Emulsion polymerization
@i; PROYECTOCONACYT
Contributors A. Berge D. C. Blackley A. S. Dunn T. Ellingsen Carlton G. Force Robert G. Gilbert A. E. Hamielec F. K. Hansen A. A. Khan Gottfried Lichti J. F. MacGregor P. C. M0rk Donald H. Napper Mamoru Nomura R. H. Ottewill Gary W. Poehlein Vivian T. Stannett J. Ugelst~d V. 1. Yeliseyeva
'.
EMULSION
POLYMERIZATION
Editad by
IRJA PIIRMA Institute of Polymer Science The Uníversity of Akron Akron, Ohía
ACADEMIC
PRESS
A Subsidiary of Harcourt Brace Jovanovich, Publishers
New York London -Toronto Sydney San Francisco 1982
----
COPYRIGHT @ 1982, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLlCATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGEANO RETRlEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLlSHER.
ACADEMIC PRESS, INC.
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United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON)
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7DX
Ubrary of Congress cataloging Main entry under ti tle:
LTD.
in Publication .
Data
Emulsion polymerization. Includes bibliographies and index. l. Emulsion polymerization. l. Piirma, QD)B2.E48E48 660.2'8448 ISBN 0-12-556420-1
81-17626 AACR2
PRINTED IN THE UNITED STATES OF AMERICA 82 83 84 85
.
9 8 7 6 S 4 3 2 J
Irja,
Contents Contributors Preface
ix xi
1 The Stability and Instability of Polymer Latices R. H. Ottewi/l 1. Introduction 11. The Nature of Polymer Latex Particles 111. The Effect of Electrolytes on a Latex IV. The Theory of the Stability of Lyophobic Colloids V. Coagulation as a Kinetic Process VI. An Alternative Approach to the Critical Coagulation Concentration VII. The Determination of ccc Values VIII. The Effect of lons That Interact with Water IX. Secondary Minimum Effects X. The Effects of Organic lons: Added Surfactants XI. lonic Head Group with a Charge of the Same Sign as the Particle XII. lonic Head Group with a Charge of Opposite Sign to the Particle XIII. Nonionic Surfactants XIV. Mixed Electrolyte Systems xv. Heterocoagulation XVI. Surface Coagulation XVII. Peptization XVIII. The Effects of Adsorbed or Grafted Macromolecules XIX. Particle Stability in Emulsion Polymerization XX. Summary References
.
1 2 6 8 14 16 17 19 22 26 27 28 31 35 36 39 40 42 45 47 47
2 Particle Formation Mechanisms F. K. Hansen and J. Ugelstad
1.
Introduction
11. Micellar Nucleation: The Smith-Ewart 111. Radical Absorption Mechanisms IV. Micellar Nucleation: Newer Models V. Homogeneous Nucleation VI. VII.
Theory
Particle Coagulation during the Formation Period Nucleation in Monomer Droplets References
v
51 54 56 63 73 82 86' 91
Contents
vi
3 Theoretical Predictions of the Particle Size and Molecular Weight Distributions in Emulsion Polymerizations Gottfried Lichti, Robert G. Gilbert, and Donald H. Napper 1. 11.
Prediction of the PSD Molecular Weight Distributions 111. Separability of MWD and PSD IV. Conclusions References
4 Theory ofKinetics ofCompartmentalized Reactions
94 115 141 142 143
Free-Radical Polymerization
D. C. Blackley 1. Introduction 11. Reaction Model Assumed 111. The Time-Dependent Smith-Ewan Differential Difference Equations: Methods Available for Their Solution IV. Solution for the Steady State V. Solutions for the Nonsteady State VI. Predictions for Molecular Weight Distribution and Locus-Size Distribution VII. Theory for Generation of Radicals in Pairs within Loci List of Symbols References
5
146 149 156 164 167 183 185 187 189
Desorption and Reabsorption of Free Radicals in Emulsion Polymerization Mamoru Nomura
1. Introduction 11. Polymerization Rate Equations Involving Free-Radical Desorption 111. Derivation of Rate Coefficient for Radical Desorption from Panicles IV. Effect of Free-Radical Desorption on the Kinetics of Emulsion Polymerization List of Symbols References
191 192 199 210 217 219
6 Effects of the Choice of Emulsifier in Emulsion Polymerization A. S. Dunn 1. Introduction Monomer Emulsification 11. 111. Emulsion Polymerization with Nonionic Emulsifiers IV. Emulsion Polymerization with lonic Emulsifiers V. Latex Agglomeration Other Effects of Emulsifiers JVI. References
:¡
221 224 229 230 236 237 243
I
Contents
vii
7 Polyrnerization
of Polar Monorners
V. l. Yeliseyeva 1. Introduction 11. Interface Characteristics of Polymeric Dispersions 111. Relationship between Emulsifier Adsorption and the Difference in the Boundary-Phase Polarity IV. Mechanism of Particle Generation V. Colloidal Behavior of Polymerization Systems VI. Kinetics of Emulsifier Adsorption VII. Mechanism of Formation and Structure of Particles VIII. Polymerization Kinetics IX. Relationship between Polymerization Kinetics and Adsorption Characteristic of the Interface Nomenclature References
247 249 250 257 261 268 27q 278 283 286 287
8 Recent Developrnents and Trends in the Industrial Use of Latex Car/ton G. Force 1. 11. 111. IV. V. VI.
289 291 300 312 313 314 316
Introduction Factors in Adhesion Bonding Applications Construction Applications Rubber Goods Properties of Various Latexes References
9 Latex Reactor Principies:
Design, Oneration,
and Control
A. E. Hamie/ec and J. F. MacGregor 1. Introduction 11. Batch Reactors 111. Continuous Stirred-Tank Reactors: Steady-State Dperation IV. ContinuQus Stirred-Tank Reactors: Dynamic Behavior V. Dn-Une Control of Continuous Latex Reactors VI. Summary Nomenclature References
10
319 320 333 339 345 351 351 353
Ernulsion Polyrnerization in Continuous Reactors. Gary W. Poeh/ein
1. Introduction
. 11.
Smith-Ewart Case 2 Model for a CSTR 111. Deviations from Smith- Ewart Case 2 IV. Transient Behavior bf CSTR Systems V. Strategies for Process and Product Development VI. Summary References
357 361 367 375 378 381 381
Contents
viii
11
Effect of Additives on the Formation and Polymer Dispersions
of Monomer
Emulsions
J. Uglestad, P. C. MrjJrk, A. Berge, T. Ellingsen, and A. A.Khan 1. Introduction 11. ThermodynamicTreatment of Swelling and Phase Distributions 111. Rate of Interphase Transport IV. Preparation of Polymer Dispersions V. Effectof Additionof Water-InsolubleCompounds to the Monomer Phase VI. Emulsificationwith Mixed EmulsifierSystems Listof Symb91s References
383 384 392 396 401 408 411 412
12 Radiation-Induced Emulsion Polymerization Vivían T. Stannett 1. Introduction 11. Laboratory Results with Different Monomers 111. Copolymerizations IV. Radiation-Induced Emulsion Polymerization Using Electron Accelerators V. Pilot Plant and Related Studies References
lndex
415 418 433 436 437 447
451
Contributors Numbers in parentheses indicate the pages on which the authors' contributions begin.
A. Berge (383), SINTEF, Applied Chemistry Division, 7034-NTH, Trondheim, Norway D. C. Blackley (145), National College of Rubber Technology, The Polytechnic of North London, Holloway, London N7 8DB, England A. S. Dunn (221), Chemistry Department, University of Manchester Institute of Science and Technology, Manchester M60 lQD, England T. Ellingsen (383), SINTEF, Applied Chemistry Division, 7034-NTH, Trondheim, Norway Carlton G. Force (289), Westvaco Corporation, Research Center, North Charleston, South Carolina 29406 Robert G. Gilbert (93), Departments of Physical and Theoretical Chemistry, University of Sydney, New South Wales 2006, Australia A. E. Hamielec (319), Department.of Chemical Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada F. K. Hansen (51), DYNO Industrier, Lillestr~m Fabrikker, N-2001 Lillestrs6m, Norway A. A. Khan (383), E. 1. du Pont de Nemours & Co., Polymer Products Department, Experimental Station, Wilmington, Delaware 19898 Gottfried Lichti (93), Australian Institute of Nuclear Science and Engineering, New South Wales, Australia J. F. MacGregor (319), Department of Chemical Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada P. C. Mr)rk (383), Laboratory of Industrial Chemistry, The University of Trondheim, N-7034 Trondheim, Norway Donald H. Napper (93), Department ofPhysical and Theoretical Chemistry, University of Sydney, New South Wales 2006, Australia Mamoru Nomura (191), Department oflndustrial Chemistry, Fukui University, Fukui, Japan R. H. Ottewil/ (1), School of Chemistry, University of Bristol, Bristol BS8 1TS, England Gary W. Poehlein (357), School of Chemical Engineering, Georgia Institute ofTechnology, Atlanta, Georgia 30332 Vivian T. Stannett (415), Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27650 ix
x
Contributors
J. Uge/stad (51,383), Laboratory of Industrial Chemistry, The Norwegian Institute of Technology, The University of Trondheim, N-7034 Trondheim, Norway V. l. Ye/iseyeva (247), Institute ofPhysical Chemistry, Academy ofSciences USSR, Moscow, Union of Soviet Socialist Republics
.
x
Contributors
J. Ugelstad (51, 383), Laboratory of Industrial Chemistry, The Norwegian Institute of Techno1ogy, The University of Trondheim, N-7034 Trondheim, Norway V. l. Yeliseyeva (247), Institute ofPhysical Chemistry, Academy ofSciences USSR, Moscow, Union of Soviet Socialist Republics
.
1m
Preface Emulsion polymerization has been a very successful industrial process for four decades. In recent years it has undergone revitalization: while some old factories are closing, new and much more sophisticated ones using emulsion polymerization are sprouting. Historically, in an attempt to produce synthetic rubber, the polymerizations involving the use of an aqueous emulsifier solution resulted in a product that in physical appearance resembled nature's latex. It also gave a greatly improved synthetic rubber over that produced previously by other processes, e.g., the sodium-butadiene process. This industrial success was subsequently followed by a more theoretical approach to the problem during the 1940s that resulted in the publication of the first scientific papers in this field. Even then, since emulsion polymerization had been established first as an industrial process, the theories proposed by the scientists were primarily concerned with trying to put the industrial observations into a general and workable scientific framework. Unfortunately, the emulsion polymerization of styrene and the copolymerization of styrene-butadiene fit beautifully into a simple kinetic scheme proposed by Smith and Ewart, and during the two decades that followe9 almost all research efforts in the field attempted to make the other monomers fit into this framework. We now know that emulsion polymerization is not just another polymer synthesis method and that the complexity of the interactions, whether chemical or physical, must be considered before any control is possible over the outcome of the reaction. The creation and nucleation of particles, for example, is not necessarily and simply explained by the presence or or absence of micelles, but needs the understanding of interactions of all the ingredients present. Variables such as hydrophilic and hydrophobic associations or repulsions, polarity of the monomers, chemical structure of the surfactants, have to be taken into account. Research in the field is flourishing all over the world, and although numerous papers have been published and collections of papers have appeared recently, they have the disadvantage of presenting fragments of the subject and never the total picture. This book presents a collection of chapters, each written by scientists in their fields of expertise. These experts come from all over the world and thus sometimes represent different viewpoints of the same subject. It is the hope ofthe editor and the contributors that we have been successful in presentirig a total picture of the current understanding ofthe subject. xi
'"
1 xii
Preface
1 would like to thank Silvia Dolson for providing her time and talents to assist in the book's cover designo
1 !1 S ~ -
1 The Stability and Instabiliíy 01 Polymer Latices R. H. Ottewill
1. Introduction . 11. The Nature of Polymer Latex Particles 111. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII. XIV. xv. XVI. XVII. XVIII. XIX. XX.
l.
.
The Effect of Electrolytes on a Latex . The Theory of the Stability of Lyophobic Colloids Coagulation as a Kinetic Process . An Alternative Approach to the Critical Coagulation Concentration The Determination of ccc Values . The Effects of lons that Interact with Water Secondary Minimum Effects . The Effects of Organic lons: Added Surfactants lonic Head Group with a Charge ofthe Same Sign as the Particle lonic Head Group with a Charge of Opposite Sign to the Particle Nonionic Surfactants Mixed Electrolyte Systems . Heterocoagulation . Surface Coagulation Peptization The Effects of Adsorbed or Grafted Macromolecules. Particle Stability in Emulsion Polymerization Summary. References
1 2 6 8 14 16 17 19 22 26 27 28 31 35 36 39 40 42 45 47 47
Introduction
Over the last two decades work on the formation and properties of polymer latices has developed extensively, and a very substantial amount of work has been devoted to the study of the processes of formation of polymer particles in a latex and to the characterization of the particles once formed (see for example, Fitch 1980). It is now generalIy recognized that in 1 EMULSION POLYMERIZATlON Copyright @ 1982 by Academic Press. Inc. AIl rights of reproduction in any form reserved. ISBN 0-12.556420-1
I
~
R. H. Ottewill
2
the majority of latices, the particles are within the size range 1 nm to 1 pm, which designates them as colloidal, and the name "polymer colloids" is becoming commonly used to describe this type of system. Consequently, the entire field of polymer latex manufacture and utilization is very dependent on an understanding of the basic principIes of colloid science in the widest sense whether it is to stabilize or coagulate the particles or to control the rheological properties of latex formation. In using the word stability in the colloidal sense we understand that the particles in the dispersion will remain for long periods of time, often years, dispersed as single entities in Brownian motion. The size range 1 nm to 1 pm is chosen to exclude at the lower end of the range small single ion s and molecules and at the higher end to exclude particles that settle under the influence of gravity and do not remain dispersed by Brownian motion. These are definitions of convenience rather than rigor and in considering polymer latices we shall frequently need to consider particles with a size. greater than 1 pm; in this case the colloidal arguments can be maintained but, in addition, the effects of gravity have to be included. When the la,tex loses its stability because the particles aggregate under the influence of chemical additives or mechanical action, the terms coagulation and flocculation are applied (see later). By the term rheology we describe the flow and deformation properties of the system, Le., whether it is viscous (either Newtonian or non-Newtonian) or elastic or whether it possesses both these properties and is viscoelastic.
ll.
The Nature oí Polymer Latex Particles
A typical polymer latex particle will be composed of a large number of polymer chains, with the individual chains having molecular weights in the range of about 105 to 107. According to the arrangement of the polymer chains within the particle, the latter can be amorphous, crystalline, rubbery, or glassy. Moreover, in many cases monomer is retained by the particle and hence the particles can also be, in cases where the polymer is soluble in the monomer, either extensively or minutely swollen. The physical state of the particle can be important in close-range interactions and in drying. For example, if the particles are soft, coalescence of the particles can occur to give continuous film formation, whereas with hard particles their individuality is retained in the dry state. In determining the colloidal behavior of a latex, the surface properties playa very important role, and these are directly related to the preparative . method employed. They frequently depend on (i) groupings arising from the initiator used; (ii) adsorbed or grafted surfactants; and (iii) adsorbed or grafted polymers, particularly, those soluble in the dispersion medium.
I j j
I j
j!
,
~
3
1. The Stability and Instability of Polymer Latices
In aqueous-based emulsion polymerizations using water-soluble initiators, the surface groupings formed are frequently determined by the nature of the initiator used (Ottewill et al., 1967; van den HuI et al., 1970; Goodwin et al., 1973) and the following have been reported: from hydrogen peroxide, persulfate, bisazocyanopentanoic acid
Weak acid
Strong acid
-0-S03
or
from persulfate
CH3 NH2 Base
Nonionic
I
,f'
-C-C~, I NH2 CH2 } -OH
+
from azobisisobutyramidine
from hydrogen peroxide or hydrolysis sulfate groups
of
In addition, latex particles with mixed anionic and cationic groups on the surface can be prepared (Bolt, 1978). In an ionizing medium of high relative permittivity (e.g., water) the acidic and basic groupings exist in the ionized form, depending on their pKa and pKb values and the pH, and consequently the surface of the particle becomes electrically charged. In addition the adsorption of other ionic species, such as surface-active ions, can also contribute to the surface charge. In physical terms the water is a good solvent for the ions and poor for the latex particle; that is, most of the polymers used for latex preparation are totally insoluble in water. A schematic illustration of this situation is shown in Fig. 1 where the particle surface is shown to be that of a smooth sphere with the charges evenly distributed over the spherical surface. The condition of electroneutrality is maintained by balancing the charge on the latex surface by the charges on small ions of opposite sign in the solution phase (counterions). This forms the so-called electrical double layer in which an equilibrium is set up between electrostatic forces and diffusion forces. As a consequence of its surface charge, the lat.ex particle surface has an electrostatic surface potential rjlswhich can be either positive or negative, depending on the nature of the surface groupings, relative to 'earth. This potential falls off exponentially with distance from the surface of the sphere according to the equation rjlr= rjls(a/r)exp[
-
K(r - a)]
(1)
where rjlris the surface potential at a distance (r - a) from the surface of the' sphere where a is the radius of the sphere. K is defined by (2) K2 = (8ne2NAl1000ekT)I
4
R. H. Ottewill
- -+ - -
,,/
o +
/ I I
"-
+ "-
+ \
+ \ \ I I
++
\ \
-
-
+
\
+ "-
"-
-
+
/
+
-- +
/
.,//
Fig. 1. SchematiciIlustration of a negatively charged spherical polymer latex particle with an electricaldouble layer. --- representsthe rangeof influenceof electrostaticforces.
and is dependent on the ionic .strength 1 of the solution phase, e the fundamental electronic charge, NA Avogadro's number, and ¡; the dielectric constant of the medium. It is K that determines how rapidly the electrostatic potential falls off with distance from the particle surface and consequently the range of electrostatiC interaction forces. The dashed line in Fig. 1 indicates that the range of electrostatic forces can extend well beyond the physical size of the particle. When latices are prepared in nonaqueous media such as hydrocarbons then charged-surface groups no longer pro vide a practical means of stabilizing the particles formed. Under these conditions polymer chains, soluble in the dispersion medium, can be grafted to the core polymer particle which remains insoluble in the dispersion medium. A typical example is the use of poly(12-hydroxystearic acid) chains to stabilize particles of poly(methyl methacrylate) in dodecane. This leads to what might be termed a "hairy particle" with the noncharged "hairs" extending into the solvent medium as shown in Fig. 2. Again the range to which the chains extend is important as it determines the distance at which one particle of this sort can start to interact sterically with another, giving the so-called sterically stabilized systems. Returning again to ionizing media, a combination of these two effects can be employed by grafting to a polymer core particle polyelectrolyte chains. This is illustrated schematically in Fig. 3. It pro vides a combinatorial effect of electrostatic and steric interactions. These will have different interactive ranges as illustrated in Fig. 3 by the dotted line for the electrostatic range and the dashed line for steric effects.
1.
5
The Stability and Instability of Polymer Latices
"-
\ .\ \ I ,
/
/
/ Fig. 2.
SchematiciIIustrationof a nonchargedpolymerlatex particlewith adsorbed or
grafted nonionic
polymer chains. ---
represents
the range of inftuence of steric forces.
The chains shown in Fig. 3 are those of long poly(ions) deliberately added. However, there is sorne evidence to indicate that even in conventional ernulsion polyrnerizations the particles forrned rnay not be as srnooth as those shown in Fig. 1, and the charged groups rnay be floating a short distance in the rnediurn as "rnicrohairs." In practice one should not be rnisled by the convenience of the srnooth sphere rnodel for theoretical rnodeling of colloidal phenornena.
. . . . . .'".. . +
.
'
+
.,
+
- .
. +
.+
+ +
. +
+
.
+
+ . . .. . . .
Fig. 3. Schematic iIIustration of a polymer latex core with grafted polyelectrolyte chains attached to the core surface. represents the range of electrostatic forces, and --represents the range of steric forces.
6
R. H. Ottewill
From this qualitative description of latex particIes we can immediately recognize the origins of three basic forces that ha ve to be considered in understanding the behavior of dispersions in both aqueous and nonaqueous media. These can be summarized as 1. Electrostatic effects: usualIy repulsive but opposite charges on particIes can lead to attraction. 2. Steric effects: arising from the geometry and conformation of adsorbed or grafted mo.1ecules. 3. Solvation effects: arising from the organization of solvent molecules near an interface or between the chains of adsorbed macromolecules. It will be noticed that these effects do not take into account to any great extent the bulk phase of the particIe. However, this also has to be taken into account and both the polarizability and the density are of importance in determining the attractive forces between particIes. Thus, we can add to the list
4. Attractive effects: which have their origin in molecular dispersive interactions (oftentermed van del Waals interactions).
m.
The Effect of Electrolytes00 a Latex
In an aqueous latex that has been cIeaned to remove various materials such as surface active agents one is dealing in many cases with a dispersion of charged spherical particIes. FrequentIy, the distribution of particIe sizes is very narrow and the term monodisperse is used to describe latices of this type. In an attempt to obtain a concise overview of the properties of aqueous latices in electrolyte solutions some of the essential features are summarized schematicalIy in Fig. 4. At intermediate electrolyte concentrations (-10-3 mol dm-3) and at low volume fractions of the dispersed phase, the charged particIes occupy random positions in the system and undergo continuous Brownian motion with transient repulsive contacts when the particIes approach each other. The range of the electrostatic repulsive forces is represented by the dashed circIe in Fig. 1, which implies that when a similar circIe on another particIe overlaps with it on a collision trajectory, a transient electrostatic repulsion occurs and the particIes move out of range. With most latices the particIes .have a real refractive index and their visual appearance is "milky" white. Ir, however, either the electrolyte concentration is reduced to about
10- 5 mol dm- 3, which increases the range of the eIectrostatic repulsive forces, or the concentration of the particIes is increased, a situation is
~
7
1. The Stability and Instability of Polymer latices Order Regular lattice Strong repulsion
Electrolyte 10- M 5
Remove electrolyte Imixed-bed ion exchang~
Dlsperslon Electrolyte
- sol 10-
3
resin)
Disorder Random arrangement of particles Brownian motion Repulsive contacts
M
Add electrolyte
Stable Unstable Electrolyte 0.2 M
Schulze
.
Hardy Flocculatlon Disorder Weak attraction
Fig. 4. partides
Coagulation Disorder Strong attraction
The effectof electrolyteand partide size on the properties of polyrner latex
in an aqueous
rnediurn. (Reproduced
with perrnission
of Chem. ¡nd. (London).
reached where the partic1es must maintain repulsive contacts over a long period of time. Con sequen tIy, an ordered arrangement.of the partic1es is set up so that the partic1es sit in lattice positions but remain well separated, Le., a "liquid crystal" arrangement is formed (see Fig. 4). When the interpartic1e spacing is of the order of the wavelength of light, Bragg diffraction effects become superimposed on the scattering from the partic1es and bright iridescent colors can be seen visually. This is well demonstrated with mono disperse latices which, in the right size and concentration range, show brilliant colors (Hiltner and Krieger, 1969; Hachisu, 1973; Goodwin et al., 1980).
R. H. Ottewill
8
In the lower part of Fig. 4 a schematic illustration is given of the transition from a stable dispersion, where all the particles exist essentially as single entities, to an unstable state where aggregation of the particles occur. This change from stability to instability has received a great deal of attention from several generations of colloid scientists. It is usually associated, when inorganic electrolytes are used, with the names of Schulze (1882, 1893) and Hardy (1900) who investigated this phenomenon at about the turn of the century. Today, our explanations of colloidal particle aggregation processes are largely based on the theories of interactions between particles that were first enunciated in quantitative form in the 1940s by Derjaguin and Landau (1941) and Verwey and Overbeek (1948), frequently now termed the DL VO theory in honor of the four authors.
IV.
The Theory of the Stability of Lyophobic CoUoids
The quintessence of the ideas put forward by DL VO was that the potential energy of electrostatic repulsion VRbetween the particles and the potential energy of the van der Waals attraction VAcould be added together to obtain the total potential energy of interaction VT. When the very shortrange Born repulsive energy was included, a potential energy against distance of surface separation curve of the form shown in Fig. 5 was obtained. This type of curve exhibits a number of characteristic features. At short distances, a deep potential energy minimum occurs, the position of which decides the distance of cIosest approach ho and is hence termed the. primary minimum. At intermediate distances, the electrostatic repulsion makes the largest contribution and hence a maximum occurs in potential energy of magnitud e Vm;this position is termed the primary maximum. At greater distances, the exponential decay of the electrical double layer term causes it to fall off more rapidly than the power law of the attractive term and another min!mum occurs in the curve, of depth VSM, termed the secondary minimum. In more quantitative terms VRfor weak interactions can be written in the form VR =
3.469 X 1019 B(kT)2ay2 exp( -
Kh)/V2
(3)
where Bis the dielectric constant of the dispersion medium, k is Bolzmann's constant, T is"the absolute temperature, v the magnitud e of the valency of the counterion, and y = [exp(velj¡s/2kT)- 1J/[exp(velj¡sl2kT)+ 1J with e as the fundamental electron charge. This expression given by Reerink and Overbeek (1954) is for the electrostatic interaction between two spheres of equal radius a of constant
1.
9
The Stability and Instability of Polymer Latices 10
Primary Maximum
. ...
.
l....
o Secondary Minim~m
Pri';;a~y- , Mínimum
h Fig. 5.
SchernaticiIIustration of a potential energy against distance of surface sepa-
ration curve to illustrate the rnain features used in discussing colloid stability. ~ Vr= energy barrier to coagulation;
~Vb
=
energy barrier to peptization;
i'd = dispersion
free energy of the
polyrner-water interface; Vm= height of the prirnary rnaxirnurn; VSM= depth of the secondary
rninirnurn.
surface potential and material 1 separated by a distance h in a medium 2 (Fig. 6). It is valid for the Ka range 3 to 10. For Ka < 3 and Ka > 10 useful expressions for small potentials are, respectively VR = [ea21jJ;/(h VR = tealjJ;
+ 2a)] exp( -'Kh)
ln[l + exp(- Kh)]
(4) (5)
The question of interaction at constant surface charge has also been discussed by several authors (Frens, 1968; Wiese and Healy, 1970; Gregory, 1975).
R. H. Ottewill
10
Fig. 6. Interaction betweentwo sphericalparticlesof material 1 in a liquid mediumof material2. a = radius of sphericalparticle;h = distanceof surfaceseparation.
For the attractive part of the interaction it was shown by Hamaker (1937) that VAcan be given for two spheres of the same radius and the same material by the expression V A-
-
A
1
1
12{ X2 + 2x+ X2+ 2x+ 1+
2l
X2
+ 2x
n(X2+ 2x+ 1)}
6)
(
where x = hl2a and A = the composite Hamaker constant for the particles in the mediumas givenby (7) TABLEI Values of Reported Hamaker Constants for Various Polymers
Material Poly(vinyl acetate) Poly(vinyl chloride) Poly(methyl methacrylate)
Styrene-butadiene Polytetrafluoroethylene
Polystyrene
AII/J (x 10-2°) 8.84 12.4 10.0 6.3 5.6 3.7 7.6
a Lifschitz, small separation distances. b Lifschitz, long separation distances.
AjJ (xlO-21) 5.4 5.5 7.2 5.5 3.0-3.8 4.0 2.9 3.6 3.5 9.0 3.2 6.5 7.0
Reference Dunn and Chong (1970) Evans and Napper (1973) Visser (1972) Visser (1972) Friends and Hunter (1971) Evans and Napper (1973) Force and Matijevié (1968a) Fowkes (1967) Rance (1976) Gingell and Parsegiana (1973) Visser (1972) Krupp et al. (1972) Gingell and Parsegiana (1973) Gingell and Parsegianb (1973) Evans and Napper (1973) Lichtenbelt et al. (1974)
11
1. The Stability and Instability of Polymer Latices
= the Hamaker constant of the particIes and A22 that of the medium. The Hamaker constant is directly related to the nature of the material by the expression
with All
(8) where Vj is the dispersion frequency of the material (c/A.o,with A.o= the dispersion wavelength), Ctjis the static polarizability and qj is the number of atoms/molecules per unit volume of the material. Some typical values of
A 11 for polymericmaterials are listed in Table I. For conditions such that x ~ 1 a useful approximation is obtained from Eq. (6),in the form (9)
VA = - Aa/12h
As the distance of separation between the particIe surfaces increases, particularly beyond 100 nm, a weakening of the attraction starts to occur,
150 11
\
\
\
., 100 t+--
\
\
.
\ \
\ \
\.,
:i.
11.
kT
50¡¡':'
\
.
\
.
\
\
\
'\ "-
\ \
o
...
.\
"-
"". -- .;-..,
.. .........
"........
,.,
- - =.= .'::..~,
10
...-.--.-20
h (nm) Fig. 7. Potential energy diagrams for the interaction between two spherical latex particles of radius 0.1 Jlm at a constant potential of 1/1,= 50 mV, with A = 7.0 X 10-21 J and T=298.2°K in a 1:1 electrolyte. -, 1O-3moldm-3; ---, 1O-2moldm-3; -'-', 0.075 mol dm-3; 0.5 mol dm-3.
R. H. Ottewill
12
100 VT kT
,......,
,
I!
~
r:
.,
"
.
'.
,
.'.
e.-- ..
'.
......-.
- .-.
k~..".-
O . ..-"
-8-
-
:: V..a.~.- . _8-
--
-
..- -¡ '8.~ I...:e-=."\:
f¡ h (nm)
Fig. 8.
Potential energy diagrams for the interaction between two spberical latex
partic1es of radius 0.1 Jlm at a constant
1:1 eIectrolyte
concentration
of 10-3 mol dm-3
A = 7.0 X 10-21 J. T = 298.2°K. and various values of "', as follows:
37.5mV;-u-o 25mV;
12.5mV;
5 mV.
-.
witb
50 mV'; -'-,
the so-called retardation effect, and this has to be allowed for in the calculation of VT. Equation (9) can then be rewritten in order to allow for retardation as (Kitchener and Schenkel, 1960) VA = -(Aa/h)(2.45/p
- 2.17/180p2 + 0.59/420p3)
(10)
with p equal to 21th/A.o.Usually, A.ocan be taken as -100 nm and Eq. (10) is a reasonable approximation for a ;p h and 0.5 < p < oo. An alternative treatment of attractive interactions between particles is that given by Lifshitz and co-workers (1961); it is beyond the scope of this article but is discussed by Ninham and Parsegian (1970, 1971) and Richmond (1975). From the various equations given, under the appropriate conditions of Ka, h. etc. the total potential energy of interaction between the particles can be calculated from the basic DL VO assumption that for lyophobic dispersions, (11)
"=""
13
1. The Stability and Instability of Polymer latices
" \
200H-'I I I
,
I I
\ \ \ \ \ \
100
O""'O\
'o
\
r! ,1
~,f o
!II-:! 8_'-..1 -=
~ -= .":--'::. 20
h
-- ~ _8-:--=30
(n m)
Fig. 9. Potential energydiagramsfor the interactionbetweensphericallatexparticlesin a 1:1 electrolyte at a concentration of 1O-2moldm-3 with A=7.0xl0-2IJ and T = 298.2°Kover a range of particle radii: -, a = 2 Jlm;---, a = 1Jlm;-'-, a = 0.5Jlm; , a = 0.1Jlm,t/J, = 25 mV. .
-
-. -
A number" of curves of VT against h are given in Figs. 7 to 9 to illustrate various points. For example, Fig. 7 shows the effect of electrolyte for spherical particles of radius 0.1 J1.mat a constant surface potential t/ls.For the same particle radius Fig. 8 shows the effect of changing t/ls at a constant electrolyte concentration of 10- 2 mol dm - 3. The effect of particle size for particles of the same t/ls at the same electrolyte concentration is demonstrated in Fig. 9. It is apparent from these curves that when the magnitude of Vmis greater than about 10kT conditions are favorable for the formation of a stable dispersion. Moreover, the form of the potential energy curve obtained by this approach indicates that the dispersion exists in a higher free energy state than that of the solid polymer with the depth of the primary rpinimum equal to twice the dispersion free energy of the polymer (Fowkes, 1964). The stability of the dispersion is kinetic in origin as a consequence of the large activation energy ~Jréwhich renders the forward transition into the primary minimum improbable. It also becomes apparent that because the activation
R. H. Ottewill
14
energy for the backward reaction /!:;. Vbis much larger than /!:;. Vr(see Fig. 5), and a decrease of free energy in the system has occurred once the primary minimum has been accessed, then spontaneous redispersion is unlikely to occur and mechanical work is needed to redisperse the aggregated particles. Móreover, time has to be considered in this context since prolonged contact of particles in the primary minimum can lead to welding of the particles, as interparticle diffusion of polymer chains occurs.
V. Coagulation as a Kinetic Process In a fundamental paper von Smoluchowski (1917) presented a theoretical model for the kinetics of the coagulation process. He showed that in the initial stages of coagulation the rate of disappearance of the primary particles, i.e., those present as single particles in the original dispersion, could be written as -dN/dt
.
= kN~
(12)
where No is number of primary particles per unit volume present initially and k is arate constant. For rapid coagulation, i.e., coagulation in the absence of an energy barrier, the process is diffusion controlled and k
= ko = 8nDR
where D is the diffusion coefficient of a single particle and R
the collision radius of the particle. In subsequent analyses it was shown that if diffusion in the presence of an energy barrier is considered (Fuchs, 1934; Overbeek, 1952) then the initial rate of disappearance of the primary particles could be written as -dN/dt
= koNUW
(13)
where W, termed the stability ratio, is related to VTby W
= 28 r'1) exp(VT/kT) Jo
dh
(14)
(h + 2a)2
In the absence of an energy barrier, i.e., setting VT = O,we find W = 1 and the equation for rapid coagulation is obtained. In the presence of an energy barrier VTbecomes positive and W becomes greater than unity and, clearly for these conditions, the rate of coagulation is slowed down; hence slow coagulation occurs. In practice at intermediate electrolyte concentrations
and medium potentials (ljIs'" 50 mV) W can attain values of the order of 107 so that coagulation is imperceptible on a reasonable time scale. The approach emphasizes the kinetic nature of the stability of lyophobic colloids.
15
1. The Stability and Instability of Polymer Latices
Measurements of the rate of coagulation of latex particles can be carried out by a number of techniques, two of those most commonly used being particle counting and light scattering (Ottewill and Shaw, 1966). These give values for the rate constant k and since a well-marked transition usually occurs between the slow and rapid coagulation regions the assumption is usually made that for rapid coagulation W = 1, whence for this region k = ko, and thus in the slow coagulation regíon, W can be obtained from the ratio ko/k. A typical example of the type of experimental data obtained is shown in Fig. 10 plotted in the form log Wagainst log C., where C. is the concentration of electrolyte in the dispersion after mixing has occurred at zero time. As can be seen, the transition between slow and rapid coagulation is clearly marked and a well-defined electrolyte concentration can be obtained from the graph at this point. This electrolyte concentration is termed the critícal coagulatíon concentratíon and will be abbreviated as cee. As a further development, it was shown by Reerink and Overbeek (1954)
:: C» o ...J
0.5
o
-2.5
-2.0 Log
-
--~
.
-1.5
ce
Fig. 10. Log W against log C. eurve for a polystyrene latex (a = 0.21 Jlm) in barium nitrate solutions (Ottewill and Shaw, 1966). indieates results obtained from light-seattering
measurements; O indieates resuIts obtained using a partic1e eounting teehnique; cee value.
i
indieates
R. H. Ottewill
16
that the gradient of the curve just before the cee was given as a first approximation, based on Eqs. (3) and (9), by (15) From this equation it is clear that the gradient should be directly proportional to the particle radius a and inversely proportional to the square of the valence of the counterion used. A number of experimental studies have been made tha~ do not seem to confirm these predictions (Ottewill and Shaw, 1966) and even more refined treatments of the kinetic process have not removed the discrepancy (Derjaguin and Muller, 1967; Honig et al., 1971). There is little doubt that as a kinetic process coagulation is rather complicated; further discussion on this point will be given later.
VI.
An Alternative Approach to the Critical Coagulation Concentration
From the previous discussion.it is apparent that provided the magnitude of Vmis substantial the probability of transition into the primary minimum is small. However, as shown above when VT = Vm = Othe transition is facile (Fig. 11) and the particles coagulate. Therefore, we can define conditions for the onset of instability as (Verwey et al., 1948) and
(16)
whence using Eqs. (3) and (9) we find Kcrit= 2.04 X 1O-Sy2/Av2
(17)
Distance >~
IJ) c: W
...
,
...
...
...
,
-
/
Fig. 11. Sehematie potential energy eurve to iIIustrate eonditions leading to a theoretical definition ofthe cee. -, VT;---, VAonly.
f
17
1. The Stability and Instability of Polymer Latices
and since for a symmetrical electrolyte 1( can be related directly to the concentration of the electrolyte C expressed in mol dm - 3 by 1(2
= 81tv2e2NAC/ekTx103
(18)
with NA = Avogadro'snumber, wethen find using Eqs. (17)and (18)that, CCril=
3.86 x 1O-25y4 -3 mol dm A 2v ~
(19)
where Ccritis the ccc and we note the inverse dependence on the sixth power of the valence of the counterion. For low surface po tentials, t/ls< 25 mV, a further simplification can be made to give mol dm-3
(20)
which gives an inverse dependence on the square of the valence, so that for univalent, divalent, and trivalent counterions, we obtain
The DL VO theory thus enabled theoretical significance to be given to the valence sequence in coagulation experiments that had been observed many years earlier by Schulze (1882) and Hardy (1900). Although expressions of this type are useful in a qualitative predictive sense, the implication that there is a simple rule applicable to alf systems must be treated with considerable caution. It must be borne in mind that coagulation is a complicated phenomenon involving quite a range of kinetic and specific ion effects.
VD.
Tbe Determination of eee Values
From an experimental viewpoint, however, there is no doubt that the ccc is a very important quantity to know for a polymer latex, since it represents the electrolyte concentration at which complete loss of stability occurs. Experimentally, the ccc can be obtained by a variety of methods and the use of light scattering and partic1e counting ha ve already been mentioned. Possibly the simplest method of all is visual observation in test tubes containing the same concentration of latex and different concentrations of electrolyte. A slightly more elaborate version of this method is to use a simple spectrophotometer to measure the optical density of the dispersion at specific time intervals after addition of electrolyte; the most convenient
R. H. Ottewill
18
time period having been determined from some preliminary experiments (OttewilI and Rance, 1977). An example is given in Fig. 12 of a plot of optical density against pH which shows the boundary between slow and rapid coagulation regions. Extrapolation of the rapidly descending portion of the curve to the abscissa yields a value for the cec. As can be seen the value obtained wilI be time dependent so that for comparative purposes, e.g., to evaluate the effectiveness of different electrolytes, standardization of the time period of the experiment is essential. The time dependence is not unexpected since each time corresponds to a different stage in the overall kinetic process. There is no doubt that the most precisely defined value is that obtained from the log Wagainst log Ce curve using initial rates, since this is always defined as t -+ O. We can anticipate that there will be some variation in the actual values of the ccc obtained by different methods and also between different workers. The general pattern of the results observed, however, should not change with either of the latter factors.
0.2
-
>-
VI c: CD
o
c. O 0.1
2.4
2.0
1.6 pH
Fig. 12. Optieal density against pH al various times after addition of hydroehlorie aeid. -0-,1 hr; -8-, 2 hr; -/;:,.-,26 hr; ---, cee 1 hr; -'-', cee 2 hr; , cee 26 hr.
1.
19
The Stability and Instability ot Polymer latiees TABlE
11
cee Values tor Various Polymer latiees Latex Polystyrene (Carboxylsurface) Polystyrene (Amidinesurface) Divinylstyrene Styrene-butadiene
Poly(vinyl chloride)
Counterion
cccjmmol dm - 3
H+ Na+ BaH La3+ (pH 4.6) CIBr1Na+ Na+ K+ MgH BaH La3+ (pH 3) Na+ MgH
1.3 160 14.3 0.3 150 90 43 160-560 200 320 6 6 0.5 50-200 2-10
Reference Ottewill and Walker (1968) Storer (1968) Ottewill and Shaw (1966) Ottewill and Walker (1968) Pelton (1976)
Neimann and Lyashenko (1962)
Force and Matijevié (1968a)
Bibeau and Matijevié (1973)
The cee values for a number of polymer latiees have been determined and some typical values are reported in Table II. The trends observed are qualitatively in agreement with those expected fram the theoretieal approach for particles with smooth surfaces, with 1/1.everywhere the same, using simple eleetrolytes, i.e., those which do not interact chemically with water to form new ionie species. These yalues should only be used for qualitative guidance since, in addition to the factors already mentioned, there can be variations of the cec with particle size, type and density of surface groupings, and the presence or absence of stabilizing materials such as surfactants. In practice it is advisable to determine the actual value for a particular latex system.
VIII.
Tbe Effects of IODSTbat Interact with Water
So far, the assumption has been made that the ions used in the coagulation experiments do not interact with water. In a number of cases, however, the ions do react with water under certain pH conditions to form hydrolyzed species. For example, in the case of aluminum, the AI3+ ion exists at pH values below about 3.3 as the hexaaquo ion, with six water molecules in the octahedral coordinate positions. As the pH is slowly increased, reaction occurs with water to form a sequence of species. The chemistry involved in these reactions is somewhat complex and has not
1-
l 20
R. H. Ottewill
been fulIy resolved but a plausible reaction scheme can be proposed, for the present purpose, as ~20
¡20 H20
¡ :
",
,
--.
'~'~I~+ ""
H;O
:
H20: .'.
Ji20
: '. ..
¡
/
H20: ". --.
''':~I~+ '.. '......
¡
..........
lI20
~20 OH
'. H20
H;O
OH
/i..... HO
'H20
¡
/
: : "AI+
H20
"H20
¡
H20
/ 1+
H'~ r~~",r~H "~I
/'~H/'" [ HO
.. ¡
~!
((
lI20
.. ¡
"'}{20
]
1120
1 Alx[OHy]"+
where Alx[OHy]n+ represents an inorganic polymer soluble in water. Polymeric species of this type can adsorb strongly onto negatively charged particles and reduce the effective surface potential on the particle to zero. As anticipated from Eq. (3) this situation leads immediately to coagulation. At higher concentrations of the aluminum species, superequivalent adsorption can take place, thus conferring a positive charge on the particle and leading to restabilization of the dispersion as one containing positively charged rather than the original negatively charged particles. In addition, it is also possible for the positive polymeric species to "bridge" two negatively charged particles. The exact nature of the polymeric species in solutions of aluminium salts at the pH conditions for charge reversal is not known with certainty. It is possible that several species coexist, depending on their stability constants, and that these also change with time with the ultimate product of hy-' drolysis being aluminum hydroxide particles. A number of species ha ve been pro posed in the literature and Matijevié et al. (1964) ha ve provided evidence for the existence of Als(OH)1t from coagulation studies. The higher valence of this type of species again reduces the concentration of ions
1.
21
The Stability and Instability of Polymer Latices
required to produce coagulation. The combined effects of high valence and reduction of the surface charge to zero makes aluminum salts very effective coagulants in the pH range of about 4 to 5.5. Coagulation can be achieved at very low salt concentrations and since most of the aluminum is adsorbed by the particles there is little salt left in the filtrate after remo val of the coagula. This factor is exploited in the use of aluminum salts for the treatment of potable water. The basic pattern of the coagulation of polymer latices with aluminum salts has been clearly demonstrated by the work of Matijevié and his collaborators (1968) using styrene-butadiene, poly(vinyl chloride) (1977), and PTFE (1976) latices. The results obtained by Matijevié and Force (1968b) for the coagulation of styrene-butadiene latices using alumirium nitrate are shown in Fig. 13. From these it can be seen that up to a pH of ",3.4 the ccc remains constant at 5 x 10-4 mol dm-3 and then decreases between pH 3.4 and 4.8 to reach a constant value of
'"
'";; O z
-2
~
c:
.2 -3 -;¡; ... ¡:
Q) () c: o Ü
RESTABILlZATlON
... -4 al o ~ ti' o ...J
STABlE
-5
REGION
2
3
5
..
6
7
pH Fig.13. Log[(AIN03h/mol dm-3J against pH showing the positions of the coagulation domains for a styrene-butadiene latex. Curves constructed from the data of Matijevié and Force (1968); reproduced with permission of Ko/loid Z.u.Z.fur Polymere.
.. ..
R. H. Ottewill
22 3.0
- 3.4
~
E
"O
<5 E "-
,.., u u u
':::! 3.8
'"
3
4.2
pH
Fig. 14.
Log[ccc] against pH for a PTFE latex using aluminium
nitrate
as the
coagulating electrolyte.
'" 2.5 x 10- 6 mol dm - 3
between pH 4.8 and 6.0. The region of restabili-
zation as positively charged particles can also be seen on this "domain" plot. In the case of PTFE latices the behavior seems to be strongly dependent on the amount of stabilizer present in the system. Kratohvil and Matijevié (1976) found evidence for both charge reversal and restabilization. On the other hand, Ottewill and Rance (1979) using well-dialyzed PTFE latices obtained the results shown in Fig. 14. The change in cee with pH is clearly defined but the cee above pH 5 is at a fairly high concentration of electrolyte and insufficient positive charge is built up to stabilize the dispersion. It is also possible with this system that the very hydrophobic polytetrafluoroethylene parts of the surface do not adsorb the hydrolyzed species, and in the well-dialyzed system adsorption can only occur on the sparsely charged sites.
IX.
Secondary MinimumEtIects
One of the pronounced features of the curve of VT against h shown in Fig. 5 is the secondary minimum, and as can be seen from Fig. 9, although this is a feature that is not very pronounced for small-diameter particles, it becomes more distinctive as the particle size increases. With an increase in
1.
23
The Stability and Instability of Polymer Latices
salt concentration, for a constant particle radius, the depth of the secondary minimum increases; and although the magnitud e of Vrnis reduced, it nevertheless remains distinct and positive. These trends can be clearly seen in Fig. 15. The form of the potential energy curves indicates the possibility that over this range of electrolyte concentration, once a particle enters a secondary minimum, it will have a long residence time there and remain separated from the second spherical particle by distances of the order of 6 to 10 nm. However, there remains a substantial primary maximum in po tential energy to be overcome before the particles can come into contact or enter the primary minimum. Association in the latter state clearly corresponds to a condition where the particles come into close contact, providing the possibility with subsequent thermal diffusion that they will 20 o
,"' , '.
100
l'
i/\
\
... .' \ \ \
:!:L kT
o
'
-',-'.- \ \
'.
". .
:,
-100
:.,I
'.
------
,
;',.y
-----
--_o .....;;-;:.-:~._- - - - -
00'
,,"
1
:,
h (nm) Fig.
15.
VT/kT against
h for spherical
partic1es
of radius
= 1.62
J.lm at various
con-
centrations of al: 1 eIectrolyte. -, 0.05 mol dm-3; -'-, 0.1 mol dm-3; -"-, 0.15 mol dm-3; ,0.3 mol dm-3; ---,0.4 mol dm-3; 1jI,= 25 mV; and A = 7 X \0-21 J at a temperature of 298.2°K.
i;
~
R. H. Ottewill
24
fuse together. Under these conditions, therefore, one would expect the units formed to be hard, compact, and essentially nonreversible, and there is compelling logic to term this state coagulation. On the other hand, when association occurs in a secondary minimum, the particles remain separated by a liquid film, which renders thermal diffusion of polymer chains between the solid particles unlikely, and leaves the possibility that by decreasing the salt concentration the particles can redisperse. The logical term for this state is flocculation and there are strong reasons for distinguishing between the coagulated and flocculated states when simple electrolytes are used to produce them. It is clear from Fig. 15 that with continued addition of electrolyte, a transition from the flocculated to the coagulated state should also occur. The spherical nature of the particles and the high degree of monodispersity in polystyrene latices makes them ideal systems for testing such a hypothesis and exploring its practical implications. In some preliminary experiments by Mardle (1980) the ccc values were determined for a series of latices of different particle sizes; and then over a range of salt concentrations at and above the ccc he examined the effect on the associated state of using dialysis to remove the salto The results obtained are summarized in Table III. TABLE
111
Reversibility of Aggregates Formed on Addition of Electrolyte Particle diameter (Jlm)
eee/mol dm - 3 value for NaCI
0.21
0.208
0.208
Large aggregates Nonreversible
0.40
0.155
Some redispersion Some redispersion Nonreversible
0.58
0.150
1.34
0.108
3.24
0.158
0.155 0.25 0.40 0.150 0.60 0.70 1.00 0.108 0.400 1.500 0.158 0.400 1.0
Eleetrolyte NaCI eone (mol
dm - 3)
Behavior on dialysis
Some redispersion Some redispersion Some redispersion Nonreversible Redispersion Redispersion Redispersion Redispersion Redispersion Redispersion
1.
25
The Stability and Instability of Polymer Latices
On a kinetic basis the presence of a pronounced secondary minimum should lead to a steady-state condition in which the rate of particles entering the secondary minimum to form associated units should be balanced by their rate of return to single particles. Direct evidence for this situation has been obtained recently by Cornell et al. (1979), using optical microscope observations on particles of 2-Jlm diameter. The results are given in Fig. 16 as plots of the percentage of the total number of particles remaining as single particles as a function of time at several difIerent electrolyte concentrations. A marked dependence of the rate of disappearance of single particles on electrolyte concentration is apparent. In the most dilute electrolyte, 10- 5 mol dm - 3 sodium chloride, no change was observed in the number of single particles present over a period of 6.3 hr. At salt concentrations of 3 x 10-3 and 10-2 mol dm-3 the percentage of single particles initially decreased and then subsequently became constant over an extended period of time, indicating a steady-state condition in the
C/') :: 60 UI 41
o
:u 40 Q. ~
20
200
100 Time
300
(min)
Fig. 16. Experimental determination of percentage of particles remaining at various times after addition of electrolyte using a polystyrene latex with a particle radius of 1 Jlm. Sodium chloride concentrations. -0-, 10-5 mol dm-3; -e-, 3 x 10-3 mol dm-3; -f:::,-, 10-2 mol dm-3; -Á-, 6 x 10-2 mol dm-3.
R. H. Ottewill
26
aggregation process. Assuming that at this stage doublets form the predominant associated units the rate of disappearance of single particIes becomes (21) where k1 is the rate constant for entry into the secondary minimum, k2 the rate constant for exit from the secondary minimum, N1 the number of single particIes, and N2 the number of doublets. For a steady-state condition we have . -dN/dt
=O
(22)
and consequentiy the number of doublets is given by N2
= k1NI/k2
(23)
From these arguments it would be anticipated that once a steady-state condition was achieved the percentage of single particIes would become constant. With a further increase in electrolyte concentration, however, a deepening of the secondary minimum would occur and therefore more particIes would reside in secondary minima. The experimental observations shown in Fig. 16 appear to be in accord with this. With this size of latex particIe it becomes possible to make direct observations on particIes over a period of time and record them with a high-speed camera. Using this technique Comell et al. (1979) discovered that particIes in an associated unit could be quite mobile. It was observed that as well as so~e particles leaving the aggregated unit as single particIes and retuming to the disperse phase there was a continued rearrangement of the particles. This was also observed with floccules at salt concentrations well above the cee. These observations clearly support the contention that association can occur in a secondary minimum and that in this situation a liquid film is maintained between the particles.
x.
The Effects of Organic Ions: Added Surfactants
In general, the types of surfactant added to a latex will be either anionic, cationic, or nonionic as classified by the nature of the head group. If it is assumed that the latex particle has a surface free of adsorbed materials and is negatively charged, then the various possibilities of adsorption of the surfactant can be envisaged by the schematic diagram given in Fig. 17. The discussion of the various phenomena observed can then be based on these models.
27
1. The Stability and Instability of Polymer Latices
ANIONIC ENHANCEO
/:~
STAS ItlTY
COAGU LA TI ON
CATIONIC
RESTAS ItI ZATION
STASltlTY
--
..
Fig. 17. Schematic iIlustration of the adsorption of anionic, cationic, and nonionic surfactants on anionic polystyrene latex particles.
XI.
Ionie Head Group with a Charge of the Same Sigo as the Particle
In this situation the hydrophobic chains of the surfactant adsorb onto the hydrophobic areas of the latex particle and hence leave the anionic group exposed to the solution phase, thus increasing the overall surface charge on the particle. The phenomena can be illustrated by data obtained by Ottewill and Rance (1977) using polytetrafluoroethylene (PTFE) latices. With welldialyzed latices the cee values were those recorded in the first column of Table IV. After it had been established that the perfluorooctanoate ion can adsorb on PTFE particles to give a monolayer, with an area per adsorbed perfluorooctanoate ion of 54 A2, at ~20% of the critical micelle con- . centration (2.4 x 10- 2 mol dm - 3) the cee values were redetermined in 2.5 x 10-2 mol dm-3 ammonium perfluorooctanoate. The results are given in Table IV. In the presence of ammonium perfluorooctanoate, it can be seen that with sodium chloride and aluminum nitrate the stability of the PTFE latex
R. H. Ottewill
28
TABLEIV cee Values for PTFE latiees
-
Eleetrolyte NaCI Ba(N03h AI(N03h (pH 3.0)
1
I
eee/mol dm - 3 dialyzed latex
eee/mol dm 3 in the presenee of 2.5 x 1O-2moldm-3 ammonium perfluoroaetanoate
4.7 X 10-2 7.4 X 10-3 1.6 X 10-4
2.2 X 10-1 7.4 X 10-3 5.4 X 10-3
increased and that nearly an order of magnitude increase in salt concentration was needed to produce coagulation. On the other hand with barium nitrate the ccc value did not change. The explanation was that barium perfluorooctanoate is essentially insoluble in water and the addition of Ba2+ ions to the solution phase stripped the adsorbed perfluorooctanoate ions from the surface. A further important point arises in the context of adsorption. It was found that despite the fact that both fluorocarbons and hydrocarbons are hydrophobic dodecanoate ions are only very weakly adsorbed on a PTFE latex surface and do not form a monolayer, whereas perfluorooctanoate forms a monolayer at relatively low concentrations (Rance, 1976). Compatibility of the polymer surface and the surfactant is therefore an important factor to consider if enhanced stability is required from addition of the surfactant. On basically hydrocarbon-hydrophobic substrates such as polystyrene, it is well established that even on the negatively charged partic1es there is adsorption of surfactant anions via the hydrocarbon chains. This is demonstrated in the work of Kayes (1976), who found a substantial increase in the electrophoretic mobility of polystyrene latices with increase in the concentration of dodecyl sulfate in the system, and in the work of Cebula et al. (1978) on the adsorption of dodecanoate ions on polystyrene latex partic1es.
XII.
Ionic Head Group with a Charge oí Opposite Sigo to the Particle
As illustrated in a very simple fashion in Fig. 17 in the case of a negatively charged partic1e, the first stage of adsorption of a cationic surfactant is via the positive head group to neutralize the charge on the r
:¡ L
IJ!!II
1.
29
The Stability and Instability of Polymer Latices
particle, whence IjIs = O and consequently VR= O also. In this region on a hydrocarbon surface it is probable that the hydrocarbon tails lie flat on the surface. Some data obtained for the coagulation of polystyrene latices by a series of alkyl trimethylammonium halides are shown in Fig. 18 in the form of curves of log Wagainst log Ce; for comparison results are also included for a simple 1: 1 electrolyte, potassium bromide (Connor, 1968; Ottewill, 1980). It can be seen from these data that the range of concentrations over which coagulation occurs is very narrow and that the cee is strongly dependent on the chain length of the hydrocarbon tail of the surfactant molecule. Studies of the electrophoretic mobility of the particles confirm that at the cee the particle mobility becomes zero (Connor and Ottewill, 1971). Once the negative charges on the particle surface have been neutralized further adsorption of the surfactant occurs via the tail onto the hydrophobic patches of the surface and also by association of the hydrocarbon chains. Detailed adsorption studies on polystyrene latices have been reported (Connor and Ottewill, 1971). The additional adsorption pro vides a positive charge to the particles and restabilization occurs. The sharpness of this phenomenon is clearly illustrated by the experimental data 2
;: 1 c> o ..J
o
-1
Log [Cone, S. A.A./ moI dni3] Fig. 18. Log W against the log of the concentration of alkyl trimethyl ammonium bromidesof variouschain lengths: ., C16; ., C12;., CIO;O, Cs; O, C4. For comparison, data for potassium bromide is included. f:::,..Radius of polystyrene latex particles Reproduced
with permission
of American
Chemical
Society.
= 48 nm.
R. H. Ottewill
30
given in Fig. 18, and it has also been examined theoretically (Ottewill et al., 1960). At much higher additions of surfactant the electrolyte concentration is appreciably increased and compression of the electrical double layer occu.rs, leading to a second coagulation region. Under these conditions, i.e., with the ionic groups of the surfactant exposed to the solution phase, the particles are well-wetted and the coagula usually sink if the density of the particles is greater than that of the media. The conditions of the first coagulat"ion region, however (i.e., zero surface potentiaI with hydrocarbon chains orientated' toward the solution phase) leads to particles that are easily dewetted and flotation is frequently observed (Connor, 1968). In Fig. 19 values of the logarithm of the ccc obtained with a series of alkyl trimethylammonium bromides are plotted against the chain length of the surfactant for the coagulation of polystyrene latices. The curve is essentially linear for chain lengths between C4 and Cl2 but deviates from linearity for the short- and long-chain materials. A similar trend was reported by Tamaki (1960) for the coagulation of silver iodide soIs by alkylamine hydrochlorides. It appears that for chain lengths shorter than C4 the ions behave in a manner similar to hydrated inorganic ions and that the short hydiocarbon chain is'hydrated by the solvation sheath of the head
-1
-2 r--r
'" le -3 "C 'O
e
-4 L
Ü Ü Ü
I
'" -5 o ...J
-6
2
4
6
8
Carbon
Atoms
10 in
12
14
Chain
Fig. 19. Log cee against ehain length for the eoagulation of a polystyrene latex (radius = 48 nm) by alkyl trimethyl ammonium bromides.
31
1. The Stability and Instability of Polymer Latices TABLE V Coagulation of Polystyrene and PTFE Latices by Cationic Surfactants eee/mol
Surfaetant CaH17 NMe; BrC1oH21 NMe; BrC12H2SNMe; Br-
polystyrene
dm - 3
eee/mol dm -
latex
PTFE latex
1.59 X 10-4 1.99 X 10-5 2.93 X 10-6
3
4.5 X 10-5 3.1 X 10-5 2.9 X 10-5
I
l¡ ¡ L
~
i g
i
I i I
group. In the case of the hexadecyl trimethylammonium bromide there .is some evidence for dimerization in solution, which would help to screen the hydrophobic nature of the hydrocarbon chain. In the coagulation of PTFE latices by cationic hydrocarbon surfactants, however, a different behavior is observed in that only very small differences are observed in the magnitude of the ccc with variation of chain length (Richardson, 1979). This effect is illustrated by the data in Table V. Again, it appears to demonstrate the lack of affinity of hydrocarbon chains for fluorocarbon surfaces.
XIII.
Nonionic Surfactants
The most extensively studied type of nonionic surfactant is that with a head group of ethylene oxide units. It was shown by Ottewill and Walker (1968) that these materials can adsorb on polystyrene latex particles, below the cloud paint of the surfactant, to give a monolayer on the surface with the alkyl chains adsorbed on the particle surface and the ethylene oxide groups extending into the solution phase, as illustrated in Fig. 17. By means of ultracentrifugation studies they measured the thickness of the adsorbed layer O and for dodecylhexaoxyethylene glycol monoether [C12H2S(CH2CH20)60H(C12E6)] found that the adsorbed layer contained as much as 70% water. Such a homogeneous hydrated layer pro vides a steric barrier to the approach of the particles and Íts effect needs to be considered in some detail. In order to account for the steric effects, an additional potential energy term V., which pro vides a measure of the steric interaction, needs to be introduced. On the assumption that the adsorbed layer is homogeneous and using Flory-Krigbaum (1950) statistics to describe the mixing of the two layers, the expression found by Ottewill and Walker (1968) for V. was V.
= (41tC;kT/3V1P~)(t/Jl -
Xl)(O - h/2)2(3a + 20 + h/2)
(24)
R. H. Ottewill
32
where Ca the concentration of the surfactant in the absorbed layer, VI the molecular volume of the solvent molecules, P2 the density of the adsorbed material, rf¡l an entropy parameter which for ideal mixing can be taken as 0.5, and Xl a parameter characterizing the interaction of the surfactant with
the solvent. It is immediately clear that if rf¡l is taken as 0.5, then for Xl < 0.5, V. is negative and the term becomes attractive, whereas for Xl < 0.5, V. becomes positive and the term becomes repulsive. Moreover, for this type of interaction no effect would be anticipated until h = 2<5,when the adsorbed layers touch. An extension of this model which allows for a redistribution of the adsorbed material during interaction has been proposed by Dorozklowski and Lambourne (1971), and application of similar models to adsorbed polymer layers has been extensively examined by Napper (1977) and his collaborators. The various models may be too simple. but it does appear that for well-solvated materials XI is less than 0.5 and in general, the interaction energy rises fairly steeply once the adsorbed layers touch. The net effect of v., when it can be used in these circumstances, is to impart considerable stability to the dispersion since it effectively presents the particles from entering the primary minimum. The form of V. against h is 'shown schematically in Fig. 20. It will, however, seldom if ever act on its own, and usually the van der Waals
'. \ 1
..
+
'.\ 1 .\
'
.\ >-
O)
.. Q)
c: W
.~
-
-Co Q)
o Q.
'.\ .. '.\ '. \ ..
..
..
.. ........
h Fig. 20.
Schematic potential energy curves. -.-',
VT= Vs + VR+ VA,
Vs only;
, vT = Vs+ vA; -,
33
1. The Stability and Instability of Polymer Latices attraction will act in combination with
v.,so that
VT = Vs+
(25)
VA
a situation that can give rise to a shallow energy minimum, as shown in Fig. 20, and to a flocculated state in a dispersion that is easily reversed by mechanical energy (Long et al., 1973). In addition in an aqueous dispersion there will be some charge on the layer, and hence for this situation VT = Vs
+ VR + VA
(26)
and a potential energy curve of the form shown in Fig. 20 is obtained. Such a system will be very well stabilized at low electrolyte concentrations and will remain stabilized even at very high electrolyte concentrations since Vs still provides the repulsive interaction energy. Data which illustrate the latter point were obtained by Ottewill and Walker (1968, 1974) using polystyrene latices of various sizes and various electrolytes in th~ presence of nonionic surfactants. Figure 21 shows the 2
C)
o
...J
o
-4
-3 Log [La (N03h/mol
-2 drñ3J
Fig. 21. Log W against log concentration of lanthanum nitrate at pH 4.6 for a polystyrene latex (radius = 52 nm) in the presence of various concentrations of a nonionic surface active agent, C12E6. -0-, CI2E6 absent; -e-, lO-s mol dm-3 C12E6; -D.-, 1.5 x lO-s mol dm-3 C12E6; -0-, 2 x lO-s moldm-3.
R. H. Ottewill
34
curves of log Wagainst log C. obtained using polystyrene particles of 103nm diameter at various concentrations of C12E6 using lanthanum nitrate as the coagulating electrolyte. It is clear that the ccc moves to higher lanthanum nitrate values as the concentration of C12E6 is increased. At 10-5 mol dm-3 C12E6, well below the critical micelle concentration, the increase in ccc is over an order of magnitude. Close to the critical micelle concentration with the system containing 5 x 10- 5 mol dm - 3 C12E6 the latex was stable even at 0.3 mol dm - 3 lanthanum nitrate. The effectiveness of C12E6 as a stabiiizing agent to the addition of electrolyte is particlesize dependent its effect being greatest with the smallest particles. This is demonstrated by the data given in Table VI. It should be noted, however, in connection with the use of nonionic surfactants that tlocculation is usually observed at a temperature just below that of the cloud point of the surfactant. The exact temperature at which this occurs, however, can depend on the type of salt used and the presence of other surfactants. An interesting feature occurs in the use of nonionic surfactants with PTFE latices. Experiments indicate that PTFE particles adsorb ethylene TABlE VI Coagulation of Polystyrene latices by Lanthanium Nitrate at pH 4.6 in the Presence of C12E6 Number average particle diameter (nm) 60:t 10
Total C12E6 eoneentration
Equilibrium C12E6 eoneentration (mol dm-3)
zero X 10-6 x 10- 5 x 10- 5 x 10- 5 zero 1 X 10-5 1.5 X 10-5 2 x 10- 5 5 x 10- 5 zero 1 x 10- 5 2 x 10- 5 5 x 10- 5 10-4
zero 2 X 10-6 3 X 10-6 7 X 10-6 -
2.8 6.9 1.7 4.2
zero 6 X 10-6 1 x 10- 5 1.4 X 10-5 -
5.6 3.3 3.2 5.2
x 10-4 X 10-4 X 10-3 X 10-3 sa x 10-4 X 10-3 X 10-3 X 10-3
zero 9.5 X 10-6 1.9 X 10-5 5.0 X 10-5 10-4
5.2 2.0 2.0 1.0
sa x 10-4 X 10-3 X 10-3 X 10-2
5 1 2 5
103 :t 8
368 :t 17
a
S indieates
b cee eould
eee/mol dm - 3 La(N03h
(mol dm - 3)
that eoagulation not be determined
did not occur in 0.3 mol dm - 3 lanthanium but very
slow eoagulation
oeeurred.
_b nitrate.
1.
35
The Stability and Instability of Polymer latices
oxide-type surfactants (Bee, 1978). Since as indicated earlier hydrocarbon chains are reluctant to adsorb on polytetrafluoroethylene surfaces the circumstantial evidence is strong that the initial adsorption occurs via interaction of the ethylene oxide group with the ionie groups on the PTFE latex partic1es. Indeed experimentally a small drop is noted in the cee value at low concentrations of C12E6, which supports this idea. Subsequent adsorption of the nonionic surfactant can then nuc1eate around the hydrocarbon chain of the head-group "down" molecules to give eventually monolayer coverage and enhanced stability.
XIV.
Mixed Electrolyte Systems
In many cases mixed electrolyte systems can be added to a latex either adventitiously or deliberately. Their effects on the stability of dispersions can best be summar~zed by Fig. 22. The axes of this figure are plotted as a percentage, so that the abscissa is the cee value of salt 1 expressed as a pereentage of its cee value in the absenee of the second salt; salt 2 is expressed on a similar basis. Thus, the simplest possible case is additivity in
\ 80
-
C\I Cii
60
CI)
.. .
\ '. \ \ \ \
~
'\. 40
"
"
20 100 Yo
-,
Salt
1
Fig. 22. Various effects obtained using mixed electrolyte systems as coagulating agents. antagonism; ---, superadditivity; , additivity; -'-', syngergism.
R. H. Ottewill
36
,
,
,,
,,
,
20
,,
,,
,,
,,
,,
,,
,,
,
...o.100
o
. Fig. 23. Results obtained for the coagulation of a polystyrene latex (radius = 0.109 pm) using mixtures of magnesium sulfate and sodium nitrate at pH 8.5 and 298.2°K. Percentages are expressed in terms of the molar concentrations of the salts; --- indicates additivity.
which case the plot joining the two values is a straight line. Superadditivity gives a curved line which is convex to both the abscissa and the ordinate. Antagonism gives an even more pronounced convexity and the gradient at the point of intersection on the ordinate is distinctly positive. The fourth case is that of synergism, Le., when the curve is concave toward the axes. Some results obtained by Storer (1968) using well-dialyzed polystyrene latices at pH 8.5 and mixtures of magnesium sulfate and sodium nitrate as the coagulating electrolytes are shown in Fig. 23. Distinct synergism was observed over the entire concentration range. The use of activities of the ions in the mixed systems, rather than concentrations, gave a reasonable explanation for the form of the data, but it is also of interest that the discrete-ion treatment of Levine and Bell (1965) also predicts synergism for certain cases.
