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n / A at low frequencies, indicating the occurrence of a relaxation process t h a t is n o t diffusion-controlled, b e c a u s e the latter would call for a n angle between 0 a n d n / A (see sec. 4.5c, ii). So there is evidence for a relaxation process in the layer itself. The a u t h o r s found similar behaviour for Langmuir monolayers of fatty acids a n d monoglycerides with u n b r a n c h e d carbon c h a i n s containing 12 or more c a r b o n a t o m s . This relaxation process could satisfactorily be interpreted quantitatively in t e r m s of a m e c h a n i s m by which alcohol molecules exchange between t h e original (parent) monolayer a n d the particles originating from the collapse. Use was made of a variant of [3.6.72], and K^ and t a n 0 were computed a s a function of ft), a s in [3.6.73 a n d 74]. Illustrations of the agreement are given in fig. 3.47 for 3.5 h CieOH
^-r^-^^'
y
S
u
/ '14^
2.5 tUD O
/o
1.5
/ c 12OH
_L
-
2
-
1
0
logo; (ft; in s"^)
3
-1 0 logft;(ft; in s~^)
Figure 3.47. Rheology of collapsed monolayers of long-chain fatty alcohols. Comparison between measured (—) moduli (fig. a) and loss tangents (fig. b) and those computed by a model as described in the text ( ) The surface pressures for C12OH, Cj40H and CjgOH are 47, 41 and 43 mN m"i, respectively. (Redrawn from Veer and van den Tempel, loc. cit.)
3.124
LANGMUIR MONOLAYERS
three alcohols. The rate c o n s t a n t r in [3.6.72] was found to be 0.58, 0.033 a n d 0 . 0 0 1 9 s-i for C12OH, C14OH a n d CigOH, respectively. This trend conforms to expectation. A correlation between K^° and a two-dimensional interaction p a r a meter similar to w in [3.4.37] w a s also established. This is one of the few wellelaborated examples. For insoluble monolayers of cholesterol a n d dipalmitoyl choline the relaxation at p r e s s u r e s below t h e collapse point were studied by J o o s et al.^^ using oscillatory a n d s t r e s s relaxation techniques. They found experimental evidence (and presented theory) for a double-exponential decay, representing two consecutive processes. The longer T'S are 0(10^ s) a n d 0(10^ s) for cholesterol and the lipid, respectively, so these relaxations are relatively slow a n d may therefore be overlooked, especially in a u t o m a t e d a p p a r a t u s . No molecular mechanism w a s proposed; the two T'S did not exhibit a clear relationship with the surface pressure at which the experiments were carried out. Figure 3.48 gives am illustration for proteins. Protein monolayers will be mostiy deferred to Volume V, b u t they are virtually insoluble, i.e. behave a s Langmuir monolayers. Hence, observed relaxations m u s t be attributed to processes inside the layer. The behaviour of the two proteins is similar. The surface concentration is the primary determining variable; even pH changes affect the results only in a s far a s different pH values lead to different F ' s . In the plateau region, ( r > 1.6 mg m"^) the m o d u l u s becomes independent of the surface concentration. Here, relaxations 100 0
S E
X
pH
80
0 3.6 A 4.7 X 7.6
40
•
A
x/
n 6.5 60
A.^vO
/ •
A
9.2
/ f
/
20 -
X ^
\
0.4
L.
ni,
0.8
i
1
\
1.2
1.6
^
L
r / m g m" Figure 3 . 4 8 . Dilational m o d u l u s of bovine s e r u m a l b u m i n a n d ovalbumin m o n o l a y e r s . (Courtesy of J . Benjamins).
^' P. J o o s , M. van Uffelen a n d G. Serrien, J. Colloid Interface Set 1 5 2 (1992) 5 2 1 .
LANGMUIR MONOLAYERS
3.125
occur at time scales of 0(10"^ s)^h The c a u s e of this relatively fast process is not entirely understood. Most likely the molecules can at this rate expand a n d compress; they behave like 'soft discs'. Knowledge about the occurrence of relaxations is very relevant in practice, even if the cause is not established. 3.6i
E^quivalent
mechanical
circuits
Now we r e t u r n to steady state m e a s u r e m e n t s , considering t h e q u e s t i o n of whether for s u c h non-oscillatory experiments it is difficult to decompose m e a s u r e d viscoelastic characteristics into viscous a n d elastic c o m p o n e n t s . The a n s w e r is t h a t this c a n n o t be done unambiguously b u t t h a t some progress c a n be m a d e by analyzing stress-strain behaviour in terms of equivalent
mechanical
circuits. These
aire models for the real system, consisting of one or more purely viscous a n d one or more purely elastic elements, connected in s u c h a way as to represent optimally the observed monolayer rheology. Based on s u c h a model, stress-strain-time relations are formulated and fitted to the experimental data to obtain quantitative values for surface viscosities a n d elasticity moduli. In b u l k rheology working with s u c h models is familiar; discussions can be found in most of the textbooks. For monolayers the method is less popular, p e r h a p s because of the prevalence of oscillatory measurements-^^. In this section we introduce the matter of equivalent mechanical circuit^ on a n e l e m e n t a r y level. First we restrict ourselves to linear viscoelastic b e h a v i o u r . Second, to show the basic elements, idealized cases will be emphasized (mainly strain retardation a n d stress relaxation), ignoring for the time being the problem of how to carry out s u c h experiments. As a rule, however, we keep in mind t h a t stress-wise the monolayer is always at equilibrium, and strain h a s to adjust to it. In this section only dilational rheology will be considered, b u t this is not a real restriction because for shear the formalism is the same mutatis
mutandis.
By way of introduction, consider the dilational experiment of fig. 3.49. At t = t the monolayer is instantaneously subjected to a stress r^ = z^ = T^ , which is kept c o n s t a n t till t = t , after which it is suddenly removed. Panels (b) and (c) refer to the s t r a i n r e s p o n s e AA/A
for a purely elastic a n d a purely viscous monolayer, res-
pectively. The elastic monolayer directly follows the applied stress; after cessation it relaxes instantaneously. The viscous one s t a r t s to flow; after cessation of the s t r e s s t h e flow stops. The height of the block in panel (b) is equal to r^ / K^ (compare [3.6,18]) whereas in panel (c) the interfacial (dilational) viscosity follows from the slope a s
^^ R.D. Ludescher, Molecular Dynamics of Food Proteins. Experimental Techniques and Observations, in Trends in Food Set and Technmol Dec. (1990) 145. ^^ For monolayers Joly describes these in some detail, using 2D-tensor notation for interfacial stresses and strains. See the reference in sec. 3.10d,
3.126
LANGMUIR MONOLAYERS
AA A (b]
AA A
(c)
to
te
t
Figure 3.49. Application of a block-shaped stress profile (panel a) and the ensuing strain for a purely elastic (panel b) and purely viscous (panel c) monolayer.
^^
dlnA/dt
[3.6.75]
(compare [3.6.20]). The diagrams of fig. 3.49 are idealized. First there is the problem of experimentally applying a block-shaped stress. Second, elastic response is not fully i n s t a n t aneous (elastic waves propagate at about acoustic speeds) and viscous flow is subject to inertia, b o t h at t h e s t a r t a n d cessation of the stress. Leaving this relatively academic issue aside, the point is t h a t the two required parameters K^ a n d rf^ are obtainable for the idealized limiting cases, b u t t h a t reality always involves more complex behaviour, governed by both elastic a n d viscous contributions. Hence, generally strain-time and stress-time diagrams are more complicated, a n d further analysis is needed. It is here t h a t modelling in terms of equivalent circuits comes
LANGMUIR MONOLAYERS
3.127
( a ) spring
[ b ) dashpot
Figure 3.50. Icons for equivalent mechanical circuits.
( c ) slider
into the picture. S u c h circuits are constructed on the basis of three elementary units; a spring, a dashpot a n d a slider, which are sketched in fig. 3.50. Following computer language, we call these pictures icons. Icon (a) mimics a purely elastic spring, icon (b) the purely viscous movement of a piston in a viscous liquid. The slider (c) represents a system with a yield stress, i.e. where a minimum force is required to achieve flow. Here, we shall only consider icons (a) and (b). In mechanical models we c o n s t r u c t circuits consisting of a n u m b e r of springs and a n u m b e r of d a s h p o t s , arranged in s u c h a way t h a t the experimental observations are optimally accounted for. The two simplest circuits are sketched in fig. 3.51a and b . In a Voigt (or Kelvin) element tlie spring a n d d a s h p o t are parallel. If a s t r e s s is suddenly applied the spring cannot respond immediately because of the resistance caused by the viscous flow (delayed elasticity). Monolayers with a two-dimensional network a n d viscous material between the cross-links will display s u c h behaviour. So, the increase of the strain is retarded. Eventually the m a x i m u m strain T^ / K^ is attained, see fig. 3.52a. After cessation of the strain the energy stored in the spring relaxes, again with a rate determined by the parallel viscosity, till AA—> 0. Behaviour like this is semi-solid.
In the limit of 77(^-> 0 the block diagram of fig. 3.49b
is retrieved.
a a ( a ) Kelvin or Voigt element
( b ) Maxwell element
Figure 3.51. The two simplest equivalent mechanical circuits.
3.128
LANGMUIR MONOLAYERS
(5/j^O
Figure 3.52. Strain-time behaviour of a Voigt (a) and a Maxwell monolayer (b). For Maxwell elements
the spring and dashpot are in series. Now the strain is the
s u m of those of the elastic a n d viscous parts. If a stress is suddenly applied it is felt equally a n d simultaneously by the elastic and viscous parts, and the d a s h e d lines in the scheme of fig. 3.52b would ensue. The initial vertical rise corresponds to the i n s t a n t a n e o u s extension of the spring, followed by viscous flow, proportional with time, with slope determined by [3.6.75]. Langmuir monolayers exhibiting p u r e Maxwell behaviour are rare. The sole illustration is a homogeneous layer with one single relaxation m e c h a n i s m and exactly the same relaxation time r everywhere. For observation times far below r the behaviour is elastic; far above r it is viscous, with a transition range in between. In three dimensions Tunny putty', or 'bouncing putty' is a striking example. If thrown, balls of such materials bounce but, if left to gravity for a while they flow a n d spread. After cessation of the applied stress (at t = t ] t h e elastically stored energy c a n be retrieved b u t the v i s c o u s p a r t is dissipated, so AA does not return to zero. Behaviour like this is semi-liquid.
In the
limit of purely viscous behaviour fig. 3.49c is obtained. In practice it is not possible to apply t h e s t r e s s i n s t a n t a n e o u s l y to the elastic a n d viscous p a r t s , so t h e behaviour is r a t h e r like t h a t of the drawn curves in fig. 3.34b. In addition, for a n u m b e r of systems the elastic recovery becomes smaller when t - t is larger. So, single Maxwell elements are not usually satisfactory. Alternatively, the difference
LANGMUIR MONOLAYERS
3.129
between the drawn and dashed parts in fig. 3.52b can be accounted for by modifying the element. For instance, behaviour a s in fig. 3.40, exhibiting both i n s t a n t a n e o u s a n d delayed elasticity can be interpreted with a Maxwell element in series with a Voigt element. Most monolayers exhibit behaviour which is too complicated to be a c c o u n t e d for by j u s t one Voigt or j u s t one Maxwell element. More of them, or combinations, are needed, either parallel or in series, and hence more interfacial moduli a n d viscosities are needed to describe the system adequately. In some cases a s p e c t r u m of p a r a m e t e r values is needed. For instance, one could try a n d interpret the curved p a r t s in fig. 3.52b in terms of Voigt elements. The question t h e n arises a s to w h a t the physical meanings of these p a r a m e t e r s are. One model of fair generality is the Burgers element consisting of a Voigt and Maxwell element in series a n d a n o t h e r is a set of parallel Maxwell elements also known as a generalized
Maxwell element
We
shall not consider s u c h generalizations, except for noting t h a t equivalent m e c h a n ical circuits n o t only serve to analyze strain-time curves u n d e r applied s t r e s s [strain
retardation
or creep) b u t also to s t u d y stress
relaxation
u n d e r applied
strain. The computation of K^ and rj^ from strain retardation or stress relaxation curves requires anadytical expressions derived from solving differential equations. Before giving some results it is appropriate to recall t h a t equivalent circuits are also currently u s e d in interfacial electrochemistry. There, dissipation is embodied in a resistance [R] a n d storage in a capacitance (C). We have used them before; see for instance figs. 1.5.12 a n d 11.3.31, which are modified electrical Voigt elements. It so h a p p e n s t h a t the electrical icons are more or less the reverse of t h o s e in rheology, b u t this is not likely to give rise to confusion. More helpful is t h a t we can borrow' the m a t h e m a t i c s to suit our purpose. In electrochemistry, equivalents of the different s t r e s s - s t r a i n - t i m e s c h e m e s can also be found; for i n s t a n c e , t h e c u r r e n t c a n be studied a s a result of a n applied voltage or the tension build-up can be followed resulting from a n imposed c o n s t a n t current. In passing, in electrochemistry the distinction between (tension) relaxation and (current) retardation is not made. For a Voigt element the part between t = t and t = t obeys
A
K^
1 - exp
K^'t^
[3.6.76]
I ^l
where t is counted from t . The rate at which the final value z^ / K^ is attained o
depends on the ratio K^ / rj'^. The larger the viscosity, the slower the process. We can also introduce the retardation time T = rj^ / K^ and rewrite [3.6.76] as
3.130
LANGMUIR MONOLAYERS
AA A
f
"
T^
K^
1-exp L V
\
t T..
[3.6.77]
vyj
This equation c a n be derived by realizing t h a t at any time the strain of the spring and the dashpot is the same; during the retardation the stress r^ redistributes over t h e two b r a n c h e s . Initially it is all in t h e viscous b r a n c h (r^ = T^(visc)) b u t eventually it is all a c r o s s t h e elastic b r a n c h (T^=T^(el)). During t h e p r o c e s s T^ = T'^(el) + T^(visc). Writing T^(el) = K^AA / A and T^(visc) = r7^(AA/A)/ dt
A
'd
dt
[3.6.78]
We have h a d more or less the same equation before; [3.6.21]. Integration leads to [3.6.76]. So, from the final value of the strain a n d the rate of retardation the two rheological characteristics K^ and r]^ can be obtained. For a Maxwell element t h e s e two p a r a m e t e r s follow from the (extrapolated) vertical p a r t s a n d the slope, respectively. If a mathematical elaboration is required the starting point is the converse of t h a t for a Voigt element; now the s t r a i n s are additive (AA/A = AA(el)/A + AA(visc)/A). Therefore, Maxwell elements are more suitable for interpreting experiments where a strain is applied a n d t h e e n s u i n g s t r e s s a d j u s t m e n t is followed. To illustrate the converse n a t u r e a s compared to strain retardation over a Voigt element, [3.6.77], let u s at t = 0 suddenly apply a given strain AA / A which is subsequently kept at t h a t value. At t = 0 the response will be elastic, b u t with increasing time this p a r t will decrease in favour of t h e viscous part at a rate d(AA / A) / d t . Writing d(AA / A(el)) / dt = ( K ^ l ' M r ^ / d t for the elastic p a r t a n d d(AA / A(visc)) / dt = T^ / r]^ for the viscous part, a n d s u b s t i t u t i n g T,^ for n^ / 77^, one obtains a d(AlnA) r dt
^r^
dr^ M dt
= T.
[3.6.79]
from which, u p o n integration
^ =^
d(AA/A) 1 - exp dt
[3.6.80]
is obtainable. We can now identify T as the stress build up time. As a result of the above process, the stress r^ is built u p . If at t = t
we finish
applying a strain, stress relaxation will take place, obeying
-f"l or
exp
[3.6.81]
LANGMUIR MONOLAYERS ( T^-T^U )exp
t_
3.131
\
where T (t ) = K (AA/A)
[3.6.82]
is t h e s t r e s s at t h e time t h a t either t h e externally
applied stress or the applied rate of shear is removed. The stress remaining in the system, stored in the spring, relaxes over t h e d a s h p o t . The p h e n o m e n o n is equivalent to Maxwell-Wagner relaxation of a n JRC-circuit where the p r o d u c t of R a n d C (i.e. the ratio of C and the conductivity) h a s the dimension of time, see sec. II.3.13d. For extensions a n d further elaborations of these principles see Joly's review, mentioned in sec. 3.10d, and s t a n d a r d textbooks on bulk rheology^^. The translation from three-dimensional to two-dimensional systems is not difficult. 3.7
Measuring monolayer properties
Over a long period of time experimental r e s u l t s on amphiphilic monolayers were limited to surface pressure-area (;r-A) isotherms only. As described in sections 3.3 a n d 4, from n{A) isotherms, measured u n d e r various conditions, it is possible to obtain 2D-compressibilities, dilation moduli, thermal expansivities, a n d several t h e r m o d y n a m i c characteristics, like the Gibbs a n d Helmholtz energy, t h e energy a n d entropy per unit area. In addition, from breaks in the K{A) curves p h a s e t r a n s i t i o n s c a n in principle be localized. All this information h a s a p h e n o m e n ological n a t u r e . For instance, notions a s common a s 'liquid-expanded' or liquidcondensed' c a n n o t be given a molecular interpretation. To penetrate further into u n d e r s t a n d i n g monolayers at the molecular level a variety of additional experimental techniques is now available. We will discuss these in this section. To illustrate the desirability of additional information, we note that, a l t h o u g h in principle p h a s e b o u n d a r i e s can be determined from isotherm m e a s u r e m e n t s , the required c h a n g e s in slope are often subtle a n d a variety of experimental difficulties can confuse the interpretation. For example, the non-horizontal n a t u r e of the plateau exhibited in the isotherms of many lipid monolayers h a s been a c a u s e for debate on the order of the LE-LC transition for a long time; even the very existence of a distinct LC p h a s e h a s been questioned. However, since the early eighties fluorescence
microscopy gave unequivocal evidence t h a t there are two p h a s e s in
the LE-LC region^^ This technique a n d many other recent experimental developm e n t s have revealed a world of rich a n d intriguing p h e n o m e n a regarding t h e ^^ See for instance H.A. Barnes, J.F. Hutton and K. Walters, An Introduction to Rheology Elsevier (1989), sec. 3.3 (for the 3D equivalent). 2) V. von Tscharner, H.M. McConnell, Biophys. J. 36 (1981) 409; R. Peters, K. Beck, Proc. Natl Acad. Set USA 8 0 (1983) 7183; M. Losche, E. Sackman and H. Mohwald, Ber. Bunsenges. Phys. Chem. 87 (1983) 848. See also the discussion of fig. 3.7 with a few more recent references.
3.132
LANGMUIR MONOLAYERS
morphology a n d d y n a m i c s of monolayers at the air/liquid interface. In recent y e a r s t h e application of X-ray diffraction a n d n e u t r o n reflection, reflection IR spectroscopy, fluorescence, a n d nonlinear spectroscopies s u c h a s second harmonic generation (SHG) a n d s u m frequency generation (SFG) have m a d e it possible to investigate these monolayers at the molecular level. Technological advances, s u c h a s the increased availability of synchroton radiation (for X-rays) a n d slow n e u t r o n b e a m s , have m a d e existing techniques, like ellipsometry, IR absorption spectroscopy a n d X-ray diffraction, sufficiently sensitive to allow the study of monolayers. Other techniques, like n e u t r o n reflection a n d nonlinear optical spectroscopy, are interface-specific and therefore intrinsically suitable for the investigation of monolayer properties. The purpose of this section is to discuss the various methods which can be a p plied for the study of monolayers. For a n u m b e r of these the measuring principles have already been treated in Volumes I a n d II to which, where appropriate, the reader is referred. Here, the m e t h o d s are divided into reflection a n d diffraction, spectroscopic techniques (invohring excitation of molecules), scanning probe techniques, rheology, a n d Volta potential m e a s u r e m e n t s . This overview does not cover every technique t h a t is applicable in monolayer research a n d the division is somew h a t arbitrary, since in some m e t h o d s different techniques are combined. For example, spectroscopic t e c h n i q u e s are frequently combined with reflection to obtain interfacial specificity; surface potential a n d
fluorescence
measurements
may be performed using a scanning device. An overview of the techniques discussed here, together with the information t h a t can be extracted from the experimental data, is given in table 3.5. In table 3.6 the acronyms used for describing these techn i q u e s are listed with their m e a n i n g s a n d the (sub)section in which they are introduced. For h i g h - r e s o l u t i o n imaging u s i n g s c a n n i n g probe t e c h n i q u e s
Langmuir
monolayers m u s t be transferred to solid s u b s t r a t e s . Some other t e c h n i q u e s are also restricted to supported monolayers, e.g. scanning electron microscopy a n d attenuated total reflection (ATR) IR spectroscopy. Therefore, and because of the freq u e n t u s e of supported monolayers, bilayers and multilayers a s model systems in f u n d a m e n t a l research, the next section will start by discussing t h e transfer of Langmuir monolayers onto solid s u b s t r a t e s . 3.7a
Monolayer
transfer
on solid
substrates:
Langmuir-Blodgett
films
Only two y e a r s after Langmuir published the design of his surface film balance ^^ now known a s the Langmuir trough, his co-worker Miss Katharine Blodgett developed a technique for transferring monolayers from the a i r / w a t e r interface to
1^ I. Langmuir. J. Am. Chem. Soc. 39 (1917) 1848.
LANGMUIR MONOLAYERS
3.133
Table 3 . 5 . Measuring techniques for the investigation of monolayers. Method
Type of information obtainable
Restrictions
Pressure-area (;r(A)) isotherms
Phase transitions, packing densities, compressibilities, thermodynamic characteristics.
Molecular interpretation very limited.
EUipsometry
Adsorbed amounts/coverages; phase transitions; thickness and refractive indices. Identification of interfacial molecules.
For interpretation in terms of molecular structure model profiles across the interface are needed. Problems: monolayer anisotropy, and different profiles may match the experimental data; additional (independent) information required.
Spectroscopic ellipsometnj Imaging ellipsometry
Domain formation and shape (coexisting phases); internal structure of condensed phases; resolution O (1 ^im).
Restricted to interfaces exhibiting a Brewster angle of incidence. Resolution is that of optical microscopy.
Brewster angle microscopy (BAM)
As imaging ellipsometry.
X-ray and neutron specular reflection
Molecular structure across the See ellipsometry. interface, laterally averaged over the beam area X-rays: electron density profiles; neutrons: scattering length density profiles of the nuclei of atoms). With neutrons different parts of the monolayer can be studied independently by selective H/D substitution.
X-ray grazing incidence diffraction
Lateral ordering in crystalline parts of monolayers (molecular lattice characteristics and average crystallite size); tilt angles and tilt directions.
Vibrational spectroscopy (ATR-FTIR, IRRAS, Raman) UV/visible spectroscopy
Identification of interfacial ATR-FTIR restricted to the molecules; orientational order ATR-crystal/fluid interface. (second-rank order parameter (S^)], and conformational order. Orientational order {{S^)]. Measurement of adsorption and monolayer penetration.
Structural information across the interface limited: tilt angles and directions only obtainable using simple models for the molecular shape of the amphiphiles.
Restricted to monolayers containing molecules with chromophoric groups.
3.134
Table 3 . 5 .
LANGMUIR M O N O L A Y E R S
M e a s u r i n g t e c h n i q u e s for t h e i n v e s t i g a t i o n of m o n o l a y e r s ( c o n t . ) .
Method
Type of information obtainable
Restrictions
Fluorescence techniques
In general: orientational order {{S^) a n d (S^>), rotational a n d translational mobility (on the time scale of fluorescence, i.e., 1 - 10 n s ), molecular environment, aggregation state. Domain formation a n d s h a p e (coexisting phases); resolution O (1 |im). With polarized radiation: local orientational order. Translational diffusion, aggregation Translational diffusion. With a b u r s t of polarized radiation: rotational diffusion. Adsorption kinetics. Orientational order.
Generally, extrinsic probe molecules have to be introduced in the monolayer: possible perturbation of the monolayer s t r u c t u r e a n d dynamics.
Adsorption kinetics, interfacial coverage, reaction kinetics, p h a s e transitions, orientational order (average tilt angle), surface chirality.
Intensity of the signal reflects the combined effect of interfacial coverage a n d orientational order. Tilt angles only obtainable if all non-zero elements of the hyperpolarizability tensor z^^^ can be determined.
Fluorescence microscopy
FCS FRAP
TIRF
Nonlinear optical techniques (SHG. SFG)
SHG spectroscopy SFG spectroscopy
Restricted to monolayers a n d multilayers on optically transparent substrates.
Electronic transitions. Vibrational transitions; identification of interfacial molecules.
Quantitative analysis complicated; knowledge of hjrperpolarizabilities of e a c h vibrational mode required.
S c a n n i n g probe microscopy (STM, AFM, ...)
High resolution topology (nm scale) in 3D; local physico-chemical properties depending on specific technique (e.g., mechanical stability, adhesion, potential).
Restricted to solid/fluid interfaces., i.e., s u p p o r t e d monolayers a n d LB films; precautions to avoid deformation a n d damage of the layers may be necessary.
Surface rheology
Viscoelasticity of the monolayer; differentiation between fluid a n d solid p h a s e s . Surface elasticity a n d viscosity in the transversal a n d longitudinal mode; wave d a m p i n g characteristics. Relaxation processes in monolayers.
Mechanical stability of the monolayer. Interpretation often complicated b e c a u s e several molecular processes may be involved a n d b e c a u s e viscous a n d elastic components may both contribute.
Volta potential measurements
Electrical surface polarization. Film homogeneity arfd limited d a t a on the orientation of the molecules or molecular groups.
Sequestering of the dipolar contribution is often ambiguous.
LANGMUIR MONOLAYERS
3.135
Table 3 . 6 . List of acronyms for optical and scanning techniques u s e d in analyzing monolayers. Abbreviation
Meaning
Section where introduced
AFM = SFM
atomic force (scanning force) microscopy/microscope
3.7d
ATR
attenuated total reflection
3.7c.i
BAM
Brewster angle microscopy/microscope
3.7b.ii
DFG
difference-frequency generation
3.7c.v
FCS
fluorescence
FFM = LFM
correlation spectroscopy
friction force (lateral force) microscopy/microscope
3.7c.iv 3.7d
FLIM
fluorescence
lifetime imaging microscopy/microscope
3.7c.iv
FRAP
fluorescence
recovery after photobleachlng
3.7c.lv
FRETT
fluorescence
resonance energy transfer
3.7c.iv
FTIR
Fourier transform Infrared (spectroscopy)
3.7c.i
IR
Infrared (spectroscopy)
3.7c.l
IRAS = IRRAS
infrared reflection-absorption spectroscopy
3.7c.i
NSOM
near-field scanning optical microscopy/microscope
3.7c.iv/3.7d
PCSA
polarizer-compensator-sample-analyzer
3.7b.i
PFM
polarized fluorescence microscopy/microscope
3.7c.lv
PSA
polarizer-sample-analyzer
3.7b.i
RA
reflectance-absorbance
3.7c.i
RF^
resonance Raman spectroscopy
3.7c. 11
SERS
surface-enhanced Raman spectroscopy
3.7c. 11
SFG
sum-frequency generation
3.7c.v
SHG
second harmonic generation
3.7c.v
SPM
scanning probe microscopy/microscope
3.7d
STM
scanning tunneling microscopy/microscope
3.7d
TIRF
total internal reflection
3.7c.iv
TIRFM
fluorescence
total internal reflection fluorescence microscopy/
3.7c.lv
microscope UV
ultraviolet (spectroscopy)
3.7c.ill
WRS
waveguide Raman spectroscopy
3.7c. 11
sohd supports s u c h a s glass slides. However, the first formal reports describing this technique did not appear until 1934 and 1935^^. Buflt-up monolayer assemblies are now referred to as Langmuir-Blodgett
(LB) films to distinguish t h e m from Langmuir
films, a term reserved for floating monolayers. The field of LB films lay relatively
1^ K.B. Blodgett, J. Am. Chem. Soc. 56 (1934) 495 (deposition of one monolayer); 5 7 (1935) 1007 (deposition of successive monolayers).
3.136
LANGMUIR MONOLAYERS
d o r m a n t until in the 1960s Kuhn and co-workers ^^ began their experiments on monolayer organization, a n d industry became interested because of t h e possible applications of LB films (organic films with tailored properties). Unfortunately, d u e to the difficulties encountered in preparing LB films on a large scale a n d bec a u s e of their mechanical and thermodynamic instability, there are still no practical applications except a s model systems in fundamental research. In the Langmuir-Blodgett technique a solid plate, the support, is moved vertically t h r o u g h a monolayer on the aqueous s u b p h a s e kept at a certain pressure in a Langmuir trough-^^. Different supports can be used, each with their specific applications. As plate materials glass a n d quartz are commonly used, b e c a u s e of their availability a n d optical transparency, transferred films can be easily examined by optical a n d spectroscopic techniques. For electron microscopy investigations thin polymer layers on electronmicroscope grids are nusually used a s the support, and, for conductivity experiments, semi-conducting plates. If the support h a s a hydrophilic surface, e.g., glass and metal (oxides), deposition follows the sequence of events depicted in fig. 3.53. On the first downward
iMlii. water
iiiiWiiii support-
^ ^
support
water
support
stroke
water
water
support
Figure 3.53. Schematic representation of monolayer and multilayer transfer (type Y) on a hydrophilic support. Not to scale! For details see the text.
^^ See H. Kuhn, D. Mobius and H. Bucher, in Techniques of Chemistry, A. Weissberger, B.W. Rositer, Eds., Wiley, New York, 1973, Part Illb, Vol. 1. ^^ In this section we shall distinguish the terms support (for the mostly solid material onto which deposition takes place) and subphase (the, almost exclusively aqueous, fluid onto which the monolayer is spread). In the literature the term 'substrate' is sometiems used for both.
LANGMUIR MONOLAYERS
3.137
the s u b p h a s e wets the surface, b u t this does not result in monolayer transfer. On the following, first upward
stroke the m e n i s c u s (which is still t u r n e d up) slides
over the surface a n d leaves behind a monolayer in which the hydrophilic g r o u p s are directed towards the hydrophilic support surface. The second immersion into the s u b p h a s e differs from the first in t h a t the surface is now hydrophobizedr the m e n i s c u s t u r n s down a n d a second monolayer is deposited with its hydrophobic tails in contact with the hydrophobic tails of the molecules already on the support. Repeated dipping gives (in principle) a s t r u c t u r e in which those are pointing tow a r d s each other. This type of deposition, in which layers are laid down each time the s u b s t r a t e moves across the interface, is called Y-type transfer. Only for a limited n u m b e r of surfactant molecules is Y-type transfer possible; some molecules, e.g. aromatic molecules, can only be deposited on a downstroke (X type) or only on a n upstroke (Z-type). See fig. 3.54. If the s u p p o r t is hydrophobic, e.g. silanized glass or silicium, deposition will normally s t a r t on the first immersion into the s u b p h a s e . For Y-type transfer there will be a n even n u m b e r of layers deposited at the end of each completed cycle, in contrast to the odd n u m b e r of layers transferred to hydrophilic supports. It should be noted t h a t the schemes depicted in figs. 3.53 and 3.54 are highly idealized a n d Y-, X- or Z-transfers do not always give the corresponding (perfect) multilayer structure. For the preparation of LB films usually the s u b p h a s e is water or a n aqueous electrolyte solution. In some cases mixtures of water a n d other solvents (for example, glycerol, ethanol a n d butanol) are used. When the monolayer consists of ionizable molecules, the pH and the concentration and valency of electrolj^e ions in the s u b p h a s e a r e i m p o r t a n t variables. An appropriate pH value keeps the molecules 1—0 o—1 vJ 1
f——vj
K o ^
p» L^ \^
r\ KJ KJ
L/
■o—o\j r\
.11
^u 1 \j 1 1 1'—-nj
1\ 1 " ^ " T
1
~\j
1
"^ —^
11 11
1
■Vj
(a) Figure 3.54. X-type transfer (a) and Z-type transfer (b).
(b]
3.138
LANGMUIR MONOLAYERS
dissociated; divalent counterions keep the solubility low and hence stabilize the monolayer. The s u b p h a s e should be free of surface-active impurities, not only b e c a u s e these would be incorporated into the monolayer, b u t also b e c a u s e their presence might c a u s e failure of the transfer process. It is therefore necessary to work with very clean water and pure substances. In order to m a i n t a i n c o n s t a n t conditions during transfer the surface p r e s s u r e m u s t be kept c o n s t a n t using one of the m e t h o d s described in section 3.3. The surface pressure which gives optimal results depends on the type of monolayer and s u b s t r a t e , a n d is established empirically. Generally, materials can seldom be successfully transferred at surface p r e s s u r e s below 10 m N / m , and at surface p r e s s u r e s higher t h a n 40 m N / m when collapse and film rigidity often give rise to problems. After compression of the monolayer to the chosen surface pressure, the monolayer should be allowed to relax before transfer, the criterion being that the area of the monolayer will not change anymore. The transfer rate (dipping rate) should not be too high. The s u b p h a s e that is dragged along upon the lifting of the support should get a chance to drain. Furthermore, the monolayer on the s u b p h a s e should be given time to adapt and stay homogeneous. Deposition rates of about 1 m m / s are common, depending on the trough area-surfactant ratio. The transfer
ratio, i.e. the ratio of the area of the monolayer removed from the
s u b p h a s e to the area of the support coated by the monolayer, is often used a s a m e a s u r e of the quality of deposition. Usually transfer ratios a r o u n d unity (0.951.05) are taken as a criterion for good deposition. However, this is not a guarantee t h a t the LB film h a s the same structure as the monolayer at the air/water interface, a s we will discuss later in this subsection. Occasionally, there is a large b u t consistent deviation of the transfer ratio from unity; this points to a major, reproducible c h a n g e in the molecular organization during transfer. Changing transfer ratios are a sign of unsatisfactory film transfer. Using a double trough it is possible to form films consisting of alternate monolayers of different composition. Such a trough has, at either end, a moveable barrier and a device to measure and control the surface pressure. The two ends are sepa r a t e d from each other by a barrier at the a i r / w a t e r interface which does not extend to the bottom of the trough. At either side of this barrier a monolayer is spread and compressed to a prespecified surface pressure. A mechanical device dips the s u b s t r a t e t h r o u g h the monolayer at the a i r / w a t e r interface at one side of the trough, p a s s e s it u n d e r the barrier, lifts it through the monolayer at the other end a n d t h e n p a s s e s it over the barrier. Repetition of this process gives a multilayer consisting of a l t e r n a t e monolayers of the two materials spread on the water surfaces in the two halves of the trough. Another way of transferring monolayers to solid s u b s t r a t e s is the horizontal dipping method, first applied by Langmuir and Schaefer to deposit proteins onto
LANGMUIR MONOLAYERS
3.139
hydrophobic surfaces ^^ Here the support is parallel above the interface a n d moved downward until contact is m a d e with the monolayer. After u p to, say, 30 to 4 0 seconds the support is either withdrawn from the interface or p u s h e d through with the aim t h a t the monolayer will remain adhered to it. It is obvious t h a t the s u p p o r t should be perfectly horizontal a n d t h a t air bubbles between s u b s t r a t e a n d monolayer m u s t be avoided since these interfere with proper deposition. This method is a conceivable alternative for monolayers t h a t are too rigid for normal LB transfer or for polymerized monolayers. Phospholipids are known to be very difficult to transfer in more t h a n one layer using the s t a n d a r d LB technique. A combination of vertical a n d horizontal dipping h a s been successfully applied to produce supported bilayers a n d multilayers with h y d r o p h i l i c o u t e r s u r f a c e s ^ ) . Alternatively, p h o s p h o l i p i d bilayers on solid s u b s t r a t e s can be created by vesicle adsorption^^. One of the issues is whether they remain intact. Apart from the LB technique, there are several alternative ways of forming ordered layer s t r u c t u r e s of amphiphilic molecules on solid s u p p o r t s which, are sometimes less c u m b e r s o m e or quicker. One of these is the self-assembly technique, in which ordered monolayers or multilayers are formed by chemisorption or physical adsorption. Reviews of this and other techniques are given in Refs "^K When u s i n g tramsferred monolayers to study the properties of Langmuir monolayers, a major concern is obviously whether the final s t r u c t u r e of t h e film is representative of the s t r u c t u r e on the water surface before transfer^^. There is no reason to a s s u m e t h a t the equilibrium s t r u c t u r e of the parent monolayer a n d the transferred one are identical. In the first place, the interaction of the amphiphiles with t h e s u p p o r t (or with previously deposited layers) m a y be d r a m a t i c a l l y different from those experienced at the w a t e r / a i r interface. Secondly, the surface p r e s s u r e variable of the Langmuir monolayer is no longer there to keep it in the parent state. As well a s these aspects of equilibrium there are kinetic features to consider. Molecular transport towards the support to replace molecules deposited in the LB film creates a complicated flow p a t t e r n t h a t t e n d s to deform the morphology of domains - domains may elongate in the dipping direction - a n d / o r induce a prefer-
1^ I. Langmuir, V.J. Schaefer, J. Am. Cherru Soc. 6 0 (1938) 1351. 2) L.K. T a m m , H.M. McConnell, Biophys. J. 4 7 (1985) 105. ^^ See, for example, E. Kalb, S. Frey a n d L.K. Tamm, Biochim. Biophys. Acta 1 1 0 3 (1992) 307. ^' A. Ulman, An Introduction to Ultrathin Organic Films, Academic P r e s s , (1991); R.H. Tredgold, Order in Thin Organic Films, C a m b r i d g e University P r e s s , (1994); R.H. Tredgold, J. Mater. Chem. 5 (1995) 1095. ^^ For elaborate d i s c u s s i o n s on this m a t t e r a n d a n overview of s t u d i e s performed for m a p p i n g out potential LB artefacts, see D.K. Schwartz, Surface Set Reports 2 7 (1997) 2 4 5 ; C M . Knobler, Physica A 236 (1997) 11.
3.140
LANGMUIR MONOLAYERS
ential orientation in the molecules. The rate of transfer may affect the structure of the transferred monolayer; a relatively fast transfer may reduce the extent of perturbation, resulting in monolayer s t r u c t u r e s more closely resembling that of the parent monolayer. Generally, at high enough deposition rates the packing density before a n d after transfer differs by a few percent at the most, equivalent to the typical uncertainty in transfer ratio m e a s u r e m e n t s . The t h e r m o d y n a m i c stability of the transferred monolayer d e p e n d s on n u m erous factors, s u c h a s the n a t u r e of the monolayer-forming molecules and, closely connected with this, their lateral coherence which may persist in different orienta t i o n s , t h e c o m p o s i t i o n of the s u b p h a s e from which t h e m o n o l a y e r s
are
transferred (pH, electrolyte composition), support-monolayer interactions and for multilayers - coupling between s u b s e q u e n t layers. Structural r e a r r a n g m e n t s towards equilibrium may occur during or after deposition. For example, if the amphiphiles prefer a denser packing on the support than on the s u b p h a s e , surface phase separation may take place, resulting in condensation and dewetting of the former surface. If the packing density changes during transfer, a transfer ratio of unity will not be the proper indicator of a defect-free homogeneous film. Moreover, m u l t i c o m p o n e n t monolayers may p h a s e - s e p a r a t e on the support. If one of the c o m p o n e n t s is preferentially transferred this may lead to the formation of a p a t t e r n of a l t e r n a t i n g stripes perpendicular to the dipping direction of both enriched a n d depleted p h a s e s in this component. The p h e n o m e n o n h a s l^ecn explored by Riegler and Spratte^^ in a series of experiments for mixed monolayers of DPPC a n d
fluorescent-labeled
DMPE. Because of preferential deposition of
DPPC on the support used (silica), an area near the support on the subphase surface is depleted of DPPC during transfer. Alter deposition of a certain area of DPPCenriched monolayer, a meniscus instability occurs and a strip of DMPE-enriched monolayer is transferred. As might be expected, the width a n d spacing of the alternating strips on the support were found to vary with the transfer rate. The evolution of LB films of various fatty acids prepared from s u b p h a s e s containing c a d m i u m ions h a s been followed by atomic force microscopy-^). While no significant s t r u c t u r a l effects on the local lattice s t r u c t u r e or on the n u m b e r of defects were observed when the films are aged in air over several m o n t h s , significant reorganization occurs when they are aged under water for periods of minutes to h o u r s , depending on the length of the hydrophobic tail. The initially uniform films start to reorganize by forming terraces with pitches of a n u m b e r of bilayers a n d eventually change into individual crystallites with distinctive edges. The driving force for reorganization h a s been attributed to reduction of both head groupie H. Riegler, K. Spratte, Thin Solid Films 210/211 (1992) 9: K. Spralte. H. F^iegler. Langmuir 10 (1994) 3161. 2) D.K. Schwartz. R. Viswanathan and J.A.N. Zasadzinski. J. Phys. Chem. 96 (1992) 10444.
LANGMUIR MONOLAYERS
3.141
s u p p o r t a n d headgroup-water interactions; the head groups prefer to *wet' each other r a t h e r t h a n the water or the support. This effect is of great practical significance for building u p multilayer systems using LB deposition. The organization of the layers can be severely disrupted if the film-coated support is allowed to rest in t h e s u b p h a s e for a n y length of time, for example, while changing one type of monolayer from the a i r / w a t e r interface and replacing it with another. 3 . 7 b Reflection
and
diffraction
When electromagnetic radiation impinges on a n interface, the c h a n g e s in this radiation can, in principle, be derived from the Maxwell a n d Fresnel e q u a t i o n s , given in Volume I (sees. 1.7.2 a n d 1.7.10, respectively). These e q u a t i o n s form a general theoretical framework for describing reflectivity. The significance of reflectivity in the study of interfaces stems from the measurability of the deviation of t h e a c t u a l reflectivity from t h a t of a Fresnel interface, i.e. a n infinitely flat interface w i t h o u t defects. This difference is determined by t h e m e a n index of refraction profile normal to the interface. In the first p a r t s of this subsection (i Hi), we will focus on the reflection of light. X-rays a n d n e u t r o n s . It h a s b e e n shown ^^ t h a t for n e u t r o n reflection the intensities of the reflected a n d transmitted b e a m follow the s a m e laws a s for reflection of electromagnetic radiation with the electric field vector perpendicular to the plane of incidence. It is typical for reflection t h a t the incident a n d reflected b e a m s are in the s a m e plane a s , a n d at the same angle to, the surface normal (so-called specular tions). Reflectivity p r o b e s the m e a n density profiles normal
condi-
to t h e interface.
Information on lateral correlations is contained in the scattering intensity in offspecular directions, a s m e a s u r e d by scattering
a n d diffraction
t e c h n i q u e s . Light
scattering by interfaces h a s already been discussed in sections 1.7.10 a n d 1.10. For solid interfaces it provides information on the surface r o u g h n e s s , while for fluid interfaces, thermally or mechanically created u n d u l a t i o n s c a n be studied from which the interfacial tension a n d the interfacial dilational m o d u l u s , respectively, can be derived. The same kind of information, on smaller length scales, c a n be obtained from X-ray a n d n e u t r o n scattering at interfaces-^h Scattering s t u d i e s are most appropriate for layers t h a t have no structure because for those systems they are the only ones available; scattering will not be considered here any further. When s t r u c t u r e in monolayers is the issue and X-ray b e a m s the source, diffraction is the more suitable technique, as will be discussed in part iv of this subsection. (i) Ellipsometry.
Ellipsometry is a well-established optical t e c h n i q u e for t h e
investigation of films, b o t h on liquid a n d on solid surfaces. The theoretical
1) M.L. Goldberger, F. Seltz, Phys. Rev. 7 1 (1947) 294. 2) See, for example S.K. Sinha, Acta Phys. Polonica A 89 (1996) 2 1 9 .
3.142
LANGMUIR MONOLAYERS
b a c k g r o u n d h a s been e x p o u n d e d in 1.7.10. Various versions of ellipsometry analyze the change in polarization as a beam of monochromatic polarized light is reflected from a n interface. A good overview of commonly used set-ups is given in ref. ^^. A s e t - u p u s i n g only two polarizers is the polarizer-sample-analyzer (PSA) ellipsometer. In a null-ellipsometer a polarizer and a quarter-wavelength plate, commonly referred to a s the compensator, are used to adjust the elliptic state of the incident b e a m in s u c h a way t h a t the reflected beam is linearly polarized. The reflected b e a m c a n t h e n be extinguished by changing the orientation of the analyzer (PCSA set-up). A null-ellipsometer gives very accurate results. The drawb a c k s are t h a t it is limited to single-wavelength m e a s u r e m e n t s d u e to the wavelength-dependent behaviour of the compensator, and the relative slowness of the m e a s u r e m e n t s . A fast b u t less accurate technique is polarization-modulation ellipsometry (time resolution ca 1 ms)^^. The change in polarization upon reflection is contained in the two measurable ellipsometric coefficients, tani//and A. These are related to the complex reflectivity coefficients, f,, and r^, parallel and perpendicular to the plane of incidence, i.e. the plane through the incident and reflected light beams. The coefficient A gives the change u p o n reflection of the phase difference between the parallel a n d normal (to the plane of incidence) polarized components of the light beam, whereas tani// is a m e a s u r e of the change in the amplitude ratio of these components (eq. [1.7.10.13]). In favourable cases, i.e. for smooth a n d homogeneous films a n d provided t h a t the optical characteristics of the ambient media are properly determined, from these coefficients both the optical (ellipsometric) thickness and the refractive index of the film can be determined. The tacit assumption is that the density (and refractive index) profiles are step-functions. Generally, for the interpretation of reflectivity data, models are used in which the interfacial region is divided into a n u m b e r of parallel h o m o g e n e o u s a n d optically isotropic layers with s h a r p b o u n d a r i e s , onto which the
Fresnel
e q u a t i o n s are applied^^ Comparison with the data lets u s verify the a s s u m e d profile a n d assign parameter values, like the thicknesses of subsequent layers and their refractive indices. An intrinsic problem is that the solution obtained is not unique; different profiles may m a t c h the same experimental data. For adsorption layers the p a r a m e t e r s obtained from the model fit allow for the calculation of the adsorbed a m o u n t F. It is generally found that this result is hardly dependent on the c h o s e n profile'^^ so t h a t F c a n be calculated in an easy way by a s s u m i n g a n
1) P.S. Hauge. Surface Set 96 (1980) 108. 2) J. Meunier, J. Phys. Paris Lett 46 (1985) L-1005. ^^ O.S. Heavens, Optical Properties of Thin Films, Butterworth (1955); W.N. Hansen, J. Opt. Soc. Amer. 58 (1968) 380; M. Born, E. Wolf. Principles of Optics, Pergamon (1970); J. Lekner. Theory of Reflection, Nijhoff (1987). '^^ See, for example, F. Tiberg, M. Landgren. Langmuir 9 (1993) 927.
LANGMUIR MONOLAYERS
3.143
homogeneous adsorbed film of thickness dr
a n d refractive index rir. The m o s t
commonly u s e d equation is^^ r=
/ . / dr dn/dc J
[3.7.11
with n^ the refractive index of the solution from which adsorption t a k e s place. In this approach it is a s s u m e d t h a t the refractive index increment d n / dc is c o n s t a n t over the whole concentration range. EUipsometiy h a s a thickness resolution of ca 0.1 n m and therefore s e e m s to be very suitable for determining the t h i c k n e s s a n d optical properties of layers of molecular dimensions. However, in the case of monolayers, the interpretation of ellipsometric d a t a is complicated by the fact t h a t these layers generally consist of ordered molecules a n d therefore exhibit significant refractive index anisotropy. Even without any lateral inhomogeneity in the monolayer t h e n u m b e r of independently measurable variables is less t h a n the n u m b e r of p a r a m e t e r s to be determined. This n u m b e r c a n not be increased either by variation of t h e angle of incidence or by variation of the wavelength-^^ Determination of quantitative d a t a by ellipsometry is only feasible if s t r u c t u r a l d a t a of the monolayer a r e k n o w n from independent measuring techniques. For example, by combining ellipsometry a n d X-ray scattering Paudler et al.*^^ have determined the anisotropy a n d refractive indices for a monolayer of behenic acid. Notwithstanding these limitations, ellipsometry on its own c a n reveal valuable information on monolayers. An important application is spectroscopy w h e r e t h e wavelength of the light is varied. In particular, w h e n infrared radiation is used, it is possible to identify molecules at the interface; for monolayers on solid s u b s t r a t e s even the type of binding to the s u b s t r a t e can sometimes be determined. F u r t h e r m o r e , ellipsometry is a very sensitive m e t h o d for detecting s t r u c t u r a l c h a n g e s in Langmuir monolayers. These changes are most significant a t p h a s e transitions. Phase changes t h a t are sometimes h a r d to see in n(A) i s o t h e r m s may be clearly observed in A(A) isotherms. A being the p h a s e of the complex reflection ratio (see [1.7.10.131). An example is given in fig. 3.55. Figure 3.55a shows a n(A) i s o t h e r m for a monolayer of d i m y r i s t o y l p h o s p h a t i d y l e t h a n o l a m i n e d o p e d with 5 % biotin-functionalized
(DMPE)
dipalmitoylphosphatidylethanolamine
(DPPE) (in order to study specific streptavidin binding). The onset of t h e LE-LC coexistence region is clearly visible, b u t there is no clear evidence for any further transition on compression of the monolayer. The ellipsometric isotherm is given in fig. 3.55b, which exhibits a second p h a s e transition. The different p h a s e regions ^^ J.A. de Feijter, J. Benjamins and F.A. Veer, Biopolymers 17 (1978) 1759. 2^ R. Reiter, H. Motschmann and W. Knoll, Langmuir 9 (1993) 2430. ^^ M. Paudler, J. Ruths, B. Albert! and H. Riegler, Makromol Chem., Macromol Symp. 46 (1991) 401.
3.144
LANGMUIR MONOLAYERS
50
(a)
40
30 20 10 0
0.3
1
1
1
0.5
0.6
0.7
1
0.4
\ .
J
L
0.9
1.0
•v.
•x
181.0
T^^
0.8
(b)
\
•a
\ \
180.5
> \
180.0 0.3
1
1
0.4
0.5
1
1
0.6
0.7
1 ^
0.8
^
1
0.9
1.0
Qj / n m ^
Figure 3.55. (a) 7i[a.] isotherm of a DMPE monolayer containing 5 mol% biotinylated DPPE at T = 20 °C. The subphase contained 0.5 M NaCl. (b) Ellipsometric A{a^] isotherm for the same monolayer. (Redrawn from R. Reiter, H. Motschmann and W. Knoll, Langmuir 9 (1993) 2430.) seem to be characterized by straight lines with different slopes. The three last data points may actually indicate the end of the coexistence phase. Perhaps the most interesting recent development in the field of ellipsometry is the possibility of imaging any arbitrary reflecting interface. One way of obtaining lateral resolution is to focus the incident beam onto a small spot and scan the sample ^^ However, the smallest spot, and therefore the best lateral resolution to be obtained, is of the order of 20 \Jim and a relatively long time is required to capture a complete picture of the interface. It is not possible to focus onto smaller spots b e c a u s e then there is too m u c h variation in the angle of incidence. An alternatlxc method is to transform lateral inhomogeneities of the sample into microscopic^ images with a n ellipsometric contrast. To achieve this the detector of a conven-
^^ B. Drevillion, J. Perrin, R. Marbot, A. Violet and J.L. Dalby, Rev. Set Instr. 53 (1982) 969; F. Heslot, A.M. Cazabat and P. Levinson, Phys. Rev. Lett. 64 (1998) 1286.
LANGMUIR MONOLAYERS
3.145
tional null-ellipsometer is replaced by a lens a n d a position-sensitive detector^K Images obtained with s u c h a n ellipsometric
microscope have a lateral resolution of
the order of 1 |im, m a k i n g it possible to visualize the formation a n d s h a p e of d o m a i n s in coexisting p h a s e s in Langmuir monolayers. Lateral variation in optical anisotropy in condensed p h a s e s caused by different moleculair orientations can also be visualized. By changing the extinction settings of the ellipsometer, the contrast of the images can be varied and inverted. Together with the Brewster angle microscope (BAM, see next subsection) t h e ellipsometric microscope offers a valuable alternative to fluorescence microscopy, because no (fluorescence) probes, which might affect the monolayer properties, are needed. In contrast to imaging with a BAM, ellipsometric imaging is not limited to the Brewster angle. Therefore, it can be applied to any perfectly reflecting s u p p o r t a n d at different angles of incidence. So far, however, the t e c h n i q u e is not in widespread use. (ii) Brewster
angle microscopy.
In 1991 the Brewster angle microscope (BAM)
was independently introduced by two groups-^K For a molecularly smooth interface the technique u s e s t h e m i n i m u m reflectance for parallel polarized light a t t h e Brewster angle of incidence (1.7.10). The presence of a monolayer alters t h e optical properties of the interface, resulting in e n h a n c e d reflectivity in film-covered regions. For monolayers at the a i r / w a t e r interface this allows visualization of t h e morphology in the LE-LC coexisting phase region. By introducing a polarizer in the reflected b e a m p a t h (making the set-up equivalent to t h a t of a PSA ellipsometer) optical a n i s o t r o p y in t h e monolayer, resulting from long-range orientational ordering of molecules, is detected. In this way the inner s t r u c t u r e of c o n d e n s e d p h a s e s also becomes visible (fig. 3.56). The lateral resolution of the i n s t r u m e n t is of the s a m e order a s t h a t of the ellipsometric microscope, i.e. ~ 1 |im. The instrumentation h a s been described in detail in ref.^^. BAM h a s b e e n widely u s e d for studying the formation a n d morphological features of condensed domains in the LE-LC coexistence region a n d to observe a n d analyze t h e p h a s e diagrams of Langmuir monolayers^K Upon rapid compression of a monolayer across a p h a s e transition, non-equilibrium s t r u c t u r e s like dense-
^^ One of the first papers dealing with microscopic imaging ellipsometry is by R. Reiter, H. Motschmann, H. Orendi, A. Nemetz and W. Knoll, Langmuir 8 (1992) 1784. A detailed discussion of the design features of the imaging ellipsometer is given by M. Harke, R. Teppner, O. Schulz, H. Orendi and H. Motschmann, Rev. Set Instr. 6 8 (1997) 8. 2) D. Honig, D. Mobius, J. Phys. Chem. 95 (1991) 4590; S. Henon, J. Meunier, Rev. Set Instr. 62 (1991) 936. ^^ D. Honig, G.A. Overbeek and D. Mobius, Adv. Matter. 4 (1992) 419; D. Vollhardt, Adv. Colloid Interface Set 64 (1996) 143. "^^ Nice examples are the studies by Teer et al. (E. Teer, CM. Knobler, C. Lautz, S. Wurlitzer, J. Kildae, T.M. Fisher, J. Chem. Phys. 105 (1997) 1913) and by Vollhardt and coworkers (see D. Vollhardt, Adv. Colloid Interface Set 6 4 (1996) 143 and references therein).
3.146
LANGMUIR MONOLAYERS
Figure 3.56. BAM image of a monolayer of pentadecanoid acid on water at pH 3 in the LELC coexistence region. The picture shows the familiar circular domains formed by the condensed phase. They do not have a uniform intensity but exhibit regions slightly differing in intensity, indicating differences in tilt angle and/or tilt direction. (From M.A. Cohen Stuart, R.A.J. Wegh, J.M. Kroon and E.J.R. Sudholter, Langmuir 12 (1996) 2863.) b r a n c h e d and dentritic domains of the more condensed phases, which subsequently relax into circular domains, are often formed^I BAM m e a s u r e m e n t s have been invoked to a s s e s s the line tension of monolayer domains by following the deformation during shear distortion and the subsequent relaxation^). However, the caveat m u s t be m a d e t h a t the m e a s u r e m e n t of line tensions is, even u n d e r simpler conditions, not yet established (see sec. 5.6). An induced flow may also reorient the molecules in condensed p h a s e s . BAM studies have also been performed to examine the effect of LB transfer on the organization of monolayers of different types of a m p h i p h i l e s ^ ) . Using BAM, Melzer and Vollhardt"^) have provided evidence t h a t monolayers of soluble surfactants can also show a two-dimensional p h a s e behaviour in that, during their adsorption at the a i r / w a t e r interface, condensed p h a s e domains may be formed. (Hi) X-ray and neutron rejlection. X-ray and n e u t r o n reflection and -scattering techniques have recently emerged as powerful tools for the investigation of interim U. Gehlert. D. Vollhardt, Langmuir 13 (1997) 277. 2) S. Riviere, S. Henon, J. Meunier, G. Albrecht, M.M. Boissonade and A. Baszkin, Phijs. Rev. Lett. 75 (1995) 2506; E.K. Mann, S. Henon. D. Langevin, J. Meunier and L. Leger, Phys. Rev. E. 51 (1995) 5708. ^^ See CM. Knobler, loc. cit. 4) V. Melzer, D. Vollhardt, Phys. Rev. Lett. 76 (1996) 3770.
LANGMUIR MONOLAYERS
3.147
faces. Due to the advent of well-collimated, high-intensity n e u t r o n reactor a n d s y n c h r o t o n X-ray s o u r c e s these t e c h n i q u e s allow for the d e t e r m i n a t i o n of t h e vertical a n d in-plane s t r u c t u r e a n d fluctuations of interfaces with a resolution a p p r o a c h i n g t h e atomic level. Since most bulk p h a s e s are relatively t r a n s p a r e n t for X-rays a n d n e u t r o n s , buried interfaces can also be studied. The r e a s o n t h a t high-intensity b e a m s are needed to study interfaces is t h a t X-ray a s well a s n e u t r o n radiation is only weakly scattered a n d the n u m b e r of a t o m s confined within t h e interfacial region is small. Only high-intensity sources allow for a c c u r a t e d a t a collection within a reasonable time. Apart from that, the weak scattering h a s the advantage t h a t the interpretation of reflection a n d scattering p a t t e r n s in t e r m s of the underlying s t r u c t u r e becomes relatively simple a n d reliable (but not unequivocally a s we will discuss later) due to the validity of the B o m approximation. Highintensity n e u t r o n a n d X-ray reflectometers are nowadays available t h r o u g h o u t the world in c e n t r a l facilities. The i n s t r u m e n t a t i o n h a s b e e n d e s c r i b e d in t h e l i t e r a t u r e ^^. Generally, reflection a n d scattering of electromagnetic radiation t a k e place u p o n interaction with matter, exhibiting refractive index inhomogeneities. The s a m e processes do also take place with X-rays and n e u t r o n s . Basically X-rays are electromagnetic waves a n d hence can be treated with the corresponding m a t h e m a t ical formalism. Their scattering is mainly determined by the electrons, w h e r e a s the scattering of the uncharged neutrons is dominated by the atomic nuclei. Hence, the two techniques provide complementary information. Scattering of electromagnetic radiation leads to diffraction,
b e c a u s e of the interference of the radiation
scattered by different atoms. When these atoms are arrcmged in a n ordered, fixed pattern, containing a large n u m b e r of scatterers, a s in a crystal, a discrete diffraction p a t t e r n is produced, exhibiting dots or rings, depending on the m e t h o d of m e a s u r e m e n t (see below, part (iv) of this subsection). For monolayers the density is only large e n o u g h in the tangential direction. Hence, incident b e a m s m a k i n g a very small angle with t h i s layer (grazing
incidence)
are required to o b t a i n
significant signals. Regarding the phenomenological description in t e r m s of refractive indices, n, for non-magnetic materials, generally and to a good approximation one c a n write n = l-d
+ ip
[3.7.2]
The imaginary c o m p o n e n t of n arises when the m e d i u m is absorbing (section 1.7.2c). For X-rays the term 8 is given by
^' For neutron reflectometers see, for example, J. Penfold et al., J. Chem. Soc, Faraday Trans. 9 3 (1997) 3899; J. Penfold, R.K. Thomas, J. Phys.: Condens. Matter 2 (1990) 1369; T.P. Russell, Mater, Set Reports 5 (1990) 171. For X-ray reflectometers: T.P. Russell, see his review in sec. 3.101; J. Als-Nielsen, D. Jacquemain, K. Kjaer, F. Leveiller, M. Lahav and L. Leiserowitz, Phys. Reports 246 (1994) 251,
3.148
LANGMUIR MONOLAYERS
^X=^Pe^^
13-7.31
in which r^ is the Thompson
radius of an electron (also referred to as the
classical
electron radius, 2.82 x 10"^^ m) and p^ the electron density. For wavelengths below = 1 n m the absorption term can frequently be ignored without introducing a significant error. This, however, is not the case if high atomic n u m b e r c o m p o u n d s are present. For neutrons, S =—pX^
13.7.4]
with p,j the scattering length density, which is related to the chemical composition and density of the medium through p =ynb
13.7.51
J
where n. is the n u m b e r density of nuclei of type j and b. their scattering length. For n e u t r o n s , the absorption factor is also negligible in most cases, except for materials containing strong absorbers s u c h as lithium, borium, cadmium, s a m a r i u m a n d gadolinium. Since S and ^^are generally of the order of 10'^ - 10~^ ^\ the X-ray or n e u t r o n refractive index deviates only slightly from 1, the refractive index of air or a vacuum. For X-rays the real part of the refractive index, 1 - ^ ^ ' ^^ always smaller t h a n 1, b e c a u s e 5
is always positive. This implies t h a t for a i r / s o l i d a n d a i r /
liquid interfaces there is a critical grazing angle 6 (given by cos 6 = n, with 6 defined with respect to the interfacial plane; n is the refractive index of the solid or liquid) below which total reflection occurs (see section 1.7.10). Critical grazing angles are very small. For n e u t r o n s d
may be either positive or negative. Most
isotopes have a positive scattering length b., b u t there are some exceptions, the most notable one being the proton. The result is t h a t the refractive index for n e u t r o n s is greater t h a n unity for normal (light) water and less t h a n unity for heavy water. Therefore, total reflection of neutrons from a light water surface does not occur. The reflectivity of X-rays a n d n e u t r o n s from a water surface is illustrated in fig. 3.57. In a n X-ray or neutron reflection experiment the specular reflection, R (the ratio between the reflected and incident intensities), is measured as a function of the scattering vector q; q = fcr" ^i^ (where k- and k^ are the incident and reflected wave vectors, respectively (sections 1.7.4 and 10^^. Since in reflection m e a s u r e m e n t s the angle of incidence and the detection angle are equal, q is always exactly normal to
1^ Typical values for 5x and d,, are tabulated bv T.P. Russell. Mater. Set. Repts. 5 [1990] 171. ^^ In scattering jargon q's are also called wave vector transfers'.
LANGMUIR MONOLAYERS
3.149
X-ray HgO or D2O — — — - neutron neutron D2O D2O neutron H2O
Figure 3.57. The reflectivity of the cdr/water interface as a function of the scattering vector Qz for X-rays £ind neutrons. Note the significant difference between H2O and D2O for neutrons. (Redrawn from J. Als-Nielsen, D. Jacquemain, K. Kjaer, F. Leveiller, M. Lahav and L. Leiserowitz, Phys. Reports 246 (1994) 251.) the surface a n d its magnitude is given by [3.7.6]
-— cos 6 = —— sin 6. X A ^
where Q. is the grazing angle of incidence, Q is the angle of incidence with respect to t h e interface normal, a n d A is t h e wavelength of the incident X-ray or n e u t r o n radiation. The variation of R with q^ (the rejlecttvity
profile) d e p e n d s u p o n t h e
refractive i n d e x profile n o r m a l to t h e interface. The s p e c u l a r reflection of n e u t r o n s a n d X-rays provide a spatial resolution in t h e direction normad to t h e interface, down to ca. 0.1 n m w i t h p e n e t r a t i o n d e p t h s over h u n d r e d s of n a n o m e t e r s . Lateral variations in density are averaged over the b e a m area. As t h e refractive index differs only slightly from unity, relative v a r i a t i o n s in refractive index in t h e interfacial region are also very small a n d t h e reflectivity m a y be treated a s the Fresnel reflectivity between two bulk p h a s e s modulated by small interference effects from the interfacial region. Neglecting refraction, which is justifiable for the u s u a l situation t h a t q »
q {= q
a t t h e critical angle), a n d
absorption this leads to the kinematic or Bom approximation^^ R(o) =
16;r^
I
|2
13.7.7]
In this equation P(q ) is t h e one-dimensional Fourier transform of t h e density
^^ For a derivation see, for example, J. Penfoid, R.K. Thomas, loc. cit, or J. Als-Nielsen, K. Kjaer, in Phase Transitions in Soft Condensed Matter, NATO ASI Series, Plenum Press, (1989) 113-138, in this section referred to as J. Als-Nielsen, K. Kjaer, loc. cit.
3.150
LANGMUIR MONOLAYERS
profile p{z) at the interface: +00
^ ( q , ) = jp(z)exp(iq^z)d2
[3.7.8]
For a Fresnel interface, the density profile is a step function and the Fourier transform e q u a l s (Apf / q^, with Ap the difference in density between the two phases. T h u s , in the B o m approximation,
R^iciJ-'-^^^^ f
z
[3.7.91 q^ ^z
Equation [3.7.7] is equivalent to the following expression, which is also often encountered in the literature: R(qJ = R^iqj\P^'\q,j\^ where P^^\q ) is the Fourier transform of the gradient
[3.7.10] of the density profile across
the interface. The Born approximation h a s been found to be accurate for describing reflectivity d a t a from monolayers on water when grazing angles exceed twice the critical angle; the remaining discrepancy can be repaired by including of a refraction correction ^K In the analysis of X-ray reflectivity data one a t t e m p t s to derive the electron density profile across the interface. However, as in all reflection and scattering t e c h n i q u e s p h a s e information is lost: R(q ) c o n t a i n s only the s q u a r e of the Fourier t r a n s f o r m of the density profile. This information is not e n o u g h to establish the profile uniquely, since more t h a n one profile can produce the same R[q ). One could try a certain model profile p{z) and use [3.7.8 and 7] to obtain R(q);
i n t r o d u c i n g a d j u s t m e n t s or iterations until the outcome m a t c h e s t h e
e x p e r i m e n t . Alternatively, calculations of the reflectivity profile for a given (model) density profile can be made using the same method a s described in the previous subsection, i.e. by dividing the interfacial region into a set of parallel layers of c o n s t a n t refractive index a n d o b t a i n i n g a n iterative solution by matching b o u n d a r y conditions at each interface. Since different profiles may fit the data equally well, the credibility of the model used should be checked carefully. Of course, in this there is no s u b s t i t u t e for i n d e p e n d e n t additional pieces of information. In general, t h e oscillations observed in the reflectivity profile (the so-called Kiessig fringes)
yield a characteristic thickness in the system u n d e r study. These
may be t h o u g h t of a s interference fringes from scattering by the top and bottom
^^ J. Als-Nielsen, K. Kjaer, loc. cit.
LANGMUIR MONOLAYERS
3.151
2.5 h 60
(a;
R/Rv
E 40
2.0
20
o
1\\
1.5
I
1
Aj-is
0
V \
O
\
1
O
0.20
,
1
.
0.22
1
.
0.24
1
0.26
.2 a, / nm-^
1.0
0.5
\ _L
_L
_L
Qz/ "f"
-1H/2
PT
tail
S.
-1H/2 + 1H/2
head
p
'^H
^
► p(z)
Y^ water
\
nb )
^^ Figure 3.58. (a) Normalized X-ray reflectivity [RIR^] as a function of the scattering vector transfer q for arachidic acid monolayers on pure water (T = 20°C). For better visibility the curves marked ^, / a n d 5 are displaced upward by 0.25, 0.5 and 1.0, respectively. Here a, j3, / a n d 5 correspond to the surface pressures indicated in the n{a^ isotherm of the insert, (b) Two-box density profile used to fit the data in (a). The boxes describing the tail region (T) and the polar head region (H), respectively, are smeared by a Gaussian, as indicated by the solid line. (Redrawn from J. Als-Nielsen and K. Kjaer, loc. cit.)
3.152
LANGMUIR MONOLAYERS
interfaces of a distinct layer of thickness A. Using [3.7.7] it can be shown t h a t the resulting m a x i m a in R{q ) are separated by Aq = 2;r / A. The occurrence of s u c h oscillatory p a t t e r n s m a y serve to restrict t h e models u s e d for c a l c u l a t i n g reflectivity profiles to be compared with experimental data. For example, fig. 3.58a shows X-ray reflectivity profiles obtained from Langmuir monolayers of arachidic acid at various surface p r e s s u r e s . A shift of the extrema in the profiles to lower q^ with increasing surface pressure can be seen, indicating t h a t t h e monolayer t h i c k n e s s increases. The full lines represent fits with a simple box-model of the monolayer as depicted in fig. 3.58b a n d using the Born approximation. The s h a r p box edges are smeared out by a Gaussian function of which the Fourier transform can readily be written down. In this example the n u m b e r of fitting p a r a m e t e r s w a s further reduced by taking for the tail box dimension at the highest surface pressure the all-trans hydrocarbon chain length t h a t follows from molecular models. Generally, when molecular dimensions are known, the average tilt can be inferred from the m e a s u r e d thickness, except at small angles, where the thickness is insensitive to the tilt. The analysis of n e u t r o n reflectivity data is carried out in a similar way a s for Xray reflection. However, n e u t r o n reflection allows one to obtain more detailed information t h a n with X-ray reflection; since protons a n d d e u t e r o n s have very different n e u t r o n scattering properties, with n e u t r o n reflection it is possible to highlight different p a r t s of monolayers a n d study these independently. This is accomplished by the selective substitution of protons by deuterons in the monolayer molecules. Moreover, the refractive index of the a q u e o u s solvent may be matched to t h a t of air by adjustment of the H2O/D2O ratio [null reflecting water). In m a n y c a s e s sufficiently different m e a s u r e m e n t s , with differently labelled combinations, can be made to overdetermine a problem or to enable a n analysis t h a t is much less sensitive to the choice of a model. For instance, to elucidate the structure of amphiphilic monolayers at the a i r / w a t e r interface from n e u t r o n reflectivity data, Simister et al.^^ used partial structure factors for head groups, hydrophobic c h a i n s a n d solvent. In this approach the scattering length density profile across the interface is written in t e r m s of the n u m b e r density profiles a n d scattering lengths of these components. The individual s t r u c t u r e factors can be determined i n d e p e n d e n t l y by performing n e u t r o n reflection m e a s u r e m e n t s at
different
isotopic compositions of the system. (iv) Grazing incidence
diffraction
of X-rays.
Irradiation of an interfacial region
containing a periodic s t r u c t u r e results in diffraction.
Surface diffraction of X-rays
is the two-dimensional analogue of three-dimensional scattering of X-rays by crystals, or of light by colloidal dispersions. The first X-ray diffraction data from
1^ E.A. simister, E.M. Lee, R.K. T h o m a s and J . Penfold, J. Phys. Chem. 9 6 (1992) 1373.
LANGMUIR MONOLAYERS
3.153
diffracted from evanesc. beam
grazing incidence
side view
PSD
top view specularly reflected Figure 3.59. Top and side-view of the experimental set-up for grazing incidence X-ray diffraction measurements on Langmuir monolayers. The 'footprint' of the incident beam is indicated by the darker area. Only the crossed-beam area ABCD contributes to the detected scattering. The Soller collimator selects a horizontal scattering angle of 20\ the positionsensitive detector (PSD) has its axis vertical and measures the Bragg rod profiles. In this geometry one has the ability to determine the lateral (q ) as well as the vertical (q^) components of the scattering vector. (Redrawn from J. Als-Nielsen and K. Kjaer, loc. cit. Langmuir monolayers were reported by Mohwald a n d co-workers in 1986^^ Since then, scattering of X-rays h a s been successfully applied to elucidate the s t r u c t u r e of condensed p h a s e s of monolayers at the water surface, self-assembled monolayers a n d LB films. In addition, it h a s become possible to monitor by diffraction t h e growth a n d dissolution of 2D crystalline aggregates a s well a s s t r u c t u r a l c h a n g e s in monolayers i n c u r r e d u p o n p h a s e t r a n s i t i o n s . There a r e several overviews of w h a t h a s been achieved '^\ As stated, surface-specific investigations u s i n g X-ray diffraction are tied to ^^ H. Mohwald, in The Physics and Fabrication of Microstnictures and Microdevices, M.J. Kelly, C. Weisbuch, Eds., Springer Verlag, (1986); K. Kjaer, J. Als-Nielsen, C.A. Helm, L.A. Laxhuber and H. Mohwald, Phys. Rev. Lett 58 (1987) 2224. 2) J. Als-Nielsen et al., loc. cit.; H. Mohwald, H. Baltes, M. Schwendler, C.A. Helm, G. Brezesinski and H. Haas, Jpn. J. Appl Phys. 34 (1995) 3906; S. Dietrich, A. Haase, loc. cit.: S.K. Sinha, Curr. Opinion Solid State Mater. Set 1 (1996) 645; P. Dutta, Curr. Opinion Solid State Mater. Set 2 (1997) 557; A. Datta, J. Kmetko, A.G. Richter, C.-J. Yu and P. Dutta, Langmuir 16 (2000) 1239.
3.154
LANGMUIR MONOLAYERS
grazing incidence to obtain sufficient sensitivity and to s u p p r e s s the bulk background scattering. Therefore, narrow well-collimated b e a m s are required to obtain sufficiently high intensities at the sample surface to predominantly probe the monolayer. In a typical experiment, carried out at a grazing incidence angle ol 10~2 radians a 100 \im vertical slice of a collimated beam is spread over a 1 cm long strip of the sample surface in the direction of incidence. Thus, the intensity of the beam is effectively reduced by a factor of 100. Usually, the incident beam is at a fixed grazing angle which is smaller t h a n the critical angle for total reflection. Under conditions of total reflection, the only wave penetrating into the s u b p h a s e is the evanescent wave. So, scattering from the bulk is substantially reduced, althoughit is non-zero. For a water surface the penetration depth of the evanescent wave is limited to a few n a n o m e t e r s (section 1.7.10). Figure 3.59 shows the geometry of a grazing incidence diffraction (GID) experiment. For more detailed information on the instrumentation the reader is referred to the literature^I The in-plane s t r u c t u r e of the interface is probed by m e a s u r i n g the scattered intensity a s a function of the angle 20 (fig. 3.59), or, equivalently, a s a function of the horizontal component of the wave-vector, q
If the molecules in the interface
are arranged in a two-dimensional periodic structure, diffraction occurs when q^^^ coincides with a reciprocal lattice vector q d^^ -2K I q -
d
, fulfilling the Bragg condition
is the lattice spacing. The Miller indices h,k indicate the posi-
tions of the diffraction p e a k s in the reciprocal lattice. There is no restriction on the z-component of the Bragg-scattered beam. In other words, a two-dimensional lattice confines the scattering to Bragg rods, not to Bragg points
as for a three-
dimensional crystal. Diffraction p a t t e r n s from monolayers at the a i r / w a t e r interface show the c h a r a c t e r i s t i c s of a 2D 'powder' s p e c t r u m , implying t h a t s u c h monolayers are composed of 2D crystallites randomly oriented on the water surface. The sizes of these crystallites can be estimated from the width of the Bragg peaks at half m a x i m u m . The grazing incidence diffraction signal at fixed 20 corresponding to a Bragg reflection a s a function of q , is called a Bragg rod scan and the result a Bragg rod profile. This can be measured, for example, with a vertical position-sensitive detector a s in fig. 3.59. Like a specular reflectivity profile, a Bragg rod profile contains s t r u c t u r a l information perpendicular to the interface. Nevertheless, the information provided by these two types of d a t a sets is not identical. Specular reflection m e a s u r e s an average density profile across the interface, including cont r i b u t i o n s from the s u b p h a s e (or solid s u b s t r a t e ) . Bragg rod profiles provide s t r u c t u r a l information in the z-direction for crystalline
parts
of the
monolayer
only. Neither non-crystalline p a r t s nor the s u b p h a s e contribute to the diffraction ^^ See, for example, J. Als-Nielsen, D. Jacquemain, K. Kjear. F. Levelller, M. Lahav and L. Laiserowitz, Phys. Repts. 246 (1994) 251; G.J. Foran, I.R. Gentle, R.F. Garrett, D.C. Crea.i^. J.B. Peng and G.T. Barnes, J. Synchroton Rad. 5 (1998) 107.
LANGMUIR MONOLAYERS
3.155
pattern; they J u s t give rise to a flat background signal which h a s to be s u b t r a c t e d from t h e total intensity. The intensity distribution along t h e Bragg r o d s is d e t e r m i n e d by t h e u n i t cell s t r u c t u r e factor, i.e. the Fourier transform of t h e electron density profile in the z-direction. For the case t h a t there is one molecule per u n i t cell, t h e s t r u c t u r e factor is identical to the molecular form factor. Therefore, using a model for the s h a p e of the molecules, it is in principle possible to d e d u c e from t h e Bragg rod profiles molecular tilt angles with respect to t h e interfacial plane a n d tilt directions in the u n i t cell^^ However, one generally observes only a few Bragg rods over a limited q
range, a n d therefore one h a s to
resort to simple molecular models, s u c h a s a rod or a cigcir. Nevertheless, in-plane diffraction experiments with the capability of m e a s u r i n g t h e Bragg rod intensity m o d u l a t i o n provide a very powerful m e t h o d for d e t e r m i n i n g t h e m o l e c u l a r s t r u c t u r e of monolayers in crystalline p h a s e s . For example, in t h e p h a s e diagrams of m a n y s a t u r a t e d fatty acid Langmuir monolayers the assignment of the p h a s e s to a molecular arrangement h a s been m a d e on the basis of X-ray diffraction data-^^ It
0.20
0.24
0.22 ttj / nm^
Figure 3.60. Tilt angle 6^ as a function of molecular area a for arachidic acid monolayers on pure water (T = 20°C) determined from X-ray diffraction data (•). For comp£irison, the tilt angle as calculated from reflectivity data (from the ratio between the thickness of the tail region and the length of the tail) is also shown (O). The drawn curve represents the function a. - a^/cos6 , with a^ = 19.8 nm^, and the agreement between this curve and the experimental values indicates that compression does not increase the density of the tail region, but merely decreases the tilt angle. The transition from the until ted state to the tilted state appears to be continuous. (Redrawn from H. Mohwald, C. Bohm, A. Dietrich and S. Kirstein. Liq. Cryst 14 (1993) 265.) 1) J. Als-Nielsen. K. Kjaer, loc. cit. 2) R.M. Kenn, C. Bohm, A.M. Bibo, I.R. Peterson, H. Mohwald, J. Als-Nielsen and K. Kjaer, J. Phys. Chem. 9 5 (1991) 2092; H. Mohwald, C. Bohm, A. Dietrich and S. Kirstein,. Liq. Cnjst 14 (1993) 265 and references therein; P. Dutta. loc. cit. and references therein.
3.156
LANGMUIR MONOLAYERS
is found t h a t at high surface p r e s s u r e s the molecules are always untilted, i.e. the acyl c h a i n s are parallel to the normal of the a / w interface (see, e.g., fig. 3.60). At lower p r e s s u r e there are tilted p h a s e s , with tilt either towards a nearest neighbour or a next-nearest neighbour. The so-called 'swivelling transition' between a nearest neighbour tilted state to a next-nearest neighbour tilted state could also be studied by X-ray diffraction a n d was found to proceed through an intermediate state, with the tilt in a n intermediate direction ^^ At low temperatures the lattice is distortedhexagonal when seen in the plane t h a t is normal to the acyl chains, the distortion being d u e to the non-circular cross-section of the molecules. At higher temperatu r e s the lattice is hexagonal. This h a s been attributed to rotation of the molecules along their long axes (although it is more likely t h a t the molecular cross-sections are orientationally disordered); these p h a s e s are therefore called rotator 3.7c
Spectroscopic
phases.
techniques
A n u m b e r of spectroscopic techniques have already been discussed in Volume I (sees. 7.11-13). Here, we will focus on the application of vibrational (infrared and Raman) a n d UV/visible spectroscopy, fluorescence and second-order nonlinear optical techniques for the study of monolayers. The type of information obtained with these techniques refers to the chemical composition, surface coverage, molecular conformation a n d orientation, and dynamics of monolayers. The principle of deriving orientational information from spectroscopic m e a s u r e m e n t s is a s follows. Polarized electromagnetic radiation is directed onto the sample. The probability of excitation is proportional to the overlap between the electric field vector E of the radiation and the relevant absorption dipole moment /i of the molecules, i.e. to cos^a, where a is the angle between E and fi. The result is t h a t excitation is dominated by t h a t population of molecules with their absorption m o m e n t oriented in the direction of electric field vector of the radiation (or at a small angle to it). This concept is called photoselection.
By measuring the degree of
absorption or (in the case of fluorescence) emission as a function of the polarization angle or angle of incidence of the radiation, we obtain information on the orientation of specific parts of the molecules. For radiation in the infrared region of the s p e c t r u m this concerns the orientation of specific b o n d s (conformational order); in the case of excitation by UV or visible light, we extract information on the orientation of chromophoric or fluorescent groups. For organized lamellar s t r u c t u r e s , like monolayers, Langmuir-Blodgett films a n d b u l k lamellar p h a s e s of amphiphiles, the orientation distribution of t h e molecules
is u s u a l l y
described
using
an
axially
symmetric
orientation
distribution function, N{6), with ^ t h e a z i m u t h a l tilt angle. This d i s t r i b u t i o n
1^ M.K. Durbin, A. Malik, A.G. Richter, R. Ghaskadvi, T.Gog and P. Dutta, J. Phys. Chem. 106 (1997) 8216.
LANGMUIR MONOLAYERS
3.157
function can be expginded in Legendre polynomials as
N(e)
AmU n n=0
Jcos0)
[3.7.11]
in which c = n
■(2rn-l)" <Sn> 2
[3.7.12]
where (S^) are the moments of the distribution function, the so-c£illed order parameter s^\ The brackets <) denote a time or ensemble average, the two being identical. The orientation distribution is fully characterized if aill the order parameters <S ) are known. On the basis of symmetry considerations (no difference between N{0) and N(18O°-0)), the odd coefficients c„ are generally taken a s zero. The second-orientational order parameter can be obtained using absorption spectroscopy and is defined as (S^lcos^ e)) = i (3(cos^ e) -1)
[3.7.13]
where (S^) rcinges from - 0 . 5 for 0 = 90° (with respect to the interface normal) to 1.0 for 9=0°.
For intermediate values sometimes an average tilt angle is directly
calculated from (S^), but without further information on the orientation distribution this is misleading, since its value depends on both the angular position and the shape of the orientation distribution^^ However, it is safe to state that as (S^) has a value more close to 1, the average tilt angle is smaller and the degree of ordering in the layered structure is higher. From two-photon processes like fluorescence it is possible, in principle, to derive (S^) in addition to (S^). The fourth order parameter is given by (S^) = i (35(cos^ e) - 30(cos2 G) + 3)
[3.7.14]
Knowledge of both (S^) and (S^) gives much more insight into the orientation distribution than having only (S ). For example, a random distribution in 6 and a (sharp) distribution with its maximum at 9= 54.7° both have a (S^) value of zero. Knowing (S^> one cam readily distinguish between these distributions; for a random distribution (S^) is also zero, while for a sharp distribution around 9= 54.7° ^^ We keep to the nomenclature used before, see [1.6.5.58] and [3.5.1], where S{s) equals S^ in [3.7.13], the small s referring to the number of the chain element. In the spectroscopic literature usually the S3mibol P is used. ^^ Model distributions to show the relationship between the shape, width, and angular position, and examples illustrating the magnitude of the errors that cam be introduced in calculations of the tilt angle from {S^ > in the case of distributions of finite widths or of a bimodal character are given by C.P. Lafrance, A. Nabet, R.E. Prud'homme cmd M. Pezolet, Can, J. CheTTL 73 (1995) 1497.
3.158
LANGMUIR MONOLAYERS
J <S4)
Figure 3 . 6 1 . Relation between the order parameters (S,^) and <S^>. The physical boundaries of (S^) and <S^), which follow from [3.7.13 and 14], are indicated by solid curves. The dashed curve indicates combinations of the two order parameters which correspond to Gauss type distributions. The insets show the shapes of the distribution function N{6) for 6 between 0° and 90° as calculated using the maximum entropy method. (Adapted from M.A. Bos and J.M. Kleijn, Biophys. J. 68 (1995) 2566.) (S ) a m o u n t s to - 0 . 3 6 . From the two order parameters together a n estimation of the orientation distribution may be obtained by a s s u m i n g a model distribution (e.g. of the G a u s s type) or by applying the maximum-entropy method ^^ In this latter approach no a priori a s s u m p t i o n s have to be made w^ith respect to the shape of t h e d i s t r i b u t i o n function; the underlying idea is t h a t the m o s t probable distribution is the one that can be realized in the greatest n u m b e r of distinguishable ways, subject to the knov^ni constraints, (see fig. 3.61). Anticipating the discussion on fluorescence techniques later in this subsection, it is mentioned t h a t , d u e to the time scale on which fluorescence takes place.
1) R.M. Bevensee, Maximum Entropy Solutions to Scientific Problems, Prentice-Hall Inc., (1983); see also, for example, M.A. Bos, J.M. Kleijn, Biophys. J. 68 (1995) 2566.
LANGMUIR MONOLAYERS
3.159
rotational movement of the molecules affects the polarization of t h e emission. Therefore, time-resolved
fluorescence
m e a s u r e m e n t s allow one to obtain inform-
ation on b o t h ordering a n d rotational dynamics. (i) Infrared
spectroscopy.
Infrared spectroscopy is b a s e d on t h e absorption of
electromagnetic radiation by m a t t e r d u e to different vibrational m o d e s of t h e chemical b o n d s (see 1.7.12). In Fourier transform infrared spectroscopy (FTIR) the sample is i n s t a n t a n e o u s l y exposed to radiation frequencies over the whole releva n t IR s p e c t r u m , after which the obtained interferogram is transformed to a n intensity-wavenumber spectrum. S t r u c t u r a l d a t a are inferred from the observed w a v e n u m b e r positions of t h e absorption p e a k s , a n d information on molecular conformations a n d local environments is deduced from line widths a n d frequency shifts in the spectra, a s compared to molecules in the gas p h a s e . From polarization s p e c t r a of oriented s a m p l e s information on the ordering of specific s t r u c t u r a l u n i t s is obtained. As a r e s u l t of t h e large n u m b e r of vibrational m o d e s , IR s p e c t r a of large molecules are generally very complex a n d not well-resolved in m a n y regions of t h e s p e c t r u m . However, absorption b a n d s at distinct frequencies c a n be assigned to specific functional g r o u p s in amphiphiles like fatty acids a n d lipids. There a r e overviews of IR vibrational modes t h a t are useful for the analysis of hydrocarbon chain configurations a n d orientations, a n d for the evaluation of the polar regions of a m p h i p h i l e s 1^. For a long time the investigation of monolayers at the a i r / w a t e r interface using IR spectroscopy w a s thwarted by strong absorption by water molecules, hiding the spectral region, where the most interesting molecular information is to be found. A way to circumvent this problem is by transferring the monolayer onto a solid s u b strate a n d using attenuated total reflection (ATR) or IR external reflection spectroscopy. ATR is a kind of wave-guiding technique where, before it is focused on the detector (II.2.5c), t h e IR b e a m is subjected to multiple reflections inside a n i n f r a r e d - t r a n s p a r e n t crystal of, for example, silicon, g e r m a n i u m or c a l c i u m fluoride.
IR external reflection spectroscopy, also referred to a s IR reflection-
a b s o r p t i o n s p e c t r o s c o p y (IRRAS or IRAS), is a direct reflection
technique,
comparable with ellipsometry. For a long time after its introduction in t h e late 1950s^^ it w a s only possible to apply it to films on high-reflectivity (metallic) s u b s t r a t e s . D u e to t h e a d v e n t of specific FTIR i n s t r u m e n t a t i o n a n d
new
experimental designs specifically developed for thin films, it is now feasible also to acquire IRRAS spectra on low-reflectivity s u b s t r a t e s , like glassy carbon, a n d
1^ R. Mendelsohn, J.W. Brauner and A. Gericke, Ann. Rev. Phys. Chem, 46 (1995) 30; L.K. Tamm, S.A. Tatulian, Quart. Rev. Biophys. 30 (1997) 365. 2) S.A. Francis. A.H. Ellison. J. Opt. Soc. Am. 49 (1959) 131.
3.160
LANGMUIR MONOLAYERS
(more importantly) directly on the a i r / w a t e r interface ^K One of the problems, interference from w a t e r v a p o u r absorption, c a n be overcome by polarization modulation. In ATR-FTIR excitation occurs only in the immediate vicinity of the surface of the reflection element, in a n evanescent wave resulting from total internal reflection. The intensity of the evanescent field decays exponentially in the direction normal to the interface with a penetration depth given by [1.7.10.121, which for IR radiation is of the order of a few h u n d r e d s of nm. Absorption leads to an attenuation of the totally reflected beam. The ATR spectrum is similar to the IR t r a n s mission s p e c t r u m . Only for films with a thickness comparable to, or larger than, the penetration depth of the evanescent field, do the band intensities depend on the film t h i c k n e s s . Information on the orientation of defined structural units can be obtained by measuring the dichroic ratio defined as R = A^^/Aj^, where A^/ and A^ are the b a n d a b s o r b a n c e s for radiation polarized parallel a n d perpendicular with respect to the plane of incidence, respectively. From this ratio the second-order p a r a m e t e r of the orientation distribution (eq. [3.7.13]) can be derived^^ ATR-FTIR h a s b e e n extensively u s e d to s t u d y t h e conformation a n d ordering in LB m o n o l a y e r s , bilayers a n d multilayers of fatty acids a n d lipids. E x a m p l e s of various studies can be found ^h In IRRAS a n IR s p e c t r u m of a thin organic film is obtained by reflecting the incoming radiation from the three-phase ambient-film-subphase system'^l measuring the reflected intensity a s a function of wavenumber and then dividing this spectrum by the spectrum obtained from the two-phase a m b i e n t - s u b p h a s e system. The data are presented a s plots of reflectance-absorbance (RA) vs. wavenumber. RA is defined as -log(R/RJ where R is the reflectivity signal of the film-covered surface and RQ is t h a t of the bare surface. As for ellipsometry, the theoretical description of IRRAS is b a s e d u p o n the Maxwell a n d Fresnel equations, applied to a system consisting of a n u m b e r of parallel, optically isotropic layers. The analysis h a s been extended in different ways to include the anisotropic n a t u r e of monolayers and LB films^^ In spectra obtained from monolayers at the air/water interface RA p e a k s may be positive or negative, depending on the angle of incidence, polariz-
^' The first IR reflection spectrum of a monomolecular layer on a water surface with an acceptable signal-to-noise ratio was reported by R.A. Dluhy and D.G. Cornell, J. Phys. Chem. 89 (1985) 3195. 2) See, for example, P.H. Axelsen, M.J. Citra, Progr. Biophys. Molec. Biol 66 (1997) 227. ^^ M.H. Greenhall. P.J. Lukes, M.C. Petty, J. Yarwood and Y. Lvov, Thin Solid Films 2 4 3 (1994) 596; R.A. Dluhy, S.M. Stephens, S. Widayati and A.D. Williams, Spectrochim. Acta A 51 (1995) 1413; N. Vila, M. Pugelli and G. Gabrielli. Colloids Surfaces A 119 (1996) 95: D.J. Neivandt, M.L. Gee. M.L. Hair and C.P. Tripp, J. Phys. Chem. B 102 (1998) 5107. "^f For the instrumentation of IRF^S see R. Mendelsohn et al., loc. cit.. or R.A. Dluhy et al., loc. cit. ^^ T. Hasewaga, S. Takeda, A. Kawaguchi and J. Umemura, Langmuir 11 (1995) 1236; R. Mendelsohn et al., loc. cit.
LANGMUIR MONOLAYERS
3.161
•eo 0)
-0.002 h
-0.004 h
2959.9
2923.3
2900
2853.6
2800 cm"
wavenumber Figure 3.62. IRRAS spectra of a monolayer of dipalmitoylphosphatidylcholine at the air/ water interface at different surface pressures. The C-H stretching region between 3000 and 2800 cm"^ is shown. Peaks may be positive or negative; their heights increase with increasing surface pressure. (Redrawn from R.A. Dhuly et al., Spectrochim, Acta A 5 1 (1995) 1413.) ation s t a t e of t h e incident radiation a n d the direction of t h e relevant transition dipole moment. An example is given in fig. 3.62. For metallic s u p p o r t s RA p e a k s are always positive. Like in IR t r a n s m i s s i o n s p e c t r a IRRAS b a n d s a r e directly correlated with molecular s t r u c t u r e s amd configurations, although t h e w a v e n u m ber positions may differ slightly from those in transmission spectra. Besides the m u c h lower reflectivity of the water surface (approaching zero a t the Brewster angle), there is a distinct difference between reflection spectroscopy on water s u b s t r a t e s and on metallic supports. At a metal surface the parallel polarized component of the electromagnetic radiation undergoes a p h a s e shift of ISO"" u p o n reflection for all cingles of incidence. Since for metals a t infrared frequencies the reflection coefficients are close to unity, t h e incident a n d reflected parallel polarized components cancel at the surface, so t h a t the electromagnetic field h a s only a perpendiculcirly polarized component, which is a kind of rectification. This is the origin of the so-called surface
selection
rule, which s t a t e s t h a t vibrational
transition m o m e n t s with a n orientation normal to the surface a p p e a r with strong intensity in t h e IRRAS spectrum, while vibrational modes oriented parallel to t h e surface c a n n o t be seen at all. Provided t h a t a n infrared s p e c t r u m of r a n d o m l y organized molecules is avedlable, the surface selection rule c a n b e employed to o b t a i n orientational information on monolayers. On t h e o t h e r h a n d , a t t h e a i r / w a t e r interface the pcu-allel a n d perpendicularly polarized c o m p o n e n t s of t h e
3.162
LANGMUIR MONOLAYERS
a i r / w a t e r interface the parallel and perpendicularly polarized components ol the radiation b o t h have finite values. This implies t h a t polarized IRRAS spectra contain information on all three orthogonal orientations of the monolayer film. Second order p a r a m e t e r s of structural units in the molecules can be obtained by changing the polarization state of the incident radiation. Additional information on the shape of the isotropic spectra is not needed. IRRAS h a s become a n important tool for studying Langmuir monolayers and LB films. Much work h a s been done, in particular on the acyl chain conformational order in monolayers of single chain amphiphiles and phospholipids a s a function of surface p r e s s u r e a n d on the occurrence of p h a s e transitions ^^ Examples of IRRAS studies on LB films can be found ^1. Reviews of the applications of IRRAS are given by Dluhy et al. and Mendelsohn et al.^^. (ii) Raman
spectroscopy.
In contradistinction to infrared absorption, R a m a n
scattering is a second-order phenomenon, governed by induced dipoles (section 1.7.12). R a m a n spectroscopy is complementary to IR spectroscopy in the sense that it provides information on molecular chain order a n d low-frequency vibrational modes t h a t are not easy to study by IR spectroscopy. The Raman spectrum is found entirely in the visible region; excitation with visible light of frequency v. results in emission at frequencies (v - v ) ('Stokes') and [v.+v ^,
.
i
V
I
) ('anti-Stokes'), with v
V
V
the vibrational frequency. Vibrational b a n d intensities obtained in R a m a n spectroscopy are inherently m u c h weaker t h a n in IR spectroscopy, and this is only partly compensated by the fact t h a t detectors in the visible region of the spectrum are more sensitive t h a n those in the infrared. Therefore, Raman spectroscopy h a s been very rarely applied to single-monolayer characterization, the experiments primarily limited to cond i t i o n s in w h i c h special e n h a n c e m e n t m e c h a n i s m s c a n be employed increasing the R a m a n intensities. The techniques involved are Raman spectroscopy Raman
spectroscopy
(SERS), waveguide
Raman spectroscopy
for
surface-enhanced
(WRS) and
resonance
(RRS). In SERS the s u b s t r a t e is a metal surface t h a t is
roughened, giving rise to Raman scattering intensities enhancement by u p to seven orders of magnitude. To explain this effect different theories have been proposed, either b a s e d u p o n a n increase of the electromagnetic field due to surface plasmon resonances or on models in which charge transfer to or from the surface or ima^e dipole effects play a central role. For details the reader is referred to the extensive ^) R.A. Dluhy, M.L. Mitchell, J. Am. Chem. Soc. 110 (1988) 712; A. Gericke. J.W. Brauner. R.K. ErukuUa, R. Bittmann and R. Mendelsohn, Thin Solid Films 292 (1997) 330; CR. Flach, A. Gericke and R. Mendelsohn, J. Phys. Chem B 101 (1997) 58; F. Wu, A. Gericke. C.R. Flach, T.R. Mealy, B.A. Seaton and R. Mendelsohn, Biophys. J. 74 (1998) 3273. ^^ T. Hasegawa et al., loc. cit.; T. Hasegawa, J. Umemura and T. Takenaka, J. Phys. Chem. 97 (1993) 9009. ^^ R.A. Dluhy et al., loc. cit.,; R. Mendelsohn et al.. loc. cit.
LANGMUIR MONOLAYERS
3.163
l i t e r a t u r e ^^ In WRS the light b e a m is confined in the film to be studied u s i n g a waveguide prism-coupling device. This gives a high light intensity in t h e film; a t the s a m e time the scattering volume is increased b e c a u s e of the increased p a t h length of t h e light b e a m . The lower limit of film t h i c k n e s s e s suitable for
yjRS
investigation is ca. 80 n m ^h WRS is mainly used for studies on thin polymer films. Finally, RRS c a n be applied to supported monolayers a s well a s to monolayers at t h e a i r / w a t e r interface, provided t h e monolayer c o n t a i n s c h r o m o p h o r e s , e.g. porphyrin complexes*^^. In this technique e n h a n c e m e n t of the R a m a n scattering is obtained by tuning the excitation wavelength v- into resonance with a n electronic absorption of the molecules. Since water is a poor R a m a n scatterer, t h e w a t e r s u b p h a s e poses no interference problems. Due to technical developments it h a s now become feasible to apply u n e n h a n c e d R a m a n spectroscopy to supported monolayers and to monolayers at the a i r / w a t e r interface, a s demonstrated by a n u m b e r of pioneering works'^K (Hi) UV/visible
spectroscopy.
In comparison with IR a n d fluorescence spectro-
scopic t e c h n i q u e s , UV/visible s p e c t r o s c o p y is only occasionally u s e d
for
characterizing monolayers. It can be applied if the monolayer contains molecules with 71-electron s y s t e m s of which the electron transitions are in the UV/visible p a r t of the spectrum. By measuring polarized transmission spectra or reflectionabsorption spectra at different angles of incidence, the second order p a r a m e t e r of t h e a b s o r p t i o n t r a n s i t i o n dipole m o m e n t in the chromophoric g r o u p s c a n b e determined. In the case of a reflection-absorption configuration, the underlying theory is similar to t h a t of IRRAS, i.e. based u p o n calculation of the reflection a n d t r a n s m i s s i o n coefficients in a stratified-layer system a n d extended to a c c o u n t for the anisotropic n a t u r e of m o n o l a y e r s ' ^ UV/visible spectroscopy h a s been used, for example, to examine the molecular orientation a s a function of the surface pressure in a Langmuir film of chlorophyll a^K
to investigate the influence of long-chain a l k a n e s on the ordering of por-
phyrin molecules in LB layers^^ a n d to study the molecular orientation a n d degree
^f For example, R.K. Chang, T.E. Furtak, Eds., Surface Enhanced Raman Scattering, Plenum Press, (1982); J.A. Creighton, in Spectroscopy of Surfaces, Vol. 16, R.J.H. Clark, R.E. Hester, Eds., John Wiley, (1988) 37. 2) J.F. Rabolt, J.D. Swalen, in Spectroscopy of Surfaces Vol. 16, R.J.H. Clark, R.E. Hester, Eds.. John Wiley. 1988. 3) G.A Schick, M.R. G'Grady, Thin Solid Films 215 (1992) 218. ^^ S.B. Dierker, CA. Murray, J.D. LeGrange and N.E. Schottler, Chem Phys. Lett 137 (1987) 453; T. Kawai, J. Umemura and T. Takenaka, Chem. Phys. Lett. 162 (1989) 243; W.R. Thompson. J.E. Pemberton. Langmuir 11 (1995) 1720; N. Castaings. D. Blaudez. B. Desbat and J.M. Turlet, Thin Solid Films 285 (1996) 631. ^^ T. Hasewaga, Y. Ushiroda, M. Kawaguchi, Y. Kitazawa, M. Nishiyama, A. Hiraoka and J. Nishijo. Langmuir 12 (1996) 1566. ^) E. Okamura, T. Hasegawa and J. Umemura, Biophys. J. 69 (1995) 1142 ^^ R. Azumi, M. Matsumoto, Y. Kawabata, S. Kuroda, M. Sugi, L.G. King and M.J. Crossley, J. Phys. Chem 9 7 (1993) 12862.
3.164
LANGMUIR MONOLAYERS
of p e n e t r a t i o n of a chromophoric d r u g (chlorpromazine) in a phospholipid LB filmD. (iu) Fluorescence
techniques.
Experiments based on the p h e n o m e n o n of fluor-
e s c e n c e may yield information on ordering, rotational a n d lateral mobility, molecular environment, association and concentration of species. Despite the fact t h a t in general extrinsic fluorescent probes, which may perturb the structure, have to be introduced,
fluorescence
spectroscopy is frequently applied in the study of
organized assemblies of amphiphiles. In particular, it is widely used for investigating of biological m e m b r a n e s a n d their model systems. Below, some of the basic c o n c e p t s of
fluorescence
spectroscopy wfll be briefly discussed, followed by a
n u m b e r of m e a s u r i n g techniques applied for the investigation of monolayers. A fluorescent molecule (fluorophore)
generally contains a n aromatic or hetero-
cyclic group. Upon absorption of UV or visible radiation the
fluorescent
group
undergoes a transition to one of the vibrational levels of its first excited electronic state. After excitation, vibrational energy is lost thermally and the molecule drops to the g r o u n d vibrational s t a t e of the excited electronic state. Excitation a n d vibrational relaxation take place within picoseconds. Fluorescence occurs as the molecule r e t u r n s to one of t h e vibrational levels of the ground electronic state u n d e r emission of radiation. The lifetime of the excited electronic state, the fluorescence lifetime r
is 0 ( 1 - 10 ns), comparable to the time scale of molecular
dynamics. Besides fluorescence nonradiative depopulation of the excited state also takes place. The q u a n t u m yield, defined a s the ratio of the n u m b e r of p h o t o n s emitted to the n u m b e r of p h o t o n s absorbed, reflects the relative importance of these two relaixation processes. By exposing
fluorophores
to high-intensity light,
molecules in the excited state may undergo a n irreversible chemical transition and hence not fluoresce anymore. This process is called
photobleaching.
Each fluorophore h a s its characteristic absorption a n d emission spectrum. The emission m a x i m u m is at a higher wavelength t h a n the absorption peak, b u t in general t h e r e is a n overlap between the absorption a n d emission spectra. The emission s p e c t r u m (peak position), q u a n t u m yield and
fluorescence
lifetime are
d e p e n d e n t on the physical a n d chemical environment of the fluorophore. It is this dependence a n d the favourable time scale, together with the possibility of filtering excitation light from the fluorescence signal, which allows one to observe a wide range of interesting molecular properties and processes with
fluorescence
tech-
niques. Interactions between p r o c e s s e s like fluorescence excimer formation.
fluorophores resonance
a n d with other molecules are reflected in energy
transfer
(FRET), quenching
and
These p h e n o m e n a can be used to study lateral diffusion a n d
1^ T. Hasewaga et al. (1996), loc. cit.
LANGMUIR MONOLAYERS
3.165
aggregation, and to determine disteinces and concentrations. FRET (also known as Forster energy transfer^^) occurs when a fluorophore (the donor) in the excited state transfers its excitation energy to another fluorophore (the acceptor), which then fluoresces. For this process to take place there has to be an overlap between the relevant part of the emission spectrum of the donor and the absorption spectrum of the acceptor. This energy transfer does not involve the transmission of a photon, but is the result of resonance dipole-dipole interactions between donor and acceptor. FRET is observed either as a reduction of donor fluorescence in the presence of the acceptor, as an increased emission of the acceptor when excited at the absorbance wavelength of the donor, or, in timeresolved fluorescence measurements, as a decrease in fluorescence lifetime of the donor. The photobleaching time of the donor also shortens, since photobleaching occurs from the excited state. FRET is extensively used as a 'spectroscopic ruler' since the efficiency of energy tramsfer depends on the inverse sixth power of the distance between donor and acceptor. The scsde of this ruler is 1 - 10 nm. The fact that the energy transfer efficiency also depends on the relative orientation of the donor and acceptor may complicate the determination of distance parameters. There are certain substcmces, called quenchers, which have the property of reducing the fluorescence in a concentration-dependent way. Examples of quenchers are oxygen, iodine, acrylamide and a number of metal ions. In dynamic quenching the fluorescence intensity decreases as a result of collisions between excited fluorophores and quenchers, upon which excitation energy is lost without emission of light. The probability of quenching is proportioned to the fluorescence lifetime and depends on the concentrations and diffusion coefficients of fluorophore and quencher. Dynamic quenching is observed as a reduction of the fluorescence intensity and lifetime. In static quenching, a nonfluorescent quencher-fluorophore complex is formed. Any remaining free fluorophore will fluoresce with the unquenched lifetime. Upon this process the fluorescence intensity goes down. Static and dynamic quenching processes may occur simultaneously. For some fluorophores (well-known examples are pyrene and its derivatives) the emission spectrum depends dramatically on their concentration. This is due to the formation of excited-state dimers, so-called excimers, consisting of a groundstate and an excited-state monomer. For instance, lipids that are substituted with a pyrene moiety in each of their acyl chains can be used to study intramolecular excimer formation. In this way information on lateral organization and intramolecular dynamics can be obtaiined. All these phenomena have been observed both for bulk systems and for monolayers.
1^ After T. Forster, Ann. Phys. 2 (1948) 55.
3.166
LANGMUIR MONOLAYERS
E x p e r i m e n t s with polarized light to excite
fluorophores
permit the study of
orientational order a n d rotational diffusion. Polarized radiation selectively excites probes of which the direction of the absorption dipole moment is parallel to, or at a small angle with, the electric field vector of the exciting radiation. The light emitted by a fluorophore is polarized along the direction of its emission dipole moment. T h u s , if the fluorophores do not change their orientation significantly on the time scale of fluorescence, i.e. if they are strongly hindered in their rotational motion, the resulting fluorescence will have a marked polarization. In the opposite case of rapid rotation without restriction, the fluorescence will be completely depolarized. As stated at the beginning of this subsection, from fluorescence data not only the second order parameter (S ) b u t also the fourth-order parameter (S^) of the o r i e n t a t i o n d i s t r i b u t i o n of a collection of fluorophores
may be
obtained.
Assuming that the absorption and emission steps are independent, we can write for the polarization component of the fluorescence intensity that is measured: lit] = c(cos2 a{0] cos^ p[t])P{t)
(3.7.151
where aiO) is the angle between the absorption dipole moment and the electric field vector of the exciting radiation at the time of excitation (t = 0), /3(t) gives the direction of the emission dipole moment at time t with respect to the polarization direction detected, and P{t) is the probability t h a t a fluorophore is still excited at time t (if t h e
decay
is s i n g l e - e x p o n e n t i a l
this
probability
amounts
to
( l / r ) e x p ( - t / T )). The brackets ( ) denote averaging over all available molecular orientations. The c o n s t a n t C accounts for s u c h p a r a m e t e r s a s the incident light intensity, the q u a n t u m yield and properties of the detection system. From 13.7.15] it is easily understood t h a t fluorescence data contain more orientational information t h a n absorbance data, because two transition dipole moments are involved; s u b s t i t u t i o n of e x p r e s s i o n s for the (time-dependent) directions of the two transition dipole m o m e n t s eventually leads to an equation in which both (cos^ o) a n d /cos"^ o) t e r m s appear, with 0 the azimuthal tilt angle of the cylindrically symmetric probe. These t e r m s can be converted readily into (S^) a n d (S^> (see 13.7.13 a n d 14]). Detailed derivations of equations used to analyze
fluorescence
data in terms of molecular orientations can be found in the literature; these depend on the specific technique used. Steady-state
fluorescence
m e a s u r e m e n t s may be
employed for systems in which the orientation of the fluorophores does not change significantly on the time-scale of fluorescence^^ Time-resolved
fluorescence
tech-
niques can reveal not only the order parameters (S^) and <S^) b u t also lead to a n average rotational diffusion coefficient of the fluorescent molecules, or, in the case
1) See, for example, M.A. Bos, J.M. Kleijn, loc. cit.; X. Zhai, J.M. Kleijn, Biophys. (1997) 2 5 6 6 .
J. 7 2
LANGMUIR MONOLAYERS
5-dodecylamino fluorescein
1 -pyrenedecanoic acid
3.167
NBD-DPPC
DPHpPC
Figure 3.63. Examples of fluorophores used in the study of monolayers, LB films and membranes. NBD-DPPC; dipalmitoylphosphatidylcholine, labeled with NBD (7-nitrobeno2-oxa-l,3-diazole); DPHpPC; a diphenylhexatriene-labeled phosphatidylcholine. of rodlike probes, the so-called "wobbling' diffusion coefficient for reorientation of the long molecular axis^K In studies of Langmuir monolayers by fluorescence techniques usually a small a m o u n t of t h e fluorescent probe, which itself is amphiphilic, is a d d e d to t h e solution before spreading on the aqueous p h a s e in the Langmuir trough. The probe concentration is typically in the range 0 . 1 - 2 mole% of t h e monolayer a m p h i philes, b u t concentrations two orders of magnitude lower aire also used. Sometimes s y s t e m s are studied in which all molecules are labelled or w h e r e they are all intrinsically fluorescent. A variety of probe molecules is available, including labeled single-chain surfactants a n d labeled phospholipids. Some examples are
^f B.W. van der Meer, H. Pottel, W. Herreman, M. Ameloot, H. Hendrix and H. Schroder, Biophys. J. 46 (1984) 515; R.P.H. Kooyman, M.H. Vos, and Y.K. Levine, Chem. Phys. 8 1 (1983) 461; H. van Langen, C.A. Schrama, G. van Ginkel, G. Ranke and Y.K. Levine, Biophys. J. 55 (1989) 937.
3.168
LANGMUIR MONOLAYERS
given in fig. 3.63. The choice of the probe molecule depends on the system u n d e r study a n d on w h a t kind of property is to be m e a s u r e d . For example, there are p r o b e s t h a t a r e s u i t a b l e for t h e d e t e r m i n a t i o n of orientational order (like d i p h e n y l h e x a t r i e n e , DPH, a n d its derivatives in t h e c a s e of p h o s p h o l i p i d monolayers), for the study of lateral diffusion (like pyrene and its derivatives) and probes t h a t are sensitive to pH (e.g., fluorescein), electric field, etc. A detailed description of the properties of virtually all available fluorescent probes and many useful references can be found in ref.^^. Intrinsically fluorescent molecules include porphyrins a n d tryptophan-containing proteins. The discussion below indicates the variety of options for studying monolayers a n d related systems, which underlies the relative popularity of fluorescence techniques. At the s a m e time the caveat m u s t be repeated t h a t extrinsic probes have to be introduced in the monolayer. This insertion does affect the s t r u c t u r e and the question r e m a i n s by how m u c h the perturbed layer differs from the original one. The a r g u m e n t t h a t the disturbance is inconsequential if the mole fraction of the probe is low does not hold b e c a u s e by fluorescence m e a s u r e m e n t s typically only the modified part is seen. Fluorescence
microscopy
on Langmuir monolayers exploits the fact t h a t the
density, solubility or quenching of fluorescent probes in two coexisting 2D p h a s e s may differ, leading to brighter and less bright regions in the fluorescence image. In this way domain morphology in coexistence regions and p h a s e transitions can be studied. In fluorescence microscopy two illumination geometries are used, i.e. t r a n s m i t t e d i l l u m i n a t i o n a n d incident or epi-illumination^^ The use ot an inverted geometry in which the objective is immersed in the water s u b p h a s e . leaves the space above the surface free for other manipulations. A disadvantage of this geometry in the study of Langmuir monolayers is the restriction of the observation to a single spot on the surface, which may not be representative. In the epi-illumination geometry the entire water surface of a Langmuir trough can be s c a n n e d . Both geometries can also be used to study films on solid substrates; of course, for transmitted illumination the s u b s t r a t e h a s to be optically t r a n s p a r e n t . The spatial r e s o l u t i o n of fluorescence microscopy is the s a m e a s for light microscopy. However, single objects, m u c h smaller t h a n this resolution limit, can be detected if they emit light strong enough to be distinguished from the background. Nowadays detectors are available t h a t are sufficiently sensitive to detect the fluorescence of one single molecule (photon counting).
By combining scanning probe microscopy
with other optical techniques, the resolution is no longer limited by the wavelength of light a n d can be improved down to ca 25 n m [near-field scanning
optical
^^ R.P. Haugland, Handbook of Fluorescent Probes and Research Chemicals, Molecular Probes, sixth edition (1996). ^^ For the instrumentation see, for example, the review of K.J. Stine and CM. Knoblcr. Ultramicroscopy 47 (1992) 23.
LANGMUIR MONOLAYERS
3; 169
microscopy, NSOM, see section 3.7d). This combination of techniques, however, can only be used for films on solid substrates. Since the fluorescence intensity is sensitive to the relative orientations of the polarization direction of the incoming radiation and the absorption transition moment of the probe molecule, it is possible to image local ordering in monolayers by using polarized radiation. This is realized in polarized fluorescence microscopy (PFM). In particular, in a phase in which the hydrocarbon tails of the amphiphiles are tilted away from the normal to the monolayer, regions of different azimuthal tilt direction can be distinguished. Thus PFM, like BAM and imaging ellipsometiy, can provide direct information about the structure of, and transition between, condensed phases^^. With fluorescence lifetime imaging microscopy (FUM) one can map various environments of the probes in terms of locations where processes like energy transfer and quenching occur. In fluorescence correlation spectroscopy (FCS) a small volume element (or a small area) of a sample is illuminated by a laser beam and the autocorrelation function of fluctuations in the fluorescence is determined by photon counting. From this autocorrelation function the mean number densities of the fluorophores and their diffusion coefficients can be extracted. Measurement and analysis of higher order correlation functions of the fluorescence has been shown to yield information concerning aggregation states of fluorophores-^K Fluorescence recovery after photobleaching (FRAP) is used to measure translational diffusion rates (see also 1.7.15). In this technique a burst of illumination powerful enough to cause irreversible photobleaching of the fluorophores is locally applied to the monolayer. Usually, a periodic pattern is bleached by using, for example, interfering laser beams. After the bleaching burst, the fluorescence recovery caused by diffusion of intact fluorophores into the bleached areas is optically monitored, again using the same periodic pattern, but now with the intensity attenuated by a factor 10^ - 10^. If a burst of intense polarized radiation is applied to a sample then an asymmetric depopulation of the ground state occurs. The relaxation of the resulting fluorescence anisotropy can be used to measure rotational diffusion in the technique known as polarized FRAP. The use of an evanescent wave to excite fluorophores selectively neair a solidfluid interface is the basis of the technique total internal reflection fluorescence (TIRF). It can be used to study theadsorption kinetics of fluorophores onto a solid surface, and for the determination of orientational order and dynamics in adsorption layers and Langmuir-Blodgett films. TIRF microscopy (TIRFM) may be combined with FRAP and FCS measurements to yield information about surface diffusion rates and the formation of surface aggregates. ^^ D.K. Schwartz, CM. Knobler, J. Phys. Chem. 97 (1993) 8849 and references therein. 2) A.G. Palmer, N.L. Thompson, Biophys. J. 52 (1987) 257.
3.170 (v) Second-order
LANGMUIR MONOLAYERS non-linear optical techniques.
Second-order non-linear optical
processes are the result of the interaction of intense optical fields with non-centrosymmetric media. These processes involve frequency conversion of light. Technical application became feasible with the development of high-power (pulsed) lasers. The p h e n o m e n o n of second harmonic generation (SHG) (the generation of light with a frequency twice t h a t of the incoming light) w a s first d e m o n s t r a t e d by Franken et al. ^Mn a quartz crystal. The technique is now widely used to extend the frequency range of laser light sources using non-centrosymmetric crystals. The foundations of the theory behind these optical p h e n o m e n a were laid by Bloembergen a n d Pershan^). Due to the fact t h a t second-order optical processes are electric dipole forbidden in centrosymmetric media, they are highly interfacespecific a n d c a n be exploited to investigate equilibrium properties and dynamic processes in all interfaces accessible to light. Practically all everyday optical p h e n o m e n a are linear, meaning t h a t emitted a n d incident intensities are proportional to each other. This implies t h a t optical material properties like absorption coefficients a n d refractive indices do not depend on the intensity of the applied light sources. The electron distribution of a molecule in s u c h a relatively weak electromagnetic field responds harmonically to the field a n d a n oscillating dipole may be induced. The magnitude of this induced dipole is proportional to the strength of the electric field component, E, of the incident radiation (1.7.3b). However, in the intense light of high-power lasers, the response of the electrons is no longer harmonic and higher powers of E m u s t be included to describe the induced polarization. As the molecules now behave a s a n h a r m o n i c oscillators, not only dipole oscillations at t h e frequency co of the incoming laser field are generated, b u t also overtone oscillations at frequencies 2CO, 3(JL> etc. Oscillating dipoles emit electromagnetic radiation a n d hence one expects o u t p u t radiation from the medium at frequencies co, 2co, 3(o and so on. In the SHG technique attention is focussed on the frequency 2(o. The induced second-harmonic polarization per unit volume, P^'^\2(o], can formally be written as^^ P^^\2co) = X^'^h E[co)E(co) = ^ X^^^,^^
|3.7.16|
i.j.k
The second-order non-linear susceptibility Z^'^^ is a third-rank tensor, which, in Cartesian coordinates, is defined by a set of 27 elements x^-^v!^ with i,J and k r e p resenting X, y or z. X^"^^ is a characteristic of the medium, depending on the n u m b e r
^^ P.A. Franken, A.E. Hill, C.W. Peters and G. Weinreich, Phys. Rev. Lett. 7 (1961) 118. ^^ J.A. Armstrong, N. Bloembergen, J. Ducuing and P.S. Pershan, Phys. Rev. 127 (1962) 1918; N. Bloembergen, P.S. Pershan, Phys. Rev. 128 (1962) 606. ^^ Y.R. Shen, Principles of Nonlinear Optics, Wiley, 1984; Ann. Rev. Phys. Chem. 40 (1989) 327.
LANGMUIR MONOLAYERS
3.171
density N a n d hyperpolarizability tensor p of the molecules:
F^ = NiP)
[3.7.17]
in w h i c h t h e b r a c k e t s () denote orientational averaging over t h e system u n d e r s t u d y . The hyperpolarizability is a h i g h e r - r a n k polarizability, a s felt in n o n linear p h e n o m e n a . It is different from t h e common polarizability a, which h a s 9 components. For a centrosymmetric m e d i u m incoming fields E{co) emd -E{co) m u s t induce polarizations P^'^\2co) and - P^^\2co], respectively. This, however, is not consistent with equation [3.7.16] u n l e s s Z^^^ is zero, indicating t h a t SHG is forbidden. At a n interface t h e inversion symmetry is b r o k e n a n d SHG is n o longer forbidden. Interfacial non-linear radiation is emitted by a sheet of coherently driven dipoles oscillating a t the same frequency. Therefore, non-linear emission is coherent a n d h a s a well-defined direction, in contrast to linear optical processes like Raleigh and Raman scattering (see 1.7.3 and 1.7.8). When the incoming field E consists of two frequencies, co^ a n d co^, dipoles nonlinearly oscillating a t frequencies {co -\- co ) and [co^ - co^) are induced a s well. In the sum-frequency
generation
(SFG) technique one focusses on t h e o u t p u t a t frequency
(ft)j + co^) and in the difference frequency generation (DFG) technique on [co^-co^]. As is the case with SHG, SFG a n d DFG are electric dipole-forbidden in centrosymmetric media. The m a n y systems t h a t can be investigated with SHG and SFG^^ include monolayers a t the a i r / w a t e r interface aind LB films. The experimental a r r a n g e m e n t s for detection system detection system
laser 2 interface (a)
(b)
Figure 3.64. Experimental arrangement for SHG (a) and SFG (b) from an interface. The basic elements are one, resp. two lasers (usually, but not necessarily, pulsed), and a photodetection system. F denotes the filtering system that rejects incident frequency light but passes the second harmonic. In SFG light at frequency [co^ - ^ 2 ^ ^^ emitted at an cingle that conserves momentum pciredlel to the interface.
^^ For an overview see, for example, R.M. Com, D.A. Higgins, Cheni. Rev. 94 (1994) 107.
3.172
LANGMUIR MONOLAYERS
both techniques are fairly simple. The basic elements are given in fig. 3.64^^ The large difference in fundamental and o u t p u t frequencies of interest m a k e s filtering of the signal against unwanted background straightforward. To achieve monolayer sensitivity high-gain photodetectors are needed. At the a i r / w a t e r interface the contributions of organic molecules to the surface non-linear susceptibility usually dominate the second-harmonic
response.
Depending on the hyperpolarizability of the molecules involved, a sensitivity down to 0.01 - 0.02 of a monolayer can be achieved. The molecular specificity provided by X^^^ h a s led to the application of SHG to the study of chemical (including photochemical a n d electrochemical) transitions at interfaces. In this way, for example, the polymerization of octadecylmethacrylate monolayers spread on a water surface by irridiation with UV light h a s been followed^^ The time-dependent r e s u l t s provided a check for existing theoretical models for polymerization in a t w o - d i m e n s i o n a l s y s t e m . V a r i a t i o n s in t h e p o p u l a t i o n s of p r o t o n a t e d
and
deprotonated species as a function of pH in monolayers are also easily monitored by SHG^K Association a n d dissociation of protons result in changes in the hyperpolarizability of t h e a m p h i p h i l e s and therefore into (sometimes d r a m a t i c ) , changes in their SHG response. From m e a s u r e m e n t s of the various p a r a m e t e r s t h a t characterize SH a n d SF light waves, different types of information can be obtained. The intensity of the emitted light is proportional to I J^^h^ and hence reflects the combined effect of the degree of coverage a n d the orientational order in the monolayer. Dictated by the symmetry of t h e interfacial system, m a n y tensor elements of J^^' are zero or d e p e n d e n t on the others. With different combinations of input and o u t p u t beam polarizations, the independent non-zero elements of ^^^^ may be established from SHG m e a s u r e m e n t s . In favourable cases this allows an average molecular orientation (tilt angle) to be determined. An example is given in fig. 3.65. The p h a s e of the SH or SF light waves with respect to the incident radiation fields (which can be m e a s u r e d by interference methods) c a n be u s e d to d e t e r m i n e t h e a b s o l u t e molecular direction, i.e. it tells whether the molecules are oriented 'up' or 'down'. Second-order non-linear optical techniques have been applied for monitoring the adsorption of soluble surfactants at the air/water interface and to characterize the resulting (sub)monolayers'^^ For Langmuir monolayers SHG allows the observ^^ For more details concerning the instrumentation see for SHG, for example, Y.R. Shen, loc. cit.; R.M. Corn, D.A. Higgins, loc. cit.; for SFG see CD. Bain, J. Chem. Soc, Faraday Trans. 9 1 (1995) 1281. 2) G. Berkovic, T. Rasing and Y.R. Shen, J. Chem. Phys. 85 (1986) 7374. ^' See, for example, X. Zhao, S. Subrahmanyan and K.B. Eisenthal, Chem. Phys. Lett. 171 (1990) 558. ^^ See, for example, J.C. Conboy, M.C. Messmer and G.L. Richmond, J. Phys. Chem. 100 (1996) 7617; M.S. Johal, R.N. Ward and P.B. Davies, J. Phys. Chem. 100 (1996) 274: S. Bae, M. Harke, A. Goebel, K. Lunkenheimer and H. Motschmann, Langmuir 13 (1997) 6274 and references therein.
LANGMUIR MONOLAYERS
3.173
1.5 a c 'So I
o X
CO
oh
1.5
O X 00
(b) 0
Figure 3.65. Polar diagram of SHG intensity as a function of the polarization angle of the linearly polarized incident beam with respect to the plane of incidence, as measured from the interface between an aqueous surfactant solution and air. The anionic surfactant is sodium 2-[4-((4-trifluoromethyl-phenyl)azo)phenoxy]-ethanesulfonate. The s)mibols represent experimental data; the drawn curves refer to a model fit yielding the unknown elements of x^^^. (a) Polcirization setting of the cinalyzer in the detection path perpendicular to the plane of incidence, (b) parallel. The data are in agreement with an isotropic azimuthal distribution and give an average tilt angle of 38° with respect to the normal of the interface. (Redrawn from S. Bae, M. Harke, A. Goebel, K. Lunkenheimer and H. Motschmann, Langmuir 13 (1997) 6274.) ation of p h a s e transitions ^^ Focussing the incident b e a m to a spot of less t h a n 10 ILim on t h e a i r / w a t e r interface provides information on the t h e r m a l translational a n d orientational motions of interfacial surfactant clusters from
fluctuations
in
t h e SH signaPK The possibility of determining the orientation of tails a n d h e a d g r o u p s of amphiphilic molecules a n d t h e t r a n s - g a u c h e conformations in t h e hydrocarbon tails h a s , in particulair, m a d e SHG a n d SFG important tools for investigating of Langmuir monolayers'^^ a n d LB films^^. Recently, it h a s been shown t h a t SHG from t h i n molecular films provides a sensitive p r o b e of surface chirality^^ With t h e help of t u n a b l e l a s e r s SHG a n d SFG c a n be u s e d for
surface
1) P. Guyot-Sionnest, J.H. Hunt and Y.R. Shen, Phys. Rev. Lett 59 (1987) 1597. 2) X. Zhao, M.C. Goh, S. Subrahmanyan and K.B. Eisenthal, J. Phys. Chem. 9 4 (1990) 3370; X. Zhao, K.B. Eisenthal, J. Chem. Phys. 102 (1995) 5818. 3) For example, D. Zhang. J. Gutow and K.B. Eisenthal, J. Phys. Chenh 9 8 (1994) 13729; C. Hirose, N. Akamatsu and K. Domen, Appl. Spectrosc. 46 (1992) 1051. ^f See, for example, G.J. Ashwell, G. Jefferies, CD. George, R. Rcinjcin, R.B. Charters and R.P. Tatam, J. Mater. Chem. 6 (1992) 131 and references therein. ^^ M. Kauranen, T. Verbiest and A. Persoons, J. Modem Optics 45 (1998) 403.
3.174
LANGMUIR MONOLAYERS
spectroscopy.
When, in the case of SHG, COOT 2coapproaches
a resonance frequency
of the interface layer, the corresponding X^^^ exhibits a resonance e n h a n c e m e n t . SHG a n d SFG spectra can be used to identify chemical species at interfaces and to study (photo)chemical and charge-transfer processes. SHG spectroscopy is limited to electronic transitions in the visible light; b e c a u s e of the low sensitivity of IR detectors it is not possible to perform vibrational spectroscopy adequately. This problem is avoided in SFG spectroscopy. In SFG vibrational spectroscopy two laser b e a m s , one in the visible a n d the other in the IR p a r t of the spectrum, are superimposed on a sample a n d light emitted at the s u m of the two incident frequencies (in the visible region of the spectrum) is detected. The intensity of the m e a s u r e d signal changes if the IR laser is in resonance with a n appropriate vibrational mode of a molecule at the interface. Scanning the frequency of the IR laser therefore yields a vibrational spectrum. As a result of the selection rules for second-order non-linear optical processes, a molecular vibration is only SF-active if it is b o t h IR a n d Raman-active^^. Quantitative analysis of SFG spectra is m u c h less straightforward t h a n t h a t of conventional IR or R a m a n spectra. Vibrational peaks are not only convoluted with a n y n o n - r e s o n a n t b a c k g r o u n d signal b u t also with each other. Therefore, curve fitting is a n e c e s s a r y step in the analysis a n d this requires knowledge of t h e hyperpolarizabilities of each vibrational mode. Unfortunately, this information is not always available. Moreover, since the contribution to the SFG signal per molecule d e p e n d s on its orientation, absolute coverages c a n n o t be calculated without first making some a s s u m p t i o n s about the orientation distribution-^^. 3.7d
Scanning
probe
microscopy
Scanning probe microscopes (SPM's) are a family of i n s t r u m e n t s used to m e a s u r e properties of surfaces. The m o s t well-known m e m b e r s of this family are t h e scanning
tunneling
microscope
(STM) and the atomic force microscope
known a s SFM, scanning force microscope),
(AFM, also
already introduced in section 1.7. l i b
a n d described in more detail in section II. 1.2. The common feature a n d h e a r t of each SPM is a piezoelectric scanner (the 'piezo') which allows movement of a probe with extreme precision very close over the sample surface to be studied. The s c a n n e r c a n be controlled to provide motion increments of less t h a n 0.1 n m in three dimensions. Depending on the design of the instrument, the s c a n n e r either moves the sample or s c a n s the probe over the sample surface. In the first case only samples of area smaller t h a n about 1 cm^ can be investigated. However, this design is more suitable for obtaining images with high (molecular) resolution. In STM the tunneling of electrons between the probe, a thin metallic wire, a n d 1) Y.R. Shen, loc. cit. ^^ The main steps in the analysis have been outlined by CD. Bain, loc. cit.. See also C. Hirose et al., loc. cit.
LANGMUIR MONOLAYERS
3.175
sample surface is m e a s u r e d a s a result of a n applied voltage. Since the tunneling c u r r e n t falls off exponentially with distance to the surface, it c a n be u s e d to let the probe follow t h e surface profile. To apply this technique, the sample h a s to be conducting. It is possible to image thin organic films, biological macromolecules (DNA, proteins) a n d even complete cells on conducting s u b s t r a t e s , b u t the imaging principle for these non-conducting materials is still unclear from a physical point of view ^^ Other SPM's, including the AFM, u s e the force between sample surface a n d probe (commonly referred to a s the 'tip') a s a feedback signal for the movement of t h e probe relative to the sample surface. Generally the tip is m o u n t e d on a flexible cantilever, t h e deflection of t h i s cantilever reflecting t h e interaction with t h e sample (fig. 3.66). In the most common design a laser beam is reflected off the b a c k of the cantilever onto a segmented photodiode. This system h a s the sensitivity to detect normal motions (in the z-direction) of 0.01 n m a s the tip s c a n s the sample surface. In the basic mode of operation, the so-called 'contact' or 'repulsive' mode, the cantilever h a s a n upward deflection a n d exerts a spring force to the sample surface in the range of 1 - 10 nN depending on the conditions. At high feedback the system tries to keep the differences between the c u r r e n t s of the u p p e r a n d lower diodes c o n s t a n t at a certain preset value a n d the movement of the z-piezo gives the height information ('constant force' or 'height' mode); at low feedback the deflection of t h e cantilever a s monitored by the photo diode c o n t a i n s the topografic information ('constant height' or 'deflection' mode). In their first applications, SPM's were solely used for m e a s u r i n g surface topography. As opposed to optical microscopes a n d s c a n n i n g electron microscopes quadrant photodetector
laser
cantilever
o u a;
touching
non-touching
repulsive
t
touching
attractive
sample piezo a)
piezo travel
(b)
Figure 3.66. (a) Diagram of the most common AFM set-up; (b) Deflection of the cantilever as a function of the z-position of the piezo.