XV. Heterocoagulation In the previous section the strong affinity of cationic surfactants for negatively charged polystyrene latices was noted. This concept of a single po sitive ion interacting with a negative charge on a surface can be extended
-
37
1. The Stability and Instability of Polymer latices
to the interaction between a positively charged particIe and a negatively charged particIe. Moreover, the particIes of different charges can have the same chemical composition or be composed of different materials. Thus, mixing of latices contaíning particIes of opposing charge can lead to coagulation
and this phenomenon
is usually. termed heterocoagulation.
.
Measurements of heterocoagulation can be made in much the same way as were measurements for the addition of an electrolyte to a latex. For example, with an appropriate mixing device (Cheung, 1979) an anioníc latex can be added to a cationic one and the progress followed by turbidity measurements to obtain a stability ratio. Results of this type are shown in
Fig. 24 in the form of log Wagainst N-/(N + + N-) where N+ and N_are the number concentrations of the cationic and anionic lattices respectively. The anionic latex used was composed of polystyrene particIes (diameter
-
~
0.1 6
O> o
...1
0.0 8
0.1
Fig. 24.
0.2
0.3
004
Log W against N_/(N- + N+) for mixtures of an anionic polystyrene latex
(particleradius = 26 nm) and a cationic polystyrenelatex (particleradius = 22 nm). N+ and N-
= the
number concentration of the cationic and anionic lattices, respectively. Sodium
chloride concentration
= 10-3
mol dm-3.
3~
R. H. Ottewill
52.7 nm) with sulfate. groups on the surface; the cationic latex was also polystyrene (diameter 43.4 nm) with surface amidine groups. It can be seen from Fig. 24 that the system becomes completely unstable w~en the ratio N_/(N+ + N_) reaches -0.25. When the particles are of different sizes complete coverage of the bigger particles by the smalIer can occur (Goodwin et al., 1978). This is demonstrated by the scanning electro n micrograph shown in Fig. 25. An "alternative method of studying heterocoagulation is to use the spinning disk technique, a method that provides well-defined hydrodynamic conditions for examining the deposition of spherical particles on planar surfaces. The method was used by Clint et al. (1973) to examine the heterocoagulation of polystyrene latex particles (diameter 418 nm) onto planar polystyrene surfaces in the presence of barium nitrate. The highest rates .of deposition of the latex particles began to occur at about 0.02 mol dm - 3 barium nitrate. This corresponded to IjIs values of about 10 mV on the particles and about 6 mV on the planar surface. The experiments were satisfactorily explained using the Levich theory (1962) of diffusion to a rotating disk, with modification to include a potential energy of interaction between the plate and a sphere.
Fig. 25. Scanning electron micrograph showing the heterocoagulation of cationic latex particles (radius = 22 nm) onto a negativeIy charged particle (radius = 1.07 11m).
.
1.
39
The Stability and Instability of Polymer Latices
XVI.
Suñace Coagulation
There are a number of cases with polymer colloid systems where the coagulation process can occur at the liquid-air interface under conditions of electrolyte concentration that are far removed from those required to produce coagulation in the bulk solution. The processes that occur in this type of coagulation are illustrated schematically in Fig. 26. The effect was originally called mechanical coagulation, by Freundlich, but waf! more appropriately termed surface coagulation by Heller and Peters (1970) who, in conjunction with several co-workers, have carried out an extensive investigation of this phenomenon. A theory of surface coagulation was developed by these authors based on the following assumptions: 1. That the coagulation process proceeded exclusively at the liquid-air interface and was a biparticle association. 2. That the contribution of aggregates to the rate could be neglected. Moreover, since the aggregates returned to the bulk phase they had an insignificant effect on the interfacial area available for occupation by unreacted primary particles. 3. That sufficient convection occurred to exclude the diffusion of particles to and from the interface as a rate-determining factor. 4. That a steady state occurred for the distribution of primary particles between the bulk dispersion and the surface, and this distribution could be described by a Langmuir adsorption isotherm. 5. That the rate of adsorption was la,rge enough relative to the rate of formation of fresh surface for the adsorption equilibrium to be unaffected. Thus, putting the Langmuir adsorption isotherm in the form
c/r
= K1
+ K2c
(27)
where c is the concentration of colloidal particles in the bulk phase, r the
surface concentration, and K I and K 2 are constants, and taking the biparticular surface reaction rate as (28) they obtained (29) Air -----..
Water
o
o
o
Dispersion Fig.26.
Schematic
(5
Adsorption illustration
co Surface Coagulation
of the process of surface coagulation.
Redispersion
40
R. H. Ottewill
When S is the surface area at a constant rate of surface renewal and Vis the volume of solution, the rate at which the bulk concentration was changed was given by -dcjdt = (KOSjV)C2j(K2
+ K2c)2
(30)
From a seriesof experimentsHelleret al. (1970b,1971a,b)found that
1. Colloidal dispersions that required a relatively large amount of electrolyte in order .to obtain conventional coagulation in the bulk phase were not susceptible to surface coagulation. . 2. Coagulation at the surface required a low dispersion stability although the latter could be adequate to avoid coagulation occurring in the absence of a renewable liquid-air interface. 3. The rate data indicated a lack of participation of the secondary and tertiary aggregates in the surface reaction. In some cases the aggregates formed by surface coagulation were found to differ in form from those formed in bulk coagulation processes. They appeared to be laminar aggregates, as indicated by the "silkiness" exhibited in mildly agitated dispersions. The mechanism appears to be connected with dewetting of the particle at the water-air interface either as a consequence of desorption of stabilizing surfactant or the fact that the particle surface is not homogeneous. PTFE latices are particularly prone to surface coagulation and this may be partly due to their nonspherical shape. The latter is a consequence of crystallinity and polymer chain folding which may mean that the ionic surface groups at the chain ends are concentrated on some surfaces, whereas the other surfaces are devoid of stabilizing entities. Consequently,the latter have a high contact angle against water. One method of preventing surface coagulation is to store the latex in containers without a water-air interface.
.
XVll.
Peptization
The reverse of the coagulation process is peptization. It is well known from analytical chemistry that fresh precipitates are easier to disperse than old ones, which indicates qualitatively that an aggregate of colloidal particles is not in equillibrium and that irreversible, time-dependent processes occur in coagulation. As pointed out by Frens and Overbeek (1971) the interpretation of peptization phenomena with aggregated systems is not possible unless the data are obtained in experiments with a shorter time scale than the aging time of the aggregate. They demonstrated that it was possible to follow the kinetics of peptization by suddenly diluting the sol
~
t 41
1. The Stability and Instability of Polymer Latices
containing electrolyte after a short period of coagulation. From their experiments they concluded that peptization was a rapid, spontaneous process and that electrical double-Iayer repulsion probably provided the driving force. The process of peptization can be explained in terms of potential energy diagrams following the suggestions of Overbeek (1977). The relevant diagrams are shown in Fig. 27 for systems that do not have pronounced secondary minima. In Fig. 27a, for the reason explained earlier, peptization is unlikely to occur since going from L to R involves an increase in free energy and a substantial energy of activation. In Fig. 27b the transition from L to R involves a free energy decrease, which is favorable for peptization; but stilI a high activation energy barrier has to be surmounted and again peptization is unlikely to occur. The most favorable conditions for peptization are those ilIustrated in Fig. 27c and d; these involve a decrease in free energy and only a small activation energy barrier of the order of 1 kT. Thus, the question arises as to how can this be achieved in practice.
>-
~
R
Q)
c:
w
L-- ( a)
.
(b)
Distance
-------
Fig.27. repeptization.
AVb-kT
~
AVb-kT
.
L
R
R
(e)
(d)
Potential energy curves to iIIustrate the differences between coagulation and
42
R. H. Ottewill
One possibility is to provide the particles with a thin steric barrier such as the "micro hairs" which could occur on the surface of a latex by solvation of the polymer chain beyond the ionic end group. Indeed some evidence for this occurs with certain latices. For example, Smithan et al. (1973) have reported evidence of steric stabilization with polystyrene latices with a high content of carboxyl groups on the surface prepared by an essentially conventional emulsion polymerization method. Microsteric stabilization with latices could be an important factor and this is undoubtedly an area that needs more extensive investigation.
XVffi.
The Effects of Adsorbedor Grafted Macromolecules
Space prohibits a detailed discussion of this topic but a few general points can be made following the comments made in the previous section. With hairy particles of the type shown in Fig. 3, polyelectrolyte molecules can be chemically linked to the surface or adsorption can occur by several mechanisms, including ionic bonding-particularly via charges of opposite sign-hydrogen bonding, coupliñg with multivalent inorganic ions, and by hydrophobic bonding of the hydrophobic regions of the marcomolecule to the surface. The net result is shown schematically in Fig. 28. Instead of the array of surface charges leading to a well-defined surface charge density and surface potential there is now a distribution of charges in space which contri bu te to the electrical double layer surrounding the particle. At low electrolyte concentrations the latter will extend into the space beyond the polyelectrolyte layer so that VR will be significant. However, with increase in electrolyte concentration and compression of the electrical double layer, VR can become small or zero. However, under these conditions the particle will still be coated with an extensively hydrated layer of polymeric molecules which provide a steric barrier V.. Hence, this type of system provides a twotier mechanism of stabilization against electrolyte additions and the classical protective agents for colloidal particles such as gelatin, gum arabic, etc. almost certainly act in this way. A number of polymer latices falling into this category have been described in the literature but they are still relatively novel and have not received the extensive attention given to the more conven.tional latices. Probably the systems of this type most extensively characterized are those described by Hoy (1979) and Bassett and Hoy (1980) which were prepared by copolymerizing methyl methacrylate, butyl acrylate, and ethyl acrylate with an unsaturated acid such as itaconic, acrylic, or methylacrylic. The particles obtained appeared to consist of a spherical core particle sur-
I
t~
I
íf
43
1. The Stability and Instability of Polymer latices
I I / POLYION /
LAYER /
-
/'
Fig. 28. Schematic ilIustration of a latex partic1e with an adsorbed or grafted layer of polyelectrolyte. represents the extension in space of the adsorbed layer, and --- represents the extension in space of the electrical double layer. 'Reproduced with permission. of American Chemical Society.
rounded by an acid-bearing polyion shell. The latter expanded at high pH values as the acid groups were neutralized to give a structure similar to that shown schematically in Fig. 28. These authors have carried out extensive ultracentrifugation studies on this type of system as a function of pH in order to determine values for the expanded shel1thickness (see c5in Fig. 17). Latices prepared by grafting polyacrylate chains onto a polystyrene core have also been described recently by Buscall and Comer (1980). These authors also examined the stability behavior of their latices as a function of the degree of neutralization of the polyacrylate and as a function of temperature at different electrolyte concentrations. As can be seen from the results given in Fig. 29 the systems were stable over a certain range of temperature and degree of neutralization but flocculated both on heating and on cooling. The behavior at the upper temperature appears to be similar to that observed with nonionic surfactants as stabilizing molecules at or near the c10ud point of the surfactant and basically arises as a
R. H. Ottewill
44
20
Fig. 29. Data iIIustrating the temperature behavior of a latex with a polystyrene core stabilized by grafted poly(acrylic acid) in 1.10 mol dm - 3 sodium chloride solution; IX= degree of neutralization of the latex.
consequence of desolvation of the chains; in the polymer terms the cloud point would be close to the () temperature. The authors explain the lower temperature behavior as a consequence of the dissimilarity between the free volume of the polymer and the solvent. The behavior of this type of polyelectrolyte system is of fundamental interest and it is hoped that in the near future more detailed stability studies will be reported. An interesting feature from the point of view of polymer morphology is whether all the chains are on the surface or some are buried in the particle. The behavior of aqueous latex dispersions, in which the polymer core particles were stabilized by block copolymers of poly(ethylene oxide) and a vinyl or acrylic monomer, has been investigated in some detail by Napper (1969). The particles in these latices were shown by electrophoresis to be noncharged. Flocculation occurred when the solvency of the dispersion medium for the polymer chains was decreased as, for example, by raising the temperature when a critical flocculation temperature was observed that was found to be insensitive, over a limited range, to the molecular weight of the poly(ethylene glycol) chains. The influence of a number of other factors on the stability of the latices was also investigated (Napper, t970a) including the nature of the anchoring groups of the stabilizing polymers, the
r
I
~
I
1. The Stability and Instability of Polymer Latices
45
nature of the disperse phase, the particle size, the surface coverage and the molecular weight of the stabilizing polymer. It was found that to obtain colloid stability, it was necessary to use a dispersion medium that was better than a () solvent for the stabilizing chains. The implication of this observation was that the second virial coefficient of the stabilizer needed to be po sitive so that the segmental excluded volume was also positive. Under these conditions once overlap of the stabilizing polymer layers occurred, the configurational entropy of the molecules in the overlap region would become less than that of the molecules in the dispersion medium and an excess osmotic pressure would occur in the overlap volume. As a consequence of this, molecules of the dispersion medium would difIuse into the overlap region, forcing the stabilizing layers apart. This is essentially the basis upon which Eq. (24) was formulated. It was found that with this type of system that peptization could be achieved spontaneously after centrifugation or flocculation,' as would be anticipated from Fig. 27d. Napper (1970b) also investigated the flocculation of poly(vinyl acetate) particles stabilized by poly(ethylene glycol) chains with a series of electrolytes. The order for the cations was
The controlling factor appeared to be the capability of the ion to convert water into a ()solvent for the stabilizing chains.
XIX. Particle Stability in Emulsion Polymerization Any consideration of the stability of polymer latices would be incomplete without some discussion of the stability of the colloidal polymer particles formed during the course of an emulsion polymerization. As pointed out by Dunn and Chong (1970) the adsorption of the emulsifier plays a major role in determining the surface charge density of the particle and hence in determining the final particle size. The case in which there is an absence of added emulsifier has been considered by Goodwin et al. (1978) on the basis that" the particulate units initially formed contain only a small number of chains; they therefore have a low surface charge and are colloidally unstable. Hence, coagulation occurs until the particles formed reach values of surface charge density and radius sufIciently large to render them stable colloidal particles. The arguments can be developed in terms of the stability ratio starting with Eq. (13), which gives the rate of coagulation, and recapitulating that as W becomes greater than unity the rate of coagulation is reduced. Some
R. H. Ottewill
46
fundamental questions therefore arise, namely, At what size does the particle become a colloidally stable entity and at this, point what is its surface charge density and how many polymer chains does it contain? A further point of importance is to understand how this size varies with the ionic strength of the aqueous phase. In order to obtain a qualitative understanding of these points we can proceed by making some simple assumptions. These are (i) the particles formed are spherical, (ii) each polymer chain has the same molecular weight Me, (iii) each chain has two end groups, and (iv) all the end groups are anchored on the surface of the particle. Hence, if the latex particle has a molecular weight M L and a density of PL, then the number of polymer chains per particle is given by Ne
= 4na3PLNAi3Me = MdMe
(31)
The number of charged end groups per particle is therefore given by Ne
= 2Ne = 8na3 PLN Ai3Me
(32)
and the surface charge density by (33) Thus, as is directly proportional to a. For spherical particles the surface potential1/ls is given by 1/Is
= 4naa./[B(1 +
Ka)]
(34)
an equation which holds reasonably well up to 1/Isvalues of 50 mV. From this we find that, taking Me = 150,000: for a = 5 nm, 1/Is= 8 mV; for . a = 10 nm, 1/1.~ 20 mV; and for a = 22 nm, 1/1.~ 50 mV. Using a combination of Eqs. (4) and (6) to calculate VT as a function of h it is then possible to calculate W by numerical integration of Eq. (14). Since 1/Isis known as a function of particle size, then W can also be obtained as a function of r at an appropriate ionic strength. The results obtained are shown in Fig. 30 in the form of curves of log W against a. It is clear from these curves that the size of the first stable colloidal particle formed is controlled to a large extent by the ionic strength of the dispersion medium, i.e., at 4 x 10-4 mol dm - 3 log W = 2 is achieved with a = 3.7 nm, where to achieve the same Wat 4 x 10-3 mol dm-3 a has to grow to 11.3 nm. Since the size of the initial stable particles controls the nu~ber concentration of the latex during the diffusional growth period, then for the same initial monomer concentration and for the same percentage conversion of monomer, the final particle diameter in the medium of higher ionic strength will be the larger. This conforms to the clear trend found in the preparation
-
47
1. The Stability and Instability of Polymer Latices 12
10
8
:;: O>
:
+ 2
.' 5
10 Radius
15
20
(nm)
Fig. 30. Log Wagainst latex partic1eradius as a function of the concentration of 1: 1 electrolytein the system; ,4 x 10-4 mol dm-3; -, 4 x 10-3 mol dm-3.
of polystyrene latices in the absence of added emulsifier (Goodwin et al., 1976). XX.
Summary
In this chapter I have attempted to show in a broad sense how the application of the basic principIes of colloid science can be applied to develop our understanding of the various mechanisms involved in the stabilization of polymer latices. In the space available, it was not possible to go into very specific details of the many systems that have been investigated nor to deal with nonaqueous polymer latices. The latter, however, have been discussed in the recent comprehensive book by Barrett (1975). The literature on polymer colloids appears to be growing exponentially and to the authors of the many excellent papei-s which I have not quoted, I offer my sincere apologies. References Barrett, K. E. J. (1975). "Dispersion Polymerization in Organic Media." Wiley, New York. Bassett, D. R., and Hoy, K. L. (1980). In "Polymer Colloids 11" (R. M. Flitch, ed.), pp. 1-25. Plenum Press, New York.
R. H. Ottewill
48
Bee, H. (1978). B.Sc. thesis, Univ. of Bristol. Bibeau, A. A., and Matijevié, E. (1973). J. Colloid Interface Sci. 43,330. Bolt, P. (1978). B.Sc. thesis, Univ. of Bristol. Buscall, R., and Comer, T. (1980). Org. Coat. Plast. Chem. 43, 203. Cebula, D. J., Thomas, R. K., Harris, N. M., Tabony, J., and White, J. W. (1978). Faraday Discuss. Chem. Soco 65, 76. Cheung, W. K. (1979). Ph.D. thesis, Univ. of Bristol. Clint, G. E., Clint, J. H., Corkill, J. M., and Walker, T. (1973). J. Colloid Interface Sci. 44,121. Connor, P. (1968). Ph.D. thesis, Univ. of Bristol. Connor, P., and Ottewill, R. H. (1971). J. Colloid Interface Sci. 37, 642. Comell, R. M., Goodwin, J. W., and Ottewill, R. H. (1979). J. Co/loid Interface Sci. 71, 254. Derjaguin, B. V., and Landau, L. (1941). Acta Physicochim. URSS 14, 633. Derjaguin, B. V., and Muller, V. M. (1967). Dokl. Phys. Chem. 176, 738. Doroszkowski, A., and Lamboume, R. (1971). J. Polym. Sci. Part C 34,253. Dunn, A. S., and Chong, L. C-H. (1970). Br. Polym. J.2. 49. Dzyaloshinskii, 1. E., Lifshitz, E. M., and Pitaevskii, L. P. (1961). Adv. Phys. 10, 165. Evans, R., and Napper, D. H. (1973). J. Co/loid Interface Sci. 45, 138. Fitch, R. M. (1980). "Polymer Colloids 11." Plenum Press, New York. Flory, P. J., and Krigbaum, W. R. (1950). J. Chem. Phys. 18, 1086. Force, C. G., and Matijevié, E. (1968a). Kolloid Z. Z. Polym. 224, 51. Force, C. G., and Matijevié, E. (l968b). Ko/loid Z. Z. Polym. 225,33. Fowkes, F. M. (1964). Ind. Eng. Chem. 56, 40. Fowkes, F. M. (1967). In "Surfaces and Interfaces" (J. J. Burke, ed.), Vol. 1, p. 199. Syracuse Univ. Press, New York. Frens, G. (1968). Doctoral thesis, Univ. of Utrecht. Frens, G., and Overbeek, J. Th. G. (1971). J. Co/loid Interface Sci. 36, 286. Friends, J. P., and Hunter, R. J. (1971). J. Co/loid Interface Sci. 37, 548. Fuchs, N. (1934). Z. Phys. 89, 736. Gingell, D., and Parsegian, V. A. (1973). J. Co/loid Interface Sci. 44, 456. Goodwin, J. W., and Ottewill, R. H. (1978). Faraday Discuss. Chem. Soco 65, 338. Goodwin, J. W., Heam, J., Ho, C. c., and Ottewill, R. H. (1976). Co/loid Polym. Sci.60, 173. Goodwin, J. W., Ottewill, R. H., Pelton, R., Vianello, G., and Yates, D. E. (1978). Br. Polym. J.
10,173.
.
Goodwin, J. W., Ottewill, R. H., and Parentich, A. (1980). J. Phys. Chem. 84, 1580. Gregory, J. (1975). J. Co/loid Interface Sci. SI, 44. Hachisu, S., Kobayashi, Y., and Kose, A. (1973). J. Co/loid Interface Sci. 42, 342. Hamaker, H. C. (1937). Physica 4, 1058. Hardy, W. B. (1900). Proc. R. Soco London Ser. A 66, 110; Z. Phys. Chemie. 33.385. Heller, W., and Peters, J. (l970a). J. Co/loid Interface Sci. 32, 592. Heller, W., and Peters, J. (1970b). J. Co/loid Interface Sci. 33, 578. Heller, W. and de Lauder, W. B. (l97Ia). J. Co/loid Interface Sci. 35, 60. Heller, W. and de Lauder, W. B. (197Ib). J. Co/loid Interface Sci. 35, 308. Hiltner, P. A., and Krieger, 1. M. (1969). J. Phys. Chem. 73, 2386. Honig, E. P., Roeberson, G. J., and Wiersema, P. H. (1971). J. Colloid Interface Sci. 36, 97. Hoy, K. L. (1979). J. Coat. Technol. SI, 27. Kayes, J. B. (1976). J. Co/loid Interface Sci. 56,426. Kitchener, J. A., and Schenkel, J. H. (1960). Trans. Faraday Soco 56, 161. Kratohvil, S., and Matijevié, E. (1976). J. Co/loid Interface Sci. 57, 104. Krupp, H., Schnabel, W., and Walter, G. (1972). J. Co/loid Interface Sci. 39,421. Levich, V. G. (1962). "Physico-chemical Hydrodynamics." Prentice Hall, Englewood ClilTs, New Jersey.
,, ¡ ~ r
t
1. The Stability and Instability of Polymer Latices
49
Levine, S., and Bell, G. M. (1965). J. Colloid Sci. 20, 695. Lichtenbelt, J. W. Th., Pathmamanoharan, C., and Wiersema, P. H. (1974). J. Colloid Interface Sci. 49, 281. Long, J., Osmond, D. W. J., and Vincent, B. (1973). J. Colloid Interface Sci. 42, 545. Mardle, R. (1980). B.Sc. thesis, Univ. of Bristol. Matijevié, E. (1977). J. ColJoid Interface Sci. 58, 374. Matijevié, E., and Force, C. G. (1968). KolJoid Z. Z. Po/y. 225,33. Matijevié, E., Janauer, G. E., and Kerker, M. (1964). J. ColJoid Interface Sci. 19, 333. Napper, D. H. (1969). J. ColJoidInterface Sci. 29, 168. Napper, D. H. (1970a). J. ColJoid Interface Sci. 32, 106. Napper, D. H. (1970b). J. ColJoidInterface Sci. 33, 384. Napper, D. H. (1977). J. ColJoid Interface Sci. 58, 390. Neiman, R. E., and Lyashenko, O. A. (1962). ColJoidJ. USSR (English Trans.) 24, 433. Ninham, B. W., and Parsegian, V. A. (1970). J. Chem. Phys. 52, 4578. Ottewill, R. H. (1980). Chem. Ind. 377. Ottewill, R. H., and Rance, D. G. (1977). Croatica Chem. Acta SO,65. Ottewill, R. H., and Rance, D. G. (1979). Cr,oatica Chem. Acta 52, 1. Ottewill, R. H., and Shaw, J. N. (1966). Discuss. Faraday Soco 42, 154. Ottewill, R. H., and Shaw, J. N. (1967). KolJoid Z. Z. Po/y. 218, 34. Ottewill, R. H., and Walker, T. (1968). KolJoid Z. Z. Po/y. 227, 108. Ottewill, R. H., and Walker, T. (1974). J. Chem. Soco Faraday 170, 917. OttewilI, R. H., Rastogi, M. C., and Watanabe, A. (1960). Trans. Faraday Soco 56, 854. Overbeek, J. Th. G. (1952). In "ColIoid Science" (H. Kruyt, ed.), Vol. 1. Elsevier, Amsterdam. Overbeek, J. Th. G. (1977). J. ColJoid Interface Sci. 58, 408. Parsegian, V. A., and Ninham, B. W. (1971). J. Col/oid Interface Sci. 37, 332. Pelton, R. (1976). Ph.D. thesis, Univ. of Bristol. Rance, D. G. (1976). Ph.D. thesis, Univ. of Bristol. Reerink, H., and Overbeek, J. Th. G. (1954). Discuss. Faraday Soco 18, 74. Richardson, R. (1979). B.Sc. thesis, Univ. of Bristol. Richmond, P. (1975). In "ColIoid Science" (D. H. Everett, ed.), Vol. 2, p. 130. Chemical Society, London. Schulze, H. (1882). J. Prakt. Chem. 25, 431. Schulze, H. (1883). J. Prakt. Chem. 27, 320. Smitham, J. B., Gibson, D. V., and Napper, D. H. (1973). J. ColJoid Interface Sei. 45, 211. Storer, C. S. (1968). Ph.D. thesis, Univ. of Bristol. Tamaki, K. (1960). KolJoid Z. 170, 113. van den HuI, H. J., and Vanderhoff, J. W. (1970). Br. Po/y. J. 2, 121. Verwey, E. J. W., and Overbeek, J. Th. G. (1948). "Theory of the Stability of Lyophobic ColIoids." Elsevier, Amsterdam. Visser, J. (1972). Adv. ColJoid Interface Sei. 3, 331. von Smoluchowski, M. (1917). Z. Phys. Chem. 92,129. Wiese, G., and Healy, T. W. (1970). Trans. Faraday Soco 66, 490.
í
I
~¡ \
-
2 Particle Formation Mechanisms F. K. Hansen and John Ugelstad
1. 11. 111. IV. V. VI. VII.
Introduction. Micellar Nucleation: The<Smith-Ewart Theory . Radical Absorption Mechanisms. ". Micellar Nucleation: Newer Models . Homogeneous Nucleation. Partide Coagulation during the Formation Period. Nucleation in Monomer Droplets References .
51 54 56 63, 73 82 86 91
l. Introduction The nuc1eation stage constitutes the so-called Interval I in an emulsion polymerization, the initial period in which the partic1e number is changing. In Intervals n and nI the paftic1e number is believed to be essentially constant. Nuc1eation of new partic1es may in some cases also take place during Intervals n and In. This phenomenon is often referred to as secondary huc1eation and may be encountered in systems with poor stability (coagulation) or with changing composition (continuous and semicontinuous polymerizations). The present chapter will attempt to treat all mechanisms that may lead to formation of polymer partic1es, in whatever stage of the polymerization they take place. All discussions of partic1e nuc1eation start with the Smith-Ewart theory in which Smith and Ewart (1948) in a quantitative tre!ltment of Harkins' micellar theory (Harkins, 1947, 1950) managed to obtain an equation for the partic1e number as a function of emulsifier concentration and initiation and polymerization rates. This equation was developed mainly for systems of monomers with low water solubility (e.g., styrene), partly solubilized in micelles of an emulsifier with low critical micelle concentration (CMC) and p'?"Ts{lIlíedto work well for such systems (Gerrens, 1963). Other authors have, ,
however, argued against the Smith-Ewart theory on the grounds that (i) . partic1es are formed even if no micelles are present, (ii) the equation for the 51 EMULSION POLYMERIZATlON
Copyright«; 1982 by Academic Press, Inc. Al! rights of reproduction in any form reservcd.ISBN 0-12-556420-1
52
F. K. Hansen and J. Ugelstad
partic1e number gives an estimate that is a factor of 2 higher than that found experimentally even for styrene, (iii) more water-soluble monomers do not fit the theory, and (iv) a maximum in polymerization rate at the end of the nuc1eation period is predicted, but has rarely been observed. On this basis other theories for the nuc1eation have been put forward, based on the idea of self-nuc1eation of oligomer radicals produced in the aqueous phase. These mechanisms of partic1e formation were first treated quantitatively by Fitch and Tsai (1971). These ideas, which have been further elaborated by other authors, seem to have solved the first problem of the theory of partic1e nuc1eation but leave open the question of whether the micelles, when present, play any role at all in partic1e formation. More recent work seems not only to confirm the importance of the micelles but to stress the necessity of inc1uding more detailed features of absorption and reaction in micelles . and particles in order to explain the other discrepancies of the Smith-Ewart theory. Usually, monomer droplets are believed not to play any role in'emulsion polymerization other than as a source of monomer. Ugelstad and associates ha ve shown, however, that in cases with very small monomer droplets, these may become an important, or even the sole, loci for partic1e nuc1eation. The system may then be regarded as a microsuspension polymerization with water-soluble initiators. It has therefore been pointed out (Hansen and Ugelstad, 1979c) that partic1e nuc1eation models should inc1ude a~l three initiation mechanisms-micellar, homogenous, and droplet-since all these mechani~ms may compete and coexist in the same system, even if one of theni usually dominates. Figure 1 illustrates the main components and phases in an emulsion polymerization system. The arrows indicate the possible distribution ofthe components between the phases. Monomer (i) will usually exist as monomer droplets; (ii) some monomer, depending on water solubility, will be dissolved in the continuous phase; and (iii) some monomer will be solubilized in micelles. Emulsifier (i) will be partly dissolved in the continuous phase; (ii) if concentration is above the CMC, the excess will form emulsifier inicelles; and (iii) some emulsifier will be adsorbed on monomer droplets, and may even be dissolved into the droplets. lnitiator (i) will mostly be dissolved in the continuous phase as watersoluble initiators are usually applied. For special applications partly or completely oil soluble initiators may be used. These will be distributed similarily to the monomer. A so-called ordinary emulsion polymerization, Le., similar to the case treated by Smith and Ewart, is characterized by large monomer droplets
'2. Particle Formation Mechanisms
53
Honamer H
Hice//es
Drap/ets
¡nitiatar
~
Emu/sifier
, Aqueaus sa/utian Fig. 1.
Schematic iIIustrationsof the components and phases usually present in an
emulsion polymerization among phases.
system. The arrows indicate
the possible distribution
of components
with consequently smaIl total surface, miceIle-forming emulsifiers with reIatively low CMC, and ionic initiators that decompose either by a thermal andjor by a redox mechanism. In the Smith-Ewart theory as weIl as in other treatments, the primary radicals formed by decomposition of the initiator in the continuous phase were assumed to enter emulsifier miceIles and polymer partieles. It has been pointed out by several authors (Alexander and Napper; 1971, Nomura et al., 1975; Barrett, 1975) that these usuaIly ionic, very water-soluble radicals are rarelyabsorbed directIy into a miceIle or partiele but must add some monomer units in the aqueous phase to become sufficientIy oil soluble to be absorbed. It now seems to be generaIly accepted that formation of these oligomers in the aqueous phase is the first step in the nUeleation (and polymerization) process. The presen'ce and molecular weight of oligomers in some systems have been analyzed by means of GPC and spectrophotometric methods (Fitch and Tsai, 1971; GoodaIl et al., 1975; Chen and Piirma, 1980). Degrees of polymerization have been found to lie between 1 and 6070. The water-soluble oligomers may be destroyed or may nUeleate partieles. The different possibilities are listed in Table I. It should be added that oligomers that are surface active may also be adsorbed onto the surface of partielesjdropletsjmiceIles rather than being absorbed into the interior. Being on the end of the oil-soluble chain, the active site of the radical wilI no doubt' be able to propagate into the interior.
11
54
F. K. Hansen and J. Ugelstad TABLEI Reaction Possibilities of an Oligomer Radical in the Aqueous Phase and the Probable Result Process
A B e D E F G
Result Micellar initiation
Absorption into a micelle Absorption into a monomer droplet Absorption into an earlier formed particle Propagation in the aquous phase Termination in the aquous phase
Droplet initiation. Radical disappearance
(particle growth)
Higher oligomers "Dead" oligomers (may or may not lead to nucleation) HoIt1ogeneous nucleation
Precipitation in the aquous phase (self-nucleation) Mixed-micelle formation (with or without emulsifiers)
Nucleation
(homogeneous
or micellar)
This may lead to a core and shell morphology. Process E in Table 1, termination in the aqueous phase, may also lead to homogeneous nucleation if the "dead" molecules are sufficiently water insoluble. When partic1es have been formed, transfer reactions to monomer (or chain transfer agent if present) willlead to monomer radicals, which may be desorbed into the aqueous phase. This is also indicated in Fig. 1. The monomer radicals may act in a way similar to the initiator radicals. ~elow is given a detailed description of the different processes listed in Table 1 and of the theories that have been advanced for these processes.
n.
MiceUar Nucleation: The Smitb-Ewart Theory
Smith and Ewart (1948) proceed as follows: radicals are absorbed into monomer-swollen emulsifier micelles which then are transformed into polymer partic1es; the rate of radical absorption Is equal to the rate of initiator decomposition p¡, which means that dN/dt
= p¡
(1)
where N is the partic1e number. The rate of growth of a partic1e is assumed to be constant and is expressed as dv/dt
=
J1.
(2)
where v is the volume of the partic1e. The number of micelles will decrease as the partic1es grow, giving an increasing surface which will adsorb
-
2.
55
Particle Formation Mechanisms
emulsifier. Particle formation stops when a11emulsifier is adsorbed on the particles, which means that the particle surface area Ap is equal to the total surface area of emulsifier asS where as is the specific surface area per unit of emulsifier and S the amount of emulsifier. To be precise S should be the amount in excess of the CMC. The difference will not be of any importance if the CMC is much lower than S. As dv/dt is assumed to be constant, Ap may be expressed by J1.and t by integration over a11formation times from O to t (3) where (4) From Eq. (3) one obtains the time tl when Ap = asS,which inserted in Eq. = Pitl' The result is
(1)givesthe particle number N
(5)
This is the so-ca11edupper limit equation. The lower limit is derived in a similar way. In this case it is also assumed that polymer particles may absorb radicals leading to a decrease in the rate of nucleation. For computational purposes the rate of radical absorption is set as proportional to the particle surface area, Ap =
¿ api'
where
apj is the surface
area of one
particle. Equation (1) is then transforme9 to (6) The total area Ap is expressed by an integral equation in a way similar to that for the upper limito Inserting for Ap in Eq. (6) gives by a somewhat complicated integration (7) which is identical to Eq. (5) except for the constant. From diffusion laws (Fick's first law) it is expected that the radical absorption rate is proportional to the particle surface area divided by the radius (i.e., 4nrN) so that sma11 particl~s absorb more radicals per unit area than do large particles. This fact was realized by Smith and Ewart who stated that the true value of k should be between 0.37 and 0.53 and accordingly the particle number somewhere between those values predicted by Eqs. (5) and (7). It may be shown (Section IV) that this procedure is not quite correct, the constants and ~will also be slightly altered (the former decreased and the latter increased). In addition the constancy of dv/dt = is somewhat doubtfuI, both because the average radical number per particle in the lower case wilI
t
J1.
-
56
-
I
I
.
F. K. Hansen and J. Ugelstad
not be constant (willdecrease)and because the monomer concentration in the particles is expected to increase with increasing size. These two factors will counteract each other and are not expected to have a great influence on the value of N. The Smith-Ewart theory has been successful in describing the experimental results with some systems,especiallythe predicted orders of N with respect to initiator and emulsifier as obtained from double logarithmic plots of N against the two variables (Gerrens, 1963). Other authors have, however,found a wide range of exponents(citedby Fitch, 1973).AIso,other discrepancies exist, as mentioned in the introduction. The Smith-Ewart theory has been modified and recalculated by several worker~ (Parts et al., 1965; Gardon, 1968a-f, 1971; Harada et al., 1972). Parts et al. applied a numericaf integration of the nucleation equations and reached the same conclusions as Smith and Ewart. They found ihat the average number of radicals per particle ñ is approximately 1 through the entire nucleation period because the rate of radical adsorption in micelles is so much higher than that in new particles (very large number of micelles). They propose that the absorption efficiency of micelleshas to be lower in order to explain experimental findings. Gardo~ has recalculated the lower limit of the Smith-Ewart theory by a seminumerical method and finds that ñ decreases from 1 to 0.67 during the formation periodo This does not, however, significantly influence the exponents 0.4 and 0.6. The particle numbers (or more correctly, particle sizes) calculated by Gardon were found to describe some experimental results for styrene and methyl metacrylate fairly well, whereas other data on particle numbers were 2-3 times lower than predicted. Another feature of the Smith-Ewart theory is that the reaction rate at the end of the nucleation period is expected to be higher than in the steady state because ñ is higher than the steady-state value of 0.5 (Smith-Ewart Case 2 kinetics). There is little experimental evidence for such a maximum in rate (Ugelstad and Hansen, 1976), and this discrepancy may be explained by more details about the radical absorption rates in micelles and particles. Before any further discussion of particle-formation mechanisms, it therefore seems logical-to review the mechanisms responsible for radical absorption,
111. Radical Absorption Mechanisms
Gardon based his calculations on a geometric derivation of the radical absorption rate which gave the result that the rate should be proportional to the particle surface area. This derivation, which also was adopted by Fitch and Tsai (1971), has been criticized for not taking the concentration
-
2. Partiele Formation Meehanisms
57
gradient of radicals around a particle into account (as in Fick's laws) (Barrett, 1975; Ugelstad and Hansen, 1976; Hansen and Ugelstad, 1978). This was also realized by Fitch and Shih (1975) who, using seeded experiments, found the expected proportionality of the absorption rate to Nr. Similar conclusions may also be drawn from the seed experiments of Gatta et al. (1969), the kinetic results of Ugelstad et al. (1969) with vinyl chloride, and the recent findings of the authors (Hansen and Ugelstad, 1979a) using a polystyrene seed. Fick's first law for the diffusion of a component A in a stationary medium B around a spherical particle may be written (Byron Bird et al.; 1960) (8) where 1)ABis the diffusion constant for A in B, e is the total molar, concentration of A and B, and XA is the molar fraction of A. For the geometric configuration see Fig. 2. '\
\ \ \
\ \
\ 1 I
R
/
Halar fraction, Concentration
r.e
.
XAW'CW
/
---
------
o
r
R Distance
Fig. 2. Geometric and concentration conditions around an absorbing spherical partic1e. e is concentration and X is molar fraction of dilfusing species.
F. K. Hansen and J. Ugelstad
58
Assuming a stationary diffusion layer outside the particle of thickness b one has for dXAldR. dXAldR
= (r/R2)[(r + b)/b](l -
Inserting into Eq. (8) for R
XA) In[(1
-
XAa)j(l - XAw)]
(9)
=r (10)
Usually the molar fraction of the diffusing species (A) is much smaller than that of the' stationary component (B) so that 1 - XA ~ 1 and In(l - XA) ~ XA, which gives (11) where (12a) and (12b) Ir b ~ r, Eq. (11) simplifies to. ñA = -Dw4nr(Cw- Ca)
(13)
Ir one has an electrostatic repulsion between charged oligomers and equally charged particles the diffusion rate is given by (Hansen and Ugelstad, 1978) (14) ñA = -4nDwr(Cw - CaeZ)/W' where z = et/lo/kTand W' is given by ,
W=r-
.
r+~
r+ b b f.r
et/lodR
exp--
( kT ) R2
(15)
where R is the distance from the oligomer to the center of the particle, e is the electronic charge, and t/lois the (effective)surface potential. The value of W' has been calculated by numerical integr~tion for the case where b ~ r and has been given as a function of et/lo/kT and Kr where K. is the inverse double-Iayer thickness (Hansen and Ugelstad, 1978). The term eZin Eq. (14) may be considered as an activation energy (Boltzmann factor) and accounts for the fact that in order to become absorbed the charged radical s have tq surmount an energy barrier at the surface. The'term W' is the' integral of this activation energy factor giving the retardation of a unit charge upon diffusion to the surface. In the case where Cw~ Caez Eq. (14) reduces to' (16)
\.
..
2.
59
Particle Formation Mechanisms
Equation (16)describesthe situation with irreversiblediffusionand seems to apply to cases of relatively large particles. The folIowing simplifications are inherent in Eq. (16):
o
1. The concentration of the diffusing component has to be low (lower than 1 M). This condition is always fulfilIed for free radicals. 2. The stationary layer "thickness" (<5)has to be much larger than the particle size. UsualIy, <5is believed to be on the order of 10 ¡.,tm,decreasing with increasing stirring intensity. For particles in the nucleation range (220 nm) this condition is very welI fulfilIed; for seeded experiments with larger particles the assumption may be doubtful. 3. The .concentration of particles has to be low, so that the "stationary layers" do not overlap. This condition is equivalent to saying that <5will be dependent on particle size, with the same consequences as above. 4. The concentration at the particle surface must be much smalIer than in the bulk, meaning that the particles must act as a radical "sink." This last condition is the most doubtful, especialIy in the case of smalI particles. A thorough treatment of diffusion rates, based on Eq. (13), has recentIy been presented (Hansen and Ugelstad, 1978). In this derivation the concentration profile inside the particles, as illustrated in Fig. 2, is also taken into account. The derivation is based on the equations for diffusion with chemical reaction (Danckwerts, 1951), expressing the steady-state rate of diffusion at the inside particle surface by ñA
= -4nrDpC*(X ooth X - 1)
(17)
where Dp is the diffusion constant inside the particles and
X
= r(k/Dp)1/2
(18)
k
= kpMp + nktp/vp
(19)
with
Here kp is the propagation constant, Mp the monomer concentration in the particles, n the number of radicals in the particle, ktp the bimolecular termination constant in particles (in molecular units), and vp the particle volume. . The total rate of absorption is obtained by assuming a rapidly established equilibrium distribution for the radical between the inner and the outer surface of the particle. Assuming no radical accumulation at the interface the value of ñA in Eq. (14) is equal to that in Eq. (17). The equilibriu.m distribution between the inner and outer surface of the particles is expressed by C*
= aCa
(20)
60
F. K. Hansen and J. Ugelstad
leading to the following expression for the rate of absorbtion per particle
nA= 4nrDwCwF
(21) ,
where the "efficiency factor" for absorption F is given by the expression 1/F = (Dw/aDp)[1/(X coth X - l)]eZ + W'
(22)
Note that in Eq. (21) nA has a positive sign since it stands here for rate of absorption. It will appear from Eqs. (21) and (22) that if W' ~ (Dw/aDp)[1/(X coth X
-
1)]eZ
the value of nAwill in any case be given by nA = 4nrDwCw/W'
(23)
which corresponds to Eq. (16). Equation (23) describes the situation when the transport of the oligomer radical to the outer surface is the ratedetermining step in the absorption process. In the case where W' 1 ::::::
(24) Figure 3 gives 1/F as a function of r for some probable values of the parameters involved and with W' obtained by numerical integration of Eq. (15). The more important features of Eq. (22) are evident from the figure. 1. When particles are large (r > 1000 nm) and a h¡¡.sa high value (oil-
soluble oligomericradicals)then F::::::1 and the absorption folIowsEq. (24) (irreversible absorption) with W' equal to unity. 2. When particles are smalIer (r < 1000 nm), the absorption rate is lower than that given by Eq. (24), and may be very low if the particles are small and/or the radicals are relevatively water soluble. Radicals with a very high water solubility (a ~ 1) will not be absorbed. 3. The electrostatic repulsion may playa role when F < 1. The electrostatic effect may be diminished by the so-calIed tunneling
effect(Fitch and Shih, 1975)in which the uncharged end pulls the oligomer through the surface or reacts while the charged end still is in the aqueous phase. This may be important especialIy for higher oligomers and may be calculated if the van der Waals attraction is included in the activation energy termo Equation (22) may in some limiting cases be simplified. Condition A: X ~ 1
i.e.
X coth X
-
r(k/Dp)1/2~ 1
(25)
1 '" X2/3
(26)
b
2.
61
Particle Formation Mechanisms
10
10 r{nm} Fig. 3.
Inverse absorption
efficiency factor 17F as a function
of particle radius r for
distribution constants a = 1 and 104. Elfective surface potential i/to = O (1), 50 mV (11),and 100mV (III). Other parameters: Dw = 5 X 10-8 dm2jsec, Dp = 1 X 10-8 dm2jsec, kp = 300 dm3jmol sec, Mp = 5 moljdm3, T= 298 K.
which
gives (27)
Case A usually implies that the term W' in Eg. (22) may be neglected. In this case Eg. (27) describes the curves with a slope of - 2 iti Fig. (3). The rate of absorption is then (28) In this case the concentration gradients both on the agueous and the particle side may be neglected. The rate of absorption is proportional to the ~
rate of reaction of the radical inside the particle and thus to the particle volume.
62
F. K. Harsen and J. Ugelstad
Condition B:
x ~ 1 i.e. r(k/Dp)1/2~ 1 X cothX - 1 "" X
(29) (30)
which gives (31) If condition B is operating it is more like1ythat W' is the dominant term in the equation for "l/F, leading to the conclusion that the irreversible absorption Eq. (23) will be operating. With low values of a and Dp and/or high values of Z one may also find that the term W' may be neglected in this case. Equation (31) then describes curves with a slope of -1, as found in part of the most righthand curve in Fig. 3. The absorption rate will if the term W' is neglected be lÍA= 41tr2a(kDp)1/2/e'= apa(kDp)1/2/e'
(32)
where ap is the particle surface area. AIso in this case the concentration gradient on the aqueous side may be neglected. The rate-determining step is diffusion with reaction inside the particle, and the absorption rate is proportional to the particle surface. This rate will also be low compared to the case for irreversible absorption, although not lowered to the same degree as when Eq. (28) is operating. Condition B, including also the negligible influence of W', gives a situation wherein Gardon's absorption equation is applicable. Both Eqs. (28) and (32) (with F ~ 1) describe cases where the electrostatic repulsion should be determined by the Boltzmann factor e'. When the particle size and/or the value of a are large, the value of F is determined chiefly by the value of W'. The rate of absorption is then given by Eq. (23). The electrostatic repulsion will be relatively small. Usually the value of W' willlie between 1 and 10. Contrary to the above treatment it may be argued that it would be more correct to express the equilibrium distribution between the inner and outside particle surface by (33) where ao is a constant for the case where z = O.This means that the value of a applied above is given by (34) The term eZ in the expression for l/F is said to take into account the fact that the charged radical at the outside surface of the particle is brought up to a higher energy level, expressed by the Boltzmann factor e'. However,
2., Particle Formation
63
Mechanisms
this fact should also come into play in that it leads to an increase in the value of a with the same factor. Application of a value of a given by Eq. (34) transforms Eq. (22) to the form
! F
-
Dw
[
1
]
aoDp X coth X - 1
+ w'
(22a)
Similarly,for Eqs. (28)and (32),respectively (28a)
ñA = vpaokCw
ñA = apao(kDp)
1/2
(32a)
Equation (23) for irreversible absorption will remain the same, the only necessary condition for Eq. (23) should be to replace eZlawith 1lao.
IV. Micellar Nucleation: Newer Models It has been suggested that the charged radicals are not at all able to enter the micelles and that the micelles only act as a reservoir for emulsifier. Roe (1968) showed that the Smith-Ewart expression for N may be derived from a homogeneous nucleation mechanism, substituting the critical micellar concentration with a critical stabilization concentration somewhat lower than the CMC. This result is not surprising, since he applied exactly the same assumptions for the nucleation rate,'radical absorption, and constant volume growth as did Smith-Ewart. The experimental arguments of Roe were among others based upon the fact that a fairly constant number of micelles in a mixture of nonionic and anionic emulsifier system gives widely varying particle numbers. However, on the basis of the absorption equations in the preceding section it may well be that micelles give differing particle numbers if the radical absorption rate varies significantly because of variations in micellar size, monomer content, internal diffusion constant and oligomer solubility. Piirma and Wang (1976) have shown that particle numbers vary with micellar size in a mixed-emulsifier system. The results of Dunn and AI-Shahib (1980) show that styrene polyrnerization rates, and hence particle numbers, are constant when the molar concentration of micelles is constant, irrespective of CMC, in the case of potassium alkyl soaps (Cs-Cd and sodium alkyl sulfates (CS-C1S)' One main objection to the micellar theory has been that even if the particle number determined by polymerization of sparingly water-soluble monomers like styrene or octyl acrylate changes steeply at or directly below the CMC, this is not the case for more water-soluble monomers (Sütterlin
~I
64
F. K. Hansen
9 seed
O
J. Ugelstad
Nsrs.1(
O
ea
and
O 11..9
21..21.
M 'e
~
1016
'Z /' ./ ;'
-
.,/
C=O
CMC
1 101' 001
0.1
1.0
e (free 50S) Fig. 4.
Emulsion polymerization of styrene.Number
the freeconcentration of SDS 60°C,
initiator
K2S20S
10.0
(g dm-3) of new partic1esN as a function of
with and without seed. Seed partic1e radius
(0.6 gjdm3).
(Reproduced
by permission
80 nm, temperature
of J. Polym. Sci.)
et al., 1976, 1980; Ugelstad et al., 1969). The often undramatic change in N at the CMC may well be explained by homogeneous nucleation. The question still remains as to whether the micelles present above the CMC play any important role in the nucleation process. One method for investigating the competition between homogeneous and micellar nucleation uses seed experiments. Results from such runs are shown in Figs. 4 and ~ for styrene and methyl metacrylate, respectively. The log(new particle number) is plotted as a function of log(free emulsifier concentration) both in . seeded and unseeded runs. Free emulsifier denotes the concentration of emulsifier not adsorbed on seed particles. In the case of styrene the curve for the unseeded runs shows a sharp increase at CMC. Above the CMC, the increase in particle number with increasing emulsifier concentration becomes smaller but is still significant.
.
2.
Particle Formation Mechanisms
65
MMA
z
u ~ .u 0.1
1.0
10
Free SDS(gdm-3¡ Fig. 5. Emulsion polymerizatjon of methyl metacrylate.Number of new particles, N as a fimction of the freeconcentration of SDS witb and witbout seed"
With seed present the particle number is drastically decreased at emulsifier concentrations below the CMC. Above the CMC the curves without and with seed almost coincide. The results indicate that above the CMC the far more numerous micelles are the loei for particle nuclea"tion both with and without seed. For the case of methyl methacrylate the result without seed is strikingly different from that with styrene in that there is no noticeable change in the slope of the curve as one passes the CMC. This fact has previously been used as an argument for asserting that with methyl methacrylate the micelles do not play any role.in particle formation. It would appear from Fig. 5 that the application of seed leads to a drastic decrease in the number
66
F. K. Hansen and J. Ugelstad
of particles below the CMC when compared to the case without seed. Slightly above the CMC, however, the curves with and without seed coincide completely. This would seem to indicate that with methyl methacrylate also the particle formation takes place in micelles when operating above the CMC. It seems as if the main difference between styrene and methyl methacrylate is that the chance for self-nucleation is better for the latter. In conclusion it may be said that the seed experiments pro vide strong arguments for the importance of micellar nucleation even for more watersoluble monomers. . Further derivations based on the micellar theory have been advanced to create a more detailed picture than that of Smith-Ewart. With these theories the equations become so complex that a simple analytical solution, like that of Smith-Ewart, cannot be given. Instead, numerical methods must be applied to the integrations. Apart froIl1the calculations of Parts et al. (1965) and Gardon (1968) already mentioned, such work has been performed by Harada et al. (1972) (styrene), Nomura et al. (1976) (viny) acetate), and Hansen and Ugelstad (1979b, styrene and 1979d, different monomers). For most of these calculations nonsteady-state equations are used to calculate the rate of particle nucleation and rate of volume growth given by the average number of radicals per particle (ñ). Generally, the rate of micellar nucleation may be expressed by (35)
wherePAis the total rate of radical generationin the aqueous phase and Pm is the probability of absorption of radical s (oligomers) in the micelles. Often (as in the Smith-Ewart theory) PA is set equal tú 'Pi, the rate of initiator splitting. Generally, radicals desorbed from the particles should also be included in PA (Nomura et al., 1976; Ugelstad and Hansen, 1976). The expression for PAwill then be PA
= Pi +
kdñN
(36)
where kd is the rate constant for desorption. . In Eq. (36) no aqueous-phase termination is taken into account. Because the particles are small, they will hardly be able to contain more than 2 (or even 1) radicals, and ñN may be expressed by (37) . where Ni and N2 are the numbers of particles containing 1 and 2 radicals, respectively. Neglecting the N2 particles the rate of formation of Ni particles is (38)
,
r
2.
Particle Formation Mechanisms
67
where Po and Pt are the probabilities for radical absorption in particles with O and 1 radical, respectively. The rate of particle growth is given by
(39) where kp is the propagation constant, N A Avogadro's number,
.
limit case. By setting Pm = 1 - Ap/asS, Po = Apo/asS, and Pt = Ap¡/asS one arrives at the Smith-Ewart lower limit case. The important question is therefore the magnitude of the parameters involvedin the above equations. Expressions for kd may vary depending upon whether the monomer radicals are transported back and forth between particles without addition of monomer in the aqueous phase or if they add monomer in the aqueous phase before reentering the particles (i.e., reversible or irreversible absorption, Ugelstad and M0rk, 1970). The two possibilities may be combined in the equation (Hansen and Ugelstad, 1979d) (40)
where kf is the transfer constant to monomer, k~ the propagation constant for a monomer radical (to distinguish it from a polymer radical), Mp the molar concentration of monomer in particles,and q = ñ (reversibleabsorption) or 1 (irreversible absorption). The parameter kdm, the diffusional desorption constant, is (41) where (42) where a is the distribution constant for the monomer radical between the particle and water. Equations (40)(with q = ñ), (41), and (42)were also derived by Harada et al. (1971)and Nomura et al. (1971)by a somewhat differentapproach. The probability for radical absorption may be calculated from the ratio of
68
F, K, Hansen and J. Ugeistad
.
absorption rate ¡nto the particle in question to the sum of all absorption rates. For instance, the probability for absorption into micelles is given by (43) where Nm is. the number of micelles presento The appropriate rates of absorption to be inserted into Eq. (43) is obtained from Eq. (21) with the value of F given by Eq. (22). Because oligomers of different degrees of polymerization may be absorbed, the expression for P may become much more complex than Eq. (43). AIso, because the efficiency constant F for initiator radicals may differ from monomer radicals, one should in fact operate with different probabilities for those two radicals, which leads to further complications. These problems will be dealt with in the next section. Satisfactory results have been obtained with the relatively simple model outlined above. Nomura et al. (1978) expressed Pmby (44) where (45) Here Mm is the agregation number for the micelles. It is seen that Eq. (44) is identical to Eq. (43) if the efficiency factor in particles containing O and 1 radicals is the same. By numerical integration, using constants for vinyl acetate, Nomura et al. found (46) where So and lo are the initial emulsifier and initiator concentrations, respectively. Equation (46) explained well their experimental results with vinyl acetate when B was held constant (1.2 x 107). A very important result of these calculations is that the exponents in Eq. (46) are higher and lower, respectively, than the Smith-Ewart values 0.6 and 0.4, respectively. This has been shown
to be a common
feature
when desorptionjreabsorption
.
be-
comes important (Nomura, private communication; Hansen and Ugelstad, 1979b,d). The present authors used a steady-state approximation for the average radical number ñ, as well as a constant value for ¡fJmp'The value of " Pm was expressed
by
,
(47) Here b is an efficiency factor for radical capture in a micelle relative to a particle of the same size and x is the order of capture rate with respect to radius.
~
2.
69
Particle Formation Mechanisms
From the discussion of absorption rates (Section III) it follows that 1 :::;;x :::;;3, and furthermore that ñm!ñp = (j(rm/rpt. The steady-state radical number was expressed by (Harada et al., 1971; Ugelstad and Hansen, 1974) (48) .Some results of calculations of particle numbers for different monomers are given in Figs. 6 and 7. In these calculations, q in Eq. (40) and the values of (j and x are all set equal to unity. Figures 6 and 7 give particle number as a function of concentration of micellar emulsifier at a given initiator concentration and as a function of initiator concentration at a given emulsifier concentration, respectively. It will be observed that only with styrene, when the value of the desorption constant is low due to a low value of kf and a low water solubility of the monomer radical (Le., a high value of a in Eq. (42)), - do the results approximately conform to the Smith-Ewart equation. The results with the other monomers deviate considerably from this scheme, the
0.1
1 10 50/(9 dm-3)
100
Fig. 6. The number of partic1es N as a function of the initial emulsifier concentrations, So, calculated by numerical integration of Eqs. (35) and (39) with Pmfrom Eq. (47) and ñ from Eq. (48). Parameters: p¡ = 1 x 1016 radicals/dm3 sec, b = 1, x = 1, q = 1. Monomers: MMA, methyl metacrylate; BMA, n-butyl metacrylate; S, styrene, VAc, vinyl acetate; ve, vinyl chloride. (Reproduced by permission of Makromol. Chem.)
70
F. K. Hansen and J. Ugelstad 102°,
ve
1019
.... ....
...
-",,'" --~.,,-'" .... .......... 1_"''''''
'upper
,....-
... I ~Iower
5-E
1017 10'5
1017
p¡!(dm-3
Fig. 7.
Sol)
The number of particles N as a function of the rate of initiator decomposition p;
calculated by numerical integration. So by permission of Makromo/. Chem.)
=
I gJdm3, other parameters
as in Fig. 6. (Reproduced
more so the higher the value of the e[ective desorption constant. It turns out that the particlenumber may be expressedby (49) where 0.6 < Z < 1.0. Equation (49) was first obtained by Nomura et al. from a nonsteadystate treatment. The value of Z increases as the desorption and reabsorption of radicals increases. This also leads to an increase in the particle number because desorbed radicals may also produce new particles. On the other hand the polymerization rate per particle diminishes as the high degree of desorption and reabsorption of radicals leads to a value of. ñ~1. The above calculations explain well the qualitative results with monomers like vinyl chloride, vinyl acetate, methyl methacrylate, and styrene. Quantitatively, the correlation between theory and experiment will depend on the magnitude of J and x, which may also change during the formation periodo Generally, if Z > 0.6, the particle number, as well as the value of Z,
2. Particle Formation Mechanisms
71
will decrease with increasing values of x and decreasing values of b. The effect of x will be relatively low if Z ~ 1, because then ñ ~ 1, which means that the particIes will grow more slowly. It may be estimated that the value of rpjrm is approximately 10 and 3 for styrene and vinyl acetatejvinyl chloride, respectively. The experimental results indicate that with a value of x = 3 the value of b is approximately unity for styrene. For vinyl chloride nnd vinyl acetate the value of b is 1.0 x 10- 3 and 1.6 x 10-4 for x = 3 and with q equal to ñ in Eq. (40), which seems to be the more probable situation for vinyl chloride and vinyl acetate. Ir q in Eq. (40) is set to unity (irreversible absorption) the value of b increases, most significantly for vinyl acetate. In any case, it appears that the apparent value of b is considerably lower for vinyl chloride and vinyl acetate than for styrene and the acrylates. This may be taken to indicate that the values of b for the radicals formed by chain transfer are considerably lower than for the polymer radicals, which in tum may be explained if the radicals formed by chain-transfer reactions are less reactive than the polymer radical s (Hansen and Ugelstad, 1979d). For styrene, a nonsteady-state calculation has been carried out without the simplifications used above (Hansen and Ugelstad, 1979a). Thus, instead of Eq. (35), the following equation was used for the rate of particIe formation (50) where PImand PMmare absorption probabilities for radicals stemming from initiator and monomer radical s, respectively. AIso, a distinction is made between Po and P1. In the calculation of the absorption probabilities, the complete expressions for nobtained from Eqs. (21) and (22) were used. In addition the monomer volume fraction in particIes (
72
F. K. Hansen and J. Ugelstad
t51
-I
I
I
I
r7.5
I
N
tO
5.0;I
E
g,
J
" IC
I
0.5
)(
o
o
2
2.5
,
--ñ
o
,
3
z
5
t (min) Fig. 8. The number of particles N mean radical concentration, ñ, and monomer volume fraction in particles, rPmp,as a function of time from numerical. integration of Eqs. (38-39) with P m from
Eq. (43) and ñ from
Eq. (21-22).
Monomer,
styrene;
emulsifier
SDS with
So
=
7 g/dm3,
initiator K2S20S (0.6 g/dm3), temperalure 60°C, Dw = 5 X lO-s dm2/sec, Dp = I X lO-s dm2/sec, 1/10~ 100 mV, kp = 300 dm3/mol sec, a = lOs, k~p= 7 X 107 dm3/mol seco(Reproduced by permission of J. Polym. Sci.)
(19) becomes less. However, radical absorption may still be practically irreversible because of more space for diffusion inside the particles. From Fig. 8 it appears that the usual assumption of a constant 4Jmpseems to be relatively good except in the early stages of the formation periodo The ca1culations showed good agreement between theoretical and experimental particle numbers and reaction rates both in seeded and unseeded runs and turned out to be little sensitive to the choice of distribution constant (a) for the radical s between particles and water (103-105). The results were somewhat more sensitive to the surface potential of the micelles and particles, which were set to 100 mV. It therefore seems that both electrostatic repulsion and reversible diffusion are important factors for the absorption efficiency of micelles and very small particles. In all theories hitherto cited, it has been assumed that only one sort of (oligomeric) radical stemming from the initiator is absorbed, even if this happens reversibily. This means that oligomeric radicals with a lower degree of polymerization are not absorbed at all, or only to a very low degree. For some monomers with low water solubility (as styrene) this may be justified, for other monomers the assumption is more doubtful. A more detailed discussion of the mechanistic aspects of oligomer growth and absorption is given below, including a treatment of the mechanisms for homogeneous particle formation.
73
2. Particle Formation Mechanisms V. Homogeneous Nucleation
Homogeneous nuc1eation is a result of processes shown as D-G in Table 1, in which the initiator radical propagates in the aqueous phase to form an oligomer which will then be the nuc1eus for a new partic1e. The exact mechanism for this nuc1eation has been discussed and several propositions have been set forth. The best-known theory on this subject, and one of the few quantitative treatments, has been proposed by Fitch and co-workers (Fitch and Tsai, 1971; Fitch, 1973; Fitch and Shih, 1975). They base their model on process F, involving the self-precipiation of the oligomer radical when a critical degree of polymerization is reached. Nuc1eation will be hindered if the oligomers are absorbed in earlier formed partic1es (process C) before they reach the critical chain length. The rate of partic1e generation is given by (51) dN/dt = p¡ - PA Aqueous-phase termination was not considered as a separate rate process but was inc1uded as anefficiency factor for p¡. The rate of radical absorption, PAwas expressed by PA= np¡LNr~ (52) where L is the average diffusion distance of an oligomer before selfnuc1eation. This parameter was expressed by Einstein's relationship (53) where t is the time between initiation and precipitation and was expressed by t = jcr/kpMw
(54)
Fitch and Tsai applied their theory to describe homogeneous partic1e formation for the case of methyl methacrylate. The critical degree of
polymerizationUcr) was found by GPC analysisof the aqueous phase to be ~65. The time dependence of rp was calculated from the volume growth which Fitch et al. (1969) found could be described by homogeneous kinetics during the formation period, Le., polymer formation as well as termination takes place mainly in the aqueous phase. The expression for the partic1e
volumeis then
.
(55) where v is the molar volume of the repeating unit in the polymer, ktw the aqueous-phase termination constant (in molecular units) and cjJppthe volume fraction of polymer in partic1es. The rate of partic1e formation is then from Eq. (51) dN/dt
= p¡[1 -
(nN)1/3{[3vkpMw/(4ktwcjJppNA)]
x In[cosh(p¡ktw)1/2t]}2/3L]
(56)
..
74
F. K. Hansen and J. Ugelstad
The partic1e number was obtained by numerical integration of Eq. (56). It was found that, in order to achieve agreement with experimental data, one had to assume a very low initiator efficiency. This does not seem unreasonable, taking into account the high degree of aqueous-phase termination. The more formal argument against the Fitch theory maintains, as mentioned, that it assumes that the absorption rate is proportional to the partic1e surface area [Eq. (52)]. This assumption is in sharp contrast to Eqs. (23) and (24) and has been criticized by several authors. Equation (52) will lead to a lower absorption rate and thereby to a higher partic1e number than Eq. (24). The fact that Eq. (56) seems to give reasonable results for methyl metacrylate may possibly result from a balance between the low rate of collision implied in Eq. (52) and the assumption of an irreversible absorption. As stated above, it is more likely that the rate of collision should be given by the diffusion theory which will result in a much higher rate of collision, and that this in small partic1es may be counteracted by a reversible absorption. One may look upon the homogeneous process as a chain reaction in which every chain has its specific probability for propagation, termination, and absorption and then choose the most probable mechanism by which new partic1es are formed. Such a treatment has been proposed by several authors (Barrett, 1975; Peppard, 1974; Hansen and Ugelstad, 1975, 1978; Arai et al., 1979). These authors all use the basic assumption of Fitch and co-workers, namely that the oligomers have to reach a certain critical degree of polymerization at which they self-nucleate (process F in Table 1). Arai et al. also inc1ude a second mechanism. If termination by combinátion in the aqueous phase leads to an oligomer which by this reaction reaches a chain length that exceeds the critical chain length this oligomer may precipitate to form a partic1e. This possibility has been neglected by other authors because it has been assumed that such a terminated molecule with two ionic end groups would be soluble as long as each of the terminating oligomers were soluble. It is possible that this argument is more valid for sparingly water-soluble monomers such as styrene, where the critical chain length is low (4-5), than for more soluble monomers with higher critical sizes and thereby a decreased influence of end group on oligomer solubility. The possibility for nuc1eation by mixed-micelle formation (process G) has also been proposed (van der Hoff, 1960), and quite recently experimental work has investigated this mechanism (Munro et al., 1979; Chen and Piirma, 1980). Evidence has been found indicating association of the surface active oligomers in systems both with and without emulsifiers (below the CMC). No quantitative treatment was given by these authors. It may be questioned whether there is any real difference between the self-nuc1eation and the mixed-micelle models. When emulsifier is absent, there is c1early a
.
2.
Particle Formation Mechanisms
75
strong coagulation among the small "primary" particles, because their surface charge is too small to give stability. Coagulation will lead to higher surface charge density and thereby to a greater stability (so-called limited coagulation). This phenomenon was also observed by Fitch and Tsai (1971). Emsulsifiers will decrease this coagulation tendency up to the point where all new particles formed are stable. It may be argued that this coagulation and the association into mixed micelles are in reality the same process, determined by the same physical parameters (diffusion rates, repulsion, and attraction energies). An argument against apure mixed-micelle model stems from the fact that, with VC and VAc, desorbed monomer radicals produce new particles. These radicals are uncharged and therefore not surface active. Most often the problem encountered in describing the particle formation quantitatively involves formulating a mathematical model that is close enough to the real process but not so complex as to make a solution impossible. Common to the chain-reaction models is the fact that a simple solution for the particle number is difficult to obtain analytically without considerable simplification. Below are given the rate equations for the chain model based on a previous treatment (Hansen and Ugelstad, 1978). In addition the present model includes the desorption of monomer radical s and the different
absorption rates, as outlined in Table 1.