1^ A. Ikai, Surface Set Reports 26 (1996) 261.
3.176
LANGMUIR MONOLAYERS
(SEM's) they m e a s u r e surface structures in three dimensions; x, y and z. With little or no sample preparation surfaces can be studied down to n a n o m e t e r or better (molecular or atomic) resolution, in ambient air, v a c u u m a n d liquids. Surface processes, like adsorption and electrochemical metal deposition can be followed in situ. In the relatively short time since the introduction of SPM's^^ many variations on the scanning probe theme have been invented and the scope of applications h a s grown explosively. SPM's are either used to m e a s u r e topography or to image the surface for a specific physical property. For example, it is possible to m e a s u r e the friction force between probe a n d sample by monitoring the lateral deflection (torsion) of t h e cantilever while the tip is moving over the surface (friction lateral force microscopy,
or
FFM or LFM). Surface potentials and dielectric properties
can be imaged by applying a n electric field across the gap, magnetic forces by using a magnetic tip. An elegant combination of SPM with optical techniques is nearfield scanning optical microscopy (NSOM), in which the probe consists of a very thin (sub-wavelength size) glass fibre. The light source is at the other end of the optical fiber. Using force feedback, the end of the probe m a i n t a i n s c o n s t a n t separation from the sample (a few nm's). As the light e m a n a t e s from the tip, it only illuminates a n area of the sample approximately equal to the aperture size, which may be less t h a n 2 5 n m in diameter. Any collected optical contrast, either reflected from the sample or emitted by excited fluorophores, originates from this small area. T h u s , resolution is limited not by the wavelength of light, b u t by the size ot the aperture. Another i m p o r t a n t application nowadays is the u s e of the AFM a s a surface force a p p a r a t u s ^ K A plot of the force interaction between the tip a n d a sample surface a s a function of their separation is generally referred to as a 'force curve'. It yields the disjoining
pressure.
The interacting a r e a s are small and need to be
smooth a n d homogeneous only on a small scale. The force is calculated from the deflection and the spring c o n s t a n t of the cantilever according to Hooke's law; it is referred to zero at large separation. It is not possible to determine the absolute zero of separation, which in some cases poses a problem. Instead of using a n AFM tip one can p u t a colloidal particle ('colloidal probe') or a bacterial cell at the end of the cantilever a n d m e a s u r e its interactions with a surface. Modifying the probe, either chemically or by physisorption, enables one to make a chemical image of the surface by m e a s u r i n g the adhesive forces at different positions at the surface^^ By
^^ The first SPM w a s the STM, described in the literature by G. Binnig, H. Rohrer. C. Gerber a n d E. Weibel, Phys. Rev. Lett. 4 9 (1982) 57. ^^ This application of AFM was introduced by W.A. Ducker. T.J. Senden and R.M. Pashley, Langmuira (1992) 1 8 3 1 . ^^ See, for example, C.E.H. Berger, K.O. van der Werf, R.P.H. Kooyman. B.G. de GrooLh a n d J . Greve, Langmuir 11 (1995) 4188; a review on chemical imaging is given by A. Noy, D.V. Vezenov a n d C.M. Lieber, Ann. Rev. Mater. Set 2 7 (1997) 3 8 1 .
LANGMUIR MONOLAYERS
3.177
modifying the tip and surface with complementary groups (e.g. of antibodies a n d cintigens) bond strengths have been determined. New SPM techniques a n d i n s t r u m e n t s in which SPM is combined with other techniques continue to be developed. Papers reviewing the state-of-the-art are p u b lished regularly. A n u m b e r of these are included in the reference list in sec. 3 . lOe. The importance of SPM for the study of monolayers is t h a t it allows t h e visualization of the s t r u c t u r e a n d defects of transferred a n d self-assembled monolayers on solid substrates at length scales from < 0.1 n m to > 10 fim. It is not (yet?) possible to image monolayers a t liquid/fluid interfaces with SPM techniques. However, it h a s already been shown t h a t it is feasible to m e a s u r e interaction forces between a colloidal particle a n d s u c h interfaces in the presence and absence of monolayers'^. In the p a s t a major concern a n d point of criticism h a s been t h a t the tip would d a m a g e soft organic surfaces s u c h a s LB films. However, it h a s t u r n e d o u t t h a t normal imaging forces are too weak to damage compact organic layers, a l t h o u g h t h e tip m a y p e n e t r a t e the layers to some degree^^. S t r u c t u r a l d a t a on LB films obtained with AFM are generally in agreement with results from other techniques. For example, molecular-resolved AFM images of compact fatty acid a n d p h o s p h o lipid monolayers show well-ordered lattices with u n i t cell characteristics comm e n s u r a t e with those, obtained from X-ray diffraction data^^K For less compact layers where the molecules are not firmly attached to the s u b s t r a t e , there is a risk of shifting the molecules a r o u n d over the surface. To avoid problems of s a m p l e deformation new techniques have been developed, for example m e a s u r i n g in t h e tapping mode^)- In this mode the contact time between tip a n d sample is reduced to a m i n i m u m . For imaging in air or gas a stiff cantilever is forced to oscillate vertically at a certain distance from the sample surface while s c a n n i n g laterally. When the tip-sample distance decreases, the frequency a n d amplitude of oscillation changes. The feedback system then lowers the position of the sample so t h a t the cantilever r e s u m e s its original amplitude of oscillation. The tapping mode in liquid is operated in a slightly different way; a m u c h softer cantilever is used. In this mode forces acting laterally to the sample are virtually eliminated a n d the frequency of oscillation is so high t h a t the collisions between tip a n d sample surface are generally completely elastic.
'^ P. Mulvaney, J.M. Perera, S. Biggs, F. Grleser and G.W. Stevens, J. Colloid Interface Set 183 (1996) 614; M. Preuss, H.J. Butt, Langmuir 14 (1998) 3164. '^f See, for example, L.F.Chi, M. Anders, H. Fuchs, R.R. Johnston and H. Ringsdorf, Science 259 (1993) 213. ^' See, for example, J.A. Zasadzinski, R. Viswanathan, L.Madsen, J. Gamaes and D.K. Schwartz, Science 263 (1994) 1726; S.M. Stephens, R.A. Dhuly, Thin Soiid Films 2 8 4 / 2 8 5 (1996) 381. "^^ Tapping mode is a registered trade name by Digital Instruments, Santa Barbara, CA, USA. A description of the technique in air and in liquid is given, for example, by C.A.J. Putman, K.O. van der Werf, B.C. de Grooth, N.F. van Hulst, and J. Greve, Appl Phys. Lett 64 (1994) 2454.
3.178
LANGMUIR MONOLAYERS
nm
Figure 3.67. AFM image of a dipalmitoylphosphatidylcholine (DPPC) monolayer transferred onto a quartz plate at a surface pressure of 30 mN m'^. On this hydrophilic substrate the phospholipids have their head groups on the surface. Therefore, the bright spots should correspond to the end-methyl groups of the DPPC hydrocarbon chains. This is corroborated by the finding that the area per bright spot (averaged over many images) corresponds to half of the value for the area per phospholipid molecule as found from the 7i{A) isotherm at 30 mN m'^. (Courtesy of X. Zhai and J.M. Kleijn^M Although the size of s t a n d a r d AFM tips is large relative to molecular dimensions (the tip apex h a s a radius of curvature of the order of 10 nm), it is very well possible to see the molecular arrangement of compact LB films or self-assembled monolayers on flat s u b s t r a t e s (mica, glass, quartz etc.). An example is given in fig. 3.67 a n d m a n y more can be found in the literature^^ Only if a monolayer is transferred at low surface pressure may the image be blurred because of the size and shape of the tip. This is a general problem in imaging small features lying apart; in a n AFM image they reflect the size and shape of the tip^^. Molecular resolution images from both STM and AFM on compact monolayers show a wealth of lattice structures, which can conveniently be analyzed in terms of lattice p a r a m e t e r s u s i n g their two-dimensional Fourier transforms. Using a n NSOM the molecular orientation in an LB monolayer was presented in polarized fluoresence images'^K With STM it is not only possible to image the arrangement of
1^ Details on this study can be found in X. Zhai, J.M. Kleijn. Thin Solid Films 304 (1997) 327. 2) J.B. Peng, G.T. Barnes, Thin Solid Films 252 (1994) 44. ^^ See, for example, P. Mulvaney, M. Giersig, J. Chem. Soc. 92 (1996) 3137. 4) A. Jalocha, N.F. van Hulst, J. Opt. Soc. Am. B. 12 (1995) 1577.
LANGMUIR MONOLAYERS
3.179
t h e molecules in a monolayer or bilayer on a conductive s u b s t r a t e , b u t chemical groups may also be identified. A possible explanation is t h a t the different polarlzabilities of functional g r o u p s influence t h e work function of t h e s u b s t r a t e to different extents^^; the work function of the s u b s t r a t e is one of the m a i n factors determining the tunneling probability. Experience h a s shown t h a t double C-C b o n d s , aromatic rings, amide, thiol a n d disulfide groups are imaged brighter t h a n s a t u r a t e d aliphatic backbones; carboxyl, hydroxyl a n d CI groups are less visible t h a n the saturated aliphatic backbone. By studying t h e s t r u c t u r e of LB monolayers a s a function of transfer p r e s s u r e different p h a s e s have been visualized, mostly on a mesoscopic scale-^^ Domain changes a n d p h a s e transitions, e.g., a s a function of temperature, have also been studied*^^. If the r o u g h n e s s of the underlying s u b s t r a t e precludes domain imaging by n o r m a l force m e a s u r e m e n t s , d o m a i n s might be imaged t h r o u g h lateral force m e a s u r e m e n t s ^ ^ The inner structure of condensed-phase domains can b e visual-
13.3 ^m height 11.2 n m
0
13.3 ^m amplitude 0.178 n m
Figure 3.68. AFM images of a LB film of stearic acid-forming domains on a polyethyleneimine/mica substrate. The left image shows the topography as measured in the contact mode. On the right the cantilever was oscillating. The resulting image reveals regions of different molecular tilt in the domains that are neither visible in the contact mode nor in the lateral force (friction force) mode. (From D. Kriiger, B. Anczykowski and H. Fuchs, Ann. Physike (1997) 341.)
1^ B. Venkataraman, J.J. Breen, and G.W. Flynn, J. Phys. Chem. 99 (1995) 6607; A. Ikai, loc. cit.. -^^ For example, L.F.Chi, M. Anders, H. Fuchs, R.R. Johnston and H. Ringsdorf, Science 2 5 9 (1993) 213. ^) H.D. Sikes, D.K. Schwartz, Ixingmuir 13 (1997) 4704. 4) M. Fujihira, H. Takano, Thin Solid Films 243 (1994) 446.
3.180
LANGMUIR MONOLAYERS
ized by u s i n g a vibrating cantilever which enables a stiffness c o n t r a s t to be obtained^^ (see fig. 3.68). Comparison with the structure of the monolayers before transfer (as obtained by other imaging t e c h n i q u e s like BAM) allow the determination of the effects of the transfer process and the influence of the s u b s t r a t e on the organization a n d defect formation in LB monolayers. Modifications of LB films, whether caused by the SPM probe or by some other external force, are easily characterized and can provide insight into film s t r u c t u r e a n d -dynamics. With a n AFM tip u n d e r high force it is possible to make holes in a n LB film. From t h e image of the hole the thickness per monolayer a n d n u m b e r of monolayers can be determined. Virtanen et al.-^^ induced defect 'pores' in bilayers of stearic acid a n d cadmium stearate by the application of electric pulses between a n STM tip a n d film surface. Real-time STM images measuring the rates at which t h e s e pores 'refill', provide a m e a n s of determining the viscosity of nanometerscale regions of deposited molecular films. AFM is a n ideal tool for investigating the quality of LB films and their longt e r m stability in various environments, which are important i s s u e s regarding their contemplated applications. Potentially useful films should be homogeneous a n d defect-free. In section 3.7a we already mentioned a n AFM study concerning the evolution of LB films of fatty acids in water and in air. The effect of polymerization of monolayers before or after transfer - in order to increase the mechanical stability of the resulting LB films - h a s also been studied using AFM'^^ 3.7e
Rheology
A large variety of techniques for measuring interfacial rheological p a r a m e t e r s exists. A first classification can be made between techniques suited for measuring interfacial s h e a r a n d interfacial dilational properties. A recent review of t h e various techniques can be found in a review by Miller et al.'^^ In order to prevent u n d u e fragmentation of the text, here we shall also describe techniques t h a t work better for Gibbs monolayers. (i) Determination
of interfacial
shear
properties
Interfacial s h e a r properties can be determined either by steady state or by oscillatory m e a s u r e m e n t s (see sec. 3.6f). In the latter case dynamic s h e a r moduli are obtained; in the former the interfacial shear m o d u l u s or the interfacial s h e a r viscosity is obtained. Direct measurements.
By direct measurements
we shall u n d e r s t a n d procedures
where the monolayer is sheared at some place and the resulting motion or stress at ^^ D. Kriiger, B. Anczykowski and H. Fuchs, Ann. Physik 6 (1997) 341. 2) J.A. Virtanen, S. Lee, W. Li, and R.M. Penner, J. Phys. Chem. 98 (1994) 26637. ^^ See, for example, H. Vithana, D. Johnson, R. Shih and J.A. Mann, Phys. Rev. E. 5 1 (1995) 454; D.F. Gu, C. Rosenblatt and Z.. Li. Liq. Crystals 19 (1995) 489. 4) R. Miller, R. Wiistreck, J. Kragel and G. Kretzschmar, Colloids Surf A l l l (1996) 75.
LANGMUIR MONOLAYERS
3.181
a different position is measured. The classical instruments for the direct determination of interfacial shear properties consist of a circular measuring body suspended from a torsion wire such that this body Just touches or, preferentially, is positioned in the interface containing the monolayer, which is contained in an outer cylindrical vessel. In the most common set-up the vessel rotates at a certain rate and the torsion stress determines what is required to let the measuring body rotate over a certain angle or with a certcdn speed. Alternatively, the inner body rotates and the torsion on the outer one is measured. Such interfacial viscometers are known as flat disc surface (or interJaciaJ) viscometers. The most common set-up is that the outer vessel rotates at a certain speed and the torsion exerted on the measuring body is determined. When the outer cylinder of the suspended measuring body rotates steadily, results are interpreted in terms of the interfacial shear viscosity rj^. The sensitivity of these viscometers is of the order of r]^ >0.01 mN sm"^for an air-water interface. Creep measurements can also be carried out in this way by applying a small rotation to the torsion wire, and measuring the resulting small rotation of the inner cyinder as a function of time, see sec. 3.6f, under (i). A complication is that this rotation causes the shear stress to vary with time. A great problem is that for (visco-) elastic interfacial layers, such as spread or adsorbed protein layers, any major deformation partly destroys the network at the interface. This is expected to cause a strong inhomogeneity of the local shesir rate and interfacial viscosity over the gap between the measuring body and the outer vessel. Then the obtained apparent r]^ reflects some average over the local values. For a small deformation, as usually applied in creep or relaxation experiments, the problem of inhomogeneous deformation of the interface is reduced. Moreover, it is smaller for a smaller gap width between the measuring body and the outer vessel.
Figure 3.69. Flat disc surface viscometer.
3.182
LANGMUIR MONOLAYERS
The s h a p e of the measuring body may vary. A simple form is that of a flat disc (see fig. 3.69). If the containing vessel rotates, a torque is exerted on the disc. It consists of a contribution from the viscous friction by the adjacent fluids above a n d below the disc a n d from the interface. For a n air-liquid interface a n d the limits t h a t ari^ » rj and a«h,
R, the torque T exerted on a rotating disc is given
by Goodrich a n d Chatterjee^^. T = -a^rico 3
+ 4na'^r]''co ^
IN m-M
13.7.18]
where (o is the angular frequency of the rotating ring and the other symbols may be read from the figure. (For arj^ « rj the numerical coefficient in the first r.h.s. term of [3.7.18] becomes 16/3.) For the case t h a t the contribution of the bulk viscosity can be fully neglected and for a narrow gap between vessel and disc, (R - a) «
a,
instead of [3.7.18] [3.7.19]
T = 4nri''o)\
[R^-a^
As the torque a n d all other parameters can be measured, rj^ is obtainable. An alternative for the flat disc viscometer for liquid-liquid interfaces is the biconical disc interfacial
viscometer.
A disadvantage of the (thin) flat and biconical
disc interfacial viscometers is the delicate placement of the disc "in" the interface. Moreover, s t a n d a r d theoretical analyses do not a c c o u n t for incomplete wetting and, for the flat disc viscometer, for the finite thickness of the disc. P a r t s of t h e s e problems are circumvented by using the classical surface
viscometer
developed by Brown et al,
knife-edge
1958^^ a n d variations of it as the
double knife-edge surface viscometer and the blunt knife-edge viscometer. For each of these it is crucial t h a t the knife j u s t touches the monolayer, b u t does not break it. Therefore the knife-edge h a s to be non-wetting. However, placing the knife precisely in the surface remains a cumbersome manipulation. Theoretical expressions for the torque upon the torsion wire have been derived for the various types. Benjamins a n d van Voorst Vader^^ describe a modified double ring surface r h e o m e t e r consisting of two concentric glass rings, which both lie flat in the interface. They used it for the determination of dynamic interfacial s h e a r moduli. The outer ring could oscillate periodically a r o u n d its axis whereas the inner ring w a s stationary and connected to a torque-measuring device. The advantage of s u c h a set-up is t h a t the adjacent bulk solution and the inner ring are both stationary, as a result of which the viscous drag by the bulk solution on the inner ring can be neglected. The oscillatory motion of the outer ring will generate a damped t r a n s it F.C. Goodrich, A.K. Chatterjee, J. Colloid Interface Set 34 (1970) 36. 2) A.G. Brown, W.C. Thuman and J.W. McBain. J. Colloid Set. 8 (1953) 491. ^^ J. Benjamins and F. van Voorst Vader, Colloids Surf 65 (1992) 161.
LANGMUIR MONOLAYERS
3.183
verse shear wave in the surface due to the hydrodynamic coupling between the surface and the solution in contact. This coupling may be neglected if the penetration depth of this shear wave is small compared to the distance between the two rings. This condition is satisfied if the interfacial shear modulus G^ exceeds a certain minimum value which increases with the square of the gap width between the rings and with o;^^^. Petkov et al.^^ described a sensitive method of obtaining 77^; a small spherical particle floats at the interface £ind moves under the action of an applied capillary force. From the measured drag coefficient rj^ is computed. Results for aqueous solutions of Na^DS" and C^gTMA^Br" agree reasonably with those in the literature. One can consider this method to be the 2D equivalent of the Stokes method for measuring bulk viscosities. Surface shear wave propagation and damping can also be used to determine the two dynamic shear moduli. Such waves are generated by mechanically applying the desired mode of vibration (longitudinal or transverscd) at the desired frequency to a bar or rod in the interface. The propagation and/or damping is recorded by a detector, placed at some distance in the monolayer. Various contraptions have been devised to operate wave generator and detector-^^ Standing waves can be studied stroboscopically. To generate a wave it is not necessairy for the driving object to be in the interface; it can also be placed in the air just above it, but without touching (-100 ^m apart). Vibrations in the object (say a needle) lead to wave generation in the surface because of differences in dielectric permittivity across the surface^^. The ensuing propagating waves can be probed by optical diffraction of a laser beam which yields the wave vector k and the damping coefficient p. Using the dispersion equation of sec. 3.6g K^ and rf^ can be obtained. Damping coefficients and the wavelength are completely defined by the density and viscosity of the bulk solution, the absolute shear modulus and loss cingle of the surface, and the wave frequency. The technique is difficult to apply for interfaces between two liquid bulk phases. Moreover, the evaluation of the shear moduli is cumbersome, as discussed in some detail in sec. 3.6g. Indirect measurements. Indirect methods for determining the interfacial shear viscosity include procedures in which the liquid underneath, together with the monolayer are brought into motion and the ensuing dissipation consists of a bulk and interfacial contribution. Theory is required to compute these two contributions and to subtract the former. An old method for determining the interfacial shear viscosity is the canal surface viscometer. It is based on the determination of the flow rate of a film through a narrow canal or slit under an applied two-dimen-
1^ J.T. Petkov, K.D. Danov, N.D. Denkov, R. Aust and F. Durst, Langmuir 12 (1996) 2650. 2) J.A, de Feyter and J. Benjamins, J. Colloid Interface Set 70 (1979) 375. ^) K. Ito. B.B. Sauer, R.J. Skarlupka, M. Sano and H. Yu, Langmuir 6 (1990) 1379
3.184
LANGMUIR MONOLAYERS
stationary cylinders 1 [ ,'
p
p
j:
j ^ ^ '■/VV//^^//V V//// 1 1 1 1 1 1 1 1 1 1 1
-
-
^h—^ L
_4.
^.''//y//.'>///AA^//.'^
\ 4^ 1 y
1 1
1 1 1 1 1 11 11 11 1 1
(a
A,
1 1 1 rot disk 1 1 rotating 1 1 1 1
(b:
Figure 3.70. Deep channel surface shear viscometer according to Mannheimer and Schechter (loc. cit.): (a) side view, (b) top view. sional pressure difference ^K.
For Newtonian flow of the film ?]" can be calculated
from the rate of film flow Q through a canal of width a and length i according to ,3
C= for f»
[3.7.20]
n
a a n d if the walls are smooth and parallel and there is no slip of the film
along the wall. The second term on the right h a n d side corrects for the contribution of the viscosity of the underlying bulk. A more m o d e r n modification is the deep-channel
surface
viscometer
which
consists of the two concentric, stationary vertical cylinders forming a ring-shaped canal a n d a rotating Petri dish containing the liquid. The canal h a s a rectangular cross-section. The cylinders are positioned in s u c h a way t h a t they almost touch the bottom of the dish. The dish can rotate at a known angular velocity, (see fig. 3.70 for a sketch). By m e a n s of a hydrodynamic analysis the shear stress exerted by the rotating dish via the viscous liquid on the liquid surface can be calculated. The centreline surface velocity inside the capillary can be determined by bringing veiy small particles into the surface. This velocity is reduced by the surface s h e a r viscosity a n d from the experimentally
determined velocity r]^ can be calculated
LANGMUIR MONOLAYERS
3.185
for laminar. Newtonian flow, both for liquid-gas^^ a n d liquid-liquid^^ interfaces. (ii) Determination
of dilationcd interfacial
properties
Dilational interfacial properties c a n be determined in various ways b o t h a t small a n d a t large strains. In the former case results are normally interpreted in t e r m s of interfacial dilational storage moduli, interfacial dilational loss moduli or dynamic interfacial dilational viscosities a n d the loss t a n g e n t s a s a function of applied deformation frequency, see sec. 3.6f. For large s t r a i n s one o b t a i n s t h e interfacial dilational viscosity. Various t e c h n i q u e s have been d i s c u s s e d in t h e reviews by Miller et al. a n d Prins, mentioned in sec. S.lOd. For the wave behaviour, see fig. 3.45. (iia) Small strains.
Wave propagation
and damping.
Measurement of wave
propagation a n d damping is a n important technique for the determination of dilational interfacial properties at small deformations. The theoretical foundations were presented in sec. 3.6f. Wave propagation and damping are usually measured in a Langmuir trough. S u c h t r o u g h s were described in sec. 3.3a.
To m a k e t h e m
suitable for wave damping experiments a device is needed to impose a n oscillation on the barrier. Usucdly to t h a t end a steppen motor, provided with a n eccentric, is u s e d to convert t h e rotatory movement into a transversal or longitudinal h a r monic motion. The response is measured at some distance from the barrier, often using a Wilhelmy plate a s the probe. Basically three regimes c a n b e distinguished, depending on the ratio P~^ / £ between the reciprocal damping coefficient a n d the trough length. For pi«l reached; for p(.»\
damping is complete before the end of the t r o u g h is
multiple reflection of waves between barrier a n d t h e t r o u g h
end take place, leading to a stationary state; a n d for j3^ = 0(1) a complicated intermediate state is created, of which analysis is difficult. S u c h trough experiments suffer from two d r a w b a c k s in the determination of dilational interfacial properties. First, the deformation in a Langmuir trough always contains a s h e a r contribution c a u s e d by flow along the sides of the trough. Only if the s h e a r moduli aire small c o m p a r e d with t h e dilational ones m a y t h e c o n t r i b u t i o n of t h e s h e a r deformation be neglected compared with the dilationad deformation. For surfacta n t s this can be better realized t h a n for protein monolayers. Second, it is very h a r d to avoid leakage along the moving barrier. We also draw attention to QL funnel
technique^^ in which a hydrophobic funnel is
moved across a LG surface in order to compress or expcind its area isotropically. A c o u n t e r - b o d y c o m p e n s a t e s for the displaced liquid by moving in t h e opposite direction. In this way the meniscus level remciins constant. Relaxation processes, induced by the funnel movement are monitored through a Wilhelmy plate. In this 1^ R.J. Mannheimer and R.S. Schechter, J. Colloid Interface Set 32 (1970) 195. 2) DT. Wasan, L. Gupta and M.K. Vora. Am. Inst Chem. Ing. J. 17 (1971) 1287. ^^ O. Senkel, R. Miller and V.B. Fainerman, Colloids Surf A143 (1998) 517.
3.186
LANGMUIR MONOLAYERS
A
1
1
►
1
llh
I
7 6
tl \^3
(c)
Figure 3.71. Scheme of the ring trough technique, (a) Perspective view; (b) side view. The arrows indicate the oscillatory movements of the ring; (c) measuring scheme (1) ring. (2) solid cylinder, (3) Wilhelmy plate, (4) transducer, (5) linear potentiometer, (6) power supply and (7) recorder. (Modified after J.J. Kokelaar, A. Prins and M. de Gee, J. Colloid Interface Set 146 (1991) 507.) way, y(A,t) c a n be m e a s u r e d and, hence, the relaxation studied both for compression a n d expansion. (iib) Improved
trough techniques.
A more recent method for relaxation experi-
m e n t s a n d for applying strain in harmonic oscillation is the so-called ring technique
trough
(see fig. 3.71 for a n illustration from Prins' group). A ring which is
completely wetted by the contracting liquid, is moved perpendicular to the surface. In this way a p u r e dilational deformation of the liquid inside the ring is e n s u r e d a n d a n y leakage of the barrier is ruled out. The resulting change in interfacial tension is measured, for instance by a Wilhelmy plate in which the plate is kept in
LANGMUIR MONOLAYERS
3.187
permanent contact with the interface in the centre of the ring. Applied changes in the relative interfacial area can be vgiried between 0.01 and 15%. Changes in the height of the liquid interface are compensated by vertically moving a cylinder with the same horizontgd cross-sectional area as the ring opposite to the movement of the ring (item 2 in fig. 3.71). Another instrument in which the deformation is also purely dilational and leakage completely prevented has been described by Benjamins and van Voorst Vader^). They make use of an elastic square of rubber bands placed in the interface. At the four comers the bands are connected to vertical metal bars which can be moved sjnichronously along the diagonals of the square, in this way chcinging the area. A disadvantage is the possible leakage of interfacisd active material from the rubbers, but this can be checked by canying out blank experiments. The problem of leakage of the barrier is also circumvented in various other modifications of the Langmuir technique. Loglio et al. described cin apparatus in which a stainless steel elastic ring, placed horizontally in the interface, is deformed by two normal inward forces, imposing small area changes-^^ Murray*^^ used a rhomboidally shaped teflon frame or barrier of one continuous piece, consisting of four rigid sides which are hinged at the comers. The area inside the barrier is expanded or compressed by driving two opposite comers to and from each other. The interfacial tension is usually measured using a Wilhelmy plate. In contrast to the first two techniques the deformations applied in the other instruments are not exactly dilational, but for small deformations the error is small. (Hi) Drop techniques. Various methods make use of pendent drop techniques and modifications thereof. A drop is prepared at the lower tip of a vertical capillary. Let us assume that the intricate manipulation of applying an insoluble monolayer on the drop surface has been successfully completed. Its volume can accurately be monitored by using a syringe. The shape of the drop is determined by an imaging technique, allowing the interfacial tension to be determined with an accuracy better than ±0.1 mN m-^ (sec. 1.4). These techniques eire now used to study the relaxation behaviour of an interface after cin applied transient interfacial area disturbance. For Langmuir monolayers they aire less appropriate. Harmonic interfacial disturbances can be induced by bringing an air bubble at the tip of a capillary in oscillation by a piezoelectric excitation system. In more modern instruments pressure variation in the bubble is directly monitored by pressure transducers. Such a set-up allows the determination of interfacial dynamic moduli. Figure 3.72 shows a dynamic drop tensiometer in which the volume of a ^^ J. Benjamins, F. van Voorst Vader, Colloids Surf. 65 (1992) 161 and older references. 2) G. Loglio, U. Tesei and R. Clini, Rev. Set Instmm,, 59 (1988) 2045. 3) B.S. Murray. Colloids Surf, A.125 (1997) 73.
3.188
LANGMUIR MONOLAYERS
motor
^ -^
^^ ^^
PC
syringe
Figure 3.72. Measuring principle of a dynamic drop tensiometer. Controlled level changes in the syringe lead to concomitant changes in the drop volume. (Redrawn from Benjamins et al., (1996).) or rising drop is controlled by a dc motor drive. The droplet profile is analyzed by using a CCD camera^^ and a n image processing unit. Several times per second, drop area, volume a n d interfacial tension are calculated. The area of the droplet c a n be m a d e to oscillate sinusoidally by letting the drop volume fluctuate sinusoidally a t a c h o s e n a m p l i t u d e a n d frequency^K The a p p a r a t u s is well suited for oil-water interfaces. Compared to traditional Langmuir trough experiments it avoids t h e problem of strong damping through viscous friction in the adjoining bulk p h a s e s , leading to non-uniform deformation of the interface, a n d of leakage p a s t t h e moving barrier which is more difficult to prevent in oil-water systems. A variant is the drop pressure
relaxation
technique*^-^ in which the p r e s s u r e
across a drop is measured (e.g. by a pressure transducer) a s a response to volume deformations. T h u s , yit) is obtained. Time scales down to 10"^ s could be mastered. (iv) Large strains.
Below we will d i s c u s s various t e c h n i q u e s in which a pre-
d o m i n a n t l y s t e a d y s t a t e dilational deformation is applied. In m o s t of t h e s e techniques there may be a s h e a r contribution to the total straiin. Whether this contribution can be neglected depends, among others, on the properties of the interface (ratio of s h e a r m o d u l u s to dilational modulus). Overjlowing cylinder. In this a p p a r a t u s the deformation of the interface is purely dilational. The liquid u n d e r investigation is p u m p e d from below to the top of a vertical cylinder, where it is allowed to flow over the top rim and downwards along
^^ CCD stands for charge-coupled device; it is a chip with many image-sensitive elements. 2^ J. Benjamins, A. Cagna and E.H. Lucassen-Reynders, Colloids Surf., A 114 (1996) 245. ^^ R. Nagarajan, D.T. Wasan, J. Colloid Interface Set 159 (1993) 164.
LANGMUIR MONOLAYERS
3.189
(b; pump
Figure 3.73. Schematic representation of the overflowing cylinder technique; (a) side view, (b) top view, indicating the radial velocity i; (r). (Courtesy of A. Prins et al.) t h e outside wall of the cylinder, thereby returning to the p u m p again (fig. 3.73). In this way a radiadly expanding liquid interface is obtained at the top of the cylinder. Experimentally it is found t h a t u n d e r steady state conditions t h e radial surface velocity initiadly increases linearly with distance, starting from zero in t h e centre (stagnation point). Near the rim the velocity increases more t h a n linearly with t h e distance. It can be easily shown t h a t in the linear part dlnA/dt
= 2v / r . At a n y
position r the surface tension can be m e a s u r e d by the Wilhelmy plate or a similar technique. For air-water interfaces v^ h a s been determined by m e a n s of laser Doppler anemometiy^). The found relative surface expansion rate vairied from roughly 1 s"^ for p u r e water to 10 s~^ for a commercial surfactant (teepol) solution. For p u r e liquids the surface flow is hydrodynamiccdly driven, b u t in the presence of surface active components a surface tension gradient may develop which accelerates a thin layer on top of the b u l k flow (Marangoni effect). The relative expansion r a t e s are affected by t h e flow rate and, for small height, by the height of the falling film along the outside wall of the cylinder. Free-falling
film
technique.
The liquid u n d e r investigation is allowed to flow
t h r o u g h a narrow slit in the bottom of a container u n d e r s u c h conditions t h a t it forms a free-falling film. Nylon wires a t both sides of the film stabilize it during its downward movement. The film becomes thinner during its fall d u e to its increased velocity. The expansion of the film is related to t h e vertical velocity g r a d i e n t
1^ D.J.M. Bergink-Martens, H.J. Bos and A. Prins, J. Colloid Interface Set, 165 (1994) 221.
3.190
LANGMUIR MONOLAYERS
(2
1)
^C=:s^ Figure 3.74. Sketch of a caterpillar trough. (1) and (2); Wilhelmy plates in fixed positions. The black squares represent the moving barriers. To the right the monolayers are expanded, to the left they are compressed. (Courtesy of A. Prins et al.) according to d\nA/dt
= dv , where v
direction. J u s t after the slit d In A/dt
is the interfacial velocity in the vertical (z) may be as high as 100 s~^ ^\ It decreases with
increasing distance from the slit. The surface tension of the film can be m e a s u r e d by a n adapted Wilhelmy plate technique. Caterpillar
trough
technique.
Large a n d more or less steady state dilational
deformations c a n also be obtained by using the so-called caterpillar trough technique, (ee fig. 3.74). It consists of a Langmuir trough provided with two Wilhelmy plates (marked 1 a n d 2 in the figure) and a n u m b e r (4-6) of barriers fixed to a n endless belt which are moved caterpillar-wise one after the other over the liquid surface in the way suggested in the figure. In this way the surface can continuously b e e x p a n d e d or c o m p r e s s e d . However, t h e relative r a t e of e x p a n s i o n
or
compression is not constant during one stroke of a barrier and leakage between the barriers a n d the trough may give rise to problems. The method can be used for low deformation r a t e s (< 0.2 s"^); at higher rates the moving barriers disturb the bulk liquid too m u c h . For Langmuir monolayers this method is not adequate. 3.7/
Volta
potentials
One of the central electrostatic characteristics of a monolayer is the potential difference y/^ created across the layer as a result of assembly a n d ionization of surfactants. Figure 3.17 gave a n illustration. Important a s this parameter may be for modelling a n d for controlling deposition of monolayers on solids, there is no way of m e a s u r i n g It. We refer to the issue of measuring potentials in general, discussed In detail in sees. 1.5.5a. Basically, y/° is the electric work of transferring, isothermally a n d reverslbly, a unit charge from the bulk of the (aqueous) p h a s e to the bulk of the vapour p h a s e . However, a s unit charges always have a non-zero volume, taking t h e m from one p h a s e to the other also Involves non-electrostatic, or chemical, work a n d there Is no u n a m b i g u o u s way of splitting the total reversible work into A. Prins, see the reference in sec. S.lOd,
LANGMUIR MONOLAYERS
3.191
its electric and chemical contributions. Briefly stated, it is impossible to measure the Galvani potential difference between two chemically different phases. Two alternatives may be considered. (i) A probe is introduced into the monolayer; the electric state of the probe's environment induces a change that may be optically measured. For instance can the extent of dissociation depend on the local potential. Although this technique has certainly contributed to the understanding of monolayers and micelles it suffers from the uncertainty mentioned above that the probe itself contributes to the composition so that the chemical contribution is non-zero. (ii) Measuring Volta potenticd differences between the monolayer and substrate. Recall that the Volta potential of a phase is the potential just outside that phase, beyond the (short range) chemical interactions. Volta potentials are measurable but much more difficult to interpret than Galvani potentials because they reflect the sum of all electric contributions (caused by free and bound ions and dipole orientation in any layer). At issue now is how they can be measured. Before discussing experiments a note on nomenclature is appropriate. In the literature Volta potentials are often called surface potentials but this term has other meanings as well, so we shall not use it. The usual symbol is AV, but in line with our convention (sec. 3.4.1) the appropriate symbol is V^^\ i.e. it is the Volta potential of the monolayer minus the same for the blank at the other side of the barrier. The latter is not zero and depends on the orientation of water molecules at the interface, and in the presence of electroljrtes, a double layer may form, giving rise to a non-zero V'^^. In sec. II, we discussed the relevsmt measurement and gave results for various electrolytes. In sec. II.3.9 we concluded that for pure water, according to the best experiments presently available, ji^^ > 0 (the j^-potential is the potential of water with respect to water vapour caused by the spontaneous polarization of the interface). This means that the water dipoles at the surface are preferentially oriented with their negative sides "out". The value of x"^ is not certain; probably it is less than 0,1 Volt. So, V^^^ contains a x^^^ ^^^ ^ ¥°^^^ contribution (four terms). The basics of the measurement date back to Frumkin^) and Yamins and Zisman-^). The principle has been given before (II, fig. 3.74). A plate R is brought parallel, and very close to, the monolayer. The potenticd difference between R and the solution is measured, first for the monolayer, then for the reference surface, the difference being V^^K Classically there are two options for measuring the potential. If it is done potentiometricadly, the air between R and the surface has to be made conducting, mostly by having the air gap ionized, for instance by using an
1^ A.N. Frumkin. Z. Physik. Chem. (Leipzig]lie (1925) 485. 2) N.G. Yamins. W.A Zisman, J. Chem. Phys. 1 (1933) 656.
3.192
LANGMUIR MONOLAYERS
monolayer
/ barrier
reference
Figure 3.75. Sketch for the potentiometric determination of the Volta potential of a monolayer. The compensation setting of E for R' is subtracted from that for R. a-emitter like polonium or the 241 isotope of americium as a coat on the metal plate JR. The s c h e m e looks like fig. 3.75. This is a n extension of the procedure described before (sec. II.3.10f). An alternative is to u s e a vibrating electrode. In this situation the gap between electrode a n d liquid acts a s a condenser of oscillating capacitance; the emitted AC current can be measured in an external circuit. This current depends on the Volta potential. As compared to fig. 3.75 the electrode now vibrates n o r m a l to the surface a n d instead of a potential difference a current is m e a s u r e d . This method is more precise t h a n the former but also more prone to malfunctioning. For a discussion with more details see Gaines' book, mentioned in sec. 3.10b, a n d Pethica et al^^ In passing, the streaming jet method, u s e d by Randies to study the free surface of water and aqueous electrolyte solutions^l can also be used, although V^^^ for a flowing monolayer may differ from t h a t at rest. Measuring V^^^ from the capacitance of a static plate is p e r h a p s also possible. Venselaar et al.^^ have given the theoretical background for this and J a c o b s et al."^^ proved t h a t the method worked. One of the conditions is that the electrode should not pick u p stray charges, which might pose a problem for Teflon troughs. For the interpretation one can write y(a) ^ ^o(a) .
X
(o)
where i/^^^^^ = i/°-"^
(3.7.211 y/^'^ (m = monolayer, r = reference), a s before. The m i n u s sign
to x^^^ is needed because in j ^ water is referred to the vapour whereas y/^ is the potential in the vapour referred to that in the water.^^
1) B.A. Pethica, M.M. Standish, J. Mingins, C. Smart, D.H. lies, M.E. Feinslein, S.A. Hossain and J.B. Pethica, in Monolayers, E.D. Goddard Ed., Adv. Chem. Ser. 144, Am. Chem. Soc. (1975) ch. 9. 2) J.E.B. Randies. Trans. Faraday Soc. 52 (1956) 1573. ^^ J.L.M. Venselaar, A.J. Kruger, L.M.H. Verbakel and J.A. Poulis, J. Colloid Interface Set 70 (1979) 149. 4) J.C. Jacobs, A.J.M. Buuron, P.J.M. Renders and A.F.M. Snik, J. Colloid Interface Set 84 (1981) 270. ^^ Note that in the literature other conventions are sometimes used.
LANGMUIR MONOLAYERS
3.193
no salt
160 80
^ -^v-v-v-^ 10"^ M MgCl2 10-^ M CaCl2 50
> E
0 -80
E
40
S ^
30h
20 h 10 0 0.18
0.20
0.22 0.24 nm'^ / molecule
Figure 3.76. Stearic acid monolayers; surface pressure (lower curves) and Volta potentials (upper curves). Influence of bivalent electrolytes. (Redrawn from E.D. Goddard, J.A. Ackilli, J. Co\\o\d Set 18 (1963) 585.) As V^^^ c o n s i s t s of four t e r m s , its interpretation is n o t straightforward, although in some cases simple double layer models (for y/^) a n d simple models for x may work. For the latter sometimes N X =
p{cos6) [3.7.22] £ £
or v a r i a n t s thereof, are used. The equation applies to a monolayer of N
dipoles
per unit area; p is the magnitude of the dipole moment, (cos 6} the average orientation to the surface a n d £ £ the dielectric permittivity. The equation is not very useful b e c a u s e polarization is rarely restricted to a monolayer a n d it is not clear what value h a s to be substituted for £. Mostly, V^^^ m e a s u r e m e n t s are u s e d to complement K{A) curves. Anticipating more illustrations in sec. 3.8, fig. 3.76 gives a first example. From the positive sign of V^^^ it may be concluded t h a t the dipolar contribution x^^^ exceeds that of xj/^^^^. The effect of the counterion is very pronounced; Mg2+ions bind somewhat, a n d Ca^^ ions bind strongly, to stearic acid. Apparently in t h e latter case strong electric charge compensation s u p p r e s s e s t h e (excess) potential to almost zero. This trend is reflected in n a n d in the rheological properties (not shown).
3.194
LANGMUIR MONOLAYERS
More illustrations of the techniques described in this section can be found in sec. 3.8. Needless to say, combining disparate techniques to one and the s a m e monolayer is the preferable approach. 3.8
Case s t u d i e s
The open literature contains several tens of t h o u s a n d s of monolayer studies. From t h e s e a small fraction will be discussed in this section. The main purpose is to provide illustrations of the techniques and interpretations treated so far. Our selection is mainly dictated by illustrating certain aspects; it is not a beauty contest'. Nevertheless we try to avoid sources of error. For a systematic review, see Ter-Minassian-Saraga's lUPAC report, mentioned in sec. 3.10a, which includes a checklist. Much practical information can be found in the monolayer h a n d b o o k s , mentioned in sec. 3.10b, particularly in t h a t by Gaines. For a rapid entry to the vast literature the compilation by Mingotaud et al., cited in sec. 3.10g, can be consulted. 3.8a
A note on equilibrium
and
reproducibility
Let u s start the systematics with a short general note on problems incurred in preparing well-defined a n d reproducible monolayers. Possible sources of errors are two-fold; they may be of a chemical or methodical n a t u r e , a n d can often be traced back to the issue of equilibration. Of course leakage around the barrier, and similar methodical errors are a s s u m e d to be absent. Langmuir monolayers are not at thermodynamic bulk p h a s e s , i.e. there is no external
equilibrium
with the adjacent
equilibrium. Unlike Gibbs monolayers, they
are not formed by adsorption from solution. A detour h a s been needed to force all monolayer-molecules into the interface (sec. 3.2). Solubility (in the liquid phases) a n d vaporazibility (in the gas phase) are never absolutely zero. Hence, in principle, dissolution a n d / o r evaporation should always occur. However, experience h a s shown t h a t m a n y monolayers are kinetically stable, i.e. remain unaltered over sufficient periods of time to carry out significant m e a s u r e m e n t s . In other words, they are at internal equilibrium. In our language; De (internal processes) «
De
(external processes). Gaines (loc. cit) gives a n example; monolayers of stearic acid in a s t a n d a r d trough, containing about 0.1 mg of acid, are stable for long periods without dissolution even though the aqueous s u b p h a s e , given its solubility, could absorb 1.5 mg of the acid. Absence of external equilibrium can lead to a variety of p h e n o m e n a . Freshly prepared Langmuir films do not necessarily have constant properties because they may still contain r e m n a n t s of the spreading liquid. These may evaporate; moreover some dissolution and evaporation of the surfactant may take place, depending on its n a t u r e , (for instance, fatty acids are more easily lost by dissolution, fatty
LANGMUIR MONOLAYERS
3.195
100 %
6 85% t=t
4
" * ^
68%
^ - j
10
20
30
J 40
L 50
X 60
70
t/min Figure 3.77. Influence of the relative humidity (given in %) on the surface pressure relaxation of myristic acid monolayers at pH = 2 (from HCl). T = 21.0 ± 1°C. (Redrawn from Bilkadi and Neumann, loc. cit.) alcohols by evaporation). Disappeairance of molecules from the monolayer leads to a reduction of the surface pressure. How m u c h loss is incurred in the later stages depends on the waiting time observed before s u b s e q u e n t compression a n d t h e rate of compression. As compression increases, the Helmholtz energy of the film (sec. 3.4b), which is the driving force for further disappearance, also increases, b u t b e c a u s e of t h e closer packing the rate of dissolution tends to decrease. As all of this also d e p e n d s on the n a t u r e of the system, general rules cannot be given. Long ago Ter M i n a s s i a n - S a r a g a studied t h e s e p h e n o m e n a systematically for lauric a n d myristic acid monolayers ^K She found the desorption r a t e s to d e p e n d on t h e surface pressure, the length of the hydrocarbon chain, the size a n d n a t u r e of the hydrophilic group a n d its degree of dissociation. Figure 3.77 illustrates t h a t t h e surface p r e s s u r e relaxation also depends on the relative humidity of the gas phase; t h e less it is a t equilibrium with the water p h a s e , the faster t h e dissolution^^ Evaporation can also be reduced by avoiding air flow above the trough. Dissolution into t h e s u b p h a s e c a n be diminished by adding acids (for fatty acids to s u p p r e s s dissociation) or (NH4)2S04 a s a salting-out agent. However, s u c h additives modify the s t r u c t u r e of the head group-water boundauy, which is reflected in c h a n g e s in Volta potential*^^ The i s s u e of external (dis)equilibrium by (suppression of) dissolution a n d / o r 1^ L. Ter Minassian-Saraga, J. Chim, Phys. 52 (1955), 80, 99, 181. 2) Z. Bilkadi, R.D. Neumann, J. CoUoid Interface Set, 82 (1981) 480. > ^^ See, for example E.D. Goddard, Ionizing Monolayers and pH Effects, in Adv. Colloid Interface Set 4 (1974) 45.
3.196
LANGMUIR MONOLAYERS
evaporation may be juxtapositioned to t h a t of internal (dis)equilibria. (Too) rapid compression of films can lead to pockets of film having deviating, internally nonrelaxed properties. For instance, Bommarito et al. investigated the p h a s e diagram of Langmuir monolayers a n d concluded t h a t previous m e a s u r e m e n t s were incorrect b e c a u s e the layers were not sufficiently relaxed ^K When this requirement is not met, there may be areas of differing tilt, a n d this can have consequences for defining average film properties. High surface dilational viscosities can promote s u c h irregularities. One way of finding s u c h inhomogeneities is by using a technique by which the surface can be scanned, like grazing incidence X-ray reflection (sec. 3.7b, iii) or Volta potential m e a s u r e m e n t s (sec. 3.7f). By way of illustration, D h a t h a t h r e y a n a n d Mobius found p r e s s u r e gradients for monolayers of 0^3 C^gCOOH^^ a n d studied them by reflection spectroscopy. At the moving barrier n always exceeds t h a t at the fixed barrier in the trough. The gradient VK increases with chain length a n d with K and can become a s high as 0.5 m N / m " ' cm"^ Condensation of the film leads to a strong further increase of V/r. Surface pressure gradients have also been reported for polymers by Peng and Barnes^^ Although nowadays we have sophisticated optical (sec. 3.7b a n d c) a n d rheological tech-
20
20
(a)
E
E
2 15
Z 15
E
E C13COOH
10
(b)
C17COOH
10
5h
ZSs^ 0.3
0.4
0.5 a: / nm^
0.6
0.1
0.2
0.3 a I nm^
0.4
Figure 3.78. n{a.] isotherms for myristic (left) and stearic acid (right). pH = 2, T = 25°C; the influence of the compression rate is given; x, 0.788; , 0.395; O, 0.296 and V, 0.197 nm-^ molecule"^ min"^ (Redrawn from Motomura et al., loc. cit.)
^^ G.M. Bommarito. W.J. Foster, P.S. Pershan and M.L. Schlossman, J. Chem. Phys. 105 (1996) 5265. '^^ See table 3.7 for the meaning of this code. 3) J.B. Peng, G.T. Barnes, Langmuir 6 (1990) 578; 7 (1991) 1749.
LANGMUIR MONOLAYERS
3.197
niques (sec. 3.6g a n d 7e), it is a pity t h a t these techniques are rsirely simultaneously applied. Another illustration of history dependence is given in fig. 3.78^K For myristic acid, CjgCOOH, K w a s found to depend on the rate of compression, whereas for stearic acid, C17COOH, itdid not. The higher solubility of the former w a s probably responsible, because it allowed leakage. Reversibility of film properties u p o n cycles is a general prerequisite for internally a n d externally equilibrated, well-spread layers. For 7t[A) cycles at fixed T this requirement can be formulated a s \>ndA = 0
13.8.11
Similar cyclic integrals m u s t be zero a s a function of t e m p e r a t u r e . Many K[A] curves below t h e collapse point have been found to satisfy this criterion. W h e n collapse does occur in the chosen n[A] interval, reversibility is mostly lost b e c a u s e p a r t of the monolayer material is pressed out. As a rule, compression c a n be performed with impunity until the ;r-value, exceeds the spreading p r e s s u r e . Figure 3.79 gives a n illustration. In this case, transition p a s t the collapse point leads to irreversible loss, after which the curve is repeatable at lower a.. In t h e figure, collapse takes place at area a^{3]; in a (I) the a q u e o u s surface is fully covered, b u t the acid molecules are not yet vertically aligned. At a (2) they are closely packed a n d oriented vertically. In passing we note that, for some acids 'spikes' have b e e n
["^^^
1
6 60 'Z
s
«
^*>. ti
■2
40
20
.2
0
"^
1 1
a
0, E V
i>
a, (3)
'
' t^ 1 \t «
\
1
C
1
'
1
"
^
1 1 1
I
U
1
8
Wi(2)
\''
\
1 's , 0.1
VOid) 1
0.3
0.2 a: I nm^
Figure 3.79. Compression until beyond the collapse point a (3), followed by expansion and recompression. Tetracosanoic acid T= 25°, pH = 3. (Redrawn from McFate et al., loc. cit.) ^^ K. Motomura, A. Shibata, M. Nakamura and R. Matuura, J. Colloid Interface Set 2 9 (1969) 623.
3.198
LANGMUIR MONOLAYERS
found in the compression i s o t h e r m a l Another issue is the purity of the chemicals used. Depending on the n a t u r e of t h e film a n d
the conditions,
impurities
m a y h a v e negligible or
drastic
consequences. We consider four below. (i) The requirements of the spreading solvent were discussed in sec. 3.2. It w a s concluded t h a t sometimes small differences were observed between monolayers spread from different solvents. The reason(s) is (are) not entirely clear. Part ot the s p r e a d i n g solvent molecules may remain in the monolayer; this solvent might have contained surface active impurities or the rate of evaporation may have given rise to frozen non-equilibrium s t r u c t u r e s in the monolayer. For polymers, the solubility in different spreading solvents will be different a n d this may t r a n s l a t e into different extents of unfolding which do not fully relax upon spreading. (ii) Impurities in the (aqueous) s u b p h a s e . Some kinds of monolayers (fatty acids) are sensitive to traces of Ca^^ (originating from the glassware or c a u s e d by the w a t e r - h a r d n e s s ) , o t h e r s (fatty alcohols) not a t all. The pH should always be controlled; for molecules with dissociable head groups this is obvious b u t specific influences of acids on non-dissociable groups have also been reported. Ionic cont a m i n a n t s also affect AV. In the p a s t ignoring this phenomenon h a s given rise to confusion w h e n using buffers* of different compositions. (iii) Impurities in the gas p h a s e . S p u r i o u s organic c o n t a m i n a n t s or CO2 may interfere, the latter for cationic monolayers. (iv) Impurities in the surfactant. Whether a reportedly '99.9% pure' sample is clean or dirty d e p e n d s on the surface activity of the non-reported 0 . 1 % . When the impurity is j u s t a close homologue of the main constituent the effect may be negligible. The ultimate check of reproducibility is to compare results obtained by different a u t h o r s u n d e r identical conditions b u t with different methods and chemicals. To t h a t end we give in fig. 3.80 a collage of six n{a.) curves for a stearic acid monolayer, one of t h e most stable a n d reproducible types. Although there is a fair a m o u n t of agreement, quantitative differences are also noticeable, for i n s t a n c e with respect to the presence of a break, demarcating the 2D liquid a n d a 2D solid p h a s e . Some of t h e s e differences may be significant a n d c a u s e d by differing experimental conditions, others are caused by differences with respect to experimental detail. Several a u t h o r s do not present data points, mostly b e c a u s e they have plotted the curve so often. The reader may judge for him(her)self. It is likely t h a t the accordance is no better for other fatty acids. Let u s conclude this subsection by reviewing with what kind of molecules Langmuir monolayers can be made. The requirements are clear; they m u s t contain one
1) C. McFate, D. Ward and J. Olmstedt, Langmair 9 (1993) 1036.
LANGMUIR MONOLAYERS
3.199
Figure 3.80. Surface pressure curves for stearic acid (CjyCOGH). Comparison between results of different authors, (a) Motomura et a l . l ^ pH = 2 (HCl), spread from benzene, 25 ± 0.1 °C, constant compression rate (cr), results independent of rate between 0.197 and 0.788 nm^ mol"! min-^; (b) Menger et al.^), 0.03 M H2SO4, spread from hexane, 23.0°C, cr. 0.4 nm^ mol"^ min"^; data points by Mingotaud c.s. ; (c) TomoaiaCotisel et a l . ^ ^ pH = 1-3 (no difference), spread from hexane after dissolution in ethanol, 22 ± 2°C, no dependence on cr. (range not indicated); (d) T. Murakata et al.4), 5x10-4 NaHCOg + 3 x 10"^ M BaClg, spread from chloroform, 17°C, cr. not given; (e) Dorfler and Rettig^l pH = 2 (HCl), spread from benzene, 25°C, cr. 77.6 cm^min'^; (f) Halperin et al.^), pH = 2 (HCl), spread from chloroform-heptane mixture, 21°C. cr. 0.9 cm min"^ (the lowest rate attainable on the Lauda apparatus).
ttj / nm^
^^ K. Motomura, A. Shibata, N. Nakamura and R. Matuura, J. Colloid Interface Set 2 9 (1969) 623. 2) F.M. Menger, M.G. Wood, S.D. Richardson, Q.Z. Zhou, A.L. Elrington and M.J. Sheirod, J. Am, Chem. Soc. 110 (1988) 6797. ^^ M. Tomoaia-Cotisel, J. Zsako, A. Mocanu, M. Lupea and E. Chifu, J. Colloid Interface Set 117 (1987) 464. "^J T. Murakata, T. Miyashita and M. Matsuda, Langmuir 2 (1986) 786. 5) H.-D. Doriler, W. Rettig, Colloid Polym. Set 260 (1982) 802. ^^ K. Halperin, J.B. Ketterson and P. Dutta, Langmuir 5 (1989) 161.
3.200
LANGMUIR MONOLAYERS
or more hydrocarbon (or fluorocarbon) tail to render them insoluble in water and to i n d u c e coherence, a n d a head group t h a t h a s enough affinity for water to promote the proper orientation. Alkanes without head groups j u s t float on the water a s thin layers (for the lower ones) or droplets (for the higher ones). This 'wetting transition' can be interpreted in terms of Van der Waals forces (sec. 4.3). Fluorocarbons c a n be a n exception in t h a t they can be oriented in the layer upon compression. The head group m u s t have a great affinity for water. It is not always realized t h a t this implies t h a t they repel each other. No films at all can be m a d e with -1, -Br, -CI or -NO2 as the end group; esters only give unstable films. Stronger hydrophilic groups (-OH, -COOH, -CN, -CONH2, -CHrNOH, -NH2) can give stable films if the chain h a s at least 16 CH2 groups. When the affinity of the head group for w a t e r i n c r e a s e s further by dissociation
(-SO~ - OSO^, - N(CH^)^, etc.)
the
molecules dissolve a n d may form micelles. Chains shorter t h a n about 10-12 tend to be too soluble a n d give too little coherence in the layer to attain sufficient stability^l The presence in the chain of cis double bonds or side groups is detrimental to close packing. In figs. 3.10 and 3.11 we already gave examples. Nowadays the surface properties of other t h a n long chain amphiphilics have been the subject of study; phospholipids, cholesterol derivatives, polymers, polyelectrolytes a n d proteins. Some of these form very stable films and illustrations will be given in the following s u b s e c t i o n s . 3,8b
Fatty
acidSf fatty
alcohols
and related
compounds
Molecules belonging to this category may be considered 'parent' s u b s t a n c e s for insoluble monolayers. Langmuir himself already studied them in his pioneering work,2), a n d these systems are not obsolete yet. Names and formulas for the acids a n d alcohols are collected in table 3.7. Familiar n a m e s prevail for molecules with even n u m b e r s of carbon atoms. The reason is that these s u b s t a n c e s are naturally occurring in animal a n d vegetable fats. For the simpler ones we shall sometimes u s e the given abbreviations. All the molecules listed belong to the category of monolayer formers'. To the side of the lower molecular m a s s e s the transition between soluble and insoluble is not s h a r p . Of course the shorter molecules are more soluble. Insolubility can be boosted by salting out. Charging is another matter; dissociation of the head groups improves solubility. Long chain molecules with strong head groups like sodium dodecylsulphate dissolve m u c h better t h a n the corresponding fatty acid at low pH, u n d e r the formation of micelles. The longer molecules form insoluble monolayers more easily; on the other h a n d the higher homologues are often heterodisperse. It
^^ Many of these rules can already be found in N.K. Adam's book (1941) mentioned in sec. 3.10b. 2) 1. Langmuir, J. Am. Chem. Soc. 39 (1917) 1848.
LANGMUIR MONOLAYERS
3.201
Table 3.7a. Normal long chciin fatty acid and fatty alcohols, used in monolayer studies. Formula
1 CgHigCOOH
Formal n a m e
Other a n d / o r familiar n a m e
Abbreviation
n-decanoic acid
capric a c i d
C9COOH
^lO^l^H
1-decanol
CJQH2JCOOH
n-hendec£inoic a c i d
undecanoic
^11^23^^
1-hendecanol
undecanol
CijOH
CJJH23COOH
n-dodecanoic acid
lauric acid
CijCOOH
^12^25^^
1-dodecanol
lauryl alcohol (dodecyl alcohol)
C12OH
n-tridecanoic acid
tridecylic a c i d
C12CX3OH
^13^27^^
1-tridecanol
tridecyl a l c o h o l
C13OH
CJOHQ-TCOOH
n-tetradecanoic acid
myristic acid
C13COOH
^14^29^^
1-tetradecanol
myristic alcohol (tetradecyl alcohol)
C14OH
C24H2gCOOH
n-pentadecanoic acid
^15^31^^ CisHg^COOH
1 -pentadecanol
pentadecyl alcohol
C15OH
n-hexadecanoic acid
palmitic acid
C15COOH
12^^5^^^^
CioOH acid
CioCXX)H
C14COOH
^16^33^^ CjgHggCOOH
1-hexadecanol
cetyl a l c o h o l
CieOH
n-heptadecanoic acid
margaric acid
CigCOOH
C17H35OH
l~heptadecanol
heptadecylalcohol
C17OH
n-octadecanoic acid
stcciric a c i d
C17COOH
^18^37^^ CjgHgyCOOH
1-octadecanol
octadecyl alcohol
CisOH
n-nonadecanoic acid
nonadecylic acid
Ci8CXX)H
C19H39OH
1-nonadecanol
nonadecyl alcohol
C19OH
^19^39^^^^
n-eicosanoic acid
arachidic acid
C19COOH
^20^41^^
1-eicosanol
arachic alcohol (eicosyl alcohol)
C20OH
1 CiyHoeCOOH
1 C20H41COOH
n-heneicosanoic acid
C20COOH
^21^43^^ 1 C21H43COOH
1-1-heneicosanol
C21OH
1-docosanoic acid
behenic acid
C21COOH
1 C23H^yCOOH
1-tetracosanoic acid
lignoceric a c i d
C23COOH
C24H49OH
1 C^sHs^COOH
C24OH
1-tetracosanol 1-hexacosanoic acid
cerotic a c i d
C25COOH
Note; nomenclature for other fatty molecules is similar; CigH33NH2 = cetylamine, abbreviation C^gNHg, etc.
3.202
LANGMUIR MONOLAYERS
Table 3.7b. As table 3.7a; compounds containing a double bond (indicated by Formula
Name
Familiar n a m e
CgHi^CH; CH(CH2)7COOH
trans-9 octadecenoic acid
elaidic acid
ibid
cis-9 octadecenoic acid
oleic acid
CgHj^CH; CH(CH2)70H
trans-8 octadecenyl alcohol
elaidyl alcohol
cis-8 octadecenyl alcohol
oleyl alcohol
CgHi^CH; C H ( C H 2 ) H C O O H
trans-13 docosenoic acid
brassidic acid
ibid
CIS-13 docosenoic acid
erucic acid
iibid
may be interesting to note t h a t for the acids the melting point increases in a n alternating way with chain length, each odd-numbered compound melting slightly below the next lower even-numbered one. However, the alcohols do not show s u c h a n odd-even
alternation.
The difference m u s t be sought in differences in crystal
s t r u c t u r e of the corresponding solids. Odd-even alternations have not been directly observed in 7t{A) curves, at least not in the G, LE a n d LC state. However, Sims and Zografi^l who systematically studied the pressure loss a s a function of time upon keeping the film at constant A below the collapse pressure for the C15COOH- C20COOH series, found differences in film stability between odd and even-fatty acids. The odd-numbered ones were more resilient against pressure loss. On the other hand, u p to the transition pressure, at any rate of compression there is a gradual increase of this pressure with the chain length^). Starting with (pseudo-)equilibrium K(A) curves, we may first recall fig. 3.9, showing the influence of the chain length of three undissociated acids, fig. 3.14, showing ;r(a.,T) curves for C13COOH and fig. 3.80, the collage of 7i{a.) curves for stearic acid, obtained by different a u t h o r s . The curve for C13COOH in fig. 3.9 a n d the (interpolated) one in fig. 3.14 are very similar b u t not exactly identical. This difference is a n o t h e r m e a s u r e of the absolute reproducibility. Diagrams like t h a t of fig. 3.9 have already been obtained long ago by Harkins* g r o u p ^ l Their results have not been substantially modified over the years. The same can be said of the thorough studies by Adam et al.^.S) ^Iso recall fig. 3.76 where Volta potentials of stearic acid monolayers were presented. The high p r e s s u r e part is not very different between the three acids, although at very high pressures subtle differences between the three are observed. We concluded
1) B. Sims. G. Zografi, J. Colloid Interface Set 41 (1972) 35. 2) B. Sims. G. Zografi, Chem. Phys. Lipids 6 (1971) 174. 3' G.C. Nutting, W.D. Harkins. J. Am. Chem. Soc. 61 (1939) 1180. "^^ N.K. Adam, Proc. Roy. Soc. AlOl (1922) 456, 516. ^^ N.K. Adam, G. Jessop. Proc. Roy. Soc. A112 (1926) 362.
3.203
LANGMUIR MONOLAYERS
before t h a t a^^, obtained by extrapolation a s indicated in fig. 3.9, i n c r e a s e s somewhat with increasing cheiin length. This area m u s t reflect the packing of t h e hydrocarbon chain. However, if d a t a for many monolayer studies are considered, a decrease with increasing chain length is also observed 1^. From a molecular point of
view b o t h t r e n d s c a n be accounted for; closer packing of longer c h a i n s is
energetically favourable b u t entropically unfavourable. It is possible t h a t , with increasing p r e s s u r e , a transition from the one to the other m e c h a n i s m m a y take place; k i n k s in the curve may result from t h a t (as in fig. 3.9). S u c h kinks, or more gradual increases of pressure, make the extrapolation very sensitive to t h e qucdity of the data. It is striking t h a t for CjgCOOH and CjyCOOH n o measurable pressure is built u p down to a r e a s of 0.28-0.30 nm^. It m e a n s t h a t there are very few kinetic u n i t s in the film, p e r h a p s b e c a u s e of the formation of small aggregates. In other words, the horizontal, cilmost zero part from very low a down to about 0.30 nm^ is a two-phase range.
44
s
40
E 36 32 28 24 20 16 12
r\a ^V
8 4
2s.
V
^v
I
0 0.18
japannn.!
-4—L
'0.20 s a,
0.221^
0.24
a„ Qj / n m ^
Figure 3.81. K{a^] curves for stCciric acid at two temperatures. The data points refer to different runs. (Redrawn from Casilla et al.)
^^ G.L. Gaines, Insoluble Monolayers at Liquid-Gas Interfaces, Interscience (1966) p. 223.
3.204
LANGMUIR MONOLAYERS
Systematic t h e r m o d y n a m i c analyses, along the lines shown in sec. 3.4c, in combination with a comparative study of different equations of state (table 3.3) have, to the author's knowledge, not (yet) been carried out. This is a pity because it would be interesting to find out w h e t h e r 2D equations of state, derived from partition functions for mobile a d s o r b a t e s do function better for the G a n d L+G range t h a n those based on a fixed lattice model. On the other hand, lattice models should satisfy for the condensed parts of the isotherm, although there the choice of the lattice size becomes critical. One of the reasons for the absence of such studies m a y be t h a t e x p e r i m e n t s in the G-state are very s u s c e p t a b l e to t r a c e s of contamination. One example h a s been given by Rakshit et al.^^ who used [3.4.17] to obtain the Helmholtz energy
F^
for monolayers of C13COOH, C15COOH, Ci^COOH a n d
CjgCOOH, substituted fatty acids and u n s a t u r a t e d acids. The integration was carried out from (almost) infinite area to ;r = TT , the equilibrium spreading pressure. For t h a t value of F"^ the a u t h o r s interpreted the result in terms of the 2D Van der Waals equation [3.4.40al. F/" decreased from 6.6 via 1.4 to 0.9 kJ mole"^ with increasing length from C j g - ^ Cj^COOH. As there is a prespecified integration boundary, these values do not say m u c h about interactions and affinities in the film. T h e c o n s t a n t
a^ w a s r e m a r k a b l y i n d e p e n d e n t of the n a t u r e of the
amphiphile, so w a s a
, (except for a few). There is clearly room for more detailed
elaborations along these lines. The influence of the temperature is exemplified in fig. 3 . 8 1 , taken from a study by Casilla et al.^^. The stearic acid was spread from benzene, b u t the rate of compression w a s not given. The a u t h o r s made a point of establishing the molecular cross-sections of a compressed film in the solid ^
a^.
a n d the liquid a^.
mi
^
state.
mi
Figure 3.82 gives the trends. Similar results have been reported by other investigators. Differences between literature d a t a depend on minor variations in the manipulation, the quality of the chemicals (Ca^^ interferes) a n d the way in which the extrapolation is carried out. See also fig. 3.80. In the present example in the 3D crystalline state the cross-section is 0.182 nm^, slighdy depending on temperature. So, in the film the monolayer r e m a i n s a bit more open t h a n in the solid. The a u t h o r s also derived compressibilities from the slopes using [3.3.1). L-films are a b o u t a factor of ten more compressible t h a n S-films (9 a s compared to 0.9 mN"M. The /c!^-values showed a n irregular temperature dependence t h a t deserves more attention. For palmitic acid, C15COOH, Pallas and Pethica studied the
L ^ G transition
between 15 and 40°^l Using a 2D-Clapeyron equation , see [3.4.24], they determined ^^ A.K. Rakshit, G. Zografi, I.M. Jalal and F.D. Gunstone, J. Colloid Interface Set 80 (1981) 466. 2) R. Casilla, W.D. Cooper and D.D. Eley, J. Chem. Soc. Faraday Trans. (1)69 (1973) 257. 3) N.R. Pallas, B.A. Pethica, J. Chenh Soc. Faraday Trans. (I) 83 (1987) 585.
LANGMUIR MONOLAYERS
3.205
0.206|-^i^ 0.204
10
12
14
16
18
20
22
temperature Figure 3.82. Molecular cross-section for monolayers of stearic acid in the liquid (top) and solid (bottom) state, obtained by extrapolation. Source as in fig. 3.81.
0.2
0.3
Figure 3 . 8 3 . Surface pressure isotherms of stearic acid, spread from hexane; temperature. 22 ± 2°, no influence of compression rate. The pH is vairied (using NaOH for pH > 9 and a borate buffer at pH 8); the ionic strength changes somewhat, (a) primary data, (b) corrected for losses by dissolution. Curve (1), pH 8; curve (2) pH 9.7; curve (3) pH 10.7; curve (4) Na stearate, spread at pH 10.7. (Redrawn from Tomoaia-Cotisel et al., loc. cit.)
3.206
LANGMUIR MONOLAYERS
the isosteric heat of the transition. From 20° to 40°C AH"" decreased from 15.6 to 9.5 k J mol~^ The trend and the magnitudes are very similar to those observed for myristic acid, see table 3 . 1 . For behenic acid monolayers it was possible to induce two different L-phases by applying a dilational flow; they could be identified by Brewster angle microscopy^^ (sec. 3.7b). The next variable is the pH. By increasing it, fatty acid monolayers become charged, with marked consequences for the layer properties. The overall behaviour is complicated because of two counteracting trends^^: (i) Charging of the molecules m a k e s them more soluble. As a result molecules escape from the monolayer and K decreases if A is kept constant. This issue counts more for the lower homologues, say for acids below CjgCOOH. (ii) When the molecules do not dissolve, as is the case for CiyCOOH and higher, at not too high pH (- u p to 9 for CiyCOOH), the head groups acquire a charge and repel each other; a n electric double layer is formed, which leads to a surface p r e s s u r e increase, (see sec. 3.4h). To identify the intrinsic role of the double layer one h a s to account for dissolution or pre-empt it. One, not very appealing procedure is to compress very rapidly to avoid dissolution. An alternative is to experiment with films of longer chain fatty acids at not excessively high pH. Figure 3.83 is a n example for stearic acid., given by Tomoaia-Cotisel et al.^K In this case the a u t h o r s found that the collapse pressure w a s the same (51 mN m"^) for each pH, b u t collapse took place at different
Figure 3.84. As fig. 3.83, lower pH values (same source). Qj / n m
^> M.C. Friedenberg, G.G. Fuller, C.W. Frank and C.R. Robertson. Langmuir 12 (1996) 1594. 2) See, for example J.A. Spink, J. Colloid Set 18 (1963) 512. ^^ M. Tomoaia-Cotisel, J. Zsako, A. Mocanu, M. Lupea and E. Chifu. J. Colloid Inlerjace Set 117 (1987) 404.
LANGMUIR MONOLAYERS
3.207
a.-values. These last differences were attributed to material loss. The authors tried 1
to account for this loss by shifting curves, obtaining in fig. 3.83(b) essentially merging curves in the LC ramge and little spread in the range of lower pressures. If this procedure is correct, the extrapolated molecular cross-section is about the same as that for pH 2 and it is inferred that in the condensed range charging does not lead to appreciable expansion; the cohesion of the tails is strong enough to keep the head groups together. The difference between pH = 2 and pH = 5.6 is indicated in fig. 3.84. At pH = 2 there are two linear parts in the condensed curves, as found before (figs. 3.80 and 81). Of these only one persists at pH 5.6. For charged monolayers additional information can be obtained from Volta potential measurements. The data in figs. 3.83 and 84 are not so suitable for that because different buffers were used (phosphate for pH 6-9 and citrate for pH 3-7) which are known to affect V^^^ see ref.^^. Figure 3.85 contains surface pressure and Volta potential isotherms for behenic acid monolayers, showing the influence of the nature of the counterion-^^. A small, but distinct lyotropic sequence from Li^ -^ K^ is seen, with a more drastic influence of trimethylammonium (TMA^) and triethylammonium (TEA^) ions. An increase of expansion in K{A) (larger area at given pressure) is paralleled by a higher (more positive) V^^K At higher ionic strengths, the trends in the surface pressure become more pronounced, whereas those in V^^^ are suppressed. So, for the specific interaction with the carboxyl groups we conclude Li-" > Na-" > K-" > TMA-" > TEA"" This sequence is more often observed, not only for fatty acid but also for fatty alcohols. For instance, Ralston and Healy*^^ found for CjgOH monolayers Mg^"" > Ca^"" » Li"^ > Na"^ > K^ > Rb^ - NH^ > Cs^ - TMA^ Later, Perzon et al."^^ reported the same sequence for the influence of electrolytes on the stability of CjgCOOH monolayers. In sec. II.3.10h, (see table II.3.8), we discussed and interpreted lyotropic sequences for double layers on a variety of solids. It depends on the nature of this solid how the sequence looks. It now appears that the present sequence is the same as it is on oxides like a-Fe203 and Y-AI2O3. For Li^ as the counterion the interaction with the head groups is mainly of an electrostatic origin, and strong. For the large, hydrophobic cations TMA^ and TEA^ this type of
^^ Recall that our V^^^ is usually written as Vand called the surface potential'. 2) E.D. Goddard, O. Kao and H.C.Kung, J. Colloid Set 18 (1963) 385. This paper gives many more examples. ^^ J. Ralston, T.W. Healy, J. Colloid Interface Set 42 (1973) 629. "^^ E. Perzon, P.M. Claesson, J.M. Berg and D. Vollhardt, J. Colloid Interface Set 138 (1990) 245.
3.208
LANGMUIR MONOLAYERS
100
H0 >
32
-100
_| o
-200
'>
-300 2: S
24
16
0.2
0.4
0.6
0.8
1
1.2
1.4
Figure 3.85. Surface pressure and Volta potential isotherms for behenic acid. Influence of the nature of the counterion. AlkaUne solutions of IQ-^ M NaOH, KOH, etc. 26°C. {Redrawn from Goddard et al., loc. cit.) interaction is impossible, so the double layer is mainly diffuse, and the specificity is not electrostatically determined. Quantitative interpretation of Volta potentials is not straightforward b e c a u s e several p h e n o m e n a contribute, and as these contributions are not necessarily additive, d a t a are easily overinterpreted. In fact, most a u t h o r s refrain from detailed a t t e m p t s . A comparison of trends in V^^^ between different molecules, or between molecules u n d e r different conditions can sometimes help to find out what is going on. In the present case the observed ion specificity may help. Let it first be repeated that V^^^ is the Volta potential of the monolayer minus same
of the carrier electrolyte,
the
a n d not t h a t of p u r e water. In fig. II.3.75 (sec.
II.3.1 Of) it w a s shown t h a t most simple electrolytes make the water surface more negative. The reason is t h a t in electrolytes s u c h as alkali chlorides and nitrates, the anions are usually more easily dehydrated t h a n the cations, so that they enrich the surface (KF is a n exception). Creation of this negative potential is mainly determined by the anion; the bigger it is, the larger the effect. Cation specificity is only a minor effect. For simple carboxylates, like K2CO3 or KHCO3 the surface m u s t also be negative with respect to the bulk. The observation that V^^^ < 0 for the three
LANGMUIR MONOLAYERS
3.209
alkali b e h e n a t e s m e a n s t h a t the presence of the hydrocarbon chaiin reinforces t h e trend; this is entirely, according to expectation. To t h e a u t h o r ' s knowledge, for TMA^ and TEA^ electrolj^e surfaces no data for Av^^ are avaiilable, b u t a s these big cations are also expelled from the water, the surface potential is less negative, or even positive. The positive V^*'^ for TEA"*^ a s the counterion may then m e a n t h a t the hydrocarbon tail promotes the expulsion of TEA^ more t h a n it does the carboxyl group. In fact, there is more evidence t h a t counterions c a n p e n e t r a t e into t h e monolayer provided they are sufficiently hydrophobic ^^ Interpretations like this may serve a s a first qualitative step, b u t there is a long way to go before t h e story becomes quantitative. In the first place, t r e n d s a t different electrolyte concentrations (not shown) differ substantially from those in fig. 3 . 8 5 . From t h e modelling point of view, q u e s t i o n s have to be a n s w e r e d regarding the positioning of the counterions with respect to the head group (below, next to, or above it?) a n d how this changes when the film is compressed. At high p r e s s u r e s t h e coherence in the film becomes strong a n d c o u n t e r i o n s become squeezed out. Then the double layer structure stsirts to resemble classical ones in solids t h a t are of the G o u y - S t e m type (chapter II.3). However, even u n d e r this simplified condition model interpretation is a multiparameter issue b e c a u s e m a n y major variables are not known. The real surface charge, a ° , i.e. t h a t of a fully dissociated layer of fatty acid molecules can be assessed, b u t what counts is how the countercharge is distributed. Although cr° may be a s high a s 60-80 |iC cm-^, t h e diffuse charge a^ is not likely to exceed about 6 ^C cm"^. These d a t a are derived from electrokinetic s t u d i e s on droplets covered with a s u r f a c t a n t monolayer, setting y/^ -^
a n d finding a^ from y/^ using Gouy theory (sec. II.3.5). So, most of
t h e potential decay t a k e s place over t h e S t e m layer b u t there the field s t r e n g t h dy^ / d z , a n d hence the contribution to V^^^ is elusive. There h a s been no lack of attempts to correct existing 2D equations of state for the effect of the double layer. Most of these are based on the diffuse double layer model, a n d therefore remain limited to the low p r e s s u r e range, i.e. to t h e least interesting p a r t s of 7t{A) curves. Henderson-Hasselbalch interpretations, u s i n g [II.3.6.53 or 54] c a n n o t be carried o u t for lack of information on the degree of dissociation a. Basically, the route for incorporation of double layer formation into 2D-equations of state is embodied in [3.4.53] in combination with [3.4.48] a n d [3.4.16]. Equation [3.4.53] h a s four parameters, viz. a ° , a^, (or y/^, t h e two are coupled), C and C . When G^ can be obtained from the surface concentration a n d representative electrokinetic d a t a are available to find y/^ (from Q a n d hence
a^,
[3.4.53] r e d u c e s to a two-parameter expression. If eventually C^ a n d C^
are
obtained a s fitting parameters to account for experimental 7i(A] curves one h a s at
1^ V. Shapovalov, A. Tronin, lAingmuir 13 (1997) 4870.
3.210
LANGMUIR MONOLAYERS
least information on the inner double layer part available. It a p p e a r s t h a t s u c h a route h a s not yet been undertaken. Another a t t e m p t to obtain more insight into the polarization distribution a c r o s s a monolayer, u s i n g a comparison of experimental d a t a between very similar layers, h a s been p r e s e n t e d by Vogel a n d Mobius^K Their idea w a s to c o m p a r e linear fatty acid type layers with a layer consisting of a mixture of molecules; 5 0 % of t h e m h a d two head groups b u t one tail, the other 50% were apolar a n d m a d e u p for the space between the tails. They found a V^^^ difference between s u c h a 5 0 / 5 0 monolayer and one consisting for 100% of the fatty acid. Assuming similarity of the head group sides between the two layers they inferred t h a t the w-CHg group in the chain h a s a net dipole moment of 0.35 D, the positive side pointing to the air^^. The assumption being debatable, it would be nice to have i n d e p e n d e n t model experiments for confirmation. A terminal (co-) dipole in the chain is relatively more effective t h a n one in the water p h a s e because it acts in a m e d i u m of a very low dielectric permittivity. This does not e x h a u s t the possibilities for obtaining additional information on charged or u n c h a r g e d fatty acid (and related) monolayers. Basically all the other 30 NaCl CdCl2 PbCl2 20
C0CI2 CaCl2 BaCl2 MgCl2
10
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
Figure 3.86. Surface pressure isotherms for stearic acid monolayers. Influence of bivalent counterions (1 mM), pH = 6.0. (Redrawn after Yazdanian et al., loc. cit.) 1) V. Vogel, D. Mobius, J. Colloid Interface Set 126 (1988) 408. ^^ For a comparison with dipole moments of polar molecules, see table 1.4.1 in sec. 1.4.4. IDCebye) = 3.33564 x IQ-^O Cm.
LANGMUIR MONOLAYERS
3.211
t e c h n i q u e s of sec. 3.7, qualify, in conjunction with n[A) d e t e r m i n a t i o n . For i n s t a n c e , t h e extent of dissociation of h e a d g r o u p s c a n be obtained from FTIR \ (change in t h e stretching frequency of the
C = 0 bond). If carried o u t system-
atically, information for a Henderson-Hasselbalch, a n d other double layer-type analyses becomes available. Oishi et al.^^ u s e d this procedure to d e m a r c a t e t h e various 2D p h a s e s in C^gCOOH monolayers. Daillant et al.-^^ studied reflection fluorescence
a n d X-ray reflectivity of charged monolayers of C21COOH in t h e
presence of Mn^"*^ ions, exploiting the propensity of Mn^^ of becoming excited by CuKaj radiation. From the fluorescence they learned t h a t u n d e r the experimental conditions (pH = 7.5, 10-^ M, MnCl2) 4 7 ± 6% of t h e Mn2+ ions were b o u n d per carboxyl group (bidentate adsorption) a n d reflectivity showed t h e m to be very close to t h o s e g r o u p s . In other words, Mn^"^ b i n d s so tightly t h a t t h e double layer is admost entirely of the S t e m type. Recall t h a t fig. 3.76 also indicated strong binding of Ca^^ ions, in t h a t case inferred from Volta potential m e a s u r e m e n t s . T h e s e r e s u l t s were confirmed a n d extended to a variety of bivadent counterions (Ba^^, C o ^ \ Cd^"^ a n d Pb^^ besides Mg^^ a n d Ca^^) and C17COOH or C19COOH monolayers^). See fig. 3.86 for the K(A) isotherms. Specific binding of t h e s e ions c a n promote t h e formation of ordered p h a s e s . Incidentally, this know-how is currently exploited in preparing deposited layers. Pb^^ and Cd^^ have t h e m o s t significant effects'^). In a later study from the s a m e group^^ these binding results were confirmed by ellipsometry, a n d the surface wave d a m p i n g t e c h n i q u e of Ito et al., 40
(b:
E pb-2+
S30 20
10
0 10-1
_i
I—I I I 11 il
I
I
o X
I
10" 10^ ft) (10^ Hz)
10r l
0 0 0 0 0 X XX.X.J
10"
. C d 2+ . B a'2+ Na-*-
0 0 ooooa X xx^x-x.^; M i l l
10^ CO (10^ Hz)
Figure 3.87. Surface dilational data for stearic acid monolayers, a^ = 0.205 nm^, pH = 6; 1 mM solutions, 25°C. The cation is indicated. (Redrawn from Yazdanian et al., (1992).) 1) Y. Oishi. Y. Takashima, K. Suehiro and T. Kajiyama, Langmuir 13 (1997) 2527. 2) J. Daillant, L. Bosio, J.J. Benattar and C. Blot, Langmuir 7 (1991) 611. 3) M. Yazdanian, H. Yu, and G. Zografi, Langmuir 6 (1990) 1093. "^J See also G. Veale, I.R. Peterson, J. Colloid Interface Set 103 (1985) 178. ^^ M. Yasdanian, H. Yu. G. Zografi and M.W. Kim. Langmuir 8 (1992) 630.
3.212
LANGMUIR MONOLAYERS
briefly described in sec. 3.7e.^^. The dilational storage a n d loss m o d u l u s (the latter as (orj^) are presented in fig. 3.87. The exceptional role of Pb^^ a s the counterion is obvious. C a d m i u m is also higher t h a n Ba^^ a n d Na^ b u t by a m u c h smaller margin. The role of Pb^^ w a s confirmed by the influence of the PbCl^ concentration on the loss angle a n d Volta potential. The binding ratio Pb^"^ / COO" is almost one to one, which would imply reversal of the diffuse charge sign (not measured). This work is a nice illustration of the potentialities of applying a variety of techniques to the s a m e system. As a n additional technique, binding of ions can also be studied using a quartz micro balance. The horizontal plate of this balance is lowered until it touches the (tail end of the) monolayer and its frequency recorded u p o n injection of the electrolyte, containing bivalent ions. When the ions bind, the frequency goes down b e c a u s e of t h e increased m a s s of the monolayer. M a t s u u r a et al.^^ applied this technique to s t u d y the interaction between Pb^^-ions a n d C COO~ m o n o layers. They concluded t h a t the binding w a s almost stoichiometric; 1 Pb^^ per 2 COO" groups. Another interesting a p p r o a c h in which interfacial rheology is applied to fatty acid monolayers h a s been proposed by Halperin et al.*^^ They called it the 'orthogonal Wilhelmy plate' method because they used two Wilhelmy plates, one oriented parallel to the Langmuir trough (i.e. in the direction of compression) a n d the other n o r m a l to it (orthogonal to the direction of compression). Obviously, for purely viscous monolayers there can be no difference between surface p r e s s u r e s obtained by these two plates. However, for solid-like (elastic) behaviour, differences may be picked u p . The a u t h o r s found no differences between n
and n for C14COOH, b u t
such differences were found for C17COOH and C23COOH at sufficiently high pressure {> 20 mN m"M. The differences amounted to a few mN m"^ The above-mentioned examples for dissociated and undissociated fatty acids act a s our 'paradigm' for similar investigations on other straight-chain molecules. Of the n u m e r o u s illustrations available we chose a few. Fatty a m i n e s a p p e a r to be somewhat more difficult monolayer-formers t h a n the corresponding fatty acids. They are charged at low pH b u t uncharged at high pH. The c o u n t e r i o n s are a n i o n s a n d this can c a u s e interference w h e n buffers are needed. We have already mentioned that buffers also affect the Volta potential. Surface p r e s s u r e isotherms, reversibility a n d hysteresis studies, a n d p r e s s u r e relaxation studies can for instance be found in two papers by Ganguli et al.^'^K As is the case with solid surfaces, the specificity of anions a s counterions is more ^R.P. Enever and N. Pilpel, Trans. Faraday Soc. 6 3 (1967) 781 found that Ca^^-ions markedly incresed the surface shear viscosity of stearic acid monolayers. 2) N. Matsuura, D.J. Elliot, D.N. Furlong and F. Grieser, Colloids Surf. 126 (1997) 189. ^^ K. Halperin, J.B. Ketterson and P. Dutta, Langmuir 5 (1989) 161. "^^ P. Ganguli, D.V. Paranjape and F. Rondelez, Langmuir 13 (1997) 5433. ^^ P. Ganguli, D.V. Paranjape, K.R. Sastry and F. Rondelez, Langmuir 13 (1997) 5440.
LANGMUIR MONOLAYERS
3.213
pronounced than that of cations. In the low pressure range, at given a^, n increases in the order HCl < H PO, < H^SO, < HCIO, 3
4
2
4
4
but at higher pressures the sequence changes because the 7t{A) slopes, and hence the compressibilites, differ substantially. The resilience against collapse is also strongly dependent on the nature of the anion. These measurements have not yet been extended by other measuring techniques. Lx)ng chaiin amine oxides appear suitable monolayer formers. Fig. 3.88, taken from work by Goddard and Kung^^ serves as an illustration. The docosyldimethyl amine oxide, DCDAO or CggNOCCHglg) molecule has a high dipole moment caused by the NO-group (N^^O^"). It is a very weak base which at low pH can pick up a proton, to become positively charged (C22(N+OH)(CH3)2). Figure 3.88 is a pendant of fig. 3.85. It shows that, unexpectedly, charged films (low pH) are less expanded than those in the uncharged form. The transition between the two regions is relatively sharp; it must be over this range that the molecules in the monolayer acquire their charge. 700
1 40
500 S
S 30
300
S 20
100
10
int(V/^.
0.2
0.8
1
1.2 a^ I nm^
1.6
Figure 3.88. Surface pressure and Volta potential isotherms for n-docosyldimethylamine oxide. 25°C, ionic strength (NaOH or HCl, +NaCl) lO'^ M. pH indicated. (Redrawn from Goddard and Kung, loc. cit.)
1^ E.D. Goddard. H.C. Kung, J. Colloid Interface Set 4 3 (1973) 511.
3.214
LANGMUIR MONOLAYERS
Explanations m u s t be sought in the a r r a n g e m e n t of the polar head groups, the positioning of any protons between these, and the orientation of adjacent water molecules. Additional techniques are needed to study this further. One of these, Volta potential m e a s u r e m e n t s , h a s been carried out by the a u t h o r s and results are included in the figure. Over the entire range V^^^ is positive, increasing with increasing n. The effect of protonation is weak a n d the rather s u d d e n transition of 7t (pH) is not found; apparently the dipole moment of the uncharged molecule plays a d o m i n a n t role. The hydrocarbon tail c a n be modified in several ways. Some examples have already been given, see fig. 3.10 for the effect of a side-branch and fig. 3.11 for t h a t of double bonds. We shall not discuss these further here. A special category is t h a t of (semi-) fluorinated hydrocarbon monolayers ^^ Fluoridation affects chain flexibility and its packing, so it is a n interesting vehicle for the study of p h a s e s in condensed films. Blockwise fluorinated hydrocarbons, of the type F(CF2)m(CH2)n. abbreviated F H , deserve particular attention. There is now evidence t h a t some molecules of this type can, without the help of head groups, form
(reverse) micelles a n d fairly s t a b l e L a n g m u i r m o n o l a y e r s .
Gaines^)
concluded t h a t for FgHj2, 1^10^12 ^ ^ ^ ^12^18' ^ P ^ ^ rapid compression. ;r(A) cur\'cs could be obtained, resembling those described before. Huang et al.^^ subjected these, a n d similar semifluorinated hydrocarbons to a more systematic study. Stability improves if the length of the fluorinated block increases; grazing incidence X-ray diffraction of Fj2Hjg monolayers indicated the formation of ordered s t r u c t u r e s , defined by hexagonal packing of the Fj2 blocks. Reflectivity
measurements
revealed that the molecules orient with the F-part 'up' and the H-part 'down'. As a last representative group belonging to this category, we mention fatty alcohols. The p h a s e diagram of C^gOH from 1-35°C h a s been studied in detail by Lawrie a n d Barnes'^K The close correlation with other single chain amphiphiles points to the significant contribution of the tail to the phase behaviour. In general, CjgOH monolayers are complicated; they show not yet u n d e r s t o o d
pressure
relaxation^^ Volta potentials have been mapped for C^g, C^g, C20 and C22OH by Kuchhal et al.^K They found V^^^ to increase with TZ and to grow with chain length at fixed n. In addition, there was a parallel with the phase behaviour as found from ;r(A,T) curves. Understanding s u c h monolayer properties, especially their phase behaviour, is ^^ Such layers have already been studied a long time ago by M.K. Bernett and W.A. Zisman, J. Phys. Chem. 67 (1963) 1534. 2) G.L. Gaines, Langmuir 7 (1991) 3054. "^^ Z. Huang, A.A. Acero, N. Lei, SA. Rice, Z. Zhang and M.L. Schlossman, J. Chem. Soc. Faraday Trans. 92 (1996) 545. 4) GA. Lawrie. G.T. Barnes. J. Colloid Interface Set 162 (1994) 36. ^^ A.G. Bois, J. Colloid Interface Set 105 (1985) 124. ^^ Y.K. Kuchhal, S.S. Katti and A.B. Biswas, J. Colloid Interface Sci. 29 (1969) 521.
LANGMUIR MONOLAYERS
3.215
crucigd for the application of long chain alcohol monolayers as evaporation inhibitors. Another interesting observation is that fatty alcohol monolayers promote ice nucleation^^ which exhibits an odd-even alternation; for the odd alcohols freezing points are less negative than for the even ones. This phenomenon must have a crystallographic origin. From this, somewhat haphazard, anthology of monolayer investigations with the most simple category of monolayer formers it may be concluded that there is much room for further study, especially by appljring different techniques to one and the same well-defined system. In particular, the combination of opticad and rheological techniques seems an underexposed domain, probably because few research groups have advanced appciratus of both approaches in house. As an entry to the literature the compilation by Minotaud et al., mentioned in sec. 3. lOg is repeated. 3.8c Phospholipids Phospholipids play an important role in the structure of biological membranes. Human adults have about 100 g lipids for 10"^ m^ of membrane. So it is not surprising that phospholipid monolayers have traditionally been used as model systems for understanding molecular interactions in biological membranes. As first proposed by Singer and Nicolson^^ in biological membranes a bilayer structure of lipids forms the membrane matrix. A lipid monolayer at the air/water interface may be considered as representative for half a bilayer membrane and the phase behaviour of the monolayer exhibits properties that may be relevant for bilayers as well. Compared to, for example, liposomes (lipid vesicles) such monolayers are well-defined systems of which the thermodynamic, structural and mechanical properties can be measured with high accuracy. Studies on monolayers can be performed in a well-controlled way, because their surface concentration, the two-dimensional molecular density, composition and temperature can be varied systematically. Although the title of this section is 'phospholipids', we in fact will, as a case study, concentrate on the most frequently studied class, viz. the diacylglycerophospholipids^^. The molecules of these compounds consist of two fatty acids and a phosphate-containing hydrophilic moiety, connected by ester bonds to glycerol. Some representative structures are shown in Table 3.8. Of these the phosphatidyl-
1^ M. Gavish, R. Popovitz-Bloro, M. Lahav and L. Leiserowitz. Science 250 (1990) 973; R. Popovitz-Biro, J.L. Wang, J. Majewski, E. Shavit, L. Leiserowitz and M. Lahav, J. Am. Chem, Soc. 116 (1994) 1179. 2) J.S. Singer, G.L. Nicolson, Science 175 (1972) 720. •^^ For a classification of phospholipids and the structure of other phospholipid classes, the reader is referred to K.P. Strickland, in Form and Function of Phospholipids, G.B. Ansell, J. Hawthorne and R.M.C. Dawson, Eds., Elsevier (1975) 9.
3.216
LANGMUIR MONOLAYERS
Table 3 . 8 . The chemical s t r u c t u r e of glycerophospholipids. The generic term 'phosphatidyl-' s t a n d s for l,2-diacyl-sa-glycero-3-phospho-, in which sn denotes 'stereospecific' n u m b e r i n g ' ^ ' (in the D/L nomenclature this corresponds to 2,3diacyl-D-glycero-1-phospho-). The OH-groups of the glycerol t h a t are not b o u n d to the head group are esterified to fatty acid. X-group
Name of head group and abbreviation phosphatidic acid (PA)
CHp-CH-CH^-0-P-O-X O"
CH2CH2NH3+
phosphatidylethanolamine (PE)
CH2CH2N(CH3)3+
phosphatidylcholine (PC)
CH2CH(NH3+)COO-
phosphatidylserine (PS)
CH2CH(OH)CH20H
phosphatidylglycerol (PG)
cholines (or lecithins) are one of the most important groups of lipid components in a n i m a l cell m e m b r a n e s . In virtually all biological s y s t e m s the double layer potential on the outside of m e m b r a n e s is negative owing to the presence of negative charges caused by dissociation of the phosphate groups. Phospholipids are ideal systems to form Langmuir monolayers; their solubility in water is extremely low a n d b e c a u s e of their molecular s h a p e (resembling a cylinder for p h o s p h o l i p i d s with a relatively small head group area, a n d a truncated cone in the case of large head group areas) they have no tendency to form micellar s t r u c t u r e s in solution. Furthermore, the asymmetry of the C-2 atom of the glycerol backbone gives the opportunity to study the role of chirality in Langmuir monolayers. In s u c h 'oriented' two-dimensional systems ('oriented' since the top differs from t h e bottom) c h i r a l i t y - d e p e n d e n t i n t e r a c t i o n s are e n h a n c e d
as
compared to three-dimensional systems because of the more limited orientational degrees of freedom of the molecules. (i) Phase
behaviour
In the 1960s the first K{A) isotherms of phospholipid monolayers were publi s h e d ^ ^ One of t h e most extensive a n d thorough experimental s t u d i e s is by
^^ The stereospecific numbering of acylglycerols has been introduced by H. Hirschmann (J. Biol Chem. 2 3 5 (1960) 2762) and is widely accepted, although its application is limited. See H. Hauser, G. Poupart, in The Structure of Biological Membranes, P. Yeagle (Ed.), CRC Press, Boca Raton, Florida, 1992. 2^ See for example, L.L.M. van Deenen, U.MT. Houtsnijder, G.H. de Haas and E. Mulder. J. Pharm. Pharmacol 14 (1962) 429; M.C. Phillips, D. Chapman, Biochim. Biophys. Acta 163 (1968) 301.
LANGMUIR MONOLAYERS
3.217
501- •
50 -hX (a)
^1
■I
z
40 h -§
1
E 30 h
20
i
'^g
I\ I \
.1 \
30
-\
20 h -
10
(b)
-
\
A \\ \\
10 h °\)
X«tfL
Koi 0.4
0.6
0.8
1.0
0.4
0.6
,
1 0.8
^^j=..j_ 1.0
1.2
Qj / nm^
Figure 3.89. Pressure-area isotherms for monolayers of saturated phosphatidylethanolamines (a) and saturated phosphatidylcholines (b) on an aqueous 0.1 M NaCl solution at 22°C. From bottom to top: (a) dicapryl-PC (CIQ). dimyristoyl-PC (C14), dipalmitoyl-PC (Cie), distearoyl-PC (Cis) and dibehenoyl-PC (C22): (b) dicapryl-PE (length of the hydrocarbon tails; Cio). dilauroyl-PE (C12). dimyristoyl-PE (C14) and distearoyl-PE (Cig). The curve for dilauroyl-PC (C12) is not depicted since it coincides almost completely with the one for dimyristoyl-PC. (Redrawn from M.C. Phillips, D. Chapman, Biochim. Biophys. Acta 163 (1968) 301.)
Albrecht et al.^^ who investigated monolayers of several phospholipids and lipid mixtures at various temperatures. The different phases of phospholipid monolayers as reflected in K[a] isotherms have already been discussed in section 3.3b and are illustrated in the schematic isotherm depicted in fig. 3.6. In fig. 3.89 experimentally obtained isotherms are given for two homologous series of saturated glycerophospholipids. This figure shows the influence of the hydrocarbon chain lengths on the phase behaviour of phosphatidylethainolamines (PEs) and lecithins (PCs). If the hydrocarbon chains are relatively short, monolayers are in the gaseous (G) or liquidexpanded (LE) state, while for sufficiently long chains condensed monolayers are formed. These monolayers are already in the coexistence state between gaseous (G) and condensed phase at a surface pressure of about zero and their 7t[A] isotherms exhibit no plateau region at accessible temperatures. In two cases increase of the surface pressure above a particular value TT results in a first order phase transi-
1) O. Albrecht, H. Gruler and E. Sackman, J. Phys. (Paris) 3 9 (1978) 301; J. Colloid Interface Set 79 (1981) 319.
3.218
LANGMUIR MONOLAYERS
tion from the LE to a liquid-condensed (LC) phase and an LE-LC coexistence region is observed. From comparison of the isotherms in fig. 3.89a and b it can be seen t h a t the molecules in a completely condensed monolayer of PE are m u c h more closely p a c k e d t h a n in t h e equivalent PC monolayer. The larger limiting a r e a per molecule found for PCs as opposed to the PEs reflects the larger space required by the larger and more hydrated PC head groups. Variation in the 7i(a.) isotherms with temperature h a s been illustrated in fig. 3.8 for monolayers of dimyristoylphosphatidic acid (DMPA). In fig. 3.14 these curves were thermodynamically elaborated. In fig. 3.90 we show the corresponding case of dipalmitoylphosphatidylcholine (DPPC) monolayers. The critical temperature T for the LE-LC p h a s e transition, defined as the temperature above which the 7t(a.) isotherms no longer show an inflection, it is close the Kraffi
temperature
of the corresponding phospholipid bilayers (for DPPC bilayers ca 41°C). The Krafft t e m p e r a t u r e is the temperature at which bilayer m e m b r a n e s undergo a transition from the crystalline (gel) p h a s e to the liquid-crystalline (fluid) p h a s e . Generally, u n d e r physiological conditions most m e m b r a n e lipids are in the fluid state; the lateral mobility of the molecules is high a n d fluid-like while their movements perpendicular to the m e m b r a n e surface ('flip-flop' and exchange with the water phase) are strongly restricted. When decreasing the temperature (passing the Krafft point), the liquid-crystalline bilayer is converted into the gel state where movem e n t in the plane is impossible. The i s o t h e r m a l LE-LC t r a n s i t i o n in lipid Langmuir monolayers is t h e r m o dynamically related to the thermotropic fluid-gel transition in lipid bilayer mem-
Figure 3.90. Pressure-area isotherms for dipalmitoylphosphatidylcholine (DPPC): • 34.6": A 29.5°: ■ 26.0°: x 2 1 . 1 : O 16.8 : A 12.4°: 6.2°. (Redrawn from M.C. Phillips, D. Chapman, Biochim. Biophys. Acta 163 (1968) 301.)
LANGMUIR MONOLAYERS
3.219
branes, both sometimes referred to as 'the maiin transition' of the system under consideration. The heats and entropies associated with these phase transitions are similar. With respect to their surface concentration and mobility the LE phase of monolayers resembles the fluid phase of bilayer membranes. For example, the lateral diffusion coefficient in the LE phase as obtsiined by FRAP using a surface active fluorescent probe^^ has been found to be of the order of 10~^ nr^ s~\ comparable to data on fluid bilayer membranes. The diffusion coefficient of the LC phase is at least two orders of magnitude lower than that in the bulk^^. DPPC is prominent in the lipid bilayer making up the cell membrane and is also a major constituent of lung surfactant {'pulmonary surfactant). The lung membrane resembles a mixed surfactant monolayer at the air/water interface. Since the temperature in a lung is below the critical temperature for DPPC monolayers, the LE-LC transition may be of significance in the continuous compression and expansion loops that this membrane undergoes during respiration. We will say more about this in sec. 3.9. As mentioned before (sec. 3.3) the LE-LC transition region in the monolayer isotherms does not have a zero slope. In fact, the slope of this region increases with temperature, indicating a decrease in the compressibility K^ of the monolayer (eq. [3.3.1]). Because of the finite slope the assumption that the transition is of first order has been questioned for a long time. In the early 1980s the newly developed technique of fluorescence microscopy (sec. 3.7c) revealed the coexistence of two phases in the transition region^^ implying that the phase transition is indeed of first order. At first this conclusion was challenged because the technique depends on the incorporation of a fluorescent probe in the monolayer. However, the coexistence of phases has now been confirmed by microscopic techniques that do not need potenticdly disturbing probes, like imaging ellipsometry and Brewster angle microscopy. Meanwhile, several suggestions have been put forward to explain the non-horizontality of the isotherms in the transition region. One of these suggestions is the presence of surface-active impurities. Indeed, it has been found that intentional addition of such impurities results into an increase of the slope^^; extensive purification of the lipids, the water and cleaning of the trough, decreases the slope^^. but generally a residual slope remains. Another suggestion is that the transition is of limited, or partial co-operativity. From the slopes of their
1) R. Peters. K. Beck, Proc. Natl Acad. Set USA 80 (1983) 7183. 2) R. Peters, K. Beck, loc. cit.; M. Seul, H.M. McConnell. J. Phys. 47 (1986)1587. ^^ V. von Tschamer, H.M. McConnell, Biophys. J. 36 (1981) 409; R. Peters, K. Beck, Proc. Natl. Acad. Set USA 80 (1983) 7183; M. Losche, E. Sackman and H. Mohwald, Ber. Bunsenges. Phys. Chem. 87 (1983) 848. "^^ H.M. McConnell, L.K. Tamm and R.M. Weiss. Proc. Natl. Acad. Set USA 81 (1984) 3249; A. Miller, W. Knoll and H. Mohwald. J. Chem. Phys. 86 (1987) 4258. ^) M.C. Phillips, D. Chapman, loc. cit.; N.R. Pallas. B.A. Pethica, Langmuir 1 (1985) 509.
3.220
LANGMUIR MONOLAYERS
DPPC isotherms in the LE-LC coexistence region Albrecht et al.^^ estimated a size of the order of 10^ molecules per co-operative unit. Using optical microscopic techniques (fluorescence microscopy, Brewster angle microscopy a n d microscopic ellipsometry) t h e formation, size a n d s h a p e of d o m a i n s in the LE-LC coexistence region of phospholipid monolayers have been s t u d i e d extensively. F u r t h e r m o r e , s t r u c t u r e s within condensed d o m a i n s a n d p h a s e s have b e e n visualized, the contrast resulting from the optical anisotropy c a u s e d by long-range tilt orientational order. The morphology of t h e d o m a i n s in the LE-LC coexistence region is very sensitive to the rate of compression of the monolayer. As for other monolayer forming molecules, at very low compression r a t e s the c o n d e n s e d p h a s e of a phospholipid monolayer forms compact domains, while at high compression rates fractal-like s t r u c t u r e s are formed a s expected for diffusion-limited aggregation. For p h o s p h o l i p i d s t h e s h a p e s of t h e d o m a i n s formed compression
v a r i e s from
circular,
bean
or S - s h a p e d
at relatively
slow
to t r i s k e l i o n s
and
multilobes-^^ Klopfer and Vanderlick^^ found t h a t keeping a DPPC monolayer in the two-phase coexistence region for a long time (over 12 h) renders the LC domains nearly circular. The compact domains exhibit a n inner structure characterized by segments in which the molecular orientation changes in a continuous way"^^; at the b o u n d a r i e s of these segments there is a j u m p in the molecular tilt direction. The s h a p e a n d s h a p e t r a n s i t i o n s of d o m a i n s in lipid monolayers are reviewed by McConnell^^ with e m p h a s i s on the theoretical description of those experimental observations t h a t are best understood. No differences can be observed between the 7t{A] isotherms for pure enantiomers of a particular phospholipid and racemic mixtures. Apparently, energetic differences are too small to give significantly different isotherms. However, the morphological properties of the monolayers show t h a t chirality can affect both the shape and inner structure of the LC phase domains^^. (ii) Molecular ordering of the different
phases
The molecular s t r u c t u r e of the different p h a s e s of phospholipid monolayers have been revealed by a n u m b e r of techniques, in particular X-ray diffraction and IR reflection. With s y n c h r o t o n X-ray diffraction
at grazing incidence
the
m o l e c u l a r p a c k i n g of the d e n s e r p h a s e s (LC a n d S) h a s been investigated.
^^ O. Albrecht, H. Gruler and E. Sackman, 1978, loc. cit. 2) R.M. Weis, H.M. McConnell, Nature 3 1 0 (1984) 47; K.J. Klopfer, T.K. Vanderlick, J. Colloid Interface Set 182 (1996) 220; D. Vollhardt, Adv. Colloid Interface Sci. 64 (1996) 143. 3) K.J. Klopfer, T.K. Vanderlick, loc. cit. "^^ D. Vollhardt. loc. cit. ^ H.M. McConnell, Ann. Rev. Phys. Chem. 42 (1991) 171. ^^ R.M. Weis, H.M. McConnell. loc.cit.
LANGMUIR MONOLAYERS
3.221
Systematic studies have been performed by Mohwald, Als-Nielsen and coworkers ^K In the compact monolayer phases the hydroccirbon chains of the lipids are packed in a periodic structure, exhibiting nearest-neighbour or next-nearestneighbour tilt, or no tilt at all. Although in phospholipids two chains are coupled to one head group, this coupling is not observable in the lattice chgiracteristics of the unit cell. The positional correlation length in the LC phase is in the order of tens of nanometers, while the orientational order can persist over distances of - 1 0 0 ^un. Diffraction signals from the head groups in Langmuir monolayers have never been measured, probably because lack of ordering. From X-ray diffraction on phospholipid single crystals, however, it has been found that the head groups prefer to orient parallel to the bilayer plane^). The effect of the head group on the chain packing and ordering in monolayers has been studied systematicadly. For lipids with the phosphatidylethanolamine (PE) head group the chain tilt continuously decreases with increasing surface pressure until the chains are oriented normal to the monolayer. For these lipids the head group is sufficiently small that the tails determine the lateral density. However, the structure still depends on the head group chiredity. Whereas a racemate assumes a rectangular lattice, that of chains connected to either of the enantiomers is oblique*^^. For the phosphatidylcholines the hydrated head group is significantly larger than the cross-sections of the two tails, measured perpendicular to the tail direction. Hence, there is a mismatch between head and tails if the molecules would attempt to align their tails in normal order. This is why even at high surface pressures monolayers of DPPC exhibit a rather large tilt angle of ca 30° ^\ The influence of the head group interactions has further been studied by attaching he PC head groups to the chains via flexible spacers^h When the spacer length is increased, the head groups C£in arrange more freely in lateral as well as normal direction; this allows for a smaller tilt cind a smaller area per molecule in the monolayer. Natural phospholipids have one or two double bonds in the aliphatic tails. These generally create disorder and reduce the transition temperature for bilayers, and - equivalently - the transition pressure for Lcingmuir monolayers. An gdtem-
^^ See, for example, C.A. Helm, H. Mowald, K. Kjaer and J. Als-Nielsen, Europhys, Lett 4 (1987) 697; C. Bohm, H. Mohwald. L. Leiserowitz. K. Kjaer and J. Als-Nielsen, Biophys. J. 6 4 (1993) 553; H. Mohwald, C. Bohm, A. Dietrich and S. Kirstein. Liq. Crystals 14 (1993) 265; G. Brezesinski, A. Dietrich. B. Dobner and H. Mohwald. Prog. Colloid Polym. Set 9 8 (1995) 255; H. Mohwald, H. Baltes. M. Schwendler, C.A. Helm, G. Brezesinski and H. Haas, Jpn. J. Appl Phys. 34 (1995) 3906; G. Brezesinski. M. Thoma. B. Struth and H. Mohwald. J. Phys. Chem., 100 (1996) 3126. 2^ H. Hauser, G. Poupart. in The Structure of Biological Membranes, P. Yeagle (Ed.). ORG Press, Boca Raton, Florida. 1992. ^) C. Bohm et al.. loc. cit. 4) C.A. Helm et al.. loc. cit. 5) H. Mohwald et al.. 1995. loc. cit.
3.222
LANGMUIR MONOLAYERS
ative way to create disorder is to attach ethyl- or methyl-groups to the hydrocarbon tails. Branched chain phospholipids have been prepared and studied^^. When the b r a n c h is near the head group and as long as the main chain, one may consider the molecule as a lipid with three or four chains per head group. Then, the molecular area is given by the area per chain and this area determines the packing. Information on the conformational state of the hydrocarbon c h a i n s and their orientation h a s been obtained from external infrared reflection absorption spectroscopy (IRRAS). The first systematic IRP^S studies on phospholipid Langmuir monolayers were reported by Dluhy et al-^^ (see, for instance fig. 3.62). For DPPC m o n o l a y e r s in t h e LE p h a s e the p o s i t i o n s of t h e
conformation-sensitive
symmetric a n d anti-symmetric C-H stretching b a n d s in the IRRAS spectra were found to be at the same positions a s for bilayer systems of DPPC above the Krafft t e m p e r a t u r e . In the LC p h a s e the frequencies of these b a n d s indicate t h a t the hydrocarbon chains of the lipid molecules are in the sd\-trans^^ conformation (i.e. zig-zag) a n d analysis of polarized IRRAS spectra"^^ show that their average tilt is ca 35° relative to the monolayer normal. This is in reasonable agreement with the tilt angle of 30° obtained from X-ray diffraction on DPPC monolayers (30°). Vibrational modes of the phospholipid polar head g r o u p s (in particular the symmetric a n d anti-symmetric PO^ stretching vibration) reflect their ionization a n d hydration state. The hydration state of the head group of DPPC was found to change u n d e r monolayer compression or by addition of cations s u c h a s Ca^^ ^). There are indications t h a t the transition at % (to the solid state S, see fig. 3.6) involves ordering a n d dehydration of the head groups. Also u s i n g IRRAS, Mendelsohn a n d co-workers have studied monolayers of phospholipids with deuterated acryl chains. In such systems C-H a n d C-D stretching vibrations c a n be monitored simultaneously. This permits, for example, observation of individual components in a mixed lipid monolayer^^ or conformational analysis of different p a r t s of the acryl chains. M e a s u r e m e n t s on monolayers consisting of tail-end deuterated DPPC molecules showed that the c h a i n s posses more conformational order adjacent to the head group than at their tails^l
^> G. Brezesinski, W. Rettig, S. Grunewald, F. Kuschel and L. Horvath. Liq. Crystals 5 (1989) 1677; G. Brezesinski et al., 1995, loc. cit. 2) R.A. Dluhy, J. Phys. Chem. 90 (1986) 1373; R.A. Dluhy. N.A. Wright and P.R. Griffiths, Appl Spectrosc. 42 (1988) 1289; M.L. Mitchell, R.A. Dluhy, J. Am. Chem. Soc. 1 1 0 (1988)712; R.D. Hunt, M.L. Mitchell and R.A. Dluhy, J. Mol Struct 214 (1989) 93. ^' A better term would be all-antiperiplanar (terminology of W. Klyne and V. Prelog, Experientia 16 (1960) 521) to avoid confusion with trans as being used for one of the geometric isomers of double bonds and ring systems [cis-trans system). ^^ R.A. Dluhy, S.M. Stephens, S. Widayati and A.D. Williams, Spectrochim. Acta A 5 1 (1995) 1413. ^) R.D. Hunt et al, loc. cit. ^) C.R. Flach, J.W. Brauner and R. Mendelsohn. Biophys. J. 65 (1993) 1994.4 '^^ A. Gericke, D.J. More, R.K. Erukulla, R. Bittman and R. Mendelsohn. J. Molec. Struct. 379 (1996) 227.
LANGMUIR MONOLAYERS
3.223
(b)
DMPE^*
\/DPPC -1.
20
30 40 n (mN m"M
0.4
0.5
0.6
0.7
0.8
0.9
Qj / n m ^
Figure 3.91. Surface shear viscosity (a) and dilational modulus (b) of DPPC (L-a-dipalmitoylphosphatidylcholine) and DMPE (L-a-dimyristoyl phosphatidylethanolamine) monolayers. Inset; n[a^ curves. (Redrawn from Kragel et al., loc cit.) (iiij Rheology Lipid monolayers have also been studied by surface rheology, which yields complementary information. The present author is not aware of systematic studies in which optical amd rheological investigations have been carried out on one and the same seimple under the same conditions. Figure 3.91 gives an illustration, based on a study by Kragel et al.^K The inset gives the, independently measured, 7t{a) curves. For both lipids a relatively horizontal part is observed. At given molecular cirea, the pressure is higher for DPPC, because the moleculsir head group is larger. At high pressure large differences in surface shear viscosity are observed, which reflect differences in dissipation between the two. The smaller DMPE head group adlows for denser packing and mechanically more stable films. At low pressures T]^ is insignificant. The dilational moduli also increase with increasing surface concentration. The minima of the curves in fig. 3.91b coincide with the pseudo-horizontal LE-LC coexistence parts in the n(a^] isotherms. There the relaxation may be identified as caused by rapid exchcinge of lipid molecules between the two phases. In the more compact layers the relaxation is slower. However, both belong to the category of relaxations in Langmuir monolayers mentioned in sec. 3.6h. 3.8d Cholesterol Cholesterol is an essential constituent of biological membranes in animal (including human) tissues. The fraction of cholesterol in some of these
1^ J. Kragel, J.B. Li, R. Miller, M. Bree. G. Kretzschmar and H. Mohwald. Colloid Polym. Set 274 (1996) 1183.
3.224
LANGMUIR MONOLAYERS
m e m b r a n e s , e.g. those in erythrocytes, may be as high a s 50%. There is evidence t h a t cholesterol acts as a plasticizer, i.e. it helps the membrane to exist in a (semi-) fluid state . On the other hand, cholesterol may separate out of the m e m b r a n e to form a bulk-like phase. This process may play a role in artherosclerosis . For these a n d other (practical and academic) reasons the behaviour of cholesterol in monolayers a n d bilayers, both being effective model systems, is often studied. Here, we discuss some results regarding the fluidity of cholesterol monolayers a n d the formation of cholesterol exudates upon monolayer collapse. (i) Fluidity of cholesterol
in monolayers.
The mobility of a molecular residue in
t h e p l a n e of t h e monolayer may be expressed in t e r m s of its lateral diffusion coefficient. Stroeve a n d Miller^^ have studied the lateral diffusivity of cholesterol in monolayers by bringing into contact two cholesterol monolayers, one of which contained radioactive cholesterol, having equal interfacial p r e s s u r e s . For this purpose, they used a specially designed trough. They measured the penetration of the radiolabeled cholesterol into the non-radioactive layer by two methods: 1..after a given contact time the radio-activity in each layer w a s determined (integral method). 2. the radioactivity profile in the contact zone between the two monolayers w a s recorded in time (differential method). The m e a s u r e m e n t s were performed on a cholesterol monolayer spread at a n a i r / w a t e r interface and at a temperature of 22 ± 0.5 °C. The m a s s concentration for the radioactive tracer molecule in the monolayer is given by Fick's second law lor surface diffusion [1.6.5.46] — = D ^ dt dx"^
[3.8.2]
where D^ is t h e interfacial diffusion coefficient a n d F the interfacial concentration of the radiolabeled material. The initial distribution (at t = 0) at the b o u n d a r y (x = 0) between the radioactive a n d the non-radioactive monolayers is F = F for X > 0 a n d r = 0 for x < 0. Taking into account these boundary conditions [3.8.2] is solved: r(x,t)
= nerfc
[3.8.3] 2(D^t)^^^
This is the two-dimensional equivalent of [1.6.5.24]. In the differential method, the broadening of the radioactivity profile with time is fltted to [3.8.3] using D" as the fitting p a r a m e t e r . In the integral method, the a m o u n t of radioactive cholesterol, M{t), that h a s dif-
P. Stroeve, I. Miller, BiochiirL Biophys. Acta 401 (1975) 157.
LANGMUIR MONOLAYERS
3.225
1
^
r/To
^cA-^cApffFO——A—Q
r
0.5 /
J —•A-
0 -10
PA* /
A
-J-
-8
A
1
b*A^oi-P-^ 1
1
-6
1
1
-2
1
1
1
1
1
6 x(mm)
8
10
Figure 3.92. Distribution of radioactive cholesterol at the boundary between a radioactive and a non-radioactive layer, as a function of contact time o initial distribution, • distribution after 15.5 h (D^ = 0.61 x 10"^^ m^ s'^; A, distribution after 41.5 h, it = 40 mN m-i [D'' = 0.58 X 10-11 m^ s'M; ° distribution after 19.5 h ( D'' = 2.0 x lO'^^ m^ s'l). (Redrawn from Stroeve emd Miller, loc. cit.) fused after a time t into the initially non-radioactive monolayer is related to D^ by M{t) = Lr
W't
xl/2
[3.8d.3]
where L is the distance over which the penetration of the radioactive molecules is measured. The experiments according to the differential method were performed a t a^ = 0.38 nm^/molecule which is below a
, i.e. in the p a r t of t h e isotherm w h e r e t h e
cholesterol molecules are tightly packed leading to a n interfacial p r e s s u r e of ca. 4 0 m N m - i . See fig. 3.13. Figure 3.92 shows the fit of the experimental d a t a to eq. [3.8.3] for t = 0, 15.5 h a n d 4 1 . 5 h. It follows t h a t in a closely packed, fully condensed monolayer t h e lateral diffusion coefficient of cholesterol is in the rsmge of lOr^'^-lQ-^^ m^ s~^. The m e a s u r e m e n t s according to the integral method were performed a t various values for a^, both before a n d beyond a^^ (= 0.39 nm^). Figure 3.93 shows results obtained after 24 h. As in the differential method, the diffusion coefficient a t a packing density of 0.38 nm^/molecule is «10-ii m^ s-^. At 0.40 nm^/molecule t h e monolayer is still closely packed, b u t t h e interfacial p r e s s u r e h a s dropped to nearly zero, and, correspondingly, D^ h a s strongly increased. Beyond 0.40 n m ^ / molecule it is a l m o s t i n d e p e n d e n t of t h e cholesterol c o n c e n t r a t i o n in t h e monolayer a n d equal to ~ 10-i° m^ s'^
3.226
LANGMUIR MONOLAYERS
10" 0)
S
10r l O
10r l l 0.2
0.4
0.6
0.8 a. / nm^
Figure 3.93. Lateral diffusion coefficient of cholesterol in a monolayer spread at an air/water interface, as a function of the molecular area in the interface. The numbers in the figure indicate the number of measurements. For comparison, a value of = 10"^ m^ s"^ h a s been reported for the bulk diffusion coefficient of cholesterol dissolved in toluene at 20°C^^. Clearly, the lower diffusivity in the monolayer is consistent with the lower fluidity. On the other h a n d , values ranging between 10"^^-10"^^ m^ s"^ are reported for steroids in biological and artificial lipid bilayers^^ Evidently, crowding of the cholesterol molecules in the interface u p to a (crit) only slightly affects t h e fluidity of the monolayer, b u t really tight p a c k i n g (a. < a. (crit)) severely impairs lateral movement resulting in a diffusion coefficient comparable to t h a t of cholesterol in biological m e m b r a n e s . It may well be t h a t p a c k i n g density t h u s plays a n i m p o r t a n t role in controlling the fluidity a n d lateral t r a n s p o r t in biological m e m b r a n e s . Hi) Collapse
of monolayers
of cholesterol
The 7r(a.) isotherm for cholesterol
spread on a n a i r / w a t e r interface, a s displayed in fig. 3.13, indicates tight packing of t h e cholesterol molecules at a. < 0 . 4 0 n m ^ . According to the m e c h a n i s m 1
^
depicted in fig. 3.7 collapse of the monolayer leads to a decrease of the interfacial p r e s s u r e a s a function of time, at c o n s t a n t interfacial area. Collapse is a n important p h e n o m e n o n in monolayer systems t h a t are subjected to compression a n d expansion cycles, a s is also the case in arterial walls and in alveoli. Here, we will consider some experimental d a t a on the collapse of a cholesterol
^C.K. Yun, A.G. Frewderickson, Mol Cryst Liq. Cryst 12 (1970) 7 3 . 2) M. Edidin, Ann. Rev. Biophys. Bioeng. 3 (1974) 179-201.
LANGMUIR MONOLAYERS
3.227
monolayer, obtained by Baglioni et al.^K Realizing that in bulk cholesterol undergoes a phase trcinsition at 37°C 2) they studied the collapse {= expulsion from the monolayer to form a bulk phase) over the temperature range 15-45°C. As expected for condensed monolayers, the n{a^) isotherms are invariant with temperature. The collapse was followed by monitoring the decrease in ;r at a^ = 0.282 nm^. Up to 35°C collapse was found to occur in two stages. The first stage, lasting ca. 15-20 minutes is well described by the Prout-Tompkins model'^^ which at given a^ implies a lineeir dependency of ln(;r - n{t)) / n{t) on In t, where 7c^=n at t = 0. This stage is thought to reflect monolayer separation and nucleation of a threedimensioned phase, see fig. 3.7. The second stage lasts from 100 to 140 minutes. It satisfies second order kinetics, i.e. a linear relation between [l/;r(t)-l/;r^] and t, and is attributed to the growth of the nuclei formed in the first stage. For both stages the rates depend on the temperature. It was possible to estimate the corresponding activation energies. At 25°C they amounted to 25.5 ± 2 . 1 kJ mol-i for the sepsiration and nucleation stage and 35.1 ± 2.9 kJ mol "^ for the growth stage. The activation energy for the first stage is very close to the heat of fusion of cholesterol in the bulk, 28.2 kJ mol'^ (loc. cit.^)). This similarity is indicative of the disruption of the tightly packed condensed two-dimensional structure during the first stage of the collapse. At 40°C and 45°C the variations in the interfacial pressure with time are too small to establish kinetic constants. The difference in n{t] behaviour between T< 35°C and T> 40°C, could be due to different structures of the collapsed phase in the two temperature ranges (as has been reported for cholesterol in the bulk phase, loc. cit.^). which, in turn, could affect the mechanism of the collapse. The fact that the structure of collapsed cholesterol monolayers changes in the physiologic2d temperature range of mammals, whose biological membranes may contain large amounts of cholesterol, is probably not fortuitous. 3.8e PMA at the air/water interface As our first case study, dealing with poljrmers, we consider Langmuir monolayers of poly(methacrylic ester), PMA, at the water-air interface. Data for these layers can be used to illustrate some trends and principles, laiid down in sec. 3.4i. In that section we discussed how the surface pressure of physisorbed polymers depends on surface concentration. In a dilute monolayer of pancakes, the surface pressure was found to be given by the ideal term plus an excluded-area contribution. We rewrite [3.4.56] in terms of the adsorbed amount F = n^/A = N^/{N^^A) in moles of chgiins per unit area
IJ P.Baglionl, G. Cestelli, L. Del, G. Gabrielli, J. Colloid Interface Set 104 (1985) 143. 2) L.Y. Hsu, C.E. Nordman. Science 220 (1983) 604. 3) E.G. Prout, F.C. Tompkins. Trans. Faraday Soc. 42 (1946) 468.
3.228
RT
LANGMUIR MONOLAYERS
r + A^n
RTF
1 +A^r
13.8.5a,b|
where t h e two-dimensional virial coefficient A^ = N 2
B^N'^ is of the order of the av
2
area per mole of pancakes. As derived in sec. 3.4i, in a good solvent A^ is expected to scale as M^^^, where M = NM
is the polymer molar m a s s . According to |3.8.5b|
a plot of 7t/r against F should produce a straight line, the slope of which should give A^. By way of illustration we now discuss some results of Vilanove et al.^^ for poly(methyl acrylate) (PMA) at the a i r / w a t e r interface. These a u t h o r s performed very a c c u r a t e m e a s u r e m e n t s on PMA (and PMMA) monolayers obtained by spreading small volumes (~ 30 [li) of dilute solutions of PMA in chloromethylene. Taking extreme p r e c a u t i o n s to avoid impurities, they
were able to m e a s u r e surface
p r e s s u r e s with a sensitivity of the order of a few }iN m"^ Figure 3.94 shows a typical plot for the dilute regime, (0 < r < 0.02 |imoles m"^ and 10 < TT < 100 fiN m~^). For two molar m a s s e s and two temperatures, very nice straight lines were obtained. In the temperature range considered (15 and 25°C), there is no temperature dependence. From the figure we found for the shorter chains (M = 4.2 kg/mole, N = 49) A^ to be a b o u t 3 5 m^/jimole, whereas for the longer ones (M = 12 kg/mole, N = 140), A^ = 220 m2/|imole. The ratio 2 2 0 / 3 5 = 6.3 between the two values of A^ should be compared with the theoretical ratio (140/49)^/^ = 4.8. The agreement is not perfect b u t quite reasonable, also considering that the values of N are possibly
M= 12,000
M = 4,000
0.01 r/fdmol
0.02
Figure 3.94. Surface pressures for spread PMA films, plotted as K/Rrr as a function of F. The molecular mass is indicated. Open symbols, 15°C, closed symbols 25°C. (Redrawn Irom Vilanove el al.. loc. cil.
m"^
^^ R. Vilanove, D. Poupinet and F. Rondelez, Macromoiecules 21 (1988) 2880.
LANGMUIR MONOLAYERS
3.229
too small for the above scaling relation to apply. By dividing the values for A^ by N^^, these may be converted to nm^ per chciin, i.e. per pancake. The result is 60 nm^ for N = 49 and 400 nm^ for N = 140. In order to get a feeling for the segment density in a pancake, we have to estimate the area per monomer in an imaginary fullypacked monolayer where each backbone unit (C-C) is at the interface and the side groups (-COOCH3) point towards the water phase. To that end, we use the empirical rule that the adsorbed amount of polymers from a good solvent is generally of the order of 1 mg/m^, which corresponds to about one monolayer. For PMA, with a segment molair mass of 86 g/mole, this implies about 6.6 segments per nm^ or a segment area of 0.15 nm^. If we interpret A^ / N as the area per pancake, we find for N = 49 that the segments themselves occupy about 7 out of the 60 nm^, corresponding to 12% internal psincake coverage. For N = 140 the pancake is more dilute; 21 out of the 400 nm^ is taken by segments, equivalent to a fractional coverage of 5% within each pancake. Obviously, these numbers are only rough estimates, but they lead to a realistic picture; the pancakes are rather dilute. So are polymer coils in a 6) solvent. Vilanove et al. edso performed measurements at higher coverages. Figure 3.95 gives a double-logarithmic K[r) plot. In the region 10 < ;r < 100 |iN m"^ which is the pairt covered by fig. 3.94, there is a clear chain-length dependence, as discussed above. However, at higher coverages, n becomes independent of N. This is the region where there is strong overlap between the pancakes; the term 1 / N in [3.4.57) may then be neglected. For ;^ = 0 this equation now reads ^ ^ = -ekT
In(l-e)
13.8.61
For simplicity, we have, dropped the index 1 for 0, assuming that all segments are at the interface. The strsiight line in fig. 3.95 was drawn by the authors to prove their seeding picture; the line has a slope of 2.8, corresponding to ;r - 0^^. On the basis of this power-law assumption, the authors argue that this exponent 2.8 is consistent with the power law R ~ N°^® for the radius of a pancake, which is close to the theoretical exponent of 3/4 as discussed in sec. 3.4i. We omit the details of their derivation. This type of reasoning is appccding because of its simplicity; all dependencies are assumed to be power laws and a double-logarithmic plot is sufficient to find the required exponent. However, in this case there is an alternative. The scaling picture is based upon the existence of individual pancakes (which is correct in the dilute regime as described by fig. 3.94 and, for higher coverages, on (smaller) subpancake regions where the typical size is no longer determined by the chain length but rather by the coverage 6. However, the values of 0 in the approximately linear part of fig. 3.95 £ire so high that a mean-field picture as expressed in eq. [3.8.6] is
3.230
LANGMUIR MONOLAYERS
10^
o^
2 ^3,
10-^
10^
M = 4,200 M = 12.000
lOl 0.01
Figure 3.95. Same system as in fig. 3.94 but now plotted double logarithmically for the concentrated regime.