The differential rate expression aqueous phase are as follows:
for the different types of radicals in the
lnitiator radicals
dR¡/dt
= p¡ -
kp¡R¡Mw
Monomer radicals (desorbed)
-
ktw¡R¡Rw
-
R¡
Lp kaipNp
(57)
,
(58) l-mers from initiator radicals (59) l-mers from monomer radicals (60)
76
F. K. Hansen and J. Ugelstad
j-mers from initiator radicals
dRr d/ = kpRIO-1)Mw- RIj kpMw+ ktwRw + ~kaIjpNp
(
)
(61)
j-mersfrom monomerradicals (62) Here R¡ and RM are the concentrations of radicals produced from the initiator and by chain transfer to monomer, respectively, RIj and RMjare the concentration of j-mers originating from these radical s, and Rw is the total concentration of alI radicals in the aqueous phase jIcr
Rw = R¡
+
L:
jMcr RIj
+ RM +
j=l
L:
(63)
RMj
j=l
The sum of all absorption rate terms ¿p is L: kaIjpNp p
¿kaMjpNp
== kaIjmNm
== kaMjmNm
+ kaIjONO + kaIjlNl + kaMjoNO +
kaMj1N1
+ kaIjdNd + kaMjdNd
(64)
(65)
p
Here index m denotes micelIes,index Oand 1 particles with Oand 1 radical, respectively (i.e., "dead" and "living" particles), and d monomer droplets. The absorption rate "constants" ka, are generalIy expressed by Eq. (21) (omitting the concentration). For instance (66) (67) for absorption into micelIes. Similar expressions are obtained for particles and monomer droplets, applying the proper expressions for radius (r) and efficiency factor (F). The rate of particle formation is given by (68) which means that oligomers stemming from initiator and monomer radicals precipitate as particles when they propagate beyond their respective critical degrees of polymerization jIcr and jMcp which may or may not be equal.
2.
77
Partiele Formation Meehanisms
Probably, jMcr will be less than jIcr because the monomer radical is uncharged. The rate of formation of living (N1) particles is
and the rate of formation of dead particles (No)is obviously dNo/dr
= dN /dt -
dN¡/dt
(70)
The total rate of particle growth is expressed by Eq. (39), only the micellar volume Vrnshould be exchanged by the volume of the precipitated oligomers. We do not differentiate between the volumes of dead and living particles, since the particles rapidly change from active to inactive and vice versa. Equations (57-70) may be integrated numerically, expressing F by Eq. (22). A simplification may be obtained by means of the steady-state approximation, in which all rates of radical change in the aqueous phase are set equal to O,expressing Rj by means of Rj-1 RIj/RIO-1) RMj/RMO-1)
= kpMw/(kpMw + ktwRw + LpkaIjpNp)
= fJIj
= kpMw!(kpMw + ktwRw + Lp kaMjpNp)= fJMj ,
(71) (72)
Thus, fJ is the probability for propagation of a j-mer. By multiplication of all f3Ijand fJMj,independently, and inserting into Eq. (68),one obtains dN jlcr jMcr (73) = Pi~i n f3Ij+ kdN1f3Mn fJMj dt j=1 j=1 By writing out the expressions for fJ and dividing each term in the denominator by kpMw, one obtains
(74) where (75)
78
F. K. Hansen and J. Ugelstad
and PM = 1 + ktwMRw + Lp kaMpNp kpMMw kpMMw
(76)
The expression for Rw is obtained by expressing Eqs. (71) and (72) as j p¡ Rlj
(77)
= k p M w p¡ T1 PII 1=1
and j kdN1 RMj
(78)
= k p M w PM T1 PMI 1=1
FinalIy we have
R.~ k:~A~+%Q]p,.)] (79)
+ ::Z~PM[[+%(QPM.)]
In the first paper on this subject (Hansen and Ugelstad, 1978) desorption of monomer radical s was neglected. Furthermore, in order to simplify Eq. (74), Pi was set equal to 1 (Le., termination and absorption of initiator radicals was neglected). AlI ka1jpvalues were set equal to some average absorption constant Kc(when micelIes are absent). As an approximation, Rw could then be expressed by Rw
= {[(KcN)2 + 4p¡ktw]I/2
-
KcN}/2ktw
(80)
and dN /dt by dN/dt
= p¡(1 + ktwRw/kpMw + KcN/kpMw)-hcr
(81)
Ir I
= (p¡/ktw)I/2
(82)
and N(t)
..
= {[k1P¡jcrt +
(k2 + l)jcr]IUcr - k2
-
1}/k1
(83)
..
2.
79
Particle Formation Mechanisms
where (84) and kz = (ktwpY/Z/kpMw
(85)
Because r will increase with time, ke will also increase, and dN/dt will fall off
more with time than is expressedby Eq. (81). By using a plausible average value for r, Eq. (83) may give an idea of the number of particles that may be expected to be formed homogeneously. Assuming jer = 5, as found by Goodall et al. (1975) for styrene, and F = 1 (irreversible absorption) it turns out that N will be of the same order of magnitude as found experimentally in emulsifier-free systems. In systems with emulsifiers, below the CMC, the experimental particle numbers are much higher, indicating that the value of ke (and F) is in reality much lower. The low particle number in emulsifierfree systems must therefore be attributable to limited coagulation. By numerical integration of Eq. (73) it was shown (Hansen and Ugelstad, 1979b) that after 1 hr the ca1culated particle number was close to the experimental particle number for styrene with SOS as emulsifier, Le., immediately below the CMC. The following simplifications were made: (1) no aqueous phase termination and (2) radical s with lower degree of
polymerizationthan jer are not absorbed. The rate of nucleation is then dN/dt in close resemblance
= P¡PIh + kdN¡PMh
to Eq. (50) for nucleati~n
(86)
in micelles. Here
(87) and PMh
= [1 +
(88)
(Lp4nDwrpNpFMp)/kpMwrl
with FIpand FMpexpressed by Eq.(22). The total rate of radical absorption may be expressed by jIcr
pA
=
jMcr
L (RIj Lp k.IjpNp) + j=O L (RMj Lp k.MjpNp) j=O
(89)
where R1j and R.¡.¡jare given by Eqs. (77) and (78). It is obviously very difficult even to estimate PA from Eq. (89). One method of simplification may be the second one given above. This leads to Lp k.1pNp
PA =p. 1 kpMw
d
(
)
+ ktwRw + Lp k.1pNpkpMw+ ktwRw
k N
+
j¡cr
kpMw
1 kpMw
+
kpMw Lp k.MpNp ktwRw + Lp k.MpNp kpMw + ktwRw
(
jMCr
)
(90)
F. K. Hansen and J. Ugelstad
80
Ir the absorption rate of the critical oligomers is high (spontaneous), the absorption probability for radicals stemming from the initiator is PAI
= (1 +
ktwRw/kpMw)-her
(91)
ktwRw/kpMw)-jMer
(92)
and for radical s from chain transfer PAM
= (1 +
The fraction 1 - PAIwill therefore represent the probability for termination of radicals stemming from initiator in the aqueous phase before they can be absorbed. It is expected that the value of PAIwill be c10se to unity for monomers like vinyl chloride and vinyl acetate where the values of kpMw are high. In the case of styrene, kp = 240 dm3/mol sec and Mw= 4 X 10-3 mol/dm3 (50°C).With a value of k¡ = 1.0 X 10-6 sec-I, ktw = 7 X 107 dm3/mol sec, and jlcr = 4 the values of PAIat [I] = 10-4, 10- 3, and 10- 2 mol/dm3 are, with Rw expressed by Eq. (82), 0.72, 0.38, and 0.082, respectively. Quite recently, Hawkett (1980) investigated the seed polymerization of styrene at various initiator concentrations..From exact measurements of conversion as a function of time at low conversions, so that the approach to the steady state is taken into account, he c1aims to have determined separate values for the rate of absorption PAland the desorption rate constant kd for the special latex applied (N
= 4.9
x 1016 dm
- 3, diameter
93 nm). Hawkett's
values for
PAI at the above values of [I] are approximately 0.2, 0.09, and 0.03, respectively. Hawkett points out that ktwmay have a higher value than that given above based upon measurements in dilute polymer solution, since the termination reactions in water involve the reaction between small molecules. It should be pointed out that the above treatment do es not involve competition between termination and absorption as in Eq. (90). From this equation we should expect an influence of partic1e number and micelles on absorption efficiency. The assumption of such a low efficiency as found by Hawkett, where the order of PAlwith respect to [I] approaches 0.5 with increasing [I], seems to be in contradiction to both the absolute value of partic1es formed (both below and above the CMC) and even more so with the observed exponent in Eqs. (5) or (7) (i.e., 0.4). AIso, it would seem to contradict the well-known fact that at high values of [I] (i.e., high a' = 2ki[I]Vp/Nk~) the rate of polymerization is proportional to [I] 1/2 even in Interval II (Smith-Ewart Case 3). The effect of termination in aqueous-phase on partic1e formation will depend on whether the terminated and usually doubly charged molecules stay in solution, are absorbed on existing partic1es, or form the nuc1eus for a new partic1e. It seems unlikely that doubly charged styrene oligomers with
2.
81
Particle Formation Mechanisms
low degrees of polymerization (1-8) would form new partic1es, whereas it seems more probable that more water-soluble monomers, forming higher oligomers, may react according to this mechanism. A model for homogeneous partic1e formation applying this mechanism has recently been pro posed by Arai et al. (1979). These researchers also make the distinction between active and inactive partic1es, and their expressions for the rate of formation are (using our terminology)
-dN1 = kpRicrMw+ 4n(foNo dt -dN. o = (1 - A)!ktw jcr d t
¿
L DwjRj
jcr
f1N1)
(93)
j= 1
jcr
L R,
Rjcr+l-j
j=1
1=1 jcr
+ 4n(f1N1 - foNo)
L DwjRj
(94)
j=1
where Dwj is the diffusion constant for j-mers in water and A is the ratio of termination by disproportionation to the overall termination reaction. The first term in Eq. (93) accounts for the partic1e formation by precipitation of
oligomers that have a total degree of polymerization higher than jcr. The rate expressions for the soluble oligomers Rj, otherwise c10sely follow Eqs. (59-62). Arai et al. assume that Dwjfollows Wilke's equation DWJ. = Dw/':1.0.6 (95) They do not take into account desorption of monomer radicals or the possibility for decreased rates of desorptioll'. The equations for dNldt and dR/dt, as well as for dVldt [Eq. (39)J are solved by numerical integration for the polymerization system MMAK2S20S-water, with rate constants obtained from the literature. The initiator efficiency was set-equal to unity. Partic1e numbers between 1014 and 1015were obtained for initiator concentrations of 10-3-10-2 mol/dm3. The calculations showed that N should be almost independent of the chosen value of jcr for values between 5 and 70 (in strong contrast to our calculations). The reason for this is probably that aqueous-phase termination with subsequent precipitation is the dominant partic1e-formation mechanism in Arai's model, even more so with increasing initiator concentration. The theoretical partic1e-formation time was on the order of 2 sec, a very low value compared to the experimental results of Fitch and Tsai. Arai et al. found that their calculated partic1e numbers were approximately in accordance with the experimental results of Yamazaki et al. (1968) for emulsifier-free polymerizations. Arai's model does not inc1ude any coagulation mechanisms. It will therefore have the same shortcomings as most other models, namely that the strongly increased partic1e number in
82
F. K. Hansen and J. Ugelstad
systems with emulsifier (below CMC) cannot be explained. A modification of the radical absorption rates could possibly lead to a higher particle number for this model too. If the parameters of Arai et al. are inserted into the very simplified equation Eq. (83), almost the same particle numbers are obtained. In conclusion it may be said that there is still too little experimental evidence to determine the exact mechanism of homogeneous particle formation, except that the production of oligomers in the aqueous phase seems to be the essential initial mechanism. A problem of special importance to homogeneous particle nucleation involves coagulation processes. It has usually been assumed that all new particles will be stable if the concentration of emulsifier is just below the CMC. With decreasing amounts of emulsifier, an increasing amount of coagulation sets in, up to the point where no emulsifier is added and the particles are only stabilized by surface groups ipherent in or produced by the reaction. Roe (1968) proposed the use of some sort of absorption isotherm of emulsifier on particles to account for the influence of the emulsifiers. This would then have to be connected with corresponding stability criteria (W ratios). Also, kinetic aspects of compeition between absorption and coagulation might be of importance. No quantitative model explaining the influence of emulsifier below the CMC (except for Roe's modified Smith-Ewart calculation) has yet been presented. Although this may seem less important than the mechanism for particle formation above the CMC, as most practical applications use supermicellar consentrations, it still represents both a theoretical and practical problem of considerable interest.
VI.
Particle Coagulation during the Formation Period
Because of the transient character of the reaction, analysis of particle numbers during the formation period is not as easy as the case where the number has reached a constant value. Sampling has usually been performed in one of two ways, either by fast sampling from the reaction mixture with some sort of short-stop procedure or by direct observation of a monomer drop-free system by some light-scattering technique. The former method was used by Fitch and Tsai (1971) in their homogeneous MMA-water system. The short-stop was achieved by spraying onto an electron microscope grid directly from the reactant mixture. When no emulsifier was used, a pronounced maximum in particle number was observed, and the final value was much less than the value at the maximum. A maximum was also observed in systems with SDS as emulsifier, but the maximum became less pronounced with increasing SDS concentration. Furthermore, formation
2.
83
Particle Formation Mechanisms
and coagulation took place during a longer time interval when emulsifier was used, and the total particle number both at the maximum and at the steady-state level increased. Fitch and Watson (1979) also used a light-scattering technique to investigate the early stages of the reaction in a homogeneous solution of MMA in water. They used a photoinitiation procedure by which free radical s could be p~oduced by means of a light flash, after which Rayleigh ratios (Rgo) were measured as a function of time. Within the experimental time scale of '" 2 min, Rgo increased linearly with time, indicating particle coagulation. The rate of coagulation was clearly dependent on SDS concentrations and was most pronounced in emulsifier-free runs. The stability of a dispersion may in the most simple way be described by Smoluchowski's coagulation equation (96) -dNddt = kllNf and in the integrated form 1/N1
= l/No +
kllt
= l/No(1 +
t/1:)
(97)
Here k11 is the second-order coagulation constant and 1:the half-life time l/Nokll' This treatment assumes that kll is constant during the coagulation, which is only approximately correct during the early stages. When no force exist between the particles, the coagulation was regarded as a diffusion process with a value of kll given by kll
= 4nDllrll .
(98)
where Dll and rll are the total diffusion constant and the collision radius of the particles, respectively. Expressing Dll by the Stokes-Einstein relationship leads to the familiar expression for kll (99) k11 = 4n(2D1,)(2r1) = 16n(k:T/61ttlr1)r1 = 8kT/3r¡ When repulsive forces exist between the particles, the rate constant is decreased and the ratio kll(slow)/kll(fast) is usually expressed as kll(slow)/kll(fast) in which W(fast) 1S usually set ratio, expressed by
= 1.
= W/W(fast)
The parameter
reo W = 2rlo exp(J!;ot/kT)
dh
(100)
W is
Fuchs' stability (101)
where J!;otis the total potential energy and h is the distance between the particles. The parameters for this equation [Eq. (101)] have been extensively discussed in the literature (Derjaguin and Landau, 1941; Verwey and Overbeek, 1948).
84
F. K. Hansen and J. Ugelstad
For our purpose, it is often convenient to describe the stability during particle formation through the variation in W with time and experimental conditions. In the experiments cited above, Fitch and Watson (1979) found the linear relationship
(102) where S is the molar concentration of SDS and is less than 9 x 10-4 M (0.26g/dm3).Becauseof the linear relationship of Rayleigh ratios with time, W wasindependentof time for a specificexperiment,whichindicatesthat W is independentof particlesize. This was also found by Ottewill and Shaw (1966) to be the case for larger particle. When the total particle surface is small, and also at low SDS concentrations, the surface charge density will probably be independent of particle size and increase linearly with S. This would seem to imply that W has a linear dependence on surface charge density in the experiments described by Fitch and Watson. Munro et al. (1979) and Goodall et al. (1980) investigated particle nucleation in emulsifier-freepolymerizationsof styreneby means of electron microscopy, light scattering, and photo correlation spectroscopy, the latter in unstirred reactions in which 11 styrene layer was kept on top of the saturated water solution. The initiator was potassium persulfate. Particle numbers were found to decrease with time from an initial high value (Le.,a maximum); the maximum was more pronounced the higher the polymerization temperature. The time scale for the decrease was 10-100 min and involved particles up to a size of about 75nm. GPC analysis of both the aqueous phase and the particles during these early stages showed that the predominant molecular weight of the species present in the aqueous phase, measured as polystyrene, was about 520 and that of the polystyrene in the particles about 1000. In addition, the particles contained some higher molecular weight polymer (up to 106), the fraction of which increased after the formation period was finished. The conclusions drawn were that if these low molecular weight species are produced by termination by combination it would appear that the water-soluble oligomers are produced from 2-3 mers and the oligomers in the particles from 4-5 mers. This is the basis for assuming that in the case of styrene jcr = 4-5. In the work on emulsifier-free polymerization of styrene Hansen and Ugelstad (1979a) also concluded that coagulation during the formation period was of great importance. By seeded polymerizations, it was found that by including coagulation between new particles and seed particles one could describe qualitatively the number of new particles formed. For the homocoagulation between new particles, Eq. (96) was applied with ku given by Eqs. (97-100).Heterocoagulation between seed (Nz) and the new particles (NI) is described by (103) -dN¡/dt = klZNINz
~
2.
85
Particle Formation Mechanisms
where k12
= 41tp12r12/W¡2 = 2kT/317[(1/r¡
= 41t(D¡ + D2)(r¡+ r2)/W¡2 + 1/r2)(rl
(104)
+ r2)/WI2]
The expression for W¡2 is similar to that given in Eq. (94), exchanging 2r with rl + r2' In order to calculate particle coagulation during the formation period the distribution in size of the coagulating new particles should be included, with the coagulation rate generally expressed by Eq. (103). Such a procedure would lead to very complex calculations. It would be necessary to calculate W12as a function of size and surface charge density, which will vary during the reaction. AIso, particle growth by propagation should be included leading to higher particle sizes and lower charge densities. The present authors (1978) have made an attempt to perform such a calculation, without including propagation. Values for W12 were calculated from the DL VO theory for different degrees of coagulation of primary pafticles with one surface charge. The rate of formation of new particles was expr.essed by Eq. (68) with Rj from Eqs. (59-65) (without monomer radical desorption). The result of this calculation was a particle number which increased up to t
= 2.7
sec and then decreased.
The size distribution
also went through
a
maximum which increased with time. It seems that this result is in qualitative agreement with the results cited above, the calculated time for reaching the maximum particle number is, however, far too short, and in addition the maximum is too shallow. Both discrepancies are probably explained by the fact that the value of the efficiency factor F was set equal to unity at Dw = 10-8 dm2/sec, resulting iij a considerable underestimation of the number of new particles formed. This number should probably be increased up to two orders of magnitude which would result in both more pronounced maxima and a larger time scale. Hansen and Ugelstad (1978) also proposed a simplified steady-state description of the particle formation with coagulation. In this case the following equation was applied: dN¡jdt
= p¡kpMw/(kpMw + kcN¡ + kcsN2) -
where kc and kcs are the absorption
constants
kllNi
-
k12N1N2
(105)
in primary and seed particles,
respectively. Only oligomers at the critical degree of. polymerization are assumed to be absorbed, and aqueous-phase termination is neglected. This could be included by applying Eq. (90) for the absorption rateo AIso, desorption of monomer radicals could easily be included. The solution of Eq. (105) when dN¡jdt
=
O and N2
=
O with kcN ~ kpMw is
N = !(p¡317kpMwWu/4nDwkTrF)
(106)
To arrive at more exact solutions, including the increase in r and change in Wll and F, numerical methods have to be applied.
.
F. K. Hansen and J. Ugelstad
86
VII.
Nucleation in Monomer Droplets
Usually, particle formation by initiation in the monomer droplets is not considered important. This is because of the low absorption rate of radicals into the droplets, relative to the other particle formation rates. Only in cases where the monomer droplets are made very small may they be an important source for partic1e formation. In a series of papers, Ugelstad and co-workers have made a strong case for droplet nuc1eation in systems with especially effective preparation and stabilization methods for making and keeping the monomer in a very fine-dispersion (Ugelstad et al., 1973; 1974; Hansen et al., 1976; Azad et al., 1976; Hansen and Ugelstad, 1979c). The fine monomer dispersions were produced either by spontaneous emulsification by means of a mixed emulsifier system consisting of an anionic or cationic emulsifier in combination with a long-chain fatty alcohol or amine or by high pressure homogenization of monomer and water, using ionic emulsifiers and a water-insoluble compound (e.g., hexadecane) to stabilize against degradation by Ostwald ripening. The latter experiments are very illustrative in this context. Electron micrographs of latexes produced with a total concentration of 2 g/dm3 of'SDS (constant) with potassium persulfate as initiator are shown in Fig. 9. The variation in partic1e size was obtained by variation of the homogenizing conditions. Case A is an ordinary polymerization with no homogenization. The degree of monomer subdivision by the homogenization increases in the order B-E. In case A the normal emulsion polymerization with initiation in the aqueous phase leads to formation of large number of particles. The increasing partic1e size in going from A to B and possibly C may still be explained by :in aqueous-phase nuc1eation. The partic1es become larger because some emulsifier is adsorbed on the monomer droplets, leaving less emulsifier in the aqueous phase and thereby leading to the formation of a smaller number of partic1es. In cases E and D when practically all emulsifier is adsorbed on the monomer droplets the initiation obviously takes place solely in the monomer droplets. The number of partic1es in case E is even larger than that obtained in case A. There are two factors that influence the particle formation conditions: the adsorption of emulsifier on the droplets, which leaves less emulsifier in the aqueous phase to facilitate partic1e formation. there, and the rate of radical absorption in monomer droplets. The former factor may be evaluated' by taking into account the adsorption isotherm of emulsifier on monomer droplets. Using a modified Langmuir adsorption isotherm in combination with a mass balance gives an expression for the aqueous phase concentration of emulsifier C ifO
= t[(K2 + 4CXS)1/2 -
K]
(107)
2.
87
Particle Formation Mechanisms
.
..
..tt-
Fig.
9.
Electron micrographs
of poly-
styrene latexes produced without (A) and with (B-E) monomer homogenization. Total SDS, So = 2 gfdm3, initiator K2S20S (0.6 gfdm3), temperature 60°C, monomer concentration 300 cm3fdm3 H20. Concentration of free SDS (gfdm3): (A) 2.0, (B) 0.95, (C) 0.27, (D) 0.14, (E) 0.12. (Reprinted by permission of J. Polym. Sci.)
. 88
F. K. Hansen and J. Ugelstad
where K
=
[{ex
(108)
+ CMC)/CMC](Ad/as) - S + ex
ifC;?;CMC C=S-
(109)
Ad/as
Here S is the total emulsifier concentration, exthe constant in the Langmuir adsorption equation, Ad the total monomer droplet surface, and as the specific surface per unit amount of emulsifier. The expression for Ad is Ad
= 3VJrd
(110)
where J-d and rd are the total volume and surface average radius of the monomer droplets, respectively. The rate of radical absorption in monomer droplets is given by Eq. (89) if index p is taken to represent monomer droplets, or simplified by an equation similar to Eq. (90)
PAd
ka1dNd
= p. I kpMw
+ Pd
kpMw
(
hcr
)
+ ktwRw + ¿p ka1pNp kpMw+ ktwRw
(
kaMdNd
kpMw
)
jMcr
kpMp + ktwRw + ¿p kaMpNp kpMw+ ktwRw
(111)
where the index p in Np as usual represents all kinds of particles, droplets and micelles and Pd is the desorption rate from all particles containing radicals. The terms enclosed in parenthesis may, if Rw is constant, be taken as the initiator/monomer radical absorption efficiency and the two fraction terms containing Nd as the efficiency of droplet initiation relative to all other initiation mechanisms. If, for simplicity, termination in the aqueous phase and monomer radical desorption are neglected, Pd at the start of the reaction is given by P d--
4nDwrdNdFd
+ 4nDwrdNdFd + 4nDwrmNmFm
kpMw
(112)
and the efficiency of homogenuous nucleation Phby P,h--
kpMw kpMw
+ 4nDwrdNdFd + 4nDwrmNmFm
(113)
where Nm is the number of micelles which when C > CMC is given by Nm
= N~iC - CMC)
(114)
where N~ is the number of micelles per unit amount of emulsifier. The absorption efficiency factors Fm and Fd are as usual given by Eq. (22). An illustration of the effect of monomer droplet size on emuIsifier
..
--
1
I
,
2.
89
Particle Formation Mechanisms
adsorption and initiation efficiencies in droplets and by homogeneous nucleation calculated by means of Eqs. (107-110) and (112-113) are shown in Table n. The values for Fm and Fd are taken from Fig. 3 with a = 104 and IjIom= 100 mV. In these calculations the total volume of monomer was constant (300 cm3/dm3 water) and the specific surface area of SDS on the monomer was set to 50
A2
per molecule.
The other parameters
are given in the table
footnote. It appears that absorption of emulsifier on the monomer droplets surface starts to become significant at droplet radii '" 5 p.m. With S = 2 g/dm3 H20 one passes the CMC for the emulsifier at a droplet diameter of about 1.5 p.m, with 5 g S the corresponding value is ",0.2 p.m. With droplets below that size one should expect that the droplets may become the important loci for particle nucleation. It also appears from Table n that the probability of homogeneous nucleation decreasesmarkedly as the monomer droplet radius decreases. In considering the number of new particles that may be formed below CMC, the stability and the growth of the new particles must also be taken into account. The reduction in Nh most probably is lower than would be expected from the decrease in Ph. Ir one operates at e > CMC the number of micelles will usually be much higher than the number of monomer droplets and consequently the number TABLE 11 Number of Monomer Droplets. Free Emulsifier Concentrations. for Droplet and Homogeneous Initiation8
S rd (pm) 0.05
0.10 0.15 0.25 0.50 1.00 2.00 5.00 10.00
Nd(dm-3) 5.73 7.16 2.12 4.58 5.73
x x x x x
1017 1016 1016 1015 1014
7.16 8.95 5.73 7.16
X 1013 X 1012 X 1011 X 1010
= 2 gJliter
e (gJliter)
Pd
0.04
-1 -1 -1 -1
0.09 0.14 0.26 0.65 1.18 1.57 1.83 1.91
-1 0.997 0.847 0.162 0.037
S Pb
e (gJliter)
and Probabilities
= 5 gJliter Pd
1.7 x 10-5
0.11
4.2x 10-5
0.30
8.0x 10-5
0.61
-1
1.9 x 6.8 x 2.7 x 9.0 x 1.1 x 1.0 x
1.56 3.28 . 4.14 4.57 4.83 4.91
0.997 0.781 0.379 0.116 0.019 0.005
10-4 10-4 10-3 10-3 10-2 10-2
-1
-1
Pb
1.7 x 10-5 4.2 8.0 1.9 5.3 1.0 1.2 1.3 1.3
x x x x x x x x
10-5 10-5 10-5 10-4 10-3 10-3 10-3 10-3
Calculated from Eqs. (107-110) and (112-113) as a function of average droplet size rd' Monomer volume 300cm3/dm3 H20. Other parameters: Dw = 5 X 10-8 dm3/sec; Dp = 1 X 10-8 dm2/sec; kp = 300 dm3/mol sec; Mw= 4 X 10-3 mol/dm3; Mp = 5 mol/dm3; a = 104; 1/10"; 100 mV, K = 5 X 108 m-I, CMC = 1.5 g/dm3. Q
90
F. K. Hansen and J. Ugelstad
of particIes stemming from the micelles Nmmuch higher than Nd. It should be pointed out, however, that this does not necessarily mean that there is no initiation in droplets. They will, however, in most cases be difficult to detect and even to separate from particIes initiated in the aqueous phase. The higher total rate of consumption of monomer in the large number of particIes initiated in the aqueous phase implies that even if monomer droplets have become initiated they will during polymerization shrink because of transfer of monomer to the growing particIes initiated in the aqueous phase. The experimental results shown in Fig. 10 illustrate the condition for droplet initiation. In this figure the total number of particIes at the end of polymerization is plotted as a function of the concentration of free emulsifier in the aqueous phase for three different levels of emulsifier concentrations. One moves from right to left in the figure as the degree of
~
../
E
'
\
0\"
~~. 8,<:,0
~
4,\
~o
~~
\KtA8~ .... I E
~~~,yl
"
z
VP' ~L~
7. I ~
.
A 1015. 0.1
~~
,
8
~it. 2g 5.. 10..
PPS ~ 4 Ct
1.0
BP <> V 10.0
e (free 50S) (g dm-3) Fig. 10. Total number of particlesafter styrene emulsion polymerizations as a concentration of free SDS in the water phase before polymerization. Initiators K2S20S (PPS) and dibenzoyl peroxide (BP). Other experimental conditions as in Fig. 9. Theoretical curves A-E calculated from the absorption isotherm, Eq. (107-108). Curves A-B, ex= 4 gjdm3, curves C-E,
ex= 0.4 gjdm3.(Reprintedby permissionof J. Polym.Sci.)
.
2.
Particle Formation Mechanisms
91
homogenizationof the monomer-water-emulsifier with a constant amount of total emulsifier is increased. The particle number decreases because the particle formation in this region still takes place in the aqueous phase, because the emulsifier concentration in the aqueous phase decreases, and because with increasing homogenization more emulsifier becomes adsorbed on the surface of the monomer droplets. As the degree of homogenization is further increased the particle number goes through a minimum and then increases steeply, with a slope of - 3, when the monomer droplets have become the dominating loci for particle formation. Figure 10 also includes a curve from "normal" emulsion polymerization experiments where the particle number is plotted as a function of the amount of emulsifier added. It appears that with sufficient homogenization one may get a higher number of particles formed in monomer droplets than will be formed by a "normal" emulsion polymerizat.ion with the total amount of emulsifier in the aqueous phase. Experiments with benzoyl peroxide show that with the oil-soluble initiator, initiation takes place solely in the monomer droplets under the same conditions as in Fig. 9. No minimum in the curves is encountered as the degree of homogenization of the monomer-water-emulsifier mixture is reduced. References Alexander, A. E., and Napper, D. H. (1971). Prog. Polym. Sci.3, 145. Arai, M., Arai, K., and Saito, S. (1979). J. Polym. Sci.. Polym. Chem. Ed. 17,3655-3665.
Azad,A. R. M., Ugelstad,J., Fitch, R. M., and Hansen,F. K. (1976).Am. Chem.SocoSymp. Ser. 24, 1-23. . Barrett, K. E. J., (1975). "Dispersion Polymerization in Organic Media." Wiley, New York. Byron Bird, R., Stewart, W. E., and Lightfoot, E. N. (1960). "Transport Phenomena." Wiley, New York. Chen, C-Y., and Piirma, I. (1980). J. Polym. Sci. Polym. Chem. Ed. 18, 1979-1993. Danckwerts, P. V. (1951). Trans Faraday Soco 47. 1014. Derjaguin, B. V., and Landau, L. (1941). Acta Physicochim. USSR 14, 633. Dunn, A. S., and Al-Shabib, W. A. (1980). In "Polymer Colloids 11" (R. M. Fitch, ed.), pp. 619-628. Plenum Press, New York. Fitch, R. M. (1973). Dr. Polym. J. 5, 467. Fitch, R. M., and Shih, L-B. (1975). Prog. Colloid Polym. Sci. 56, 1. Fitch, R. M., and Tsai, C. H. (1971). In "Polymer Colloids" (R. M. Fitch, ed.), p. 73. Fitch, R. M., and Watson, R. C. (1979).J. ColloidInterfaceSci. 68, 14-20. Fitch, R. M., Prenosil, M. B., and Sprick, K. J. (1969). J. Polym. Sei. Part C 27,95. Friis, N., and Hamielec, A. E. (1976). Am. Chem. Soco Symp. Ser. 24, 82-91. Gardon, J. L. (1968a). J. Polym. Sci. Part A-l 6, 623. Gardon, J. L. (1968b). J. Polym. Sci. Part A-l 6, 643. Gardon, J. L. (1968c). J. Polym. Sci. Part A-l 6, 665. Gardon, J. L. (1968d). J. Polym. Sci. Part A-l 6, 687.
92
F. K. Hansen and J. Ugelstad
Gardon, J. L. (1968e). J. Po/ym. Sci. Part A-I 6, 2853. Gardon; J. L. (1968f). J. Polym. Sci. Part A-I 6, 2859. Gardon, J. L. (1971). J. Po/ym. Sci. Part A-I 9, 2763. Gatta, G., Benetta, G., Talamini, G. P., and Vianello, G. (1969). Adv. Chem. Ser. 91, 158. Gerrens, H. (1963). Ber. Bunsenges. Phys. Chem. 67, 741. Goodall, A. R., Wilkinson, M. C., and Heam, J. (1975). Prog. Colloid Interface Sci. 53, 327. Hansen, F. K., and Ugelstad, J. (1975). Preprint, Nato Advanced Study Institute on Polymer Colloids. Hansen, F. K., and Ugelstad, J. (1978). J.Po/ym. Sci. Po/ym. Chem. Ed. 16,1953-1979. Hansen, F. K., and Ugelstild, J. (l979a). J. Po/ym. Sci. Po/ym. Chem. Ed. 17,3033-3045. Hansen, F. K., and Ugelstad, J. (l979b). J. Po/ym. Sci. Po/ym. Chem. Ed. 17, 3047-3067. Hansen, F. K., and Ugelstad, J. (l979c). J. Po/ym. Sci. Po/ym. Chem. Ed. 17,3069-3082. Hansen, F. K., and Ugelstad, J. (1979d). Makromo/. Chem. 180,2423-2434. Hansen, F. K., Ofstad, E. B., and Ugelstad, J. (1976). In "Theory and Practice of Emulsion Technology" (A. L. Smith, ed.), pp. 13-21. Academic Press, New York. Harada, M., Nomura, M., Eguchi, W., and Nagata, S. (1971). J. Chem. Eng. Jpn. 4, 54. Harada, M., Nomura, M., Kojima, H., Eguchi, W., and Nagata, S. (1972). J. App/. Po/ym. Sci. 16, 811. Harkins, W. D. (1947). J. Am. Chem. Soco 69, 1428. Harkins, W. D. (1950). J. Po/ym. Sci. S, 217. Hawkett, B. S. (1980). Thesis, Dept. of Physical Chemistry, Univ. of Sydney. Morton, M., Kaisermann, S., and Altier, M. W. (1954). J. Colloid Sci. 9, 300. Munro, D., Goodall, A. R., Wilkinson, M. c., Randle, K., and Heam, J. (1979). J. Colloid Interface Sci. 68, 1-13. Nomura, M., Harada, M., Nakagawara, K., Eguchi, W., and Nagata, S. (1971). J. Chem. Eng. Jpn.4, 160. Nomura, M., Harada, M., Eguchi, W., and Nagata, S. (1975). Po/ym. Preprint Am. Chem. Soco div. Po/ym. Chem. 16,217. Nomura, M., Harada, M., Eguchi, W., and Nagata, S. (1976). Am. Chem. Soco Symp. Ser. 24, 102-121. Ottewill, R. H., and Shaw, J. N. (1966). Discuss. Faraday Soco 42, 154. Parts, A. G., Moore, D. E., and Watterson, J. G. (1965). Makromo/. Chem. 89, 156. Peppard, B. D. (1974). Thesis, Iowa State Univ. Piirma, l., and Wang, poCo(1976). Am. Chem. Soco Symp. Ser. 24, 34-61. Roe, C. P. (1968). Ind. Eng. Chem. 60, 20. Smith, W. V., and Ewart, R. H. (1948). J. Phys. Chem. 16,592. Sütterlin, N., Kurth, H-J., and Markert, G. (1976). Makromol. Chem. 177, 1549-1565. Sütterlin, N. (1980). In "Polymer Colloids 11" (R. M. Fitch, ed.), pp. 583-587. Plenum Press, New York. Ugelstad, J., and Hansen, F. K. (1976). Rubber Chem. Techno. 49, 536-609. Ugelstad, J., and Merk, P. C. (1970). Brit. Po/ym. J. 2, 31. Ugelstad, J., Merk, P. C., Dahl, P., and Rangnes, P. (1969). J. Po/ym. Sci. Part C 27,49-68. Ugelstad, J., EI-Asser, M., and Vanderhoff, J. W. (1973). J. Po/ym. Sci. Po/ym. Lett. Ed. 11,505. Ugelstad, J., Hansen, F. K., and Lange, S. (1974). Makromo/. Chem. 175, 507-521. Ugelstad, J., Hansen, F. K., and Kaggerud, K. (1977). Faserforsk. Texti/tech. 28, 309-320. Verwey, E. J. W., and Overbeek, J. Th. G. (1948). "Theory of the Stability of Lyophobic Colloids." Elsevier, Amsterdam. Yamazaki, S., Fukuda, M., and Himachima, M. (1968). Kobunshi Kagaku 25, 203.
,
3 Theoretical Predictions of the Particle Size and Molecular Weight Distributions in Emulsion Polymerizations Gottfried Lichti, Robert G. Gilbert, and Donald H. Napper
1. Prediction of the PSD . A. Simple Approximate Approaches to the PSD B. Population Balance Models of PSD . C. Batch Polymerizations . D. Semicontinuous Emulsion Polymerizations. E. Continuous Emulsion Polymerizations . F. Experimentallnvestigations of the PSDs G. Conclusions on the PSD '. 11. Molecular Weight Distributions A. Introduction . B. ElementaryConcepts . . C. General Theory of Emulsion Polymer MWDs D. Sample Evaluationof MWDs . E. Alternative Formulations of the MWD . F. ExperimentalDeterminationof the MWD . 111. Separability of MWDand PSD IV. Conclusions . References
.
94 95 96 99 105 105 109 114 115 115 116 120 124 134 139 141 142 143
The technique of emulsion polymerization is characterized by the formation of the polymer in the form of a latex. The particle size distribution (PSD) of the latex and the molecular weight distribution (MWD) of the contained polymer are two important measurable parameters of the latex. Not only do they inftuence the end-use behavior of the product, but they also reftect the growth history of the emulsion polymerization process. In what follows, we review the theories that have been developed to describe the PSD and MWD of emulsion polymers. 93 EMULSION
POLYMERIZATION
Copyright 1982 by Academic Press, Inc. Al! rights of reproduction in any form reserved. ISBN 0-12-556420-1
94
l.
Gottfried Lichti el al.
Prediction of the PSD
AlI the observable properties of an emulsion polymerization, such as the PSD and MWD, are goverÍ1ed by a single set of rate coefficients for the various microscopic processes occurring therein. Although the two distribution functions are interconnected, it is possible, without loss of generality, to discuss separately the mathematical modeling required to compute these two observables (see Section III). It must be recognized, however, that the various rate coefficients that can be determined empiricalIy are themselves commonly a function ofthe PSD and, less commonly, ofthe MWD. We now consider the problem of predicting the PSD (or the inverse problem of deducing rate coefficients from an observed PSD) without reference to the nature of the MWD generated. There have been two broad strategies adopted with respect to the prediction and interpretation of experimental PSDs. The first, exemplified by the work of Min and Ray (1974), is a "global" strategy which recognizes the considerab1e complexity of industrial-type emulsion polymerizations. The system is modeled on the basis of plausible theoretical arguments for each of the many microscopic kinetic processes included therein and incorporates rate coefficients taken from the literature for similar or analogous types of systems. In contrast, the second approach, which has been favored by the present authors (Hawkett et al., 1980; Lansdowne et al., 1980; Lichti et al., 1981), adopts a more pragmatic strategy in that simple model systems are studied experimentally' and theories constructed to permit several different determinations to be made of each required parameter. This obviates the need to appeal to literature values that may not be applicable to the systems in question. The global approach has the advantage that it considers problems of direct interest to industry. It is open to criticism in that the results may be ambiguous: the same agreement between theory and experiment could often have been reached with a different set of parameters and/or other equally plausible theoretical premises. Literature values for many rate coefficients for polymerization processes display considerable variation. For example, the reported values of the propagation rate constant (kp) for styrene at 50°C span the range 100-400 dm3 mol-1 sec-l, yet values of the average number of free radicals per particle (ñ) are often calculated by selecting one specific determination of kp. The proponents of the more pragmatic approach, on the other hand, have confined their attention to well-characterized "model" systems. Such studies are, as yet, of limited relevance to industrial systems, although the determination of an unambiguous set of rate parameters should in the long term permit a better understanding of systems of technical importance.
í
-
95
3. The Particle Size and Molecular Weight Distributions
A. Simple
Approximate Approaches to the PSD
We define the PSD by n(O", t), the relativenumber of latex particles of size O"at time t; O"may be the volume (V),area, or diameter (D)of a swollenor unswollen particle. The most rudimentary method of describing a PSD is to specify the average particle size, together with the breadth of the distribution. This method was adopted by Ewart and Carr (1954), who used two separate measures for the breadth of the PSD. These were the mean square deviation of (i) the particle diameter and (ii) the cube of the particle diameter. The former is defined by (1) with an analogous definition for the latter. In terms of the continuous distribution function n(O",t), where O" == D, we can write
~D =
{[f
D2n(D, t) dD
I f n(D,
t) dD
]-
[f Dn(D,
t) dD
If n(D, t) dD J}
1/2
It may appear at first sight that 15 and ~D in fact are the only measures of the PSD necessary (in a unimodal system), because of the following argument. If one supposed that each latex particle in an emulsion polymerization were to grow at constant rate in terms of the volume added per unit time, then the mean square volume deviation of the PSD would be constant after Interval I (the nucleation period). The PSD expressed in terms of volume would thus translate along the volume axis (i.e., the distributions would be superimposable) as the experiment progressed in time. On the other hand, if each particle were to grow ata constant rate in terms of radius added per second, then the radius distribution would translate along the radius axis after Interval 1. In fact, a real latex system cannot obey either type of behavior exactly because not all particles actually contain a growing free radical at any given instant. The foregoing argument involving the translation of the PSD on the size axis remains valid provided only that the fluctuations in the average polymerization times from particle to particle be negligible. This permits the real particle tha~ polymerizes for half the time to be replaced by an "equivalent" particle that grows continuously at half the rate of a particle containing one free radical. Such considerations are clearly of only limited value, and more complete measures of the PSD are required. Another measure of the PSD, one used by Gerrens (1959), is the mean square volume deviation, which is directly proportional to the mean square deviation of the diameter cubed. Gerrens was aware that such a description
Gottfried Lichti et al.
96
is only meaningful when all the PSDs to be compared have the same Gaussian or normal distributions. His experimental evaluation of several PSDs of polystyrene latexes showed that the distributions were almost Gaussian when expressed in terms of the particle volume. An additional measure of the PSD is the skewness parameter s, defined by Gardon (1968b) as the exponent of the radius such that the PSD expressed in the size parameter (radius)' is most nearly Gaussian. The preceding approaches to characterizing the PSD are adequate if the PSDs always closely approximate a particular type of distribution. If, however, the shape of the PSD changed markedly during polymerization, or if the PSD do es not conform to a recognizable functional form, greater mathematical sophistication is required.
B.
Population Balance Models of PSD
A comprehensive theory of the PSD should account for the time evolution of the PSD throughout the emulsion polymerization. The basic concepts widely accepted as describing the growth of polymer latex particles were originally advanced by Harkins (1945, 1946, 1947, 1950) and Smith and Ewart (1948). Each latex particle contains an integral number i (O,1,2, 3, ...) of polymerizing free radicals. Henceforth, i will be referred 'to as the "state" of the latex particle, The fraction oflatex particles that are in st'ate i at any time t is denoted by N¡(t). These Ni values relate directiy to the rate of polymerization through the average number of free radical s per particle, ñ = L¡ iNi (with the normalization condition L¡ Ni = 1). The Smith-Ewart equations describing the time evolution of N¡ are dN;/dt
= p(Ni-l - N¡}+ k([i + 1JNi+l - iNi) + e([i + 2J[i + lJN¡+2 - i[i -1JNi)
(2)
for all i ~ O. Here p is the first-order rate coefficient for the entry of free radicals into latex particles, k the first-order rate coefficient for exit (desorption) of free radicals from the particles and 2e pseudo-first-order rate coefficient for the annihilation of pairs of free radical s by bimolecular termination. Note that in Eq. (2), the term with a negative state coefficient (for i
= O) is
ignored and that bimolecular
termination
only contributes
if
i ~ 2. Note, too, that p and kñ give, respectively, the average number of free radical s that enter and exit from each particle in unit time and that the average lifetime of an isolated pair of free radicals in a latex particle is about !e.
¡,;
-
...
3. The Particle Size and Molecular Weight Distributions
97
The quantity N¡(t) alone contains insufficient information to specify the PSD of the growing latex because it refers to the fraction of particIes in state i at time t, irrespective ofparticle size. To circumvent this problem, it is necessary to define the number density distribution of particles of size (1in state i at time t by nM, t). The actual fraction of particIes with sizes in the range (a, b) can be evaluated from the integral of n¡«(1, t) between these limits. Thus, n¡«(1, t) is related to the previously defined N¡(t)through
N¡(t)
=
(3) 100
n¡«(1, t) d(1
from which it can be seen that the dimensions of n¡«(1, t) are (size)-l. The observable PSD n«(1,t) at any time during the experiment may be calculated from n¡«(1, t) by a summation over all states: n«(1,t) =
L¡ n¡«(1, t)
(4)
The n¡«(1, t) term is a function of two independent variables, (1and t. The equations describing them are a family of partial differential equations. The basic forro of these equations, as derived from population balance considerations, has been recognized by many authors (O'Toole, 1969; Sunberg and Eliassen, 1971; Pis'men and Kuchanov, 1971; Min and Ray, 1974; Lichti et al., 1977) and may be written in the compact but general form . onlot
= en - o(Kn)lo(1+ e
(5)
Here n«(1,t) i~ a vector whose (i + l)th component represents the distribution n¡«(1, t) and e is a square matrix formed from the kinetic parameters p, k, and c. The nature of e may be recognized by expressing Eq. (2) in matrix form and identifying the resulting square matrix with e. e is called here the Smith-Ewart coupling matrix because its elements in Eq. (5) describe how latex particIes change state as a consequence of the SmithEwart mechanisms (entry, exit, and bimolecular termination). The matrix K in Eq. (5) is a diagonal matrix ~hose (i + 1, i + l)th element specifies the rate of growth of a latex particIe in state i. The term -o(Kn)lo(1 in Eq. (5) accounts for the particIe growth process whereby particles of size (1 are lost to the population n¡«(1, t) when they grow to another size (1+ d(1,whereas particles are gained in the population n¡«(1, t) when particIes of size (1 d(1 in state i grow to size (1(Lichti et al., 1977). One common assumption regarding K is that
-
K¡+l,¡+l = iK
(6)
98
Gottfried Lichti el al.
where K = rate of growth of a partiele in state 1. This assumption, which asserts that a partiele containing i free radicals grows i times more rapidly than a partiele containing one free radical, is valid provided that partiele growth is not limited by, for example, monomer diffusion. Note that K = kpCrJNA where CMequals monomer concentration in the latex partieles and NA is Avogadro's constant. The vector c in Eq. (5) describes the creation in, andjor remo val oflatex partieles from, the system. The creation component may arise from in situ partiele formation (e.g., in Interval 1) or from the flow behavior in a continuous stirred-tank reactor system (CSTR) with an arbitrary number of reaction vessels. Partiele remo val terms may be required if coagulation occurs or in the context of CSTR operation. All the parameters in Eq. (5) may be functions of (J and t. Equation (5) may also be coupled to other mass balance equations, for example, that for the total amount of monomer present in the system. Certain parameters, e.g., the entry rate coeffcient p, may themselves be functions oe n¡«(J,t). Such would be the case if a radical that exists from one particle may enter another (Ugelstad and Hansen\ 1976). This results in highly nonlinear behavior. Equation (5) reduces to the Smith-Ewart equation [Eq. (2)] if c is sef equal to zero and if both sides of Eq. (5) are integrated between (J = O and (J = oo. This reduction further requires the assumption that all rate coef-
ficients forming the elements of a are independent of (J. It is evident that the population balance Eq. (5) are considerably more general in scope than the Smith-Ewart equation because the inelusion of the size parameter enables the formalism to model the partiele formation process, as well as both the kinetics and the evolution of the PSD. The Range of Applicability of the Populat~onBalance Equations The population balance equations are very general and may be applied to batch, semicontinuous, and continuous emulsion polymerizations. Furthermore, both seeded and ab initio polymerizations are comprehended by Eq. (5) in all (or part) of the three commonly considered polymerization intervals. The following sections show how the different possibilities are reflected in different functional forms of the elements of the matrices a and K and of the vector c. It should be remembered, however, that certain conceivable situations are not comprehended by Eq. (5); for example, if the monomer molecules are not freely exchanged between the latex partieles so that the monomer concentration inside each latex partiele is determined by its growth history.
.
3. The Partiele Size and Moleeular Weight Distributions C.
99
Batch Polymerizations 1. lnterval II
Interval 11 of an emulsion polymerization is characterized by polymerization in a constant number of latex particles in the presence of monomer droplets (Le., nucleation is absent). This situation usually exists in an ab initio polymerization immediately on completion of Interval 1; however, for a seeded system, it may exist from the commencement of polymerization. Clearly, if no new particles are formed and coagulation does not occur, the vector e in Eq. (5) is zero. Moreover, in the presence of monomer droplets, the concentration of monomer at each polymerizing site in the particles is approximately constant. The growth factor K is thus known. The remaining parameters p, k, and e in Eq. (5), or rather size-averaged values for them, can be evaluated from kinetic studies (Hawkett et al., 1980, 1981; Lansdowne et al., 1980). All the parameters in Eq. (5) are then specified and it is possible to predict uniquely the time evolution of the PSD. Of course, the initial distribution n~q, t = O)must also be specified (Lichti et al., 1977). Provided that a relatively monodisperse seed latex is used, the size-averaged kinetic parameters can be employed without introducing significant error. In this way, the predictions of Eq. (5) can be tested against experiment and, e.g., the accuracy of the kinetic parameters checked by PSD evolution data. Additional experiments with polydisperse seed latexes may permit the size dependence of the parameters to be specified. a. The Solution of the Population Bala'lce Equations. The solution of Eq. (5), given the initial conditions and all the requisite parameters, can be achieved in at least three different ways: (i) by analytic solutions, if they exist; (ii) by finite difference numerical solutions which may always be generated (Carnahan et al., 1969), although they may require considerable computing time and are prone to inaccuracy; or (iii) by the method of moments (Bamford and Tompa, 1954) which provides an efficient numerical procedure for certain systems. Analytic solutions for Eq. (5) provide the most direct path of the prediction of PSD evolution. For batch polymerizations in Interval 11, however, analytic solutions have only been achieved forothe so-called zeroone system (Lichti et al., 1981). These are systems wherein negligibly few particles contain two or more free radicals because of the rapidity of the bimolecular termination reaction (e.g., in styrene emulsion polymerizations with smalllatex particles). In this case, Eq. (5) may be written as follows: ano/at = - pno + (p + k)n¡ (7) andat = pno (p + k)nl - aKndaq (8)
-
Gottfried lichti et al.
100
The appearance of the term pnl in Eq. (7) reflects the fact that entry into a . state 1 latex particIe causes a state zero latex particIe to be formed as a consequence of rapid bimolecular termination. Ir all the paramaters p, k, and K in Eqs. (7) and (8) can be taken to be independent of time, while being permitted to be arbitrary functions of size, analytic solutions may be generated for arbitrary initial conditions (Lichti et al., 1981). These solutions encompass the more restricted cIass of analytic solutions provided by O'Toole (1969) and Watterson and Parts (1971). The use of the term analytic is retained Qere even though, for arbitrary initial conditions, one numerical integration is required; such integrations are very rapidly performed numericalIy. The importance of this analytic solution is that it enables one to make a thorough comparison between experimental PSDs and theoretical predictions, with a wide range of assumptions as to the values and functional forms of the various contributing rate coefficients. The analytic solution derived by Lichti et al. is applicable to any zeroone system in lnterval n, with no restrictions on the rate coefficients except that they be independent of time (but may depend on size). Although a zero-one description is applicable to some important systems, it is not universally
valid. For systems where ñ exceeds
t, general
analytic solutions
have yet to be developed, and we now examine methods for solving Eq. (5) for systems of arbitrary ñ. The second method for solving the PSD evolution equations is bruteforce numerical solution using first-order finite difference. Whereas a solution can always be obtained by this technique, it suffers from numerical instability, from the lack of any automatic check on accuracy, and from requiring large amounts of computer time. The third method for solving Eq. (5), the method of moments, was exploited by Katz et al. (1969) in connection with MWDs (see Section n,E,2) and by Sundberg and Eliassen (1971) in connection with PSDs. This method is numerically efficient. The kth moment mf of the population n¡(a,t) is defined by mNt) = 1<0akn¡(a,t) da
(9)
Equations involving only a finite number of mf may be derived from Eq. (5) under appropriate cIosure approximations. As only one variable (t) is then involved, the moment equations may be readily solved and the populations n¡(a,t) generated. This method will often fail, however, when Eq. (5) is nonlinear (e.g., if reentry is important) or if large numbers of moments are equired (e.g., for a polymodal PSD). b. Theoretical Results. To illustrate the use of the analytic solutions mentioned above and to highlight the general behavior exhibited by the
3. The Particle Size and Molecular Weight Distributions
101
PSD in Interval II batch reactions, the results of a sample calculation are provided (see Fig. 1). In this caIculation for a zero-one system, it was assumed that p = 1, k = O,K = 1 and e ~ p, the units being arbitrarily, but appropriately, chosen. The initial condition selected, which is typical of a seeded emulsion polymerization system, was that
no(O",t = O)= 10 exp[ -1t(0" - 2)2] =0
0">0 O"~O
and (10) which corresponds approximately to a Gaussian distribution function. In Fig. 1, we chose O"= V (volume) as the size variable. Figure 1 depicts the evolving population no(O", t) and nl(O"'t), as well as the overall observable PSD n(O",t). Initially, alllatex particles are nongrowing. As polymerization proceeds, more particles enter the growing state. After some time, the total number of latex particles in each state is equal (Le., ñ = 0.5), although the population nl(O"'t) is marginally further advanced in size than the nongrowing population no(O", t). This must be so because the population nl(O"'t) is growing. The overall PSD moves along the size axis and broadens (as measured by the decreasein peak height of the normalized curves) with increasing time. The rate of broadening is greatest when the polydispersity is least (e.g., the PSD broadens significantly more in the initial time interval 0-2 than in the next interval 2-4). It is stressed that the PSD may be expressed as a function of any arbitrary size variable. For example, distributions n(V) and n(r)expressed in terms of the particle volumeand radius, respectively,are related by n(V) dV = n(r) dr
(11)
n(V) = n(r)/41tr2
(12)
For spheres, this implies that
Equation (12)has the interesting,but often overlooked,.consequencethat a series of evolving PSDs if expressed in volume may broaden with time; yet the sameseries if expressedin terms of radius may become more monodisperse. This can be seen from Eq. (12) to arise because each element of n(V) must be multiplied by 41tr2 to yield the distribution n(r); consequently, elements with larger values of V (and r) are weighted more and so become more peaked than elements with smaller V values. It is therefore mandatory to specify the size variable in which a PSD is expressed before commenting on the nature of the evolving PSD.
102
Gottfried
Lichti el al.
(o) 100 r 80 60 > o c: 40 20
O
1
2
V
3
4
5
3
4
5
3
4
5
(b)
100 r 80 60 > c: 40 1=2
20f
O
. 1
2
1
2
V
(c) 100 r 80
60 >
e
40
20
O
Fig. 1.
V
Parlic1esizedistribution functionsno, nI' and n (= no + ni) for p = K = 1 and
k = O,as functions of time t; size variable is volume V.
3. The Particle Size and Molecular Weight Distributions
103
It should also be noted that the functional dependence of the growth factor K in Eqs. (5), (7), and (8) is strongly influenced by the size variable used to describe the PSD. Suppose, for example, K is constant when expressed as a function of particle volume (Le., K(V) = K), which would pertain if each free radical incremented the host latex particle by a constant volume in unit time:
dV/dt
=K
(13)
If the same PSD is now expressed in terms of the radius, the term K(r) corresponds to the radius increment to the host particle in unit time as a result of growth of a single free radical. Equation (13) yields dr/dt
= K/4nr2 = r(r)
(14)
which is the requisite form of the same growth factor expressed in terms of the new variable r. 2.
lntervall
The prediction of the evolution of the PSD in Interval n is simpler than that in the other intervals and it was for this reason that it was discussed first. Even the qualitative
features of particle formation
in Interval I are in
doubt and the relative importance of homogeneous (Le., oligomeric précipitation) versus heterogeneous (Le., micelIar) nucleation mechanisms are not fully understood. For this reason, detailed solutions to Eq. (5) in this Interval, when e is nonzero, appear to be premature. Moreover, in many emulsion polymerizations, the precise detail~ of events occurring in Interval I are masked by the subsequent particle growth in Intervals n and nI. The global strategy endeavors to enCQIIlpass all possible nucleation and coagulation m~chanislI\s. Min and Ray (1974) have identified four different mechanisms that lead to a change in the number of particles, although this list may not be exhaustive: (i) the coagulation of latex particles with micelles, (ii) the mutual coagulation of latex particles, (iii) the entry of free radical s into micelles, and (iv) the precipitation of an aqueous-phase oligomeric radical that has exceeded its criticallength. The four processes all contribute to the vector e in Eq. (5). These terms are evaluated in a nonrigorous fashion. For example, the rate of coagulation of particles of volume V1 with those of volume V2 is taken by Min and Rayas proportional to the product of the respective numbers of particles, the constant of proportionality being given by kc
= C1 exp( -
E* /kB T)(Vl V2)-1/3
(15)
In Eq. (15), E* equals the activation energy for coagulation and Cl is a constant.
Gottfried Lichti el al.
104
With this type of approach, two comments must be borne in mind: first, at this level of complexity, the proliferation of adjustable parameters almost assures that any experimental data can be fitted (Le., the model is virtuaIly unfalsifiable experimentaIly); second, only plausibility arguments were used to establish Eq. (15). It might be argued, for instance, that E* should be a function of particle size for charged species and that a formalism that treats miceIles and smaIl latex particles in an identical fashion is unrealistic. Furthermore, all particle sizes under consideration in Interval I are relatively smaIl «10 nm typicaIly); arguments leading to Eq. (15) have only been validated for considerably larger particles. These criticisms are meant only to stress that the coIloid science associated with Interval I is still poorly understood. Progress in this are a is therefore likely to be slow. Fortunately, as mentioned previously, particle formation by whatever mechanisms are operative usuaIly produces particles whose size is smaIl relative to that attained at the end of Interval In. It then becomes possible to assume with little loss of accuracy that aIl particles are formed at the same (smaIl) size.
3. IntervalIlI .
Interval nI is characterized by polymerizationin a constant number of latex particles in the absence of monomer droplets. The concentration of monomer in the latex particles CM thus declines as polymerization progresses. The principal modification required for the application of Eq. (5) in modeling Interval nI is its coupling with a monomer balance equation and the modification of the growth factor K to incorporate the declining monomer concentration. A full monomer balance equation for a batch reactor demands the consideration of the monomer consumed in both the aqueous phase and the particles (Min and Ray, 1974). Frequently, however, the aqueous phase consumption is relatively smaIl so that only consumption in the latex phase is significant. The latter is given by
-
dCM/dt
= AñCM
(16)
where A is kp/NAVSand Vs the average swoIlen volume ofthe paiticles. Equations (16) and (5) are mutuaIly coupled as foIlows: CMenters the" evaluation of the growth parameter K [see Eq. (6)] and thus the matrix K in Eq. (5); conversely, ñ is required in Eq. (16) and is ca1culated by reference to Eq. (5) through the relationship
ñ
= i~O
f
n¡(a,t) da
(17)
Solutions to these relationships have been developed by Wood et al. (1981).
...
3. The Partid e Size and Molecular Weight Distributions
105
Other materials balance equations may be coupled with Eq. (5) in an way analogous to the monomer balance equation. This is necessary if the availability of some species changes significantIy with time, e.g., when the initiator has a half-life comparable to (or shorter than) the polymerization half-life. .Jt D.
Sem;cont;nuous
Emuls;on Polymer;zat;ons
Semicontinuous emulsion polymerizations are characterized by the continued addition of monomer to the reaction vessel. This permits the production of latexes with high weight percentage solids while allowing the initial burst of nuc1eation to be achieved in substantially aqueous surroundings. The theory for semicontinuous systems is substantially that set forth for Interval In of batch polymerizations, except that the materials balance equations [Eq. (17)] must be modified to inc1ude the flow of new material into the reactor. The effect of the monomer input is twofold: first, the mass of material present in the system is increased and second, the concentration of other reagents may be reduced. From a practical viewpoint, a semicontinuous process may be used to increase the duration of Intervals n or In. Thus, for example, by extending the duration of an Interval In which displays a Trommsdorff gel effect with its concomitant rate acceleration, a shorter reaction time may be achieved. E.
Cont;nuous Emuls;on Polymer;zat;ons
.
A continuous emulsion polymerization is characterized by (i) the continual addition of monpmer, surfactant, and initiator to the reaction vessel and (ii) the withdrawal of a steady stream of reactor fluido Several such reaction vessels may be set up in series with one another so that the effiuent from the first feeds the second, etc. Any species in such a system remains in the reaction vessel for a finite time, termed the "residence time." Such reactor vessels may be either completely or incompletely mixed and operate under either isothermal or nonisothermal conditions. The incompletely mixed, nonisothermal reactor is characterized by the existence of spatial concentration and temperature gradients in the reactor. The principal advantage of continuous reaction vessels is that they operate (after an initial transient period) under steady-state conditions that are conducive to the formation of a highly uniform and well-regulated product. In this section, we shall confine the discussion to continuous stirred-tank reactors (CSTRs). These reactors are characterized by isothermal, spatially uniform operation.
106
Gottfried lichti et al.
Equation (5) may be used to model a eSTR by modifying the vector e to allow for the removal of latex particles in the effluent stream while incorporating the particle creation terms of the type discussed above. The form of the term describing latex particle removal is given simply for all i by c¡ =
-NJr
(18)
where t is the mean residence time. This may be readily caIculated from the volume of the reactor and the efflux rateo The addition of a term such as that in Eq. (18) to Eq. (5) makes a profound difference to the evolution of the PSD in time. For example, true steady-state solutions to Eq. (5) may be generated by setting the lefthand side equal to zero. The PSD does not evolve in time in that case but remains static under the competing influences of particle nucleations and remo val. This type of behavior is unique to continuous systems. Uually, steady-state conditions prevail in eSTRs only after a period equal to several mean residence times has elapsed. Thompson and Stevens (1977) have numerically solved the steady-state version of Eq. (5) for a multistate emulsion eSTR, allowing for all the usually considered free-radical events. The problem contains only one independent variable, the particle size (1.It may be solved with considerable precision using sophisticated finite difference methods. The actual shape of the steady-state PSD is quite unlike that observed in the batch process (see Fig. 2), being a monotonically decreasing function of particle volume rather than a peaked function. This feature of the PSDs of eSTRs arises from the greater probability of removal of particles in the effluent as their times of residence (Le., growth times) increases. It is emphasized that the foregoing argument is valid only when the PSD is expressed in terms of volume; the PSD produced in a eSTR does show a maximum when expressed in terms ofradius [see Eq. (12)]. The PSDs produced in emulsion eSTRs tend to extend over a wider range of particle sizes than those generated in a batch process. This arises from the constant creation of new particles in a eSTR compared with the short burst of nucleation in a batch system. One consequence of this broadness is that reasonably accurate predictions of the steady-state PSD can be achieved in such reactors without considering "stochastic" broadening factors (Le., broadening caused by the distribution of free radicals among the particles, as illustrated in Fig. 1 for a batch system). The formalism of Eq. (5) fully encompasses the contribution from stochastic broadening by considering the portion of the overall population in each state i. eSTR PSDs often display insensitivity to stochastic broadening. This insensitivity to stochastic broadening considerably simplifies the problem of predicting the PSD in a eSTR system. De Graaf and Poehlein
3. The Particle Size and Molecular Weight Distributions
107
(a)
>-
t-
¡¡¡ Z t.s e
lb)
a: t.s ID ~ => z
VOLUME
Fig. 2.
Schematic comparison of the PSDs produced by (a) batch and (b) CSTR
emulsion polymerizations.
(1971) showed that it was possible to calculate the PSD from an expression for the distribution of residence times (and hence growth times), as well as a growth rate parameter that depends upon the particle size [see Eq. (21)]. The crux of their argument will now be presented, The lifetime distribution of any species in the CSTR g(t) is given by g(t)
=
Co exp(
-
tlr:)
(19)
if the effiux rate is uniformo Here Cois a normalizing factor. Suppose that it is possible to assign a unique value of particle size O'(t)to a particle that leaves the reactor after a residence time t. This assumption actually disregards stochastic broadening by ignoring the fact that particles that leave the reactor after residence time t will in reality possess a size distribution. The lifetime distribution expressed by Eq. (19) can then be transformedinto the steady-statePSD as follows[cf. Eq."(11)]: g(O')
=
Co exp[
- t(O')Ir:](dtldO')
(20)
where t(O') is obtained by inverting O'(t). In order to calculate t(O'),or equivalently O'(t),an equation describing the average growth rate of the particle is used: dO'ldt
= Kñ"
(21)
Gottfried Lichti et al.
W8
where ñ",is the size-dependent average number of free radicals per particle calculated from a knowledge of the size-dependent parameters p, k, and e [see Eq. (2)]. The foregoing argument is equivalent to the approach of Stevens and Funderburk (1972), who used a more abstract line of reasoning. Suppose that a summation of Eq. (5) is performed over all states i (Le., all the rows are summed). Then Eq. (5) becomes .0
L ni/ot = -oKL inJoa- L n;/r:
(22)
Equation (22) follqws from Eq. (5) if the vector e is given the form appropriate to CST,s [see Eq. (18)] for removal of latex particles in the effluent stream and if the particle creation terms are considered as boundary conditions operating at a = o. The term involvingthe Smith-Ewart coupling matrix vanishes on summation because of the conservation of particle numbers. The value of ñ",is given by (23)
ñ",= L ini/L ni so that Eq. (22) may be rewritten,as on/ot
(24)
= - oKñ", n/Ba - n/-r:
where n represents the overall PSD (Le., n = Li n¡). For steady-state conditions, Eq. (24) becomes (25)
oKñ", n/oa = -n/-r: This equation
has the general solution
n where
= coex{
Co is the number
-(f:da/Kn",-r:)JIKñ
of newly formed
particles
(26) present
at a
= O.