0.1 r ///mol m
probably adequate. The problem in applying this equation is the occurrence of the logarithm; since 6 = F / F , where F
is the surface concentration corresponding
to 0 = 1, it is not possible to rearrange [3.8.6] s u c h that a straight line is obtained from which the u n k n o w n F
follows.
m
From the d a t a in fig. 3.95, it is nevertheless possible to estimate F , using two points and a s s u m i n g [3.8.6] to be applicable. In the following, we express F and F in m a s s per unit area, where F and n^ at F^ are known, F 2
^2
2
is expected to be of the order of 1 mg/m^. If 7t^ at F^
can be found by solving m
J
t5
_^2/^m^M^-^2/^m)
^1 ~
13.8.7]
^l/^m^Ml-^l/^m)
We did this for fig. 3.95, estimating from the graph K^ = 10^^ |iN m"^ at F^ ^ 10 -2/-A mg/m2 and K^ = 10^^ |iN m"^ at F^ = 10"^^^ m g / m ^ . The result is F^ = 0.54 m g / m ^ . which is in the expected range; it corresponds with a
= 0 . 2 6 nm^ r a t h e r t h a n the
above e s t i m a t e of 0 . 1 5 nm^. With this value of F , t h e d a t a p o i n t s for F > 0.1 m g / m 2 in fig. 3.95 fall perfectly on a plot of log;r against \og\-0 - \n(l - 0)]. Hence, in this region a mean-field picture describes the d a t a quite well. The added advantage is t h a t the monolayer adsorption capacity F
is obtained, the value of
which is quite reasonable. Finally, we note t h a t the value a
= 0 . 2 6 nm^ derived from K{F] at high cover-
ages leads, in the dilute regime, to somewhat higher pancake densities than those estimated from the discussion of fig. 3.94, a s s u m i n g F
= I m g / m ^ . Now for the
LANGMUIR MONOLAYERS
3.231
fractional coverage within a panceike around 22% would be found for N = 49 and about half of that for N = 140. These values might give a slightly more realistic description of the internal pancake structure. Anyhow, the beautiful data of Vilanove et al. give a rather detciiled picture of monolayers of physisorbed polymers in a good solvent, even though some uncertainty about the precise value of a remains. The same authors also studied monolayers of poly(methylmethacrylate) at the air/water interface, believed to be representative of monolayers in a theta solvent. If that were the case, the second virial coefficient in [3.8.5] should be zero, and higher-order terms would have to be tciken into account. However, it was found that A^ is not zero in this case, but slightly negative. A plot such as fig. 3.94 starts with a negative slope at extremely low F, followed by an upward swing at higher F . This is interpreted as a situation with pancakes under conditions worse than a theta solvent. For more details we refer to the original publication. Of the many more aspects of spread macromolecular layers we mention again the possibility that differently prepared monolayers of the same material may have the same surface pressure but nevertheless possess different conformations. Equation [3.4.56] shows that this observation is not at odds with the theory; the r.h.s. contains sums 0[z) and different distributions can have the same sum. So, the surface pressure is not necessarily an exclusive characteristic; layers of identical pressure represent different frozen-in non-equilibrium situations and may react differently if subjected to certain experiments. Some time ago^^ we came across an illustrative case, concerning a block co-polymer of polyacrylic acid (PAA) and partially esterified polyacrylic acid (PAA-pe) at the water-paraffin oil interface. Because of the carboxylic groups in the chain this polymer has polyelectrolyte properties. In particular, n depends on pH. It is possible to prepare monolayers at pH = 4 in several different ways. One of these was spreading or adsorbing at that pH, or preparing the monolayer at pH = 9, thereafter slowly reducing the pH to 4. In both case the final result for n is the same. However, the resulting layers are structurally different £md this shows up when afterwards the pH is rapidly increased to 9 again. In the former case the molecule almost completely desorbs, whereas in the latter case it remains anchored. We speak of memory effects, because the monolayer suddenly remembers its history. Obviously here we are considering frozen non-equilibria; had we carried out the experiments infinitely slowly, no such memory would have been observed. 3.8/ PEO brushes In this section we discuss some recent result of Currie et al.-^^ and Bijsterbosch et 1^ J.Th.C. Bohm. J. Lyklema, J. Colloid Interface Set 50 (1975) 559. 2^ E.P.K. Currie, F.A.M. Leermakers, M.A. Cohen Stuart and G.J. Fleer, Macromolecules 32 (1999) 487.
3.232
LANGMUIR MONOLAYERS
al.l^ on monolayers of PS-PEO A-B block copolymers at the a i r / w a t e r interface. The relatively s h o r t b u t highly insoluble poly(styrene) (PS) blocks terminally a n c h o r the soluble poly(ethylene oxide) (PEO) chains to the interface. Water is a moderately good solvent for PEO b u t at the same time EO segments do adsorb at the a i r / w a t e r interface. Hence, we expect PEO to form p a n c a k e s at low coverage a n d extended b r u s h e s at high coverage. For the b r u s h region we derived in sec. 3.4j the scaling laws H ~ No^^^ for the b r u s h thickness H and n -- Na^^^ for the surface p r e s s u r e K . Here, N is the chain length of the PEO-moiety and a is the chain density (number of chains per unit area). The purpose of the present case study is to investigate how well these relations hold for PS-PEO monolayers on water. Currie et al.^^ based their analysis upon earlier m e a s u r e m e n t s of Bijsterbosch et al.^^, who used block copolymers with short PS anchors and varying PEO lengths; N = 90, 148, 2 5 0 , 4 4 5 , a n d 700. With these samples they performed n e u t r o n reflectivity experiments to determine the b r u s h thickness H and Langmuir-trough m e a s u r e m e n t s to find the surface pressure n. In both cases the coverage a was varied over a wide range. Bijsterbosch et al.^^ combined their H{a] data for all live polymer s a m p l e s to find t h e overall scaling relations. Their best fit gave H ~ N^-^a^"^^, suggesting that H would increase less t h a n linearly with N and more strongly with
a
t h a n a c c o r d i n g to t h e theoretical e x p o n e n t
1/3.
Similar
deviations have been reported by several a u t h o r s on a variety of experimental systems; for more details we refer to the paper of Currie et al. However, averaging over long and short polymer samples is dangerous because scaling laws apply for long chains only. Moreover, from K{G) data, to be discussed 70 h H / nm 50
N = 700 o.o^
30
10 0.01
0.1 a ^ I nm^
Figure 3.96. Brush height as a function of grafting density for terminally anchored PEO chains. The chain length (N) is indicated. (Redrawn after Currie et al.. loc. cit.)
^^ H.D. Bijsterbosch, V.O. de Haan, A.W. de Graaf, F.A.M. Leermakers. M. Mellema, M.A. Cohen Stuart and A.A. van Well, Langmuir 11 (1995) 4464. 2^ E.P.K. Currie et al., loc. cit.
LANGMUIR MONOLAYERS
3;233
below, deviating behaviour for s h o r t c h a i n s could be deduced. If only t h e two longest chains (N = 445 and 700) are considered, the results seem better, a s shown in fig. 3.96. The fitted exponents are 0.33 for iV= 700 a n d 0.35 for N = 4 4 5 a n d are in excellent agreement with the theory. Moreover, the ratio between the t h i c k n e s s e s is, a s expected, quite close to the ratio of chain lengths. In this case a n a c c u r a t e exponent could not be obtained since only two samples of sufficiently high N are available. In the remainder of this section we concentrate on the 7i{a) dependence. In sees. 3.4i and j we found that n should equcd kTa for extremely low a (ideal gas region) and 71 ~ Ncj" in the b r u s h regime (high cr), where a = 5 / 3 in a good solvent a n d a = 2 in a t h e t a solvent. The latter two dependencies should apply w h e n the only contribution to 7t is t h a t caused by b r u s h segments, so, when trains would play no role here. Hence, these relations should be tested on the non-adsorbing segments. As a first check, Currie et al. performed numericcd c o m p u t a t i o n s with the SF model. They chose p a r a m e t e r s representative for PEO (bond length 0.35 n m , corresponding to a
= 0.12 nirf) but set
x^ equal to zero (which is not the case for PEO at the
a i r / w a t e r interface). Tlie results are shown in the double-logarithmic plot of fig. 3.97, covering a wide range of a. Note that a~^ is plotted along the abscissa, so t h a t a mirror image of fig. 3.95 is obtained; the ideal gas region is now to the right, the b r u s h regime to the left. The scaling exponents are as expected; a = 1 for very low a, a = 5 / 3 for a b r u s h in a good solvent, and a = 2 for a b r u s h in a theta solvent. As stated above, PEO adsorbs at the air/water interface, which m e a n s t h a t x^ is non-zero. Figure 3.98a shows the theoretical SF results for ;^® = 1 for three values of N, which may be compared with the experimental d a t a of Bijsterbosch et al. (loc. cit.) given in fig 3.98b. In this case a linear scale is used for both n a n d a"^ To the far right (outside the range shown in fig. 3.98) we have the ideal gas region. Upon compression (lower values of a"^) the pancakes first start to interact (in t h a t region a virial expansion a s discussed in sec. 3.4i applies) a n d then overlap to form a more or less homogeneous monolayer (which is still r a t h e r flat, corresponding to
10
10^
10^ a ' V nm^
0^0^
Figure 3.97. Surface pressure isotherms for end-grafted PEO chains. SF lattice theory, N = 700, i = 0.35 nm, two values of X (indicated).
3.234
LANGMUIR MONOLAYERS
of order unity, or a~^ ~ Na ). Upon further compression, loops and tails develop b u t the train density remains more or less constant. Since in this range trains give t h e d o m i n a t i n g contribution to 7i (see sec. 3.4i), there is a region in the 7r{a) isotherm which is nearly horizontal (semi-plateau), especially so for long c h a i n s . In passing, recall the discussions in this chapter a b o u t the horizontal p a r t s in isotherms in relation to p h a s e separation. Eventually the degree of compression becomes so high t h a t the chains are forced to form a b r u s h . In this b r u s h region, which will be analyzed in more detail below, n increases strongly with increasing coverage a. It is, however, important to note t h a t in this b r u s h region the train layer is still present, with 6 close to unity. A highly schematical picture of the concentration profile in the b r u s h region is shown in fig. 3.99. In this picture, the b r u s h region itself is simplified a s a step function, in line with the scaling picture as discussed in sec. 3.4i. In fig. 3.98 there is semi-quantitative agreement between the theoretical model a n d t h e e x p e r i m e n t a l d a t a , especially at high coverages. The s h a p e s of t h e isotherms are the same, the semi-plateaus are found in the same region of a a n d have roughly the same level; a r o u n d 8 m N / m in fig. 3.98a a n d around to 10 m N / m in fig. 3.98b. This level is also close to independent experimental evidence by Cao a n d Kim^^ on monolayers of PEO homopolymers at the a i r / w a t e r interface who found n = 9.8 m N / m for long PEO chains; these a u t h o r s also observed a slight increase of n with chain length, a s is also visible in fig. 3.98. At low densities (high a " \ to the right in fig. 3.98) the theoretically predicted behaviour is correct qualitatively b u t quantitatively to a lesser extent. This is characteristic for meanfield models, which cannot cope with lateral inhomogeneities.
300 a
I nm
Figure 3.98. Surface pressure isotherms for end-grafted PEO chains, (a) SF lattice theory. I - 0.35 nm. ;t' = 0. ;t^ = - 1 . taken from Currie et al.. loc. cit.; (b) Experiments by Bijstorbosch et al., loc cit.
B.H. Cao and M.W. Kim, Faraday Discuss. Roy. Soc. Chem. 98 (1994) 245.
LANGMUIR MONOLAYERS
3.235
Figure 3.99. Simplified sketch of a PEG brush consisting of trains at the surface (with 6^, close to unity) and a brush region of volume fraction 6 and thickness H.
Finally, we consider the scaling dependencies for n in the brush region. Bijsterbosch et al. (loc. cit.) tried unsuccessfully to verify the power-law exponents. One reason was that they included the data for short chains, as discussed above (fig. 3.96). For interpreting the surface pressure data, a more important effect is that the train layer contribution should be treated separately and sequestered. If this is done, the scaling relations only apply to the brush part of fig. 3.99. The train layer obeys quite different rules. Recall from [3.4.56] that n is found from summing the contributions of all layers. For physisorbed pol)nTiers the train segments dominate. However, this is no longer the case for a train plus brush structure as depicted in fig. 3.99. In that case the brush contribution may be found by subtracting the train contributions from K. The remaining part, ;r (hairs) should obey the laws for brush hairs. The result is seen in fig. 3.100. This figure was obtained by choosing ;r(trains) = 9.8 mN m"^ for N = 700, as reported by Cao and Kim (loc. cit.) £ind which is consistent with fig. 3.98. The figure also contains data obtained from SF lattice theory. A power law is now obeyed with the exponent 5/3, solving a dispute in the 'scaling world'. The stronger dependence of ;r(h2iirs) on G for lower coverage (in the lower right comer of fig. 3.100 is an artefact. The exponent 5/3 was also found for PEO chains with N = 445; in this case ;r (trains) a slightly lower value (9.2 mN/m) had to be taken, in agreement with the data of Cao and Kim, but the width of the brush regime is smaller. For short chain lengths (N = 250 and below), no brush region with ;r(hairs) - a^^^ could be found, demonstrating again that only long chains can be described with scaling theory. As shown in fig. 3.100, the numerical theory still works for short chains; however, the results do not correspond to power laws. This last case study is a recent demonstration of the power and limitations of scaling, amd lattice approaches. 3.9 Applications This chapter is one of the longest ones in FIGS even though we have restricted ourselves mainly to low molecular weight molecules at water-air interfaces. Its length
3.236
LANGMUIR MONOLAYERS
-
E 4r z E .£ -S 2 -
^^^^c^
• PS-PEO
^^^Cn
D SCF
^ V .
"•o.o.
^ ^^ ^v . C
^
0
-«a'•o>. \ °*^n-
°K
^ -2
1
1
1
I
1
L ^
^
In (T ^ {G Mn nm^) Figure 3.100. SF lattice results for the monolayer of fig. 3.97, double logarithmic scale. The drawn straight line has a slope of 5/3. is not surprising in view of the r i c h n e s s of physical a n d chemical p h e n o m e n a involved. Applications can be found in various domains of the living and
non-
living world. It is of historical Interest t h a t compression of monolayer u p to compaction was one of t h e older t e c h n i q u e s for obtaining tangible information on the crosssection of molecules. There exists a recording of a seminar, given by Debye in his birthplace, Maastricht, in which he discusses this approach u n d e r the title T h e Measuring of Molecules'. Some other applications a n d extensions recur in FIGS. In the following chapter on Gibbs m o n o l a y e r s , material exchange with t h e b u l k is a n essential new element. Expansion of a n d compression of interfaces t h e n typically give rise to adsorption a n d desorption, respectively. The rate at which the former takes place is often determined by the rate of supply from the solution, i.e. by the surfactant c o n c e n t r a t i o n s a n d its diffusion
c o n s t a n t . In c o m p a r i s o n with
Langmuir
monolayers, p a r a m e t e r s like c and D enter the equations. Some of the information of this c h a p t e r is also needed to interpret wetting, both its statics and dynamics (chapter
5).
Extensions
to
monolayers
of
macromolecules
(polymers,
polyelectrolytes a n d proteins) are p l a n n e d for Volume V. Liquid-liquid (o/w) interfaces remained underexposed in this chapter. However, our t r e a t m e n t may readily be extended. For instance, in thermodynamics there is not m u c h difference (because insoluble monolayers are supposed to be insoluble in both phases); in molecular t h e r m o d y n a m i c s the ;^-parameters will change; in rheology viscous dissipation will take place in both bulk phases, to an extent determined by the two viscosities.
LANGMUIR MONOLAYERS
3.237
Free liquid films, or liquid films on solid supports, are usually stabilized by soluble surfactants. (Here, we anticipate the following chapter.) They may be interpreted as consisting of two monolayers, either identical or different, separated by a thin layer of liquid. The static properties of such films, in particular their equilibrium thicknesses, are determined by the same forces that control colloid stability; Van der Waals forces (discussed in detail in chapter 1.4), electrical forces (if the monolayers cire charged) and steric ones. Consequently, such films constitute excellent models for studying these forces and hence we intend to discuss these in Volume TV. Besides this, thin films play a role in their own right, say in foams. The trend is that no stable films C£in be made for G-monolayers, whereas films made from LC-monolayers can be kept for a long time. Preparation and breaking of foams are interesting, practically relevant but very complex processes about which the last word has not yet been said. However, it is obvious that liquid transport, and hence surface rheology plays an important, if not decisive, role. Similar things can be said about the preparation, stabilization and coalescence of emulsions. These topics are planned for Volume V, but, anticipating that, it is appropriate to say a few words about the emulsiflcation process. Two immiscible liquid phases (here called 'oil' (o) and 'water' (w) are vigorously sheaired with the aim of causing fluid threads to break up and form droplets. Surfactsmts (here called emulsifiers') are needed to accomplish this emulsiflcation. They serve three purposes: (i) They lower the oil-water interfacial tension, which facilitates elongation. Although this is the most obvious function of emulsifiers, it is not the most important one; most of the mechanical energy input is dissipated as heat; (ii) They stabilize the emulsion, once formed; (iii) Under the dynamic condition of breeiking and recoalescence of droplets (rates of shear 10~^-10"^ s) they create /-gradients which give rise to viscous traction which, in turn, keeps the just-created droplets long enough apart to be stabilized by newly supplied surfactants. This is the most important feature. The process is complicated because regions of higher and lower shear may exist side by side. It is obvious that monolayers under dynamic conditions play a crucial role. As the solubility of the surfactants play an important role we shall come back to this process in sec. 4.9. Comparisons between monolayers and similar layers on solids is of interest, both academically and for applications. The academic one is that the two layers are complementary and that it is interesting to find out what structural similarities and dissimilarities exist. Complementcirity is expressed by the fact that for the Langmuir monolayer K can be measured, whereas for layers on, say mica, the disjoining pressure can be estimated. For one of the many illustrations see^^
1^ P.M. Claesson, P.O. Herder, J.M. Berg and H.K. Christenson. J. Colloid Interface 1 3 6 (1990) 5 4 1 .
Set
3.238
LANGMUIR MONOLAYERS
Of the applications t h a t will not be treated in FIGS let u s first consider some biological examples. Langmuir monolayers have often been denoted a s half of biological m e m b r a n e s ' . Although in reality s u c h monolayers are a far cry from the complex biological reality of living m e m b r a n e s , they are nevertheless useful in learning to u n d e r s t a n d some of the elementary processes, like ion permeation or the resilience against local external perturbations. Applications are for instance found in drug delivery (preparing devices containing membrane-coated capsules from which d r u g s are released at a controllable rate) and the spraying of stagnant tropical w a t e r s to combat malaria. The idea behind the latter is to detach the larvae of t h e malaria mosquitos from the water surface, to which they a d h e r e through their hydrophobic abdomen, through which they also breathe. One of the other challenging biological applications of Langmuir monolayers c o n c e r n s lung
(or pulmonary) surfactant
mixtures.
This i s s u e w a s already
mentioned on the first page of Volume 1, and briefly explained thereafter. With the experience of the p r e s e n t chapter we now come back to it and give it a broader background. The biological, a n d in some cases medical, issue is that breathing requires the surfaces of t h e alveoli in the lung to e x p a n d a n d c o m p r e s s continually at frequencies of the order of a hertz, depending on the excitement of the person u n d e r study. Nature h a s t a k e n care of the propensity of healthy lungs to do so with a m i n i m u m of energy dissipation, by creating a surface layer t h a t not only h a s a low surface tension, b u t also a low surface dilational m o d u l u s . This is achieved by having the surface enriched by w h a t is commonly called the lung surfactant.
In
reality it is a mixture, consisting of = 5 5 % d i p a l m a t o y l p h o s p h a t i d y l c h o l i n e
of
DPPG, of =35% of other lipids and of = 10% by proteins^l The resulting monolayers exhibit negligible d e s o r p t i o n / r e - a d s o r p t i o n upon compression-expansion cycles so they are essentially of the Langmuir type. The precise composition, still a matter of study, is not person-specific; in fact this is not expected for a n organ t h a t h a s no genetic or immunochemical function, although the protein can give rise to (immuno-chemical) problems. One of the medical problems already raised in sec. I.l, is t h a t premature babies may not have produced enough of the surfactant mixtures, leading to so-called respiratory distress
syndrome
(EDS). This disease is nowadays readily overcome by
letting the baby inhale a spray containing the mixture. The remedy is facilitated by the non-specificity of the mixture; the composition is not a s critical a s it would have been in say, implants. The action of lipid-protein mixtures, mimicking those of physiological lung surfactants can be, and h a s been, studied in Langmuir troughs. For instance, in one of s u c h studies the monolayers were subjected to compression-expansion cycles. At 1) S.H. Yu, N. Smith, P.G.R. Harding and F. Possmayer, Lipids 18 (1983) 522.
LANGMUIR MONOLAYERS
3.239
a frequency of about 2 5 s per cycle, tJiere is no indication of material loss from the monolayers a n d cycles are perfectly repeatable^K The surface tension d r o p s from the rest-state of about 25 mN m'^ to less t h a n 5 mN m"^ upon compression by about 3 5 % a n d the 2D isothermal compressibility K^, defined in 13.3.1] is a r o u n d 0.014 m / m N . The reciprocal of this quantity, K^ is m i n u s t h e interfacial dilational modulus, see [3.4.4]. These values a n d conditions are more or less representative of intact lipid films. In fact, the protein does not seem to contribute m u c h to t h e s u r f a c e activity itself, a l t h o u g h it a p p e a r s to facilitate t h e
phospholipid
adsorption in a way t h a t is still subject to further study. For hysteresis to occur in t h e s e model-monolayers it is necessary to increase the frequency a n d , especially the compression rate; the resulting high surface p r e s s u r e s t h e n lead to incipient collapse. Physiologically speaking, hysteresis is not desirable b e c a u s e it implies additional energy dissipation. So, n o r m a l l u n g s u n d e r n o r m a l conditions will avoid this happening. At any rate, this illustration shows how monolayer s t u d i e s C£Ln contribute to the understanding of the functioning of lung surfactants^^. On t h e more technical side, monolayers have been u s e d to retard
evaporation
a n d in this way help to conserve water in arid regions, particularly in t h e dry season where otherwise several tens of a cm could be lost by evaporation. Under laboratory conditions the rate of evaporation can be obtained by placing a d e s s i c a n t j u s t above the water level a n d m e a s u r i n g its weight increase. Comp a r i s o n of t h i s r a t e with the r a t e after application of a monolayer provides information o n t h e inhibiting effect. From t h e a c a d e m i c viewpoint, t h e r a t e reduction c a n be interpreted in t e r m s of molecular processes of permeation, for which a n u m b e r of models have been proposed. However, the m e a s u r e m e n t s are not simple a n d very sensitive to local d i s t u r b a n c e s , a s for instance those incited by t e m p e r a t u r e gradients c a u s e d by n o n - h o m o g e n e o u s evaporation; a n d to minor impurities. In view of the contents of this chapter it is expected a n d observed, t h a t evaporation inhibition is ameliorated by monolayers having a high
surface
p r e s s u r e a n d a high surface dilational viscosity, i.e. a strong Marangoni-type resilience against rippling. The ensuing 'stillness' condition of the water surface h a s t h e additional effect t h a t water t r a n s p o r t is diffusion-limited r a t h e r t h a n convection-limited; the former being the slower process. For application in t h e field the monolayer material m u s t spread easily, be non-toxic for aquatic life a n d be c h e a p . Experience h a s shown t h a t long chain aliphatic alcohols (hexadecyl, octadecyl alcohol or mixtures of these) are most effective. The ins a n d o u t s of this ^^ See, for instance, J.Y. Lu, J. Distefano, K. Philips, P. Chen and A.W. Neumann, Respiration Physiol 115 (1999) 55. -^^ For overviews of the state-of-the-art, see R. Herold. R. Dewitz, S. Schurch and U. Pison, Pulmonary Surfactant and Biophysical Function, in: Drops and Bubbles in Interfacial Research, D. Mobius, R. Miller, Eds., Elsevier (1998) p. 433-474 and Biochim. Biophys. Acta 1408 (1998) which is entirely dedicated to the present theme.
3.240
LANGMUIR MONOLAYERS
technique have been described in an old anthology ^^ and in a review by Barnes-^K Experience h a s shown t h a t evaporation retardation is not only determined by the monolayer material a n d the way in which it is spread, b u t also by the (weather) conditions, the effect being most marked when, in the absence of the monolayers, evaporation is substantial. Transfer of w a t e r molecules (in evaporation control), t r a n s p o r t of solvent across monolayers at oil-water interfaces (in Ostwald-ripening of emulsions) and transfer of ions across s u c h interfaces (as models for ion conduction in bilayers a n d membranes) can often be treated in terms of surface concentration
fluctua-
tions. Their magnitudes can be expressed in standard deviations (a^ for the stand a r d deviation in t h e surface c o n c e n t r a t i o n ) , w h i c h are m e a s u r e s of t h e probability t h a t r a n d o m 'holes' are formed in the layer, allowing m a t e r i a l transport. We have presented the formal treatment in sec. 1.3.7. From this section we c a n immediately obtain a
= kT{dr / d/j)
, for a Gibbs monolayer, with
G^ I r ~ f'^^"^, indicating t h a t these fluctuations become relatively smaller at large r . Some conversion is required to obtain the equivalent for Langmuir monolayers. For a n application to lipid monolayers see^^ L a n g m u i r m o n o l a y e r s play some part in the preparation of multi-layer systems, now mostly referred to a s self-assembled
monolayers
or multilayers
(SAM's).
However, this role is modest b e c a u s e it is difficult to m a k e Langmuir-Blodgett layers sufficiently perfect and stable to function in new materials, s u c h a s electronic a n d bio-mimetic devices. One approach of stabilizing LB films is by working with molecules having double b o n d s that, after deposition, are polymerized. S u c h layers are stable enough to serve as a substrate for protein adsorption^^. Surface rheology also plays a role in the formation of LB films, particularly during transfer from a i r / w a t e r to the solid surface. In a study by B u h a e n k o et al.^'^^ it w a s shown that, for instance with Ca-docosonate monolayers, under conditions of high surface s h e a r viscosity and relatively low elasticity the monolayer did not deposit effectively. Neither was good deposition obtained in the opposite case, presumably because the monolayer is then too rigid and brittle. So, a compromise had to be established and interfacial rheology could help in finding it. Chemical
reactions
in monolayers
constitute a field of study in its own right.
Several types of reactions can be distinguished, including reactions between mono-
^^ Retardation of Evaporation by Monolayers, V.K. La Mer, Ed., Acad. Press (1962). ^^ G.T. Barnes, The Effects of Monolayers on the Evaporation of Liquids, in: Adv. Colloid Interface Sci. 25 (1986) 89-200; See also G.T. Barnes, J. Hydrol. 145 (1993) 165 and G.T. Barnes, Colloids Surf A126 (1997) 149. ^^ J.A. Fornes, J. Procopio, Langmuir 11 (1995) 3943. 4^ See for instance, W. Norde, M. Giesbers and H. Pingseng, Colloids Surf B5 (1995) 255. ^^ M.R. Buhaenko, J.W. Goodwin, R.M. Richardson and M.F. Daniel, Thin Solid Films 134 (1985) 217. ^) M.R. Buhaenko, J.W. Goodwin and R.M. Richardson, Thin Solid Films 159 (1988) 171.
LANGMUIR MONOLAYERS
3.241
layer molecules or with r e a c t a n t s coming from the liquid or gas p h a s e . For t h e former, the rheological consequences have been briefly addressed in sec. 3.6h. The kinetics a n d m e t h o d s of m e a s u r e m e n t differ substantially from those in bulk. For further reading the books by MacRitchie and (sec rV^.8 of) Adamson a n d Gast may be consulted, (see sec. 3.10b). As the final application 2D colloids deserve mentioning. These are monolayers, n o t consisting of low M molecules b u t of colloidal particles. S u c h particles c a n r e m a i n in t h e interface provided they are not too hydrophilic. For monolayers between two liquids, studies of s u c h layers have been carried o u t in connection with the stabilization of emulsions by solid particles, so-called Pickering
stabiliza-
tion. This is mainly a wetting issue (see sec. 5.11c). A more m o d e r n variant, requiring homodisperse colloids is to m a k e the positions of the particles visible, counting the n u m b e r of particles in a narrow ring a r o u n d a central one to obtain 2D radial distribution
functions
(for the traditional 3D case see sec. I.3.9d). S u c h
functions yield interesting information on the interaction between the particles a n d on the p h a s e formation ('2D
crystallization')^^
This s u m m a r y is more brief t h a n the topic merits, b u t nevertheless demonstrates the richness in the applications. 3.10
General references
Note, this list contains several older reviews t h a t have been included where they contain useful b a c k g r o u n d information a b o u t facts, m a n i p u l a t i o n s , cleanliness, do's a n d dont's a n d other experiences from the monolayer world. 3.10a
lUPAC
Reporting
Recommendations
Experimental
Pressure-Area
Data with Film Balances,
publication by L. Ter-Minassian-Saraga, Pure Appl
prepared for
Chem, 5 7 (1985) 6 2 1 . (Data
representation, experimental precautions, checklist). The lUPAC recommendation Manual of Symbols chemical Quantities Colloid and Surface
and Terminology for
and Units; Appendix II Definitions Terminology Chemistry,
Part 1.13 Selected
Symbols for Rheological Properties, Pure Appl
Definitions,
Physico-
and Symbols Terminology
in and
Chem. 5 1 (1979) 1213 also contains
r e c o m m e n d a t i o n s for surface rheology. Only p a r t of t h e m a r e heeded in t h i s chapter.
^^ For recent illustrations, see for example K. Strandburg, Rev. Mod. Phys. 60 (1998) 161 (2D-melting), and M. Kondo, K. Shinozakl, L. Bergstrom and N. Mizutani, Langmuir 11 (1995) 394 (hydrophobed silica at air-liquid interfaces).
3.242 3,10b
LANGMUIR MONOLAYERS MonographSf
reviews
N.K. Adam, The Physics
and Chemistry
of Surfaces,
Oxford University Press
(1941). (Classical text on interfacial science with some emphasis on monolayers.) A.W. Adamson, A.P. Cast, Physical Chemistry
of Surfaces,
6th ed. Wiley (1997).
(The successor of the s t a n d a r d book by Adamson; in their chapter IV they discuss Langmuir monolayers, b u t less extensively t h a n in the present chapter.) J.T. Davies, E.K. Rideal, Interfacial
Phenomena,
Academic P r e s s (1961).
(Classical text, containing three chapters on monolayers; (ch. 5, properties, ch. 6, reactions a n d ch. 7, diffusion through monolayers); represents the state-of-the-art around 1960.) G. L. Gaines jr. Insoluble
Monolayers
at Liquid-Gas
Interfaces.
Interscience
(1966). (Relatively broad a n d introductory; m u c h practical information experimental techniques, examples and applications. Theory is very elementary.) Micelles,
Membranes,
Microemulsions
and Monolayers,
W.M. Gelbart, A. Ben-
S h a u l a n d D. Roux, Eds., Springer (1994). (Collection of contributions, of which several deal with monolayers a n d related topics.) E.D. Goddard, Ionizing Monolayers
and pH Effects, Adv. Colloid Interface Set. 4
(1974) 45-78. (Older review b u t not dated because it contains m u c h basic information on surface p r e s s u r e s and Volta potentials for ionized monolayers.) E.D. Goddard, Ed., Monolayers,
Adv. Chem. Ser. 1 4 4 , Am. Chem. Soc. (1975).
(Proceedings of a symposium dedicated to the memory of N.K. Adam, one of the British 'Grand Old Men' in this area. The book contains a n anthology of monolayer studies.) W.D. Harkins, The Physical Chemistry
of Surface Films, Reinhold (1952). (One of
the 'classics' in the field of surface science.) V.M. Kaganer, H. Mohwald a n d P. Dutta, Structure Langmuir
Monolayers,
and Phase Transitions
in
in Rev. Mod. Phys. 7 1 (1999) 779-819. (Review, over 200
references.) F. MacRitchie, Chemistry
at Interfaces, Academic Press (1990). (Emphasis on the
'real' interfacial chemistry, i.e. reactions, particularly in monolayers. In passing a variety of monolayer techniques and properties are reviewed. ) G. Roberts (Ed.), Langmuir-Blodgett
Films,
Plenum (1990). (Collection ol
c o n t r i b u t i o n s on monolayers, multilayers, deposited layers, Langmuir-Blodgett layers a n d their applications.)
LANGMUIR MONOLAYERS
3.243
T. Smith, Monomolecular Films on Mercury, Adv. Colloid Interface Set 3 (1972) 161-22. (Review; techniques, including electrical ones, examples for various simple molecules in the interfaces.) D. Vollhardt, Morphology and Phase Behavior of Monolayers, Adv. Colloid Interface Set 64 (1996) 143-171. (Review emphasizing the various structures and patterns that can be observed in monolayers, mostly obtained from Brewster Angle Microscopy.) 3.10c Classical and molecular thermodynamics CM. Bell, L.L. Combs and L.J. Dunne, Theory of Cooperative Phenomena in Lipid Systems, Chem. Revs. 81 (1981) 15-48. (Review of lipid monolayers, phase tra.nsitions and statistical interpretations. Because of extended referencing (202 entries) good coverage of literature up to 1980.) K. Motomura, Thermodynamics of Interfacial Monolayers, Adv. Colloid Interface Set 12 (1980) 1-42. (General thermodynamics of Langmuir and Gibbs monolayers; the author's convention differs from the one adopted in this chapter.) 3.10d Interfacial rheology D.A. Edwards, H. Brenner and D.T, Wasan, Interfacial Transport Processes and Rheology, Butterworth-Heineman, Boston (1991). (Rather advanced. Further reading to our sections 3.6 and 3.7e.) M. Joly, Rheological Properties of Monomolecular Films, in Surface and Colloid Science, E. Matijevic, Ed., Vol. 5 Wiley (1972), Part I Basic Concepts and Experimental Methods, p. 1; Part II Experimental Results. Theoretical Interpretation, Applications, p. 79. (Extensive review with several illustrations; further reading to sees. 3.6 and 3.7e.) P. Joos, Dynamic Surface Phenoma, VSPO (The Netherlands), 1999. (Dynamic surface tension, rates of adsorption/desorption, surface rheology, emphasis on Gibbs monolayers. The team of editors consisted of V.P. Fainerman, G. Loglio, E.H. Lucassen-Reynders, P. Petrov and R.H. Miller.) E.H. Lucassen-Reynders, J. Lucassen, Properties of Capillary Waves, Adv. Colloid Interface Sci. 2 (1968) 347. (Further reading to sec. 3.6.7.) E.H. Lucassen-Reynders, Surface Elasticity and Viscosity in Compression/ Dilation, in Anionic Surfactants; Physical Chemistry and Surfactant Action; E.H. Lucassen-Reynders, Ed., Marcel Dekker (1981). (Review of dilational rheology mode, emphasis on Gibbs monolayers; includes discussion on 2D equations of state.)
3.244
LANGMUIR MONOLAYERS
J.A. Mann, Dynamic
Surface Tension and Capillary Waves, in Surface and Col-
loid Set, 1 3 , E. Matijevic, R.J. Good, Eds., Plenum Press (1984), 145-212. (Review, somewhat on the formalistic side.) R. Miller, R. Wiistneck, J . Kragel and G. Kretzschmar, Dilational Rheology of Adsorption
Layers at Liquid Interfaces,
and
Shear
Coll Surf A l l l (1996) 75-118.
(Paper with the n a t u r e of a review; 2 3 3 refs., covers theory, experiments, a n d illustrations; some e m p h a s i s on mixed monolayers) A Prins, Dynamic New Physico-chemical
Surface
Tension
Techniques
and Dilational
Interfacial
for the Characterization
Properties,
of Complex Food
in Sys-
tems, E. Dickinson, Ed., Blackie Academic (1995), chapter 10. (Review of dynamic techniques.) J.C. Slattery, Interfacial
Transport Phenomena,
Springer (1990). (Very thorough
a n d long treatise, encyclopedic in n a t u r e . Parts are highly abstract a n d detailed, b u t m a n y applications are also discussed.) M. v a n den Tempel, Surface Mechanics
Rheology,
in Journal
of Non-Newtonian
Fluid
2 (1977) 205-19. (Review with a phenomenological e m p h a s i s ; opera-
tional definitions a n d coupling to bulk rheology.) 3.10e
Characterization
J . Als-Nielsen, D. J a c q u e m a i n , K. Kjaer, F. Leveiller, M. Lahav and L. Leiserowitz. Principles Scattering
from
and
Applications
Ordered
of Grazing
Molecular Monolayers
Incidence
X-ray
at the Air-Water
and
Neutron
Interface,
Phys.
by Internal
Reflec-
Reports 2 4 6 (1994) 251-313. (Review paper.) P.H. Axelsen, M.J. Citra, Orientational tion Sectroscopy,
Order Determination
Progr. Biophys. Mol Biol 6 6 (1997) 227-253). (Good review paper.)
B. Berge, P.-F. Lenne a n d A. Renault, X-ray grazing monolayers
incidence
diffraction
on
at the surface of wate, in Curr. Opinion Colloid Interface Set 3 (1998)
3 2 1 . (Short update.) N. Bloembergen a n d P.S. Pershan, Light waves
at the Boundary
of
Non-linear
Media, Phys. Rev. 128 (1962) 606. (Theoretical background on non-linear optics.) L.A. Bottomley, J . E . Coury and P.N. First, Scanning
Probe Microscopy,
Anal
Chem. 6 8 (1996) 185R; idem 7 0 (1998) 425R. (Review paper on SPM, state-of-theart. Covering October 1994 - December 1995; both papers contain sections devoted to SPM on LB films.)
LANGMUIR MONOLAYERS
3.245
R.W. Carpick and M. Salmeron, Scratching the Surface; Fundamental Investigations ofTribology with Atomic Force Microscopy,in Chem. Rev. 9 7 (1997) 1163. (Review; relevant technical aspects using AFM for nanotribology, results on bare interfaces and model lubricant films (SAM's and LB films), aimed at atomic-scale understanding of processes such as friction, the onset of wear, nanometer-scale elasticity, plasticity aind adhesion.) J.A. DeRose, R.M. Leblanc, Scanning Tunneling and Atomic Force Microscopy Studies of Langmuir-Blodgett Films, Surface Set Reports 22 (1995) 73. (Review concerning STM and AFM studies of LB films, covering 1987-1994.) R.A. Dluhy, S.M. Stephens, S. Widayati and A.D. Williams, Vibrational Spectroscopy of Biophysical Monolayers. Applications of IR and Raman Spectroscopy to Biomembrane Model Systems at Interfaces, Spectrochim. Acta Part A51 (1995) 1413. (Review on biomembrane model systems studied by surface-sensitive vibrational spectroscopic methods. In particular the following methods are surveyed: external reflectance IR spectroscopy, wave-guide Raman spectroscopy and SERS.) S. Dietrich and A. Haase, Scattering of X-rays and Neutrons at Interfaces, Physics Reports 260 (1995) 1-138. (Review and systematic analysis of the theory of scattering at interfaces.) Fluorescence Studies on Biological Membranes, Subcellular Biochemistry, H.J. Hilderson, Ed., Vol. 13, Plenum Press, 1988. (Compilation of reviews on the advances in fluorescence studies on biological membranes, highlighting subcellular aspects and clearly written. The first chapter, 'Biomembrane structure and dynamics viewed by fluorescence' by B.W. van der Meer, is a very useful introduction to this field of reseairch.) K.B. Eisenthal, Photochemistry and Photophysics of Liquid Interfaces by Second Harmonic Spectroscopy, J. Phys. Chem. 100 (1996) 12997. (Article; among the topics discussed are dynamics of photo-induced structure changes, transport of charge across an interface, the rotational motions of interfacial molecules, intermolecular energy transfer within the interface, interfacial photopolymerization, and photoprocesses at a semiconductor/liquid interface.) A. Ikai, STM and AFM of Bio/organic Molecules and Struchxres, Surface Set Reports 26 (1996) 261. (Review paper.) K.D. Jandt, Developments and Perspectives of Scanning Probe Microscopy (SPM) on Organic Materials Systems, Mater. Set Eng. Reports 21 (1998) 221-295. (Recent developments in instrumentation and particularities in connection with SPM on
3.246
LANGMUIR MONOLAYERS
soft organic s y s t e m s ; m a n y examples, including polymers, liquid crystals, LB films, p h a s e separation and molecular manipulations.) J.R. Lu, R.K. T h o m a s a n d J . Penfold, Surfactants Adv.
Colloid Interface
at Air-Water
Interfaces,
in
Sci.84 (2000) 143-304. (Extensive review, emphasizing
reflection a n d diffraction techniques.) R. Mendelsohn, J.W. B r a u n e r , a n d A. Gericke, External Absorption
Spectrometry
of Monolayer
Infrared
Reflection
Films at the Air-Water Interface,
Ann.
Rev.
Phys. Chem. 4 6 (1995) 3 0 5 . (Reviev^; theory a n d practice of IRRAS a s applied to L a n g m u i r monolayers; determination of conformational s t a t e s of h y d r o c a r b o n tails a n d H-bonding, ionization states of head groups, a n d molecular orientation; illustrated with experimental results on monolayers of single-chain amphiphiles, phospholipids a n d proteins.) D. Mobius, Morphology layers by Brewster
and Structural
Angle Microscopy,
Characterization
of Organized
Mono-
Curr. Opinion Colloid Interface Set 3 (1998)
137. (Literature update.) J . Penfold a n d 19 other a u t h o r s , Recent Advances Surfaces
and Interfaces
by Specular
in the Study
Neutron Reflection,
of
Chemical
J. Chem. Soc,
Faraday
Trans. 9 3 (1997) 3899-3917. (Review describing advances in instrumentation and m a n y applications, including Langmuir monolayers, LB films a n d polymeric a d s o r b a t e s at air/liquid, liquid/liquid and solid/liquid interfaces.) Scattering,
Reflection
and Surface
Current Opinion Colloid Interface
Interactions,
J . Penfold, L. Magid, Eds., in
Set 4 (1999) 173-221. (Update. It is likely t h a t
more of t h e s e will a p p e a r in t h e s a m e j o u r n a l after closing of the p r e s e n t manuscript.) G.L. Richmond, J.M. Robinson and V.L. S h a n n o n , Second Harmonic Studies
of Interfacial Structure and Dynamics,
Generation
Prog. Surf. Set 2 8 (1988) 1. (Review,
theory a n d experiment; investigations of a variety of solid materials in vacuo, air, solutions a n d in contact with other solids are considered, as well as studies at the liquid/liquid interface.) T.P. Russell, X-ray and Neutron Reflectivity
for the Investigation
of
Polymers,
Mater. Set Reports 5 (1990) 171-271. (Basic theoretical and experimental concepts of specular reflection, and application to polymer science.) Y.R. Shen, The Principles of Nonlinear Optics, Wiley, (1984); Optical Second monic Generation
at Interfaces,
Har-
Ann. Rev. Phys. Chem. 4 0 (1989) 327. (Theoretical
basis of SHG, experimental set-up, examples of applications to show what types of information are obtained from SHG measurements.)
LANGMUIR MONOLAYERS
3.247
K.J. Stine and CM. Knobler, Fluorescence Microscopy; A Tool for Studying the Physical Chemistry of Interfaces, Ultramicroscopy 47 (1992) 23. (Review; short introduction to fluorescence and fluorophores; basic instrumentation for fluorescence microscopy and extensions to study dynamics and resonance energy transfer, confocal scanning microscopy; results obtained with Langmuir monolayers.) 3.1 Of Langmuir-Blodgett layers S.B. Peng, G.T. Barnes and I.R. Gentle, The Structures of Lxingmuir-Blodgett Films of Fatty Acids and their Salts, Adv. Colloid Interface Set (in press, 2000.) G.G. Roberts (Ed.), Langmuir-Blodgett Films, Plenum Press, (1990). (General and extensive review of thesubject.) D.K. Schwartz, Langmuir-Blodgett Film Structure, Surf Set Reports 27 (1997) 245-334. (Review on structural and thermodynamic properties of LB films; brief description of characterization techniques.) R.H. Tredgold, Order in Thin Organic Films, Cambridge University Press, Cambridge, (1994). (Films formed by LB, self-assembly and other techniques; concentrates on systems for which an effort has been made to characterize the degree of order.) R.H. Tredgold, Ordered Organic Multilayers, J. Mater, Chem, 5 (1995) 1095. (Short review; basics of LB, self-assembly and other techniques; interesting developments and aspects of particular scientific importance.) A. Ulman, An Introduction to Ultra Thin Organic Films, Academic Press, (1991). (Reviews both Langmuir-Blodgett films and films formed by the self-assembly technique.) J.A. Zasadzinski, R. Viswanathan, L. Madsen, J. Gamaes and D.K. Schwartz, Langmuir-Blodgett Films, Science 263 (1994) 1726. (Comprehensive overview of the progress made in LB technology with SPM, in terms of film structure, stability, and the substrate influence on these. Specific results for Langmuir-Blodgett films of fatty acids.) 3.10g Data collection A.F. Mingotaud, C. Mingotaud and L.K. Patterson, Handbook of Monolayers. (Contains about 1300 examples of ;r(A), or K(a) curves, with references and some experimental information. Only for aqueous subphases. Not critically evaluated.) Volume 1, long chain amphipolar aliphatic compounds, phospholipids, macrocyclic and inorgcinic compounds; Volume 2, dyes, polymers, steroids, amino acids and polypeptides, and other natural products. Academic Press (1993).
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4 GmBS MONOLAYERS 4.1 Introduction 4.2 The surface tension of miscible binary mixtures 4.2a General features and thermodynamics 4.2b From F^"^ to y 4.2c From r to F^"^ 4.2d A note on surface excess entropy 4.3 Dilute solutions of simple molecules 4.3a Experimentad techniques 4.3b Theory 4.3c A case study: alcohols 4.4 Simple electrolytes 4.4a The pristine surface of water 4.4b Electrolytes at the air-water interface 4.4c Electrolytes at water-oil interfaces) 4.4d Some practical implications 4.5 Rheology and kinetics 4.5a Identification of basic transport phenomena 4.5b Basic mathematics 4.5c Experimental techniques 4.6 Surfactants 4.6a Surfactants in solution 4.6b Surfactant monolayers. General features 4.6c Non-ionics 4.6d Ionic surfactants 4.7 Curved interfaces 4.8 Apphcations 4.9 General references
4.1 4.2 4.2 4.6 4.18 4.20 4.20 4.21 4.22 4.27 4.34 4.35 4.36 4.41 4.45 4.46 4.48 4.51 4.58 4.68 4.69 4.73 4.76 4.83 4.93 4.97 4.99
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4
4.1
GIBBS MONOLAYERS
Introduction
Gibbs monolayers are adsorbed monolayers. Unlike Langmuir monolayers they are the result of the spontaneous enrichment or depletion of one or more components at the interface. At equilibrium, the interfacial tensions are related to surface concentrations and the composition of the adjacent phases through Gibbs' adsorption law, the most important equation of interfacial science. The derivation of this equation (sec. 1.2.13) is purely thermodynamic, i.e. no model assumptions are needed. For systems at equilibrium, violation of this law is therefore impossible, because that would imply the possibility of creating a perpetual motion. However, the application of the Gibbs equation to real systems is not always simple. In this connection the following note on measurabilities is appropriate. In contrast to Langmuir monolayers, for which the surface concentration F is generally known and where n is measurable, here the determination of F may cause problems when the area A is too small to allow reliable analytical estimations. This restriction is partly offset by the possibility of measuring / as a function of composition and from there inferring F using Gibbs' law. However, this conversion is not always straightforward. What is d^^ in a mixture? How should F be counted for a polymeric adsorbate? What is the consequence of moving the Gibbs dividing plane as a result of adsorption? etc. Large areas are of course encountered in foams and emulsions but these are not at thermodynaimic equilibrium; in the sense that they do not form spontaneously although adsorption equilibrium with the bulk is mostly retained. When it is possible to determine the area, these systems can be used to obtaiin physical information on the monolayer (e.g. the packing density of surfactants) but there is no guarantee that the composition of the monolayer is identical to that obtained by adsorption at a quiescent surface of fixed area. It is an implicit consequence of this discussion that verifying Gibbs' law is not easy for Gibbs monolayers. Such testing checks the applicability of this law to real systems, rather than its validity. Gibbs monolayers are widespread. The simplest system is that of the surface of a fully miscible binary liquid. More complex ones are: monolayers of uncharged molecules adsorbed from dilute solutions (example: aliphatic alcohols from aqueous solution); electrolytes; surfactants (non-ionic or ionic); polymers and polyelectrolytes and yet more. On the other hand, the methods for characterizing
4.2
GIBBS MONOLAYERS
the monolayers are not so different from those for Langmuir monolayers. Hence, there is no need to d i s c u s s these techniques again. One exception is the surface rheology, t h e interpretation of which h a s to be drastically modified b e c a u s e comp r e s s i o n / e x p a n s i o n of t h e monolayer now leads to d e s o r p t i o n / a d s o r p t i o n . The relative r a t e s of t h e s e p r o c e s s e s become i m p o r t a n t variables, b e c a u s e they determine the deviations from equilibrium. With t h i s in mind, this chapter will be set u p system-wise, working from t h e more simple t o w a r d s the more complex monolayers a n d inserting a section on surface rheology a s soon a s it is needed. In order to contain the t r e a t m e n t within r e a s o n a b l e limits, we shall mostly restrict ourselves to b i n a r y s y s t e m s . E a c h section s t a r t s , where possible a n d appropriate, with the required (thermodynamic, statistical, electrostatic, ...) background. Recadl from sec. 3.1 that, at equilibrium, surface equations of state are the same a s for Langmuir monolayers. Liquid-vapour surfaces a n d liquid-liquid interfaces will mostly be considered in conjunction, with some e m p h a s i s on the former. 4.2
The surface t e n s i o n of miscible binary mixtures
In t h i s a n d t h e following sections we shall mostly restrict ourselves to fully miscible m i x t u r e s . P h a s e s e p a r a t i o n in t h e b u l k or at t h e surface l e a d s to i n h o m o g e n e o u s s u r f a c e s , of w h i c h t h e t e n s i o n c a n n o t b e
unambiguously
m e a s u r e d . For a n illustration of s u c h ain anadysis, see ref.^^ which concerns t h e influence of t h e t e m p e r a t u r e on w a t e r - 2 , 6 dimethylpyridine m i x t u r e s w h i c h phase-separate below T, = 33.87°C. 4.2a
General features
and
thermodynamics
Surfaces of b i n a r y liquid m i x t u r e s are t h e simplest Gibbs monolayers t h a t exist. We are considering the surface tension y a s a function of the mole fraction X = x^. It r u n s from the value / * for pure component 1 to /* for p u r e 2. t h a t is from X = 0 to X = 1. Often s u c h curves are convex with respect to the x-axis (as curves 2 a n d 3 in fig. 4.1), implying the tendency of the interface to be richer in the comp o n e n t with the lower / * . At the same time this is the most volatile component. S u c h convex behaviour is the rule for mixtures of simple molecules, like liquid Ar, CH4, Ng, CO, etc. b u t h a s also been observed for binary mixtures of the Kr-ethenee t h a n e triod^) a n d for molten salt mixtures^^. Concave curves (2' in the figure) require the surface to be enriched by the component with the higher 7*, b u t s u c h
^^ T. Mainzer-Althof, D. Woermann, Ber. Bunsenges. Phys. Chem. Chem. Phys. 101 (1997) 1014. 2^ B.S. Almeida, V.A.M. Scares, LA. McLure and J.C.G. Calado, J. Chem, Soc. Faraday Trans. 8 5 (1989) 1217. ^^ J. Goodisman, J. Colloid Interface Set 7 3 (1980) 115.
GIBBS MONOLAYERS
4.3
Figure 4.1. Surface tension of binary miscible mixtures. Examples of trends: (1), near-ideal; (2) and (2) many organic mixtures; (3) ethanol +water.
behaviour is restricted to more complicated mixtures. Certain energetically favourable interactions in the interface are needed to enrich the component with the higher y*. Only for fully ideal mixtures is y[x) linear. Linearity may occur when the fluids and surfaces are both ideal: d^u^ = RTd ln(l - x], d//^ = i ^ d In x , F^ = a(l - x) and r^=ax,
then dy = -r^dfi^- F^dpi^ is proportional to d x . Examples approaching
this behaviour are mixtures of hydrocarbons with similar chain length (line 1 in fig. 4.1), but linccirity has also been observed for mixtures of dioxane + benzene or dioxane + nitrobenzene ^K Surface tensions for a variety of mixtures are collected in appendix 1, tables A l . 16-18. Subjecting y{x) curves to analysis in terms of Gibbs' law immediately confronts u s with the basic issue of where to locate the dividing plame. Let u s start from Gibbs' law at constant pressure
dy =
-sldT-r^d^^-r^dfi^
[4.2.1]
In this equation F^ and F^ are real excesses in the interface. At issue now is whether these are identical to the analytically determined ones, using some depletion technique. The problem is that in such methods one measures the decrease of the solute concentration by adsorption, but how can one do that in practice when the system contains more solute than solvent? We discussed this issue in detail in sees. II.2.1 and 4. Let u s briefly elaborate this for constant temperature. In [4.2.1] d/x^ and dju^ are coupled by the Gibbs-Duhem relation ( l - x ) d / i j +xd/d^ = 0 , so we can eliminate either one of the chemical potentials, obtaining these alternatives
dr = -
(l-x)
d/^.
1' S.K. Suri, V. Ramakrishna, J. Phys. Chem. 72 (1968) 3073.
I4.2.2al
4.4
GIBBS MONOLAYERS 2
dy =
^1--
d//j
[4.2.2b]
These equations show that it is impossible to define F^ and F^ independently. In dilute solutions, x « 1, we can get away with defining F^\ that is the surface excess of the solute (component 2) with respect to the solvent (component 1) which is present in excess. This locates the Gibbs dividing plane (GDP). In sec. 4.3, where only dilute solutions will be considered, this reference is appropriate. However, in the present case the entire range of x from 0 to 1 has to be considered, so the distinction between solvent and solute becomes very impractical; it makes no sense to define F^^ as the excess of 2 with respect to 1 when the system contains negligible amounts of 1, not that there would be a way of measuring this quantity properly. Basically the issue is that [4.2.1] reflects a surface excess isotherm, as already encountered in the adsorption of binary mixtures on solid surfaces (sees. II.2.3 and 4). Adsorption of the one component cannot be effected without depletion from the surface of the other, and because splitting these two processes is inoperational, thermodynamics tells us that only the two adsorptions together are measurable ^^. The solution of the dividing plane problem is that the adsorptions are not referred to a zero value of one of the two components, but that F^^^ and F^^^ are introduced where F^^"^ is the surface excess of 1 per unit area over the amount of 1 in a reference system of uniform composition with x^ = (1 - x) and x^= x. This is the excess that is measured in surface excess isotherms and which determines the surface tension. The definitions are p(n) _ 1
F^-il-xHF^^F^)
(4.2.3a]
-(n) _
obeying ^^(n) ^ pM ^ 0
[4.2.4]
So, only one surface excess is obtainable; the positive adsorption of the one component equals the negative adsorption of the other. For small x,
rf^-(l-x)rf
[4.2.5]
as discussed in sec. II.2.3a, so F^^^ -^ F^^ in dilute solutions. Similarly, for A: -^ 1 p(n) 1
p(l) 1 •
The behaviour of F^"^ as a function of x is a curve starting from 0 and ending at 0. Three possible trends are given in fig. 4.2. Similar curves have already been encountered for the solid-liquid interface (fig. II.2.8a,b). For a F^^\x) curve to be ^^ For historical interest the paper by J.J. Kipling. J. Colloid Set 18 (1963) 502, in which the meanings of the various F's arc analyzed, can be consulted.
GIBBS MONOLAYERS
4.5
V 2
\ \ \ \
(a)
/
\
\ *^ **»^ \ V ^ ^1 A ^ xyl / ^^—^ /
(b;
Figure 4.2. Some trends of r^^' and r^'. (a) Low and almost symmetrical (with respect to -(n) (n) x); (b) skewed; (c) containing an azeotrope. At any x, r.^"' perfectly sjrmmetrical, as in fig. (a), F^"^ should first be symmetrical with respect to the mole fraction x^ in the interfacial region and second, x^ and x should be identical. Such high extents of ideality aire rare. Substituting definitions [4.2.3a and b] of the surface excesses in the Gibbs equation yields [4.2.6]
d / = - S^^^^dT - Fj^^^d/ij - F f^dAi2
Here we have re-introduced the surface excess entropy. It is noted that this entropy is now referred to the same reference as selected for the F^"^'s. In sec. 4.2d we shall elaborate this in detail. Because of [4.2.4], [4.2.6] reduces to [4.2.7a]
dy=-Sf"^dT-F/'^^(d//^-d/i2) or to
dy=-Sf"^dT-F^"^(d//2-ciAzJ
[4.2.7b]
Using the Gibbs-Duhem equation (1 - x)d/i = -xdfi
, one of the chemical potentials
can be eliminated, leading to this pair of equations dy = -S''^"^dT-
r/"^d/i^
[4.2.8a]
X.
dv = -S^^"^dT- ^ ^ ^ ^ (1-x)
[4.2.8b]
These two expressions are rigorous for binary systems at fixed pressure. In [4.2.8a and b], S^^"^ stands for S^ - rl^'^S and S^ - r}!^^S , respectively. Here, S a
a
molar entropy of the bulk (S
i
m
a
2
m
*
^
= S /(n + n )), see sec. 4.2d.
'
'
is the m
4.6
GIBBS MONOLAYERS
Basically there are two ways to exploit the pair [4.2.8a and bj. The first is by making some assumption about the x-dependencies of the two T^"^ 's and on the chemical potentials, thereafter integrating the equations to predict y(x) and checking the result ag£iinst experiment. The alternative is by deriving F^"^ and F^^ from experimental data by differentiation of the surface tension with respect to the appropriate chemical potential. The latter route is more in line with the nature of Gibbs monolayers because the surface excesses, rather than the tensions are the unknowns. Let us nevertheless first consider the former case. 4.2b From /^"^ to y The analysis can be carried out at several levels. The most elementary is by making some assumption regarding the trend F^^ as a function of x. For instance, one could empirically try to account for the fully symmetrical case of fig. 4.2a by letting F^^ = F*^x[l- x), where F* is a kind of capacity concentration, to which we shcdl return below. If this is substituted in [4.2.8bl, with d^^ = jRTdx/x it is found that at fixed temperature d y / d x is a constant, i.e. the linear case of fig. 4.1 is retrieved. However, this model is unrealistic because, if surface and bulk are both ideal, there is no reason why the one component would enrich the interface over the other, i.e. F^^O and /* -^ /*; when two liquids are identical they must have identical surface tensions. In practice this implies that trend (1) in fig. 4.1 is found only in the limiting case of horizontality of the y{x) line. This limit is never fully attained. Hence we should start at a higher level to account for the more frequently encountered /(x) curves. In doing so it is expedient to recall that F^"^ and F^^ are the excesses in the composite isotherm, which are not identical to the excesses that can be computed for single component adsorption from very dilute solutions (except for the trivial limiting cases x « 1 and (1 - x ) « 1). Hence, we can neither indiscriminately use the isotherm equations nor the matching equations of state, say Langmuir, Volmer, FFG or 2D Van der Waals. However, the principles underlying these equations can be used to obtain the required surface excesses. In sec. II.2.4 a number of such isotherms have already been derived for SL interfaces, albeit under a number of simplifying assumptions. One of these was that the surface layer was considered monomolecular. This approximation is better for SL than for LL or LG interfaces because in the former systems the molecular density profile p^{z) has a maximum close to the solid (see figs. II.2.4 and 2.6) where most of the adsorption takes place, whereas for the latter the surface layer is more extended and P^(2) rather has a tanh-like profile (chapter 2). To render this matter concrete, consider the simplest case that adsorption takes place in a monolayer only, that all molecules are spherical, have the same size and mix athermally in solution (as in sec. II.2.4c). Equilibrium between surface layer and bulk is based upon the coupled exchanges of the two components and governed
GIBBS MONOLAYERS
4.7
by the equality ju^ - ja^ = ^\- ^\' see [II.2.4.11]. The exchange equation is
l-e
=K-^^ 1
[4.2.9]
where 6 = 6^ is the mole fraction of component 2 in the surface monolayer and the exchange constant K follows from ^^K
= -A^,^G^ = A^r - Hi' - < • + H^,-
(4.2.101
Here, the asterixes refer to the pure liquids. We are not looking for the real fraction 6 of component 2 in the interface, but for its excess with respect to the bulk, i.e. for 6-x. From [4.2.9] we obtain
, _ , = (^ziH£z^
14.2.111
1 + (K - l)x The larger K, the stronger the preference of component 2 for the surface layer. When K = 1 there is no preference and composition in surface and bulk aire identical. We see that 6{x) is an increasing function of x, running from 0 = 0 at x = O t o 0 = l a t x = l, with the initial slope increasing with K. On the other hand, the excess 6-x runs from 0 at x = 0 to 0 at x = 1, passing through a maximum which is higher and more skewed toward lower x for higher K (fig. II.2.11). The derivation of [4.2.9] implied r^ = r^, which is Just the number of moles that can be accommodated in the surface layer, i.e. the monolayer capacity, F* rl"^ =(9- x)r' = ^ ' ( ^ - 1 ) ( ^ - ^ ^ ) 2 l + (K-l)x
[4.2.12]
This relation is illustrated in fig. 4.3. Infinitely high values of K are needed to let r^^ approach T* because such a skewed equilibrium is entropically very unfavourable. In fact, for K» 1, F^^ -^ r^(l- x), i.e. the maximum should be found at x-^0. When the molecules have different sizes, F^ ^ F^, and equations more complicated than [4.2.9] are then needed; see below. Having found F^\x), [4.2.12] can be substituted in the appropriate Gibbs equation, [4.2.7b]. The result is dy = -
a
-F\K-
-1) " ^ ^ 2
l + (K-l)x
[4.2.13]
Integration at constant temperature allows / to be computed at any x as Y(x) = y\-KrF\K-\) \ ^ '^\^ , ^ J 1 + (K - l)x
[4.2.14]
x'=0
where djU^ has been replaced by RTd In x', because the liquid mizture is assumed ideal, and x! is the mole fraction variable. Whatever the value of K, y(x' = !) = /*:
4.8
GIBBS MONOLAYERS
0.6h r{n)
0.4h
0.2
Figure 4.3. Surface excess isotherms according to 14.2.12). For conditions see the text. K is the exchange constant. The curves correspond to the drawn ones in fig. II.2.11, after normalization.
r;-r[=-RTr\K-i)
J — x'=0
dx' (K-l)x'
[4.2.15]
For K = 1 (no preference for the surface) y* = 7* in this model a n d the trend y{x] is a horizontal line. In this case fluids 1 a n d 2 are identical. For arbitrairy K t h e definite integral in [4.2.15] equals In K / ( K - 1). Hence, using [4.2.10] * I
'2
ads
[4.2.16]
m
The difference between the two surface tensions is determined by the Gibbs energy of replacing t h e one liquid surface by the other, multiplied by a capacity factor. This r e s u l t is intuitively expected. Alternatively, one might write t h i s a s A ^ G° = (yl - y,*)cL*, where a* = 1 / F* is the molar area in the surface. ads
m
^'2
'1'
'
For intermediate vadues of x r(x) = y* - RTr*^ ln[l + (K - l)x]
[4.2.17a]
y(x) = y* + RTF* ln[x + K(l - x)]
[4.2.17b]
Results are plotted in figs. 4.4a and b, showing the absolute values of the surface tension a n d the difference Ay from linearity (y{lin) = ( 1 - x ) y j + x y * ) , respectively. The latter way of plotting is often seen in the literature. These two graphs show
GIBBS MONOLAYERS
4.9
/i+8 -
6
^(_
(a)
-
K= 1/20/
"
4
^^^^1^
-^
2
1/2
- ^^_
1
0
2 -<—
-2 5 -4
"^
-6
_
rl-s
20
" "^~
i
1
i
0.2
3 -
1
1
0.4
1
0.6
K =: 2 0
i
0.8
(b)
Ar 2
1 \
1
5
1
2
0
t:
■^^^..^^^^
/
-1
\
1/2
/A
1/5
-2
^y/^
—-"^^.^^i/^o
\
-3 -ji
J
0.2
1
0.4
1
1
0.6
0.8
1 -
Figure 4.4. Surface tensions of binary mixtures according to the exchange principle. Monolayer approximation (eq. 14.2.17]) with fixed areas per molecule. Capacity factor (T^) corresponds to 0.4 nm^/molecule. Exchange constant K is a measure of the relative preference of the two components for the surface according to (4.2.10]. Top: curves plotted with respect to y^ = 0 ; bottom: absolute value A/of the deviation from linearity. t h a t even t h e simple monolayer picture already c a p t u r e s m a n y experimentally observable t r e n d s . Figure 4.4a shows that, with increasing deviation of K from unity, t h a t is, with increasing difference between the molecules 1 a n d 2, the difference between /* and /* grows and the curves become more skewed. From fig. 4.4b it is seen t h a t for K > 1 the deviation from linearity is positive, for K < 1 it is negative. Equation [4.2.17] explains the background of the sign of A/: it is positive (curve 2' in fig. 4.1) if K > 1 and negative (curves 2 and 3 in that figure) for K < 1. So the n a t u r e of the curvature is determined by the relative preference of the two components for the surface, that is: by the signs of F^^^ and T^^^ in fig. 4.2.
4.10
GIBBS MONOLAYERS
Figure 4.5. (a) Surface excess isotherms for a non-ideal binary system according to [4.2.18]. Parameters: K = 5, r*= 5, x^ = -2; the value of x^ is indicated, (b) Surface tension for the same parameters. This elaboration c a n be extended to cover more complicated cases. We give two illustrations. Non-ideality in t h e regular solution model yields the following excess isotherm equation (see II.2.4.21) for a monolayer
e Lx^ii-2e)^jA :.x'^n-2x) 1-xJ i-e\
[4.2.18]
GIBBS MONOLAYERS
4.11
where x"^ ^^^ X^ ^^ Flory-Huggins type pair energy pcirameters in the surface and bulk, respectively. These parameters measure the energetic preference the unlike molecules have for each other over that between identical pairs. The lower x» the better the mixing; high positive x -values lead to de-mixing. In order to show the effects of surface non-ideality we have kept K and x^ constant, letting x^ vary. (This construction is somewhat academic; usually there will be some parallel between x^ ^^d x^ -) In fig. 4.5a, F^"^ / F^ = (0 - x) is plotted as a function of x for various x"" • Unlike the ideal case of fig. 4.3, loops are developing, which become more pronounced for more positive x^ • ^o^ X^ - ^ the lower x part exhibits a surface that is strongly enriched in component 1, whereas the higher part of x has a strong excess of component 2. For still higher values of ;^^, phase separation would occur, with the surface covered by pure component 1 at low x and by pure component 2 at high x. (In practice this situation is unlikely because then demixing would also occur in the bulk.) For x^ = -4 mixing in the interface is more favourable tham in the bulk; this situation resembles the types of curves in fig. 4.3c. The surface tension follows from a variant of [4.2.14]. The integration is carried out numerically. For d/x^ the Flory expression d^ = [ 1 / x - 2;i^^(l- x)dx] was used, keeping x^ =-^ constant. For results see fig. 4.5b. All curves approach the same values of 7* at X -> 1, determined by [4.2.16]. With /* = 35 rtiN m-^ F* = 5 mole nr^ and A ^ G° =-RT\nK = - R T l n 5 , y! = 22.6 mN m-^. For x"" = "4 the curve is ads
m
'2
^
convex. For j*^ = -1 the curve is already slightly concave; here the interaction in the surface is less attractive than in the solution. For less negative or positive x^ this trend becomes more pronounced. The other illustration concerns oligomers, adsorbed flat in a monolayer. For an r-mer we derived [II.2.4.33] using a lattice model: — ^
=^
K[r) — ^
[4.2.19]
Here, cp is the volume fraction of the r-mer, (1 - cp] that of the solvent aind z^ and z^ are the co-ordination numbers in the surface layer and in the bulk, respectively. Results are presented in fig. 4.6. In order to emphasize the r-effect we fixed z^K{r) / z^ at 5, meaning that the enthalpic preference of the oligomer was forced to be independent of the chain length. What was left variable is the configurational factor, characterized by the denominators (1 - 6Y and (1 - (pY. Figure 4.6a shows that, for configurational reasons, the longer the chain, the lower the surface excess of the solute. This feature was observed before (fig. II.2.14). The corresponding relative enrichment of the monomer is reflected in the ensuing stronger depression of A/ (fig. 4.6b) with increasing r. In the integration, leading to this latter graph the chemical potentials were considered to obey Flory theory.
4.12
GIBBS MONOLAYERS
0.6
-H
r{n) ^2
(a)
r= 1
0.4
-]
3
0.2
-.,,
1..
0.2
1
*"""^^--^
i
0.4
,
1 0.6
.
r
^7-
0.8
Figure 4.6. Surface excess isotherms (top) £ind surface tension (bottom) of a binary mixture of an r-mer and a monomer. z^K(r)/z^ = 5. These two extensions illustrate how the simplified monolayer model m a y be extended. The t r e a t m e n t s have t h e advantage of being relatively p h e n o m e n o l ogical. A variety of elaborations can of course be made, say to cover more realistic density profiles across the surface, or to include more-component systems. Several alternatives for describing surface t e n s i o n s of binary m i x t u r e s have been suggested a n d elaborated in the literature. For the sake of compgirison, let u s d i s c u s s a n o t h e r thermodjnnamic alternative, which h a s received m u c h attention^^
^^ See for instance J.W. Helton, M.G. Evans, Trans. Faraday Soc. 4 1 (1945) 1; J.C. Eriksson, Adv. Chem. Phys. 6 (1964), 145; R. Defay, I. Prigogine and A. Bellemans (English transl. D.H. Everett), Surface Tension and Adsorption, Longmans (1966), Chapters XII and XIII; F.B. Sprow, J.M. Prausnitz, Trans. Faraday Soc. 6 2 (1966) 1105; S.M. Bardavld, G.C. Pedrosa and M. Katz, J. Colloid Interface Set 165 (1994) 264.
GIBBS MONOLAYERS
4.13
At equilibrium, for each component i, fi^ = }i^, where the superscript L stands for the liquid. For fJL^ one writes /x°^ + KT In J x . but for the surface phase //[^ = ii^"" + RT In f^e^ - yA^
[4.2.20]
where A. is the partial molar area of i. The idea behind this equation is that transporting a molecule to the interface requires work against the surface tension. For the pure fluid i ^oa_^oL =y*^Al
[4.2.21]
where A* is now the molcir area of i in the surface. From the equilibrium condition it follows that yA* = 7* A* + RT In
[4.2.22]!)
If this model is applied to an ideal binary system on the same level of approximation as in the derivation of [4.2.17], J^ = J^ = l; A^ = A^ = A* =AI-^A yA = YlA + RT Inf ^ ^ 1 = r*^A-\-RT l n f - 1
[4.2.23]
In sec. II.2.4, eq. [II.2.4.46], we showed that from [4.2.23] it is also possible to derive SchuchowitskCs equation e-yA/RT ^ ^ _ ^ j g - y ; A / R T ^^^-y^A/RT
[4.2.24]
For the sake of comparison with our approach, [4.2.23] is written as
In this way [4.2.9] is retrieved, however, with RT In K = -A^^^G^ replaced by v\~^2)^' ^^ ^^ interesting to consider the background of this analogy. The configurational (logarithmic) terms £ire identical in the two approaches; this is an expected result. On the other hand, in [4.2.9] the exchange constant RT In K is a combination of standard chemical potentials, i.e. of reversible work per mole, whereas in [4.2.23] it is the reversible work of replacing area of type 1 by that of type 2. Ultimately this is a difference of convention. According to [4.2.20] the Gibbs energy of a flat surface would be G^ = Xi ^i^^ ~ M whereas in the lUPAC
!) This equation has already been derived by J.A.V. Butler, Proc. Roy. Soc. A135 (1932) 348.
4.14
GIBBS MONOLAYERS
convention, adhered to by us, G^ = ^^ A^j'^l'- See appendix 2 and, for a discussion of the background, sec. 1.2.10. The surface Gibbs energy in [4.2.20] corresponds rather to our surface Helmholtz energy. Matters of convention may of course never lead to ambiguities in relations between operational variables and in the present approximation the identity of -A ^^G^ and (YI-YO)^
^^ readily verified, considering
[4.2.16]; the area per mole being the inverse of F*. The other difference is that in our approach we do not have to introduce single chemical potentials in the surface layer (//l^'s) because these are automatically equated to those in the bulk via Gibbs' law. So, making some assumption regarding the shape of the relation between JLI^ and n'^ is not necessary. This does not mean that it is not possible to derive such a relation. In fact, in the model for exchange in a binary system as in [4.2.9] we would not find ju^ but the difference JJ.^ - fi^, which depends on composition through an RTlnO/(\-6)
term, the Rr\n(\-6)
contribu-
tion taking the place of the yA in [4.2.20]. The conclusion is that, after all, there is no difference of principle, rather of convenience and convention. We adhere to the lUPAC recommendation and to the fundamental exchange principle. However, for more-component systems the alternative thermodynamic approach has advantages because exchange is then more cumbersome to describe. The remaining problem is how to interpret the parameters in the equation, particularly for non-ideal mixtures and/or mixtures with molecules of different sizes. For instance, in equations like [4.2.20] there is some ambiguity in the way of assigning parts of the deviations from ideality to RT In J^ and to yA^, since both terms refer to intermolecular interaction. Regarding the surface excess, it may be repeated that r^^ and r^^ are ill-defined; what is analytically measured from depletion of the bulk is F^"^ = -FJ"^, hence this excess should occur in the equations. We shall not analyze this interesting issue further. These models do by no means exhaust the literature. Several of them are variations and have little independent meaning. Eberhart^^ assumed that the tension of the mixture could be represented as the weighted average of the components y = {\-e)y\
+Oyl
[4.2.26]
Deeper analysis requires of course another assumption for the isotherm
6(x].
Gaines^^ modified our lattice approach for r-mers (sec. II.2.4e) in the ' / A ' approach, including a pair interaction energy parameter p. His equations are * Y = Y,-^
RT , ^i r-1 / a \ — 1 - ^ ^ — ( < - ^ ^ ) - ^{(Pof A -^
1^ J.G. Eberhart, J. Phys. Chem. 70 (1966) 1183. 2) G.L. Gaines Jr., J. Phys. Chem, 73 (1969) 3150.
[4.2.27a]
GIBBS MONOLAYERS
^2
FT rA
4.15
[4.2.27b]
where the cp's are volume fractions. He found a good fit for m i x t u r e s of hydrocarbons, liquid metals a n d several organic mixtures ^K A third group of interpretations is b a s e d on the statistical t h e r m o d y n a m i c s of surfaces; essentially either u s i n g [2.3.5 a n d 2.4.6] or extending t h e molecular dynamics simulation of sec. 2.7 to multi-component systems. The advantages a n d disadvantages of these approaches have been discussed before. An essential elem e n t is t h e proper choice of the intermolecular interaction pairameters a n d their distance dependence. Often there is some arbitrariness in this choice, which can be a posttori validated by showing t h a t sets of d a t a also serve well in accounting for other experimental observations. If Lennard-Jones pair interactions are used, the distance (cr ) a n d energy (u ) p a r a m e t e r s for a pair of dissimilar a t o m s or molecules are often related to those of the like-like interactions in first approximation via a n algebraic (cr^. = i ( o " +o- )) a n d geometric average (u.. =(u^.u )^^^), respectively, w h e r e t h e latter average c o r r e s p o n d s to t h e Berthelot principle, [2.11.18]. Truncation of the range of interaction is another issue. As compared to single component interfaces, mixtures require more computer time a n d t h e rule is
Figure 4.7. Excess surface tensions as a function of the mole fraction of the second component for carbon monoxide + nitrogen (T = 83.82 K), methane + argon (T = 90.67 K) and for carbon monoxide + methane (T = 90.67 K). The excess is counted with respect to linearity. (Data taken from F.B. Sprow, J.M. Prausnitz, Trans. Faraday Soc. 6 2 (1966) 1105.) Drawn curves are only meant to guide the eye. 1) G.L. Gaines Jr., Trans, Faraday Soc. 65 (1969) 2320.
4.16
GIBBS MONOLAYERS
t h a t it is relatively easier to obtain density profiles in t h e interface for t h e two c o m p o n e n t s t h a n t h e surface tension a n d its t e m p e r a t u r e dependency. Illustrations a r e s c a n t y ^^ b u t more may be expected w h e n more powerful c o m p u t e r s become available. S u c h simulations c a n also contribute to deconvoluting r^"^ a n d r^^ into analytical excesses. By way of illustration we shall now discuss some examples from the literature. The first c o m e s from Sprow a n d P r a u s n i t z a n d c o n c e r n s m i x t u r e s of simple liquids (fig. 4.7).The figure does not give absolute values of y{x) b u t r a t h e r t h e deviation from linearity, i.e.
from y(x) = (1 - x)/* + x / * . The limiting values a r e
7* = 7.42 mN m-i at 83.82 K, /* IN^
= 17.78 mN m'^ at 90.67 K. /
i^il^
= 9.02 mN nr^ a t CO
83.82 K and 7.65 mN m-^ at 90.67 K and y* = 11.65 mN m-^ at 90.67 K. These d a t a ' Ar
are very close to those in table A1.4. The curves illustrate well t h e t r e n d s found above; with increasing non-ideality (downward in the figure), the deviation from the straight cross-over (Ay = 0) increases a n d a t the same time the curve becomes more skewed. The a u t h o r s u s e d [4.2.23] for their analysis, interpreting the activity coefficient via t h e Hildebrand method, a n d finding A^ from the molar volume of i in solution. In t h i s way they could account satisfactorily for the d a t a in fig. 4.7. Making a choice for Aj is a recurrent a n d cumbersome issue-^^ since in real binary liquid surfaces the molar volumes are larger t h a n in bulk, a n d depend on position 2.
Following sec. 4 . 2 . 1 , negative values of Ay m e a n surface e n r i c h m e n t with t h e lower y* c o m p o n e n t . As long a s t h e mixing is simple (mixing m o r e or l e s s a t h e r m a l , n o t too large size differences, n o specific p a i r interactions)
this
behaviour is the expected one, and the above example is a good illustration. On t h e other h a n d , if special s t r u c t u r e s are built in the interface, say by hydrogen bridges or b e c a u s e the s t r u c t u r e s of the molecule promote a special packing, positive Ay's may also be expected. The triad CH4 + Kr, Kr + NO a n d CH4 + NO exhibits negative Ay's, although NO associates in the liquid state. This triad w a s also analyzed by a microscopic m e a n field theory, using a grand potenticil^\ Most organic mixtures have negative Ay's, for instance n-pentane + dichlorometheme'^^ see fig. 4.8, a n d benzene + n-hexane and acetone + iso octane^^, all at 20 or 25°C. On the other heind, n-dodecane + n hexane, a n d n-dodecane + 2.2.4-trimethylpentane showed positive
^^ Examples are M. Matsumoto, Y. Takaoka and Y. Takaoka, J. Chem, Phys. 9 8 (1993) 1464 (water-methanol) and A. Pohorille, I. Benjamin, J. Chem. Phys. 9 4 (1991) 5599 (water-phenol). 2) See for instance S. Nath, J. Colloid Interface Set 209 (1999) 116. ^^ J.C.G. Calado, A.S. Mendonga, B.J.V. Saramango and VA.M. Soares, J. Colloid Interface Set 185 (1997) 68. ^^ M.L.G. de Soria, J.L. Zuvita, MA. Postigo and M. Katz, J. Colloid Interface Set 1 0 3 (1985) 354. ^^ D. Papaioannou, C. Panayiotou, J. Colloid Interface Set 130 (1989) 432.
GIBBS MONOLAYERS
4.17
0.4
0.6
0.8 X (pentane)
Figure 4.8. Excess surface tension A/ for the dichloromethane-n-pentane system at 298.15 K, as a function of the mole fraction of the second component. Redrawn from de Soria et al., loc. cit. A/'s^K Bardavid et al.^) reported positive deviations A/ for m i x t u r e s of 1,1.1,trichloroethane a n d propanols a t 2 9 8 . 1 5 K. Positive A / ' s were also found for mixtures of 1-propanol a n d n-propylamine or n-butylamine^K The sign of Ay is determined by which of the two components preferentially enriches t h e surface (fig. 4.4b). An example of a convex /(x) curve, relating to hydrogen-bonding
fluids,
is given in fig. 4.9. The reader can find more data on the surface tension of mixtures in appendix 1, tables A 1.16-18. The molecular interpretation of y(x) or A/(x) curves r e m a i n s so far mainly restricted to the simpler systems. Molecular dynamics simulations s u p p o r t t h e conclusion t h a t if A7 < 0 the lower 7* liquid enriches the surfaces, see refs. ^'^^• Sullivan^) derived analytical expressions for the distributions p^z) a n d p^z)
in
the surface on the basis of van der Waals' theory (sec. 2.5), a s s u m i n g t h a t for a
1) R.L. Schmidt. H.L. Clever, J. Colloid Interface Set 26 (1968) 19. 2) S.M. Bardavid, G.C. Pedrosa and M. Katz, J. Colloid Interface Set 165 (1994) 264. ^^ D. Papaioannou, A. Magopoulou, T. Talilidou and C. Panayotou, J. Colloid Interface Set 156 (1993) 52. 4) D.J. Lee, M.M. Telo da Gama and K.E. Gubbins. Mol Phys. 53 (1984) 1113. ^) E. Salomons, E. Mareschal, J. Phys. Condens Matters (1991) 3645. 6) D.E. Sullivan. J. Chem, Phys. 77 (1982) 2632.
4.18
GIBBS MONOLAYERS
s e
Figure 4.9. Surface tension of mixtures of water (component 1) and sulphuric acid (o) or hydrazine (A) at 25°C (component 2). Graphs constructed at 50°C from data by ^\ mixture the a - p a r a m e t e r obeyed Berthelot's rule: a
=(^11^22^^^^ ^ ^ ^ a s s u m i n g
equal sizes. Tarek et al.^) mimicked t h e e t h a n o l - w a t e r surface by MD. This mixture exhibits relatively strong negative deviations from linearity, a s sketched in fig. 4 . 1 , curve 3 . At a mole fraction for the adcohol of 0.1 they found t h a t at t h e surface t h e latter molecules orient with the OH-moiety towards the solution; b e n e a t h this alcohol layer there w a s a water-rich layer, apparently b e c a u s e water molecules prefer hydrogen b o n d s with other water molecules over those with the hydroxyl group of t h e alcohol. This, a n d similar simulations, are extensions of those for mono-component fluids, discussed in sec. 2.7. 4.2c
From yto
7^"^
The starting equation is [4.2.8b], from which, at constant temperature ,
r
(n) _ _ j n ( n )
_
-r;"'=-(i-x)
[4.2.281
^^ C. Wohlfarth, B. Wohlfarth and M. Lechner, Surface Tension of Pure Liquids and Binary Liquid Mixtures, Springer (1997). 2) M. Tarek, D.J. Tobias and M.L. Klein, J. Chem, Soc. Faraday Trans. 92 (1996) 559.
GIBBS MONOLAYERS
4.19
^ 6 ^ 6 " ^6^14
0.4
0.6
0.8 X (linear he)
Figure 4.10. Surface excess isotherms of linear alkanes (he), with different chain length n, in mixtures with benzene. Temperature 30°C. (Redrawn from Schmidt and Clever, loc. cit.) The differentiation needed can be carried out if the relation between /i^ a n d x is known, t h a t is, if activity coefficients in the bulk are available. It is noted t h a t activities in the surface layer are not needed; this simplifies the analysis. By way of illustration fig. 4.10 gives some r e s u l t s for b i n a r y h y d r o c a r b o n mixtures by Schmidt a n d Clever ^^ The surface excess isotherms are derived from [4.2.28] for mixtures of benzene a n d linear hydrocarbons of varying lengths n. The b u l k w a s a s s u m e d ideal, b u t in a few cases where activity coefficients were available a n d introduced, this did not significantly affect the results. In t h e surface, linear h y d r o c a r b o n s are preferred over benzene. It is seen t h a t with increasing length the m a x i m u m shifts to lower x^
values. In the mixture with dodecane the
excess isotherm even exhibits a concave over part of the isotherm. Qualitatively, this trend agrees with the earlier observation t h a t t h e more volatile c o m p o n e n t enriches the surface. However, the trend predicted in fig. 4.3 for the position of the m a x i m u m in relation to the excess F^"^ is not recovered. Apparently, t h e model underlying t h a t figure is too simple for the present system. The set of surface excess isotherms c a n n o t be u s e d to derive individual isot h e r m s ; eq. [4.2.3bl c o n t a i n s two u n k n o w n s . So a n additional a s s u m p t i o n is needed. The a u t h o r s took F^A^ "''^2^2 " ^ (results not shown). Equation [4.2.26] might be a n alternative. Analyses like the one leading to fig. 4.10 can of course be extended to all literature d a t a available.
1^ R. Schmidt, H.L. Clever, J. Colloid Interface Set 2 6 (1968) 19.
4.20
GIBBS MONOLAYERS
In this way we reach the limit of what thermodynamics can tell us. The results obtained may be amplified and validated by additional experimental techniques (as in sec. 3.7) and/or by simulations. 4.2d A note on the surface excess entropy If the temperature dependence of the surface tension is known, it is possible to obtain additional structural information by thermod5niamic means. In principle, by differentiation of the surface tension with respect to the temperature we can obtain the surface excess entropy, which carries such information. However, the required analysis demands some scrutiny. Consider [4.2.7], which is rigorous (at given pressure) and contains S^, the excess entropy per unit area with reference to the surface entropy that a reference system with mole fractions (1 - x) and x would have up to the surface. From [4.2.7] we eliminated one of the chemical potentials using the Gibbs-Duhem rule as (1 - x)d)Uj + xd^^ - ^ • However, if the temperature becomes variable, the Gibbs-Duhem rule must be extended to S dT + (1 - x)d//, + xd/i, = 0 m
' 1
[4.2.29]
' 2
where S^ is the molar entropy of the bulk {=S/(n^ "•"^2^^' ^^^ [1.2.13.5]. So, if [4.2.29] is used to eliminate one of the chemical potentials, the surface excess entropy acquires an additional term; in [4.2.8a and b] sf""^ stands for (S^ - T^^^^S^) or (S^ - r^^S^). respectively; dy =- (S^ - rl^'^S )dT - - i — ^ '^
'
a
i
m
'
[4.2.30a]
^
r^^^dii dv = - (S^ - ri^'^S )dT - - 2 _ I 2 . ^
' a
2
m'
[4.2.30b]
(l_j^)
Considering these equations it becomes clear how elaborate the analysis is, all terms, except x depend on T. However, as, in principle, y[T,x) is measurable, so is r^"^ at each T, and hence, r^''\T,x). As ju^ =/i° + KT In/^x^, differentiation gives -S^ + K In f^x^ + RTd In JJdT. Only if all these terms are properly accounted for can S^ be obtained. This procedure requires extremely accurate data over wide ranges of T and x. Although surface entropy computations have been published in the literature the author is not aware of studies executed with such detailed scrutiny. Certainly much remains to be done. 4.3 Dilute solutions of simple molecules As a counterpart to the previous section consider now solutions of sparingly soluble substances, consisting of uncharged, non-polymeric molecules. As long as the solutions remain dilute (x, « x ) the Gibbs surface excess r/"^ or r/^^ now i
w
i
i
GIBBS MONOLAYERS
4.21
coincides with the analytical surface concentration F^, see sec. 1.2.22c, so t h a t we arrive a t the most simple variant of the Gibbs equation d / = - S ^ d T - r^djd^
[4.3.1]
dy = - r^d/ij
(T const)
[4.3. la]
dy =- RTr^ d In Xj = - RTF^d In c^
(T const; ideal solution)
[4.3. lb]
By m e a s u r i n g / a s a function of I n c t h e adsorption i s o t h e r m is immediately found: r= i
^ RTdlnc.
[4.3.2]
Since for c^ -^ c^(sat) the surface also becomes s a t u r a t e d with i, a concave r^(c^) isotherm with a n initial steep rise a n d a plateau is often obtained. 4.3a
Experimental
techniques
The b a s i c determination of interfacial tension w a s adequately described in c h a p t e r 1. It may be noted t h a t for some a d s o r b a t e s the recoverable range is narrow, so t h a t accurate experiments will be needed. W h e n t h e solute is only sparingly soluble b u t volatile, m e a s u r i n g t h e partial vapour p r e s s u r e may help to determine d^^. For the dilute systems u n d e r consideration Dalton's law for the pressure in the mixture, (p^ + p^)V = RT{n^ "•" '^w^' ^^^ [1.2.17.3], is vcdid. Then we may u s e [1.2.17.19] for the chemical potential; ^^(sol.) = fi^ =iil + RThix^+RT
ln(p / p^)
[4.3.3]
where t h e daggers refer to s t a n d a r d states; jj.^ being equal to G^^, the s t a n d a r d molar Gibbs energy of i in the vapour. The partial pressure of i can be introduced via p^ = XjP, so that at fixed T dfd. (sol.) = RTd In p^
[4.3.4]
This method w a s described some time ago by Ottewill's group ^K For a n u m b e r of organic s u b s t a n c e s , including n - p e n t a n e , n - h e x a n e , anisole, chloroform a n d c a r b o n tetrachloride, 7t{p ] or y(p ) isotherms appeared convex a n d obeyed t h e Szyszkowski equation (see below, [4.3.13]). Long ago McBain a n d co-workers-^^ tried to verify Gibbs' law by actually determ1) See for instance, D.C. Jones, R.H. Ottewill, J. Chenh Soc, (1955) 4076; D.C. Jones, R.H. Ottewill and A.P.J. Chater, Proc. 2nd Int. Congress Surface Activity, Butterworth, (1957) 4076; M. Blank, R.H. Ottewill, J. Phys. Chem. 6 8 (1964) 2206. 2) J.W. McBain. C.W. Humphreys, J. Phys. Chem. 3 6 (1932) 300; J.W. McBain, R.C. Swain, Proc. Roy. Soc. A154 (1936) 608.
4.22
GIBBS MONOLAYERS
ining adsorbed a m o u n t s . They did so by slicing off a thin layer (~ 0.1 mm) from a large area (- 1 m^). This procedure is known a s the microtome method. S u c h types of p a i n s t a k i n g experiments do of course neither confirm, nor challenge the validity of rigorous thermodynamic equations b u t r a t h e r check their applicability to real systems. Another a p p r o a c h for finding adsorbed a m o u n t s a s a function of vapour composition is by gas chromatography. Karger et al.^^ gave a n example. Water w a s immobilized on a porous support. The gas p h a s e percolated over s u c h a plug. First this p h a s e w a s presaturated with water; then organic vapours were added a n d the retention m e a s u r e d . One of their findings w a s t h a t aliphatic hydrocarbons mostly enriched the surface, whereas aromatic compounds accumulated both in the surface a n d the bulk. Given the better solubility of the latter group of compounds, this difference is a s expected. However, / cannot be found by this procedure. Besides t h e s e specific methods, the general arsenal of techniques described in sec. 3.7 r e m a i n s available. So, optical and Volta potential m e a s u r e m e n t s are often invoked to obtain structural information on the monolayers. These techniques do n o t basically differ from t h e c o r r e s p o n d i n g o n e s for L a n g m u i r m o n o l a y e r s . However, surface rheology differs drastically because for Gibbs monolayers t r a n s port to a n d from the bulk is possible. Differences start to appear if the molecules are not very smcdl a n d therefore diffuse with time scales comparable (or shorter) t h a n those of t h e m e a s u r e m e n t s . Therefore this theme will be devloped separately before surfactant monolayers are discussed, see sec. 4.5. 4.3b
Theory
Three characteristics can be used to define the simple Gibbs monolayers t h a t are now u n d e r discussion, viz. the surface tension / (or surface pressure ;r), the surface concentration P. amd the bulk mole fraction x or concentration c,. Between these 1
1
i
there exists a triad of relationships; (i) /"j(Cj) or rXx ) or 0 [x ], the adsorption
isotherm,
(ii) 7t(r^), the surface equation of state, (iii) 7t{c.). Of these, (i) a n d (ii) have been encountered over a n d again. Adsorption isotherms were discussed in some detail in chapters 1.3 and II. 1 and 2. Appendix 1 of Volume II gives a survey of t h e most relevant isotherm equations. The corresponding 2D e q u a t i o n s of s t a t e are repeated a n d extended in table 3.3 in sec. 3.4e. Now we consider set (iii). For each isotherm 7r(c^) is fully determined by ;r(r^) and r^ic^), b u t a s we also have t h e Gibbs equation, relating F to changes
in n a n d c there is
redundancy; 7t[c ) can be obtained in more t h a n one way .
^J B.L. Karger, P.A. Sewell, R.C. Castells and A. Hartkopf, J. Colloid Interface Set 3 5 (1971) 328.
GIBBS MONOLAYERS
4.23
(i) Absence of lateral interaction. Let us first elaborate this for the Langmuir case, accepting the Langmuir premises to be valid. First some technical remarks have to be made. Regarding the choice of parameters, four options for the adsorption isotherm are available; r^(Cj), ^^ix^), 0^{c^) and 0^{x^). The choice is not trivial because in the equations either the product K^c^ or K^x^ occurs, where the Langmuir constant K has different dimensions in these two cases. As to the surface concentration, conversion of the surface concentration F (in mol m"^) into the dimensionless fractional coverage 0j = r / r^Cmax) requires knowledge of the plateau adsorption or, for that matter, of the molecular cross-section in a compact monolayer, a . This quantity is not a priori known, but can be obtained by linearization (sec. II. 1.4a). In fact, linearization is a useful exercise anyway, because it tells us whether the Langmuir equation applies at all. Below we shsdl mainly use the dimensionless sets 0^(x^] and Tt^iOJ, as being the most general. As only one adsorbing component will be considered (which in the present situation is thermodynamically allowed) the subindex i will be dropped. So the starting equations aire (see Il.app. 1) ^ K,x L
l-e
or
e =
Kx ^ 1 + ^L^
[4.3.5]
;ra^=-fcTln(l-^)
[4.3.6]
In [4.3.5] K^ is dimensionless and equal to exp(A^^^Lr^ / KT) = exp(A^^^u/kT) where A^^^LT^ and A^^^u stand for the molar and molecular adsorption energy, respectively. It followed from the derivation (sec. I.3.6d) that A^^^LT^ is an energy containing intrinsic subsystem-dependent entropic contributions, i.e. those entropies that can be counted per adsorbing molecule, say those caused by changes in hydration or vibration. The important configurational entropy is not included; this contribution is accounted for by the shape of the ^dependence. At given temperature, the corresponding dimensionless Gibbs equation reads e =
—
[4.3.7]
KTnniax)d In x Conversion of [4.3.5-7] into other units is straightforward, using e = r/ r(max) x=V
with
a^ = (N^^nmax))'^
[4.3.8a,b]
n
[4.3.9]
m.l
with V
the molar volume of the solvent (component 1). Hence, from [4.3.5 and 6] r
=KV r r(max)-r ^ ™i
or
KV r(max)c j^ ^ __L_nu l + KV c L
m.l
[4.3.10a,b]
4.24
GIBBS MONOLAYERS
and K = RTr(max)ln|
r(max)-r r(max)
[4.3.11]
respectively. Equation [4.3.1 Ob] is often written a s
Kc
[4.3.12]
l + fc^c The two constants k^ and k^ have different dimensions.
With these conversions in mind 7r{x) can be directly obtained by elimination of e between [4.3.5 and 6] 7ta
[4.3.13a]
=kT ln(l + K x)
or Tt = RTrimax)
[4.3.13b]
ln(l + K^x]
Alternatively, from [4.3.5 a n d 7]
dK = RTr{max)\
-—^^— | d In x l + Kx. L J A.
K = RTr(max]
J x*=0
K , d x ' "l 1 + K X' ,
= [4.13b]
It is a matter of taste which route is preferred. Equation [4.3.13] is the Szyszkowski
equation,
after B. von Szyszkowski who
proposed y= l-bln|--l
[4.3.14]
for t h e normalized capillary rise (h - h(pure water)) of a q u e o u s fatty acid solutions^ J. Here x is the concentration of the fatty acid a n d a a constamt. The Szyszkowski equation h a s proved useful for describing the relatively simple adsorptions u n d e r consideration. However, its foundation is at issue b e c a u s e the Langmuir equation was not derived for mobile b u t for localized adsorbates; the translational entropy is not properly accounted for. We r e t u r n to this issue below, in the m e a n time accepting [4.3.13] a s a useful empirical expression. Corresponding analyses c a n be carried o u t for the other i s o t h e r m s a n d 2D equations of state t h a t we have derived. For the simple Henry region everything is linear. The isotherm is N^ / A = K^x 1^ B. von Szyzskowski, Z. Phys. Chem, (Frankfurt) 64 (1908) 385.
4.25
GIBBS MONOLAYERS a n d t h e equation of state r e a d s nA - kTN^.
In this case no 6 c a n be defined
b e c a u s e there is no reference for the maximum n u m b e r of molecules adsorbed. For this reason K ^ is not dimensionless. Elimination of N^ leads to M
7t =
[4.3.15]
kTKx M
The Henry c o n s t a n t depends on the u n i t s in which the concentration is expressed. Linear initial 7t{x] relations are also obtained from the Langmuir a n d Volmer isotherms (see below). Apart from its dimension, K^, (or K^ or K^) is a m e a s u r e of the affinity of the molecule for the surface. The higher it is, the steeper
-[dy/dx]^^^
or (d;r/dx)^^^. More interesting is t h e mobile equivalent of the Langmuir equation. For this case the Volmer model applies. We already derived (see II. 1.5.22 and 23) ^ ^e/n-e) 1-^
[4.3.16]
K^x
and [4.3.17]
kT-
na
a-o) for t h e adsorption isotherm a n d 2D equations of state, respectively. The easiest way of obtaining 7t{x] is to eliminate 6 /{I-6]
between [4.3.17 and 16]. The result is
1.5
1.0
/ y^ ^^
^^^.^^"^
0.5
1
1
1
0.1
0.2
0.3
1
0.4
Figure 4.11. Surface pressure as a function of solution composition. Comparison between mobile ( ) and localized ( — ) adsorbates.
4.26
GIBBS MONOLAYERS
!^^^^m/^
=K^x
[4.3.181
This is the mobile equivalent of the Szyszkowski equation [4.3.13a]. Alternatively, a mobile equivalent of [4.3.13b] could be formulated. It is interesting to establish by how much the surface pressure differs between a localized and a mobile adsorbate. To that end such a comparison is made in fig. 4.11. All curves are convex with respect to the concentration axis. (For these models the surface pressure is conueAras a function of 6, see fig. 11.1.15b). However, the curvature differs between the two types of adsorbates. In practice, mostly the initial part of 7t{c) will be analyzed; because for sparingly soluble solutes only low values of x are attainable. Moreover, for interpretational reasons, at higher ;r's the premise of absence of lateral interaction breaks down. So, if experimental data are interpreted in terms of one of these models only this part tends to be investigated. From the figure it then transpires that by adjusting K^ one can satisfactorily match the, theoretically preferable, 'mobile' curve. Regarding the value of the constant, for a given type of molecule K^ should exceed K^ by about a factor of e ~ 2.7, corresponding with the two degrees of freedom (2 x i kT) that a mobile molecule possesses over a localized one. (The Henry slope in G{c) for a mobile adsorbate exceeds that of a localized one by this factor, see fig. II. 1.15a). Therefore in fig. 4.11 the pair to be compared is the K^ = 9 with (about) the K^ = 3 curve. These differ substantially. However, in practice one gets away with applying the (localized) Szyszkowski equation with the (mobile) constant K^. (ii) Presence of lateral interaction. All of the above is restricted to the initial parts of the isotherms. One step further would be to account for lateral pairwise interaction. For both types of monolayers this can be implemented via the virial route, or in terms of the Frumkin-Fowler-Guggenheim (FFG) or 2D Van der Waals equation, applying to localized and mobile monolayers, respectively. For monolayers the latter is the more appropriate. The relevant equations are, see Il.app.l, _6_
^em-B) ^-2a<'«/a„M- ^ ^ ^ ^
( 4 3 ^g,
for the adsorption isotherm, and f K +
^ao ^^r 2 ^
[A-Najj = NhT
Ka =fcT - ^ [i-ej
- ^5L.5/2 a^
[4.3.20a]
[4.3.20b]
for the 2D equation of state, respectively. As compared to [4.3.16 and 17] the additional parameter is the 2D Van der Waals constant for the surface layer, a^.
GIBBS MONOLAYERS
4.27
Elimination of 6 between [4.3.19 a n d 20bl is cumbersome; numerical solutions appear more suitable. (Hi) Surface excess entropies.
Basically, from the t e m p e r a t u r e d e p e n d e n c e of
the surface tension S^ can be derived. For binary mixtures, this is a complicated procedure (sec. 4.2d). However, for dilute solutions it is easier. Equations [4.2.8a and b] for the Gibbs equation now reduce to d r = S^dT - r d l n ^ = - S ^ d T - RTF din fx
[4.3.21]
where S^ and F may now be identified with the real, or analytical, surface excess entropy per u n i t area a n d surface concentration, respectively. In the m o s t right h a n d expression /
a n d x are the activity coefficient a n d mole fraction of t h e
solute, respectively. Experiments on the t e m p e r a t u r e dependence of the surface tension are invariably carried out at fixed composition. When /
d e p e n d s on the
temperature, activity data are needed to convert constant x into c o n s t a n t fx.
For
this dependence no genered rules can be given, although of course parametrization in t e r m s of a model is possible (say, in terms of a regular solution model). Here we shall a s s u m e t h a t / is independent of the temperature. Differentiation of [4.3.21] with respect to T jrields
-^1 =-S°
[4.3.22]
For t h e implied infinitesimal c h a n g e s of y with T the factor RTF c o n s t a n t . Generally, however, the derivative dy/dT
remains
also d e p e n d s on T . From
[4.3.22] S^ will eventually be obtained a s a function of x and T . As, for each T, F is accessible a s a function of x , it is also possible to derive the surface excess entropy a s a function of the monolayer composition. Accurate d a t a are, a s before, a prerequisite. From S^ the surface excess enthalpy H^ = TS^ is obtainable. Alternatively, one c a n differentiate y/T
with respect to the temperature, obtaining the
enthalpy directly using the appropriate Gibbs-Helmholtz relation. 4.3c
A case study;
alcohols
Primary, u n b r a n c h e d , aliphatic alcohols belong to the groups of most-studied solutes b e c a u s e they are uncharged and, by varying the chain length, t h e entire s p e c t r u m between full miscibility with water (C^OH-CgOH)^) via partial miscibility a l m o s t to insolubility, c a n be covered. Notwithstanding t h e simple molecular structure, the n(x, T) curves exhibit a n u m b e r of interesting fine-structures. Figure 4.12 is taken from a study by N e a m a n d Spaull-^^ Surface tensions were m e a s u r e d by the drop-volume method a s a function of chain length (C40H-CgOH)
^^ We use the same abbreviation as in sec. III.3.8b, table 3.7a. 2) M.R. Neam, A.J.B. Spaull, Trans. Faraday Soc. 65 (1969) 1785.
4.28
GIBBS MONOLAYERS
2 3 molal xlO~^ Figure 4.12. Surface pressure isotherms for aqueous solutions of n-C40H (a) and n-CgOH (b). The temperature is indicated. (Redrawn after Neam and Spaull, loc. cit.) a n d t e m p e r a t u r e over a limited range (10°, 25° a n d 40°C). The figure gives K(C) curves, the concentrations expressed a s molalities, for the lowest a n d highest term of the series. The others (not shown) take intermediate positions. Similar curves have been obtained by other authors^-^'^^'^l The first, a n d expected, trend is t h a t the surface activity increases steeply with increasing chain length (compare t h e abscissa axes in panels (a) a n d (b). In this direction the solubility decreases rapidly, b u t the two t r e n d s are not exactly similar because transport of molecules from the solution to the pertaining bulk p h a s e is different from t h a t to a n adsorbed monolayer. The lower m e m b e r s have concave n(c) curves, for which a Szyszkowski or Volmer equation should be tried (which Nearn a n d Spaull did not do). For t h e higher members (C^OH and CgOH), the initial part is convex. This w a s also found by Clint et al^l (In passing, curves plotted a s ;r(lnc) are convex over the entire concentration rainge, j u s t as is the ;r(ln p) curve for adsorption from the vapour p h a s e (see 14.3.4 a n d 21]). So, the initial affinity of the higher alcohols is relatively lower t h a n t h a t at higher pressure. 1) W.D. Harkins, R.W. Wampler, J. Am. Chem. Soc. 53 (1931) 850. 2) A.M. Posner, J.R. Anderson and A.E. Alexander, J. Colloid Set 7 (1952) 623. 3^ J.H. Clint, J.M. Corkill, J.F. Goodman and J.R. Tate, J. Colloid Interface Set 28 (1968) 522. "^J R Vochten, G. Petre, J. Colloid Interface Set 42 (1973) 320. ^^ loc cit.
GIBBS MONOLAYERS
4.29
74< \ 72<
\
1
\
B 70,
g \ ^ ^^ 66 64
\
\
\
\
\
■ "^x \
\
\
62 V
60
\
N. N . >y25°C 40°cN>
58 1
i
0
1
1
■
?
■
1
8xl0"2molal
Figure 4.13. Surface tension of aqueous butanol solutions at three different temperatures. (Redrawn from Neam and Spaull, loc. cit.) There is a small, but systematic, decrease of the surface pressure with increasing temperature. As K equals 7(pure water) - /(monolayer) the temperature coefficient represents 0 ( 0 ) _ oOTn
[4.3.23]
using the symbols of sec. 3.4b. We note that S^^^ is the small difference between two, almost equal, large quantities. The temperature effect is better bom out if /(c) is plotted at different temperatures. For C4OH this is shown in fig. 4.13. For c up to about 0.04 molal the curves are almost peirallel, implying that d / / d T for pure water and for C4OH monolayers is very much the same. In other words, the presence of butanol molecules in the interface has, at the degrees of coverage considered, little influence on the number of degrees of freedom, compared with that in the bulk of the solution. In sec. 2.9a the relative invariance of S^ over a large group of different pure fluids (fig. 2.14) was attributed to the combination of two features; (i) S^ is primarily determined by the entropy of the mixing of holes and molecules and (ii) the density distribution is essentially of the tanh z type. The finding that for monolayers of alcohols S^ differs so little from that of pure water should then imply that the density distribution is not significantly perturbed. Neutron scattering
4.30
GIBBS MONOLAYERS
2
3
4
N^/ A (molec. nm"^) Figure 4.14. Volta potentials for Gibbs monolayers of n-butanol (•) and n-heptanol (o) as a function of surface concentration. Temperature, 25°C. (Redrawn after Posner et al., loc. cit.) experiments on Gibbs monolayers of b u t a n o l a n d hexanol confirmed this conclusion 1^. Two other pieces of structural information can be derived from this scattering study. First, the molecules are oriented almost normal to the surface, a n d second, the molecules a d s o r b with their hydrophobic moieties out of the water. This last feature is according to expectation a n d we have met this orientation before a t water-silver iodide interfaces, see fig. II.3.77 (in sec. II.3.12d). A n o t h e r a r g u m e n t for t h e vertical orientation s t e m s from Volta potential m e a s u r e m e n t s , see fig. 4.14. The surface concentrations cover the range u p to n e a r saturation. (According to Vochten and Petre (loc. cit) the molecular cross section a t near-saturation a m o u n t s to 0.27 nm^ for the series from n-C40H to n-CjoOH.) So, given the linearity of the AV -plot, there is no argument for a change in orientation with coverage. In addition, there is little influence of the chain length either. As AV = pN (cosO)/ £ £, see [3.7.22], this m e a n s t h a t most of the normal component of the dipole m o m e n t is determined by the orientation of the OH-group, or, more precisely, the excess orientation of the OH-groups over t h a t of the p u r e water. In sec. II.3.9 we concluded t h a t at the free surface of water the negative sides of the water molecules are pointed outward, with a surface ;^-potential of a b o u t 80-130 mV. So we may conclude t h a t the presence of the hydrophobic group reinforces this orientation, in line with expectation. From the slope of the lines in fig. 4.14 t h e ratio p ^ / £ c a n be deduced, b u t further analysis is academic b e c a u s e e is n o t ^^ Z.X. Li, J.R. Lu, R.K. Thomas, A.R. Rennie and J. Penfold, J. CheirL Soc. Faraday Trans, 92 (1996) 565.
GIBBS MONOLAYERS
4.31
known. This ratio is systematically somewhat lower for heptanol t h a n for b u t anol. Two explanations for this difference c a n be p u t forward; either t h e heptanol molecules a r e more tilted, or a slight compensating polarization takes place inside t h e h y d r o c a r b o n c h a i n . However, given t h e relatively large deviations from linearity a t low N^, the trends m u s t not be overinterpreted. Although S^ a n d AV a r e relatively aspecific quantities, t h e surface excess e n t h a l p y H^ a n d related e n t h a l p i e s a r e specific, reflecting t h e c h a i n length influence on t h e adsorption energetics. Recall t h a t a similar trend is observed for evaporation a n d for t h e creation of surfaces of p u r e liquids (sec. II.29a); for t h e s e two p h e n o m e n a t h e enthalpies cire specific, whereas t h e corresponding entropies are r a t h e r generic (Trouton's rule for evaporation a n d for surface formation). T h e most detailed study h a s been cairried o u t by Vochten emd Petre^^. These a u t h o r s observed t h a t if wider temperature ranges are studied u n d e r several conditions, t h e surface tension does not continue to decrease, b u t passes through a m i n i m u m (fig. 4.15). T h e inference is t h a t a t high t e m p e r a t u r e s H^ =TS^ m a y reverse sign.
70
E 6 •^0^
"^^^o—o—o—o—o
60
-6.31 xlO""^ -8.00 xlO-^ -1.00x10"^ -1.30x10"^ -1.59x10"^ -2.00x10"^
50
. / o**^
5.00x10"^
^**o ^ 0 — 0 ^ 0 — 0 — 0 - ^
"\.
40
. /
7.60 xlO"^
^^o 'O*—iO—.0—0-—O**
30
_L
0
20
JL
40 60 °C temperature
Figure 4.15. Temperature effect of the surface tension in Gibbs monolayers of n-heptcinol, the concentration of which is given in moles dm"^. (Redrawn from Vochten and Petre, loc. cit.)
R. Vochten, G. Petre, loc. cit.
4.32
GIBBS MONOLAYERS
I5h*< o
10
s 5h ^
C40H
< C50H CgOH
-10
C70H
-15 -20
CgOH -25
C9OH
-30
J_
0
10
20
J_
30 40 50 temperature
-1_ 60
70 °C
Figure 4.16. Enthalpy of adsorption of n-alcohols at the water-air interface for concentrations close to saturation. (Redrawn from Vochten, Petre cind Defay (1973) loc. cit.) indicating a change in the driving force balance for adsorption. The adsorption of C7OH continues to decrease with increasing temperature. To obtain H^ a more complete equation t h a n [4.3.22] is needed; since large variations of y with t e m p e r a t u r e are now considered, F may no longer be considered constant. It c a n be obtained from the y(lnx) plots. Vochten et al.^^ elaborated this in detail and, taking the proper reference condition in the solution into account, eventually arrived at the reversible enthalpy of adsorption. Figure 4.16 gives one of their r e s u l t s . It refers to n e a r - s a t u r a t i o n a n d d e m o n s t r a t e s t h e enthalpy reversal a n d the chain length effect. In the studies by Clint et al., a n d Nearn a n d SpauU, mentioned before, m u c h narrower t e m p e r a t u r e r a n g e s were s t u d i e d . Nevertheless, t h e last-mentioned a u t h o r s did also observe t h e sign reversal a n d found adsorption enthalpies comparable to those in fig. 4.16. For t h e interpretation of this figure (not given by the authors) two observations deserve attention; (i) t h e sign reversal, from e n d o t h e r m i c to exothermic, a s a function of increasing temperature a n d
1^ R. Vochten, G. Petre and R. Defay, J. Colloid Interface Set 42 (1973) 310.
GIBBS MONOLAYERS (ii) the magnitude of A
4.33 H
.
As to the former, positive values of A ^ H
imply t h a t a d s o r p t i o n is ener-
getically unfavourable, so t h a t the process m u s t be entropiccdly
driven. At higher
t e m p e r a t u r e s adsorption is also energetically driven (probably in conjunction with a n entropic drive). As to item (ii) A
H ^ is low. It is m u c h less t h a n t h e
enthalpy of breaking or forming hydrogen b o n d s . The enthalpy of s u c h a b o n d is 0 ( 2 0 kJ). For 4 to 9 CHg-groups, if each of these, upon leaving the water, would lead to the reformation of only one such bond, the total enthalpy effect would be 80 - 180 k J mole-^ According to recent insight into hydrophobic bonding ^^ these two features aire typical. Because of the open structure in fluid water, CHg-groups can be introduced or removed without making or breadcing hydrogen b o n d s . The enthalpy effect is mainly determined by changes in the n u m b e r of repulsive H2O-H2O contacts, a n d the entropy gain upon removal of a CHg-group results from the increase in the configurational n u m b e r s of freedom of forming the various intramoleculcir contacts. In the mccin time the features of sign reversal a n d low absolute enthalpies have been experimentally observed over a n d again for processes involving hydrophobic bonding, s u c h a s adsorption of surfactants on hydrophobic adsorbents a n d micelle formation. So, against this b a c k g r o u n d the t r e n d s of fig. 4.16 are immediately interpreted a s being primarily caused by hydrophobic bonding. On top of this come Van der W a a l s interactions. Upon transfer of a n alcohol molecule from t h e solution to t h e monolayer, the attractive CH2-water interaction is lost, b u t CHgCH2 interactions are gained because, a s found above, the hydrophobic c h a i n s stick out a n d interact laterally (bear in mind t h a t fig. 4.16 deals with near-saturation). From the observation t h a t the C9OH curve is more negative t h a n the C4OH one, it is inferred t h a t on balance the Van der Waals exchange is slightly favourable. We repeat though, t h a t A H
is mainly determined by the hydrophobic effect; the
sign inversion persists also at low surface concentration. The vertical distance between the curves depends on T, b u t it a m o u n t s to a b o u t 2-2.5 k J per mole of CH2-groups, which at room temperature corresponds to about 1 RT per mole. This is typical a n d sometimes referred to as the quantitative rule (sec.
Traube
IA.5G)'^\
Let u s finally consider w h a t h a p p e n s w h e n the OH-group is not at t h e end position. Table 4 . 1 , also t a k e n from Vochten a n d Petre, illustrates the position effect for nonanol. When the OH-group is shifted from the end to half-way along the chain, t h e molecular cross-section increases, implying a n increasing t r e n d to
^J N.A.M. Besseling, J. Lyklema, J. Phys. Chem. 101 (1997) 7604. (This paper revisits the treatment given in sees. I.4.5e and 1.5.4.) 2) After I. Traube, Ann. 265 (1891) 27, who observed that for each additional CH^-group the concentration needed to produce a certain surface tension lowering was reduced by about a factor of 3. (RTln3 = 2.67 kJ mole"').
4.34
GIBBS MONOLAYERS
Table 4.1. Molecular cross-sections and adsorption energies of nonanols. Temperature 15°C. Type of molecule
a , 1 nm^ mi '
1-nonanol 2-nonanol 3-nonanol 4-nonanol 5-nonanol
0.27 0.33 0.42 0.50 0.52
A,H ads
/kJmole"^ m
5.65 9.21 13.10 14.94 15.50
adsorb flat. Energetically speaking, upon this shift it becomes more difficult to adsorb. The probable reason is the decreasing options for CH2-CH2 contacts in the monolayer. Displacement of the OH-group from the end to the centre of the molecule makes it more surface active. This was experimentally confirmed by Jachimska et al.^^ for butanols. These authors found that in this direction the foamability also improved. As upon this displacement the enthalpy of adsorption becomes more endothermic, the increased surface activity must be entropically determined. In conclusion, this case study illustrates how such Gibbs monolayer studies, if carried out over sufficiently wide temperature ranges, with enough related adsorbates and analyzed with scrutiny, do give a consistent picture and hence contribute to the understanding of the mechanism of the underljring transfer processes. 4.4 Simple electrolytes In this section we introduce the development of electric double layers under the most elementary conditions, viz. those caused by simple electrolytes. By 'simple' we understand; containing ions without sizeable hydrophobic groups that would drive these ions towcirds the interface. This matter has already been discussed in sees. II.3. lOf and g and in sec. II.3.9 we looked at the poleirization of the surface of pure water, as judged by Volta potential measurements. Here we shall briefly repeat the main findings, extending and updating them. Let us first review the basic assets. (i) Double layers at water-fluid interfaces form spontaneoush^. The driving force is chemical in the sense of 'non-electrostatic'. Electrostatic interactions oppose double layer formation. The situation is the same as for all double layers in dispersed systems (sec. II.3.1). (ii) Double layers are electroneutral They only exist because of the spontaneous unequal distribution of cations and anions at the interface.
1) B. Jachimska. K. Lunkenheimer and K. Maiysa, J. Colloid Interface Set 1 7 6 (1995) 3 1 .
GIBBS MONOLAYERS
4.35
(iii) It follows from (i) that, thermodynamically, the adsorption of electrolytes can be described in terms of electroneutral combinations of ions. For all practical cases this means 'of sadts'. (iv) The resulting surface concentration F of a salt s, can be positive or negative. In the former case adsorption leads to a reduction of y or an increase of n; in the latter case it is the other way around. (v) For phenomena involving tangential flow it is relevant that the surface viscosity of water is the same as that in the bulk. 4.4a The pristine surface of water The density distribution p{z) of water molecules at the water-vapour interface differs drastically from that near a solid (hard) wall. In the latter case p{z) shows some oscillations (sec. II.2.2c), whereas in the former p{z) is gradual, with a distribution resembling that of a tanh(z / ^) profile, depending on the temperature, as discussed in sec. 2.8. The transition layer between bulk water aind bulk vapour is only a few molecular diameters wide, except close to the critical temperature. The surface excess entropy of water is not different from that for all other fluids at temperatures not too far above their melting point (fig. 2.14). According to the best available experiments the surface potential of water, ;i:^ is positive, meaning that in the surface of water either the dipoles are oriented with their negative sides outward and/or OH" ions preferentially enrich the outer sides. In order to build on this information, experiments for obtaining the f-potential of the pure water-vapour interface have been carried out. Such experiments are not easy. First, the water must be extremely pure; even trace amounts of impurities, leaching from vessel walls or CO2 from the atmosphere might adsorb at the interface and drastically eiffect the outcome. If carried out in cells, electro-osmosis has to be eliminated, or accounted for. Then, it is difficult to carry out electrophoresis on rising bubbles and, finally, as LG interfaces in their pristine state cannot resist slip, the Helmholtz-Smoluchowski equation (11.4.3.4] has to be modified. An often applied procedure for mechanically stabilizing bubbles is to rotate them in cylindrical tubes towards the centre. Quincke ^^ applied this idea as long ago as 1861. Kelsall et al.-^^ reviewed this matter 2ind added their own measurements, mostly in the presence of electrolytes. Intentionally added electrolytes obviously swamp the H^ and OH" ions stemming from the intrinsic dissociation of water. Kellsall et al. used a double laser-Doppler apparatus by which the difference between the bubble rise velocity with and without the applied field could be measured. They found the mobility to depend on size and pH, but it could at least be
1^ G. Quincke, Ann. Prog. 113 (1861) 513. 2^ G.H. Kellsall. S. Yang, S. Yurdakul and A.L. Smith, J. Cheni. Soc. Faraday Trans. 92 (1996) 3887.
4.36
GIBBS MONOLAYERS
concluded that at neutral pH the f-potential was negative. Graciaa et al.^^ overcame a number of problems involved in the rotating cylinder technique. For the mobility they used 3.6 f eC
[4.4.1]
T]a(ft)p/r])^/2
where p is the water density and rj the bulk viscosity. This equation was derived by Sherwood^). In its denominator the factor cop/rj has the units [m]"^, so that a[cop/ri)^^^ is dimensionless. Note that we do not have to worry about rj^ being different from rj. Under the right conditions (relatively small bubbles) Graciaa et al. found the ^-potential to be independent of droplet size a and rotational frequency co. Their result for f was -67 mV. The negative sign confirms that of the ;^-potential, and also gives a foundation for the mechanism. Electrophoresis requires chairge separation and, as dipoles camnot charge-separate, the minus sign must be caused by the enrichment of protons to the inner, amd hydroxyl ions to the outer side of the water-vapour interface. This is in line with the generally observed difference in behaviour between cations and anions, see sec. II.3.10f and subsec. 4b below. With respect to the absolute value of the mobile charge, it is very low. Presuming the double layer part at the solution side to be diffuse, with C - V^"* = - 6 7 mV and c = 10"^ M [II.3.5.13a] can be used, to ^
^
s
obtain cj^ = -0.02 ^iC cm"^. It is because of the low salt concentration that such a low mobile charge can give rise to a substantial f-potential. At the same time it is appreciated that only traces of electrolytes will swamp this pristine behaviour. In conclusion, a consistent picture has emerged. Progress continues to be made with theoretical studies and (MD) simulations of the water-vapour interface. For an update see the study by Sokhan and Tildesley*^^ In such studies the dipole and quadrupole orientations are discussed in detail, but the incorporation of free H^ and OH" ions is mostly ignored. Finally, it is interesting to note in passing that the observed spontaineous charge separation becomes manifest if airborne droplets partially freeze. This phenomena is probably at the root of the development of atmospheric electricity. 4.4b Electrolytes at the air-water interface The basic set of information is a collection of /(c ), or K{C ) curves, preferentially as a function of T. As typically low sadt concentrations are involved (mostly ^^ A. Graciaa, G. Morel, P. Saulner, J. Lachaise and R.S. Schechter, J. Colloid Interface Set 172 (1995) 131. 2) J.D. Sherwood. J. Fluid Mech, 162 (1986) 129. ^^ V.P. Sokhan, D.J. Tildesley, The Free Surface of Water: Molecular Orientation, Surface Potential and Non-linear Susceptibility (Molecular Physics Lecturej, Mol Phys. 92 (1997) 625.
4.37
GIBBS MONOLAYERS
below 1-2 M, i.e. x < 0.02), these plots are linear. If plotted a s a function of In x the slope yields the surface excess F . Recall from [II.3.10.25b] t h a t d / = - S^dT - vKTF d In y^c^
[4.4.2]
where v = v + v_, v a n d v being the n u m b e r s of cations a n d anions, created by the dissociation of one molecule of electrolyte, respectively. Factor v a c c o u n t s for t h e n u m b e r of kinetic u n i t s in solution, b u t F a n d c refer to t h e electroneutral s
s
electrolyte. As to t h e n a t u r e of the electrolyte t h e trend is clear; t h e easier t h e ion is dehydrated, the more such aisly it is found at the outside and the more s u c h asly it is positively adsorbed. It is noted, b u t not further discussed here, t h a t the molecular picture of (de-)hydration in a n interfacial layer may differ substantiedly from t h a t in bulk, the latter being well understood (sees. 1.5.3 Eind 4). In fig. II.3.73 in sec. II.3.10f we gave illustrations for K-salts a n d acids. KPFg is positively adsorbed, KCIO3, KNO3, KCl a n d K^SO^ increasingly negative, in t h a t order. For t h e acids H2SO4 is negatively adsorbed. HCl almost not at all, HNO3, HCIO3 a n d HPFg are increasingly positively adsorbed. These trends cire reflected in the Volta potentials (fig. II.3.75)
5h NH4C1
S S
< -5
l\\
N C3NH4CI
-10 C4NH4CI -15 CgNH^Cl -20 0.5
1.0
M
1.5
Figure 4.17. Surface tension increments of aqueous solutions of alkylammonium chlorides; influence of the chain length. Temperature 25°C. (Redrawn from Tamaki^\) 1^ K. Tamaki, Colloid Polym. Set 252 (1974) 547.
4.38
GIBBS MONOLAYERS
Figure 4.18. As previous figure; surface tensions obtained from surface light scattering. Temperature 25°C. (Redrawn from Hard and Johannson, loc. cit.) Figures 4.17 and 18 are additional illustrations. Hexylammonium chloride adsorbs strongly; it resembles a classical surfactant. With decreasing alkyl chain length the surface activity decreases until methyl ammonium chloride and ammonium chloride, which are adsorbed negatively. In line with the trend, replacement of the counterion CI" by Br" or I" favoured the trend towards positive adsorption. Figure 4.18, taken from a paper by Hard and Johannson^^ has the additional feature that the surface tensions have been obtained from surface light scattering, and that a very large bulk concentration range has been studied. As far as comparison with Randies' data, fig. II.3.73 is possible, the two sets of measurements agree well. Specific ionic effects and lyotropic sequences for electrolytes at interfaces can also be inferred from Volta potential measurements^^ Sometimes the question is asked how it is possible that the surface tension of pure water increases by the addition of electrolytes that are depleted from the surface. The answer must be found in the excess nature of molar Gibbs energies (or chemical potentials) in the interface, as compared with those in the bulk. If, by adding a substance to the solution fj. decreases more than ^^ , the surface tension should rise. In formulas, such as /i = //* -i-0RTln(l- x), see [1.2.18.5], where ^ is the osmotic coefficient, /z decreases if x increases. Let a similar equation be vadid for the surface, with 9 replacing x, one arrives at j^^ = jJ*^ + 0°RTln(l- 0), so if 6 increases less than x, fj,^ would become higher than /i , implying an increase S. Hard, K. Johansson, J. Colloid Interface Sci 60 (1977) 467.
2) N.L. Jarvis, M.A. Scheiman, J. Phys. CherrL 72 (1968) 74.
GIBBS MONOLAYERS
4.39
of 7 . In principle, differences between 0 and 0^ can also contribute to the slope of
dy/dlnc. Many more data on y(c) plots for simple electrolytes can be found in two p a p e r s by Weissenbom and Pugh^^ From 7(ln c) plots the surface concentration F can be obtained a n d from these t h e surface charge CT°, a s s u m i n g complete dissociation. We already p r e s e n t e d results in fig. II.3.76 which demonstrated t h a t <7° = 0 ( l - 5 ^iC/cm^), exceeding the contribution by the intrinsic dissociation of water to the double layer by a factor of 102. Using [4.4.21. surface excess entropies can be computed if the surface tension is available a s a function of temperature. Hey et al.^^ and Matubayashi et al.*^^ b o t h found t h a t there is not m u c h difference between dy / dT in electrolyte solution a n d in p u r e water. By way of illustration fig. 4.19 gives surface excess entropies for fairly concentrated solutions of electrolytes with differently charged cation. The inferred values of 0.162 m J K"^ m"^ for S^ of p u r e water is slightly higher t h a n o u r best value 0.141 (table 1.4, average value of -A). Electrolytes have only a m i n o r effect, even u p to 3 mole kg"^ For NaCl a t the water-hexane interface, Ikeda et al."^^ observed a similar trend. For this system, the absolute value of S^ is a b o u t 0.09 mN m"2. In passing, these a u t h o r s cdso gave results on the influence of p r e s s u r e . 0.17-
^ 0.16 ^
V
MgCl2 0.15k
0.14
A
Figure 4.19. The surface excess entropy of aqueous solutions for three electrolytes.. Temperature 25°C. (Redrawn from Matubayashi et al., loc. cit.)
1^ P.K. Weissenbom, R.J. Pugh. Langmuir 11 (1995) 1422; J. Colloid Interface Set 184 (1996) 550. 2) M.J. Hey, D.W. Shield. J.M. Speight and M.C. Will, J. Chenh Soc. Faraday Trans. (I) 7 7 (1981) 123. '^^ N. Matubayashi, H. Matsuo, K. Yamaoto, S. Yamaguchi and A. Matuzawa, J. Colloid Interface Set 209 (1999) 398. 4^ N. Ikeda, M. Aratono and K. Motomura, J. Colloid Interface Set 149 (1992) 208.
GIBBS MONOLAYERS
4.40 They found t h a t {dy/dp]^
is almost the s a m e between the interface with a n d
without electrolyte. So, we arrive at the s a m e conclusion a s with w a t e r - b u t a n o l mixtures (sec. 4.3c); S^ is a fairly invariant property having more or less the s a m e value for p u r e liquids as for mixtures. In this connection it is interesting to note t h a t the dynamics of p u r e water a n d water + electrolyte surfaces are cdso similair. Pcul of the evidence is the similarity between statically a n d dynamicEilly m e a s u r e d surface tension changes (similarity between figs. II.3.73 a n d 4.18). The other refers to t h e relaxation of a q u e o u s surfaces, measured by the oscillating jet method (sec. 1.14). In fig. 1.29 we gave y(t) results for pure water which were characterized by relaxation times T ^ = 0(10"^ s). Figure 4.20 gives corresponding results for NaCl-solutions. In this study the Volta potential relaxation Axit) w a s measured, where Ax s t a n d s for xW ~ X^^^-) • Relaxation times do not differ between pure water a n d electrolyte solutions. The sign of Xit), interesting for its own sake, does not affect our conclusion. It is related to the (re-)distribution of ions n e a r t h e orifice of t h e capillary from w h i c h t h e Jet emanated. Surface tension a n d Volta potential m e a s u r e m e n t s of a q u e o u s electrolyte s u r faces c a n be s u p p l e m e n t e d by electrophoresis s t u d i e s . Although t h e technical problems are the same a s for the water surface in its pristine state, the interpretation is slightly easier b e c a u s e of t h e swamping n a t u r e of the electrolyte. We
\1
IM
50 ^X
30 h 10 10
2VA
101-3
X
^0^>n.^vAA
0
lO'-^s
/
-10
lo-y* -30
-50 Figure 4.20. Surface potential relaxation of water and aqueous NaCl solutions. Oscillating jet method. Temperature 24°C. The electrolyte concentration is indicated. (Redrawn from Kochurova et al.^M
1^ N.N. Kochurova, S. Yu. Dementev and A.I. Rusanov, Zhur. Priklad. Khim. 70 (1997) 683.
GIBBS MONOLAYERS
4.41
mention that Kellsall et al.^^ carried out such studies in NaClO^ solutions at different pH. In fact, they worked with electrolyte mixtures, the pH being fixed by adding NaOH or HCl. One of their conclusions was that round neutral pH the sign of the electrokinetic potential is negative and that it approached zero around pH = 2. Under these conditions c„^, exceeded c,, ^,^ by about a factor of 100. As we have seen before that there is only negligible adsorption of HCl at the water surface (fig. II.3.73b and 4.18), we arrive at the somewhat paradoxial conclusion that nonadsorbing HCl keeps adsorbing NaC104 out of the interface. This issue deserves further study. Kellsall et al. did not convert their mobilities into f-potentials but observed the effects of the electrolyte concentration and the nature of the anion, the mobility becoming more negative from NO" via ClO^ to SO^" (compare figs. II.3.73 and 75). The literature on the adsorption of electrolyte mixtures includes a paper by Matsuki et al.^^, on propylammonium chloride (CgNH^Cl) and LaClg mixtures. The former depresses the surface tension, whereas the latter increases it. There is one specific mixing ratio between the two electrolytes where the two trends exactly compensate each other. At that mole fraction ratio / does not depend on the total solute concentration. 4Ac Electrolytes at water-oil interfaces'^ Experimentally, water-oil interfaces are easier to handle than water-air. One reason is that the solubility of ions in the oil remains small though non-zero. The trend is that, because of its higher polarizability, the larger partner in the cationanion pair (usually the anion) enriches the oil phase. Mostly anions are the bigger ones. So, as a rule oil drops in aqueous electrolyte solutions carry negative charges. A second reason is that water-oil interfaces resist slip better than water-air surfaces. This feature is strengthened by the fact that minor impurities from the oil may also adsorb at the interface giving rise to the propensity of withstanding a tangential stress. As a consequence, it is more appropriate than for the air-water interface to interpret mobilities in terms of f-potentials using the HelmholtzSmoluchowski equation. The third experimental advantage is that it is easier to apply a stable potential difference across the interface. Below we shall briefly return to this aspect. An example of /(c) curves for the water-oil interface in the presence of electrolytes was given by Desnoyer et al.'^^ The oil was a somewhat unusuad mixture (50% tributylphosphate + 50% 'Solvesso', a commercial product), but it allowed repeat-
^^ G.H. Kellsall. S. Yang, S. Yurdakul and A.L. Smith, J. Chem. Soc. Faraday Trans. 92 (1996) 3887. -^^ H. Matsuki, N. Ikeda, M. Aratono, S. Kareshina and K. Motomura, J. Colloid Interface Set 162 (1994) 203. ^^ In this section the term 'oil' is used for all organic fluids that do not mix with water. ^^ C. Desnoyer, O. Masbemat and C. Gourdon. J. Colloid Interface Set 191 (1997) 22.
4.42
GIBBS MONOLAYERS
10
^n\
>
-]-20 -1-40
S CO
C/mV
-4 k
-60
O X
3
+
-6h -8
H-80 |f-j-H -1-100 -^-120
-10
-L 7
8
10
pH Figure 4.21. Electxophoretic mobility and electxokinetic potential of xylene in water droplets. Electrolyte, 10"^ M NaCl. Temperature 22°C. (Redrawn from Marinova et al., loc. cit.) able m e a s u r e m e n t s . It w a s found t h a t adsorption of FeCl^, NiClg a n d CoClg leads to a n increase of y, whereas HCl yields a decrease. The charge sign of the droplets w a s not established. Marinova et al.^^ m e a s u r e d electrophoretic mobilities of xylene emulsions in water containing NaCl plus HCl a n d / o r NaOH, b u t did not estimate interfacial tensions. Figure 4.21 is t a k e n from this work. The problem of stabilizing xylene droplets in water long enough to carry out electrokinetic m e a s u r e m e n t s w a s solved by first dissolving the xylene in the water at high temperature, a n d t h e n cooling the system down to the m e a s u r i n g t e m p e r a t u r e of 22°C. As a result, t h e xylene s e p a r a t e s a s small, p u r e emulsion droplets t h a t remain stable for a b o u t 10 m i n u t e s , long enough to complete the m e a s u r e m e n t s . The error b a r s in the figure give a good idea of the repeatability of the experiment. The f-potentials were obtained u s i n g t h e Helmholtz-Smoluchowski equation, [II.4.3.4]. The negative charge sign is attributable to OH" ion ad- (or ab)sorption; in fact, Marinova et al. showed t h a t inadvertently present ions s u c h a s CO^' or HCO^ only h a d a minor effect. The present a u t h o r is not aware of any systematic studies in which y a n d f m e a s u r e m e n t s have been carried out which simultaneously for a given water-oil interface. In other words, studies in which adsorbed a m o u n t s of electrolytes c a n be c o m b i n e d w i t h electrokinetically mobile c h a n g e s a r e still u n a v a i l a b l e . T h e m a x i m u m electrokinetic charge attained in fig. 4 . 2 1 , a b o u t 10 jiC cm"^, is on t h e higher side of w h a t is maximally found for solids. Clearly there is room for more systematic studies. 1^ K.G. Marinova, R.G. Alargova, N.D. Denkov, C D . Velev, D.N. Petsev, LB. Ivanov and R.P. Borwankar, Langmuir 12 (1996) 2045.
GIBBS MONOLAYERS
4.43
Water-oil interfaces can also be studied from the double layer point of view by imposing an electric field across them and measuring the resulting change in interfacial tension. This yields the water-oil analogue of the electrocapillary curves that have been so successfully studied for mercury-aqueous solution interfaces. Differentiation of the interfacial tension with respect to the applied field gives the surface charge, see [11.3.10.5]. For a review, see sec. II.3.10b. Alternatively, the differential double layer capacitance can be directly measured by some AC bridge method, as described in sec. II.3.7c. The problem of these types of studies is the uncertainty about the potentialdetermining mechanism. Recall that the distinction is basically between relaxed and polarized interfaces (see the introduction to ch. 11.3). Relaxed interfaces are in thermodynamic equilibrium; for these the isothermal Gibbs equation does not contain the applied field, but only Fdn terms. Polarized interfaces are not at equilibrium; the potential E across them is applied externally and therefore the Gibbs equation contsiins an additional cT°dE term. When charge transport across the interface is possible the former mechanism tends to dominate, but this transfer can be inhibited by working at sufficiently high frequencies. It is therefore appreciated that the basic issue to be resolved is whether Faraday currents are suppressed. The issue is compounded by the fact that investigators have a preference for working with organic liquids such as nitrobenzene, in which minor amounts of electrolyte can dissolve, as this can alleviate polairization problems at the non-aqueous electrode. However, although this makes measurement easier, it also clouds the mechanism for determining the potential. For air-aqueous electrolyte solutions the problem is not yet solved. Results are contradictory. For instance, Hurd et al.^^ found small, but reproducible chainges in surface tension (about 0.6 mN m"^ decrease for fields of 7000 V cm"^), but neither Hayes-^^ nor Jiang et ad.*^^ could detect such an effect, although their methods were sensitive enough. Pethica^^ argued that 3E / dP could be related to dy / 3(7°, using the appropriate cross-differentiation in the Gibbs equation, but this is begging the question because one caimot be sure which form of this equation has to be used. As to results for the water-oil interface, fig. 4.22 gives a charge-potential curve for the water-nitrobenzene interface. These results were obtained by Samec et al.^^ who solved the polarization problem by adding LiCl to the water and tetrabutylammonium tetraphenylborate (TBATPB) to the nitrobenzene. The former electrolyte 1^ R.M. Hurd. G.M. Schmid and E.S. Snavely, Science 135 (1962) 791. 2J C.F. Hayes, J. Phys. CheirL 79 (1975) 1689. 3^ 9.A. Jiang, Y.C. Chiew and J.E. Valentini, Colloids Surf. 83 (1994) 161. 4^ B. Pethica, Langmuir 14 (1998) 3115. ^^ Z. Same6, V. Mare^ek and D. Homolka, J. Electroanal Chem. 126 (1981) 121; 187 (1985) 31.
4.44
GIBBS MONOLAYERS
0.01 M
-150
-100
150mV
Figure 4.22. Surface charge at the aqueous side of the water-nitrobenzene interface. The aqueous concentration of LiCl is indicated. The nitrobenzene contains tributylammonium tetraphenylborate. The potential is referred to the common intersection point, taken as a zero point. Temperature 22°C. (Redrawn from Samec et al., loc. cit.) is hardly soluble in nitrobenzene, whereas TBATPB does dissolve in nitrobenzene (under dissociation) b u t hardly in water. In this way t h e interface r e m a i n e d polarized over a sizeable potential range. The differential capacitance could b e obtained from t h e impedance, m e a s u r e d with a n AC polarographic t e c h n i q u e , following a procedure similar to t h a t described in sec. II.3.7c. The capacitance curves h a d t h e typical c o s h - s h a p e , characteristic for G o u y - S t e m double layers with high Stem-layer capacitance (fig. II.3.22a, upper curves) although the absolute values are lower. Integration gives fig. 4.22, which, in turn, may be compared to the theoretical curves of fig. II.3.22b. The s h a p e s of t h e curves resemble those on oxides, see fig. II.3.59, except t h a t the absolute value of cr° is substantiedly lower. It is a pity t h a t n o electrokinetic m e a s u r e m e n t s are available for c o m p a r i s o n . Incomplete polarizability a d d s to the experimental problems ^^ Volkov^^ combined capacitance a n d electrocapillary m e a s u r e m e n t s for the s a m e a n d similar s y s t e m s , a n d found t h a t the m i n i m u m of the former did not coincide with t h e m a x i m u m of t h e latter. There are, a s yet unquantified, a m o u n t s of ions a t t h e interface. The surface potential of nitrobenzene, s a t u r a t e d with water, is a b o u t 100 mV more negative t h a n t h a t of water saturated with nitrobenzene^^ For p u r e water a n d p u r e nitrobenzene the difference is larger (240 mV). The conclusion is t h a t the first exploration of s u c h interfaces is promising b u t t h a t m u c h interesting research remains to be done.
^^ I. Paleska, J. Kotowski, Z. Koczorowski, E. Nakache and M. Dupeyrat, J. Chem. 278 (1990) 129. 2J A.G. Volkov, Langmuir 12 (1996) 3315. '^^ Z. Koczorowski. J. Electroanal Chem. 190 (1985) 257.
Electroanal
GIBBS MONOLAYERS
4.45
4.4d Some practical implications The present topic seems academic, if not esoteric, but this is not the case. It plays a decisive role in at least two techniques that have practical significance. The first is Jlotation. This is a metal ore beneficiation technique based on separating suspended particles on the basis of, intrinsic or intentioncdly achieved, differences in hydrophobicity. When air bubbles are blown through such a system these bubbles attract the more hydrophobic components, subsequently moving them upward. In practice, surfactants are also present so that a foam collar appears on the liquid, from which the hydrophobic fraction can be collected. A central theme in the attachment of a particle to an air bubble is the breaking of the intervening fluid film. Does it occur? And if so, how? And does it depend on the shapes of the particles? Figure 4.23a gives a sketch of the approach stage. When the particle S approaches the bubble, liquid has to be squeezed out from the gap between them (arrows in fig. 4.23). Usuedly the SL interface carries a double layer but, as we have just seen, this is also the case for the LG interface where, even in the absence of ionic surfactants, significant ^-potentials can be created. The ensuing double layer repulsion may keep particle and bubble apart. Hence, it is relevant to know the properties of the double layer at LG interfaces. For practical purposes it does not matter whether, after the capture of a particle by a bubble, a thin aqueous film persists on the solid surface or that this surface becomes essentially dry (except for an adsorbate). Anticipating sec. 5.3, the most such asly final situation will be that of a remaining a-film, characterized by a deep primary minimum such as in fig. 5.12b. With all of this in mind, it is not surprising to find many related studies in the metadlurgy literature. = ^ ^ ^ ;LJ^L~- ^^> ^EZ^^^ \ \_ _-^z — ■
G
y* •^~
embubble
^'fHi||fc
pir
F^^
£^^ ■
—
n--lz
--
. ^l^F ^Hi^^
— :
^ ^ ^
—
—-
rE^
_^_______ ^^^^^
(a] Figure 4.23. Elementary processes in flotation (a) and bubble coedescence (b). Liquid film thinning when a solid particle S or air bubble G, moving from right to left, approaches air bubble G.
4.46
GIBBS MONOLAYERS
The sketch and pertaining explanation are simplified. In practice the dynamics of film thinning also has to be considered. The flow can lead to Marangoni effects emanating from V/'s in the LG interface. The second example concerns bubble coalescence. Experience has shown that in fresh water, air bubbles are much less stable than in sea water. Those involved in boating may have observed that speedboats in sea water create much longer bubble tracks. What is the origin of this difference? The creation of double layers at the LG interfaces automatically comes to mind. However, the mechanism is a matter of discussion. It is known that a certain minimum electrolyte concentration is needed. Craig et al.^^ showed that the resilience to coalescence is ion-specific in the sense that the effectivity depends on the specific combination of cation and anion. All of this is in line with double layer formation as a such asly origin. However, as systematic electrophoretic data are not available, the strength of the resulting contribution to the disjoining pressure and its derivative cannot yet be established. Double layer formation can also have an indirect influence, for instance via the promotion or inhibition of Marangoni effects. It is logical to look for dynamic features; coalescence can be interpreted as resulting from the growth of spontaneous capillary waves as far as they are out of phase between the two approaching LG surfaces. However, so far, the correlation between coalescence resilience and (dA/ / dc)"^, taken as a measure of the Marangoni effect, has not been convincing^'^^ As we have argued before, an explanation in terms of changes in the surface viscosity is probably inadequate as well, because there is no enhancement in the surface. Weissenborn and Pugh^^ pointed to the correlation between dA/ / dc and the entropy of dehydration of the ions involved or, for that matter, between the Marangoni effect and the solubility of gases; the presence of micro-bubbles between the two macroscopic surface would then be responsible for the lower resilience against coalescence. We intend to come back to thin liquid films and their stability in Volume TV. The above discussion is just the tip of the iceberg and is mainly meant to underline that there remains a host of related intriguing problems to solve. 4.5 Rheology and kinetics For all practical purposes the Gibbs monolayers, discussed so far could be treated as fully relaxed. (Figure 4.20, giving measurements taken at extremely short times, illustrates the sole exception.) Complete equilibration, meaning observation at De 1^ V.S.J. Craig, B.W. Ninham and R.M. Pashley, J. Phys, Chem. 97 (1993) 10192; also see U. Hofmeier, V.V. Yaminsky and H.K. Christenson, J. Colloid Interface Set 174 (1995) 199. ^^ H.K. Christenson, V. Yaminsky, J. Phys. Chem. 99 (1995) 10420. ^^ P.K. Weissenborn, R.J. Pugh, Langmuir 11 (1995) 1422.
GIBBS MONOLAYERS
4.47
« 1, is attained because small molecules adsorb very rapidly, or more precisely, they adsorb so fast that under most experimental conditions the process may be considered instamtaneous. However, in sees. 4.6 and 4.8 larger molecules will be considered; these adsorb more slowly and under certain conditions nonequilibrium states will be encountered. Typically, the time t, or the frequency co (for oscillatory experiments), now enter the equations. This is one reason why our systematic treatment of molecules with increasing complexity will now be interrupted by a methodical section on dynamics. The other reason is that almost all applications of surfactants (emulsification, flotation, detergency, advanced oil recovery etc.) involve rapidly moving interfaces. To give some feeling for the order of magnitudes, for the lower alcohols, adsorbing at air-water interfaces, from not too dilute solutions, the Volta potential V^^^ reaches its equilibrium value after less than 5 x 10"^ s ^\ This means that processes occurring at time scales longer than that are considered equilibrium processes. However, for the longer alcohols equilibration takes longer. In both cases the equilibration time depends on the bulk concentration (because of replenishment of the surface by diffusion). Figure 4.24 illustrates this for n-octanol. With increasing chain length the molecules acquire a more amphipolar nature and their properties approach those of sur250
o o ^oo°o°°o 2 . 1 5 x 1 0 - 2
V^'^VmV V oo 200 " o, O
^ o
cO
o o ^° o °
O CO
10"^
CO
150 ^
o
CO
°
oo
0
O
o 100
o o 5 X 10-^
coCO° QCCO
Ko-'^"^ JS^
50
ooo^o o-o
0 2.5x10-4
OO
oo ^^tcotocoooooooooooooo oo o 10-4
t.
(
\
50
\
\
100
150x10-2 t/s
Figure 4.24. Volta potential for aqueous octanol solutions of various concentrations (indicated) as a function of time. (Redrawn from Geeraerts et al., loc. cit.)
1^ As measured by G. Geeraerts, P. Joos and F. Ville. Colloids Surf. A75 (1993) 243, using an oscillatory jet type of set-up, coupled to a Volta potential meter.
4.48
GIBBS MONOLAYERS
factants. The study of the dynamics of such systems in general is the subject matter of this subsection. To describe these dynamics of Gibbs monolayers we shall use the terms (interfacial) rheology and (interfacial) kinetics. By the former we shall, as in sec. 3.6, understand all phenomena involving deformation and flow, by the latter processes occurring due to the non-equilibrium state. For Gibbs monolayers rheology cemnot be analyzed without understanding the kinetics of the transport of molecules to and from interfaces. In principle, kinetics can be investigated without entering the domain of rheology; for instance, one can study the diffusional transport of surfactants to or from stationary interfaces. However, non-equilibrium liquidfluid interfaces are rarely stationary and hence, for most practical purposes rheology and kinetics will be discussed in conjunction. 4.5a Identification of basic transport phenomena As compared with sec. 3.6, the most marked distinction is the possibility of material transport to and from the interface. The following mechanisms contribute; (i) convection, meaning that surfactsmt molecules ^^ are trcinsported because of the flow of the liquid in which they are dissolved; adsorption
^ r t /
diffusion transport
—♦ \
y
r
-v^ [x)
>•
\ \ \
\
\
Figure 4.25. Pictorial representation of a non-equilibrated surface layer, indicating the transport processes that may occur in it. Cartesian co-ordinates; zl surface, counting downwairds from z = 0 in the surface; x parallel to the surface on the right; y parallel to the surface, normal to the plane of drawing. Desorption is ignored. Further discussion in the text.
^^ To simplify things, we shall, in this section call all surface-active molecules surfactants'.
GIBBS MONOLAYERS
4.49
(ii) diffusion of surfact2ints to or from interfaces as a result of a chemical potential gradient. The transport to the surface is completed by an adsorption step; (iii) As is the case for Langmuir monolayers, surfactant transport in the interface can also occur, typically in conjunction with (i) and/or (ii). Let us now consider these three phenomena systematically, on the basis of fig. 4.25, which visualizes a possible state in which a non-equilibrated interface may find itself in contact with a solution. Molecules are represented as clubs. Outside the adsorption region (far down in the figure), the solution is dilute, with the clubs randomly distributed. Association in the solution is assumed absent (concentration c^{z = oo) = Cj(oo) < c.m.c). It is also assumed that the surfactant molecules prefer to adsorb in a monolayer, with the head groups down and the tails up. In the figure, this process is not yet completed. Just to the right of the centre Ccin be seen a package of molecules in a more or less final situation (what this final state looks like is of course determined by the concentration c^(oo) with which the monolayer is at equilibrium). Surface tension gradients lead to local contraction and dilation of the interface. In this case the 'finalized' patch will be torn apart by the gradients V/. Of course, they will also dissipate by diffusion in a stationary surface but, as a rule, surface convection dominates. Liquid is entrained with this surface dilation. This flow is visualized in the figure by the sets of arrows of -v [z] and +1; (z). The solution being incompressible, liquid is supplemented from the bulk. We have indicated this convection by the set of arrows -v (z). How the replenishment takes place in detail is a matter of later concern; it is expected, and indeed observed, that a transition will develop between the regions of horizontal and vertical flow (not drawn in the figure). In general, at each position r = (A:,y,z), the velocity has a different direction and magnitude. So, generally we must write v[r) for the velocity of the convective flow. It is not difficult to think of several complications. For instance, more to the left of the figure there may be an almost uncovered patch in the monolayer. Such an area contracts at the expense of the surrounding surface and the excess liquid is carried down towards the bulk liquid. All velocity arrows now reverse sign. When dilating and compressing patches exist close to each other, Benard-type fluid circulations cells may develop. Another scenario is that of surfactant transfer across the monolayer to the upper phase, which in that case should also be a liquid. Now the accumulation at the interface, with its ensuing reduction of interfacial tension, may lead to interfacial instabilities, strongly promoting transport. We shall not consider these two phenomena here. The reader may think of further complications. So far, we have addressed items (i) and (iii), mentioned at the opening of this subsection. Let us now consider diffusion and other possible material transport mechanisms near otherwise stagnant monolayers.
4.50
GIBBS MONOLAYERS
What is the driving force? It is not the concentration gradient Vc. ^ {dc. / dz) near the surface; such a gradient does not form spontaneously. The real driving force is the difference in chemical potentied /i^ - //^ (bulk) which is really a molar Gibbs energy difference. Let us, for the sake of argument, consider an initial situation in which a surfactant solution of constant concentration c^(oo) is brought in contact with a clean, flat surface. For the present argument we will not worry about the way in which such a situation might be created. Initially the gradient VJJ,^ is very high, in the idealized state it is even infinite. Adsorption of surfactant ensues, leading to the lowering of V/x. because ja^ - u (bulk) decreases and because the distance Az over which the surfactant has to be transported by diffusion (i.e. the diffusion layer thickness) increases. The parts of the solution immediately outside the adsorption layer, sometimes called the subsurface, are depleted first. The parts further away follow later. We see that, as a result of the adsorption, a concentration gradient Vc. is created. It is the consequence of the driving mechanism, not the origin. The process continues until V//. = 0 ; any remaining concentration gradients are levelled down by diffusion, the final bulk concentration is c^{oo) everywhere and the final surface tension y is related to this concentration by Gibbs' law. For desorption the reverse path implies starting at a situation where ILi^ > //.(bulk). Molecules desorb from the surface and have to diffuse into the solution. The sign of the ensuing concentration gradient is the opposite to that in the adsorption case. Regarding the transport mechanisms and their rates, it follows from our reasoning that, in the absence pf convection, one has to consider two consecutive transport processes of which only the sum is observable; (a) adsorption or desorption in the interface; (b) diffusion to and from the interface. The slower of the two determines the rate of the overall process. As process (b) is much easier to describe than (a) there has been a tendency in the literature to overemphasize the latter. Accepting that in practice many experiments can be well described by a diffusion controlled rate, such simplifications have led to the introduction of a number of ill-defined concepts such as that of a diffusion barrier. Diffusion barriers do not exist, but diffusional transport can be slowed down when the driving force diminishes (say, as a result of progressive completion of the adsorption process) or when D is reduced by a local increase in viscosity. Alternatively, seeming diffusion barriers may be artefacts, caused by strongly adsorbing minor impurities in the surfactant which may 'block' the surface. The slowing down of the transfer of an ionic surfactant due to the repulsion of an, already present, negatively charged adsorbate, is not caused by a diffusion barrier but by a lowering of the driving force (in this case, electrochemical potentials have to be considered,i.e. V^. has to.be replaced by V/T^). Below (see the text following
GIBBS MONOLAYERS
4.51
[4.5.291) we shall argue that adsorption barriers cannot be invoked for retarding diffusion either. Subsurface concentrations do exist, but are non-thermodynamic concepts in the sense that there is no way of measuring them. In equations they appear as, sometimes unavoidable, model quantities and can then be inferred from model considerations. In this connection it is appropriate to consider the question of how far the transport of the surfactant towards the surface must have proceeded before the molecule may be considered 'adsorbed'. Operationcdly speaiking, there is no way of discriminating between 'fully adsorbed' and 'almost in the final state of adsorption', apart from noting that variables such as / d o no longer change with time and accepting the validity of Gibbs' adsorption law also under dynamic conditions. The underlying idea is that, even if the adsorption process has not yet relaxed, adjustment of the pressure tensor, and hence the interfacial tension, is instantcineous. We see that even this presumption does not suffice; under dynamic conditions in dy = RTF d i n e , F and c are both unknown. Only when adsorption establishment is fast may F^ and c be related via an adsorption isotherm equation. Here, c^ is the subsurface concentration, referred to above. If rearrangements of molecules in the monolayers took place at constant F^, giving rise to a change of the surface tension, this would be interpreted as being caused by a chamge of c , which is an unphysical model. The over-all conclusion is, therefore, that subsurface concentrations are ill-defined quantities, the use of which should be avoided as much as possible. Ultimately, the extent to which a certain kinetic model can account for experimental observations is a criterion for the quality of the theory (and perhaps, cdso of the experiments). Summarizing this subsection, we are faced with an extremely involved set of processes; convection (in three directions), adsorption and desorption, diffusion to, from and along the surface. As these processes are coupled it is virtually impossible to analyze them within the confines of FICS. However, we shall introduce the mathematics in subsec. 5b and describe experiments in subsec. 5c. One of the purposes is to find regimes, or experimental conditions, where certain mechanisms prevail. For further reading see the books by Edwards et al, by Slattery, and by Dukhin et al., mentioned in sec. 4.9. 4.5b B€isic mathematics Some of the 'building bricks' are already available in previous chapters of FICS. Here, we shall summarize, integrate and extend these. Everything we have said about interfacial rheology (sec. 3.6) remains formally valid, although the interpretation of physical characteristics requires reconsideration. In particular this is the case for the dissipative terms. In Langmuir monolayers these are exclusively attributable to relaxation processes in the layer itself (sec. 3.6h) and to viscous losses in the subsurface layer (sec. 3.6g). For Gibbs mono-
4.52
GIBBS MONOLAYERS
layers contributions caused by adsorption and desorption come on top of this. We come back to this in the experimental section, b u t anticipating subsec. 4.5c we note t h a t the balance between these various contributions to the dissipation is determined by t h e experimental conditions. For i n s t a n c e , in oscillatory e x p e r i m e n t s adsorption a n d desorption can be suppressed by working at very high frequency co. The trend is t h a t relaxation by m o m e n t u m a n d / o r m a s s transfer to or from t h e solution outweighs t h a t inside the layer. So there is ample reason to discuss t h e s e additional processes. (i) Convection.
Interfacial tension gradients in the x-direction (horizontal in fig.
4.25) can generally be described by [3.6.29] ^y
fdv^,
dv Z ^
[4.5.1]
dx=''l
For t h e two-directional c a s e (with y also varying in t h e y-direction) t h e
y-
contributions m u s t be added to the r.h.s. In sec. 1.6.4 we discussed the principles of the bulk fluid mechanics. As argued before, we may use the same (bulk) viscosity rj everywhere in the system. The m a s s flux (in mole m"^ s"^) J^ ^ is generally given by J.Jr,t]
= c^{r.t)v{r,t)
[4.5.2]
For unidirectional convective transport in, say the z-direction, J^JzA) = c.(z,t)v{z,t)
[4.5.3]
(ii) Diffusion control We consider the kinetics of m a s s transfer w h e n convection may be neglected a n d where the actual adsorption process is fast when compared to diffusion. In other words, once a molecule h a s diffused towards the surface it is i n s t a n t a n e o u s l y adsorbed. Diffusion p r o b l e m s are generally solved by starting from Fick's two laws, [1.6.5.5 a n d 7], which are essentially mass-conservation laws for diffusion t r a n s port j^^(r,
t) = -D.Vc.
(Fick I)
[4.5.4]
and ^cAr,t) —\ = Dy^c.{r^) (Fick II) [4.,5.5] ot * ^ Here, D is the diffusion coefficient of the surfactant i, t h a t we have a s s u m e d to be 1
constant. In [4.5.4] J h a s the direction of -Vc^ and in [4.5.5] V^c. is the Laplacian of c.. In Cartesian co-ordinates
'
a^c
d'^c a^c
ax^
dy"^ dz"^
GIBBS MONOLAYERS
4.53
For unidirectional diffusion in the z-direction, Kick's two laws reduce to
and acfz,t)
'd'^cXzX]
Let us briefly digress and consider the situation that diffusion and convection occur simultaneously. Then the flux becomes ''.=-'..d+''..c=-0,Vc,+c,r
14.5.9]
We can use this equation by estimating the ratio between the convective and the diffusive flux. Taken in the z -direction only, the absolute value of this ratio becomes cv^ /D^{dc^/dz). If the process if fully diffusion-controlled, 3c. / 3 z = c./A, where A is the diffusion layer thickness, so the concentration drops out and the ratio becomes i; A/D^. Generally, A is A(t) (the layer grows with time); in the stationary state A is fixed, but depends on v and D. However, to get some feeling for the order of magnitude, if ^ - 10^ m, D ~ 10"^ m^ s"^ and v^ ~ 10"^ ms"^ the ratio is ~ 10. In passing it may be noted that, however much convection may prevail over diffusion, the last part of transport towards a surface is always diffusion-controlled when the surface is inextendable. Note that ratio u A / D is z
i
just about independent of concentration. In chapter 1.6, in particular in sees, d, e and f, we solved a number of diffusion problems, mostly by using the technique of Laplace transformations, explained in Lapp. 10. Two of these are useful for the present purpose, so let us repeat them here. (a) Diffusion to or from a flat surface. Consider a solution of concentration c.(oo) instantaneously brought in contact with a surface where, at the beginning of the experiment, the concentration Cj(0,0) = 0. Such a state can be approximated by sweeping the surface free of surfactant, hoping that convection may be neglected. The surface is replenished by diffusion and the change of c^(0,t) is given by [1.6.5.191; c^(0,t) = c(oo) + —-^1 Jr _ J^ ,_M^ du (TcD^r^ J (t-uY
14.5.101
Here, u is a dummy (time-) variable. Equation [4.5.10] can be integrated when a second piece of information is available. We have discussed a few cases. One of these, the simplest, is that c (0,t) always remains zero. It is a somewhat academic case which would apply if the molecules arriving at the interface were immediately absorbed by the upper phase (a liquid, in this case). Then the process is continually diffusion-controlled and
4.54
GIBBS MONOLAYERS
J,(0,t) =
72
D.
[4.5.111
C.ioo) ^Ktj
This is the so-called Cottrell equation. The m i n u s sign on the r.h.s. is to a certain extent a m a t t e r of taste. In the present situation, where z is counted from t h e surface, it m e a n s t h a t t h e t r a n s p o r t t a k e s place in the negative z-direction. If c. (0, t) = 0 the profile c. (z, t) reads c.(x,t) = c^(oo)erf[x/2(D^t)^/2j (b) Diffusion-controlled
[4.5.12]
adsorption
on a plane surface. For this limiting case we
derived [1.6.5.3 l a and b]
r.(t) = r.(0) +
fD.V/2
[
cM-cMu)
it-u 1/2
I
du
[4.5.13]
and 1
c.(0,t) = c.(oo)
—-
[
dr/d(u) —i—TTo-du
[4.5.14]
To digress briefly, [4.5.13] can also be written a s
r.(t) = r.(0)+ 2
/^D. V/2
c.Ht^/^-
(D^]U2 J c^(0,u)
[4.5.15]
or a s
r^{t) = rp]+2
DA 7 2
c^Ht'/^-jc^(0,u)d(u^/2)
[4.5.16]
This last expression is also known a s the Ward a n d Tordai equation. (These a u t h o r s needed the subsurface concentration in their derivation, b u t our treatment does not.) For very short times and F. (0) = 0 , ;D.t
rst) r =
2\^
72
c^(^)
it-^O)
[4.5.17]
This equation is nothing b u t the integrated form of [4.5.11] (with respect to t), applying for diffusion-limited t r a n s p o r t (c (0,t) ~ 0 for all t). Equation [4.5.13] can be integrated when the adsorption isotherm, i.e. F(t) a s a function of Cj(0,t), is known. For the simplest Henry case, r^{t) = K^c^{0,t) r.(eq.) = K^c^(oo).Then r.(t) = r^(eq)- [rj(eq)- r . ( 0 ) ] e ^ ^ [ l - e r f ( a / / 2 ) ]
[4.5.18]
and
GIBBS MONOLAYERS
4.55
with a^ = Dy^ / ^ H * ^ ^ ^ ^ ^^^ ^ ^ s ^ ^ ^ simple isotherm equation the time-dependence of the adsorbed a m o u n t is r a t h e r complicated. For longer times (a^t»
1),
[4.5.18] reduces to
K fr(eq)-r(0)l Obviously, more complicated i s o t h e r m s are generally required, b u t even t h e Langmuir isotherm, itself simplified, is already difficult ^K (c) Diffusion-controlled
adsorption
on a surface of variable area. When the surf-
ace r e m a i n s homogeneous u p o n dilation a n d compression (convection negligible; mostly this implies low strain rates), this case c a n still be solved analytically using the technique of Laplace transformations^^ Instead of [4.5.7] now t h e total a m o u n t of surfactant transported is considered, viz. AT^. The equation is replaced by3) dc^(z,t)
d(Ar)
[4.5.20]
dz and [4.5.16] h a s to be extended to become r r.(u)dIn A(u)
r(t) = r(0)+ I ^ — ^
^
J
du
/'DV/2
du + 2 - ^ [K
^
J
du
0
[4.5.21] This equation contains two integrals t h a t require numerical elaboration. To t h a t end first the n a t u r e of the A(t) dependence m u s t be established. Depending on the experiment u n d e r consideration it may be linear, exponential, sinusoidal, or something else again. The sought time dependence r^(t] occurs three times in t h e equation, once in integrated form a n d twice a s the derivative with respect to time. (Hi) Adsorption
control. Now we consider t h e regime where t h e adsorption-
desorption s t e p is rate determining. As, relatively speaking, diffusion is now infinitely fast, the concentration is
c.(oo) everywhere, down to z = 0. We are
interested in dP / dt or dO / dt. We shall focus on the latter a n d also choose t h e mole fraction x in the solution a s the concentration variable. If so wanted x be replaced by cJoo)y , where V ^
-^
i
m
may
is the molar volume of the solvent. Furthermore, m
the solution is a s s u m e d dilute [x « 1) so that factors proportional to [I- x^) can be 1^ W.H. Reinmuth, J. Phys. Chem. 6 3 (1961) 473 found that in this case r[t) can be written as a power series. 2) R.S. Hansen, J. Colloid Set 16 (1961) 549. ^^ R. Miller, Colloid Polym. Set 261 (1983) 439. Also see, R. Cini, G. Loglio and A. Ficalbi, Ann. Chim. (Roma) 62 (1972) 789.
4.56
GIBBS MONOLAYERS
ignored. However, the surface is not dilute, so factors (1-0.) will not be replaced by unity. As a first step the rate of adsorption can be written as k x(l - 6) and that of desorption as k^O, so that — = k^x{l-e]-
k^e
[4.5.22]
Here, k^ and k^ are the adsorption- and desorption rate constants, respectively. Their dimensions are [tY^. At equilibrium dQ / dt = 0 and the Langmuir equation ensues: TTe = ^ t ^
14.5.231
with K^ ~^a,^^d' ^^^^ rather primitive model does not say anything interpretationally about the constants, except that K is related to the adsorption energy via K =exp(-A ^ u /kT). L
^^
ads m '
*
As a further step k can be written as k =k exp(-A a
ao
*^\
a
//CT)
act^a.m
'
[4.5.24]
J
Here, A^^^g^ ^ is the molar Gibbs energy of activation. Without insight into the precise molecular pathway of insertion into the monolayer one cannot detail this parameter. For surfactants one could imagine that molecules, already present in the monolayer, must yield a place for the newcomer and that this newcomer has to change its conformation and/or orientation transiently. The pre-exponential factor k must have the dimensions of a reciprocal time. It may be physically interpreted as a residence time, but will also contain molecular characteristics such as the molecular mass, the chain flexibility and kT (to account for the kinetic energy), the last quantities entering through the factor (2nmkT)^^'^ of the kinetic gas theory (compare the dynamic interpretation of the, much simpler, case of gas adsorption onto a solid, sec. II. 1.5a.) As these factors occur both in k and g ^
'
'
ao
^a.m
further detailed analyses are needed to make progress. In a similar fashion,
K-Ko^^-Kc.%.^'^]
I4-5-251
In reaction kinetics usually the assumption is made that A a^ - A a act"^d.m
act'^a.m
= A^^
[4.5.26]
ads"^m
where we have written A^^^g for Aj.g^^,^jQj^. The idea behind [4.5.26] is that the interacting molecules follow the same path upon association and dissociation. For adsorption of large molecules this assumption is not obvious; molecules may
GIBBS MONOLAYERS
4.57
adsorb a n d desorb in different ways. However, a s s u m i n g this to be true, the implication is t h a t t h e n also k^^ « k^^ = k^. The molecular adsorption Gibbs energy consists of the u s u a l adsorption energy A
u
and a contribution of work to be done
against the surface pressure, 7ta . With all of this in mind. d ^ = k'^[x[l-e] dt
- ae-^^ads"m + ^^m)/*^]
[4.5.27]
with <=^e^(-\cA.m/'^)
[4.5.281
Notwithstanding the imperfections of this model, a s m a d e explicit in t h e derivation, [4.5.27] is a n improvement over the Langmuir model, b e c a u s e it a c c o u n t s more specifically for surface p r e s s u r e , a n d hence, for lateral interaction a n d configurational entropy. No a s s u m p t i o n s have been needed regarding the presence of adsorption sites, either on the mobility, or localization, of the monolayer, or on lateral interaction. All of this is accounted for by the factor exp(;ra
/fcT), for
which we have our set of 2D equations of state. It is often found t h a t k « k
; for a
molecule to leave a monolayer, it m u s t be lifted out of the energeticadly favourable position in t h e interface. On the other h a n d , with increasing occupancy of the layer, the pressure goes up, with an increasing tendency to squeeze the molecule out of t h e layer. In [4.5.27] this is accounted for by the opposite signs of (negative) a n d na
A^^^u^
(positive). The 0-dependence of [4.5.27] is complicated because
K also depends on it, and it is such asly that /c will be different between dilute a n d densely occupied monolayers. At equilibrium dO/dt
i-e
= 0 and from [4.5.27] it follows t h a t
xe-^ads^m/'^^e^^m/'^^
which reduces to the Langmuir equation if the exp(;ra The term adsorption
[4.5.29] / kT) factor is ignored.
barrier is often used in the literature w h e n diffusion-lim-
ited t r a n s p o r t is observed to be slower t h a n predicted by the appropriate equation of subsec. (ii) above. Some of the many experimental examples of s u c h retardation are given in refs.^K However, the u s e of this term in the p r e s e n t context is not appropriate because adsorption does not retard the diffusional transport. Rather it is a n independent, consecutive process. Relaxation processes preceding the diffusional t r a n s p o r t in the bulk of the solution, may adso retard the overall r a t e of t r a n s p o r t , b u t may not be interpreted a s a barrier to diffusion. For i n s t a n c e ,
^^ G. Bleys, P. Joos, J. Phys. Chem. 89 (1985) 1027; J.C. Eamshaw, E. McCoo, Phys. Rev. Lett. 72 (1994) 84; C.-H. Chang, E.L Franses, Colloids Surf. AlOO (1995) 1; D.O. Johnson, K.J. Stebe, Colloids Surf. A114 (1996) 41; K.D. Wantke, K. Lunkenheimer and C. Hempt, J. Colloid Interface Sci. 159 (1993) 28.
4.58
GIBBS MONOLAYERS
Grigorev et al. found for CigPyridinium bromide monolayers an additional maximum in the wave damping which could be attributed to (de-jmicellization^^. (iv) Combined control of diffusion and adsorption. For this situation no general solution appears to be available, but partial ones can be found in the literature. One of these is to consider diffusion and adsorption as consecutive processes with the (presumed) subsurface concentration as the anchoring point^K The problem is that diffusion and adsorption are not purely consecutive; the driving force, and hence the rate, of the one depends on the extent to which the other has progressed. An attempt in this direction has a.o. been made by Adamczyk and Petlicki^^ though under a number of simplifying conditions (spherical surface in contact with finite volume). An analytical solution was given for isotherms in the Henry regime. (v) Some concluding remarks. It follows from our treatment that there is no physical argument for assuming something such as an adsorption barrier prior to entering the monolayer. Time-steps and activation Gibbs energies are entirely determined by the dynamics inside the monolayer. We have explicitly assumed that the surface tension, and hence the surface pressure, adjust themselves instantaneously. It is noted that relaixation processes inside the monolayer may be controlled by lateral diffusion. Under those conditions the overall rate may again show a V^t time-dependence, but now with a diffusion coefficient that is substantially lower than that in the bulk. We have not discussed charged systems. As far as the diffuse parts of double layers are concerned, these relax very rapidly, see sec. II.2.13d, meaning that their dynamics will not be rate-controlling. Double layers do, of course, exert their influence on the diffusional transport rate and on the activation energies for the exchange of ionic surfactants between monolayers and solution (uptake in the monolayer is inhibited, release promoted). For further reading, see chapter 5 of the book by Edwards et al. and chapter 4 of that by Dukhin et al., both mentioned in sec. 4.9, and the reviews by Kretzschmar and Miller"*^ and by Miller et al.^^ 4,5c Experimental techniques Briefly stated, the purpose of this subsection is to describe the response of
1) D.O. Grigorev, B.A. Noskov and S.I. Semchenko, Colloid J. Russ. Ac. Set 55 (1993) 658. 2) J.F. Baret, J. Colloid Interface Set 30 (1969) 1. ^^ Z. Adamczyk, J. Petlicky, J. Colloid Interface Set 118 (1987) 20. ^^ G. Kretzschmar and R. Miller, Dynamic Properties of Adsorption Layers of Amphiphilic Substances at Fluid Interfaces, Adv. Colloid Interface Set 36 (1991) 65. See also R. Miller, G. Kretzschmar, ibid 37 (1991) 97. ^^ R. Miller, G. Loglio, U. Tesei and K-H. Schans, Surface Relaxations as a Tool for Studying Dynamic Interfaeial Behaviour, Adv. Colloid Interface Set 37 (1991) 73-96.
GIBBS MONOLAYERS
4.59
adsorbed monolayers to a n imposed variation in the area. This simple s t a t e m e n t covers a range of experiments, because a variety of area chainges can be applied a n d more t h a n one response is measurable. Areas can be slowly or rapidly changed, linearly or logarithmically, once only (transiently) or periodically. M e a s u r e m e n t s include the time dependence of the interfacial tension, one of the moduli of table 3.4, t h e interfacial compliance, wave d a m p i n g or establishing non-rheological properties s u c h a s t h e surface potential V^.
In all t h e s e m e a s u r i n g m o d e s
relaxation by m a s s transport to and from the solution h a s to be accounted for, a n d here again a n y of the m e c h a n i s m s discussed in s u b s e c . 4.5b m a y be operative. Obviously there is not one sole solution to all these variants, and, h a d there been one, it would have b e e n u s e l e s s b e c a u s e of its highly formalistic n a t u r e . It is therefore not surprising t h a t the literature a b o u n d s with case s t u d i e s of partial validity. One of the t r e n d s found in the literature is to e m p h a s i z e diffusioncontrolled relaxations a n d Langmuir adsorption isotherms, b o t h b e c a u s e of their relative simplicity. Many examples of t h a t can be found in the references of sec. 4.10. Convection is often neglected. Of course, experimental conditions c a n be selected s u c h t h a t only one of the relaxation regimes prevails. For instance, one could c h a n g e t h e a r e a so rapidly t h a t adsorption a n d desorption are virtually suppressed a n d in capillary wave techniques convection can be virtually avoided if the amplitude is small compared to the wavelength. Depending on the m o d e s of m e a s u r e m e n t a n d interpretation, a variety of Deborah n u m b e r s (De) c a n b e introduced to describe limiting behaviour. In [3.6.71] we already met t h e Levich p a r a m e t e r (D / (of^'^dc / dr\ if the frequency is so high t h a t this quantity is «
1,
adsorption by diffusion is suppressed. In our terminology D e ( a d s ) » 1. However, other characteristic times may be needed to describe other conditions. (i) General theoretical
background.
In view of the diversity of analyses, we shall
group together below some relatively important methodologies. Prior to that, two notes of wider generality can be made. The first is t h a t u n d e r equilibrium conditions the dilational m o d u l u s K^ can be related to the interfacial excess Helmholtz energy F^ through f^2p<3\
K^ = A
^dA"
14.5.30]
Probably t h i s equation r e m a i n s valid for small deviations from equilibrium ^K For colloid scientists, [4.5.30] is not unfamiliar, because in three dimensions the m o d u l u s is related to the derivative of the disjoining pressure /7(h) with respect to the distance h between interacting particles a n d where /7(h) is, in t u r n , t h e derivative of the Gibbs or Helmholtz energy of interaction. There is a formal difference
1) R. Defay, I. Prigogine and A. Sanfeld, J. Colloid Interface Set 5 8 (1977) 498.
4.60
GIBBS MONOLAYERS
with the three-dimensional analogue, in that for the latter the Helmholtz energy applies to a pair of particles, the factor before the derivative containing numbers of pairs and the connectivity of the system. In our case F^ accounts for the entire monolayer; the value of F^ is determined by a number of parameters, including r.The advantage of [4.5.30] is that a link is made with the general thermodynamic formalism of sec. 3.4. Recall for instaince [3.4.13a], from which it follows that fd^F' o\ dA'
^^
'
(4.5.311
which is a generalization of Gibbs' expression K^ = - d 7 / d l n A . Thermodynamics may be helpful when other conditions have to be considered, for instance constant ju 's instead of constant n 's. For large deviations from equilibrium A and K^ become time-dependent, but it is presumed that the adjustment of y and n to changes in F is instamtaneous. The second rather general approach involves Fourier transforms, as has been largely elaborated by Loglio et al^^ We shall not enter into this formalism in depth, but recall that the principles of Fourier transformations were outlined in appendix 10 of Volume I . A certain periodic function in the time domain f(t] can be transformed into its Fourier transform J((o] in the frequency domain, using [I.A10.301 /(^) = 7r- \ me^'dt
[4.5.32]
and back-transformed , using [I.A 10.31] fit) = J f[co] e-'^^'dco
[4.5.33]
In chapter 1.7 we often relied on this transformation to handle light scattering problems. Not unexpectedly, this procedure is also useful for rheology. Lx)glio et al. showed that
JAA^^jj
f{d\nA(t)/dt}
which is a generalization of [3.6.34]. From [4.5.34] A/W = r'{Kmdif{A\nA(t)}]
[4.5.35]
1^ G. Loglio, U. Tesei and R. Cini, J. Colloid Interface Set 71 (1979) 316; Colloid Polym. Set 2 6 4 (1986) 712; G. Loglio, R. Miller, A. Stortini, U. Tesei, N. Degli Innocent! and R Cini, Colloids Surf A90 (1994) 251.
GIBBS MONOLAYERS
4.61
wiich, in principle, gives the interfacial tension response to area changes. Here /"^ refers to the back-transformation. Alternatively, the response may also be written as t
Ay{t) = j / " M K ^ (ift^),u}A In A(t-u)du
[4.5.36]
o
where u is a dummy time-variable. Integr2ils [4.5.35 or 36], depending on the experiments at hand, can be evaluated if a model is available for K^ = K°'- iK^". This technique is valid provided the system behaves linearly (response proportional to input, impljring not too Icirge deviations from equilibrium). Loglio et al. (1986) give some examples of A{t) profiles with the corresponding Fourier transforms. (ii) A first elaboration. Let us elaborate this for the case of a one-component diffusion-controlled adsorption. The starting equation is [4.5.20], where the subindex i can be dropped. From this
D(—] UzJz=o dlnr dlnA
d r dln(Ar) ^ d r rdlnA dt d l n r ~ dt U l n r "^ 1 DOc/az)^_^
1+-
^'=^
dr/dc-Oc/at)
^,^_^2^dinr_^ dr^ ^
^
.1
l^^5^3^j
dlnr -^^^(dc/dz)^__^ del dc/dt
drj
Equation [4.5.37] can be written in a more manageable way by recognizing that we can introduce a characteristic time scale for diffusion through the definition r(difr.) H -^ I : ^ I
(s)
[4.5.38]
This definition arises from dimensional considerations. Introducing the factor 2 is customeiry, but not essential. Its reciprocal is a;(diff.) = | | ^ | p j
(s-M
[4.5.39]
The derivative (dr/dc) is the slope of the adsorption isotherm. It is high in the initial acclivity but approaches zero near saturation. In this direction, T(diff.) decreases and ft)(diff.) increases. If we also replace -d/Zd In F by K^ (without circumflex, to indicate its static value), [4.5.37] reduces to
4.62
GIBBS MONOLAYERS
l + Mdiff01^/2(2o)i/2.1^^^^fl-o k"" ^K""
1-1
[4.5.40] ^
dc/dt
In order to nicike progress the behaviour of c{z,t)
has to be solved. This requires
an assumption for the nature of the time dependence of the area. Let u s consider the case that it is harmonic. Then the solution of the diffusion problem can be written as an equation of the form c{z, t] = c(oo) + const, exp(az) • exp(icyt), where a and the constant have to be determined from boundary conditions. The solution was given by Lucassen and vein den Tempel^^ and reads in our terminology and convention ^.^^.
l.(De)-'/^-i(Der'^^
14.5.41]
with its real and imaginary components K- =
K<^il-iDer^''^ I-f2(Der^/2^2/De
[4.5.41al
and K^ =icori^=
^,f^
(4.5.4Ibl
Here, we have introduced the Deborah number for diffusion, defined as De(= De(difr.)) . ^ ^ t
=- ^ co(diff.)
14.5.42]
Using the formalism of sec. 3.6. see (3.6.38, 39 and 41al we Ccin now also obtain the absolute value of the modulus as I K^ I =
—
^^
[4.5.431
[l + 2 ( D e r ^ / ^ + 2 / D e ] and the loss tcingent via , tanO
^
K^' = —-r
[De]-^^^ = —
1 rr^ =
fytcZAA^ ryT
4.5.44
These expressions qusuitify the intuitively expected trends. For large De (far from equilibrium because of relatively short observation times) K^ -^ K^, becoming frequency-independent. Then the Gibbs monolayer has no time to desorb and, hence, behaves virtually as if it were a Langmuir monolayer. In the opposite limit
^J J. Lucassen, M. van den Tempel, Chem, Eng. Set 27 (1972) 1283. (Their C corresponds to our De~^/^ and they have a convention for complex numbers, which is different from ours.)
GIBBS MONOLAYERS
4.63
2
Q
2;
E
a
40° ^o^..^
1.5
^S^^D
30° -
1
O O
) 0.5
20° q
I
-2
1
1
0 1 \og(o{(i) in s~^)
1
2
1
1
-2
-1 logfi)(fi> ins~^)
Figure 4.26. Absolute value of the surface dilational modulus (left) and loss single (right) for monolayers of dodecanoic acid. Surface wave technique. Concentrations; O, 2.0 x 10~^ M; A, • 4.5 xlO-5 M; n, ■. 1.0 x 10"^ M (left) or 3.0 x lO'^ M (right); room temperature. (Redrawn after Lucassen and van den Tempel, loc. cit. ) of full equilibration, De -> 0; then the modulus becomes proportional to oo^''^. For the loss angle the corresponding story is t h a t for diffusion-controlled adsorption t a n Q varies between zero for large De (0 -^ 0 b e c a u s e there is no time for losses) a n d unity for De -^ 0 (0 -> 45°). When, experimentally, a loss angle larger t h a n 45° is found, it follows t h a t diffusional exchcuige is not the limiting factor. In fact, we already used this a r g u m e n t in interpreting fig. 3.46. An illustration t a k e n from the work of Lucassen a n d v£in d e n Tempel, cited before, is given in fig. 4.26. The system w a s a n a q u e o u s solution of n-dodecgmoic acid; small-angle sinusoidcd longitudinal waves were created in a Lauigmuir trough where the resulting changes in the surface tensions were measured. Two sets of data (open a n d closed points) are given; they reflect (slight) differences in the m e a s u r i n g technique b u t show identical trends. At low frequency the slope of the double logarithmic plot is 0.5 (this is the pure Gibbs monolayer behaviour), at high frequencies the slopes level off. Eventually they would become zero, characteristic for the Langmuir regime. This transition between Gibbs (fully relaxed equilibrium v a t h t h e bulk) a n d Langmuir (no transfer a t all) monolayers is reminiscent of t h a t between fully relaxed a n d polarized electric double layers (introduction to ch. II.3); the silver iodide solution interface is fully relaxed, b u t Ccui be polarized artificially by working at s u c h high frequencies t h a t Fairadaic c u r r e n t s are s u p p r e s s e d (sec. 11.3.7c). Having derived [4.5.41 and 43], it is a trivial step to make a n a s s u m p t i o n for the adsorption isotherm equation, in order to make G;(diff.), a n d hence, De explicit. To cover the complete range, we needed isotherms with a plateau. The simplest one is t h a t of Langmuir amd, in fact, it is the one most frequently a s s u m e d , rightly or not.
4.64
GIBBS MONOLAYERS
One can even go so far as to derive the isotherm from dynamic measurements. Note that this does not mean that a dynamic Langmuir isotherm' is derived; the theory is based on diffusion-limited adsorption, so the surface is taken to be fully relaxed with respect to the sub-surface concentration. In other words, the isotherm is taken to be identical to that in the static case. This is probably correct, unless under dynamic conditions the surfactant assumes a different conformation. Generally, K^ and K^ depend on co and c. The lower co, the better equilibrium is approached and the lower \K^ \. The loss modulus tends to pass through a maximum as a function of c if cw is kept constant. At low c there is not enough material available to affect y significantly, whereas at high c there is so much surfactant available that, even at high frequencies, the surface is for all practical purposes replenished. The practical relevance of analyses such as the one given above is the central role the modulus plays in emulsification, foaming, Ostwcds ripening, particularly of foams detergency, and other processes involving area changes. Recall that the modulus is a measure of the resistance a monolayer has against creating an interfacial tension gradient. Once such a gradient has been created, the relaxation mechanism controls the rate of relaxation which is also related to the modulus. In conclusion, subsec. (ii) is meant to illustrate how an analysis may proceed. Various modifications, with respect to the nature of the A{t) dependence, the nature of the material exchange, the experimental set-up and the shape of the isotherm equation can be imagined. For elaborations, see the references in sec. 4.10; some illustrations will also be given in sees. 4.6 and 4.8. Table 4.2. Survey of techniques for studying the rheology of Gibbs monolayers Method Suitability | meaning of Time range(s)
Drop relaxation Drop p r e s s u r e relaxation
time
LG
LL
1-300 10-5 - 102
t
+
+
t
+
+
10-1 - 200
(0~^
+
+
5x103-5x103*
co~^
+
-
co~^
+
-
Surface waves in troughs
10-3 - 10-2 ia-2 - 103
Q)~^
+
Wave damping
10-2 - 105
(0~^
+
Overflowing weirs, cylinders
10-2 - 102
(dlnA/dtr^
+
- #
Surface s h e a r viscometers
10-1 - 104
ld(Ax / Ay)dtr^
+
#
5 - 104
(dlnA/dtr^
+
-
Ring trough, etc. Oscillating bubble or drop Oscillating Jet
Caterpillar trough
* Kao et al. claim down to 120 kHz ~ 0(10"^ s~i); #, have been applied to LL interfaces, though over a narrow time range.
GIBBS MONOLAYERS (iii) Experimental
techniques.
4.65 Basically all available m e t h o d s have already been
reviewed. In table 1.5 (sec. 1.14) we summarized classical m e t h o d s for obtaining interfacial tensions u n d e r dynamic conditions. These techniques are suitable for m e a s u r i n g d y n a m i c t e n s i o n s , r a t h e r t h a n interfacial rheology. We shall n o t consider t h e m again here. More pertinent are the rheological techniques discussed in sec. 3.7e. For easy reference we summarize them in table 4.2, which is a n extension of table 5.2 in the book by D u k h i n et al., mentioned in sec. 4.9. Regarding this table we note t h a t mentioning u p p e r a n d lower time b o u n d a r i e s involves some arbitrariness. Many experiments cam be extended for weeks, b u t it is difficult to tell w h a t impurities may enter during t h a t period. The higher frequency range for waves in a trough is limited by t h e need to place the oscillator a n d Wilhelmy plate very close a n d working with a n elastic r u b b e r ring at oil-water interfaces may be prohibited by the chemical n o n - i n e r t n e s s of the oil for the rubber. Oscillating b u b b l e s c a n b e analyzed by m e a s u r i n g the gas p r e s s u r e or the shape; the former procedure is faster. Two questions t h a t come automatically to mind are; (a) Do different methods yield the same results regarding /(t), r]^, K^, etc.? (b) Which method is preferable a n d when? The answer to (a) is; 'not necessarily', a n d t h a t to (b); 'that depends'. Regarding (a); we are dealing with non-equilibrium monolayers, of which the properties are partly determined by their history. Only when, in two experiments, exactly t h e s a m e histories a n d the s a m e experimental conditions c a n be m e t for t h e s a m e chemicals, may the identity of observables be anticipated. Issues t h a t play a role include the age of the interface before cycles are started; in particular w h e n t h e surfactant contains a minor, b u t very surface-active, c o m p o u n d there c a n be a s u b s t a n t i a l difference in the r e s u l t s between the situation w h e r e t h i s m i n o r c o m p o n e n t is already fully adsorbed, or s t a r t s to do so. The issue of incomplete equilibration of the monolayer also plays its role in macromolecular a d s o r b a t e s , which n o t only equilibrate notoriously slowly b u t also often exhibit non-linear behaviour. Once s u c h a partly-equilibrated layer is subjected to compressionexpansion cycles, the possibilities of further equilibration will depend on quantities s u c h a s AA a n d co, a n d these may be different in different m e t h o d s .
Non-
linearity of the p h e n o m e n a may be another problem. In a sense, this qualitative reply to query (a) also a d d r e s s e s (b). Academically, one would like to have comprehensive studies, in which the above-mentioned problems are avoided a s well as possible and in which a variety of surfactants are studied. As far as the present author is aware, such investigations have not yet been published, although many examples can be found in the literature which a d d r e s s (small) p a r t s of the problem (say, only valid for very low co). From a more practical point of view the emswer to (b) is strciightforward; choose t h a t method which b e s t
4.66
GIBBS MONOLAYERS
mimics the practical conditions at h a n d . Before presenting a few examples, let u s first note t h a t sometimes additional information of a non-rheological n a t u r e is available. Obviously only those m e t h o d s in sec. 3.7 t h a t are fast enough to capture the non-equilibrium states will qualify. In this respect we should give more attention to exploiting the potentiadities of all t h e optical m e t h o d s of t h a t section. We mention ellipsometry^^ which h a s b e e n u s e d for overflowing cylinders. For monolayers the coefficient of ellipticity for CjgTMA bromide monolayers w a s found to vary quadratically with radial distance from the centre, in agreement with earlier models. Ellipsometry h a s also been used for m e a s u r i n g t h e adsorption kinetics of cationic s u r f a c t a n t s via a liquid j e t t e c h n i q u e ^ ^ H u h n e r f u s s et al.^^ m e a s u r e d Volta p o t e n t i a l s . A l t h o u g h
the
quantitative interpretation in t e r m s of adsorbed a m o u n t s a n d orientation of the molecules r e m a i n s esoteric, the variation of V^ with time enabled a s s e s s m e n t of the phase angle 6. Let u s now compare techniques with sinusoidally changing areas. As rheological techniques with s u c h harmonic strains, the wave £ind oscillating bubble technique have m u c h in common. The former was discussed in sec. 3.7. In the latter, a small a m p l i t u d e radial p e r t u r b a t i o n is applied a r o u n d equilibrium. The p h a s e angle between the change in bubble radius a n d the variation in gas p h a s e p r e s s u r e is measured; it relates to the imaginary part of the m o d u l u s , i.e. to the dilational viscosity 77^. For a n a l y s e s of t h e i s s u e , see refs.^) a n d t h e brief review in Kretzschmar-Miller (1991), mentioned in sec. 4.9. It seems well established t h a t at low frequency the oscillating bubble technique gives a proportional increase of the absolute value of t h e m o d u l u s \K°\
with w^^'^ (experiments with n-octanol a n d
dimethyl decyl p h o s p h i n e oxide^'^K This trend agrees with our prediction for D e - > 0 , see below [4.5.44], a n d with longitudinal wave t e c h n i q u e r e s u l t s for dodecanioc acid. Figure 4.27 gives a n illustration of oscillating b u b b l e r e s u l t s obtained by W a n t k e et al.^^ The open symbols refer to the oscillating b u b b l e experiments. These d a t a have been extended by oscillating barrier m e a s u r e m e n t s
^^ S. Manning-Benson, C D . Bain and R.C. Darton. J. Colloid Interface Set 189 (1997) 109. '^^ J. Hutchison, D. Klenerman, S. Manning-Benson and C. Bain, Langmuir 15 (1999) 7530. ^^ H. Huhnerfuss, P.A. Lange and W. Walter. J. Colloid Interface Set 108 (1985) 430. 4) G. Kretzschmar, K. Lunkenheimer, Ber. Bunsenges. Phys. Chem. 74 (1970) 1064; R.L. Kao, D.A. Edwards. D.T. Wasan and E. Chen, J. Colloid Interface Set 148 (1992) 247 (for a dispute on this paper, see the same journal 155 (1993) p. 516 and 518.); C.H. Chang, E.I. Franses. J. Colloid Interface Set 164 (1994) 107; D.O. Johnson. K.J. Stebe, J. Colloid Interface Set 168 (1994) 21. ^) K. Lunkenheimer. G. Serrien and P. Joos, J. Colloid Interface Set 134 (1990) 407. ^^ P. Warszynski, K-D. Wantke and H. Fruhner, Colloids Surf A139 (1998) 137. ^^ K-D. Wantke. H. Fruhner, J. Fang and K. Lunkenheimer, J. Colloid Interface Set 2 0 8 (1999) 34.
GIBBS MONOLAYERS
4.67
60
2
50 h
S 40 30 20 10 0 0.001
0.01
0.1
100
1 10 frequency (Hz)
Figure 4.27. Absolute value of the surface dilational modulus technique (closed symbols) and from oscillating bubbles (open tridecyldimethyl phosphine oxide; A, A c = 2 xlO"^ M; O, • c = 5 x fit to [4.5.431. Temperature 22°C. (Redrawn from Wantke et al. (loc.
obtained by the wave symbols). Surfactant, 10"^ M. Drawn curves; cit.).)
(filled symbols), to cover the low frequency range. It a p p e a r s t h a t the two sets of d a t a connect well. Their wave technique w a s insufficient to attain the high-frequency plateau, b u t this defect could be made u p by oscillating bubble experiments. Wantke et al.'s d a t a compare well with those presented in fig. 4.26. The implication is t h a t nowadays we have two 'grown-up' t e c h n i q u e s available for t h e s t u d y of surface rheology a n d t h a t u p to five frequency d e c a d e s c a n be covered. The oscillating bubble technique is p e r h a p s less m a t u r e t h a n surface wave t e c h n i q u e s b u t h a s the advantage t h a t the experimental set-up is simpler. In particular, this is so because nowadays pressures can be rapidly measured by pressure transducers. J u s t a s Lucassen and van den Tempel (fig. 4.26), Wantke et al. found t h a t [4.5.43] described their data reasonably well, except a t high concentrations (not shov^m). By way of illustration, in table 4.3 their fitting p a r a m e t e r s are given for a n u m b e r of surfactants. We refer to the original for a discussion on the steps tsdcen to arrive at, a n d the accuracy of, these data. It is observed t h a t a s a function of c K^
first
i n c r e a s e s somewhat, t h e n levels off. From fi)(diff) t h e Deborah n u m b e r c a n be assessed, using [4.5.42]. Other examples will be given in the following subsections. We note t h a t the wave technique can also be applied to liquid-liquid interfaces ^K
1^ See, for instance C. Lemaire, D. Lemgevin, Colloids Surf. 65 (1992) 101.
4.68
GIBBS MONOLAYERS
Table 4 . 3 . Surface Theological parameters according to Wantke et al. (1999). Material*) C13DM phosphine ox
c/M
K^/mNm"^
w(diff)/s-^
5 x 10^
32.5
0.0036
1 X 10-5
51
0.009
2 x 10-5
53
1.40
5 x 10-5
53
C9COOH
5 x 10-5
37.5
I x 10^
47.5
CgCOOH
2 x 10-^
4.5
57.2
5x10-4
6.5
45.5
I x 10^3
10.0
74.4
2 x 10-3
11.1
59.4
5.x 10-5
8.5
2.2
I x 10-4
16.3
1.4
2 x 10^ 3 X 10-4
27
1.3
30.7
2.1
5 X 10-4
31.3
3.7
1 X 10-4
4.4
2.5
C9OH
CgOH
Triton X-100
44.2 0.3 1.11
3x10-4
4.6
10
6 X 10-4
16.8
25
I x 10-3
19.8
70
2 x 10-3
21.5
90
1 X 10-5
39.7
5x10-5
48
0.23 11
1.5 X 1 0 ^
51.1
210
2.5 X 10-4
55.1
865
* Codes as in table 3.7a. 4.6
Surfactants
Perhaps it is fair to state that surfactant monolayers are the most abundant representatives of Gibbs monolayers. Scientific literature abounds with entries on their measurements, theory and applications. Given the scope of FICS, a selection has to be made in which fundamental aspects are emphasized. To that end, we shall mostly adhere to the following scheme: (i) We shall discuss the interfacial behaviour, not the bulk properties. Items such as micelle formation, and bulk phase behaviour will be postponed until Volume V. However, some basic features of surfactant solutions will be reviewed in subsec. 4.6a.
GIBBS MONOLAYERS
4.69
(ii) We shall emphasize solutions containing, in addition to the solvent (mostly water), only one surfactant and only one low molecular weight solute. (iii) We shall consider both non-ionic and ionic surfactants, with some emphasis on those with simple structure. Polymers are for most practical purposes insoluble, although it is possible to force parts of the chain out of the surface by applying high pressures. For this reason we treated these in chapter 3, sees. 3.4i and j , and 3.8e and f. Proteins will be deferred to Volume V. (iv) We shall consider both LG and LL interfaces. The difference between these two systems is often of a quantitative, rather than a qualitative nature. In cases where the distinction is trivial, we shall concentrate on LG surfaces. (v) We shall discuss both equilibrated and non-equilibrated monolayers. (vi) In addition to measuring the classical /(In c) curves, the 'beginning of much wisdom', we shedl also discuss more modem techniques for obtaining information on the statics £ind dynamics. The required methods are available in chapter 1 and sec. 3.7. They include dynamic interfacial tension measurements, optical, electrical and rheologiccd characterization. As is our habit, examples given are an anthology rather than a beauty contest, the main purpose being that they serve to illustrate a given point. For a review of the physicochemical properties of surfactants, see^^.
4.6a
Surfactants
in solution
Strictly speaking, all dissolved molecules having a high affinity for a given interface may be called surfactants.
However, in practice the name is reserved for
those substances of which the molecules have a hydrophobic and a hydrophilic moiety. Choosing these terms implies that we take explicitly water as one of the phases. If one wants to consider surfactants in an apolar liquid one could use the terms lyophobic and lyophilic. Interfaces can be formed between the aqueous surfactant solution and either a solid, an oil (i.e. a liquid with which water does not mix) or a gas (vapour) phase. We shall designate them as SL, w / o or L/L and LG, respectively. Only the last two are now under consideration. We refer to sec. II.2.7d for non-ionic surfactant adsorption at SL interfaces and to sec. II.3.12 for electrosorption of ionic surfactants. Surfactants have a part that feels well at home in the water, and another part that prefers to be expelled from it. This internal contrast renders the molecules kind of schizophrenic. This nature is sometimes expressed by calling s u c h molecules amphipolar or amphiphilic. 'Amphi' stems from the Greek a|i(t)i, meaning on both sides', so the first term is not adequate (the surfactant molecules are not polar on both sides) and the second is at least debatable. (The hydrophobic moieties
^^ N.M. van Os, J.R. Haak and L.A.M. Rupert, Physico-chemical Properties of Anionic, Cationic and Nonionic Surfactants, Elsevier (1993).
4.70
GIBBS MONOLAYERS
may such as an oil, but have no affinity for vapour.) For practical purposes the notion of hydrophile-lipophile balance (HLB) is sometimes used to scale surfactants in terms of the relative predominance of their hydrophilic amd hydrophobic parts. The HLB is an empirical quantity, which ranges from zero (virtually insoluble in water) to about 20 (very soluble in water, not in oils). The trend is that surfactants with a low HLB are w/o emulsifiers, those with intermediate values are wetting agents, whereas high HLB surfactants promote the formation of o/w emulsions. This trend is in line with Bancroft's rule, see sec. 4.8 In fact, this discussion of terms teikes us to one of the basic issues of surface activity and micelle formation; what is the driving force for these processes? In not too dilute aqueous solution micelles can be formed, i.e. small, often spherical, aggregates of some tens of monomers, arranged in such a way that the hydrophobic parts are inside and hydrophilic moieties outside. So, the hydrophobia of the latter is resolved by becoming screened from the water via the hydrophilic coat. The driving force of micelle formation cannot be the affinity between the hydrophilic groups. On the contrary, these groups repel each other across water, so the tendency of the hydrophobic parts to associate must be responsible. Why then do they aggregate? Mostly by hydrophobic bonding, meaning by an increase in entropy of the water. Recall subsec. 4.3c on the adsorption of short chain alcohols. The energetic contribution of the Van der Waals attraction between the hydrophobic groups is small, if it is attractive at all. Note that it is not the pure hydrophobe-hydrophobe attraction which counts but its excess with respect to mixing with water; Hamaker constamts of the lower alkanes across water are attractive, (also see sec. 5.3d) but very low; (about 1 fcTat room temperature), see table I.A9.2. Evidence for all of this has to come from thermodynamic measurements; calorimetry or equilibrium micelle formation studies as a function of temperature, followed by an interpretation using Gibbs-Helmholtz relationships. The balance between the three contributions (head group repulsion, hydrophobic bonding and Van der Waals attraction between the hydrophobic groups) depends on the nature of the micelle, i.e. on the kind of surfactant. Hydrophobic bonding cannot occur in apolar solvents. MiceDes in such media have the hydrophilic groups inside, the hydrophobic ones sticking out. Their formation must be primarily enthcdpically determined. The spontaneous aggregation into micelles is also known as self-assembly. The term also covers the more complicated structures, formed from solutions of higher concentration. Micelles are the best known examples of association colloids. A wide variety of surfactants exist. Fundamental studies can best be done with those that are well-defined and have a relatively simple structure, i.e. consisting of one unbranched aliphatic chain as the hydrophobic tail and one head group. Moreover, all molecules in the sample should be identical. This conditions implies homodispersity (or monodispersity), meaning that all molecules have the same tail
GIBBS MONOLAYERS
4.71
length. Commercial seimples are usually heterodisperse mixtures. Head groups can be non-ionic or ionic. The most familiar non-ionic head group is a polyoxyethylene oligomer. Ionic surfactants may have an anionic (say, sulphate-) or cationic (say, tetramethyl-ammonium) head group. Homodisperse surfactants have a sharp critical micelle concentration (c.m.c), that is the bulk concentration above which micelles form. For concentrations above the c.m.c. adding more surfactant leads to £in increased number of micelles but hardly to an increase of the intermicellar solution concentration nor in the micellar size (unless the concentration becomes very large). The micellar size is mainly determined by the comprising number of monomers and their packing. For ionic micelles this number is some tens, or even above one hundred, depending on the indifferent electrolyte concentration. The higher the concentration, the better the charged head groups are screened smd the larger the micelles. It can be shown by a straightforwcird statistical argument ^^ that the less the micellar size varies with Table 4.4. Some representative critical micelle concentrations (25°C, 1 atm, unless otherwise stated). Category
Surfactant
Anionic
CgSO^Na^
1.33x10-1
C^^SO;Na^
3.33 X ia-2
C^^SO^Na^
8.3 X 10-3
ibid, 55°
9.8^ X 10^
C, SO-Na^
2.1x10-3
14
Cationic
Non-ionic
(linear)
c.m.c./M
4
Cj^TMA^Br"
1.5x10-2
CjgTMA^Br"
3xia^
Ci2Pyridinium+Bi^ (30°)
1.18x10-2
ibid, 65°
1.63x10-2
^16^9
2.09 X 10-«
^16^15
3.09 X 10-^
^16^1
3.89 X 10-«
^10^9
0.9 X 10-3
^12^9
8.7 X ia-5
^14^9
1.0x10-5
TMA = tetramethylammonium; E^ = ethylene oxide, x-mer. Source; P. Mukerjee and K.J. Mysels, Critical Micelle Concentrations of Aqueous Surfactant Systems, NBS, Washington (1971). 1^ P. Mukerjee. J. Phys. Chem. 76 (1972) 565.
4.72
GIBBS MONOLAYERS
the total surfactant concentration, the more homodisperse is the system a n d the s h a r p e r t h e c . m . c . Several surfactants in apolar media form cylindrical micelles of which the length increases with concentration. For those systems there is no sharp c.m.c. Some typical c.m.c.'s are collected in table 4.4. For a given type of surfactant the length of the hydrocarbon chain is the dominant variable. Considering the driving force, this is not surprising. For non-ionics the c.m.c.'s are m u c h lower t h a n for the ionic surfactants, because no work h a s to be done to overcome the adverse electrostatic repulsion between the head groups, although for non-ionic surfactants t h e head g r o u p s of course also repel each other. For the same reason the addition of electrol3rtes significantly lowers the c.m.c. of ionic surfactants. Between cationics a n d anionics of given chain length there is a small b u t distinct difference.
This
difference m u s t be related to the packing of the head groups. As a trend, cationic head groups are bulkier t h a n anionic ones a n d so are the corresponding counterions (Cl~ a n d Br" ions are bigger t h a n Na+-ions, see table 1.5.4). The influence of the temperature on the c.m.c. is important for establishing the driving force. For m a n y anionic s u r f a c t a n t s the c.m.c. h a s a m i n i m u m a s a function of temperature. (See the reference to table 4.4 a n d ^^). The position of t h e m i n i m u m depends on the n a t u r e of the surfactant b u t is usually found between 15 a n d 30°C. It is possible to derive that, a s a first approximation, the s t a n d a r d Gibbs energy of micellization AG° (mic) d e p e n d s on the c.m.c. (expressed a s a mole fraction) through^^ AG^(mic) = RTlnlc.m.c.l
[4.6.1]
where the subscript m refers to 'molar' (per monomer). If t h e c.m.c. is known a s a function of T, the micellization enthalpy c a n immediately be derived, using the following Gibbs -Helmholtz relation (see [I.2.15.8a] a(AG°(mic)/Tl
a(T-M
'
= A H (mic)
[4.6.2]
So, a t t h e m i n i m u m , where ln[c.m.c.] is ~ independent of T, AH(mic)~0. Below this temperature,
AH(mic) > 0
(micelle formation
endothermic),
above
it,
AH(mic) < 0 (exothermic). Both the low magnitude and the sign change are in line with hydrophobic bonding a s the main driving force. For cationic surfactants
not
so m a n y detailed studies are available, b u t the same trend is expected. In order to observe the minimum, careful m e a s u r e m e n t s are required over a long temperature IJ V.D. Yakovlev et al., Zhur Prikl Khim. 52 (1979) 2471. (Transl.: J. Appl Chem. 5 2 (1979) 2340.) 2^ See, for Instance, R.D. Void and M.J. Void, Colloid and Interface Chemistry, Addison (1983), sec. 18.3b.
GIBBS MONOLAYERS
4.73
range. In several experiments measurements at only two or three temperatures are recorded and in other cases only data above the minimum are available; hence the minimum escaped attention. Anjrway, the temperature dependence is not very pronounced and it has taken a while to establish the proper trend. Nowadays the sign change of AH (mic) is confirmed calorimetrically^^ For non-ionic surfactants of the familiar C E type, the c.m.c. decreases with increasing temperature^^. This trend is related to the decreasing solubility in this direction. This observation does not imply that micellization does not involve hydrophobic bonding. Rather, the weak enthalpic effect of this phenomenon is outweighed by that of the EO-water interaction. With respect to the non-ionics, it is noted that lengthening the polyethylene oxide groups increases the c.m.c, whereas lengthening the aliphatic chain reduces it; the latter trend is far more pronounced. Micelles are dynamic entities. They can form and decay rapidly, the shorter the chains, the faster this occurs. The interior hydrophobic phase' is in the liquid state and can chcinge conformation rapidly. The outer sheaths of head groups are mobile as well and not aligned on the surface of a sphere; that would be both energetically and entropically very unfavourable*^^ From nuclear magnetic resonance the decay process has become more transparent. There are two time scales involved, one in the 10-10^ |is range, caused by the exit of one monomer; the other in the 1-10^ ms range, related to the decay of whole micelles. This latter step is so much slower because the micelle has to pass through a Gibbs energetically very unfavourable transient state^K 4.6b Surfactant monolayers. General features We are now interested in the structure and physical properties of surfactant monolayers at LL and LG interfaces. The primary physical characteristic is / . Let us first consider equilibrium states. Then, y can be related to the composition of the solution via Gibbs' law. In solution, with increasing concentration c , surfactant association takes place. This happens suddenly or gradually, depending on the (homo- or hetero-) dispersity of the micelles to be formed. The difference between 'gradual' and 'sudden' is not sharp, and therefore it is debatable whether micelle formation may be considered a first-order phase transition. Automatically the question also arises whether at the interface association t£Lkes place if c is increased, and ^^ See, for instance, M.Mehrian, A. de Keizer and J. Lyklema, Colloids Surf. A71 (1993) 255. 2) M.J. Schick, J. Phys. Chem. 67 (1963) 1796. ^^ The popular artist's view of a micelle, with the head groups positioned on a sphere and the tails represented as straight lines toward the centre, faiils on all accounts. ^^ E.A.G. Aniansson, Ber. Bunsenges. Phys. Chem. 82 (1978) 981; E.A.G. Aniansson and eight other authors, J. Phys. Chem. 80 (1976) 905.
4.74
GIBBS MONOLAYERS
whether such association, if any, takes place before or beyond the c.m.c. In other words, is it easier for surfactants to build condensed parts in the monolayer or to form micelles? As far as interfacial tension measurements are concerned, general observation suggests a gradual increase of F with increasing c , the plateau being attained before the c.m.c. Figure 4.28 shows a prototype y(logc ) isotherm. (Of course, y can also be plotted as a function of c . Such curves are convex with respect to the abscissae axis. However, most features show up better in the semilogarithmic mode. Moreover, in the latter plot the slope can, 2ifter conversion of concentrations into activities, be directly related to F , using Gibbs' law, see below.) The first part (A) is nearly horizontal. If extrapolated to the left, / -» /(water). On the surface there are only a few adsorbed molecules, probably obeying the ideal 2D gas law. Without further information we do not know whether the tails stick out into the vapour phase or prefer to lie flat. This molecular configuration is the result of a subtle balance of forces; a flat orientation is energetically more favourable whereas protrusion is preferable for entropic reasons. On the basis of Gibbs' law we cannot decide. Some feeling can be derived from simulations, although the result of course depends heavily on the parameter choice. An example is the molecular dynamics study of Kuhn and Rehage^^ who found the molecules of the non-ionic C12E5 to lie almost flat on water surfaces at infinite dilution, in line with neutron reflection studies-^^. However, when the upper phase is an oil, sticking out is more probable. Region A of fig. 4.28 is also characterized by low moduli \K^ \.
log c.m.c. lOgCg
Figure 4.28. Generic y(logc ) diagram for surfactants. Here, c is the total surfactant concentration. ^) H. Kuhn, H. Rehage, Phx^s. Chem. Chenh Phys. 2 (2000) 1023. 2) J.R. Lu, M. Hromadova, R.K. Thomas and J. Penfold, LangmuirS (1993) 2417.
GIBBS MONOLAYERS
4.75
In region B, F^ has increased and I K^ I is high. Had intermediate association to dimers, trimers, etc., taken place then a horizontail region in the plot would have appeared. Examples of such behaviour are not known to the author. Region C is often linear. Constancy of d y / d l n c means constancy of F , at least if the activity constant remains the same, and it is physically realistic to interpret this range as representing the saturated monolayer. Here, I K^ I is low again (in this situation surfactant is abundant; the surface is instantaneously replenished). From the plateau value F (oo) of F as the molecular cross-section per surfactant molecule can be computed, see [4.6.5], a
=\F{OO)/N, m.s
L s^ "
V Av J
[4.6.3] ^
'
Parameter a is the average cross section per surfactant molecule in the monolayer. From the fact that it increases with the hydrocarbon tail length, one may infer that these tails are not packed linearly. For ionic surfactants a markedly decreases with increasing salt concentration. In passing, and anticipating illustrations to follow in this section, the determination of cross sections according to [4.6.3] is by no means a foregone item. Drawing a straight line through a limited number of data points tends to be subjective, establishing the data can have its problems (minor impurities, time effects, accounting for non-ideality, etc.). Anticipating fig. 4.33, giving adsorption isotherms obtained by neutron reflection, it also is a bit arbitrary to decide whether the c.m.c. is in the ascending part or in the plateau. The break at D is interpreted as being caused by the micelle formation in solution. This break is one of the familiar ways for obtaining c.m.c.'s. Evidence for the correctness of this method stems from the ifact that the c.m.c, obtained in this way, is identical to that obtained by other methods, such as light scattering or conductivity. Beyond the c.m.c. any added surfactant is accommodated in micelles; the monomer concentration hardly increases any more, and y is almost constant (region E). The stereotype /(logc ) curves of fig. 4.28 can also be used as a touchstone for identifying deviating behaviour. For instance; (i) Impurities may lead to a minimum in the curve around the c.m.c. The explanation is that before the c.m.c. the impurities are adsorbed, thereby reducing y. Once micelles have been formed the impurities are incorporated into the interiors of the micelles, hence solution and interface are scavenged, and y rises again. Such an incorporation process is known as soiubilization-This picture only works for substances that are surface active and solubilizable. So, absence of the minimum is a good, but not sufficient indicator for the purity of the surfactant The d5niamic test of sec. 1.14c is more sensitive.
4.76
GIBBS MONOLAYERS
(ii) Heterodispersity leads to less sharp breaks at the c.m.c. (ill) Insufficient equilibrium leads to curves that are shifted to the right. When the monolayer relaxes slowly as compared to the formation of micelles the c.m.c. is overestimated. So, /(log c ) curves can adso act as a diagnostic tool. For the interpretation of the slope, the Gibbs equation can be used. Consider first a solution, containing one undisssociated surfactant s plus an undissociated additive A at constant pressure. Then the equation assumes the form dy = -S^dT - r dA/^ - r^dfi^
[4.6.41
Unless otherwise specified, the solutions are assumed dilute; hence the surface excesses with respect to F = 0 may be identified with the analytical surface concentrations and the superindex ^^^ dropped, see sec. 1.2.22c. Moreover, the d/i's may be replaced by Rid In fx or Rid In yc d7 = - S ^ d T - R r r d l n y c -RTrdlnyc^ S
S
S S
A
[4.6.5] A A
from which F and F can be obtained provided accurate and detailed /(logy^c ,logy^c^) curves are available. Moreover, [4.6.5] allows computation of S^ from the temperature dependence, along the lines of sec. 4.3. When surfactant and additive aire dissociated, the d^ factors require a factor v to account for the number of kinetic units per molecule. Counting this number requires some scrutiny, and we shall return to it in subsec. 4.6d. When A is very surface active, it is called a co-surfactant Under appropriate conditions, mixtures of surfactant and co-surfactants C£in give rise to interfacial tensions that are so low that the Gibbs energy of increasing the airea can be outweighed by the entropy gain of forming new droplets. This is the basis for the formation of micro-eniulsions, which we shall not further consider here. 4.6c Non-ionics A wide variety of this group of surfactants is commercially available. They include some of the Tritons (adkyl phenol additives, as far as they are non-ionic), Tweens (sorbitan fatty acid ester polyoxyethylene ethers). Spans (sorbitan fatty acid esters) and alkyl polyoxyethylenes [C^E^, where n and x stand for the number of CH2- or CH3-, and CH20-groups in the hydrophobic and hydrophilic parts of the molecule, respectively). Given our interest in the fundamentals we shcdl emphasize only the last-mentioned group, and only when n and x are sharply defined and the two moieties are either linear or branched in a defined way. Unless specified otherwise, there is an OH-group at the end of the E-chain. Notwithstanding the non-ionic nature of these molecules, micelles sometimes appear to cany a (low) charge; probably caused by preferential uptake of ionic species.
GIBBS MONOLAYERS
4.77
Non-ionics of the C^Ej^-type have a very typical solubihty behaviour, which is related to the EO-water interaction, hydration for short. First, poly(ethylene oxide), (PEO)j^ is fairly soluble in water at room temperature, but poly(propylene oxide) (PPO)x is not (as expected), and neither is polyfmethylene oxide) (PMO)^^ (unexpected). This irregular trend reminds us that solubility is not only determined by hydration in solution, but also by the Gibbs energy in the crystalline phase, which will be related to the molecular packing therein. Based on this difference in solubility, and hence in adsorbability, surface active polymers of the PEO-PPO type have been synthesized [Pluronics); they have a wide scope of application. Another typical property of Cj^Ej^-non-ionics is that they become less soluble with increasing temperature. For the great majority of the other solutes this trend is the other way around. There exists a rather well-defined cloud point T , that is the temperature above which the surfactant becomes insoluble. This point is also known as the lower consolute point (LCP). Its value depends on the nature of the surfactant and on surfactant concentration (it passes through a minimum as a function of c ). Typically, cloud points for Cj^E^^-type non-ionics are between 60 and 80°C. At given n, T increases with x; for instance, for n = 8, T increases from 60 to 95° if x is increased from 5 to 8. The lowering of the c.m.c. with increasing temperature agrees with this lowering of the solubility. The statement that the decreased solubility with increasing temperature is caused by decreased hydration is a tautology and begs for a molecular interpretation. Not only are PEO-water interactions involved, those internally between PEO
KSCN
A— urea
0.6 M Figure 4.29. Cloud point of 5 x IQ-^ M CigEyi influence of added electrolytes and urea. (Redrawn after K. Deguchi, K. Meguro. J. Colloid Interface Set 50 (1972) 223.)
4.78
GIBBS MONOLAYERS
molecules or between water molecules also play a role. A further piece of information is t h a t electrolytes do affect the cloud points, b u t a t higher b u l k concentrations t h a n are needed to screen electrostatic repulsion. Figure 4.29 is a typical i l l u s t r a t i o n . T h e electrolyte KSCNimproves t h e solubility of t h e
surfactant,
w h e r e a s t h e others are salting-out agents. The order of salting-out effectiveness is SO^" > C r > Br" > NOg. Schick found the same for Cg^E^^ (^ s t a n d s for a phenyl group) 1^ a n d the series also agree with older work by other investigators, often with less-defined s u r f a c t a n t s . So this result a p p e a r s well-established. The role of t h e cation is minor, a n d p e r h a p s not definitively established. Urea is a n o t o r i o u s hydrophobic b o n d breaker; t h e fact t h a t it h a s only a minor effect on T^ is additional evidence t h a t we are concerned with a s a l t i n g - i n / o u t of t h e ethoxy groups, a n d not with a n influence on the hydrophobic bonding between the hydrocarbon c h a i n s . For a thermodynamic discussion of salting-in/out phenomena, see the last paragraph of sec. 1.5.4. The above observations regarding chain length effects a n d influences of T a n d c m u s t also be reflected in monolayer properties. Here we are not in the first place interested in t h e positions of the b r e a k p o i n t s of /(logc ) curves b e c a u s e t h e s e virtually m e a s u r e b u l k properties. Rather we should now consider t h e absolute value of 7 , the slope d y / d l n c
before the c . m . c , a n d whatever optical, electriced
a n d rheological properties of sec. 3.7 may appear suitable. Of this we shall now give some examples to illustrate trends. 80 14 13
12
11
10
9
70
6 60
^^^^N^^
50
^ 40 h
\
\
\
\
WWW
30 h
10"
10"
10"
10"
10"
101-4
10"
10-2 M
Figure 4.30. Surface tension -logc plots for non-ionic surfactants of the C^Eg type at 298.15 K. The value of n is indicated. (Redrawn from M. Ueno, Y. Takasawa, H. Miyashige, Y. Tabata and K. Meguro. Colloid Polym. Set 259 (1981) 761.) 1^ M.J. Schick, J. Colloid Set 127 (1962) 801; J. Phys. Chem. 6 7 (1963) 1796.
GIBBS MONOLAYERS
4.79
Figure 4.30 illustrates the effect of the hydrophobic chain length on y(logc ) curves. Most striking is the decrease of the c.m.c. with increasing hydrocarbon c h a i n length, in agreement with the trend discussed before (table 4.4). It is also observed that, a t a n d above the c . m . c , / decreases slightly with increasing length a n d t h a t t h e slope J u s t before t h e c.m.c. i n c r e a s e s in t h i s direction. B o t h observations are in line with a (slightly) increasing compaction of t h e surfactant monolayer, caused by lengthening the hydrocarbon moiety. On closer inspection, these observations also demonstrate the interesting odd-even
effect
see fig. 4 . 3 1 .
This feature can only be observed if the hydrocarbon chains are u n b r a n c h e d a n d in a semi-solid packing; t h e increased lateral attraction compel increasingly, b u t stepwise, the EO moiety in a less favourable configuration. The even c h a i n s pack better t h a n the odd ones. Further along the /(log c ) curves, t h a t is, at lower surface concentrations, s u c h parity phenomena are not observed. Branching of the C- a n d / o r E-moiety c a n have a s u b s t a n t i a l effect. Note t h a t b r a n c h i n g of t h e hydrocarbon chain also h a s consequences for t h e packing, a n d hence for the configurational entropy, of the E-part. Good d a t a can t h e n be £inalyzed by statistical theories a s discussed in sec. 3.5.c.d or e. So far s u c h studies are rare b e c a u s e of the difficulty of synthesizing the required molecules. An example is fig. 4.32 where a
is given for two different surfactants, both b r a n c h e d in the C-E
contact by introducing a glycerol (G) group. It is seen t h a t in case (a) t h a t lengthening the E-chain (increase of x) increases a
, whereas in case (b) this is not so.
Evidently the area is then determined by the gemini hydroccirbons. With r e s p e c t to t h e t e m p e r a t u r e effect, /(logo ) c u r v e s h a v e b e e n mostly analyzed with t h e aim of u n d e r s t a n d i n g the t h e r m o d y n a m i c s of micellization. 45
0.8
s
6 C
0.7
B 40
0.6
3 ^
0.5 35
0.4
10
_I_ 11
30
JL
12
13
14
15
n u m b e r of carbons in chain Figure 4.31. Odd-even effects in the monolayers of fig. 4.30.
4.80
GIBBS MONOLAYERS
(a) 0.9
0.8
0.7
Figure 4.32. Influence of different modes of forking on the molecular cross-section just above the c.m.c. (a) Ci4G(Ej^/2)x'' (t>) (CyjgGE^. Temperature 20C. (Redrawn from K. Kratzat, H. Finkelmann, Langmuir 12 (1996) 1765.) Nevertheless, from these d a t a information regarding y{T) and CL^(T) is obtainable. For instance from the work of Meguro et al. on several Cj^Eg non-ionics^^ (n = 1015) it c a n be inferred that, with increasing temperature, y and a
both decrease,
implying increasing compaction caused by decreasing affinity of the EO-groups for w a t e r in t h i s direction. From t h e negative y{T) coefficient follows a positive interfacial entropy, see [4.6.5]; very detsdled d a t a £ire required to obtain S^ a s a function of T ; the result probably depends on the nature of the surfactant^). Aratono a n d Ikeda also present the influence additives may have on
yilogcj-
curves, b u t most of their examples refer to electrolytes with chairgeable non-ionics or to mixtures of ionic cind non-ionic surfactamts. The above discussion illustrates how m u c h can be learnt from /(logc ) a n d / ( T ) - m e a s u r e m e n t s . There are of course other chciracteristics. One of these is the Volta potential. Although their interpretation is esoteric for t h e complicated surfactants u n d e r study, these potentials can be measured on the m s range, see fig. 4.20, a n d are h e n c e suitable for investigating rates of adsorption^'"*). Moreover, they are sensitive. Faviaini et al.^) used s u c h m e a s u r e m e n t s to analyze the purity of drinking water in Firenze, (Italy), after standardizing the method with non-ionics.
^^ K. Meguro, Y. Takasawa, N. Kawahashi, Y. Tabata and M. Ueno, J. Colloid Interface Set 8 3 (1981) 50. 2^ M. Aratono, N. Ikeda, Adsorption of Surfactants at a Gas-Liquid Interface, ch. 2, in Structure-Performance Relationships in Surfactants, K. Esumi, M. Ueno, Eds., Marcel Dekker (Surfactant Series # 70) (1997). 3) M.J. Schick. J. Colloid Set 18 (1963) 378. 4) N.N. Kochurova, A.l. Rusanov, Colloids Surf A76 (1993) 1. ^^ A. Faviana, M. Costa and S. Bordi, J. Electroanal Chem. 47 (1973) 147.
GIBBS MONOLAYERS
4.81
14 X 10'^ Figure 4.33. Adsorption isotherms for non-ionics of the Cj2Ex type at the air-water interface, obtained from neutron scattering. Arrows indicate c.m.c.'s; the value of x is indicated. (Redrawn from J.R. Lu, T.J. Su, Z.X. Li, R.K. Thomas, E.J. Staples, I. Tucker and J. Penfold, J. Phys, Chem. BlOl (1997) 10332.). Several optical chciracterizations can be found in the review by Lu et al., mentioned in sec. 4.9. Optically, surface excesses can cdso be obtsilned, but the added vgdue of scattering experiments is that they can help to establish density profiles. For neutron scattering; with the possibility of blanking parts of the molecules by deuteration, profQes of parts of the molecules can be made visible. Figure 4.33 gives adsorption isotherms for CigE^ obtained by neutron reflection. Arrows indicate c.m.c.'s. As the isotherms do not show definite plateaus, the values for a are probably less accurate than those obtained from /(logc ) curves, as in fig. 4.30. For the C12E3 surfactant a comparison can be made with a^ in fig. 4.31. The thicknesses as a function of packing could be well accounted for by a statistical thermodynamical rotational isomeric state (RlS)-model^^. Table 4.5 gives some molecular data obtained from neutron scattering, which can be compaired with the corresponding data obtained by other methods. Density distributions are given in fig. 4.34. One of the inferences of this figure is that, with growing EO length, more overlap between the EO part and the hydrocarbon moiety takes place. So, the structure of the monolayer has a three-layer nature; hydrocarbon, mixed, ethylene oxide. Because of this, the width of the alkyl chain region decreases only by a small amount, cdthough a increases strongly. Such types of information cannot be obtained from surface tension measurements only.
^^ C. Sarmoria, D. Blankschtein, J. Phys. Chem. 96 (1992) 1978.
4.82
GIBBS MONOLAYERS
Table 4 . 5 . P a r a m e t e r s of non-ionic monolayers a t the c.m.c Surfactant
C.m.c./ICHM
a
/nm^
/ ( c . m . c ) , mNm"^
m'
^12^
0.33
0.33
25.5
^12^3
0.55
0.36
27.6
^12^4
0.69
0.44
28.6
^12^5
0.64
0.50
30.0
^12^6
0.8
0.55
33.5
^12^8
1.0
0.62
36.1
^12^12
1.25
0.72
38.5
1
Rheological m e a s u r e m e n t s on non-ionic monolayers have also been carried o u t a n d a n example is the study by Lucassen a n d Giles ^K The dilational moduli were m e a s u r e d for CjgEg, C j g E e ^ ^ ^ ^ u ^ e monolayers and their absolute values I K^ I were found to p a s s t h r o u g h a m a x i m u m a s a function of c , with a b r e a k a t t h e c.m.c. By studying the frequency dependence, the loss cmgle (and hence the imaginary p a r t of the modulus) could also be obtained. Interpretation along the lines of
1
0
1
Figure 4.34. Peirtial volume fractions normal to the surface for four non-ionics, obtained by neutron scattering and reflection. Identification ( —) chains, ( ) heads, ( ) water, ( ) total. (Redrawn from Lu et al., see sec. 4.9.)
1^ J. Lucassen, D.Giles, J. Chem. Soc., Faraday Trans. 171 (1975) 217.
GIBBS MONOLAYERS
4.83
subsec. 4.5b showed that the loss could be entirely attributed to diffusion-limited transport. Diffusion control to and from the monolayer persists above the c.m.c. The rather sharp reduction of I K^ I above the c.m.c. is caused by the rate at which the subsurface concentration is affected by the rate of dissociation of micelles. So, indirectly, experimental information on this rate is also obtainable. For an illustration of surface tensions under dynamic conditions, see^K Nonionics at interfaces have also been analyzed by lattice statistics^K 4,6d Ionic surfactants The presence of charges on the surfactant ion leads to a number of differences between these and the non-ionics considered in the previous subsection. (i) The c.m.c.'s are much higher (table 4.4), so y(logc ) can be studied over a larger concentration range. This difference can be annihilated by working in swamping electrolyte. (ii) The structure of the monolayers is affected by charging; the charged head groups repel each other electrostatically. (iii) The monolayer tends to minimize its Helmholtz energy by screening this repulsion through counterion uptake. In the most simple situation (only one surfactant) there is one (monovalent) counterion for each (monovalent) surfactant ion. These ions will form a double layer as discussed in sec. 3.4h. Screening is stronger in the presence of an electrolyte. Because of specific counterion adsorption lyotropic sequences may be observed. (iv) Because of the repulsion that an incoming surfactant experiences from the monolayer, the rate of supply by diffusion is retarded^^. (v) The presence of electrolytes in the solution modifies the number of kinetically active entities in the solution and consequently there appears a stoichiometric coefficient in the Gibbs equation if it is written in terms of activities. As the Gibbs equation remains our primciry tool, let us start with item (v). Some time ago this issue has given rise to a lively discussion in the literature but the issue is now resolved. Originally the question was whether for a fully dissociated ionic surfactant such as A"Na^ or C^Br" the adsorption term in the Gibbs equation (F d// ) should be written as RTF d In c or 2RTr d In c if the solution is s
s
s
s
s
s
ideal. We shall now anadyze the problem thermodynamically. The first thing to note is that the factor does not have anything to do with the fact that at the surface the surfactant consists of two kinetic units, the surfactant ion and the counterion. Rather it is caused by the number of kinetically independ1^ B.V. Zhmud, F. Tiberg and J. Klzling, Langmuir 16 (2000) 2557. 2) N.A.M. Besseling, B.P. Binks, Faraday Discuss. 104 (1996) 167. 3) C.A. Macleod, C.J. Radke, Langmuir 10 (1994) 3555.
4.84
GIBBS MONOLAYERS
ent species into which the surfactant dissociates in the solution. This is typical for Gibbs monolayers; Langmuir monolayers are not at equilibrium with the substrate, so the Gibbs equation does not apply cind neither do the chemical potentials of dissolved species play a role. Let us take by way of example a surfactant of the A"Na^ type, (abbreviated ANa) such as sodium dodecyl sulphate. For cationic surfactants the reasoning is similar. Let the solution also contain dissolved NaCl. For this system the Gibbs equation [4.6.4] becomes dy = - S^dT- r ^ dfi^^ - F '
a
ANa '^ANa
da
[4.6.6]
NaCl '^NaCl
We note that, because monolayer and solution are electronetutral, the surface composition is completely determined by adsorption and depletion of electroneutral entites. Because of this, only two Fd/j. terms suffice. Some authors prefer to write the r.h.s. in terms of ionic components (r..d//._, T., +d//.. +, etc.) which gives one A
A
Na
iMa
term more but also an auxiliary condition, viz. that of electroneutrality. It is to a certain extent a matter of taste which choice is preferred. From an academic point of view it is not elegant at the very outset to make the concession of introducing single ionic activities, i.e. thermodynamically inoperable quantities. On the other hand, in the later elaborations, working with single ionic activities is often unavoidable, particularly when the system contains many components. We discussed this matter in some detail in sec. 11.3.4. Anyhow, we shall start with [4.6.6] and see how far we get. Before elaborating the djj, terms, it must be realized that F^^ > 0 whereas F < 0; electrolytes are negatively adsorbed by charged particles and monolayers. This is the Donnan effect. The ionic components of charge are a^_(=a°) = - F r , . = - F r ^ ^ (4.6.7al
^cr=-^^cr=-^^Nac.
>4.6.7c|
The sum of these charges is zero. As r , ^, < 0, cr, . < -CT°; the surface charge is not =>
NaCl
Na
°
compensated for 100% by counterions; the deficit, cj^^- = -^^^acr ^^ ^ positive contribution due to negative adsorption of co-ions. In principle F^^^ and F^^^^ are obtainable if detailed y(u^^, , u^, ^,) sets are available; these two surface concen' '^'^ANa
'^NaCr
trations follow from dy / djd^^ at constant /^^^^^^ and from dy / d^^^^^ at fixed jd^ , respectively. So, the ionic components of charge are thermodynamically operable quantities. Translating changes in chemical potentials into changes in concentration is the next problem and it requires some scrutiny. We now have to split the dju's into their ionic components; d^^^ = d^^. + d//^^^and d^^^^^ = d^^^^ + d/i^^. and then
GIBBS MONOLAYERS
4.85
assume that all these terms can be written as d//^ = RTd In y^c^, where y^ is the activity coefficient of ionic component 1 in the mixture. In subsec. 1.5.1b we discussed the ins and outs of this assumption. The result is dy = -S^-dT - i ? r r ^ J d l n ( y ^ . c , _ ) + dln(y,^.c,^jl 14.6.8]
Using [4.6.7] the terms can be grouped together to render the ionic components explicit dy = - S°dT - Krr^.dln(y^_ c^.) - i?TVdln(y^^.c,^J
^^ ^ ^^
- RTr^,-dln(y^,.c^,J Solving this equation requires knowledge of activities in solution, which have to be measured separately. It is noted that such measurements yield mixed activity coefficients iy^g^f^i ~ ^^Na'^^cr^^^^ ^^^ ^ pure NaCl solution, etc.), and that a model is needed to split them. Under some conditions this assignment is easy; for instance, ^^ ^Naci ^^ ^ANa ^^^^S^^ in c^^ do uot affcct y^j-. Once this has been established the remciinder is simple because c^. =c,^, » c^, + = c^, ^, +c^„ and c_,_ = c^, ^,. For ^
A
ANa
Na
NaCl
ANa
Cl
NaCl
a somewhat simplified elaboration, see^^. Another elaboration of [4.6.8] is to discriminate between the two extremes of pure surfactant (c^^^^ = 0) and surfactant in swamping electrolyte [c^^^^ » c^^). In the former case the last two terms on the r.h.s. disappear; Cj^^+ = c^ , yANa=f^A-?^Na^)'^''S«that
dr = - SldT - 2 K T r ^ , d l n ( y ^ ^ c ^ J
(no salt)
[4.6.10]
In the opposite case, the last three terms on the r.h.s. of [4.6.8] disappear because dc^, + and dc^,. are equal to dc^, ^,, which is zero for fixed NaCl concentration. As Na
01
^
NaCl
a result dr = - S^dT - Krr^^d I n t y ^ . c ^ J
(excess salt)
[4.6.11]
This equation contains a single activity coefficient. However, as the activity of the surfactant anion is dominated by its interaction with the abundantly present Na^ ions and hence virtually constant, d In y = 0. Hence, d/ = - S^dT = -KTF ,, dine,,, a
ANa
(excess salt)
[4.6.12]
AiNa
So the problem of distinguishing between the Tactor 1' and factor 2' is really a matter of working in the presence or absence of excess (and constant) electrolyte. 1) S. Ozeki, M-A. Tsunoda and S.Ikeda, J. Colloid Interface Set 64 (1978) 28.
4.86
GIBBS MONOLAYERS
Basically the reason is that in the former case there is one degree of freedom less because the activity of the counterion is fixed. Intermediate and more complicated situations require further analysis. Let u s briefly indicate in what direction solutions can be found. (i) Intermediate
values of the surfactant and salt concentration.
For dlnCy.c^) we
write [1 + (d In y^ / d In c^)] d In c^. From [4.6.8]
dy = - S'^dT - RTF
1+
dlny^-1 dine A - ;
dlnc,_ + 1 +
dlnyM,0 d In c,
Na*
A
[4.6.13]
^^y^.^
-RTrNaCl
dlny^^ Na* 1+ |dlnc^j_ l ^ ^ " ^ N a ^ " | l d l,,_ dlnc^, + / cr ; • Na J
The advantage of converting the equation into this form is that In y^ depends less strongly on In c^ than y^. Simplifying to the case that adl d In y^ / d In c^ terms are small compcired to unity, [4.6.13] reduces to dy - - S ' ^ d T - R T F dlnfc (c + c ,)]-JRTr,dlnfc ,(c +c ,)] '
a
s
L s
s
elj
el
I el
s
[4.6.14]
el J
where for convenience of writing we set ANa = s £ind NaCl = el, for surfactant and electrolyte, respectively. Equation [4.6.14] cannot be elaborated further without making an assumption about F , i.e. about the Donnam exclusion. It depends in a known way on the potential y/^ and the concentration, because, for negative adsorption, Gouy theory is adequate (see sec. II.3.5b). This consideration helps somewhat but not completely, because v^^ is not known. (ii) Surfactants
and electrolytes
of other stoichiometry.
This requires additional
book-keeping but does not basically pose new problems. For single electrolytes dju = vRTdlny c , already used in [4.4.2], where v is the sum of the number of kinetic entities into which the electrolyte dissociates. For instance, for a surfactant of the type (A J^Mg^^, if fully dissociated, v = 3 . (iii) Weak surfactants
and/or
electrolytes.
If a fraction a is dissociated, this
fraction can be treated along the lines described above together with a fraction ( 1 - a ) as an uncharged component. Note that by thermodynamic means one cannot discriminate between bound (associated) and free (diffuse) counterions in the monolayer. (iv) Surfactants
and electrolyte
have no ion in common. Example: A Na^ in a
solution of KCl. There is not much difference compared to the pure Na^ case because of ion exchange. The c
+ / c + ratio in the solution is determined by the
concentration ratio surfactant/electrolyte. For two ions as similar a s Na^ and K^ it is such asly that this ratio will be about the same in the monolayer (ion exchange constant K^^++close to unity); for more dissimilar ions i and j , K will deviate more from unity and will be related to the lyotropic sequence.
GIBBS MONOLAYERS
70
4.87
•CO-r^#l
s 6 ^^ 50 40 h No—o-#
Q.
30 h J -5
-4
L -3 -2 log Cg ( Cg in M)
Figure 4.35. Surface tension-logc curves for C.gDMA^Cr. The electrol)rte concentration is indicated; it is either made up from NaCl (•) or from HCl (o). Temperature 25°C. (Redrawn from 8. Ozeki, M. Tsunoda and S. Ikeda, J. Colloid Interface Set 6 4 (1978) 28.) For reviews see ref. ^^ a n d the chapter by Aratono a n d Ikeda, mentioned in sec. 4.9. These a u t h o r s follow a somewhat different analysis b u t elaborate more c a s e s a n d give more examples. Of course, [4.6.6] is a general thermodynamic equation. Instead of NaCl a s the second c o m p o n e n t we could also have written it for a low MW additive, a cosurfactant or acid or base. Examples for charged monolayers c£in be found from the literature by more or less following t h e s c h e m e u s e d for non-ionics, i.e. first d i s c u s s w h a t c a n b e obtained from surface tension m e a s u r e m e n t s a n d then consider other techniques, obviouslywith a certain emphasis on the electrostatics. We shall not consider the classes 'anionic' a n d 'cationic' separately, notwithstanding the sometimes significant difference in behaviour and application. A n u m b e r of monolayer properties involving charge effects have already been included in sec. 3.8b. There, lyotropic sequences were edready discussed. Figure 4 . 3 5 is our first illustration; it shows a n u m b e r of typical t r e n d s . With increasing electrolyte concentration the c.m.c. goes down. As to the n a t u r e of the electrolyte, there is no difference between HCl a n d NaCl. This m e a n s t h a t HCl behaves a s a n indifferent electrolyte; it does not react chemically to hydrolyze t h e monolayer. With increasing c , y diminishes, m e a n i n g t h a t F i n c r e a s e s . The reason is the increased screening of the adverse double layer effect. The 'factor 2' ^^ S. Ikeda, The Gibbs Adsorption Isotherm for Aqueous Electrolyte Solutions, Adv. Colloid Interface Set 18 (1982) 93.
4.88
GIBBS MONOLAYERS
70 h
X X>\
S
2 E 60 h
\ 14\\l3
\ \ \ 12\\11 10\ 9 \ 8 \
\ 7\
50
\
(a)
\
\ \
40 -4
\
\
\
\
\ \
-2
\.
-1
log Cg ( Cg in M)
10 11 12 13 number of carbon atoms in the chain Figure 4.36. Gibbs monolayers of C^SO^Na"^. (a) Surface tension; (b) molecular crosssection near saturation. No salt added. Temperature 25°C. (Redrawn from K. Lunkenheimer, G. Czichocki. R. Hirte and W. Barzyk. Colloids Surf. 101 (1995) 187.) effect in t h e Gibbs isotherm is not well borne out b e c a u s e c^^ is n o t large a s compared to c , particularly not so close to the c.m.c. Figure 4.36 tells a similar story, b u t this time for a series of homologeous anionic s u r f a c t a n t s which were meticulously purified. The interesting feature is that a
p a s s e s through a minimum a s a function of the hydrocarbon chain length
a n d exhibits a pronounced odd-even effect. J u s t a s with non-ionics (fig. 4.31) t h e odd values are higher. Odd-even disparity h a s also been observed with micelle formation ^^ so the effect a p p e a r s established. We will come back to the shortly.
1) P. Mukerjee, Kolloid-Z. 2 3 6 (1970) 76.
a
data
GIBBS MONOLAYERS
4.89
Counterion specificity, for ionic surfactants, is another interesting piece of information. We have already seen that the lyotropic sequence depends on the nature of the head group. For the alkali dodecyl sulphates, counterion binding increases in the sequence Li^ < Na^ < K^ < Rb^ < Cs^ and consequently the area a^ in close packing, changes in the opposite direction (table 4.6). It is gratifying that the packing densities obtained from the maximum slope of the y(ln c ) curves agree well with those from neutron reflection. The areas a in table 4.6 are in line m
with general experience for single chain ionic surfactants with not too bulky head groups. In contrast with that, the a -values for the shorter chains in fig. 4.36 are somewhat enigmatic; they are definitely too low and the decrease with increasing hydrocarbon chain length for the lower members is not readily accounted for. The authors themselves noted that their surfactaints behave as if they were non-ionic; in wjocj case the factor 2 in [4.6.10] would disappear and a doubled. However, it is hard to see why in the bulk of the solution the lower terms would be nondissociated, in contrast to the higher terms. This issue is still open. The areas increase with temperature, as expected because of the increase in thermal motion. The c.m.c. decreases somewhat with Tfor the Li^- and Na"^-surfactants (micellization exothermic) but increases for the K^-, Rb^- and Cs"^-surfactant (micellization endothermic). However, to establish the sign of A^^^H, data over a longer range are needed. As explained before, it is such asly that the c.m.c. passes through a minimum. Table 4.6. C.m.c.'s and molecular areas a at the c.m.c. for alkalidodecylsulphates. Data from /(logo ) curves and from neutron relfection. (J.R. Lu, A. Marrocco, T.J. Su, R.K. Thomas and J. Penfold, J. Colloid Interface Set 158 (1993) 303.) Surfactant
Temp. °C
c.m.c./M
a
/nm^
from;
Y1 mN m ^
m
C^^SO-.Li^
C^^SO^Na^
C^^SO-^K^ C^^SO-^Rb^ C^^SO-^Cs^
d / / d In c
n-refl. 0.50 - 0.51
at c.m.c. 43.7
25.0
8.68 X 10-3
0.493
33.0
8.46 X 10-3
0.519
40.0
8.25 X 10-3
0.556
25.0
8.15 X 10^
0.474
33.0
8.10X 10-3
0.488
40.0
40.0
8.05 X 10^
0.500
39.8
33.0
6.71 X 10-3
0.425
35.3
40.0
6.90 X 10^
0.431
35.4
33.0
5.90 X 10^
0.366
35.0
40.0
6.01 X lO^
0.384
35.3
33.0
5.90 X 10-3
0.389
40.0
6.10X 10-3
0.397
43.8 43.0 0.44
0.37 - 0.38
40.6
34.7 34.9
4.90
GIBBS MONOLAYERS
It fits into the lyotropic sequence t h a t from Li^ to Cs^ the surface tension at the c.m.c. decreases. These sequences find their origin in water structure-mediated anion-cation interaction. S u c h interaction is determined by the sizes of cationanion pairs. Hence, the sequence depends not only on the size of the counterion. b u t also on t h a t of t h e surfactant h e a d group (sees. 1.5.4 a n d Il.S.lOh). So, for C^^anionic s u r f a c t a n t s with other head groups it may be the other way around^'2)^ w h e r e a s for other anionics with t h e s a m e h e a d group (say C^^SO^ i n s t e a d of C SO") the series should be the same. An illustration of the latter can be found in n
4'
ref.^^ For C^^^SO^ monolayers the binding order is indeed Li^ < Na^ < NH^ < K^ a n d for the bivalent ones it is Mg^^ « Ca^^ < Sr^^. For the cationic Cj2Py^ monolayers, counterion binding increases in the sequence F" < CI" < Br~ < NO" < I" < SCN4.5)
A similar s e q u e n c e holds for C i e T M A - h a l i d e s ^ ^ We have already
encountered lyotropic sequences in fig. 3.76 (stearic acid, dramatic effect of Ca^^ binding), fig. 3.85 (behenic acid, Li^ > Na"" > K"^ > TMA"" > TEA"", i.e. j u s t the reverse of the sulfates) a n d fig. 3.86 (bivalent counterions on stearic acid). For practical r e a s o n s it is i m p o r t a n t t h a t some anionic surfactants strongly bind Ca^"^. For example, if a detergent h a s to be used in h a r d water one could consider the u s e of cationics (which have the propensity of a d s o r b i n g on glass surfaces) or t h e a d d i t i o n of a Ca^"^-sequestering agent. For the time being, /(logc^), or, for insoluble monolayers, 7t(A) m e a s u r e m e n t s remain the primary source for studjring these sequences. Neutron scattering/ reflection is not free of interpretational steps (are all the counterions seen?). Electrokinetic, flotation a n d similar experiments with surfactant-covered b u b b l e s are often not sensitive enough; moreover t h e r e m a y b e interpretational problems^'^^. It follows from [4.6.8ff| t h a t the interfacial excess entropy can in principle be obtained from t h e t e m p e r a t u r e dependence of the surface tension. S u c h experim e n t s require some scrutiny both technically (how to prevent evaporation?) a n d interpretationally (now to a c c o u n t for the t e m p e r a t u r e coefficients of chemical potentials at fixed concentrations?). Detailed studies are welcome. However, one striking t r e n d m a y be mentioned^K Adsorption of (at least some) non-ionics is accompanied by a n increase of entropy, whereas for the cationic
0^2^^^^^^^' ^
d e c r e a s e is observed. Again, more systematic s t u d y s e e m s appropriate, before
1) I. Weil, J. Phys. Chem. 70 (1966) 133. 2) V.E. Haverd, G.G. Warr, Langmuir 16 (2000) 157. 3^ K.D. Dreher, J.E. Wilson, J. Colloid Interface Set 32 (1970) 248. 4^ B.C. Parreira, J. Colloid Interface Set 29 (1969) 235. ^^ E.D. Goddard. O. Kao and H.C. Kung, J. Colloid Interface Set 27 (1968) 616. ^J M.M. Knock, C D . Bain, Langmuir 16 (2000) 2857. "7) J.D. Morgan, D.H. Napper, G.G. Warr and S.K. Nicol, Langmuir 10 (1994) 797, ^^ P. Saulnier, J. Lachaise, G. Morel and A. Graciaa, J. Colloid Interface Set 182 (1996) 395. ^^ M. Aratono, S. Ikeda, see sec. 4.9.
GIBBS MONOLAYERS
4.91
inferences c a n be drawn regarding the entropic contribution to the driving force 1^. The present a u t h o r anticipated this effect to be the other way around.) In the s a m e vein, the influence of urea a s a co-adsorptive deserves attention; this s u b s t a n c e is a hydrophobic bond-breaker and its influence on c.m.c.'s is well documented2'3.4) Ionic monolayers can be, a n d have also been, analyzed theoretically either with advanced lattice theories or with Monte Carlo or molecular djniamics simulation. Basic principles a n d some illustrations of monolayer compositions have already been discussed in sec. 3.5. The step from Langmuir to Gibbs monolayers is theoretically realized t h r o u g h the choice of the adsoption energy. As before, the selection of the various parameters ( x -interaction p a r a m e t e r s in lattice theories, c o n s t a n t s in t h e L e n n a r d - J o n e s . i n t e r a c t i o n s in MD, etc.) a n d approximations (choice of lattice, accounting for stereoisomery, or extent of truncation, respectively) r e m a i n a central i s s u e . In view of t h e growing power of c o m p u t e r s , increasingly b e t t e r results may be expected in the near future. By way of illustration we refer to a publication by Van Os et al.^^ which unites a n u m b e r of elements t h a t are relevant for our purpose: (i) the surface tension / is
SOoNa* SOgNa"^
log Cg ( Cg in M) Figure 4.37. Computed interfacial tension at the water-decane Interface in the presence of CjQ -p^SOgNa"^. Influence of branching. Temperature 25°C. (Redrawn after van Os et al., loc. cit.) ^^ For instance, Lu et al., (see table 4.6 for a reference) note that for Cj2SO^Li"*^ d y / d T > 0, whereas d y / d T < 0 for all other alkali-counterions. 2) P. Mukerjee, A. Ray, J. P\v^s. Chem, 67 (1963) 190. 3^ M.J. Schick, J. Phys. Chem. 68 (1964) 3585. 4^ J.M. Corkill, J.F. Goodman, S.P. Harrold and J.R. Tate, Trans. Faraday Soc. 6 3 (1967) 240. ^^ N.M. van Os, L.A.M. Rupert, B. Smit, P.A.J. Hilbers, K. Esselink, M.R. Bohmer and L.K. Koopal, Colloids Surf. A81 (1993) 217.
4.92
GIBBS MONOLAYERS
c o m p u t e d , essentially from [2.3.5] or 12.7.1] for the lattice model or t h e MD simulation, respectively.; (ii) y is related to the equilibrium concentration a n d (iii) the results of the two theories are not only compared with each other, b u t also with new experimental data, in this case for a b r a n c h e d anionic surfactant. Some of these d a t a are given in fig. 4.37. The /(logc )-curves have the u s u a l shape, except t h a t the absolute values are lower, because oil-water interfaces are now considered. The total hydrocarbon length is fixed, b u t the position of the paraphenylsulphonate group is Vciried along the chain. Not m u c h difference is seen between this group on the second or third carbon atom, b u t with the group in the fifth position t h e interfacial tension a n d t h e c.m.c. is higher. Apparently, in the last-mentioned case, packing of t h e surfactant in monolayer a n d micelle are impeded. Analysis in t e r m s of the m e a n field lattice theory or of MD simulation support this conclusion, t r a n s l a t i n g it in t e r m s of density distributions of t h e various s e g m e n t types normal to the interface. The two theoretical approaches agree at least qualitatively, whereby it can be noted t h a t the molecular picture behind the MD simulations is oversimplified. Ionic Gibbs monolayers have also been studied rheologically. An illustration is given in fig. 4.38 taken from a study by Monroy et al. ^^. These results were obtained by a longitudinal wave technique, described in a n earlier paper^). This surfactant very well d e m o n s t r a t e s the m a x i m u m a s a function of c at given (o, a s predicted. 20
6
K"
e 15 13
i
10
' K = 6)7]^
o
•
o o -4
-3
-2 log Cg ( Cg in M)
Figure 4.38. Real and imaginary parts of the surface dilational modulus for Cj2TEt^Br~ mono-layers as a function of surfactant concentration. Frequency 800 Hz, temperature 22°C. (Redrawn after Monroy et al., loc. cit.)
F. Monroy, J. Giermanska and D. Langevin, Colloids Surf. A143 (1998) 251. 2) C. Stenvot, D. Langevin, Lxingmuir 4 (1988) 1179.
GIBBS MONOLAYERS
4.93
see [4.5.41a and b]. The loss tangent is given by [4.5.44]. In the initial part the monolayer behaves as if it were of the Langmuir type. Monolayers of C^^TEt^Br" and CjgTEt^Br" behaved in a less exemplary manner. Finally, we recall that surface light scattering is another modem technique. Essentially, thermal capillary waves can be studied and this enables us to derive interfacial tensions and binding constants. We discussed this matter in sec. 1.10. 4.7 Curved interfaces So far, the Gibbs monolayers treated in this chapter have been flat, or only slightly curved, as in capillary wave experiments. Phenomena can then be interpreted in terms of surface concentrations, interfacicd tensions and in quantities related to them, such as surface pressures and rheological moduli. Now we address interfaces that are so strongly curved that, in addition to the Gibbs energy of extension, the Gibbs energy of bending must also be accounted for. However, we shall not consider interfaces that are so strongly curved that the very notion of interfacial tension loses its meaning. In this section we shall discuss the thermodynamic background within this curvature window. In sec. 1.15 the foundations of such a treatment were cdready laid in connection with the aim of measuring the bending moduli. Now we shall make a further step by considering explicitly how the quantities characterizing the curvature are related to the composition of the solution, that is, to the various chemical potentials /i^, fi^ fi^ Our present aim is to do the spadework for the formation of micro-emulsions and complex phase behaviour that can be observed in concentrated systems of surfactants, co-surfactants and other admixtures. (These systems are planned for Volume V.) One of the new elements that has to be considered is that, say in concentrated micro-emulsions, so much material is withdrawn from the solution that it becomes depleted. At fixed composition (all n^ fixed), this means constraints on the chemical potentials and, hence, on the curvature. Two types of bending have to be considered, see fig. 1.34; simple bending and 'saddle splaying'. Upon bending, the two principal curvatures c^ and c^ have the same sign. (Recall that c =R\^ and c =i^2^. where R^ and ^2 ^^^ ^^^ principal radii of curvature; c^ and c^ have the dimensions of reciprocal lengths.) Bending has to be considered in the formation of micro-emulsion droplets (for which c^ = c^) or of oblong structures. When saddles are formed, c^ and c^ have different signs; the surface is spatially folded in such a way that the direction of the bending in one plane is opposite to that normal to that plane. Two-phase spatial structures built from these units give rise to bicontinuous structures, also known as 'plumber's nightmares'. For practical reasons we adhere to the common habit of working with
4.94
GIBBS MONOLAYERS
J = c^+c^ cind K = c^c^, instead of with c^ and c^ individually. Here, J is called the first or mean, curvature,
K is the second, or Gauss curvature. J and K together
suffice to describe the curvature completely at any point on an interface ^K For a flat interface K = J = 0; for a sphere {c = c = c), J = 2c, K = c^, for a plumber's nightmare c^ = - c , J = 0 and K = -c^. Changes of curvature at a given point are completely given by dJ £ind dK. In [1.15.3] we have extended the Gibbs equation with the terms C^dJ and C^dK to account for Gibbs energy changes as a consequence of changing the curvature; d / = - S ^ d T - Y rdn '
a
itui
i '^i
+ C d J + C,dK 1
[4.7.1]
2
where formally (Nm)
[4.7.2a,b]
T./i's.J
Cj and C^ are called the Jirst £ind second bending moment, respectively. The next step is to derive a relation between //^, J and K. It is a matter of taste, or convenience, which of these variables to take as the independent variable. For adsorption from dilute solutions it is customary to take the concentration (i.e. ju^) as independent. On the other hand, for many theoretical analyses it is easier to assume a certain spatial geometry and then find out the JLL^ of the solvent with which the curved interface is at equilibrium. Let u s follow the second route, i.e. we want to establish Bja^ / dJ and 3^^ / dK. These differential quotients can be obtained from [4.7.1] by changing variables and cross-differentiation. For instance.
5' + S ^i^i
= ~ ®ad^ + q d J + C,dK + X,M,dr, 'dC^
T,K,r's
^^i
V ^^ JT,K,A,nls
V
i /T.j.K.r's^rj
(BAC^) V
i J T.A.J.K.n^'s * nf
V
i JT,A,J,K,n'l's*nf
[4.7.3a]
Similarly,
M y"^^ ^T,J,A,nls
[4.7.3b]
^^ Other combinations of Cj and C2 have also been elaborated.
GIBBS MONOLAYERS
4.95
Because of [4.7.3a eind b] it appears that each chemical potential can be expressed in terms of J and K (or conversely). So. we may write idiLi.)^ =
M
^^i
[4.7.41
dK T,J
which can be substituted in [4.7.1], to give
^r-Zn, a j ,
dy = - S ° d r +
dJ +
^2-I/i
T,K
r;^„ Bn,\
[4.7.5]
dK
,9K,
In this way, the n u m b e r of independent variables h a s been reduced to three, b u t the coefficients have changed;
^A^L*z4'^ [dj)
dJ JT^K
dK). T,J
Zr, dK)
[4.7.5al
T,K
[4.7.5b] T,J
Because of [4.7.3a and b] the differential quotients of //^ can be eliminated. Equation [4.7.5] informs u s in a thermodynamic way how, at fixed temperature, / d e p e n d s on J and K . Now we may compare this with the mechamical equivalent, proposed by Helfrich^^ 7(J,K) = 7(0,0) + -^{j-jj"
[4.7.6]
+ k^K
w h i c h is a n extension of [1.15.2]. The s u b i n d e x o refers to the s p o n t a n e o u s curvature, t h a t is the curvature the interface prefers to a s s u m e in the a b s e n c e of external forces. Helfrich set K = 0 . The constants /c, and k^ are the first, or 1
o
2
'
mean,
'
a n d the second, or Gauss bending modulus, respectively^). Both fc's have the dimensions of a n energy and are of the order of kT (table 1.6). Here, always k > 0 b u t k^ c a n be negative, m e a n i n g t h a t b i c o n t i n u o u s s t r u c t u r e s develop s p o n t a n e o u s l y . T h a t the [J - J ) term h a s a square, whereas the term in K is linear is a consequence of dimensional considerations. See the definitions [4.7.2]. The term 7(0,0) refers to the interfacial tension for which J = J
a n d K = K = 0 , t h a t is for t h e o
o
equilibrium state in the absence of external forces. Elaboration of [4.7.6] leads to y{J,K) = 7(0,0)
+ -^J-^-kJ
J + KK
IJ W. Helfrich. Z. Naturforsch. 28c (1973) 693; 33a (1978) 305. ^^ For alternative symbols, see sec. 1.15.
[4.7.7]
4.96
GIBBS MONOLAYERS
from which the bending moduli can be expressed in t e r m s of differential quotients of 7 with respect to J a n d / o r K;
Mo=-[S
K=0
"^ = (S.=o
[4.7.81
These differential quotients m a y now be identified with those in [4.7.5], considering t h a t [4.7.5 a n d 7] both give the same, complete, information. The results are
k,J 1
= O
^i-I.^.
I.^.
k -A
S/.
14.7.9al
dj
dK
T.K
dj
[4.7.9bl T.K
I4.7.9cl T,J
The zeroes a t t h e s q u a r e b r a c k e t s indicate t h a t the differentiations have to b e carried o u t a t t h e u n b e n d e d interface. So, t h e above derivation essentially d e s cribes a perturbation of the ground state. For stronger deviations from the ground state higher t e r m s are needed (say, by a Taylor expansion, retaining more terms). Equations [4.7.9] are thermodynamic interpretations of the bending moduli for t h e case t h a t the c u r v a t u r e a n d the chemical potential are coupled. This is t h e situation we wanted to describe. De-coupling can, for instance, take place in dilute micro-emulsions; t h e n the adsorption or desorption involved in bending the interface, or m a k i n g more droplets, leads to a negligible change in concentration a n d hence to almost c o n s t a n t chemical potentials. In t h a t limit.
Vo=-Ki
^aCj^
aj
K = (^2)0
[4.7.6a,b,c]
/o
This situation is em extension of t h a t described before, see the text a r o u n d [1.15.9]. Note t h a t there the bending w a s referred to the flat interface (J = 0, K = 0), whereas we now refer to the interface in the equilibrium state, (subindex o) which may have a spontaneous curvature. For further reading a b o u t this matter, see Safran's book, mentioned in sec. 4.9 a n d ref.^^.
^^ M. Gradzielski, Bending Constants of Surfactant Monolayers, in Curr. Opinion Colloid Interface Set 3 (1998) 478.
GIBBS MONOLAYERS
4.97
4.8 Applications Few phenomena find a wider range of application than Gibbs monolayers, even though they are rarely recognized, let alone given this name. They are encountered in detergency, flotation, advanced oil recovery, extraction processes, pharmaceutical products, the preparation, stability and breaking of foams and emulsions in wetting/de-wetting phenomena, ... briefly, they seem ubiquitous. One of the central issues is recognizing the basic monolayer properties, accepting that in most practical situations these layers will consist of more than one component. And, if one is not so lucky, one could well encounter a layer of which not all components are known; it can be a nightmare to detect the presence of an unknown minor component in the system, and control its properties. Some applications have already been discussed in sec. 3.9; in connection with fig. 4.23 we briefly touched on the thin film stability problem and in chapter 5 the role of Gibbs monolayers in wetting will be addressed. Volumes TV and V will also contain several applications. Let us therefore select one illustration, the preparation of (macro-) emulsions, as a paradigm. This topic is of great practical relevance and it is tjrpical in that, as in most applications, Gibbs monolayers under dynamic conditions are involved. Emulsions are commonly prepared by mixing the oil (o) and water (w) in the presence of one or more emulsijiers, under vigorous agitation. Emulsifiers are substances that adsorb strongly at the oil-water interface. We shall assume that there is only one, and call it 'the surfactant'. The type of emulsion that is formed depends primarily on the nature of the surfactant. According to the empirical Bancroft rule this type tends to be such that the phase into which the surfactant is more soluble becomes the continuous one. So, hydrophilic surfactants promote the formation of oil-water emulsions, for hydrophobic surfactants it is the other way around. A host of commercial emulsifiers are available, tailor-made for certain purposes, but the above rule remains generally valid. Emulsions are thermodynamically unstable. They will never form spontaneously. Their Helmholtz energy is higher than that of a phase-separated system with the same overall composition, because of the large interfacial area [AF^ is large). It follows that the emulsifier has a dual task; (i) it acts as an agent which lowers the interfacial tension; (ii) it works as an agent preventing coalescence of just-formed droplets (coalescence is the merging of droplets to form bigger ones). In practice, emulsifiers are often mixtures in which one, or more, act in the former sense, the other(s) in the latter. The thermodynamic.instability of emulsions is generally recognized but has led to the misunderstanding that the work done by the machine in preparing the emulsion (such machines are also called 'emulsifiers') is needed to create the interface. Quantitatively, only a small fraction of this work is transformed into excess
4.98
GIBBS MONOLAYERS
interfacial Helmholtz energy; most of it is dissipated into heat. A simple 'back-ofthe-envelope' computation will prove this; if a n emulsion were to coalesce completely, a n d the lost interfacial Helmholtz energy were fully dissipated into heat, the t e m p e r a t u r e of a n average system would increase by less t h a n 10"^ deg. However, the increase of the temperature, accompanying the emulsification process is higher by factors of 10^-10^, depending on the n a t u r e of the emulsion. The related m i s u n d e r s t a n d i n g is t h a t t h e primary t a s k of the s u r f a c t a n t is to lower t h e interfacial tension. Rather t h i s t a s k is related to t h e dynamics
of t h e droplet
formation - a n d stabilization process. Recall t h a t thermodynamic instability of a s y s t e m implies t h a t t h e properties (type, size a n d size distribution) a r e n o t determined by t h e state variables b u t by the history. In this history it is not so much y t h a t plays a role, b u t the rate and extent to which / is adtered w h e n a r e a s are increased. Technically speaking, we are interested in the interfacial rheology, with the m o d u l u s I K^ I a s the m a i n characteristic. In fact, model s t u d i e s on t h e formation of emulsions ^^ a n d foams-^^ in which the interfacial rheology is actively a c c o u n t e d for d e m o n s t r a t e t h i s r e l a t i o n s h i p , exhibiting t h e
characteristic
m a x i m u m a s a function of concentration. On the other hand, theoretical interpretations in which the type of emulsion is related to the spontaneous curvature (J^ in sec. 4.7) in the presence of surfactants with a certain structure ('cylinder', wedge', cone', etc. ...) are b o u n d to fail, even if only on the account of size sccdes; radii of emulsion droplets exceed those of surfactant molecules by a factor of 10^, so from t h e point of view of a surfactant molecule all water-oil interfaces in a n emulsion are flat. It is far beyond this chapter to discuss all the intricacies of emulsion preparation. For Volume V we plan £in entire chapter devoted to emulsions. However, let u s d i s c u s s one fragment in the chain of events, viz. the dynamics of t h e s t e p s preventing the re-coalescence of just-formed droplets. A s s u m e t h a t by external force, large streaks, or feathers, of liquid are formed a n d t h e n b r e a k u p u n d e r t h e influence of the Rayleigh instability. Fresh oil-inwater a n d water-in-oil droplets will form. The question is now which of t h e two types
is more coalescence-resilient u p o n a following encounter. Generally t h e
disjoining p r e s s u r e between the incipient drops is not enough to keep t h e m apart; u n d e r the prevailing highly dynamic conditions drops are not yet fully covered by s u r f a c t a n t s , a n d t h e mechanical forces are strong. Rather, we have to look for m e c h a n i c a l c o u n t e r forces. Two situations are sketched in fig. 4.39. In (a) t h e s u r f a c t a n t is in the c o n t i n u o u s p h a s e , in (b) it is dissolved in t h e drops. W h e n droplets are formed in s u c h a way t h a t the surfactant is in the continuous p h a s e ,
1^ J.J.M. Janssen, A. Boon and W.G.M. Agterof, Am. Inst. Chem. Eng. 40 (1994) 1929. 2^ R. Tuinier, C.G.J. Bisperink, C. van den Berg and A. Prins, J. Colloid Interface Set 179 (1996) 327.