Equation (26) is identical to Eq. (20),ifviewed in conjunction with Eq. (21). The utility of the steady-state CSTR methods lies in the fact that the problem of the steady-state PSD may be couched in terms of uncoupled equations that are considerably easier to solve than the full problem. Some caution must be exercised in omitting the stochastic termo The results of the comprehensive calculations of Thompson and Stevens (1977) show that in certain instances, the steady-state PSD is sensitive to stochastic broadening. Finally, we note that the PSD in a CSTR is strongly sensitive to the residence time distribution, which may be varied over a wide range. Consequently, the production of a latex with a desired PSD is usually more readily achieved with a CSTR process than a batch or semicontinuous process, for the latter depend in a complex manner upon many mechanisms. The production of monodisperse latexes is an exception to this rule: these
3. The Particle Size and Molecular Weight Distributions
109
are more readily prepared by a batch or semicontinuous process since the CSTR product has a much broader distribution.
F. Experimentallnvestigations of the PSDs 1.
Batch Polymerizations
Min and Ray (1974) in their review article detailed many experimental studies on the PSDs of emulsion polymers. In this section, some more recent results that compare the predictions of the population balance equations [Eq. (5)] with experimental data will be discussed. The actual acquisition of reliable experimental PSD data is a task of considerable complexity. Such techniques as soap titration, turbidity, ultracentrifugation, and light scattering (Morton et al., 1954; Kerker, 1969; Shaw, 1970) usualIy pro vide only average values for the particle diameter, although some of these methods can provide PSD data if some functional form for the distribution function is assumed. The Coulter Counter can usualIy be exploited only for particles oflarger size (> 0.5 ,um), although it is not an absolute method (Eckhoff, 1967). Fractional creaming of latexes has also been proposed as a method for determining PSD (Schmidt and Kelsey, 1951; Schmidt and Biddison, 1960). This method is based on a relationship between the concentration of creaming agent and the size of the creamed particles, which is claimed to be independent of the nature of the dispersed particles. It has the advantage of simplicity, but again calibration is mandatory. Hydrodynamic and liquid exclusion chromatography (Nagy et al., 1980; Singh and Hamielec, 1978) have also been proposed as methods for determining the PSD, although difficulties still exist in relating the detector signal to the PSD. By far the most direct method for the measurement of PSDs is the use of transmission electro n microscopy. The measured PSD is a distribution expressed in terms of the unswolIen radius (or diameter) of the particles. AlI sizes are treated with the same statistical weight (provided they are able to be resolved); this is not the case with some of the sizing methods listed above (e.g., light scattering), which weight the larger particles more heavily. One major difficulty with electro n microscopy is that so me latex particles are adversely affected by the electro n beam. Shadowing techniques and hardening procedures (Corio et al., 1979) can sometimes be used to overcome this problem. A further difficulty inherent in any PSD measurement by electro n microscopy resides in the need to measure a large number of images of latex particles on a photographic print. Gerrens (1959) has stated that at least 3000 particles must be measured in order to obtain a statisticalIy meaningful distribution. This involves considerable human
Gottfried Lichti et al.
110
effort because current attempts to automate the procedure have thus far foundered on the difficulty of resolving the extensively overlapping particles thát inevitably occur in samples of sufficient number density to give meaningful statistics. It seems likely that sophisticated image analysis software andjor software that can resol ve overlapping particles will become commercially available in the near future. An additional complication arises with relatively mono disperse samples in that slight changes in the focus of the electro n microscope introduce random errors in the exact magnification of the final print. These problems of focus adjustment can be corrected for by the use of an internal standard (frequently another polymer latex with a significantly larger average particle size). It is usually mandatory for the PSD of the internal standard to be completely separate from the PSD of the sample. Sundberg and Eliassen (1971) ha ve compared the predictions of their population balance formalism with the experimental PSD data obtained by Gerrens (1959) for polystyrene latexes. Their model is a zero-one system with no exit (desorption) from the particles. Although the neglect of radical desorption for particles of this size is questionable (Hawkett et al., 1980; Lansdowne et al., 1980), the theoretical curves are in qualitative agreement with the experimental PSDs (see Figs. 3 and 4). It must be stressed, however, that the experimental PSDs were taken at the conclusion of the 6
32
1 2 3 4 5 6
28
"> o H "
24 20
lO' [1]0 (g cm-3) 3.61 .5.41 10.8 18.0 28.9 54.1
16 12 8 4 O
500
1000
1500
2000
1018 VOLUME (cm3)
Fig. 3.
Experimental PSDs for polystyrene latexes obtained by Gerrens (1959) for
various initiator concentrations [1]0. Gerrens' d('r.%)/dV, the derivative of the cumulative PSD, is proportional to n(O',t) with O'= volume (V). (After Gerrens, 1959; adapted with permission of Springer- Verlag.)
3. The Partide Size and Molecular Weight Distributions
111
4
z 0.6 52 1Ü Z ~
I.J... Z O
¡: 0.4 ~ m a: 1IJ)
o
w
~ 0.2 ...J O >
o Fig. 4.
0.5
1.0 1.5 VOLUME
2.0
Theoretical PSDs for polystyrenelatexes predicted by Sundberg and Eliassen
(1971). Initiator concentration curves (mol dm-3): 1, 1.1 x 10-3; 2, 2.2 x 10-3; 3, 5.5 x 10-3; 4, 1.1 x 10-2. Volume is dimensionless. (Reproduced with permission of Plenum Publishing Corp.)
polymerization reaction and SO incorporate information from the entire range of kinetic processes (e.g., nuc1eation, monomer-depleted growth, etc.). It is therefore difficult to assess whether the qualitative agreement between theory and experiment is significant or whether it results from a fortuitous cancellation of errors in the theory, especially as the data in Figs. 3 and 4 do not correspond to the same recipe and temperature conditions. Min and Ray (1978) have compared the predictions of the population balance model with the experimental results obtained by Gerrens (1959) on poly(methyl methacrylate) latexes. The correspondence between theory and experiment is qualitatively acceptable, and the same kinetic parameters model the kinetic behavior ofthe polymerization process (see Fig. 5). Again, the PSD was measured at the conc1usion of the polymerization reaction, raising once more the problem of cancelling errors in the theory. Min and Ray (1978) used literature values for all but two of the rate coefficients
112
Gottfried Lichti et al. 0.3
N I
.
o ~
0.2
>-
1Vi Z UJ e ...J
~ 0.1
Ir o Z
80 PARTlCLE
Fig. 5.
DIAMETER
160 Inm)
.
Comparison of experimer,ttaland theoretical PSDs for poly(methylmethac-
rylate) latexes prepared with various initial initiator concentrations: [1]0 = 1.8 x 10-3 g cm-3, ... [1]0 = 3.6 x 10-4 g cm-3, predictions of Min and Ray (1978); O and 1::" corresponding experimental data of Gerrens (1959). Ordinate is "normal density," proportiomi.l to n(u, t) with u = D (diameter). (After Min and Ray, 1978; adapted with permission of Journal 01 Applied Polymer Science. Also after Gerrens, 1959; adapted with permission of Springer-Verlag.) .
required in the polymerization. As noted above, such literature values frequently display large variations from one source to another. Lichti et al. (1981) examined the evolution of the PSD during a seeded styrene emulsion polymerization. The polymerization was sampled only during Interval 11, thus removing any uncertainties associated with monomer-depleted growth. The use of well-characterized seed particles obviates the difficulties associated with nucleation in Interval I and provides the initial condition for Eq. (5). Exhaustive kinetic studies on this system showed that the zero-one approximation was obeyed so that Eqs. (7) and (8) were applicable. The same kinetic studies yielded independent, precise estimates for the values of the parameters p and K, the effects of desorption being negligible; values of p and K were then chosen to optimize the agreement between the theoretical and experimental PSDs at the later time. Figure 6 shows the good agreement achieved between the calculated and measured PSDs at the later time (t = 45 min). A comparison between the values of p and K obtained by the kinetic and PSD experiments was also presented and excellent agreement found. These experiments demonstrate that consistent rate parameters may be determined using the kinetic and
113
3. The Particle Size and Molecular Weight Distributions RADIUS (om) 40 5 102 ('._1 1025 K
4
7e ~
60
50
PSD KINETICS 2.2 2.3 2.3
2.4
m3 $-1
3
2: e
Ñ
I o
2
~\
\ .\
,\
o
2
4
6
8
10
Fig. 6. Comparison of theory and experiment for a seeded emulsion polymerization. Continuous lines: smoothed partic1e size distribution obtained experimentally; broken line: theoretical fit using values of p and K shown in inset (values of p and K from kinetic study also shown) at t = 45 mino (After Lichti et al., 1981; reproduced with permission of Journal of Polymer Science.)
PSD approaches; alternatively, they demonstrate that the PSDs may be reliably calculated from o , kinetic data alone.
2. Continuous Emulsion Polymerizations De Graaf and Poehlein (1971) and Stevens and Funderburk (1972) have compared the predictions of the simple residence-time theory for the CSTR with experiment. However, the results of Stevens and Funderburk must be treated with caution in view of their use of only 30ü-400 particles to establish the PSD. Figure 7 shows the comparison of theory with experiment for the cumulative PSD obtained by De Graaf and Poehlein for a styrene CSTR with a mean residence time of 59 mino The agreement obtained was good provided that the Stockmayer solution for ñ in terms of p and e was used (k = O), rather than the Smith-Ewart Case 2 (i.e., ñ was greater than t). Note, however, that De Graaf and Poehlein assumed that free-radical desorption need not be taken into account; moreover, they assumed that the initiator capture efficiency was 100%. Both assumptions
Gottfried lichti et al.
114 1.0
z 0.8 O i= => ID
Q? 1- 0.6 VI i5 ILI >
~ 0.4 -1 =>
~
=>
00.2
O'
/
/
/
o
100.
200
300
PARTICLE DIAMETER(n m) Fig. 7. A comparison of theory with experiment for the normalized cumulative PSD, proportional to Son(O',t) dO',where O'= diameter, obtained by De Graaf and Poehlein (1971) for a polystyrene CSTR: --- ñ = 0.5; ñ > 0.5; O experimento (After De Graaf and Poehlein, 1971; adapted with permission of Journal of Polymer Science.)
are of dubious validity for the small particle sizes studied (Hawkett et al., 1980). G.
.
Conc/usions ofthe PSD
Because of the large number of mechanistic processes opera tive in emulsion polymerizations, complete theories for the PSD are necessarily complex. Nevertheless, they can be formulated by a population balance approach. Much remains to be done, however, to clarify the basic colloid science that underpins the nucleation process in Intervall. The experimental challenge in evaluating the predictions of the theory for PSDs resides not only in the attainment of agreement with experiment but also in showing that such agreement is not merely fortuitous but arises from the . correct mechanistic scheme. Considerable experimental work will be required to establish the validity of mechanistic assumptions for any particular monomer.
3. The Particle Size and Molecular Weight Distributions
115
11. Molecular Weight Distributions
A. lntroduction The molecular weight distribution (MWD) of a polymer generated by emulsion polymerizations can be fundamentally different from that generated in solution or bulk. For example, in styrene emulsion polymerization the MWD of formed polymer has a much higher average molecular weight than may be obtained using other methods. The basic reason for this was postulated by Smith and Ewart (1948) to be the compartmentalization of the polymerization reaction inside the latex particles which leads to the isolation of free radicals. This isolation reduces the probability of bimolecular terminations and hence increases the degree of polymerization. The fundamental difficulty in constructing a theory for the MWD in emulsion polymers is to account for the compartmentalized nature of the system. In the commonly occurring situation where particles contain only a few free radical s at any given time, it is obviously incorrect to consider that each latex particle behaves like a "mini-bulk" reaction vessel, and so the conventional methods used for bulk polymerizations are inapplicable. Nevertheless, some assumptions which introduce only minor errors may often be made. The most important such assumptions is that the evaluation of the MWD may be separated from that of the PSD. In other words, provided that the MWD being produced at any given moment is the same as would be formed in an equivalent set of monodispersed latex particle systems [as expressed in Eq. (27) below], then the MWD evolved in a system that is polydispersed in size may be computed trivially. Formally, this is expressed as follows. Let S(M, a, t) be the MWD formed in a monodisperse' system 'Of size a at time t; here M is the molecular weight variable. In a polydisperse system with PSD n(a, t) the overall MWD at any experimental time te, defined as S(M, te),is postulated as "" re (27) S(M, te)= O dt O da n(a, t)S(M, a, t)
ii
A detailed critique of the validity of Eq. (27) is given in Section III. In brief, two criteria are required for this validity, both of which are well satisfied in ordinary emulsion polymerization systems. These are (i) that the time required for formation of a single polymer chain be much less than that over which significant changes occur in the rate coefficients governing the MWD and (ii) that the average number of free radicals per particle of size a is close to its steady-state value.
116
Gottfried Lichti el al.
Equation (27) may be expanded to incorporate the contribution to the MWD from newly formed latex particles by assuming that these enter the system at some small volume and calculating the MWD in the new particles separately. Since latex particles grow to many times their original volume during the course of polymerization, the component of the MWD produced by nucleation is often negligible (at least, when measured as a weight average). Any aqueous-phase polymerization may also be included in the same way. We now show how to evaluate the MWD in a monodisperse compartmentalized system. It will be seen that the problem may be solved with complete generality if chain-branching reactions do not occur; moreover, analytical solutions can be obtained for the steady-state regime. B.
Elementary Concepts
In this chapter, the term MWD refers to the number density MWD, S(M), which gives the relative number of polymer molecules of molecular weight M. Another commonly used measure is the weight density MWD, W(M), giving the relative weight of polymer molecules. The two distributions are related by .
W(M)
= MS(M)
(28)
Thus, the relative number of chains in the sample with molecular weights in the range MI::;;;M ::;;;M2 is given by N[MI,M2J = rM2S(M)dM
.
(29)
JMI
and the relative number in a small range M to M + 11M by S(M) 11M. The normalization (and thus the dimensions) of S(M) will be specified later. In the ensuing development, S(M) will refer to the "instantaneous" MWD, Le., the contribution to the MWD created over a comparatively short time periodo Ir all polymerization occurs under steady-state conditions, S(M) then gives the final MWD of formed polymer directly via Eq. (27); otherwise, the final MWD is given by a simple time integration over S(M), as given in Eq. (27) and amplified in Section II,C,2. 1. Review of Bulk MWD Theory In bulk or solution polymerizations, the following free-radical mechanisms are usually considered: initiation, propagation, chain transfer (to monomer, polymer or transfer agent), and bimolecular termination (by
3. The Particle Size and Molecular Weight Distributions
117
combination or disproportionation). Except for initiation, all these reactions are bimolecular. Initiation and transfer are chain-starting reactions, whereas transfer and bimolecular termination are chain-stopping. A particularly simple theory for the MWD in bulk or solution polymeri. zations
is obtained if long-chain branching mechanismsare ignored and if
the growth of chains is envisaged as a continuous rather than a discrete process. The latter approximation is valid for almost all systems of interest, since the average degree of polymerization is usually large. The molecular weight of a chain is proportional to the growth time t' of this chain: M = kpCMMot' ==al'
(30)
where kp is the propagation rate coefficient, CMthe monomer concentration, and Mo the molecular weight of monomer. We note at this point that a may be a function of time, as it is during Interval III when CMdecreases; this point will be pursued in Section II,C,2. G(t),the distribution of growing chains of growth time t', is then G(t') = Goexp(-Jet')
(31)
where Go is a constant given by the rate of formation of new, growing chains (involving initiation and transfer rates) and Jerelates to the stopping of growing chains (involving bimolecular termination and transfer rates). Equation (31) expresses the fact that, once formed, a growing chain continues growing unless it undergoes a chain-stopping reaction. As Flory (1953) has pointed out, these kinetic probabilities imply a chain distribution that is of the most probable type, which to a good approximation is exponential. The required MWD is then given by the distribution of dead (nongrowing) chains; this is readily found as follows from G(t'). For those chainstopping reactions ih which the identity of the growing chain-stopping remains intact (i.e., transfer to monomer or to chain-transfer agent and disproportionation), the distribution of dead polymers produced which have (previously) polymerized for t' is simply proportional to G(t'). Denoting this distribution by Str.iM), we thus ha ve
.
Str.iM) oc exp( - Jet')
(32)
where we have used Eq. (31) together with Eq. (30) to relate M and t'. However, in the case of chain stoppage by bimolecular combination, pairs of free radicals join together to form a chain whose "equivalent" growth time t~q is the sum of the growth times of the two contributing chains. Now, for bulk or solution polymerization, the product G(l'¡)G(tí) specifies the distribution of pairs of growing chains of growth times t'¡ and tí, since in a bulk system any growing chain is equally likely to undergo
118
Gottfried Lichti et al.
bimolecular combination with any other chain (it will be seen that this does not hold in a compartmentalized system). The distribution of dead chains created by bimolecular combination with equivalent growth time t~q, denoted Sbc(M) (where M = at~q) is thus proportional to the sum of alI possible pairs of growth times giving this equivalent growth time:
i
t~q
Sbc(M
= at~q)oc. o
(33)
G(t' - t~)G(t~)dt~
Thus, from Eq. (31) we have Sbc(M)oc t~qexp( -
(34)
At~q)
The overalI MWD is then the sum of Sbcand Str,d' In order to facilitate comparison between MWDs, it is customary to define a dimensionless quantity P, the polydispersity of the MWD, which is the ratio ofthe weight average to the number average tnolecular weight: P = [1'X) M2S(M) dM LX)S(M) dM
J/[LooMS(M)
dM
J
(35)
If alI chains have the same molecular weight, P = 1; otherwise P > 1. For monomodal MWDs, the larger the value of P, the broader the distribution. For the MWD of Eqs. (32) and (33), P = 2 and 1.5, respectively. 2. Emulsion Polymer MWDs: Concepts and Limiting Cases The concepts introduced above require extension and revision when we turn to an emulsion polymerization. In view of the above discussion, we may take the system to be monodisperse in volume. First, we briefly consider the kinetics of such a system. As described in Section I,B, this is given by the distributions N¡(t), which are in turn given by the first-order rate coefficients for entry (p), desorption (k) and bimolecular termination (c). We note here that c
= Cbc + Cd
(36)
where Cbcand Cdare the (pseudo-first-order) rate coefficients for bimolecular combination and disproportionation, respectively. It is convenient to introduce at this point a further pseudo-first-order rate coefficient, that for transfer, given the symbolf We write f
= ktr.MCM + ktr.A[A]
(37)
where ktr.Mand ktr.Aare the rate coefficients for transfer to monomer and to chain transfer agent A; we assume that if transfer of free radical activity to A occurs, the species so produced polymerizes further. It is postulated that
3. The Particle Size and Molecular Weight Distributions
119
desorption, if it occurs, proceeds by transfer of free-radical activity to a small molecular weight species that subsequently leaves the latex particle. Thus, f as given in Eq. (37) includes desorption as well as true propagative transfer. To resolve this ambiguity, we redefine f as the rate coefficient for transfer events that do not result in desorption, i.e., we set
f = ktr.MCM + ktr.A[A]- k
(38)
We will consider the MWD in two simple cases. The first is when chain transfer is sufficiently rapid to ensure that all other chain-stopping events can be ignored. In such a situation, whereas the compartmentalized nature of the reaction may affect the rate of initiation of new chains, it will not affect the lifetime distributions of the chains once they are formed. The MWD may then be found from the bulk formulas, provided only that ñ, the average number of free radicals per particle, is known. Such an approach has been used by Friis et al. (1974) to calculate the MWD evolved in a vinyl acetate emulsion polymerization. These authors included in addition the mechanisms of terminal bond polymerization and of transfer to polymer (both of which cause broadening). The formulas required for the incorporation of these mechanisms could be taken from bulk theory. It is important to note that, even in this present limiting case of a transfer-dominated system, the chain-stoppage mechanism can be changed by compartmentalization. Thus, the MWD formed in the polymerization of styrene appears to be transfer-dominated in some emulsion systems (Piirma et al., 1975) but to be combination dominated in bulk or solution (George, 1967). This difference occurs because, in ~tyrene emulsion systems, the rate of radical entry into a particle is slow, and most particles usually contain either zero or one free radical. In the "state one" particles (Section I,B), the growing free,radical ras time to undergo several transfer reactions before a further entry causes radical annihilation. The second simple case we consider in this section arises in a zero-one system (Section I,C,l,a), where the average time between successive entries of free radicals into a latex particle is short compared with the time taken for a growing chain to undergo a transfer reaction. In this case, most chains cease growth by bimolecular termination. Ir this happens by combination with a low molecular weight entrant species, the following approach is possible. When entry occurs in a state zero particle, a free radical is formed and grows uninterrupted until the next entry event. Since the rate coefficient for entry is essentially constant, Eq. (31) gives the distribution of growing chains. Since the terminating free radical is of negligible molecular weight, the MWD will then be given by Eq. (32). The average chain growth time A.-1 is the average time between successive entries into the same particle (viz., p -1; i.e., p = },).
120
Gottfried Lichti el al.
In concluding this section, we note that except for the limiting cases given above, the phenomenon of long-chain branching has not thus far been incorporated into the models for emulsion polymer MWDs. In the general MWD formulation given below, it is assumed that these branching events occur with negligible frequency. C.
General Theory 01 Emulsion Polymer MWDs 1. "Singly Distinguished" Particles
The development here follows that of Lichti et al. (1980). By analogy with the MWD calculation for bulk and solution polymerizations presented earlier, the MWD formalism for monodisperse emulsion systems requires the evaluation of certain types of free-radical growth time distributions. Because of the variable nature of the reaction loci (depending on the state i), a separate growth time distribution is required for the population of particles in each state i. It is therefore convenient to define the distribution of singly distinguished latex pa¡;ticles in state i, denoted N;(t, t'), as the relative number of latex particles inside which a certain free radical began growth at time t, and continued growing in an uninterrupted manner for a further growth time t'. The state of the latex particle at time t + t' equals i. The free radical with growth time t' is called the distinguishing free radical. When the distinguishing free radical ceases growth, the latex particle is no longer said to be distinguished. These N; are analogous to (but quantitatively different from) the G for bulk systems (Section U.B.1). Note that for a distribution of singly distinguished free radicals N;(t, t') evaluated at experimental time te, we have
te = t + t'
(39)
from the above definition. It will be seen that this feature of the formalism has the important consequence that the evolution equations governing N;(t, t') are simply differential equations containing terms in only one of the independent variables, viz., t'. For N;, the minimum value of i is unity, not zero, since the definition requires the presence of at least one growing chain. If N;(t, t') is integrated over all values of the growth time t', the resulting integral counts each of the ¡free radicals inside the particle. Thus, from Eq. (36), we have the following normalization: rte
iNi(te)
= lo
N;(te - t, t') dt'
Since Ni is dimensionless (by the normalization condition dimensions of reciprocal time.
(40)
L Ni = 1),N; has
3.
The Particle Size and Molecular Weight Distributions
121
Because N¡(t, t') is a function of two independent variables, it would at first appear that the concomitant family of evolution equations would be, for example, coupled partial differential equations, and thus difficult to solve. Indeed, some formalisms for emulsion polymer MWDs (Katz et al., 1969) are based on distribution functions that suffer from this difficulty. However, N¡(t, t') is defined such that this problem is avoided, since the evolution equation separates into equations in t' alone with t being merely parametric. In fact, we have oN¡/ot' = pN;-l - [p + ik + f + i(i - l)cJN¡ + ikN¡+l + i(i + l)cN¡+2
(41)
This has been derived in detail by Lichti et al. (1980). In brief, this equation states that singly distinguished latex particles in state i form (i) by entry into an N¡-l type particle, (ii) by desorption of nondistinguishing radicals from an N¡+l particle, (iii) by termination among any of the (i + 1) nondistinguishing radicals in an N¡+2 particle. Similar statements hold for the loss term in Eq. (41). Since Eq. (41) involves variation in t' only, it may be solved given the initial conditions, viz., N¡(t, t' = O). These last quantities are the distributions of ordinary latex particles in state i inside which a new chain begins growth at time t: N¡(t, t' = O)= pN¡-l(t) + ifN¡{t)
(42)
Equation (42) asserts that entry and transfer (involving any of the i chains present) are the only chain starting reactions. Note that since N¡(t, t') usually decay monotonically in t', no steady-state approximati<:>ncan ~e made to simplify Eq. (41). Nevertheless, there are only a set of differential equations in one variable (as noted above) which can readily be solved (e.g., as in Section II.D.2). Having specified N¡, we now show how to compute the required MWD, or more specifically, the component of the MWD arising from the mechanisms considered in this section. This is the distribution of dead chains formed as a result of transfer, exit (desorption), and termination by disproportionation. We denote the components ofthe instantaneous MWD arising from each of these mechanisms by Str(t., M), S.it., M) and Sd(t., M), where t. is the experimental time. We have
L fN¡(t., t') S.x(t., M) = L kN;(t., t') i~l Stit., M) =
Sd(t., M) =
(43)
i;?;l
L 2(i -
i?t2
I)CdN¡(t., t')
(44) (45)
122
Gottfried lichti et al.
Here t' and M are related by Eq. (30). The right-hand sides of Eqs. (43-45) are the rates at which the distinguishing growing chain can cease growth by each of the events considered. It can be seen that Stn Sex, and Sd each has dimensions of(time)-z. The meaning of these distribution functions is as follows: the number of chains formed by transfer whose growth times are between t' and t' + dt', over the range of experimental time from te to te + dte, is given by SIrdt' dte (a dimensionless quantity), and similarly for Sex and Sd' Note that the expression for Sd is simpler than that given by Lichti et al. (1980), although the more complex expression for Sd given by these authors reduces to Eq. (45) after suitable manipulation. 2. " Doubly Distinguished" Particles The N; values are insufficient to account for the contribution to the MWD from bimolecular termination by combination: since tfiis requires a knowledge of the growth times of each of a pair of growing chains. In the bulk system considered in Section II,A,l, the distribution of free-
radical pairs with growth times '1/1 and t~ was shownto be givenby the product G(t~)G(t~).However, the equivalent relation in an emulsion system does not hold. A simple counter example will illustrate this. We consider a system containing only two particles in state 2. Let particle 1 contain growing chains with growth times t~ and tB' and particle 2 contain growing chains with growth times t~ and tD' The fraction of particles in state 2 which contain a chain of growth time t~, which we denote N~(t~), is 0.5, and similarly for N~(tB)'N~(tC),and N~(tD)' Note that, as in Eq. (40) N~(t~) + N~(tB)+ N~(t~) + N~(tD) = 2 since each particle is counted twice in this expression. Now, the fraction of particles that contain a pair of chains of growth times t~ and t~ is evidently zero, 110t N2,(t~)N~(tC)= 0.25, as would be given by the product formula. The reason for this difference between bulk and compartmentalized systems is that whereas all free radicals in a bulk system are mutually accessible, in an emulsion system only radicals inside the same latex particle are mutually accessible for bimolecular termination. We therefore define a new distribution N?(t, t', t") as being that of "doubly distinguished" latex particles in state i, Le., particles in which one free radical began growth at time t and continued growing for a time t', at which time (t + t') another free radical began growth in the same particle, and both are still growing at time t" later, the particle being in state i. From this definition, the experimental time te is given by te
= t + t' + t"
(46)
3. The Particle Size and Molecular Weight Distributions
123
The two free radical s which started at t and t + t' are termed "distinguishing," and the latex particle ceases to be doubly distinguished when either or both of these distinguishing free radicals cease growth. Obviously, the minimum value of i for which N7 is nonzero is 2. We define N;' to be normalized such that the integral of N7 over all possible values of t' and t" counts all possible pairs of growing free radicals in particles in state i. Since the number of pairs in a single particle in state i is ti(i
-
1), we have fte ftte
Jo Jo N;'(t. - t' - t", t', t") dt' dt" = ti(i - I)N¡(t.) (47) Note that this definition corrects a minor error in the work of Lichti et al. (1980). From Eq. (47),we see that N7 has dimensions of(time)-2. Although N;'(t, t', t'') is a function of three independent variables, the evolution equation governing variation with t" can be shown to contain t and t' only parametrically, analogous to that for N;(t, t'). In fact, it may be shown (Lichti et al., 1980) that ON;'/ot" = pN;'-l - [p + 2f + ik + i(i - l)c]N;' + (i - l)kN;'+l + i(i - l)cN;'+2 i ~ 2 (48) The usual population balance methods are used to derive this equation: thus entry into an N;'-l particle creates an N;' particle, and so on; note in particular that transfer occurs with arate coefficient of 2f, since f is that for transfer of a single free radical, and we here have two distinguishing free radicals. Since Eq. (48) involves variation with respect to t" only, it may be solved if the initial conditions N;'(t, t', t" = O) are known. These initial conditions are the distributions of singly distinguished particles in state i inside which a new chain starts growing at time t + t'. Thus N7(t, t', t" = O)= pN;-l(t, t') + (i - l)fN;(t, t') (49) because only entry and transfer are chain-starting reactions. The coefficient (i - 1) arises because the chain-starting transfer must not involve the first distinguishing radical. We see therefore from Eqs. (49), (48), (42), and (41) that the multiplevariable distribution functions represented by N7(t, t', n are in fact obtained as the solutions of sets of coupled hierarchical ordinary or simple partial differential equations: the solution of one set [for N¡(t)] pro vides the initial conditions for another set of partial differential equations [for N;(t, t')] which in turn pro vides the initial conditions for N7(t, t', t"). Obviously, this could be extended to n-tuply distinguished distributions, but this is unnecessary since the order of polymer-producing reactions never exceeds two.
Gottfried Lichti et al.
124
We now show how to use N¡' to obtain the contribution to the MWD arising from bimolecular termination by combination. When two distinguishing chains, one of which has been growing for time t" (this being the second chain formed)
and the other for t'
+ t"
(this being the first) undergo
combination, the resulting single dead chain has an equivalent growth time of t~q= t' + 2t". The rate coefficient for this event is 2c/(the factor of 2 arising from the usual definition of c as being per pair of free radicals). Thus, the relative number of chains of equivalent growth time t~qpresent at experimental time te formed by bimolecular combination is
f
t,~q
Sbc(te, M) =
O
dt" L: 2ccN¡'(te i
-
t~q
+ t", t~q-
2t", t")
(50)
where at~q = M as usual. Equation (50) is obtained as follows. First, the upper limit of the integral is the maximum value of t" such that a chain of growth time t~q can be produced by combination. Second, the integral is performed over all pairs of chains (after summation over all doubly distinguished particles in all states i) one of whose growth time is t" and the other whose growth time is such as to give a chain of growth time t~q, after combination has occurred. The te - t~q + t" is the starting time for such chains so that the time at which combination occurs is te; note here that since the lifetime of chains is normally much less than experimental times,
one has te - t~q + t"
~ te
to an excellent approximation.
Equation (50) defines a distribution as do Stn Sex, and Sd, so that the number of chains formed of growth time in the range t~qto t~q+ dt~q over the experimental time te to te + dte, is Sbc dt~q dte. These four contributions to the instantaneous MWD may thus be directiy summed to give the overall instantaneous MWD from all sources, S(te, M): S(te, M) = SIr + Sex + Sd + Sbc te,
(51)
Finally, we recall that the instantaneous MWD, S(te, M), may vary with The accumulatedoverall MWD of formedpolymer at time t* is simply Ct'
S(M, t*) ~ Jo S(te, M) dte
(52)
If S is independent of te, one simply has S = teS; such is the case, for example, during the Interval n steady state. In other cases (e.g., Interval In) the variation of quantities such as CM (and hence a) with time will be known from the kinetics; the evaluation of Eq. (52) is then a simple quadrature.
D.
Samp/e Eva/uation 01 MWDs The formalism given in Section n,e involves a large number
of equations
whích, although posing no difficulties so far as developing solutions, can best be understood by examining their behavior in limiting cases.
3. The Particle Size and Molecular Weight Distributions
125
1. Zero-One-Two Systems We first consider a system in which the maximum number of free radicals per latex particle is 2. This is termed a "zero-one-two" system. An analytic solution to the MWD equations for such a system in the Interval II steady state has been developedby Lichti et al. (1980). The zero-one-two model accurately describes systems wherein ñ (the average number of free radical s per particle) does not exceed 0.7; it is thus applicable to small-particle styrene (Hawkett et al., 1980),vinyl acetate (Ugelstad and Hansen, 1976), and vinyl chloride (Friis and Hamielec, 1975) emulsion polymerizations. In the Interval II steady state, the analytic solutions to the various functions involved in the MWD obtained by Lichti et al. (1980)are as follows; in these expressions,the dependence on te is suppressed since a steady state is assumed (53) N'l(t') = B1 exp( - A+t') + El exp( - Aj) N~(t') = B2 exp( where
-t{all
},+ t')
+
E2 exp(
-
Aj)
(54)
= N;(O) - E¡, E¡ = [(a¡l + },+)N'I(O) + a¡2N~(0)]/(},+- A_), A:t = + a22:t [(all + a22)2 - 4(alla22 aI2a21)]1/2}, N'¡(O) = pNo + fNI,
B¡
-
N~(O)= pNI + 2fN2, whereNo = 1- NI - N2,NI = p(p + 2k + 2c)/rx,N2= p2/rx,with rx= p(2p + 3k + 4c) + 2k(k + c), and the aij are the elements of the matrix
-p-f - k
[
p
k + p/2 -p-2k-f-2c
]
We further have N;(t',I t") = [pN'I(t') + fN~(t')] exp( - Qt")
(55)
where Q = p + 2(f + k + c). These results give the singly and doubly distinguished particle contributions for i = 1 and 2 (no higher value of i being required for our zero-one-two system) in terms of the various rate coefficients for the microscopic processes involved. The various components of the instantaneous MWD are then found from Eqs. (43-45) and (50). Using the above results, Eq. (50) is found to reduce to
Sbc(M)= 2cc{(fB2 + pBI)[exp(-A+t~q) - exp(-tQt~q)]/(Q- 2A+) + (fE2 + pE¡}[exp(-A_t~q)- exp(-tQt~q)]/(Q - 2A_)}
(56)
Finally, there is an additional contribution to the MWD arising from the artificial truncation used in a zero-one-two system, Le., from the assumption that entry into a particle in state 2 causes instantaneous termination. We denote this additional term Sit(M), and find (57)
126
Gottfried Lichti el al.
This term is in fact a numericaIly inconsequential component of the overaIl MWD (if ñ < 0.7). Eqs. (53-56), (43-45), and (30) may then be used to compute MWDs for some cases of interest; because we are considering an lnterval II steady-state system, the overall MWD is simply proportional to the instantaneous MWD: s(t., M) = t.S(t., M) = t.(Str + S.x + Sd + Sbc+ Sit). Figure 8 shows the MWD produced in a zero-one-two system where values of the various rate coefficients have been chosen to give a MWD dominated by transfer and exit: p = 0.1 sec-l, k = 0.3 sec-l,f= 0.9 sec-1, e = Osec-1. This gives a steady state ñ of 0.34. Before discussing the form of the curves, we pause to consider the axes employed in this figure. Because we are considering a steady state system, we may use as abscissa either M (molecular weight, in a.m.u.) or t' (growth time, in s). We use both
0.5
o
0.4
4
2
10-5M 6
2
( b)
(o)
0.4
N I U Q) ~ 0.3 z O ¡:: ::> ~ 0.2 a:: ti> 5
0.3
0.2
0.1
0.1
O O
O 2
341 GROWTH TIME (sec)
2
3
4
Fig. 8. Plots of instantaneous molecular weight distribution S arising from instantaneous termination, stoppage, and transfer, as a function of growth time (Iower abcissa) and molecular weight (for a typical styrene system; upper abcissa), for a steady-state transferdominated zero-one-two emulsion polymerization, with e = O, p = 0.1 sec-I, k = 0.3 sec-I, f = 0.9 sec-I. (a) Curves I and 2 give conlribulions lo S from N'I and N2, respeclively. (b) Overall MWD, S. (Mter Lichli et al., 1980; reproduced wilh permission of Journal of Polymer Science.)
127
3. The Particle Size and Molecular Weight Distributions
for illustrative purposes, with the value of a computed for styrene emulsion polymerization at 50°C, using kp = 258 dm3 mol-1 sec-1, CM = 5.-8mol dm - 3 (Hawkett et al., 1980). The ordinate of the instantaneous MWD plot has dimensions (time)-2, the dimensions of S; the conversion from S to the relative number of chains of a given molecular weight was given in Section n.c.l. We consider the curves given in Fig. 8. In Fig. 8A, curves 1 and 2 give the instantaneous MWD arising from distinguished partic1es in states 1 and 2, respectively. Fig. 8B gives the overall instantaneous MWD, which is a monotonically decreasing function approximating a single exponential. This behavior, which for a transfer dominated system is identical with that in the bulk, will be further discussed in Section n,D,3. Figure 9 shows the instantaneous MWD computed for a zero-one-two system where the rate coefficients have been chosen to give domination by combination: p = 0.1 sec-1, Cc = 1 sec-l, k = O, f= O, Cd = O. This gives a
steady state ñ of 0.55. Figure 9A showsthe contributions to the MWD from Sbc [Eq. (56)] and the artifactual Sil term [Eq. (57)]. It can be seen that Sil indeed contributes but little to the MWD, showing that the artificial truncation method used to reduce the problem to a zero-one-two case (so 0.004 (b)
(o)
.-
...
I <.> CII
'"
5.... 0.002 ::> ID
ir \ñ e TT
o o
1.0
2.0
1.0
2.0
EQUIVALENT GROWTH TIME (sec) Fig. 9.
(a) Plots
of components
of instantaneous
molecular
weight
distribution
S
arising from bimolecular combination (Sbe' labeled BC) and instantaneous termination (Sil' labeled TI) for a steady-state zero-one-two system with termination by combination only, assuming Ce= I sec - 1, P = 0.1 sec - 1, k = f = Cd= O. (b) Plot of S, the overall instantaneous MWD, for the same system. Note ñ = 0.55. (After Lichti et al., 1980; reproduced with permission of Journal of Polymer Science.)
128
Gottfried Lichti et al.
as to obtain analytic solutions) does not affect physical content. It can be seen from Fig. 9B that the overall MWD shows a distinct maximum. This resembles the behavior in bulk or solution, but as will be seen the similarity is only qualitative. Figure 10 shows the MWD for a zero-one-two system with rate coefficients chosen to give a disproportionation-dominated process: p = 0.1 sec-l, Cd= 0.3 sec-l, Cc= O= k = f. This gives ñ = 0.64. Here the MWD is seen to be monotonically decreasing, again a resemblance to solution and bulk behavior which is only qualitative. 2. Systems of Arbitrary ñ We next consider the evaluation of the instantaneous MWD for systems where ñ may be arbitrarily large. For simplicity we confine our discussion to a steady-state system in Interval II; the minor adjustments required to extend the computation to Interval III have been mentioned in Section n,e,2. For systems of arbitrarily large ñ, analytic solutions as given in Section n,D,l are no longer possible. Nevertheless, the numerical evaluation of S for such systems will be seen to require negligible computational effort. The procedure is as follows: first, from a given set of values of p, k, and c, one numerically solves the steady-state Smith-Ewart equations for Ni, i.e., Eq.
0.03 .... I
o
(\)
'" ~
0.02
z o ~
:J CD
g:0.01 IJ)
e
o
O
10 GROWTHTIME (sec)
20
Fig. 10. Plot of instantaneous MWD S as function of growtb time in a zero-one-two Interval 11 system witb termination by disproportionation only, assuming p = 0.1 sec-1, Cd = 0.3 sec-1, c<=
J = k = O. (After
oJPolymerScience.)
Licbti et al., 1980; reproduced
witb permission
of Journal
.
3. The Particle Size and Molecular Weight Distributions
129
(2) with appropriate modification to allow for truncation at a sufficiently large value of i (Ballard et al., 1981).Equation (41) is then solved numerically by expressing them in matrix terms: (58)
oN'jot' = O'N'
where N' is the vector whose elements are N'l' N~, oo.,and the elements of the matrix n' are defined in Eq. (41); the solution to Eq. (58) is N'(t') =
I
j
exp(Ajt')Lej[RejN'(t'
= O)]
(59)
where the Aj, Lej and Rej are the eigenvalues, left (column) and right (row) eigenvectors of n'. The initial conditions N'(t' = O)are determined from Eq. (42) using the values of the Ni obtained as described above. Solution of Eq. (59) thus requires a single numerical eigenvalue determination for a comparatively small matrix (e.g., a 10 x 10 matrix for ñ = 3). Sd' SIn and S.x are then found from Eqs. (43-45). The next step is the evaluation of the N7. These are obtained by writing Eq. (48) in matrix form, as in Eq. (58), carrying out the eigenvalue evaluation, and then determining Ni from the equivalent of Eq. (59). The initial conditions N7(t', t" = O) are found from Eq. (49) using the results obtained in N;(t') computation. Specifically, we expand Eq. (59) to give
N;(t')=
Ij a;j exp(Ajt')
where
Im Le;m(pNm-1
a;j = Re;j
+ mfNm)
Re;j and Le;m'being tbe ith components of the jth right and mth left eigenvectors of n' (corresponding to Aj), and Ni being the above-mentioned steady-state solutions of the Smith-Ewart equations. Writing Eq. (48) in matrix notation, we have oN"jot" = n"N" whose solution is written using the eigenvalue expansion as N;'(t', t") =
Ij a;j exp(Ait")
(60)
the Aj being the eigenvalues of n". The a;j depend on t', and one finds that Eq. (60) may be rewritten as N;'(t', t") =
Lj LI bijl exp().;t'
+ Ait")
Gottfried Lichti el al.
130
where b¡jl
= Reíj L Le;;'lpaí.m-l m
+ (m - l)faím]
from Eq. (49). Finally, substituting into Eq. (50),one finds Sbc(t., M) = 2cc
L LL {b¡jl[exp(tAjt') -
¡;>2
j
exp(l.ít')]/[Aj- 2Aí]}
1
Some typical resu"lts found using the above formulas are shown in Fig. 11, where the MDS from a combination-dominated high ñ system are shown (ñ=1.72, obtained with p=0.5sec-1, cc=O.lsec-l, k=Cd= f = O) and, for comparison, a combination-dominated low ñ system (ñ = 0.51,using p = 0.5 sec-1, Cc= 50 sec-l, k = Cd= f = O).Note that the MWDs have been normalized, and for cIarity of graphical presentation that for ñ = 0.51 has been re-scaled by a factor of t. The pronounced difference between Sbc for ñ
= 0.51
and 1.72 is a dramatic
illustration
of the effects of
compartmentalization, a point amplified in the following section. Note too that the polydispersity
ratio P for: ñ
= 0.51
is greater than for ñ
= 1.72.
This
0.04
(ñ
=
0.51 )
0.03
~
'" I
(ñ=1.72)
~ 0.02
<11 '"
o ~ ~ 0.01
o O
5 GROWTHTIME (sec)
10
Fig. 11. Comparison of instantaneous MWD for combination-dominated systems (where S = Sbc) with ñ = 0.51 and 1.72, assuming p = 0.5 sec-I, k = Cd= f = O, with Cc= 50 sec -1 and 0.1 sec -1, respectively.
131
3. The Particle Size and Molecular Weight Distributions occurs even though the MWD for ñ broader than that for ñ
= 0.51.
= 1.72
appears from Fig. 11 to be
This highlights the fact that Pis a measure
of relative, rather than absolute, broadness. 3. Polydispersity Ratios It will be recalled that the polydispersity ratio P, defined in Eq. (35), gives a compact description of the MWD. It is instructive to compare values of P computed from bulk and solution MWD theory with equivalent values of P for a compartmentalized system, Le., from the theory developed in Sections n,D,l and 2. As stated in Section n,B,l, for bulk or solution polymerization, Pis 2 for a system dominated by transfer or disproportionation but 1.5 for domination by combination. For compartmentalized systems P may be computed analytically from the expressions given in Sections n,D,l and 2. For the transfer- and exit-dominated system shown in Fig. 8, it is found that P = 2.0. This result shows that compartmentalization does not alfect the MWD of polymer in transfer-dominated systems, vis-a-vis their bulk/solution counterpart. Briefly, the reason for this is that the chain-stopping mechanism does not involve free radicals other than those on the growing chain, and so compartmentalization has no elfect. For the combination-dominated compartmentalized system shown in Fig. 9, the polydispersity ratio is found to be 1.9. Here it can be seen that compartmentalization has a significant elfect, this value for P being appreciably greater than the bulk value of 1.5. Thus, for compartmentalized combination-dominated systems the MWD is significantly broader than in the equivalent bulk system. In the disproportionation-dominated system of Fig. 10, P = 2.2, showing again a significant broadening
compared
with the bulk value of P
= 2.
It is particularly informative to compute P as a function of ñ for combination-dominated and disproportionation-dominated systems (note incidentally that 0.5 is the lower limit of ñ in such a system). It will be seen
. that
when ñ;(; 2, the compartmentalized
system is indeed
a "minibulk"
system, with compartmentalization elfects becoming more pronounced as ñ becomes smaller. The P versus ñ results shown in Figs. 5 and 6 were obtained by fixing p and systematically varying either Cc(Fig. 12) or Cd(Fig. 13). The values of P were obtained from the MWD expressions given in Sections n,D,l (valid for ñ < 0.7) and n,D,2 (valid for any ñ). Figure 12 shows P versus ñ for a combination-dominated system, obtained
by varying Cc and with p
= 1 sec-1.
This type of plot was first
presented by Katz et al. (1969), whose work in this area will be reviewed in Section n,E,2. We show P computed both from the zero-one-two analytic
132
Gottfried Lichti et al. 2.0 + + +
"c: ~ v 1.5 '"'-
---
----
"~
~ v
1.0 0.5
1.0
1.5
ñ
2.0
Fig. 12. Plot of polydispersity ratio P = (Mw>/(Mn>, as function of ¡¡ for system where termination is by combination alone. + zero-one-two system; - complete analysis. p = l sec - 1, k = 1 = Cd = O,CC varied.
4.0
3.0
2.0
1.0 0.5
--------------
1.0
ñ
1.5
2.0
Fig. 13. Plot of polydispersity ratio, P = (Mw>/(Mn>, versus ñ for system where termination is by disproportionation alone. + zero-one-two system; - complete analysis. p = I sec-I, k =1= '.c = O,Cdvaried.
133
3. The Particle Size and Molecular Weight Distributions
formulas and from seminumerical formulas of Section 11,0,2, so as to show the validity range of the former (i.e., ñ < 0.7). Figure 12 shows that in the totally compartmentalized limit (ñ = 0.5), P approaches 2, as shown above for the MWO of Fig. 9. As foreshadowed above, the transition from P = 2 (compartmentalized limit, for small ñ) to P = 1.5 (bulk limit, for large ñ) occurs in the range 0.5 ;5 ñ ;5 2. Figure 13 shows the analogous P versus ñ plot for a disproportionationdominated system, found by putting p = 1 sec-1, k = f = Cc= O,and letting Cdvary. In the totally compartmentalized limit (ñ = 0.5),P = 4. This can be understood as follows. When ñ = 0.5, only state Oand state 1 particles are present: the entry of a second free radical causes instantaneous termination. This termination leaves a contribution to the MWO with P = 2, as in the combinatioil-dominated system. However, with a disproportionation mechanism operative, the entrant free radical leaves in addition a low moleeular weight species for each longer dead chain formed. These two contributions to the MWO add, to halve the number-averaged molecular weight, leaving the weight-averaged molecular weight essentially unaffected. Thus, the overall P changes from 2 to 4. The P versus ñ curves computed in Figs. 12 and 13 were for systems where no desorption occurred (k = O)and thus gave a lower limit of 0.5 to ñ. By choosing a nonzero value for k, values of ñ anywhere between O and 00 can be obtained. Figure 14 shows the P versus ñ curve obtained 4.0
A ¡;;;
3.0
~ v ""A ~
~V
-------
2.0'~-------
1.0
0.5
i'i
1.0
1.5
Fig. 14. Plot of polydispersityratio P = <Mw>I<Mn>versus ñ for system where chain stoppage is by exit and disproportionation. k = 10-3 sec.l, Cd= 10-1 sec-I, f= Ce= O, O varied.
Gottfried Lichti et al.
134
for a system showing disproportionation and exit: k = 10- 3 sec-1, Cd= 10-1 sec-1,f = O= cc, where p is varied systematically. It is seen that P passes through a distinct maximum at ñ = 0.5 (for k = O,the maximum value of P is 4, as in Fig. 13). For ñ ~ 0.5, the system is exit-dominated (P ~ 2), whereas for ñ ~ 0.5, the bulk value of P is equal to 2 for a disproportionation-dominated system. E.
Alternative Forinulations 01 the MWD
We have reviewed (above) a complete theory of the MWD in an emulsion polymerization (in the absence of long-chain branching). We now relate this to alternative formulations. 1. Zero-One Systems In these systems (Section I,C,l,a) Gerrens (1959) recognized that if combination is the only chain-stopping event, then the number-average molecular weight (Mn)is inversely proportional to the entry rate coefficient: Mn IXp-l
(61)
This result may indeed be proved by taking the appropriate limits (k = O, f = O, p ~ e) to the results discussed in Section n,D,1. Gardon (1968a) extended this concept to make allowances for p varying as a function of the fraction conversion of monomer to polymer in Interval n (arising from the increase in particle size). Gardon however concluded incorrectly that, in such a system, 1 < p < 1.33. Gardon's error lay in his assumption that the instantaneous MWD is perfectly monodisperse (P = 1),Le., that all chains formed at a given instant have the same molecular weight, this being given by Eq. (61). In fact, this assumption does not hold, and P has, for example, a value in the range 1.5 ~ P ~ 2 for domination by combination. Since P at any instant exceeds 1.5, the overall P must also exceed 1.5. Lin and Chiu (1979) developed a theory for the MWD in a zero-one system that correctly predicts (where M is continuous rather than discrete) the free-radicallifetime distribution N'1 leading to a value of 2 for P. The formalism of Lin and Chiu involves calculating the number of chains containing m monomer units. Their final results involve sequence summations over the range 1 ~ m ~ oo. 2.
Formulatíon of Katz et al.
The first comprehensive theory of the MWD in an emulsion polymerization system was given by Katz et al. (1969). These authors considered a monodisperse system in which the only mechanisms operating were freeradical entry, chain propagation, and bimolecular termination by combination. They defined a distribution function Pi(te,MI, M2, ..., Mi), as the
135
3. The Particle Size and Molecular Weight Distributions
relative number of particles in state i at experimental time te containing one growing chain of molecular weight MI, another of M2, and so on, with MI > M2. The equations that describe the evolution of the p¡ are
fJPifJt.= -a
I
j<'
+ 2c
fJP,lfJMj - [p + i(i -1)c]P, + pP'-1t5M;.o
I I
'<j~'+2
ff
p,+2(MI, oo.,M" .oo,Mj, ..., M'+2) dMj dM,
(62)
Here a is defined in Eq. (30). The Kronecker t5 term gives the source terms for each P,. These coupled partial integrodifferential equations in the variables t, MI, oo.,Mn were derived by population balance applied to each microscopic process. Since bimolecular termination by combination is the only chain-stopping mechanism considered, Sbc is the only contribution to the instantaneous MWD; this is given by
f ~j~
Sbc(t., M) = 2ccP~
x t5(Mj + M,
P,(te, MI, oo.,M¡}
-
(63)
M) dMI, oo.,dM,
Here t5 is the Dirac t5 function and p is a normalizing factor. The inner summation in Eq. (63) accounts for combination between all possible pairs of free radicals. Equation (63)was derivedassumingthat the polymerization is occurring in the steady-state regime. Because of the complexityof these equations, Sbcmust be evaluated by numerical means. Katz et al. used the method of moments to generate a measure of the MWD called the cumulative distribution of the tail, defined . as
F(M)
=
f: Sbc(M)dM
(64)
The development of Katz et al. properly encompasses all compartmeIltalization effects in a system where combination is the only chain-stopping mechanism. It has been shown (Lichti et al., 1980) that the equations in Eq. (62) are equivalent to the evolution equations for N; and N;' given in Section n,e,
with the restriction
that k
= f = Cd = O. The
P, and N;(t., t')
and N;'(t., t', t") are related by N;(t.
-
Mrla, Mrla) =
f
j~.i P,(t., MI, ..., Mj-I'
M.. Mj+l' oo.,M,)
dMI, oo.,dMj-1dMj+l' oo.,dM, N;'(t. - Mrla, (Mr - Ms)la,Msla) =
fI L
i~ 1
(65)
P,(t., MI, .oo,Mj-I'
l<j~i
M.. Mj+l' dMj+l'
oo.,M'-I,
oo.,dM'-1
M.. MI+I, dM,+I'
oo.,M,) dMI, .oo,dMj-1
.oo,dM,
i ~ 2
(66)
136
Gottfried Lichti el al.
Plots of the type shown in Fig. 12 (P versus ñ) were first given by Katz et al. Their treatment, however, suffers from a number of limitations. These are (i) the numerical labor involved in generating the moment expansion, (ii) the imperfect resolution involved in generating the cumulative distribution [Eq. (64)] rather than the fuIl distribution, and (iii) the neglect of exit, transfer, and bimolecular combination by disproportionation. Point (ii) may be iIIustrated as foIlows. Consider a combination-dominated system in two limits: the fuIly compartmentalized case of ñ = 0.5, when one has Sbcex exp(-ca'), and the bulk case, where ñ = 00, when one has Sbc ex t exp( - at'), where a is a parameter proportional to ñcc' Figure 15
e ~ ~
z o ¡::
=> m ir 1(J)
e w >
~
~ =>
~
=> (,)
o
2
4
GROWTH TIME
Fig. 15.
Plot
combination-dominated
curve 2 ñ = oo.
of instantaneous
MWD
system, as functions
(S) and
cumulative
of growth time (arbitrary
distribution
(F) for
units). Curve 1 ñ
= 0.5;
3. The Particle Size and Molecular Weight Distributions
137
shows plots of Sbcand F [from Eq. (64)] for these two limits, with a = 2. It can be seen that plots of the MWD, Sbc' show a pronounced qualitative ditTerence between the compartmentalized and bulk limits. However, the equivalent plots of F, the cumulative distribution of the tail, are qualitatively similar, and only show smalI quantitative ditTerences.This is because the greatest ditTerencesbetween the Sbcfor the bulk and compartmentalized limits occurs at smalI values of M (or t'), to which F(M) is insensitive.
3.
Formulation of Min and Ray
Min and Ray (1974) have presented a theory in which the MWD and PSD evolutions are considered together. The proposition that these quantities may be evaluated separately is considered in Section III of ~his chapter. The treatment of Min and Ray is applicable to a system which is mohodisperse in volume if one omits both particle nucleation terms and terms involving O/OV,and if the volume dependences of any rate coefficients are ignored. For such a system, Min and Ray define a function fm(i, te), the distribution of latex particles in state i at experimental time te that contain a growing radical with m monomer units. This is directIy related to the singly distinguished distribution function Ni(te, t') by
Ni(te
-
t', t') = fm(i, te)
(67)
where t' = mMo/a, where Mo is the molecular weight of monomer. The evolution of fm(i, te) is given by simple coupled ditTerential equations in te, one for each m. There would typicalIy be thousands of such equations; this is to be compared wi'th the sma:lI number of simple coupled ditTerential equations required to evaluate Ni. The formulation of Min and Ray alIows for exit, in the form of permitting desorption of growing chains of any length, rather than the exit of smalI oligomers alone permitted in the general formulation given here. This assumption of Min and Ray does not relate desorption to any chaintransfer evento If growing chains of any length could d~sorb, it would seem as likely that dead chains would also desorb; this possibility is however not encompassed within Min and Ray's formalismo Their formalism in addition has no analog of the doubly distinguished distribution functions Ni. Instead they approximate the contribution to the MWD by combination by
a convolution expression involving products of the fm and indeed acknowledge that this assumption is open to question. It was shown in Section II,C,2 by use of a particular example that such a product approximation is
138
Gottfried Lichti et al.
invalid. We now give a more specific illustration. Consider the correct form for Sbcin a zero-one-two system:
i
it'
Sbe(te' t' ) =
o
" N"2e' (t t' - 2t" , t" ) dt
(68)
with the equivalent convolution expression of Min and Ray, which we denote Sbc:
sbe(t e' tI) =
tO
pio
NI 2e' (t
tI
-
t" ) N' 2e' (t
t") dt"
Here the normalization constant pis. chosen so that Figure 16 shows Sbc and Sbc for p
=
~~
JSbcdt' = J
SbC
dt'.
1 sec-1, Cc = 10 sec-1, k = f = Cd = O
(giving ñ = 0.55). It is clear that the product assumption is both quantitativeiy and qualitatively inaccurate. Indeed, the limiting , .value of the
2
NI o ~ ~
~
o 31 ~
2
3
4
EQUIVALENT GROWTH TIME (sed Fig. 16. Comparison of predictions of the formalism of (1) Min and Ray (1974) with that of (2) Lichti et al. (1980) for the MWD of a combination-dominated system assuming p = 1 sec -1, C, = 10 sec -1 and k = f = Cd = O. Ordinate cissa is growth time (sec).
is instantaneous
MWD
(sec - 2), ab-
3. The Particle Size and Molecular Weight Distributions
polydispersi"ty ratio P as ñ approaches 0.5 is P correct value of P = 2. F.
= 2.5 for Sbc, rather
139 than the
Experimental Determination 01 the MWD
We now briefly consider experimental methods of determining the MWD, in order both to test and to apply the theory. In relating theory and experiment, it is clearly insufficient to consider a single measure of the MWD alone, e.g., the number average, since interpretation of a single datum is prone to ambiguities. Hence, experimental techniques that only give such a datum (e.g., light scattering) are inadequate for the present purpose. Even the polydispersity P, being the weight-to-number-average ratio, is ambiguous unless it can be established unequivocally that the MWD is monomodal, and even then different-shaped MWD curves can give similar values of P. It is clear that a measure of the full molecular weight variation of the MWD is necessary to pro vide useful information. The best procedure at present for obtaining this appears to be gel permeation chromatography (GPC). As this is relatively new technique, full MWD data are sparse. Friis and Hamielec (1975) have used GPC to study the MWD development in vinyl acetate and vinyl chloride emulsion polymerizations. For these monomers, the main chain-stopping mechanism is thought to be transfer, and so the compartmentalized nature of the system is relatively unimportant. These workers found that the MWDs produced at early times, where branching reactions are unimportant, have a P value close to 2, as expected for transfer-dominated reactions. A careful experimental study of the MWD produced in a highly compartmentalized system has been carried out by James and Piirma (1976) and Piirma et al. (1975). Ah ab initio emulsion polymerization was used which produced particles small enough ('" 75 nm unswollen radius) to ensure low ñ values in the Interval 11 part of the reaction. P was found to be constant during Interval 11, with a value somewhat in excess of 2. The fact that P (which as measured experimentally is of course from the cumulative rather than the instantaneous MWD) remains constant implies that the P of the instantaneous MWD is also close to 2 throughout this interval. This value of P may be rationalized on the assumption that either transfer or combination (in the ñ = 0.5, i.e., compartmentalized limit) are the main chainstopping mechanisms. Piirma et al. showed that in fact transfer to monomer was dominant, since the number-average molecular weight observed corresponded closely to that predicted from transfer domination. This result is interesting, in view of the fact that the main chain-stopping mechanism for styrene solution or bulk polymerization is combination. This result is thus a
140
Gottfried Lichti et al.
clear example of how compartmentalization can change the dominant chain-stopping mechanism. This is because free radicals inside the growing latex particles polymerize in isolation for periods of time sufficiently long to make the MWD transfer limited. The work of James and Piirma and of Piirma et al. is important because, inter alia, it highlights the role of several commonly used surfactants (e.g., Triton X) as transfer agents. This discovery complicates the interpretation of many experimental results reported in the literature. Included in this category is the rise in molecular weight with conversion in Interval 11,used by Grancio and Williams (1970) as evidence for the core-shell model of latex particle morphology. Lin and Chiu (1979) have reported measurements of P as a function of time for an ab initio styrene emulsion polymerization. They also found that P was slightly in excess of 2 for a considerable part of the reaction, but their actual molecular weight averages were much lower than those of Piirma et al. (1975). This suggests that their surfactant may have been acting as a chain-transfer agent. De Graaf and Poehlein (1971)'have measured the MWD of styrene in a continuous stirred-tank reactor. A wide range of particle sizes were present, and thus interpretation of the data is hindered by an inadequate knowledge of the size dependence of the various rate parameters. However, the values reported for the average molecular weights suggest again a transferdominated process; this is also consistent with the value obtained for P which was close to 2, for a variety of conditions. The influence of particle size on MWD has been investigated by Morton et al. (1954). They showed that the average molecular weight of the polymer produced was insensitive to the latex particle size. This is consistent with the molecular weight being dominated by chain transfer to monomer, a conclusion that holds irrespective of any differential swelling of particles of different sizes. The foregoing experimental review includes the major studies in which polydispersity ratios (as distinct from average molecular weights) were reported. The experiments are somewhat piecemeal in nature, dealing with systems for which reliable estimates of the rate coefficients which govern the MWD (p, etc.) were not available. It would clearly be advantageous, in terms of mechanistic understanding, to carry out MWD measurements on systems that are well characterized kinetically. The simplest experiment to interpret would be on a seeded system (thereby obviating problems as to the MWD formed during particle nucleation, as will be shown later), employing a volume monodisperse latex with polymerization being carried out in lnterval 11 under steady-state conditions and without significant particle growth during the course of polymerization. Methods have been established
3. The Particle Size and Molecular Weight Distributions
141
for obtaining the various rate coefficients klP p, k, kp, and e from kinetic studies (e.g., Hawkett et al., 1980, 1981). The theoretical evaluation of the MWD is then trivial. For systems with a significant polydispersity in volume, the MWD can readily be calculated using Eq. (27), given the volume dependence of the various rate coefficients; however, it was pointed out above that uncertainties in these quantities make an unambiguous relation between theory and experiment impossible in such an experiment. Experiments on a volume-monodisperse Interval III system could again be readily compared with theory, using known values of the time variation of CM, etc. (obtained from the kinetics), and integrating the instantaneous MWD over time. The ideal seeded experiment would be where seed Iatex particles are prepared in which the MWD of the seed is significantly different from that formed during subsequent seeded polymerization. The instantaneous MWD formed at early times could then be estimated directly. Seed latexes of different sizes could be used to probe the effect of compartmentalization (we stress again that if the system is transfer-dominated, the MWD of formed polymer should be independent of particle size). The experimental strategy outlined above would give a unified set of rate parameters to describe the kinetics, MWD, and PSD. If no such consistent set could be found, new mechanisms may pro ve to be important. For example, aqueous-phase termination, which is not usually incorporated in MWD theories, would give rise to extensive low molecular weight fragments, which would significantly influence the MWD if these fragments are subsequently incorporated into the latex p~rticles.
111. Separa~iIity of 1YIWDand PSD Most of the theory surveyed in this chapter is based on the premise that, although the MWD and PSD of a system are governed by the same fundamental set of rate coefficients (p, klP kp, etc.), it is nevertheless possible to decouple the computation of these quantities. This is required, for example, for the validity of Eq. (27). The basis of this premise '¡s the separation of time scales over which the various proc~sses governing these quantities occur. This concept was first introduced by O'Toole (1969). We now consider its validity. It is frequently the case that the time required for a Iatex particle to increase its volume by a measurable amount (say by 10%) is large compared with (i) the time taken for the growth of a polymer chain and (ii) the time taken for the distribution of free radicals inside the latex particles to reach a steady-state value (for a given particle volume). This separation of time
142
Gottfried Lichti el al.
scales is plainly invalid at very early reaction times, when most of the volume of the partic1e may be that of a single chain. However, since latex partic1es usually contain many individual chains, the time scale separability assumption for volume versus chain growth [i.e., (i) above] is c1early relevant to mO$tof the growth process. We now consider the second time scale separability, (ii) above. Again, this will obviously break down at early times, but again will be valid for most of the polymeriz.ation. This occurs for three reasons. 1. As partic1es increase in volume, a fixed percentage increment of growth takes longer to achieve. 2. With increasing time, the system will attain and maintain its steady state in the distribution of free radical s in all partic1es, with the possible exception of growth during a particularly rapid Trommsdorff gel effect. 3. The PSD becomes smoother with the passage of time (e.g., Fig. 1),so that partic1e growth [which disturbs steady state through the o/ay term in Eq. (8)] becomes less significant. . Since the separate time scale aondition is c1early valid for most of the polymerization process, one may say that each polymer chain is formed inside a partic1e of unchanging size, wherein all rate coefficients are constant and the distribution of free radicals has its steady-state value, for each volume V. Any residual effect of the PSD on the MWD would reside presumably in the effects of the PSD on the kinetic parameters (e.g., p, e, and to a lesser extent k). Conversely, the MWD would possibly influence the PSD through its effects on the swelling of the partic1es by the monomer; the effect, if it exists, is likely to be small.
IV. Conclusions The theoretical tools required to describe the evolution of the MWD and PSD of an emulsion polymerization, in terms of a consistent set of rate coefficients for the various microscopic processes involved, are fairly well developed. Whereas chain branching (transfer to polymer) has yet to be inc1uded, it is likely that bulk theories for this process (Bamford and Tompa, 1954) can be readily modified to the emulsion polymer case. Although the general theory is well developed, a real understanding of the details of the processes involved is limited by the paucity of unambiguous experimental results to enable theory to be tested, modified, and applied.
143
3. The Particle Size and Molecular Weight Distributions Acknowledgments
The support of the Australian Research Grants Committee, and of an Australian Institute for Nuclear Science and Engineering postdoctoral fellowship for GL, are gratefully acknowledged.
References Ballard, M. J., Gilbert, R. G., and Napper, D. H. (1981). J. Polymer Sci. PoI. Phys. Edn., (in press). . Bamford,C. H., and Tompa, H. (1954).Trans. Faraday Soco SO, 1097-1115. Camahan, B., Luther, H. A., and Wilkes, J. O. (1969). "Applied Numerical Methods." Wiley, New York. Corio, l., Mara, L., and Salvatore, O. (1979). Makromol. Chem. 180,2251-2252. De Graaf, A. W., and Poehlein, G. W. (1971). J. Polym. Sci. Parl A-2 9, 1955-1976. Eckhoff,R. K. (1967).J. Appl. Polym. Sci. 11, 1855-1861. Ewart, R. H., and Carr, C. 1. (1954). J. Phys. Chem.58, 640-644. Flory, P. J. (1953). "Principies ofPolymer Chemistry." Comell Univ. Press, 1thaca, New York. Friis, N., and Hamielec,A. E. (1975).J. Appl. Polym. Sci. 19,97-113. Friis, N., Goosney, D., Wright, J. D., and Hamielec, A. E. (1974). J. Appl. Polym. Sci. 18, . 1247-1259. Gardon, J. L. (l968a). J. Polym. Sci. Parl A-I 6, 665-685. Gardon, J. L. (1968b). J. Polym. Sci. Parl A-I 6, 687-710. Gerrens, H. (1959).Forlschr. Hochpolym.Forsch. 1, 234-328. George, M. H. (1967). /n "Vinyl Polymerizations" (G. E. Ham, ed.), Vol. 1, part 1, p. 165. Dekker, New York. Grancio, M. R., and Williams, D. J. (1970). J. Polym. Sci. Parl A-I 8,2733-2745. Harkins, W. D. (1945).J. Chem. Phys. 13, 381-382. Harkins, W. D. (1946). J. Chem. Phys. 14,47-48. , Harkins, W. D. (1947). J. Am.Chem.Soco69, 1428-1444. Harkins, W. D. (1950). J. Polym. Sci. 5, 217-251. Hawkett, B. S., Gilbert, R. G., and Napper, D. H. (1980).J. Chem.SocoFaraday Trans. /76,
1323-1343. .
.
Hawkett, B. S., Napper, D. H., and Gilbert, R. G. (1981). J. Chem. Soco Faraday Trans. / (in press). James, H. L., and Piirma, l. (1976)./n eds.), pp. 197-209. American
"Emulsion
Polymerization"
(1. Piirma and J. L. Gardon,
Chemical
Society, Washington, D.C. Katz, S., Shinnar, R., and Saidel, G. M. (\969). Adv. Chem. Ser. 91, 145-157. Kerker, M. (1969). "The Scattering of Light." Academic Press, New York.
Lansdowne, S. W., Gilbert, R. G., Napper, D. H., and Sangster, D. F. (1980). J. Chem. Soco Faraday Trans./76, 1344-1355. Lichti, G., Gilbert, 1957-1971.
R. G., and Napper,
D. H. (1977). J. Polym. Sci. Polym. Chem. Ed. 15,
Lichti, G., Gilbert, 1297-1323.
R. G., and Napper,
D. H. (\980).
Lichti, G., Hawkett,
B. S., Gilbert,
R. G., Napper,
Sci. Polym. Chem. Ed. 19, 925-938.
J. Polym. Sci. Polym. Chem. Ed. 18,
D. H., and Sangster,
D. F. (1981). J. Polym.
144
Gottfried Lichti el al.
Lin, C. c., and Chiu, W. y. (1979). J. Appl. Polym. Sci. 23, 2049-2063. Min, K. W., and Ray, W. H. (1974). J. Macromol. Sci. Rev. Macromol. Chem. C 11, 177-255. Min, K. W., and Ray, W. H. (1978). J. Appl. Polym. Sci. 22, 89-112. Morton, M., Kaizerman, S., and Altier, M. (1954). J. Colloid Sci. 9, 300-312. Nagy, D. J., Silebi, C. A., and McHugh, A. J. (1980). In "Polymer Colloids II" (R. M. Fitch, ed.), pp. 121-137. Plenum Press, New York. O'Toole, J. T. (1969). J. Polym. Sci. Part C 27, 171-182. Piirma, J. Kamath, V. R., and Morton, M. (1975). J. Polym. Sci. Polym. Ed. 13,2087-2102. Pis'men, L. M., and Kuclianov, S. I. (1971). Vysokomol. Soedin. A13, 1055-1065. Schmidt, E., and Biddison, P. H. (1960). Rubber Age 88, 484-490. Schmidt, E., and Kelsey, R. H. (1951). Ind. Eng. Chem. 43, 406-413. Shaw, D. J. (1970). "Introduction to Colloid and Surface Chemistry." Butterworths, London. Singh, S., and Hamielec, A. E. (1978). J. Appl. Polym. Sci. 22, 577-584. Smith, W. V., and Ewart, R. H. (1948). J. Chem. Phys. 16,592-599. Stevens, J. D., and Funderburk, J. O. (1972). Ind. Eng. Chem. Process Res. Dev. 11, 360-369. Sundberg, D. C., and Eliassen, J. D. (1971). In "Polymer Colloids" (R. M. Fitch, ed.), pp. 153-161. Plenum Press, New York. Thompson, R. W., and Stevens, J. D. (1977). Chem. Eng. Sci. 32: 311-322: Ugelstad, J., and Hansen, F. J. (1976). Rubber Chem. Tech. 49, 53Cr609. Watterson, J. G., and Parts, A. G. (1971). Die Makromol Chem. 146, 11-20. Wood, D., Lichti, G., Napper, D. H., ~nd Gilbert, R. G. (1981), to be published.
4 Theory 01 Kinetics 01 Compartmentalized Free-Radical Polymerization Reactions D. C. Blackley
1. Introduction. A. Definitionsand Introductory Concepts B. Practical Significance of the Theory C. Scope of Chapter . 11. Reaction Model Assumed A. Description. B. Constancy and Uniformity of Monomer
111.
IV. V.
VI. VII. VIII.
Concentration within Reaction Loci C. Mechanism of Fundamental Processes; Influence of Locus Size , The Time-Dependent Smith-Ewart Differential Difference Equations; Methods Available for Their Solution A. Derivation . B. Methods Available for Their Solution . Solution for the Steady State Solutions for the Nonsteady State . A. Case in which Radical Loss 15 Predominantly by First-Order Processes B. Case in which Generation of New Radicals Ceases . C. Approximate .. Poissonian" Solution to the General Case. D. Other Approximations Predictions for Molecular-Weight Distribution and Locus-Size Distribution . Theory for Generation of Radicals in Pairs within Loci . List of Symbols. References .
146 146 147 149 149 149 151 153
156 156 160 164 167 167 172 176 177 183 185 187 189
145 EMULSJON POL YMERIZA TION Copyright ~ 1982 by Academic Press, Inc. AII rights 01 reproduction in any lorm reserved. ISBN 0-12-556420-1
146
D. C. Blackley
l. Introduction A.
Definitions and Introductory Concepts
By the term "compartmentalized free-radical polymerization reaction" is meant a free-radical polymerization reaction that is taking place in a large number of separa te reaction loci. These loci are dispersed in a contiguous external phase. They are "separate" from each other in the sense that material contained within one particular locus is presumed to be capable of transferring to another locus only insofar as it is capable of being lost from the first locus to the external phase, and then of being subsequentIy absorbed by the second locus from the external phase. The number of separate reaction loci is presumed to be "large" in the sense that it is at least of the same order of magnitude as the number of propagating free radicals present within the reaction system as' a whole. It therefore follows that the average number of radicals per single reaction locus is small; it is convenient to regard 10 as the absolute upper limit, 5 as the usual upper limit, and 0.01-2 'as the range that covers many reaction systems of practical significance. The term "compartmentalization" as applied to free-radical polymerization reactions of the type considered here seems to have first been introduced by Haward (1949). The mechanism of the polymerization reaction is presumed to be essentially that of a homogeneous bulk or solution free-radical polymerization. The concern is exdusively with the polymerization by double-bond opening of carbon compounds that contain at least one carbon-carbon double bond. The reactive species that propagates to produce the polymer chain is a free radical formed by opening of the n-bond of the carbon-carbon double bond. The basic steps of the polymerization reaction are initiation, propagation, termination (by various means), and various transfer reactions. The structure of the polymer produced is determined by the balance of the propagation, termination, and transfer reactions. Whereas the polymerization mechanism is essentially that of homogeneous bulk or solution polym~rization, there are significant differences attributable to compartmentalization as the term has been defined above. The most important of these is that, unlike free-radical polymerizations taking place in a homogeneous medium, there are physical barriers that prevent interaction between the various propagating radicals present in the reaction system at a given time. To a large extent, the propagating radicals are physically isolated from each other, each very small group of radicals being provided with its own reaction vessel. This is, in fact, the significance of the adjective "compartmentalized." An important consequence of the compartmentalization of the propagating radicals is that opportunities for
4.
Kinetics of Compartmentalized
Free-Radical Polymerization Reactions
147
the mutual termination of radicals are reduced relative to the case of a similar polymerization occurring in a homogeneous medium at the same overall concentration of propagating radicals within the reaction system as a whole. The model for the reaction system will be considered in detail in Section 11.However, it is convenient to note here that, in principie, the free radical s that initiate the polymerization may be generated either within the external phase (external initiation) or within the reaction loci themselves (internal initiation). Whereas very brief reference will be made at the conclusion of this chapter to reaction systems of the latter type, the concern here will be almost exclusively with reaction systems of the former type. Insofar as the initiating radicals are generated exclusively within the external phase (and therefore ha ve to be by some means acquired by the loci by absorption from the external phase), we have a further important distinction between homogeneous and compartmentalized reactions. In the latter case, the processes that lead to the generation of the initiating radical s are physically isolated from the propagation, termination, and transfer reactions. One minor consequence of this is that transfer-to-initiator reactions may be virtually eliminated in the latter case. The primary objective of the theory of compartmentalized free-radical polymerization reactions is to predict from the physicochemical parameters of the reaction system the nature of the "Iocus population distribution." By this latter term is meant collectively the proportions of the total population of reaction loci which at any in~tant contain O,1,2,. ", i,... propagating radicals. The theory is concerned with the prediction of these actual populations and also with such characteristics of the locus population distribution as the average number of propagating radical s per reaction locus and th~ varian~e of the distribution of locus populations. .,
B.
Practical Significance of the Theory
Apart from intrinsic interest, the theory of compartmentalized freeradical polymerization reactions is of importance primarily because it is believed that ITIost of the polymer which is formed in the course of an emulsion polymerization reaction is formed via reactions of this type. The general shape of the conversion-time curve for many emulsion polymerization reactions suggests (see Fig. 1) that the reaction occurs in three more-orless distinct stages or "intervals." The first of these, the so-called Interval 1, is interpreted as the stage of polymerization in which the discrete reaction loci are formed. In the second and third stages - Intervals 11 and 111- the polymerization is believed to occur essentially by compartmentalized freeradical polymerization within the loci which were formed during Interval l.
148
D. C. Blackley
c. o
.~ Q)
> e o <>
INTERVAL m
time
Fig.1.
Conversion-time
curve for typical unseeded emulsion
polymerization
reaction.
The feature that distinguishes IntervallI from Interval 111is that monomer droplets are present as a separate phase during the former only. The theory also has relevance to the so-called "seeded "emulsion polymerization reactions. In these reactions, polymerization is initiated in the presence of a "seed" latex under conditions such that new particles are unlikely to formo The loci for the compartmentalized free-radical polymerization that occurs are therefore provided principally by the particles of the initial seed latex. Such reactions are of interest for the preparation of latices whose particles have, for instance, a "core-shell" structure. They are also of great interest for investigating the fundamentals of compartmentalized freeradical polymerization processes. In this latter connection it is important to note that, in principIe, measurements of conversion as a function of time during nonsteady-state polymerizations in seeded systems offer the possibility of access to certain fundamental properties of reaction systems not otherwise available. As in the case of free-radical polymerization reactions that occur in homogeneous media, investigation of the reaction during the nonsteady state can provide information of a fundamental nature not available through measurements made on the same reaction system in the steady state.
4. Kineticsof Compartmentalized Free-Radical PolymerizationReactions 149. C.
Scope 01 Chapter
Detailed consideration will first be given to the nature of the reaction model assumed. Such consideration is important in order to gain an appreciation of the limitations of the theory that is subsequently developed. This will be followed by derivation of the equations that govern the behavior of compartmentalized free-radical polymerization reactions and a discussion ofmethods that are available for their solution. This will be followed by brief consideration of the solution of these equations for reaction systems that have attained a steady state. This part of the subject is not recent and will not be dealt with in detail. The main part of the chapter will not be concerned with the solution of the equations for reaction systems in the steady state but with those that are approaching it. This aspect of the subject is of relatively recent development. Brief reference will then be made of the evolution of the particle-size and molecular weight distribution during a compartmentalized free-radical polymerization; although this subject is of recent development, it will be dealt with in detail elsewhere in this book. The chapter will conclude with brief reference to reaction systems in which the initiating radicals are generated in pairs within the reaction loci.
11. Reaction Model Assumed A.
Description
The number of reaction loci is assumed not to vary with time. No nucleation of new reaction loci occurs as polymerization proceeds, and the number of loci is not reduced by processes such as particle agglomeration. The monomer is assumed to be only sparingly soluble in the external phase (a typical example is styrene as monomer and water as the external phase), and thus polymerization is assumed to occur exclusively withip the reaction loci and not within the external phase. The monomer is assumed to be present in sufficient quantity throughout the reaction to ensure that monomer droplets are present as a separa te phase, and the rate of transfer of monomer to the reaction loci from the droplets is .assumed to be rapid relative to the rate of consumption of monomer in the loci by polymerization. The monomer concentration within the rea<,:tionloci is then taken to be constant throughout the reaction. This assumption is important if an attempt is made to relate the overall rate of polymerization to the average number of propagating radicals per reaction locus. The assumption will therefore be examined in further detail below.
150
D. C. Blackley
In general, radicals are presumed to be generated in the external phase at a constant rate and to enter the reaction loci at a constant rate. Thus, the rate of acquisition of radicals by a single locus is kinetically of zero order with respect to the concentration of radicals within the locus. The principal concern is with reaction systems that initially contain no free radicals, and therefore in which the rate of polymerization is zero. Then, at a certain instant, which is taken as the zero of subsequent time, radical s begin to be generated in the external phase at a constant rateo It is then required to predict the behavior of the reaction system as it approaches the steady rateo Important exceptions to these generalizations include the following: (i) where the interest is primarily with the steady state rather than with the approach to the steady state; (ii) where the rate of generation of new radicals varies with time, e.g., because of initiator depletion; (iii) where the rate of generation of new radicals in a polymerizing system is suddenly reduced to zero and the interest is in predicting the subsequent decay of the reaction; and (iv) where new radical s are generated in pairs within the reaction loci. Once a radical enters a reaction locus, it is presumed to initiate a chain polymerization reaction which then continues at a constant rate until the activity of the radical is lost. The processes whereby the activity of the propagating radicals is lost from the reaction loci can be classified into two broad types: 1. Processes that are kinetically of first order with respect to the concentration of radicals within the reaction locus. These processes include exit from the locus into the external phase, termination by reaction with monomer within the locus, termination by reaction with adventitious impurities in the locus, and spontaneous deactivation. 2. Processes that are kinetically of second order with respect to the concentration of radicals within the reaction locus. The most important of these processes is bimolecular mutual termination between pairs of propagating radicals within the same reaction lo~us. In attempting to analyze the behavior of reaction systems in the nonsteady sta te, it is generally necessary to make the assumption that radicals lost from the reaction loci by exit to the external phase are not able subsequently to reenter the reaction loci and reinitiate polymerization. They are not, therefore, regarded as being added to the "bank" of radicals in the external phase available for entry into reaction loci. This is undoubtedly a restrictive assumption that cannot be justified rationally. It is unfortunately
an assumption that often has to be made in order for the mathematics describing the behavior of the reaction system to remain tractable. Although some progress has been made in removing this restriction, it
J
4.
Kinetics of Compartmentalized Free-Radical Polymerization Reactions 151
nevertheless remains a general feature of the theory developed for nonsteady state reactions. A further general assumption is that the physicochemical parameters that characterize the rates at which the various processes occur remain constant throughout the reaction. However, as will appe~r subsequently, there is one particular instance where it has been possible to remove this restriction. Important consequences of this restriction are that the polymerj monomer ratio in the reaction loci should not vary significantly as the reaction proceeds, and that the volume of the reaction loci should not change greatIy as a consequence of polymerization. The latter requirement will be most obviously realized in a seed emulsion polYp1erization in which the size of the initial seed is large and the extent of polymerization is small. B.
Constancy and Uniformity of Monomer Concentration within Reaction Loci
There has been much discussion in recent years concerning the question of whether or not, in a reaction system of the type considered in this chapter, the concentration of monomer in the reaction loci is constant as the reaction proceeds and uniform across the reaction locus. Morton et al. (1954) made the reasonable proposal that the equilibrium swelling of polymer partic1es by excess monomer in a system such as is envisaged here is determined by the balance of two factors: (i) the decrease of free energy that accompanies mixing of polymer and monomer and (ii) the increase of interfacial free energy that accompanies the concomitant swelling of the polymer partic1es. Theoretical considerations predict that at equilibrium large partic1es should imbibe more monomer than small partic1es, and that reduction of the interfacial free energy between polymer partic1e and external phase shoulcl lead to increased swelling. Polymer molecular weight is not a significant factor in determining equilibrium imbibition, but the polymer-monomer solution interaction parameter is. Morton et al. (1954) and Allen (1958) have provided experimental evidence to support these predictions, the polymers used being polystyrene and natural rubber, respectively.Further information has been provided by Vanzo et al. (1965) concerning the solubilities of vinyl acetate, vinyl hexanoate, styrene, and benzene in poly(vinyl ,acetate), poly(vinyl hexanoate), and polystyrene latices. Morton et al. (1954) also provided evidencein support ofthe view that, as long as excess monomer is present as a separate droplet phase, the monomer-swollen polymer partic1es remain essentially in the same state of equilibrium imbibition during polymerization as in the absence of polymerization. This implies that the process of diffusion from droplets to polymerization loci occurs rapidly relative to the rate of polymerization, so that the
152
D. C. Blackley
consumption of monomer by polymerization has little effect on the concentration of monomer at the polymerization loci. A further implication is that the concentration of monomer is uniform throughout the polymerization locus. The views summarized in the preceding paragraph were generally accepted without serious challenge for reaction systems for which monomer and polymer are miscible, until Grancio and Williams (1970) proposed that the monomer-swollen polymer particles in a styrene emulsion polymerization are nonuniform, and that in fact they consist of an expanding polymer-rich "core" surrounded by a monomer-rich "shell," the latter being the major locus of polymerization. The "core-shell" model was suggested by kinetic evidence and supported by evidence obtained by examining ultra-thin sections of latex particles by electro n microscopy. These ideas have been further elaborated by Williams (1971), by Keusch and Williams (1973), and by Keusch et al. (1973).Friis and Hamielec(1973)have challengedGrancio and William's interpretation of their kinetic data and have suggested that the observations can be explained by means of a homogeneous particle model in which allowance is made for decrease in the rate coefficient for termination as polymerization proceeds. Napper (1971) has also criticized the core-shell morphology proposed by Grancio and Williams, and has argued in favor of a core-shell morphology of the reverse kind, Le., a particle that comprises a monomer-rich core surrounded by a polymer-rich shell. Williams (1973) has challenged this view. Keusch et al. (1974) have discussed the nature of the distribution of polymer segments in a swollen latex particle and find that the concentration of segments should be high in the central region of the particle and fall to zero at the particle surface, thus supporting a core-shell morphology of the Grancio-Williams type. The evidence for and against concentration gradients in polymerizing monomerpolymer particles in a reaction system of the type envisaged here has been reviewed by Gardon (1973). Theconclusion reached is that such concentration gradients as may form within such a particle are unlikely to be large enough to affect the rate of polymerization significantly. A further review of this subject has been published recently by Vanderhoff (1976). Blackley and Haynes (1977) have argued that the marked reduction in the rate of the emulsion polymerization of styrene that occurs when certain organic diluents (e.g., ethylbenzene) are added is consistent with the view that the equilibrium concentration of monomer in the polymerization loci is less when polymerization occurs than when it does noto This interpretation has recently been challenged by Azad and Fitch (1980). The conclusions to which the present evidence seems to lead can be summarized as follows: 1. The monomer concentration is probably essentially uniform across the polyermization locus if the monomer is a good solvent for the polymer.
4. Kineticsof Compartmentalized Free-Radical Polymerization Reactions 153 However, the equilibrium concentration during polymerization may be somewhat less than that attained if no polymerization is occurring. 2. The monomer concentration will remain constant as polymerization proceeds only if the following conditions are fulfilled (or if, fortuitously, the opposing effects which they tend to have upon equilibrium swelling happen to balance): (a) the size of the loci remains essentially unchanged as polymerization proceeds and (b) the interfacial free energy associated with the interface between the loci and the external phase remains unchanged as polymerization proceeds. If the loci increase in size only to a small extent as a consequence of polymerization, and the amount of adsorbed stabilizer in the system remains constant, then condition (b) will probably be fulfilled. Furthermore the extent to which polymer particles are swollen by excess monomer is usually such that the polymer/monomer ratio at the polymerization locus is high, even from the earliest stages of the reaction. The viscosity of the reaction medium is therefore high, and allowance must be made for this when assigning values to the rate coefficients for processes such as propagation and termination.
C.
Mechanism 01 Fundamental Processes; lnfluence 01 Locus Size
Although this chapter is concerned primarily with the derivation of theoretical predictions-and for this purpose the various fundamental processes that occur within the reaction system are characterized by appropriate physicochemical parameters regardless of underlying mechanism-it is nevertheless desirable to consider briefly the mechanism of some of the fundamental processes in order to appreciate the significance of the physicochemical parameters. 1. Acquisition of Radicals by Loci Formally, the rate of acquisition of new radicals by loci is characterized by the average rate of entry of radical s into a single locus. Denoted by a, this quantity is equal to p/N, where p is the overall rate of entry of radicals into all the loci contained within unit volume of the reaction system, and N is the number of loci of all types contained in' unit volume of the reaction system. p is not necessarily equal to the rate of generation of new radical s within the external phase. There may be wastage, and the extent of wastage may depend upon, inter alía, the rate of generation of new radicals and the value of N. Thus, Hawkett et al. (1980) and Gilbert et al. (1980) have recently shown that, for the seeded aqueous emulsion polymerization of styrene initiated by potassium persulfate, the capture efficiency for radicals is only about 1% at an initiator concentration of 8.33 x 10- 2 M, but rises to about 50% at 1.6 x 10- 5 M.
154
D. C. Blackley
Controversy has surroundecÍ the question of whether it is mainly primary unreacted initiator fragments (e.g., sulfate radical ions) that enter the reaction loci, or whether some polymerization of monomer dissolved in the external phase occurs first, and then it is the oligomers (which may well be surface-active) formed by this process that are acquired by the reaction loci. Present opinion tends strongly to favor the latter view, especially when the monomer is appreciably soluble in the external phase. A related matter. concerns the physical mechanism by which radical s (primary or oligomeric) are acquired by the reaction loci. One possibility, first proposed by Gardon (1968) and subsequentIy developed by Fitch and Tsai (1971), is that capture occurs by a collision mechanism. In this case, the rate of capture is proportional to, inter alia, the surface area of the particle. Thus, if the size of the reaction locus in a compartmentalized free-radical polymerization varies, then u should be proportional to r2, where r is the radius of the locus. A second possibility (Fitch, 1973)'is that capture occurs by a diffusion mechanism. In this case, the rate of capture is approximately proportional to r rather than to r2. A fairly extensive literature now exists concerning this matter (see, e~g., Ugelstad and Hansen, 1976, 1978, 1979a,b). The consensus of present opinion seems to favor the diffusion theory rather than the collision theory. The nature of the capture mechanism is not, however, relevant to the theory discussed in this chapter. It is merely necessary to note that both mechanisms predict that the rate of capture will depend on the size of the reaction locus; constancy of u therefore implies that the size of the locus does not change much as a consequence of polymerization. 2. Exit of Radicals from Loci Of the various possible first-order processes by which radicals can be lost from reaction loci, the most likely is that of exit from the locus back into the external phase. It is reasonable to suppose that the likelihood of a propagating radical being lost from a reaction locus by this process falls off sharply as the degree of polymerization increases. It is the monomeric radicals and very short-chain oligomers that are likely to be lost in this way. For this reason, the favored molecular mechanism for radical exit is transfer to monomer followed by exit of the monomeric radical or of a short-chain oligomer formed from it. In fact, the product of the transfer-to-monomer rate coefficient (relative to that for propagation) and the solubility of the monomer in the external phase is sometimes taken as a rough index of the tendency for radicals to be lost from reaction loci by exit. Whatever may be the exact nature of the molecular processes that lead to exit, the rate of loss of radical s from a single reaction locus by exit is written simply as ki, where i is the number of radicals in the locus and k is a
4. Kinetics of Compartmentalized Free-Radical Polymerization Reactions 155 composite coefficient. As with (1,the parameter k almost certainly depends on the size of the reaction locus. Thus, results published by Hawkett et al. (1980) and also by Gilbert et al. (1980) indicate that k is inversely proportional to r-2. This is consistent with an exit mechanism that involves the diffusion of a species (e.g., a monomeric radical) from a spherical particle. On the other hand, Smith and Ewart (1948) assumed k to be expressible in the forro koa/v (Le., k IX.r-l), where a is the surface area of the reaction locus, v is its volume, and ko is a constant. ko then expresses the tendency of radical s to diffuse across a unit area of the surface of the reaction locus when radical s are present in the locus at unit concentration. Again, for the purposes of this chapter, the precise functional dependence of k on r matters little; it is merely necessary to note that there are good reasons for supposing that k varies with the size of the reaction locus. 3.
Propagation and Termination
Little needs to be said here except to note that (i) the rate of propagation is unlikely to be appreciably dependent on the size of the reaction locus, whereas the rate of termination is likely to be appreciably size-dependent and (ii) the rate of both propagation and termination will be reduced if the viscosity of the reaction medium rises, but the rate úf termination will be reduced more than that of propagation. The physical reason why the rate of propagation is not appreciably size dependent is simply that a propagating radical is always surrounded by the same concentration of monomer molecules wherever the radical is in the reaction locus and, to a first approximation, whatever the size of the locus. However, to the extent that the monomer/polymer ratio in the reaction locus depends on the size of the locus (see Section II,B), then some dependence of rate of.pro paga tion on locus size will be observed. Since most of the monomer in a compartmentalized free-radical polymerization reaction is consumed in the propagation reaction, it is customary to write the overall rate of polymerization as dM/dt
= 1Nkp[M]
(1)
where 1 is the average number of propagating radical s per reaction locus, kp is the rate coefficient for propagation, and [M] is the concentration of monomer in the reaction locus. (For discussion of the precise meaning of dM/dt, see Blackley, 1975.) From the above discussion, it is clear that there may be some slight size dependence of dM/dt through [M]. The rate of propagation in a single reaction locus containing i radicals is written forroally as kpi[M]. . In the case of the termination reaction, the rate is expected to be appreciably size dependent because it involves the interaction of two radical
156
D. C. Blackley
speciesthat have to find each other. Formally, the rate of termination in a single locus is written as k,i(i - 1)/v, where k, is the rate coefficient for mutual termination (see Blackley, 1975 and Smith and Ewart, 1948). This expression can be most easily justified by regarding (i - 1)/v as the concentration of free radical s with which any one of the i free radical s may react. An important consideration is that possibly the effect of locus size, and almost certainly the. effect of locus viscosity, will depend on the degree of polymerization of the propagating radicals seeking to interact. The larger these radicals have grown, the more pronounced should be the effect of increasing locus size and viscosity in reducing the rate of termination relative to propagation.
111. The Time-Dependent Smith-Ewart Differential DifIerence Equations; Methods Available CorTheir Solution
A. Derivation The fundamental equations that govern the behavior of a compartmentalized free-radical polyrnerization reaction in which the radicals are generated excIusively in the external phase are most readily derived by considering the rates of the various processes by which loci containing exactIy i propagating radicals are formed and destroyed. These processesare illustrated in Fig. 2 as transitions between various "states of radical occupancy" of the loci, each state of occupancy being defined as the number of 0+2)0 +l)ni+2X
(j + Oni+1 k
i+2
i+1 in¡k
i(j -I)n¡x
njO'
H ni-lO'
j-2 F.ig. 2. Transitions betweenstatesof radical occupancyrequired for derivation of timedependentSmith-Ewart differential differenceequation for state i. .
4.
Kinetics of Compartmentalized Free-Radical Polymerization Reactions 157
propagating radical s present in the locus.* Only those transitions are shown that affect the value of ni, the number of reaction loci per unit volume of reaction system which contain i propagating radicals. This type of locus is referred to henceforth as a "Iocus of type i." There are three processes by which loci of type i can be formed. These are (i) from type i
-
1 loci by acquisition
of a radical, (ii) from type i + 1
loci by loss of a radical, and (iii) from type i + 2 loci by mutual termination within the loci. Likewise there are three processes by which loci of type i can be destroyed: (i) by acquisition of a further radical, thereby becoming a locus of type i + 1; (ii) by loss of one radical by exit, thereby becoming a locus of type i - 1; and (iii) by loss of two radicals by mutual termination, thereby becoming a locus of type i - 2. The differencebetween the sum of the rates of the first group of processes and the sum of the rates of the second group of processes gives dn;/dt, the overall rate at which loci of type i are formed. The result for dn¡/dt is readily found to be dl1;/dt
= (11¡-1 -
11¡)O'+
{(i +
l)n¡+1
-
il1¡}k
+ {(i + 2)(i + 1)11i+2- i(i - l)n¡}(kt/v)
.
(2)
where i = 0,1,2, ..., and n-1 = O. It will be convenient subsequently to denote the ratio kt/v by the single symbol X. It is c1ear that constancy of the coefficient X implies that v is constant as well as kt (apart from the unlikely possibility that simultaneous variations in v and kt fortuitously balance each other). These equations comprise an infinite set of linear differential difference equations, conveniently known as the "time-dependent SmithEwart differential difference equations" because they are a generalization to the nonsteady-state of the infinite set of equations first derived by Smith and Ewart (1948) fOl;steady-state reaction systems. The first term on the right-hand side of Eq. (2) represents the net effect of radical acquisition on dn¡/dt. The second and third terms likewise represent the net effects of firstorder radical loss and bimolecular mutual termination, respectively. The equations originally given by Smith and Ewart (1948) for the steady state follow immediately from the Eq. (2) by setting all the dn;/dt equal to zero. The time-dependent Smith-Ewart differential difference equations can also be derived by an alternative method first used by O'Toole (1965) for the steady state. In this method, one considers the rates of transition of locus populations across a notional barrier situated between two neighboring states of radical occupancy. The barrier is illustrated in Fig. 3, where the * In faet, as Gilbert and Napper (1974) have pointed out, there is a useful analogy between the oeeupaney of quantized energy states and the presenee in reaetion loei of free radieals whose basie "quantum" is the free radical
158
D. C. Blackley
1+2 n..,. I
---1---1_--1--
i+1
- -------------
i-I 1-2 .
.
these transltlons not relevant
Fig. 3. Transitions between states of radical occupancy required for derivation of O'Toole equation for rate of transition of loci across notional barrier between states i and i + 1.
.
barrier has been drawn between the states i and i + 1. The O'Toole approach is simpler than the earlier approach of Smith and Ewart (1948) (which considers the balance of transitions from a particular state of radical occupancy, as illustrated in Fig. 2) to the extent that only four transitions
have to be considered instead of six. Of these four, three (i + 1 ~ i, i ~ i + 1,and i + 2 ~ i)are identicalto those of the Smith-Ewart approach. The remaining three Smith-Ewart transitions (i ~ i - 1, i - 1 ~ i, and i ~ i - 2) are irrelevant because they do not involve transitions across the barrier between states i and i + 1. The fourth transition
that has to be taken
into account in the O'Toole approach is i + 1 ~ i - 1; this is irrelevant to the Smith-Ewart approach because it does not affect the number of loci which contain i radicals. However, although the O'Toole approach is simpler than the Smith-Ewart approach in that fewer transitions have to be considered, and although application to steady-state reaction systems is simple, application to nonsteady-state reaction systems is not as simple as in the case of the Smith-Ewart treatment. O'Toole presents his argument in terms of what he calls "the probability of i-fold occupancy." This probability is mathematically equivalent to the fractional frequency of occurrence of loci that contain i radicals, Le., to ni/N. Such fractional frequencies will bC?denoted by Vi in this chapter. However, the argument can equally well be presented in terms of actual
locus populations ni, Inspection of Fig. 3 shows that the overall rate of
4. Kineticsof Compartmentalized Free-Radical Polymerization Reactions 159 transition of loci upward across the barrier between states i and i + 1 is given by R¡-+i+l = n¡(1- (i + l)n¡+lk - {(l + l)in¡+l + (i + 2)(i + 1)n¡+2}x (3) To obtain the equation that must be obeyed by the locus populations in the steady state, one merely equates R¡-+¡+ 1 to zero. It will be shown subsequently that the resulting equation is exactly equivalent to that obtained from Eq. (2) by setting dn;/dt
= O. If
the reaction system is not in the steady
state, then Eq. (3) gives merely the overall rate of transition of loci upward across the barrier. To obtain an expression for dn;/dt, it is necessary to observe that this quantity is the rate of accumulation of loci in state i, and that this in turn is equal to the difference between the rate of transition upward across the barrier between states i - 1 and i and the rate of transition upward across the barrier between states i and i + 1 (see Fig. 4). Thus, we have (4) Equation (2) then follows immediately by noting that R¡-l-+i
= n¡-l(1-
in¡k - {i(i - l)n¡ + (i + l)in¡+¡}x
(5)
It is desirabIe to mention briefly the matter of the dimensions and units of the physicochemical parameters (1, k, and X. The dimensions of the left-hand side of Eq. (2) are [lociJ[timer 1. The dimensions of (1, k, and X are therefore, respectively [timer 1, [radicalsr 1[timer 1, and [radicalsr2[timerl. To the extent that numbers of loci and numbers of radicals are regarded as "mere numbers'! and therefore dimensionless, the dimensions of the left-hand side of Eq. (2) become [timer 1, and those of (1, i+2 i+1
---
- - - --- - - - - -1-1
1-2 la)
lb)
Fig. 4. Transitions between states of radical occupancy required for derivation of dnJdt by the O'Toole approach. (a) shows transitions across barrier betwe~n states i and i + 1; (b) shows transitions between states i - l and i.
160
~o Co Blackley
k, and X are also all [timer
lo
The dimensions of the k¡{= Xv) of Eqo (2) are
then [radicalsr 2[volumeJ[timer
l
or [volumeJ[timer 1, according to
whether the dimensionality of number of radicals is or is not recognisedo B.
Methods Available for Their Solution lo Matrix Methods The objective is in general to obtain explicit expressions for either the
actual locus populations n¡(t) (i = 0,1,2,ooo,) as functionsof t, or the fractional locus populations v¡(t) (i = 0,1,2, oo.,) as functions of to The mathematical procedures for obtaining v¡(t) are identical to those for obtaining n¡(t),because the form of Eqo (2) is unaltered by dividing through by No In the special case where the reaction system is in the steady state, the objective is to obtain the steady-state values of n¡(or'V¡). The feasibility of the matrix approach to solving the time-dependent Smith-Ewart differential difference equations depends on the fact that each of these equations is linear in certain n¡ Thus, the typical equation of the o
set [Eq (2)Jcan be rearranged to read o
dn¡/dt
= an¡-I - {a + ik + i(i - l)x}n¡ + (i + l)kni+1 + (i + 2)(i + 1)Xn¡+2
(6)
The infinite set of equations can therefore be written as the single matrix equation d[n¡]/dt = [nJ[n¡] (7) where [n¡]T is the matrix [nonl n2 . . .J and [nJ is a matrix of coefficientso The structure of [nJ is such that the jth row contains the following elements in the U - l)th,jth, U + l)th, and U + 2) columns respectively, and all the other elements of the jth row are zeros: a
- {a + U- l)k + U- l)U - 2)x} jk U + l)jx
(8) .
To the extent that the elements of the matrix [nJ are dependent neither on time nor on the n¡nor on each other, it is possible immediately to write down in matrix form the solution ofthe differential matrix Eq. (7). It may, however, be preferable first to transform the differential matrix equation, eogo,by using a suitable similarity transformationo Having solved the transformed equation, the n¡ can then be obtained from the matrix of transformed ni by applying the inverse transformation. It should be noted that, beca use the set of equations contained in Eq. (2) is theoretically infinite in number, the matrices [n¡] and [nJ of Eq. (7) are infinite with respect to the number of elements they contain. What is done
4. Kineticsof Compartmentalized Free-Radical Polymerization Reactions 161 in practice is to truncate the set of equations in Eq. (2) at some value of i which is believed to be such that the fraction of reaction loci that contain more than this number of propagating radicals is negligible. An alternate way of regarding the matter is to place a limit on the maximum number of propagating radicals that a locus can contain. Denoting this maximum Qumber of radicals by s, [Q] then has the form of an (s + 1) x (s + 1) square matrix. As a consequence of this truncation, it may be necessary to adjust the coefficients of the final equation of the set in Eq. (2) in order to preserve constancy of the totallocus population. This adjustment inevitably introduces a slight distortion into the set of equations, but the distortion will be negligible if the maximum value of i is taken sufficiently large for the reaction system whose behavior is being represented.
2. Use of a Locus-Population
Generating Function
In this method, the infinite set of linear differential difference equations [Eq. (2)] is also con verted into a single equation, but by a different approach to that used in the matrix approach. A new function 'P(~, t) is introduced, defined by the equation 00
'P(~, t) =
L v¡(t)~¡ ¡=o
(9)
where ~ is an auxiliary variable. This function is described as a "locuspopulation generating function," because once it is known, all the fractional locus populations at all times can in principIe be obtained from it by making use of the fact that 1 0¡'P (10) v¡(t) ="1 ::I}'i lo
( ) u,>
~=o
Furthermore, the average number of propagating radical s per locus at any 'instant Y(t) can be found from
0'1'
00
Y(t) = 1=1 .L iy¡(t)
=
() ~u,>
(11)
~=l
and the variance of the distribution of locus populations at any instant can be found from 00
V(t)
=
-
-
L (i -
¡=o
~ { o~
(
Y)2y¡(t)
~0'P
= L i2V¡(t) -
o~ )} ~= 1
-
0'1'
/2
2
(o~ )~=
(12) 1
162
D. C. Blackley
The function 'P(~, t) c1early has the additional property that CJ)
'P(I, t) = L: v¡(t)= 1 ¡=o
(13)
for all values of t. Thus, the time dependency of 'P(~, t) should always disappear when the substitution ~= 1 is made-this is a consequence of the assumption that the number of reaction loci in the system remains constant. The function 'P(~, t) has another interesting property which as yet hasnever been exploited as fai:as is known. Ir the substitution ~ = - 1 is made; then we obtain 'P(-I, t) = vo(t) - v¡(t) + V2(t)- v3(t) + ... (14) Thus, 'P(-I, t) gives at any time the difference between the fraction of the total number of loci that contain an even number of propagating radicals and those that contain an odd number, the fraction containing an even number inc1uding within it those containing no propagating radicals at all. Ir it is desired to know the fraction of the total number of loci that do not contain any propagating radicals, then this can be obtained from the relationship vo(t) = 'P(O,t) -(15) Thus, it is c1ear that the single function 'P(~, t) is capable of yielding a great deal of information concerning the distribution of locus populations in the reaction system. There are at least four important advantages to using locus-population generating functions as compared with the matrix approach: 1. It is quite unnecessary to truncate the set of equations contained in Eq. (2); in fact, the logic of the method requires that the set be maintained infinite in extent. There is therefore no possibility that the set of equations actually being solved is a distorted representation of the behavior of the reaction system being investigated. To the extent that the requisite mathematical operations ha ve been correctly performed, the resultant expressions for v¡(t),etc. are free from approximation errors. 2. It is possible in several cases to obtain expressions for v¡(t), etc. in c10sed analytic form rather than as somewhat unwieldy algebraic expressions. 3. The method using the locus-population generating function is more readily applicable to systems in the steady state. 4. It is in principIe possible to make inferences concerning the nature of the distribution of locus populations if the generating function can be recognized as that of the frequencies of some known distribution. It should perhaps be pointed out that in several previous publications (e.g., Stockmayer, 1957; Birtwistle and Blackley, 1977, 1978: Birtwistle et al.,
4. Kineticsof Compartmentalized Free-Radical Polymerization Reactions 163 1979) the function 'P(~, t) has been detined using the actual locus 'populations n¡(t) and not the fractionallocus populations v¡(t).The difference is trivial. The function as detined by these previous writers is merely N times the function as detined here, N being the total number of reaction loci in unit volume of the reaction system. The advantages of the present detinition over the alternative detinition are that (i) the analytic expressions for 'P(~, t) are simplitied to the extent that they do not contain N as an arbitrary multiplier and (ii) the expressions for i(t) and v(t) in terms of 'P(~, t) are somewhat simpler. It should be noted, however, that if 'P(~, t) is detined using n¡(t)in place of v¡(t),then the right-hand side of Eq. (10) gives n¡(t),and not v¡(t). In order to convert the set of differential difference equations in Eq. (2) into a single differential equation with 'P as the dependent variable, each equation for dn;/dt is multiplied by ~¡/N [the factor N-1 changes n¡(t)into the corresponding v¡(t)], and then all the equations so obtained are added together. It is then noted that
(16)
where in each case the summations cover all possible values of i. The resultant single differential equation then readily transforms to .8'P -
8t
t = O\~ - 1)'P + k(l - ~)-8'P + X(l - ~2)-82'P
8~
8~2
(17)
This is the partial differential equation for 'P(~, t) which has to be solved for each particular case. The solution has to be subject to the initial (boundary) conditions appropriate to that particular case. For the special case of reaction systems that are in a steady state, n¡(t) are invariant with time, and therefore 'P(~, t) is not a function of t. It is therefore denoted by 'P(~) in this case. Thus, in this case 8'P/8t = O,and the righthand side of Eq. (17) must be zero. What were hitherto partial differential coefficients of 'P(~, t) with respect to ~ become ordinary differential coefticients. Dividing through by the factor 1 - ~ then gives d'P d2'P a'P - k- X(l + J:) -
d~
-
..
de
=O
(18)
164
D. C. Blackley
as the ordinary differential equation to be solved for 'P in this case. This is identical to the differential equation first given by Stockmayer (1957) for the locus-population generating function that characterizes the behavior of reaction systems in the steady state. Equation (18) can also be obtained from the infinite set of equations for the steady-state as given by O'Toole (1965). It will be recalled that this is the set of which Eq. (3) with the lefthand side set equal to zero is the typical member. Again the procedure is to multiply each eq\lation by ~i/N, add together all the equations so obtained, and then note the relationships summarized in Eq. (16) together with the additional relationship . ¿¡2'P ¿(i + 1)ivi+l~1 = ~ ¿¡~2
(19)
The resultant single differential equation can then readily be transformed into Eq. (18). Thus, it becomes clear that the O'Toole (1965) formulation of the steady-state problem is exactIy equivalent to that of Smith and Ewart (1948), notwithstanding that the approach to the problem is somewhat different. 3.
Approximation Methods
As has already been explained, the matrix approach involves some degree of approximation because of the necessity of truncating the set of equations in Eq. (2). There have, however, been other attempts to solve the Smith-Ewart differential difference equations by approximation methods that have not used the matrix approach. These methods have been used for steady-state systems as well as for nonsteady-state systems. Again the procedure is to set a limit on the maximum number of propagating radicals which a single locus can contain. This maximum number is sometimes qujte low, e.g., either one or two. The resulting set of equations is then solved by conventional methods for simultaneous linear algebraic equations (in the case of equations representing the steady state) or simultaneous linear differential equations (in the case of equations representing the nonsteady state).
IV. Solution for the Steady State The general solution to the Smith-Ewart differential difference equations for reaction systems in the steady state is most readily obtained using the locus-population generating function approach. This was first demonstrated by Stockmayer (1957) and subsequentIy by O'Toole (1965). It is convenient to introduce two new parameters ¡:;and m defined as ¡:;= av/kt = a/x,
m = kv/kt = k/X
(20)
4. Kineticsof Compartmentalized Free-Radical Polymerization Reactions 165 It is subsequently convenient to introduce a third parameter h defined by the equation (21) The parameter e is a measure of the rate of radical entry relative to the rate of bimolecular termination within loci. Similarly, the parameter m is a measure of the rate of radical exit relative to the rate of bimolecular termination within loci. The ratio e/m = CT/kis a measure of the rate of radical entry relative to radical exit. The so-called Case 1, Case 2, and Case 3 of Smith and Ewart (1948) correspond to the following circumstances: Case 1: m large relative to e; Case 2: k = O,kt = 00 (Le., e = m = O); Case 3: e large relative to m. Note that both e and m increase linearly with locus volume v if CT,k, and kt remain constant, but the ratio e/m is independent of both v and kt. The first step is to solve Eq. (18) for 'P(~). Introducing the parameters e and m, this equation becomes (1 + ~) d2'P/d~2 + m d'P/d~ - e'P = O
(22)
Two new variables x and y are introduced. These are defined by the equations x
y = 'P(~)/xl-m
= 2)e(1 + ~),
(23)
Equation (22) then becomes X2 d2y/dx2 + x dy/dx
-
{(1 - , m)2
+
X2}
y
=O
(24)
This is a modified Bessel equation of order 1 - m. Except for the physically improbable case wliere 1 - m is exactly an integer or zero, the general solution to Eq. (24) is y = AIl-m(X) + Blm-l(X) (25) I
where Il-m(x) and Im-l(X) are modified Bessel functions of orders 1 - m and m - 1 respectively, and A and B are constants. Physical considerations (see O'Toole, 1965) indicate that the A must always be zero. The value of B is determined by the requirement that 'P(1) = 1. The final result for 'P(~) is
(\/+fl+1)
2(m-1j/2
'P(~) = Im-l(h) (1 +
~)(1-m)/2Im-l
(26)
Application of Eqs. (10) and (11) gives h
hi2m-1-3i and
Vi
= i! Im-l(h)
Im-l+i
(J2)
(27)
(28)
166
D. C. Blackley
Factors such as Im(h)/Im-l(h) have been convenientIy referred to by van der Hoff (1958, 1962) as "subdivision factors." In effect, they quantify the extent to which the overall concentration of propagating radical s in the reaction system as a whole is enhanced by compartmentalization of the propagation steps into a large number of small reaction loci. An important further contribution to the analysis of steady-state reaction systems has been made by Ugelstad et al. (1967). They have shown how account can be taken of the likely possibility that radicals that exit from the reaction loci contribute to the stationary concentration of free radicals in the external phase which is available for entry into a reaction loci. For this purpose, it is necessary to distinguish bimolecular mutual termination between radical s that occurs in the reaction loci (i.e., within polymer/ monomer partic1es)from that which occurs in the external phase. The rate at which the former reaction occurs is characterized by the rate coefficient ktP, the rate of the latter reaction by ktE. The total rate of entry of radicals into all loci within unit volume of reaction system is th~n expressed as the sum of three contributions. The first derives from the rate of formation of new "acquirable" radicals within the external phase; the second derives from the rate at which acquirable radicals become present in the external phase by the process of exit from the loci; the third (which is negative) allows for the fact that radicals can be lost from the external phase by bimolecular mutual termination within the external phase. The resultant equation is 00
p = p' + k
I
i= 1
ini - 2ktE e2
(29)
where p is the total rate of entry of radicals into all the N loci in unit volume of reaction system, p' is the rate of generation of new radicals within unit volume of reaction system, and e is the stationary concentration of radicals within the external phase. The form of this equation implies that all the radical s that become present in the external phase (whether by generation or by exit from the loci) are potentially available for reentry, except insofar as they are destroyed by mutual termination. Dividing through by N, setting a = p/N, a' = p'/N, and y = pie, and introducing parameters
e = av/ktP'
e' = a'v/ktp,
m = kv/ktP,
Z = 2NktpktE/yZv
(30)
Eq. (29) readily transforms to e = e' + mf - Ze2
(31)
Ugelstad et al. have used Eq. (31) in conjunction with Eq. (28) to calculate y as a function of e' for various values of m and Z. It is valid to regard the e of
4.
Kinetics of Compartmentalized
Free-Radical Polymerization Reactions
167
Eq. (31) as equivalent to the h of Eq. (28) because the reaction system is presumed to have reached a steady state in which, inter alia, ¡¡,¡¡/,and 1 have attained stationary values.
V. Solutionsfor the NonsteadyState A.
Case in which Radical Loss is Predominantly by First-Order Processes
Considerable progress has been made in recent years in obtaining solutions to the time-dependent Smith-Ewart differential difference equations for various special types of reaction system in the nonsteady state. Although it has so far not pro ved possible to give an entirely general solution to these equations, it has pro ved possible to obtain a general solution to a modified set of equations which, under certain circumstances, approximate to the exact set of equations. The simplest case for which an exact solution has been obtained is that of a reaction system in which radicals are lost from reaction loci almost exdusively by first-order processes. Initially, the reaction system is devoid of free radicals, so that no polymerization is occurring. Then, at a time taken as the zero of subsequent time, radicals begin to be generated in the external phase at a constant rateo This case has been discussed in detail by BirtwistIe and BIackley (1977, 1979) using the locus-population generating function approach, and by Gilbert and Napper (1974) using the matrix approach. The expressions for the locus-population generating function, for v¡(t), and for l(t) haye also been given by Weiss and Dishon (1976), but without discussion of the significance of the result. Setting X = O,the partial differential equation to be solved for this case is
..
o\f/ot
= c¡(~-
1)\f + k(1 - ~)o\f/o~
(32)
The boundary conditions are vo(O)= 1 v¡(O) = V2(0)
= ... = O
(33)
and, furthermore, for all t 00
L
;=0
v¡(t)
=
vo(O)
=
1
(34)
Equation (32) with these boundary conditions is amenable to solution by the method of separation of variables, in which the function \f(~, t) is assumed to be of the form 2(~)'11:t),where 2(~) is a function of ~ only, and
168
D. C. Blackley
T{t) is a function of t only. The details of the process whereby the solution can be obtained have been given by Birtwistle and Blackley (1977). The result for 'P(~, t) is 'P(~, t) = exp{(o-¡k)(~ - 1)(1 - e-k/)}
(35)
It follows immediately from this that at all times the distribution of locus populations with respect to radical occupancy is Poissonian, and that the parameter of the distribution at any instant is (O"/k)(1- e-k/). These conclusions follow because the expression for 'P(~, t) is recognizable as the frequency-generating function for a Poisson distribution (see Kendal and Stuart, 1965). It then follows that
{
v.(t) = .!. ~(1 , i! k
- e-k/)
} { ¡ eXP
-~(1
k
- e-k/)
}
(36)
and
(37)
T~t) = (O"/k)(1- e-k/)
Alternatively, the results embodied in Eqs. (36) and (37) can be derived from Eq. (35)using Eqs. (10)and (11).The general result for v¡(t) then shows that the distribution of locus populations must always be Poissonian with timedependent
parameter
(O"/k)(1- e-k/). Setting t
= 00 in
these results givcs the
following predictions for the reaction system when it has attained the steady state: 'P(~,oo)
= e(O'/k)(~-l)
1 O" i v¡(oo)=i! k e-O'/k
()
Y(oo) = O"/k
(38)
Approximate solutions for vo(t),Vl(t),and V2(t)have been given for this case by Gilbert and Napper (1974). These solutions were obtained using the matrix method. The expressions obtained are algebraically cumbersome compared to the general result embodied in Eq. (36), but can, of course, be readily handled using modern computers. Provided that O"/k is small compared to unity, the solutions given by the two methods predict almost identical numerical results for Vi(t);in fact the ratio of the values given by the two methods is e-O'/k/(1- 0"/2k)2,which is almost unity for O"/k~ 1. An example of the numerical predictions that this theory gives is shown in Figs. 5 and 6. Figure 5 shows the fractionallocus populations vo(t),Vl(t), and
V2(t)
as functions of t for a reaction system for which
= 1 x 10- 5 sec-l, k = 5 X 10-4 sec-l, and X is zero. It is seen that the steady state is reached after approximately 104 sec, and that at all times most of the reaction loci are devoid of propagating radicals. Of those loci that contain radicals, most contain only one. Figure 6 shows the prediction for T(t) as a function of t for this reaction system. Again this shows the O"
4. Kinetics of Compartmentalized Free-Radical Polymerization Reactions 169 1.0 í=O i=I
;,;-0.5
i=2
o
5
10
15
20
time (sec) x 10-3
Fig. 5.
Fraetional locus populations, v¡(t),as functions of time t for i = 0,1,2 for
reaction system for whieh radiealloss from reaction loei is exclusively by first-order processes. Values taken ror (] and k are 1 x lO-s sec-¡ and 5 x 10-4 see-¡ respeetively. The ordinates for i = Oare vo(t); those for i = 1 are 40 v,(t); those for j = 2 are 2 x 103 v2(t).(Reproduced with permission of J. Chem. SocoFaraday l.)
2
.. Q
,x
O
5
10
15
20
time (sec) x 10-3
Fig. 6. Average number of radieals per loeus I(t) as a funetion of time t for reaetion system to which Fig. 5 refers. (Reprodueed with permission of J. Chem. SocoFaraday l.)
170
D. C. Blackley 10
-
5
i
O
10
5
15
20
time (se e) x 10-3 Fig. 7. Conversion of monomer to polyrner M(t) as a function of time t for reaction system to which Figs. 5 and 6 refer. (Reproduced with permission of J. Chem. Soco Faraday l.)
steady state being reached after about 104 seco The average number of radical s per locus in the steady state is small (0.02) for this case. The amount of monomer M(t) converted in a unit volume of the reaction system after the eIapse of time t can be obtained by substituting for T(t) in Eq. (1) from Eq. (37), and then integrating
over the range t
= O to t = t.
The
result is (39) The prediction for M(t) as a function of t for the reaction system to which Figs. 5 and 6 refer is shown in Fig. 7. Marked deviation from linearity in the predicted curve for conversion as a function of time occurs over the range t < 5 X 103 seco An interesting generalization to the case X = O has been given by Birtwistle and Blackley (1979). In this generalization, the theory is extended to include cases where a and k are time dependent. In order to emphasize the time dependence of a and k they are written as a(t) and k(t). What Birtwistle and Blackley (1979) have shown is that the solution to Eq. (32) always has the form 'I'(~, t) = e<~-1)8(t)
(40)
where O(t) is a function of time that satisfies the ordinary differential equation dO(t)/dt = a(t) - k(t)O(t) (41)
4. Kineticsof Compartmentalized Free-Radical Polymerization Reactions 171 and is subject to the initial condition 0(0) = Ofor reaction systems for which the boundary conditions are as stated in Eq. (33). This result for 'I'(~, t) shows that the distribution of locus populations with respect to radical occupancy is at aIl times Poissonian, notwithstanding the time dependence of a and k, and that the parameter of the distribution is always equal to O(t).It therefore foIlows that always 7(t) = O(t)
(42)
and -8(/) v¡(t) = {O(tW ., e lo
(43)
If a and k are not time dependent, then O(t)has the value (a/k)(1 - e-kl) and the results are identical to those obtained previously. The foIlowing particular cases of time-dependent a and k have been considered in detail by BirtwistIe and BIackley (1979): 1. The case where a decays exponentiaIly with time, and k is constant. 2. The case where a decays linearIy with time, and k is constant. 3. The case where a decays as a consequence of second-order depletion of initiator, and k is constant. 4. The case where a is constant, but k varies because the loci grow at a constant rateo 5. The case where a varies because radicals lost to the external phase are available for reinitiation, and k is constant. Of these cases, the first is probably of greatest interest because the decomposition of moSt dissociative initiators is kineticaIly of first order with respect to initiator concentration, and therefore both the initiator concentration and the rate of decomposition of the initiator wilI decay exponentiaIly with time. Setting a(t) = aoe-al, the solution for O(t)is
(44) except for the unlikely special case where o: = k, in whichcase the result for O(t)is O(t)= aote-kl
(45)
Figure 8 shows examples of the variation of O(t)[and hence of T(t)] with t for a reaction system for which k has the constant value 5 x 10-4 sec-l and a decays exponentiaIly with time with ao = 1 x 10- 5 sec- I and o: taking various values between zero and 5 x 10-3 sec-I. It appears that the exponential decay of a has little effect upon the variation of O(t) with t, provided that o:/k< '" 10- 2. But in aIl cases the effectof ~ nonzero o:is to
D. C. Blackley
172 2
a/k
=O
a/k =0.01
.. Q X
,11
~
q;
15
20
Fig. 8. Loeus-populationdistribution parameter O(t)and the average number of radieals per loeus T(t) as funetions of time t for reaetion system for whieh radiealloss from reaetion loei is exc1usively by first-order proeesses and rate of radical entry deeays exponentially with time. The values taken for (10and k are 1 x 10- s see-¡ and 5 x 10-4 see-¡, respeetively; eurves are given for various values of c(, indieated by the C(/k ratios (Reprodueed with permission of J. Chem. Soco Faraday l.)
appended
to the eurves.
cause 8(t) to rise to a maximum and then eventually to decay to zero. This ultima te decay to zero is a consequence of depletion of the source of radicals. It carries the implication that eventually all v¡(t) for i > O themselves decay to zero and vo((0) = 1.
B.
Case in which Generation oi New Radicals Ceases
Birtwistle et al. (1979) have obtained an explicit analytic solution to Eq. (17), and hence to the general time-dependent Smith-Ewart differential difference equations, for the case where the rate of formation of new radical s in the external phase is zero (Le., (f = O).Of course, if no radicals ever ha ve been generated within the external phase of the reaction system, then the problem becomes trivial and admits of an obvious and simple solution, namely, that allloci are at all times devoid of propagating radical s and the rate of polymerization is always zero. This solution is c1early of no interest. The case that is of interest is that of a reaction system in which radical s have been generated within the external phase, so that a certain rate of polymerization has developed; then the rate of generation of new radicals is suddenly reduced to zero, so that the reaction rate then decays. It is with the characteristics of the reaction during this period of decay, following the cessation of the generation of new radicals, that this aspect of the theory of
4.
Kinetics of Compartmentalized Free-Radical Polymerization Reactions 173
compartmentalized free-radical polymerization is concerned. Possible ways in which the rate of generation of new radicals might suddenly be reduced to zero include (a) sudden release of an efficient radical scavenger into the external phase of the reaction system and (b) cutting off the source of radiation in the case of a radiation-initiated reaction. It is convenient to regard the elapsed time as measured from the time at which the generation of new radicals ceased. It is necessary to consider two distinct cases,namely, the general case of reaction systems for which m is nonzero, and the special case for which m = O. It will be recalled that m denotes the ratio kv/k" Le., k/X [see
Eq. (20)J.Thus, a nonzero value of m implies that radicals can be lost from reaction loci by first-order processes,whereasa zero value of m impliesthat either radicals cannot be lost from reaction loci by first-order processes or k, is truly infinite. The latter possibility seems physically unlikely. Whatever the value of m, the equation to be solved is Eq. (17) with (1set equal to zero, Le., (46) subject to an appropriate
boundary
condition.
In any particular
case, the
boundary condition is determined by the particular distribution of locus populations that prevailed at the instant when the formation of new radicals in the external phase ceased. Equation (46) can be solved by the method of separation of variables; full details are given in the paper by Birtwistle et al. (1979). The function 'P(~, t) is assumed to be of the form E(~). T(t). The function T(t) is found to h~ve the form
T(t) = Ae).x
(47)
where A.is the "separation constant" and A is a constant whose value may depend upon that of A..It is necessary to give careful consideration to the
values of
A. that
are physically acceptable. It turns out that these are all
negative and are of the form - x(m + b)(b
+ 1) where b =
0,1,2,
....
The equation which the function E(~)must obey is found to be (48) By means of the substitution x = (1 + W2, this equation can be readily transformed to x(1
-
x) d2E/dx2 + m(1 - x) dE/dx - (A./X)E= O
(49)
This differential equation is of hypergeometric form, and so solutions in terms of hypergeometric functions are readily available. It is at this point that it is necessary to distinguish between the cases m # O and m = O. The latter case requires separate treatment.
174
D. C. Blackley
1. Casein which m is Not Zero For this case, the result for 'I'(~, t) is found to be 00
(50)
¿ BpJr 1.m-l)(~)e-t/tp
'I'(~, t) =
p=o
where 7:pis defined by the equation . 7:p= 1j[Xp(P
+m-
1)]
(51)
p = O, 1,2, ...
the Jpare Jacobi polynomials, and the Bpare coefficients whose values are determined by the requirement that 'I'(~, t) at zero time must have a particular form 'I'(~,O). The particular form for 'I'(~,O) in any given instance is that which characterizes the distribution of locus populations which prevailed at the instant when the generation of new radicals ceased. The general results obtained for v¡(t), T(t), and M(t) are as follows:
1 v¡(t) =
2¡.,1.
.
00
¿.'Bip p='
+
m
(52)
- l);1~¡:/,m+¡-l)(O)e-t/tp
00
T(t) =
t ¿ Bp(p + m -
(53)
l)e-t/tp
p=l
and 00
M(t) = M(O) + tkp[M] N
¿ Bp7:p(p+ m p=l
1)(1-
(54)
e-t/tp)
where a symbol of the type (U)Kis a Pochhammer symbol denoting the function r(u + K)jr(U). Equation (50) shows that the nature of the decay of the reaction following the cessation of the generation of new radicals is characterized by, inter aUa,a set of relaxation times 7:p' The number of these relaxation times is in general infinite, although there may be special cases for which the number is effectively finite. The values of 7:pdo not depend on the nature of the initial distribution of locus populations from which the reaction system is decaying, insofar as the nature of the initial distribution does not affect the allowable values of p. Rather, tp are a property of the reaction system itself and not of any particular distribution of locus populations from which it may be decaying. It should be noted that one of the relaxation times (that corresponding to p = O)is infinite in value, and its presence ensures that a second boundary condition which obviously applies in this case, namely 'I'(~, (0) = 1, can be fulfilled. Birtwistle et al. (1979) have applied the general solution embodied in Eqs. (50-53) to the decay of the reaction from the following three types of \
4. Kineticsof Compartmentalized Free-Radical Polymerization Reactions 175 initial distribution of locus populations: (i) a distribution of the Stockmayer-O'Toole type, for which 'P(~, O) is given by Eq. (26); (ii) a Poisson distribution, for which 'P(~, O)is of the form ell(~-¡)where J.lis the parameter of the distribution; and (iii) a ..homogeneous" or ..uniform " distribution, Le., a distribution in which all the reaction loci contain the same number of propagating radicals. For the case of decay from an initial distribution of locus populations which is of the Stockmayer-O'Toole type, it is found that the coefficients Bp are given by
= 2p +
B
2.
m
-
1 12p+m-¡(h)
p + m- 1
p
(55)
Im-¡(h)
Case in which m = O
Setting m
= O in
Eq. (48) gives d2,:=
A.
(1 - ~2) d~-; - xE
(56)
=O
as the differential equation that must now be satisfied by the function E(~). This equation is a special case of the Gegenbauer differential equation. The result obtained for 'P(~, t) is C()
(57)
L KpC~-¡/2)(~)e-t/tp
'P(~,t) =
p=o
where "pare defined by the equation 1
.
=
..
p
Xp(p
-
(58)
p = O,1, 2, ...
1)
q-¡/2)(~) is a Gegenbauer polynomial of order p and parameter -!, and Kp are coefficients whose values are determined by the form of 'P(~, O). The general results for v¡(t),I(t) and M(t) for the case m = Oare as follows:
2¡
" C()
. ( 1)(P-/)/2
v¡(t)= l'l. P=I L, . Kp -
r[(p + i - 1)/2]
e -t/tp
r(i - 1/2)r([(p - i)/2] + 1)
(59)
where the summation extends over all values of p ~ i such that p - i is even C()
I(t)
=-
L Kpe-t/tp
(60)
p=!
and (61)
176
D. C. Blackley
The separate term for p = 1 in Eq. (61) arises because '1 is infinite in this case, as well as 'o. There is a very simple physical consideration that underlies the need for separate treatment in the case m = O,and which explains in particular the fact that the summation for v¡(t) given in Eq. (59)does not contain terms that correspond
to p
-
i odd. It is that, if m truly is zero, and this situation
does not arise because k, is infinite, then there is no mechanism by which the number of radicals in a reaction locus can alter by other than - 2 (it being recalled that in the type of reaction system under consideration here no new radicals are being generated). There is thus an essential physical discontinuity in passing from reaction systems for which m is small but nonzero to those for which m is truly zero. One consequence is that loci that initially contained an even number of propagating radicals must continue always to contain an even number of radicals (inc1uding no radical s at all); likewise "odd" loci must always remain "odd." It is this feature that gives rise to the absence of terms corresponding to p - i od!=iin the expression for v¡(t). Again, this general result has been applied to the decay of the reaction from initial locus-population distributions of the Stockmayer-O'Toole, Poisson, and homogeneous types. For the case of decay from a Stockmayer-O'Toole distribution, the coefficients Kp are found to be given by Kp
= -(p - !)[I2p-l(h)/L l(h)J
(62)
It should be noted that this result does not follow from Eq. (55) by setting m = O. However, the 'p for the case m = O can be obtained from those for the case m # O by putting m
C.
= O.
Approximate" Poissonian" Solution to the General Case
Although it has so far not been possible to obtain a completely general explicit analytic solution to Eq. (17) [and therefore to the set of equations in Eq. (2)J for the case of reaction systems initially devoid of radicals and in the external phase of which radicals suddenly begin to be generated at a constant rateo Birtwistle and Blackley (1981a) have shown that it is possible to obtain an explicit analytic solution to a modified form of Eq. (17) which under certain circumstances can be expected to be a reasonable approximation of Eq. (17). The modified equation is o\f!/ot
=
a(~
-
1)\f!
+ k(l - ~) o\f!/o~ + X(1- ~) o2\f!/O~2
(63)
e
Le., in the third term of the right-hand side of Eq. (17), the factor ~ is replaced by the factor 1 -~. Some mathematical justification for the
4.
Kinetics of Compartmentalized Free-Radical Polymerization Reactions 177
approximation can be given if it is noted that (i) the use which is made of the function 'P(~, t) is such that it is required at the extremities of the range O::;;~ ::;;1 only, (ii) over this range 1 ~ is a reasonably good approximation for 1 - ~2, and (iii) 1 - ~ and 1 - ~2 have the same values at the extremities of this range. Equation (63) can be obtained from a modified set of time-dependent Smith-Ewart differential difference equations in which the coefficient of kt/v in the final term on the right-hand side of Eq. (2) is replaced by {(i + 2)(i+ 1)ni+2-(i+ l)ini+¡}' The modified set ofequations is thus expected to be a reasonable approximation, provided that the rate of loss of radical s from reaction loci by second-order processes is not so great as to be in effect the dominant radical-los s mechanism. The solution of Eq. (63) subject to the boundary condition 'P(~, O)= 1 is found to be
-
'P(~, t) = e(~-l)
(I)
(64)
where fjJ(t)is a function of time which satisfies the ordinary differential equation (65) dfjJ(t)/dt= a - kfjJ(t) - X{fjJ(t)}2 and is subject to the initial condition fjJ(O)= O. Solution of Eq. (65) gives the following explicit form for fjJ(t): ,¡"
'f'(t) = 2 a
.
tanh(at/2)
(66)
where a = (4aX + k2)1/2. The function 'P(~, t) is immediately iecognizable as the frequencygenerating function .of a Poisson distribution whose parameter is fjJ(t).It therefore follows that, for reaction systems whose behavior is described by Eq. (63),the distribution oflocus populations is Poissonian at all times; this is the justification for describing the approximation as "Poissonian." Thus, the conclusion reached concerning the distribution of locus populations in reaction systems for which X = O has been shown to be of much wider applicability in that this will be approximately the case for all reaction systems for which Eq. (63) is an adequate representation of behavior. Since the parameter of the distribution is always the function fjJ(t),it follows that I(t) and v¡(t)are given by equations analogous to Eqs. (42) and (43) in which fjJ(t)replaces O(t). D.
Other Approximations
Hawkett et al. (1975) ha ve used the matrix method to obtain approximate predictions of the nonsteady-state behavior of reaction systems for
178
D. C. Blackley
which radical loss from reaction loci is predominantly by second-order processes. Loss by first-order processes, such as radical exit, is assumed to be negligible. Reference has been made (see Section V,A) to the paper by Gilbert and Napper (1974) in which the matrix method was used to obtain approximate predictions of the nonsteady-state behavior of reaction systems for which radical loss is predominantly by first-order processes, the rate of loss by second-order processes being negligible by comparison. The paper to which r~ference is now made pro vides approximate solutions for what is in effect the complementary problem. In particular, solutions are given for reaction systems for which no radicalloss by first-order processes occurs at all (Le., k = O). To the extent that the rate of radical loss by second-order processes is large relative to the rate of radical entry (Le., a/x ~ 1), then such reaction systems should conform to Case 11 of the classification scheme of Smith and Ewart (1948). For such systems, it is known that 1(00)= -0.5. The results which Hawkett et al. (1975) give for vo(t),Vl(t), and v2(t) for this latter case are as follows: . vo(t) =!<1 -
P + P2)
+ 4(1 +
P+
p2)e-2at -
p2e-(2x+a-a2/20X)t
Vl(t) =!<1 - i~2) -!<1 - ip2)e-2at
(67)
V2(t)= !