GIBBS MONOLAYERS
/ ^ \
4.99
(a)
(b)
Figure 4.39. Explanation of Bancroft's rule. Two droplets just after their formation. (a), in the initial stage the freshest parts of the surface (those directed towards each other) have transiently a higher interfacial tension because it takes a certain time for the surfactant to penetrate between the drops and replenish the interfaces. As a consequence of these transient gradients, liquid is sucked in between the droplets (arrows in fig. (a)), pushing them apairt, until the surfaces carry enough surfactcint to ensure stability. In case (b) such Marangoni effects are much less efficient and stability is more difficult to reach. In this way the principle behind Bancroft's rule can be understood ^^ but at the same time it is appreciated that there is more under the sun. (How to make this quantitative? What cire the forces and rates involved? What is the rate of adsorption? Are there surface active minor components? Are there micelles, of which the rate of decomposition is rate determining?, etc.). For an overview on emulsion formation, including interfacial rheology aspects, see the review by Walstra and Smulders-^K It is hoped that the contents of this chapter will help the reader to find a way through this, and other, challenging labyrinths. 4.9
General references
Note, Most of the references to chapter 3 also apply to the present chapter; except for a few they are not repeated. Aut. Div. Much information on surfactants can be found in Marcel Dekker's Surfactant Series, (Various editors; some emphasize Gibbs monolayers.) M. Aratono, N. Ikeda, Adsorption of Surfactants at a Gas-Liquid Interface, chapter 2 in; Structure-Performance Relationships in Surfactants. K. Esumi, M. Ueno, Eds., Marcel Dekker (Surfactant Series #70) 1997. (Further reading and update to sec. 4.6.) ^^ M. van den Tempel, Proc. 2nd Int. Congress Surface Activity, 2 (1960) 573. 2^ P. Walstra, P.E.A. Smulders, Emulsion Formation, in Modern Aspects of Emulsion Science, B.P. Sinks, Ed., Roy. Soc. Chem. (1998) chapter 12,
4.100
GIBBS MONOLAYERS
R. Defay, I. Prigogine and A. Bellemans, (revised and translated into English from the original French version (1951) by D.H. Everett), Surface Tension and Adsorption. (Chapters VII-XIII deal with Gibbs monolayers; their convention differs from ours.) S.S. Dukhin, G. Kretzschmar and R. Miller, Dynamics of Adsorption at Liquid Interfaces, Elsevier (1995). (Considers adsorption phenomena with a variety of applications; some emphasis on diffusion-controlled interpretations.) D.A. Edwards, H. Brenner and D.T. Wasan, Interfacicd Transport Processes and Rheology, Butterworth (1991). (More advanced than our sec. 4.5, but very readable. Also contains a variety of applications. The book has an engineering slemt and contains problems.) P. Joos, Dynamic Surface Phenomena, VSP (Netherlands) 1999. (Covers and extends our sections on surface relaxations. Rather rich in formulas.) G. Kretzschmar, R. Miller, Dynamic Properties of Adsorption Layers of An^)hiphilic Substances at Fluid Interfaces, Adv. Colloid Interface Set 36 (1991) 66124. (Review, 227 refs. Background reading of sec. 4.5. This review is not very different from: R. Miller, G. Kretzschmar, Adsorption Kinetics of Surfactants at Fluid Interfaces, Adv. Colloid Interface Set 37 (1991) 97-121.) H. Lange, P. Jeschke, Surface Monolayers in Nonionic Surfactants; Physical Chemistry, M.J. Schick, Ed., Marcel Dekker (Surfactant Series #23) 1987. (A bit dated review by one of the earlier 'grandmasters' in the field; covers our sec. 4.6c.) D. Langevin, J. Meunier, Interfacicd Tension; Theory and Experiment, in Micelles, Membranes, Microemulsions and Monolayers, W.M. Gelbart, A. Ben-Shaul and D. Roux, Eds., (Springer, 1994). (Reviews several themes belonging to the present chapter. The techniques mostly apply to adsorbed monolayers. The book as a whole contains much interesting background reading. J.R. Lu, R.K. Thomas and J. Penfold, Surfactant Layers at the Air-Water Interface; Structure and Composition. Adv. Colloid Interface Set 84 (2000) 143304. (Extensive review, over 300 references of the optical characterization of surfactant monolayers; further reading to our subsecs. 4.6c and d.) E.H. Lucassen-Re5niders, Adsorption of Surf octant Monolayers at Gas/Liquid and Liquid/Liquid Interfaces, in Progr. Surface Membrane Set, D.A. Cadenhead, J.F. Danielli, Eds., 10 (1976) 253, and Adsorption at Fluid Interfaces, chapter 1 in Anionic Surfactants; Physical Chemistry and Surfactant Action, E.H. LucassenReynders, Ed., Marcel Dekker (1981). (Two reviews by the same author; she emphasizes adsorption thermodynamics and 2D equations of state.)
GIBBS MONOLAYERS
4.101
E.H. Lucassen-Reynders, Surface Elasticity and Viscosity in Compression/ Dilation, in Anionic Surfactants: Physical Chemistry of Surfactants, E.H. LucassenReynders, Ed., Marcel Dekker (1981). (Principles are emphasized, additional reading to sec. 4.5.) R. Miller, P. Joos and V.B. Fainerman, Dynamic Surface and Interfacial Tensions of Surfactant and Polymer Solutions. Adv. Colloid Interface Set 4 9 (1994) 249. (Review of methods for obtaining dynamic interfacial tensions. 211 refs.) S.S. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes, Addison-Wesley (1994). (Interpretation of interfacial tensions, capillarity; further reading to sec. 4.7.) J.C. Slattery, Interfacial Transport Phenomena, Springer (1990). (Thorough and comprehensive treatise. Contains highly abstract and detailed parts, but applications are also considered.) M. van den Tempel, E.H. Lucassen-Reynders, Relaxation Processes at Fluid Interfaces, Advan. Colloid Interface Set 18 (1983) 281. (Review in which various relaxation mechanisms £ire considered.) A. Watts, T.J. VanderNoot, The Electrical Double Layer at Liquid-Liquid Interfaces, in Liquid-Liquid Interfaces; Theory and Methods, A.G. Volkov, D.W. Deamer, Eds., CRC Press (1996). (Review with many useful references. Other contributions to this book are also relevant for Gibbs monolayers.)
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5 WETTING 5.1 General considerations 5.1a Principles and definitions 5. lb The laws of Young and Neumann 5.2 Thermodjniamics of wetting and adhesion 5.3 The relation between adsorption and wetting. Wetting films 5.3a The disjoining pressure in wetting films 5.3b Film formation by adsorption 5.3c Case studies 5.3d A note on film thinning 5.4 Measuring contact angles 5.4a Factors affecting contact angles 5.4b Sessile drops and captive bubbles on a flat surface 5.4c Contact angles from forces on objects in interfaces 5.4d Tilted plates 5.4e Capillary rise or depression 5.4f Vertical plates and cylinders 5.4g Fibres 5.4h Individual colloidal particles 5.4i Powders and porous materials 5.4j Concluding remark 5.5
Contact angle hysteresis 5.5a The phenomenon 5.5b Origins 5.5c Interpretations 5.5d Hysteresis on model surfaces 5.6 Line tensions 5.7 Interpretation of static contact angles 5.8 Dynamics 5.9 Porous systems 5.10 Influence of surfactants 5.11 Applications 5.1 la Characterization of the wettability of solid surfaces 5.11b Flotation 5.11c Particles at interfaces 5.lid Various other applications 5.12 General references 5.12a lUPAC recommendation 5.12b Books, Reviews and Symposium Proceedings
5.3 5.3 5.10 5.12 5.22 5.23 5.28 5.33 5.38 5.39 5.39 5.41 5.47 5.47 5.48 5.50 5.53 5.54 5.56 5.58 5.59 5.59 5.60 5.63 5.66 5.68 5.73 5.77 5.83 5.89 5.93 5.94 5.96 5.98 5.101 5.103 5.103 5.103
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5
WETTING
Wetting is an umbrella term describing all phenomena involving contacts between three phases, of which at least two are fluid. At that line of contact three interfaces meet, each with its own excess Helmholtz energy and interfacial tension. Wetting phenomena are very relevant in the living and non-living world and many examples can be mentioned. Wetting of solid objects (plates, rings) by a liquid the surface tension of which had to be measured, was encountered in chapter 1. Every-day illustrations can be observed all around us. For example; with cars, mostly the lacquer surface is hydrophobic, either intentionally by waxing or because of dirt. Hence, raindrops will not spread on it but form isolated droplets on the surface. They do spread, however, on cleamed windscreens. It is said that sufficiently hydrophilic surfaces aire completely wetted by water, whereas hydrophobic surfaces are only partially wetted or even not wetted at all. Similarly, hydrophobic objects may float on water, even if their density exceeds that of the water, whereas exactly the same items with a hydrophilic surface would sink immediately. The practical relevance is immediately obvious; think of the necessity of dispersing pigment particles in an aqueous solution to prepare a water-based paint, or of dispersing cacao powder in milk to make a chocolate drink. As long as a situation of partial wetting is encountered, the contact angle that the liquid makes with the solid is the discriminating parameter. Already in chapter 1 of Volume 1 we discussed some related phenomena. The story of how 'they went to sea in a sieve' in Lear's Nonsense Songs, is not necessarily nonsense provided the sieve is fine and hydrophobic; the weight it can support is determined by the balance between gravity and capillary pressure. Light objects like whirligigs can therefore 'walk' on a clean water surface, but will sink if the water is polluted by surfactants. (More precisely, the capillary pressure keeps them afloat but metabolic action is needed to obtain locomotion.) In 1902 Lord Rayleigh reported as a curious observation 1^ that certain iron gauzes, pressed under a thin layer of mercury on the bottom of a glass vessel remained down, although iron has a lower specific density than mercury. Rayleigh interpreted the phenomenon as being caused by the 'ferrophobicity' of mercury. The term 'ferrophobicity' is phenomenologically correct, but not with respect to content; iron £ind mercury do not repel ^^ The Scientific Papers of Lord Rayleigh. Dover Reprints. New York, Vol. IV (1964) 430.
5.2
WETTING
each other 'as the 'phobicity' suggests) but attract each other strongly; rather the glass of the vessel prefers contact with iron over that with mercury. Entrained air bubbles, preferring the mercury over the iron, could also have played a role. Numerous other practical illustrations can be given where either good or poor wetting is desirable. Rain cloth and canvas tents should preferably be waterrepellent. Many plant leaves and flowers are hydrophobic. The observer will enjoy the beauty of rain drops on rose petals or on a lotus leaf. Nevertheless, water-based agricultural sprays should preferably wet the leaves for which they are intended. The capillary rise of ground water in soils allows agriculture above the ground water table. This rise can also be observed when the surface of tea in a cup is touched by a sugar cube; the liquid is first sucked up before the sugar dissolves. More quantitative is the issue of the selective wetting of mixtures in minerals, used as a basis of separation in the technical process known as Jlotation. Many wetting features are also encountered in detergency and enhanced oil recovery. Ink jet printing requires a controlled extent of wetting of the paper. Nature itself presents us with more examples. The engulfment of antigens by leucocytes, known as phagocytosis, is an interesting illustration. Another biological example that comes to mind is that of cobwebs which Ccin be seen more clearly on damp autumn days because of the tiny dewdrops sitting on the threads. However, it is not obvious to infer from the almost spherical shapes of the droplets that the threads are hydrophobic because the droplets are much larger than the diameter of the thread; the contact angle between drop and thread is not easily observed by the naked eye. Ducks have water-repellent feathers, into which water cannot penetrate. Such feathers act as an 'airbag', making the ducks lighter and protecting them from the cold. If the water is polluted by surfactants, it can penetrate into the feathers, threatening the life of the animals. It is also interesting to compare the consequences of rain falling on a dry and a wet soil; in the former case the drops often do not wet the soil, whereas in the latter they do. This is a typical example of how the history of a process affects the degree of wetting. Figures 5.1 and 5.2 are photographs of partial wetting situations. In fig. 5.1 the surface was intentionally made hydrophobic by applying wax to it. The droplets are heterodisperse; the bigger ones are flattened and the contact angle is obtuse. Figure 5.2 shows how the addition of detergent improves the wetting; this is one step in textile laundering. Without visual aids one cannot infer from these pictures whether the uncovered support (metal or fibre) carries a thin adsorption layer or a thicker aqueous film. In other words, the presence of drops does not tell us whether or not the surface in between is completely wet or not. It follows from these pictures and the preceding discussion that the contact angle a is at least one parameter in characterizing the extent of wetting. For a-^ 0 the situation of complete wetting is approached (we shall not discuss whether zero
WETTING
5.3
Figure 5.1. Water droplets on a hydrophobized metal surface. (Courtesy J. Maas.) situations up to almost complete non-wetting (obtuse, or 'blunt' contact angle). For liquids on solids, contact angles above 120° are rare, mercury droplets on glass being one of the examples. For liquid-liquid-solid systems such high angles can be observed more often. Bubbles that appear to float on a surface exist by virtue of the resilience against breaking of the intervening fluid film. Severed more examples of wetting phenomena can be given, and there is every reason to try to understand and control these wetting phenomena. To do so systematically is the purpose of this chapter. 5.1 General considerations 5.1a Principles and definitions The above already leads us to recognize a number of objects and problems for
5.4
>"^wp—g
WETTING
III
m
^
Figure 5.2. Drops of water on a textile fibre. From top to bottom the detergent concentration increases, resulting in improved wetting. (Photo courtesy of P. van der Vlist.)
further study, including; - measurement and interpretation of contact angles - history effects (hysteresis). There are differences between singles measured for advancing liquid fronts and for retracting, or receding, fronts. Can these differences be reproducibly measured? What is their origin? In this connection, is there a difference between statics and dynamics? - effects on external forces on the droplet (so-called/orced wetting): do they alter the contact angle? - complete wetting; under what conditions can a surface be fully covered by a thin homogeneous layer of liquid? And what is the relation between wetting layers and drops? - dewetting, the reverse of wetting, in which, for instance, an originally thick liquid layer on a support, thins (by evaporation, gravity or suction at its borders) to form a thin unstable film that breaks up in droplets. What are the conditions for break-up? - spreading tensions, introduced in sec. 3.2 as the driving forces for the spreading of a liquid over a liquid surface. How do they change during the spreading? And what about spreading over a solid surface? - adhesion vs. cohesion. When a liquid spreads over a solid, the driving force is the adhesion between the two; spreading takes place against the internal cohesion
WETTING
5.5
of the liquid. Can we define and measure heats of adhesion and heats of cohesion. How are these related? - line tensions, one-dimensional forces in the three-phase contact line, promoting its contraction or extension, depending on the sign of the tension. Do they exist? What is their origin? Can they be measured? - influence of surfactants. Their adsorption at the SL and LG interface lowers the two interfacial tensions, improving wetting, but they also affect the rates of wetting and spreading. The list is not complete, but indicates the versatility of wetting problems. Systematizing these is not always straightforward because they are interwoven. Nevertheless we shall try. Before doing so let us briefly discuss the notions of hydrophilicity and hydrophobicity. These names are used for macroscopic surfaces and for (parts of) molecules to indicate affinity for water, and we shall follow this custom. It is noted that the two phenomena are typically collective, i.e. involving many molecules. In a vacuum, a water molecule attracts any molecule, hydrophobic or not, and this is also true for a drop of water amd a drop of oil. In wetting science, the surface of a substance is Ccdled 'hydrophilic' when a water droplet on it spreads or forms drops with a (very) low contact angle. Can these notions be made quantitative? The concept of wetting is not restricted to water aind aqueous solutions. One can also speak of the wetting of a surface by an oil. In that case, the notions of (relative) hydrophilicity and hydrophobicity have to be replaced by (relative) lyophilicity and lyophobicity. For a liquid droplet in contact with a solid (i.e. for a GLS-system) the contact angle is understood to be the one through the L-phase. For LjLjS cases we shall indicate through which phase the contact angle is measured. Upon further consideration it treinspires that five distinctions have to be made. (i) With respect to the scale. One can, and often has to, distinguish between a macroscopic, colloidal and molecular scale, where in some circles it has become fashionable to replace 'colloidal' by 'mesoscopid, to give it a modem flavour. The phenomena mentioned in the introduction all deadt with macroscopic systems. On this scale, typically phenomenological, thermodynamic approaches are required, or, for moving systems, hydrodynamics and thermodynamics together. Surface and interfacial tensions refer to macroscopic amounts of fluids and solids and the three-phase contact line is just a curve without molecular structure. However, on the molecular scale, classical three-dimensional thermodynamics does not work well and has to be replaced, or complemented, by statistical thermodynamics which, in turn, is based on explicit assumptions about molecular interactions. Monomoleculcir layers on surfaces also belong to this category. Between these two scales, say for fluid layer thicknesses 0(1-10^ nm), we have the colloidal range.
5.6
WETTING
where among other things Van der Waals and double layer forces play a role. Mostly these require a thermodynamic interpretation, sometimes with a mix of statistics (for instance if steric forces caused by adsorbed polymers are involved). A typical distinction between molecular and macroscopic scales is encountered in the notion of surface hydrophobicity, as already discussed. One cannot say that a surface is hydrophobic because it repels water molecules. On the contrary, from the gas phase such molecules are adsorbed to any surface, even to the most hydrophobic ones, by Van der Waals forces. Hydrophobicity is typically a multimolecular phenomenon; if water is repelled from a surface this is because water-water attractions outweigh those between the water and the surface. This brings up the question of the transition of interactions between only one molecule, a few of them, or a large collection. The scale argument also plays its part in the hydrodynamics of spreading. Consider a hydrophilic surface onto which a water droplet is placed. It will spread, but how fast? The rate will be determined by the driving force and the resistance to flow. The driving force is the unbalanced sum of interfacial tensions acting on the perimeter. For instance, for a droplet L on a horizontad flat solid surface it is ySG _ ^SL _ ^LG cos a, where a is the contact angle. When spreading has progressed so far that a - ^ 0, this force becomes y^^ -y^^ -y^ ^ which in [3.2.1] we have identified as the spreading tension S gSGCL) _ ^SG _ ySL _ yLG
[5^ j ,
Definition [5.1.1] can also be applied under conditions where the spreading tension is so large that a thin film (the precursor Jilrrii is pulled out of the droplet. The conditions for this to happen will be discussed in sec. 5.8. The spreading tension can be interpreted as the isothermal reversible work per unit area of replacing the SG interface by an SL and an LG interface. In sec. 5.2 we shall further specify the gSG(L) rpj^g resistance has a macroscopic component, quantified by the viscosity of water and a molecular one, determined by the progress of the leading liquid molecules spreading over the as yet unwetted surface. Obviously, there will be a mechanistic transition in the colloidal range. This is another challenge of the kinetics of wetting. Finally, the scale distinction is also recognized in the interpretation of contact angles. In sees. 2.5c and 2.11b we saw that surface tensions, and hence contact angles, can to a first approximation be interpreted in terms of an additive contribution of dispersion forces and a non-dispersive contribution (say, hydrogenbridging in water). These forces act across the entire bulk of each phase and, at least for London-Van der Waals forces they have a colloidal range. On the other hand, a limited adsorption of surfactants, which only act over a molecular range, drastically modifies the wetting behaviour.
WETTING
5.7
►!<
macroscopic range
U<
colloidal range
molecular range
Figure 5.3. Static partial wetting, indicating the three distance ranges for a drop on a surface. The picture is not to scale in the vertical direction. Discussion in the text. Figure 5.3 illustrates a possible profile. It is not to scale; the molecular p a r t h a s a t h i c k n e s s of 0 ( 1 nm), the colloidad reinge of Ofl-lO^ nm), the macroscopic range above t h a t . Most of t h e techniques for m e a s u r i n g profiles of d r o p s described in c h a p t e r 1 a n d sec. 5.4 c a n n o t see the deviations from macroscopic behaviour, resulting from interactions in the coUoidcd range. Hence, extrapolation of the LG interfacial profile (dashed), leads to a macroscopic contact angle a, which h a s a value t h a t would have been obtained h a d there not been colloidal interactions. It is determined by the interfacial tensions y^,
y^^ and y^^. These three tensions are
modified by adsorption at the corresponding interfaces; hence a is also determined by adsorption a t the SG interface, which is in the molecular range. Deviations from the macroscopic behaviour of the LG profile occur in the colloidal range. They are upwaird or downward, depending on the sign of the disjoining pressure
^^ As to
its molecular interpretation, the contact angle is determined by s u m m i n g over all i n t e r a c t i o n s , including t h o s e over t h e colloidal d o m a i n . Accounting for t h e deviations in the profile, caused by the disjoining pressure, requires special techniques. Anticipating sec. 5.4, we refer to a paper by Kolarov et al.-^^ who obtained t h e profile u s i n g a microscopic interference t e c h n i q u e . T h e s e a u t h o r s could account for the deviations a s s u m i n g reasonable values for the disjoining p r e s s u r e . It is probably also possible to obtain profiles using AFM with very small droplets. For obtuse contact angles these techniques become cumbersome a s far a s illumination (or approach) from above is involved. An interesting problem is w h a t consequences very high positive or negative disjoining p r e s s u r e s may have for the stability of the drop. Yeh et al.'^^ a u g m e n t e d t h e equations for the sessile drop
^^ The notion of disjoining pressure was introduced in sec. 1.4.2 and expressions for its Van der Waals part can be found in sees. 1.4.6 and 7. There will be further discussion of this in sec. 5.3a. 2) T. Kolarov, Z. Zorin and D. Platikanov. Colloids Surf. 51 (1990) 37. 3J E.K. Yeh, J. Newman and C.J. Radke, Colloids Surf. A156 (1999) 525.
5.8
WETTING
profiles of sec. 1.2 to account for a variety of disjoining pressure-distance relationships. In this way they could account for a variety of wetting situations. This paper also reviews earlier work along these lines. In fig. 5.3 we have drawn the SG interface as a very thin film, but it can be anything between just a sub-monolayer adsorbate up to a film of colloidal dimensions. As already stated, under dynamic advancing conditions the droplet may be preceded by a 'foot' or precursorJUnt (ii) With respect to the driving force for partial wetting. Two cases have to be distinguished. A drop brought onto the surface can either spread spontaneously to a certain extent (spontaneous partial wetting) or it can be induced to do so by application of an external force (forced wetting). In the former case the spreading tension is the driving force; in the latter the force is externally applied, or superimposed on the spreading tension. As will be seen, the contact angle differs between these two processes, an aspect that has to be kept in mind if, in practice, surfaces or powders have to be wetted rapidly. (iii) With respect to the attainment of equilibrium. For a droplet at equilibrium with the surface onto which it sits, the contact angle is a suitable macroscopic characteristic. Equilibrium means that no net force acts on the system, so equilibrium conditions can be derived mechanically (from a balance of surface tension components) or thermodynamically (minimalization of the Helmholtz energy at given V and T). On either of these bases Young's equation for the contact angle can be derived (sec. 5.2).
(b]
S Figure 5.4. The phenomenon of contact angle hysteresis.
WETTING
5.9
When equilibrium is not attained, the contact angle changes with time. When the driving force is determined by surface forces we can refer to the text leading to [5.1.1]. Typically, thermodynamic equations now have to be replaced by kinetic expressions, involving p a r a m e t e r s like molecular friction or diffusion coefficients (on the molecular scale) or viscosities (on the coUoidad a n d macroscopic scale). In the stationary state the driving a n d friction forces balance each other. For forced wetting the issue is even more complicated. (iv) With respect to the ideality of the surface. There is a great deal of difference between perfectly smooth, homogeneous (so-called Fresnel-) surfaces a n d those usually encountered in practice, which are mostly heterogeneous with respect to geometry a n d composition. P e r h a p s liquid s u b s t r a t e s (as met in w a t e r c o n t a c t angles on clean mercury) are the sole examples of Fresnel surfaces. The m o s t typical consequence of these two types of surface heterogeneity is t h a t of angle hysteresis,
that is the phenomenon in which the advancing
contact
contact angle,
a(adv) differs from the receding contact angle, cir(rec). Here, 'advancing' m e a n s a change in contact line in s u c h a way t h a t the s u b s t r a t e surface not covered originally b e c o m e s wetted. 'Receding' refers to the reverse. F u r t h e r specification is required, because a(adv) and a(rec) are contact angles at rest, i.e. they are static entities. Nevertheless, the process preceding the m e a s u r e m e n t plays a central role so, strictly speaking, one needs a djmamic step, even if only infinitesimal, in order to define a static quantity. (This is reminiscent of the necessity of considering a process, in this case a reversible process, when defining thermodynamic equilibrium.) We shall therefore define a(adv) and a(rec) a s the contact angles j u s t before the wetting line starts to advance or recede, respectively.
a
V (rec.)
0
V (adv)
Figure 5.5. Forced wetting. Trends in the dependence of the contact angle on the rate of displacement.
5.10
WETTING
To illustrate how this works out in practice, consider fig. 5,5, which shows the typical trend for the dependence of the contact angle on the rate v of wetting. This rate is not specified for the moment; it may be different in different p a r t s of the drop or film. The trend is t h a t advancing angles become larger the faster the front advances, whereas for receding angles it is the other way ciround^K The hysteresis remaining for u = 0 is the common' hysteresis. For definiteness we shall, in the following, call the difference a(adv v ^0)-
a(rec LJ -> 0) the hysteresis. In doing so,
it is realized that, in practice, sometimes m e a s u r e m e n t s a t non-zero v are carried out, invariably leading to a larger hysteresis. Basically, contact angle hysteresis is not completely understood, b u t it is certainly related to t h e geometric a n d chemical heterogeneity of the solid surface. Most real surfaces contain p a t c h e s of different wettability. If a liquid spreads, t h e advancing contact line will avoid the poorer wettable zones. By the s a m e token, retraction is resisted in the better wettable zones. Hysteresis will lead to some irregularity on a molecular scale of the advancing front, a n d hence to a dependence of the macroscopic contact angle on details of the (pretreatment of the) surface. Contact angles on Fresnel surfaces, free of hysteresis, will be called ideal angles
contact
(some a u t h o r s call these intrinsic contact angles). Strictly speaking, only
ideal contact angles can be interpreted by equilibrium thermodynamics. There cire indications t h a t during advancement on, or retraction from, a non-Fresnel surface the liquid front gets stuck in successive, metastable positions. Around these metastable situations thermodynamics can also be applied, and, a s conditions are rarely ideal, recommending certain contact angle Vcdues becomes a real issue. This h a s to be kept in mind w h e n considering our compilation of contact gmgles in app. 4. Hysteresis will be treated more systematically in sec. 5.5; we will d i s c u s s t h e definite values of the contact singles in sec. 5.4a. (v) Wetting and dewetting.
Dewetting
is the removal of a drop or wetting layer
from a surface cind in m a n y respects it is the converse of wetting, both in the static a n d dynamic sense. It may occur spontcineously (a film may break u p into droplets) or t h e p r o c e s s c a n be externally forced, say by blowing away a droplet or by replacing a drop by another, better wettable fluid. Of course, both in SLG a n d SLjLg systems, wetting by the one fluid (L or Lj) m e a n s dewetting of the other (G or L2). The hydrodynamics of dewetting will differ from t h a t of wetting; the contact angle is a(rec) which is rate-dependent (fig. 5.5). 5.1b
The laws of Young and
Neumann
The above discussion illustrates t h a t for liquids on surfaces, besides spreading 1) R.A. Hayes and J. Ralston, J. Colloid Interface Set 159 (1993) 429, collected literature examples of forced wetting and presented them (their table 1). In their note Langmuir 10 (1994) 340 the same authors illustrated fig. 5.5 for the systems water aind water-glycerol on poly (ethylene terephtalate).
WETTING
5.11
tensions, contact angles are prime wetting characteristics. They can be measured (sec. 5.4) but the interpretation is only straightforward for very well-defined systems, which is no comfort for everyday practice. Similar things can be said about Young's law, which we derived in sec. 1.1 and which, for a liquid drop on a solid reads ySG _
cos a =-^^
SL
^—
15.1.2]
This equation is valid only for mechanical equilibrium, so it does not apply when spreading takes place. It is also assumed that the line tension is negligible. For a floating drop, as sketched in fig. 5.6, three measurable LL interfacial tensions, 7"^, 7^ and y°^ and contact angles, a^, a^ and a", can be distinguished. Such systems aire stable provided each of the interfacial tensions is lower than the sum of the other two. The three angles and interfacial tensions are related through y^y
- ^ ^ sm a
yYtt
yttP
= ^—J = - ^ ^ sm a^ sm a^
15.1.31
which is known as Neumann's triangle, after Franz Neumann who formulated it long ago^^ In [5.1.3] a" +a^ +a^ = 360°, so one of the angles does not need to be measured. Equation [5.1.3] is more general than [5.1.2], to which it reduces for a flat undeformable support. Moreover, Young's equation cannot be tested experimentally because surface tensions of solid surfaces cannot generally be measured. Notwithstanding this. Young's equation will play a central role in this chapter; its basic correctness for the conditions for which it has been derived is unchallenged. Other relevant wetting chairacteristics are enthalpies of wetting. Of these, several kinds exist (sec. 5.2) most of them referring to advancing wetting fronts. For fluid mixtures the interpretation has already been dealt with in sec. II.2.3d; it often also involves contact aingles. From this discussion it also follows that the qualitative notion of (relative) hydrophobicity or hydrophilicity of a surface can be made quantitative either by basing it on the water contact angle on the substrate or on one of the enthalpies of wetting. The former is usually chosen because of easier measurability but some care has to be exercised, not least because of the difference between the advancing and receding contact angle. Certainly, all of this only leads to a chciracteristic on the macroscopic scale and there is no unambiguous way to translate this to the molecular scale. We shall return to this, but already note that interpretation in terms of contact angles implies characterization in terms of Gihbs or Helrnholtz ^^ F.E. Neumann, Vorlesungen uher die Theorie der Capillaritdt, A. Wangerin, Ed., Teubner Verlag, (Leipzig, 1894).
5.12
WETTING
(a:
(c)
energies,
Figure 5.6. Floating drop (a) with identification of the three angles and interfacial tensions (b). Construction (c) is known as 'Neumann's triangle' in the stricter sense.
whereas t h a t in terms of heats is a n enthalpic interpretation. The latter
does not include a n entropic contribution. 5.2
T h e r m o d y n a m i c s of w e t t i n g and adhesion
In this section we consider the statics of wetting, emphasizing the roles of spreading t e n s i o n s a n d contact angles for ideally flat surfaces. Only o n e - c o m p o n e n t liquids will be discussed. The process of wetting involves the creation of new types of interfaces at t h e expense of others. For example, when a liquid droplet spreads over a solid, more of the SL a n d LG interface is created, whereas (part of the) SG interface h a s vanished. All these changes are accompanied by changes in thermodynamic characteristics, s u c h a s the Gibbs or Helmholtz energies of the system. Here, thermodynamics is useful to
WETTING
5.13
1
(d;
Figure 5.7. Attachment of spherical particles or droplets to (solid) surfaces, (a) h -^ «>, no interaction; (b) h of colloidal range; interaction determined by the disjoining pressure across phase 2; (c) attachment; (d) attachment of a rectangular particle; (e) spreading of an attached drop until the contact angle is a; (f) droplet deforms but does not wet [a = 180°); (g) complete wetting; (h) partial wetting on a completely wetting film. (i) define operationally the required (or gained) work (ii) formulate equilibrium conditions. The restriction is t h a t all steps in the process should take place reversibly. Phenomenologically speaking, wetting a n d adhesion are related. Adhesion is the a t t a c h m e n t of particles, or drops, onto surfaces, or of two macrobodies of whatever geometry to each other. Consider a solid or liquid sphere, approaching a surface S, through medium 2, until a t t a c h m e n t a n d spreading, if possible, occurs (see fig. 5.7). This process can be divided into two steps. 1) The approach from infinitely large shortest distance h between the surfaces
5.14
WETTING
until touch-down (fig. 5.7a-c). Upon passing this range the interaction is given by the disjoining pressure
/7(h) across phase 2. This is the domain of colloid stability.
Usually, /7(h) has positive (repulsive) and negative (attractive) parts as in fig. 5.13b. When phase 2 is a vacuum, attraction prevails. The sign of /7(h) dictates whether or not attachment (adhesion) takes place. The integral over /7(h) from h = oo until h = 0 is the Gibbs energy of adhesion. Steps (a) - (c) belong to the domain of colloid science, which will be deferred to Volume IV. We now consider what happens after attachment has taken place. For a solid sphere this is the end of the process (situation (c)). Attachments of a solid pcirticle which has flat facets on its surface (as in case (d)) can lead to a common interface between particle amd surface. 2) When 'particle' 1 is a liquid, it may spread completely (fig. 5.7g), to some extent until a certain contact angle a is attained (fig. 5.7e), or special situations may arise (figs. 5.7f and h). Cases 5.7d , e, g and h differ fi*om the other ones in that a new type of interface is formed, that between S and 1, at the expense of those between 1 and 2 plus S and 2. Each of these interfaces is the seat of a Helmholtz energy, so that interfacial tension badances can be set up. In situation (e) it is seen that the extent of spreading is determined by the competition between the work of cohesion of 1 (a measure of the tendency of keeping the molecules of type 1 together) as compaired to the work of adhesion between 1 and 2. Whether the droplet wets the surface partially, to form a finite contact angle, or spreads completely, may depend on a number of factors, like the chemical nature of the phases and the temperature. When a change in one of these variables reverts complete wetting into partial wetting, or conversely, one says that a wetting transition has taken place. Sometimes the film between fluid 1 and a solid is resilient against coalescence. One can then see the droplet 'float' on the surface (fig. 5.7f). Floating droplets are also sometimes observable in reactors if S is a fluid and phase 2 a vapour. A number of phenomena may be responsible for that. The most common reason is that the intervening film is kinetically stable, but stability can also have a thermodynamic origin (disjoining pressure positive). We note that in situations of figures 5.7f-h, thin films of liquid 1 between solid and phase 2 occur. J u s t as between the spheres and the surfaces in cases (a) - (c) the Gibbs energy of this film is determined by the disjoining pressure /7(h) across the film, where h is now the film thickness. We shall discuss the thermodynamics of such films in some detail, mostly in sec. 5.3a. In the further elaboration a general phenomenological framework for wetting can be developed. Because of its thermodynamic nature, this framework is macroscopic and static; it refers to equilibrium or to reversible processes. So, the kinetics of wetting cannot be analyzed in this way and only one contact angle, the equilibrium angle, can be considered. It remains an issue how this thermodynamic contact angle relates to the one that is physically measurable. Another typical feature is that interfaces are always taken to be at equilibrium with the adjacent
WETTING
5.15
contact perimeter
( a ) spreading wetting
[ b ) adhesional wetting
( c ) immersional wetting
Figure 5.8. Three kinds of wetting, illustrated for the gas-liquid (lightly hatched) - solid (darker hatched) system. The work involved is indicated. The solid is idealized as a cube with flat faces. p h a s e s . For instance, interfacial tensions are determined by p , T, a n d t h e chemical potentials of t h e components in these p h a s e s . Transient gradients in t h e s e tensions are not supposed to occur. In practice, this situation c a n be attained if t h e adjoining p h a s e s are not depleted, which is a s s u m e d to be the case now. Depletion may occur in practice, for instance in the penetration of a surfactant solution into a dry powder, where the advancing liquid front can become depleted of surfactcint, with ensuing consequences for wetting. (See further sec. 5.9.) Thermodynamically, three types of wetting c a n be distinguished; adhesional
a n d immersional
wetting.
spreading,
Figure 5.8 shows the underlying physical
phenomena, illustrated for the case of a solid, a liquid and a gas. Spreading
wetting, or j u s t spreading,
s t a n d s for the process which occurs w h e n
the solid is spontaneously wet by the liquid. Recall t h a t in [5.1.1] we defined the spreading
tension a s S^^^^^ = y^ - y^ - y^^. According to Ross a n d B e c h e r ^ l this
condition for spreading goes b a c k to Marangoni (1865). In 1922 H a r k i n s a n d Feldman introduced it (but calling it 'spreading coefficient') for a liquid a t the oilwater interface a s ( y ^ -y^^
- y^^) 2) They also introduced a 'penetration coef-
ficient' ( 7 ^ + y^^ - y^^) which is akin to our work of immersional wetting.
1^ S. Ross, P. Becher. J. Colloid Interface Set 149 (1992) 575. ■^^ Recall that we prefer the term 'spreading tension' over the less precise spreading coefficient' and 'spreading parameter'. Our spreading tension is also known as work of spreading, w^^^.
5.16
WETTING
The notion of spreading tension deserves further specification. It represents the Helmholtz energy gain if a unit area of dry SG interface is replaced by a liquid film, which is thick enough for its Helmholtz energy to be characterized by the s u m of the two tensions (y^^ + 7 ^ , see fig. 5.8a. Spreading will occur only if S > 0 , For S = 0 the system is at equilibrium and for S < 0 the droplets retracts its perimeter, leading to partial wetting (as in fig. 5.7e). The situation of fig. 5.7f is not usually obtained by the s p o n t a n e o u s formation of a film between fluid 1 a n d solid b u t from a n a p p r o a c h i n g d r o p t h a t c a n n o t completely r e a c h t h e solid surface ^^ For practical application it m a k e s sense to distinguish between the initial
spreading
tension a n d the s a m e at later stages. Several phenomena can give rise to a lowering of S during spreading. In sec. 3.2, w h e n dealing with the spreading of one liquid over another, m u t u a l saturation was noted a s a cause. Recall the classical example of b e n z e n e on water, which initially s p r e a d s (S > 0) b u t in later stages r e t r a c t s (S < 0) to eventally attain equilibrium contact angles. For the spreading of a droplet on a n originally dry surface evaporation of droplet material with s u b s e q u e n t adsorption at the SG interface may be another reason. In t h a t case 7^^ diminishes with time. So, a more general definition is gSGCDj^j = ySG* _ ;pSG(^j_ ^SL _ ^LG
[5 2.1]
sSG(L)(f) = y^^it)-
[5.2.1b]
or y^^ - y^
where 7^^* is the original surface tension of the solid a n d ;r^^ the surface pressure a t t h a t interface, c a u s e d by adsorption, see [3.1.2]. So, for the initial spreading tension sSGH-'dnje
QSG(L
[5.2. Ic]
Ht ^ 0)
and Ss°»-'(eq) =: y S G . - ;r(eq) -. y S L . . sSG(L)(in) - S^^^^Heq) = ;r(eq)
yLG
[5.2. Id] [5.2. le]
For t h e spreading of one liquid on a n o t h e r S^i^^^2^ (in a n d eq) are accessible from t h e c o n s t i t u e n t three interfacial tensions (The tables for liquid-liquid interfacial t e n s i o n s in appendix 1 refer to mutually s a t u r a t e d systems so from t h e s e only S(eq) is obtainable). Examples of initial a n d equilibrium spreading tensions
^^ On liquid supports (Lj) spontaneous intrusion of a liquid (L2) film between Lj and G is more common. See, for example, R.B. Heady, J.W. Cahn, J. Chem. Phys. 58 (1973) 896; M.R. Moldover, J.W. Schmidt, Physica 120 (1984) 351.
WETTING
5.17
c a n be found in the literature 1'-^^. However, spreading coefficients for liquids on solids a r e experimentally inaccessible; although estimations c a n be m a d e from contact angles a n d information on the surface p r e s s u r e . Alternatively, theoretical relations containing the spreading tension can be a s s u m e d correct. By way of example, E n d o h et al.'^) determined
S^i^^^s^ from t h e t h i c k n e s s of a floating,
flattened liquid lens, using a n equation derived by Langmuir'^^ Takii a n d Mori^^ extended t h i s work. They reported spreading coefficients for Ce-Cio aliphatic hydrocarbons between 0° a n d 50°C on water. Here, we shall not consider situations in which y^^ and y^^ also depend on time, for instance by relatively slow adsorption of surfactants. Adhesional
wetting means that an adhesional or adhesive Joint between solid and
liquid is formed, a s in fig. 5.8b. However, in this type of wetting t h e solid is not completely engulfed by the liquid. Adhesional wetting across air always o c c u r s because London-Van der Waals interactions between condensed bodies across gases are attractive. However, adhesional wetting across a liquid may be repulsive; this is for instance the case when the Hamaker constant A. ^„ . is negative (ch. 1.4). It may give rise to the stable films of fig. 5.7f. Adhesional wetting leads to a situation characterized by a system-specific contact angle. Immersional
wetting (fig. 5.8c) takes place if the solid is completely wet, t h a t is,
it is the result of spreading for S > 0 during the entire process, a s in case (a). It is a less general p h e n o m e n o n t h a n a d h e s i o n a l wetting. It is n o t e d t h a t
forced
immersion of only partially wettable objects in a liquid leads in practice to t h e entrainment of air bubbles on the surface. The arrows in figs. 5.8b a n d c indicate the adhesion a n d immersion process, respectively. The corresponding work w of adhesion is the isothermal reversible work needed to create one unit area of SG interface, plus one unit area of LG interface u n d e r the simultaneous annihilation of 1 unit are of SL interface. For further thermodynamic elaboration it is useful also to bring the work of cohesion
into the picture. Generally speaking, upon spreading, as in fig. 5.8a, the
internal cohesion of the liquid h a s to be overcome in order to achieve a d h e s i o n between liquid a n d solid. Figure 5.9 indicates how the work of cohesion is defined. An infinitely long column of unit cross-section is cut into two halves a n d w^^^ is t h e i s o t h e r m a l reversible work required to achieve that. Only for liquids or c
1^ A.W. Adamson, A.P. Oast, Physical Chemistry of Surfaces, 6th ed., (Wiley, 1997), their tables IV-2. 2) G.J. Hirasaki, J. Adh. Set Technol 7 (1993) 285, collected after R.E. Johnson, R.H. Dettre, J. Colloid Interf Set 21 (1966) 610. LA. Girlfalco and R.J. Good. J. Phys. Chem. 6 1 (1957) 904, and others. 3^ K.I. Endoh, A. Mikami and Y.H. Mori, Colloids Surf 46 (1990) 99. 4) I. Langmuir, J. Chem. Phys. 1 (1933) 756. ^^ T. Takii, Y.H. Mori, J. Colloid Interface Set 161 (1993) 31.
5.18
WETTING
ompletely ductile solids is this process operational for the same reasons as expounded in sec. 1.13. The next step is to interpret the various u;' s in terms of thermodynamic characteristics. Which one? We want an interfacial excess function per unit area. The choice is between U^, F^, G^, Q^ and y (see sec. 2.2). Of these, U^ is of course not a
a
a
a
'
a
suitable because the entropy term would be disregarded. F° and G^ have the drawback that they contain ^J^^l^^ terms (see sec. 2.1) which means that changes in the adsorption upon wetting have to be accounted for. Therefore, Q^ is the preferred quantity, because it represents the excess entropy and energy in an interface if it is extended by one unit area under equilibrium with its surroundings. Statistically, it means that we are working grand canonically, see [2.1.19]. The various surface concentrations F^ adjust automatically by ad- or desorption, provided the process is carried out reversibly. As before, the requirement that all ^^'s remain constant implies that the adjacent phases should be infinitely large, so as not to become depleted if Icirge new areas are created. We shall restrict ourselves to systems where this premise is satisfied. As Q^ = yA and 12° = / , the grand potential per unit area is the thermodynamic equivalent of the mechanical' interfacial tension, interpreted as a force per unit length. With this in mind, for adhesional wetting o(LG) Q ,a(SG) + Q Q ,a(SL) [5.2.2a] adh ySG ^ ^LG _ ^SL
[5.2.2b] [5.2.2c]
= /^^(l + cosa)
where we have used the Young equation [5.1.1]. Equation [5.2.2b] was derived long ago by Dupre^^, and we shall therefore refer to [5.2.2b and 2c] as the Dupreequation. The equation applies to the adhesion of a solid to a liquid, where it has been ^---^
;
'
7T-
1
1
1
i>
l£_
"'coh
, -(^—
^
>r '
^^^ 1
1 -J ■
T1 "
k
Figure 5.9. Definition of the work of cohesion. ^^ A. Dupre, Theorie Mecanique de la Chaleur, Gautiers-Villars (Paris) (1869) 369.
WETTING
5.19
a s s u m e d t h a t t h e c h a n g e in liquid surface a r e a is negligible. In t h e opposite situation (interchange S a n d L in fig. 5.8b) substantial changes in this area m a y occur, depending on drop size and contact angle, with a concomitant contribution to w ^^ 1). adh
As for the meaning of / ^ ^ in [5.2.2b and c], we proceed a s in connection with the spreading tension, see [5.2.1]. When, before adhering to the liquid, the solid particle is completely dry, y^^ is y^^\
In that case, w^^^ is identified a s t h e initial work of
a d h e s i o n . u;^^j^(in). However, in practice this situation is not easily realized; mostly t h e solid will have been exposed to the vapour of the liquid a n d hence 7^^* h a s to be replaced by y^^* - 7t{t). For solids at equilibrium with the v a p o u r before adhesion, y^^ is Just the equilibrium solid-gas interfacial tension. Only u n d e r t h a t condition is S^^^^^ = 0 and does Young's equation apply. For immersional wetting, similarly w. = x2^(SG)_ ^o(LG) imm
a
[5.2.3a]
a
= y^^ - y^^
[5.2.3b]
= 7^^ cos a
[5.2.3cl
a n d for cohesion w ^ = 2X2^^^^ = 2 7 ^ coh
a
[5.2.4a,bl
'
It is seen that w
I
' J
is always positive; work h a s to be done to remove solid particles
floating on the surface of a liquid. Immersion requires cos a >0 or 0 < 9 0 ° . Between the spreading tension a n d the various types of work, simple relationships c a n be derived, provided they all apply to exactly the s a m e conditions. For instance, for initial spreading a n d adhesion on a n SG surface in its pristine state, from [5.2.2a and 4b], S^^^^Hin) = w^^-w
,
adh
coh
W ^^ = W^ +^W adh
imm
2
[5.2.5a] ^
^
coh
[5.2.5b] *■
Equation [5.2.5a] agrees with intuition. The spreading coefficient c a n only b e positive if the work of adhesion exceeds t h a t of cohesion. When t h e SG interface carries a n a d s o r b a t e , t h e s e equations r e m a i n valid on t h e u n d e r s t a n d i n g t h a t ^a(SG) ^g j^Q^ lower by a n a m o u n t of n. When this surface carries a liquid film, ^o(SG) j^^g ^Q ^^ replaced by the corresponding film tension, say 7^. For thick films 7^ -^ 7^^ + 7^^; in this case the situation of fig. 5.7h will not arise; to achieve that, 7^ m u s t differ from 7^^ + 7^^ by a n a m o u n t determined by the disjoining p r e s s u r e /7(h) across that film (sec. 5.3). 1^ M.E. Schrader, Langmuir 11 (1995) 3585.
5.20
WETTING
Figure 5.10. Derivation of the Young equation for the equilibrium contact angle. Regarding t h e heat, or enthalpy,
of (immersional) wetting we refer to sec. Il.l.Sf. The
q u a n t i t y c a n b e experimentally determined. Q. ^ = ~ ^ w ^ ~ ^imm^ ~ ~ ^ i m m ^ ' a n d we related it to adsorption from t h e gas p h a s e . We u s e d a Gibbs-Duhem relationship to obtain SL^
ySL _ J 3 r dT
A H w
a
^^^cosa- T
SG^
ySG_^3y dT
dy^
cosa
[5.2.6al
[5.2.6b! 1)
dT
In sec. II.2.3d immersional enthalpies were analyzed for binary liquid mixtures, including dilute solutions. All quantities on the r.h.s. of [5.2.6b] are operational, with t h e qualification t h a t by virtue of the m e a s u r i n g procedure a = or(adv) a n d depend on t h e history, (how dry is the solid prior to immersion?). A t h e r m o d y n a m i c derivation can also be given for Young's law, a s a n alternative to t h e mechanical one in sec. 1.1. This law h a s a long history. It dates back to, a n d obtained its n a m e from, Thomas Young, who a s long ago a s 1805, derived it in w o r d s ^ ^ T h e m a t h e m a t i c a l formulation is more recent a n d probably s t e m s from Gauss*^^ Sometimes [5.1.1] is called the Young-Dupre equation, though Dupre did not formulate that, b u t rather (our) [5.2.2b], so we shall not follow this custom. Achieving t h e thermodynamic counterpairt of the mechanical derivation requires minimalization of t h e grand potential of the system v^th respect to changes in t h e contact angle at fixed chemical potentials of the s u r r o u n d i n g s . Because equilib-
1) A H in [II. 1.3.42 and 43] should be A H . r>-
w
'
w
a
2) T. Young, PhU. Trans. 9 5 (1805) 65, 82. ^^ See J.C. Melrose, Advan. Chem. Series 4 3 (1964) 158. Other references for more rigorous derivations are R.E. Johnson jr., J. Phys. Chem. 6 3 (1959) 1655 and D.H. Everett, PureAppl Chem. 52 (1980) 1279.
WETTING
5.21
rium with t h e s u r r o u n d i n g s is maintained, Q^'^^^K Q"^^^^^ a n d £2"^^^^ r e m a i n constant when the three areas A^^, A^^ and A^
vary a s a result of a change in cos a.
Consider t h e simple situation of a spherical drop segment, a s in fig. 5.10. Sphericity is n o t really a restriction b e c a u s e it is always atteiined w h e n t h e d r o p s a r e small enough to neglect flattening by gravity. Of course, contact angles are indepe n d e n t of t h e size of t h e drop provided it remains macroscopic. In this spherical cap t h e contact angle follows from cosa
= -^ 5r^ +h'^ which is attained a t fixed volume V
[5.2.7]
=-h{3r^+h^]
cap
6
^
[5.2.8] ^
The total interfacial grand potential of t h e system is ^a
^ ^ a ( S G ) ^ S G ^ ^ a ( S L ) ^ S L _^ ^a(LG)^LG a a a
= {A- Kr^)af''^ + nr^Qf^^ + K{r^ + h^jx^f ^^^
[5.2.9]
w h e r e A is t h e total area of t h e b a s e . Now t h e variation d ^ ^ is required a s a function of a n infinitesimal change in r, d r with concomitant c h a n g e s in cos a and h; dn^ = - 2nrdra^^^^^ + 2nrdrn^^^^^ + n(2rdr + 2Mh) = 0
[5.2.10]
u n d e r t h e auxiliary condition dV
= - (6rhdr + Sh^dh + S r ^ d h k = 0 cap
g \
[5.2.11]
/
These two expressions can also be written a s rdr(i2^^^^^ +12^^^^^ - 12^^^^^ + hQ^^^^dh = 0 \
a
a
a
/
[5.2.12]
a
and 2 r h d r = (r^ + h ^ ) d h = 0
[5.2.13],
respectively. Using [5.2.13], dh c a n be expressed in dr, which is s u b s t i t u t e d in [5.2.12]. Again using [5.2.7], it is found t h a t n^^^^^ + n^^^^^ cos a - Q^^^^^ = 0. As y = Q^ the required equation ySG _ ySL
cos a = ^
^—
(a = a{id] = a(eq))
[5.2.14]
is immediately retrieved. This derivation is longer t h a n t h a t using surface tensions a s mechanical forces.
5.22
WETTING
but has the advantage that no assumptions have to be made about the existence of tangential forces in solid-fluid interfaces. At the same time it is transparent what assumptions have been made; equilibrium, absence of gravity, inertness of the solid, flatness of the surface, absence of line tension and constancy of the three interfacial tensions. The equation only considers ideal contact angles and the earlier discussions defines the conditions for ideality. Some of these restrictions will be relcixed, or at least addressed, in later sections. Absence of gravity is not an issue of principle; gravity siffects the shapes of sessile drops but not the contact angles. In the absence of gravity all macroscopic fluid-fluid interfaces are spherical; this is a consequence of the fact that the Laplace pressure is the same everywhere, see [1.1.2 and 3], and of the equality of JR^ and K^, or c^ and c^ for axisjmimetrical systems. Gravity is negligible if the drop is small enough. Larger drops are flattened, so the profile is different. Recall that the capillary length ll.3.3al is given by
which is 0(mm) (see table 1.1). It quantifies the size below which body (gravity) forces are negligible with respect to surface forces. For SL1L2 systems, the droplets may be larger. When an experimental observation is at variance with one of these premises, further consideration is required. For instance, sometimes it is found that the contact angle depends on the size of the droplet; action of the line tension has been put forward as one of the reasons (sec. 5.6) but something else may be involved as well. The usual reason is contact angle hysteresis and the fact that different-sized drops sample different surface heterogeneity. Further it is noted that there is no way of experimental verification of [5.2.14] because y^^ and y^^ are inoperational. At best the difference y^^ - y^^ is accessible. Finally, reconsider fig. 5.6. At equilibrium there should be a force balance orthogonal to the directions of all menisci. For instance, for the 1,2 meniscus, 7^2 sin(K - Cfg) = /j2 sin(7c -a^).As sin(7c -a] = sin a, one may also write y^^ sin a^ = 7j2 sina^, or y^^ /sina^ = y^^ /sina^. This gives two equalities of [5.1.2] to which the third is readily added. Alternatively, the Neumann triangle construction of fig. 5.6c, in combination with the sine rule of trigonometry yields [5.1.2] immediately. 5.3 The relation between adsorption and wetting. Wetting Hlms This topic can be subdivided into two parts; (i) the relation between adsorption of molecules from the drop-forming liquid onto the solid surface and the wetting that may ensue for high surface concentrations. In other words, what are the phenomena taking place when a liquid layer is built up on a surface stairting from the adsorbent in pristine condition? (ii) The reverse process. What will happen if we start from a very thick liquid
WETTING
5.23
layer on the surface, letting it thin, say by evaporation? Consider first a flat solid surface in contact with a monocomponent v a p o u r a t pressure p. Gas molecules will adsorb, more of t h e m at higher p. The relation between the adsorbed a m o u n t and p is the adsorption isotherm, which may obey one of t h e isotherm equations, discussed in sec. II.1.5f-g. At i s s u e now is w h a t h a p p e n s if p approaches its saturation value p . Under w h a t conditions will the adsorbed layer gradually thicken, leading to complete wetting, or form s e p a r a t e droplets with between t h e m either a complete or incomplete monolayer or a t h i n film? The answer h a s to be found in the stability of the thin liquid film, formed at the interface between solid a n d vapour. Colloquially stated, w h a t is stronger, t h e internal cohesion of the adsorbate or the adhesion between adsorbate a n d surface? In colloidal parlance, is the disjoining pressure /7(h) across a film of t h i c k n e s s h positive or negative, a n d how does FJ change as a function of h ? The reverse approach, thinning of macroscopic layers, leads to the s a m e issue; u p o n decreasing h a t a given m o m e n t the colloidal range is reached. T h e n it d e p e n d s on the sign of /7(h) w h e t h e r the film s p o n t a n e o u s l y d r a i n s further or attains a stable thickness. So, both for the 'bottom u p ' and 'top down' approach it is essential to u n d e r s t a n d the behaviour of /7(h) in wetting films. This will be o u r next theme. To remain within the domain of 'Fundamentals' we shall restrict the d i s c u s s i o n to monocomponent liquids without surfactants, t h o u g h low concentrations of electrol5^es are a s s u m e d present, because these are needed to control the electric contribution to /7(h). 5.3a
The disjoining
pressure
in wetting
films
The behaviour of /7(h), already encountered in the previous section, is the most central t h e m e of colloid stability a n d this issue will be dealt with extensively in Volume IV. Here, we shall anticipate this discussion by reviewing t h e m a i n elem e n t s . The disjoining p r e s s u r e w a s already introduced in sec. 1.4.2. For two colloidal particles, or macroscopic phases, a distance h apart, let the Gibbs energy of interaction be G{h). For the present purpose only the interaction between flat surfaces h a s to be considered. The macroscopic p h a s e s are the (mostly solid, b u t in some cases liquid) support S (or LJ and the vapour G, interacting across the liquid
Figure 5.11. Definition of a wetting film.
5.24
WETTING
film L (or Lg) of thickness h, see fig. 5.11. Wetting films are typical representatives of systems determined by hetero interaction (G and S are different materials). Symmetrical systems like SLS films (in colloid stability) or GLG films (in foams) involve homo interaction. From G{h], -/7(h) is obtained by differentiation with respect to h. A variety of interaction forces contribute to G(h) and /7(h), each with its own sign, magnitude and typical decay as a function of h. One of them is the LondonVan der Waals force, also known as dispersion force, cind already described extensively in chapter 1.4. For wetting films G[h) may be positive or negative, depending on the sign of the Hamaker constant A , examples of which can be found in appendix 1.9. (See under A for water as the wetting liquid.) For such forces, ^vdw^^^ "^ ^vdw^^^ ^^^ ^vdw^^' decay as h"^ and h"^, respectively, provided the layers are thin enough to remain within the non-retarded range but thick enough to be of colloidal range, which is often the case, see [1.4.6.2 and 6). London-van der Waals forces are ubiquitous. Moreover, they will be virtually identical for films of pure water and films of dilute solutions of surfactants and electrolytes. The interesting point is that A can be either positive or negative. In the latter case ^vdw ^ ^' meaning that dispersion forces tend to stabilize thick films. Seemingly in that case air or a vacuum and the solid repel each other; in reality this apparent repulsion reflects the fact that L attracts S more than it attracts itself. The second contribution to G{h], G Ah), stems from the overlap of electric double layers. So, this term will contribute if a double layer develops at both the SL and LG borders. For pure non-aqueous liquids hardly any double layer can be formed gind even for pure water G Ah) will be small, even though at the water/solid boundary some surface charge may be created by preferential adsorption of H^ or OH" ions. However, no surface charge of any consequence will be found at the water-vapour interface. Hence, to create significant values of G^^{h) additives are needed, either ionic surfactants or just acids or bases to charge the two surfaces (see sec. Il.S.lOf). As a rule the SL and LG interface will carry charges of the same sign and then G^^(h) and 77 (h) > 0, but negative signs also occur, for instance when the two double layers are formed by electrolyte adsorption only. The structure of isolated electric double layers has already been described in detail in chapter II.3, but not yet the forces resulting from double layer overlap. As a trend, 77 Ah) decays as e"'^^ where K is the reciprocal Debye length, amd with a pre-exponential factor proportional to the product y/^-^^y/^-^^ ^ where y/^ is the potential of the diffuse part of the double layer. Electric interactions are strongly dependent on the electrolyte concentration; if c^^^ is increased, the two v^^'s go down and the decay becomes steeper. As v^^ is not measurable, the best practical solution is to replace the v^^'s by the corresponding electrokinetic potentials f. In turn, these potentials are obtainable electrokinetically, for instance from electrophoresis or streaming potential measurements. Interpretation of these experiments in terms of ^-
WETTING
5.25
p o t e n t i a l s is not u n a m b i g u o u s . For SL interfaces surface c o n d u c t i o n in t h e s t a g n a n t layer h a s to be accounted for; a s this is rarely done, many reported ^ - d a t a are u n d e r e s t i m a t i o n s . (Fig. II.4.31 shows quantitatively t h e deviations from the routinely applied Helmholtz-Smoluchowski equation.) As a result, m a n y computed n^^{h) curves are too low, b u t correction is not usually feasible for lack of the required surface conductivity d a t a . For the LG interface, t h e problem is n o n rigidity w h e n air b u b b l e s move in a q u e o u s solution. However, t h i s problem is mostly a c a d e m i c b e c a u s e invariably s u r f a c t a n t s are needed for stabilization, suppressing the development of local interfacial tension gradients. Next to nothing is k n o w n a b o u t surface conduction in s u c h systems. Tables for FJ
for v a r i o u s
combinations of the two f potentials a n d differing electrolyte concentrations are available in t h e literature ^^ b u t the computations can also easily be carried o u t with a simple cedculator. It is noted t h a t electrolytes may have a drastic effect on 77^^ (because they may lead to a double layer at the LG border) b u t hardly any on cos a (because they affect the SL a n d LG interfacial tensions to only a minor extent, see fig. II.3.73). There also are solutes for which these trends are the other way around. Below, a thermodynamic relation between cos a , y ^ a n d the integral of /7(h) will be derived, see [5.3.91. A third contribution to 77(/i) finds its origin in steric
interactions,
i.e. t h o s e
induced by adsorbed polymer layers. The adsorption of polymers a n d polyelectrolytes, b u t not their influence on stability, was discussed in chapter II.5. Import a n t p a r a m e t e r s are the strength a n d extent to which the polymer is b o u n d , the solvent quality, expressed in terms of the Flory-Huggins p a r a m e t e r x» the molecular m a s s a n d composition (homogeneous chain, block copolymer, grafted chain, etc.). Theory is available b u t not always easy to implement. For t h i n liquid films on non-hairy surfaces, steric forces are often absent. One of t h e problems is in assessing this hairiness or, for t h a t matter, its absence. Polyst5n*ene latex surfaces may inadvertently contain short hairs a s left-overs of the polymerization process and some silicas may carry polysilicic groups a s a result of surface dissolution. For accurate work we recommend checking for the absence of s u c h hairs by appljang t e c h n i q u e s to remove them, s u c h a s h e a t t r e a t m e n t for latices a n d fluoric acid t r e a t m e n t for the silica. Solvent-structure
(mediated) forces enter when h is so small t h a t overlap occurs
between the liquid layers adjacent to the two boundaries. Close to these surfaces the ordering of the fluid molecules differs from t h a t in the bulk, a s discussed in sec. II.2.2. If h is reduced, the overlap of two such layers requires work to be done by or on the system, t h a t is, it leads to a n additional contribution to G{h) a n d to 77(h).
^^ O.K. Devereux, P.L. de Bruyn, Interaction of Plane-Parallel Double Layers, M.I.T. press, Cambridge (Mass. USA), 1963.
5.26
WETTING
Such forces are also known as hydration forces', 'structure forces' or hydrophobic forces' (for hydrophobic surfaces), but we prefer the generic, less specific name. Solvent structure forces certainly play a role in wetting films. According to present insight, such forces decay exponentially with distance, see [5.3.9], exhibiting oscillations if h becomes commensurate with a few times the molecular diameter. For examples see figs. II.2.2 and 3. In sec. 1.5.4 we discussed such forces between solutes. On top of these 'intrinsic' contributions to 77 there may be additional ones, like capillary suction (exerted on the ends of the film) and external fields such as gravity. The overall FJ, , (h) is the sum of these contributions ; tot ^
n
fh) = n^,,Jh)+ 77,(h) + n , tot^ '
vdW^ '
er
'
{h] + n , Ah]+...
ster^ '
solv.str^
[5.3.1]
'
As all terms depend in a different way on h, 77 (h) is generally a complicated function. The problem is compounded by the fact that some of these forces are not always additive. Only in relatively simple situations can /7(h) be theoretically predicted; for the rest, establishing such curves is a matter of ongoing research, including, but not restricted to, that on thin liquid films on substrates. In fact, investigations with isolated soap films and wetting layers have both contributed to our understanding of the forces responsible for the disjoining pressure. We intend to come back to such model studies in some detail in Volume IV. For SLS systems the stable parts of /7(h) curves can be experimentally measured, using the so-called surface force apparatus or atomic force microscopy. Illustrations of such measurements have already been presented; figs. 1.4.19, II.2.2 and 3. For isolated (soap) films /7(h) can be established by recognizing that, at equilibrium, the sum of all forces acting on it is zero, so /7(h) is obtained if the outer forces (vapour pressure, capillary force, and gravity for vertical films) are known. The thickness has to be independently measured, for instance from light reflection. For wetting films /7(h) can also be obtained by the consideration that the liquid in the film is at equilibrium with the vapour. Equating chemical potentials leads to /7(h) = - ^ In - - £ — V^ p(sat)
[5.3.2]
where p/p(sat) is the relative vapour pressure, h is a function of p and V is the molar volume of the liquid. A kind of manometric technique can also be used, in which the film is connected to a U-tube containing the liquid film via a porous ring; /7(h) follows from the meniscus level difference between inner and outer tubes. Alternatively, a vapour bubble can be pressed against the solid across the liquid, measuring h as a function of the applied pressure. Also for these systems h must be measured independently (light reflection, interference, ellipsometry, ...).
WETTING
5.27
Gjnin (sec.)
Figure 5.12. DLVO-type interaction curve (a) and the disjoining pressure resulting from that (b). Discussion in the text. An equation similar to [5.3.2] was derived, in the section on capillary condensation, see [II. 1.6.16]. For the moment it is concluded that the stable parts of i7(h) curves are experimentally accessible. Technical details will be deferred until Volume IV. It is noted that often 'toppled' /7(h) curves are drawn, in that h is plotted as a function of FI. Plots of this type cire anedogous to adsorption isotherms in which the mass adsorbed is plotted as a function of relative pressure. An illustration follows in fig. 5.16. In principle G{h) is obtainable from /7(h) by integration. Alternatively, if G[h) is known, /7(h) can be found by differentiation. Figure 5.12, which is cin elaboration of fig. 1.4.2 gives an illustration. Figure 5.12a is typical for a DeryaginLandau-Verwey-Overbeek (DLVO) type of interaction. For the case at hand (flat plates) G is expressed per unit area; SI units are J m-^. The upper curve consists of an attractive Van der Waals pari:, a repulsive electrostatic component and a very short range steep repulsion. Such behaviour may be representative for various wetting films. The G{h] curve displays one maximum, G , and two minima, the relatively deep primary minimum G^^^(prim) at low h and a more shallow secondary minimum G j^(sec) at much higher h. These three extremes result from the combined behaviour of the three constituent forces. The very steep rise towards distance of
5.28
WETTING
close approach reflects the repulsive solvent-structure component. It has a short range, beyond which the attractive Van der Waals contribution is responsible for the primary minimum. The maximum is caused by electrostatic repulsion. The typical behaviour with one maximum and two minima, finds its origin in the way in which the Van der Waals and electric contribution depend on h. For h -> 0, G^^ remains finite, whereas G goes to -oo, and this state would have been reached, had not a repulsive G^^^^ taken over. Beyond the primary minimum there is a range where G outweighs G , but as the former decays more rapidly with h at large h, eventually the shallow secondary minimum is created . From G{h) one finds i7(h) by differentiation; /7(h) = - ( ^ ^ ]
[5.3.31
which has the dimensions of a pressure (N m-^ in SI units). The consequences of this differentiation are visible in fig. 5.11. 77 = 0 at the extrema of G and n exhibits extrema where G{h) has inflection points; i.e. when
(d^Gih)]
fmhy] I 5^ Jp,T
= 0
[5.3.4]
dh^
Conversely, when i7(h) is known, G(h) is obtainable by integration; h
G(h) = - J /7(h')dh' = J /7(h')dh' oo
[5.3.5]
h
where h' is the distance variable. 5.3b Film formation by adsorption Let us return to the case of a pure vapour, adsorbing on a flat surface until p ~> p(sat) cind beyond. At issue now is over what (ranges of) values of h the film is stable. For the case that /7(h) is positive and decays monotonically to zero, the layer thickness would grow indefinitely with increasing p/p(sat) until at p/p(sat) = 1, vapour would condense massively. The BET-theory predicts such a trend, see fig. II. 1.24a. In the more general case, for arbitrary 77(h), stability as a function of h requires 77(h) = 0
— <0 [5.3.6] dh These two situations concur with the primary and secondary minimum in G[h), see fig. 5.12. The combination 77 =Owith d77/dh > 0 coincides with the maximum of G(h), which is a metastable situation. Let us assume that double layers have been developed, without asking how.
5.29
WETTING
For the given type of interaction curve there are two viable film thicknesses at saturation (p = p(sat)); (i) one corresponding to the primary minimum, which, following the Russian literature we shall call 'a-films'. The thickness h is of the order of a nm and -^
a
mostly determined by solvent structure-mediated and Van der Waals forces. (ii) one corresponding to the secondary minimum, [p-films), with h determined by Van der Waals attraction and double layer repulsion and hence being of order K:"\ which varies with the electrolyte concentration. It may be up to 100 nm. Between the two there is the maximum, which acts as a barrier, inhibiting the free a ^ p transition. This barrier can be crossed only when the required activation (Gibbs) energy is available. Whether a thin liquid film is stuck in the a-state or the p-state, or partly in one and partly in the other, depends not only on the activation Gibbs energy but also on the direction from which the equilibrium situation was approached. In this respect there is a difference between liquid films created from gas adsorption and those obtained from thick liquid layers subjected to drainage. We shall now consider the former case, treating the latter in sec. 5.3d. Upon increasing p/p(sat) an adsorbed layer will be formed that gradually increases in thickness. Let us for the moment assume that G(h) and /7(h) have the shapes of figures 5.12a and b, respectively. After adsorption has progressed for a while G^^^(prim) has been reached, where /7(h) = 0. Both thermodynamically and mechanically this is a stable situation. If more liquid is condensed, one enters an unstable state, where G would increase again and where /7 becomes negative. The additionally added liquid cannot spread further over the film; rather it will form droplets on the surface, characterized by a certain contact angle a, as sketched in fig. 5.13. The inability of a liquid to spread over a very thin layer of itself, is known as autophobicity. We encountered this phenomenon before (sees. II.1.5h and 6e, in connection with multimolecular adsorption and capillary condensation, respectively). The deeper the primary minimum, the larger the contact angle a. Autophobicity requires the thin layer to be structurally different from that of the bulk. In principle, the story repeats itself for the secondary minimum, but as this is shallow, the contact angle will be very low and difficult to measure.
Figure 5.13. Partial wetting of an a-film.
5.30
WETTING
The depth of the G{h] minimum Ccin be related to the contact angle. Mechanical equilibrium of the contact perimeter requires /
= ^SL_^ 7 ^ cos a
[5.3.7]
where y^ is the interfacial tension of the thin (a-) film. Because this is a very thin film, we cannot replace y^ by y^^ + y ^ (in fact this would mean absence of a disjoining pressure and complete spreading, cos a = 0). A contribution G{h) has to be added, accounting for the work to be done in bringing the SL and LG surfaces from infinity to distance h. For this we have [5.3.5]. Hence, h
Y^ = ySL ^ yLG _ J /7(h')dh' = 7^^ + y^ +G{h)
[5.3.8]
so that y^^il - cos a] = J n(h')dh' = - G(h)
[5.3.9]
h
It is appropriate to stress that the above argument is thermodynamical, and hence phenomenological. The transition from the film, with tension 7^ to the droplet, with surface tension 7 ^ , is taken as sharp, just as in the macroscopic treatment of contact angles. In other words, it is ignored that on a colloidal scale 7^^ may change gradually, in which case the contact angle is ill-defined. Equation [5.3.8] was derived by de Feijter and Vrij^^ for soap films, assuming 7 to be variable in the transition zone. Prior to that, similar equations have been proposed by the Russian School, see for instance^^. Equation [5.3.9] is important because contact angles can be measured. In this way information on the disjoining pressure or on the interaction Gibbs energy is obtainable. Particularly for a-films this information is interesting because the behaviour is sensitive to detciils of the molecular structuring. Sometimes, minor changes in the conditions (temperature, nature of the surface) can make all the difference between continued wetting or autophobicity. Recall the notion of wetting transition, introduced in sec. 5.2 and already illustrated in fig. II. 1.41. Such transitions are very conspicuous features and draw much attention. It is appropriate now to reconsider the shapes of adsorption isotherms leading to complete or partial wetting. The former type, indicated by w in fig. 5.14, represents the classical BET isotherms, except that we have plotted r{p) instead of V(p/p(sat)). However, partial wetting implies that adsorption in the first instance can only proceed until a certain limiting value, say F at p -> p(sat), see curve pw in the same figure. This is followed by a metastable range, characterized by a 1) J. Feijter, A. Vrij, J. Electroanal Chem. 37 (1972) 9. 2) A.N,. Frumkin. Acta Physicochim. USSR 9 (1938) 313.
WETTING
5.31
Figure 5.14. Difference between adsorption isotherms leading to complete (w) or partial (pw) wetting. When, as a function of T, a jump from w to pw isotherms takes place, one crosses the wetting transition. P (sat)
loop^K The physical m e a n i n g is t h a t if p infinitesimally exceeds p(sat) all additional condensed vapour appears a s macroscopic drops. Between curves w a n d pw, Intermediate situations may be found, displajmig a shorter loop a t lower p. In t h a t case there is a sub-monolayer on the surface between the drops. Cahn^) h a s argued t h a t the transition is first order when d / ^ ^ / d T h a s a discontinuity. Recall from 3.12 t h a t a t a given value of F the surface pressure 7t equals / * - / , where y* is the surface tension of the uncovered (pristine) surface a n d / t h a t for the surface, covered by a n adsorbed amount F. At any F
15.3.10]
n = RT \ r d l n p
i.e. 71 is RT times the area u n d e r the adsorption isotherm, written a s F(p). With this in mind the hatched area can be found for a pw-type isotherm by carrying out the integration from F' = 0 to « and then subtracting the same for T' = 0 to F^. We find for the former
y^ - r^^- y^ = ^^ \ r ' d i n p
15.3.111
o
(which is identical to the spreading tension) a n d for the latter
^^ Such an interpretation was first proposed by B.V. Derjaguin (= Deryagin) and Z.M. Zorin, 2nd Int. Congress Surface Activity, London, Proc. Butterworth (1957) 2, 145 2) J.W. Cahn, J. Chem. Phys. 66 (1977) 3667.
5.32
WETTING
[5.3.12]
/ ^ - / o = RT \ r d l n p
where y^o is the film tension at the point where F = F . Subtracting [5.3.12] from [5.3.11] yields hatched area in fig. 5.14
= J r d l n p = 7^0 - ySL_ yL ^ J /7(h')dh'
[5.3.13]
where for the last transition we have used [5.3.5]. The lower integration border h is the thickness corresponding to the adsorbed a m o u n t F . According to [5.3.9] this area is J u s t t h e Gibbs energy difference between the states where F = F a n d t h a t where F = oo. The theory developed above offers a framework for t h e further s t u d y of t h e relationships between colloidal interactions a n d wetting behaviour. If /7(h) is known on the b a s i s of obtained insight into intermolecular forces, the n a t u r e of the wetting can be predicted. We already did so for fig. 5.14. The most simple case is fig. 5.15, which m a y apply to simple n o n - a q u e o u s liquids, interacting with t h e solid only t h r o u g h Van der Waals forces, a p a r t from the ubiquitous short range repulsion. If enough liquid material is available thin a-films are formed, b u t a n y additional m a t t e r forms droplets. Hence, this /7(h) behaviour leads to the
floating
drop case of fig. 5.7h. ^^ Wetting transitions correspond to chainges from isotherms of the pw-type to the w-type in fig. 5.14. Mostly they are first order, particularly so for a-films. In
/7(h)
Figure 5.15. Disjoining pressure isotherm for a Van der Waals liquid.
1^ For a state-of-the-art review see G.H. Findenegg, S. Herminghans, Curr. Opinion Colloid Interface Set 2 (1997) 301.
WETTING
5.33
practice attempts are often made to obtain such a transition by changing the temperature; essentially the w-curve describes an adsorbate above its critical point. It is not easy to obtain wetting transitions for films for which /7(h) is solely determined by 77^^ and 77^^^, because these components are not very temperaturesensitive. More success has been achieved with films in which hydrophobic interactions play a role with, for instance two-component liquids which demix at a given temperature or with films containing surfactants which modify the two film surfaces. Finally we will illustrate the various transition steps between a solid surface under pristine conditions and the completely immersed state, (see fig. 5.16). Panels (a), (c) -> (d) -> (e) -> (g) refer to a wetting system. Examples are water on various hydrophilic mineral oxides. Sometimes the surfaces of materials are called 'high energy surfaces'. However, we shall avoid this term because it does not refer to the energy of the surface proper but rather to the interaction of that surface with a special liquid, viz. water. Panels (b), (c) -> (d) -> (f) -> (g) represent a non-wetting system, such as water on Teflon ('low energy surface'). Panels (a) and (b) are adsorption isotherms. The initial parts obey BET theory, with for cases (a) and (b) a high and a low C-constant, respectively, see fig. II. 1.24a. In panel (b) two different isotherms are sketched. The two series (c) -^ (g) indicate what happens when the supply of water increases from zero to bulk amounts. The work of immersion, identified as the Gibbs energy difference between panels (g) and (c), is obviously different between the two solids. In panel (d) the F's and ;r's are different between the two solids. In both cases F follows from the adsorption isotherm (panels (a) and (b)) and 7t follows from F, using [5.3.10]. The thickness of the film in panel (f), which is at equilibrium with the drop, is determined by the depth of the minimum in the 77(h) curve across the film; mostly this will be an a-film, for which the thickness is virtually independent of F. Along these lines the various steps and processes, discussed above, can be visualized. Interactions in adsorption and wetting can also be quantified calorimetrically; in this way enthalpies rather than Gibbs energies are obtained^^. 5.3c Case studies; water on silica and liquids on liquids From the abundance of investigations on wetting films we select two typical cases. (i) Water, or dilute aqueous solutions on silica. This is one of the best studied systems. Silica can be made in various modifications such as glass and quartz, subjected to various surface treatments (for instance hydrophobing) and since beautifully flat surfaces can be made, the thin layers can be relatively well studied
^^ See for instance, J.M. Doillard, M. Elwafir and S. Partyka, J. Colloid Interface Set 164 (1994) 238.
5.34
WETTING
complete wetting
partial wetting
combination
Figure 5.16. Schematic representation of various adsorption and wetting situations, indicating adsorbed amounts (where appropriate) and interfacial tensions. Two solids, both called S, are considered; one is wetted, the other is not. Discussion in the text. (Redrawn after L.J.M. Schlangen, L.K. Koopal, M.A. Cohen Stuart and J. Lyklema, Colloids Surf. 8 9 (1994) 157.)
WETTING
5.35
optically. Moreover, the properties of the layers can be modified by adding small a m o u n t s of acid or b a s e (to change the pH amd create double layers) cind indifferent electrol5rtes (to create double layers at the water-vapour interface a n d to s u p p r e s s double layer interactions). We a s s u m e these chemicals are present in low a m o u n t s , b u t exclude surfactants a n d polymers. Several studies on this sytem have been published, see for example^'^'^''^•^•^'^•^^ These reflect the parallel growing insight into t h e colloid science of the p r e s e n t system a n d t h a t of stability in general. Kitchener a n d Read^^ observed very thick wetting layers, persisting after meticulous cleaning and concluded that there should be a non-zero 77^^, i.e. the LG border should c a n y a double layer. Pashley and Kitchener proposed the (what we now call) solvent structure-mediated component, for which the Russian School^'^^ formulated the exponential expression /7 , Ah) = Ke"^/^
[5.3.131
solv.str^ '
^
*
where K is a measure of the strength and A of the range. For water on quartz, glass a n d mica K = 0(10^ Nm~^), i.e. K is very high; A = 0(nm), i.e. short range. The 10 - n m h^ ' 'o " 8 \ ^5 6^0^
4 2 0 10
^o 1
1
\
20
30
40
\ ^ \ , 50 60 temperature
70 X
Figure 5.17. Ellipsometrical thickness of a-films for water on quartz as a function of temperature; p/p(sat) = 1. (Redrawn after G.F. Ershova, Z.M. Zorin and N.V. Churaev, Koll Zhur. 3 7 (1975) 208.)
1) B.V. Deiyagin, M.M. Kusakov, Izv. Akad. Nauk. SSSR 5 (1936) 741, 1119; Acta Physicochim USSR 10 (1939) 25. 153. 2^ B.V. Derjaguin (= Deryagin), Discuss. Faraday Soc. 18 (1954) 85. ^U.A. Kitchener, A.D. Read, The Thickness of Wetting Films, in Wetting (Soc. Chem. Ind. (1967); A.D. Read. J.A. Kitcherner. J. Colloid Interface Set 30 (1969) 381. ^^ T.D. Blake. J.A. Kitchener. J. Chem. Soc. Faraday Trans (I) 6 8 (1972) 1435. 5) R.M. Pashley. J.A. Kitchener, J. Colloid Interface Set 71 (1979) 491. ^^ B.V. Derjaguin (= Deryagin). N.V. Churaev, Properties of Water Layers Adjacent to Interfaces, in Fluid Interfacial Phenomena, C.A. Croxton. Ed., Wiley (1986) Ch. 15. p. 663. '^^ B.V. Derjaguin (= Deiyagin). N.V. Churaev, Langmuir 3 (1987) 607. ^^ RR. Mazzoco. P.C. Wayner. J. Colloid Interface Set 214 (1999) 156.
5.36
WETTING
t 1.
300 nm
h
p
, ^
(a)
200
o o'>
/ p °/?
of - 100 a 1
,
T - ^ 200 0
\
1 - - '
1 —T
-200
-400Nm-2
n
1
-2xlO^Nm-2
n
Figure 5.18. Wetting water films on quartz. Drawn curves, theory; data points, experimental. Figure (a), the long distance range (p-films, metastable); figure (b), short distance range with h^ indicated. Further discussion in the text. (Redrawn from Derjaguin and Churaev, loc. cit., 1986) trend for A is to decrease with temperature, b u t wide temperature ranges have not been systematically studied. By way of example, Perevertaev et al.^^ reported A to decrease from 3.3 to 0.8 n m for water films on mica if the temperature was raised from 2 9 3 to 3 1 3 K. For this system a = 10°. Systematic d a t a for t h e relation between a, K a n d A would be welcome, b u t intuitively one would expect better wetting at higher temperatures. That h
decreases with increasing temperature is
illustrated by fig. 5.17. In modelling /7^^^, values in the indicated range have to be selected. Figure 5.18 gives a n impression of the agreement between theory a n d experiment, choosing representative parameter values. The London-Van der Waals component w a s computed from the Lifshits theory, a s described in sec. 1.4.7. For water a n d silica the H a m a k e r c o n s t a n t s are similar, a s a result these forces do n o t contribute substantially, except at very low h, where 77^^^^ ^^ is also strong. The electrical contribution w a s computed for hetero-interaction a s s u m i n g y/^ = - 1 5 0 a n d - 5 5 mV for the quartz-water a n d water-air interface, respectively. Eventually K and A were used a s adjustable parameters. The pairs K = 0.2 x lO^N m"^ and A = 2 n m , a n d K = 3 x l O ^ N m " ^ a n d A = 0.3 n m gave the best fits. Accepting t h e uncertainties, a picture is obtained t h a t conforms to expectation. The thickness of p-films is mainly electrostatically determined, w h e r e a s electrostatics play a minor role for a-films. In t h e Derjaguin-Churaev review, some values for contact angles are also given (not reproduced here). The trend is that a is not very sensitive to c^^^ (increase by
IJ V.D. Perevertaev, M.S. Metsik and L.M. Golub, Koll Zhur. 41 (1979) 159.
WETTING
5.37
about 5° upon a thousand fold increases in c^^). but slightly more to pH, with the tendency to increase when pH approaches the point of zero charge. The last word has not yet been spoken because there is substantial hysteresis, which should not occur for a droplet partially wetting a thin fluid film. Mazzoco and Wayner (loc. cit.) improved and augmented these studies. The film and film-border profile were studied using an image-analyzing interferometer. The influences of the temperature and traces of organic impurities on the, otherwise meticulously cleaned, surface were systematically investigated. Deryagin and Churaev's results were grosso modo confirmed. When electrolytes are added in low concentrations and the surface is cleaned by HF, stable films of about 60 nm are obtained at pH 12. On the other hand, films of pure water were metastable; after a couple of hours they disproportionated into droplets and thin films (h < 10 nm). The apparatus allowed them to follow the breaking process; waves on the film surface grew unimpeded, with tramsient temperature gradients contributing (thermocapillarity and vapour recoil; evaporation and condensation in the crests and valleys of the waves give rise to temperature- and surface tension gradients, i.e. to Maraingoni effects). Studies like this one are also relevant to the understanding of heat transfer. While doing so, it must always be kept in mind that traces of surface active contaminaints may play a role. As the thickness of a-films is determined by the layering of the liquid molecules adjacent to the solid, more than one thickness (stratificatiori) could in principle be expected. For pure water films or dilute aqueous solutions in the absence of dissolved surfactants or pol3miers, such stratification has never been observed. However, the phenomenon has been found for free aqueous films of concentrated surfactants and for wetting layers of large spherical organic molecules ^^ (ii) Liquids on liquids. Adsorption of low molecular mass vapours on the surface of a liquid substrate into which it does not dissolve, can be followed by surface tension measurements. We discussed methods and theory for this in sec. 4.3 where some illustrations were also given. Other examples of hydrophobic vapours on a water surface include work by Baumer and Findenegg-^^ by Lou and Pethica^^ and by Pfohl et al.'^^ The last-mentioned reference addresses the present issue, viz. what happens when the adsorbed layer becomes thick. Does the condensed liquid form a wetting layer and/or droplets? An advantage of this LjI^G-system over the SLG system (to which water films on silica belong) is that measurements can be carried out with pure liquids; the spreading liquid (L2) does not require electrolytes or surfactants to control its IJ F. Heslot, N. Fraysse and A.M. Cazabat, Nature 388 (1989) 640; S. Villette, M.P. Valignat, A.M. Cazabat. L. Jullien and F. Tiberg, Langmuir 12 (1996) 825. 2) D. Baumer, G.H,. Findenegg, J. Colloid Interface Set 85 (1982) 118. ^^ A. Lou, B.A. Pethica, Lxingmuir 13 (1997) 4933. "^^ T. Pfohl, H. Mohwald and M. Rlegler. Langmuir 14 (1998) 5285.
5.38
WETTING
disjoining p r e s s u r e . The choice between complete a n d partial wetting is solely determined by London-Van der Waals forces, for which theory is available, see c h a p t e r 1.4. The principles a n d a collection of Hamaker c o n s t a n t s were given, in t h a t c h a p t e r a n d in a p p e n d i x 1.9, respectively. For the p r e s e n t p u r p o s e t h e interesting observation is t h a t this constant, called A
c a n be either positive or
negative (table I.A9.2), meaning t h a t the liquid on liquid system is very suitable for s t u d y i n g t h e theory of dispersion forces. A d r a w b a c k of t h e s y s t e m is t h a t meticulous experimental control is required (constant vapour pressure, absence of evaporation, continually m u t u a l s a t u r a t i o n , etc.). Here we find ourselves a t a cross-roads between current theoretical a n d experimental issues. For a l k a n e s on water, according to table I.A9.2, A
increases with c h a i n
length n, b u t different theories disagree about sign reversal (and even then, at w h a t n). Negative H a m a k e r c o n s t a n t s imply a positive disjoining p r e s s u r e a c r o s s t h e film which, in t u r n , m e a n s unconditionally stable films. One of t h e theoretical i s s u e s is the b a l a n c e between short-range a n d long-range contributions to t h e force. This b a l a n c e is sensitive to the orientation of the molecules at t h e surface a n d m a y be temperature-sensitive, giving rise to possible wetting transitions. The study by Pfohl et al., (loc cit.) addresses this issue. These investigators studied the wetting of hexane (Cg), heptane (Cy) and octane (Cg) from their saturated vapours on water by ellipsometry, a n d Brewster angle microscopy. For Cg a n d Cy a n ultrathin film of molecular dimensions w a s found, topped by droplets of |im-size, whereas Cg only adsorbed a s a submonolayer film. Detailed steps a s a function of time could also be seen; they are probably related to changes in orientation of the adsorbed molecules. More detailed s t u d i e s along t h e s e lines are welcome, t h e more so b e c a u s e of the extreme sensitivity to evaporation. Finally, floating lenses of liquids offer a p a b u l u m for the development of theory to describe t h e involved c u r v a t u r e s mathematically. Comparison with experim e n t s allows t h e e s t a b l i s h m e n t of t h e three contact angles, see for i n s t a n c e refs.^'^'^K Aveyard a n d Clint"^^ reviewed the stability a n d capillarity of
floating
droplets in the presence of surfactants. 5.3d
A note onjilin
thinning
So far we have described in some detail the development of wetting layers by accretion. Obviously, the other direction is also possible; a thick, macroscopic liquid layer on a solid can thin (by gravity, evaporation or capillary suction) until t h e layers become of colloidal t h i c k n e s s . Eventually, t h e s a m e final s i t u a t i o n should be attained, unless the dynamics of dewetting leads to hysteresis. 1^ H.M. Princen, in Surface and Colloid Science, E. Matijevic, Ed., Wiley (1969). Vol. 2, 1. 2) P.R. Pujado, L.E. Scriven, J. Colloid Interface Set 40 (1972) 82. 3) I.H. Balchin, E.A. Boucher and M.J.B. Evans, J. Colloid Interface Set 134 (1990) 312. "^^ R. Aveyard, J.H. Clint, J. Chem, Soc. Faraday Trans. 91 (1995) 2681.
WETTING
5.39
For free soap films the drainage is well-studied. Such films will drain under the influence of capillary suction (at the film borders) and gravity (for vertical films); they will stop doing so once the secondary minimum has been reached. This thickness is sensitive to the electrolyte concentration; it corresponds to p-films. Some types of films, depending on the nature of the surfactant and counterion, may Jump spontaneously into the primary minimum, at thicknesses not very much exceeding twice the extended chain length of the surfactant molecules. Such (a-) films are called Newton Jilms. Their thickness is independent of c^^^, indicating that double layer overlap is not a significant contribution. For the dynamics the question is what happens with the excess liquid created by the, initially local, thinning. In vertical films it forms a rim around the growing hole, which breaks down into small droplets via Rayleigh instability; these droplets flow down. With horizontal wetting films, sideways movement is often inhibited, giving rise to ring and drop structures on the surface after cessation of drainage. So, non-equilibrium situations can be frozen in for hydrodynamic reasons. An illustration, showing holes with fingering instabilities for polystyrene films on silicon wafers was given by Shcirma and Reiter^l When wetting transitions do occur as a function of temperature, and drgiinage is hysteresis-free, it is attractive from an academic point of view to play around with /7(h,T) phase diagrams which may look like the /7(A,T) diagram of fig. 3.15. Above a certain critical point thinning is gradual, below it there are dewetting steps. On closer inspection, even the distinction between binodcd and spinodal demixing can be analyzed this way. There is no need to state that on heterogeneous surfaces all of this changes drastically. 5.4 Measuring contact angles In this section we shall discuss the measurement of macroscopic contact angles under conditions that are as close as possible to equilibrium. These contact amgles are not necessarily identical to those on a molecular scale and certainly not to contact angles with a precursor film. In other words, we are essentially discussing macroscopic measuring techniques. Even these macroscopic angles depend on a variety of factors. Some of these are the very object of investigations, others may Just be a nuisance. Before starting a measurement one should therefore be conscious of factors that may affect, or interfere with it. Therefore, we shall start with a brief consideration of such factors. 5.4a Factors (iffecting contact angles Contact angles reflect the wettability of a substrate by a liquid, but results may 1) A. Sharma, G. Reiter, J. Colloid Interface Set 178 (1996) 383.
5.40
WETTING
differ markedly for samples that have been subjected to different pretreatments, for advancing and receding fronts (fig. 5.4), for substrates in a different state of comminution (flat polished plates as compared with powders) and even between the same liquids, obtained from different suppliers. Even if surfaces optically look like Fresnel surfaces, they may contain microgrooves, asperities, pores, etc., and as these features affect the contact angle, if only through its hysteresis, it becomes difficult to determine 'recommended standard contact angles'. The sensitivity of contact angles to all these features poses at the same time both a challenge and a problem. Consider first contact angle hysteresis. The difference between receding and advancing contact angles is a recurrent observation implying that some non-reversible history effect is unavoidable. This makes it difficult to apply thermodynamics, which is based on the premise of full equilibrium. We shall discuss the origins of contact angle hysteresis in sec. 5.5, but in anticipation we should distinguish between real hysteresis and measurement at non-zero Deborah number. Real hysteresis means that the system on the advancing track differs from that on the way back, for instance with respect to the filling of microheterogeneities on the surface. We encountered the same phenomenon in capillary condensation, see sec. II.1.6e. Hysteresis means that advancing and receding fronts pass through a series of metastable intermediate states. When the contact perimeter is stuck in one such state, thermodynamics may be applied to both angles. On the other hand, if the measurement is too fast to ensure equilibrium to be established on all the three interfaces involved (say because of slow adsorption processes, or slow evaporation of the liquid, to produce an adsorbate on the substrate), it is inappropriate to tcdk of hysteresis. Then one should rather speak of lack of patience', and thermodynamics is not readily applied, unless the process towards equilibrium is so slow that real hysteresis is approached. Worth reading is a discussion of the magnification effect and the consequences of hysteresis on the contact angle by Decker et al.^^ These authors also refer to the influence of mechanical disturbances; vibrations may help the perimeter to cross unfavourable intermediate positions by providing the required activation energy, reducing the hysteresis. The familiar illustration is that tapping on a windscreen makes raindrops roll down. In this connection we should also recall that in forced wetting the angle becomes rate dependent, as sketched in fig. 5.5. We are interested in how pristine the three involved interfaces are; similar things can be said, as has been done, in connection with the measurement of LG and LL interfacial tensions (chapter 1). Impurities may adsorb slowly, but rapid measurements have the disadvantage that intrinsically slower processes may not 1) E.L. Decker, B. Frank. Y. Suo and S. Garoff. Colloids Surf. A156 (1999) 177.
WETTING
5.41
come to completion (adsorption of macromolecules, evaporation of the liquid with subsequent re-adsorption at the SG interface). See, for instance ref.^K Impurities may also enter via the vapour phase, say evaporated hydroccirbons from the heated oil of a vacuum pump. Solid surfaces should be clean and not touched prior to measurement, unless studying the effect of impurities happens to be the objective of the investigation. For various methods of cleaning solid surfaces and assessing their pristine state see Goldfinger's book^). When all precautions have been taken, the variability of substrates, samples and methods of preparation remain and all of this may give rise to results differing between different investigators. Measurements of contact angles can be classified into two categories: (i) Actual measurement of the angle by observation or some optical technique. This is perhaps the simplest and most direct method, but putting a tangent to a curved surface is subjective, the more so since the profile can be optically distorted. (ii) Methods not giving a but / cos a. Many of these have already been treated in chapter 1, but then with the determination of interfacial tensions as the primary goal. Such methods usually involve a force measurement, or compensation of a capillary force and can be carried out precisely and automatically. Moreover, they are less susceptible to errors of judgement than methods requiring visual inspection of enlarged images. The drawback is of course that y has to be known. In a number of modem techniques, meniscus curvatures are scanned; from these image analyses the interfacial tension and the contact angle (from extrapolation) are both obtainable. We shall now review some of these techniques, more or less in order of increasing complexity. Regarding the 'ycosa methods' frequent reference will be made to chapter I. Strictly speaking, a measurement is incomplete unless both the advancing and receding angle are obtained. By this strict criterion, the literature does not contain mainy 'complete' measurements. According to Marmur (see below), the drop volume is also an important parameter. 5 Ah, Sessile drops and captive bubbles on a flat surface This is the most frequently used technique. In chapter 1 these systems were studied to obtain the surface or interfacial tension from the shapes, see figs. 1.3 and 13. In fig. 5.19 they are redrawn with the contact angles indicated for two different cases of partial wetting. In principle, a can be measured by direct observation, obtciined from a photograph, or by interference microscopy, which will be described later. Observations are usually carried out using a travelling tele(micro)scope, as used in cathetometers, equipped with a goniometer eyepiece. So, 1^ G. Mchale, S.M. Rowan, M.I. Newton and M.K. Banerjee, J. Phys. Chem. B102 (1998) 1964. 2) Clean Surfaces, G. Goldfmger, Ed., Marcel Dekker (1969).
5.42
WETTING
Figure 5.19. Contact angles, measured through the liquid, in sessile drops and captive bubbles. The vapour phase can be replaced by smother liquid. with this technique y and a can both be estimated. Usually the set-up consists of: (i) a horizontal stage onto or below which the flat surface is mounted. (ii) a device to put a droplet on the surface, or a bubble underneath it. Often the droplet is formed with a micropipette. By applying either pressure or suction, with the pipette in contact with the droplet, advancing and receding angles can be obtained. Droplets can also be deposited by picking them up on a cleaned platinum wire, which is then brought close to the surface until the droplet flows off the wire. For captive bubbles a narrow bore through the surface C£in be used or the bubble is deposited from below. (iii) an enclosure to prevent interference of vapour-bome impurities and to secure saturation of the vapour. Evaporation may give rise to temperature fluctuations. For the value of the contact angles precise pressure control is much less critical than that of temperature because contact angles are more sensitive to the latter. For captive bubbles the liquid around them acts as both enclosure and as thermostat. (iv) a light source to illuminate the three-phase contact region from behind. It should be equipped with a heat filter to prevent temperature fluctuations and, hence, convection. The light can be either diffuse or coUimated, with different effects. Experience has shown that diffuse illumination (yielding a silhouette) is preferable for closed-circuit television (CCTV) imaging, whereas coUimated light is suitable for telescope-type measurements. (v) the telemicroscope which magnifies the contact area (or the whole drop, depending on its size). It must be able to travel along when the drop advances or recedes. Nowadays cameras are usually replaced by CCTV's, provided with
WETTING
5.43
appropriate software to process the image and determine the contact angle. It should contain a goniometer dial to read the angle. The choice of the magnification is a matter of compromise; the higher it is, the more accurate the readings, but the more rapidly the contact area moves out of the field of visibility and the shorter the focal length. (vi) (optional) a camera, coupled to the telemicroscope. Measuring photographs is more accurate than taking goniometer readings but more time-consuming; this drawback especially plays a role when moving contact lines are studied. The choice between a sessile drop and a captive bubble is mostly a matter of convenience but it may also be appropriate to match the technique to the type f surface. Droplets require only small amounts of liquid but run the risk of interference by evaporation. Droplets may be as small as a few mm cross-section (i.e. of a size comparable to the capillary length). The advantage is that gravity plays a negligible role so that the shape is nearly spherical, enabling easier establishment of the contact angle in some elaborations. A drawback is that for small droplets hysteresis may be larger. Maintaining a micropipette needle in the drop or bubble may locally affect the curvature, and interfere with the optical measurement, but it can of course not modify the angle. For the information to be complete, generally a(adv) and a(rec) are both needed. On surfaces that are not specially prepared, hysteresis may be anisotropic. In the magnified image of the drop it may sometimes give rise to an edge at the contact perimeter and, if observed from above, the perimeter is not always circular but may display irregulcirities. Interpretation of these also takes us into the domain of line tensions (sec. 5.6). For verifying isotropy, a set-up is needed in which the contact region can be observed from all directions, for instance by rotating the droplet around its axis, requiring meticulous rotational stability. Spontaneously spreading films may have a real thin precursor film, advancing in front of the droplet itself, but here that is not at issue (see sec. 5.8).
Figure 5.20. Interferometry of the contact region. Explanation in the text.
5.44
WETTING
Mutatis m u t a n d i s , the approach can also be applied to L1L2S interfaces. For several practical p u r p o s e s s u c h m e a s u r e m e n t s are relevant, for instance in detergency a n d in t h e flooding of oil fields. However, for forced wetting the droplet method is not so suitable. Depending on the composition of the liquid a n d the quality of the s u b s t r a t e , a precision of a b o u t 5° can be attained for small and very large angles b u t t h a t a b o u t 2° is easily obtainable n e a r 90°, especially if the droplet is reflected in t h e s u b s t r a t e . However, t h e accuracy (between different experiments carried o u t by t h e same investigator using the same routine of manipulations) may be a s good a s 1°. It may be added that in wetting studies cos a counts, rather t h a n a; t h e sensitivity of cos a to errors in a is negligible for or ^ 0 a n d maximal at a = 90, above which it decreases again. Obtuse angles above 130° are rare, except for liquid-liquid (instead of liquid-vapour) systems. For m a n y technical details see the literature 1^. The liquid profile n e a r a flat horizontal surface, a n d hence the contact angle, c a n in a n u m b e r of cases also be obtained interferometrically'^^.
The principle is
sketched in fig. 5.20. Light from a source A p a s s e s t h r o u g h lens L to become a horizontal b u n d l e , reflecting against the half-silvered mirror SM, m o u n t e d at 45° with respect to the surface of the solid. The light arriving at M is the superposition of t h e b e a m s reflected by t h e u p p e r a n d lower surface of the liquid. Fringes resulting from sequential destructive (dark) a n d constructive (light) interference c a n be observed in t h e microscope. Dark fringes occur w h e n the optical p a t h difference £ is equal to (p + i)A / 2n^ where A is the wavelength of the incident light, n^ the refractive index of the liquid and p a n integer, indicating the order of the interference. So, between two adjacent dark rings f=X/2n^ As i/x
[5.4.1]
= t a n a, where x is the distance between two adjacent fringes,
a = tan-^(A/2n^x)
[5.4.2]
relating the contact angle to the distance between fringes. This m e t h o d requires reflecting surfaces; at any rate, the reflectivity of t h e surface should exceed t h a t of the liquid. Michelson interferometers can be used to a s s e s s surface r o u g h n e s s . However, by this technique no contact angles c a n be
^ ^ For instance the review Techniques of Measuring Contact Angles by A.W. Neumann and R.J. Good, mentioned in sec. 5.12. In this section we shall refer to it as Neumann and Good, loc. cit. 2) G.W. Longman, R.P. Palmer, J. Colloid Interface Set 29 (1967) 185; I.C. Callaghan, D.H. Everett and A.J.P. Fletcher, J. Chem. Soc. Faraday Trans. (I) 79 (1983) 2783; T. Kolarov, Z. Zorin and D. Platikanov, Colloids Surf 51 (1990) 37.
WETTING
5.45
Figure 5.21. Contact angle from light reflection. The situation is drawn for the limiting angle, beyond which no reflection is seen anymore. measured. Measurements with t r a n s p a r e n t s u b s t r a t e s are also possible. S h e n a n d Ruth^^ proposed a grating shearing interference method to obtain contact angles a n d m e n i s c u s profiles for low contact angles. This method m a y also be useful u n d e r dynsmiic conditions. The quality of the outcome depends on the resolution of the fringes a n d on t h e value of a. The method is of particular merit for small drops a n d low angles (less t h a n a b o u t 10°). Changes with time are reflected a s displacements of t h e fringes. Interferometry c a n also contribute to the detection a n d analysis of irregularities (deviations from circular shape) of the perimeter. Contact angles of sessile drops can also be conveniently determined by specular reflection. The method dates back to Langmuir a n d Schaeffer^^ a n d w a s improved by Fort a n d Patterson^^ a n d by Allain et al.'^^ The idea is to let light from a source m o u n t e d on a b e a m pivot around a n axis in s u c h a way t h a t the LG border is scanned. Upon pivoting the beam a r o u n d its axis the orientation at which the reflection disappeeirs is determined (fig. 5.21). The angle between b e a m a n d n o r m a l is t h e n equal to the contact angle, which can be established with a n accuracy of about 1°. In sec. 1.4 we described in some detail how the contour of a sessile drop c a n be m e a s u r e d a n d how the profile can be interpreted in terms of [1.3, 9, 12 or 14]. In that
Figure 5.22. Contact angle from the shape of a drop.
1^ C.H. Shen, D.W. Ruth, J. Colloid Interface Set 168 (1994) 162. 2) I. Langmuir, V.J. Schaefi"er, J. Am, CheirL Soc. 59 (1937) 2400. 3^ T. Fort, H.T. Patterson. J. Colloid Set 18 (1963) 217. ^^ C. Allain, D. Ausserre and F. Rondelez, J. Colloid Interfaee Set 107 (1985) 5.
5.46
WETTING
/ I
u
111 I j t u r n t ' M t J
Mf|[
lilnrii
)< llli'vlul
«
Figure 5.23. Contact angle from the height of a very small drop.
-2r section t h e m e t h o d w a s u s e d to determine the surface tension. However, t h e procedure is more versatile since it can also give the contact angle, which equals K-cp where (j) is indicated in fig. 1.13, see fig. 5.22. We recall one of t h a t the most advanced variants of this technique is the ADSA procedure which w a s developed by N e u m a n n a n d h i s group a n d h a s b e e n perfected in great detail since its inception. This m e t h o d a n d v a r i a n t s of it h a s appeared in a large n u m b e r of publications, including methodical reviews I'^'^-'^h In these publications, useful information can be found regarding experimental details (preparation of surfaces, methodical errors, digital image processing of profiles, etc.). Li et al. claim a n a c c c u r a c y of b e t t e r t h a n 0.1 degrees u n d e r favourable conditions. Agreement within this margin with Wilhelmy plate results w a s observed for water, glycerin, ethylene glycol a n d dodecane on a n u m b e r of polymer surfaces. However, there are also some snags. One of these is t h a t only advancing angles are given a n d t h a t this contact angle d e p e n d s on the drop radius r in a way t h a t cannot be accounted for theoretically. Anticipating sec. 5.6, r a d i u s dependence may be c a u s e d by line tensions. For not too strong curvature this dependence is proportional to r " \ a s in [5.6.1], for very strong curvature it is different. In the present set of m e a s u r e m e n t s the observed dependence is not exactly proportional to r"^ a n d the line tension is overestimated by several orders of magnitude. When the droplet is very small, a n d therefore spherical, a s in fig. 5.22, t h e contact angle can be related to the height and width via t a n ( a / 2) = h / r
[5.4.3]
This is a very simple equation b u t only applicable u n d e r limiting conditions. Equation [5.2.7] is more precise. ^^ D. Li, P. Cheng and A.W. Neumann, Contact Angle Measurement by Axisymmetric Drop Shape Analysis (ADSA), Adv. Colloid Interface Set 3 9 (1992) 347, and references to the Neumann group in sec. 5.12; D.Y. Kwok, A.W. Neumann, Contact Angle Measurement and Contact Angle Interpretation, Adv. Colloid Interface Set 81 (1999) 167-249. 2^ F.K. Skinner, Y. Rotenberg and A.W. Neumann, J. Colloid Interface Set 130 (1989) 25. ^^ D.Y. Kwok. T. Gietzelt, K. Grundke, H.-J. Jacobasch and A.W. Neumann, Langmuir 13 (1997) 2880. "^J O.I. Del Rio, D.Y. Kwok, R. Wu, J.M. Alvarez and A.W. Neumann, Colloid Surf. A 1 4 3 (1998) 197.
WETTING 5.4c.
5.47
Ck}ntact angles from forces
on objects
in
interfaces
Pull, on objects kept in cin interface is invariably related to y c o s a , already described in sec. 1.8. So the method works if y is k n o w n or m e a s u r a b l e . For instance, / c a n first be established with a n object t h a t is fully wetted: thereafter the measurements can be repeated to obtain a for partially wetted objects. The i n s a n d o u t s of the m e a s u r e m e n t s have already been discussed in c h a p t e r 1^^ For c o n t a c t angle determination, flat plate symmetry is preferred, so t h e Wilhelmy plate method (sec. 1.8a) is viable. Regarding the oscillation mode of t h e Wilhelmy plate technique, speciad reference is m a d e to fig. 1.21 which allows t h e distinction between advancing a n d receding angles. The force-height plots t e n d to be somewhat contorted. This may be caused by surface microheterogeneity a n d the role it plays in hysteresis; a s a consequence the plates may be irregularly wetted over t h e contact line. Conversely, the irregularities give a n impression of t h e s e heterogeneities. As long a s the rates of the height edterations remain below a b o u t lO"'* ms~^ the oscillatory mode of the Wilhelmy plate technique r e m a i n s suitable for rapidly assessing the rate influence on the contact angle^h The Wilhelmy plate method may have its problems for surfactant solutions. Adsorption of these on the plate will generally affect the contact angle, and, hence, the extent of hysteresis. Besides plates, contact angle m e a s u r e m e n t s are also possible with s p h e r e s . We refer to work by Zhang et al.'^^ Huethorst and Leenars'^^ obtained the cingles from the centrifugal force needed to pull a sphere through the interface. 5.4d
Tilted
plates
This t e c h n i q u e , typically developed for m e a s u r i n g c o n t a c t angles w a s n o t considered in chapter 1. The principle is sketched in fig. 5.24. This plate, TP in the figure, c a n be rotated around a n axis normal to the plane of the paper. The idea is to do so until the liquid on the one side is perfectly horizontsd, by which time t h e angle between plate a n d liquid surface is j u s t the contact angle. The horizontality of the liquid level is relatively easily verified, for instance by viewing it over t h e s h a r p straight edge of a razor blade or by illuminating meniscus and plate t h r o u g h a n a r r o w slit. The light lines on the liquid surface are s t r a i g h t / c u r v e d w h e n t h e surface is
flat/curved.
This method w a s devised specifically for measuring contact angles. It goes b a c k to Adam a n d Jessop^^ who also developed m e t h o d s for optical observation. By ^) For a description of forces on objects at interfaces and fluid profiles we also refer to the literature in sec. 1.17c. 2) R.A. Hayes, A.C. Robinson and J. Ralston, Langmuir 10 (1994) 2850. 3J L. Zhang, L. Ren and S. Hartland, J. Colloid Interface Set 192 (1997) 306. 4) J.A.M. Huethorst, A.F.M. Leenaars. Colloids Surf. 50 (1990) 101. ^^ N.K. Adam, G. Jessop, J. Chem. Soc. (1925) 1863; See also, N.K. Adam, The Physics of Chemistry of Surfaces, e.g. 3rd ed., Oxford Univ. Press (1941).
5.48
WETTING
Figure 5.24. Contact angle by the tilted plate method.
establishing t h e tilt angle, using two micrometers, a n accuracy of 0.1° is attainable ^^ The a p p a r a t u s is simple, no fancy instrumentation, b u t a fair a m o u n t of liquid is needed. P e r h a p s the only problem arising is which c o n t a c t angle is actually measured; the advancing or receding one or something between. As is the case with the Wilhelmy plate a n d vertical plate, if the surface is microheterogeneous, a kind of average angle over the contact line is measured. Yamold-^^ applied the idea to measuring the contact angle hysteresis of spherical objects in a mercury surface, obtaining horizontality in two directions. He found large differences between a(adv) and a(rec), depending on pretreatment. For some reason the method h a s lost most of its popularity, probably b e c a u s e sessile droplet m e t h o d s can nowadays be carried out routinely, providing both the interfacial tension a n d contact angle. Simultaneously obtaining these two q u a n tities is also feasible with a combination of the Wilhelmy plate method a n d t h a t of t h e capillary rise a t a stationary vertical plate (see sec. 5.4g). The former gives u; = 2 y ^ c o s a if b « ^ and the latter gives h^ = 2y{l - sin a) / Apg, see [1.3.16]. So we have two equations with two u n k n o w n s between which / can be eliminated a n d a obtained using sin^ a + cos^ a = I. For details, especially in the presence of surfactants, see refs. ^'"^K 5.4e
Capillary
rise or
depression
This group of methods can be subdivided into two subgroups (a) rise or depression inside thin capillaries or pores a n d (b) t h a t outside objects. The former is the more p r o n o u n c e d feature; rises can be substantial w h e n the capillary is narrow a n d well-wetted. Moreover, it is of great practical relevance. A drawback is t h a t precise profile m e a s u r e m e n t s may be difficult b e c a u s e of optical distortion^^ W h e n t h e capillary is long a n d thin a n d the m e a s u r i n g liquid is a s u r f a c t a n t
1^ A.L. Spreece. C.P. Rutkowski and G.L. Gaines, Rev. Set Instr. 28 (1957) 636. 2) G.D. Yarnold, Proc. Phys. Soc. (London) 58 (1946) 120, ^^ A.W. Neumann, W. Tanner, Ten$ide 4 (1967) 220. 4) J. Kloubek, A.W. Neumann, Tenside 6 (1969) 4. ^^ See, for instance, S. Ross, R.E. Kombekke, J. Colloid Interface Set 9 8 (1984) 223.
WETTING
5.49
solution, the solution can become depleted upon rising, by adsorption at the solidliquid border. The second category is less conspicuous; outside macroscopic objects the rise is of the order of the capillary length, K* = (7 / ^pg)^^^, see [1.3.3] which is 0(mm), see table 1.1 in sec. 1.3a. On the other hand, when the objects have a weU-defined geometry, the profiles can nowadays be accurately measured. We must resort to those approaches when no capillaries of the material to be studied can be made. In this subsection we shall discuss the former group; the latter follows in sees. 5.4f and following. The rise h of a liquid inside a partially wetted capillary (a < 90°), or the depression (a > 90°) is related to y cos a, so that from h the contact angle can be obtained if 7 and the meniscus profile are known. In sec. 1.3a this method was used the other way around, i.e. to obtain 7 if a is known. Usually fully wetted cylinders are then used so that the contact angle does not enter the equations. What was said there about the profile remains applicable. This also applies to the deviations in the Laplace profile, incurred as a result of disjoining pressure^^. For the independent measurement of 7 and cos a, the present method has little significance, because it is much easier to work with drops on flat supports, sec. 5.4b. To achieve that goal the profile of the meniscus should be measured. This has to be done optically, but the interpretation of light reflection inside, and partially outside, narrow capillaries is cumbersome. One of the few examples is that of mercury in glass capillaries; the meniscus is relatively easy to measure because of the high reflectivity of the metal. An example was given by Good and Paschek^^ who described a set-up and measured in this way the contact angle of mercury on Pyrex glass and fused silica under various conditions with respect to relative humidity and outgassing temperature of the substrate. For Pyrex a small but measurable increase of a(adv) and a(rec) with relative water vapour pressure was found, viz. from about 136° to 139° for the former and from about 122° to 124° for the latter, for relative pressure ranging from 0.2 to 1.0. It may be noted that for the measurement of 7 narrow capillaries are preferred, whereas for the determination of a, wide capillaries have advantages in that the meniscus profile is more easily accessible optically. Assessing contact angle hysteresis is no problem, because measurements can be done with rising and falling menisci. A problem with solutions of surfactants is that if upon capillary rise depletion takes place, which gives rise to a slow step in the establishment of the meniscus profile. In two respects capillary penetration (or depression) does give rise to independ-
IJ B.V. Deiyagin, (Russian) Colloid J. 56 (1994) 32. -^^ R.J. Good, J.K. Paschek, in Wetting, Spreading and Adhesion, J.F. Padday, Ed., Acad. Press (1978) 147.
5.50
WETTING
ent, derived methods. The first is the pressure
compensation
method, originally developed by Bartell
a n d Walton 1^. The principle is t h a t it is not the capillary pressure t h a t is m e a s u r e d (as the weight of a liquid column) b u t the pressure required to compensate for it, t h a t is; the p r e s s u r e to keep the height inside the capillary at the s a m e level a s outside. This principle h a s found application in the m e a s u r e m e n t of the wetting of powders, to which we shall return in sees. 5.4i. The second is the rate of penetration,
(dh/dt)
method. The principle is t h a t from
the driving force for the penetration (a < 90°), i.e. the capillary pressure, the liquid flux c a n b e c o m p u t e d , u s i n g the Poiseuille equation. For t h e ideal c a s e of horizontal homogeneous capillaries a n d a spherical meniscus, d h _ a / c o s Of dt 4rih
[5.4.4]
a n d is known a s the Washburn
equation. Here, a is the inner capillary radius a n d rj
the viscosity of the liquid. In the real world the situation is rarely so simple, b u t capillary p e n e t r a t i o n is a p h e n o m e n o n of great practical relevance. We shall derive a n d d i s c u s s this equation and the associated problems in sec. 5.4i, b u t note now t h a t Mumley et al.^^ analyzed this method in some detail for liquid-liquid interfaces. 5.4f
Vertical
plates
and
cylinders
The vertical plate case h a s been covered in sec. 1.3b. We refer to [1.3.181 for t h e relationship between the ascending height h and sin a. N e u m a n n a n d Good*^^ give details of t h e cathetometric determination of h. Later, Budziak a n d Neumann^^ proposed a new method t h a t is less susceptible to h u m a n error. This approach combines a digital image analysis with a high precision (resolution O(10~^ cm)) tramslational stage determination. As a corollary to the previous s u b s e c t i o n consider now t h e c o n t a c t angle between a liquid a n d t h e outside of a massive cylindrical solid. Keeping t h e cylinder vertical in the LG interface offers the two u s u a l options; (i) m e a s u r e t h e capillary pull on it a s 'Padday's pencil', sec. 1.8c. This again yields y^^ cos a with the implications already discussed. (ii) m e a s u r e the capillary rise (or depression) of the liquid h against the solid a n d find the contact angle from that. The outer radius should be large a s compared to t h e capillary length. As for a cylinder h is lower t h a n for a flat plate, t h i s
1) F.E. Bartell, C.W. Walton, J. Phys. Chem. 38 (1934) 503. 2) F.E. Mumley, C.J. Radke and M.C. Williams, J. Colloid Interface Set 109 (1986) 398. 413. 3^ A.W. Neumann, R.J. Good, loc. cit. p. 53ff. 4) C.J. Budziak, A.W. Neumann, Colloids Surf 43 (1990) 279.
WETTING
5.51
Figure 5.25. Horizontal liquid near submerged cylinder. Front view. Discussion in the text; equality of a(adv) and a(rec) assumed.
method is less accurate, hence it offers no advantages and should be used only if the solid h a p p e n s to be available a s a cylinder only. However. Gu, Li a n d Cheng^^ improved this method; they ancdyzed the liquid profile a r o u n d a conical cylinder. New situations arise with the cylinder horizontal in the interface. Two alternatives p r e s e n t themselves. In the first the cylinder is p u s h e d so far into the liquid t h a t the liquid level is horizontal, j u s t a s in the case of the tilting plate (fig. 5.24). The geometry is simple, see fig. 5.25. If h is m e a s u r e d (optically or from the displaced volume) the contact angle follows immediately from cos a = (a -
h]/h
[5.4.51
By rotating the cylinder a r o u n d its axis, the difference between the advancing a n d receding angle can be made visible^). For the rest, all remarks m a d e before regarding surface heterogeneity remain vadid. As a variant, the force required to keep the cylinder submerged in this position can be measured and equated to the capillary plus buoyancy force, to again yield y^^ cos a . The second option is mathematically involved; the cylinder is left floating on the surface and y cos a is computed from a force balance. Of course, the relevance of this system goes beyond j u s t measuring contact angles; we only have to remember the introduction to Volume I of FIGS, example 3 . Princen gave a n account of this a n d other systems^^. For a cylinder of radius a, long enough to neglect end effects, h e derived the following pair of equations .GA
2sin(0 + a) + ( p ^ - p ^ ) 5 2 _ VP
n- a + s m a cos a
2 sin a\ —
0
[5.4.6] 1) Y.Gu. D. Li and P. Cheng. Colloids Surf. 112 (1997) 135. 2) R. Ablett, PhU. Mag, 46 (1923) 244. ^^ H.M. Princen, The Equilibrium Shape of Interfaces, Drops, and Bubbles. Rigid and Deformable Particles at Interfaces, in Surface and Colloid Science 2, E. Matijevic, F.R. Eirich, Eds., Academic Press (1969) chapter 1. See A.V. Rapacchietta and A.W. Neumann, J. Colloid Interface Set 59 (1977) 555 for a modification, and H.M. Princen, R.N. Vaidya, J. Colloid Interface Set 174 (1995) 68, for spinning horizontal tubes.
5.52
WETTING
Figure 5.26. Infinitely long cylinder, floating at the interface between two immiscible fluids (here designated as L and G). zf
_ 2 [ l + cos(0-«)]ya^
Here 0 and a have the usual meaning; these parameters and z are Indicated in fig. 5.26. In these equations y is 7 ^ , b u t the formulas also apply w h e n G is a second liquid, t h e n y becomes 7^^ a n d the densities have to be adjusted accordingly. Between [5.4.6 a n d 7] 0 c a n b e eliminated, t h o u g h not analytically. Measurem e n t of z (cathetometrically) yields a if 7 is known. Alternatively, t h e liquid profile c a n be scanned to obtain a optically. The coefficient of the term in square brackets in [5.4.6] scales with the crosssectional area of the cylinder. For very thin cylinders ('threads') this term goes to zero, i.e. 0 = a approaches 180°, meaning t h a t the liquid level becomes completely horizontal. This situation is also a t t a i n e d for high surface t e n s i o n s a n d low density differences (p^ - p^) or (p^2 - pW). The inverse of the systems depicted in figs. 5.25 and 26 ('cylinders on liquid') is t h a t of a liquid drop on a cylinder. One advantage is t h a t only small a m o u n t s of liquid are needed. Another one is t h a t constructions can be made to allow distinction between advancing a n d receding angles. For instance, the cylinder c a n be mounted horizontally in s u c h a way t h a t it can be rotated along its long axis. The drop is then brought on top of it and kept in position by connecting it to the tip of a needle, platinum wire or micropipette. The contact angle is measured directly with the aid of a goniometer with a n eyepiece. The geometry is somewhat more difficult to handle t h a n with drops on flat plates, because there is no axial symmetry. However, t h e possibility of looking specifically for surface heterogeneities, a n d their anisotropy is a n advantage; this can be accomplished by the above-mentioned axial rotation of the cylinder a n d by varying the droplet size (via contact with a micromanipulator). Schwartz et al. have experimented with this technique^'-^^ a n d d e m o n s t r a t e d its viability. 1) A.M. Schwartz, F.W. Minor, J. Colloid Set 14 (1959) 572. 2) A.M. Schwartz, C.A. Rader, IV Int. Congress Surface Activity (Brussels, 1964) Proc. Vol. 2, Gordon & Breach (1967) 383.
WETTING 5,4g
5.53
Fibres
The distinction between long, thin cylinders a n d fibres is quantitative, r a t h e r t h a n qualitative. Nevertheless we shall make the distinction b e c a u s e there is great technical relevance; n a t u r a l fibres (cellulose), synthetic ones (nylon), non-woven fabrics, etc., are materials belonging to this group. The wettability of b u n d l e s or m a t s of fibres a n d woven fabrics is of prime importance
for clothing, t e n t s a n d
several other industrial products. Regarding wetting properties, distinction h a s to be m a d e between individual fibres a n d collections of t h e m ('cloths'). The second group h a s the greater practical relevance. However, the overall wettability is to a large extent determined by t h e geometry of the fibres array, and the apparent contact angle of, for example, water on s u c h a woven fabric is not identical to the contact angle on individual fibres, reducing the relevance of the latter type of measurement. We shall now only consider individual fibres. When a fiber is completely wetted, a n unstable situation arises, j u s t like a liquid cylinder b r e a k s u p into small droplets according to the Rayleigh instability. Basically, the driving force is the minimization of the surface area. For a filament, t h e resulting state is a series of droplets 'on a string', a n d the angle t h a t is formed in this way is often the purpose of the measurment. The stability of ultrathin films on fibers h a s been studied by Brochard-Wyart a n d di Meglio^^; Goren^^ analyzed the instability. In practice, fibres are often anisotropic, either by the way they grow in n a t u r e or are made in industry, e.g. by spinning from nozzles a n d / o r drawing. As a result, the contact angle a n d its hysteresis may also depend on the direction in which the liquid front is moved; in the direction of the fibre or circumferential to it. The m e a s u r e m e n t of the contact angle anisotropy or hysteresis anisotropy is therefore a challenge with practical implications. However, the technicalities of s u c h a m e a s u r e m e n t are by no m e a n s simple. They d e m a n d magnification a n d observation in directions with different curvature a n d this is not easy for the situation where the r a d i u s of the drop strongly exceeds t h a t of the fibre; in t h a t case the influence of the fibre on the curvature of the drop n e a r the fibre becomes very small. Compare the discussion in the previous subsection; w h e n a in fig. 5.27 becomes very small the geometry of fig. 5.24 is approached, t h a t is the situation for a n undisturbed surface. Figure 5.27 shows the way in which such a n experiment can be carried out^^ The drop is kept in position in a small horizontal ring in the field of the microscope. The filament is suspended vertically between support posts and p a s s e s t h r o u g h the
1^ F. Brochard-Wyart, J.-M. di Meglio, Ann. Chim. 77 (1987) 275. 2) S.L. Goren, J. Colloid Set 19 (1964) 81. 3) W.D. Bascom, J.B. Romans, Ind. Eng. Chem., Prod. Res. Develop. 7 (1968) 172.
5.54
WETTING
droplet
Figure 5.27. Fibre through droplet, captured in a ring.
drop. By moving t h e fibre u p a n d down hysteresis in t h e axial direct ion c a n b e measured; if the fibre c a n be made to rotate airound its axis the axial symmetry c a n be verified. An advantage of working with a thin fibre is t h a t microscopic focusing on t h e edge of t h e fibre a n d t h e meniscus profile poses few problems. Yamaki a n d Katayama analyzed this profile^^. Contact angles of fibres a n d drops have also been measured by light reflection, a d a p t i n g t h e procedure of Fort a n d Patterson, depicted in fig. 5 . 2 1 ^ ^ J o n e s a n d Porter^J described a n a p p a r a t u s for measuring angles u p to about 75'' on fibres a s thin a s 2.5 |Li diameter. Other relevant references are ref.^^ a n d ref.^^. In addition, t h e required contact emgles have also been obtained from t h e m e n i s c u s s h a p e , from flotation a n d using a Wilhelmy thread' technique. Bascom^^ reviewed these m e t h o d s a n d gave a n u m b e r of results. Gu a n d Li^^ extended their m e t h o d for vertical cylinders, quoted in sec. 5.4f, to fibers crossing a n oil-water interface. 5.4h
Individual
colloidal
particles
Anticipating t h e m e a s u r e m e n t of contact angles in large collections of particles (subsec. 5.4i), let u s now d i s c u s s a t t e m p t s t h a t have been m a d e with individual particles of colloidal size. The literature is very thin, which is not surprising, given the delicate problem of handling s u c h small particles a n d simultaneously controlling t h e forces. A paper by Mingins a n d Sheludko^^ is seminal. These a u t h o r s studied 20-50 |LI s p h e r e s individually, measuring u n d e r a n optical microscope t h e radius of the three-phase contact line of these spheres, attached to the surface of a pendent drop. From this radius the contact angle could be evaluated.
1) J.-I. Yamaki, Y. Katayama, J. Appl Polymer Set 19 (1975) 2897. -^^ A.M. Schwartz, C.A. Rader, loc. cit. 3) W.C. Jones, M.C. Porter, J. Colloid Interface Set 24 (1967) 1. 4) B.J. Carroll, J. Colloid Interface Set, 57 (1976) 488. 5) H.D. Wagner, J. Appl Phys. 67 (1990) 1352. ^^ W.D. Bascom, The Wetting Behaviour of Fibers, in Modem Approaches to Wettability: Theory and Applications, M.E. Schrader, G.I. Loeb, Eds., Plenum (1992), chapter 13, p. 359. ■7) Y.G. Gu, D.Q. Li, J. Colloid Interface Set 206 (1998) 288. ^J J. Mingins, A. Sheludko, J. Chem. Soc. Faraday Trans. I. 75 (1979) 1.
WETTING
5.55
colloidal sphere cantilever spring
position Figure 5.28. Schematic picture of the interaction between a (dark) sphere and a bubble, obtained via AFM. Discussion in the text. (Redrawn from Preuss et al.) The advent of atomic force microscopy (AFM) has improved matters, because the particle can be glued to the tip, which is connected to a standardized cantilever spring. The particle is then pressed onto (or into) a liquid-fluid interface such as an air bubble and the force recorded^'-^J. Figure 5.28 shows the principle. It relates the force to the height of the particle with respect to the bubble (the 'position'). In the sketch other forces apart from capillary ones are ignored and the sphere is assumed partly wetted by the liquid. At a large distance (position A), the cantilever is not deflected. This is the reference for the force. Now the particle is brought downward; at the very moment that it touches the bubble it is spontaneously drawn down, forming an (receding) contact angle a, (see jump line B in the picture). Pressing the particle further down (arrow C) makes the three-phase contact line shift over the particle. A force has to be applied to achieve this. Having arrived at this point, the process is reversed(arrow D) until eventually the particle is drawn off the interface (Jump line E). On the way up, the contact angle is advancing. The authors show that cos a(rec) = 1 - -
[5.4.8]
where a is the particle radius and d is indicated in fig. 5.28. In addition, for the 1^ M. Preuss. H.-J. Butt, J. Colloid Interface Set 208 (1998) 468. 2) S. Ecke, M. Preuss and H.-J. Butt, J. Adhesion Set Techn. 13 (1999) 1181.