(68)
where A is constant. With regard to functional dependence on time, this is of the same form as Eq. (39) for reaction systems in which radical loss is exclusively by first-order processes. [Equation (39) can also be derived by using the matrix approach.] The conclusion is therefore reached that it is unlikely that it will pro ve possible to discriminate between these two very different types of reaction system on the bases of the shapes of plots of M(t) as a function of t. Hawkett et al. (1977) have also succeeded in obtaining approximate predictions of the nonsteady-state behavior of completely general reaction
40 Kinetics 01 Compartmentalized
Free-Radical Polymerization Reactions
179
100
-= ;;;- 005
i=2-
o
30
60
lime {mio} Fig. 9. Fractional locus populations, v~t), as functions of time t for i = 0,1,2 for reaction system for which radical loss from reaction loci is exclusiveiy by second-order processes. Values taken for (f and X are l x 10- 3 sec-¡ and 1 x 103, respectively. The ordinates for i = O and i = 1 are vo(t) and v¡(t), respectively; those for i = 2 are 2 x 106V2(t). (Reproduced
with permission
of Jo Chemo Soco Faraday lo)
systems using the matrix method. They agree that the locus-population generating function method is more dir~ct than the matrix method, but correctly point out that treatment of the general case by the locuspopulation geneniting function method has so far not been possible. For the case where all the loci are initially devoid of propagating radical s and (f ~ (k + X), the general solution is given by Hawkett et al. (1977) as co
v¡(t)
= L l~r~eAp'
p=o
(69)
where l~ is the zerotb component of the pth left eigenvector of the matrix [O], r~ is the ith component of the pth right eigenvector of [O], and Ap is the pth eigenvalue of [O]. The expression given for M(t) is (70) where A is a constant. Thus, the problem of obtaining predictions for the v¡(t)and for M(t) reduces to that of finding the eigenvalues and eigenvectors
180
D. C. Blackley
of En]. The method which Hawkett at al. (1977) use is to express the matrix En] in tHeform En]
= [no] + 0"[n1]
(71)
where
-1
O -1
[O,]
=
~
O O oo. O O oo.
1 -1
O ...
(72)
[ and [no] is the matrix whose elements are obtained by subtracting O"times those of [na from the corresponding elements of En]. Since O"is assumed to be small compared with k and X, the eigenvalues and eigenvectors of En] can be obtained by using non-Hermitian perturbation theory and treating 0"[n1] as a perturbation on [no]. Hawkett et al. consider that the restriction O"~ (k + X) is fulfilled by most, though not all, compartmentalized free-radical polymerization re'actions in which the external phase is aqueous. Of the somewhat grosser approximations, consideration will be given first to the "two-state" model of Lichti et al. (1977). Reaction systems that conform to this model are those in which very few loci ever contain more than one radical, Le., the rate of entry of radical s into loci is much less than the sum of the rates of radical loss by first- and second-order processes. Thus, the only significant populations that have to be taken into account in calculating l(t) are those of loci for which i = O and 1. The number of loci that contain three or more radicals is assumed to be strictly zero. The number of loci containing two radical s is assumed to be very small and stationary. Although the number of such loci is assumed to be insignificant with regard to contribution to 1(t), the assumption that dn2/dt is zero can be used to eliminate n2 from the expressions for dn¡jdt and dn2/dt. The following treatment of the model is essentially that of Birtwistle and Blackley (1981a). Setting n3 = n4 = O in the equation for dn2/dt [Le., Eq. (2) with i = 2], and setting dn2/dt = O,gives n2 = O"n¡j[O" + 2(k + X)]
(73)
from which it is evident that n2 ~ n1 implies that O"~ O"+ 2(k + X),and thus that O"can be neglected relative to 2(k + X). Substituting for n2 from Eq. (73) into the equations for dno/dt and dn¡jdt [Le., Eq. (2) with i = O and i = 1, respectively] gives equations for dl1o/dt and dn¡jdt which can be expressed in matrix form as
~ dt
no
[J n1
=
O" -q
no
[- O" qJ[ n1J
(74)
4. Kineticsof Compartmentalized Free-Radical
Polymerization
Reactions
181
The general solution of this differential matrix equation is known to be of the form ... no(t)
[ ]
= c [ A ] e)."
nl(t)
1
+c
1
[A ] 2
(75)
e).21
2
where Al and A.2are the eigenvalues of the matrix of coefficients in Eq. (74), [Al] and [A2] are the corresponding column eigenvectors, and CI and C2 are arbitrary constants. The following results for vo(t), VI(t), and f(t) are obtained by this method: vo(t) f(t)
=~
{
O'+q
= VI(t)
1+
(76)
~e-(<1+q)/
}
q O'
= -{1-
(77)
e-(dq)/}
O'+q
= k + O'X/(k+ X). Solutions for a "three-state" model have been published by Brooks
where q
(1978,1979).In this model, it is assumed that the n¡{t)values are strictly zero for i > 2, so that the only locus populations that have to be considered are
'°1
:+
e
y.
D
F
o
2
3
4
kt Fig. 10. Predictions for average number of radicals per locus I(t) as a function of time t obtained by numerical solution of time-dependent Smith-Ewart differential difference equations, showing effect of increasing /. keeping (1 and k constant. Values taken for (1and k are both 1 x 10-3 sec-'. Values taken for /. are as follows: A, O; B, 1 X 10-5 sec-'; e, 1 x 10-4 sec-I; D, 1 X 10-3 sec-t; E, 1 X 10-2 sec-'; F, I X 10-' sec-'. (Reproduced with per'mission of J. Chem. Sal'. Faraday /.)
182
D. C. Blackley
those for which i = O, 1, and 2. No assumptions are made concerning the variation of n2(t) with t. Brooks gives explicit expressions for vo(t),Vl(t), and V2(t)from which T(t)can be readily obtained as (78) Brooks regards his approximation as valid for reaction systems in which T((0) is smalI (up to 0.4). The matter of the decay behavior of a seeded emulsion polymerization reaction following the cessation of the generation of new radicals in the external phase has recently been treated by Lansdowne et al. (1980) using the matrix approach. Numerical procedures have been devised for solving the set of equations in Eq. (2) in particular instances. Birtwistle and Blackley (1981b) have described one such procedure. Examples of the results of their calculations are shown in Figs. 10 and 11. These calculations refer to reaction systems 0.6
0.4
-
,-
0.2
A time (sec) Fig. 11 . Predictions for average number of radicals per locus, ¡(t), as a function of time t obtained by numerical solution of time-dependent Smith-Ewart differential difference equations, showing effect of decreasing k and increasing X, keeping u constant. Value taken for u is 1 X 10-5 sec-I. The values taken for k and X are as follows: A: k = 1 X 10-3 sec-I, X = 1 X 10-8 sec-I; B: k = 1 x 1O-4sec-1, X = 1 X 10-6 sec-I; C: k = 1 X 10-5 sec-I, X=lxl0-4sec-l; D: k=lxl0-6sec-l, X=lxl0-2sec-l; E: k=lxl0-7sec-., X = 1 x 10° sec-I. (Reproduced with permission of J. Chem. SocoFaraday l.)
4.
Kinetics of Compartmentalized
Free-Radical Polymerization Reactions
183
that are initially devoid of radical s and in which, at a certain time (taken as t = O),radicals suddenly begin to be generated in the external phase at a constant rateo Figure 10 illustrates the effect of increasing Xon the variation of l(t) with t, (1,and k being held constant. As expected, an increase in the value of X leads to a reduction in the value of "t at any instant. Figure 11 shows the effect of increasing X and decreasing k on l(t) as a function of t, with (1being held constant. As expected, for large values of X/k, the value of i(t) at long times approaches the Smith-Ewart Case 2 value of 0.5. Numerical solutions have also been obtained by Brooks (1980) using his three-state model (see above). The relevant simultaneous differential equations were solved by Euler's method. Brooks has included in his examples the case where (1 decays exponentially with time. In all the cases investigated, he finds that allowance must be made for bimolecular mutual termination of radicals and for the re-entry of desorbed radicals into reaction loci; he concludes that failure to take account of these possibilities can lead to serious errors.
VI.
Predictions for Molecular-Weight Distribution and Locus-Size Distribution
This chapter has been concerned exclusively with predictions for the distribution of locus populations within a compartmentalized free-radical polymerization reaction system. Other matters of considerable interest are the distribution of polymer molecular weights which the polymerization reaction produces, and the distribution of sizes of the reaction loci at the end of the reaction. A significant literature concerning both these aspects is beginning to develop, but beca use of the complexity of the subject and limited space, oniy a brief summary of the various contributions can be given here. The distribution of molecular sizes produced by a given addition polymerization reaction is determined by the balance of processes such as propagation, termination, transfer; branching, and cross-linking. In fact, the final polymer molecule produced is the "corpse" of the kinetic chain by which it was produced, as modified by transfer, branching, and crosslinking reactions. Early attempts to consider the distribution of molecular weights produced by a compartmentalized free-radical polymerization reaction were made by Katz et al. (1969) and by Saidel and Katz (1969). These workers derived a set of coupled partial differential equations, from the solution of which the molecular-weight distribution can, in principIe, be predicted. However, except for a few simple cases, solutions were restricted to predicting the lower moments of the molecular-weight distribution, and
184
D. C. Blackley
even these predictions required moderately extensive numerical calculations. Furthermore, the treatment did not take into account several important molecular events, such as the possibility of mutual termination with disproportionation, and the various transfer reactions. An alternative treatment, given by Min and Ray (1968), is also restricted to the prediction of the lower moments of the molecular-weight distribution. More recently, Sundberg and Eliassen (1971) have attempted a prediction of molecular-weight distribution for a reaction taking place isothermally in a well-mixed batch reactor. Micelles are assumed to be the only source of reaction loci. Both micelles and loci receive radicals at arate proportional to surface area. All the radicals produced in the external phase are absorbed by micelles and loci. Termination takes place immediately when two radical s become present in a locus and combination is the outcome. Allowance is made for the reaction of transfer to monomer. The predicted molecular-weight distribution is of the Flory "most probable" type with a polydispersity ratio of 2.0. As might be expected, the value of the rate coefficient for transfer to monomer relative to that for propagation has an important effect on both the average molecular weight and the distribution of molecular weights. An extensive treatment of this subject has been given very recently by Lichti et al. (1980),and a brief summary was given in an earlier paper (Lichti et al., 1978).The model assumed for this treatment is a three-state model in which i is O,1,or 2. An earlier paper (Lichti et al., 1977)applied a similar treatment to a two-state model in which i is O or 1. The treatment allows for the possibility that mutual termination may result in either combination or disproportionation. It also allows for the possibility of transfer to monomer. It has not, however, been possible to make allowance for branching and cross-linking. Prediction of the full distribution of molecular sizes, and not merely of particular moments of the distribution, has been achieved. The conclusion has been reached that compartmentalization of the reaction leads to a broadening of the molecular-weight distribution. An early contribution to the cognate matter of the prediction of the eventual distribution of locus sizes was made by Ewart and Carr (1954). The two principal factors that affect the nature of this distribution were considered to be (i) the distribution of locus sizes present when locus nucleation ceases, and (ii) the manner in which the loci grow subsequently as a consequence of polymerization. A third factor that may influence the growth pattern is the tendency for large loci to imbibe more monomer than do smallloci. O'Toole (1969) has discussed the extent of stochastic (as contrasted with deterministic) con tribu tion s to the polydispersity of locus sizes. He con-
4. Kineticsof Compartmentalized Free-Radical Polymerization Reactions 185 eludes that for moderately large loci, stochastic contributions are significant if the ratio of propagation to termination rate coefficients is greater than about 0.1. Sundberg and Eliassen (1971) have also made predictions of locus-size distribution using their modeI. The subject has also been discussed by Watterson and Parts (1971a,b). BirtwistIe and Blackley (in press) ha ve recently applied the locuspopulation generating function approach to the problem of the evolution of the locus-size distribution in compartmentalized free-radical polymerization reactions. They have introduced a generalized locus-population generating function 'P(~, t, v), defined as 00
'P(~, t, v) =
L
v¡(t, v)~¡
¡=o
(79)
where the function v¡(t,v) is such that v¡(t,V)DVis the fraction of the total number of reaction loci which at time t contain i propagating radical s and which also ha ve a volume that lies between v and v + DV.The relationship between this locus-population generating function and the generating function 'P(~, t) which has been used previously is elearly 'P(~, t) =
Vll.
(80) Loo
'P(~, t, v) dv
Theory for Generation of Radicals in Pairs within Loci
This problem was first treated in detail by Haward (1949). He considered the case of a bulk' polymerization that has been compartmentalized by subdividing the reaction system into a large number of separate droplets, each of volume v. Radicals are generated exelusively within the droplets and always in pairs. An example would be the polymerization of styrene in emulsified droplets dispersed in water initiated by the thermal decomposition of an oil-soluble initiator which partitions almost exelusively within the monomer droplets, In the model considered by Haward, radicals are unable to exit from the droplets into the external phase. The only radical-Ioss process is in fact bimolecular mutual termination. It therefore follows that all the droplets must always contain an even number (ineluding zero) of propagating radicals, and that the state of radical occupancy will change in increments of :t2. The conelusion reached by Haward is that in this case the effect of compartmentalization is to reduce the overall rate of polymerization per unit volume of disperse 'phase. The physical reason for this is that, as the volume of the droplets is reduced, so are the opportunities for a radical to escape from the others-and hence to avoid mutual
186
D. C. Blackley
termination. Compartmentalization therefore enhances the rate of termination relative to propagation, and therefore reduces the rate of polymerization; indeed, according to Haward, polymerization can be effectively suppressed altogether if the degree of compartmentalization is sufficiently great. The average degree of polymerization of the polymer produced is also reduced by compartmentalization. The expression derived by Haward for the overall rate of polymerization per unit volume of disperse phase in the steady state is as foUows: d[M]/dt
=
-kp[MJX/2k\)1/2
tanh{(X/2k\)1/2vNA}
(81)
where X is the rate of formation of new radicals containing one monomer unit, in unit volume of monomer, k\ is the rate coefficient for bimolecular mutual termination, and NAis the Avogadro number. Comparison with the corresponding equation for bulk polymerization without subdivision shows that the effect of compartmentalization is expressed by the factor tanh(vNAi.jX/2k,), and this is, of course, always less than unity. A more detailed treatment of, this problem has been given by O'Toole (1965). In this treatment, allowance is made for the possibility that radical s can exit from the loci into the external phase. However, no allowance is made for the possibility that radicals which do so exit may reenter the reaction loci and reinitiate polymerization there. The transitions which affect the numbers of loci which cross a notional boundary between states of radical occupancy i and i + 1 are illustrated in Fig. 12. The condition for the steady state is readily found to be k(i + l)n¡+1 + x(i + l)in¡+1 + x(i + 2)(i + l)n¡+2 = !CT(n¡ + n¡-I) {j+2)(i+l)n¡+2X
(i+l)ni+lk
(i+ I)lnl+lx
(82)
1+2
i+1
---- -- - - -- -- - 1--- - --n¡cr/2 i-I nl-lcr/2 Fig. 12. Transitions between states of radical occupancy required for derivation of OToole equation for rate of transition of loci across notional barrier between states i and i + 1 in the case where radicals are generated in pairs within reaction loci.
4. Kineticsof Compartmentalized Free-Radical Polymerization Reactions 187 where (j is now the rate of formation of single radicals within a single locus, and therefore (j/2 is the rate of formation of pairs of radicals within a single locus. The remaining symbols have their previous significances. Introducirig the parameters 8 and m as defined previously, this equation becomes
(m + i)(i + l)n¡+1 + (i + 2)(i + l)n¡+2= t8(n¡ + n¡-l)
(83)
An equation of this type must be satisfied at notional boundaries between each pair of neighboring states of radical occupancy, if the reaction system as a whole is to be in a steady state. By introducing the locus-population generating function 'P(~) as defined previously, this infinite set of equations can be combined together to give the single equation d2'P/d~2 = Cm/O
+ ~)J d'P/d~ - (8/2)'1' = O
(84)
The solution of this equation consistent with the physical constraints of the reaction system is l-m
'P(~) = A(l
h
+ ~)-r-Im;1 { 4(1 + ~)}
(85)
where A is a normalizing constant and h is as defined previously. The result obtained for Viis
where the combinatorial symbols have their usual meanings, and ¿j is zero for even values of i.and unity for odd values of i. The average number. of propagating radical s per locus is found to be given by
-1 =-h I(m+ 1)/2(h/2) 4I(m-1)/2(h/2)
(87)
For the case where loss of radical s by first-order processes is of negligible significance, the expression for 't'assumes the simple form 1=
ih tanh(h/4)
List of Symbols A [AJ,(AzJ a B Bp
constant column eigenvectors (4
(88)
188 b q-I/21(~) nCr e C¡,C2 h l. ; 1
Jt..lm j Kp k ko kp kt ktE k,p [o p M [M] m N NA ni
D. C. Blackley 0,1,2, ... of order p and parameter
stationary
of radicals in external phase
concentration
constants associated with [A ¡] and [A 2] (80)1/2 modified Bessel function of order t¡ number of propagating radicals in single reaction locus average number of propagating radicals in single reaction Jacobi polynomial of order p row of matrix [O]
rate coefficient for propagation rate coefficient for bimolecular
mutual
rate coefficient for bimolecular rate coefficient for bimolecular
mutual termination mutual termination
concentration kvlkt
of monomer
q
k+~
x y
of matrix [O]
locus
number of reaction loci in unit volume of reaction system Avogadro number number of loci in unit volume of reaction system which contain ; propagating radicals matrix of ni values
T(t) t V v X
in external phase in reaction loci
= klx
0,1,2, oo.
rip
at.reaction
loci
termination
zeroth component of pth left eigenvector amount of monomer
p
s
locus
constant associated with term containing e-ti'. coefficient characterizing rate of exit of radicals from reaction kvla
[n;]
R¡-i+l
-1-
Gegenbauer polynomial combinatorial symbol
k+X rate of transition of loci across national boundary between states of radical occupancy ; and ; + 1 radius of sphericaI reaction locus ith component of pth right eigenvector of matrix [O] maximum number of propagating radicals in single reaction locus part of 'I'(~, 1) which depends only on 1 time variance of distribution of locus populations volume of reaction locus rate of formation of new radicals containing one monomer unit, in unit volume of monomer 2';6(1 + ~) o/' (1 + W2 'I'(~)
xl-m
Z ex
2Nk,pk,Jy2v see (10
p r
(1/2X
y
pIe
gamma function;
(u). is a Pochhammer
symbol which denotes r(u + K)/r(u)
4. Kinetics of Compartmentalized Free-Radical Polymerization Reactions 189 o for evenvaluesof i and 1for odd valuesof i uv/k,= u/X
e e'
u'v/k,
O(t)
).
AI,A2 Ap J1 Vi
E(~)
~ p p' u u' Uo and C(
, 'p q,(t) X
'P [n]
= u'/x
time-dependent parameter of Poisson distribution separation constant eigenvalues associated with [A tJ, [A2] pth eigenvalue of matrix [n] parameter of initial Poisson distribution of locus populations fraction of loci which contain i propagating radicals part of 'I'(~, t) which depends only on ~ auxiliary variable of locus-population generating function rate of entry of radicals into all reaction loci in unit volume of reaction system rate of formation of new acquirable radicals in unit volume of reaction system average rate of entry of radicals into a single locus reaction locus, i.e., p/N, or rate of formation of radicals within a single reaction locus p'/N are such that u = u o r" average number of propagating radicals in single reaction locus I/XP(P + m - 1) time-dependent parameter of Poisson distribution kJv locus-population generating function matrix of coefficients
[no], [nI] are such that [n]
= [no]
+ [ntJ
References Allen, P. W. (1958). J. Col/oíd Sci. 13,483-487. Azad, A. R. M., and Fitch, R. M. (1980). Paper presented
at Am. Chem. Soco Emulsion
Symp.. Las Vegas Pr~prints, pp. 537-542. Birtwistle, D. T., and Blackley, D. C. (1977). J. Chem. Soco Faraday Birtwistle, D. T., and Blackley, D. C. (1979). J. Chem. Soco Faraday Birtwistle, D. T., and Blackley, D. C. (l98Ia). J. Chem. Soco Faraday Birtwistle, D. T., and Blackley, D. C. (198Ib). J. Chem. Soco Faraday
Polym.
173, 1998-2009. 175, 2051-2064.
177, 413-426. 177,1351-1358. Birtwistle, D. T., Blackley, D. c., and JefTers, E. F. (1979). J. Chem. Soco Faraday / 75, 2332-2358. Blackley, D. C. (1975). "Emulsion Polymerisation: Theory and Practice," Science, London. Blackley, D. C., and Haynes, A. C. (1977). Br. Polym. J. 9, 312-321. Brooks,
B. W. (1978). J. Chem. Soco Faraday /74,
p. 95. Applied
3022-3056.
Brooks, B. W. (1979).J. Chem.SocoFaraday /75, 2235. Brooks, B. W. (1980). J. Chem. Soco Faraday 176, 1599-1605. Ewart, R. H., and Carr, C. 1. (1954). J. Phys. Chem. 58, 640-644. Fitch, R. M. (1973). Br. Polym. J. 5, 467-483. Fitch, R. M., and Tsai, C. H. (l97Ia). Plenum Press, New York.
"Polymer
Colloids"
(R. M. Fitch, ed.), pp. 73-102.
Fitch, R. M., and Tsai, C. H. (I97Ib). Plenurn Press, New York.
"Polyrner
Colloids"
(R. M. Fitch, ed.), pp. 103-116.
Friis, N., and Hamielec, A. E. (1973). J. Polym. Sci. Polym. Chem. Ed.2,3321-3325.
190
D. C. Blackley.
Gardon, Gardon,
J. L. (1968). J. Po/ym. Sci. Part A-/6, 623-641. J. L. (1973). J. Po/ym. Sci. Po/ym. Chem. Ed. 2, 241-251.
Gilbert,
R. G., and Napper,
D. H. (1974). J. Chem. Soco Faraday 170, 391-399.
Gilbert, R. G., Napper, D. H., Lichti, G., Ballard, M., and Sangster, D. F. (1980). Paper presented at Am. Chem. Soco Emu/sion Po/ym. Symp., Las Vegas Preprints, pp. 527-530. Grancio, M. R., and Williams, D. J. (1970). J. Po/ym. Sci. Part A-1S, 2617-2629. Hansen, F. K., and Ugelstad, J. (1978). J. Po/ym. Sei. Po/ym. Chem. Ed. 16, 1953-1979. Hanseii, F. K., and Ugelstad, J. (1979a). J. Po/ym. Sei. Po/ym. Chem. Ed. 17,3033-3046. Hansen, F. K., and Ugelstad, J. (1979b). J. Po/ym. Sci. Po/ym. Chem. Ed. 17, 3047-3068. Haward,
R. N. (1949).
Hawkett,
B. S., Napper,
/
Po/ym.
Sci.
4, 273-287.
D. H., and Gilbert, R. G. (1975). J. Chem. Soco Faraday 171,2288-2295.
Hawkett, B. S., Napper, D. H., and Gilbert, R. G. (1977). J. Chem. Soco Faraday 173,690-698. Hawkett, B. S., Napper, D. H., and Gilbert, R. G. (1980). J. Chem. Soco Faraday 176,1323-1343. Katz, S., Shinnar, R., and Saidel, G. M. (1969). Adv. Chem. Ser. 91, A.C.S., p. 145-157. Kendal, M. G., and Stuart, A. (1963). In "The Advanced Theory ofStatistics," 2nd ed., Vol. 1, p. 30. Griffin, London. Keusch,
P., and Williams,
Keusch, P., Keusch, P., Lansdowne, Faraday
D. J. (1973). J. Po/ym. Sci. Po/ym. Chem. Ed. 11, 143-162.
Prince, J., and Williams, D. J. (1973). J. Macromo/. Sci.-Chem. A7(3), 623-646. Graff, R. A., and Williams, D. J. (1974). Macromo/ecu/e~ 7,304-310. S. W., Gilbert, R. G., Napper, D. H., and Sangster, D. F. (1980). J. Chem. Soco 176, 1344-1355.
Lichti, G., Gilbert,
R. G., and Napper,
D. H. (1977). J. Po/ym. Sci. Po/ym. Chem. Ed. 15, 1957-
1971. Lichti, G., Gilbert, R. G., and Napper, Latex Conf, London Paper No. 1. Lichti, G., Gilbert, 1323. Min, K. Morton, Napper, O'Toole, O'Toole,
R. G., and Napper,
D. H. (1978). Paper presented
at P/ast. Rubb. Inst. lnt.
D. H. (1980). J. Po/ym. Sci. Po/ym. Chem. Ed. IS, 1297-
W., and Ray, W. H. (1968). J. App/. Po/ym. Sci. 22, 89-112. N., Kaizerman, S., and Altier, M. W. (1954). J. Col/oid Sci. 9, 300-312. D. H. (1971). J. Po/ym. Sci. Part A-19, 2089-2091. J. T. (1965). J. Appl. Po/ym. Sci. 9, 1291-1297. J. T. (1969). J. Po/ym. Sci. Part C 27, 171-182.
Saidel, G. M., and Katz, S. (1969). J. Po/ym. Sci. Part C. 27, 149-169. Smith, W. V., and Ewart, R. H. (1948). J. Chem. Phys. 16,592-599. Stockmayer, W. H. (1957). J. Po/ym. Sci. 24, 314-317. Sundberg, D. C., and Eliassen, J. D. (1971). In "Polyrner Colloids" (R. M. Fitch, ed.), pp. 153-161. Plenum Press, New York. Ugelstad, J., and Hansen, F. K. (1976). Rubber Chem. Techno/. 49, 53/Hi09. Ugelstad, J., Merk, P. c., and Aasen, J. O. (1967). J. Po/ym. Sci. Part A-I 5, 2281-2288. van der Hoff, B. M. E. (1958). J. Po/ym. Sci. 33, 487-490. van der Hoff, B. M. E. (1962). In "Polyrnerization and Polycondensation Processes," Adv. in Chem. Ser. 34, pp. 6-31. American Chemical Society. Vanderhoff, J. W. (1976). Proc. Water Borne Higher Solids Coating Symp. Paper No. 6. Vanzo, E., Marchessault, R. H., and Stannett, V. (1965). J. Col/oid Sci. 20, 62-71. Watterson, J. G., and Parts, A. G. (1971). Makromo/. Chem. 146, 11-20. Weiss, G. H., and Dishon, M. (1976). J. Chem. Soco Faraday 172,1342-1344. Williams, D. J. (1971). J. E/astop/ast. 3, 187-200. Williams,
D. J. (1973). J. Po/ym. Sci. Po/ym. Chem. Ed. 2, 301-303.
5 Mamoru Nomura
1. Introduction . 11. Polymerization Rate Equations Involving FreeRadical Desorption . A. Reaction Locus . B. Polymerization Rate Equations 111. Derivation of Rate Coefficient for Radical Desorption from Particles. A. Definition of Radical Desorption and Reabsorption B. Derivation of Mass- Transfer Coefficient for Radical Desorption and Reabsorption . C. Derivation of Rate Coefficient for Radical Desorption IV. Effect. of Free-Radical Desorption on the Kinetics of Emulsion Polymerization A. Effect on the Rate of Emulsion Polymerization. B. Effect on Micellar Particle Formation V. List of Symbols . References
l.
192 192 194 199 199 202 204 210 210 214 217 219
Introduction
The kinetic behavior of ernulsion polyrnerization is greatly atfected by radical desorption from polymer particles. This has been shown by Ugelstad et al. (1969), Lítt et al. (1970), Harada et al. (1971), Friis and Nyhagen (1973), and Nomura et al. (1971). It is believed that the deviation of the kinetic behavior of the emulsion polyrnerization of water-soluble monorners such as vinyl acetate and vinyl chloride from the Srnith and Ewart (1949) Case 2 kinetic theory is mainly due to dominant desorption of 191 EMULSION
POLYMERIZATION
Copyright It> 1982 by Aeademie Press. 1ne. AIl rights of reproduetion in any form reserved. ISBN 0-12-556420.1
192
Mamoru Nomura
radical s from particles. Although the importance of this physical phenomenon was pointed out by Smith and Ewart in the 1940s, the quantitative understanding was insufficient to explain the kinetic deviation of vinyl acetate and vinyl chloride emulsion polymerizations from the Smith-Ewart Case 2 kinetic theory. Recently, Ugelstad et al. (1969) proposed a semiempirical rate coefficient for radical desorption in vinyl chloride emulsion polymerization. On the other hand, Nomur.a et al. (1971, 1976) have derived arate coefficient for radical desorption theoretically with both stochastic and deterministic approaches and have successfully applied it to vinyl acetate emulsion polymerization. They also pointed out that radical desorption from the particles and micelles played an important role in micellar particle formation. Friis et al. (1973) also derived the rate coeffieient for radical desorption in a different way. Litt et al. (1981) discussed in more detail the chemical reactions incorporated in the physical process of radical desorption in the emulsion polymerization of vinyl acetate.. In this chapter, the polymerization rate equations for emulsion polymerization will be reviewed briefly: Then, the rate coefficient for radical desorption from the particles will be derived theoretically, and the effect of radical desorption on the rate of emulsion polymerization and the micellar particle formation will be discussed.
11. Polymerization Rate Equations Involving Free-Radical Desorption A.
Reaction Locus
Harkins (1947) and Smith and Ewart (1948) assumed that in emulsion polymerization the polymerization loei were inside the particles because the rate of styrene emulsion polymerization, for example, was proportional to the number of polymer particles presento However, the polymerization loci in the emulsion polymerization of water-soluble monomers such as vinyl acetate and vinyl chloride have long been discussed because the rate of emulsion polymerization of these monomers was not proportional to the number of polymer particIes presento Patsiga et al. (1960) and Giskehaug (1965) carried out the seeded emulsion polymerizations of vinyl acetate and of vinyl chloride, respectively, and found that in both systems the rate of polymerization was proportional only to the 0.15-0.20 power of the number of polymer particles. From this finding they concIuded that the main locus of the emulsion polymerization of water-soluble monomers must be in the water phase. This conclusion seems reasonable because the solubilities of these monomers are about 100
5. Desorption and Reabsorption of
Free Radicals
193
times greater than that of styrene. But this inference may be excluded from the following simple discussion. Let us consider a seeded emulsion polymerization where no particle formation occurs and hence the number of polymer particles is constant. At a steady state, the overall rate of radical entry into the particles PA is expressed by
= PA
rate of radical production in the water phase
[ -
J+
rate of radical desorption from polymer particles J
[
rate of radical termination
[
in the water phase
J
(1)
Since the value of PA is not so different from the value of Pw, the rate of radical production in the water phase, we get (2) It must be noted here that the quantities PA and Pware different from one another. Ir the diffusion law can be applied to the radical entry into the particles, PA is given by
PA = ka[R~JNT~ 2ndpDw[R~JNT
(3)
where [R~J is the radical concentration in the water phase, NT is the number of polymer particles, dp is the diameter of a particle, ka is the rate coefficient for radical entry into the particles, and Dw is the diffusion coefficient for the radical s in the water phase. Using Eqs. (2) and (3), one can calculate the average residence time for a radical to be in the water phase before entering into the particles tred, the average time needed for a radical to add one monomer unit in the water phase tadd, and the average time needed for a radical to be deactivated by the mutual termination reaction in the water phase ttermfrom the following equations: tred= [R~J/PA ~ 1/2ndpDwNT
(4)
tadd= l/kp[MwJ
(5)
tterm= [R~J/2ktw[R~J2 ~ ndpDwNT/ktwpw
(6)
where kp is the propagation rate constant, [MwJ is the monomer concentration in the water phase, and ktwis the termination rate constant in the water phase. The values of tred, tadd' and ttermare calculated to be -10-5, -4 x 10-4, and - 103 sec, respectively, when the following numerical constants are used: ktw= 6 X 108 (dm3/mol sec), Pw= 1016(molecules/dm3 sec),
194
Mamoru Nomura
[Mw] = 0.5 (mol/dm3), dp = 10-7 (m), Dw= 10-9 (m2/sec), kp = 5000 (dm3/mol sec), and NT = 1017(particles/dm3 water). Comparing the values of (red' (add, and (term,one can conclude that the radical s in the water phase enter the particles without adding any monomer unit or terminating with other radicals in the water phase under normal conditions. This indicates that the pro paga tion and mutual termination reactions in the water phase can be neglected, and hence that these reactions occur practically in the particles under normal conditions. B.
Polymerization Rate Equations
For emulsion polymerization systems where polymerization takes place exclusively in the particles, the rate of emulsion polymerization can be expressed in the same way as in other radical polymerizations
.
Rp
= -dM/dt = kp[Mp][R;]Mw .
(7)
where Rp is the rate of emulsio~ polymerization [kJdm3(water) sec], M is the monomer concentration in the water phase [kJdm3 (water)], kp is the propagation rate constant (dm3/mol sec), [Mp] is the monomer concentration in the polymer particles (mol/dm3), and Mw is the molecular weight of monomer (kJmol). [R;] and NT can be expressed as follows in terms of the number of polymer particles containing n radicals Nn. <XJ
[R;] = (Ni + 2N2 + 3N3 + ... + nNn + ...)/NA <XJ
NT=No+Ni+N2+...+Nn+"'=
¿Nn n=O
=
¿
n=i
nNn/NA
(8) (9)
where NA is Avogadro's number, [R;] is given in mol/dm3 water, and Nn in particles/dm3-water. The average number of radicals per particle ñ is defined by ñ
= (~i nNn)j NT
(10)
Thus, the rate of emulsion polymerization given by Eq. (7) is also rewritten as Rp = kp[Mp]ñNTMw/NA
(11)
In order for the rate of emulsion polymerization to be predicted by Eq. (7) or (11), Nn must be represented as a function of the properties of the emulsion polymerization system in question. Smith and Ewart proposed the steady-state equation for Nn in terms of the rate of radical entry into the particles, the rate of radical desorption
195
5. Desorption and Reabsorption of Free Radicals
from the particles, and the rate of radical termination within the particles. For the nonsteady state dNn dt
PA
() -( )
N T Nn-l
+ k eap
PA
n+ I
(~ ) ()
N n+l
+ k tp
n
NT Nn - keap vp Nn - ktp [
[
(n + 2)(n + I) N n+2
~
n(n - I) vp
J Nn
J
(12)
where ke is the rate constant for radical desorption from the particles (m/sec), ap is the surface area of a particle (m2), vp is the volume of a particle (m3), and ktp is the rate constant for termination (m3/molecule sec). Since the rate constant for radical desorption should depend on the radical chain length, the rate constant ke represents an average value. The rate coefficient for radical desorption from the particles kr is defined as (13) wh~e (14) where kj is the rate constant
for radical desorption
from the particles for
j-
mer radical s, 'j is the ratio of the number of j-mer radicals to the total number of radicals nNn contained in Nn particle, and j = O indicates the initiator radical. By solving Eq. (12) for Nn and introducing it into Eq. (10), one can calculate the value of ñ, and accordingly, 'the rate of emulsion polymerization by Eq. (11).. Although many investigations have been reported concerning the solution of Eq. (12), only the principal work will be reviewed briefly here. For more details, the readers should refer to the review article by Ugelstad et al. (1976). Smith and Ewart (1948) did not obtain a general solution for Eq. (12) but rather solved it for three limiting cases, applying a steady-state hypothesis, i.e., dNn/dt = O. Case 1 PA/NT ~ kr In this case, the following relation holds: (15) Further, (a) When termination in the water phase is dominant (ktp/vp ~ kr, Pw~ 2ktw[R~]2) (16)
Mamoru Nomura
196
where md indicates the partition coefficient of radicals between the particle and water phases defined by Eq. (38). (b) When termination in the particles is dominant (ktP/vp~ kr, Pw~ 2(pAiNT)N1) ñ = (Pw/2krNT)1/2 ~ 0.5 Case 2
(17)
kr ~ pAiNT ~ ktP/vp
ñ
= 0.5
(18)
Equation (18) is most generally known as the Smith-Ewart theory. Case 3 pAiNT ~ ktp/vp ñ
= (PAvp/2ktpNT)1/2 ~
0.5
(19)
Further, when the termination of radicals in the water phase or the desorption of radicals from the particles could be neglected, Eq. (19) is rewritten as ñ =.(Pwvp/2ktpNT)1/2
(20)
Stockmayer (1957) obtained a general solution for Eq. (12), applying a steady-state hypothesis, and expressed ñ by the modified Bessel function of the first kind. O'Toole (1965) later extended it and gave a physically more acceptable solution for ñ as follows: ñ
= -!a[Im(a)/Im-l(a)]
(21)
where a2 = 80(
O(= PAvp/ktpNT
(22)
and m = krvJktp
(23)
Gardon (1968) has solved Eq. (12) numerically for the case of negligible desorption of radical s from the particles without assuming the steady state, stating that the Stockmayer solution for ñ is incorrect because there is no steady state in principie and because Eq. (12) includes the time-dependent parameter vp' However, the results of numerical calculation by Gardon coincide almost completely with those predicted by the Stockmayer solution for no radical desorption from the particles. This also supports the validity of applying the steady-state hypothesis to the solution for Eq. (12) under normal conditions for emulsion polymerization. Noting that in the treatments by Smith and Ewart, by Stockmayer, and by O'Toole the "fa te " of the desorbed radicals was not necessarily specified,
5.
197
Desorption and Reabsorption of Free Radicals
Ugelstad et al. (1967) claimed that Eq. (12) should be solved simultaneously with the following balance equation on the radicals in the water phase. (24) Since the steady-state hypothesis is applicable to Eq. (24), it is rewritten in the same form as Eq. (1): PA = ka[R:JNT = Pw
+ ¿kfnNn - 2ktw[R:J2
(25)
Considering that ¿nNn = ñNT, Eq. (25) is rewritten in a dimensionless form a = a' + mñ - Ya2 (26) where a = PAVp/ktpNT a' = Pwvp/ktpNT
(27)
m = kfVp/ktp
(23)
= 2ktwktp/k;NTvp
(28)
and y
Ugelstad et al. (1967) solved the simultaneous equations Eqs. (21) and (26) for ñ and plotted the calculated value of ñ against the value of a' at fixed value of Y, varying the value of m as a parameter. Since the radical termination in the water phase is negligible under normal emulsion polymerization conditions as mentioned in Section ~I,A,the condition Y = Ois most important for usual emulsion polymerizations. Figure 1 shows a plot of 10'
y=o
IC
164
10-2
104
a' Fig. 1. Relationship between ñ and IX'when termination in the water phase is neglected. IX'= Pwvp/NTk,pand m = kfVp/k,p. (Reprinted with permission of Journal of PolyrnerScience.)
198
Mamoru Nomura
logñ versus logO(', varying the value of m for the case of Y = O. The treatment by Ugelstad et al. (1967) is most general and correct, and hence, Eqs. (21) and (26) are important in predicting the value of ñ, that is, the rate of emulsion polymerization. Since it is inconvenient to use Eqs. (21) and (26) directly, however, several empirical or approximate equations for ñ are derived for the case where Y=O. 1. When m = O
-
1
1/2
0('
( )
n= -+4 2
(29)
2. When instantaneous termination is dominating in the particles and ñ < 0.5 ñ
= !(- e + J c2 + 2e)
e = O('/m= Pw/kfNT
(30)
Equation (30) leads to
ñ = 0.5
(31)
when e -4 00, and when e < 10-2 ñ = (Cj2)1/2
(32)
3. When ñ < 0.2 -
0('
[(
n= -
2
4.
1+-
1 1/2 m)J
(33)
When m -4 00 or ñ ~ 0.5 ñ = (0('/2)1/2
(34)
Equation (29) is an empirical equation presented by Ugelstad and Merk (1970) and may be useful in styrene emulsion polymerization because the value of mis about 10-\ or less than that under normal reaction conditions in this system. On the other hand, Eqs. (30) and (33) are applicable to vinyl acetate and vinyl chloride emulsion polymerizations (Ugelstad et al., 1969; Harada et al., 1971; Friis and Nyhagen, 1973). Equation (34) explains very well the rate of aqueous dispersion polymerization of vinyl acetate in the absenceof emulsifier(Nomura et al., 1978). It is clear from the discussion so far that as long as the value of the rate coefficient for radical desorption from the particles kf cannot be estimated quantitatively, the rate of emulsion polymerization is impossible to predict. In the next section, therefore, the quantitative expression for kf will be derived.
5. Desorption and Reabsorption of Free Radicals
199
111. Derivation of Rate Coefficient for Radical Desorption from Particles Ugelstad et al. (1969) first suggested experimentally that in vinyl chloride emulsion polymerization kf may be expressed in the following form kf
= kv-2/3 = k'd-2 p p
(35)
Nomura et al. (1971) also discussed this problem almost at the same time and derived the theoretical expression for kf, which was inversely proportional to the square of particle diameter, as shown by Eq. (35). In this section, the derivation of kf by the Nomura and Harada method is mainly explained (Harada et al., 1971; Nomura et al., 1976; Nomura and Harada, 1981). A.
Definition 01 Radical Desorption and Reabsorption
As shown in Fig. 1, the value of ñ becomes independent of the value of kf in the range of ñ ~ 0.5. This means that the rate coefficient for radical desorption from the particles is important in the range (ñ < 0.5) where the polymer particle contains at most one radical. For this reason, we consider an emulsion polymerization system where (i) the particles contain at most one radical and (ii) instantaneous termination takes place when another radical enters the particle that already contains a radical. In this case, the rate coefficients for radical desorption and reabsorption are defined in the following balance equation on the active particles containing one radical (36) where N* is the number of active polymer particles containing one radical, ka is the rate coefficient for radical entry into the particles, and No is the number of dead particles containing no radicals. The first term on the righthand side of Eq. (36) shows the rate of decrease in the number of active polymer particles due to radical desorption from the particles containing a radical. The second term usually expresses the rate of increase in the number of active particles containing two radicals if instantaneous termination does not occur when another radical enters the particle already containing one radical. However, since we supposed that instantaneous termination does occur in this case, this term represents the rate of decrease in the number of active particles containing a radical, and accordingly, should be negative. The third term indicates the rate of increase in the number of active particles by radical entry into the dead particles. Let us consider the diffusion of radicals. According to the two-film theory developed by Lewis and Whitman (1924) for mass transfer across the
200
Mamoru INTERFACE I WATER PHASE
PARTlCLE
-
-DISTANCE
Fig. 2. (Reprinted
Nomura
Schematic diagram of concentration gradients near phase boundary. with permission of Journal of Applied Polymer Science.)
Cp
= n/vp.
interface between two phases, the concentration gradients near the phase boundary can be assumed to' be as shown in Fig. 2. Applying Fick's diffusion law, the rate of radical desorption from a single particle that contains, for example, n radicals with same chain length, is generally expressed by JRo= -d(vpCp)/dt = -dn/dt = ksap(Cp- Cpi)= kwap(Cwi- Cw) (37) where ks and kw, respectively, denote the film mass-transfer coefficients for the inner and outer diffusion films adjacent to the interface between the particle and water phases, Cp is the concentration of radical s in the particle, Cw is the concentration of radical s in the water phase and i denotes the interface. The concentration of radicals at the interface, which is at equilibrium and usually very low, can be expressed by the linear relationship , Cpi
= rnd Cwi
(38)
whererndis the partition coefficient. Using Eqs. (37)and (38),we have J. = RO
-
dn = Cp dt (l/ksap)
- rndCw
-
+ (rnd/kwap) -
Ksap(Cp
rndCw)
(39)
(40)
here
=
l/ks + rnd/kw
(41)
l/Kw = l/rndks + l/kw
(42)
l/Ks
5. Desorption and Reabsorption of Free Radicals
201
where Ks and Kw are the overall mass-transfer coefficients. Equations (41) and (42) show that the overall resistance for mas s transfer is the sum of individual ones. From Eqs. (41) and (42) we obtain (43) Since we are considering an emulsion polymerization system where the particle contains at most one radical, the rate of decrease in the number of active particles containing a j-mer radical equals the desorption rate of jmer radicals from the particles. Thus, applying Eq. (39) we have
= Ksjap[(l/vp)
-dNlfdt
- mdJR:J]N/ + Ksjap[(O/vp) - mdJR:J]
x (No + N,* + Nt + Ni +.oo + N/-1 + N/+1 + oo.)
(44)
where N/ is the number of active particles containing a j-mer radical, mdj is the partition coefficient for j-mer radicals between the water and particle phases, Nt is the number of polymer particles containing an initiator radical, and [R:J is the concentration ofj-mer radical in the water phase. The first term on the right-hand side of Eq. (44) represents the desorption rate of a j-mer radical and the last term expresses the absorption rate of jmer radical s from the water phase into the particles containing no j-mer radicals. Rewriting Eq. (44) we get dNj/dt here
= -Ks/ap/vp)NJ
+ KsjapmdlR:j]N* + KsjapmdlR~j]No (45)
N* = Nt + Ni + Ni + ... + N/-'l + N/ + N/+1 + ...
(46)
Summation of Eq. (45) with respect to Nj* leads to dN*/dt
= d ¿Nlfdt = -('1 KsjN/Hap/vp)+ (¿KSjmdlR:J)apN* + (¿ KSjmdJR:j])apNo
(47)
The second term on the right-hand side of Eq. (47) usually represents the absorption rate of j-mer radical from the water phase into the active particles that already contain a radical, and hence represents the rate of increase in the number of particles containing two radicals, one of which is a j-mer radical. However, this term must be changed from positive to negative because it expresses the rate of decrease in the number of active particles when instantaneous termination in the particles is assumed. Thus, using Eq. (43), Eq. (47) can be rewritten as dN* /dt = - ('1KsjN/)(ap/vp)- (¿ KWjmdJR:j])apN* (48)
202
Mamoru
Nomura
Equation (48) defines the radical desorption and reabsorption in the polymer particles and corresponds to Eqo (36)0Thus, comparing the corresponding terms in Eqso (36) and (48), we obtain the following equations
whichdefinethe coefficientskf and ka
o
kf
= LKsiNNN?i')(ap/vp) = LKOJ{NNN*)
ka = (LKw~[R:j]/[R:])ap
KOj =
= ¿Kai[R:j]/[R:])
Ksiap/vp) (49)
Kaj = Kwjap (50)
where [R:] = [R:.J + [R:¡] + [R:2] + o.. + [R:j_¡] + [R:j] + 0.0 (51) In this case, ke and (j defined in Eqso (13) and (14) are, respectively, represented by ke =
B.
¿
KSJ{Nf/ N*)
Derivation 01 Mass-Transler and Reabsorption
(j
= (NNN*)
Coefficient lor Radicql Desorption
In order for the rate coefficients kf and kaodefined by Eqso (49) and (50), to be predicted it is necessary to know how KSj and Kwj are expressed in terms of the chemical and physical properties involved in the desorption and reabsorption processeso First of all, let us consider the mass-transfer coefficient for a j-mer radical in the individual diffusion filmso There is a large number of published studies concerning the mass-transfer coefficient in an external diffusion film around a spherical particleo One of these is the following semitheoretical equation proposed by Ranz and Marshall (1952) Sh
=2 +
006R~/2S~/3
(52)
where Sh is the Sherwood number (kwAJDwj), Re the Reynolds number (dpuP//l), and Sc the Schmidt number (J1/pDwj)o Since such small spheres as emulsion polymer particles will move with the eddies of the fluid, there will be no relative velocity u between the surface of the particle and the fluid (water)o Therefore, the value of Re can be regarded as zero, and hence Sh = 2. From the value of Sh = 2 we get kwj = 2Dwidp
(53)
On the other hand, mass-transfer inside the viscous polymer particles will occur by molecular diffusiono According to an analytical solution to the diffusion equation inside the particles, average mass-transfer coefficient between time O", t,ks is given as follows (Newman, 1931):
_k 0= SJ
- dp 1n 6 t
[~ ~ 2- ( 2 L-
1tn=¡n
2 exp
4n21t2Dpl dp2
)]
(54)
203
5. Desorption and Reabsorption of Free Radicals
Since this coefficient is too complicated to employ for our present purpose, we use an approximate mass-transfer coefficient derived by the following simple treatment. The average time t spent by a radical inside a particle before it escapes from the particle can be ca1culated using the Einstein diffusion equation. Nomura and Harada (1981) used the following value for t:
(55a) Recently, Chang et a/. (1981) considered two cases: (1) when a radical enters at the edge of the particle t is given by (55b) and (2) when a radical is generated anywhere in the particle t is given by (55c) We assume that the rate of radical desorption from the particle can be ca1culated approximately using the following equation obtained from Eq. (37) by neglecting the term Cpji because the value of Cpji is usually very low compared to that of Cpj. (56) Using Eq. (56), the average time t spent by a radical inside the particle before it escapes fram the particle will be given by t =. (CpjVp)/lR*= (Cpjvp)/ksjap Cpj = dp/6ksj By comparing
Eqs. (55) and (57) we obtain ksj
= /3(Dp/dp)
/3 = i
-i
(57)
(58)
Substitution of Eqs. (53)and (58)into Eqs. (41)and (42)leadsto K . = 2Dwj 1 + SJ
mdjdp
(
2Dwj /3mdjDpj
)
-1
= 2Dwj
bj
(59)
mdjdp
and KWj
= m.K dJ
sj
- 2Dwjb. l
(60)
dp
where (61)
Mamoru Nomura
204
where bj is the ratio of the external film mass-transfer resistance to the overall mass-transfer resistance for j-mer radicals (mdikwj)/(l/Ksj)' C.
Derivation 01 Rate Coefficient lor Radical Desorption
To simplify the subsequent treatments, we make the following five assumptions: (i) polymer particles contain at most one radical, (ii) a radical with no longer than s monomer units can desorb from and enter into the particles with the same rate irrespective of chain length, (iii) instantaneous termination occurs when another radical enters the particle already containing a radical, (iv) no distinction is made between radicals with or without an initiator fragment on its end, and (v) water-phase reactions such as propagation, termination, and transfer can be neglected from a kinetic point of view, as shown in Section n,A. Under these assumptions, the rate coefficient for radical desorption from the particles is derived with both deterministic and stochastic approaches. 1. Deterministic Approach* According to the assumptions [(ii) and (iv)] given above, we can regard the values of KOj and Kaj defined by Eqs. (49) and (50) to be constant and equal to Ko and Ka regardless of radical chain length, j, respeCtively. Moreover, no radicals longer than s monomer units will be found in the water phase according to the assumption of (ii). Thus, Eqs. (49) and (50) can be rewritten as
kf
= KQI(~I:)+ Ko(~~) + Ko(Z!) + ... + Ko(~:)
k
[R~I
[R~l]
[R~2]
[R~s] "-
a = Kal [R~] + Ka [R~] + Ka [R~] +... + Ka [R~] = Ka
(62)
(63)
where KQIand Kal are the coefficients for initiator radical s and Ko and Ka are the coefficients for radicals other than initiators. Discrimination between the initiator and other radicals is made here because their chemical and physical properties are very different. Thus, the values of KQIand Ko are different. In order to get the relationship between Nj and N*, we have the balance equations with respect to N1*and Nf which contain an initiator radical and * See Nomura
et al., 1976 and Nomura
and Harda,
1981.
5.
205
Desorption and Reabsorption of Free Radicals
a j-mer radical, respectively. Applying a stationary-state hypothesis to these equations we obtain dNNdt
= KaI[R:¡]No -
(ka[R:] + kmr[Mp]+ kTf[Tp] + k¡[Mp] + KOI)N,*
=0
~~
dNT/dt = Ka[R:¡]No + k¡[Mp]N¡*+ (kmf[Mp] + kTf[Tp])N*
dNNdt
(ka[R:] + kmf[Mp] + kTf[1;,] + kp[Mp] + Ko)Ni
= Ka[R:j]No
= O
+ kp[Mp]Nt-¡
- (ka[R:] + kmf[Mp]+ kTf[Tp]+ kp[Mp]+ Ko)Nt = O dN.*fdt = Ka[R:s]No - (ka[R:]
~~ ~~
+ kp[Mp]Ns*-1 + kmrEMp] + kTf[Tp] + kp[Mp]
+ Ko)Ns*
=
O
~~
where k¡ is the initiation rate constant, kTfis the chain transfer rate constant to chain transfer agent, [Tp] is the concentration of chain transfer agent in the polymer particles and kmf is the chain transfer rate constant to monomer. Furthermore, by taking a balance on the water-phase radicals and applying a steady-state hypothesis we have (68) d[R:¡]/dt
= KoNi -
Ka[R:¡]NT
=O
(69)
d[R;j]/dt
= KoNt -
Ka[R:j]NT
=O
(70) (71)
Since high molecular weight polymers are usually produced in emulsion polymerization, it can be assumed that ka[R:], kmr[Mp],kTf[Tp] ~ kp[Mp], k¡[Mp],Ko" Ko
(72)
From Eqs. (64),(68), and (72) and the definition N* = ñNT,weobtain N,* =
Pw(1- ñ) -
n~
KOIñ + k¡[Mp]
By similar treatments, we have
n~
206
Mamoru Nomura
and j-¡
fVt
=
kp[AIp] Kon + kp[AIp]
(
) )[( )+ ( )fV* + (~ ) fVt
j
=(
kp[AIp]
kmr
kTf[Tp]
kp
kp[ AIp]
fVt
kp
]
(75)
Inserting Ego (75) ioto Ego (62) we get
kmr
fVt
kr = KOI
kTr[Tp]
k¡fVt
~
kp[AIp]
j
( )+ Ko[(k;)+ (kp[AIp])+ (kpfV*)] j':¡ (Koñ + kp[AIp]) fV*
(76) Introduction of Ego (73) and fV* = ñfVTinto Ego (76) leads to
k - K r-
[
Pw(1- ñ)
O( (KO(ñ + k¡[AIp])ñfVT
I(
kp[AIp]
] ) [k; + j
kmr
+ Ko j= ¡ Koñ + kp[AIp]
kTf[Tp]
PW(1- ñ)k¡
kp[AI!,] + (KO(ñ
+ k¡[AIp])kpñfVT] (77)
Application of kr given by Ego (77) to a real emulsion polymerization system will be shown latero 20 Stochastic Approach In this treatment (Harada et al., 1971) we make the same assumptions as given aboveo A radical in the particle has the probability of undergoing the following four events in the particle: (i) initiation and propagation reactions, (ii) chain transfer to monomer, polymer, emulsifier, and so on, (iii) termination reaction when another radical enters the particle, and (iv) desorption from the particle into the water phaseo If the probability for a radical to escape from the particle within the time interval for which the radical needs to add one monomer unit is designated as q, the probability for the radical not to desorb within the time interval p is given" by
p=l-q
(78)
Since a radical with no longer than s monomer units is assumed here to escape from the particles with the same rate, irrespective of chain length, the probabilities p and q should be constant regardless of radical-chain lengtho Considering Figo 3, the fraction
207
5. Desorption and Reabsorption of Free Radicals
containing (s+l) units
Fig. 3. Scheme for radical escape from polymer partic1e. (Reprinted with permission of Journal of Chemical Engineering, Japan.) transfer to monomer or transfer agent to desorb from the particles before growing to (5 + 1)-mer radical is given by
(79)
The rate of radical production by chain transfer to monomer and transfer agent can be expressed as (kmr[Mp]+ kTf[1;,])N*
(80)
Part of these radicals will escape from the particles before growing (5 + 1)-
mer radical s and that fraction is given by (81) This quantity also represents the desorption rate of radicals generated originally by chain transfer to monomer or chain transfer agent. The appearance of small radicals that can desbrb from the particles also occurs by entry of initiator radicals. Since termination in the water phase can be neglected (as shown in Section n,A), all initiator radicals generated in the water phase enter the particles. The entry of initiator radical s into the particles containing no radicals results in an increase in the number of polymer particles containing an escaping radical, with the rate given by (82) Let <1\be the probability for an initiator radical to escape the particle before it adds one monomer unit. Then, the desorption rate.of radicals that have grown from the initiator radicals is expressed by (83) The first term represents the desorption rate of initiator radicals that enter the particles and the last term represents the desorption rate of the radicals that have grown from initiator radicals. At steady state, the concentration of radical s in the water phase is constant. This means that the rate of
208
Mamoru Nomura
radical entry into the partic1es should be the same as that of radical desorption from the partic1es. Therefore, the decrease, due to radical desorption, in the number of partic1es containing escaping radicals is partly recovered by radical entry into the partic1es containing no radicals. Let N be the number of polymer partic1es containing an escaping radical. Then, KoN represents the rate of radical desorption, and KoN(N o/NT)is the rate of recovery in the number of partic1es containing an escaping radical by radical entry into. the partic1es containing no radicals. Therefore, the apparent (or net) rate of radical desorption per partic1e containing an escapingradical is given by (84)
[KoN - KoN(N o/NT)]/N = Koñ
For initiator radical s Ko in Eq. (84) should be replaced by Ko). Considering the rate for each event (ii) to (iv) to occur, only events (i) and (iv) are usually important in calculating the probability, p. The probability p is therefore expressed by p
=
1 -'q
=
(85)
kp[Mp]
Koñ + kp[Mp]
Substitution of Eq. (85) into Eq. (79) leads to
~ = Koñ f.
(
kp[Mp]
) j
= 1-
kp[Mp]j= 1 Koñ + kp[Mp]
s
kp[Mp]
(Koñ+ kp[Mp])
(86)
. In the same way we obtain cI\ =
(87)
KOJñ
Ko)ñ + k¡[Mp]
It must be noted here that the rate coefficient for radical desorption kr is related not to the apparent (or net) rate but to the true rate of radical desorption by molecular diffusion. Using Eqs. (81) and (83), therefore, the apparent (or net) rate of radical desorption from the partic1es can be expressed by the use of the coefficient kr as krN* -
krN*(No/NT)
= <1>M(kmr[Mp]
+ kTf[Tp])N*
+ Pw(No/NT)[<1» + ~(1
- <1»)]
(88)
Introducing Eqs. (86) and (87) into Eq. (88) and rearranging leads to Eq. (77). kr
= KOJ
+
[
-
Pw(1
- ñ)
-
(KOJn+ k¡[Mp])nNT Pw(1 -
ñ)k¡
kmr
] [ ]i (
(KOJñ+ k¡[Mp])kpñNT
+Ko
-
kp
+ -kTf[1;'] kp[Mp]
kp[M p]
j= 1 Ko ñ
+ kp[M p]
j
)
(77)
209
5. Desorption and Reabsorption of Free Radicals
Initiator radical s are so reactive that initiator radicals would initiate polymerization before escaping from the particles and hence, the number of polymer particles containing an initiator radical will be maintained at a low value. Moreover, when transfer to monomer is dominant, that is, the value of kmf/kp is large, it is reasonable to consider that the term N,*/N* in Eq. (76) can be neglected. Thus, kr given by Eq. (77) is simplified as kr = Koz where Z
=
(
)
kmr + kTf[Tp] kp
I(
kp[Mp]
kp[Mp]
(89)
j
)
(90)
j= 1 Koñ + kp[Mp]
The value of Z depends upon the values of Koñ and kp[Mp] and satisfies the following inequality: o< Z < s (91) If it is supposed further that only monomer radicals can escape from a
particle(that is, s = 1) and that Koñ ~ kp[Mp] Eq. (89)becomes kp[Mp]
(Koñ + kp[Mp])(
kr = KO
kmr + kTf[Tp] kp
kp[Mp]
)
(92)
where Ko is the desorption rate constant for monomer radicals defined by Eq. (49), and it is supposed that Ko is also applicable to a chain transfer agent radical. According to Eqs. (49) and (59),therefore, Ko is given by Ko = Ks(aJvp) = 12Dw¡)/rndd~ Considering that the value of {3is i most likely value for l, we have
~
(93)
1, because Eq. (55c) seems to give the (94)
Since the physical properties of a monomer radical will be almost identical to those of monomer, the values of Dw, Dp, and rndused here are those for monomer. We have derived Eq. (92) under the assumption that the physical and chemical properties of a chain transfer agent radical are approximately equal to those of a monomer radical. However, if we take into account the difference of physical and chemical properties between the chain transfer agent and monomer radicals, Eq. (92) should be modified as k
-
r-
K
(
kmr[Mp]
o Koñ + kp[Mp]
) ( +K
kTf[1;']
OT KOTñ
+ kiT[Mp]
)
(92')
where KOTand kiT are the desorption rate constant and the reinitiation rate constant for chain transfer agent radical s, respectively.
210
Mamoru
Nomura
In the absence of transfer agent, when the rate of radical desorption from the partic1es and the reactivity of monomer are very high, as with vinyl acetate and vinyl chloride, the condition kp[Mp] ~ Koñ is fulfilled. For such systems Eg. (92) is simplified further to kf
= Ko(kmelkp) = (12DwDlrndd~)(kmelkp)
(95)
Consider here the value of D. In the beginning of the polymerization, D seems to be unity because the partic1es are saturated with monomer, and hence the decrease in the value of Dp, the self-diffusion constant of a monomer radical in the partic1e, is not so remarkable. However, in a higher conversion range the value of Dp decreases with the progress of polymerization due to an increase in the viscosity inside the partic1es. For this reason, the value of Dwill decrease in a higher conversion range. When the condition 2DwlprndDp~ 1 is satisfied in Eg. (94), that is, the diffusion resistance inside the partic1es becomes dominant, the rate coefficient for radical desorption kf given by Eg. (95) is written in the f?rm kf --
6pDp
2 dp
kmf ~ 6Dp
kp
-
kmf
(96)
2 dp kp
Using Eg. (55a), Friis and Nyhagen (1973) derived the following expression for kf: kf
= (2Dpld~Df~:[Mp])
kmf[Mp]
(97a)
When the condition kp[Mp]~ 2Dpld~is fulfilled,Eg. (97)is simplifiedto k
f
= 2Dp kmf d2p
kp
(97b )
This is the same as Eg. (96) except for the value of the numerical constant. Ugelstad and Hansen (1976) also derived arate coefficient for radical desorption similar to those given by Egs. (92) and (95). IV.
A.
Effect of Free-Radical Desorption on the Kinetics of Emulsion Polymerization Effect on the Rate 01 Emulsion Polymerization
1. Verification of Applicability of kf
In the emulsion polymerization of vinyl acetate and vinyl chloride, for example, the polymer partic1e contains at most one radical, under normal conditions. For such emulsion polymerization systems, the steady-state
211
5. Desorption and Reabsorption of Free Radicals
hypothesis can be applied to the following balance equations for the number of active particles N* and the radical concentrations [R:] in the water phase dN*/dt
= ka[R:]No -
kfN*
-
ka[R:]N*
=O
d[R:]/dt = Pw+ kfN* - ka[R:]NT = O
(98) (99)
Substituting Eq. (99) into Eq. (98) and solving for ñ, we reproduce Eq. (30): ñ
= 1(- e + ~ C2 + 2C)
e = pw/kfNT
(30)
In Fig. 4, theoretical values of ñ calculated by Eq. (30) are plotted against the value of e = Pw/kfNT. Experimental values of ñ obtained at the conversion point in vinyl acetate and vinyl chloride emulsion polymerizations where monomer droplets disappear in the water phase (20 -- 40%) are also plotted in Fig. 4 and compared with the theoretical values. The numerical values of constants used here are shown in Table I. The rate of radical production in the water phase was calculated from Pw = 2kd[Io]
(100)
where kd is the rate constant for radical decomposition, f is the initiator efficiency,and [lo] is the initiator concentration. It has generally been accepted that the main interruption reaction of the growing polymer chain is first order with respect to the concentration of
monomor
10-1,
50.C
Yinyl chlaride
SO.C
kfNy
literature 4 5,7 22 1 Ihalsgd (1 .6. Gi......... 11 L:. Peggion. 24
key () o
.
resean:he1's
Frils " Nomura Zollars
Id
IcJ3
k
te.
vinyl acotate
[-J
Fig. 4. Comparison between theoretical and experimental values of ñ: (a) calculated from conversion versus time curve and the number of polyrner particles. (Reprinted with permission of Journal of Applied Polymer Science.)
212
Mamoru Nomura
TABLEI Numerical Values of the Constantsa Constants
(units)
Vinyl acetate
kp (Iiterjmolsec) kmrjkp md Dw (cm2jsec) . kd (Iiterjsec) [Mp). (molj1iter) z b
3340 2 X 10-4 28 1.9 x lO-s b 1.5 X 10-6 e 8.9 1.0 1.0
a 500C. Reprinted with permission Applied Polymer Science.
Vinyl chloride
10,000
1.2x 10-3 35
2.5 X lO~sb 1.5 X 10-6, 6.2 1.0 1.0 of the Journal of
b From Wilke and Chang (1955). From Morris and Parts (1968).
e
growing polymer chains. This was supposed to result from a chain transfer to monomer and the rate of the interruption reaction rf was experimentally analyzed according to the expression rf = k[R .][M]
(101)
where [R -] is the concentra tion of growing polymer chains, [M] is the concentration of monomer, and k is the rate constant of the interruption reaction. Ir the main interruption reaction of growing polymer chains is a chain transfer to monomer, the value of k corresponds to the value of kmf, the rate constant of chain transfer reaction to monomer. However, Ugelstad (1980) recently pointed out that although the rate of interrupting the reaction of growing chains is represented by Eq. (101) in vinyl chloride polymerization, k is not equal to kmf but is composed of many rate constants because a growing polymer radical, after the head-to-head addition to monomer, undergoes several reactions and finally terminates by splitting off CI. or H- radicals. This finding, however, does not affect the present treatment as long as the experimental value of k, based on Eq. (101), is used as kmf in the coefficient kf, in the case of vinyl chloride emulsion polymerization. As can be seen in Fig. 4, a comparison of the theoretical and experimental values of ñ, assuming the value of Z = 1, gives a good agreement. From this and the fact that the value of Koñ is about an order of magnitude smaller than that of kp[Mp] in vinyl acetate and vinyl chloride emulsion polymerizations, we can conclude that the radical that can escape from a particle seems to be principally a monomer radical. Furthermore, it can be
213
5. Desorption and Reabsorption of Free Radicals
conc1uded that Eqs. (30) and (95) are applicable to vinyl acetate and vinyl chloride emulsion polymerizations. On the other hand, for such monomers as methyl methacrylate and styrene which are less reactive and less soluble in water than vinyl acetate or vinyl chloride, Eqs. (30) and (76) [or (77)] are essentially applicable, although the value of the term (kJkp)(N¡*jN*) may not necessarily be neglected comparing the value of the term kmr/kp. The rate coefficient for radical desorption in emulsion copolymerization was also derived in the same way as described in Section III, and it was successfully applied to explaining the rate of emulsion copolymerization of methyl methacrylate and styrene (Nomura et al., 1978, 1979). 2. Effect of Radical Desorption on Rate of Emulsion Polymerization Let us consider the rate of emulsion polymerization Rp where Eqs. (30) and (95) can be applied. From Eqs. (30-32), it is c1ear that Eq. (30) can be written in the form (102) The values of a varies from ! to O with an increase in the value of C. Combining Eqs. (95) and (102) we have I ] av2a/3 R p oc ñN T oc N1-a (103) ] ad2aoc N1-a T [I Op T [ Op After the complete absorption of monomer existing as monomer droplets in the water phase, the following relationship holds: NTvp= Vp
(104)
where Vpis the total volume of the partic1e per unit water volume. Inserting Eq. (104) into Eq. (103) leads to R p oc N(3 (105) T - saJ/3[ I °] aJl:2a/3 p When radical desorption Eq. (105) becomes
from the partic1es can be neglected
R p oc N1.0 T [I °] 0Jl:0 p
(Le., a = O)
(106)
This corresponds to Smith-Ewart Case II kinetics and is applicabie to styrene emulsion polymerization under normal conditions. On the other hand, when radical desorption from the partic1es is dominant (Le., a = !) Eq. (105) leads to R p oc Nl/6 T [ I °] 1/2Jl:1/3 p
(107)
This theoretical equation explains very well the rate of seeded emulsion polymerization of vinyl acetate and vinyl chloride found by Patsiga et al.
214
Mamoru Nomura
(1960) and Giskehaug (1965). Recently, Ugelstad et al. (1969) reported that when the number of polymer particles present was large, the rate of vinyl chloride emulsion polymerization is proportional to the 0.15 power of the number of polymer particles and to the 0.3 power of the total volume of polymer
particles
~.
Nomura
et al. (1971, 1976), found
that
Eq. (107)
explained the dependence of the rate of vinyl acetate emulsion polymerization on NT, [/0], and ~. Van der Hoff (1956) reported that even in styrene emulsion polymerization, the rate of polymerization was proportional to the 0.17 power of the number of polymer particles when the number of polymer particles was very large. These experimental findings support the validity of the theory developed in this chapter.
B.
Effect on Micellar Particle Formation
Smith and Ewart (1948) proposed two idealized situations for the formation of polymer particles, assuming that (i) partiéle nucleation occurs in monomer-swollen emulsifier micelles, (ii) the volumetric growth rate of a particle is constant in the interval of particle formation, and (iii) radicals do not desorb from a particle. Case 1: Ir only micelles can absorb initiator radicals, then dNT/dt = Pw
(108)
In this case the number of polymer particles formed is given by NT = 0.53(pw//l)0.4(asSo)0.6
(109)
where /l is the volumetric growth rate of a particle, as is the surface area per unit amount of emulsifier, and Sois the total amount of emulsifier per unit volume of water. Case 2: Ir both particles and micelles absorb radicals at arate portional to the surface area, then dNT/dt = pw[A.,J(Am + Ap)]
pro-
(110)
where Am and Ap are the total surface areas of micelles and polymer particles, respectively. In this case NT
=
0.37(pw//l)0.4(asSo)0.6
(111)
However, when radical desorption from particles takes place in the interval of particle formation, Pwin Eqs. (108) and (111) should be changed to PA, the overall rate of radical entry into micelles and particles, and the volumetric growth rate of a particle can no longer be a constant.
215
5. Desorption and Reabsorption of Free Radicals
Noting this, Nomura et al. (1972, 1976; Nomura, 1975) studied the effect of radical desorption on the formation of polymer particles from micelles for the case Y = o. They used the following non-steady-state treatment under the assumption that the polymer particles contain at most one radical. Particle formation: dNT
k1ms[R:J klms + kzNT[R:J = PA klms + kzNT
(
dt = PA -
k1ms[R:J
) (
PA
1 + aNT/Sm
) (112)
where (113) and PA
= (k1ms + kzNT)[R:J = Pw+ kfN*
(114)
and where Mmis the aggregation number of a micelle. The number of polymer particles containing a radical, N*; d~* = (k1ms + kzNo - kzN*)[R:J - kfN* = [1 + (aNT/Sm)(l- 2N*/NT)](pw + kfN*)/[l + (aNT/Sm)]- kfN* (115) Monomer conversion: (116) where Mw is the molecular weight of monomer, Mo is the initial monomer concentration, and NAis Avogadro's number. Emulsifier balance: (117) where (118) The second term on the right-hand side of Eq. (117) represents the amount of emulsifier adsorbed on the surface of polymer particles. These equations correspond to the Smith and Ewart Case 1 model of particle formation when the conditions a = Oand kf = Oare employed; they further correspond to the Smith and Ewart Case 2 model of particle
216
Mamoru Nomura
formation when the conditions k1 = nd~, k2= nd~,and kf = O are employed (where dmis the diameter of a micelle). Nomura et al. (1972) solved Eqs. (112) to (118) on a digital computer and analyzed the particle formation in styrene emulsion polymerization where kf = O approximately held under normal conditions and found that the value of 8 was 1.3 x 105. This value is about 102 times greater than that predicted by the diffusion theory which assumes that k1 = 2nDdm and k2 = 2nDdp,and whereD is the diffusioncoefficientof a radical in the water phase. On the other hand, in vinyl acetate emulsion polymerization the value of 8 was 1.2 x 107 (Nomura et al., 1976). This value is also about 104 times greater than that predicted by the diffusion theory. The reason for this may be that radical s have greater difficulty in entering micelles than polymer particles, or it may be that radicals, having entered a micelle, may escape from the micelle too rapidly to cause initiation, because the micelle has too small a volume. Both factors will decrease the apparj::nt value of k1 and hence increase the value of 8. Therefore, 8 can be regarded as a factor that represents "the radical capture efficiency of a micelle relative to a particle." Furthermore, they studied the effect of radical desorption from the polymer particles on the particle number formed in Internal 1 of emulsion polymerization, using above equations, and showed that radical desorption leads to an increase in the number ofparticles. The reason for this is that: (1) The desorbed radicals reenter the micelles and take part in particle nucleation: (2) Radical desorption decreases the particle growth rate and hence, results in a decrease in the rate of micelle consumption. This also increases the chance of radical entry into the micelles. They also showed that radical desorption brought about the change in the orders of particle number with respect to emulsifier and initiator according to the following relationship: NT oc S~p~-a
(119)
The value of a increases from 0.6 to 1.0 with increasing radical desorption. For vinyl acetate and vinyl chloride emulsion polymerization, the calculated
values of order with respectto Soand Pw are 1 and O,respectively.Theseare in good agreement with experimental results (Ugelstad et al., 1969; Nomura et al., 1976). For other monomers and details see the recent paper by Hansen and Ugelstad (1979). Chain transfer agents such as CCI4, CBr4, and mercaptan promote the desorption of radicals from the particles and result in an increase in the value of kf, as can be seen from Eq. (92) (Nomura, 1975; Whang et al., 1980; Nomura et al., in press). Thus, increasing the amount of chain transfer agent charged initially causes both a decrease in the rate of emulsion polymerization and an increase in the number of polymer particles formed.
5. Desorption and Reabsorption of Free Radicals
217
Furthermore, the value of a in Eq. (119) increases from 0.6 to 1.0 with increasing transfer agent (Nomura, 1975; Nomura et al., in press).
List of Symbols a ap a, Am Ap C Cp Cp; Cw Cw; dm dp Dp f I Im,/m-1 [lo] j Jpo
k. kd k¡ k¡ kj'
(8:x)1/2 surface area of a partic1e partic1e surface area per unit amount total surface area of micelles
total surface area of polymer partic1es (J.'/m concentration of radicals in a particle concentration of radicals in particle at interface concentration of radicals in the water phase concentration of radicals in the water phase at the interface diameter of micelle diameter of particle self-dilfusion constant of a monomer initiator efficiency subscript denoting initiator radical Bessel functions of the first kind initiator concentration subscript denoting denotes an initiator
radicals radical
rate of radical desorption rate coefficient for radical rate constant for initiator rate coefficient for radical initiation rate constant
kTf k. kw m md 'n~ Mm Mw [Mp] [Mw]
radical in a particle
with j number
of monomer
film mass transfer interface between rate constant for rate constant for rate constant for
units, j = O
from a single partic1e entry into the partic1es decomposition desorption from the partic1es
(j = 1,2,3, ) rate constant for radical desorption j-mer radicals rate constant for transfer to monomer
propagation rate constant
k,p k,w
of emulsifier
from the partic1es for
.
coefficient for the inner dilfusion film adjacent the partic1e and water phases termination in the partic1es termination in the water phase transfer to transfer agent
rate constant for radical desorption from the partic1es film mass transfer coefficient for the outer dilfusion film adjacent interface between the partic1e and water phases k¡l'plk,p partition coefficient for radicals at the particle-water concentration of micelles per unit volume of water aggregation number of a micelle molecular weight of monomer concentration of monomer in partic1es concentration of monomer in water phase
interface
to the
to the
218
Mamoru Nomura
Mo n ñ N N* NA N.,
initial
monomer
number
concentration
of radicals in a particle
average number
of radicalsper particle
number
of particlescontaining an escaping radical
number
of particlescontaining one radical
Avogadro's number (n =
NT P
0, 1,2, 3...)
n
number
of particles containing
number
of polymer particlesper unit volume of water
radicals
probability of a radical not escaping fron:¡a particleduring the time in"terval of adding one more monomer
q
of adding one more monomer
Re Rp [R:] [R:] 5 Sc Sh So Sm t
unit
probability of a radicalescaping from a particleduring the time interval unit
Reynold's number overallrate of polymerization concentration of radicalsin the particlesper unit volume of water totalconcentration of radicalsin the water phase maximum number of monomer units in a desorbed radical Schmidt number Sherwood
number
totalamount amount
of emulsifierper unit volume of ~ater
of micellaremulsifierper unit volume of water
average time spent the
by a radical inside a particlebefore itescapes from
particle
tadd
average time for a radicalto add one monomer
¡red
average residence time of a radical in the water phase before entering a
unit in the water phase
particle
fterro
average time for a radical to be deactivated by mutual
termination in
the water phase
[1;,] Vp Vp Xm
concentration of transferagent volume
of a particle
totalvolume of particlesper unit volume of water fractionalmonomer conversion
ex
parameter defined by Eq. (22)
ex'
parameter defined by Eq. (27)
P
numerical
°l
constant, !- i ratio of the outer film mass-transfer resistance to the overall mass-
transfer resistance for j-mer
Cl J1
ratio of number
radicals
ofj-mer radicalsto the totalnumber
of radicals
volumetric growth rate of a particle
PA Pw
rate of radical production
<1>m
fraction
overall rate of radical entry into the particles
of
tbe
transfer agent
in the water
radicals
to desorb
generated from
phase
by
chain
transfer
the particles before
to
growing
monomer to (5 +
or 1)-mer
radicals <1>¡
probability of initiatorradicals escaping out of the particles before
t/lc
monomer
adding one monomer
unit
weight fraction
in the particles
atsaturation
with monomer
5. Desorption and Reabsorption of Free Radicals
219
References Chang, K., Litt, M., and Nomura, M. (1981). Macromolecules (to be published). Friis, N., and Nyhagen, M. (1973). J. Appl. Polym. Sci. 17, 2311. Gardon, J. L. (1968). J. Polym. Sci. Part A-l, 6, 665. Giskehaug, K. (1965). Symp. Chem. Polym. Process, London, April. Hansen, F. K., and Ugelstad, J. (1979). Macromol. Chem. ISO, 2423. Harada, M., Nomura, M., Eguchi, W., and Nagata, S. (1971). J. Chem. Eng. Jpn. 4(1), 54. Harkins, W. D. (1947). J. Am. Chem. Soco 69, 1428. Lewis, W. K., and Whitman, W. G. (1924). Ind. Eng. Chem. 16, 1215. Litt, M., Patsiga, R., and Stannett, J. (1970). J. Polym, Sci. Part A-l S, 3607. Morris, C. E. M., and Parts, A. G. (1968). Macromol. Chem. 119,212. Newman, A. B. (1931). Trans. AIChE 27, 310. Nomura, M. (1975). Ph.D. Thesis, Kyoto Uniy., Kyoto, Japan. Nomura, M., and Harada, M. (1981). J. Appl. Polym. Sci. 26, 17. Nomura, M., Harada, M., Nakagawara, K., Eguchi, W., and Nagata, S. (1971). J. Chem. Eng. Jpn.4(2), 160. Nomura, M., Harada, M., Eguchi, W., and Nagata, S. (1972). J. Appl. Polym. Sci. 16,811. Nomura, M., Harada, M., Eguchi, W., and Nagata, S. (1976). In "Emulsion Polymerization" (1. Piirma and J. L. Gardon, eds.), ACS Symposium Series No. 24, pp. 102-122. Nomura, M., Harada, M., and Eguchi, W. (1978). J. Appl. Polym. Sci. 22, 1043. . Nomura, M., Yamamoto, K., Fujita, K., Harada, M., and Eguchi, W. (1978). Preprints, 12th Fall Meeting ofthe Soco ofChem. Engrs., Okayama, Japan, GS-207, pp. 439-440. Nomura, M., Yamamoto, K., Harada, M., and Eguchi, W. (1979). Preprints, Int. Conf Surface Col/oid Sci., 3rd, Stockholm, Sweden, pp. 148-149. Nomura, M., Minamino, Y., Fujita, K., and Harada, M. J. Polym. Sci., (in press). Patsiga, R., Litt, M., and Stannett, V. (1960). J. Phys. Chem. 64, 801. Ranz, W. D., and Marshall, W. R. (1952). J. Chem. Eng. Prog. 4S, 141. Smith, W. V., and Ewart, R. H., (1948). J. Chem. Phys. 16, 592. Stockmayer, W. H. (1957). J. Polym. Sci. 24, 313. O'Too1e, J. T. (1965). J, Polym. Sci.9, 1291. Ugelstad, J. (1981). Pure Appl. Chem. 53, 323-363. Ugelstad, J., and M0rk, P. C. (1970). Dr. Polym. J. 2, 31. Uge1stad, J., and Hansen, F. K. (1976). Rubber Chem. Technol.49, 536. Uge1stad, J., M0rk, P. c., and Aasen, J. O. (1967). J. Polym, Sci. Part A-l 5, 2281. Uge1stad, J., M0rk, P. C., Dahl, P., and Rangnes, P. (1969). J. Polym. Sci. Part C 27,49. Van der HotT, B. M. E. (1956). J. Phys. Chem. 60, 1250. Wang, B. C. Y., Lichti, G., Gilbert, R. G., and Napper, D. H. (1980). J. Polym. Sci. Po/ym. Letter Edi. IS, 711. Wilke, C. R., and Chang, P. C. (1955). AIChE J. 1,264. Zollars, R. L. (1979). J. Polym. Sci. 24, 1353.
.
6 Effects of the Choice of Emulsifier in Emulsion Polymerization A. S. Dunn
1. Introduction . 11. Monomer Emulsification A. Hydrophile-LipophileBalance B. Effects of Mixtures of Anionic and Nonionic Emulsifiers . C. Preparation of Monodisperse Latexes 111. Emulsion Polymerizationwith Nonionic Emulsifiers IV. Emulsion Polymerizationwith lonic Emulsifiers. A. Effectof Emulsifieron Numberof Latex Particles Formed B. The Effectof Micelle Size . V. Latex Agglomeration VI. Other Effects of Emulsifiers A. Monomer Solubilization B. Polymer Solubilization . C. Initiator Decomposition Induced by Emulsifier. D. Catalysis of the Initiation Reaction . E. Transferto Emulsifiers . References
221 224 225 227 228 229 230 233 234 236 237 237 238 239 241 242 243
l. Introduction Despite the name, neither the emulsification of monomer nor the stabilization of polymer particles formed is an essential characteristic of emulsion polymerization. The essentlal feature of emulsion polymerization is that polymerization occurs in a large number of isolated particles that normally contain no more than a single polymerizing radical: this permits high molecular weight polymer to be formed at a high rate of polymerization, by contrast with bulk or solution polymerization in which an 221 EMULSION POLYMERIZATION Copyright It 1982 by Aeademie Pres,. Ine. AJI righlS of reproduetion in any fonn reserved. ISBN 0-12-556420-1
222
A. S. Dunn
increase in the rate of polymerization generally resuIts in a decrease in the molecular weight of the polymer produced. Emulsion polymerization without the use of an emulsifier may be achieved even with a monomer with water solubility as low as that of styrene provided one uses an initiator such as potassium persulfate which introduces ionic end groups into the polymer that can stabilize the polymer latex particIes produced electrostatically. Emulsifier-free emulsion polymerization is advantageous when the object is to obtain a well-characterized model colloid for use in experiments on colloidal stability, etc. Then it is usually desirable that the surfaces of the colloidal particIes be cIean. When an emulsifier is used in the preparation, its removal (e.g., by dialysis) is generally so incomplete that it is simpler to avoid its use in the first place. However, emulsifier-free latexes are necessarily dilute and consequentIy of little interest for commercial applications. When an emulsifier is used, its type and concentration primarily affects the number of latex particIes formed, which in turn determines the rate of polymerization and, depending also on the rate of initiation, the molecular weight of the polymer formed.' AIthough the physical properties of the polymer are primarily dependent on its molecular weight and molecular weight distribution, the properties of the latex depend on its concentration, averageparticIe size, particIe size distribution, and the viscosity of the aqueous phase, which may be enhanced by addition of a thickener-a water-soluble polymer not adsorbed by the polymer phase which does not affect the course of the reaction. For applications in which the stability of the latex to mechanical agitation, exposure to low temperatures, etc. is a prime consideration, it may be expedient to add additional amounts of surfactants after the polymerization is complete: in general the effect of such post-additions differs from the effect obtained when the same amounts are added prior to polymerization. The best emulsifiers for stabilizing the mo~omer emulsion are not necessarily those that are best for stabilizing the polymer latex. Normally, mechanical agitation is provided to keep the monomer dispersed during polymerization, whereas the latex is likely to be required to remain in dispersion for a prolonged period without agitation. The fact that the latex particIes are much smaller than the monomer droplets in the original emulsion facilitates stabilization of the latex, but emulsifiers will usually have to be chosen with. a view to stabilizing the latex rather than the monomer emulsion. When it is desired to maximize the solids content of the latex, controlled agglomeration of the latex particIes may be needed. Again, if the uItimate application of the latex is as an adhesive or a paint vehicIe requiring formation of a continuous film from the polymer latex particIes after evaporation of the water, the effect of the emulsifiers on film properties
6.
Effects of the Choice of Emulsifier in Emulsion Polymerization
223
(e.g., water sensitivity) may be of the utmost importance. Hence, extensive practical testing is likely to be required to determine the least expensive emulsifying system that will give acceptable results in a given application. Synthetic butadiene-styrene rubber production accounts for the greatest volume of polymer production by emulsion polymerization. Most synthetic rubber is not used as a latex but coagulated to isolate the polymer for subsequent compounding. Consequently, it is convenient to continue to use carboxylate emulsifiers, fatty acid or resin acid soaps that permit the latex to be coagulated simply by acidification. The presence of emulsifier residues in the polymer is not objectionable in synthetic rubber because zinc stearate is an important ingredient of must rubber compounds. Coagulation of latexes stabilized by sulfate, sulfonate, and nonionic emulsifiers is frequently difficult, although these do coalesce to form more or less coherent films above the minimum film-formation temperature (MFT) of the polymer: this is related to the glass transition temperature of the polymer (Tg) but is generally conspicuously lower because of plasticization of emulsion polymers by water. The effects of emulsifiers in emulsion polymerization systems may be enumerated as follows: (1) stabilization of the monomer in emulsion, (2) solubilization of monomer in micelles, (3) stabilization of polymer latex particles, (4) solubilization of polymer, (5) catalysis of the initiation reaction, and (6) action as transfer agents or retarders which leads to chemical binding of emulsifier residues in the polymer obtained. Commercial emulsifiers are mostly mixtures of homologs, which are difficult or impossible to purify or even 3;nalyze. Differences in the composition of the mixture are likely to account for differences observed in the effects of similar 'materials from different sources (Blackley, 1975). Consequently, comparisons between the effects of different emulsifiers are relatively rare. The authors of a number of important publications have prudently confined their investigation to a single batch of a particular emulsifier, although it may have been used over a range of concentrations. When comparisons are made between different emulsifiers, it is difficult to ensure that they are made at corresponding concentrations. The obvious procedure is to use equal concentrations by weight (cf. Hopff and Falka, 1965): since emulsifiers are sold by weight, this is the proper procedure to determine the best value for money. However, the molecular weights of emulsifiers differ so much that a more chemically satisfactory procedure would use equal molar concentrations. This should be valid provided the concentration chosen is greatly in excess of the critical micelle concentration (CMC) of all the emulsifiers. Micellar nuc1eation of latex partic1es dominates in the polymerization of monomers of low water solubility (e.g., styrene), wherein the rate of polymerization may increase by a factor of 100
A. S. Dunn
224 4
o
O
2.5
5.0 102¡SJ/mol
7.5
10.0
dm-3
Fig. 1. Dependence of the rate of polymerization (in Interval 11) of styrene emulsions on the concentration of the emulsifier (sodium dodecyl sulfate) at 60°C. Initiator: 0.2% K2S20S on aqueous phase. (From AI-Shahib, 1977.)
as the concentration of the emulsifier is increased through the CMC (Fig. 1). In such a case a comparison between equal co'ncentrations of two emulsifiers, one above its CMC and the other below, is useless; and it is logical to choose concentrations at which the amounts of each emulsifier that will be present as micelles under the conditions of the experiment are equal, despite the fact that the total concentra tion s of the emulsifiers present may differ greatly. The conventional anionic emulsifiers (typified by sodium dodecyl sulfate) are much less strongly adsorbed by polar polymers [e.g., poly(vinyl acetate)] than they are by hydrocarbon polymers (e.g., polystyrene). For monomers of moderate (Le., 1-3%) solubility in water (e.g., methyl methacrylate, vinyl acetate), the dominant mechanism of latex partic1e nuc1eation is oligomeric precipitation (Fitch and Tsai, 1971), and there is no perceptible effect of the presence of emulsifier micelles. In such cases, corresponding concentration should probably be chosen so as to give equal surface concentrations on the polymer (i.e", the emulsifiers would have the same effect in stabilizing the' polymer latex partic1es), but the paucity of adsorption isotherm data makes it difficult to arrange this at present.
11. Monomer Emulsification The emulsification of the monomer is not usually of primary importance in emulsion polymerization, although it has been shown (Ugelstad et al., 1973; Ugelstad and Hansen, 1979) that if the size of the emulsion droplets can, by the use of special methods of emulsification, be reduced considerably below that which would normally be attained, the emulsion
6.
225
Effects of the Choice of Emulsifier in Emulsion Polymerization
droplets can compete effectively for initiator radical s and become a significant or even dominant locus of polymerization. It may occasionally be desirable to have a monomer emulsion sufficiently stable to permit stirring to be dispensed with (e.g., this would facilitate the use of the dilatometric method for determining the rate of an emulsion polymerization), but the difficulty here is that an emulsion that is stable so long as it is not polymerized will break as polymerization proceeds because of depletion of emulsifier from the monomer droplets by adsorption on the latex paitic1es. This might be prevented by the use of sufficiently large concentrations of emulsifier .
A. Hydl'ophile-LipophileBalance Hydrophile-lipophile
balance
(HLB)
pro vides a useful guide
to the
selection of a suitable emulsifier system for a given disperse phase particulady when nonionic emulsifiers are to be used. Several studies of the effect of HLB in emulsion polymerization
have been published.
The HLB scale was introduced by W. C. Griffin of Atlas (now LC.L America) (1949, 1954, 1980) as an aid particularly to the use of nonionic surfactants in the formulation of cosmetics. His scale (Table 1) is related to the solubility of the materials in water: for nonionic surfactants on poly(ethylene
oxide) the HLB number may be found simply by dividing the
percentage of ethylene oxide in the product by five (Griffin, 1954). Davies (1957) has devised group constants that permit ca1culation of HLB values for other types of surfactant (Table 11). Greth and Wilson (1961), also of TABLEI The HLB Scale and Water Solubility of Surfactantsa Solubility
HLB number
in water
Not dispersible Poorly dispersible Unstable milky dispersion Stable milky dispersion Translueent solution
{!6
Clear solution
{ a After Adamson,
Applieation
8 10 12 14 16 18
1976. Reprodueed
Emulsifiers for Water in Oil Emulsions Wetting agents Emulsifiers
Detergents Solubilizers
with permission
}
for oil in water
Emulsions
of John Wiley & Sons, lne.
\
226
A. S. Dunn TABLE
11
Group Constants for Calculations Hydrophilic
groups (constant)
-S04Na
(38.7)
-COOK -COONa -S03Na -COOH -OH -0-{CH2CH20)-
(21.1) (19.1) (1l.0) (2.1) (1.9) (1.3)
of HLBa Valuesb
Lipophilic
-CH2-CH= -CH3 -{CH2CH2CH20)-
a HLB = 7 + ~Jhydrophilic group constant) constants). ~ After Davies, 1957. Reproduced
groups (constant)
- Dlipophilic
with permission
(0.475)
(0.15)
group
of J.. T. Davies.
Atlas, extended the application' of the HLB system to the selection of emulsifiers for the emulsion polymerization of styrene and vinyl acetate. Emulsifiers and emulsifier blends were rated according to the stability of the polymer latexes obtained on storage at room temperature. The best results were obtained when the HLB for polystyrene latexes was in the range 13-16 and for poly(vinyl acetate) 14.5-17.5. The highest rates of polymerization were also obtained in these ranges. Benetta and Cinque (1965) found the HLB system useful for the selection of stabilizers for the suspension polymerization of vinyl chloride, but Testa and Vianello (1969) working in the same laboratory found that all blends were inferior to sodium dodecyl sulfate in the emulsion polymerization of vinyl chloride. Ono et al. (1974, 1975) found that particle size and latex stability increased as HLB was decreased by increasing the proportion of hexaoxyethylene oleyl ether (HLB 9.9) mixed with sodium dodecyl sulfate, both in the homopolymerization of methyl methacrylate in emulsion and in the emulsion copolymerization of acrylonitrile and methyl methacrylate in a molar ratio of 3 to 1. They determined latex stability by calculating the Hamaker constant for the latexes from the value of Debye and Hückel's reciprocal thickness of the ionic atmosphere 1( at the critical concentration of added electrolyte required to coagulate the latex following the procedure of Ottewill and Shaw (1966). Jagodic et al. (1975, 1976) also studied the effect of the HLB of emulsifying agents in the emulsion homopolymerization of methyl methacrylate, ethyl acrylate, and acrylonitrile and in the emulsion copolymerization of methyl methacrylate and ethyl acrylate, methyl methacrylate and
6.
Effects of the Choice of Emulsifier in Emulsion Polymerization
227
styrene, and ethyl acrylate and styrene. They found the HLB to affect reaction rate, latex stability, viscosity, and partiele size. Optimum latex stability was obtained in the range 12.1-13.7 for poly(methyl methacrylate), 11.8-12.4 for poly(ethyl acrylate), 13.3-13.7 for polyacrylonitrile, and 11.9513.05 for the copolymer obtained from a 50% (by weight) mixture of methyl methacrylate and ethyl acrylate. Eliassaf (1973) found a correlation between the HLB of the suspension stabilizer and the morphology of PVC [poly(vinyl chloride)J partieles prepared by suspension polymerization, which varied from glassy beads to porous partieles having a high plasticizer absorption. However, as pointed out by Rosen (1978) the HLB method is useful only as a rough guide to emulsifier selection since it indicates neither the efficiency of the emulsificr (i.e., the concentration required) or its effectiveness (i.e., the stability of the emulsion produced) and does not take into account the effect of temperature in varying the extent of hydration of hydrophilic groups such as polyoxyethylene, with consequent change in the action of the surfactant.
B. Effectsof Mixtures of Anionic and Nonionic Emulsijiers As shown by Ono et al. (1974, 1975) decrease of the HLB of a mixed emulsifier by use of an increasing proportion of a nonionic emulsifier increases the stability of the latex to coagulation by electrolyte addition despite an increase in its average partiele size. This is because purely electrostatic stabilization by adsorbed ionic emulsifier is supplemented by steric stabilization by the adsorbed nonionic emulsifier which effectively decreases the van der Waals attractive force between the latex partieles (which causes them to coalesce), thereby increasing their stability. All the systems studied by Ono et al. inelude a large proportion of a monomer of moderate water solubility (e.g., methyl methacrylate, acrylonitrile) so that partiele nueleation by the oligomeric precipitation mechanism (Fitch and Tsai, 1971) is likely to be dominant. In cases (e.g., styrene) for which micellar nueleation of latex partieles is dominant above the CMC of the emulsifier another effect is also important. This is the formation of mixed micelles that are much larger than those formed by the anionic surfactant alone but which have a much lower surface charge density and which may, therefore, increase the efficiency of initiation by negatively charged radicals (e.g., SO;) from the aqueous phase. Working with a mixture of sodium dodecyl sulfate and a tridecyloxypoly(ethyleneoxy)ethanol (Emulphogene BC-840, GAF), Piirma and Wang (1976) found that addition of the ionic emulsifier reduced the micellar weight from 16,800 for the nonionic
alone to 3,500 with 50 mol
% anionic
emulsifier, although
A. S. Dunn
228
the micellar weight of the anionic emulsifier alone was much larger (23,500): thus, there is a much larger number of much smaller micelles in the mixed system than is obtained with either component alone. This was reflected in an increase in the number of latex particIes formed and in the subsequent steady rate of polymerization and in a reduction of the breadth of the particIe size distribution. The highest rate and narrowest particIe size distribution was obtained with 17 mol % of the ionic emulsifier when the average micellar weight was 6,000: it was found that the probability of a micelle nucIeating a latex particIe was a maximum at this composition aIthough the probability remained low as an absolute value (0.00038).
C.
Preparation 01 Monodisperse Latexes
In the absence of particIe coalescence (i.e., when relativeiy large concentrations of emulsifiers are present sufficient to stabilize all primary particIe nucIei formed) the essential condition for the' formation of a latex with a very narrow particIe size.distribution is that the nucIei of all particIes should be formed at very neariy the same time and should subsequently grow at equal rates. The use of mixtures of anionic and nonionic emulsifiers pro vides the requisite conditions as first shown by Woods et al. (1968). AIthough initiation of emulsion polymerization with a water-soluble initiator has hitherto been credited with a 100% efficiency, the efficiency of initiation of styrene by persulfate in seeded polymerizations of styrene in which sodium dodecyl sulfate was used as the emulsifier has recently been shown by Hawkett et al. (1980) to be rather low. Using an -10% emulsion with 0.42% sodium dodecyl sulfate on the water phase, they find at 50°C an initiator efficiency of 44% at low persulfate concentrations (1.6 x 10-5 mol dm - 3) falling to only 1% at high concentrations (8.33 x 10- 2 mol dm - 3). Consequently, any improvement in initiator efficiency should increase the rate of particIe nucIeation. Evidently, the increased surface area and reduced surface charge density of mixed micelles achieves this. The seed latex used by Hawkett et al. was monodisperse: it was prepared at a high temperature (90°C) using sodium dioctylsulfosuccinate (Aerosol MA, Cyanamid) as emulsifier with persulfate initiation. The high temperature would give a high rate of radical formation from the initiator but this emulsifier, having two alkyl chains, presumably forms micelles with a lower surface charge density than emulsifiers with single alkyl chains. It has often been pointed out that the approach of a charged radical to a charged micelle requires a Coulombic repulsive energy barrier to be overcome even though counterion binding reduces the effective charge on the
6.
Effects of the Choice of Emulsifier in Emulsion Polymerization
229
micelle below that which would be inferred from the aggregation number of the micelle. Consequently, it has been surmised that a sulfate radical might hav.e to add several monomers in an aqueous-phase polymerization before the van der Waals attractive force between the growing radical and the micelle suffices to overcome the Coulombic repulsion. Some evidence in support of this is provided by the observation (Waite, 1977) that monomers even less soluble in water than styrene (e.g., tert-butylstyrene, dodecyl methacrylate) cannot be polymerized in an emulsion with a water-soluble initiator unless the monomer solubility in the aqueous phase is increased by addition of alcohol or acetone. On the other hand the only actual estimate of the magnitude of the energy barrier (Fitch and Shih, 1975) shows it to be negligible in the case of latex particles stabilized by ionic initiator end groups only. Exchange of individual emulsifier molecules between micelle and solution is rapid but a minimum Cs alkyl chain is needed for micelles to be formed at all by n-alkyl sulfates or carboxylates, from which one might infer that a minimum of four monomers must be added before a sulfate radical can enter a micelle or a latex particle. The first published formulation for producing a mono disperse polystyrene seed latex (Bobalek and Williams, 1966) involved the use of octylphenoxypolyethylene
oxide (Triton X-100, Rohm and Haas) 1.7 %with 0.08-
0.17% sodium dodecyl sulfate on the water phase. Unfortunately, as shown by Kamath et al. (1975),this nonionic emulsifierhas a labilehydrogen atom and is liable to peroxidize. Consequently, polymerization rates are not reproducible unless the emulsifier used is a fresh sample, and transfer to emulsifier invalidates any inference from molecular weight data in which this factor is neglected. Emulphogene BC-840 was introduced as a product with similar propert'ies free from this difficulty; but it is possible that equivalent results could be obtained with other mixtures of ionic and nonionic emulsifiers, indeed Renex 30 (Atlas) (a polyoxyethylene alkyl ether) in combination with sodium dodecylbenzene sulfonate has been found suitable (Doherty, 1978).
ill.
Emulsion Polymerization witb Nonionic Emulsifiers
Nonionic surfactants were developed subsequent to the ionic types and are not normally used as the sole emulsifying agent in emulsion polymerizations. Consequently, the characteristics of emulsion polymerizations using only nonionic emulsifiers have received little attention apart from a series of papers from Medvedev's group in the Soviet Union, although an understanding of these is a prerequisite for the interpretation of their action in combination with ionic emulsifiers. The Bobalek-Williams recipe produces
A. S. Dunn
230
latex partic1es of eomparatively large size (195-230 nm diameter) relative to those obtained with ionie emulsifiers (typieally about 50 nm), although smaller than obtainable by emulsifier-free emulsion polymerization of styrene (500 nm). The meehanism of emulsion polymerization with nonionie emulsifiers alone appears to differ fundamentally from that of emulsion polymerization with ionie emulsifiers. Instead of all the latex partic1es being formed during a eomparatively short initial Interval I and then remaining eonstant in number during Interval II though inereasing in size at a steady rate until all monomer is absorbed by the latex partic1es and Interval III eharaeterized by a diminishing rate of polymerization eommenees, the size of the partic1es remains eonstant throughout the reaetion but their number inereases as eonversion proeeeds (Medvedev et al., 1971). The eharaeteristies of emulsion polymerization with nonionie emulsifiers alone would thus appear to have mueh in eommon with emulsifier-free emulsion polymerization in whieh the final latex partic1es are formed by primary partic1es whieh eoalesee until a stable size is reaehed. This would imply that even though mieelles are present and presumably solubilize styrene the loeus of polymerization is exc1usively in the aqueous phase. Adsorption of the nonionie emulsifier would greatiy inerease the size whieh oligomerie radicals eould attain without preeipitating. However, the results of Piirma and Chang (1980) shed a different light on these experiments. Although they also observe a eonstant rate for the first 40% of the reaetion (an extent of reaetion exeeeded in few of the experiments reported by the Soviet group), they find a marked inerease in rate above 40%. Eleetron mieroseopy shows that this is not attributable to the gel effeet but to an inerease in the number of reaetion loei beca use of the generation of a seeond erop of latex partic1es. They attribute this to the faet that the nonionie emulsifiers are soluble in styrene, so that the emulsifier eoneentration in the water phase inereases as the monomer droplets are eonsumed and all monomer is present in the swollen latex partic1es. The Soviet workers determined partic1e size by a nephelometrie method, and it is possible that the average partic1e size may remain eonstant, as they find when there is a bimodal distribution with both large and small partic1es inereasing in size but with the number of the small partic1es inereasing while the number of large partic1es remains eonstant. There is c1early seope for further investigations of the behavior of nonionie emulsifiers in emulsion polymerizations.
IV.
EmulsioD PolymerizatioD with IODicEmulsifiers
The Smith-Ewart theory was eoneeived with referenee only to ionie emulsifiers. Ir the mode of aetion bf nonionie emulsifiers differs from that of ionie emulsifiers, the theory may be inapplieable either when nonionie
6.
Effects of the Choice of Emulsifier in Emulsion Polymerization
231
emulsifiers are used alone or when mixtures of ionic and nonionic emulsifiers are used. The parameter characteristic of the emulsifier in SmithEwart theory is as, the area occupied by an emulsifier "in a saturated monolayer at the polymer-water interface. The criterio n for the transition from Interval 1, in which the latex particles are formed, to Interval 11, in which the particles increase in size at a uniform rate while their number remains constant, is that the total surface area of the latex particles should ha ve increased to an extent sufficient to adsorb all the emulsifier originally present in the aqueous phase as micelles. It is assumed that the area occupied by an emulsifier molecule on the latex particle surface and in the micelle is the same. Since the presence of micelles containing solubilized monomer is postulated as essential to the nucleation of latex particles, it follows that it should not be possible to nucleate additional latex particles once all emulsifier has been adsorbed on the existing particles. The reason that emulsifier should adsorb on the latex particles rather than aggregate in micelles in solution is not explained, although it is an experimental fact that the micelles do usually disappear from solution (as shown by an increase in the surface tension) at approximately the same time as new latex particles cease to formo Actually, it is probable that the van der Waals interaction energy between an emulsifier molecule and a latex particle is greater than that between an emulsifier molecule and a micelle simply because the latex particle is larger, but a quantitative demonstration of this has not yet been gIven. Despite the fact that Smith-Ewart theory (or Gardon's development of it) does apply well to the emulsion polymeri?:ation of styrene at least, none of these postulates seems to be strictly true. Micelles are not essential for the nucleation of la'tex particles since the possibility of emulsifier-free emulsion polymerization has been amply demonstrated. When high concentrations of a weakly adsorbed emulsifier are used, micelles do not disappear at the beginning of Interval 11 and even remain at the end of the reaction (Bakker, 1952), it being impossible to carry out a soap titration on the latex because the surface tension has not risen above the value characteristic of the CMC of the emulsifier (AI-Shahib, 1977). The value of as is not independent of the nature of the polymer as was initially assumed [and apparently confirmed by early experiments (Sawyer and Rehfeld, 1963)] but increases with the polarity of the polymer and the temperature (Piirma and Chen, 1980) (Table III). Indeed if as were independent of temperature the van't Hoff Isochore would imply a zero enthalpy of adsorption in contradiction to the general observation that physical adsorption is an exothermic process. The real criterion for the cessation of micellar particle nucleation appears to be not the absence of micelles but the fact that the number and size of the latex particles has increased sufficiently to ensure c~pture of all radicals generated in the aqueous phase in competition with any micelles that may remain. Hence, as is probably not the parameter
A. S. Dunn
232 TABlE
111
Area (a's) Occupied by a Surfactant Molecule at a PolystyreneWater Interface at the Critical Micelle Concentration: Effect of Alkyl Chain length (a/A2) Potassium carboxylates
Chain length C10 C12 C14 C16 C18
Sodium alkyl sulfates Piirma and Chen 47°C (1980)
Maron el al. AI-Shahib 50°C 60°C (1954)Q (1977)
-
68 66 48
41 34 25 23
52 40 25
EffeCI of temperature Sodium dodecyl,sulfate Temperature¡OC a~A2 Q
(Piirma and Chen, 1980)
22 47
37 49
47 52
On butadiene-styrene rubber.
required, but if it is used it needs to be determined from measurements on the right polymer at the relevant temperature, and values derived, for example, from studies of adsorption at the air-water interface cannot be used. For non polar polymers, the magnitudes of polymer-emulsifier and emulsifier-emulsifier interactions appear to be similar so that the CMC is reached in solution at just about the concentration that is also in equilibrium with a saturated monolayer on the polymer surface. In these circumstances the soap titration method of Maron et al. (1954), involving the addition of a surfactant solution to a latex in which the particles are only partially covered with adsorbed surfactant initially, can be used to determine as reasonably satisfactorily; but in the case of more polar polymers the polymer-emulsifier interaction is evidently considerably lower than the emulsifier-emulsifier interaction and micelles are formed in solution long before enough emulsifier has been adsorbed to complete the coverage of the polymer surface (Paxton, 1969). The as value obtained by soap titration is the area occupied by a surfactant molecule on the polymer surface at the concentration at which the CMC is reached in solution, precluding any further increase of the concentration of surfactant monomers in the aqueous phase (cf. Table IV). It appears also (Drban, 1980) that a saturated monolayer may be formed at the air-water interface before micelles form in
6.
233
Effects of the Choice of Emulsifier in Emulsion Polymerization
TABLEIV Adsorption of Soaps on PVCa.b Soap Potassium Potassium Potassium Potassium
dodecanoate tetradecanoate tetradecanoate tetradecanoate
lOs (salt)jmol dm-3
a;jA2
aslA2
2.7KCI O 1.7 K2HP04 5.7 K2HP04
51 52.9 47 40
26.5 24.4 25 25
.
From Paxton, 1977.
b as was determined by soap titration, the Langmuir adsorption isotherm.
as by extrapolation
of a linear plot of
the bulk of the solution, so that differing estimates of as are obtained according to whether surface tension or conductivity measurements are used to determine the CMC. Urban used both methods on the same surfactant sample, whereas most other investigators ha ve confined themselves to a single technique and have attributed any discrepancies with literature results obtained by alternative techniques to differences in sample purity (which is certainly the major factor in explaining discrepancies in the reported results). A.
Effect 01 Emulsifier on Number 01 Latex Particles Formed
According to the theories of Smith and Ewart and of Gardon, the effect of emulsifiers on the number of polymer latex particles formed N (and hence on the rate of polym~rization during Interval 11)is determined by the area as which the emulsifier molecule occupies in a saturated monolayer at the polymer-water interface, N oc (asS)3/5
where S is the surfactant concentration. Although Bartholome et al. (1956) showed that the slope of a logarithmic plot of the rate of emulsion polymerization of styrene against surfactant concentration could indeed be fitted with a straight line with the expected gradient of 0.60, the only studies in which a series of different surfactants were used (Ivanova and Yurzhenko, 1958; Onischenko et al., 1970) showed that the latex particle size decreased rapidly and the rate of polymerization increased correspondingly as the alkyl chain length of the emulsifier increased. However, at the concentrations used in these studies the lower members of the homologous series of emulsifiers were below their CMC, and the effect is basically similar to that observed when the concentration of a single emulsifier is increased . from below to above its CMC.
A. S. Dunn
234
Using equal weight concentrations of alkyl carboxylates (all above the CMC of the emulsifier), Carr el al. (1950) observed only a slight increase in the Interval 11 rate, although there was a large difference in the time required for a steady rate to be attained. In fact, the literature values of as (Table III) decrease with increasing alkyl chain length in the homologous series of alkyl carboxylates so that when equal concentrations of these emulsifiers are used a decrease in Interval 11 rate should be expected. Actually, when equal (molar) concentrations chosen to be above the CMC of the lowest member of the homologous series are used a slight decrease in particle size with a corresponding increase in the Interval II polymerization rate is found (Dunn and AI-Shahib, 1978). However, the CMC decreases as alkyl chain length increases so that although the total emulsifier concentration is the same, the concentration of micellar emulsifier increases with alkyl chain length. Since, for styrene, a large increase in the number of latex particles formed is observed as emulsifier concentration is increased through the CMC, showing the micellar nucleation of latex particles to be dominant, this suggests that the increase in rate may be attributable to the increase in the concentration of micellar emulsifier and that it may be the concentration of micellar emulsifier that should be considered. Although the Harkins model postulaÚ~s micellar nucleation of latex particles, the micelles are not actually considered in the Smith-Ewart theory: it is assumed that the total concentration of emulsifier is all adsorbed on the latex particles at the end of Interval I and that the equilibrium concentration in solution (which is likely to be of the order of the CMC) may be neglected. This is possible for many commonly used emulsifiers that have a low CMC (e.g., potassium stearate) but it is unsatisfactory for the more weakly adsorbed emulsifiers (e.g., resin acid salts and even for sodium dodecyl sulfate). When the concentration of emulsifiers are chosen so that the micellar concentrations are equal (although total concentration may differ greatly), the size of the latex particles formed is the same. This means that the number of latex particles formed is also the same and, consequently, the Interval 11 rates of polyq¡.erization are also the same (Dunn and AI-Shahib, 1980). The duration ofInterval I does increase for the more weakly adsorbed emulsifiers, however (Fig. 2). B.
The Effect of Micelle Size
Considerable discrepancies exist between the results of different techniques for determining micelle size (Anacker el al., 1964); but it has been shown (Kratohvil, 1980) that serious discrepancies can arise from oversimplification of the treatment of experimental results and that the results of
6.
235
Effects of the Choice of Emulsifier in Emulsion Polymerization 100
ea
e 10
'
e 12
-
::./ O
e 16
/!
o
~ 40
e 14
,
LL l 600
600 Time(mio)
'
I
o
600
e la
,l
f
,
600
600
L
60
Fig. 2. Course of the emulsion polymerization of styrene at 60°C using the same concentrations (0.012 mol dm - 3)above their critical micelle concentrations of the homologous series of sodium alkyl sulfates. lnitiator: 0.20% KzSzOs on aqueous phase. (From AI-Shahib, 1977.) different techniques can be reconciled when proper allowance for the effects of counterion binding is made, although unfortunately the only emulsifier for which sufficient data exists to allow this to be done is sodium dodecyl sulfate. However, although the absolute values of the aggregation numbers may be incorrect, there is no doubt (Table V) that micelle size increases with alkyl chain length. Consequently, at constant micellar concentration the number of micelles must decrease as their size increases. Clearly the number of micelles initially present do es not determine the number of latex particles formed. However, at a given micellar concent~ation, the total surface area of the micelles is constant because the increasing size of the micelle compensates for their decreasing number as alkyl chain length is increased. Thus, it seems that the total surface area of the micelles may be theofactor determining the rate at which initiator radicals are captured by micelles and hence the number of latex particles formed. TABLEV Total Surface
Areas of the Micelles in Solutions of Sodium Alkyl Sulfates Containing 0.012 mol dm-3 Micellar Surfactant Alkyl chain length
Aggregation numbera 10 - 3 Total surface area m z dm - 3 b a b
From Aniansson et al., 1976. From Al-Shahib, 1977.
27 4.4
CIO
CIZ
CI4
CI6
41 4.5
64 4.3
80 4.4
100 4.5
CIS
A. S. Dunn
236
Because of their greater size, the efficiency of capture of initiator or oligomer radicals by the latex particles is greater than that of the micelles. Consequently, when the area of the latex particles has increased sufficiently to ensure capture of all initiator radical s, particle formation ceases because there is no chance of any remaining micelles capturing radicals. The small micelles of the lower members of homologous emulsifier series are less efficient in capturing initiator radical s than the larger micelles of the higher members of the series, which leads to a longer duration of Interval I which should mean that the particle size distribution is much broader when the critical surface area of latex particles is ultimately attained. The efficiency of radical capture by micelles will differ for different emulsifiers and will be the factor determining the breadth of the particle size distribution in batch polymerizations.
. V. Latex Agglomeration The size of the latex particles obtained by an emulsion polymerization using an ionic emulsifier is in the 3O-100-nm range. Particles exceeding 100 nm in diameter can be produced by multistage seeded emulsion polymerizations: and although this technique has been used in the laboratory to obtain model colloids it is not suitable for use on an industrial scale, although latexes with an average diameter in excess of 100 nm are required for some applications. The viscosity of dispersions increases with decreasing average particle size although it also depends on particle size distribution. The solids content of a latex produced by the mutual recipe using 100 parts by weight of monomer to 180 parts water carried to a 70% conversion is 28% after the residual monomer has been removed. This is much too low for many applications in which the product is used as a latex: solids contents in excess of 60% are often required. However, if the latex is concentrated by evaporation it sets to a stiff paste when the solids concentration rises to about 40%. This can be avoided if the average particle size is increased by agglomeration. The principIe of agglomeration is that the latex is destabilized slightly when particle coalescence occurs until the total surface area of the particles has been reduced sufficiently for stability to be restored. This may be brought about by the addition of a solvent that swells the particles and which has to be removed after agglomeration, by partial neutralization of carboxylate emulsifiers, by addition of electrolytes, or by freezing which increases the effective electrolyte concentration when some of the water separates as ice. Unfortunately, all these processes are more or less difficult to control and generally re'Sult in partial coagulation of the latex as well as agglomeration. The process of pressure agglomeration
6.
Effects of the Choice of Emulsifier in Emulsion Polymerization
237
developed by the International Synthetic Rubber Company (1971) appears to have overcome these difficulties; this process involves subjecting a stream of latex in turbulent flow to a large drop in pressure. Although no investigations into the mechanism of this process have been reported, it may depend on the surface of the latex being less than completely covered with emulsifier at the end of the polymerization. The drop in pressure might cause rapid desorption of some emulsifier permitting some coalescence to occur until equilibrium is established again at the lower pressure. For the process to be successful the initial solids content has to be raised to about 35% by evaporation. After agglomeration the solids content may be raised to 60% by further evaporation before the latex viscosity exceeds 20 P, becoming too viscous to handle conveniently. Ir the critical factor in pressure agglomeration is, in fact, the rates of desorption and readsorption of emulsifier in comparison with the rate of slow coalescence of the latex particles, the result obtained should depend on the emulsifier used and might provide a means for studying rates of emulsifier adsorption.
VI.
Other Effects of Emulsifiers
Various other effects of emulsifiers have been observed in particular systems but systematic studies of these effects in relation to emulsifier structure have not yet been undertaken. A.
Monomer So/ubilization
In general the amount of hydrophobic monomer that can be solubilized in emulsifier micelles increases with the alkyl chain length of the emulsifier parallel to an increase in micelle size. In the case of styrene there is a definite correlation between solubilizing power of the emulsifier and the rate of polymerization during Interval I (Fig. 3), although the number of latex particles ultimately formed and consequently the ultimate rate of polymerization during Interval 11 is independent of the amount of monomer solubilized (Fig. 2). Although no investigation of particle size distribution in relation to amount of monomer solubilized has been published it is to be expected that the width of the particle size distribution would decrease with increase of the amount of monomer solubilized and consequent decrease in the duration of Interval I. Although emulsifiers do also solubilize the more polar monomers, which have a greater solubility in wath, to about the same extent as nonpolar monomers. this amount is usually negligible compared with the amount of
A. S. Dunn
238 P,'I
~'" 1.2
I (a)
""
.. ~O.B ;Q
" ~
00°.4
< ~ o
°
O
8 16 24 Ofopolymerizedin 3 hr
P,'I-;241(b) ""
32
o
'" :o.. .1:1
~"
16
'O
.. ~ 8 .. .. >. ~ O O
0.4 0.8 1.2 DMAB solubilized(gdm'3)
Fig. 3. (a) Correlation of the initial (Interval 1) rate in the eopolymerization of butadiene and styrene with the amount of dimethylaminobenzene (DMAB) solubilized in the surfaetant solution. (b) Correlation of the amount of styrene solubilized in surfaetant solutions with the solubilization of DMAB. Surfaetants: O Rubber Reserve Soap; O sodium rosinate; D. potassiumtetradeeanoate: O potassiumdodeeanoate: \l sodiumoleate. (From Kolthoffet al., 195\. Reprodueed with permission of John Wiley and Sons, Ine.)
monomer present in true solution so that it has no discernible effect on the course of the polymerization in such cases. B.
Po/ymer So/uhi/ization
When the surfactant concentration is high relative to the polymer concentration sufficient surfactant may be adsorbed on individual polymer molecules to prevent their coalescence to form latex particles or indeed to disperse preformed polymer to form clear solutions in which the solute behaves as a polyelectrolyte. But the influence of such effects on the course of emulsion polymerization reactions has not been elucidated. Sata and Saito (1952) showed that poly(vinyl acetate) precipitated from acetone solution with water could be solubilized in sodium dodecyl sulfate solutions after removal of the acetone by dialysis. To obtain a clear solution at 20°C, a weight of surfactant 5-10 times that of pol~mer was required. Although this greatly exceeds the surfactant concentrations normally used in emulsion
6.
Effects of the Choice of Emulsifier in Emulsion Polymerization
239
polymerizations this effect could mean that the lowest molecular weight fractions of polymer could remain in the aqueous phase at high surfactant concentrations. C.
lnitiator Decomposition lnduced by Emulsifier
Medvedev and Sheinker (1954; Medvedev, 1957) advanced a theory of emulsion polymerization in which the reaction was supposed to take place within the adsorbed emulsifier layer. Induced decomposition of the initiator by radical s derived from the emulsifier formed an essential step in his kinetic scheme. Although Ryabova et al. (1975a,b) subsequently showed that the experimental evidence on which Medvedev's theory was based was unreliaqle, it is nevertheless important to know whether decomposition rate constants for initiators derived from experiments in homogeneous solutions are applicable (as is usually assumed) in the presence of emulsifiers and emulsified monomer. It is plausible that the electrical double layer surrounding micelles and emulsified monomer droplets might affect the rate of decomposition of ionic initiators, although if it did the rate of decomposition might also be expected to be affected by the ionic strength of aqueous solutions whereas, in the case of persulfate at least, no effect was found (Kolthoff and Miller, 1951). Nevertheless, there is a considerable body of evidence in the literature that the rate of persulfate decomposition may be increased by a factor of two or thereby in the presence of monomers. Although this would mean that the rate of consumption of initiator would be greater than otherwise ~xpected, it does not necessarily mean that the rate of initiation would also be enhanced. Where titrimetric methods are used' to determine persulfate concentrations, higher concentrations have to be used than would be used in polymerizations: the effect of second-order reactions involving persulfate might be negligible at lower concentrations. Induced chain decompositions of persulfate, e.g., SOi R.
+ RH = R. + S20~- = RSOi
+ HSOi + SOi
may be prevented in the presence of monomer if all the primary radicals react with the monomer. Although such an induced chain decomposition increases the rate of consumption of the initiator, it would usually affect the radical concentration little. Dunn and Tonge (1972) used diphenylpicryl hydrazyl as a radical scavenger to measure the rate of initiation (rather than the rate of decomposition) of persulfate under polymerization conditions, although 50% ethanol solutioQs had to be used beca use diphenylpicryl hydrazyl is insoluble in watef'. No evidence was found for any large enhancement of the initiation rate by persulfate due to the presence of ..
A. S. Dunn
240
additives as was implied by the results reported by Morris and Parts (1968): their results refer to rates of persulfate decomposition but they seem to ha ve been vitiated by interference by the additives in the titrimetric method used for determining persulfate concentrations. Yurzhenko and Brazhnikova (1956) reported that hexane or toluene, dispersed in water without an emulsifier, increased the rate of decomposition of persulfate by a factor of two or three. van der Hoff (1967) showed that the rate of decomposition of persulfate was much increased in dispersions of octane or benzene. Vinogrado v et al. (1962) found that whereas persulfate decomposed at a much enhanced rate in an emulsion of xylene with potassium oleate as emulsifier compared with a similar emulsion using the same concentration by weight of sodium dibutylnaphthalene sulfonate, the rate of polymerization of styrene emulsions was actuaIly greater with the latter emulsifier! Volkov and Kulyuda (1978) found nOl1ionicsurfactants to enhance the rate of persulfate decomposition: the effect of a polyethyleneoxyalkylphenol was grea~er than that of a polyethyleneoxymonododecyl maleate, which exceeded that of poly(vinyl alcohol), which in turn was greattr than that of polyethyleneoxymonotetradecyl maleate; but the rate of polymerization of styrene was greater with the second of the above emulsifiersthan with the first. Ryabova et al. (1977) found that persulfate decomposed 50 to 100% faster in potassium decano ate solutions than in water, whether the concentration was above or below the CMC of the emulsifier: emulsification of styrene resulted in a further 100% increase in the decomposition rateo Liegeois (1971) found that the rate of initiation of vinyl chloride in aqueous solution by persulfate was that expected from the rate of decomposition in the absence of additives, although the rate of decomposition was increased by a factor of three in the presence of vinyl chloride. Similariy, AIIen (1958) found that the rate of initiation of methyl methacrylate emulsions by persulfate (as inferred from measurements of overaIl polymerization rate and the degree of polymerization of the polymer) did not vary as the concentration of sodium dodecyl sulfate emulsifier was increased. The general conc1usion is that the presence of emulsifiers and emulsified monomers does not increase the rate of initiation by persulfate but that the induced chain decomposition may increase the rate of consumption of the initiator by a factor of three or more. Thus, the effect will usually be negligible in laboratory studies in which conditions are usually chosen so that the decrease in the concentration of the initiator will be negligible in the duration of the polymerization reaction, but under industrial conditions wasteful consumption of persulfate could lead to premature exhaustion of the initiator and incom-
pletepolymerization.
.
6.
D.
Effects of the Choice of Emulsifier in Emulsion Polymerization
241
Catalysis 01the lnitiation Reaction
From the discussion above, it is cIear that there is no evidence for catalysis of persulfate initiation in emulsion polyrnerization systems. However, many ionic reactions have been shown to be subject to large catalytic elfects in the presence of emulsifier micelles (Fendler and Fendler, 1975) so that the question arises as to whether there are any radical reactions that are subject to micellar catalysis and whether this phenomenon plays any part in any emulsion polymerizationsystems. Prima Jacie evidence that micellar catalysis may be important when emulsified monomer is allowed to polymerize thermally is provided by the work of Asahara et al. (1970, 1973)who find that several emulsifiersdecrease the energy of activation for thermal initiation of alkyl methacrylate and styrene. In particular, the energy of activation for thermal initiation of styrene emulsified with sodium tetrapropylene benzene solfonate was reported as
53 kJ mol- 1, much lower than any value determined in bulk. Hui and Hamielec's value of 115 kJ mol-I (1972) seems to be representative of the data available on th(;:rmalinitiation in bulk. The concIusions of Asahara et al. are based on observations of the temperature dependence of the degree of polymerization and are open to several objections. 1. The viscosity-average degree of polymerization is measured when the number.oaverage degree of polymerization is required, although this will not lead to any error in deriving an energy of activation provided the molecular weight distribution does not change with temperature. 2. It is assumed that all transfer reactións can be neglected so that the kinetic chain length can. be taken as half the degree of polymerization: this seems dubious when it is generally agreed that the degree of polymerization of thermally polymerized styrene in bulk is limited by transfer to monomer and when the possibility of using oil-phase initiation for emulsion polymerization is dependent on the escape of one of a pair of.radicals generated in the oil phase to the aqueous phase which seems likely to involve transfer either to monomer or to emulsifier. 3. In their calculation, they seem to have confused the energy of activation for propagation with the overall energy of ~ctivation for polymerization: when this is corrected the energy of activation for initiation becomes 80 kJ mol- 1 which is still significantly lower than the bulk value of 115 kJ mol- 1 but which may stiII be incorrect if the second objection above is justified. An alternative method of calculating the energy of activation for initiation in emulsion polymeriza60n was introduced by Bartholomé et al.
A. S. Dunn
242
(1956). It depended on the variation of the number of latex partic1es formed N with temperature. Unfortunately, they have overlooked the fact that the partic1e growth rate J1which appears to the power -~ in the Smith-Ewart expression for the number of latex partic1es formed contains the propagation rate constant kp which is temperature dependent. It has also recentIy been realized that another factor on which N depends, the area occupied by a surfactant molecule at the polymer-water interface as, is also temperature dependent. Dunn et al. (1981) observed that the temperature dependence of N in the thermal polymerization of styrene differed from different emulsifiers. It seems unlikely that the differences can be wholly explained by differing enthalpies of adsorption of the emulsifiers and, if not, this observation implies that the energy of activation for thermal initiation of styrene in emulsion depends on the emulsifier used. Participation of emulsifiers in thermal initiation (and probably also in initiation by oilsoluble initiators) is most probably attributable to transfer to emulsifier and desorption of the emulsifier radical from the micelle .or latex partic1e into the aqueous phase: the rates of these processes are likely to differ with the
emulsifier.
'
E. Transfer lo Emu/sifiers The extent and importance of transfer reactions to emulsifier molecules in emulsion polymerization has not been extensively investigated. Tr.ansfer to an emulsifier molecule that is subsequentIy desorbed from the micelle or latex partic1e would seem to be an attractive mechanism that would facilitate the escape of radicals of the less water-soluble monomers to the aqueous phase, a process of greater importance than had previously been thought. However, most emulsifiers do not contain any particularly active hydrogen or other substituent atoms, and the topology of the system implies that transfer constants determined from experiments in homogeneous solution do not necessarily apply to latex systems. Thus, Okamura et al. (1958) found from experiments in homogeneous solution that the rate constant for the transfer of poly(vinyl acetate) radicals to poly(vinyl alcohol) (35 x 10-4 dm3 mol-l sec-l) was much higher than that to poly(vinyl acetate) (1.5 x 10-4 dm3 mol-1 sec-1) so that it might be expected that when incompletely hydrolyzed grades of poly(vinyl alcohol-acetate) are used as emulsifiers in the emulsion polymerization of vinyl acetate, the extent of formation of graft copolymers of poly(vinyl acetate) with the emulsifier sho~ld be expected to decrease with acetyl content. In fact, the contrary trend was observed. The acetyl blocks form the hydrophobic portion of poly(vinyl alcohol-acetate) emulsifiers and are the only parts of the molecule readily accessible to poly(vinyl acetate) radicals in the latex
6.
Effects of the Choice of Emulsifier in Emulsion Polymerization
243
particIes: consequently,most of the transfer that does occur must occur to these acetyl blocks. Extensive studies of the removal of adsorbed emulsifiers have been made only with polystyrene latices. Exhaustive dialysis does not seem to be a satisfactory procedure (Edelhauser, 1969) as it fails to remove all the emulsifier, but it does seem to be possible to do this either by ion exchange (Vanderhoff et al., 1970) provided the resin used has been properly prepared or by the serum replacementtechnique (Ahmedet al., 1980).AftercIeaning, the number of sulfate groups per polystyrene molecule is less than two. When persulfate initiation is used two sulfate end groups per molecule would be expected, but hydrolysis of the sulfate ester end group is quite facile so that some of the original end groups may have been replaced by hydroxyl. However, no critical experiment has yet been attempted. This might involve the use of an initiator (e.g., sodium azobiscyanopentanoate) that could only introduce carboxylate end groups in conjunction with radioactively labeled sulfonate emulsifier (since there is no danger of sulfonate groups being hydrolyzed): radioactivity remaining in the polymer after removal of adsorbed emulsifier would enable the extent of transfer to emulsifier to be determined. Kamath et al. (1975)showedthat the nonionic octylphenoxypolyethylene oxide emulsifier Triton X-I00 contains a labile pro ton so that the molecular weight of polystyrene prepared using this emulsifier is abnormally low because of extensive transfer to the emulsifier. In general, transfer to emulsifier does not appear to be very important in the emulsion polymerization of styrene, a1though it has recently become evident (cf. Hawkett et al., 1980) that even in this case, escape of radicals from latex particIes' cannot be neglected. However, there is no evidence available to show whether emulsifiers participate in the escape>process. Transfer processes are likely to be more important in the case of those radicals (e.g., vinyl acetate) that are more active than styrene but very little data indeed pertaining to these has been published.
References Adamson, A. W., (1976). "Physics and Chernistry ofSurfaces," 3rd ed. Wiley, New York. Ahmed, S. M., EI-Aasser, M. S., Micale, F. J., Poehlein, G. W., and Vanderhoff, J. W. (1980). In "Polyrner Colloids 11" (R. M. Fitch, ed.), p. 265. Plenum Press, New York. Allen,P. W. (1958).J. Polym. Sci. 31, 206. AI-Shahib, A. W. (1977). Ph.D. Thesis, Manchester. Anacker, E. W., Rush, R. M., and Johnson, J. S. (1964).J. Phys. Chem.68, 81. Aniansson, E. A. G. et al. (1976). J. Phys. Chem.SO,905. Asahara, T., Seno, M., Shiraishi, S., and Arita, Y. (1970). Bull. Chem. Soco Jpn. 43, 3895.
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244
Asahara, T., Seno, M., Shiraishi, S., and Arita, Y. (1973). Bul/. Chem. Soco Jpn. 46, 249. Bakker, J. (1952). Phi/ips Res. Rep. 7, 344. Bartholomé, E., Gerrens, H., Herbeck, R., and Weitz, H. M. (1956). Z. E/ektrochem. 60, 334. Benetta, G., and Cinque, G. (1965). Chim. Ind. (Mi/an) 47, 500. Blackley, D. e. (1975). "Emulsion Polymerisation: Theory and Practice," p. 308, Fig. 7.22. Applied Science, London. Bobalek, E. G., and WiIliams, D. A. (1966). J. Po/ym. Sci. Part A-/ 4, 3065. Carr, C. W., KoltholT, J. M., Meehan, E. J., and WiIliams, D. E. (1950). J. Po/ym. Sci. 5, 20\. Davies, J. T. (1957). Proc. InI. Congr. Surface Activity, 2ndVol. 1, p. 426. Butterworths, London. Doherty, J. V. (1978). Unpublished work. Dunn, A. S., and AI-Shahib, W. A. (1978). J. Po/ym. Sci. Po/ym. Chem. Ed. 16,677. Dunn, A. S., and AI-Shahib, W. A. (1980). In "Polymer Colloids 11", (R. M. Fitch, ed.), p. 619. Plenum Press, New York. Dunn,
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13, 126\.
Dunn, A. S., Said, Z. F*, and Hassan, S. A. (I98\). In A.C.S. A. E. Hamielec, eds.), p. 11 \. American Chemical Society, Edelhauser, H. A. (1969). J. Po/ym. Sci. Part C 27, 29\. Eliassaf,J. (1973). Polim. Vehomarim P/ast. 3, 9 (in Hebrew); cf. Fendler, J.~., and Fendler, E. J. (1975). "Catalysis in Micellar Academic Press, New York.
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(R. M. Fitch, ed.), p. 73. Plenum
Greth, G. F., and Wilson, J. E. (l96\). J. App/. Po/ym. Sci. S, 135. Griffin, W. C. (1949). J. Soco Cosmet. Chem. 1, 31\. Griffin. W. C. (1954). J. Soc. Cosmet. Chem. 5, 249. Griffin. W. e. (1980). Emulsions Kirk-Othmer "Encyc1opedia of Chemieal Teehnology" 3rd Edn. 8, 900. Hawkelt, B. S., Gilbert, R. G., and Napper, D. H. (1980). J. Chem. Soc. Faraday Trans./76, 1323. HoplT. H., and Falka. \. (1965). Makromo/. Chem. 88, 54 (in German); Br. Po/ym. J. 2, 40 (1970). Hui, A. W., and Hamielec, A. E. (1972). J. App/. Po/ym. Sci. 16,749. lntemational Synthetie Rubber Co. (D. A. Bennett) (I97\). U.S.P. 3 573 243. lvanova. N. Y.. and Yurzhenko, A. l. (1958). Kol/oid Zh. 22, 37 [English trans.: Col/oid J. USSR 22,39J. Jagodie, F., and Fajt. B. (1976). Kem. Ind. 25, 13 (in SJovenian); cf. Chem. Abstr. 86,44067g (1977). Jagodie, F., Abe. M., and Ogrizek, N. (1975). Kem. lnd. 24, 591, 659 (in Slovenian); cf. Chem. Abstr. 85, 33460h, 63365y (1976). Kamath, V., Morton, M.. and Piirma, l. (1975). J. Po/ym. Sci. Po/ym. Chem. Ed. 13,2087. KoltholT, J. M., and MiIler. J. K. (1951). J. Am. Chem. Soco 73, 3055. KoltholT, J. M.. Meehan, E. J., and Carr, e. W. (1951). J. Po/ym. Sci. 6, 73. Kratohvil, J. P. (1980). J. Col/oid Interface Sci. 75, 271. Liegeois, J. M. (1971). J. Po/ym. Sci. Part C 33, 147. Maron, S. H., Elder, M. E., and Ulevitch, l. N. (1954). J. Col/oid Sci. 9, 89. Medvedev, S. S. (1957). In Proc. InI. Symp. Macromo/. Chem.. Prague p. 174. Pergamon, Oxford. Medvedev, S. S., and Sheinker, A. P. (1954). Dok/. Akad. Nauk. SSSR 97,111. Medvedev~ S. S., Zuikov, A. V., Gritskova, J. A., and Dudukin, V. V. (1971). Vysokomo~. Soedin. A13, 1397 [English trans.: Po/ym. Sci. USSR, 13, 1572J. Morris, C. E. M., and Parts, A. G. (1968). Makromo/ Chem. 119,212. Okamura, S., Yamashita, T., and Motoyama, T. (1958). Kobunshi Kagaku 15,170; ef. Chem. Abstr. 56, 953i (1960).