5.56
WETTING
d e t a c h m e n t force, F(detachm) = In ay sin^ f ^ i ^ ^ l
[5.4.9]
So, the two angles can both be obtained, a n d from these the hysteresis. Alternatively, the advancing angle can be obtained by interchanging the liquid a n d the air phase in the set-up of fig. 5.28. In their experiments the a u t h o r s worked with gold-coated silica spheres, with self-assembled monolayers of mixtures of undecanethiols a n d co-hydroxy u n d e cane thiols, to vary the contact angle between 20 cind 100°. The results were compared with sessile drop m e a s u r e m e n t s on the same system. A systematic difference (up to 20° for the receding angles) between the two sets of results w a s observed, b u t since these differences depend on the n a t u r e of the solid surface it w a s not possible to p i n p o i n t t h e origin definitely. A r e m a r k a b l e feature w a s t h a t in t h e AFM method, hysteresis w a s very small, if not absent. Anyhow, this a p p e a r s to be a promising technique. 5Ai
Powders
and porous
materials
At p r e s e n t it is virtually impossible to m e a s u r e contact angles of isolated, irregular, particles; indeed, the question h a s to be asked whether s u c h quantities have a physical meaining. At best, some average can be obtained for a large collection of s u c h pcirticles. The issue is relevant in practice because it is met in a host of examples; wetting of dry soils by rain, of pigment particles by a solvent, of powdered food by water, etc. In all these cases one is interested in the 'ease' of wetting, which for practical situations mostly refers to both the statics a n d the dynamics. The first method t h a t comes to mind is to make a compressed cake of the powder a n d m e a s u r e the contact angle of a droplet - or larger volume - of the liquid on it. To obtain sensible results the caike should be consolidated £ind should not redisperse u p o n c o n t a c t with the liquid, which may p r e s e n t a particular problem for low angles. But t h e n m a n y industrial workers would not worry too m u c h a s long a s dispersion is the objective. For higher angles, more or less reproducible m e a s u r e m e n t s c a n be obtained, depending on the system. For instance, for deposited bacterial lawns, (bacteria are homodisperse so they may form a relatively s m o o t h sediment), advancing angles reproducible within 1-2° have been be obtained^^. However, for various commercial powders the reproducibility is m u c h poorer. Whether the contact angles t h a t are eventually obtained are identical to the real contact angle on a flat surface of the s a m e material is a question t h a t , in all probability, h a s to be answered negatively. Both theoretical, (comparing the angle
1^ M.C.M. van Lx)osdrecht, J. Lyklema, W. Norde, G. Schraa and A.J.B. Zehnder, AppL Environ, Microbiol 5 3 (1987) 1893.
WETTING
5.57
on a porous and a non-porous surface ^^ and experimental analysis (comparing angles on a compressed cake and an evaporated film of the same material, which was smooth under the scanning-electromicroscope-^^), underlines this difference. So, the conclusion is that only semiquantitative results are obtainable, however reproducible they may be. Nevertheless for many systems this is the only information available. A number of attempts have been made to improve upon this method. Kossen and Heertjes^^ found that more stable drops were obtained if the compressed cake was pre-soaked by the liquid. The question of what the measured angle meant was more difficult to answer. Current procedures are based on the penetration of liquids into the porous material. Two variants can be distinguished; (i) the dynamic mode; the rate of liquid uptake is measured and interpreted by the Washburn equation [5.4.4] or a variant of it. (ii) the static mode; the pressure needed to prevent a liquid front from advancing or receding is measured and, via the Laplace pressure, related to menisci profiles, and hence to the contact angle. The Washburn equation applies to ideal cylinders (constancy of radius a and contact angle a along its length) and is derived on the basis of the Laplace pressure Ap = (2/ cos a)/ a as the driving force for a Poiseuille-type flow rate, d V / dt = d(7ca^h) / dt, where h is the penetration depth of the intruding liquid and rj the liquid viscosity. For obtuse angles d h / d t < 0 . So, dh ^ Apa'^ ^ ya cos a dt Srih 4T]h
^
which we had before [5.4.4]. Direct application of [5.4.10] to a porous plug means that the pores in it are represented as a set of parallel cylindrical pores, which is an obvious over-idealization. In real powders a, a and h change from place to place and at best some average can be measured. The radius a is obviously a kind of average (a), but it is difficult to say which average. In fact, the rate is very sensitive to the way of packing. The irregularities of real porous systems may lead to fluctuatng meniscus curvatures which, in turn, may lead to different results for advancing and receding fronts, apart from any local contact angle hysteresis. Perhaps the best one can do is repeat the experiment with a fluid of known a, assuming that the average found this way also applies to the unknown sample. Experiments with model pores (say, hexagonal arrays of homodisperse spheres)
1^ R. Shuttleworth. G.L.J. Bailey, Discuss. Faraday Soc. 3 (1948) 16. ^^ A.W. Neumann, D. Renzow, H. Reumuth and I.E. Richter, Fortschr. KoUoide PolyrrL 55 (1971) 49. 3) N.W.F. Kossen, P.M. Heertjes, Chem. Eng. Set 20 (1965) 593.
5.58
WETTING
have only academic meaning, because it is the very deviation from regularity t h a t causes part of the problem. We return to this in sec. 5.9. In a variant, known a s thin layer wicking, the ascent or descent of the liquid is m e a s u r e d t h r o u g h a packed thin layer, supported on a glass microscopic slide. Constanzo et al.^^ showed t h a t for a n u m b e r of model systems this method give r e s u l t s for cos a agreeing with those obtained from direct m e a s u r e m e n t s on a deposited a n d dried lawn. We repeat the caveat t h a t the dyncimic methods fail w h e n for surfactcint solutions, depletion takes place. The static (compensation) method goes back to Bartell et al., cited in sec. 5.4e. For porous media it h a s been elaborated by D u n s t a n and White^J and is based on a n earlier t h e r m o d y n a m i c a p p r o a c h by White*^^ In this theory t h e average capillary radius in Ap = [2y cos a) /(a) is related to the specific surface area A (a>=2(k:^
via 15.4.111
where (p is the volume fraction of the solid a n d p the solid density. This a p p r o a c h obviates m a n y of the restrictions to the dynamic methods. Diggins et al.^^ elaborated the method to study contact angle and specific surface cireas of quartz powders. 5.4j
Concluding
remark
No definite answer can be given to the key question; 'do all these m e t h o d s yield the same result?' As far as we know, the reply is 'probably not'. One issue is t h a t it is very difficult to exactly replicate m e a s u r i n g conditions. Systematic c o m p a r i s o n s of a wide variety of m e a s u r e m e n t s , applied to the same system do not exist. Even p a p e r s t h a t , according to their titles, claim to m a k e s u c h a comparison usually consider only a few s y s t e m s a n d a few methods^*^^. In fact, m o s t experimental studies do include some comparisons. Rarely are exactly identical results reported for a vciriety of methods, except for ideal systems u n d e r perfect conditions. The r e a s o n s are probably of a n intrinsic n a t u r e ; hysteresis a n d p r e t r e a t m e n t m a y work t h o u g h in different ways in different approaches. These intrinsic uncertainties should be a warning not to overinterpret the data. We present some contact angle data from the literature in appendix 4; the reader can judge for himself how reproducible these data are.
IJ P.M. Costanzo, W. Wu, R.F. Giese and C.J. van Oss. Langmuir 11 (1995) 1827. 2) D. Dunstan, L.R. White, J. Coloid Interface Sci. I l l (1986) 60. 3) L.R. White, J. Colloid Interface Set 90 (1982) 536. ^^ D. Diggins. L.G.J. Fokkink and J. Ralston, Colloid Surf 44 (1990) 299. ^^ Y. Uyama, H. Inoue. K. Ito, A. Kishida and Y. Ikada, J. Colloid Interface Set 141 (1991) 275. ^J L.M. Lander, L.M. Siewierski, J.W. Brittain and E.A. Vogler, Langmuir 9 (1993) 2237.
WETTING
5.59
5.5 Contact angle hysteresis 5.5a The phenomenon The term contact angle hysteresis refers to the generad observation that contact angles depend on their history. In particular, the advancing contact angle always exceeds the receding one. Hysteresis should be considered as a real physical feature. When it occurs, the system is characterized by more than one equilibrium state, all of which may be, or are, metastable. Therefore hysteresis also is a nuisance; with contact angles one should adways specify under what conditions they have been measured, and in (thermodynamic) interpretations, the question as to which of the various values is the ideal angle, if such an item exists at all, must always be asked. In daily life the phenomenon is well known. When rain falls on a soil after a period of draught the first droplets appear unable to wet. Isolated droplets tend to be formed with obtuse contact angles. However, once the soil is soaked, wetting does no longer pose a problem. Water-colour artists know that dipping a dry paint brush in water will not give even wetting because small air drops will remain stuck between the haiirs. After removing these bubbles by squeezing them out, the brush is well wetted and the painting may begin. Numerous other examples could be mentioned. For basic studies, model experiments have to be carried out and anadyzed. We shall mostly consider liquid (L) drops on horizontal solids (S) in a vapour phase (G), because in such a system hysteresis is most manifest. A simple set-up is sketched in fig. 5.29. The droplet on a tilting plate (fig. 5.32) is an alternative. In fluid-fluid systems (L^Lg^)* ^^Y ^^ o^^ ^^^^P floating on water, or a water droplet on mercury, hysteresis may be absent, but then the interpretation is more complex because the vertical component of the surface tension (/^^ sin a) has also to be considered because the liquid substrate cannot support a vertical stress. In other words, analysis requires Neumann's triangle [5.1.3] rather than Young's law [5.1.2]. Hysteresis is a static phenomenon, but its measurement requires displacement of the contact line (fig. 5.4). Immediately the question is raised as to what are the
Figure 5.29. A simple set-up for obtaining advancing or receding contact angles for a sessile drop.
5.60
WETTING
rate, direction and reason (driving force) for this movement. Displacement can be spontaneous (when the spreading tension is > 1) or externally applied, i.e. forced. For instance, a stream of air can be used to blow-dry the droplets from a surface. We have already seen that the faster an advancing front is moved, the more obtuse a(adv) and the faster the receding front, the lower a(rec) is, see fig. 5.5. In practice this implies that the stronger external force is applied, the more we find Nature against us. For our purpose it means that we should let the contact line move as slowly as possible, or if possible, measure a as a function of the rate of displacement and extrapolate to zero rate. The qualification 'if possible' is needed because for slow displacements, the contact angle and the speed are often no longer uniform. Stick-slip steps, and other irregularities may occur. So the dilemma is that if the front is moved too fast, we come into the range of forced wetting or forced dewetting, whereas metastable situations may be frozen if the applied force is too low to overcome the required activation energy to dislodge the front from one metastable state into the next. General rules for finding a way out are not easily formulated because the choice of the optimum rate will depend on the origin of the hysteresis, which may be different for different systems. In this connection, it is not surprising that different investigators report different extents of hysteresis for one and the same system. Small changes in pre treatment or mechanical stability may make a large difference; for instance vibration of the solid may reduce the difference between a(adv) and a(rec)^^ The reason for this last phenomenon may be that the additional mechanical energy helps to move the system from one metastable state into the next. Systems that are fully hysteresis-free are rare. 5.5b Origins There is a vairiety of possible causes of contact angle hysteresis. For some of these model experiments are available, but other origins are more elusive. We shcdl now review the main cases. (i) Surface roughness is the most familiar and best-recognized origin and Deiyagin^^ realized that this phenomenon could give rise to a series of metastable states. Solid surfaces are rarely flat and homogeneous on a submicroscopic scale. This scale is small as compared to visibility by the naked eye, but large as compaired to the sizes of the molecules of the liquid. On this scale, the local contact angle, even if it has the ideal equilibrium value everywhere, is not generally identical to the one macroscopically measured by one of the methods of sec. 5.4, because the surface slope may vary locally. Figure 5.30 illustrates this. Suppose we are in the advancing situation with the liquid moving from the left to the right.
IJ G.D. Nadkami, S. Garoff, Langmuir 10 (1994)1618. 2) B.V. Deryagin, Doklady AkacL Nauk. SSSR 51 (1946) 361.
WETTING
5.61
► X
macroscopic surface
Figure 5.30. Hysteresis caused by surface roughness. Even if the equihbrium contact angle a is the same in A and B, the angle under which the liquid L meets the macroscopic surface is much larger in the second position. Macroscopically, the liquid p a s s e s over patches t h a t seemingly have a lower a n d higher contact angle, a n d which therefore behave a s if they are more hydrophilic a n d more hydrophobic. The result is a jerky 'move a n d stick'-like motion. On the other h a n d , on a n u m b e r of practical rough surfaces channelling, or working along grooves) c a n e n h a n c e spreading (or retraction, if a > 90°). Another p h e n o m e n o n is the 'pinning' of wetting lines. Generally speaking, geometrical details of the surface play a d o m i n a n t role; hence also the relevance of carrying o u t experiments with model surfaces. All of this is a n interpretation b a s e d on viewing the interface a s three-dimensional, r a t h e r t h a n two-dimensional. We stated t h a t the r o u g h n e s s in fig. 5.30 should be larger t h a n the molecular size of the liquid. For a liquid of which t h e molecules are »
these irregulcirities there is no reason for r o u g h n e s s to induce
hysteresis. An illustration w a s given by W. Wijting^^ who worked with colloidal fluids. The system w a s a sol of ludox HS40 (a colloidal silica with particles of 13 nm), coated by stearyl alcohol in cyclohexane, to which the non-adsorbing polym e r poly(dimethylsiloxane) w a s added. By depletion
flocculation
t h i s polymer
induced p h a s e separation into a silica-rich (the colloidal fluid') a n d a silica-poor (the colloidal gas') fluid. The interfacial tension w a s very low, a n d so w a s t h e capillary length. For the present purpose it is pertinent t h a t the contact angle with a glass fiber (25°) w a s hysteresis-free. Surface roughness does not only occur in the x- b u t also in the y-direction. The c o n s e q u e n c e is t h a t the perimeter of a drop on a surface m a y exhibit irregular deviations from circularity.
1^ Private comm. (1999).
5.62
WETTING
(ii) Chemical or surface composition heterogeneity. The stoiy is similar to that under (i) except that the apparent contact angle heterogeneity is now a real feature of the surface if its local equilibrium contact angle is not everywhere the same. The conclusion that heterogeneity tends to inhibit spreading is also confirmed for this case. In fact it is quite possible that real surfaces are at the same time geometrically and chemically heterogeneous. Distinguishing between the two types of hysteresis is then difficult. Experience appears to indicate that chemical heterogeneity produces larger hysteresis than surface roughness ^^ (Hi) Failure of adsorption equilibration. Origins (i) and (ii) apply when the three tensions involved have their equilibrium values, i.e. when all adsorption processes are relaxed. However, incomplete adsorption at any of the three interfaces also gives rise to differences between a(adv) and a(rec). This phenomenon is not a real type of hysteresis but rather the result of lack of patience; if we wait long enough the Deborah number De = T(ads)/t(obs) becomes « 1. Here T(ads) is the characteristic time for the establishment of adsorption equilibrium and t(obs) the measuring time. However, as these phenomena are often observed, we shall include them in the present discussion. A typical illustration, already referred to in connection with 13.2.1] is that of a benzene droplet placed on top of pure water. First it spreads, but later it retracts to form a droplet. The reason is that it takes some time to equilibrate benzene adsorption at the water-air interface. The following adsorptions have to be accounted for; (1) Adsorption of the vapour of the liquid at the SG interface which, depending on such conditions as the pretreatment of the system and the size and volatility of the drop, may be slow or fast. When equilibration is very slow, experiments cam be done with the essentiadly dry surface, pre-empting vaporization and subsequent adsorption. Illustrations are to be found in the investigations by the French School on the rate of spreading of PDMS, to which we return in sec. 5.8. As a rule however, we need y^^ as the surface tension of the solid, in equilibrium with the vapour. Some authors therefore write y^^ as y^^* + n^^, but as y^^* is an inaccessible quantity, this does not take us any further. Experience has shown that this liquid transport through the vapour phase is usually much more efficient than diffusion of molecules out of the droplet onto the solid around it. See for instance^^ (2) Adsorption of adsorptives (surfactants) at the SL and LG interfaces. These processes are usually relatively rapid (De « 1). However, for extremely fast spreading, transport towards the three-phase line may become a limiting factor. (3) Adsorption of surfactants at the SG interface, by 'creeping' over the surface.
IJ C.W. Extrand, Y. Kumagai, J. Colloid Interface Set 191 (1997) 378. 2) V.J. Novotny. A. Marmur, J. Colloid Interface Set 145 (1991) 355.
WETTING
5.63
This phenomenon is mostly not prominent. (iv) Phenomena caused by non-inertness of the solids. This may occur when solvent or adsorptives penetrate into the solid. Some substrates exhibit swelling by the solvent, possibly aided by surfactants. Another mechanism is that of elastic waves. At the contact point, the solid experiences an upward stress 7 ^ sin a which is O(10mN m"^). It is not obvious over what area this force acts because the threephase line may have a 'foot', but when such a foot is absent the thickness of the interfaciad layer is 0(1 nm) (chapter 2), so that the vertical pressure exerted on the solid is 0(10^ Nm"2). Most solids can resist such pressures, meaning that no significant strain results. In such cases spreading can be retarded, but there is no mechanism for real hysteresis. However, if the contact line moves, this elastic pressure has to follow and real hysteresis may arise when the solid has defects, across which the wave cannot be trgmsmitted. In those situations the moving front can be locked in a metastable state. The phenomenon is difficult to quantify. Softer substrates are lifted at the contact line, forming a wedge. Moving such a wedge leads to viscoelastic dissipation in the substrate^--^K In extreme cases wetting may lead to surface reconstruction. As different measuring techniques sometimes involve different rates of spreading or retraction, one should account for any methodical difference between a(adv) and a(rec), obtained by differing experimental approaches. See for instance*^'"^'^K 5.5c Interpretations Given the various considerations just presented, no general theory for hysteresis can be developed, although some attempts have been made to account for parts of it, or for special cases. Everett^^ gave a very formal analysis, which also applies to other hysteresis phenomena like those in gas adsorption and magnetization. He used two important criteria to distinguish real hysteresis (the system passes through a sequence of metastable states) from lack of patience (or retardation of contact line movement) in terms of the repeatability and the possibility of scanning across hysteresis loops. The possibility of complete scanning means that all metastable states are accessible. These observations are of practicad relevance. Two simple equations in the literature are sometimes cited as accounting for hysteresis. The first is the Wenzel equation^*^^ 1^ M.E.R. Shanahan, A. Carre, Ixingmuir 11 (1995) 1396. 2) C.W. Extrand. Y. Kumagai, J. Colloid Interface Set 184 (1996) 191. 3) J. Drelich, J.D. Miller and R.J. Good. J. Colloid Interface Set 179 (1996) 37. 4) A. Marmur, Colloids Surf 136 (1998) 209. 5^ M. Miyama, Y.X. Yang, T. Yasuda, T. Okuno and H.K. Yasuda, Langmuir 13 (1997) 5494. ^> D.H. Everett, Trans. Faraday Soc. 50 (1954) 1077. '^^ R.N. Wenzel. Ind. Eng. Chem. 28 (1936) 988. S^ R.N. Wenzel. J. Phys. Colloid Chem. 53 (1949) 1466.
5.64
WETTING
cos a(obs) = (r> cosa(id)
[5.5.1]
where (r> is some averaged ratio between the real solid surface area and the smoothed, macroscopic one. Equation 15.5.1] minimizes the global Helmholtz energy emd, hence, is meant to account for surface roughness only. The relevance of the equation is very limited. In the first place, it is not clear how (r) is averaged; secondly, the equation can only account for one metastable state whereas real hysteresis demands the description of a series of metastable states. One of the odd features is that for a < 90° a(obs) decreases with r, whereas it increases for a < 90°. At a = 90° no roughness effect is predicted at all. Its applicability is limited to surfaces without chemical heterogeneity and droplets with a radius » roughness scale ^^. The second set of equations come from Cassie and Baxter-^'^l Cassie considered a smooth, but chemically patchwise heterogeneous solid surface, composed of fractions /^ and /^ with ideal contact angles a^ and a^, respectively. For the average he wrote the Cassie equation^^ y^ cosa(obs) = f^iy^i^ - 7^1^) + f^iy^^^
- y^^^)
[5.5.2]
which, for a multi-heterogeneous surface becomes y^ cosa(obs) = ^ ^ f^iy^P - y^h
[5.5.3]
with
X,/,=l
(5.5.41
Alternatively, the Cassie equation can also be written as cos a(obs) = / j cos a^ + f^ cos a^
[5.5.5]
and similarly for [5.5.3 and 4]. The Cassie-Baxter equation'^^ applies pairticularly to porous surfaces and reads cos a(adv, obs) = f^ cos a (adv) - /^
[5.5.6a]
cos a(rec, obs) = f^ cos a (rec) - f^
[5.5.6b]
where /^ and /^ now refer to the SL and the LG area, respectively, projected on the smoothed flat area. Similar objections can be raised against [5.5.2 and 6] as against [5.5.1]. Most importantly, the equation describes only one metastable state. Nevertheless, ^iG. Wolansky, A. Marmur. Coll Surf. A156 (1999) 381. 2) A.B.D. Cassie, S. Baxter, Trans. Faraday Soc. 40 (1944) 546. ^^ A.B.D. Cassie, Discuss. Faraday Soc. 3 (1948) 11. ^^ A.B.D. Cassie, S. Baxter, loc. cit.
WETTING
5.65
Figure 5.31. Wetting of an array of parallel cylinders. Cross-section. experience has shown that as a first approximation the equation serves well. Cassie and Baxter applied their formulas to a set of parallel cylinders (model for a woven fabric), as illustrated in fig. 5.31. From their model they inferred that the familiar water repellence of ducks is caused by the structure of their feathers, rather than by the exceptionally obtuse contact angles. In passing, Israelachvili and Gee^^ proposed to average /^(l + cosa^)^ rather than f^ cos a^, as being applicable to heterogeneity on a near-molecular scale but Johnson and Dettre contested their derivation and applicability^). A theory of a different genre was developed by de Gennes and Joanny^K For the case of small angles they supposed the horizontad surface to contain small, independent non-wetting defects (N per unit area), which inhibit the progress of an advancing liquid front. The resulting perturbation of the contact line lead to a deformation energy U per defect, which could be related to the mciximum force that such a defect can withstand. For the hysteresis, defined as [a(adv)- alrec)]^^^, see fig. 5.5, they found y^[cos a(adv) - cos a(rec)] = N dU d
[5.5.7]
if the defects are independent, that is, far apart as compared to the capillsiry length. The application of this equation to real systems gives rise to problems similar to those encountered before; one does not know how the surface looks like in reality, there is no way of finding N^ and U^ and only one metastable state is predicted. The overall conclusion is that the present problem is not solved; the main culprit is a lack of information on the submicroscopic properties of the solid surface, and the real world is very much more complex than discussed so far; think of the influences of the line tension (which intermingles in a complicated fashion with surface roughness and heterogeneity) and surfactamts (which may lead to continuing changes even after the application of a force has been stopped).
^J J.N. Israelachvili, M.L. Gee, Langnmir 5 (1989) 288. 2) R.E. Johnson, R.H. Dettre, in Wettability, J.C. Berg, Ed., Marcel Dekker (1993), especially p. 16. 3^ J.F. Joanny, P.G. de Gennes, J. Chem, Phys. 81 (1984) 552.
5.66
WETTING
120 ^ 100
a (adv) ^ ^ s ^
'00
^ u
80 -1 or (Cassie)^V^
3 §
60 40 - V
i
^^^ a (rec)
20 1
20
1
1
1
i
1
1
1
40 60 80 hydrophilic fraction of surface
1
100
Figure 5.32. Three types of contact angles computed for a model-heterogeneous surface with concentric circular bands. (Redrawn from Johnson and Dettre, loc. cit.) 5.5d
Hysteresis
on model
surfaces
Given t h e m a n y problems involved in defining heterogeneity a n d surface roughn e s s a n d their consequences for hysteresis, a n u m b e r of attempts have been m a d e to p r e p a r e surfaces of well-defined irregularity a n d / o r chemical composition. S u c h model s t u d i e s also have practical relevance, for instance in microprinting (pinning of liquids by wetting barriers) a n d for the u n d e r s t a n d i n g of t h e overall hydrophilicity/hydrophobicity' of heterogeneous surfaces. J o h n s o n a n d Dettre carried out a n u m b e r of seminal studies, referred to by them in ref.^^ from which fig. 5.32 is taken^^. The model-heterogeneous surface consists of concentric rings, alternately with a high and low contact angle. The boundaries were supposed to be infinitely s h a r p a n d not to contribute to the Gibbs energy (which is a n idealization). From this figure it c a n be seen t h a t a(adv) a n d a(rec) a r e p a r t i c u l a r l y a s s o c i a t e d with regions of low a n d high wettability, respectively. The curve m a r k e d Cassie' w a s computed by [5.5.51; in this case the rings were too narrow a n d h e n c e the d i s t a n c e s between the high a a n d low a too s h o r t to p r o d u c e m e t a s t a b l e s t a t e s . The narrower the heterogeneous rings, the closer a(adv) a n d a(rec) approach a (Cassie). In a n o t h e r study*^^ the s a m e a u t h o r s looked in a similar way, at wetting on a chemically homogeneous surface with a sinusoidal corrugation. From this s t u d y emerged the relevance of the energy barriers, t h a t separated metastable states.
1) RE. Johnson, R.H. Dettre, in Wettability, J.C. Berg, Ed.. Marcel Dekker (1993), chapter 1, sec. III. 2) R.E. Johnson, R.H. Dettre, J. Phys. Chem. 68 (1964) 1744. 3^ R.E. Johnson, R.H. Dettre, Adv. Chem, Ser, 4 3 (1964) 112.
WETTING
5.67
Without striving for completeness, let u s discuss a few follow-ups. Eick et al.^^ investigated capillary rise at a vertical saw-tooth solid wall. The grooves were horizontal a n d so w a s the contact line. The new element w a s the inclusion of gravity. These a u t h o r s also found a finite n u m b e r of metastable states, separated by energy barriers. A follow-up of this study was given by Schwartz a n d Garoff^^ H u h , Mason a n d c o - a u t h o r s studied surfaces with various types of grooves (cross-grooves, hexagonal a n d radial grooves) a n d other k i n d s of r o u g h n e s s , theoretically a n d experimentally*^'"^K These investigations are of a solid, fundamental n a t u r e . Interesting elements are features of texture in addition to those of fraction of roughness on the surface. The, often observed, unsteady, jerky, advance (of parts) of spreading drops, which leads to 'corrugated' perimeters is apparently c a u s e d by t h e fact t h a t only a limited n u m b e r of metastable configurations with constant curvature are accessible. These kind of processes can be mimicked. Studies like these also take u s to the kinetics of wetting. Anticipating sec. 5.8 we mention s u c h a s t u d y by Fraciije et al.^^ who investigated stick-slip j u m p s on otherwise hydrophilic glass surfaces of which the heterogeneity w a s controlled by the application of thin hydrophobic ink lines. Sauer a n d Camey^^ studied advancing a n d receding angles on single glass fibers, treated with silane a n d fluorocarb o n m o n o l a y e r s . They also observed c o n t a c t line pinning; t h e h y d r o p h o b i c patches are commensurate with the fiber diameter (down to 10 |im). In a series of mostly theoretical model studies Marmur et ed.^'^'^^ investigated the role of the drop volume for smooth surfaces, containing oscillatory chemical heterogeneities. The idea, t h a t m a n y metastable s t a t e s m a y exist for r o u g h a n d heterogeneous surfaces, was p u s h e d aihead by showing t h a t the dependence of the a (rec)
a (adv) Figure 5.33. Droplet on a tilted plate.
1^ J.D. Eick, R.J. Good and A.W. Neumann, J. Colloxd Interface Set 53 (1975) 235. 2) L.W. Schwartz, S. Garoff, J. Colloid Interface Set 106 (1985) 422. 3) C. Huh, S.G. Mason. J. Colloid Interface Set 60 (1977) 11. 4) J.F. Oliver, C. Huh and S.G. Mason, Colloids Surf 1 (1980) 79. ^J J.G.E.M. Fraaije. M. Cazabat, X. Hua and A.-M. Cazabat, Colloids Surf 41 (1989) 77. ^J B.B. Sauer, T.E. Carney, Langmuir 6 (1990) 1002. 7) A. Marmur. J. Colloid Interface Set 168 (1994) 40. ^) S. Brandon, A. Marmur. J. Colloid Interface Set 183 (1996) 351. 9J S. Brandon, A. Wachs and A. Marmur, J. Colloid Interface Set 1 9 1 (1997) 110 (hysteresis in three dimensions).
5.68
WETTING
metastable angles on the volume was the reason for t±ie hysteresis. Drelich et al.^^ studied wetting on smooth surfaces with well-defined chemical heterogeneities, obtained by p a t t e r n i n g self-assembled monolayers. One of their findings w a s a large difference between situations with the contact line parallel or normal to the direction of hydrophobic strips. They found t h a t [5.5.5] applies provided it is extended by a line tension term. Off-hand, however, there is no reason to expect the t e r m s in the Cassie equation a n d the line tension contribution to b e additive, unless the surface heterogeneity is very regular. Finally, droplets on a tilted plate (fig. 5.33) can also serve a s a suitable model system for studying hysteresis. By changing the tilt, the combination of cf(adv) a n d a(rec) t h a t j u s t prevents the droplet from sliding can be established. S u c h studies have for instance been carried out by Briscoe a n d Galvln^^ Quere et al.*^^ a n d by Extrand a n d Kumagai'^K A point to keep in mind here is t h a t at the instance of first movement t h e extreme values of cir(adv) a n d a(rec) are not necessarily attaiined simultaneously. A variant, avoiding tilting, is a horizontal plate with a drop on it, which is s p u n radially in a centrifuge^). With the later method it w a s found t h a t roughening increased the retention force and the critical elongation of the drop. 5.6
Line t e n s i o n s
Line tensions (r) are forces acting in the three-phase contact perimeter. Their SIunit is N. When T > 0 the line tension tries to shorten the perimeter, for r < 0 the trend is the other way around. Line tensions are typically excess quantities in t h a t their action comes on top of t h a t of the three interfacial tensions constituting t h e contact angle, a n d which are related through Young's law or Neumann's tricingle. It is historically interesting t h a t the notion of line tension can already be found a s a footnote in Gibbs w o r k s ^ l He also noted that, because of the action of the line tension, the m e a s u r e d contact angle should differ slightly from the macroscopic one predicted by the Young equation [5.1.2] a n d Mysels a n d Frankel^^ pointed to the effect of a line tension in interpreting so-called 'black spots' (i.e. p a t c h e s of afilms) in soap films. In fact, line tensions have generally been invoked to account for the size-dependence of contact angles. It is straightforward to modify Young's e q u a t i o n in order to a c c o u n t for t h e line tension. To t h a t end t h e derivation leading to [5.2.14] is repeated b u t now with the additional term 27CTr in [5.2.9]. The IJ J. Drelich, J.D. Miller, J.D. Kumar and G.M. Whitesides, Colloids Surf. 9 3 (1994) 1. 2) B.J. Briscoe. K.P. Galvin, Colloids Surf. 52 (1991) 219. ^J D. Quere, M.-J. Azzopardi and L. Delattre, Langmuir 14 (1998) 2213. 4) C.W. Extrand, Y. Kumagai, J. Colloid Interface Set 170 (1995) 515. 5) C.W. Extrand, A.N. Gent. J. Colloid Interface Set 138 (1990) 431. ^^ J.W. Gibbs. The Scientific Papers 1, Dover reprint (1961) p. 288. ^^ K.J. Mysels, K. Sinoda and S. Frankel. Soap Films. Studies of their Thinning and a Bibliography, Pergamon (1959).
WETTING
5.69
result is y^
cos a(obs) = y^ cos a(Young) - -
[5.6.1]
where r s t a n d s for the contour length (as in fig. 5.7). Several a u t h o r s have given this equation, or v a r i a n t s of it, including Scheludko et al.^^ De Feijter a n d Vrij (for soap films)2), Pethica*^^ a n d Ivanov et al.'^^ More advanced analyses indicate t h a t r"^ term applies only if the curvature of the contact line is not too strong, later in this setion we shall come back to the precise meaning of r. E q u a t i o n [5.6.1] shows t h a t b e c a u s e of the action of the line tension the contact angle of a sessile drop c a n become size-dependent. According to the not-extended Young equation t h i s s h o u l d not be the case. Another consequence of this action is t h a t small particles, droplets or bubbles, rising in a denser liquid towards the LG p h a s e (as in fig. 5.25) do not necessarily reach this interface because the contractile tension in the t h r e e - p h a s e line c o u n t e r a c t s this, at least if r > 0. S u c h t r e n d s b e c o m e observable only for very small droplets, depending on the value of r. Line tensions also influence condensation and nucleation^^ This is. in a nutshell, the line tension story. However, on closer inspection some subtleties emerge t h a t we shall not avoid discussing. Let u s first a p p r o a c h t h e p h e n o m e n o n from the theoretical side. We take the stance that, a s Young's equation is purely macroscopic, deviations from the p u r e Laplacian behaviour in t h e drop profile n e a r a n d at the contact line are disregarded. It follows t h a t the additional term in [5.6.11 should account for all these deviations or, more precisely, for the corresponding grand potential per unit length of the line in the contact region, in excess of t h a t accounted for by Young's equation. J u s t a s in Gibbs' t r e a t m e n t of the interfacial tension where all p r e s s u r e excesses are assigned to a n infinitesimally thin plane, the surface of tension (see sec. 1.2.23b), here all the excesses contributing to t h e force are assigned to a n infinitesimally thin contact line, the line of tension.
The logic b e h i n d this a p p r o a c h is that, in practice, contact angles are
mostly m e a s u r e d macroscopically, i.e. p a r t s of the c o n t o u r s are in some way m e a s u r e d a n d extrapolation to the t h r e e - p h a s e contact gives the experimental angle. The range of the profile over which the extrapolation t2ikes place usually is not usually studied. However, this is j u s t t h e range where the deviations from
1^ A. Scheludko (= Sheludko), B.V. Toshev and D.T. Bojadjiev, J. Chem. Soc. Faraday Trans. (I) 72 (1976) 2815. 2) J. de Feijter. A. Vrij, J. Electroanal Chem. 37 (1972) 9. 3) B.A. Pethica, Rept Progr, Appl Chem. 46 (1961) 14, J. Colloid Interface Set 6 2 (1977) 567. ^^ I.e. Ivanov, B.V. Toshev and B.P.R. Radoev, On the Themiodynamics of Contact Angles, Line Tension and Wetting Phenomena in Wetting, Spreading and Adhesion, J.F. Padday, Ed., Academic Press (1978) p. 37. ^J J.E. Lane, J. Colloid Interface Set 52 (1975) 155.
5.70
WETTING
Laplacian behaviour, induced by the proximity of other interfaces, and giving rise to the line tension, act. Our treatment is not exclusive; one could also ignore line tensions, but then one should accurately measure the profile in the 1-10 nm remge and probably refrain from speaking of the contact angle. Perhaps this is what Gibbs had in mind when making the historical note on the alteration of the contract angle, mentioned at the beginning of this section. With this in mind, the starting point for theoretical evaluations becomes clear; one has to evaluate the sum of all contributions to the grand potential that are not accounted for by the three macroscopic tensions. Generally, these involve the disjoining pressure /7(h) in that range of the contour where the SL and LG (or LjLg and LgG) interface approach each other closely. The nature of the system determines which contributions to /7(h) prevail. Electrostatic interactions may be absent but dispersion forces and liquid structure-mediated forces are ubiquitous. Regarding the latter, recall that molecules in liquids near solids are stacked in an oscillatory fashion, whereas at the LG boundary the profile is of the tanh type. Close to the three-phase line boundary these mismatching structures overlap and the Gibbs energy of this contributes to r. It also follows that line tensions can in principle be positive or negative, depending on the sign of the prevailing interaction, and that r may indirectly depend on the contact angle a. The argument that negative line tensions do not exist because they would lead to the continuous growth of drops, and eventually to spreading, fails because of the resistance of contact angles to takevalues at variance with Young's equation. In other words, the length of the perimeter cannot be varied without simultaneously changing the SG, SL and LG areas, so there is no thermodynamic argument to dictate the sign of r. As to the computation of r, the previous discussion indicates more or less the path that can be followed, but the detailed execution of this task is not simple. A variety of theories have been elaborated in the literature using different assumptions on the nature of the three phases, the types of interactions and the geometry. Indekeu has reviewed this matter ^^ and for free and wetting films the thermodynamics were reviewed by Babak^K Rusanov^^ classified three types of line tension interpretations, addressing the issue of the deformability of the solid. The most formal approach is perhaps that of density functionals in the style of van der Waals and Cahn (sees. 2.5a and 2.6). Examples of such elaborations were given by Qu et al."^^ and by Dobbs^^. Qu et al. noted that r can be either positive or negative.
1^ J.O. Indekeu, Int. J. Modem Physics B8 (1994) 309. 2) V.G. Babak, Colloids Surf. A156 (1999) 423. ^^ A. Rusanov, Surface Set Repts. 23 (1996) 173. 4^ W.L. Qu. C. Yang and D.Q. Li, Colloids Surf. A144 (1998) 275. 5) H. Dobbs, Langmuir 15 (1999) 2586.
WETTING
5.71
Dobbs considered n-alkanes on water, for which r = 0(10-^2 j^j Marmur^) followed a n o t h e r p a t h , in which h e a s s u m e d the interfacial tensions to c h a n g e over t h e contact a r e a (see our earlier comment on this approach). Although he could not solve the complicated differential equations, he could predict t h a t r should be less t h a n 5 x 10"^ N and vary a s coth a, being positive for acute angles a n d negative for o b t u s e o n e s . Getta a n d Dietrich^^ found from a n analysis b a s e d on pair interactions, T-values of order 10"^^ N a n d a similar trend in the sign reversal a s a function of contact angle a s w a s found by Marmur. Line tensions of 0(10-^^ N) were also theoretically predicted by Rowlinson a n d Widom*^^ a n d by Solomentsov a n d White^). So, in conclusion the present state of the theory is t h a t r = 0(10-^^-10-^^ N). Hence t h e action of t h e line tensions c a n only be observed for d r o p s s u b s t a n tially below the 1 |i cross-section range. For instance, let in [5.6.1] r = 1 |i, y= 0 ( 1 0 mV m-i), it follows t h a t r / r = 0(10"^ N ur^), which is less t h a n a p e r c e n t of y^^ cos a . This is below the u s u a l sensitivity of the m e a s u r e m e n t s a n d m u c h less t h a n t h e u n c e r t a i n t y c a u s e d by hysteresis. The implication is t h a t for m o s t practical p u r p o s e s the effect of line tension is eclipsed, or at least it becomes a n esoteric quantity. Given t h e low value of r , m e a s u r i n g t h i s q u a n t i t y r e q u i r e s very sensitive procedures. Experimental values have among others been obtained by Scheludko et al.^^ from t h e r e s i s t a n c e of m i c r o s p h e r e s to a t t a c h to LG b o u n d a r i e s . Their estimate w a s 10~® - l O ' ^ N . Later, Mingins a n d Scheludko reported 10-^^ N from similar measurements^^. Drelich a n d Miller^^ reported similar r e s u l t s . However, in Neumcinn's group^^ values 0(10"^ N) were found from the drop size dependence of contact angles. The N e u m a n n group d a t a were confirmed by J e n s e n a n d Li^K studying capillary rise inside conical t u b e s . These last-mentioned d a t a were only obtained with advancing angles, for which the r"^ dependence was found to hold. In fact, interpretation of t h e r a d i u s - d e p e n d e n c e of contact angles is fraught with uncertainties b e c a u s e of hysteresis; the way in which the contact perimeter folds itself a r o u n d microscopic roughnesses is strongly determined by the line tension.
1) A. Marmur, J. Colloid Interface Set 186 (1997) 462. 2) T. Getta, S. Dietrich, Phys. Rev. E57 (1998) 655. ^^ J.S. Rowlinson, B. Widom, Molecular Theory of Capillarity, Clarendon Press (1982); see also J. Szeifler, B. Widom, Mol Phys. 75 (1992) 925. 4) Yu. Solomentsov. L.R. White. J. Colloid Interface Set 218 (1999) 122. ^^ A. Scheludko, B.V. Toshev and D.T. Bojadjiev, J. Chem. Soc. Faraday Trans (I) 7 2 (1976) 2815. ^> J. Mingins. A. Scheludko, J. Chem. Soc, Faraday Trans. (I) 75 (1979) 1. "7) J. Drelich. J.D. Miller, J. Colloid Interface Set 164 (1992) 252. ^^ A. Amirfazli, D.Y. Kwok. J. Gaydos and A.W. Neumann. J. Colloid Interface Set 2 0 5 (1998) 1; A. Amirfazli. D. Chatain and A.W. Neumann. Colloids Surf A 142 (1998) 183. 9) W.C. Jensen, D. Li. Colloids Surf A156 (1999) 519.
5.72
WETTING
(a)
Figure 5.34. Corrugations of the three-phase line caused by surface heterogeneity, (a) top-view (|i-range), (b) perspective view of a section of the perimeter (horizontal: |i-range, vertical up to ~ 0.1 ^i). (Redrawn after Pompe et al.) For a sketch see fig. 5.34. Note t h a t in [5.6.1] t h e actual r in t h e denominator is often orders of magnitude smaller t h a n t h e macroscopic r a d i u s of a sessile drop. Several a u t h o r s have reported this trend ^♦'^^. For reviews see ref.^^ and, for a more physico-phenomenological approach, ref. ^\ However, quantitative utilization of perimeter corrugations h a d to await t h e advent of atomic force microscopy. Very nice results have been obtained by Pompe et al.^'^^. These a u t h o r s applied AFM in the tapping mode to determine the details of the corrugated profile of liquid drops, deposited on a surface with controlled (stripe-wise) hydrophobicity (periodicity 4 0 0 - 1000 nm). For t h e liquid, hexaethylene glycol w a s chosen (for a n u m b e r of practical reasons). Top views of the droplets looked like those in fig. 5.34a, though with more
regularity in t h e corrugations b e c a u s e of t h e control of t h e hetero-
geneities. To obtain r , the a u t h o r s plotted locciLly cos a versus t h e reciprocal local radius, a n d found linearity a s predicted by [5.6.1]. From t h e slope, the line tension is directly found. They reported - 6 x 10'^^ N and - 3 . 5 x 10"^° N for t h e more hydro-
IJ R.J. Good, M.N. Koo, J. Colloid Interface Set 7 1 (1979) 283. 2) D.Q. Li, Colloids Surf. A116 (1996) 1, 2^ A. Rusanov, Surface Set Repts. 2 3 (1996) 173. 4) E.M. Blokhuis. B. Widom, Current Opin. Colloid Interface Set 1 (1996) 424. ^^ T. Pompe, A. Fery and S. Herminghaus, J. Adh, Set Technol 13 (1999) 1155. 6) T. Pompe, S. Herminghaus, in press (2000); the author appreciates receiving a preprint.
WETTING
5.73
philic ( a = 18°) a n d t h e more hydrophobic (a = 34°) domains, respectively^K This promising technique therefore provides results t h a t are entirely in line with theoretical predictions, a n d so resolve the issue of size (and sign) of the line tension. Given t h e difficulties involved in precisely m e a s u r i n g details of profiles, alternative methods also deserve attention. Examples are the line tension effect on vapour condensation on surfaces, studied by t h e Bulgarian School-^•'^^ a n d t h a t on the size a n d stability of floating liquid lenses, a s investigated by Aveyaird et al.^''^^ GenerEilly, s u c h studies confirm the low values, for instance - 1 . 9 x 10"^^ N in ref.^^ a n d +1.6 X IQ-^^ N in ref.'^l The advantage of floating liquid lenses is t h a t they a r e (almost) hysteresis-free. Stockelhuber et al. reported line t e n s i o n s in t h e n a n o meter range for water lenses on dodecane^^. In a similar vein, D u s s a u d a n d VignesAdler^^ analyzed t h e role played by line tensions in wetting transitions of a l k a n e s on saline solutions. Their values for T are +0.9-2 x 10"^^ N, again in the same range. For details of experiment a n d interpretation see the originals. Let u s finailly note t h a t line tensions have also been analyzed by MD simulations. We have t h e restrictions a n d possibilities discussed before, b u t note t h a t , from the models, line tensions of about 5 x 10"^^ N were also found'^K 5.7
Interpretation of static c o n t a c t angles
In this section we shall a s s u m e t h a t for a given t h r e e - p h a s e system t h e ideal contact angle(s) h a s (or have) been measured, a n d now a s k for a molecular interpretation. We shall specify our t a s k by considering only SLG a n d SL^L2 s y s t e m s , where t h e two solid surfaces are co-planar, so t h a t only one contact angle suffices to describe t h e static wetting. The choice of choosing flat solid s u p p o r t s h a s t h e dual p u r p o s e of allowing u s to apply Young's equation, [5.12], a n d to a d d r e s s t h e issue of characterizing surface properties of solids in t e r m s of their wettabilities. This is of prime practical relevance a n d will be discussed in sec. 5 . 1 1 . Unless otherwise stated, t h e solid shall be considered mechanically a n d chemicsdly inert a n d free of heterogeneities. Only p u r e liquids will be considered, on t h e u n d e r standing t h a t in SLG systems the vapour will be taken saturated by t h e liquid a n d t h a t for SL^Lg systems the two liquids are mutually saturated. Liquids containing surfactants are a tale in their own right; these systems will be discussed in sec. 5.10.
1) R. Aveyard, J.H. Clint, D. Nees and V. Paunov, Colloids Surf. A 1 4 8 (1999) 95; R. Aveyard, J.H. Clint and D. Nees, Colloid Polym. Set 278 (2000) 155. 2) A.D. Scheludko. J. Colloid Interface Set 104 (1985) 471. ^^ B.V. Toshev, D. Platikanov and A. Scheludko, Langmuir 4 (1988) 489. 4) R. Aveyard, J.H. Clint, J. Chem. Soc. Faraday Trans. 9 3 (1997) 1397. 5J K.W. Stockelhuber, B. Radoev and H.J. Schulze, Colloids Surf 156 (1999) 323. ^^ A. Dussaud, M. Vignes-Adler, Langmuir 13 (1997) 581. "7) F. Bresme, N. Quirke, Phys. Chent Chem. Phys. 1 (1999) 2149.
5.74
WETTING
In the previous section we airgued that contact angles can be interpreted on two levels; (i) in terms of the three macroscopic surface and/or interfacial tensions, measured at some distance from the three-phase contact line. (ii) in terms of a molecular picture of all interactions in and close to the threephase contact zone. Following our approach in sec. 5.6, all contributions of nature (ii) are subsumed in the line tension, which has already been discussed. Hence, for the present section only item (i) remains. For the LG and L^L2 phase boundaries we have already treated the corresponding tensions in some detail in chapter 2. There is no need to repeat that. Interpretation of the two tensions involving solids is avoided because these are unmeasurable. The only issue left is how the various models and interpretations work out for a set of three phase boundaries. To that end, let us itemize the various interpretations of chapter 2. Where relevant, it is assumed that y^^ is the equilibrium value; the SG interface may cairry an adsorbate. (a) Thermodynamics and statistical thermodynamics. What has been saiid about thermodynamic interfacial excess functions (especially F° and Q^] remains valid for all three phase boundaries. This is a consequence of the general phenomenological nature of thermodynamics. Although the formalism leading to the relations between interfacial tensions and interfacial pressure tensors (sec. 2.3) and distribution functions (sec. 2.4) also remains unaltered, the shapes of the functions p. (z), as in [2.3.5], and g^^\z^, z^^,r). as in [2.4.6], become very different. Recadl that at the LG border the p(z) profile obeys a hyperbolic tangent profile, whereas at an SL border it behaves in an oscillatory way. At the SG border a step function is expected for the density. For an inert solid the corresponding surface tension has a relatively high energetic contribution. Any mismatch resulting from overlap between these three profiles in the threephase contact zone leads to a positive or negative excess in Q^ per unit perimeter length and hence to a (positive or negative) contribution to the line tension. (b) Van der Waals and Cahn-Hilliard mean field interpretations. As above, the formalism remains the same; for each interface the Helmholtz energy per unit area is obtained by minimizing a density functional of the F^lp^(z]] type, as in [2.5.18] or [2.6.1]. However, the shape of p^(z) is again different for the SL interface, (c) The Hamaker-De Boer approximation. Recall from [2.5.43 and 44] that for the surface tension of a liquid a y'^^Ajen^^ and for the interfacial tension between two liquids a and p.
[5.7.1]
WETTING
5.75
where ^ is the thickness of the transition zone (taken identical for t h e a - v a p o u r a n d a-P interface) a n d the A's are H a m a k e r c o n s t a n t s , defined in |2.5.2]. If a n expression similar to [5.7.1] may be written for the surface tension of the solid, basically the information is avaiilable to relate the contact angle to two (for liquid a on solid S) or three (for liquids a a n d p on solid S), Hamaker c o n s t a n t s . As, for m a n y materials, these c o n s t a n t s are known (see table in appendix 1.9) a n estimation of the contact angle is in principle possible. The weak point in the method is t h a t ^ is a sensitive, t h o u g h esoteric quantity. We discussed its Vcdue for fluid interfaces in sec. 2.8, where we concluded t h a t the order of magnitude is well established b u t t h a t a precise value is difficult to assign. For SG interfaces we did not develop a theory; in those systems § r e p r e s e n t s the d e p t h over which the a t o m s n e a r the surface a s s u m e m u t u a l positions differing from those in the bulk of the solid. However, we shall show below t h a t for contact angles the choice of ^ is less critical t h a n it is for interfacicd tensions. In a n u m b e r of alternative approaches, equations similar to [5.7.1 a n d 2] are derived, ignoring t h e finite t h i c k n e s s of the interfacial region, a n d / o r applying Lifshits theory to obtain (the equivalents of) Hamaker c o n s t a n t s (eq. [1.4.7.7] or its variants). In s u c h models our parameter ^ is replaced by the distance r of shortest approach between t h e adjoining p h a s e s . However, a s r is a s esoteric a s <^, if only b e c a u s e surfaces are rarely flat on a molecular scale, these alternatives offer little comfort. We recall t h a t our 'wedge' approach (fig. 2.7) obviates the introduction of r . By way of illustration we refer to the following equation, derived by D r u m m o n d a n d Chan^) for the SLG system
2^SL
cos a = — ^ ^ ^L
2
/^,'o.LL
-1
[5.7.3]
V'o.SLy
This equation c o n t a i n s only two H a m a k e r c o n s t a n t s a n d two r 's, b e c a u s e t h e corresponding p a r a m e t e r s for the SG interface were eliminated u s i n g the Young equation. The a u t h o r s call r t h e 'contact surface separation'. The advantage of [5.7.3] is that the absolute values of r are not needed b u t rather the ratio of two r 's. ^
o
*
o
A s s u m p t i o n s c a n be m a d e about this ratio, without having any knowledge of the a b s o l u t e v a l u e s . For i n s t a n c e , one could simply e q u a t e t h e two r 's, t a k e a geometric m e a n like r^^, =r ^^ x r „ , or otherwise. The u p s h o t is t h a t (cosines of) *=*
o.SL
o.SS
o.LL
*
contact angles are m u c h less sensitive to the values assigned to (^ or r t h a n surface tensions. The overall conclusion is t h a t this group of methods provides semi-quantitative 1^ C.J. Drummond, D.Y.G. Chan, Langmuir 13 (1997) 3890.
5.76
WETTING
results a n d enable one to grasp the essential features quickly. (d) Quasi-thermodynamic
approaches.
In sec. 2.9a we found t h a t the temperature
coefficient of the surface tension, i.e. the surface excess entropy S^, is a r a t h e r generic quantity. The interpretation t h a t we offered in connection with fig. 2.16 implies t h a t for LL-boundaries a very similar value for S° m u s t b e expected. For solids one does not know d y / d T , b u t if this dependence is also generic, this may m e a n t h a t (cosines of) contact angles are m u c h less t e m p e r a t u r e sensitive t h a n interfacial tensions. Indeed this is often observed. Kinks in a(T) curves may t h e n indicate s t r u c t u r a l trcinsitions in the solid^J. (e) Antonow's rule. This rule reads ySL = yS _ ^L
jfQj. ^S > ^Lj
[5 7 4]
for SLG-systems. It is p e r h a p s the oldest attempt to find a n interfacial tension if the constituent surface tensions are known. We have used this equation before, see [2.11.12] a n d refer to Winter's review for a s t a t u s report a n d a historical introduction*^'. Antonow's a n d Young's rules may be juxtaposed; the former is exact for complete wetting, w h e r e a s the latter only applies for partial wetting. Antonow's rule may be a good approximation for low contact angles. (f) Geometric mean methods.
Much research h a s been carried out on the basis of
Fowkes' equation [2.11.191 which, for a solid-liquid interface, reads f^=y^
+ y^-2{Yyf
15.7.5]
It c a n be derived from Antonow's rule, [5.7.4], applying it to partial wetting b u t accounting for the adhesion between solid a n d liquid, a s s u m i n g it to be dominated by the Van der Waals, or dispersion, p a r t s of the surface tensions, y^ ^^^
7^ •
Various studies have shown t h a t [5.7.5] is quite effective for materials t h a t mainly interact
through
dispersion
forces
and
that
it
remains
a
reasonable
approximation for systems in which other interactions also operate. The root in the r.h.s. of [5.7.5] s t e m s from the a s s u m p t i o n t h a t Berthelot's principle may be applied. In sec. 2.11b we argued t h a t this principle may be applied only to t h e energetic part of the interfacial tensions and t h a t a more correct form is ySL =y^ ^y^.TA '
'
*
S"" - 2lu''l U^M^^^ adh a
\
a.d
[5.7.6]
a.d/
Where A^^^S^ is the adhesion entropy per unit cirea of the SL p h a s e boundary a n d
1) A.W. Neumann, Adv. Colloid Interface Set 4 (1974) 105. 2) A. Winter, Heterog. Chem. Revs. 2 (1995) 269.
WETTING
5.77
the LT^^'s stcind for the dispersion parts of the corresponding surface tensions. Equation [5.7.6] can be combined with Young's equation, to give TA S^ 2(1;^^ L/^M^^^ cos a = - 1 + —ad^_^_ ^ V ^'^ ^ ' ^ / —
[5.7.7]
Fowkes' own expression does not contain the entropic contribution b u t h a s a term accounting for the surface pressure of the SG interface (we do not need t h a t b e c a u s e our y^ is the surface tension of the solid in the presence of vapour). Equation [5.7.5], a n d variants thereof, have been widely invoked to a s s e s s the surface t e n s i o n of solid surfaces by working with organic liquids ( s u c h a s hydrocarbons) in which dispersion forces prevail. For those one may set y^ =y^ so t h a t the equation can be solved for y^, which, in turn, may be equated to 7^ for a Van der Waals solid. However, we see from [5.7.7] t h a t t h e situation is more complicated. First, neglection of the TAS term is not allowed, it may a c c o u n t for 2 0 - 3 0 % of t h e interaction Helmholtz energy. Second, even if a n a s s u m p t i o n is made on A^^^S^, or if it is directly m e a s u r e d from the heat of adhesion, only the energetic part of y^ can be assessed. Here it is interesting to recall fig. 2.15 and its discussion. Aveyard found t h a t the work of adhesion and hence, cos a , interpreted in terms of [5.7.5] w a s satisfactory if it could be a s s u m e d t h a t the a l k a n e s lie flat on t h e interface ^^ Later Fowkes concluded something similar^^ independent of the chain length. According to our interpretation [5.7.5] is satisfactory when A
S^ in [5.7.7] is low, and independent
of the c h a i n length. Considering [2.11.22] this is the case w h e n adhesion affects only slightly the molecular configuration in the interface. We shall therefore not elaborate these equations any further, b u t consider t h e m a s useful approximations^^ 5.8
Dynamics
Rates of wetting are of great practical a n d theoretical interest. They are relevant in pigment dispersion, in food science, in oil flooding a n d almost everywhere where wetting is involved. In practice, wetting rates are mostly controlled by working with surfactants (to lower the contact angle between liquid a n d solid, a n d hence to increase the driving force) and, where possible, to work with fluids of low viscosity 77 (to reduce the viscous resistance). However, surfactant addition is double edged, b e c a u s e it also leads to surface tension lowering, w h e r e a s a high t e n s i o n is
1) R. Aveyard, J. Colloid Interface Set 52 (1975) 621. 2) F. M. Fowkes, J. Phys. Chem, 84 (1980) 510. ^^ For a recent, but rather specialistic review, see D.Y. Kwok, A.W. Neumann, Adv. Colloid Interface Set 81 (1999) 167.
5.78
WETTING
required for high rates. This can also be seen in [5.4.10]. As fair a s hydrodynamics is involved, it is not surprising t h a t the quotient of viscosity a n d surface tension, written in dimensionless form a s the capillary
number
Ca^nR
[5.8.1]
is a n important characteristic. Here, v is the velocity. The n u m b e r Ca occurs in m a n y equations describing wetting rates from a fluid dynamics point of view. In this section we shall only a d d r e s s wetting of solids by p u r e liquids, emphasizing spontaneous wetting. For the influence of surfactants, see sec. 5.10. The theoretical description involves the major challenge t h a t wetting r a t e s are determined by a combination of regimes that do not easily match; flow in the drop a n d close to the contact perimeter obeys different laws. It is no surprise t h a t s u c h i s s u e s offer fodder for theoretical physicists. The problems involved generally s u r p a s s the confines of FICS, b u t we shall nevertheless try to point out where the basic problems are, a n d in which way solutions can be sought. In a seminal paper by de Gennes^^ these basic issues are clearly recognized. To find a rate, one m u s t generally identify the driving force a n d the resistance against flow. We elaborated this for a n u m b e r of examples in sec. 1.6.4. All t h e s e examples involved macroscopic a m o u n t s of fluid, moving u n d e r the influence of external forces a n d having a resistance of a viscous n a t u r e . Under s u c h conditions solution of t h e Navier-Stokes equation [1.6.1.15] or v a r i a n t s thereof, suffices to describe the fluid dynamics. For a droplet, spreading on a (Fresnel) surface, the situation is more complicated. Flow in the bulk of the drop obeys Navier-Stokes
V77777777777777Z77777777777777777777777777777777777 Figure 3.35. Schematic picture of a precursor film. The contact angle a^^ at the front is an ill-defined parameter.
IJ P.O. de Gennes, Rev. Mod. Phys. 57 (1985) 827.
WETTING
5.79
type dynamics but the part at and close to the three-phase contact perimeter behaves differently because now much thinner layers, down to molecular size, are involved. For complete wetting in the absence of external forces (which would lead to rate-dependent contact angles, as in fig. 5.5) the outward pull on the perimeter by the unbalance of capillary forces tends to draw a precursor film out of the droplet. A situation as in fig. 5.35 may arise. Beyond the precursor film the solid surface is covered by a macroscopically thick film because it is at equilibrium with the vapour. If it is not, the variation y^^(t) offers an additional complication. The precise shape of the h(x] profile depends on the system; on the (molecular) friction in the film, on the (viscous) friction in the macroscopic part of the droplet, on the possibility that slip occurs along the solid-liquid phase boundary and on the action of disjoining pressures operating in the colloidal transition zone. Precursor films have been experimentally observed, for instance by ellipsometry, interferometry, or by scanning microscopy, as described in sec. 5.4. Lin et al.^^ showed that rates of spreading can also be obtained with quartz microbalances. Precursor films are not ubiquitous, and their properties will remain objects for study for a long time. Our present interest in them concerns spontaneously spreading liquids. When precursors are observed, one may conclude that the spreading tension is positive. When, during spreading, evaporation takes place, additional driving forces may arise, caused by surface tension and/or temperature gradients. At the beginning of FICS I, we mentioned the formation of 'wine tears', rising up the inside of glasses containing (not too dilute) alcoholic drinks. Such tears, with the accompanying fingering, are appealing illustrations. Neogi-^ \ Cazabat et al.*^^ and others have analyzed the ensuing Marangoni-type flows. However, at present we shall restrict ourselves to mono-component liquids. No precursor films are expected for partiailly wetting liquids. For such systems, spreading can be achieved only by applying an external force, leading to forced wetting. Then, entirely different mechanisms prevail. Returning to our present issue, the dynamics of spontaneous spreading, we can at least make the statement that flow in the film is two-dimensional (onedimensional if the length of the film is small as compared to the radius of the droplet), whereas it is three-dimensional for the bulk of the droplet. Intuitively, one might expect a(dyn) to increase with Ca. Experimentally, this trend is corroborated with, at the extremes, a(dyn) -^ 0 for very low Ca (down to 10~^) and a(dyn) -^ n for very high Ca (10^ and higher). Cubic relationships of the nature
1^ Z.X. Lin, T. Stoebe, R.M. Hill, H.T. Davis and M.D. Ward. Langmuir 12 (1996) 345. 2) P. Neogi, J. Colloid Interface Set 105 (1985) 94. 3^ A.M. Cazabat, F. Heslot, P. Carles and S.M. Troian, Adv. Colloid Interface Set 39 (1992) 61; P. Carles, A.M. Cazabat, J. Colloid Interface Set 157 (1993) 196; X. Fanton, A.M. Cazabat, Langmuir 14 (1998) 2554. Also see S. Bardon, M. Cachile, A.M. Cazabat, X. Fanton, M.P. Valignat and S. Villette, Faraday Discuss. Chem. Soc. 104 (1996) 307.
5.80
WETTING
[a(dyn)l^ = f(C a), where / is some function, have been reported a n d theoretically derived. However, there is no reason for a s s u m i n g t h a t Ca is the sole deciding quantity. Regarding the value of a u n d e r dynamic conditions a(dyn), distinction m u s t be m a d e between forced a n d s p o n t a n e o u s wetting. The former situation is usually obtained at constant rate, so it represents a steady state process. Hence, Ca is c o n s t a n t a n d so is a, (see fig. 5.5). S p o n t a n e o u s wetting is not a steady state process. S p r e a d i n g t a k e s place, hence a d e c r e a s e s with time. Note t h a t we are discussing advancing contact angles^^. Let u s go one step further into the interpretation. Recall t h a t we m u s t describe the driving force a n d the frictiohal resistance. As a first approximation, t h e former may be identified a s F = 2K r/^^[cos a(stat) - cos a(dyn)]
[5.8.2]
if r is the r a d i u s of the droplet. During spontaneous spreading a(dyn) will change, so F = F(t). Accounting for the resistance requires a mechanistic model. We shall now briefly describe two approaches. The first is of a molecular-kinetic n a t u r e , a n d h a s been derived by Blake a n d Haynes^^ a n d by Cherry a n d Holmes*^^. Blake's theory interprets the advancement of the contact line £dong lines similar to Eyring's theory for diffusion. Molecules of the droplet, in contact with the solid, may move out of the drop a n d back, because of dynamic equilibrium. Under static conditions the two material flows are equal in magnitude, b u t w h e n a non-zero spreading p r e s s u r e acts, 'forward' j u m p s are biased in favour of 'backward' j u m p s . The bias is given by a variant of [5.8.2], a n d b e c a u s e of the difference between two activation Gibbs energies (one forth, one back) this driving force a p p e a r s in the rate i; a s a hyperbolic sine function. The result is v= 2 r ^sinh j x " ^ l c o s a ( s t a t ) - c o s a ( d y n ) l |
[
2N^hT
J
Here v is t a k e n in radial direction, £ is the average distance between sites on the surface, in the Langmuir model related to the (average) molecular area a^, N^ is the number of sites per unit area and r
is the average residence time of molecules on
the surface sites. It is typical t h a t [5.8.3] does not contain the bulk viscosity. The equation h a s a molecular foundation. It is expected to apply when viscous forces in t h e b u l k are n o t rate-determining, i.e. at high Ca. One would expect Blake's ^^ Many interpretational and experimental aspects of all this have been comprehensively reviewed by T.D, Blake, in Wettability, J.C. berg., Ed., Marcel Dekker (1993) chapter 5. 2) T.D. Blake, Ph.D. thesis, Univ. Bristol (1968); T.D. Blake, J.M. Haynes, J. Colloid Interface Set 30 (1969) 421. 3) B.W. Cherry, CM. Holmes, J. Colloid Interface Set 29 (1969) 174.
WETTING
5.81
formula to work better.for partial, t h a n for complete wetting, b e c a u s e in the latter cse the viscous part dominates. Blake (loc cit.) gives illustrations of experimental verification. Some of these do not apply to s p o n t a n e o u s b u t to forced wetting. In b o t h c a s e s t h e sinh functionality a p p e a r s to work well, a l t h o u g h there m a y be some d i s c u s s i o n on t h e p a r a m e t e r values to be assigned. For later detailed illustrations,
s e e ^ ^ De Ruijter et al.-^^ i l l u s t r a t e d t h e model by m o l e c u l a r
dynamics. The second a p p r o a c h is purely hydrodynamical a n d elaboration by Cox^^ deserves mentioning One of his results is 5[[a(stat) - a(dyn)] = Cw
ln|^K9
-0(Ca2)
[5.8.4]
Typically, this equation contains Ca, w h e r e a s all molecular properties are s u b s u m e d in t h e d i m e n s i o n l e s s phenomenological p a r a m e t e r Q. In [5.8.4] g is a. function of angle, r' is a characteristic macroscopic length (proportional to t h e drop radius r), s is a slip length parameter, which should be of molecular size b u t in practice often a p p e a r s to be m u c h less t h a n t h a t . Mostly Q < ln(r' / s). The velocity e n t e r s the equation via Ca. One of the problems to be solved w a s how to a c c o u n t for the singularity of hydrodynamic flow n e a r the t h r e e - p h a s e border. Here, the velocity is finite, whereas in the bulk viscous dissipation m u s t become infinite, b e c a u s e the fluid layer thickness h ^ 0 . So, a solution m u s t be found to obviate this problem, or r a t h e r for modelling the flow a n d dissipation n e a r t h e perimeter. Cox a s s u m e d t h a t the liquid slips close to the solid. We know from electrokinetics t h a t such slip does occur; it gives rise to the so-called slip plane, w h i c h is s i t u a t e d a few molecular d i a m e t e r s from t h e surface a n d w h i c h is primarily determined by t h e stacking of the molecules of the liquid against t h e solid'^^ Beyond this layer the liquid h a s its b u l k viscosity. From surface light scattering a n d surface rheology (sec. 3.7e) it follows t h a t this bulk value persists u p to the LG p h a s e boundary. Apart from this, the molecular picture in the derivation of [5.8.4] is only implicit. Before proceeding, let u s mention the following simple empirical equation, found by Remoortere and J o o s ^ ^ to apply for silicon oils ascending in glass capillaries: a ( s t a t ) - a(dyn) = 2[l + cosa(stat)] Ca^^'^
[5.8.5]
^^ R.A. Hayes, J. Ralston, Langmuir 10 (1994) 340; M. Schneemilch, R.A. Hayes, J.G. Petrov and J. Ralston, Langmuir 14 (1998) 7047. 2) M.J. de Ruijter, T.D. Blake and J. de Coninck, Langmuir 15 (1999) 7836. 3) RG. Cox, J. Fluid Mech, 168 (1986) 169. 4) J. Lyklema, S. Rovlllard and J. de Coninck, Langmuir 14 (1998) 5659. ^^ P. van Remoortere, P. Joos. J. Colloid Interface Set 141 (1991) 348.
5.82
WETTING
30H 30
25 20
20
15 10^
0 30 H
25J 20-1
101
(a)
5 5
10
15
20
25
30
mm,,
35
40
0
30-1 (c)
25]
10
mwm
15
20
25
UiJiiiiiii;:
30
35
(d)
20 J
15
15-1
10-1
10
' i I p M l « ; » ' xj^'xx'xv^-^xx'kXVW'.'x**' / * I f » ♦ • t ♦ ' " •* * X •* »♦ ^■»-»»xsX'xW»'»'x-*
ji-iu;^
5l 0
10
15
20
25
30
35
40
5
10 15 20 25 30 35 40 45
Figure 5.36. Molecular dynamics pictures of liquid motion near the contact line. Partial wetting. Given is the height as a function of horizontal position, both in reduced units. Panel (a) initial stage of spontaneous wetting, (c) intermediate stage, (d) final stage. Panel (b) corresponds to panel (a), but is taken with respect to the position of the contact line. The solid is at h = 0.55. (Courtesy of M. de Ruijter and J. De Coninck.) It may be useful j u s t to describe observations. Other a u t h o r s , including Petrov^^ Voinov^) a n d Rame a n d Garoff^^' considered t h e t r a n s i t i o n zone, theoretically a n d / o r experimentally, proposed various models of the rest, investigations tend to be limited to the study of scaling law^s of a limited range of validity. Experience h a s shown that, to 'explain' a(v) data, the Blake and Cox approach usually give similar results, n o t w i t h s t a n d i n g very different interpretations. So, comparative c h e c k s are not always discriminative, aihd in this respect, m u c h remains to be done. An interesting development stems from applying molecular dynamics simulations of which fig. 5.36, taken from the paper by de Ruijter and de Coninck (loc. cit.) gives a n interesting illustration. The four panels show very clearly how the pull on the perimeter leads to internal flow p a t t e r n s inside the droplet, a n d in this way visualizes how t h e molecules inside the droplet solve the singularity problem. For details of the simulations, including a discussion of p a r a m e t e r values, see t h e original paper. We further draw attention to a paper by Shikhmurzaev who devel-
1) P.G. Petrov, J.G. Petrov, Langmuir 8 (1992) 1762. 2) O.V. Voinov, J. Colloid Interface Set 201 (1998) 127. 3^ E. Rame, S. Garoff. J. Colloid Interface Set 177 (1996) 234.
WETTING
5.83
oped a new hydrodynamic theory witJi a non-equilibrium thermodynamic description of the three-phase line and the adjacent interface!^. The point of this treatment is that it contains the no-slip conditions without producing a singularity at the wetting line. Additional interesting phenomena occur when the surface is rough or chemically heterogeneous. Only when these irregularities obey a certain pattern is it possible to make distinct progress. By way of illustration we mention that systematic studies have been carried out on surfaces with controlled grooves-^K Let us finally say a few words about the reverse process, dewetting. As discussed before, upon drainage of a thick film on a flat horizontal surface, holes may appear, either because of surface heterogeneities, or because of the growth and subsequent destabilization of spontaneous fluctuations. One of the issues is how to describe this process. For theoretical work we refer to studies by Brochard-Wyart and de Gennes^K For a visualization of the process, see fig. 5.37, referring to a polymeric system, which has the advantage that the process can be followed easily because of the high viscosities. In panel (a) isolated holes have formed; they appear to be rather homodisperse, implying similarity in creation and growth. Excess liquid is visible as a lighter rim around the holes. The thickness profile can be scanned by AFM, and fig. 5.38 gives an illustration. By capillary action, the holes tend to aggregate. (Such an aggregation can also be observed with air bubbles floating on a liquid.) After some time the surface is completely filled with holes and rims (panel (b)). Because of the reasonable homodispersity a quasi-hexagonal pattern develops. In panel (c) the aggregated rims have coalesced and partially disintegrated into droplets because of the Rayleigh instability. Studies like this have obvious practical relevance. 5.9 Porous systems In this section we shall briefly review some phenomena related to the penetration [imbibition] of porous solid materials by a liquid. These phenomena have great practical relevance. Numerous processes come to mind in which they play a role; uptake of water in pharmaceutical powders, imbibition of dry soils by rain water, absorption of ink by paper, and tertiary oil recovery. In the last example one fluid (mostly gas or aqueous) displaces the other (crude) and the process is therefore forced, in contradistinction to the other examples where penetration is spon-
1) E.D. Shikhmurzaev, J. Fluid Mech, 334 (1997) 211. 2) R.R. Rye, F.G. Yost and J.A. Mann, Langmuir 12 (1996) 4625; S. Gerdes, A.M. Cazabat and G. Strom, Langmuir 13 (1997) 7258; S. Gerdes, A.M. Cazabat, G. Strom and F. Tiberg, Langmuir 14 (1998) 7052. ^> P.G. de Gennes, Rev. Mod. Phys. 57 (1985) 827. F. Brochard-Wyart, J. Phys. //4 (1994) 1727.
WETTING
5.84
^^
f*' ^
(b)|
r ;
; > ^
. ^.
, ;
•
*
#*
Figure 5.37. Three stages in the breakdown of a continuous polymer film on a polymer brush. From top to bottom; (a) isolated holes, (b) holes with rims occupy almost the entire surface; (c) coalescence has proceeded. (Courtesy J. Maas.)
WETTING
5.85
20 h
E C!
10 ^•ot) OJ
0 -10
-20 10 )U Figure 5.38. AFM profile across one of the holes in fig. 5.37a. (Courtesy J. Maas.) t a n e o u s . Generally, we are interested in t h e rate of u p t a k e a n d t h e a m o u n t absorbed. In imbibition of p o r o u s materials m a n y of the p h e n o m e n a d i s c u s s e d before converge in a compounded way. The basic mechanism - capillary rise - is readily identified. However, t h e complications a s compared to the well-defined experim e n t s with capillaries, plates, etc., t h a t we have described, are n u m e r o u s . The geometry of the pores is rarely well-defined (if known at all), pores are interconnected, surfaces are often heterogeneous and rough, a n d constrictions m a y block certain r o u t e s . The driving force d e p e n d s sensitively on t h e extent to which t h e u n w e t t e d p a r t s of the pores are already covered by vapour, which is difficult to control in actual porous systems. Wetting and dewetting are rarely reversible. It is a hopeless task to try smd develop a comprehensive theory accounting for all these features. Next to trial a n d error, the following possibilities for a p p r o a c h i n g t h e problem may be p u t forward. (i) Extend the W a s h b u r n equation [5.4.10] to any array of parallel cylinders, ignoring connections between them. (ii) Develop a formal theory, giving a general picture b u t not containing clear physical quantities. (iii) Carry out model experiments, or study model systems. Let u s consider the first possibility, and start by repeating [5.4.10] dh _ Apg _ ya cos a ~dt ~ Srih ~ 4rjh
[5.9.1]
This e q u a t i o n describes the rate at which a liquid of viscosity rj a n d surface tension y
=y penetrates into a cylindrical t u b e or capillary of fixed r a d i u s a.
Gravity is not incorporated, meaning t h a t the equation is valid for a horizontal
5.86
WETTING
pore or for a narrow vertical pore provided h is not too large. For verticed pores in which h becomes so high that the hydrostatic head can no longer be ignored, Ap becomes 2 / c o s a
Ap = —
,
r,- r^ r^i
pgh
[5.9.2] a This equation gives the maximally attainable height h(max) for Ap = 0 as ,, . 2ycoscir h(max) = —i
re o oi [5.9.3]
pgcL
We have seen this equation before, [1.3.7]. It tells us, for instance, how high groundwater can ascend in soils above the ground water table, and how much higher the rise is in narrower pores. We have tacitly assumed that the reservoirs from which the liquid is drawn are large enough to saturate the porous system. In this case the volume of liquid that is maximally absorbed in pores follows
from
V(max) = 7ca^/i(max), or __, , 2iiaycosa V(max) = P9
,- ^ .. [5.9.4]
Although the driving force (first term on the r.h.s. of [5.9.2)]) decreases with increasing radius, the imbibed volume increases in this direction. Let us, in passing, remark on the influence of surfactants on the rate of penetration. Generally they are added as wetting agents, meaning that adding them leads to an increase of cos a, which promotes the uptake. We shall discuss this in sec. 5.10. As stated before, this is only part of the story. Surfactants also lower y , which acts the other way around. Moreover, in practice, penetration over long dist£inces may lead to depletion. For the rest, cdl the remarks that have been mode concerning hysteresis, the distortion of contact angle range by disjoining pressures or as a result of the dynamics, remain vcilid. Let u s for the moment continue to discuss the ideal case. We may identify dh / dt in [5.9.1] as the rate of wetting, u, assume a to be constant, and use [5.8.1] to find for the capillary number acosa 4h which decreases with increasing h, even if gravity is excluded. When gravity is included, [5.9.1] changes into dh _ y a c o s a dt 4r]h
pga^ 8ri
In the absence of gravity [5.9.1] and fixed a can be integrated to give
[5.9.6]
WETTING
5.87
h'=m^t
(5.9.71
where the lower boundary h = 0 corresponds to t = 0; if this is not the reference state in the experiment the immersion depth at t = 0 has to be accounted for. In the presence of gravity the relation contciins an additional term. All of this applies to a single capillary. For a bundle of N identical capillaries nothing changes as far as h{t) is concerned, because the relevant expressions all refer to one single capillary. However, the maximally imbibed volume [5.9.4], becomes N times as high; V(max)=
2KaN Ycosa ^
[5.9.8]
P9
The next step is of course to consider the situation that not all the radii are identical. Generally there will be a certain pore size distribution P{a), where P[a)da represents the probability of finding a pore with radius between a and a + d a . In that case the average diameter (a) can be defined as (a) = ^ . a^P^ia^)
[5.9.9a]
for a discrete distribution, or as (a) = J aP{a)da/j
P{a)da
[5.9.9b]
for a continuous one. In [5.9.9a] the sum includes aU classes j of a and in [5.9.9b] the integration is over all a. Equations [5.9.9] do not offer much reUef because for (opaque) powders there are no easy ways to obtaiin the distribution independently. Techniques such as X-ray scattering do give some feeling for the porosity, but it is not possible to extract support for the model of paredlel cylinders. Similar things can be stated about permeability studies, discussed in some detail in sec. I.6.4f. However, it is questionable whether further analysis along these lines makes much sense, because the pores are rarely straight, and they are mostly inclined and interconnected. So, for practical reasons, the best solution is to continue using [5.9.6 and 7] but replace a by (a), considering this to be a semi-empirical parameter dh ^ 7(a) cos g dt 4nh ^2^y{a)cosa^ 2r]
pgjaf 87]
[5 9 10]
[5.9.11]
Many porous systems obey the h^{t) relationship reasonably well, at least over a given h range, which means that at least the parameters in [5.9.11] are
5.88
WETTING
independent of h. When t h a t fact is established it also m a k e s sense to repeat the experiment with fully wetting liquids, to a s s e s s ( a ) , and, by comparison, estimate the average contact angle. For a suitable package for studying this, see^^ In this way a dynamic contact angle is obtained. On the other h a n d , from t h e m a x i m u m volume 27iaN (a)Y cos a ^—^ [5.9.12] P9 the static (advancing) contact angle is derived. Here (a) follows from [5.9.9a] with V(max) =
P=N/N J
. In this connection we recall the method of D u n s t a n a n d White to cj'
c
m e a s u r e the contact angle of powders by establishing the pressure needed to keep the front stationary. These a u t h o r s related (a) to the packing a n d porosity, see [5.4. 111. Several aspects of the above were discussed by Siebold et al.-^^ We shall n o t d i s c u s s t h e v a r i o u s c o n s e q u e n c e s of p e n e t r a t i o n by limited a m o u n t s of liquid, b u t refer to the literature^'^^ The practical relevance is to discover how far ink from a pen or jet printer penetrates into the paper. When the added drops are very small this can lead to retention in the capillaries. In practice, this p h e n o m e n o n c a n be troublesome; sometimes it is referred to a s t h e J a m i n effect^^ In order to displace it, one h a s to apply a p r e s s u r e to overcome t h e difference between the advancing (at the front side of the drop) and receding (at the rear side) angles. This pressure difference across the drop a m o u n t s to ^ 27[cos a(adv) - cos a(rec)]
,^ ^ ^^,
a Schwartz et al. have studied this phenomenon extensively^^. We may add t h a t pore t h r o a t s have a great effect, where the geometry allows meniscus curvature to vary over a greater range t h a n t h a t caused by contact angle hysteresis. This is a b o u t a s far a s we shall go with item (i) mentioned at the beginning of this section. Regarding items (ii) a n d (iii) let it suffice to referr to a few examples taken from the literature. A typical example of a formal macroscopic theory is t h a t by Levine a n d Neale^^ 1) H.G. Brull, J.J. van Aartsen, Colloid Polym, Set 252 (1974) 32. ^^ A. Siebold, A. Walliser, M. Nardin, M. Oppliger and J. Schultz, J. Colloid Interface Set 186 (1997) 60. ^^ A. Marmur, Adv. Colloid Interface Set 39 (1992) 13; A. Marmur, in Modem Approaches to WettabUity, M.E. Schrader, G.I. Lx)eb, Eds., Plenum (1992) chapter 12. '^^ M. Denesuk, G.L. Smith, B.J.J. Zelinski, N.J. Kreidl and D.R. Uhlmann, J. Colloid Interface Set 158 (1993) 114; also see M. Denesuk et al., ibid. 168 (1994) 142. ^^ After J. Jamin, C.R. Acad, Set 50 (1860) 172. ^) A.M. Schwartz, C.A. Radar and E. Huey, Adv. Chem. Ser. 43 (1964) 251. ^^ S. Levine, G. Neale, A Theory of the Rate of Wetting of a Finely Dispersed Random Porous Medium, in Wetting, Spreading and Adhesion, J.F. Padday, Ed., Acad. Press (1978) chapter 11.
WETTING
5.89
In this a p p r o a c h no a s s u m p t i o n is m a d e about pore s t r u c t u r e or particle size or s h a p e . The model is adso more advanced t h a n t h a t described above, in t h a t flow at higher Reynolds n u m b e r s is taken into account, which allows taking care of fluid circulation within t h e pores between the particles. Dissipation resulting from hysteresis-induced m e n i s c u s expansion or contraction is also incorporated. All of this leads to a n extension of d'Arcy's law (sec. I.6.4f). The resulting e q u a t i o n s contain a n u m b e r of physical c o n s t a n t s , the interpretation of which in t e r m s of the microscopic geometry of the medium is not direct. Nevertheless, theories s u c h a s this one provide useful scale laws. Of the model studies we mention work with periodically variable porosities ^'^K Mason a n d Morrow studied the effects of fluid trapping between adjoining particles by looking a t triangular tubes'^^ a n d throats formed by spheres"^^. Studies s u c h a s these are particularly useful in investigating the efficiency of oil field flooding. Let u s finally draw attention to studies in which the (rates of) wetting a n d dewetting are c o m p a r e d between plugs, consisting of t h e s a m e material, b u t having a different particle shape, say random powders, homogeneously stacked s p h e r e s or filaments n o r m a l or parallel to t h e direction of penetration. S u c h c o m p a r i s o n s serve a s a m e a n s for distinguishing between intrinsic contact angle influences a n d their geometrical consequences. There are also some nice computer simulations, s u c h a s those by Cieplak a n d R o b b i n s ^ ^ demonstrating the influence of the contact angle on fluid penetration into a two-dimensional p o r o u s m a t e r i a l a n d providing a n example of selforganized criticality. 5.10
Influence of surfactants
B e c a u s e of their propensity to lower interfacial tensions efficiently, s u r f a c t a n t s have a drastic effect on static a n d dynamic wetting. When surfactants are intentionally added to improve wetting, they are called wetting
agents. When they are
fortuitously present, a n d interfere with the wetting, they are called impurities. Many wetting agents are mixtures. In the previous section we already noted t h a t a d d i n g s u r f a c t a n t s may, u n d e r certain conditions, be c o u n t e r p r o d u c t i v e . For instance, the driving force for the wetting of powders, / ^ cos a , can either increase or decrease, depending on the question of whether or not lowering / ^ ^ is compensated by increasing cos a . In this section we shall discuss some fundamentals. The bottom line of the problem is to describe the way in which added surfactants
1^ A. Marmur, J. Colloid Interface Set 129 (1989) 278. 2) A. Borhan, K.K. Rungta, J. Colloid Interface Set 155 (1993) 438. 3) G. Mason, N.R. Morrow, J. Colloid Interface Set 141 (1991) 262. 4) G. Mason, N.R. Morrow, J. Colloid Interface Set 168 (1994) 130. ^J M. Cieplak, M.O. Robbins, Phys. Rev. B41 (1991) 11508.
5.90
WETTING
affect contact angles. Let u s consider this for a sessile drop on a flat inert surface, restricting ourselves to only one single surfactant. So the picture is t h a t shown in fig. 5.19 (top sides). The obvious first step is to combine Youngs law, [5.1.2] y^^ cos a = Y^^- y^^
[5.10.1]
with Gibbs' law, t h a t we shall write as dy dine
= -RTfr
[5.10.2]
where / a c c o u n t s for the n u m b e r of kinetically active units per molecule. For nonionics this follows from [4.6.4] with T and ^ ' s constant a n d a s s u m i n g the solution to be ideal. Activity coefficients may be needed, b u t for the analysis to follow we a s s u m e t h e m to be unity. In these systems / = 1. For ionic s u r f a c t a n t s , also a s s u m i n g c o n s t a n t temperature a n d ideality in solution, we obtain the same result from [4.6.10] or [4.6.11] on the understanding t h a t / = 2 for fully ionized surfacta n t whereas / = 1 for the s a m e surfactant in excess electrolyte. For intermediate concentration ratios / can be between 1 and 2 and may change if, upon addition of surfactant t h e electrolyte concentration is not adjusted. We shall a s s u m e t h a t t h e conditions are c h o s e n in s u c h a way t h a t /
is i n d e p e n d e n t of the s u r f a c t a n t
concentration c. Differentiating [5.10.1] with respect to I n c , applying [5.10.2] leads to y^o g.^ ^ f ~ ^ 1 = RTlr^'' I, d In c y ^
- / r ^ ^ - / r ^ cos a) ^
[5.10.3]
Here, we have set / = 1 for the SG interface. When no surfactant adsorption t a k e s place here from t h e solution, neither via the v a p o u r p h a s e , nor by molecules 'walking out of the perimeter of the drop', F^^ ~ 0 . However, for L1L2 systems one h a s to be more careful; the surfactant may dissolve in both liquids a n d a d s o r b from there. Most likely, one of the liquids is apolar and surfactants dissolved in it will not dissociate, or only poorly, so t h a t / ~ 1 . However, whatever the cingle, sin a is always positive, so the sign of d a / d In c is determined by the sign of the factor between p a r e n t h e s e s on t h e r.h.s. of [5.10.3]. Figure 5.39 illustrates t h i s graphically ^K Three d o m a i n s c a n be distinguished. The top one r e p r e s e n t s de-wetting by surfactants, which is common for water on hydrophilic surfaces a n d c « c.m.c. Surfactants
a d s o r b with their polar h e a d s toward the surface a n d in this way
hydrophobize it. This is one of the ways by which materials can be m a d e repellent.The
water-
lowest trend implies improved wetting, a common p h e n o m e n o n for
^^ Analyses along these lines have been proposed by C.A. Smolders, Rec. Trav. Chim. 8 0 (1961) 650.
WETTING
5.91
r^^>f{r^^+r^cos
a]
a
r^^=/(r^^+r^^cosa)
r^^
a]
In c Figure 5.39. Influence of surfactants on the contact angle. Smolders plot for low surfactant concentration. hydrophobic surfaces a n d for hydrophilic ones for s u c h high concentrations t h a t a second adsorbed layer is formed on top of the first, b u t now with the polar h e a d s pointing outward. In the figure s u c h duplex' adsorption would lead to a s u d d e n break above a certain concentration. The contact angle p a s s e s through a m a x i m u m a s a function I n c ; mostly s u c h meixima are located before the c . m . c . in fact, in the linearly descending part of fig. 4.28. Exact null-wetting (middle line) does not occur often. Some two-liquid systems display s u c h behaviour. Note t h a t the figure only gives the variation of a with In c; the absolute value of a depends on the wettability of the surface, gmd will be higher for more hydrophobic substrates. In fig. 5.40 three situations are visualized. We note, t h a t at the three-phase contact, m i s m a t c h of the s t r u c t u r e s of the surfactant a d s o r b a t e s occurs; their contribution to t h e excess grand potential e n d s u p in the line tension. Special cases c a n sometimes be distinguished. One of t h e s e is t h a t F^^ = 0 ,
(a)
(b;
:c)
Figure 5.40. Sketch of the mode of adsorption of surfactants from a water drop on (a) an apolar surface, (b) a polar surface at low concentration and (c) a polar surface at high concentration. The absolute value of the contact angle is kept constant.
5.92
WETTING
cos a = 1
Figure 5.41. Influence of surfactants on wetting according to Lucassen-Reynders. Discussion in the text. which is for instance, common for polymeric surfactants a n d for oil-soluble surfactants in a n oil drop on a surface. When F^^ = F ^ , dy^^ = d y ^ , of course. Interpretations like the present one can be extended to study the influence of surfactants on the reversible work of adhesion, using [5.2.2c]. For m a n y fllustrations see ref.^^ An alternative way of presenting the influence of surfactant on static contact angles h a s been proposed by Lucasssen-Reynders^^ a n d is schematically presented in fig. 5 . 4 1 . She differentiates [5.10.1] with respect to y ^ , after using [5.10.2] to obtain; d(y ^ cos a ) XG
dy
psc _ jpSL
fr
LG
[5.10.4]
reducing to d(y^^cosa) dy
LG
J-SL [5.10.4a]
for r ^ ^ ~ 0 . Each l.h.s. contciins measurable quaintities only. In [5.10.4a] the factor /
cancels; this is not a consequence of some similarity between the surfactant
^J T.D. Blake. Wetting, in Surfactants, Th.F. Tadros. Ed., Acad. Press (1984) 221. 2) E.H. Lucassen-Reynders, J. Phys. Chem, 6 7 (1963) 969; see also E. Wolfram, Kolloid Z. 211 (1966) 84.
WETTING
5.93
adsorptions at the SL and LG boundaries, b u t because these two adsorptions refer to the s a m e solution, with identical degrees of dissociation of t h e ionic surfactant. S t a r t i n g from t h e zero value of t h e ordinate axis straight lines fan o u t in a direction, determined by cos a , with straight lines for cos a = +1 a n d - 1 a s t h e extremes. Systems of constant contact angles are characterized by straight lines t h r o u g h t h e origin. Practical systems will lie between t h e s e extremes. Slopes of curves in s u c h a diagram give the ratio T ^ / F ^ . The straight lines a, b and c in the figure apply to constant values F ^ / F ^ = 0 , F ^ = F ^ and F^^ / F ^ ^ = 0 , respectively. For real systems the d a t a will lie between these extremes. The experim e n t a l p o i n t s apply for a n a q u e o u s perfluorooctanoate solution o n paraffin wax^^; only in rare cases are s u c h plots linear. Variations in the slope are useful diagnostic indicators of the adsorptions at the various interfaces. Case (c) implies t h a t no surfactant a d s o r b s a t the SL interface. In t h a t case complete wetting can never be achieved, whatever the adsorption at the LG surface. In the reverse situation, case (a), complete wetting is attainable at any F ^ ^ , a n d in t h e more c o m m o n intermediate situation (b) adsorption a t t h e liquid-vapour interface m u s t lead to a lowering of /^^ t h a t is characteristic for the wettability of the solid. The general conclusion is t h a t reduction of y^^ is more i m p o r t a n t t h a n t h a t of y^^. How strongly surfactants adsorb at the two interfaces d e p e n d s on the n a t u r e a n d strength of the various contributions to the adsorption Gibbs energies. Of course surfactants also exert a strong influence on the probability a n d process of dewetting, on hysteresis a n d on the dynamics of wetting, compounding the i n h e r e n t problems a n d confounding o u r a t t e m p t s to u n d e r s t a n d p h e n o m e n a . Depending on the relative affinities for the three interfaces, a n d the rates a t which the surfactants can reach these and equilibrate, a broad s p e c t r u m of p h e n o m e n a c a n develop, either improving or frustrating wetting. If, for instance, spreading is spontameous, with a precursor film, it maikes a lot of difference whether t h e surfact a n t c a n move at the same rate a s the front, or lower thein that. In the latter case a promoting Marangoni effect develops in the precursor. Surfactant adsorbed a t the SL interface, left behind on the solid surface after retraction of t h e liquid, will affect the spreading in the next cycle and so affect hysteresis. Surfactant depletion can affect all of this. For a n introduction to these, a n d a host of other related phenomena, the reader is referred to the books on wetting, mentioned in sec. 5.12. 5.11
Applications
This fifth c h a p t e r is, in a sense, already a n application, b e c a u s e knowledge of liquid-fluid interfaces, the theme of this Volume, h a s been applied to systems also 1) R.A. Pyter, G. Zografi and P. Mukerjee. J. Colloid Interface Set 89 (1982) 144.
5.94
WETTING
involving solid surfaces. So this section can be regarded as an application of an application, which seems appropriate as a conclusion to this book. Wetting finds wide application in the living and non-living world. Here, a selection will be made. 5.11a Characterization of the wettability of solid suffaces Wetting experiments are often carried out as a meems of probing the surface of a solid. Obviously, with water as the liquid, the nature of surfaces can range from hydrophobic to hydrophilic. In practice, on flat surfaces, contact angles exceeding about 125° are rarely observed, see table A4.2 for PTFE. Angles of 0° are found on meticulously cleaned gold amd germanium, see table A4.1. Hence, on this basis, a hydrophobic-hydrophilic scale can be introduced, with gold having one of the most hydrophilic surfaces and Teflon having one of the most hydrophobic. As there is no reason to restrict the study to water, one could just as well create an alcoholphobic/philic scale or, generally, a lyophobic/lyophilic scale. The habit has developed for calling surfaces that are easily water-wetted high energy surfaces and those that are poorly wetted low energy surfaces. The terms are misleading and we shall avoid using them because it is not the surface energy that is being measured. We already discussed this issue in connection with table II. 1.3. This table contains immersion wetting enthalpies, which follow a similar trend. At best from contact angles and Young's equation, assuming equilibrium, we can derive y^^ - y^^, i.e. the difference in Helmholtz energy or grand potential per unit cirea. We can measure this difference for a family of liquids and note that this is a real surface characteristic; modification of a surface (say, hydrophobing gold by vapour deposition of silanes) drastically increases the contact angle without strongly affecting the Hamaker constant, which is a measure of the interaction between the two bulk phases. There has been no shortage of attempts to estimate surface (Helmholtz-) energies from contact angles, by invoking some model. A controversial issue is Neumann's equation of state' method ^^ which is based on the assumed validity of a second relationship between interfacial tensions, so that y^^ and y^^ can be individually estimated. Another route starts by assuming [5.7.5] to be valid. For an apolar liquid on a solid S (/^ == /^), combination with Young's law gives L\ 1/2
cos or:
[5.11.1] 7^
In this way only the dispersion contribution to /^ can be found. Moreover, [5.7.5] is inaccurate, and [5.11.1] should be replaced by the equivalent of [5.7.7]. For a
1^ D.Y. Kwok, A.W. Neumann, Adv. Colloid Interface Set 81 (1999) 1267.
WETTING
5.95
discussion of models see ref.^^ It seems more appropriate to remain within the domain of wettability characterization. This takes us to a procedure developed by Zismein^'S) and his group, which leads to an empiricad characteristic, called the critical surface tension of wetting /(crit). This notion applies to hydrophobic surfaces'*^ and represents the surface tension of a liquid that just wets the solid. Here, just wetting' is experimentally determined by comparing the contact angle for a range of liquids with different surface tension y ^ (often homologeous series), establishing the value of y^ below which the surface is fully wetted. Schematicadly, the resulting Zisman plot looks like fig. 5.42. The data points refer to homologeous series of liquids, say alkanes, ethers, alkylbenzenes, etc. Such plots are often reasonably linear; their intersection point with the cos a = 1 horizontal line is the critical surface tension of wetting. The value of y(crit) appears to be more or less the same between different series. For instemce, Zisman (loc. cit. 1964) finds for alkanes, dialkyl ethers, siloxanes and alkylbenzenes on Teflon /(crit) values between 17 and 24 mN m~^. Hence, although y(crit) is a liquid surface tension, it may, within limits, be considered as representative for a solid. Experience has shown that fluoridation of the solid surface lowers y(crit), i.e. makes its wettability poorer. Polymeric surfaces tend to have higher y(crit) values; typical values are 18, 31, 39 and 43 mN m"^ for Teflon, poly (ethylene), poly(vinylchloride) and poly(ethyleneterephtalate), respectively. The higher y(crit), the more difficult it is to wet the solid. Zisman's plot may be formulated as 1
«0« -
8 0.6 -
_Oi—O—^
\ \ \ o
0.4 _
\ \
0.2
Figure 5.42. Zisman plot (schematic). \
0 -0.2 Y (crit)
yUG
1^ J. Kloubek. Adv. Colloid Interface Set 3 8 (1992) 99. 2) H.W. Fox, W.A. Zisman, J. Colloid Set 5 (1950) 514. 3^ W.A., Zisman, Adv. Chem. Ser. 4 3 (1964) 1. (R.F. Gould, Ed., Am. Chem. Soc.) ^^ In practice, hydrophilic surfaces are often covered by hydrophobing adsorbates. The Zisman method can then also be applied, provided wetting does not lead to desorption.
5.96
WETTING
cos cf = 1 - c o n s t j / ^ - /(crit)]
[5.11.2]
where the constant is usually between 0.03 and 0.04 m mN'^ It has been combined with the other equations for cos a, such as [5.2.2c and 5.7.5] with v£irying success. Our conclusion is that /(crit) is a useful empirical parameter. The slope of the curve, i.e. the value of the constant in [5.11.2], has been interpreted in some detail by Johnson and Dettre^^; they related this quantity to the solubility of the solid surface.
5.11b
Flotation
Flotation, or froth Jlotation is a technique used to separate dispersed solids from each other on the basis of differences in wettability. The method is particularly important for separating ores from gangue in mineral processing. The technological challenge is that many ores appear only as small fractions of mined material in an excess of minerals, most of which are of no economic interest. Separation by melting is usually too costly. Alternatives such as sieving, differential sedimentation and magnetic separation only work under special conditions a n d / o r for special systems. Moreover, these methods are not 2dways sufficiently selective, and in many cases, may be too labour-intensive. However, when the solids to be sequestered have different water-wettability, or when it is possible to create this difference intentionally, they can be parted from each other by bubbling air through the slurry; the hydrophobic particles are caught and move upstream, to be collected in a foam layer on top of the reactor. Flotation is also used in other fields, for instance in the purification of waste water. The primary beneficiation act is schematically represented in fig. 5.43. Hydrophobic particles (filled) attach to the air bubbles, whereas the hydrophilic ones (open) remain dispersed. The former ones move upward. Usually there is a surfactant-stabilized foam on top of the vessel, it is here that the attached pairticles can be recovered at increased concentration. On the other hand, the unfloatable hydrophilic 'tailing' can be removed from the lower side of the reactor. Simple (and cheap!) as this upgrading is in principle, it involves a variety of steps of physicochemical background, many of which relate to the contents of this chapter. Let u s identify some of them. (i) The raw material should first be milled, to produce psirticles that are small enough to be either hydrophobic or hydrophilic. (ii) The hydrophobic particles should be downmilled to a size that is neither too large (lest the bubbles fail to carry them upward) nor too small (because then the pairticles move, together with the bulk water, around the bubbles).
1) R.E. Johnson, R.H. Dettre, in Wettability, J.C. Berg, Ed.. Marcel Dekker (1993) ch. 1.
WETTING
5.97
D
D
^
D
Figure 5.43. Elementary act of separation by flotation; ■ hydrophobic particles, hydrophilic particles. The former adhere to ascending air bubbles. (iii) Some minerals (such as graphite) are hydrophobic by nature but most must be made hydrophobic by adding (a) surfactant(s) (in floatation slang called collectors). Collectors must satisfy very strict criteria, of which selectivity is the most important one. Typical collectors are alkyl xanthogenates which, because of the sulphur in the head group, have a strong affinity to the heavy metal in sulphidic ores such as pyrite. (iv) Activators are sometimes needed; these are admixtures, promoting the selective attachment of the collector (illustration; Cu^^ ions act as activators in the binding of ethyl xanthogenate to zinc blende, or sphalerite (ZnS)). Additives inhibiting collector adsorption are Ccdled depressors. In our example cyanides act as depressors because they scavenge Cu^^ ions. (v) The hydrophobic particles should reach and stick to the bubble. This requires the proper hydrodynamics and a negative disjoining pressure across the intervening aqueous film. We discussed the constituents of this pressure in sec. 5.3a, and in sec. 5.3d, made a few remarks on the thinning of this film. For flotation of small pcirticles it is not necessary that the film ruptures, to make an actual three-phase contact; particles can also be entrained if they are separated by a thin film in the (preferentially) first minimum (i.e. the a-film which corresponds to the lower minimum in fig. 5.12a). For bigger particles rupture is required.
5.98
WETTING
Rupture of the film is also sensitive to the line tension. (vi) For practical r e a s o n s the contact angle between particle, solution a n d air (with or without a n intervening film) should not be too high b e c a u s e t h a t would lead to a dry' foam, which tends to be blown off by air flow. (vii) Last, b u t n o t least, very intricate hydrodynamics occur in t h e b u b b l e movement. Usually the surfactant adsorption is uneven over the ascending bubble, giving rise to Marangoni-type p h e n o m e n a . These are coupled to the dynamics of the particle-bubble approach. It is obvious from this review t h a t we are dealing with a n extremely complicated set of p h e n o m e n a , where know-how still plays a role. However, the contents of this chapter, together with the interfacial rheology sections 3.6 a n d 4.5 may help to identify the elementary steps. For further reading we refer to a book by Schulze^^. 5,11c
Particles
at interfaces;
engulfinent
The p r e s e n t applications have in common t h a t particles in a two-phase system c a n prefer one of the two bulk p h a s e s or the interface, depending on the relative hydrophobicity/hydrophilicity.
The principle is sketched in fig. 5.44. The sketch
is b a s e d on t h e simplification t h a t wetting is t h e only driving force for t h e distribution a n d t h a t equilibrium h a s been reached. As discussed before, the final situation may depend on the history; particles may entraiin p a t c h e s of one liquid into the other. At contact angles of a r o u n d 90°, the particles are usually found a t t h e interface; t h e r e is a gradugd transition toward preference for t h e oil/water p h a s e if the water contact angle increases/decreases. It follows from these elementary concepts t h a t we have, a t least in principle, a m e t h o d available for separating particles on the b a s i s of differences in contact
o
w
m
w
0
w
0
II
11 (a)
(b)
(c:
Figure 5.44. Positioning of a particle (hatched sphere) in an oil-water two-phase system on the basis of its wettability. In (a) the particle is hydrophobic, in (c) it is hydrophilic and in (b) it is partially wetted by oil cind water. 1^ H.J. Schulze, Physikalisch-Chemische Elementarvorgdnge des Flotationsprozesses: Eine Analyse aus Kolloidwissenschaftlicher Sicht VEB Deutscher Verlag der Wissenschaften (1981). (English translation: Physico-Chemical Elementary Processes in Flotation: an Analysis from the Point of View of Colloid Science, including Process Engineering Con-
WETTING
5.99
angles. This separation can be controlled by surfactants. So, basically a n alternative to flotation may b e developed. However, the p h e n o m e n a are also relevant in their own right. Small particles, a t t a c h e d to interfaces, c a n c o n t r i b u t e to protecting t h e s e against coalescence. A typical example is t h a t of Pickering stc±>ilization of emulsions, t h a t is stabilization against coalescence w h e n the particles c a n n o t b e removed from the oil-water boundsiry by a n approaching second emulsion droplet. Many practical examples are known; one of t h e s e is t h e stabilization of food emulsions by tiny fat crystals. In other cases s u c h stabilization is troublesome. A typical illustration is the resilience aggiinst breaking of crude oil/brine emulsions in tertiary oil recovery due to the presence of a s p h a l t e n e s . It is not difficult to recognize b o t h t h e i m m e n s e practical relevance a n d the wetting b a c k g r o u n d of these phenomena. For reviews see refs.^'-^^ Interestingly enough, u n d e r the right conditions, finely divided particles c a n not only stabilize foams, b u t also act a s a foam
breaker
or anti-foaming
agent if
added to a n existing foam. This dual function is known for highly surface active materials (such a s higher alcohols); if added a s a component during preparation of foams they m a y contribute to stabilization, whereas addition of these t h r o u g h the v a p o u r p h a s e may b r e a k the foam. The m e c h a n i s m is probably related to t h e Marangoni effect; local adsorption leads to a local reduction of the film tension, leading to local stretching a n d r u p t u r e . The anti-foaming action of simple solids requires t h e particles to be large enough to bridge the air p h a s e s on either side of the lamellae; if the receding angle between film aind particle is large enough, t h e film will eventually be p u s h e d away from the particle'^K Engulfment
is a related phenomenon, a n d fig. 5.45 gives the principle. Let P in
situation (a) be a relatively hydrophobic particle in water; O is a p h a s e t h a t does not w
/^"^
^"\
w
/ '
\
w
P
(a)
(b)
Figure 5.45. Principle of engulfment.
siderations (Elsevier).) 1) R. Aveyard, J.H. Clint, J. CherrL Soc. Faraday Trans. 9 1 (1995) 2681. 2) A.I. Abdelfattah. M.S. Elgenk, Adv. Colloid Interface Set 78 (1998) 237. 3^ G.C. Fiye, J.C. Berg, J. Colloid Interface Set 127 (1989) 222.
(c:
5.100
WETTING
mix with water, say oil. When the particle meets the droplet it becomes engulfed; the contact angle through the aqueous phase in situation (b) is obtuse. Eventually, in case (c), the particle ends up inside the drop. From a physicochemical point, the process consists of two consecutive steps; heterocoagulation between P and O across water until they come in a sticking mode, followed by a wetting step^^. The method is, for instance, used in the preparation of composite particles in material science; inorganic particles can be engulfed by polymer particles and polymers with a high glass transition temperature T can be engulfed by a polymer of low T . The best biological example of engulfment is phagocytosis . In this case O stands for a phagocytic cell. Such cells are characterized by a low interfacial tension with the serum in which they are embedded, sometimes visible through their amoebelike mobility. In the human and animal body these cells scavenge antigens such as bacteria, viruses, fungi, decaying erythrocytes and foreign colloids. Phagocytosis is therefore one of the methods by which the body wards off detrimental invaders. Phagocytosis can be aspecific (purely on the basis of preferential wetting) or, more generally, by ligand binding to receptors that are localized on the outside of the host membrane. Insofar as it is generic, a certain relationship with the cell/ particle serum contact angle is observed-^^ but mostly the process is more complicated^^. The best-known physiological phagocytic cells are the white blood cells, or leucocytes. People suffering from certain types of leukemia have a prolific
Figure 5.46. Junctions between particles by capillary bridges. 1^ R.H. Ottewiil, A.B. Schofield and J.A. Waters, J. Dispersion Set Technol 19 (1998) 115. 2^ C.J. van Oss, Ann. Rev. Microbiol. 32 (1978) 19. 3^ H.M. Chen, R. Langer and D.A. Edwards, J. Colloid Interface Set 190 (1997) 118.
WETTING
5.101
number of such cells in their blood, but these cells have lost the propensity of phagocytosis. Typically, they no longer exhibit the amoebic mobility; rather they behave as solid spheres with a high interfacial tension. Perhaps this is because a certain biosurfactcint, needed to keep this tension low, cannot be synthesized at sufficient quantity to replenish all the surface of the proliferating cells. The conclusion is that a wetting phenomenon may play a role in this disease. 5.1 Id Various other applications There is no way to do justice to the variety and wealth of applications of wetting. For one thing, we have not systematically discussed capillary phenomena, a collective term for everything involving curved interfaces, mostly in contact with solids. References can be found in sec. 1.17c; in chapter 1 analyses of fluid profiles were invoked for obtaining interfacial tensions and in sec. 5.4 the same was done for measuring contact angles. Let us now mention a few independent aspects. Figure 5.46 shows capillary bridges i.e. fluid masses remaining between the particles S of a wetted solid, in air (A). These junctions are kept in place by capillary forces. The contact angle for L on S is low, so that a negative Laplace pressure develops in the bridge, keeping the particles together. It is one of the reasons for the stickiness of hygroscopic materials in moist air and for the cohesiveness of wet snow. The resulting force can be computed from the contact angle, the surface tension and the geometry. In the sketch of fig. 5.46 the powder is assumed heterodisperse. The force is not the same for each joint, because the distance and the radius of curvature are different. So, the powder can adjust its structure under the influence of capillary bridges. Capillary bridges can also be created in liquid systems. Let, in the same fig., A be water and the hatched immiscible liquid be an oil. Then an attraction is created between the particles and this has to compete with the disjoining pressure. In practice the phenomenon is used by adding an oil as an agglomeration aid to coagulate slurries of hydrophobic pgirticles, such as coal tailings. Figure 5.47 illustrates another phenomenon in the same category. Long cylinders of liquid are unstable with respect to breaking up into droplets. It is nowadays known as the Rayleigh instability, after its discoverer. Lord Rayleigh (1879). The phenomenon is familiar to everyone who has unsuccessfully tried to let a very thin water jet flow out of the tap. The origin of the phenomenon is that the surface area is lower for the comminuted jet, so the break-up is a spontaneous process. The figure illustrates the dynamics. Usually satellite drops are also formed. We have encountered the phenomena more than once, for examples see figs. 1.17 and 5.37. Detergency is the science (or is it an art?) of removing undesired material from surfaces; in particular the term is reserved for 'soil' removal processes in which detergents play a role. This is also our present interest. Alternative ways of removal are dissolution in a suitable solvent amd/or mechanically. Wetting phen-
5.102
WETTING
(a)
O
o
<=>
ici
Figure 5.47. The Rayleigh instability. o m e n a enter especially w h e n the dirt to be removed is of colloidal size. Agitation a t higher pH a n d elevated t e m p e r a t u r e s plays a n important role. Figure 5.2, from bottom to top, suggests three p h a s e s in the removal of a liquid drop from a fibre. Commercial detergents typically consists of 10-20 components, including builders, a n t i - r e d e p o s i t i o n a g e n t s , perfumes, corrosion inhibitors a n d special p u r p o s e a d m i x t u r e s . For reviews of the underlying physico-chemical principles, see^'^^ An area closely related to detergency is the de-inking
of papers. As in so m a n y
d o m a i n s of m o d e m society, we are dealing here with a conflict of interest between the drive for good printing (i.e. good adhesion of the carbon particles to the m e s h of t h e filaments c o n s t i t u t i n g t h e paper) a n d t h e growing need for recycling (i.e. removal). Basically, c a r b o n particles are hydrophobic, p a p e r is hydrophilic. By specific surface t r e a t m e n t s optimization of the carbon-carrying ink a n d t h e p a p e r interaction is achieved. The ink should not spread too m u c h by capillary action (which would yield diffuse lettering) b u t neither too little, lest u n d u l y large droplets are formed. After drying, the carbon should remain on the paper, a l t h o u g h t h e quality of this adhesion may vary; few newspapers can be read without getting a black deposit on your h a n d s . Intentional removal is mostly achieved by w a s h i n g (size fraction l-10|i), flotation (lO-lS^i) and by other cleaning processes (stiU larger fractions). Very small particles (below l|i) are difficult to remove; partly b e c a u s e they are imbedded' in the fine s t r u c t u r e of the paper. It is mostly this remaining carbon t h a t gives recycled paper its gre3^sh colour.
^^ A.M. Schwartz, The Physical Chemistnj of Detergency in Surface and Colloid Science. E. Matijevic, Ed.. Vol. 5 Wiley-Interscience (1972) 195. 2) M.J. Schwuger, Effects of Adsorption on Detergency, in Anionic Surfactants: Physical Chemistry of Surfactant Action, E.H. Lucassen-Reijnders, Ed., M. Dekker (1981) 267.
WETTING
5.103
Electro-wetting stands for a group of techniques in which wetting is improved by the application of an electric field, leading to the lowering of the interfacial tension according to [1.1.3.6] CT°dE'
15.11.3]
Here, <7° is the ensuing surface charge and E the applied potential across the interface; the primes refer to the vsdues during the chcirging. When the double layer capacitance is known, [5.11.3] can be integrated. For a derivation, see the text leading to [1.1.3.6]. The process is most effective when y^^ and y^^ are both lowered. Recall from sec. 5.9 that, if for practical reasons only one of the two can be modified, lowering of y^^ is the more effective. It is worth keeping in mind that [5.11.3] applies to polarizable interfaces: only in that case is the applied field cin independent extra parameter. Of course, electric double layers also do form at reversible interfaces. However, in this case the double layer itself is not responsible for the lowering of the interfacial tension; it is the adsorption of chargedetermining electrolyte which counts. It leads to terms such as ^"^^0 ^^HNO ^^^ ^KOH^^KOH ^^ ^ ^ Gibbs equation which give rise to this lowering. That the ions distribute themselves spontaneously in a certain fashion, say as a diffuse double layer, has no consequences. All of this does by no means exhaust the manifold applications and occurrence of wetting phenomena in the living and non-living world. We may think of tertiary oil recovery, coatings, waterproofing, wetting of dried soils, opthalmology and many more themes. We suffice by concluding that we have laid down the fundamentals of a rich and challenging branch of natural science. A branch that is over 200 years old but still alive! 5.12
General references
5.12a lUPAC recommendation The general recommendation, Manual of Symbols and Terminology for Physicochemical Quantities and Units; Appendix; Definitions, Terminology and Symbols in Colloid and Surface Chemistry, Part I, (Prepared for publication by D.H. Everett), PureAppl Chem. 31 (1972) 578, also contains sections on wetting. 5.12b BookSf Reviews and Symposium Proceedings Wettability, J.C. Berg, Ed., Surfactant Series 49, Marcel Dekker (1993). (Covers most themes of this chapter plus some special topics.) A.M. Cazabat, Wetting; From Macroscopic to Microscopic Scale, Adv. Colloid Interface Set 42 (1992) 65. (Review, discussing dyncimics on different scales .)
5.104
WETTING
M. Schick, Introduction
in Wetting Phenomena,
in Liquids at Interfaces,
Les
Houches XLVIII, J . Charvolin, J . F . J o a n n y cind J . Zinn-Justin, Eds., North Holland (1990) 415. (Course material from 1988.) N.V. Churaev, Z.M. Zorin, Wetting Fdms, in Adv. Colloid Interface Set, 4 0 (1992) 109. (Review; forces in a q u e o u s and non-polair wetting films, experimental studies, influence of various types of surfactants.) B.V. Derjaguin (- Deiyagin), N.V. Churaev, Properties of Water Layers to Interfaces,
in Fluid Interfacial Phenomena,
Adjacent
C.A. Croxton, Ed., Wiley (1986), ch.
1 5 6 6 3 - 7 3 8 . (Review on the structural idiosyncracies of water near solid surfaces with a strong e m p h a s i s on work from the Russian School.) Contact Angle, Wettability (1963), p u b l i s h e d by t h e
and Adhesion,
P.M. Fowkes, Ed. Adv. Chem. Ser. 4 3
Am. Soc. (Book, containing t h e c o n t r i b u t i o n s to a
S y m p o s i u m , h o n o u r i n g W.A. Zisman; mostly restricted to American contributions; historically interesting because it reflects very well the state of the art in the USA a t t h a t time.) P.G. de Gennes, Wetting; Statics and Dynamics, in Rev. Mod. Phys. 5 7 (1987) 827, (Review.) G.J. Hirasaki, Structural Interactions Waals
Fluids,
in J . Adh.
Set
in the Wetting and Spreading
Technol
of Van der
7 (1993) 2 8 5 . ( N o t w i t h s t a n d i n g
the
restriction to Van der Waals fluids a n informative review because it relates d a t a on adsorption, spreading, adhesion a n d wetting. Essentially statical.) R.E. Johnson, R.H. Dettre, Wettability Surface
Science,
E. Matijevic, Ed., Wfley
and Contact Angles,
in Colloid
and
2 (1969) 8 5 . (Excellent review; basic
features, hysteresis, m e a s u r e m e n t s , illustrations.) D.Y. Kwok, A.W. Neumann, Contact Angle Measurements, ization Methods. Principles, Techniques and Applications.
in Surface
Character-
Surfactant Series no. 8 7 ,
A.J. Milling, Ed., Marcel Dekker (1999) chapter 2, p. 37-86. (Review, many practical hints, 191 refs.) D.Y. Kwok, A.W. Neumann, Contact Angle Measurement Interpretation,
and Contact
Angle
in Adv. Colloid Interface Set 8 1 (1999) 167-249. (Review. 141 refs.,
emphasizing model attempts to obtain surface tensions of solids.) A. Marmur, Thermodynamic
Aspects of Contact Angle Hysteresis
in Adv. Colloid
Interface Sci. 5 0 (1994) 121. (Review, rather formalistic, 40 refs.) Drops and Bubbles
in Interfacial Research,
D. Mobius, R. Miller, Eds. Elsevier
(1998). (Mostly on t h e experimental a n d theoretical description of interfaces; also covers the subject matters of the preceding chapters.)
fluid-liquid
WETTING
5.105
A.W. Neumann. R.J. Good, Techniques of Measuring Contact Angles, in Surface and CoRoid Science, Vol 11 (1979). E. Matijevic, Ed., Plenum Press, chapter 2, 319 1 . (Review with many practical details. Not recent but still useful and informative.) Applied Surface Thermodynamics, A.W. Neumann, J.K. Spelt, Eds., Marcel Dekker, (1996). (Also contains section on the measurement and interpretation of contact angles.) Wetting, Spreading and Adhesion, J.F. Padday, Ed., Academic Press (1978). (Proceedings of a Symposium (1976). (Covers the entire field of interest at that time; discussion remarks included.) Capillarity Today, G. Petre, A. Sanfeld, Eds., Lecture Notes in Physics 3 8 6 , Springer Verlag (1991). (Proceedings of a Symposium held in Brussels, 1990.) Modem Approaches to Wettability: Theory and Application, M.E. Schrader, G.l. Loeb, Eds. (Plenum, 1992). (Sixteen contributions on various aspects of wetting, honouring the memory of W.A. Zisman. Several of these chapters refer to applications.) Contact Angles and Wetting Phenomena, Special issue Adv. Colloid Interface Set 39 (1992), Th.F. Tadros, A.W. Neumann, Eds. (Papers presented at a symposium held in Toronto, June 1990.)
This Page Intentionally Left Blank
Al.l
APPENDIX 1 Surface Tensions of Pure Liquids and Mixtures This appendix aims at providing a useful selection from the vast literature. Most measurements reported here have been carried out under well-defined conditions, especially with respect to temperature and purity. The latter is not always verifiable, since inadvertent impurities may always be present; the trend is the higher the better', because of Gibbs' law. Data are presented either as tables or graphically, or both. Although graphs are less precise they demonstrate relevant trends better, especially variation with temperature. In setting up this appendix, earlier tabulations have been used as starting points; they have been amended, extended, or replaced by better data, where necessary and available. These 'starting references' are by Jasper^^ Korosiand Kovats^^ Wolf'^^ and Wohlfarth et al.^h Jasper gives extended data of many derivatives, mostly between 0 and 100°C at integral values of the temperature, as a rule obtained by linear interpolation [y = a - bT). The authors of ref. 2) extended the data in ^^ and compared the results. Where significant deviations were found the substances were re-examined by the capillairy rise method (CR). Study-^^ mostly refers to commercial products that were purified by the indicated method. For some substances the (gaschromatographically-determined) composition is also given. Wolf*^^ states that he 'selected the best value and, in case of doubt, repeated the experiments himself, without specifying his measurements. Some of his data are therefore included as graphs, to illustrate certain trends. As a rule, the differences between the data reported by Wohlfarth et al."^^ and those of Jasper ^^ are small. For this general case, only Jasper's data are presented. Only when the difference is not negligible are both values included, without attempting to explain the origin of the deviations. Measurements reported above the boiling points of a certain compound refer to surface tensions at higher pressure. The influence of the pressure is small, (of the order of 10"^° m, see sec. 2.9b and refs. ^'^^, except near the critical point. The method of measurement is indicated in the reference. a. Surface tension of some inorganic fluids See tables A 1.1a and b and figs. A 1.1-5. Linearity as a function of temperature is imposed by interpolation, but it applies very well provided one remains far from the critical point. The graphs clearly show the extent of consistency between different authors and, sometimes, different methods. ^~^> See the references at the end of the tables.
A1.2 Table A l . l .
Surface tensions of some inorganic fluids. 7 in mN m"^; dy/dT
mN m-^ K-i; T
in
= melting point. Accuracy of y according to ref. 1. Upper/lower
temperatures in degrees Celsius/Kelvin, respectively; yat T = T
obtained by
linear extrapolation. Absolute temperatures rounded (293.15 written as 293. etc.).
Substance and formula Bromine Bromoform CHBrg Carbon disulfide Carbon tetrachloride CCI4 Chloroform CHCI3 Mercury
y^^J
265.8
46.1
ace.
5 278
10 283
15 288
20 293
25 298
±0.6
44.7
43.6
42.9
41.8
40.9
281.45 47.0
± 0.10
162.35 51.9
±0.3
Phosphor trichloride PCI3 Silicium tetrachloride SiCl4 Water IH2O
44.87
46.18 32.32
33.81
250.19 32.13
27.65
26.43
209.65 38.13
27.97
26.67
489.6 488.6 487.5 486.5 485.5
234.28 498.6 ±2.0
Hg
1 Substance and formula
Tm
161.15 45.31 ±0.10
29.24
203.15 27.75 ± 1.0
20.28 19.78 19.29 18.79 18.29
273.15 75.84 ± 0.10
27.97
74.36 73.62 72.88 72.14
m 30 303
1 Bromine 40.0 Br2 Bromoform CHBrg Carbon disulfide 30.84 CS2 Carbon tetrachloride CCI4 Chloroform CHCI3 Mercury 484.5 Hg Phosphor trichloride PCI3 Silicium tetrachloride 17.79 SiCl4 Water 71.40
35 308
40 313
45 318
50 323
39.2
38.3
37.3
36.4
43.56
42.25
55 328
60 333
65 338
40.95
39.64
27.87
29.35 25.21
23.98
22.76
21.53
25.38
24.08
22.79
21.49
483.4 482.4 26.71
478.3
480.4
22.91
24.18
25.44 16.80
70 343
15.80
70.66 69.92 69.18 68.45
66.97
65.49
A1.3 Table A l . l . continued
Substance and formula 1 Bromine Br2 Bromoform 1 CHBrg Carbon disulfide
75 348
80 353
38.33
85 358
90 363
37.02
95 368
100 373
105 378
150 423
200 473
35.71
Carbon tetrachloride 16.64 20.31 17.86 19.09 CCI4 Chloroform 20.20 CHCI3 Mercury 459.9 449.6 474.2 470.1 Hg Phosphor trichloride PCI3 Silicium tetrachloride SiCl^ Water 64.01 62.54
Ko
Substance and formula Bromine Bromoform CHBrg Carbon disulfide CS2 Carbon tetrachloride CCI4 Chloroform CHCI3 Mercury Hg Phosphor trichloride PCI3 Silicium tetrachloride SiCl4 Water
Ko
dy/dT
r - T ( d y / d T ) References
Notes
-0.18
95.4
1. 7
-0.13
83.8
1, 8
-0.15
76.2
1, 9, 10
See fig. Al.l
-0.122
62.8
1. 11, 12
See fig. A1.2
-0.130
65.3
1, 11, 12
See fig. A1.3
-0.205
546.6
1, 13-15
See also tables A 1.2 See fig. A1.4
-0.13
65.7
1, 8
-0.10
48.0
1, 9
-0.148
116.2
1, 16-21
See sec. 1.12, table 1.4 and fig. 1.27
A1.4
40
2
s
30
20
• reference 9 o reference 22 A reference 2 3
10
273
283
293
303
323 K
313
Temperature Figure A l . l . Surface tension of carbon disulphide, linear region. Drawn line: values recommended by Jasper ^^ as in table A l . l . Other references indicated for the sake of comparison.
30 V
1 2^ v"^^., 20 A D • V o X
15
10
273
reference reference reference reference reference reference
8 24 11,12 25 26 27
J_
_L
_L
J_
283
293
303
313
323
333
343
353
363
373 K
Temperature Figure A 1.2. Surface tension of carbon tetrachloride, linear region. Drawn line: values recommended by Jasper ^^ as in table A l . l . Other references indicated for the sake of comparison. Wolf^^ gives data over a much larger temperature range, reproduced by Adamson2^^ showing that above 400K the decrease is weaker than proportional to T.
A1.5
30 -^^Oi
V ^ . •.D ?
25
"^^S-^D
20
a • V A X
15
10
273
reference reference reference reference reference
8 11,12 23 25 29
I
I
283
293
303
313
323 333 Temperature
J_
343
353 K
Figure A1.3. Surface tension of chloroform, linear range. Drawn line: values recommended by Jasper ^^ tabulated in table A l . l . Other references indicated for the sake of comparison.
30 h
?
25
20
15 V reference • reference X reference D reference
10
273
9 8 23 25
I
I
283
293
303
313
J_
323 333 Temperature
343
353 K
Figure A1.4. Surface tension of phosphor trichloride as a function of temperature in the linear range. Data from table A l . l . Other references added for the sake of comparison.
A1.6 b. Surface tensions of some molten metals The data in tables A 1.2a and A 1.2b are taken from Keene^^^ and Wolf^^ respectively. The data for dy/dT from Keene's compilation tend to be higher than those of Wolf. In general, these measurements are less reproducible than those presented in table Al.l because, at the high temperature, oxidation and other surface reactions may occur. The absolute accuracy of these data diminishes accordingly. Table A1.2a. Mean values of y and dy /dTfov molten metals as collected by Keene^^^ Where sufficient data are given, values for / and dy/dT based on the highest one-third of all the values are given in parentheses. Metal
Symbol
r /K
y /mN m"^
dy/dT
7-(dr/dT)
1 1
Aluminium
Al
933
871 (890)
- 0 . 1 5 5 (-0.182)
1060 (1016)
Antimony
Sb
903
371 (382)
- 0 . 0 4 5 (-0.063)
411 (439)
Bismuth
Bi
543
3 8 2 (389)
- 0 . 0 8 0 (-0.097)
4 2 5 (442)
Cadmium
Cd
594
637
-0.15
726
Chromium
Cr
2133
1642
-0.2
2068
Cobalt
Co
1773
1881 (1928)
- 0 . 3 4 (-0.44)
2 4 8 3 (2708)
Copper
Cu
1358
1330 (1374)
- 0 . 2 3 (-0.26)
1642 (1727)
Gold
Au
1338
1145 (1162)
- 0 . 2 0 (-0.18)
1413 (1296)
Iron
Fe
1803
1862 (1909)
- 0 . 3 9 (-0.52)
2 5 6 5 (2849)
Lead
Pb
600
4 5 7 (471)
- 0 . 1 1 (-0.156)
5 2 3 (565)
Lithium
Li
495
399
-0.15
468
Magnesium
Mfi
923
557
-0.26
797
Mercury
Hg
235
4 8 9 (498)
- 0 . 2 3 1 (0.215)
5 4 3 (549)
Nickel
Ni
1728
1796 (1834)
- 0 . 3 5 (-0.376)
2 4 0 0 (2484)
Palladium
Pd
1825
1482
-0.279
1991
Platinum
Pt
2043
1763
-0.307
2390
Potassium
K
337
110 (118)
- 0 . 0 7 (-0.065)
134 (140)
9 2 5 (955)
- 0 . 2 1 (-0.31)
1184 (1337)
Silver
Ag
1233
Sodium
Na
371
197 (203)
- 0 . 0 9 (-0.08)
2 3 0 (232)
Tin
Sn
505
5 6 2 (586)
- 0 . 1 0 3 (-0.124)
6 1 4 (638)
Uranium
U
1403
1552
-0.27
1931
Zinc
Zn
693
789 (817)
- 0 . 2 1 (-0.227)
9 3 5 (974)
1
A1.7 Table A1.2b. Values of dy/dT Metal Bismuth Gold Lead Mercury
Symbol
Temp./K
dy/dT
y-(dr/dT)
Bi
573 - 1073 1373 - 1573 623 - 1073 293 - 623
-0.067
414.5 1267 487.8 from 528 to 562
Au Pb
Hg
Silver
Afi
Tin
Sn
c. Surface
and y- [dy / dT), a s collected by Wolf^).
tension
1273 - 1423 573 - 1273
of some molten
-0.10 -0.073 from -0.206 at =335 K to -0.280 at = 600 K -0.12 -0.07
414.5 from 587.5 at 573 to 591 at 1273
halides
See table A1.3 a n d fig. A1.5. After Wolf^). Table A 1 . 3 . Values o f / a n d / - (dy/dT)
for molten alkali halides
Temp./K
dy/dT
y-T(dy/dT)
NaCl
1075 - .1395
-0.071
191.5
NaBr
1034 - 1438
-0.070
178.0
KCl
1073 - 1440
-0.071
171.6
KF
1185 - 1583
from -0.075 at 1288 K to
from 116 at 1185 K to
-0.090 at 1548 K
97 at 1583 K
Substance
750 ^
730
S 710h 690
670 6501 L 1000
•-^ KCl
1100
1200
1300
J
1400
1500
1600 K
Temperature Figure A1.5. Surface tension of some molten alkali halides. Redrawn from ref ^^
A1.8 d. Surface
tensions
of some low boiling
point
liquids.
See table A l . 4 . Table A 1 . 4 .
Surface tension of some low boiling fluids. T e m p e r a t u r e s in K.
Accuracy ± 0.1 mN m-^ Linear region. Substance Formula
T /K
Argon
Ar
83.78 13.4
Helium II
Hell
0.8
0.35
Helium III
He III
0.8
0.15
Helium IV
He IV
0.8
0.37
Hydrogen
H2
14.01 2.96
Krypton
Kr
Nitrogen
N2
115.8 8.34 17.7 63.29 12.1
Oxygen
O2
54.8
Xenon
Xe
161.2 19.0
Temperature and Surface Tension
r(^J
21.8
84 13.34 0.5 0,351 0.361 0.151 0.35 0.373 15 2.80 115 8.341 78 8.75 71 18.01 165 18.46
86 12.84 0.75 0.347 0.500 0.150 0.50 0.372 16 2.63 118 6.474 80 8.30 73 17.50 175 16.58
Substance
Formula Temperature and Surface Tension
Argon
Ar
Helium II
Hell
Helium III
He III
Helium IV
He IV
Hydrogen
88 12.34 1.00 0.345 0.574 0.151 0.65 0.370 17 2.41 120 5.896 82 7.85 75 16.99 185 14.74 dy/dT
90 11.84 1.25 0.340 0.647 0.152 0.80 0.368 18 2.29 122 5.318 84 7.39 77 16.48 195 12.96
92 11.34 1.50 0.334 30.820 0.149 0.95 0.366 19 2.12 124 4.740 86 6.94 79 15.96 205 11.23
1.75 0.327 0.910 0.147 1.10 0.360 20 1.85
2.00 0.317 1.132 0.131 1.25 0.359
88 6.49 81 15.45 215 9.55
90 6.03 83 14.94 225
7-T(d7/dT) Refs.
-0.25
34.3
1, 31
-0.04
0.4
1, 32
-0.056
0.2
1, 33
-0.02
0.4
1, 34
H2
-0.183
5.5
1, 31
Krypton
Kr
Nitrogen
N2
-0.387 (-0.187) -0.227
52.9 (39.4) 26.4
1, 35 4, 36 1. 31
Oxygen
O2
-0.263
36.2
1, 37
Xenon
Xe
-0.178
47.8
1, 38
2.1 0.313 1.639 0.111 1.40 0.354
85 14.43 245 4.94
2.328 0.069
87 13.91 265 2.30
2.992 0.028
88 13.40 285 0.28
^^ Calculated by Guggenheim-Ferguson eq.
7.94J Notes
1)
A1.9 e. Surface tensions of linear alkanes See table Al.5. As can be seen from the table, melting points of molecules with an even number of carbon atoms are relatively higher than those with odd ones. However, for the increase of the surface tension with n no even-odd irregularity is found. From this observation it can be inferred that the T -irregularity must be a property of the solid phase (say, the packing of the paraffin in a lattice).
Table A1.5. Surface tensions of liquid linear alkanes obtained by capillary rise in N2 atmosphere, taken from ref. 39, except where indicated otherwise. T = melting point, n = number of carbon atoms in the chain. Temperatures rounded, otherwise as in table Al. lb. Reproducibility ± 0.10 (0.12 for the last two). Substance
Pentane Hexane Heptane Octane Nonane Decane Undecane (= Hendecane) Dodecane Tridecane Tetradecane Pentadecane Hexadecane Heptadecane Octadecane Nonadecane Eicosane Hexacosane 1 Hexacontane _
nc
m
5
143.4
6
178
7
182
8
216.6
9
222
10
243.5
11
248
12
263.5 267.6
13 14
279
15
283
16
291
17
295
18
301
19
305
20
309.8
26
329
36
r^^J 32.58 30.13 31.02 28.9 29.54 28.38 28.7 27.96 28.2 27.76 27.93 27.67 27.74 27.56 27.58 27.47 27.35
10
20
30
40
283
293
303
313
17.15 19.42 21.12 22.57 23.79 24.75 25.56 26.24 26.86 27.43
16.05 18.40 20.14 21.62 22.85 23.83 24.66 25.35 25.99 26.56 27.07 27.47
14.94 17.38 19.17 20.67 21.92 22.91 23.76 24.47 25.11 25.69 26.21 26.62 27.06 27.45
16.36 1 18.18 19.71 20.98 21.99 22.82 23.58 24.24 24.82 25.35 25.76 26.22 26.61 26.91 27.21
ALIO Table A1.5. (continued) Substance
c
Pentane Hexane Heptane Octane Nonane Decane 1 Undecane (= Hendecane) Dodecane Tridecane
5
Tetradecane Pentadecaine Hexadecane Heptadecane Octadecane Nonadecane Eicosane Hexacosane 1 Hexacontane
14 1
Substance Pentane Hexane 1 Heptane 1 Octane 1 Nonane Decane Undecane (= Hendecane) Dodecane Tridecane Tetradecane Pentadecane 1 Hexadecane Heptadecane Octadecane Nonadecane Eicosane Hexacosane I Hexacontane
50 323
^0 333
T 70
6 1 15.34 7 1 17.20 8 9 10
11 1 12 1 13 15
16 1 17 18
19 1 20 1 26
1 80
1 14.32 1 15.24 1 16.22 18.77 1 17.81 1 16.86 18.18 20.05 19.12 21.07 1 20.15 1 19.23 21.96 21.05 1 20.15 22.70 21.81 1 20.93 23.37 22.50 1 21.63 22.22 23.96 23.09 24.50 23.64 1 22.78 24.91 1 24.06 1 23.20 25.38 24.52 1 23.68 25.77 1 24.92 1 24.08 26.07 j 25.24 1 24.40 26.38 1 25.54 1 24.71 26.33
1 90
353
363
100 373
14.26 15.91 17.24 18.31 19.25 20.05 20.75 21.35 1 21.93 1 22.35 22.83 1 23.24 1 23.56 1 23.88 25.59
1 13.28 14.96 1 16.31 17.39 18.35 1 19.16 19.88 20.48 21.07 1 21.49 1 21.99 1 22.93 1 22.73 1 23.04 24.86
1 1 14.01 15.37. 1 16.47 17.45 18.26 19.01 19.61 20.21 20.46 1 21.14 21.55 1 21.89 1 22.21 1 24.13
1 140 413
1 150 423
343
1 1 1 1
1
1 1 1 1 1 1 1 1 1 1 1 1 1
36
"c
1 110 383
1 120 393
1 130 403
1433^^^ 1
5 6 7
1 13.06 1 14.44 10 15.55 11 16.55 12 1 17.39 13 •1 18.14 14 18.74 15 1 19.36 16 1 19.79 17 20.29 20.71 21.05 20 21.38 1 26 1 23.39 1 36 1 24.48 8 9
1 ^^ 1 ^^
1 12.11 1 13.50 1 14.63 15.65 1 16.51 I 17.27 17.87 18.50 1 18.93 19.45 19.87 20.21 20.54 22.66 1 21.93 1 21.20 1 20.40 1 19.73 1 23.90 1 23.31 J 22.73 1 22.15 [21.57
ALU Table A1.5. (continued) Substance
'^c
180
Y-T{dy/dT)
dy/dT
Refs., notes
453 Pentane
5
-0.1102
48.4
1
39
Hex£ine
6
-0.1022
48.3
1
39
Heptane
7
-0.0980
48.9
1
39
Octane
8
-0.0951
49.5
1
39
Nonane
9
-0.0935
50.2
1
39
Decane
10
-0.0919
50.8
1
39
Undecane (= Hendecane)
11
-0.0901
51.0
1
39
Dodecane
12
-0.0884
51.3
1
39
Tridecane
13
-0.0872
51.5
1
39
Tetradecane
14
-0.0868
52.0
1
39
Pentadecane
15
-0.0856
52.2
1
39
1 Hexadecane
16
-0.0854
52.8
1
39
Heptadecane
17
-0.0846
52.7
1
39
Octadecane
18
-0.0843
52.0
1
39
Nonadecane
19
-0.0837
53.1
Am. Petr. Inst.
Eicosane
20
-0.0833
53.3
Am. Petr. Inst.
Hexacoscine
26
18.26
-0.07
51.5
1 Hexacontane
36
20.40
-0.06
1
1. 4 0
J , 40
_J
/ . Surface tensions of linear aliphatic n-alcohols See table A1.6 and figs. A1.6 - 10. The surface tension increases with the chciin length, with the exception that values for ethanol are syistematically slightly lower than those for methanol. Table A1.6.
Surface tensions of linear aliphatic n-alcohols. Accuracy ± 0 . 1
mN m-^ ± 0.2 for Cg-CiQ. Otherwise as in previous table. Substance
Formula
m
y^^J
10
20
30
40
50
60
283
293
303
313
323
333
Methanol
CH3OH
175.35 31.6
23.28 22.50 21.73 20.96 20.18
19.4l|
Ethanol
C2H5OH
155.85 33.8
23.22 22.39 21.55 20.72
19.06
Propanol
C3H7OH
146.1
35.1
24.48 23.71 22.93 22.15 21.37 20.60
Butanol
C4H9OH
183.2
35.2
26.28 25.39 24.50 23.61
Pentanol
C5H11OH
194
34.5
26.67 25.79 24.92 24.04 23.17 22.30
Octanol
CgHi^OH
256.3
30.4
28.30 27.50 26.70 25.91
Nonanol
^9^19^^
267.5
30.2
29.03 28.27 27.51 26.75 26.00 25.24
Decanol
^10^21^^
280
29.8
29.61
28.88 28.14 27.41
19.89
22.71
25.11
26.68
21.82
24.32
25.95J
A1.12 Table A 1 . 6 (continued). Substance Methanol
formula
70
80
90
100
343
353
363
373
CH3OH
dy/dT
7Tidy/dT)
Refs.
-0.0773
45.2
1, 8
Notes see fig. Al. 6
Ethanol
C2H5OH
-0.0832
18.23
1, 8
46.8
see fig. Al. 7
Propanol
C3H7OH
19.82
19.04
18.27
-0.0777
46.5
1, 8
Butcinol
C4H9OH
20.93 20.04
19.14
18.20 - 0 . 0 8 9 8
51.3
1. 8
see fig. Al. 8 see fig. Al. 9
Pentanol
CSHHOH
21.42 20.55
19.67
18.80 - 0 . 0 8 7 4
51.4
1, 8
see fig. ALIO
Octanol
CgHjyOH
23.52
-0.0795
50.8
1, 2 4
Nonanol
^9^19^^
24.48 23.72 22.96 22.20 -0.0759
50.5
1, 4 1
Decanol
^10^1^^
2 5 . 2 1 2 4 . 4 8 23.75^ 2 3 . 0 2 - 0 . 0 7 3 2
50.3
1. 4 1
25
-•^a.
A .A
6 S
20
15
10 • reference 8 X reference 2 7 A reference 42 D reference 4 3 01
L 273
I
I
JL
J_
283
293
303
313
J_
323
333
343
J_
353 K
Temperature Figure A1.6. Surface tension of methanol. Linear region. Drawn line, values recommended by Jasper ^h other references included for the sake of comparison.
^^ See the reference at the end of the tables.
A1.13
R^ 15
10 • reference 8 A reference 4 3 X reference 44 273
J-
I
I
283
293
303
313
323
333
343
353 K
Temperature 3) Figure A1.7. Surface tension of ethanol. Linear region. As in fig. 1.6. Wolf {re{.\ p. 31 and 32) gives data up to over 500 K, which tend to be lower than those reported here, and are not exactly linear with T over the entire range.
25 AQ-
I
20 A ° ^"^^^^
.
15
10 n • X A
273
reference reference reference reference
9 8 42 44
\
I
L
J_
_L
283
293
303
313
323
333
343
353
Temperature Figure A1.8. Surface tension of n-propanol. Linear region. As in fig. A1.6.
363
373 K
A1.14
25 h-
AX
A A
A A
I 20
A
^
343
353
15
10 X reference 9 • reference 8 A reference 4 5
5\-
273
\
I
L
283
293
303
J_
313
323
_L
333
363
373 K
Temperature Figure A1.9. Surface tension of n-butanol. Linear region. As in fig. A1.6. A
25 U A
X
°
A A
?
20
A A
6
A
X°
D X
15
10 D • X A 01
L 273
reference reference reference reference
9 8 44 46
\
I
L
_L
_L
J_
-L.
283
293
303
313
323
333
343
353
363
Temperature Figure ALIO. Surface tension of n-pentanol. Linear region. As in fig. A1.6.
373 K
A1.15 g. Surface tensions of linear aliphatic See table Al.7.
n-aldehydes
Table A1.7. Surface tensions of linear aliphatic n-aldehydes. Accuracy ±0.1 mN m"^ (± 0.3 for heptanal). Otherwise as in table A1.5. Substance
Formula
Ethanal
CH3GHO
20 293
30 303
40 313
50 323
19.82
18.46
17.10
r^^J
10 283
148.5
40.8
22.54 21.18
C3H7CHO
174.1
35.8
25.74 24.82 23.89 22.97 22.04
C4H9CHO
181.6
37.2
26.95 25.94 24.93 23.92 22.91
Heptanal
CgH^3CHO
230.1
32.6
27.72 26.84 25.84 24.96 24.08
Substance
Formula
60 333
70 343
dy/dT
Ethanal
CH3CHO
m
(acetaldehyde) Butanal (butyraldehyde) Pentanal (valeraldehyde)
yTidy/dT)
Refs.
-0.136
61.0
1. 4 7
C3H7CHO
21.12 20.19 -0.093
51.9
1, 4 8
C4H9CHO
21.90 20.89 -0.101
55.5
1. 4 8
C6H13CHO
23.19 22.20 -0.095
53.5
1, 2 4
(acetaldehyde) Butanal (butyraldehyde) Pentanal (valeraldehyde) Heptanal
A1.16 h. Surface tensions of linear n-amines. See table Al.8 and fig. A L U . For ethylamine y is slightly lower than for methylalcohol at 15°, but this feature is not observed at more elevated temperatures. Table A1.8. Surface tensions of some linear aliphatic n-amines. Accuracy ± 0.1 mN m-^. Otherwise as in table A 1.5. Substance
Formula
T /K
y^T^J
15 288
20 293
30 303
40 313
Methylamine
CH3NH2
179.6
36.8
20.64
19.89
18.41
16.92
Ethylamine
C2H5NH2
189.1
34.1
20.57
19.84
18.51
17.14
Propylamine
C3H7NH2
190.1
35.2
23.00 22.37 21.13
19.89
Butylamine
C4H9NH2
222.6
31.9
24.56 24.00 22.87 21.75 20.63
Pentylamine (amylcmiine)
C.H^^NH,
218.1
32.9
25.20 24.18 23.16 22.13 21.11
Hexylamine
C^H^gNH^
254.1
30.2
26.76 26.26 25.24 24.22 23.20 22.19
Substance
Formula
70 343
Methylamine
CH3NH2
-0.148
63.5
1, 8
Ethylamine
C2H5NH2
-0.136
59.9
1. 8
Propylamine
C3H7NH2
-0.124
58.8
1. 8
Butylamine
C4H9NH2
-0.112
56.9
1, 8
Pentylamine (amylamine)
C.H^^NH,
20.09
19.07
1 8 . 0 4 -0.102
55.2
1, 8
Hexylamine
CgH^3NH,
21.17 20.15
1 9 . 1 4 -0.102
56.0
1, 8
80 353
90 363
dr/dT
rT(d7/dT)
50 323
60 333
19.51
Refs., Notes
See fig. Al.ll
A1.17
25 k'
1 2°
-S-
15
10 • reference D reference A reference X reference
8 23 25 49
0
J_
273
283
293
323 K
303 313 Temperature
Figure A l . l l . Surface tension of n-propylamine. Linear region. As in fig. A1.6. 1. Surface tensions of n-aliphatic acids See table Al.9 and figs. A1.12 - 13. Wolf (ref. 3, his fig. 12) gives a plot for acetic acid from 400 - 600 K. which is almost linear as a function of temperature till near the criticad point. As a function of chain length these surface tensions exhibit a pronounced minimum and do not follow the rather alternating variation of the melting point. Table A1.9. Surface tensions of linear aliphatic n-acids. Accuracy ± 0.1 mN m-^ (formic acid ± 0.5; enanthic acid ± 0.2). Otherwise as in table A1.5. Substance
Formula
Methcuioic acid
15
20 293
30 303
40 313
50 323
^m/^
y^-^J 288
HCOOH
281.5
39.0
38.22 37.67 36.58 35.84 34.38
CH3COOH
289.7
27.9
27.59 26.60 25.60 24.61
C2HgCOOH
252.3
30.7
27.19 26.69 25.70 24.71 23.71
C3H7COOH
266.6
28.9
26.51 25.59 24.67 23.75
C^HgCOOH
238.6
31.9
27.13 26.24 25.35 24.46
C^H^gCOOH 2 6 3 . 1
30.4
28.61 28.18 27.34 26.49 25.64
(formic acid) Ethanoic acid (acetic acid) Propanoic acid (propionic acid) Butanoic acid (butyric acid) Pentanoic acid (valeric acid) heptanoic acid (enanthic acid)
A1.18 Table A 1 . 9 ( c o n t i n u e d ) .
r-
Refs. Notes
Substance
Formula
70 343
Methanoic acid
HCOOH
3 2 . 1 8 3 1 . 0 9 2 9 . 9 9 -0.11
70.0
CH3COOH
2 2 . 6 2 2 1 . 6 3 2 0 . 6 3 -0.1
56.7
C2H5COOH
21.73 20.74
55.8
1, 8
CgH^COOH
21.91
2 0 . 9 9 2 0 . 0 7 -0.092
53.5
1, 8
C^HgCOOH
2 2 . 6 9 2 1 . 8 0 2 0 . 9 2 -0.089
53.1
1. 8
51.3
1, 50
80 353
90 363
dy/dT
T(dr/dT)
see 1, 42 fig. A1.12 see 1, 8 figA1.13
(formic acid) Ethanoic acid (acetic acid) Propanoic acid
1 9 . 7 4 -0.1
(propionic acid) Butanoic acid (butyric acid) Pentanoic acid (valeric acid) heptanoic acid
C^H^gCOOH 2 3 . 9 4
-0.08
(enanthic acid)
45 40 h"~»''t?r^$A^
s I 35
V
p-^A V
X"^#0,.
A
30 h
-A^
25 h
D reference 9
20 h
A reference 2 5
o reference 2 3 • reference 4 2
15h lOl—i273
V reference 4 5 X reference 4 6 J-
J_
_L
_L
-L.
283
293
303
313
323
333
343
353
363
Temperature Figure A1.12. Surface tension of formic acid. Linear region. As in fig. A1.6.
373 K
A1.19
30 h-,
I 25
•3^,
x ^ i' • : i ^
°*^--*-
20 • reference o reference D reference X reference A reference V reference
15
10
8 22 23 25 42 46
_L.
_L
-L.
_L
273
283
293
303
J_
313
323
333
343
353
363
373 K
Temperature Figure A1.13. Surface tension of acetic acid. Linear region. As in fig. A1.6. J. Surface
tensions
of
n-aliphatic
nitrites
See table A L I O a n d figs. A1.14 - 16. With increasing chain length the melting points p a s s t h r o u g h a m i n i m u m . A shallow m i n i m u m is also observed in t h e surface tension, b u t the minima do not coincide.
30 h
?
25
20
15 V reference 4 3 • reference 51 X reference 5 3
10
273
-L
_L
283
293
_L
303
313
323
333
Temperature Figure A1.14. Surface tension of acetonitrile. As in fig. A1.6.
343
J-
353 K
A1.20
Table A L I O . Surface tensions of linear aliphatic n-nitriles. Accuracy ± 0.1 mN m"^ (± 0.2 for decanitrile). Otherwise a s in table A1.5. Substance*
Formula
Ethanenitrile (acetonitrlle)
CH3CN
1 227.4
37.6
1 29.29 2 8 . 0 3
26.77 25.50 24.24|
Propanenitrile (propionitrile)
C2H5CN
1 181.2
40.2
1 27.32 2 6 . 1 7
25.02 23.86 2 2 . 7 l |
Butanenitrile (butyronitrile)
C3H7CN
1 160.6
41.2
1 27.44 2 6 . 4 0
25.36 24.32 23.29!
Pentanenitrile (valeronitrile)
C4H9CN
1 177.1
38.3
1 27.41 2 6 . 4 7
25.53 24.60 23.66|
Hexanenitrlle (capronitrile)
C5HHCN
1 228.1
33.7
1 27.83 2 6 . 9 2
26.01 25.10 2 4 . 2 0 |
Heptanenitrile
CgH^gCN
Octanenltrlle (capryionitrile)
C7H15CN
Nonanltrile (pelargononitrile)
CgHiyCN
239
33.3
Decanitrile 1 (caprinitrile)
C9H19CN
258.6
33.0
Substance*
Formiala
Ethanenitrile (acetonitrile)
y^T^J
m
15 288
20 293
30 303
1 28.181 27.75 2 6 . 8 9 1 227.6
33.3
28.41
1 28.01 2 7 . 2 0
1 29.91 2 8 . 5 0 29.89
40 313
50 323
60 333
26.03 25.17
24.311
26.40 25.60 24.80|
27.68 26.87 26.05 25.32
1 29.36 2 8 . 3 0
27.24 26.17 25.11
dy/dT
yTidy/dT)
Refs. Notes
CH3CN 1
-0.126
66.3
1, 51 fig.
Propanenitrile (propionitrile)
C2H5CN
-0.115
61.1
1. 51 fig. A 1 . 1 5 |
Butanenitrile (butyronitrile)
C3H7CN
22.25 2 1 . 2 l | 20.18| -0.104
57.9
1, 51
Pentanenitrile (valeronitrile)
C4H9CN
22.72 21.78| 20.85 -0.094
54.9
1, 51
Hexanenitrile (capronitrile)
CgHjjCN
23.29 22.38| 21.48| -0.091
54.4
1. 51
Heptanenitrile
CeHjgCN
23.45 22.59! 21.73! -0.086
53.0
1, 52
Octanenitrile (capryionitrile)
C7H15CN 2 4 . 0 0 2 3 . 1 9 2 2 . 3 9 - 0 . 0 8 1
51.5
1. 5 2
Nonanitrile (pelargononitrile)
CgHj^CN 2 4 . 4 2 2 3 . 6 0 | 2 2 . 7 9 ! - 0 . 0 8
51.8
1. 5 2
C9H19CN 2 4 . 0 5 2 2 . 9 9 ! 2 1 . 9 3 ! - 0 . 1 0 6
60.5
1. 2 9
Decanitrile 1 (caprinitrile)
70 343
80 353
90 363
Substances also known as methyl cyanide, ethyl cyanide, etc.
AI.MI
fig. A1.16 1
A1.21
30 h-^,
15 D A X •
10
reference reference reference reference
9 44 45 51 _L
273
283
293
303
_L
313
333
323
343
353 K
Temperature Figure A1.15 Surface tension of propionitrile. As in fig. A 1.6.
30 h
I 25 20
15 X reference A reference • reference D reference
10
51
L 273
44 49 51 53
_L
J_
_L
_L
JL
283
293
303
313
323
J-
333
343
353
Temperature Figure A1.16. Surface tension of butyronitrile. As in fig. A1.6.
363
373 K
A1.22 k. Surface tensions of n-aliphatic isomers compared SeetableAl.il and figs. Al.17- 18. In these examples the trend is that for linear chains the melting points and the surface tensions are higher. A wealth of other data can be found in Jasper's tables^l Table A l . l l . Surface tensions of some aliphatic isomers compared. Accuracy ± 0.1 mN m-^ Substance, Formula
T /K
y{T
10 283
20 293
Butanol C4H9OH
183.2
35.2
26.28
25.39 24.50 23.61 22.71 21.82 20.93
Isobutylalcohol CH3(CH20H)CHCH
165.15 33.1
23.73
22.94 22.14 21.35 20.55
1-Pentanol (n-Amylalcohol) C,H„OH
194.1
26.67
25.79 24.92 24.04 23.17 22.30 21.42
24.96
23.95 22.95 21.94 20.94
155.65 35.4
24.94
24.12 23.30 22.48 21.66 20.84 20.02
289.85 30.3
28.30
27.50 26.70 25.91 25.11
234.5
31.1
27.14
26.32 25.50 24.68 23.86 23.04 22.22
238.6
32.0
27.13 26.24 25.35 24.46 23.58 22.69
235.6
30.3
25.51 24.62 23.74 22.85 21.96 21.08
34.5
2-Pentanol C3H7CHOHCH3 1 3-Methyl-l-butanol (Isoamylalcohol) (CH3)2CH(CH2)20H 1-Octanol 1 2-Octanol C^Hj3CHOHCH3 Valeric acid C^HgCOOH Isovaleric Acid hcH^^HCH^OH
1^ See ref. ^^ at the end of the tables.
30 303
40 313
50 323
60 333
19.76
19.94
70 343
18.96
18.93
24.32 23.92
A1.23
Table A l . l l (continued). Substance, Formula
70 343
Butanol C^HgOH Isobutylalcohol CH3(CH20H)CHCH 1-Pentanol (n-Amylalcohol) C,H„OH 2-Pentanol CgH^CHOHCHg 3-Methyl-1-butanol (Isoamylalcohol) (CH3)2CH(CH2)20H 1-Octanol
1 2-Octanol C^HjgCHOHCHg Valeric acid C^HgCOOH Isovaleric Acid (CH3)2CHCH2COH
dy/dT
r-
Refs.
Notes
51.1
1, 8
also in table A1.6
16.58 -0.08
46.1
1. 8
19.67
18.80 - 0 . 0 8 7
51.4
1, 8
17.93
16.92
15.92 -0.1
53.4
1, 2 0
19.20
18.38
17.56 -0.082
48.2
1, 8
80 353
90 363
100 373
20.93 20.04
19.14
18.20 -0.09
18.96
18.17
17.32
21.42 20.55
18.93
20.02
T{dy/dT)
fig. A1.17 also in table A1.6
23.92
-0.08
50.8
22.22
-0.082
50.4
also in 1, 2 4 table A1.6 1. 2 4
22.69 21.80 20.92 28.90 -0.089
53.1
1, 8
19.31 2 7 . 2 8 - 0 . 0 8 9
51.5
1, 8
21.08 20.19
also in table A1.9 fig. A1.18
25 h X A'—.©,
1 2°
X^'A-.
15
10 • reference 8 X reference 45 A reference 46 01
L
J_
-L
273 283 293 303
_L
313 323 333
343 353 363 373 K
Temperature Figure A1.17. Surface tension of isobutylalcohol. As in fig. A1.6.
A1.24
25 A A
A
D^*-
1 2«
x**-
nx
xB-*-
15
10 D • X A 01
L 273
reference reference reference reference
I
I
283
293
9 8 44 45 L
303
_L
313
323
333
343
J_
j _
353
363
j _
373 K
Temperature Figure A1.18. Surface tension of isovaleric acid. As in fig. A1.6. I, Surface
tensions
of some other common
aliphatic
compounds
SeetableAl.12andfigs.Al.19-- 21.
30 -
25
_-ST
°x
"IT"
Y
A
^•-*
^
20
X
X D A V • o
15
10
5
reference reference reference reference reference reference
1
1
273
283
o
9 22 27 44 54 57 1
293
1
1
303
313
Temperature Figure A1.19. Surface tension of acetone. As in fig. A1.6.
1
323 K
A1.25 Table A1.12. Surface tensions of some other common aliphatic compounds. Accuracy ± 0.1 mN m"^ (± 0.15 for acetone). Substance
Formula
^J^
r^^ra
Acetone
CH3COCH3
177.8
31.7
Temperature and Surface Tension 25 298 24.02 -70 203 25.32 15 288 17.56
1 30 303 22.90 -60 213 23.84 25 298 16.65
40 313 22.34 -50 223 22.36 30 303 16.20
50 323 21.78 -45 228 21.62
60 333 21.22 -40 233 20.88
40 313 46.65 45 318 55.34
60 333 44.87 65 338 53.66
80 353 43.09 85 358 51.97
100 373 41.31 100 378 50.71
CH3OCH3
135
35.4
^2^5^^2^5
156.9
29.5
Ethylene glycol (Glycol, 1, 2 ethane diol) Formamide
CH2OHCH2OH
260
51.4
HCONH2
275.70 58.9
Substance
Formula
Temperature and Surface Tensic n
dr/dT
Acetone
CH3COCH3
70 343 20.66
-0.068 43.7
Ether, dimethyl (Methylether)
CH3OCH3
-0.148 55.3 -30 -25 -35 248 238 243 20.14 19.40 18.67
Ether, dimethyl (Methylether) 1 Ether, diethyl (Ethylether)
1 Ether, diethyl (Ethylether) Ethylene glycol (Glycol, 1, 2 ethane diol) Formamide
20 293 48.43 25 298 57.02
yT(dr/dT)
C2H5OC2H,
-0.09
CH2OHCH2OH 1 2 0 140 393 413 39.53 37.75
-0.089 74.5
110 120 388 398 49.87 49.03
-0.084 82.1
HCONH2
43.7
Refs.
Notes
1, 5 4 fig. A1.19
1, 4 7 fig. 1, 5 5 A1.20*)
1, 5 6
* Wolf (ref. 3. his fig. 12) gives a plot of y(T) over the range 290 - 420 K.
fig. 1, 4 9 A1.21
A1.26
25
S
20 -n«x^-.
-X-jiA-.
15h
10 X n A •
reference reference reference reference
25 27 43 55 JL
_i_
273
278
383
388
393
398
303
313
318 K
Temperature Figure A1.20. Surface tension of formamide. As in fig. A1.6.
60
" " ■ ■ • - - i - - ^ _
D
E
a
X
^'
^-°-V...
_ ^
50
^X—•
—*x#-
^ >40 -
X reference A reference • reference V reference n reference
30
20
10
1
273
1
288
45 49 58 59 60
1
1
1
1
1
303
318
333
348
363
Temperature Figure A1.21. Surface tension of diethyl ether. As in fig. A1.6.
1
378
, 393 K
A1.27
m.
Surface
tensions
of some
triglycerides
See table A 1.13. The surface tensions decrease systematically with increasing chain length of the acid with which the glycerol is esterified.
Table A1.13. Surface tension of some triglycerides. Accuracy ± 2.0 mN m"^ (± 0.3 for glyceroltripalmitate and -stearate) . Substance
^J^
y^T^J
40 313
60 333
80 353
100 373
110 383
47.41 45.27 43.12 40.98 38.84 37.77
Glyceroltriformate Glyceroltriacetate (triacetine)
20 293
276.3
37.6
36.26 34.64 33.02 31.40 29.78 28.97
Glyceroltributyrate
30.85 29.49 28.14 26.78 25.42 24.74
Glyceroltrihexanoate
29.93 28.79 27.64 26.50 25.36 24.79
Glyceroltrioctanoate (Glycerol tricapry late, tricapryline)
281.4
29.8
Glyceroltridecanoate
29.21 28.17 27.13 26.08 25.04 24.52
27.64 26.54 25.45 24.36 23.81
Glyceroltridodecanoate (Glyceroltrilaurate, trilaurine)
322.1
30.1
29.36 28.26 27.17 26.62
Glyceroltrihexadecainoate (Glyceroltripalmitate, tripalmitine) Glyceroltrioctadecanoate (Glycerol tristearate, tristearine)
238.6
34.6
26.88 25.54 28.87
a 328.6 p 346.1 pi 3 3 7 . 6
27.7
28.62 27.25 25.88 25.19
Glyceroltrioleate
34.63 33.23 31.84 30.44 29.04 28.34
A1.28 Table A1.13 (continued). Substance
120 393
130 403
140 413
150 423
d7/dT
r-
refs.
T(d7/dT)
Glyceroltriformate
36.70 35.63 34.56 33.48 -0.107
78.8
1, 25
Glycerol triace tate (trlacetine)
28.16 27.35 26.54 25.73 -0.081
60.0
1, 25
Glyceroltributjo-ate
24.06 23.38 22.70 22.02 -0.068
50.8
1, 25
Glyceroltrihexanoate
24.22 23.65 23.08 22.50 -0.057
46.7
1. 25
Glyceroltrioctanoate (Glycerol trlcaprylate, tricapryline)
24.00 .23.48 22.96 22.44 -0.052
44.5
1. 25
Glyceroltrideccinoate
23.27 22.72 22.18 21.63 -0.055
44.7
1, 25
Glyceroltridodecanoate (Glycerol trllaurate, trilaurine)
26.08 25.53 24.98 24.44 -0.09
59.2
1. 25
50.6
1, 60
Glyceroltrihexadecanoate 24.20 23.52 (Glycerol tripalmi tate, tiipalmitine) Glyceroltrioctadecanoate (Glycerol tristearate, 24.51 23.82 tristearine) G lycerol trioleate
-0.067
51.5 -0.069
27.64 26.94 26.24 25.54 -0.07
1. 60 55.1
1. 25
A1.29 ji. Surface tensions of benzene and some mono-substituted See table A1.14 and figs. A1.22 - 28.
benzenes
Table A1.14. Surface tension of benzene and some mono-substituted benzenes. Accuracy 0.1 mN m~^ (1.0 for nitrobenzene). 20 293
40 313
Formula
^m/^
y^T^J
10 283
Benzene
^6^6
278.6
30.7
30.21
Phenol
CgHgOH
316
38.9
Toluene
CgHgCHg
178
42.2
29.72
28.52 27.33 26.15
Aniline Bromobenzene
C6H5NH2 CeHsBr
266.9 242
45.5 41.8
36.98
43.21 42.67 41.56 40.50 35.82 34.66 33.50
Chlorobenzene
C6H5CI
228
41.5
34.78
33.59 32.40 31.21
lodobenzene
C6H5I
241.7
45.0
40.40
39.27 38.15 37.03
Benzylalcohol
C6H5CH2OH
257.8
40.4
Nitrobenzene
C6H5NO2
278.8
45.7
Substance
Formula
50 323
Benzene
^6^6
24.69 23.67 22.40
60 333
15 288
30 303
Substance
28.88 27.56 26.25 39.27
41.71
70 343
80 353
90 363
100 373
110 383
Phenol
C6H5OH
38.20 37.13
Toluene
CgHsCHa
24.95 23.77 22.58 21.39 20.20
Aniline Bromobenzene
C6H5NH2 CeHgBr
39.41 38.33 37.24 36.15 35.06 32.34 31.18 30.02 28.86 27.70 26.54 25.38
Chlorobenzene
CeHgCl
30.01 28.82 27.63 26.44 25.25 24.06 22.87
lodobenzene
C6H5I
35.90 34.78 33.66 32.54 31.41
Benzylalcohol
C6H5CH2OH
Nitrobenzene
C6H5NO2
Substance
Formula
Benzene
^6^6
Phenol
C6H5OH
Toluene
CgHgCHg
Aniline Bromobenzene
C6H5NH2
CeHsBr
24.22 23.06 21.90 20.74
Chlorobenzene
C6H5CI
21.68 20.49
lodobenzene
C6H5I
28.04 26.92 25.80 24.67 23.55
Benzylalcohol
C6H5CH2OH
21.68
18.92
16.15
Nitrobenzene
C6H5NO2
32.46
30.14
27.83 25.51
35.00
32.86 19.01
30.29 29.17
28.58 27.20 25.82 24.44
120 393
130 403
30.72
34.77
37.08
39.40
140 413
150 423
160 433
180 453
200 473
28.59
13.39 23.20
A1.30 Table A1.14 (continued). Substance
Formula
dy/dT
7Tidy/dT]
Refs.
Notes
Benzene
^6^6
-0.13
67.0
I.Am. Petr. Inst.
fig. A1.22
Phenol
CgHsOH
-0.107
72.7
1. 61
fig. A1.23
Toluene
CgHgCHg
-0.119
63.4
1, 62
fig. A1.24
Aniline
C6H5NH2
-0.109
74.5
1, 8, 31, 42, see legend 44, 63, 64 fig. A1.28
Bromobenzene
CgHsBr
-0.117
70.1
1, 55
fig. A1.25
Chlorobenzene
C6H5CI
-0.119
68.5
1, 55
fig. A1.26
lodobenzene
C6H5I
-0.112
72.2
1. 55
fig. A1.27
Benzylalcohol
C6H5CH2OH
-0.138
75.9
1, 20
Nitrobenzene
C6H5NO2
-0.116
77.9
1, 63
fig. A1.28
30 A
s E
^ ^ ^^D»0^
^
^A^^o5(o_
25 VA'^^^O^
>D
20 • tabulated X reference 24 A reference 26 D reference 42 0 reference 4 3 V reference 44
15
10 5
1
1
1
1
i
273
283
293
303
313
1
1
323 333 Temperature
1
343
1
353 K
Figure A1.22. Surface tension of benzene. As in fig. A1.6. Wolf^^ (his fig. 15) gives a plot for 400 - 500 K.
A1.31
45
E
40 -
^V.. V D Xo
35 D reference o reference • reference A reference X reference V reference
30
25
201
L 273
_J
293
22 25 61 64 65 66
I
i_
313
333
r^^ .^^
J
353
L
373
393
413
433
453
473 K
Temperature Figure A1.23. Surface tension of phenol. As in fig. A1.6.
30 h □—J.
I 25^ D V
20 h
V reference X reference a reference • reference A reference
15h
10 h
26 42 44 62 67 _L
273
283
293
303
J_
313
_L
323
333
temperature Figure A1.24. Surface tension of toluene. As in fig. A 1.6.
343
353 K
A1.32
50
6
40 -^-.^ ^•*»^ 30
20 □ reference A reference X reference • reference
10
0
..
23 25 55 63
1
1
1
1
1
i
1
i
273
293
313
333
353
373
393
413
1
433 K
Temperature Figure A1.25. Surface tension of bromobenzene. As in fig. A1.6.
50 -
40
30
^^•c?A-
20 n reference • reference A reference X reference
10
0
__ 1
273
26 43 44 55
1
1
1
1
1
1
1
293
313
333
353
373
393
413
1
433 K
Temperature Figure A1.26. Surface tension of chlorobenzene. As in fig. A1.6. Wolf (^^ his fig. 15) gives a plot for 420 - 600 K.
A1.33
50
e
40
30 A
•-.
20 A reference 25 X reference 55 • reference 6 3
10
0
1
1
273
293
1
1
1
1
1
313
333
353
373
393
1
1
413
433 K
Temperature Figure A1.27. Surface tension of iodobenzene. As in fig. A1.6.
^ O v
X
40 v \ „
7
E z 6
X
35
AS,
>>^
30 X reference V reference o reference A reference • reference D reference
25
20
15
t
273
i
293
l
l
3.13
X >^^
9 25 42 63 61 68
A*V
.. i
333
353
1
373
1
393
1
413
1
433
1
453
1
473 K
Temperature Figure A1.28. Surface tension of nitrobenzene. As in fig. A1.6. Wolf {'^\ his fig. 15) gives a plot over the same temperature range, with fewer measuring points. Over this range he sees no difference with aniline.
A1.34 o. Surface tensions of some other cyclic
compounds
See table A1.15 and figs. Al.29-35. Table A1.15. Surface tensions of some other cyclic compounds. Accuracy 0.3 for the cresols and quinoline, 0.15 for pyrrole, otherwise 0.1. Substance
m
y^^m
5 278
10 283
20 293
25 298
30 303
40 313
o-Cresol
303.9
36.3
36.90
35.39
m-Cesol
284.5
36.9
35.69
34.31
p-Cresol
307.8
35.4
50 323
34.88
o-Xylene
248
35.3
31.41 30.31
29.21 28.11 27.00
m-Xylene
225.7
36.5
30.13 29.02
27.92 26.81 25.71
p-Xylene
286.6
29.3
28.55
27.47 26.39 25.32
Cyclohexane
279.6
26.9 27.13 26.43 25.24
24.06 22.87 21.68
Pyridine
231
45.3
34.60
37.21
Pyrrole
38.71 37.61
36.51 35.41 34.31
44.19 43.12
42.06 41.00 39.93
Quinoline
257.2
Substance
60 333
o-Cresol
33.36
31.34
29.32 27.30 26.29 25.28
m-Cesol
32.46
30.61
28.76 26.92 25.99 25.07
p-Cresol
33.02
31.17
29.32 27.47 26.54 25.61
o-Xylene
25.90 24.80 23.70
m-Xylene
24.61 23.50 22.40
21.29 20.19
p-Xylene
24.25 23.17 22.10
21.02 19.95
Cyclohexane
20.49 19.30
Pyridine
31.98
Pyrrole
33.21 31.11
Quinoline
38.87 37.81 36.75
46.9
70 343
80 353
85 358
90 363
100 373
22.60 21.50
28.72 35.68 34.62
120 393
130 403
140 413
A1.35 Table A 1 . 1 5 (continued). Substance
150 423
170 443
180 453
r-
dr/dT
Notes
Refs.
T(dy/dT)
o-Cresol
24.26 22.24 21.23 -0.101
67.1
1, 44 fig. A1.29
m-Cesol
24.14 22.30 21.37 -0.092
63.2
1, 44 fig. A1.30
p-Cresol
24.69 22.83 21.91 -0.093
63.9
1, 69
o-Xylene
-0.110
62.6
1, 19 fig. A1.31
m-Xylene
-0.110
61.4
1, 19 fig. A1.32
p-Xylene
-0.107
60.0
1. 19 fig. A1.33
Cyclohexane
-0.120
60.3
1. 70
Pyridine
-0.13
75.5
1, 48 fig. A1.34
Pyrrole
-0.11
69.8
1, 71
Quinoline
-0.106
74.3
1, 44 fig. A1.35
40
35
30
25
15
?^
• reference 44 A reference 65 X reference 69
20
_L
I
273
293
_i_
313
I
333
j_
353
373
393
413
433
Temperature Figure A1.29. Surface tension of o-cresol. As in fig. A1.6.
453
473 K
A1.36
40
6
^x^-
35
~*«^
30 h
^
\
'^v.^
25 h
^*>«^, •A^
• reference 44 A reference 6 5 X reference 69
20
15
J
273
L
293
J_
313
""^^
J
333
353
I
I
373
393
L
413
433
J
L
453
473 K
Temperature Figure A1.30. Surface tension of m-cresol. As in fig. A1.6.
^>^-2x^.
30 h
?
•AK..
25 ^•A^ ^•A^ "A*^
20 h
15 • reference 19 A reference 2 5 X reference 42
lOh 51
L 273
J
283
I
I
293
303
L
313
J
323
333
343
I
I
L
353
363
373 K
Temperature Figure A1.31. Surface tension of o-xylene. As in fig. A1.6.
A1.37
30 X V
XA
X
A*
D
25
^•*,
20
rP
15 k
• n A V X
10
reference reference reference reference reference
_J
273
283
I
293
19 25 26 44 46 L
303
313
_L
323
333
343
353
363
373 K
Temperature Figure A1.32. Surface tension of m-xylene. As in fig. A1.6.
30 "^^-%v
I
25
■*^v,OC
"^v...^ X "*v^
*4V^
20
15 • reference 19 V reference 25 X reference 42
10
273
283
_L
J_
293
303
313
323
333
343
353
Temperature Figure A1.33. Surface tension of p-xylene. As in fig. A 1.6.
363
373 K
A1.38
50 1
6
2
40
s
°—AW_^ -DA X
30
.^^ X
T^l—^A_ X
20
D X • A V
10
0
reference reference reference reference reference
22 44 48 71 72
1
1
1
1
1
1
1
1
1
1
273
283
293
303
313
323
333
343
353
363
1
373 K
Temperature Figure A1.34. Surface tension of pyridine. As infig.A1.6.
50 h D
A
I 40
A** D A
30
20 D • A X
10
reference reference reference reference
23 44 65 73 _L.
_L
273
283
293
303
313
323
333
343
353
363
373 K
Temperature Figure A1.35. Surface tension of quinoline. As infig.A1.6. p . Surface
tensions
of some binary
mixtures
See tables A1.16 - 1.18. This is a selection from the abundance in the literature.
A1.39 Table A1.16. Surface tensions of some binary mixtures of inorganic and organic compounds. (Values for pure liquids were calculated on the basis of experimental results using the fitting linear expression.) Compounds
T/K
Argon - Krypton (2)
120.5 130
140.16 150.66 163.15 177.38 Argon Nitrogen (2)
83.82
Argon(l) - Methane
90.67
Kryptone Methane (2)*
110.0 115.0 119.0
Krypton (1)Nitric oxide*
113.0 116.0 119.0
Methane (1) Nitric oxide*
102.0 108.0 113.0
Ethane (1) Nitric oxide*
111.0 115.0 119.0
Mole fraction (1) or (2) and mN m ^ 0.000 0.125 0.267 0.381 4.982 6.019 7.257 8.221 0.000 0.193 0.415 0.508 7.193 3.137 4.462 6.38 0.000 0.296 0.463 0.751 3.058 5,582 7.048 10.118 0.000 0.314 0.557 0.803 1.275 4.631 6.035 8.589 0.000 0.207 0.207 0.646 < 0.05 1.287 1.287 5.019 0.187 0.427 0.614 0.729 < 0.05 1.267 2.706 3.782 0.419 0.696 0.801 0.868 < 0.05 1.438 2.323 2.863 0.000 0.058 0.085 0.148 13.39 12.80 12.54 12.03 0.496 0.558 0.629 0.651 8.94 9.74 9.08 9.45 0.000 0.083 0.117 0.204 17.78 16.80 16.42 15.66 0.000 0.150 0.266 0.371 17.57 16.67 16.03 15.41 0.000 0.149 0.264 0.367 16.49 15.67 15.04 14.48 0.000 0.147 0.264 0.365 15.64 14.86 14.26 13.75 0.000 0.232 0.382 0.483 26.^33 21.65 19.89 18.80 0.000 0.230 0.381 0.482 25.18 20.39 18.62 17.44 0.000 0.228 0.380 0.482 24.02 19.13 17.36 16.08 0.000 0.102 0.153 0.252 30.55 22.02 20.20 18.64 0.000 0.097 0.148 0.245 28.25 21.00 19.39 17.73 0.000 0.091 0.142 0.240 26.33 20.16 18.72 16.97 0.000 0.204 0.409 0.546 27.1 27.53 28.21 29.09 0.000 0.205 0.414 0.551 25.56 26.27 27.27 27.67 0.000 0.208 0.418 0.558 24.02 25.00 26.33 26.25
Surface tension, 1 0.468 9.055 0.616 8,326 1.000 13.410 1.00 11.279 0.824 6.945 0.889 5.453 1.000 4.280 0.192 11.69 0.682 8.79 0.289 14.96 0.482 14.80 0.478 13.95 0.476 13.26 0.646 17.80 0.647 16.61 0.649 15.42 0.461 17.82 0.456 16.67 0.451 15.71 0.666 28.73 0.671 27.11 0.680 25.49
0.618 10.587 0.688 9,212
1.000 9.179 1.000 6.775
0.300 10.94 0.757 8.46 0.411 14.13 0.623 14.28 0.620 13.39 0.617 12.68 0.804 17.07 0.807 16.17 0.811 15.28 0.515 17.04 0.510 16.14 0.507 15.38 0.816 26.90 0.821 25.88 0.829 24.86
0.434 10.07 0.809 8.23 0.508 13.57 0.729 13.98 0.725 13.05 0.723 12.30 1.000 16.93 1.000 16.28 1.000 15.64 0.620 16.70 0.616 15.54 0.613 14.57 0.911 27.03 0.915 26.07 0.921 25.11
A1.40 Table A1.16 (continued) Compounds
T/K
Argon - kiypton(2)
130
120.5
Mole Fraction (1) or (2) cind Surface Tension, mN m"^ 0.843 10.666 0.813 12.807
4, 36
0.904 1.000 11.769 13.436 1.000 15.403
Argon Nitrogen (2)
83.82
1 Argon (1) -
90.67
Methane Kiyptone Methane (2)*
110.0 115.0 119.0
Krypton (1)Nitric oxide* Methane (1) Nitric oxide*
102.0
113.0 111.0 115.0 119.0
0.951 1.415 1.000 7.42 0.913 11.90
1.000 1.850
74 74 74 74 74 74
1.000 7 5 11.65
76
0.782 16.06 0.781 14.81 0.781 13.76 1.000 26.67 1.000 25.91 1.000 25.15
1.000 14.68 1.000 13.55 1.000 12.60
±0.05
±0.05
74
76
113.0
108.0
Ethane (1) Nitric oxide*
0.876 7.90 0.712 12.60 1.000 13.16 1.00 12.22 1.00 11.47
0.896 0.983 0.912 7.76 0.852 12.11
Notes
74
130
140.16 150.66 163.15 177.38 193.16 0.682
Refs.
76
76
±0.01 ±0.1
A1.41 Table A1.16 (continued) Compounds
T/K
Kiypton (1) Ethane
116.0
Mole Fraction (1) or (2) and Surface Tension,
mNm ^
Nitrogen (1) Carbon monoxide Nitrogen (1) Methane 1-Propanol (1) n-Propylamine 1-Propanol (1) n-Butylamine Benzene (1) n-Hexane Acetone(l) Isooctane n-Dodecane(l) n-Hexane
Compounds
0.000 27.36 120.0 0.000 26.69 124.0 0.000 26.07 90.67 0.000 9.02 83.82 0.000 17.78 298 0.000 21.50 0.000 298 23.12 293.15 0.000 18.42 298.15 1.000 18.36 0.000 298 17.94 303 0.000 17.43 0.000 308 16.90 313 0.000 16.38 T/K
0.211 23.70 0.202 22.52 0.191 21.34 0.099 8.77 0.133 13.72 0.050 21.75 0.051 23.18 0.099 18.78 0.101 18.23 0.2219 19.79 0.2494 19.60 0.1301 18.04 0.1930 18.03
0.306 22.00 0.259 20.93 0.282 19.87 0.192 8.53 0.200 12.32 0.101 21.95 0.101 23.25 0.200 19.23 0.202 18.23 0.4775 21.56 0.3859 20.59 0.3667 19.86 0.3976 19.68
0.454 20.33 0.441 19.27 0.425 18.22 0.268 8.40 0.341 10.25 0.200 22.33 0.130 23.31 0.325 20.08 0.297 18.24 0.7265 23.30 0.6174 22.11 0.6796 21.96 0.7248 21.70
0.559 19.44 0.546 18.36 0.530 17.27 0.445 8.05 0.429 9.49 0.301 22.66 0.201 23.44 0.455 20.81 0.395 18.31 1.000 24.69 0.7297 22.64 1.000 23.85 1.000 23.42
0.711 18.17 0.700 17.04 0.685 15.91 0.591 7.83 0.531 8.80 0.404 22.99 0.297 23.60 0.493 21.03 0.496 18.44
1 0.886 1 16.95 0.881 15.90 0.874 14.85 0.718 7.68 0.602 8.39 0.502 23.33 0.402 23.76 0.599 21.76 0.590 18.57
1.000 24.31
Mole Fraction (1) or (2) and Surface Tension, Refs. Notes mNm"^ Krypton (1) 7 7 0.01 116.0 1.000 Ethane 16.33 120.0 1.000 15.48 1.000 7 5 ± 0.01 124.0 14.62 Nitrogen (1) 90.67 0.858 0.932 1.000 Carbon monoxide 7.54 7.42 7.46 Nitrogen (1) 83.82 0.811 0.952 1.000 Methane 7.08 6.24 5.98 1-propanoic 1) 0.601 0.700 0.805 0.898 0.946 1.000 7 8 ± 0.05 298 n-propylamine 23.48 23.53 23.51 23.43 23.38 23.33 l-Propanol(l) 298 0.496 0.601 0.697 0.802 0.947 1.000 n-Butylamine 23.86 23.88 23.86 23.67 23.46 23.33 Benzene (1) 7 9 ± 0.05 293.15 0.700 0.812 0.900 1.00 n-Hexane 22.68 24.24 25.92 28.87 Acetone 1) 298.15 0.698 0.799 0.900 1.000 Isooctane 18.84 19.40 20.51 23.03 n-Dodecane(l) - 2 9 8 80 1 n-Hexane
A1.42 Table A1.17. Surface tensions of mixtures of water (1) and some inorganic and organic compounds (2). Compound (2)
T/K
Ammonia
293
Hydrogen peroxide Sulfuric acid
291
Hydrazine
298
N.N-DimethylAcetamide
298
Methanol
293
1 Ethanol
293
Propan-1-ol
323
293
1 1,2-Butanediol
298
1,3-Butanediol
298
1,4-Butanediol
298
1 2,3-Butanediol
298
Acetic acid
303
Pyridine
295
Phenol
303
Acetonitrile
293
Mole Fraction (2) and Surface Tension, mN m ^ 0.0045 72.55 0.7047 32.99 0.1278 73.22 0.000 67.80 0.000 71.96 0.000 71.89 0.000 72.75 0.000 72.75 0.000 72.75 0.000 71.97 0.5968 32.29 0.000 71.97 0.6473 39.31 0.000 71.97 0.5974 47.38 0.000 71.9 0.4912 34.70 0.00 71.25 0.000 71.98 0.000 71.02 0.000 72.60 0.169 33.38
0.0772 65.74 0.7249 31.84 0.2370 73.51 0.054 71.55 0.067 73.11 0.0212 71.99 0.029 63.46 0.020 56.41 0.016 42.51 0.0099 59.80 0.6928 31.96 0.0009 71.26 0.7154 38.85 0.0100 66.26 0.6990 46.81 0.0099 65.85 0.5996 34.05 0.03 55.45 0.049 55.6 0.0053 65.19 0.005 69.02 0.186 32.40
0.1461 62.15 0.7507 30.57 0.2814 73.67 0.101 73.55 0.105 73.68 0.077 72.27 0.059 56.87 0.042 48.14 0.032 34.86 0.0191 53.58 0.7991 31.65 0.0046 67.90 0.8097 38.24 0.0600 56.69 0.8001 46.33 0.0300 56.01 0.7315 33.31 0.05 50.70 0.102 52.8 0.0077 62.51 0.010 65.45 0.209 3.84
0.2414 58.02 0.8095 28.11 0.4431 74.13 0.132 74.33 0.205 75.10 0.163 74.69 0.090 51.83 0.065 42.72 0.05 30.87 0.0298 49.09 0.8914 31.41 0.0081 65.30 0.8919 37.73 0.0898 55.20 0.9009 45.95 0.0500 49.74 0.8993 33.03 0.08 44.96 0.302 47.9 0.0097 60.27 0.015 63.03 0.231 31.56
0.2970 55.58 0.8972 25.22 0.5927 74.67 0.171 74.99 0.265 75.41 0.227 75.45 0.123 47.86 0.089 38.56 0.091 27.08 0.0398 46.29 1.000 31.16 0.0181 60.12 1.000 37.09 0.1097 54.31 1.000 45.47 0.0699 46.43 1.000 32.47 0.13 42.41 0.493 46.6 0.0147 56.23 0.021 59.46 0.254 31.01
0.3598 52.29 0.9141 24.70 0.6083 74.73 0.215 74.94 0.339 75.47 0.313 73.59 0.194 41.67 0.115 36.09 0.114 26.41 0.0600 42.67
0.4456 1 48.08 0.9666 23.02 0.7901 75.29 0.265 74.20 0.401 75.28 0.430 67.06 0.273 37.02 0.207 30.69 0.167 25.68 0.0979 39.12
0.0294 0.0352 56.35 54.93
0.1599 0.1984 52.54 51.65
0.1000 0.1300 43.73 41.71
0.22 38.40 0.602 45.8 0.0348 46.11 0.028 56.89 0.313 30.61
0.35 36.95 0.797 43.7 0.0453 43.14 0.035 53.75 0.396 30.02
A1.43 Table A1.17 (continued). Compound (2)
T/K
Ammonia
293
Hydrogen peroxide Sulfuric acid
291
Hydrazine
298
N,N-DimethylAcetamide
298
Methanol
293
1 Ethanol
293
Propan-l-ol
323
293
1 1,2-Butanediol
298
1,3-Butanediol
298
1,4-Butanediol
298
1 2,3-Butanediol
298
Acetic acid
303
Pyridine
295
Phenol
303
Acetonitrile
293
Mole Fraction (2) and Suirface Tension, mN m ^ 0.4645 46.62 0.9718 22.78 0.9066 75.67 0.3337 2.95 0.488 74.18 0.637 55.44 0.360 33.37 0.281 28.51 0.231 25.18 0.1490 36.78 0.0649 50.37 0.2294 51.16 0.1499 40.66 0.51 33.37 0.898 41.0 0.704 38.09 0.044 49.32 0.489 29.67
0.5348 42.65 1.000 22.03 1.000 75.94 0.415 70.73 0.636 72.38 0.788 47.28 0.458 30.32 0.370 26.72 0.310 24.89 0.1999 35.48 0.1082 47.16 0.2990 49.99 0.1702 39.70 0.69 31.00 1.000 37.0 0.740 38.22 0.055 47.61 0.655 29.02
Refs. Accuracy
0.5440 0.6116 0.6364 0.6451 4, 41.63 37.90 36.40 35.87 81
0.529 66.92 0.697 71.88 1.000 36.43 0.568 27.91 0.477 25.48 0.412 24.47 0.2496 34.66 0.1599 45.13 0.3600 49.31 0.2002 38.47 0.85 29.50
0.671 61.15 0.831 69.97
0.885 54.00 0.969 67.57
1.000 51.70 1.000 66.67
0.692 25.98 0.610 24.32 0.545 24.23 0.2991 34.07 0.2487 43.18 0.3980 49.02 0.2500 37.52 1.00 26.34
0.835 24.37 0.779 23.23 0.730 23.98 0.3993 33.25 0.4248 41.06 0.4284 48.73 0.3016 36.39
1.000 22.95 1.000 22.31 1.000 23.69 0.5006 32.70 0.4995 40.41 0.4991 48.15 0.3986 35.36
0.766 38.29 0.067 45.19 1.000 28.37
1.000 38.54 0.084 41.91
0.100 39.06
0.130 35.22
4. 82 4, 83 4, 84 4, 85 4, 86 4, 86 4, 86 87 87 87 87
4. 88 4, 89 4, 90 4, 91
±0.2
A1.44 Table A1.18. Surface tensions of n-propanol in water at different temperatures. Data tciken from Glinsky et al. ^'^\ Accuracy ±0.4 mN m-^ Surface Tension, mN m"^
Mote Fraction of Alcohol 5°C
lo
74.9
lo.ooi
71.1
7.5°C
10°C
12.5°C 15°C
70.3
70.0
69.5
22.5°C 25°C
69.3
68.8
27.5°C
71.97
72.75
73.49
74.22 70.7
17.5°C 20°C
68.5
30°C 1 71.18|
68.1
67.8
67.4 1 61.9
|o.003
65.4
64.8
64.6
64.5
63.9
63.8
63.3
62.8
62.5
62.2
|o.004
63.1
62.8
62.3
61.9
61.2
60.8
60.3
59.9
59.4
59.0
58.4
|o.005
61.3
60.9
60.3
59.8
59.1
58.6
58.0
57.4
56.9
56.2
55.9
55.5
55.2
54.9
52.5
52.1 46.0
lo.ooe
59.7
59.2
58.8
58.5
57.9
57.6
56.8
56.3
|o.008
56.9
56.3
56.0
55.5
55.0
54.5
54.0
53.4
52.7
lo.oi
54.5
54.0
53.5
53.1
52.5
52.2
51.6
51.1
49.6
|o.014
50.5
50.1
49.4
49.0
48.7
48.3
47.6
47.3
46.8
46.2
|o.018
47.8
47.2
46.7
46.1
45.4
45.0
44.7
44.3
43.9
43.3
0.02
46.2
45.5
45.3
44.7
44.2
43.7
43.2
42.7
42.4
41.7
41.3
|o.03
41.1
40.6
40.2
39.4
39.0
38.3
37.9
|o.04
37.1
36.6
36.2
35.6
35.1
34.6
34.2
33.8
33.2
|o.06
31.6
31.1
30.8
30.5
30.2
29.9
29.4
29.3
29.0
28.5
28.4
|o.08
28.7
28.6
28.4
28.1
27.9
27.8
27.6
27.3
27.2
26.9
26.7
0.1
27.6
27.5
27.3
27.2
27.0
26.8
26.7
26.5
26.4
26.1
26.1
|o.2
26.6
26.5
26.1
26.4
26.0
26.0
25.7
25.6
25.5
25.3
25.2
0.3
26.4
26.2
26.1
25.8
25.7
25.6
25.4
25.4
25.2
24.8
24.7
0.4
26.2
25.9
25.9
25.6
25.5
25.4
25.1
24.9
24.8
24.6
24.5
0.5
26.0
25.9
25.5
25.4
25.2
25.0
25.0
24.8
24.7
24.5
24.3 1
|o.6
25.7
25.6
25.3
25.1
25.0
24.8
24.7
24.5
24.4
24.2
24.0
0.7
25.6
25.4
25.2
25.2
24.9
24.8
24.5
24.4
24.1
23.9
0.8
25.4
25.3
25.0
24.9
24.6
24.6
24.4
24.2
24.0
23.8
0.9
25.2
24.9
24.8
24.7
24.5
24.3
24.1
23.8
23.7
23.4
23.9 1 23.6 1 23.3 1
1.0
24.9
24.7
24.4
24.2
24.1
23.8
23.8
23.5
23.5
23.2
23.0
A1.45
References, indicating m e t h o d s where appropriate Abbreviations: CR = capillary rise; DM = d e t a c h m e n t method (including Wilhelmy plate a n d D u Nouy ring); DW = drop weight ('stalagmometer'); HD = h a n g i n g (pendant) drop; MGP = maximum gas bubble pressure; SD = sessile drop. M e a s u r e m e n t s 'in own vapour' are m e a s u r e m e n t s w h e r e t h e air h a s b e e n removed. In a few cases data are given although the method w a s not indicated. As far a s these references have been taken from J a s p e r or other references they have not been cross-checked. 1.
J.J. Jasper. The Surface Tension of Pure Liquid Compounds.
J. Phys.
Chem.,
Ref DatR 1 (1972), No. 4, 841-1010. 2.
G. Korosi, E.G. Kovats, Density
and Surface Tension of 83 Organic
Com-
pounds. J. Chem Eng. Data 2 6 (1981) 323-332. 3.
K.L. Wolf, Physik und Chemie der Grenzfldchen.
Band 1 Die Phdnomene
in
AUgemeinen. Springer (1957). 4.
C. Wohlfarth, B. Wohlfarth a n d M.D. Lechner, Surface Tension of Pure Liquids and Binary Liquid Mixtures, Springer, (1997)
5.
I. Vavruch, J. CoUoid Interface ScL 169 (1995) 249.
6.
S.S. Susnar, H.A. Hamza and A.W. Neumann, Colloids Surf A 8 9 (1994) 169.
7.
M.S. Chao, V.A. Stenger, Talanta 11 (1964) 2 7 1 . CR in own vapour.
8.
A.I. Vogel, J. Chem. Soc. (1948) 1820. CR in own vapour. (Differential CR for the amines.)
9.
W. Ramsay, J . Shields, J. Chem Soc. 6 3 (1893) 1089. (CR in air.)
10.
F. Wilbom, Jahresber.
11.
J.D. van der Waals, Z. Physik. Chem 13 (1894) 657.
Schles. Gesellsch. Vaterl Kultur, 1 2 1 2 (1910) 56. (CR
in air.) 12.
E.A. Guggenheim, J. Chem Phys. 1 3 (1945) 253.
13.
N.K. Roberts, J. Chem Soc. (1964) 1907. (SD in own vapour.)
14.
R.C.L. Bosworth, Trans. Faraday Soc. 3 1 (1938) 1501. (MBP in CO2.)
15.
C. Kemball, Trans. Faraday Soc. 4 2 (1946) 526. (SD in own vapour.)
16.
W.F. Clausen, Science 156 (1967) 1226. (CR in He-atmosphere.)
17.
G.J. Gittens, J. CoUoid Interface ScL 3 0 (1969) 406. (CR in N2.)
18.
H. Moser, Ann. Phys. 8 2 (1927) 993. (CR in air.)
19.
T.W. Richards, C.L. Speyers a n d E.K. Carver, J. Am. Chem
Soc. 4 6 (1924)
1196. (CRinair.) 20.
B.Y. Teitel'baum, T.A. Gartolova a n d E.E. Sidorova, Zhur. Fiz. Khim.
25
(1951) 9 1 1 . (CRinair.) 21.
T.F. Young, P.L.T. Gross a n d W.D. Harkins, Physical Fdms. Reinhold (1952) 79. (CR in air.)
Chemistry
of Surf ace
A1.46 22.
R.P. Worley, J. CherrL Soc. 105 (1914) 273. (in fig. 083, A1.2) acetic acid A l . 17. (CR in air.)
23.
R. Schiff, Gazz. Chim. Ital 14 (1884) 368. (In fig. A1.2 CS2, A1.3 CHCI3.
24.
W.D. Harkins, Y.C. Cheng, J. Am. Chem. Soc. 4 6 (1924) 35. (DW in air.)
25.
F.M. Jaeger, Z Anorg. Allgerih Chem, 101 (1917) 1.
26.
P. Walden, R. Swinne, Z. Physik. Chem 7 9 (1912) 700. (CCl^ fig. A1.2). (CR in air.)
27.
R. Schiff, Arm. Chem (Leipzig) 2 2 3 (1884) 47.
28.
A.W. Adamson, Physical Chemistry qfSurfaces,
29.
M. Hennaut-Roland, M. Lek, Bull. Soc. Chem Belg. 4 0 (1931) 177. (CR in air.)
30.
B.J. Keene, Intemattonal
31.
5th ed., Wiley (1991), p. 55.
Materials Reviews 3 8 (1993) 157.
R.A. Stairs, M.J. Sienko, J. Am. Chem. Soc. 7 8 (1956) 9 2 0 . (CR in own vapour.)
32.
K.R. Atkins, Y. Narahara, Phys. Rev. 138 (2A) (1965) 437. (CR in own vapour.)
33.
A.I. Vogel, D.M. Cowan, J. Chem Soc. (1943) 16. (CR in own vapour; interpolation of graph used by Jasper, see his p. 880, table 29.)
34.
M. Baccareddo, R. Baldacci, Recerca Set 2 0 (1950) 1817. (CR in own vapour.)
35.
S. Fuks, A. Bellemans, Physica 3 2 (1966) 594. (CR in own vapour.)
36.
I.I. Sulla, V.G. Baidakov, Zti. Fiz. Khim. 6 8 (1994) 6 3 .
37.
E.E.C. Balys, F.G. Donnan, J. Chem Soc. 8 1 (1902) 907.
38.
C.C. Snead, H.L. Clever, J. Chem Eng. Data 7 (1962) 3 9 3 . (CR in own vapour.)
39.
J.J. Jasper, E.V. Kring, J. Phys. Chem 5 9 (1955) 1019. (CR)
40.
R. Schenck, M. Kintzinger, Rec. Trav. Chim. Pays-Bas
4 2 (1923) 759. (CR in
air.) 41.
Y.V. Efremov, Zhw. Fiz. Khim 4 0 (1966) 1240. (CR in air.)
42.
R. Kremann, R. Meingast, Monatsh. Chem. 3 5 (1914) 1332.
43.
S. Sugden, J. Chem Soc. 125 (1924) 32. (CR.)
44.
R. Renard, P.A. Guye, J. Chim. Phys. 5 (1907) 8 1 . (CR in air.)
45.
J . Livingston, R. Morgan a n d E.C. Stone, J. Am Chem. Soc. 3 5 (1913) 1505.
46.
M.J. Timmermans, M. Hennaut-Roland, J. Chim. Phys. 2 7 (1930) 4 0 1 . (CR in
47.
O. Maass, E.H. Boomer, J. Am Chem Soc. 4 4 (1922) 1709. (CR in air.)
(DW) air.) 48.
C.T. Kyte, G.H. Jeffrey and A.I. Vogel, J. Chem Soc. 161 (1960) 4454. (MBP in air.)
49.
W.E.S. Turner, E.W. Meny, J. Chem Soc. 9 7 (1910) 2069. (CR)
50.
W.D. Harkins, G.L. Clark and L.E. Roberts, J. Am Chem Soc. 4 2 (1920) 700. (DW)
51.
G.H. Jeffeiy, A.I, Vogel, J. Chem Soc. 6 7 4 (1948) 1804. (CR in air.)
52.
A.I. Vogel, J. Chem Soc. (1952) 514. (CR in air.)
A1.47 53.
J . Livingston, R. Morgan and P.M. Chazel, J. Am, Chem. Soc. 3 5 (1913) 1821. (DW)
54.
D.M. Cowan, G.H. Jeffery a n d A.I. Vogel, J. Chem. Soc. (1940) 171. (MBP in
55.
A.I. Vogel, J. Chem Soc. (1948) 607. (CR in air.)
56.
A.F. Gallaugher, H. Hibbert, J. Am Chem. Soc. 5 9 (1937) 2574. (CR in own
air.)
vapour.) 57.
J . Livingston, R. Morgan a n d W.V. Evans, J. Am Chem Soc. 3 9 (1917) 2 1 5 1 . (DW)
58.
S.A. Mumford, J.W. Phillips, J. Chem Soc. (1950) 75. (MBP)
59.
F.H. Getman, Rec. Trav. Chim. Pays Bas 5 5 (1936) 2 3 1 . (CR in air.)
60.
P. Walden, Z Physik. Chem 7 5 (1911) 555. (CR in air.)
61.
R.B. Badachhape, M.K. Gharpurey a n d A.B. Biswas, J. Chem. Eng. Data 1 0 (1965) 143. (CR in air.)
62.
R.E. Donaldson, O.R. Quayle, J. Am Chem Soc. 7 2 (1950) 3 5 . (MBP in air.)
63.
S. Sugden, J. Chem Soc. 125 (1924) 1167. (MBP in air.)
64.
C.A. Buehler, J.H. Wood, D.C. Hull a n d E.E. Erwin, J. Am. Chem. Soc. 5 4 (1932)2398. (MBP in air.)
65.
J . Bolle, P.A. Goye, J. Chim Phys. 3 (1905) 38. (CR)
66.
N.V. Sigwick, N.S. Bayliss, J. Chem Soc. (1930) 2027. (CR)
67.
C.A. Buehler, T.S. Gardner a n d M.L. Clemens, J. Org. Chem
2 (1937) 167.
(MBP) 68.
W. Hiickel, W. Jahnentz, Chem Ber. 8 1 (1948) 7 1 . (MBP)
69.
J.T. Hewitt, T.F. Winmill, J. Chem Soc. 9 1 (1907) 4 4 1 . (CR)
70.
W. Hiickel, W. Rothkegel, Chem Ber. 8 1 (1948) 7 1 . (CR)
71.
R.V. Helm, W.J. Lanum, G.L. Cook, J . S . Ball, J. Phys. Chem. 6 2 (1958) 8 5 8 . (MBP in air.)
72.
W. Hiickel, C M . Salinger, Chem Ber. 7 7 (1944) 810.
73.
M.J, Timmermans, M. Hennant-Roland, J. Chim. Phys. 3 4 (1937) 6 9 3 . (DW,
74.
K.C. Nadler, J.A. Zollweg, W.B. Streett, LA. McLure, J. Colloid Interface
75.
F.B. Sprow, J.M. Prausnitz, Trans. Faraday Soc. 6 2 (1966) 1105. (CR.)
76.
J.C.G. Calado, A.F.S. Mendonga, B.V. Saramago, V.A.M. Soares, J. Colloid
CR) Set
122 (1988) 530 (CR.)
Interface Set 189 (1997) 273. (CR) 77.
B.S. Almeida, V.A.M. Soares, LA. McLure, J.C.G. Calado, J. Chem.
Soc,
Faraday Trans. (I) 8 5 (1989) 1217. (CR) 78.
D. P a p a i o a n n o u , A. Magopoulou, M. Talilidou, C. Panayiotou, J .
Colloid
Interface Set 1 5 6 (1993) 52. (CR) 79.
D. Papaioannou, C. Panayiotou, J. Colloid Interface Sci. 1 3 0 (1989) 4 3 2 . (CR)
80.
R.L. Schmidt, H. Lawrence Clever. J. Colloid Interface Set 2 6 (1968) 19. (MBP)
A1.48 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92.
H.H. King, J.L. Hall, G.C. Ware, J. Amer. Chem. Soc. 52 (1930) 5128. (CR in NH3.) O. Maass. W.H. Hatcher, J. Amer. Chem. Soc.,42 (1920) 2548. (CR) L. Sabinina, L. Terpugow, Z Phys, Chem. Abt A. 173 (1935) 237. (CR) N.B. Baker, E.C. Gilbert, J. Amer. Chem. Soc. 62 (1940) 2479. (CR in H2.) CM. Kinart, W.J. Kinart, A. Bald, A. Szejgis, Phys. Chem. Liq. 30 (1995) 151. (DW) G. Vazquez, E. Alvarez, J.M. Navaza, J. Chem. Eng. Data 40 (1995) 611. B. Hawrylak, S. Andrecyk, C.E. Gabriel, K. Gracie. R. Palepu, J. Solution Chem. 27 (1998) 827. (DM). E.H.M. Wright, B.A. Akhtar, J. Chem. Soc. B (1970) 151. (CR in air.) H. Hartley, N.G. Thomas. M.P. Applebey, J. Chem. Soc. 93 (1908) 538. (MBP) J. Levingston, R. Morgan, C.E. Davis, J. Amer. Chem. Soc. 38 (1916) 555. (DW) A.L. Vierk, Z. Anorg. Chem. 261 (1950) 283. (MBP) J. Glinsky, G. Chavepeyer, J.K. Platten, J. Chem. Phys. 104 (1996) 8816. (DM)
A2.1 APPENDIX
2
a. Integral characteristic functions of flat interfaces LT^ = TS^ + yA + ^
^^n^
[A2.1]
H^ = TS^ + ^
^^n^ = 17° - /A
[A2.2J
F"" =yA-\-'^
li^n^ = U^ -
G° ^ ^
TO^
jLLji^ = H° - TS° = F° - /A
12° = F° - ^ ^ /z^n^ = yA
[A2.31 [A2.4] [A2.51
b. Differential characteristic functions of flat interfaces dLr° = TdS° + ydA + ^
//.dn°
[A2.6]
dH° = TdS° - Ady + ^
/x^da°
[A2.7]
dF° = -SdT° + ydA + ] £ //^dn°
IA2.81
dG° = -SdT° - Ad/ + ] £ A/idn°
[A2.91
dr2°=-S°dT + y d A - ^ /i^dn^
[A2.10]
All functions have been derived on the basis of the Gibbs convention (V° = 0), except for 12° which is invariant with respect to the position of the dividing plane.
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APPENDIX 3 Some principles of variational calculus Functioncds are functions of functions. In this Volume we met functionads in van der Wacds' theory for the interfacial tension (sec. 2.5a) and in the mean field theory for the surface pressure of polymeric monolayers (sec. 3.4e). In these two cases equations were derived in which the excess interfacial Helmholtz energy had to be minimized as a function of a density distribution across the interface and of the spatial derivative of this profile [density Junctionals). The technique of finding the function that minimizes the Helmholtz energy is called variational calculus, or calculus of variations. The problem also occurs in other places in physics. One example is finding the energetically most favourable path that a moving object follows to get from one point to another under the influence of (conservative) external variables. An example from surface science is to find the spatial equilibrium shape of fluid interfaces under the constraint that the interface is fixed at its extremities.
Figure A3.1. Variations of density distributions. Variational calculus is an extension of common calculus. In the latter, the minimum of a function of a variable is found by setting the derivative with respect to that variable equal to zero. In Vciriationad calculus this should in principle be done by searching through the full set of functions, consistent with the boundary conditions, and look for that function which minimizes the functional. This procedure is virtually impossible. Fortunately, there are some general principles that C2in be applied to simplify the issue. We shall now discuss some of these, taking
A3.2 the density gradient across an interface as the function to be minimized. Figure A3.1 is a sketch of the basic issue. Consider the density p{z], changing from p^ for z < Zj, to p^ for z> z . Numerous distributions can be drawn, each satisfying these boundary conditions and ^2
\ p*(z)dz = const.
[A3.11
Two of these are sketched in the figure. Let curve p{z) be the 'right' solution, i.e. the density profile for which the Helmholtz energy per unit area F is a minimum. Curve p * (z) is one of the many 'wrong' ones, satisfying the boundary conditions, but not minimizing F . The difference between the two is called ri(z]. We note that r]{z) = 0 for z< z^ and z> z , One can define a family of functions by multiplying ri(z) by the scalar a, all obeying the boundary conditions. We relate the set of 'wrong' curves to the correct one by writing p * (z, a) = p(z) + aT](z)
[A3.21
Now let, quite generally, the Helmholtz energy F be a function of p * (z, a) and p*' (z, a) = dp* (z, a) I dz only, and let p * (z, a] and p*' (z, a) be independent: P^ = \
f[p*(z^(x).p*'(z.a))dz
[A3.3]
Now the problem is to find the optimum. By analogy to common calculus we achieve this by setting dF \ =0 da a=0
[A3.41
The derivative should be taken for a = 0 because only in that case is p * (z) = p[z).
OF \ da
/a=0
-i
z,
M. dp*(z,a) ^
ap*(2,a) , da
a/
ap*'(z,a)
dp*'{z,a)
da
From [A3.21 it follows that dp*{z,a]/da Hence, [A3.5] reduces to
a/ V
/a=0
dp * (z, a)
T](Z) +
M
dz
[A3.5]
= r]{z] and dp*'(z.a)/da = d7]{z)/dz.
^i^z) dz
dp*' (z, a)
dz
[A3.61
Now the goal is to rewrite the second term such that one gets something proportional to T](Z). Such simplification is realized by integration by parts. In
A3.3 doing so, the integrated part vemishes because of the fixed boundary conditions. The result is an equation where rjiz) can be taken out of the brackets:
A
(dF a.
da
df
d
M 3p*(z.of)
dz
dp*'{z,a]
r](z)dz
[A3.7]
The second term between the squcire brackets contains straight d's. Now we use the condition that a = 0 in the term between square brackets on the r.h.s. As this situation refers to the 'true' profile we may replace p * and p*' by p and p', respectively. So our condition for the 'true' function becomes
dp{z)
dz 3p'(z)
kz)dz = 0
[A3.81
This condition must be met for any arbitrary function rjiz) and the only way to satisfy it is that the terms in the square brackets vanishes: ^ ^ dp{z)
^ dx
^-^ = 0 dp'iz)
IA3.91
This equation is an example of what is known as the Euler-Lagrange
equation.
Various forms of it are known, depending on the nature of the function / . For instance, there may be more variables. Under certain conditions it can be integrated. Equation [A3.9] represents an extremum for F . Mostly, physical conditions will determine whether this extremum is a minimum (as in our case) or a maximum. If we now look back at van der Waads' treatment, sec. 2.5, several steps can be recognized. In a sense he anticipated the present method. His function to be minimized is [2.5.19]; he eliminated boundary condition [A1.3] by working grsuid canonically and [2.5.25] is his Euler-Lagrange equation. From this, F could be written as [2.5.30]!).
!^ For further reading, see Density Functionals: Theory and Application s. D. Joubert, Ed., Springer 1998. G. Arfken, Mathematical Methods for Physicists, Acad. Press, 3rd ed. (1985). For a very readable introduction by Richard Feynman, see The Principle of Least Action, in, R.P. Feynman, R.B. Leighton and M. Sands, The Feynman Lectures on Physics. Addlson-Wesley (1966). Vol. II chapter 19. The book by H.T. Davis, Statistical Mechanics of Phases, Interfaces and Thin Films, Wiley (1996), contains a chapter (9) on this matter.
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APPENDIX 4 Contact angles This appendix contains tabulations of contact angles of liquids on solids. These data have been collected, starting from a systematic literature review, covering Chem. Abstr., J. Colloid Interface Set, Colloids Surf., Langmuir and Adv. Colloid Interface Set on the basis of key words, where available. In places the data have been extended by additional entrees, without attempting to achieve completeness. In order to keep the contents within acceptable bounds, only data for pure liquids are tabulated for surfaces without intentioucdly applied adsorbates (like deposited or adsorbed surfactant monolayers). Moreover, we have restricted ourselves to water and a few other familisu- liquids. We also excluded biological surfaces. The main purpose is to give an impression of (orders of) magnitude and the extent of (dis-)agreement between different sources. Many of the disparities find their origin in different (pre-)treatments of the solid and the liquid. We found it virtually next to impossible to Judge the quality of the data because many significant pieces of information were found lacking even in, otherwise trustworthy, papers. So the collected data are not claiimed to be critically selected. However, some important pieces of information on methods and pre-treatment are included in the references. a. Contact angles on metals These data can be found in table A4.1. Tabel A4.1 Contact angles of several liquids on metals. Abbreviations: a = advamcing angle; r = receding angle; a-BN = alpha-bromonaphthalene; DIM = diiodomethane or methylene iodide. In the references methodical information can be found and there the meaming of 'other (liquid)' will also be explained. Contact angle of Water
Metal a Stainless steel
a-BN
r
a
0 0 59 42 0 71-72 71 74-76 74 8 8 5 0
0
r
Formamide
DIM a 29
r
a
r
r
a
15
22
33-36 27-30
Other
Glycerol a
24
41-44 37-42
70-75 70-74
81-86 80-81
45-48 41-45
Ref.
r 1 2 3 4 5 6a 6b 6c 6d 7a 7b 8a 8b
A4.2 Table A 4 . 1 c o n t . Contact angle of a
TitEinium
67-77 66-71 68-73 54-59 49-52 67-73 33-40 36-42
Nickel
6 7 83
Copper
Aluminium
a-BN
Water
Metal
90 7 10 0 12 18 29 54 72 90
r
a
r
Silver
Gold
30-40 50-60 66
r
a
r
Other
Glycerol a
r
a
33-35 38-42 35-40 27-30 27-29 32-36
6 3 22
16 12 25
27 32
<5 32
13 39
8 4
deer.
7 5 20 29 33 31 20 80 10 0 31 0 29 23 28 0 0
Formamide
DIM a
8 7 0
0 0 0 0 0
Ref.
r 9 10a 10b 10c lOd lOe 11a lib 7a 7b 3 12a 12b 13 7a 7b 14 29a 29b 29c 29d 29e 15a 15b 12a 12b 7a 7b 16a 16b 16c 16d 16 17 18 14 19a 19b 19c 19d 19e 20 21a 21b 21c 17
A4.3 Table A 4 . 1 c o n t . Contact angle of Water
Metal a
r
Gold
a-BN a <5 18
7
r
r
a
r
Other
Glycerol
Formamide
DIM a
a
r
14 22
a 11
0
60-65 61
55-65 Platinum
0 73 40
10
55-62 0 Germanium 0 0
30 <5 30
11
10 37
Cesium
12 32
Ref.
r 12a 12b 18 22 23 24 25 26 17 27 20 1 5 12a 12b 28
References (Abbreviations: CB = captive bubble; TP = tilting plate; WP = Wilhelmy plate; SD = sessile drop; DCA = dynamic contact angle; AFM = atomic force microscopy.) 1.
R.P. Schneider, J. Colloid Interface Set 182 (1996) 204: SD, steel surface, fine-
2.
J. Davies, C.S. Nunnerley, A.C. Brisley, J.C. Edwards and S.D. Finlayson, J. Colloid
polished and cleaned with surfactamt followed by glow dischairge. Interface Set 182 (1996) 437: DCA, cleaning with detergent solution followed by rinsing with water and dried under a Ng stream. 3.
M.A. Assanta, D. Roy and D. Monpetit, J. Food Protection 6 1 (1998) 1321: SD, other liquid = DMSO .
4.
F.W. Hyde. M. Alberg and K. Smith, J. Ind. Microbiology and Biotechnol 19 (1997) 142: SD, 316L steel, surface roughness cinalysis through AFM.
5.
R.P. Schneider, K.C. Marshall, Colloids Surf B2 (1994) 387: SD, cleaning with 10%
6.
D.J. Ryley, B.H. Khoshaim, J. Colloid Interface Set 59 (1977) 243: carbon steel, test
SDS prior to treatment with boiling water and glow discharge. of droplet contour profile analysis; (a) SD, surface finish: 180 grade of carborundum grinding powder; (b) TP, surface finish: ibid, (a): (c) SD, surface finish: 600 grade of carborundum grinding powder: (d) TP, surface finish: ibid. (c). 7.
D.J. Trevoy, H. Johnson, J. Phys. Chem. 6 2 (1958) 833: (a) CB, steel surface, polished £ind cleaned with oxidizing agent. Organic contamincints virtually absent, (b) SD.
8.
M.Mantel, Y.I. Rabinovich, J.P. Wightman and R.-H. Yoon, J. Colloid Interface Set 170 (1995) 203: SD, 304 steel, ESCA surface analysis, cleaning by argon plasma treat-
A4.4
merit, (a) a s received, d a t a affected by organic contamination: (b) water-cleaned; other liquid: DMSO. 9.
A.P.V. Serro, A.C. F e m a n d e s a n d B. de J . V. Saramago, Colloids Surf. A 1 2 5 (1997) 2 0 9 : SD.
10. D.V. Kilpadi, J . J . Weimar a n d J . E . Lemons, Colloids
Surf. A 1 3 5 (1998) 8 9 : SD,
surface r o u g h n e s s analysis via AFM a n d mechanical profile method: (a) air-dried, (b) passivated in 3 0 % (by volume) nitric acid for 2 0 m i n . a t room t e m p e r a t u r e ; (c) ibid, heat-sterilized, ibid, (d) re-sterilized, ibid, (e), heat-sterilized. 1 1 . D . E . M a c d o n a l d , B. Markovic, M. Allen, P. S o m a s u n d a r a n a n d A.L. Boskey, J . Biomedical
Materials
Res. 4 1 (1998) 120: surface r o u g h n e s s analysis via AFM: (a)
highly polished, (b) commercial sample. 12. M.K. B e m e t t , W.A. Zisman, J . Colloid Interface
Set 2 8 (1968) 2 4 3 : mirror-polished,
cubic face-centered, grease-free p u r e metal, SD: (a) 2 h r s . a t 0.6% relative humidity, (b) ibid, a t 9 5 % relative humidity; other liquid, a l p h a dibromobenzene. 1 3 . S h i h Pin Liaw, Ta-tiung
Hsueh
Pao 1 9 (1989) 1 (as quoted in Chem.
Abstr.
113
(1990) # 10567): mirror-polished clean surface. 14. M.E. S c h r a d e r . J . Phys. Chem, 7 8 (1974) 8 7 : SD, UHV-evaporated copper a n d silver films, oxygen-free water droplets. 15. J . D . B e m a d i n , I. Mudawar, C.B. Walsh a n d E.I. Frances, Int. J. Heat Mass
Transfer
4 0 (1997) 1017: SD in p r e s s u r e vessel, s t a n d a r d polishing: (a) 2 5 -120°C, (b) 120 170°C. 16. Lai-Kwan C h a u , M.D. Porter, J . Colloid Interface Set 1 4 5 (1991) 2 8 3 : SD. i.e.p. a t pH = 10.4: (a) pH = 8.0, (b) pH = 9.2, (c) pH = 9.9, (d) pH = 11.1. (e) pH = 12.0. 17. A.C. Zettlemoyer, J . Colloid Interface
Set 2 8 (1968) 3 4 3 . d a t a a s quoted by: R.A. E r b ,
J. Phys. Chem. 6 9 (1965) 1307: n o organic contamination. 18. F.E. Bartell, J . T . Smith, J . Phys. Chem
5 7 (1953) 165: v a c u u m - e v a c u a t e d , deposited
metal film, c o n t a c t angle d e t e r m i n a t i o n in evaporated water a t m o s p h e r e . Surfaces w e r e p r e p a r e d by e v a p o r a t i n g t h e m e t a l onto a g l a s s s u r f a c e in a n e v a c u a t e d c h a m b e r , c o n t a c t angle of water drops on t h e metal surfaces were determined in a water v a p o u r a t m o s p h e r e a t 25°C. 19. M.E. S c h r a d e r , J . Phys. Chem
7 4 (1970) 2 3 1 3 : SD, d i a m o n d powder-polished gold
disk, purity: 99.999+%: (a) gold disk in UHV, 560°, 2 h . (b) UHV-evaporated gold film, (c) gold disk in conventional v a c u u m , 100°. 3 h , (d) ibid, (c) 600°. 1.5 h . (e) ibid, (c) 700°, 2 h. 2 0 . K.W. Bewig. W.A. Zisman, J . Phys.
Chem
6 9 (1965) 4 2 3 8 : SD, polished gold a n d
platinum, white-hot heating in s t r e a m of high purity hydrogen. 2 1 . T. S m i t h , J . Colloid Interface
Set 7 5 (1980) 5 1 : SD, UHV-evaporated gold film on
glass: (a) exposure time to air: 0 m i n / s u r f a c e clean a t atomic level, (b) exposure time, 10 m i n , (c) exposure time, 9 0 min. 2 2 . R.A. E r b , J . Phys. surfaces.
Chem
7 2 (1968) 2 4 1 2 : s u m m a r y of d a t a on clean s m o o t h gold
A4.5 23. J.N. Plaksin, S.V. Bessonov, Dokl Akad. Nauk SSSR. 6 1 (1948) 865: clean smooth gold surface in oxygen and nitrogen. 24. M.L. White, J. Drobek, J. Phys. Chem. 70 (1966) 3432: vacuum-evaporated gold film on silica, consecutively polished with diamond abrasive and fired in oxygen. 25. M.E. Schrader, J. Colloid Interface Set 100 (1984) 372: SD, UHV-evaporated gold film, oxygen-free. 26. L.S. Penn, B. Miller, J. Colloid Interface Set 77 (1980) 574: steady state wetting data WB, solid rod-like specimen. 27. L.C. Krebs, Takanobu Ishida, Energy Res. Abstr. 17 (1992) # 9683 (quoted in CA 118 (1993) # 201151): oxide-free platinum. 28. D. Ross. J.E. Rutledge and P. Taborek. Science 278 (1997) 664. 29. A.P. Boyes. A.B. Ponter, Cheuh Eng. Techn. 45 (1973) 1250: polished with diamond paste, degreased in mild detergent, rinsed with ethanol and distilled water (as quoted by
J.D. Bemadin, I. Mudawar cind C.B. Walsh, E.I. Frances, Int. J. Heat Mass
Transfer 40 (1997) 1017: (a) 20.0°C, (b) 61.5°C, (c) 76.5°C, (d) 93.5°C, (e) 100.8°C. b, Cont€ict angles
on
polymers
See table A4.2. Abbreviations etc. a s in table A 4 . 1 ; PTFE = poly(tetrafluorethylene) or Teflon. Table A 4 . 2 Contact angles of several liquids on polymers. Abbreviations: a = advancing angle; r = receding angle; a-BN = alpha-bromonaphthalene; DIM = diiodomethane or methylene iodide. In the references methodical information c a n be found a n d there the meaning of other (liquid)' will also be explained. Contact angle of Polymers Water a Poly (propylene)
PTFE
100 110 99 104 101 9397 104 95 105 50 107 98 99 125 111 126 127
a-BN r
a
DIM r
46
a
r
56
Formamide Glycerol a
r
a
r
Other a
Refs. r 1 2 3a 3b 4 5
86
81 73 74 8692 74
6 88 71 73 93 91 97 98
45
31
64
54
51 49
77
56
102
78
68
97
56
65 42
54 27
69
71
82
90
75
6 7 8a 8b 8c 9a 9b 2 6 9a 9b
A4.6 Table A 4 . 2 cont. Contact angle of Polymers Water
PTFE (cont.)
a-BN
a
r
100 120 109 97 121124 106112 118125 120123 120123 112 108 107108 107109 108 167 108 124 118 9092 96 109 52 35 103107 115 117 109 111 114 108 108 102106 100 91 84
90 90 106 93 99101
a
DIM r
a
r
Formamlde Glycerol a
92
8186
r
88
a
101
95102
r
96
Other a
Refs. r
86
82
8486 8591
6870
11 12 13a 13b 14, 57 15 16a 16b 16c
88
17 18 19a
88
19b
64
83
73 87
88
92
100
18
90 131
32
21a 21b 7 20a 20b 22a 22b 23a 23b 23c 24
93 16 0 99103 98 93 89 66 73
72 83 88 77
25 26 27 28 29 30a 30b 31 32a 32b 32c
A4.7 Table A 4 . 2 c o n t . Polymers Water PTFE (cont.)
Contact single of Formamide Glycerol
a-BN
DIM
a
r
a
r
112 112
106
85 76 72
75
114118 99- 67104 72 |Poly101 (ethylene) 1 1 0 9093
91
r
a
r
Other a
Refs. r 58 41 47
87
105
7278
9091
8082
49 3a 3b 34a
35
53
77
5258
34b 13 15
79
9094
7883
7 35a 35b 24 25 36a 36b 36c 37 60a 60b 60c 60d 8a 8b 8c 28 38 19a
47 39 67
85
52
56
45 46
58 37
20 41
53
5152
19b 30a 30b 31 29 9a 9b 41 47
52 52 53 41
53
33 15
46
81 87
107111 101- 57103 61 94
a
9496
96103
94 94 104 87 96 110 111 95
85
r
59 82
55 102
94 96 74 88 104 94 104 116 107 86 28 30 30 99 62 63 96 88 94
a
81
8890 35
52
77
69
83
79
5356
6365
3437
49 59
A4.8
Table A4.2 cont. Contact angle of Polymers Water
Poly (styrene)
PMMA
a-BN
DIM
a
r
a
r
98101 88 91
8792
2630
9 - 1 2 1518
84 86 92 98 91 80 81 85 92 90 92 91 84 83 82 77 85 33 8286 8587 74 85 60 72 80 73 7678 74 75 95 95 6569 95 80 74 70
15
46 59
37 15
0
a
Formamide Glycerol
r
a
r
812
7780
7035
a
35
74
80
37
69
71
45 35
6
88 74
r
Other r
7880
6874
60 63
40
Refs.
a
24
73 80
67 63 65 35 78 77 76 71 40 30 10
39 40 13, 43 41 42 6 25 43 44a 44b 44c 39a 39b 39c 30a 45a 45b 45c 45d 46a 46b 47 57
6266 42
58
67
30 40 41 42
51 53 64 58
60 66 69
30 18 13 16 4749
0 11
34
49 65 62
65 18
37
57
67
52
48 49 50a 50b 13 1 14 41 17 51a 51b 33 51c 7 28 44a
A4.9 Table A 4 . 2 c o n t . Contact angle of Polymers Water a PMMA (cont.)
Nylon
PET
70 68 7274 74 80 7781 7779 74 67 71 72 64 75 73 70 70 60 53 60 70 72 70 81 81 61 70 71 67 75 65 7377 79 77 69 65 81 76 77 82 83 79
a-BN r
a
DIM r
9-10
a
r
Formamide Glycerol a
r
a
r
Other a
Refs. r 44b 44c 29
3b37 45 41
52 30a 47
14 4951 67
41
57 34
36 11 23 16 16
28
21
46 37 44 41 41
24
55 60 51
65 65 26
50
60
48
57
51 53 0
41 28 28 36
66
37 9
29 25
34
2629 48
62 23
41
23
38 24 41
46 51 62
68
15
58 36a 36b 36c 50 41 6 53 43 44a 44b 44c 30a 30b 31 9a 9b 54a 54b 54c 54d 58 41 14 55 28 44a 44b 30a 34b 29 9a 9b 56
A4.10 Table A 4 . 2 c o n t . Contact angle of Polymers Water a PVC
87 90
Polycarbonate
a-BN r
a
50
11 28
DIM r
a
22
36 50
8386
1820
4042
87 83 66
16
36 40
Formamide Glycerol
r
a
r
16
66 58
17
a
r
Other
Refs.
a
r
58
23
67
55
69
50
59
13 6 29 30a 41 6
References Abbreviations as in the references to table A4.1. R.P. Schneider, J. Colloid Interface Set 182 (1996) 204: SD, surfaces polished to a roughness below 0.1 micron. J. Davies, C.S. Nunnerley, A.C. Brisley, J.C. Edwards and S.D. Finlayson, J. Colloid Interface Set 182 (1996) 437, DCA, cleaning with detergent solution followed by rinsing with water eind dried under a Ng stream. 3.
C.W. Extrand, Y. Kamagai, J. Colloid Interface Set 184 (1996) 191: (a) as quoted by O.N. Tretinnikov and Y. Ikoda, Langmuir 10 (1994) 1606, (b) as quoted by L.S. Penn, B. Miller, J. Colloid Interface Set 78 (1980) 238.
4
F.W. Hyde, M. Alberg and K. Smith, J. Ind. Microbiol Biotechnol 19 (1997) 142: SD. surface roughness analysis through AFM surface; roughness pairameter (algebraic average) = 16.19 nm.
5.
M. Morra, E. Occhiella and F. Garbassi, J. Colloid Interface Set 132 (1989) 504: SD using de-ionized, bi-distilled water, untreated poly(propylene). L.S. Penn, B. Miller J. Colloid Interface Set 78 (1980) 238: WB, using single polypropylene filament probe; other liquid, ethylene glycol. A.C. Zettlemoyer, J. Colloid Interface Set 28 (1968) 343: review, also contains data for PTFE. PP. PE and PMMA.
8.
G. Xiao, J. Colloid Interface Set 171 (1995) 200: SD, enclosed chamber, triply distilled water; other liquid = DMSO: (a) untreated surface, (b) corona dischargetreated surface, followed by dipping in water, (c) same as (b) but untreated.
9.
Y. Ikoda. O.N. Tretinnikov. Langmuir
10 (1994) 1606. Modified WP: (a) single
sample-hole boundary, (b) both boundciries employed. 10. L.S. Penn, B. Miller J. Colloid Interface Set 78 (1980) 238: WB using single filament probe, PTFE. 11. T. Yasuda, T. Okuno and H. Yasuda, Langmuir 10 (1994) 2435: SD, drop volume: 5 . 1 - 2 1 . 6 microliter. 12. I. Noh, S.L. Goodman and J.A. Hubbell, J. Biol Set, Pol Ed., 9 (1998) 407: WP,
A4.11 using DCA, including ESCA surface characterization. 13. Souhang Wu, Polymer Interface and Adhesion, Marcel Dekker, New York, 1982, p. 142 - 146; other liquid = ethylene glycol: (a) 20°C, (b) 120°C. 14. C.W. Extrand, Y. Kumagai, J. Colloid Interface Set 170 (1995) 515: TP, average surface roughness, surface roughness parameter, determined by AFM, 207 nm, all polymers wiped with methanol before use, other liquid = ethylene glycol. 15. J. Drelich, J.D. Miller, J. Colloid Interface Set 167 (1994) 217: polymer plates, other liquid is ethylene glycol. 16. A.S. Dimitrov, P.A. Kralchvsky, A.D. Nikolov, Hideaki Nashi and Mutsuo Matsumoto, J. Colloid Interface Set 145 (1991) 279: SD, droplet height (h) and radius (a) ± 20 micron: (a) h = 945 micron, a = 638 micron, (b) h = 1613 micron, a = 1140 micron, (c) h =1925 micron, a = 1412 micron. 17. J.O. Hansen, R.G. Copperthwaite, T.E. Deny and J.M. Pratt, J. Colloid Interface Set 130 (1989) 347: WP, effect of surface roughness studied. 18. W.A. Zisman, Adv. Chem. Ser. 43 (1964) 1. Review. 19. P.M. Fowkes, D.C. McCarthy and M.A. Mostafa. J. Colloid Interface Set 78 (1980) 200: data show zero spreading pressure: (a) water droplet in water vapour, DIM droplet in DIM vapour, (b) water droplet in water vapour plus added DIM, DIM droplet in DIM vapour plus added water. 20. A.B. Ponter, M. Yekta-Fard, J. Colloid Interface Set 101 (1984) 282: SD in nitrogen saturated with water vapour: (a) commercial grade PTFE, (b) pressed at 200°F, 1400 psig. 2 1 . N.R. Morrow, Mai Dong Nguyen, J. Colloid Interface Set 89 (1982) 523: capillary rise, other liquid = ethylene glycol: (a) smooth surface, intrinsic data without hysteresis taken from K.W. Fox, W.A. Zisman, J. Colloid Set 5 (1950) 514, (b) rough surface; (in both cases) other liquid, ethylene glycol. 22. D.J. Ffyley, B. H. Khoshaim, J. Colloid Interface Set 59 (1977) 243: SD using droplet profile and droplet volume data: (a) clean surface, authors method: droplet volume ranging from 6.75 - 27.0 mm^ (b) TP. 23. D.W. Dwight, W.M. Riggs, J. Colloid Interface Set 47 (1974) 650: (a) control, (b) Na/NHg sodium-etched surface, (c) melted polymer recrystallized against a gold substrate.. 24. J.T. Kenney, W.P. Townsend and J.A. Emerson, J. Colloid Interface Set 4 2 (1973) 589: untreated PE/PTFE, surface cleaned with water, methanol and Freon TF. 25. D. Bargeman, J. Colloid Interface Set 4 0 (1972) 344: SD, PTFE and PE sheets extracted for 2 hrs with ethanol and dried under vacuum, PS-film rinsed with ethanol and bi-distilled water. 26. H.L. Rosano, W. Gerbacia, M.E. Feinstein and J.W. Swaine, J. Colloid Interface Set 36 (1971) 298: WP. 27. H. Kamusewitz, W. Possart, Int. J. Adhes. 5 (1985) 211. WP.
A4.12
2 8 . B. J a n c z u k , T. Bialopiotrowicz. J. Colloid Interface Set 1 4 0 (1990) 3 6 2 : SD; d a t a from J. Colloid Interface Set 1 2 7 (1980) 189. 2 9 . Y. T a m a i , T. M a t s u n a g a a n d K. Horluchl, J . Colloid Interface
Set 6 0 (1977)
112:
comparison with d a t a obtained with two-liquid contact angle method. 3 0 . D.K. O w e n s , R.C. Wendt, J. Appl
Polym. Set
1 3 (1969) 1 7 4 1 . (a) d a t a from E.G.
Shafrin, W.A. Zisman, N.R.L. Report 5985 (1963); u p p e r limits for t h e contact angles of liquids on solids, (b) a u t h o r ' s data. 3 1 . J.K. Spelt, Colloids Surf 4 3 (1990) 389; method used: SD. 3 2 . R.F. Mangel, E. Baer, Chem. Eng. Set
1 7 (1962) 7 0 5 : SD u p o n evaporation u n d e r
c o n s t a n t humidity: (a) time = 0, (b) time 40 - 160 min. 3 3 . J . D . A n d r a d e , S.M. Ma, R.N. King a n d D.E. Gregonis, J . Colloid Interface
Set
72
(1979) 4 8 8 . Method u s e d CB. 3 4 . J . Drelich, J . D . Miller a n d J . H u p k a , J. Colloid Interface
Set 1 5 5 (1993) 3 7 9 : SD,
static data, compared with dynamic contact angle values: (a) drop size > 2 microlitre, (b) d r o p size = 0.024 microlitre. 3 5 . A. Baszkin, L. Ter-Minassian-Saraga, J. Colloid Interface
Set 4 3 (1973) 190: SD, low
density poly (ethylene), water tridistilled from p e r m a n g a n a t e solution in all Pyrex glass a p p a r a t u s : (a) non-oxidized, (b) oxidized in a 9.09% KClOs-containing solution. 3 6 . W.J. Herzberg, I.E. Marian, J . Colloid Interface
Set 3 3 (1970) 1 6 1 : SD: (a) 5 micro
litre, (b) 10 microlitre, (c) 3 5 microlitre. 3 7 . F.M. Fowkes, J. Adhesion
Set Techn. 1 (1987) 7: other liquid = DMSO; method u s e d ,
SD. 3 8 . P. Hu, A.W. A d a m s o n , J . Colloid Interface
Set 5 9 (1977) 6 0 5 : m e n i s c u s h e i g h t
method on a vertical plate. 3 9 . B. Bouali, F. G a n a c h a u d , J . P . Chapel, C. Pichot a n d P. Lanteri, J . Colloid
Interface
Set 2 0 8 (1998) 8 1 : SD, other liquid = ethylene glycol. 4 0 . A. Nakao, Y. Suzuki a n d M. Iwaki, J. Colloid Interface
Set 1 9 7 (1998) 2 5 7 : SD, re-
distilled w a t e r , u n t r e a t e d surface before N e - b o m b a r d m e n t or Na i m p l e m e n t a t i o n whereby the contact angle gradually decreases. 4 1 . J.R. D a n n , J . Colloid Interface
Set 3 2 (1970) 3 0 2 : other liquid = ethylene glycol: (a)
Nylon 11, (b) Nylon 6,6. 4 2 . L.S. Penn, B. Miller, J. Colloid Interface
Set 7 7 (1980) 5 7 4 : WP u s i n g solid rod-like
specimen. 4 3 . A.M. Ellison, W.A. Zisman, J. Phys. Chem. 5 8 (1954) 5 0 3 : SD, polymers cleaned with Tide detergent solution, thoroughly rinsed with water, a n d finally dried in air a t 75°C. 4 4 . Y. Uyama, H. Inone, K. Ito, A. Kishida a n d Y. Ikada, J . Colloid Interface
Set
141
(1991) 2 7 5 : SD- a n d WP (data in table estimated from graphical presentation): (a) WP, (b) SD-telescope method, (c) SD-laser b e a m method. 4 5 . Z. Haq, J . Mingins, Polymer
Comm. 2 5 (1984) 269; SD, polymer films c a s t a g a i n s t
PTFE a n d glass, (a) 'top' surface not in contact with s u b s t r a t e PTFE, (b) ibid, (a) not in
A4.13 contact with glass, (c) 'bottom' surface cast against PTFE, (d) ibid, (c) cast against glass. 46. K. Esumi, K. Meguro, A.M. Schwartz cind A.C. Zettlemoyer. Bull CherrL Soc. Japan. 55 (1982) 1649, SD (a) untreated, (b) surface treated with ultraviolet radiation for 60 min in air. 47. H.J. Busscher, A.W.J, van Pelt, H.P. de Jong and J. Arends, J. Colloid Interface Set 9 5 (1983) 23: SD. 48. D.Y. Kwok, A. Leung, C.N.C. Lam, A. Li, R. Wu and A.W. Neumann, J. Colloid Interface Set 206 (1998) 44: DCA, mean values for rates between 0.260 - 0.730 mm/min. 49. C.W. Extrand, A.N. Gent, J. Colloid Interface Set 138 (1990) 431: spinning platter method, establishing the critical rotational speed for droplet movement, giving critical advancing and receding angles, other liquid = ethylene glycol. 50. C.J. van Oss, Interfacial Forces in Aqueous Media, Marcel Dekker, Inc. New York, 1994, 104: (a) and (b), two samples of PMMA. 5 1 . H.S. van Damme, A.H. Hogt and J. Feijen, J. Colloid Interface Set 114 (1986) 167, data extrapolated from figure. 52. T.B. Lloyd, Colloids Surf A93 (1994) 25. Method not specified. 53. A.M. Schwartz, S.B. Tejada, J. Colloid Interface Set 3 8 (1972) 359: SD static, comparison with dynamic contact angle data in text; other liquids (all angles are 0) include, hexane, absolute ethanol, isopropanol. 54. J.K. Spelt, E.I. Vargha-Butler, Appt Surface Thermodynamics, Marcel Dekker (1996) A.W. Neumann, Ed., J.K. Spelt, ibid, chapter 8, 1996, 379. 55. C.W. Extrand, Y. Kumagai, J. Colloid Interface Set 170 (1995) 515: TP; other liquid, ethylene glycol. 56. D. Li, A.W. Neumann, Adv. Colloid Interface Set 39 (1992) 299. 57. R.G. Craig, G.C. Berry and F.A. Peyton, J. Phys. Chem. 6 4 (1960) 541: SD in saturated vapour of the droplet liquid. 58. A. El-Shimi, E.D. Goddard. J. Colloid Interface Set 48 (1974) 242: Nylon-U. 59. K.W. Fox, W.A. Zisman, J. Colloid Interface Set 7 (1952) 428: SD in 50% relative humidity. 60. N. Inagaki, S. Tasaka, H. Kawai and Y. Kimura. J. Adhesion Set Teehnol 4 (1990) 99: (a) untreated: (b) heat treatment in NO for 10 min, (c) ibid, in O2, (d) ibid, in N2.
c. Contact angles on oxides, minerals and metalloids See table A4.3. Abbreviations etc. as in table A4.1.
A4.14 Table A4.3 Contact angles of several liquids on oxides, minerals and metalloids. Abbreviations: a = advcincing angle; r = receding angle; a-BN = alphabromonaphthalene; DIM = diiodomethsine or methylene iodide. In the references methodical information can be found and there the meaning of 'other (liquid)' wiU also be explciined. Contact angle of Water
Solid a Silica (fused)
19 20 29 43 49
Quartz
7 31 11
r
a-BN a
Diamond
50 74 11 73 57 68 62 59 80 81 87 90 86 84 84 86 86 90 0 71-78 68-75 25 12
a 31 32 34 37 39 5 45
5 33 Galena (PbS) Silicon
r
DIM r
Formamide a
r
Other
Glycerol a
r
a
Ref.
r la lb Ic Id le 2a 2b 3a 3b 3c 14a 14b 4a 4b
30 21 15 14 11
22 37
5a 42 45 41 39 63 60 69 75 66 65 68 74 74
24-34 20-30
36
27
5b 6a 6b 6c 6d 6e 6f
6g
7a 1 7b 7c 7d 7e 7f 8a 9a 9b 10a 10b
A4.15 Tabel A 4 . 3 (cont.) Contact angle of Water
Solid
Graphite
a-BN
Formamide
DIM
a
r
a
r
a
r
a
r
93 B3 85 35 0
45
17
17
35
23
64
56
Glycerol a
r
Other a
r
57
26
Ref.
11 12a 12b 13a 13b
References Abbreviations as in the references to table A4.1. 1.
J. Rayss, A. Gorgol, W. Podkoscielny, J. Widomski and M. Cholyk, J. Adhesion Sci Technol 12 (1998) 293: SD, after controlled surface oxidation: (a) 4.60, (b) 2.35, (c) 1.50, (d) 0.70, (e) 0.40 (in GH/nm^).
2.
M.E. Schrader, J. Colloid Interface Sci. 27 (1969) 743: SD using goniometer eye
3.
V.P. Safronov, L.M. Shcherbakov, V.P. Chestyanin and P.P. Ryaizontsev, as quoted in
piece: smooth, fused silica disk: (a) in absence of water, (b) water vapour admitted. Chem. Abstr. 79 (1973) # 23823r: (a) untreated, (b) HF-treatment followed by heating at 95°C in vacuum for 4 hrs, (c) hydrated at 96-97°C for 3 hrs. 4.
C.A. Prestidge, J. Ralston, J. Colloid Interface Set 172 (1995) 302: (a) sieved 150 75 micron sized particles, (b) cyclosized particles. O.M.R. Chyan, J.J. Wu and J.J. Chen, Appl Spectroscopy 51 (1997) 1905: (a) doubly polished, (b) HF-etched. R. Vera-Graziano, S. Muhl and F. Rivera-Torres, J. Colloid Interface Set 170 (1995) 515: SD 9 microlitre droplet, polished p-type single crystal pieces of silicon, other liquid = ethylene glycol: (a) red light 640.4 nm wavelength, (b) unetched; green 536.2 nm, unetched: (c) violet 402.8 nm, unetched: (d) red light, etched; (e) green, etched: (f) violet, etched.
7.
R. Vera-Graziano, S. Muhl, F. Rivera-Torres, J. Colloid Interface Set 155 (1993) 360: SD, amorphous silicon: a-Si:H = amorphous hydrogenated silicon; ibid + oxide = containing a native oxide layer after one month storage; etching is used to remove oxide layer in a standard 'p' etch solution for 5 min followed by rinsing with triply distilled water, and drying with UHP ultra high pure nitrogen prior to contact angle measurement, (a) green light, a-Si:H, after etching; (b) red, ibid.; (c) violet, ibid.; (d) green light, a-Si:H + oxide; (e) red, ibid.; (f) violet, ibid.
8.
R. Williams, AM. Goodman, Appl Phys. Lett 25 (1974) 531: SD (a) before oxidation, (b) after oxidation till oxide layer thickness > 3 nm.
A4.16 9.
J.O. Hansen, R.G. Copperwaite, T.E. Deny and J.M. Pratt, J. Colloid Interface Set 130 (1989) 347: WP, data almost insensitive to pH from 1 to 13, hysteresis due to surface roughness: (a) polished (HI), (b) ibid. (110).
10. C.J. Hartley, H.L. Shergold, Chenh Ind. (London) 6 (1980) 224: SD (a) ordinary surface, (b) surface finish; effect of surface polishing (a) ordinary surface (b) surface finish. 11. L.S. Penn, B. Miller, J. Colloid Interface Set 7 8 (1980) 238: WP using single graphite rod probe; other liquid, ethylene glycol. 12. I. Morcos, J. Colloid Interface Set 34 (1970) 469: SD (a) cleaved, (b) pre-immersed in water for a few seconds. 13. M.E. Schrader, J. Phys. Chem. 79 (1975) 2508; SD, (0001) graphite surface: (a) evacuated to 10'^^ Torr, (b) after ion bombardment. 14. M.K. Bernett, W.A. Zisman, J. Colloid Interface Set 2 9 (1969) 413. SD, 20°C at (a) 0.6% RH; (b) 95% RH.
CUMULATIVE SUBJECT INDEX OF VOLUMES I (FUNDAMENTALS), I I (SOLID-FLUID INTERFACES) AND III (LIQUID-INTERFACES) In this index bold face print refers to chapters or sections; app., £ind fig. mecin appendix, and figure, respectively. The romcin numerals I, II and III refer to Volumes I, II and III, respectively. When a subject is referred to a chapter or section, specific pages of that chapter or section are usually not repeated. Sometimes a reference is made even though the entry is not explicitly mentioned on the page indicated. Entries in square brackets I..1 refer to equations. The following abbreviations are used: (intr.) = introduced; (def.) = definition of the entry, ff = and following page(s). Combinations are mostly listed under the main term (example: for negative adsorption, see adsorption, negative), except where only the combination as such makes sense or is commonly used (example: capillary rise). Entries with surface' are often also found under 'interface' except where one of the two is uncommon. Entries to incidentally mentioned subjects are avoided. For the spelling of non-English names, see the preface to this volume. To avoid undue expansion of this index, chemical substances are mostly grouped together; for instance, for butanol, palmitic acid, sodium dodecylsulphate, hexane and dimyristoylphosphatidylethanol amine (DMPE) look under alcohols, fatty acids, surfactant, (anionic), alkanes and lipids. absorption bands; 1.7.14 absorption coefficient; 1.7.13 absorption index; 1.7.13 absorption (of radiation); see electromagnetic radiation acceptor (in semiconductor); II.3.172ff acid rain'; II.3.166, II.3.221 acoustic waves; 1.7.44 activity coefficient; 1.2.18a, 1.2.18b, 1.3.50 of (single) ions; 1.5.1a, 1.5.1b, I.fig. 5.2 Debye-Hiickel theory; 1.5.2a, 1.5.2b activator (in flotation); III.5.97 adhesion; II.2.5, II.5.97, III.5.4, III.5.2 (see also; wetting, adhesional, work of adhesion) adhesive joints; III.5.17 adiabatic (process); 1.2.3 admittance spectrum; II.3.93, Il.fig. 3.30, II.3.97 adsorbate; I.1.17(def.), 1.3.17 ideal; 1.1.17 thickness; II.2.63, II.2.76, II.2.79 ellipsometric; 1.7.10b (see further: adsorption)
2
SUBJECT INDEX
adsorbent; I.1.18(def.) adsorption; I.1.4ff(intr.), II.chapters 1-3 and 5 and diffusion; I.6.5d, I.6.5e, II. 1.6, see adsorption, kinetics energy; I.1.19(intr.), I.3.23ff, [1.4.6.1|, II.1.22, 11.1.3c, II.1.3f, II.1.44ff, Il.l.SOff, II.3.6d-e. Il.chapter 5 for heterogeneous surface; II.1.104ff enthalpy; II. 1.3c, II. 1.3d, II.1.3f, II.2.5b, Il.figs. 2.26-28, Il.figs. 3.60-61 isosteric, ILl.3c, II.1.3d, II.1.28, Il.figs. 1.8-1.10, II.2.26, II.2.49 entropy; 1.3.30, II. 1.21, II. 1.22, II.1.3c, II. 1.29, II.1.3f, Il.fig. 1.11, II.1.43, II.1.52, Il.fig. 1.16, II.1.65 from solution; 1.2.73, 1.2.85, Il.chapter 2, Il.chapter 5 electrosorption; II.3.12 exchange nature; II.2.1 basic features; II.2.2, Il.fig. 2.1 composite nature; II.2.2,11.2.3-2.6 dilute solutions; II.2.4, II.2.7, II.5.7, II.5.8 experiments; II.2.5, II.5.6 functional; II. 1.18, II. 1.33 Gibbs energy; 1.2.74, II.1.3e, II.1.3f, II. 1.45 heat; II. 1.3c, II. 1.28, Il.fig. 1.7, Ill.fig. 4.16 (see also; enthalpy) Helmholtz energy; II. 1.21, II. 1.23 heterogeneous surfaces; II. 1.7 hysteresis; Il.fig. 1.13, II. 1.42, II. 1.82, Il.figs. 1.31-33, Il.fig. 1.35, Il.fig. 1.39, II.1.6e, II.5.26, II.5.7d kinetics; II.1.45ff, II.2.8, II.5.3c localized; I.3.5b, I.3.6d, II.1.7, 11.1.5a, 11.1.5b, II.1.5d, Il.l.Se, Il.l.Sf, Il.fig. 1.21 mobile; I.3.5d, II. 1.7, II. 1.5c partially mobile; II.1.5d, Il.l.Se, Il.fig. 1.18, Il.fig. 1.21 negative; I.1.3(intr.), 1.1.4, 1.1.5, 1.1.21, 1.2.85, 1.5.93, II.3.5b, II.3.7e, Il.fig. 3.40, II.5.20ff, II.5;3e, Il.fig. 5.9 of atoms; 1.3.5b, 1.3.5c, Il.chapter 1 of biopolymers; 1.1.2, Il.fig. 5.26b, Il.fig. 5.29 of gases cind vapours; Il.chapter 1 functional; II. 1.18, (for relation to wetting, see III.5.3b, Ill.fig. 5.16 of ions; 1.1.20, II.3.6d-e (see also; double layers, electric)
SUBJECT INDEX adsorption (continued) of polyelectroljrtes; II.5.8 charge compensation; II.5.85 chemical and electric contributions; II.5.84ff, Il.fig. 5.32;, Il.figs. 5.38-39 isotherms; Il.figs. 5.32-33, Il.figs. 5.35-40 profiles; Il.fig. 5.34 theory; II.5.5g multi-Stem layer; II.5.87 of polymers; 1.1.2, 1.1.19, 1.1.23, I.fig. 1.18, 1.1.27, 1.2.72, Il.fig. 4.42, Il.chapter 5, Il.fig. 5.1, Il.fig. 5.6 applications; II.5.9 bound fraction; II.5.18, II.5.71, Il.fig. 5.22 dispersity effects and fractionation; II.5.3d, Il.fig. 5.8, II.5.7c, Il.figs. 5.29-31 energy parameter; II.5.28 experimental techniques; II.5.6 hysteresis; II.5.26, II.5.7d isotherms; Il.figs. 5.7-8, Il.fig. 5.22, Il.figs. 5.25-28 kinetics; II.5.3c layer thickness; II.5.6b, Il.fig. 5.19, Il.figs. 5.23-25, II.5.72ff electrokinetic; II.4.128, Il.fig. 4.42, II.5.63ff ellipsometric; II.5.64ff hydrodynamic; II.5.6Iff, Il.figs. 5.24-25 steric; II.5.65ff loops; II.5.18, II.5.32, figs. II 5.19-23, II.5.70ff negative (= depletion); II.5.20, II.5.3e, Il.fig. 5.9, III.2.58 (self adsorption) profiles; II.5.18, Il.fig. 5.6, Il.fig. 5.10, II.5.40, Il.figs. 5.15-16, II.5.6c, Il.figs. 5.19-20 tails; II.5.18, II.5.32 , Il.figs. 5.19-23, II.5.70ff theory; II.5.4 diffusion equation; II.5.32 excluded volume effect; II.5.5b lattice theories; II.5.30ff Monte Carlo; II.5.30 scaling; II.5.4c Scheutjens-Fleer theory; II.5.31, II.5.5 square gradient method; II.5.33 statistics; II.5.29 trains; Il.fig. 2.27, II.5.18, II.5.32, Il.fig. 5.19, Il.figs. 5.21-23, II.5.70ff
4
SUBJECT INDEX
adsorption
(continued)
of surfactants; 1.1.25. III.1.14b ionic; I I . 3 . 1 2 non-ionic; II.2.7d physical; II. 1.18, II.fig. 1.13 presentation of data; II. 1.4, II.fig. 1.12 residence time (adsorbed molecules); II.1.46ff specific; see specific adsorption s t a n d a r d deviations; II. 1.45 superequivalent; II.3.62(def.), see further: specific adsorption t-plot; Il.figs. 1.27-28, II. 1.88, Il.fig. 1.34 (statistical) t h e r m o d y n a m i c s ; I . 2 . 2 0 e , 1.2.22, II. 1.3, II.2.3, II.3.6d-e, II.3.12, U.S.5 a-plot; II. 1.90 (see also; adsorption isotherm (equation), calorimetry for adsorption a t liquidfluid interfaces, see (Gibbs) monolayers. For specific examples see u n d e r the chemical n a m e of the adsorbate) adsorption isosters; II.1.3d, Il.fig. 1.9, II.1.37, Il.fig. 1.12f, II.2.26 adsorption isotherm (equation); I.1.17ff(intr.), I.fig. 1.12, II.1.3ff, Il.fig. 1.12, I I . 1 . 5 , Il.app. 1 Brunauer-Emmet-Teller (BET); I.3.5f, Il.l.Sf, [II.1.5.47], [11.1.5.50], Il.fig. 1.24a classification, adsorption from dilute solution; II.2.7b, Il.fig. 2.24 gas adsorption; II. 1.4b surface excess; II.2.3c, Il.fig. 2.8, II.2.4 composite; 1.2.85 (see surface excess) Dubinin-Radushkevich; [II. 1.5.56] electrosorption; I I . 3 . 1 2 b , Il.S.Sg Frenkel-Halsey-Hill; [II. 1.5.55] Freundlich; 1.1.19, II.1.2, [11.1.7.7] (generalized), Il.fig. 2.24c Frumkin-Fowler-Guggenheim (FFG); I.3.8d, I l . l . S e , Il.fig. 1.19, II. 1.64, Il.fig. 1.43, [II.A1.5a], II.2.65, II.3.195 for surface excess isotherm; II.2.4d for specific adsorption of ions; II.3.6d H a r k i n s - J u r a ; [II. 1.5.57] Henry; 1.1.19, 1.2.73, 1.6.65, II.1.2, [II.Al.la], Il.fig. 2.24a heterogeneous surface; Il.fig. 1.43
SUBJECT INDEX adsorption
isotherm
J (continued)
high affinity; 1.1.19, Il.fig. 2.24d, Il.figs. 5.7-8, II.fig. 5.26, Il.fig. 5.29, Il.fig. 5.31 Hill-De Boer = Van der Waals; see there individual; see partial Langmuir; 1.1.20, 1.2.74, I.3.6d, I.fig. 3.2, 1.3.46, II.1.2, II.1.28, II.1.4a, 11.1.5a, 11.1.5b, Il.figs. 1.14-17, II.1.5d, II.1.5e, [II.1.7.7] (generalized), [II.A1.2a], Il.fig. 2.24b, II.2.86, II.3.196 binary mixture; II.2.4b, I I . 2 . 4 c , Il.fig. 2.11 local; II. 1.104, Il.fig. 1.43, II. 1.108 one-dimensional; 1.3.8a Ostwald-Kipling; II.2.3b, [II.2.3.6], [II.2.6.1] partial (= individual); Il.fig. 2.9, Il.figs. 2.11-14 partially mobile; II.1.5d, Il.fig. 1.18 potential theories; II. 1.73 quasi-chemical; I.3.8e, II. 1.57, [II.A1.6a], II.3.196 s t a n d a r d deviation; 1.3.36 statistical t h e r m o d y n a m i c s ; II.1.3ff, II. 1.5, II. 1.6, II. 1.105, II.2.4, I I . 3 . 1 2 , II.5.5 surface excess; II.2.3, Il.figs. 2.11-14, Il.figs. 2.18-23 molecules of different sizes; II.2.4e, Il.fig. 2.14 relation to interfacial tension; II.2.4f multilayer; II.2.44ff Szyzskowski; [III.4.3.14] Temkin; [II. 1.7.6] t h e r m o d y n a m i c s ; I . 2 . 2 0 e , II. 1.3, II.2.3, II.3.6d-e, I I . 3 . 1 2 , II.5.5 Van der Waals (= Hill-De Boer); II. 1.59, [11.1.5.27], Il.fig. 1.20a, Il.fig. 1.23, [II.A1.7a] virial; I.3.8f, II. 1.58, [II.A1.4a] Volmer; II. 1.5c, Il.figs. 1.15-17, [II.A1.3a] (see also; Gibbs' adsorption law) adsorptive; I.1.17-18(def.) Aerosil; see silica aerosol; I.1.5(def.), 1.1.6 AES = Auger electron spectroscopy AFIVI = atomic force microscopy ageing; 1.2.99 aggregation; 1.1.2, 1.1.6
6
SUBJECT INDEX
air bubbles, electrophoresis; II.4.130ff floating: I.fig. 1.4 submersion of; 1.1.1, 1.1.2, 1.1.11 alcohols, surface dynamics and rheology; Ill.figs. 3.46, 47, III.4.3c, Ill.figs. 4.12-16, Ill.table 4.1 surface entropy; Ill.fig. 2.15 surface tension; III.4.3c Volta potential; Ill.fig. 4.14, Ill.fig. 4.24 alkanes, surface entropy; Ill.fig. 2.15 surface djniamics and rheology; Ill.figs. 46, 47 surface tension, data; Ill.fig. 2.17, Ill.table 2.3, Ill.fig. 4.10 simulations; III.2.41-43, Ill.figs. 2.12-13 lattice theory; III.2.60 ff, Ill.fig. 2.17-19 aluminum oxide, adsorption of HCl; II.fig. 1.10 adsorption of water vapour; 11, fig. 1.28 double layer; Il.table 3.8 point of zero chcirge; Il.app. 3b amphipathic; 1.1.23{def.) amphiphilic; 1.1.23(def.) amphipolar; 1.1.23{def.) analyzer; 1.7.27, I.fig. 7.7, 1.7.98 anionic surfactants, see surfactants anisotropic media; 1.7.14 birefringence; 1.7.97, 1.7.100 scattering; 1.7.8c anisotropy; 1.7.8c, 1.7.14 of colloidal particles; see particles (colloidal), shape Antonows rule; [111.2.11.12], III.5.76 apolar media, double layers; II.3.11 electrokinetics; II.4.50 solvation; I.5.3f arable gum; see gum arable
SUBJECT INDEX
7
Archimedes principle (for interaction in a medium); 1.1.30, 1.4.42, 1.4.47, 1.4.50, I.4.69ff, Lfig. 4.15 d'Arcy's law (flow in porous media); I.6.4f area; see surface area association colloids; I.1.6(intr.), I.1.23ff association constant; 1.5.2d association of ions; see ion association association of water; 1.5.3c atomic force microscopy; 1.7.90, II.1.12ff, Il.figs. 1.3-4, II. 1.91, Il.fig. 2.17. Ill.table 3.5. III.3.7d. Ill.figs. 3.66-68. Ill.fig. 5.28 ATR = a t t e n u a t e d total reflection. a t t e n u a t e d total reflection; 1.7.81, II.1.18, II.2.54, Il.fig. 2.16 Auger (electron) spectroscopy; 1.7.11a, I.table 7.4 autocorrelation function; Lapp. 11.1 autophobicity; II. 1.80, II. 1.101 average molecular m a s s or particle size averaged radius of gyration; 1.7.63 m a s s average; 1.7.63 n u m b e r average; 1.7.26 Z-average; 1.7.63 averaging; I.3.1a(intr.) azeotrope (in adsorption from solution); II.2.23 or-method (porous surfaces); II. 1.89-90 bacteria, Corynebacteriam;
Il.fig. 4.39
halophilic; 1.1.27 Nitrosobacter,
Nitrosomonas;
II.3.122
BAM = Brewster angle microscopy Bancroft rule; III. 1.84. III.4.97 b a r i u m sulphate; Il.table 1.3 barometric distribution; 1.1.20 barycentric derivative; 1.6.5 Bashforth-Adams tables (for capillarity); III.1.18ff BBGKY = Bogolubov-Bom-Green-Kirkwood-Yvon (recurrency expression); II.3.53ff BDDT = Brunauer-Deming-Deming-Teller, II.(isotherm classification); II. 1.4b b e a m splitters; 1.7.98 beating = opticed mixing bending; Ill.fig. 1.34 bending m o m e n t of interfaces; 1.2.92
8
SUBJECT INDEX
bending moduli of interfaces; [111.1.10.2], III. 1.55, III. 1.15, III. 1.79, Ill.tables 1.6 and 1.7 (data) Berthelot principle (for interaction between different particles): 1.4.3Iff, [III.2.11.181 BET = Brunauer-Emmett-Teller; see adsorption isotherm BET transformed; II. 1.69 biaxiality (anisotropic systems); 1.7.97 binodal; 1.2.68, II.5.12, Il.fig. 5.4, III.2.26 Copolymers; 1.1.2, 1.1.27, Il.fig. 5.5 birefringence; 1.7.14 Bjerrum length; [I.5.2.30al for polyelectrolytes; [11.5.2.23] Bjerrum theory (ion association); 1.5.2d black body (radiation); 1.7.22 blob; II.5.11 body (or volume) forces; I.1.8ff(intr.), 1.4.2 Bohr magneton; 1.7.95 boiling point elevation; 1.2.74 Boltzmann equation, II.Boltzmann factor; I.3.10ff, [II.3.5.4], II.3.216 dynamic; II.3.217 Boltzmann's law (for entropy); [1.2.8.2], [1.3.3.7] (see also Poisson-Boltzmann equation, theory) Bom-Bjerrum equation (solvation); [1.5.3.4] B o m equations (solvation); 1.5.3b, II.3.123 Born repulsion; 1.4.5 Bose-Einstein statistics; 1.3.12 Boyle point; 1.2.51, 1.2.64, II.5.6 Boyle-Gay Lussac law; 1.2.51 Bragg-Williams approximation; 1.2.62, I.3.8d, I.3.49ff, II.1.56ff Brewster's angle; 1.7.74, II.2.51 Brewster angle microscopy; III.table 3.5, III.fig. 3.56 Brillouin lines; 1.7.44 Bronsted (acids, bases); 1.5.65, II.2.7 Brownian motion; 1.3.34, 1.4.2, 1.6.3a, 1.6.3d, Lapp, l i e in a force field; 1.6.3b rotational: 1.6.73 b r u s h e s (at interfaces); III.3.4J bubbles; see air bubbles Burgers element; III.3.129
SUBJECT INDEX C a b a n n e s factor; 1.7.53 Cabosil; see silica C a h n electrobalance; III. 1.44 Cahn-Hilliard theoriy (for interfacicd tension); III.2.6 calomel reference electrode; 1.5.85 calorimetry (adsorption); II.1.3c, Il.fig. 1.7, II. 1.29, II.2.5b, II.5.60 canal surface viscometer; III.3.183-184 capacitance, electric; 1.4.51, 1.5.13, II.3.7c, II.3.94, II.3.106 differential; I.5.13(def.), 1.5.15, 1.5.100, II.3.10, II.3.21, Il.fig. 3.5, II.3.29, Il.fig. 3.9, II.3.33, II.3.36, II.3.6c, Il.fig. 3.22, Il.figs. 3.42-43, Il.fig. 3.49, Il.figs. 3.50-51, Il.fig. 3.53, II.3.149, II.5.60-61 integral; I.5.13(def.), 1.5.15, 1.5.59, II.3.10, II.3.6c capillaries, electrokinetic velocity profile; Il.figs. 4.15-16 electro-osmosis; II.4.2 Iff streaming current; II.4.3d s t r e a m i n g potential; I I . 4 . 3 d capillary bridges; III.1;49, III. 1.84, I l l . S . l l d capillary condensation; II. 1.42, II. 1.6, Il.figs. 1.32-33, Il.fig. 1.35, Il.fig. 1.39 capillary depression; I.1.8ff, I.fig. 1.1, Ill.fig. 1.4b, III.5.4e capillary electrometer; II.3.139ff, Il.fig. 3.47, III. 1.20 capillary electrophoresis; II.4.132 capillary length; [111.1.3.31, III.table 1.1, capillary osmosis; I I . 4 . 9 capillary p h e n o m e n a (general); 1.1.3, 1.2.23, II.l.Gd, II.1.6e, III. 1.1, 111.1.1,111.1.2 capillary pressure; I.1.8ff, I.fig. 1.9, I.fig. 1.10, 1.2.23, II.1.6 Young a n d Laplace's law; I.1.9(intr.), 1.1.12, 1.1.15, 1.2.23b, especially [1.2.23.191, II.1.85ff, II.1.99, I I I . 1 . 1 , [III.1.1.21 capillary rise; 1.1.2, I.1.8ff, I.fig. 1.1, II.1.6e, III.1.3. Ill.fig. 1.4a, III.1.83, III.5.4e capillary waves; III.2.9c, III.3.6g, III.3.10 carrier wave; 1.7.38 carbon, graphite, AFM image; Il.fig. 1.3 adsorption of: benzene, ri-hexane; Il.fig. 1.8 carbon tetrachloride; Il.figs. 1.22-23 hexane + hexadecane; Il.fig. 2.20 krypton; Il.fig. 1.29
10
SUBJECT INDEX
carbon: adsorption
of
(continued)
long alkanes from n-heptane; II.figs. 2.28-29 n-heptane-cyclohexane mixture; II.fig. 2.18 octadecanol; II.fig. 2.17 pentane + decane; II.fig. 2.20 rubber; II.fig. 5.31 water vapour; II.fig. l . l l , II.fig. 1.28 immersion (= wetting) enthalpy; 11, table 1.3 Casimir-Polder equation (for retarded Van der Waals forces); [1.4.6.35], [1.4.7.9] Cassie equation; [III.5.5.2] caterpillar trough; III.fig. 3.74 cation exchange capacity; 1.5.99, II.3.165ff cationic surfactants, see surfactants c.c.c. = coagulation, critical concentration CD = circular dichroism; see dichroism c.e.c. = cation exchcinge capacity cell (galvanic); see galvanic cells centrifugation potential (gradient); II.table 4.4, II.4.6-7 Chandrasekhcir equation; [1.6.3.20] Chapman-Kolmogorov equation; [1.6.3.13] characteristic curve (in potential theory for gas adsorption); II. 1.74 characteristic functions (in statistical thermodynamics); 1.3.3, [1.3.3.8], Ill.table 3.2 (in Langmuir monolayers), III.fig. 3.14 charge (electric); 1.5.3, 1.5.9, I.fig. 5.1 (see also; double layer, surface charge density, space charge (density)) charge-determining ions; 1.5.5b, II.3.7, II.3.8, II.3.84ff, II.3.89, II.3.147ff charge reversal; II.3.62 charged (colloidal) particles, c o n c e n t r a t i o n polarization; II.3.206, II.3.13c, II.4.6c, [II.4.6.53], II.4.8, [II.4.8.22] contribution to conductivity; II.figs. 4.37-39 contribution to dielectric permittivity; II.figs. 4.37-39 far fields; I I . 3 . 2 0 7 , II.3.13b, I I . 3 . 2 1 1 , II.3.217, II.4.18-19, II.4.6, II.4.8 fluxes; II.3.215ff, II.4.6, II.4.8 (in) alternating fields; I I . 4 . 8 induced dipole moment; II.3.206, II.3.210, II.3.212ff, II.4.8 local equilibrium; I I . 3 . 2 1 3 , II.4.79 n e a r field; I I . 3 . 2 1 1 , II.4.6 polarization field; II.3.207, II.3.209, II.3.211ff, II.4.18-19, II.4.70, II.4.87, II.4.8
SUBJECT INDEX charged (colloidal) particles (continued) polarization in external field; II.3.13, Il.fig. 3.86, Il.fig. 3.88, II.4.3a, II.fig. 4.2, II.4.18ff, II.4.6, II.4.8 relaxation; 11.3.13d, Il.fig. 3.89, II.4.6c, II.4.8 charging of double layers; I.5.17ff, 1.5.7, II.3.5 (see also under double layer, electric: Gibbs energy; for specific examples see under the chemical name) charging parameter; 1.5.17, 1.5.106 chemical potential; I.2.11ff(intr.), 1.2.35 dependence on curvature; 1.2.23c dependence on pressure; 1.2.4Iff dependence on temperature; 1.2.40 (of) polymers; II.5.9 chemisorption; II. 1.6, II. 1.32, II. 1.18, Il.fig. 1.9, II.2.85 chirality; 1.7.100, III.3.216 cholesterol monolayers; Ill.fig. 3.13, III.3.8d, Ill.figs. 3.92-93 chromatography; II.2.47ff, II.2.88 eluate; II.2.48 high performance liquid (HPLC); II.2.47 retention volume; II.2.48 c.i.p. = common intersection point circular dichroism (CD); see dichroism circular polarization; see electromagnetic radiation, polarization Clapeyron equation chemical equilibrium; [1.2.21.11 and 12] gas adsorption; [1.3.39] solubility; [1.2.20.6] in pores; II. 1.99 two-dimensional; III.3.38 Clausius-Mosotti equation (for polarization of a gas); [1.4.4.10] clay minerals (general); 1.5.99 cation exchange capacity; 1.5.99, II.3.165ff double layer; Il.fig. 3.1c, II.3.8, II.3.10d electrokinetics; II.3.168 isomorphic substitution; II.3.2, II.3.165 structures; II.3.163ff, Il.figs. 3.66-67 sv^elling; II.3.163ff cleaving of solid surfaces; 1.2.99 cloud seeding; II.3.130 CLSM = confocal laser scanning microscopy; see CSLM
11
12
SUBJECT INDEX
cluster integrad; 1.3.65 c.m.c. = critical micellization concentration; see micellization coagulation; I.1.6(intr.), 1.1.7, 1.1.28, 1.4.7, 1.7.61 critical concentration; II.3.129ff irregular series; 11.3.62 coherence (of radiation, electromagnetic waves); 1.7.15, I.7.22ff, 1.7.69 coherence time; 1.7.22 coherent neutron scattering; 1.7.70 cohesion (in liquids); 1.4.5c cohesion (work of); 1.4.47, III.5.2, Ill.fig. 5.9 cohesion pressure; 1.3.69 cohesion (or cohesive) energy; 1.4.46 coil (of polymer molecules); 1.1.26, I.fig. 1.17, II.5.2 co-ions; I.1.21(def.) Cole-Cole diagram; 1.4.35, Il.fig. 3.30b collapse (monolayers) (def.); III.3.23, Ill.flg. 3.46, III.3.226 collector (in flotation); 1.1.25, III.5.97 coUigative properties; I.2.20f collision broadening (spectral lines); 1.7.22 colloids (general); I.1.5ff(def.), 1.1.2 electron micrographs; Il.fig. 1.1 in external fields; II.3.13, II.chapter 4 hydrophilic; 1.1.7(def.) hydrophobic; I.1.7(def.) stability; 1.1.6, I.1.22ff (see also; colloid stability, general) interaction; constant charge vs. constant potential; 1.5.108 density correlation functions; Lapp, l i e direct measurement; 1.4.8, II.figs. 2.2-3, II.3.56ff in atomic force microscopy; II. 1.13 primary minimum; I.fig. 4.2 secondary minimum; I.fig. 4.2 two-dimensional; III.3.241 virial approach; 1.7.8b irreversible = hydrophic, lyophobic lyophilic; I.1.7(def.) lyophobic; I.1.7(def.), I.1.21ff preparation; 1.1.6, 1.2.100 reversible = hydrophilic, lyophilic solvent structure contribution; II.figs. 2.2-3, II.2.10
SUBJECT INDEX colloids (general)
13 (continued)
wetting; III.5.4h (see also; particles, chcirged (colloidal) particles) colloid stability, stabilization, general; I.1.6fflintr.), I.1.21ff, Lfig. 1.14, 1.2.71, I.fig. 2 . 1 1 , 1.4.8 by surfactants; 1.1.25 by (bio)polymers (including steric stabilization); I.1.2(intr.), 1.1.7, Lfig. 1.18, I.1.27ff, II.5.96ff a n d point of zero charge; II.3.106 I.fig. 1.18, I.fig. 2.11 (see also; colloids interaction, Van der Waals interaction) colloid titration, calorimetric; II.3.98 conductometric; II.3.88, Il.fig. 3.20 potentiometric; I.S.lOOff, I.fig, 5.17, II.3.7, II.3.85, Il.fig. 3.29, I I . 3 . 1 5 1 , II.figs. 3.57-59, II.5.60 colloid vibration potential; Il.table 4.4, II.4.7, II.4.3c, II.4.5d common intersection point (in colloid titration curves); 11.3.8a, Il.fig. 3.34, Il.figs. 3.57-59, Il.figs. 3.63-64, Il.fig. 3.77, Il.fig. 3.80, II.3.206 complex quantities; Lapp. 8 composition law (polymer adsorption); II.5.40 compressibility; 1.7.46, [III.2.11.4] O m s t e i n - Z e m i k e equation; [1.3.9.32] two-dimensional; see interfacial rheology concentrated polymer regime; II.5.9, Il.fig. 5.3 condensation, homogeneous, 1.2.23d c o n d e n s a t i o n , (two-dimensional); 1.3.43, Il.figs 1.3.5-8, I.3.47ff, I.3.53ff, ILl.59ff, Il.fig. 1.20, Il.figs. 1.31-33, Il.fig. 1.35, Il.fig. 1.39, Il.fig. 1.42, II.2.66 conduction; 1.6.6 (see also; surface conductance, surface conductivity) conduction bond (solids); Il.fig. 3.68, 11.3.173 conductivity, of ions a n d ionic solutions; 1.5.51, 1.6.6a, I.table 6.5, 1.6.6b limiting; L6.6a, I.table 6.5 molar; 1.6.6a of capillaries a n d plugs; II.4.55ff, II.4.7, Il.fig. 4.34 of water; 1.5.43 of colloids: a.c. m e a s u r e m e n t s ; II.4.5e, Il.figs. 4.21-22, I I . 4 . 8 , Il.figs. 4.37-39
14
SUBJECT INDEX
conductivity (continued) (see also; surface conductivity) conductometric titration of colloids; see colloid titration configurations; 1.3.11, I.3.29ff, II.5.2 configuration integrals; 1.3.9a, [1.3.9.6] configurational energy; 1.3.46 configurational entropy; 1.2.52, 1.3.30 confocal laser scanning microscopy; 1.7.91 conformation; II.5.1, see under polymers congruence (adsorption from binairy mixtures); II.2.3e charge; II.3.198 electrosorption; II.3.198, Il.fig. 3.81 pH; II.3.155, II.3.198 temperature; 11.2.27, II.3.156 conjugate acid; 1.5.65 conjugate base; 1.5.65 conjugate force; see force conservation (of energy); see energy conservation laws; see hydrodynamics consistency test (adsorption from binary mixtures); II.2.3e, Il.fig. 2.19 contact angle; 1.1.3, 1.1.8, I.fig. 1.1, Il.figs. 1.40-41, Ill.fig. 1.1. III.chapter 5 and enthalpy of wetting; II. 1.29. III.5.2 data; Ill.app. 4 hysteresis; Ill.fig. 1.20. III.1.41ff. III.5.5. III.5.4. Ill.fig. 5.4. III.5.9-10. III.5.40 measurement (general); 111.5.4 advancing; see hysteresis captive bubbles; III.5.4b capillary rise/depression; III.5.4e fibers; III.5.4g individual particles; III.5.4h objects in interface; III.5.4c powders, porous materials; III.5.4i pressure compensation; III.5.50 receding; see hysteresis sessile drops; III.5.4b spinning drop; III. 1.53 tilted plates; III.5.4d contact angle, dynamics; III.5.8 contact angle, interpretation; III.5.7
SUBJECT INDEX continuity equation; 1.6. l a contrast matching (in neutron scattering); 1.7.70 convection; 1.6.37 convective diffusion; 1.6.7c convolution; I.A10.3 cooperativity; II. 1.48 coordination number; 1.3.45, 1.4.46, 1.5.3c correlation coefficient; I.3.9e correlation function, pair; 1.3.66, IL3.51ff time (-dependent), 1.6.31, I.7.6c, I.7.6d, 1.7.7, Lapp. 1 1 , II.2.14 total; [1.3.9.231, II.3.51ff correlation length; 1.7.46, II. 1.94, II.5.11. III.2.27 correlation time, rotational; 1.5.44 correlator; 1.7.6c, 1.7.6d corresponding states; III.2.51, III.2.53 corrosion inhibition; II.3.224 Cotton-Mouton effect; 1.7.100 Cottrell equations; [1.6.5.20, 11.21), Lfig. 6.15a Coulomb's law. Coulomb interactions; [1.4.3.1], 1.4.38, 1.5.11, 1.5.16, 1.5.17, 1.5.21, II.3.36, II.3.48ff countercharge; I.1.20(def.), II.3.2, II.3.7 counterions; 1.1.21 (def.), See, double layer (ionic components of charge), lyotropic sequencies, specific adsorption coupling parameter (Kirkwood); 1.3.68 copper phtalocyanate; II.table 1.3 creep flow; 1.6.45 for interfacial creep, see interfacial rheology critical micellization concentration; see micellization critical opalescence; 1.3.37, 1.3.69, I.7.7c interfacial; 1.7.83 critical point or critical temperature, for polymer demixing; II.5.12 in pores; Il.fig. 1.39 two-dimensional; I.3.49ff, 1.3.53, II. 1.109 critical radius (nucleation); 1.2.101 cross coefficients (in irreversible thermodjniamics); 1.6.12, 1.6.2 crystal defects (in semiconductor); II.3.172
15
16
SUBJECT INDEX
crystal growth; 11.5.9 7 CSLM = CLSM = confocal laser scanning microscopy; 1.7.91 curvature (of interfaces); I.2.23a,III.1.4ff, III.1.17, I I I . 1 . 1 5 influence on chemical potential; 1.2.23c m a t h e m a t i c a l description; III. 1.78 r a d i u s of; I.2.23a, figs. 1.2.14-15, III.1.4ff, III. 1.2 spontaneous; III. 1.78 (see also bending moment, bending modulus) CVP = colloid vibration potential Dalton'slaw; [1.2.17.2] damping (of oscillations); I.4.37ff see further interfacial rheology, wave damping dashpot; Ill.fig. 3.50 Darcy's law; see d'Arcy's law Davies equation (for ionic activity coefficient); [1.5.2.28] Deborah number; 1.2.6, 1.2.86, 1.5.77, 1.6.2, II.1.8, III.1.32, III.1.35, III.3.5, III.3.12, III.3.90 De Broglie wavelength; 1.3.23, 1.7.24 Debye equation (for polarization of gases); [1.4.4.8] Debye-Falkenhagen effect; 1.5.60, I.6.6c, II.4.111 Debye-Huckel approximation; I.5.19(intr.) Debye-Hiickel limiting law; [1.5.2.22] Debye-Hiickel theory (for strong electrolytes); 1.5.2, 1.6.6b Debye length; [1.5.2.10], I.5.19(def.), I.table 5.2, II.3.19, [II.3.5.7]ff, [II.3.10.22] Debye-Van der Waals forces; see Van der Waals forces Debye relaxation; 1.6.73 decomposition; see demixing deep channel surface shear viscometer; Ill.fig. 3.70 degeneracy; 1.3.4 degree of dissociation; 1.5.30, II.3.76, II.5.56 degrees of freedom; 1.2.36 de-inking; III.5.102 delta formation (relation to colloid stability); 1.1.1, 1.1.2, 1.1.7 demixing; 1.2.19, II.1.6e binodal; 1.2.68, Il.fig. 5.4 critical; 1.2.19, II.1.6e spinodal; 1.2.68, Il.fig. 5.4 density correlation functions; Lapp, l i b , Lapp, l i e density functional; [111.2.5.18], 111.2.34, Ill.app. 3
SUBJECT INDEX
17
density profiles, liquid-fluid interfaces; III.2.4, III.2.5. [111.2.5.31], Ill.fig. 2.6, Ill.fig. 3.29 see distribution functions (of liquids near solids and of fluid interfaces) depletion (polymer adsorption) = negative adsorption depolarization (of polarized interface); II.3.137 depolarization ratio; 1.7.54 Deryagin approximation (to compute interactions between non-flat colloids); 1.4.61, I.fig. 4.13, 1.4.64 Deryagin-Landau-Verwey-Overbeek (DLVO) theory; I.1.21ff[intr.), 1.3.59 interaction curve; I.fig. 4.2 desalination; 1.1.3 (see also; salt-sieving) Descartes' law = Snell's law desorption; I.1.5(def.) detectors (for radiation); 1.7. I c quadratic; I.7.36ff detergency; III.5.101 dewetting; III.5.4, III.5.10 dextrane, adsorption on silver iodide; Il.fig. 5.26b, II.5.80ff, Il.flg. 5.29 DFG = difference frequency generation; III.3.7c.v dialysate; I.5.86ff dichroism; 1.7.98, II.2.56 circular (CD); 1.7.99 dielectric displacement; I.4.5f, 1.7.9 dielectric dispersion of sols, low and high frequency; II.3.219, Il.fig. 3.89, II.4.110 measurements; II.4.5e, Il.fig. 4.21 theory; II.4.8 dielectric drag; 1.5.51 dielectric increment, of colloids; II.4.8, Il.fig. 4.37-39 of ions; I.table 5.10 dielectric permittivity (dielectric constant); 1.4.10, I.4.4e, 1.4.5a, 1.4.5f, 1.5.11, I.table 5.1, I.5.3e, 1.7.2, 1.7.6 complex formalism; I.4.4e, 1.7.2c, Lapp. 8 measurement; 1.4.24, I.4.5f, II.4.5e, II.figs. 4.21-22 relation to polarization; I.4.23ff relation to refractive index; 1.7.12 dielectric polarization;, see polarization
18
SUBJECT INDEX
dielectric relaixation; I . 4 . 4 e , I.4.5f, II.4.8 dielectric saturation; 1.5.11 dielectrophoresis; II.4.51 diffraction; 1.7.13, 1.7.24 diffuse charge, diffuse double layer; see double layer, diffuse (see also; surface charge) diffusion (coefficient); 1.6.3, 1.6.5, 1.7.15, Lapp, l i e along surface; I.6.5g, II.2.14, II.2.29. III.3.74 and correlation functions; Lapp. 11 and irreversible thermodynamics; 1.6.5a collective; 1.6.55, 1.7.15, Lapp, l i e concentrated sols; 1.7.66, 1.7.15, Lapp, l i e convective; 1.6.7e data; Ltable 6.4 forced; 1.6.53, 1.6.7 hydrodynamic correction; 1.6.56, Lapp, l i e in condensed media; 1.6.56 in gases; 1.6.55 in water; L5.44ff model interpretation; 1.6.5b non-linear geometry. 1.6.5f non-spherical particles; L6.69ff, I.fig. 6.19 of colloids from dynamic light scattering; 1.7.8b, L 7 . 8 e , I.7.8d, 1.7.15 rotational; 1.5.44, 1.6.20, 1.6.53, I.6.70ff, L 7 . 8 e , 1.7.59 self; 1.5.44, 1.6.53, 1.7.15, Lapp, l i e semi-infinite; 1.6.59 thermal; 1.7.44, 1.7.48 to/from (almost) flat surface; L 6 . 5 d , 11.2.8, II.4.6e, IL4.8b diffusion equation (theory for polymer adsorption); II.5.32ff diffusion impedance; 11.3.96 diffusion layer; 1.6.63, 1.6.68 diffusion potentials; 1.5.5d, 11.4.125 see also; potenticd difference diffusion relaxation; 11.3.13, 11.3.219, II.4.6, II.4.8 diffusiophoresis; 1.6.91, II.3.214, II.4.9 dilatometry (and surface excesses); 11.2.7 dilational modulus, interfacial; see interfacial rheology dipole field; L 4 . 4 b , I I . 3 . 1 3 , II.4.6, II.4.8
SUBJECT INDEX
19
dipole moment; I.4.4b(def.), 1.7.3b data for molecules; I.table 4.1 of colloids; II.3.13 dipoles; 1.4.4b ideal (point dipole); 1.4.20 induced; 1.4.22, 1.4.27, 1.7.18, I.7.93ff, II.3.13, II.4.6 of colloids; II.3.13, Il.fig. 4.1, II.4.8 oscillation; 1.7.3b, II.4.8 permanent; 1.4.22, 1.4.27, 1.7.17 Dirac delta function; I.7.40(def.) discotic fluid (2D); III.3.62 disjoining pressure; I.4.6(def.), II.1.22, II.fig. 1.37, II.1.95ff, II.1.101, [11.2.2.1], II.5.65, III.3.176, III.5.7, III.5.14-15, III.5.23, Ill.fig. 5.12, Ill.fig. 5.15 (see also; films, interactions) dispersion, of colloids; 1.1.5 dielectric; see there of refractive index; 1.4.37, 1.7.13 of transverse waves; III.3.116 dispersion forces; see Van der Waals forces displacement , of particles; I.6.18ff, I.6.30ff dielectric; see there dissipation; 1.2.7, 1.2.22, 1.4.3, 1.4.34, 1.6.9, 1.6.13, I.6.35ff, I.7.2c, 1.7.14 dissociation constant; 1.5.2d in double layers; II.3.65ff, II.3.72ff, II.3.76, II.3.82ff relation to points of zero charge; II.3.8c, II.table 3.5 dissolution, heat of; 1.2.71 dissymmetry ratio (in scattering); 1.7.58, I.fig. 7.13 distributions; 1.3. l a , 1.3.7 most probable; 1.3.7 distribution (partition) coefficient; 1.2.69 distribution (partition) equilibrium; 1.2.20a distribution (function); I.3.9d, II.3.6b, II.3.9 higher order; I.3.9e in electrolytes; I.5.28ff, I.fig. 5.9, I.5.57ff in fluid interfaces; Ill.fig. 2.1, III.2.3. III.2.4, III.2.5, III.2.24. [111.2.5.30], Ill.fig. 2.6. [III.2.5.40] in liquids near surfaces; II.1.94, Il.fig. 1.38, [II.2.1.2], II.2.6.8, Il.figs. 2.2-3, II.2.2b, Il.figs. 2.4-8, II.3.6b, II.3.9
20
SUBJECT INDEX
distribution
(function)
(continued)
in water; 1.5.3c, I.fig. 5.6 pair; 1.3.71, II.3.51ff, III.2.30 radial (or pair correlation); I.3.9d, 1.7.66, Lapp, l i e , II.3.6b singlet; 1.3.71 dividing plane; see Gibbs dividing plane DLVO = Deryagin-Landau-Verwey-Overbeek (theory) DNA, persistence length; II.fig. 5.5 D o n n a n effect; 1.1.21, 1.5.90, 1.5.93, II.3.10, 11.3.26, II.3.99 relation to s u s p e n s i o n effect; I.5.5f D o n n a n e.m.f.; 1.5.88 donor (in semiconductor); II.3.172ff donor number; 1.5.65 Doppler broadening (spectral lines); 1.7.22 Doppler effect, Doppler shift; 1.7.16, I.fig. 7.6, 1.7.19, 1.7.45, 1.7.94, II.4.46 D o m effect = sedimentation potential double layer, electric; I.1.20(def.), I.fig. 1.13, I.5.3ff, I.fig. 5 . 1 , Il.chapter 3 in apolar media; I I . 3 . 1 1 diffuse; 1.1.21, I.fig. 1.13, 1.5.3, I.fig. 5 . 1 , II.3.5 (in) asymmetrical electrolytes; I I . 3 . 5 c capacitance; I I . 3 . 2 1 , II.fig. 3.5, II.3.29, Il.fig. 3.10, II.3.33, II.3.36 (in) cavity; Il.fig. 3.16 charge; I I . 3 . 2 1 , Il.fig. 3.4, II.3.29, Il.fig. 3.9, II.3.32ff, II.3.36, II.3.37, Il.fig. 3.12, Il.table 3 . 1 , Il.table 3.2, II.3.40, Il.fig. 3.14, III.4.4 cylindrical; II.3.5f, II.5.14ff electrolyte mixtures; II.3.5d field strength; II.3.20, I I . 3 . 2 1 , II.3.29, II.3.32 Gibbs energy; II.3.23, Il.fig. 3.6 Gouy-Chapman theory; see there i n t r o d u c t i o n ; II.3.17ff ionic components; 11.3.911, II.3.5b, Il.fig. 3.8, II.3.33, Il.fig. 3 . 1 1 , Il.fig. 3.15, II.3.168 negative adsorption of co-ions; II.3.5b, II.3.7e, Il.fig. 3.33 potential distribution; II.3.24ff, Il.fig. 3.7, II.3.35, II.3.36, Il.fig. 3.12 III.4.4 spherical; I I . 3 . 5 e , Il.table 3 . 1 , Il.table 3.2 statistical t h e r m o d y n a m i c s ; II.3.6b enthalpy of formation; 1.5.108, II.3.98, II.3.155ff, II.figs. 3 . 6 0 - 6 1 , Il.table 3.6 entropy; 1.5.109, Il.fig. 3.44, Il.table 3.6
SUBJECTINDEX
21
double layer, electric (continued) equivalent circuit; I.fig. 5.11, II.3.7c, Il.fig. 3.31 examples: II.3.1, Il.fig. 3.1 Gibbs energy; 1.5.7, II.3.5, II.3.9, II.3.23, Il.table 3.6, II.3.142, II.3.146 Gouy-Stern model; II.3.6c, Il.figs. 3.20-26, II.3.6f, II.3.133ff, II.3.154, II.3.158 (see also; Gouy-Chapman theory. Stem layer) heterogeneity; II.3.83ff measurements; II.3.7 moment; [II.4.6.50] in monolayers; III.3.4h, Ill.fig. 3.17 in non-aqueous solvents; 1.5.66, II.3.36 ionic components of charge; 1.5.2, I.5.90ff, 1.5.6b, 1.6.88, II.3.5b, Il.fig. 3.8, Il.fig. 3.46, Il.figs. 3.53-55, Il.fig. 3.62 (see also; double layer, diffuse) origin; II.3.2, II.3.110, II.3.117, II.3.155ff, II.3.158 overlap; 1.2.72, II.3.24 polarization in external field; II.3.13 (see further: charged (colloidal) particles) polarized vs. relaxed; I.5.5b, II.3.1, II.3.4 poly electrolytic adsorbates; II.5.5g relaxation; I.5.5b, I.6.6b, I.6.6c, II.3.94, II.3.13d, II.4.6c, II.4.8 site binding; see Stem layer statistical thermodynamics; II.3.6b Stem layer; 1.5.9, 1.5.59, II.3.17, II.3.6c, II.3.6g, Il.S.Sg capacitance; II.3.59ff, Il.fig. 3.43, ILfig. 3.50 charge and potential distribution; II.3.6c, II.3.6d, Il.figs. 3.20-21, II.4.71, Il.figs. 5.17-18, II.5.5g Gibbs energy; II.3.6f, Il.fig. 3.26 site binding: II.3.6e, II.3.6g specific adsorption; II.3.6d zeroth-order; II.3.59, Il.fig. 3.20a, Il.fig. 3.21 surface conduction; I.6.6d thermodynamics: 1.5.6, II.3.4, II.3.110ff, Il.table 3.6, II.3.138ff, II.3.155ff, Il.figs. 3.60-61 triple layer model; II.3.61(def), II.3.6c (see also: capacitance, ionic components, surface charge. For specific examples; see under the chemical name of the material.) drainage (of films cind foams); I.fig. 1.7, 1.1.15 drilling muds; II. 1.80
22
SUBJECT INDEX
drop, in electric field; III. 1.5, Ill.fig. 1.15 pendant; 1.1.11, I.fig. 1.3 pressure relaxation; III.3.188 rheology; III.3.187, Ill.fig. 3.72 sessile; I.fig. 1.1, Ill.figs. 5.1-2, III.5.4b. Ill.fig. 5.19 (see interfacial tension, measurement. III.chapter 1) Drude equations; I.7.78ff, II.2.52 Dukhin number; [11.3.13.1], II.3.208ff, II.4.12, II.4.30, II.4.3f, II.4.35ff, II.4.59 dynamic light scattering; see electromagnetic radiation, scattering Einstein crystal; 1.3.2 Iff, I.3.6a Einstein equation (for diffusion); 1.6.20, 1.6.30, [I.7.8.12al, 1.7.64, 1.7.66, 1.7.15 efficiency (thermodynamic); 1.2.9, 1.2.22 electrical birefringence; 1.7.100 electric double layer; see double layer, electric electric capacitance; see capacitance electric charge; see charge electric current (density); 1.6.6 two-dimensional; I.6.6d electric field; 1.4.3, I.4.5f, 1.5.10, I.7.6b caused by surface charge; 1.5.11 and electromagnetic waves; I.chapter 7 electric potential; see potential electroacoustics; II.4.3e, II.4.5d, II.fig. 4.20 electrocapillary curves; I.5.96ff, 1.5.99, I.fig. 5.16, II.3.139, Il.fig. 3.48, III. 1.45 electrocapillary maximum; I.5.99ff, II.3.102, II.3.139ff, Il.fig. 3.48 electrochemical potential; 1.5.Ic, 11.5.1.18), 1.5.74, II.3.5, II.3.90 electrochemistry (general); I.chapter 5 electrodialysis; II.4.132 electrokinetic charge; II.3.90, II.4.1, Il.fig. 4.13 electrokinetic consistency; II.4.58, II.4.6e, Il.table 4.2, II.4.6f, Il.table 4.3 electrokinetic phenomena; II.chapter 4 a.c. phenomena; II.4.8 advanced theory; 11.4.6 applications; II.4.6i, II.4.10, II.5.63ff double layer relaxation; II.4.6c elementary theory; II.4.3, II.4.7a irreversible thermodynamics; see Onsager relations survey; Il.table 4.1
SUBJECT INDEX electrokinetic phenomena (continued) techniques; II.4.5 xylene in water; III.fig. 4.2.1 (see further the specific electrokinetic phenomena) electrokinetic potential; I.5.75ff, 1.6.87, 11, chapter 4 examples; Il.fig. 4.13, Il.figs. 4.29-30 interpretation; II.4. l b , II.4.4 relation to v^^; II.4.41ff, Il.fig. 4.12 electrolytes; 1.5.1b, 1.5.2 electromagnetic radiation and waves; I.chapter 7 absorption; 1.7.2c, 1.7.3, I.7.60ff secondary; 1.7.15 coherence; 1.7.15, 1.7.23 and oscillating dipoles; 1.7.3d detection; 1.7. I c in a medium; 1.7.2b, 1.7.2c intensity; 1.7.8, 1.7.33 interaction with matter; 1.7.3 in a vacuum; 1.7. la, 1.7.2a irradiance; 1.7.5, 1.7.23 Maxwell equations;.1.7.2 phase shift; 1.7.3 polarization; 1.7.la, I.fig. 7.2, I.fig. 7.4, 1.7.23, 1.7.26, I.fig. 7.8, 1.7.14 elliptical; 1.7.6, Lfig. 7.4, 1.7.98, III.3.7 circular; Lfig. 7.4 planar; Lfig. 7.4 scattering; 1.7.3 and absorption; I.7.60ff and fluctuations; 1.7.6b dynamic; I.7.6c, Lfig. 7.10, I.7.6d, 1.7.7, 1.7.8 forced Rayleigh; 1.7.103 inelastic; I.7.16(def.) Mie; I.7.60ff of colloids; 1.7.8, II.4.46 of interfaces; 1.7.10c, III.l.lO of liquids; I.5.44ff, 1.7.7, I.7.8a plane; I.7.27(def.) quasi-elastic, QELS; 1.7.16, 1.7.6, 1.7.7, II.4.46, II.5.62 Raman = inelastic Rayleigh-Brillouin = QELS
23
24
SUBJECT INDEX
electromagnetic
radiation and waves; scattering
(continued)
Rayleigh-Debye; I.7.8d secondary; 1.7.16 static; 1.7.33, I.7.6d, 1.7.7, 1.7.8 survey; I.table 7.3 wave vector; I.7.27(def.) (see also; n e u t r o n scattering, X-ray scattering) sources; 1.7.4 types of; I.fig. 7.1 electromotive force; 1.5.82 electronegative; 1.4.19, 1.4.48 electroneutrality (electrolyte solutions); 1.5.1a; 1.5.1b electroneutrality of double layers; 1.5.4, 1.5.6a electron pair acceptor; 1.5.65 electron pair donor; 1.5.65 electron spin resonance (ESR); 1.7.16, 1.7.13 of a q u e o u s electrolytes; I.5.54ff of interfaces; II.2.8, II.2.55, II.5.59 electro-osmosis; 1.6.12, 1.6.16, II.4.1, Il.table 4.4, II.4.6, II.4.3b, II.fig. 4.6, II.4.46, II.fig. 4.15 in plug of arbitrary geometry; II.4.21-22, II.4.5b electro-osmotic dewatering; II.4.132 electro-osmotic flux; II.4.23 electro-osmotic p r e s s u r e (gradient); Il.table 4.4, II.4.6, II.4.23ff electro-osmotic slip; II.4.19, II.4.2Iff electro-osmotic volume flow; Il.table 4.4, II.4.6, II.4.22ff electrophoresis; II.chapter 4 advanced theory; I I . 4 . 6 anticonvectant; II.4.131 applications; II.4.10 elementary theory; II.4.3a experiments; II.4.5a polarization retardation; I I . 4 . 3 a electrophoretic light scattering; II.4.46 electrophoretic mobility, velocity; II.4.4-5, Il.table 4 . 1 , II.4.3a, II.fig. 4.41 cylindrical particles; II.fig. 4.4, II.4.16 D u k h i n - S e m e n i k h i n equation; [11.4.6.45], II.fig. 4.29 Helmholtz-Smoluchowski equaUon; [11.4.3.4], 11.4,12-14, II.4.17-19, ILfig. 4.29 Henry; II.fig. 4.4, II.4.16
SUBJECT INDEX electrophoretic
mobility, velocity
25 (continued)
Huckel-Onsager equation; [11.4.3.5] hydrodynamics; II.4.14ff, II.4.6 influence of surface conduction; II.fig. 4.4, II.fig. 4.31 irregular particles; II.4.6h, II.fig. 4.33 measurement; II.4.5a microelectrophoresis; II.4.45ff, II.figs. 4.14-16 moving boundary; II.4.51ff, II.fig. 4.17 Tiselius method; II.4.53 O'Brien-Hunter equation; [II.4.6.44] O'Brien-White; Il.figs. 4.26-29 sol concentration effect; II.4.6g, Il.fig* 4.32 stagnant layer thickness determination; II.4.128ff, II.fig. 4.42 verification of theories; II.4.6e electrophoretic deposition; II.4.132 electrophoretic retardation (in ionic conduction); 1.6.6b, 11.4.3a electropositive; 1.4.19, 1.4.48 electrosonic amplitude; II.4.7, II.4.5d electrosorption; II.3.4(def.), II.3.12 electrostriction; 1.5.103 electroviscous effect; II.4.122ff electrowetting; III.5.103 ellipsometric coefficients; 1.7.75, II.2.51, [II.2.5.7] ellipsometric thickness; [1.7.10.17], II.5.64 ellipsometry; 1.7.10b, II.2.5c, II.5.64ff, III.2.47, Ill.table 3.5, III.3.141ff elliptical polarization; see electromagnetic radiation, polarization eluate; see chromatography emission spectrum; 1.7.14 emulsification; 1.1.3, 1.6.45, III.3.237, III.4.97 emulsifyer (biological); 1.1.3 emulsion; I.1.3(intr.), I.1.5(def.), 1.2.98 Pickering stabilization; 111.5.9 9 (see also; microemulsions) endothermic; see process energy; 1.2.4, Lapp. 3 , Lapp. 4 absorption; L 4 . 4 e , 1.7.3 configurational; 1.3.46 conservation; 1.2.8 interfacial; 1.2.5, 1.2.11, Lapp. 5, Il.table 1.2 levels (semiconductors); Il.fig. 3.68-69
26
SUBJECT INDEX
energy
(continued)
mixing (polymers); [11.5.2.12] of radiation; 1.7.5 (see also; adsorption, interaction) engulfment; 111.5.11c enhanced oil recovery; 1.1.1, 1.1.3, 1.1.11, III. 1.84 ensemble; 1.3.1c canonical; 1.3. I c g r a n d (canonical); 1.3. I c microcanonical; 1.3. I c enthalpy; 1.2.6, Lapp. 3 , Lapp. 4 interfacial; L 2 . 6 , L 2 . 1 1 , Lapp. 5 , Iktable 1.2 of chemical reactions; L 2 . 2 1 of dissolution; L 2 . 2 0 c , L 5 . 3 a of electric double layer; L5.108, IL3.98, IL3.155ff, ILfigs. 3.60-61 of hydration; I. table 5.4 of transfer; L2.69 of wetting; see wetting (see also; adsorption, enthalpy) entropy; L2.8(intr.), L 2 . 9 , Lapp. 3 , Lapp. 4 absolute; L2.24, L3.16 configurational; L 2 . 5 2 , L3.30 interfacial; L 2 . 9 , L2.42, 1.2.83, Lapp. 5 , I L l . 2 , ILtable 1.2, ILfig. 3.44 intrinsic; L 2 . 5 2 of electric double layers; L5.109, ILfig. 3.44 of mixing; 1.2.53, 1.3.28, [11.5.2.11] of solvation (hydration); 1.5.3, I.table 5.4 production of; I . 6 . 2 a , L 6 . 2 b statistical interpretation; L3.16ff (see also; adsorption entropy) e n v i r o n m e n t , double layer effects; II.3.220ff Eotvos equation (for surface tension); [III.2.11.1] Eotvos number; [III.1.3cl EPR; see electron spin resonamce equation of motion; 1.6. l b equation of state, BET; [II. 1.5.49], ILfig. 1.24b Boyle-Gay Lussac (ideal); [1.1.3.4], 1.2.17a C a m a h a n - S t a r l i n g ; [1.3.9.31] h a r d sphere fluid; [1.3.9.26]
SUBJECT INDEX equation of state
27 (continued)
one-dimensional; [1.3.8.5] Percus-Yevick; [1.3.9.29 and 30] V a n d e r W a a l s ; [1.2.18.26], [1.3.9.28] two-dimensional; 1.1.17, 1.3.42, I.3.8d, II.1.3, 11.1.3b, II.1.39, I I . 1 . 4 5 , Il.app. 1, III.3.4, Ill.table 3.3, III.4.2. III.4.3 double layer; II.3.14 electrosorption; II.3.197 Frumkin-Fowler-Guggenheim (FFG); I.3.46ff, [II.Al.5b] Henry; [II.Al.lb] Hill-De Boer = Van der Waals; see there Langmuir; I.3.6d, [1.3.6.23], II.1.45, [II.1.5.10], Il.fig. 1.15b, [II.A1.2b] polymer monolayers; III.3.4i, [III.3.4.56] quasi-chemical; I.3.8e, [II.A1.6b] V a n d e r W a a l s ; II.1.51, II.1.59, [II.1.5.28], Il.fig. 1.20b, [II.A 1.7b a n d c], III.3.4e (two dimensional) virial; [II.A1.4b] Volmer [1.5.23], Il.fig. 1.15b, [II.A1.3b] equilibrium (general); 1.2.3, 1.2.8, 1.2.12, 1.3.7 chemical; 1.2.21 frozen; 1.2.8 local; 1.6.2, I.6.2a mechanical; 1.2.22 m e m b r a n e ; I.2.33(def.), I.5.5f, III.3.29 metastable; 1.2.7, 1.2.68 osmotic; 1.2.34 partial; 1.2.7 stable; 1.2.7, 1.2.19 equilibrium constant; 1.2.77, II.3.6e equilibrium criteria; 1.2.12 equipartition (of energy); 1.6.18 equipotential planes (in gas adsorption theory); Il.fig. 1.25 equivalent circuits (electrochemistry); I.fig. 5 . 1 1 , II.3.7c, Il.fig. 3.31 equivalent circuits (rheology); interfacial rheology; III.3.6i error function; [1.6.5.25], [II.4.6.37] Esin-Markov coefficients; I.5.6d, 1.5.102, II.3.15ff, II.3.26, II.3.103ff, II.3.136, Il.fig. 3.45, II.3.144ff ESA = electrosonic amplitude
28
SUBJECT INDEX
ESCA (electron spectroscopy for chemical analysis) = XP(E)S ESR = electron spin resonance Euler-Lagrange equation; [111.2.5.25], [III.A3.9I E u l e r s theorem; 1.2.28, 1.2.14a evanescent waves; 1.7.75, 11.1.18, II.2.54 evaporation; Ill.fig. 2.16 (heat). III.2.55 (entropy) prevention (water conservation); 111.3.239 EXAFS = extended X-ray absorption fine structure exchange (adsorption from binary mixtures); I I . 2 . 1 , I I . 2 . 3 , I I . 2 . 4 constant; [11.2.3.16] excess functions a n d quantities; I.2.18b(intr.) in Regular Solutions; 1.2.18c, I.3.46ff (see also; interfacial excesses) excimers; III.3.165 excluded volume; see polymers exothermic; see process expansion coefficient (2D); [111.3.3.2], [III.3.4.5] extended X-ray absorption fine structure (EXAFS); 1.7.88 Fabry-Perot interferometer; 1.7.36, I.7.6d falling film (interfacial rheology); III.3.189ff falling m e n i s c u s (for m e a s u r i n g interfacial tensions); III. 1.11 fats (metabolism); 1.1.1, 1.1.3, 1.1.7 fatty acids; III.tables 3.7a, 3.7b (overview) fatty acid monolayers; Ill.fig. 1.32 (interfacial tension, dynamics), Ill.fig. 3.58, Ill.fig. 3.60, Ill.fig. 3.68, Ill.fig. 3.76, Ill.figs. 3.78-87, Ill.fig. 4.26 fatty amine monolayers; III.3.212, fig. III.3.88 FCS = fluorescence correlation specroscopy; III.3.7c.iv FEM = field emission (electron) microscopy; 1 . 7 . l i b Fermi-Dirac statistics; 1.3.12, II.3.172 Fermi (energy) level; II.3.172, 11.fig. 3.68, II.3.174 FFG = Frumkin-Fowler-Guggenheim; see adsorption isotherm fibres, wetting; Ill.fig. 5.2, III.5.4g Fick's first law; I.table 6 . 1 , 1.6.54, I.6.5d, I.6.5e, 1.6.67 two-dimensional; 1.6.69 Fick's second law; 1.6.55, I.6.5d, I.6.5e, II.4.78, II.4.115 field emission techniques; 1 . 7 . l i b field strength, li.electric; I.4.12ff (see also; double layer) film balance; 1.1.16, III.3.3, Ill.figs. 3.4, 3.5 film tension; I.1.12ff, I.2.5ff, II.1.95ff
SUBJECT INDEX films, liquid (free); 1.1.6, I.1.12ff, I.fig. 1.4 u p to a n d including fig. 1.11, I.fig. 2 . 1 , 1.2.5 colours; 1.7.80 flow in t h e m , drainage; 1.1.15, I.6.4d multiple reflections; 1.7.80 stability; 1.6.45 thinning; I I I . 5 . 3 d Van der Waals forces; 1.4.72, III.5.3 films, liquid (on solid supports), disjoining pressure; II.1.22, [II.1.3.15], II.1.6d, [11.1.6.18], Ill.fig. 1.14, III.5.3 (also see; wetting films) FIM = field-ion microscopy; 1 . 7 . l i b first curvature (of interfaces), see m e a n curvature First Law of thermodjmamics; see thermodynamics First Postulate of statistical thermodynamics; see statistical thermodynamics flatbands
(semiconductors); II.3.174, Il.fig. 3.69
flickering clusters; 1.5.42 FLIM = fluorescence lifetime imaging microscopy floating (objects on liquids); I.l.lOff, I.fig. 1.2, I.fig. 1.4 flocculation;
1.1.28, II.2.88, II.5.97
Flory-Huggins interaction parameter (;^); 1.3.45, II. 1.56, II.2.34, II.5.5ff flotation;
1.1.25, II.2.88, III.4.4d, 111.5.11b
flow; see viscous flow flow birefringence = streaming birefringence fluctuations;
1.2.68, 1.2.102, 1.3.1, 1.3.7, 1.4.26, 1.7.26
in surfaces; 1.7.8 Iff, II. 1.45 of dielectric permittivity; 1.7.6 fluctuation fluidity;
potential; II.3.52
I.6.52(def.)
fluorescence;
1.7.14
in surfaces and adsorbates; 1.7.11a, II.2.54, II.2.80, Ill.table 3.5 fluorescence
correlation spectroscopy; III.3.7c.iv
fluorescence
lifetime imaging microscopy; 111.3.7c. iv
fluorescence
recovery (after photobleaching) (FRAP); 1.7.104, III.3.7c.iv
fluorescence
resonance energy transfer; III.3.7c.iv
fluorophores;
Ill.fig. 3.63
flux; 1.6.5ff, 1.6.11, I.6.2b, 1.6.32 a r o u n d polarized double layers; II.3.13c radial; 1.6.68
29
30
SUBJECT INDEX
foam; I.fig. 1.7, 1.2.98 (see also; films, liquid) foam breaker; III.5.99 fog; 1.1.6 Fokker-Planck equation; I.6.3c, 1.6.73 force, conjugate; 1.6.12, 1.6.2b, conservative; 1.4.2 directional; 1.6.1, I.6.3b, electrostatic; 1.4.2 fields; 1.4.3 generalized interpretation; 1.6.1 Iff, 1.6.54 hydrophobic; see hydrophobic interaction a n d bonding internal vs. external; 1.6.13 mechanical vs. thermodynamic; 1.2.27, 1.4.2, 1.4.49 steric; 1.4.2 stochastic; 1.4.2, 1.6.1, 1.6.3 Van der Waals; see Vam der Waals forces vectorial interpretation; 1.4.3a, Lapp. 7 (see also; interaction a n d interaction force) force constant; 1.4.44 force (effect) microscope; 1.7.90 forced Rayleigh scattering; 1.7.103 forced wetting; III.5.4, Ill.fig. 5.5 form drag; 1.6.47 Fourier transform infrared (spectroscopy) (FTIR); II.2.53 Fourier transforms; Lapp. 1 0 fractionation, adsorptives of different sizes; II.2.45 FRAP = Fluorescence recovery after photobleaching free energy; see Helmholtz energy free enthalpy; see Gibbs energy free p a t h (mean); 1.6.55 freezing point depression; 1.2.75 Fredholm integrals; II. 1.108 Frenkel defects; II.3.173 Fresnel equations; 1.7.10a Fresnel interfaces; 1.7.73, II.2.5c FRET = Fluorescence resonance energy transfer Freundlich adsorption isotherm; see adsorption isotherm
SUBJECT INDEX friction; 1.4.3, 1.6.10 friction coefficient; I.6.21ff, I.6.30ff, 1.6.56, 1.7.101, Lapp. 11 frictional drag; 1.6.47 FRS = forced Rayleigh scattering FTIR = Fourier transform infrared (spectroscopy) function of state; 1.2.9, I.2.14c functional adsorption; see adsorption, functional; III.2.22, III.2.34, Ill.app. 3 fundamental constants (table); Lapp. 1 funnel technique (interfacial rheology); IIL3.185 Fuoss-Onsager equation for limiting conductivity; [L6.6.29] Fuoss theory for ion association; L5.2d Galvani potential; see potential galvanic cells; L5.5e gases, adsorption on solids; chapter 1 ideal; Ll.17, 1.2.40, L2.17a, LS.lf, L3.6b, L3.6c, L3.58 non-ideal; L3.9 Gauss distribution; L3.39, L6.21, I.6.3c, L6.63 for surface heterogeneity; II. 1.106, ILfig. 1.43 Gauss equation (surface charge and field strength); I.4.53ff, Lapp. 7e, II.3.59 Gaussian beams; 1.7.23 Gauss(ian) curvature; L2.90(def.). III.1.4ff, III. 1.15 (see also; bending moduus) gel electrophoresis; II.4.131 generic phenomena, properties; L5.67(def.), II.3.6 Gibbs adsorption law; Ll.5(intr.), 1.1.16, 1.1.25, 1.2.13, 1.2.22, II.1.2, 11.2.27 for charged species; 1.5.3, II.3.12a for curved interfaces; 1.2.94 for dissociated monolayer; 1.5.94 for electrosorption; II.3.12d for narrow pores; II. 1.96 for polarized charged interfaces; 1.5.6c, 11.3.4, II.3.138 for relaxed (reversible) charged interfaces; L5.6b, 11.3.4, II.3.138 for water-air interfaces; 11.3.178 see III.chapter 4 for many examples Gibbs convention (for locating dividing plsme); 1.2.5, Lfig. 2.3 Gibbs dividing plane; 1.2.5 (intr.), 1.2.22, 11.1.2, II.2.4, 11.2.64, 111.4.4 for curved interfaces; 1.2.23b Gibbs-Duhem relation; 1.2.10, 1.2.13, 1.2.78, 1.2.84, 1.5.92, [II. 1.3.35-36]
31
32
SUBJECT INDEX
Gibbs elasticity; III.3.30 Gibbs energy; 1.2.10, Lapp. 3, Lapp. 4 interfacial; 1.1.4, 1.2.10, 1.2.11, Lapp. 5, Il.table 1.2 of adsorption; see adsorption, II.Gibbs energy of chemical substances; 1.2.77 of double layer; 1.5.7, II.3.5, II.3.9, II.3.23, ILfig. 3.6, Il.table 3.6, Il.fig. 3.26, 11.3.142, 11.3.146, IL3.155ff of ions; I.5.17ff, (see also; solvation, hydration) of nucleation; 1.2.23d of polarization; 1.4.55 of solvation (hydration); 1.4.45, L5.3a, Ltable 5.4, L5.3f of transfer; L5.3f, Ltable 5.11, 1.5.5a self; L4.5C, 1.5.17, I.5.3a, I.5.3b statistical interpretation; 1.3.18, [1.3.3.14] Gibbs free energy; see Gibbs energy Gibbs-Helmholtz relations; 1.2.41, 1.2.15, 1.2.61, 1.2.78, IL3.156, 111.3.34 Gibbs-Kelvin equation; see Kelvin equation Gibbs-Thomson equation; see Kelvin equation Girifalco-Good-Fowkes theory (for interfacial tensions); 111.2.lib, Ill.table 2.3 glass, double layer; ILfig. 3.64 glass electrodes; 11.3.224 goethite; see iron oxide Gouy-Chapman theory (diffuse double layers); 1.5.16, 1.5.18, II.3.5 (in) cavities; II.3.5g cylindrical surfaces; II.3.5f defects; II.3.6a flat surfaces; IL3.5a-d, ILfig. 5.18 improvements; IL3.6b, Il.figs. 3.18-19 spherical surfaces; 11.3.5e (see also; double layer, Gouy-Stem model) grand potential; III.2.7 graphite; see carbon Graphon - graphite; see carbon grazing incidence; II.2.56, III.3.147, 111.3.152, Ill.fig. 59 ground water table; 1.1.1 Guggenheim convention (for treating interfacial excesses); 1.2.15, I.fig. 2.4 gumairabic; 1.1.2, 1.1.7 Gurvitsch's rule; II. 1.94
SUBJECT INDEX gyration radius; see radius of gyration haematite (a-Fe203); see iron oxides Hagen-Poiseuille law; 1.6.42, II.4.47, II.5.62 H a m a k e r constant, Hamaker function; 1.3.45, 1.4.59, [1.4.7.7], 1.4.79, II.2.5, II.3.129, (tables) Lapp. 9 a n d interfacial tensions; I I I . 2 . 5 c Hamiltonian; I.3.57ff, II.3.47ff h a r d core interaction; 1.3.65, 1.4.5, 1.4.42 heat, statistical interpretation; 1.3.16 (see also; enthalpy) h e a t capacity; 1.2.7, 1.3.36, 1.5.42 interfacial; 1.2.7, III.2.74 of ions; I.table 5.6 heavy metal pollution; II.3.221 Helmholtz energy; 1.2.10, Lapp. 3 , Lapp. 4 interfacial; 1.2.10, 1.2.11, Lapp. 5 , Il.table 1.2 statistical interpretation; 1.3.17, Il.especially 11.3.3.10] Helmholtz free energy; see Helmholtz energy Helmholtz planes; see inner Helmholtz plane and outer Helmholtz plane Helmholtz-Smoluchowski equation; see electrophoretic mobility Henderson equation, for liquid junction potential; [1.6.7.11] for solvent structure contribution to disjoining pressure; [1.6.13] for ;t-potential; [11.3.9.9] Henderson-Hasselbalch equation, plot; [1.5.2.34], [II.3.6.52, 11.53], II.3.88ff Henry adsorption isotherm; see adsorption isotherm Henry c o n s t a n t , 11. for adsorption; 1.1.19, 1.2.71 for solubility of a gas; 1.2.20b Henry's law for gas solubility; 1.2.20b Hess'law; 1.2.16 heterodispersity (of colloids); I.7.8e heterodyne beating; see optical mixing heterogeneity of surfaces; see surface, heterogeneity hetero interaction; 1.4.72, I.fig. 4.17 hexadecylpyridinium chloride (adsorption); 11.fig. 2.22 higher-order Tyndall spectra (HOTS); 1.7.61 Hill plot; 11.1.48 Hoffmeister series = lyotropic series
33
34
SUBJECT INDEX
holes (in semiconductors); II.3.171 homodisperse colloids; 1.1.14, 1.1.28, 1.7.53 homodyne beating; see optical mixing homointeraction; 1.4.72 homopolyelectrolytes; II.5.1 homopolymers; II.5.1 honeycomb symmetry; 1.1.14 HOTS = higher order Tyndall spectra HPLC = high performance liquid chromatography; see chromatography Hiickel-Onsager equation; see electrophoretic mobility hydration; 1.2.58, 1.5.3, II.3.121, Il.table 3.7 (see also; solvation) hydration number; 1.5.50 hydraulic radius; 1.6.50, II. 1.84 hydrodynamic radius, layer thickness; 1.7.50, II.5.61 hydrodynamics; 1.6.1, conservation laws; 1.6. la, 1.6. lb, II.4.6, II.4.8 in electrophoresis; II.4.3, II.4.6 in polarized double layers; II.3.215ff, II.4.6 hydrogen bonding, hydrogen bridges; I.4.5d, 1.5.3c hydrophilic; 1.1.7, 1.1.23, Il.table 1.3 (see also; colloids) hydrophilicity/phobicity; Ill.table 1.3, III.5.5, III.5.11, 111.5.11a hydrophobic; 1.1.2, 1.1.7, 1.1.23, Il.table 1.3 (see also; colloids) hydrophobic interaction and bonding, hydrophobic effect; 1.1.30, I.4.5e, 1.5.3c, 1.5.4, I.table 5.12, II.2.7d, II.3.12d (see also; lyotropic sequences) hyperbolic functions; app. 2 hypemetted chain; 1.3.69 hysteresis; 1.2.7 of adsorption, see there of contact angles, see there of monolayers, see there ideal dilute (polymer solution); II.5.9 i.e.p. = isoelectric point iHp = inner Helmholtz plane illites; II.3.165 image charges; II.3.48ff, II.fig. 3.17, Il.table 3.3 imaginary quantities; Lapp. 8
SUBJECT INDEX imaging techniques; 1.7.11b (see also; transmission electron microscopy, atomic force microscopy, etc.) immersion method (to determine points of zero charge); 11.3.105 immersion heats or enthalpies; II. 1.29, Il.table 1.3, II.2.5, II.2.6, II.2.7, II.2.3d, Il.fig. 2.10, ll.fig. 2.20, II.3.98, II.3.114, III.5.2 (see also; wetting, immersional) impedance (spectrum); II.3.92, Il.fig. 3.30, II.3.149, II.4.8 incident angle; 1.7.10a incident plane; 1.7.10a index of refraction; see refractive index indicator electrode; 1.5.82 indifferent (ions, electrolytes); II.3.6, II.3.103 inertia; II.4.2 infrared spectroscopy; 1.7.12, II.2.8, II.2.71ff, II.5.57; III.3.7c.i, Ill.fig. 3.62 infrared reflection-absorption spectroscopy; III.3.7c.i ink (Egyptian); 1.1.1, 1.1.2, 1.1.7, 1.1.27 ink jet printing; III. 1.84 inner Helmholtz plane; II.3.6Iff insoluble monolayers, see monolayers, Langmuir interaction, energy, force; 1.4.2, 1.4.8, II.figs. 2.2-3 multiparticle, Bom-Green-Yvon; 1.3.69 Carnahan-Starling; I.3.69ff h3rpemetted chain; 1.3.69 Percus-Yevick; 1.3.69 relation to distribution functions; I.3.9d, I.3.9e relation to virial coefficients; 1.3.9c pairwise; 1.3.8, 1.3.9, 1.4.1, 1.4.2, 1.4.3, 1.4.4 potential; see interaction energy sign; 1.4.4 solvent structure-originated; 1.5.15, 1.5.4, Il.table 1.5.12, II. 1.95-96, Il.fig. 2.2, II.3.184ff interaction between colloids and macrobodies, (see colloid stability. Van der Waals forces and colloids, interaction) interaction between ions; 1.5.2 interaction between molecules and surfaces; [1.4.6.1], II. 1.5, II.chapters 1, 2 and 5 interaction curves; I.fig. 3.4, I.fig. 4.1, figs. 1.4.2-3
35
36
SUBJECT INDEX
interaction energy parameter; I.3.40ff, 1.3.43-45, [1.3.8.9], II.1.56, II.2.34, II.5.5ff excess; 1.3.45, especially [1.3.8.9] interaction forces, general; I.chapter 4 interaction in solution (excess nature of); 1.1.29, 1.4.5, 1.4.6b, 1.4.7 interface; I.1.3(intr.) curved; see capillary phenomena of tension; 1.2.94 optical study; 1.7.10, 1.7.11, II.2.5c reflection of light; 1.7.10a, II.2.5c refraction of light; 1.7.10a scattering; 1.7.10c (see also, purity criteria) interfacial area; see surface area interfacial charge; see surface charge interfacial concentration; 1.1.5 interfacial energy; III.2.9a, Ill.fig. 2.14, Ill.fig. 2.16 (relation to heat of evaporation) interfacial entropy; III.2.9a, Ill.fig. 2.14-1§5, III.2.55 (relation to entropy of vaporization). III.4.2d, Ill.fig. 4.19 interfacial excess; 1.2.5, 1.2.42, 1.2.22, III. 1.2, II.2.2, Il.fig. 2.1, [II.2.1.2], II.2.3, III.2.2 isotherm; II.2.3, III.4.2 (see also; adsorption, Gibbs' adsorption law, surface excess) interfacial polarization; see potential difference, x interfacial potentiad jump (x)\ see potential difference, x interfacial potentials; 1.5.5, II.3.9, III.4.4 interfacial pressure; see surface pressure interfacial rheology; III.3.6, Ill.table 3.5 Burgers element; III.3.129 compliance; Ill.table 3.4, III.3.105 compressibility; [III.3.3.1], [111.3.4.3], III.3.93 compression; III.3.83, III.3.91 creep; Ill.fig. 3.40, III.3.61 deformation types; Ill.fig. 3.34 dilation; III.3.81, III.3.83, III.3.91, Ill.fig. 3.38 dilational elasticity (modulus); [III.3.4.4], III.3.40. III.3.81, Ill.table 3.4ff. [III.6.18-19], [III.3.6.34-39], III.3.6g, Ill.fig. 3.48, Ill.fig. 3.87, Ill.fig. 3.91, III.4.5, Ill.figs. 4.26-27, Ill.table 4.3, Ill.fig. 4.38 distance coefficient; III.3.113. Ill.fig. 3.44, III.3.117ff
SUBJECT INDEX interfacial
rheology
37 (continued)
distance damping; III.3.112 elasticity; III. 1.55, III.3.82. Ill.table 3.4 equivalent mechanical circuits; III.3.6i experimental methods; III.3.6f, III.3.7e Fourier transform method; III.4.59ff Gibbs monolayers; Ill.table 4.2 Kelvin element = Voigt element Kelvin equation (damping); [III.3.6.631 kinetics; III.4.5 loss angle; [111.3.6.12]. [III.3.6.41al, [111.3.6.66], [III.3.6.74] Marangoni effect; 1.1.2 (intr.), 1.1.17, I.6.4.43ff, III.1.35, III.1.72, III.3.81, III.3.6e, Ill.figs. 3.35-37, III.3.239 Maxwell element; Ill.figs. 3.51-52 relation to interfacial tension; III.3.92, III.3.6d recovery; Ill.fig. 3.40, Ill.fig. 3.52 relaxation (Gibbs monolayers); Ill.fig. 4.20 relaxation (Langmuir monolayer); III.3.6h, III.3.6i respiratory stress s)nidrome; III.3.238-239 shear modulus; III.3.84, III.3.92 s h e a r viscosity; III.3.84, III.3.92, [111.3.6.20], III.3.6g, Ill.fig. 3.91 s t r e s s relaxation; Ill.fig. 3.39, III.3.6i stress tensor; III.3.91ff, Ill.table 3.4 time damping; III.3.113 viscosity; III. 1.55, III.3.82, Ill.table 3.4 Voigt element; III.3.94, Ill.figs. 3.51-52 wave damping a n d propagation; III. 1.1, III. 1.58, III.3.6g, Ill.fig. 3.42-44, III.3.183, III.3.185, see also loss angle interfacial science (first review); 1.1.2, 1.1.3 interfacial tension, surface tension; I.1.4(intr.), 1.1.25, I.fig. 1.16 binary mixtures; 111.4.2 data; Ill.app. 1, III.1.12 dynamic conditions; III. 1.14b, Ill.fig. 1.31, Ill.fig. 1.32 interpretation; III.chapter 2, III.3.6d Cahn-Hilliard; III.2.6 capillary waves; 111.2.9c distribution function; III.2.4, [111.2.4.6-8], III.2.24 empirical; I I I . 2 . 1 1 a n d geometric means; III.2.11b
38
SUBJECT INDEX
interfacial tension, surface tension; empirical (continued) and grand potential; III.2.7 Hamaker-de Boer approximation; III.2.5c lattice theory; III.2.10 mechanically; III. 1.3 pressure tensor (interfacial); III.2.3, [III.2.3.5], 111.3.6d scaling; [111.2.5.35] simulations; III.2.7. Ill.figs. 2.9-10, Ill.table 2.2 statistical thermodynamics; III.2.4, III.2.30-31, III.2.5Iff thermodynamic or quasithermodynamic; 1.2.1 Off, I.2.26ff, 1.2.11, 1.2.91, III.2.2, III.2.9 van der Waals; III.2.5 measurement; 1.1.11, 1.2.5, 1.2.96, II.3.139. Ill.chapter 1 'Bugler method'; III. 1.49 capillary rise; III.1.3, (differential) III. 1.19 (in a wedge), Ill.fig. 1.10 captive drops; Ill.fig. 1.11, further see sessile and hamging drops drop oscillations; III. 1.58 drop weight; III. 1.6, III.1.72ff drops in a gradient; III. 1.5 (see also, growing drops, sessile drops, spinning drops, etc.) du Noiiy ring; 111.1.8b, III.1.72ff dynamic (conditions); III. 1.14, III. 1.3-4, III.1.53ff (also see; interfacial tension, relaxation) falling drop; Ill.fig. 1.17 (see further, drop weight) falling meniscus; III. 1.11, Ill.fig. 1.26 growing drops; III. 1.74 hanging drops; see sessile drops maximum bubble pressure; III. 1.7, III.1.72ff micropipette; III. 1.57 'Padday's pencil'; III. 1.48 pendant drop = hanging drop; see sessile and hanging drops rheology; III. 1.57 sessile and hanging drops; III. 1.4, III.1.72ff sphere tensiometry; III. 1.48 spinning bubbles; see spinning drops spinning drops and bubbles; III. 1.9, Ill.fig. 1.24 surface light scattering; III. 1.10 tensiometers; III. 1.8
SUBJECT INDEX interfacial tension, surface tension
39 (continued)
wave damping; Wilhelmy plate; 111.1.8a. III.L72ff of curved interfaces; 1.2.23, II.1.6d, I I I . l . l . III.1.15 of electroljrtes; III.4.4 of films; II.1.95ff of solid surfaces; 1.2.24. III. 1.5 m e a s u r e m e n t ; III. 1.13 p r e s s u r e dependendence; III.2.9b relation to adsorption from binary mixtures; II.2.4f relation to compressibility; III.2.11a. [111.2.11.6-71 relation to interfacial Helmholtz, Gibbs or internal energy; 1.2.11, L a p p . 5 . [Ill.l.la.b] relation to molar volume; III.2.11a relation to surface light scattering; 1.7.10c. III. 1.10 relation to work of cohesion; 1.4.47 relaxation; III.1.14. Ill.fig. 1.29 temperature dependence; 1.2.42, [11.1.3.42], III.2.9a (see also; capillary phenomena, monolayers, wetting, interfacial rheology) interfacial viscometers; III.3.180ff, Ill.figs. 3.69-71 interfacial work; 1.2.10, 1.2.3, 1.3.17 interference; 1.7.8, 1.7.15 interferometry (contact angle); III.5.43ff ion association; 1.5.2(1 ion binding; I.5.3ff, II.3.6d-e ion condensation; II.4.43 ion correlations; I I . 3 . 6 b ion vibration potential; 11.4.2 9 ionic atmosphere; 1.5.16, see double layer, diffuse ionic components of charge; see double layer, electric ion exchange; II.3.35, II.3.168ff ion m a s s spectroscopy (SIMS); 1.7.11a, I.table 7.4 ion pairs; 1.5.3 ion scattering spectroscopy (ISS); I.7.11a, I.table 7.4, II. 1.15 ion transfer resistance; II.3.95 ionization, ionization (Gibbs) energy; 1.4.29, I.5.34ff, 1.7.86 ions, activity coefficient; see there b o u n d vs. free; 1.5.1a hydration; 1.5.3
40
SUBJECT INDEX
ions
(continued)
hydrophilic; 1.5.47 hydrophobic; 1.5.46 r a d i i ; I.fig. 5.7 solvation; 1.5.3 structure-breaking; 1.5.47 structure-forming; 1.5.47 transfer; I.5.3f, II.3.9 volumes; I.tables 5.7 and 8 ion-solvent interaction; see hydration, solvation ionic surfactants; see surfactants IRAS = infrared reflection-absorption spectroscopy iron oxides goethite (a-FeOOH), electrokinetic charge; II.fig. 4.13 point of zero charge; II.table 3.5, Il.app. 3b haematite (a-Fe203); Il.fig. 1.1 adsorption of fatty acids from heptane; Il.fig. 2.26 conductivity of sols; Il.fig. 4.38 dielectric relaxation of sols; Il.fig. 4.38 double layer; II.3.94, Il.table 3.6, Il.figs. 3.59-62, Il.table 3.8 electrokinetic properties; Il.table 4.3 point of zero charge; Il.table 3.5, Il.fig. 3.37, Il.app. 3b immersion, wetting; Il.table 1.1 irradiance; 1.7.5 IRRAS = infrared reflection-absorption spectroscopy irregular coagulation series; see coagulation irreversible thermodynamics; see thermodynamics irreversible colloids = colloids, lyophobic irreversible process; see process, n a t u r a l Ising problem; 1.3.40, 1.3.43 isobaric (process); 1.2.3 isochoric (process); 1.2.3 isoconduction; II.3.215 isoelectric point; I I . 3 . 8 , II.3.103, II.3.106, Il.fig. 3.78, Il.fig. 4 . 4 1 , II.4.127ff relation to point of zero charge; II.3.8b, Il.fig. 3.35 isoelectric focusing; II.4.131ff isodisperse = homodisperse isomorphic substitution (in clay minerals); II.3.2, II.3.165 isosteric (process); 1.2.3
SUBJECT INDEX isosteric h e a t of adsorption; see adsorption, isosteric enthalpy isotachophoresis; II. 4.131 isothermal (process); 1.2.3 destination; see Ostwald ripening reversible work; 1.2.27 ISS = ion scattering spectroscopy Jones-Dole equation, coefficients (viscosity of electrolytes); 1.5.52, I.table 5.9, I.6.78ff kaolinite; II.3.164, Il.fig. 3.66 wetting; Il.table 1.34, Keesom-Van der Waals forces; see Van der Waals forces Kelvin element (rheol.) = Voigt element; see interfacial rheology Kelvin equation; [1.2.23.24], [II.1.64, [11.1.6.17), [111.1.13.3] Kelvin equation (wave damping); 111.3.6.63] Kerr effect; 1.7.100 Kiessing fringes; III.3.150, Ill.fig. 3.58 Kirkwood equation (electric polarization); [1.4.5.22] Kirkwood-Buff equation (interfacial tension); [III.2.4.6-9] Kirkwood-Frohlich equation (electric polarization); [1.4.5.23] Kozeny equation; [1.6.4.39], II.4.55 Kozeny-Carman equation; [1.6.4.41], II.4.55 Kramers-Kronig relations; [1.4.4.31, 11.32], 1.4.36, 1.4.77, 1.7.13, II.3.93 Kuhn segment = statistical chain element Lambert-Beer's law; 1.7.13, 1.7.41 Langevin equation (for forced stochastic processes); [1.6.3.4], 1.6.3d, Lapp. 11.2 Langmuir adsorption isotherm; see adsorption isotherm Langmuir-Blodgett layers; II.2.56, III. 1.42, III.3.7a Langmuir monolayers, see monolayers Langmuir trough; see film balance Laplace pressure = capillary pressure Laplace transformations; Lapp. 10 lasers; 1.7.4c laser-Doppler microscopy = QELS; see electromagnetic radiation latex, ILlatices or latexes; 1.1.6, L5.99, II.3.87, ILfig. 3.29 electrokinetics, conductivity; Il.table 4.2, ILfig. 4.34 electro-osmosis; Il.table 4.2 electrophoresis; ILfig. 4.29, Il.table 4.2 streaming potential; ILfig. 4.30, ILfig. 4.35
41
42
SUBJECT INDEX
lattice statistics; I.3.6d, I.3.6e, 1.3.8b polymer adsorption; IL5.30ff r a n d o m walk; 1.6.3d LC = liquid condensed (2D phase); III.3.3b LE = liquid expanded (2D phase); III.3.3b LEED = low-energy electron diffraction Lennard-Jones pair interaction energy; I.fig. 4.9, I.4.5b, [1.4.5.1] in adsorbates; [II.1.1.14], II.1.74 in liquids n e a r solids; ILfigs. 2.4-5 leucocytes; III.5.100 leukemia; III.5.100 Levich equations (for convective diffusion); I.6.92ff Lewis acids, bases; 1.5.65, II.3.185 Lifshits theory; see Van der Waals interaction between colloids light scattering; see electromagnetic radiation line tension; III. 1.6, III.5.5, III.5.6 lipase; 1.1.3 lipids (phosphol); Ill.table 3.8 lipids (phospholipid) monolays; Ill.fig. 3.8, Ill.fig. 3.12, Ill.fig. 3.14. Ill.fig. 3.29, III.3.140, Ill.fig. 3.55, Ill.figs. 3.62-62, Ill.fig. 3.67, III.3.8c, Ill.figs. 3 . 8 9 - 9 1 , III.3.238 Lippmann capillary electrometer; see capillary electrometer Lippmann equation (for electrocapillary curves); [1.5.6.17], 1.5.100, 1.5.108, II.3.138 liquid bridges, see capillary bridges liquid j u n c t i o n potentials; see potential difference liquid-fluid interface, general; Ill.chapter 1.2, III.2.8 (thickness). III.2.9b density profile; Ill.fig. 2 . 1 , III.2.3, [111.2.5.31], III.2.8, Ill.figs. 2.11-13, Ill.fig. 2.19 double layer; II.3.10g t h e r m o d y n a m i c s ; 111.2.2 liquids, apolar, double layers; II.3.11, II.4.50 solvation; I.5.3f in pores; II.1.6d n e a r surfaces; II.1.6d, II.3.123ff, II.4.38 London-Van der Waals forces; see Van der Waals forces longitudinal waves; III.3.110, see interfacial rheology loops; see adsorption of polymers
SUBJECT INDEX Lorentzian peaks; 1.7.50 Lorenz-Lorentz equation (electric polarization); [1.4.5.21], 1.7.43 loss angle (rheology), III.3.90, [111.4.5.44] see interfacial rheology low-energy electron diffraction (LEED); 1.7.25, 1.7.86, Il.fig. 1.2, II. 1.1 Iff lunar soil, spherules in; 1.1.1, 1.1.2 sorption of methanol; Il.fig. 1.35 lung surfactant; 1.1.1, 1.1.2, III.3.219, III.3.238 lyophilic; 1.1.7 (see also; colloids) lyophobic; 1.1.7 (see also; colloids) lyotropic series; I.5.66ff(intr.) in coagulation; 1.5.67 in ionic binding, double layer charge or double layer capacitance; I.5.66ff, II.3.15, II.3.109, II.3.132, Il.fig. 3.41, II.3.135, Il.fig. 3.53, Il.fig. 3.55, II.3.147, Il.fig. 3.75, Il.S.lOh, Il.table 3.8, II.3.203. III.3.207ff, Ill.figs. 3.85-86, III.4.89ff macromolecules; see polymers, polyelectrolytes, proteins macropores; see pores magnetic birefringe; 1.7.100 magnetic fields; 1.7.la, 1.7.2, 1.7.16, 1.7.13 magnetic induction; 1.7.2 magnetic permeability; 1.7.9 magnetization; 1.7.9 Mandelstam equation (for surface scattering); [1.7.10.24], [III. 1.10.1] manganese dioxide, double layer; Il.table 3.8, Il.app. 3b Marangoni effect; see interfacial rheology marginal (polymer concentration) regime; II.5.9, Il.fig. 5.3 Markov chain; 1.6.24 Markov process, first order; 1.6.24, II.5.30 masers; 1.7.4c mass conservation (in hydrodynamics); 1.6. l a mass, reduced; 1.4.44 maximum term method (statistical thermodynamics); 1.3.37 Maxwell-Boltzmann statistics, distribution; 1.3.12, I.6.26ff, II.3.172 Maxwell element, see interfacial rheology
43
44
SUBJECT INDEX
Maxwell equations (for electromagnetic waves); 1.7.2 Maxwell (-Wagner) relaxation; 1.6.84, II.3.219, II.fig. 3.89 Mayer function; I.3.60ff, I.3.64ff mayonnaise; 1.1.6 m e a n curvature (of interfaces); 1.2.23a, III.1.1, III.1.15 m e a n field theories; II.5.7, II.5.29, III.2.5 m e m b r a n e equilibrium; see equilibrium mercury-solution interface, double layer; I.5.6c, II.3.10b, Il.figs. 3.48-55, Il.table 3.8 interfacial tension; II.3.138ff, II.fig. 3.48 mesopores; see pores metabolism; see fats metals, points of zero charge; Il.app. 3a methylviologen; [II.3.14.1], II.3.224 mica; II.3.165 micelle; I.1.6(def.), 1.1.24, I.fig. 1.15 reverse (or inverted); 1.1.25 micellization, critical concentration of (c.m.c); I.1.24ff(intr.), III.4.6a, Ill.table 4.4 determination; I.1.25ff microelectrophoresis; II.4.45ff, Il.figs. 4.14-16 microemulsions; 1.1.3, 1.1.7, 1.2.68 micropores; see pores Mie theory (light scattering); see electromagnetic radiation mixtures, athermal; 1.2.55 h o m o g e n e o u s , thermodynamics; 1.2.16 ideal; 1.2.17 non-ideal; 1.2.18 mobility (of ions); 1.6.6a molality; I.2.45(def.) molarity; I.2.45(def.) mole fraction; I.2.44(def.) molecular condensor; I.fig. 5.1, II.3.59 Molecular dynamics; I.3.1e(intr.), electrolytes; I.5.57ff, I.fig. 5.9 liquids in pores; II.fig. 1.38 liquids n e a r surfaces; Il.figs. 2.5-7, II.3.55, Il.fig. 3.39 wetting; Ill.fig. 5.36
SUBJECT INDEX molecular m a s s (of colloids); see polymers, particles molecular sieve, adsorption of krypton; II.fig. 1.19 adsorption of methane; II.fig. 1.36 molecular state; see state molecular thermodynamics; see statistical thermodynamics moment, of a distribution; 1.3.7b of a double layer; [II.4.6.50] m o m e n t u m ; I.3.57(def.), m o m e n t u m conservation (in hydrodynamics); 1.6.lb (see also; transport of momentum) monatomic crystal; see Einstein crystal monochromatic (waves, radiation); 1.7.2 monochromator; 1.7.3 monodisperse = homodisperse monolayers (at liquid-fluid interfaces); I.fig. 1.15b adsorbed = Gibbs monolayers bending moduli; III.tables 1.6 a n d 7 binary mixtures; see Gibbs monolayers characterization; cholesterol; curved; see Gibbs monolayers; diffraction; dilute solution; see Gibbs monolayers electrolytes; see Gibbs monolayers film balances; I I I . 3 . 3 a fatty acids; alcohols; Gibbs (monolayers); III.chapter 4 binary mixtures; II1.4.2 curved; III.4.7 dilute solutions; 111.4.3 distinction from Langmuir monolayers; III.3.1 dynamics; III.1.14b, III.4.5 electrolytes; 111.4.4 Gibbs equation; 1.5.94 ionized; II.3.2, Il.fig. 3.1b rheology a n d kinetics; see interfacial rheology surfactants; III. 1.14b, III.4.6 Langmuir (monolayers); III.chapter 3
45
46
SUBJECT INDEX
monolayers (at liquid-Jluid interfaces), LAxngmuir (continued) Brewster angle microscopy; III.table 3.5 characteristic functions; 111, table 3.2 cholesterol; III.3.8d collapse; Ill.fig. 3.46 diffraction; III.3.7b distinction from Gibbs monolayers; III.3.1 ellipsometry; III.table 3.5, 111.3.7b energy-entropy compensation; III.3.37 fluorescence; III.table 3.5 hysteresis; III.3.13. III.3.8a, Ill.fig. 3.79 ionized; III.3.4h Langmuir trough; III.3.3a Lcingmuir-Blodgett; see there lattice theory; III.3.5e mixed; III.3.4f molecular dynamics; III.3.5d molecular thermodynamics; 111.3.5 Monte Carlo; III.3.5c neutron reflection; III.table 3.5, III.3.7b optical techniques; III.3.7b-c permeation; III.3.238 phase behaviour; III.3.3 phospholipids; III.3.8c polymer brushes; III.3.4J, III.3.8f polymers; III.3.4i, III.3.8e preparation; 111.3.2 reflection; III.III.3.7b relaxation; III.3.6h reproducibflity; III.3.8a, Ill.fig. 3.79 rheology; see interfacial rheology; scanning probe; III.3.7d, III.table 3.5 simulations; III.3.5c, III.3.5d spectroscopy; III.3.7c, III.table 3.5 thermodymamics; III.3.4 thermodynamics; III.3.4 transfer; III.3.7a, Ill.fig. 3.5„ Ill.figs. 3.53-54 Volta potential; see there. For the optical techniques see the entry in question X-ray diffraction; Ill.table 3.5, III.3.7b X-ray reflection; Ill.table 3.5, III.3.7b
SUBJECT INDEX monolayer formers; III.3.200 montmorillonite; I I . 3 . 1 6 5 adsorption of alcohols + benzene; II.fig. 2.21 adsorption of m e t h a n e + benzene; II.fig. 2.22 adsorption of poly(acryl amide); II.fig. 5.39b adsorption of water vapour; II.fig. 1.30 Monte Carlo simulations; I.3.1e(intr.), I.fig. 5.4, 1.5.30 adsorbed liquids; II.fig. 2.4 adsorbed polymers; II.5.30 electric double layer; II.fig. 3.18 Mountain lines; 1.7.45. moving b o u n d a r y electrophoresis; II.4.51ff, II.fig. 4.17 muscovite; II.3.165 natural; see process Navier-Stokes equation; [1.6.1.15], 1.6.51, II.4.18, (II.4.6.4]ff negative adsorption; see adsorption, negative Nernst-Einstein equation; [1.6.6.15], [11.3.13.14], [II.4.3.55] Nemst-Planck equation; I.6.7a, 1.6.89, II.2.85, [II.3.13.12], [II.4.6.2] N e m s t ' s heat theorem; 1.2.24 N e m s t ' s law for distribution equilibrium; 1.2.20a, 1.2.81 N e m s t ' s law for electrode potential; 1.2.34, 1.5.5c, I.5.5e, II.3.8, I I . 3 . 9 1 , II.3.147ff, II.3.150 N e u m a n n triangle; [111.5.1.3], Ill.fig. 5.6 n e u t r o n reflection (by surfaces); II.2.7, II.5.66ff n e u t r o n scattering (by colloids); 1.7.9, 1.7.102 Newton films; III.5.39 Newton(ian) fluids; 1.6.8, I.table 6 . 1 , I.6.4a, III.3.6b Newton's second law; [1.6.1.12], 1.6.4 NMR = nuclear magnetic resonance non-ionic surfactants; see surfactants non-linear optical techniques; III.table 3.5 non-Newton(ian) flow; 1.6.36, III.3.6b non-solvent; 1.1.27 normal stress; see stress nuclear magnetic resonance (NMR); 1.7.16, 1.7.13, 1.7.102 chemical shift; I.5.54ff, I.fig. 5.8 of interfaces; II.2.8, II.2.55, II.5.58ff, II.5.71 of pores; II. 1.90 of water; I.5.54ff, I.fig. 5.8, (see also; spin, etc.)
47
48
SUBJECT INDEX
nucleation, heterogeneous; 1.2.100, II. 1.42 homogeneous; 1.2.23d in pores; see capillary condensation number of realizations; 1.3.4 octupole moment; 1.4.19 odd-even parity; III.3.302, Ill.fig. 4.31, Ill.fig. 4.36 oHp = outer Helmholtz plane oil recovery, tertiary; see enhanced oil recovery ointments; 1.1.6, 1.1.28 Onsager formula (for limiting conductivity); [1.6.6.26] Onsager formula (for polarization); [1.4.5.20] Onsager relations (irreversible thermodynamics); 1.6.2b application to electrokinetics; 1.6.2c, II.4.2, II.4.7, II.4.21, II.4.27, II.4.61, II.4.106 Onsager theorem (for approach to equilibrium); 1.7.44, 1.7.48, Lapp. 11.3, Lapp. 11.5, Lapp. 11.7-8 optical activity; I.7.99ff optical mixing (beating); 1.7.37 heterodyne; 1.7.37, L7.6d optical axes; 1.7.14 homodyne; 1.7.37, I.7.6d ordering parameter; 1.6.73, III.3.71ff, Ill.fig. 3.61, III.3.166 open circuit potential; II.3.149 ore benification; 1.1.25, II.5.97 orientation of adsorbed molecules; 11.2.55 Omstein-Zemike equation (for compressibility); [1.3.9.32] Omstein-Zernike equation (for critical opalescence); [1.7.7.10] oscillating drop; Ill.fig. 3.72 oscillating liquid jet; Ill.figs. 1.28 and 29, III. 1.84 oscillation, harmonic; 1.4.38, 1.4.44, I.7.3d, III.3.80ff, 111.3.105ff, Ill.fig. 3.41, Ill.fig. 3.45 oscillator; 1.7.3b oscillator, harmonic; 1.3.5a, 1.4.37 oscillator strength; 1.4.38 osmotic coefficient; 1.2.18a osmotic equilibrium; see equilibrium osmotic pressure; 1.2.34, 1.2.64, I.2.20d osmotic repulsion; 1.2.72, I.fig. 2.11 Ostwald equation; [1.2.23.25], II.1.19. [III.1.13.2]
SUBJECT INDEX Ostwald ripening; 1.2.97, II.1.103, II.3.110 outer Helmholtz plane; II.3.17, II.3.59ff overflowing cylkinder (in rheology); III .fig. 3.73 oxides (in general), double layer; I.5.6a, I.5.6b, II.3.71ff, Il.table 3.5, II.3.8, II.3.71ff, 11.3.10c point of zero charge; II.3.112, Il.app. 3b, Il.table 3.5 (for specific oxides, see under the chemical name) Overbeek equations (for retarded London-Van der Waals forces); [1.4.4.23a, b], 1.4.74 overpotential; 1.5.79 paints; 1.1.22, 1.1.28 pair correlation function: 1.3.66, II.3.5Iff pair interaction; see interaction Pallmann effect = suspension effect paper electrophoresis; II.4.131 parachor; III.2.67 parameter, extensive; 1.2.10 intensive; 1.2.10 mechanical; 1.3.40 thermodynamic; 1.3.40 paraquat; [11.3.14.1] partial molar quantities; 1.2.46 particle-in-a-box problem; 1.3.23 particles (colloidal), form factor; 1.7.56, .I.7.70ff shape; I.6.5g (2), 11.(3), I.7.8c, I.7.8d, 1.7.69 size; 1.7.8, 1.7.67 see also; charged (colloidal) particles particle-wave duality; 1.7.5 partition; see distribution partition function; I.3.2(intr.), 1.3.3, 1.3.4, 1.3.5, Lapp. 6 canonical; I.3.2(intr.), 1.3.3, 1.3.4, 1.3.5, 1.3.51, 1.3.54, 1.3.59, 1.3.63, Lapp. 6 for ideal gas; I.3.6b, L 3 . 6 c for localized adsorbate; L 3 . 6 d for subsystem; 1.3.5 grand (canonical); I.3.2(intr.), 1.3.3, 1.3.4, 1.3.31, 1.3.33, I.3.54ff, 1.3.63, Lapp. 6, 11.1.95, 11.1.99
49
50
SUBJECT INDEX
partition function; grand canonical
(continued)
isobaric-isothermal; 1.3.13, 1.3.18, 1.3.19 microcanonical; I.3.2(intr.), 1.3.3, 1.3.4 separable; 1.3.20 Pascal's law; 1.2.90, III.2.9 Pauli principle: 1.4.5, 1.4.42, II.3.172 PCS = photon correlation spectroscopy = QELS; see electromagnetic radiation Pearson's rule; II.3.185 Peclet number; 1.7.97 p e n d a n t drop; see drop, pendant penetration depth (evanescent waves); [1.7.10.12] period (of a wave); 1.7.4 permeability; see porous plugs of monolayers; III.3.239ff perpetual motion; 1.2.8 of second kind; 1.2.23 persistence length; see polymers in solution persistence parameter; see polymers in solution persistence time; 1.5.45 PFM = polairzed fluorescence microscopy phagocytosis; III.5.2, III.5.100 phase angle; Lapp. 8, see further loss angle p h a s e diagrams (2D); III.fig. 3.15, Ill.fig. 3.19, (see the n(A) curves in Ill.chapter 3 p h a s e integral; 1.3.57 phase rule (Gibbs); 1.2.13 p h a s e separation transitions a n d coexistence; 1.2.19, II.5.2e in capillaries; II.1.6e in interfaces; III.2.18, III.3.3b. Ill.table 3 . 1 . III.3.4d, III.3.217ff (see also; demixing, critical point, condensation s u b two-dimensional a n d polymers in solution) phase space; I.3.57(def.) phenomenological approach; I.1.29(def.), 1.2.2 p h o s p h a t e binding (soils); 11.3.2 22 phospholipids, see lipids photobleaching; 1.7.103 photocatalysis; II.3.222 photochromic probes; 1.7.103 photoconduction; II.3.173 photocorrelation spectroscopy = QELS; see electromagnetic radiation photoelectric effect; 1.7.85
SUBJECT INDEX
51
photolysis of water; II.2.87, II.3.223 photons; 1.7.5, III.3.168 (counting) physisorption; II. 1.5, II. 1.18, Il.l.SOff pipettes, emptying; III.fig. 1.8 plant growth in arid regions; 1.1.1, 1.1.2 Plateau border; 1.1.16, I.fig. 1.11 point of zero charge; 1.5.90, I.5.6e, II.3.8, II.3.11, II.3.17, II.3.74, II.3.8, Il.app. 3, II.3.118, II.3.120, Il.fig. 3.61, II.3.162 experimental determination; 11.3.8a influence of organic additives; II.3.12d, Il.figs. 3.77-80, Il.fig. 3.82, II.3.223 influence of specific adsorption; II.3.68ff, II.3.103ff, Il.fig. 3.34 interpretation; II.3.8c pristine; 1.5.102, II.3.8, II.3.103ff, Il.fig. 3.34, II.3.140, II.3.152 relation to isoelectric point; II.3.8b, Il.fig. 3.35 tabulation; app. II.3 temperature dependence; 3.75ff, II.3.115ff, Il.figs. 3.36-37 Poiseuille's law; see Hagen-Poiseuille's law Poisson-Boltzmann equation; 1.4.16, 1.5.18, [II.3.5.6], [II.3.5.44], lll.3.5.57fn Poisson-Boltzmann theory; II.3.6a for flat interfaces = Gouy-Chapmcm theory for low potentials = Debye-Huckel theory improvements; I.5.2c, II.3.6b, Il.figs. 3.18-19 Poisson's law (electrostatics); 1.4.53, 1.5.10, [I.5.1.20-20al, II.3.19, II.3.35, [11.3.5.431, [II.3.6.14], II.3.211, II.4.18, II.4.70, [II.4.6.12]ff, II.4.115, II.5.55 polarimeters; 1.7.99 polarizability (intr.); I.4.22ff, I.4.4d, I.4.4e, 1.7.18, 1.7.53, 1.7.94 data for molecules; I.table 4.2 molar; 1.4.24 polarization, II.dielectric (phenomenon); 1.4.4b, I.4.4e, I.4.5f of interfaces; 1.5.5b, II.3.9 (see potential difference, x) polarization, dielectric (physical quantity); I.4.5f, 1.7.2, 1.7.6 polarization (of radiation, etc.); see electromagnetic radiation polarized fluorescence microscopy; III.3.7c.iv polarizer; I.fig. 7.7, 1.7.99 polairzer-sample-analyzer; III.3.7b.I polar molecules; 1.4.4b poly(acryl amide), adsorption on montmorillonite; Il.fig. 5.39b
52
SUBJECT INDEX
poly(ethylene), AFM image; II.fig. 1.3 poly(ethylene oxide or oxyethylene), adsorption on latex and Si02; II.fig. 5.25 polyampholytes; I I . 5 . 1 3 polydispersity; 1.1.13 polyelectrolytes; 1.1.6, II.5.2f adsorption; see there polyelectrolyte effect; I I . 3 . 7 1 , II.3.76 polyelectrolytes in solution; II.5.2f charge; II.5.14ff persistence length; II.5.14, II.fig. 5.5 polymer b r u s h , monolayers; III.3.8f, Ill.figs. 3.96-98, Ill.fig. 3.100 polymer melt n e a r a wall; II.5.45ff polymers in solution; I.1.2(intr.), I.fig. 1.17, 1.3.34 concentration regimes; II.5.9ff, II.fig. 5.3 conformation; II.figs. ,5.1-2, II.5. Iff end-to-end distance; II.5.4, II.fig. 5.2 excluded volume (parameter); II.5.3, II.5.2b, II.5.5b e x p a n s i o n coefficient; II.5.6ff ideal chain; I I . 5 . 3 , I I . 5 . 2 a light scattering; I.7.56ff, I.7.62fi^ molecular m a s s ; I.7.62ff, 1.7.68 overlap; I I . 5 . 2 c persistence (stiffness) parameter; II.5.4 p h a s e separation; II.fig. 5.3, II.5.2e, II.fig. 5.4 solvent quality; 11.5.2b swollen chain; I I . 5 . 3 , II.5.2b, II.5.9 thermodynamics; II.5.2c (see also; r a d i u s of g3a-ation, adsorption of polymers, colloid stability) polymers, average molecular m a s s ; I.7.62ff, I.7.68ff backbone = primary structure primary structure; II.5.3 secondary structure; II.5.3 tertiary structure; II.5.3 poly(methacrylic acid), adsorption on silver iodide; II.fig. 5.36-37
SUBJECT INDEX poly(methacrylic ester), monolayer; III.3.8e, Ill.figs. 3.94-95 poly(oxymethylene), adsorption of polylstjrrene sulfonate); II.fig. 5.35 poly(styrene), adsorption on silica; Il.fig. 5.28, ILfig. 5.30 polytstyrene) latex, adsorption of C9(|)P^x)^<m>(^o^"^o^^^)' II-fig- 2.32 adsorption of Cg(t)P^i3^E^27)(^on-ionic); Il.fig. 2.33b adsorption of poly(ethylene oxide or oxy-ethylene); Il.fig. 5.25a polyCstyrene sulfonate), adsorption on poly(oxymethylene); Il.fig. 5.35 polylstyrene co 2-vinyl pyridine), AFM image; Il.fig. 1.4 poly (vinylpyrrolidone), adsorption on Si02; Il.fig. 5.22 pores (in surfaces); II. 1.6 ad- a n d desorption of gases; II.figs. 1.32-35 classification into macro-, Il.meso- a n d micropores; II. 1.6a connectivity; II. 1.82 mesopore filling; II. 1.6b micropore filling; II. 1.82, II. 1.6c Molecular dynamics; Il.fig. 1.38 r a d i u s (effective); II. 1.84 size distribution; II. 1.85, II. 1.88 volume; II.1.84ff (see also; porosity, hysteresis, capillary condensation) porosity, m e s o p o r o s i t y ; II. 1.6b microporosity; II. 1.6c of plugs; I.6.50ff of surfaces; II.1.6, II.2.67, II.3.161 by mercury penetration; II. 1.90, II. 1.100 classification; II. 1.6a (see also; adsorption hysteresis, capillary condensation, pores (in surfaces)) porous plugs, permeability; I.6.4f, II. 1.90, II.4.55ff, Il.fig. 4.18 electro-osmosis; II.4.3b, Il.fig. 4.6, II.4.5b, Il.fig. 4.18 other electrokinetic phenomena; II.4.5b, Il.fig. 4.18-19, I I . 4 . 7 , Il.figs. 4.34-35 wetting; III.5.4i, III.5.9 porous surfaces; see pores (in surfaces)
53
54
SUBJECT INDEX
potential-determining ions; see surface ions or charge-determining ions potential difference (between adjacent phases); I.table 5.13, 11.3.7b, II.3.138 ;i:; 1.5.73-74, II.2.19, II.3.91, II.3.102, II.3.115, II.3.9, Il.figs. 3.38-39, Il.table 3.7, II.3.179, Il.fig. 3.75, Il.table 3.9, II.3.200ff, Il.fig. 3.79, III.2.47, [111.3.7.22], III.4.4a,b, Ill.fig. 4.20, Ill.fig. 4.24 electrokinetic (^); see electrokinetic potential Galvani; I.5.5a, I.5.5c, II.3.14, II.3.90, II.3.119ff, Il.fig. 3.38, II.3.138 liquid Junction (diffusion); I.5.5d, I.fig. 5.12, I.6.7b real; 1.5.75, II.3.121ff, Il.table 3.7 Volta; I.5.5a, II.3.119ff, Il.fig. 3.38, Il.figs. 3.74-75, II.3.179, III.3.7f, Ill.fig. 3.75, Ill.fig. 3.76. Ill.fig. 3.85, Ill.fig. 3.88, Ill.fig. 4.14 (see also; suspension effect) potential of a force; 1.4.3b electric; 1.4.12, 1.5.3, I.5.7ff, 1.5.10, I.fig. 5.1, II.3.3 interfacial; 1.5.5, II.3.6b in diffuse layer. Stem layer etc.; see there of mean force vs. mean potential; I.4.3c, 1.5.18, I.5.24ff, I.5.27ff, II.3.51ff potentiometric titration (of colloids); see colloid titration powder technology; II.5.97 powders (wetting); III.5.4b, III.5.9 Poynting vector; 1.7.5, 1.7.10, 1.7.97 precursor film; III.5.8, Ill.fig. 3.35 pressure, two-dimensional; see surface pressure pressure tensor; III.2.3 prefixes (table); Lapp. 2 primary minimum; see colloids, interaction primitive (liquid model); I.5.1(def.) in conduction; 1.6.79 in diffusion; 1.6.56 in hydrodynamics; 1.6. Iff in solvation; 1.5.3b principal axes (in optics); 1.7.98 principal radii of curvature; see curvature, radius of probability; 1.3.1, I.3.2d, 1.3.3 probability distributions; I.3.2d, 1.3.7b process; I.2.3(def.) endothermic; 1.2.8 exothermic; 1.2.8 isobaric; 1.2.3 isochoric; 1.2.3
SUBJECT INDEX process
(continued)
isosteric; 1.2.3 isothermal; 1.2.3 n a t u r a l (or irreversible); 1.2.4, 1.2.8 reversible; 1.2.3, 1.2.21 s p o n t a n e o u s ; 1.2.4, 1.2.8 stochastic; 1.6.3 (see also; transport) protection, of colloids against aggregation; I.1.2(intr.), 1.1.27 proteins; 1.1.23 proton acceptor; 1.5.65 proton donor; 1.5.65 PSA = polcirizer-sample-analyzer pulmonary surfactant = lung surfactant purity criteria (of interfaces); III.1.7, III.1.14c p.z.c. = point of zero charge QELS = quasi-elastic (light) scattering; see electromagnetic radiation, scattering quenchers; 111.3.165 quadrupole moment; 1.4.19, 1.5.42 quasi-chemical approximation (in statisticad thermodjmamics); I.3.8e quasi-elastic (light) scattering (QELS); see electromagnetic radiation, scattering radial distribution functions; see distribution function r a d i a n t intensity; 1.7.5 radiation; see electromagnetic radiation radius, hydraulic; 1.6.50 hydrodynamic; 1.7.51 of gyration; 1.7.57, II.5.4, II.5.6ff R a m a n scattering; see electromagnetic radiation scattering R a m a n spectroscopy; 1.7.12, III.3.7c.ii Randies circuit; II.fig. 3.31 r a n d o m coil; 11.5.3 r a n d o m flight or r a n d o m walk; 1.3.34, 1.6.3, II.5.3ff, ILfig. 5.2, II.5.24 Raoult's law for vapour pressure lowering; 1.2.74, II. 1.70 Rayleigh-Brillouin scattering; see electromagnetic radiation scattering Rayleigh-Debye (-Cans) scattering; I.7.8d, 1.7.67 Rayleigh instability; I l l . S . l l d , Ill.fig. 5.47 Rayleigh line; 1.7.44 Rayleigh ratio; !l.7.7.61(def.), 1.7.3 (table)
55
56
SUBJECT INDEX
red shift (of spectra); 1.7.19 reference electrode; 1.5.82 reference state; see state, standard reflection, multiple; 1.7.80, II. 1.18 total; 1.7.74 reflection angle; 1.7.72 reflection at interfaces; 1.7.10a, III.fig. 3.57 reflection coefficient; 1.7.73, II.2.50 reflection electron spectroscopy; see scanning electron spectroscopy reflectometry; 1.7.10b, II.2.5c, II.figs. 2.15-16, II.5.64, III.2.47 refraction angle = transmission angle refraction by interfaces; 1.7.10a refractive index; 1.7.12, 1.7.14 complex; 1.7.2c, 1.7.61, 1.7.98 Regular Solutions; L2.18c, II.2.30, II.5.8 relaxation (time); I.4.4e, I.6.6c, II.3.13, II.4.10ff, II.4.6c, II.4.8 Debye; 1.6.73 dielectric; see dielectric relaxation double layers; see there Maxwell (-Wagner); 1.6.84, II.3.219, II.4.111 of interfaces (electric); 1.5.5b in Langmuir monolayers; III.3.6h. Ill.figs. 3.46-47 retardation (in ionic conduction); 1.6.6b, 1.6.6c thermodynamic; 1.2.3 (see also; diffusion, rotational, double layer, relaxation) repulsion, electric; 1.1.2Iff osmotic; 1.2.72 (see further: colloids, interaction) residence time, and adsorption; II.1.46ff, [11.2.4.1] and hydration; 1.5.53 resonance band = absorption band resonance (electric); I.4.4e resonance frequency; 1.4.34 resonators; 1.7.4a respiratory stress syndrome; 111.3.238 retardation (of dispersion forces); see Vam der Waals forces retention volume; see chromatography
SUBJECT INDEX
57
reversible, reversibility (in thermodynamic sense); 1.2.3, 1.2.9, 1.2.8 colloids = colloids, lyophilic interfaces (in electrical sense); 1.5.5b (see also; process; for adsorption reversibility, see (adsorption) hysteresis Reynolds limit (wave damping); Ill.fig. 3.44. III.3.117ff Reynolds number; I.6.4b, I.table 6.2 rheology; I I I . 3 . 6 b see also; interfacial rheology ring t r o u g h (interfacial rehology); Ill.fig. 3.71 rotating molecule; I.3.5e rotational correlation time; see correlation time rotational diffusion (coefficient); see diffusion Rowlinson-Widom equation (for surface tension); [III.2.5.40] rubber, adsorption on carbon black; II.fig. 5.31 r u t h e n i u m dioxide, double layer; ILfig. 3.56, II.fig. 3.59 point of zero charge; Il.app. 3b XPS (= ESCA) spectrum; Il.fig. 1.5 rutile, see titanium dioxide saddle splay modulus; III. 1.79 Sackur-Tetrode equation; [1.3.1.9], 1.5.35, [111.2.9.12] (for surfaces), III.3.37 salt-sieving; 1.1.1, 1.1.3, I.1.21ff, II.3.28, II.3.223, II.4.56 salting-out; 1.5.71 saMng-in; 1.5.71 Sand equation; [1.6.5.23], I.fig. 6.15b SAMS = self assembled monolayers; III.3.240 SANS = small angle neutron scattering Saxen's rule (electrokinetics); 1.6.17, II.4.2 SAXS = small angle X-ray scattering scaling theory; I I . 5 . 1 1 , I I . 5 . 4 c , III.3.8e,f scanning electron microscopy (SEM); 1 . 7 . l i b , Il.fig. 1.1 scanning, optical; III.3.7c.iv, I I I . 3 . 7 d scanning probe microscopy (SPM); III.table 3.5 (includes STM a n d AFM), III.3.7d s c a n n i n g transmission electron microscopy (STEM); 1 . 7 . l i b scanning tunnelling microscope (STM): 1.7.90, II. 1.12, III.3.7d Scatchard plot; II. 1.48 scattering, length density; 1.7.70, II.5.66 length; 1.7.70, II.5.66
58
SUBJECT INDEX
scattering
(continued)
plane; I.7.27(def.) from surfaces; III. 1.10 wave vector; I.7.27(def.), III.1.54 scattering of: neutrons; 1.7.9b radiation; see electromagnetic radiation X-rays; 1.7.9a Schottky defects; II.3.173 Schulze-Hardy rule (for coagulation of coUoids); 1.5.67, 1.6.83, II.3.129ff Schrodinger equation; 1.3.1, 1.3.11, I.3.20ff screening (of charges); 1.5.11 second harmonics, generation; II.2.55, III.3.7c.v, Ill.figs. 3.64-65 second central moment; 1.3.35 Second Law of thermodynamics; see thermodynamics Second Postulate of statistical thermodjoiamics; see statistical thermodynamics second virial coefficient; see virial coefficient secondary ion m a s s spectroscopy (SIMS); 1.7.11a, I.table 7.4, II. 1.15, II.fig. 1.6 secondary m i n i m u m ; see colloids, interaction sediment, sedimentation; 1.1.2, 1.1.22, I.fig. 1.14, 1.6.48 sedimentation current; II.4.24 sedimentation potential (gradient); II.table 4 . 1 , II.4.6-7, II.4.3c seeds (in nucleation); 1.2.100 segment weighting factors; II.5.37ff selection rules, infrared; I.table 7.5 Raman; I.table 7.6 self Gibbs energy; see Gibbs energy self-avoiding walk; II.5.6 self-consistent field; II.5.29, I I . 5 . 5 self-diffusion; see diffusion self-similarity, in Brownian motion; 1.6.18 in scaling theory; II.5.34 SEM = scanning electron microscopy s e m i c o n d u c t o r s ; 11.3. lOe double layer; II.3.10e, II.figs. 3.60-72 intrinsic; I I . 3 . 1 7 0 n-type and p-type; II.3.173
*
SUBJECT INDEX semidilute (polymer) solution; II.fig. 5.3, II.5.2d SER = surface enhanced Raman spectroscopy SF = Scheutjens-Fleer (polymer adsorption theory) SFG = s u m frequency generation SFM = scanning force microscopy; see AFM = atomic force microscopy shear rate; 1.6.32 shear stress; see stress s h e a r thickening, thinning; 111.3.8 7 SHG = secnd harmonic generation shielding (of charges); see screening silica, silicium dioxide, adsorption of poly(oxyethylene); II.fig. 5.25b adsorption of poly(styrene); II.fig. 5.28, II.fig. 5.30 adsorption of poly(vinyl pyrrolidone); II.fig. 5.22 point of zero charge; Il.app. 3b Aerosil, adsorption of Cg(t)P^i3^E^27)(^o^'^o^^c)' H-fig- 2.33a adsorption of various organic s u b s t a n c e s from carbon tetrachloride; Il.fig. 2.27 adsorption of water vapour; Il.fig. 1.28 Cab-o-Sil, adsorption of water vapour; Il.fig. 1.26 adsorption of nitrogen, Il.fig. 1.26 double layer; II.table 3.5 hydrophilic, adsorption of Ci2^5 (non-ionic); II.figs. 2.30-31 immersion, wetting; II.table 1.3 Ludox, adsorption of CjgEe (non-ionic); Il.fig. 2.31 oxidized wafers, adsorption of C12E6 (non-ionic); Il.fig. 2.31 precipitated, adsorption of nitrogen; Il.fig. 1.34d double layer; II.figs. 3.64-65, Il.table 3.8 pyrogenic, double layer; Il.fig. 3.65 quartz, double layer; Il.fig. 3.65 wetting by water; 111.5.3c
59
60
SUBJECT INDEX
silica sols, stability; II.3.161-2 silicium dioxide-zirconium dioxide catalyst, SIMS spectrum; II.fig. 1.6 silver bromide, point of zero charge; Il.app. 3 c silver iodide, adsorption of alcohols; II.figs. 3.77-79, Il.table 3.9 adsorption of dextrane; II.fig. 5.26b, II.5.80ff, Il.fig. 5.29 adsorption of poly(methacrylic acid); 11, figs. 5.36-37 adsorption of tetraalkylammonium salts; II.figs. 3.80-81 double layer; II.3.8, Il.fig. 3.28, II.fig. 3.32, Il.table 3.6, 11.3.10a, Il.figs. 3.40-46, II.3.112, Il.figs. 3.52-53, Il.fig. 3.56, Il.table 3.8, II.3.202ff, Il.figs. 3 . 7 7 - 8 1 , Il.table 3.9 electrokinetic charge; Il.fig. 4.13 electrosorption; II.3.12d, Il.fig. 3 . 7 7 - 8 1 , Il.table 3.9 negative adsorption of ions; Il.fig. 3.40 point of zero charge; II.3.110ff, Il.fig. 3.36, Il.figs. 3.41-43, Il.figs. 3.77-80, Il.app. 3 c , Il.fig. 5.37 site binding (adsorption); II. 1.47-48, II.3.6e, II.3.159, Il.fig. 3.63 SIMS = secondary ion m a s s spectroscopy single ionic activities; 1.5. l b (see also; activity coefficient) sky (blue colour); 1.3.34, 1.7.25 slip plane, slip process; 1.5.75, I I . 4 . l b , Il.fig. 4.3 interpretation; II.4.4 sludges; 1.1.23 small-angle n e u t r o n scattering (SANS); 1.7.9b small-angle X-ray scattering (SAXS); 1.7.9a smectite, wetting; Il.table 1.3, II.3.165 smoke; 1.1.6 Smoluchowski's theorem (electrokinetics); II.4.21-22 Snell'slaw; 1.7.11, 1.7.72 soap bubbles; I.fig. 1.4, I.figs. 1.9-10 soap films; see films, liquid sodium dodecylsulphate; 1.1.24, I.fig. 1.15 surface tension; III.fig. 1.30 sodium laurylsulphate; see sodium dodecylsulphate soils (permeation in); 1.1.2, 1.1.3, I.1.22ff, 1.1.28 sol; I.1.5(def) ageing; 1.2.99
SUBJECT INDEX sol
61
(continued) colour; I.7.60ff
solar energy conversion; II.3.223 solid surfaces cind interfaces, c h a r a c t e r i z a t i o n ; II. 1.2 solid-liquid; II.2.2, Il.figs. 2.4-7 t h e r m o d y n a m i c s ; 1.2.24 (for adsorption, double layers etc. see there; also see, interfacial tension of solid surfaces) solubility, of gas in liquid; 1.2.20b of liquid in liquid; 1.2.20c of small drops a n d particles; 1.2.23c of solid in liquid; 1.2.20c solubility p a r a m e t e r (Hildebrand); 1.4.47 solutions, (ideally) dilute; 1.2.17c, 1.2.20 non-ideal; 1.2.18 solvation; 1.2.58, 1.4.42, I.4.5c, 1.5.3 solvent, quality of; 1.1.7, I.1.25ff, I.fig. 1.17, 1.1.30, II.5.2, Il.fig. 5.24 solvent structure; 1.5.3, 1.5.4 n e a r surfaces; see distribution functions of liquids near surfaces (see; interactions, solvent structure-mediated) space charge (density); 1.5.9, II.fig. 3.70 speciation; I.5.2(def.) specific binding, specifically b o u n d chcirge; 1.5.3 specific vs. generic (properties, phenomena); 1.5.67, II.3.6 specific adsorption; I.5.6d, I.5.104ff, II.3.6, II.fig. 3.20b, II.c, II.3.6d, II.3.6e criteria for absence or presence; 1.5.102, II.3.108ff, II.3.132 first a n d second kind; II.3.64 site binding models; II.3.6e spectral density; 1.7.34 (intr.) spectroscopy, of surfaces; 1.7.11, I.table 7.4, II.2.7ff, Ill.table 3.5, III.3.7c spectrum, continuous; 1.7.20 spectrum analyzer; 1.7.37 (intr.) spin-echo techniques; 1.7.102 spin (electronic); 1.7.16, 1.7.13
62
SUBJECT INDEX
spin labels; 1.7.13 spin-lattice relaxation; 1.7.96 spin (nuclear); 1.7.16, 1.7.13 spinning drop; see interfacial tension, measurement spinodal; 1.2.68, II.5.12, II.fig. 5.4 SPM = scanning probe microscopy sputtering; II. 1.110 spin quantum number; 1.7.16 spin-spin relaxation; 1.7.96 spontaneous; see process spreading; 1.1.8, III.3.2 rate of; III.3.12 spreading coefficient = spreading tension spreading parameter = spreading tension spreading tension; III.3.8, III.5.4. III.5.6, |III.5.1.1], III.5.15ff square gradient (across interfaces); [III.2.5.28I. [III.2.5.30I, III.2.28ff, III.2.36 square gradient method (polymer adsorption); II.5.33ff stability, stabilization, thermodynamics; 1.2.7, 1.2.19 (see colloids, stability of; steric stabilization, state) stagnant layer (electrokinetics); II.2.15, II.4.1b, II.4.4, II.4.128ff standard deviations; I.3.7a, I.6.19ff, [II. 1.5.11] starch; 1.1.2 Stark effect (for spectral lines); 1.7.16 state, metastable; 1.2.7 molecular; 1.2.3, 1.3.2 stable; 1.2.7 standard; 1.2.4 thermodynamic; 1.2.3 (see also; equation of, function of) state variables; 1.2.3 stationary state; 1.6.8, 1.6.13, 1.6.15, II.4.2, II.4.6 statistical chain element; I.3.5f, II.5.5 statistical mechanics; see statistical thermod5niamics statistical thermodynamics; I chapter 3 classical; 1.3.9 postulates; 1.3.2, 1.3. Id (see also; adsorption isotherm, Fermi-Dirac, Maxwell-Boltzmann interfacial tension, interpretation)
SUBJECT INDEX
63
Stefan-Ostwald rule (for surface tensions); [III.2.11.25] STEM = scanning transmission electron microscopy step-weighted lattice walk; 1.6.28, II.5.5 steric stabilization; see colloid stability Stem layer; see double layer stiffness parameter = persistence parameter, see polymers in solution Stirling approximation; [1.3.6.51 STM = scanning tunnelling microscope stochastic; see processes, forces Stokes' law; [1.6.4.30), 1.6.56, II.4.18, II.5.62 Stokes limit (wave damping); Ill.fig. 3.44, III.3.117ff strain; III.3.6b strain rate; III.3.85ff streaming, or flow birefringence; 1.7.97, 1.7.100 streaming current; I.6.16ff, Il.table 4.4, II.4.7, II.4.3d, Il.fig. 4.8, II.4.55 streaming potential; I.6.16ff, II.fig. 3.78, Il.table 4.4, II.4.7, II.4.3d, Il.fig. 4.8, II.4.5b, Il.fig. 4.30, Il.fig. 4.35, II.5.63 stress, normal; 1.6.7, III.3.6b shear; 1.6.7, 1.6.1 Iff, I.6.4a, III.3.6b stress tensor; I.6.6ff, [III.3.6.1-2], see also interfacial rheology stretching of solid surfaces; 1.2.103 structural forces; 1.4.2, II. 1.95 structure breaking; 1.5.38, 1.5.3d structure of water; see water, structure structure promotion; 1.5.38, 1.5.3d structure factor; 1.3.67, 1.7.64, Lapp, l i e substantial derivative; 1.6.5 subsystems (statistical thermodynamics); 1.3.5, 1.3.6 dependent; 1.3.5, 1.3.20, 1.3.8 independent; 1.3.5, 1.3.20, 1.3.6 sum frequency generation; III.3.7c.v supercooling; 1.2.23d supermolecular fluids; 1.7.63 super saturation; 1.2.23d surface; I.1.3(intr.), acidity/basicity (dry surfaces); II. 1.18 characterization in general; II. 1.2, Il.table 1.1, II.2.2a external vs. internal; II. 1.6a heterogeneity; I.1.18(intr.), 1.5.106, II. 1.5, II. 1.7, II.2.29, II.3.83
64
SUBJECT INDEX
surface (continued) patchwise vs. random; Il.l.lOSff 'high' vs. 'low' energy; II. 1.35 hydrophilicity/hydrophobicity; II. 1.19, II. 1.35, II.2.7, II.2.87, II.3.130 imaging techniques; 1.7.11b porosity; see porosity of surfaces reconstruction; II. 1.8 scattering by; 1.7.10c spectroscopic characterization; 1.7.11, II.1.9ff, II.figs. 1.1-6 (see also; interface, especially for 'wet' surfaces, equations of state) surface (or interfacial) area, (molecular, in monolayers), III.3.15, III.3.24, see further the n(A) isotherms in Ill.chapter 3, Ill.fig. 3.16, Ill.fig. 3.82, 111.3.84 specific; I.1.18(def.), 1.1.20, I.6.4f, II.2.67, II.2.73, II.3.7e, II.3.127, II.3.131ff surface charge (density); 1.1.20, 1.5.3, 1.5.9, 1.5.6, II.3.3, II.3.21, ILfig. 3.18, Il.fig. 3.28, ILfig. 3.41, ILfig. 3.52, Il.figs. 3.56-59, Il.figs. 3.63-65, Il.figs. 3.69-70, ILfig. 3.77, ILfig. 3,.80, ILfig. 3.82-83 determination; I.5.6e, II.3.7a dipolar contribution; II.3.126 discrete nature; II.3.46, II.3.6e for clay mineral-type particles; II.3.10d for polarized interfaces; I.5.6c, II.3.10b, 11.3.163 for relaxed (reversible) interfaces; I.5.6a, II.3.10a, IL3.10c, 11.3.163 formation thermodynamics; II.3.110ff Gouy-Stem layer; Il.figs. 3.23-25 relation to D and E; L4.53ff site-binding models; IL3.6e (from) statistical theories; ILfig. 3.18 (see double layer, diffuse, charge) surface concentration; see interfacial concentration surface conduction and conductivity; 1.5.4, I.6.6d, II.3.208, 11.4.1, II.4.28, II.4.3f, Il.fig. 4.9, II.4.91, Il.table 4.3 behind slip plane; IL4.32ff, II.4.37ff, II.4.67, II.4.94, II.4.6f, Il.table 4.3 in diffuse double layer; II.4.32ff, ILfig. 4.10 Bikerman equations; [II.4.3.591ff influence on ^-potential; IL4.6e, Il.figs. 4.29-31, IL4.6f, Il.table 4.3 measurements; II.4.5c surface correlation length; II.2.10 surface diffusion (coefficient); I.6.69ff, II.2.14, II.2.29
SUBJECT INDEX
65
surface excess; see interfacial excess surface energy; see energy surface enhanced Raman spectroscopy; III.3.7c.ii surface equation of state; see : equation of state, two-dimensional surface force apparatus; 1.4.8 surface forces versus body forces; I.l.Sff, 1.4.2 surface ions; 1.5.89 surface modification; II. 1.110, II.2.88, II.5.97 surface porosity; see pores (in surfaces), porosity of surfaces surface potential; 1.5.5 ('surface potentials' of monolayers = Volta potentials; see under potentials) surface pressure; I.1.16(def.), 1.3.17, I.3.32ff, I.3.47ff, I.3.51ff, II.1.3, 11.1.3b, II.1.28, II.1.51, Il.fig. 1.15, II.1.59ff, Il.app. 1, II.3.14, II.3.140. III.chapters 3 , 4 (see also; equation of state, two-dimensional; for measurement, see film balance) surface pressure isotherms; III.chapter 3 surface rheology; see interfacial rheology Marangoni effect; I.1.2(intr.), 1.1.17, I.6.43ff surface roughness, and Van der Waals forces; 1.4.68 in electrokinetics; II.4.39 in optics; 1.7.10 surface states (semiconductors); II.3.172ff, II.3.176 surface tension; see interfacial tension surface of tension; 1.2.93 surface undulations; 1.7.77, 1.7.10c surface wave; 1.7.75 surface work; see interfacial work surfactants; I.1.4(def.), I.1.6(intr.), I.1.23ff, Il.figs. 1.1.15-16. III.4.6a, Ill.table 4.4 anionic; 1.1.23, III.4.6d adsorption of; Il.fig. 3. Id, also see monolayers monolayers; III.4.6d, Ill.fig. 4.36 bending moduli of monolayers; III.tables 1.6 and 7 cationic; 1.1.23, III.4.6d adsorption, see monolayers interfacial tension (dynamic and rheological); Ill.figs. 3.43-44, Ill.fig. 4.17 monolayers; III.4.6d, Ill.fig. 4.35. Ill.table 4.6, Ill.fig. 4.38
66
SUBJECT INDEX interfacial tension (dynamic a n d Theological); III.fig. 1.31, III.4.6
surfactants
(continued)
monolayers; Ill.fig. 3.65, III.4.6 non-ionic; 1.1.23 adsorption of; see poly(styrene) latex, silica, a n d monolayers cloud point; Ill.fig. 4.29. Ill.table 4.5 interfacial tension (dynamic a n d rheological); Ill.fig. 1.31 monolayers; III.4.6c, Ill.figs. 4.30-34 surface tension (dynamics, rheology); Ill.fig. 1.31 s u r r o u n d i n g s (in thermodynamic sense); 1.2.2, 1.3.2 susceptibility (electric); 1.4.52 (intr.) suspension; 1.1.2, 1.1.22, I.fig. 1.14 ageing; 1.2.99 suspension effect; I.5.5f, Lfig. 5.15, II.3.105 swollen dilute (polymer solution); II.5.9, II.fig. 5.3 system, (in statistical sense); 1.3.la (in thermodynamic sense); 1.2.2 Szyzskowski isotherm; [III.4.3.14] tactoids; II. 1.80 tails; see adsorption of polymers t-plot; see adsorption tangential stress = shear stress; see stress Tate's law; [111,1.6.11 Taylor n u m b e r ; 1.6.36 Taylor vortices; fig 1.6.8 Teflon, wetting; II.table 1.3 tensiometers; III. 1.8 tensors; Lapp. 7f TEM = t r a n s m i s s i o n electron microscopy tertiary oil recovery; see enhanced oil recovery thermal diffusion; 1.6.12, 1.7.44, 1.7.48 thermal n e u t r o n s ; 1.7.25 thermal wavelength; [1.3.5.14] thermodynamic state; 1.2.3 thermodynamics (general); I.chapter 2 First Law; 1.2.4, 1.4.3 irreversible; 1.6.2, I.6.5a, 1.6.6a, 1.6.7 Second Law; 1.2.8 Third Law'; 1.2.24
SUBJECT INDEX (see also; statistical thermodynamics) theta [0] solvent; 1.6.28 thickness of adsorbed layers; see adsorbate thin liquid films; see films thixotropy, thixotropic; 1.1.23, III.3.87 tilt angle; Ill.fig. 3.60 tilted plate; III.5.4d, Ill.fig. 5.24 time correlation functions; see correlation functions TIRF = total internal reflection fluorescence titanium dioxide; Il.table 1.3, Il.table 3.6 anatase, double layer; II.3.94 point of zero charge; Il.table 3.5, Il.app. 3b rutile, adsorption of anionic surfactants; II.figs. 3.82-83 adsorption of water vapour; II.fig. 1.9 double layer; Il.figs. 3.58-60, Il.fig. 3.63, Il.table 3.8, Il.figs. 3.82-83 electrokinetic charge; Il.fig. 4.13 point of zero charge; Il.table 3.5, Il.fig. 3.37, Il.fig. 3.82, Il.app. 3b C-potential; Il.fig. 3.63 total internal reflection fluorescence (TIRF); II.2.54, III.3.7c.iv total reflection; 1.7.74, II.2.51, II.2.54 trains; see adsorption of polymers transfer in galvanic cells; I.5.5e transfer, of molecules; 1.2.18a (ions to other phases); I.5.3f, 1.5.5 (molecules to other phases); 1.2.20, 1.4.47, 1.6.44 (see also; transport, II.viscous flow) transference numbers; see transport numbers transmission angle; 1.7.72 transmission coefficient; 1.7.73, II.2.50 transmission electron microscopy (TEM); 1.7.lib, Il.fig. 1.1 transport processes; I.chapter 6 (see also; hydrodynamics, diffusion, conduction) transport, linear laws; 1.6.Ic, I.table 6.1 of charge; I.table 6.1 of heat; I.table 6.1 of mass; 1.6. la, I.table 6.1
67
68
SUBJECT INDEX through interfaces; 1.6.44
transport
(continued)
of m o m e n t u m ; 1.6.1b, I.table 6 . 1 , 1.6.4a transport n u m b e r s ; I.6.76ff, [1.6.6.14](def), transverse waves; III.3.110, III.fig. 3.43, see further: interfacial rheology Traube's rule; 1.4.51 triboelectricity; I I . 3 . 1 8 7 Trouton's rule; III.2.54 (also for surfaces) tunnelling (of electrons); 1.7.90 turbidity; 1.7.41, 1.7.47 turbulence; 1.6.4b Tyndall effect; 1.7.26, II.4.45 ultramicroscope; 1.7.26, 11.fig. 4.14 ultrasonic vibration potential; II.4.7, II.4.3e uncertainty principle (Heisenberg); 1.3.4, 1.3.58 u n d u l a t i o n s (of fluid interfaces); III. 1.78 uniaxiality; 1.7.97 UPES = UPS = ultraviolet photo-electron spectroscopy; 1.7.11a UVP = ultrasonic vibration potential vacancy (in semiconductor); II.3.171 valence b a n d (solids); 11.fig. 3.68, II.3.173 Van der Waals interactions; I.chapter 4 between molecules (general); I.4.10ff, 1.4.4 additivity; I.4.18ff London (or dispersion); 1.4.17, I.4.4d, I.table 4 . 3 , I.4.4e, 1.4.5, 1.4.6, 1.4.7 Debye; 1.4.17, I.4.4c, I.table 4 . 3 , 1.4.41 Keesom; 1.4.17, I.4.4c, I.table 4 . 3 , 1.4.41 retardation; 1.4.17, 1.4.31, I.4.78ff between colloids a n d macrobodies; 1.4.6 Hamaker-De Boer; 1.4.6 Lifshits; 1.4.7 m e a s u r e m e n t (direct); 1.4.8, I.fig. 4.19 macroscopic; see Lifshits microscopic; see Hamaker-De Boer repulsive; 1.4.72, 1.4.78 retardation; 1.4.6c in thin films; II. 1.101 Van der Waals equation of state; [1.2.18.26], [1.3.9.28], [1.4.4.1], III.2.17. [III.2.9.3] (reduced)
SUBJECT INDEX Van der Waals loops; 1.3.47, 1.4.17, Il.fig. 1.20, I I . l . l O l , II.fig. 1.42 Van der Waals' theory (interfaclal tensions); III.2.5, III.2.3.1 (generalized ) Van 't Hoff s law, for boiling point elevation; 1.2.74 for freezing point depression; 1.2.74 for osmotic pressure; 1.2.20d, 1.7.50 vapour pressure, lowering; 1.2.74 of small drops; 1.2.23c variance; 1.3.35 vector, vector field etc.; Lapp. 7 velocity correlation function; Lapp. 11a, II.2.14 velocity distribution; 1.6.2Iff, I . 6 . 3 c , Lfig. 6.4 vermiculite, wetting; Il.table 1.3 vertical plate, wetting of; III. 1.3b end effect correction; III. 1.22 vibration; 1.3.5a, 1.4.44 vibrational spectroscopy; III.table 3.5 virial coefficients; 1.2.18d, I.3.8f, L 3 . 9 c second; I.2.18d, I.3.8f, I.3.9b, [1.3.9.12], [1.4.2.8-11], 1.7.51, 1.7.57, two-dimensional; [II.1.5.24], II. 1.60 virial expansions; I . 2 . 1 8 d , I . 3 . 9 c , I.5.27ff, 1.7.51, [11.1.5.30] viscoelasticity; I.2.7(intr.), III.3.88 viscoelectric coefficient; 11.4.40 viscoelectric effect; II.4.40 viscometers, rotation; I.6.36ff viscosity; 1.5.43, I.6.10ff dynamic vs. kiiiematic; 1.6.11 (in) electrokinetics; I I . 4 . 4 examples: I.table 6.3, I.6.4g interpretation; I.6.4g s h e a r vs. elongational; 1.6.8 viscous flow; 1.6.1, 1.6.4 a r o u n d spheres; I . 6 . 4 e , II.4.6, II.4.8 between parallel plates; L6.40ff dilational vs. rotational; Lfig. 6.7 d u e to Marangoni effects; 1.1.17, 1.6.44 due to temperature gradients; 1.6.4c fluid-fluid
interfaces; I.6.42ff
69
70
SUBJECT INDEX in cylindrical tube; 1.6.4Iff
viscous flow (continued) in porous media; I.6.4f l a m i n a r linear; 1.6.4a, I.6.4d turbulent; 1.6.4b Volta potential; see potential Volmer adsorption isotherm; see adsorption isotherm volumes, of ions (partial); I.table 5.7 Vonnegut equation (for spinning drops); (111.1.9.6] vortices; 1.6.4b Warburg coefficient; II.3.96 Ward-Tordai equation; [1.6.5.36], [II.1.1.15] W a s h b u r n equation; [III.5.4.4] III.5.57ff, III.5.84ff water, interactions in; I.4.5d, 1.4.5e s t r u c t u r e ; 1.5.3c, 1.5.4, II.2.16 n e a r surfaces; II.2.2c, II.figs. 2.6-7, II.3.122ff, II.fig. 3.39, II.4.38ff water-air interface, double layer; II.3.10f, II.fig. 3.78, III.4.4, Ill.fig. 4.20 reflectivity; Ill.fig. 3.57 surface relaxation; Ill.fig. 1.29 surface tension; III. 1.12, III.table 1.2 influence of electrolytes; II.3.180, II.fig. 3.73 influence of temperature; III.1.12b, Ill.table 1.3, Ill.table 1.4, Ill.fig. 1.27 simulation; Ill.table 2.2, Ill.figs. 2.12-13 wave damping; see interfacial rheology waves, electromagnetic; I.chapter 7 evanescent; 1.7.75 in a vacuum; 1.7.1 plane; 1.7.1a polarization; 1.7. l a spherical; 1.7. l b surface; see surface wave (see also; electromagnetic radiation) wave vector; I.7.4(def.) wave vector transfer = wave vector Wenzel equation; [III.5.5.1] wetting; 1.1.2, 1.1.8, 1.1.3, I.fig. 1.13, Il.table 1.3. Ill.fig. 5.7 a d h e s i o n a l ; II.2.5, I I I . 5 . 2
SUBJECT INDEX a n d gas adsorption; II. 1.19, III.5.3, Ill.fig. 5.16 wetting
(continued)
and Van der Waals forces; 1.4.72 complete; III. 1.5, III.5.1, III.5.4 enthalpy or heat; [11.1.3.43], Ill.table 1.3, Il.fig. 1.10b, II.2.6, II.2.3d, II.fig. 2.10, Il.fig. 2.20. III.5.2. III.5.20 entropy; II.2.7 immersional; II.2.5, Il.fig. 2.10, III.5.2 liquids by liquids; III.5.30 molecular dynamics; III.fig. 5.36 partial; III. 1.5, III.5.1, Ill.fig. 5.1, Ill.fig. 5.13, scales; III.5.5 selective; II.2.88 silica by water; III.5.3c surfactant influence; III.5.10 t h e r m o d y n a m i c s ; III.5.2 wetting agents; III.5.86, III.5.10 wetting films; III.5.3 wetting transition; II. 1.101, Il.fig. 1.41, III.5.14, III.5.30, Ill.fig. 5.14 Wiegner effect; see suspension effect Wien effect (in electrolytic conductance); 1.6.6c Wilson chamber; 1.2.100 wine tears; 1.1.1, 1.1.2, 1.1.17 wolfram surface, covered with palladium; Il.fig. 1.2 work; 1.2.4 of adhesion; III.2.34, III.2.71ff isothermal reversible; 1.2.27 statistical interpretation; 1.3.15, [1.3.3.11] (see also; interfacial work, transfer, potentials) work function; 1.5.75, II.3.114, II.3.174 work hardening or softening; III.3.88 XAFS = X-ray absorption and fluorescence spectroscopy; 1.7.11a XPS = XPES = X-ray photoelectron spectroscopy; I.7.11a, I.table 7.4, II.1.15, Il.fig. 1.5 X-ray reflection a n d diffraction; III.2.47, Ill.table 3.5, III.3.7b X-ray scattering; I.fig. 5.6, 1.7.25 of colloids; 1.7.9 Young a n d Laplace's law; see capillary pressure Young's law for capillary pressure; see capillairy pressure. Young a n d Laplace Young's law for contact angle; [III. 1.1.7], 111.5.1b, [111.5.1.2], III.5.2
71
72
SUBJECT INDEX
Z-average; 1.7.63 Zeeman effect (for spectral lines); 1.7.16 zeolithe; see molecular sieve zero point of charge; see point of zero charge zero point vibrations; 1.3.22, 1.4.29 Zimm plot; I.7.57ff, I.fig. 7.12, I.fig. 7.16 zinc oxide, SEM; II.fig. 1.1 Zisman plot; Ill.fig. 5.42 zone electrophoresis; II.4.131 zwitterionic surfaces; 11.3.74 ;^-parameter (polymers etc.); see Flory-Huggins interaction parameter ;^^-parameter (polymer ads.); [II.5.4.1], II.chapter 5 X^.^: II.5.40, Il.fig. 5.22 ;^-potential; see potential f-potential; see electrokinetic potential ©-point, ©-temperature; II.5.6ff, II.5.2b