6.
245
Effeéts of the Choice of Emulsifier in Emulsion Polymerization
Onischenko, T. A., Rabinovich, M. A., and Gershenovich, A. 1. (1970). Kol/oíd Zh. 32, 886 [English transl.: Colloid J. USSR 32,744. Ono, H., Jidai. E.. and Fujii, A. (1974). J. Col/oid Interface Sci. 49, 155. Ono. H.. Jidai, E.. and Fujii. A. (1975). J. Phys. Chem. 79. 2020. Ottewill, R. H., and Shaw, J. N. (1966). Discuss. Faraday Soco 42. 154. Paxton. T. R. (1969). J. Col/oid Interface Sci. 31, 19. Paxton. T. R. (1977) B. F. Goodrich Co.. Brecksville. private communication. Piirma, l., and Chang, M. (1980). Org. Coatíngs Plast. Preprints 43, 104. Piirma, l., and Chen, S.-R. (1980). J. Col/oíd Interface Sci. 74, 90. Piirma, l., and Wang, P.-e. (1976). In "Emulsion Polyrnerization" (1. Piirma and J. L. Gardon, eds.), Am. Chem. Soe. Symp. Series 24, p. 34. American Chemical Society, Washington D.C. Rosen, M. J. (1978). "Surfactants and Interfacial Phenomenena," Wiley, New Y.ork. Ryabova, M. S., Sautin, S. N., Beresnev, V. N., and Smirnov, N. 1. (l975a). Zh. Prikl. Khim. 48, 1101 [Enf{li.fh transl.: J. Appl. Chem. USSR 48, 1148]. Ryabova. M. S.. Sautin, S. N.. and Smirnov. N. 1. (l975b). Zh. Prikl. Khim. 48, 1577 [English transl.: J. Appl. Chem. USSR 48, 1632). Ryabova. M. S.. Sautin. S. N.. and Smirnov. N. 1. (1977). Zh. Prikl. Khim. SO. 1719 [English transl.: J. Appl. Chem. USSR SO, 1648]. Sata, N., and Saito, S. (1952). Kol/oid Z. 128, 151. Sawyer, W. M., and Rehfeld, S. J. (1963). J. Phys. Chem. 67, 1973. Testa. F., and Vianello, G. (1969). J. Polym. Sci. Part C 27,69. Ugelstad, J., and Hansen, F. K. (1979). J. Polym. Sei. Polym. Chem. Ed. 17, 3069. Ugelstad, J., EI-Aasser, M. S., and VanderhotT, J. W. (1973). J. Polym. Sci. Polym. Lett. Ed. U, 503.
Urban, P. e. (1980).Polysar Ltd., Canada.Paperpresentedat 54th Col/oid Surfaee Sei. Symp., 54th, Lehigh Univ., Bethleham, Pennsylvania, June15-18 Abstr. 84. Van der HotT, B. M. E. (1967). In "Solvent Properties ofSurfactant Solutions" (K. Shinoda, ed.), Chapter 7. Dekker, New York. VanderhotT,J. W., Van den Hui, H.J., Tausk, R.J. M.,andOverbeek,J. Tb. G. (1970). In "Clean Surfaces" (G. Goldfinger, ed.), Chapter 2. Dekker, New York. Vinogradov, P. A., Odintsova. P. P., and Shitova, A. A. (1962). Vysokomol. Soedin. 4, 98 [English transl.: Polym. Sci. USSR 4. 33]. Volkov, V. A., and Kulyuda, T. V. (1978). Vysokomol. Soedin. B 20,862; cf. Chem. Abstr. 90,
122120t (1979).
.
Woods, M. E., Dodge, J. S., Krieger, 1. M., and Pierce, P. E. (1968). J. Paint Teehnol. 40, 543. Waite, F. A. (1977). 1.e.1. Ltd., Paints Division, Slough, private cornmunication. Yurzhenko, A. l.. and Brazhnikova, O. P. (1956). Zh. Obs. Khim. 26,1311 [English transl.: J. Gen. Chem. USSR 26, 1481].
7 Polymerization of Polar Monomers v. l. Yeliseyeva
1. Introduction. 11. Interface Characteristics of Polymeric Dispersions 111. Relationship between Emulsifier Adsorption and the Difference in the Boundary Phase Polarity A. Monomer-Aqueous Phase Interface B. Aqueous Phase-Polymer and Aqueous PhaseLatex Particles Interfaces. IV. Mechanism of Particle Generation . V. Colloidal Behavior of Polymerization Systems. VI. Kinetics of Emulsifier Adsorption VII. Mechanism of Formation and Structure of Particles VIII. Polymerization Kinetics IX. Relationship between Polymerization Kinetics and Adsorption Characteristic of Interface. X. Nor,nenclature . References .
l.
247 249 250 251 254 257 261 268 270 278 283 286 287
Introduction*
Experience has shown that each monomer has its own specific features in emulsion polymerization and requires a specific technology. To a certain extent this is also true of other components in the reaction system, e.g., the emulsifier and the initiator. Attempts to fit various emulsion reaction systems into one physicochemical model or theoretical scheme have therefore failed. Nevertheless, several features that are common to all polymerizations in colloidal systems have been established. They were formulated in the * There is a Nomenclature chapter.
section on p. 286 which defines the major symbols used in this
247 EMULSION POLYMERIZATION Copyright
1982 by Academic Press. Ioc. Al! rigbts or reproductioo io aoy rorm reserved. ISBN 0-12-556420-1
248
V. 1. Yeliseyeva
élassical theory of Smith and Ewart (1948) which was created in the late 1940s and which is weIl known to researchers working in the field of emulsion polymerization. The most important concIusion that foIlows from the theory is that the process takes place in an equilibrium of swoIlen polymer-monomer particIes (PMP) each of which may be "living" or "dead" at any given time depending on the presence of a free radical. Furthermore, Case 2 of the theory was developed for systems in which styrene was used as the weakly polar model monomer. An anion-active, miceIle-forming surfactant with a low CMC (critical miceIle concentration) value (such as sodium dodecylsulfate) was used as the model emulsifier and persulfate as the model water-soluble initiator. The process is characterized by a period of constant rate, the rate being proportional to the number of particIes and the average number of radical s per particIe and depending on monomer reactivity. According to the theory based on the Harkins' (1947) model oi emulsion polymerization [a similar model was independentIy developed by Yurzhenko and Mints (1945)], PM:P are formed from monomer-swoIlen emulsifier miceIles into which free radicals enter from the aqueous phase; the number bf particIes remains constant during the constant rate periodo The derived equation of the rate dependence on the emulsifier (Ce) and initiator (C¡)concentrations during the constant rate period
R '" C~.6 . C?-4
(1)
satisfactorily describes polymerization in this and similar systems, on the strength of which the theory became quite popular. Medvedev (1968) suggested that not the number of particIes and miceIles, but the value of their overaIl surface area is the rate-determining factor. Inconstancy in the number of particIes during the constant rate period is allowed, e.g., flocculation with retention of the overall surface value. On the basis of this suggestion a general equatíc:m was derived which, however, differs only slightIy from the equation of the cIassical theory shown in Eq. (1) R '" C~.5 . Cp.5 (2) With the significant increase in the number of various monomers, emulsifiers, and initiation systems used in recent years the límited applicability of the quantitative aspect of both theories quickly became apparent. Let us consider one of the reasons for this limitation. It do es not foIlow from Eqs. (1) and (2) that the polymerization rate being a function of emulsifier concentration also depends on the emulsifier activity in the given polymerization system. It has been shown in several studies, however, that emulsifier activity at the water-organic phase interface is determined by the structure of the emulsifier molecule and the
7. Polymerizationof Polar Monomers
249
polarity of the organic phase. Hence, the use of the emulsifier concentration value in the rate equation without taking into account its activity .is inadequate. Therefore, in order to extend the applicability of Eqs. (1) and (2) to the polymerization of monomers of various polarity in the presence of emulsifiers of various structure, a parameter characterizing the emulsifier activity in the given system should be introduced. Whereas this parameter may be neglected when considering polymerization of some hydrophobic monomers (hydrocarbons) with close adsorption characteristics, it must be taken into account in the case of polymerization of highly polar monomers (or their copolymerization with hydrophobic monomers) where the colloidal behavior of the system, and consequently the polymerization kinetics, depends on emulsifier activity. Since the practical importance of latexes obtained by polymerization of polar monomers or monomeric systems is rapidly increasing, a consideration of the regularities of their formation, taking into account a11important factors, is of considerable interest.
D.
InterfaceCharacteristics of Polymeric Dispersions
Polymers in the form of latex (co11oidal dispersions) acquire a novel quality not observed in bulk or solution and which is due to the strongly developed interface with the aqueous phase. The properties of this interface vary specifically with the nature of the polymer, the latter varying in a wide range for different latexes and other polymer dispersions. The most important characteristic of the interface is its energy, the interfacial free energy, which depends on the molecular interactions between boundary phases. Molecular interactions which are responsible for interfacial tension occur as a result of various we11-known intermolecular forces. Many of these forces are determined by the specific chemica] nature of the substance. On the other hand in a11 types of matter London dispersion forces exist, and they always ensure attraction between neighboring atoms and molecules independent of their chemical nature. Fowkes (1964) has suggested that the effect of dispersion interactions on interfacial energy may be predicted from the geometric mean ratio of dispersion forces of surface tension components of boundary phases. My~)1/2. Since the interfacial tension is the sum of tensions in both regions and provided that only dispersion forces exist between the phases, then the interfacial tension at the boundary of the first and second phase is Y12 = Yl + Y2 - 2M - y~)1/2
(3)
Fowkes analyzed the available experimental data on interfacial tension Y12 at the water-organic liquid interface and calculated the values of interfacial
250
V. 1. Yeliseyeva
tensions Y12 under the assumption that only dispersion interactions are operative at the interface. For all the compounds studied Y12was found to be higher than Y12' The difference between them may serve as a measure of the energy, which includes various polar interactions. Fowkes established that for most of the cases examined, interaction attributable to dispersion forces makes the highest contribution to interfacial tension, although for substances capable of forming hydrogen bonds the attraction due to dispersion forces may be approximately equal to attraction due to hydrogen bonds. Wu (1974) obtained an equation for boundary phases with various properties which relates Y12not only to dispersion interaction but also to phase polarity. In his opinion, for an interface between high and low energy phases, e.g., mercury or water and organic polymers, this dependence may be represented by the geometric-harmonic mean ratio Y12 = Yl + Y2 -
2[y1- Y~- 4y~y~/(y~+,Ym
(4)
This ratio is transformed to Fowkes' equation when the polar term is negligibly small. Using Eq. (4) and experimental data on interfaCÍal and surface tension of polymers, Wu calculated the polarity of some polymers. He estimates the contribution of the polarity to the surface tension of polymers to be considerable. Thus, for poly(vinyl acetate) it takes up 33%, for poly(methyl methacrylate) 28%, and for polychloroprene 11%. Since the polar contribution is the most important factor determining the interfacial energy, the polarity of polymers in a dispersed phase strongly influences (i) the adsorption of surfactants, (ii) the mechanism of particle formation, (iii) the particle flocculation, and (iv) the configurational behavior of the forming macromolecules. Several experimental confirmations of this have been reported elsewhere (Yeliseyeva, 1972).
III. Relationship between EmulsifierAdsorption and the Difference in the Boundary-PhasePolarity The energy state of the interface obviously determines the adsorption of a given surfactant by this interface. On the other hand, a given interface may adsorb with different energy surface-active substances of different chemical nature. Rhebinder (1927) was the first to point out that the difference in polarity between boundary phases, which affects the interfacial energies, is the main factor determing adsorption; for adsorption of a third component by the interface, the polarity of this component should lie between the polarities of the two boundary phases.
251
7. Polymerizationof Polar Monomers
In order to analyse the colloidal processes occurring in colloidal polymerization systems containing monomer, polymer monomer and polymer particles it is important to know about adsorption characteristics of the emulsifier on the monomer-aqueous phase and polymer-aqueous phase interfaces. A.
Monomer-Aqueous Phase Interface
The structure of the liquid-liquid interfacial layer depends on the difference in polarity between the two liquids (Kaeble, 1971). Asymmetric molecules of some liquids display a molecular orientation on the interface which is indicative of their structure. Thus, interfacial tension at the octanewater interface is 50.5 nm/m whereas at the octanol-water interface it is only 8.8 nm/m. Reduction of interfacial tension in the latter case points to the orientation of octanol hydroxyl groups toward water, in other words to the structure and polarity of the interfacial layer. Because of such an orientation, the stimulus for adsorption of other asymmetric molecules on the interface is decreased. A similar pattern is typical of the homologous series of lower alkyl acrylates: at the interface with water the carbonyl groups of their asymmetricaI" molecules are oriented toward water; this orientation is more effective the higher the polarization of the carbonyl, Le., the smaller the alkyl. Interfacial tension decreases in the same order from 27.2 nm/m for hexyl acrylate (Yeliseyeva et al., 1978) to 8 nm/m for methyl acrylate (datum from our laboratory by A. Vasilenko). Adsorption isotherms of n-butyric acid at various interfaces are shown in Fig. 1 where it can be seen that the greater the difference in polarity between boundary phases the higher the adsorption (differing by more than fourfold). Interfacial tension, however, cannot serve as the only criterion of adsorption. Typical surfactants with asymmetric molecules or ions consisting of a polar group and a sufficiently long hydrocarbon chain are always active at water-hydrocarbon interfaces. The greater the difference in polarity between boundary phases the steeper the orientation of surfactant molecule at the interface and the larger the reduction in free energy of the system due to adsorption. Upon substitution of a non polar organic phase (aliphatic hydrocarbon) by a polar organic liquid, with resultant decrease in the energy of interaction between the aliphatic hydrocarbon portion of surfactant and the organic phase, the free energy of the system is reduced to a lesser extent and the surfactant molecules are less oriented at the interface. Davis et al. (1972) estimated the contribution of CH2 groups to the free energy of substance transfer from aqueous phase into organic liquids of
.
252
V. 1. Yeliseyeva
0.1 0.2 0.3 Concmtration of n-lJutyr¿cacid (mol/tim!)
.
Fig.1. Adsorption isotherms of'n-butyric acid at the interfaces: (1) water-air; (2) waterhexane; (3) water-benzene; (4) water-olive oil. T, 318 K. various polarity (~G). It was established that this value decreases with increasing polarity of the organic liquido For nonpolar liquids such as cycJohexane, hexane, and heptane, this value is 3.6 kJ/mol, whereas for polar liquids (alcohol s, nitro-compounds, ethers) it decreases to 1.892.98 kJ/mol. . Using the stalagmometric method, we determined the adsorption energy (E'ds) of sodium dodecylsulfate (SDDS) at the water boundary with the homologous series of alkyl acrylates at 293 K (Yeliseyevaet al., 1978). Calculations were performed from the initial section of the surface tension isotherm using the Langmuir equation. Table 1 lists values of the initial interfacial tension Y12;the overall free energy of adsorption, E'ds>and the TABLEI Energy Characteristics of SDDS Adsorption on WaterAlkyl Acrylate Interface Depending on Alkyl Acrylate Polarity YI2
E.d'
Acrylate
(mJ/m2)
(kJ/mol)
t:.G (kJ/mol)
Methyl Ethyl Butyl
8 13.7 23.2
20.0 22.1 25.6
1.69 1.85 2.10
253
7. Polymerizationof Polar Monomers
free energy of adsorption LlG per methyl group of the alkyl (assuming that the entire alkyl portion of the emulsifier is immersed in the monomer phase). Data presented in Table I indicate a decrease in the energy of interaction between the hydrocarbon portion of the emulsifier and the organic phase (alkyl acrylate) with an increase in the polarity of the latter. Accordingly, the overall adsorption energy also decreases. Several important practical conc1usions may be drawn from these data. On the one hand, dispersions of polar monomers are stabilized to a lesser extent than nonpolar monomers by emulsifiers containing an aliphatic hydrocarbon in the oleophilic part of the molecule. Although the overall adsorption energy increases only slightly with increasing length of the hydrocarbon portion, as follows from data presented in Table 11,the solubility of the emulsifier in water is significantly reduced, which may hinder its practical use. Therefore, on the other hand, in order to increase the energy of interaction of the oleophilic part of the emulsifier molecule with the polar organic phase, polar groups should be introduced into its structure. This has been confirmed in practice. A consideration of the adsorption kinetics is very important in an estimation of the effectiveness of surfactants under the dynamic conditions of emulsion polymerization. In a stalagmometric study of dynamic and static adsorption of emulsifiers of various structure at the air-water interface, it was established that adsorption values of micelle-forming surfactants differ significantly in the period of drop formation (Nikitina et al., 1961). This was explained by the consider~ble period needed for establishment of adsorption equilibrium connected with the kinetics of adsorption layer formation. The authors conc1uded that for usual concentrations of surfactant solutions the period of establishment of adsorption equilibrium can be taken as equal to 2 mino Figure 2 shows the adsorption isotMrms of TABLE 11
Energy Characteristics of Adsorption Alkylsulfates on Ethyl Acrylate-Water Interface8
Alkyl su,lfate C12H2SS04Na C14H29S04Na CI6H31S04Na a The
E.d. (kJjmol) 22.1 23.3 24.6
of
I:1G
(kJjmol) 1.85 1.69 1.55
absence of proportionality between I:1Gand
increase of the hydrocarbon radicallength indicates that for polar organic liquids Traube's rule is not valid.
254
V. 1. Yeliseyeva
-10
rmxa =3.ifx!O
moZ/cm2
1
.
2;5 5.0 Concfntration
Z5
10.0
of lIerosol (tOsmoZ/ dm J)
Fig. 2. Adsorption isotherms of Aerosol AT plotted according to data of (1) static (2 min) and (2) dynamic (2 sec) values of surface tension.
.
Aerosol AT solutions (sodium dioctylsulfosuccinate) .plotted according to both dynamic (drop formation period 2 sec) and static (drop formation period 2 min) values. The diff~rence in the shape of the isotherms clearIy indicates the significance of the time of surface formation for effective emulsifier adsorption and stabilization at the interface. Apart from the emulsifier structure, the process may depend on the difference in polarity between the contiguous phases. Stalagmometric determination of the SDDS adsorption at the aqueous solution-ethyl acrylate interface dependence on the rate of drop formation (volume 0.03 cm3) were carried out in our laboratory by Vasilenko. The measurements showed that establishment of adsorption equilibrium at the CMC occurs at drop formation periods of 15-20 sec, i.e., at surface formation rates not exceeding 10-6 m2/sec. Adsorption kinetics acquires considerable importance in analysis of the mechanism of particle formation during emulsion polymerization, when the rate of organic phase formation and the rate of adsorption layer formation may be commensurate. B.
Aqueous Phase-Polymer and Aqueous Phase-Latex Particle lnterfaces
The general ideas developed for adsorption of surfactants on liquidliquid and liquid-air interfaces obviously cannot be completely transferred to adsorption on interfaces with a solid phase. Wolfram (1966) caIculated the packing density of surfactant molecules on the polymer surface from the adsorption value at the CMC and showed that it varies with polymer polarity. Thus, the adsorption area of a SDDS molecule on various surfaces takes the following values (nm2): paraffin 0.41,
7. Polymerization of Polar Monomers
255
polyethylene 1.21, poly(methyl methacrylate) 1.32, poly(ethylene terephthalate) 1.42, and polycarbonate 1.48. On the basis of the results obtained the author introduced the concept of "required area" of a surfactant molecule and conc1uded that this area increases with increasing polarity of the polymer. The established relationship he explains by the existence of other interactions such as orientation, induction, and hydrogen bonds between contiguous phases, in addition to dispersion forces. Because of these interactions the molecules adsorbed on the solid phase-liquid interface may acquire a nonvertical orientation: they may be arranged with greater planarity the more intensively the field (depending on polymer polarity) acts upon the polar part of the surfactant molecule. Several investigations have determined the absorption behavior of surfactant adsorption on partic1es of aqueous polymer dispersions by adsorption titration. The results have been similar to those observed by Wolfram for adsorption on aplanar polymer surface determined from the wetting angle. Thus, Paxton (1969) established that the area occupied by a sodium dodecylbenzylsulfonate molecule in a saturated adsorption layer (AS1im)on the surface of PMMA latex partic1es is 1.31 nm2, whereas on the surface of polystyrene latex partic1es it is only 0.53 nm2. The author considers that previous studies of adsorption of this emulsifier, which gave adsorption area (ASlim)of 0.50 nm2, were carried out on interfaces with similar adsorption characteristics. The intermolecular forces involved in adsorption between water and air or water and hydrocarbon solvent or nonpolar polymer are nearly the same. In his opinion the differences observed in surfactant adsorption on polymers of different nature allows one to use the molecular adsorption area value as a polarity characteristic of the polymer phase. Dunn and Chong (1970) determined the value of ASlim for sodium dodecylsulfate on poly(vinyl acetate) latex partic1es; it was fountl to be 1.24 nm2, i.e., 2.4 times higher than the minimal adsorption area of this emulsifier. Zuikov and Vasilenko (1975) showed that the ASlim value for sodium dodecylsulfate increases with polarity of the polymer and is inversely related to the interfacial tension at the interface of the corresponding monomer with water. A correlation was established (Yeliseyeva and Zuikov, 1976) between ASlimof a given emulsifier and its adsorption energy at the corresponding monomer-water interface. The same correlation is observed between ASlimof emulsifier at the given polymer-water interface and its adsorption energy at the interface between the monomer and water for the homologous series of alkyl sulfates (Table III). It follows from the results obtained that the factors determining the adsorption value of a given surfactant at the water interface with the monomer and with the corresponding polymer are the same. Since with the increase in the adsorption energy on the emulsifier-monomer interface, the
256
V. 1. Yeliseyeva TABLE
111
Adsorption Characteristics of Surfactants on Water-Monomer and Aqueous Phase-Polymer Particle Interfaces
Monomer
Emulsifier
MA EA EA EA BA HA Sty
C12H2SS04Na C12H2SS04Na C14H29S04Na C16H31S04Na C12H2SS04Na C12H2SS04Na C12H2SS04Na
.
aAt polymer-water
1'12 monomerwater (mJjm2)
-8 13.7 13.7 13.7 23.2 27.2 33.8
a
E.d' (kJjmol)
ASHm (nm2)
20.0
1.51 0.92 0.82 0.74 0.67 0.52 0.48
22.1 23.3 24.6 25.6 -
interface.
value of the surfactant adsorption increases at the interface with the polymer (Le., ASlimdecreases) which means that the packing density of its molecule in the adsorption layer increases. In a study of the adsorption characteristics of alkyl acrylate and alkyl methacrylate latexes Sütterlin et al. (1976) obtained values for adsorption areas of sodium dodecylsulfate which support the values listed in Table III. The authors, however, attributed the established regularity of ASlimvariation not to polarity but to hydrophilicity of the polymer, the increase of which leads to reduction of the equilibrium emulsifier concentration on the latex particle surface. Since in the homologous series of alkyl acrylates and alkyl methacrylates the increase of hydrophilicity of the monomer occurs parallel to the polarity of the interface, the established relationship may also be attributed to the latter factor. In an attempt to apply Wu's (1974) ratios to calculation of the polar component of interfacial tension at the interface with aqueous phase for polymers of difIerent polarity, Vijayendran (1979) estimated ASlimin latexes of the same polymers on the basis of the obtained results. The values are in good agreement with reported experimental data (Yeliseyeva et al., 1978; Sütterlin et al., 1976). The coincidence of adsorption areas for molecules of a given emulsifier on latex particles of polymers of difIerent polarity obtained by difIerent authors points to the determining role of this factor in adsorl'tion in the case of usual latexes prepared by emulsion polymerization. However, in general when determining the adsorption areas of surfactant molecules other factors, such as electrolyte concentration, temperature, and particle size, should also be considered .(Piirma 'ind Chen, 1980).
7.
IV.
257
Polymerization of Polar Monomers
Mechanism of Particle Generation
Numerous experimental data are available which suggest that both the solubility of the monomer in water and its polarity affect the mechanism of particle generation. Whereas during a conventional emulsion polymerization of styrene (or other hydrophobic monomer) examined by Harkins (1947) and Yurzhenko and Mints (1945) the most important sites of particle generation are monomer-swollen emulsifier micelles; with the increase of monomer solubility in water particle generation in similar systems may be shifted to the aqueous phase. Thus, the possibility of preparing concentrated and stable latexes by polymerization of methyl acrylate and ethyl acrylate in the absence of an emulsifier was demonstrated by Yeliseyeva and Zaides (1965) and by Yeliseye~a and Petrova (1970). It is also well known that styrene latexes may be obtained by emulsifier-free polymerization; such latexes are characterized, however, by larger particles and much lower concentrations. In all such cases the process initiated by persulfate begins in the aqueous phase with the formation of water-soluble, surface-active polymeric radicals which, after growing to a certain critical size, precipitate to form particles; subsequent polymerization proceeds mainly within these particles. The higher the solubility of the monomer in water, the more surface-aciive radical s and therefore primary particles are formed and the higher the stability and the concentration of the latex. A kinetic curve of the emulsifier-free polymerization of ethyl acrylate confirming this scheme is shown by Curve 1 in Fig. 3 (Yeliseyeva anq Petrova, 1970). The process
.
5
15 t(mini
25
Fig. 3. Conversion kinetics (g/100 g of aqueous phase) of ethyl acrylate (1) in the absence of emulsifier and (2) in the presence of 0.5 mol % of emulsifier E-30. Ammonium persulfate, 0.33%; tert-dodecyl mercaptan, 0.33% in aqueous phase; T, 60°C; phase ratio, 1: 3.
258
V. 1. Yeliseyeva
beginning in the aqueous solution is characterized by a low initial rate which rapidly increases, evidently due to the formation of partic1es and the transfer of the polymerization mainly into these partic1es. At the initial stages the surface tension of the system decreases and then increases with conversion. Estimation of the total activation energy of emulsifier-free polymerization of ethyl acrylate showed it to be 100 kJjmol initially, but it markedly decreases in the course of the process in accordance with the increase in the termination energy occurring in the partic1es typical of emulsion polymerization. In the presence of emulsifier (Fig. 3, Curve 2), the process proceeds from the beginning at a high rate and a low activation energy (53.5 kJjmoI), suggesting formation of partic1es from the very beginning of the process and participation of the emulsifier in the mechanism of partic1e generation. The slight difference in the vaIues of the integral molecular mas s of the poIy(et~1 acrylate) oDtained in the absence and in the presence of an emulsifier supports the assumption that in both cases the process mainly follows the mechanism of emulsion polymerization; the viscosity average molecular masses of this polymer obtained under identicaI conditions, both without emulsifier and in the presence of 2% (based on monomer) SDDS, are approximately 4 x 106 and 7 x 106, respectively (Mamadaliev, 1978). The slightly lower integral molecular mas s in the former case may be explained by a larger contribution of polymerization in aqueous solution at the initial stages of the process. Hence, the difference in the mechanisms of partic1e formation of ethyl acrylate (solubility in water 2.5%) in the absence and presence of emulsifier at concentrations above CMC consists in the first case of poIymerization in the aqueous solution with the formation of" own" surfactants which precede the generation of partic1es, whereas in the second case partic1es are formed from the very beginning. Whether own surfactants are formed in the latter case and the role they play is yet to be determined. After generation of partic1es, when their concentration becomes quite high, polymerization in the aqueous phase probably results in the formation of low molecular weight oligomer radical s which are captured by the partic1es before they grow to critical size. Their role in the subsequent process consists of initiation and termination of polymerization in the formed partic1es according to the usual behavior of water-soluble, active radicals. In the case of their termination in the aqueous phase they may also act as own surfactants contributing to the stabilization of partic1es. Zuikov and Soloviev (1979) studied the effect of monomer polarity on both the size and the size distribution of partic1es in the forming latexes. As a criterio n of polarity they took the solubility of the monomer in water, which in this case has an independent significance as well. Polymerizations of styrene, methyl methacrylate, butyl methacrylate, and methyl acrylate
i
Polymerization of Polar Monomers
259
initiated by ammonium persulfate(0.05%in aqueous phase) in the presence of SDDS at concentrations below the CMC were investigated. As can be seen from the electro n microphotographs of the latexes (Fig. 4), with increasing monomer solubility in water the size of particles decreases and their distribution broadens. This is also illustrated by plots shown in Fig. 5. The results obtained may be associated with the effects of both monomer solubility in water and polarity of the forming interface on the mechanism of particle formation. Since in all experiments the emulsifier concentration was below the CMC, particle generation in the case of the water-soluble initiator began in the aqueous phase. Because of the lower solubility of styrene, the concentration of polymer radicals initially formed is lower than for MMA and MA. Accordingly, a smaller number of large particles is formed. The critical size of polymer radicals increases with the solubility of the monomer in water (according to literature data it is 8 monomer units for styrene and 65 for MMA). The period of particle formation also increases, leading to higher polydispersity. Moreover, as previously discussed, the emulsifier adsorption decreases with increasing polarity of the interface; and therefore for the formation of a given surface less emulsifier is consumed, which also increases the period of particle generation and
...
'. 2
,
1.1"~
Fig. 4. Electron micrographs of latex particles obtained by polymerization of (1) styrene; (2) methyl methacrylate; and (3) methyl acrylate. SDDS, 0.066%; ammonium persulfate, 0.05% in aqueous phase; T, 80°C; phase ratio, 1: 10.
260
V. 1. Yeliseyeva
250 200
~t:: 150f4 4'
1J
0.7
100
1 2 J '+ 5 MonomerSolu.bilitgin water (%) Monodispersity coefficient (K) and diameter(D)of latexparticlesformedby
Fig. 5.
polymerization of monomers differing in solubility in water: (1) styrene; (2) butyl methacrylate; (3) methyl methacrylate; (4) methyl acrylate. For conditions see legend to Fig. 4.
decreases the coefficient of monodispersity. This facilitates the increase of the overall surface area, because of a decrease in particle size. As can be seen from Fig. 5, the broadest particle size distribution is observed for the most polar monomer, MA. Due to the increased critical size of radical s and the smallest consumption of emulsifier by the forming interface, this corresponds to the longest period of particle formation.
""
I
0.8
"-
.
.
I
1
0.0'+
0.05
I 0.05
/3
I
0.7 I
.
I
0.01
o
.
0.02
0.03
[s1)1)8] <%) Fig. 6. The effect of SDDS concentration (% in aqueous phase) on the monodispersity coefficient of latex particles obtained by polymerization of (1) styrene; (2) methyl methyacrylate; and (3) methyl acrylate. Ammonium persulfate, 0.05% in aqueous phase; T, 80°C; phase ratio, 1: 10.
7. Polymerizationof Polar Monomers
261
A comparative study of the dependence of the monodispersity coefficient K on the SDDS concentration for polymerization of styrene, MMA, and MA was carried out in the same work. The results obtained, similar to data of Yakovlev el al. (1971), indicate that for styrene polymerization the polydispersity of the latex sharply increases in the region where the initial emulsifier concentration equals the CMC (Fig. 6). This is explained by a change of particle-formation mechanism, a transition from homogeneous to micellar, and accordingly, by an increase of the particle-generation periodo In the case of MMA (solubility in water 1.5%) the transition of SDDS concentration from below to above CMC affects the polydispersity coefficient to a lesser extent, since in the polymerization of this monomer particle formation apparently follows both the homogeneous mechanism and the micellar mechanism, In the case of polymerization of the most soluble monomer (MA, solubility 5.2%), an increase in the emulsifier concentration smoothly decreases the monodispersity coefficient, which is not affected by passage over the CMC. The contribution of micelles to the formation of particles is evidently negligible in this case.
V.
Colloidal Behavior of Polymerization Systems
The differences in the polymerization kinetics and colloidal behavior of polymerization systems based on monomers of different polarity may be illustrated (Bakaeva el al., 1966; Yeliseyeva and Bakaeva, 1968) by the polymeri;ation of the model monomers, methyl acrylate and butyl methacrylate, at various concentrations of sodium alkylsulfonate (C15H31S03Na). The fact that the solubility of the monomers in water differs by two orders of magnitude (5.2 and 0.08%, respectively) was used as a criterio n of polarity. An additional advantage to comparing these two monomers is that their polymers have rather close glass transition temperatures which is important for coalescence of particles at later stages of polymerization. As can be seen from Fig. 7, variation of the initial emulsifier concentration from 0.5 to 5% in the aqueous phase results in an increase in the BMA polymerization rate (conversion after 30 min) by about 15 times, whereas the MA polymerization rate essentially does. not change with changing emulsifier concentration. The data in Table IV show how emulsifier concentration affects particle size and, accordingly, number. AJthough for both monomers an increase in the emulsifier concentration results in a decrease in the size and an increase in the number of particles, the effect is much weaker in the case of MA"polymerization. A comparison of run 2 with runs 3, 4, and 5 in Table IV indicates that at the same initial emulsifier concentration the number of particles in 1 dm3 of the latex is an
262
V. 1. Yeliseyeva 50
40
--
1
s:::
"Jt .... '-> -b.
s::: 1:: 20
A
/.
.
.
4.-
"" Q.. 10
O
2 ,
Fig. 7.
J
5
[RSOaNa](%)
Dependence of conversion (%) over 30 min on sodium alkylsulfonate
concentration in polymerization of (1) methyl acrylate and (2) butyl methacrylate. persulfate, 0.01% (1) and 0.1% (2) in aqueous phase; T, 60°C; phase ratio, 1: 1.5.
Ammonium
order of magnitude higher for BMA polymerization. Since in both cases the polymerization begins with the formation of very small particles, it may be assumed that the flocculation of particles occurs during MA polymerization, even with excess emulsifier (run 4), and does not occur (or occurs on a much smaller scale) during BMA polymerization. Morover, as can be seen from Figs. 4 and 5, during the polymerization of 'polar monomers (MMA TABLE IV Colloidal Characteristics of MA and BMA Latexes Depending on Initial Concentration of Sodium Alkylsulfonate in Aqueous Phase
No.
Emulsifier concentration in aqueous phase (%)
Monomer
1 2 3 4 5
0.5 1.0 1.0 3.0 3.0
MA MA BMA MA BMA
y (mJ/m2) 41.6 38.1 " 31.0 (-CMC) -"
Partic1e diameter (nm)
Number of partic1es in 1 dm3
217 . 178 86 148 60
7.5 x 1016 1.4 xl017 1.25 x 1018 2.45 x 1017
3.7 X 1018
"We are unable to determine y precisely because of rapid film formation on the surface of the p-BMA latex.
7. Polymerizationof Polar Monomers
263
and MA) a larger number ofparticles of lesser size is generated (and retained in dilute latexes) than for the less polar monomer (styrene). This also indicates flocculation of particles during MA polymerization (shown in Table IV). This explains why Eq. (1) does not describe polymerization of both investigated monomers equally well. The relationship between colloidal behavior of polymerization systems and monomer polarity has also been observed in other works. Thus, in an adsorption titration study (Zuikov and Vasilenko, 1975) of alkyl acrylate and styrene latexes synthesized with SDDS it was shown that the amount of emulsifier additionally adsorbed by 1 g of polymer is sharply reduced by an increase of interface polarity and is 40 times less for the methyl acrylate latex than the styrene latex (Table V), the methyl acrylate latex particles being much larger. The area occupied by an emulsifier molecule (ASllm)on a particle surface at CMC increases with interfacial polarity in agreement with the experimental data described above. Two characteristics of the adsorption area of emulsifier molecules are given in Table V: As, the calculated area per molecule on latex particles and ASlim'the area occupied by molecule of the given emulsifier at saturation determined by adsorption titration. The p¡ value [(AS1¡m/As)100]may be used as a characteristic of the degree of adsorption saturation but not of the degree of filling of the adsorption layer and therefore not of latex stability, as usually assumed when dealing with butadiene-styrene latexes. Because of the hydrophobic nature of the particle surface, ASlimfor most rubber latexes is close to the minimal .value corresponding to the most dense packing of emulsifier molecules on surface, and therefore p¡ may cparacterize the degree of filling of the adsorption layer and thus of latex stability. But in the general case, when ASlimis a variable dependent on polymer polarity and which may acquire high values, even at p¡ = 100%, the degree of filling of the adsorption layer and latex stability may be quite low. Thus, from data presented in Table V it follows that on the one hand with an increase in interface polarity the limiting adsorption of emulsifier decreases, whereas on the other hand the degree of adsorption saturation of latex particles increases: in the ~ethyl acrylate latex the p¡ value is close to 100%. Allowing flocculation of primary particles it may be considered that in the case of MA it proceeds almost to the limiting degree of saturation which however is not sufficient for the required stability of particles during polymerization (formation of coagulum was observed). In the case of styrene latex the degree of saturation at the given emulsifier concentration is '" 50%, but As is lower (the degree of filling of the adsorption layer is practically twice as high as in the methyl acrylate latex) which ensures a higher aggregate stability of the particles during polymerization (absence of coagulum). It is noteworthy that at a higher initial concentration of emulsifier (Table V) its consumption during styrene polymerization is higher (surface tension of the resultant latex is higher) than in alkyl acrylate polymerization.
TABlE V Colloidal Characteristics of Acrylate and Styrene Latexes Synthesized with SDDS
Monomer
Initial SDDS conc in aqueous phase (mol/dm3 x 103)
Latex conc (%)
Coagulum: monomer (%)
MA EA BA St
8.68 17.36 26.64 26.04
20 18.7 20 19.1
0.20 0.11 0.00 0.00
Particle diameter (nm)
)' (mJjmZ)
As (nmZ)
Additional adsorbed amount of SDDS (moljg of polymer x 103)
49.5 47.5 53.6 63.9
1.92 1.24 1.06 0.95
0.347 2.01 5.78 13.23
125 96 88 71
TAlE
Degree of adsorption saturation ASlim (nmZ)
( )
1.75 0.86 0.61 0.49
90.6 78.2 63.8 51.7
A:m
VI
Colloidal Characteristics of Acrylate and Styrene Latexes Synthesized with AAEOS Latex stability
Monomer
Solubility in water (%)
Latex conc (%)
Coagulum: monomer (%)
Viscosity (cp)
)' (mJjmZ)
MA EA BA 2-EHA BMA St
5.2 2.6 0.34 0.01 0.08 0.03
34.4 34.3 34.3 34.0 33.8 33.7
0.17 0.06 0.00 0.68 0.36 0.18
6.0 12.3 29.2 13.9 18.5
41.7 49.4 59.5 67.0 62.0 -
a
Mechanical
stability was determined
on a Marone-Ulevich
instrumento
Particle diameter (nm) 150 150 MO 97 120 100
Number of particles . in 1 dm3 (x 10-17) 1.66 1.67 2.19 6.17 . 3.58 6.10
Overall surface in 1 cm3 (m-Z)
As (nmZ)
mechanical (% formed coagulum)a
eIectrolyte (mi 0.1 M CaClz)
11.7 11.8 13.5 18.5 16.1 19.1
1.05 1.12 1.31 1.87 1.51 1.80
2.1 1.6 O 0.2 1.0 0.5
0.75 0.95 1.25 0.15 0.05 0.02
7.
Polymerization of Polar Monomers
265
Yeliseyeva et al. (1975) investigated the effectiveness in emulsion polymerization of the alkyl acrylates, butyl methacrylate and styrene, in the presence of another type of emulsifier, alkylac polyoxyethylenesulfate (AAOES), obtained by exhaustive sulfonation of Triton X-100 (Rohm and Haas, Philadelphia, Pennsylvania) with sulfamic acid and subsequent neutralization with ammonia. Polymerizations were carried out under identical conditions by the batch method. Emulsifier concentration in aIl runs was 26.4 x 10- 3 mol/dm3 in aqueous phase, ammonium persulfate concentration 1.1 x 10- 3 mol/dm3 for MA and EA polymerization and 2.2 x 10-3 mol/dm3 for polymerization of the other monomers. AIl in dices characterizing the latex stability have optimal values for the monomer with medium solubility in water, namely for butyl acrylate (Table VI). However, latexes based on more polar monomer are more stable when using this emulsifiér than latexes based on less polar, hydrophobic monomers. Surface tension in the latter case is considerably higher, indicating a higher capacity of the surface to adsorb the given emulsifier when formed during polymerization of less polar monomers. As in the case of alkylsulfonate (Table IV), at the same initial concentration of the emulsifier a smaIler number of larger particIes are formed in the case of polar monomers, where the surface is better protected by the emulsifier. Thus, the area As occupied by the emulsifier molecule on the surface of styrene latex particIes is 1.7-fold larger than for the methyl acrylate latex, the diameter of the polystyrene latex particIes being smaIler. The l0l" stability to electrolytes of latexes based on hydrophobic monomers obtained in the presence of AAOES play therefore be explained by the rarefied adsorption layer on the particIe surface. Conversely, the enhanced stability to' electrolytes of latexes of polar monomers may be attributed to the denser packing of emulsifier molecules in the adsorption layer at a given emulsifier concentration. The somewhat higher mechanical stability of latexes based on hydrophobic monomers may be associated with their higher stability to orthokinetic fIocculation which is attributable to the smaIler size of particIes, which to a certain extent compensates for the fact that their surface is les s protected by the emulsifier. Similar data on the adsorption saturation of acrylate latexes (based on EA, BA, and 2-EHA) synthesized with the same emulsifier were obtained recentIy by Snuparek and Tutalkova (1978). A lesser degree of filling of the adsorption layer, 46.5 and 49.6%, was observed for more hydrophobic monomers (2-EHA and BA): with a greater degree being observed in the polymerization of the more hydrophilic EA, 66.3%. Summarizing the described results, it may be concIuded that when using the emulsifiers described above, the coIloidal behavior of polymerization systems is mainly determined by monomer polarity. Latexes of polar
266
V. 1. Yeliseyeva
monomers are characterized by larger particles with surfaces close to limiting saturation, which, due to high values of Aslim, correspond to low degrees of filling of the adsorption layer. Since polymerization invariably begins with the formation of very small particles, the observed difference in colloidal behavior is associated with tlocculation to a certain size at the initial stages of polymerization of polar polymer-monomer particles (PMP) and with the formation of secondary particles. The better protected PMP of hydrophobic monomers retain stability to higher conversions at which their protection may become insufficient due to the consumption of most of the emulsifier. Flocculation of primary PMP of polar monomers up to a certain limit ("limited tlocculation") may be explained by the kinetics of the adsorption layer formation under dynamic conditions of polymerization. This leads to a reduction of the real filling of the adsorption layer of primary particles in relation to equilibrium adsorption which is lower than in the case of hydrophobic monomers. Equilibrium adsorption is attained on particles of the resultant latex (or in the course. of the process when formation of new particles is terminated) ensuring at sufficient emulsifier activity the necessary aggregate stability of the system. In the above-mentioned cases of polymerization of lower alkyl' acrylates, because
of the high rate of the process
kp
=
1260 dm3/mol sec for MA
(Bagdasar'yan, 1966) and the high monomer concentration in particles (Gerrens, 1964), the surface of the monomer-polymer phase increases at a rate that may exceed the rate of attainment of equilibrium adsorption. On the other hand, the 'PMP formed during polymerization of hydrophobic monomers are better protected by the emulsifier because of the high adsorption capacity of the surface (low value of Aslim)' In addition, their polymerization rate (kp = 190 dm3/mol sec for styrene) (Bagdasar'yan, 1966) and monomer concentration in particles (Gerrens, 1964) are lower, which ensures a lower rate of interface growth and creates conditions for achieving adsorption equilibrium during PMP formation, which in turn hinders tlocculation up to high degrees of conversion. Flocculation in this case occurs only when most of the emulsifier is consumed at high values of As. It should be noted that particles of hydrophobic monomers may remain descrete at lower degrees of filling of the adsorption layer (styrene, BA, Table V) which is possibly connected with the reduced interparticle interaction (Hamaker's constant) and the lower monomer concentration in them. For retention of stability, particles of polar monomers should be better protected by the emulsifier, apparently because of stronger interparticle interaction and the higher content of monomer in them. The lower stability of smaller particles which follows from the DL VO theory may be one of the factors affecting limited tlocculation of particles during polymerization of polar monomers. The importance of this factor ','
7.
267
Polymerization of Polar Monomers
was noted by Dunn and Chong (1970) in a study of the mechanism of particle formation during polymerization of vinyl acetate in aqueous solution. They also concluded that flocculation throughout the process occurs between smalI, newly formed particles and larger "oId" particles. It should be noted, however, that such flocculation is not typical of hydrophobic monomers. The restricted adsorption of anion-active emulsifier during polymerization of polar monomers (vinyl acetate) has also been reported in other work. Breitenbach et al. (1970) established that in the case of polymerization initiated by a,a-azobis(methyl butylonitrilesulfonate Na) the emulsifier (sodium dodecylsulfonate) content in the resuItant latex twice exceeded the CMC value, Le., the emulsifier was not exhausted by the forming interface. The polymerization rate was found to depend on emulsifier concentration to the power of 0.1. According to data obtained by Okamura and Motoyama (1953), adsorption of anion-active emulsifiers by the surface of vinyl acetate latex particles is also limited: an increase in emulsifier concentration (sodium dodecylsulfate and dioctylsulfosuccinate) above a certain limit does not produce an increase in adsorption. The authors found that the ratio of the amount of adsorbed emulsifier to the mas s of formed polymer remains constants and concluded that part of the emulsifier is located inside particles of the polar monomer, in contrast to hydrophobic polymers where it is found only on the surface of particles. In our opinion, the presence of emuIsifier jnside latex particles may be due to the flocculation of primary particles from the surface of which not alI the.emulsifier is transferred to the surface of secondary particles. Of the two emulsifiers studied by Okamura and Motoyama (1953).the molar quantity of dioctylsulfosuccinate adsorbed by 1 g of polymer is 1.8-fold higher than that of dodecylsulfate, pointing to the higher adsorption energy of the former on the surface of poly(vinyl acetate). It was established by Yeliseyeva and Bakaeva (1968) that in the polymerization of polar monomers (MA) the decrease of emulsifier adsorption depends on the structure of the latter and for some types of emuIsifiers may reach limiting values. This was observed in the polymerization of MA in the presence of a mixed type of emulsifier, partialIy sulfurated. with suIfuric acid oxyethylated alkylphenol (emulsifier "C-lO"). Its adsorption on the particle surface increases with the initial concentration and reaches 100% filling of the adsorption layer, conditionalIy corresponding to 0.35 nm2 per molecule. Stable, concentrated latexes with smalI particles are formed. Therefore, emulsifier adsorption and the mechanism of particle formation associated with it depends not only on monomer poIarity but also on the chemical structure of the emulsifier. ~
..
V. 1. Yeliseyeva
268
VI. Kinetics of Emulsifier Adsorption In view of the specificity of latex system formation, which is directly related to the adsorption capacity of the forming interface, it is of interest to examine the kinetics of effective adsorption of emulsifiers of various structures in the course of polymerization of monomers of various polarity (Yeliseyeva and Petrova, 1972; Yeliseyeva et al., 1973, 1976). The consumption kinetics of SDDS and AAOES during the polymerization of methyl, ethyl, and butyl acrylates was studied by Yeliseyevaet al. (1976). Benzoyl peroxide was used as the initiator, and experiments were carried out in a special dilato meter with platinum electrodes connected to a conductometer so as to monitor the rate of emulsifier consumption with increasing conversion via variation of electroconductivity. Since the initator used is poorly soluble in water, the possibility of polymerization in the aqueous phase and the formation of "own" surfactants that may mask adsorption of the introduced emulsifier are exc1uded. In order to obtain colloidally stable systems 0.1% (with respect' to monomer) tertdodecylmercaptan was added to all runs; the effectiveness of such addition had been previously shown by Yeliseyeva and Petrova (1972~ The dependence of adsorption of both emulsifiers on conversion during polymerization of the three monomers is shown in Fig. 8. At a certain degree of conversion (varying with the monomer used) a limiting adsorption value is reached, a value which decreases with increasing interface polarity from BA to MA. It differs only slightly for both emulsifiers during BA polymerization. With an increase in the polarity of the interface, both the effective
20
.
un
J
I (8)
J
.. . .... '1::-,0
,
"':
n
I
I
20
40
o
I
20
I
40
COT!1rersion(%)
Fig. 8.
Adsorption kinetics of emulsifiers AAOES (A) and SDDS (B) in polymerization
of (1) methyl acrylate;
(2) ethyl acrylate;
and (3) butyl acrylate.
Recipe m.p.: monomer,
benzoyl peroxide, 0.2; emulsifier, 2; tert-dodecyl mercaptan, 1; water, 900. T, 45°C.
100;
7.
269
Polymerization of Polar Monomers (11')
30
3
(S)
90
30
90
t (min) Fig. 9. Conversion (%) kinetics during polyrnerization of (1) rnethyl acrylate; (2) ethyl acrylate; and (3) butyl acrylate in the presence of SDDS (A) and AAOES (B). For recipe see Fig.8.
rate and the equilibrium value of the adsorption of AAOES increases as compared with SDDS. During the MA polymerization the amount of adsorbed AAOES is twice as high as SDDS. This is apparentIy the reason for the higher effectiveness of AAOES in emulsion polymerization of lower alkyl acrylates: increase of the rate and equilibrium value of adsorption of this type of emulsifier reduces the flocculation of primary particles dui-ing polymerization and facilitates the formation of coIloidaIly stable systems with smaIler particles. Kinetic. curves of the polymerization of these monomers in the presence of both emulsifiers with their initial concentration close to CMC are shown in Fig. 9. As can be seen the initial polymerization rate, at the same rate of radical formation (the same concentrations of initiator and the same temperature), decreases from MA to BA in accordance with the decrease of the chain propagation rate constant in these monomers (Bagdasar'yan, 1966). SubsequentIy, however, the polymerization rate of the MA becomes much lower than the rate of other monomers, a fact which apparently is associated with the coIloid behavior of the system (reduction of the number of polymerization centers as a result of flocculation). Similar resuIts were obtained by Yeliseyeva et al. (1973, 1975) when studying the sodium alkylsulfonate emulsifier adsorptiQn kinetics during polymerization of butyl acrylate and its copolymerization with such watersoluble monomers (3%) as methacrylic acid, N-methacrylamide, and Nmethylolmethacrylamide. In aIl cases the introduction of water-soluble comonomers resuIted in a decrease of the effective rate and in the value of the emulsifier adsorption. The authors attributed this to the hydrophilization and increase of polarity of latex particle surfaces.
270 VII.
V. 1. Yeliseyeva
Mechanism of Formation and Structure of Particles
Using the method of flow ultramicroscopy by Kudryavtseva and Deryagin (1963), we investigated the variation in the number of partic1es during polymerization of ethyl acrylate with ammonium persulfate in the presence of three types of emulsifiers: anion-active sodium alkylsulfonate, nonionogenic oxyethylated (30) cetyl alcohol ("C-30"), and mixed type (AAOES)(Y eliseyeva and Zuikov, 1976; Yeliseyeva et al., 1975)(Fig. 10).For all three emulsifiers, the number of partic1es value goes through a maximum, indicating flocculation. Similar curves were observed by Fitch and Tsai (1971) when studying MMA polymerization in dilute aqueous solutions of the monomer. Judging from the number of partic1es in the resultant latex (Fig. 10), which in the case of AAOES is twice as high as that for alkylsulfonate, partic1es flocculate to a smaller extent when using the emulsifier of the mixed type, indicating their higher stability. Indeed, an estimation of the adsorption energy of these emulsifiers on a water-ethyl acrylate interface (see above) gave the following values (kJ/mol): 22.2' for sodium alkylsulfonate, 25.6 for oxyethylated (30) cetyl alcohol, and 25.6 for ammonium alkylphenylpolyoxyethylenesulfate. These data indicate a higher adsorption energy for emulsifiers which result in a smaller degree of flocculation. However, because of their small size the number of partic1es formed at the beginning of the process could not be determined by flow ultramicroscopy. The nature of partic1e flocculation occurring during polymerization may be
J 12 o
.
4-
o
20
40
60
Con1rers¿on
(Dio)
o
. -¡ 80
Fig. 10. Variation of the number of particles during polymerization of ethyl acrylate in the presence of emulsifiers: (1) sodium alkylsulfonate; (2) oxyethylated (30) cetyl alcohol; and (3) AAOES. Recipe m.p.: ethyl acrylate, 100; emulsifier, 4.0; ammonium persulfate, 0.5; water, 900. T, 60°C.
7. Polymerization of Polar Monomers
271
assessed from electro n micrographs of ethyl acrylate latex at 38.0% conversion (Fig. 11A) (before preparation the latexes were irradiated by a 60Co source, at 20 Mrad, in order to avoid particle deformation). A similar pattern is observed during the polymerization of a mixture of MMA and BA (55:45) at 60% conversion (Fig. llB). The complex structure ofparticles of carboxyl-containing acrylate latex MMA-BA-MAA (55:40:5) may be revealed by increasing the pH above 9 (Fig. llC). The desaggregation which occurs is attributable to the electro static repulsion of dissociated carboxyl groups present in the macromolecules of primary particles. We were able to reveal the structure of latex particles and films of polar polymers (acrylate latexes) using a special technique for preparing samples
Fig. 11. Electron rnicrophotographs of latex particles: (A) ethyl acrylate at 38 % conversion; (B) rnethyl rnethacrylate-butyl acrylate copolyrner (60:40) at 60% conversion; (C) rnethyl rnethacrylate-butyl acrylate-rnethacrylic acid terpolyrner (55:40:5) at pH 9 and 100% conversion.
272
V. 1. Yeliseyeva
Fig. 12. Electron micrographs of polystyrene latex particles (A) before etching and (B) after oxygen etching.
for electron microscopy (Yeliseyeva et al., 1967, 1968). The method of lowtemperature etching with active oxygen formed in an electrodeless highfrequency discharge was used. Under such conditions the less ordered, looser regions are" burned out" initially, revealing the denser morphological regions (Jacobie, 1960). The latexes were placed on quartz supports, . subjected to oxygen etching and shaded with platinum at a 20° angle. The structure of films was studied by the method of single-step carbon replicas shaded with platinum. Optical periods of etching were determined empirically. The effectiveness of this procedure may be assessed by comparing electro n micrographs of polystyrene latex particles which were subjected (Fig. 12B) and not subjected (12A) to oxygen etching. As can be seen, these particles, contrary to expectation, are not coils of tangled macromolecules but an arrangement of rather clearly defined polymeric globules (this may provide a new insight into the mechanism of particle formation during styrene polymerization). On the other hand, examination of the structure of poly(vinyl acetate) emulsion particles by the same method gave quite different results (Fig. 13A and B).
7. Polymerization of Polar Monomers
273
A study of the structure of polar polymer particles was carried out on MA-BA copolymer latexes; in some experiments methacrylic acid was added in order to change polymer polarity. Latexes were synthesized at a phase ratio of 1: 1.5, with the emulsifier concentration in aqueous phase being 0.07%. Polymerization was carried out by gradual addition of the monoiners and emulsifier solution into the reaction mixture at 75-78°C. Composition and properties of the latexes are listed in Table VII. The efIect of oxygen etching on the particle structure is demonstrated in Fig. 14 which shows electron micrographs of latex number 3 particles (Table VII) at various periods of etching. As can be seen, they consist of a spherical shell filled with smaller particles in the form of globules. After 2 min of etching (Fig. 14A) the shell is ruptured by oxygen and forms a dense ring on the substrate at the periphery of the particles. At longer periods of etching (10 min, Fig. 14B) the size of primary globules decreases and the peripheral ring is found to consist of primary globules of the same sizes as those inside the particles. Because of the den ser arrangement in the ring on the substrate
274
V. 1. Yeliseyeva
(B)
lefA) Fig. 13.
.
Electron micrographs of poly(vinyl acetate) emulsion particles (A) before
etching and (B) after oxygen etching.
they are the last to disappear (after 20 min of etching, Fig. 14C). After etching for an hour all trace of particles on the substrate disappears. In order to estimate the size of primary globules and their content in latex particles, etching was carried out of films obtained by drying of the same latexes (Table VII). Electron micrographs of replicas of films obtained by drying latexes numbers 1, 2, and 3 (Table VII) at room temperature after 20 min oxygen etching are shown in Figs. 15A, 15B, and 15C. In the comer of each micrograph a medium-sized particle of the corresponding latex at the same enlargement is shown. The main structural elements of films are primary globules which are much smaller than latex particles. Taking the diameter of primary globules as the distance between their centers, for latex number 3 (Table VIII) we conclude that these distances coincide in micrographs of particles and films, i.e., the structural element of both particles and films is a
7.
275
Polymerization of Polar Monomers TABLE VII
Composition and Properties of Latexes used in the Study of Particle Structure
MAA
Latex conc (%)
Molecular mass of polymer (10- 3)a
O 2.6 4.3
37.95 39.34 39.6
214 203 227
Polymer composition (%mol) No.
MA
BA
1 2 3
65 63.3 62.3
35 34.1 . 33.4
a
Molecular
mass of copolymers
was calculated
Partic1e diameter (nm)
Latex pH
118-210 120--220 118-200
from specific viscosity of their solutions
2.9 2.8 2.8 in
dioxane using Staudinger's coefficient for poly(alkyl acrylates) Staudinger and Trommsdorff, 1933).
globule that apparently constitutes thé primary particle formed at the initial stages of the process. The size of primary particles is different for different latexes; they decrease with increasing polymer phase polarity (Fig. 15). Data of approximate calculation of sizes of primary particles, the number of macromolecules in them, and the content of primary particles in particles of the resultant latex are given in Table VIII; data for a butyl methacrylate latex synthesized under similar conditions wherein primary particles were not revealed by the same oxygen etching method are also presented in this ~~.
.
From this discussion it may be concluded that latex particles forming during the polymerization of polar monomers are the result of limited flocculation of primary particles. The mechanism of flocculation may be as follows. In the case of a water-soluble initiator, the process begins in the aqueous phase. Upon reaching a critical degree of polymerization polymeric radical s -S04(M)nM precipitate aggregating into nuclei of primary particles which are stabilized partially by the polarity of the polymer itself (polar groups such as S04, COO-, COOH, COOR) and partially by the dynamic adsorption of the emulsifier. Increase in the size of primary particles may result from two factors: polymerization of the absorbed monomer and aggregation with other polyme~ic radicals. The latter is increasingly slowed down with increasing surface charge density of polymeric radical s and with hydrophilization of their surface. Indeed, as can be seen from data in Table VIII primary particles differ in size, and for a polymer of medium molecular weight may contain from a few to several dozen macromolecules, depending on the polarity of the polymer phase (the size of primary particles decreases with increasing polarity).
276
V. 1. Yeliseyeva
Fig. 14. Electron micrographs of polyacrylate latex particles (Table VII. run 3) after oxygen etching for: (A) 2 min; (8) 10 min; and (C) 20 mino
Under dynamic conditions of emulsion polymerization the process of formation and aggregation of primary particles is accompanied by establishment of an equilibrium adsorption of the emulsifier on the polar surface . of particles. As a result of competition of these processes.. "secondary" particles of complex structure are formed (Figs. 11 and 14). The rate of attainment of equilibrium adsorption, depending on monomer polarity and the nature of the emulsifier, determines the degr~e of limited tlocculation of primary particles at which aggregate stability of the "secondary" latex particles is reached. The formation of nuclei from micelles during the
7.
277
Polymerization of Polar Monomers TABLE VIII
Structural Characteristics of Latex Particles of Acrylic Polymers of Various Polarity
No.
2
3 4
Polymer composition (%rnol) BA-MA (65:35) BA-MA-MAA (63.3:34.1:2.6) BA-MA-MAA (62.3:33.4:4.3) BMA"
Partic1e diameter (nm) latex
prirnary
Numbers of primary partic1es in latex partic1e
Number of macromolecules in primary partic1e
118-210
40
-120
-90-150
120-220
25-30
-530
- 25-40
118-200
15-20
-1000
15-40
no
no
-5-10
u In order to ensure necessary stability of the latex during polyrnerization of BMA the initial ernulsifier concentration in aqueous phase was taken equal to 3.3%.
polymerization of hydrophobic monomers, which polymerize more slowly and better adsorb the emulsifier, is accompanied by the establishement of equilibrium adsorption of the emulsifier on account of which "organized" flocculation does not occur and as a result of which much smaller particles are formed. However, at a high adsorption capacity of the forming nonpolar surface, the emulsifier is initially rapidly consumed, and the formation
Fig. 15. Electron rnicrographs of replicas frorn the surface of polyacrylate latex filrns: (A) run 1, Table VII; (B) run 2, Table VII; (e) run 3, Table VII.
278
V. 1. Yeliseyeva
of particles at the end of the processwith poorly protected surfacemay lead to an avalanche of unlimited flocculation and precipitation of coagulum. When using more active emulsifiers of the C-10 type (Yeliseyeva, 1966) the effective rate and the equilibrium value of adsorption increase in the polymerization of polar monomers, which reduces the intensity of the processes of initial flocculation. Moreover, in this case the charge density is not the only stabilizing factor; it is supplemented by the enthalpy factor which arises from hydration of oxyethylenic chains of emulsifier molecules. The presence of these emulsifiers creates conditions that enable the obtainment of polar polymer latexes of high stability. Generalizing, it may be concluded that the limited flocculation of primary particles depends on the ratio of the rate of formation of their overall surface (S) to the rate of establishment of equilibrium adsorption (r) of the emulsifier by the surface. For formation of particles stabilized by the emulsifier dr/dt = K dS/dt
(5)
where K is the proportionality constant which takes into account the value of equilibrium adsorption. In reality however it may occur that dr/dt < K dS/dt
(6)
,. Depending on whether or not the condition [Eq. (5)] is met the mechanism of particle formation will be different. When this condition is satisfied the forming surface of the polymer phase is stabilized by the adsorbing emulsifier and the formed particles may remain discrete at high degrees of conversion. In this case the polymerization rate is described by Eq. (1) which is derived by assuming a constancy in the number ofparticles. In the case of inequality, as expressed by Eq. (6) for example, at low surface activity of the emulsifier on the polar polymer surface and at high polymerization rates, particles appear whose surface is insufficiently protected by the emulsifier. Under conditions of high temperature and intensive agitation, such particles rapidly flocculate with each other and an equilibrium adsorption of the emulsifier is established at the formed aggregates latex particles. In such cases the polymerization rate does not obey Eq. (1).
VIn.
Polymerization Kinetics
.
In the study of emulsion polymerization kinetics which depend on monomer polarity, the homologous series of alkyl acrylates and alk.yl methacrylates are usually used because of their wide ranges of solubility in
279
7. Polymerizationof Polar Monomers
water, their reactivity, and the fact that they do not display any particularly specific features of polymerization (as do vinyl chloride and vinyl acetate which have a high constant of transfer onto the monomer or as do vinyl chloride and acrylonitrile where there is low solubility of polymer in monomer). The differences in polarity of alkyl acrylates (alkyl methacrylates) is understood as the difference in polarity at the interface with water, since taken separately lower alkyl acrylates have practically equal dipole moments (Granzhan, 1969). However, the structure of the alkyl acrylate-water interface layer changes with increasing alkyllength: the polarization of the carbonyl group, which determines polarity of the asymmetric alkyl acrylate molecule at the water boundary, decreases as a result of an increase of the induction effect of the alkyl group. The degree of orientation of monomer molecules decreases and interfacial tension increases. Medvedev (1956) proposed that molecules of some acrylic monomers have a negative charge in aqueous phase. Yeliseyeva et al. (1976) studied the polymerization kinetics of polar acrylic monomers using ethyl acrylate. The dependence of the polymerization rate on the initiator concentration (ammonium persulfate) was examined at equal ionic strength in the presence of two emulsifiers, sodium dodecylsulfate and oxyethylated (30) cetyl alcohol. Polymerization was carried out in a dilato meter at 45°C, monomer-water phase ratio 1:9, and ammonium persulfate concentration 0.44-4.4 x 10-3 mol/dm3. The obtained loagrithmic dependence is shown in Fig. 16. In each cases the 1.5
0.5
1.0
1.5
2.0
-4 +tg Ct(mol/dm') Fig. 16. Dependence of ethyl acrylate polymerization rate (R mol/dm3 sec) on a~monium persulfate concentration (mol/drn3) in the presence of (1) 13.8 x 10-3 mol/drn3 SDDS; (2) 2.55 x 10- 3 rnol/drn3 oxyethylated (30) cetyl alcohol. Phase ratio, 1: 9; T, 45°C.
280
V. 1. Yeliseyeva
dependence is represented by a straight line with the same slope, the tangent being equal to 0.5. It should be noted that such a clearcut dependence is not observed when the ionic strength is not controlled. This may be associated .
with the effectof this factor on polymer-monomer solubility [which was established by Klein et al. (1973) for the vinyl acetate-poly(vinyl acetate) system] and on the degree of particle surface protection by the emulsifier (Piirma and Chen, 1980). Typical curves of the dependence of ethyl acrylate polymerization rate on conversion in the presence of sodium dodecylsulfate and initiated by persulfate are shown in Fig. 17 together with the variation in the number of particles determined by flow ultromicroscopy with increasing conversion (Kudryavtseva and Deryagin, 1963). As can be seen, the number of particles significantly varies during the constant rate period: after formation of a large number of particles at the beginning, their number gradually decreases; the number of particles also decreases when emulsifier concentration in the resultant latex exceeds the CMC value ,(Curve 2). However, within the range of concentrations studied, the resultant number of particles increases as does the polymerization rate with emulsifier concentration. The ethyl acrylate polymerization rate remains constant up to 38-40% conversion (Fig. 17), whereas according to data on equilibrium swelling of ethyl acrylate latex particles (Mamadaliev, 1978) the monomer phase disappears at 20% conversion. Hence, the polymerization rate remains constant after the disappearance of the monomer drops. Since the monomer drops
6
2
. o Fig. 17. Variation of polymerization rate (R mol/dm3 sec) (Curves I and 2) and of the number of partic1es (N) (Curves l' and 2') with conversion (5) during polymerization of ethyl acrylate in the presence of (1) 0.3% and (2) 0.8% SDDS with respect to the monomer. Phase ratio, 1: O; T, 45°C.
7.
281
Polymerization of Polar Monomers
maintain the equilibrium concentration of the monomer in the partic1es, in the absence of a monomer concentration gradient in the partic1es a constant rate should have been observed only untiJ disappearance of the monomer phase. On the other hand, this inconsistency in continuation of the constant rate period after the disappearance of the monomer phase does not take place in the case of alkyl acrylate polymerization initiated by benzoyl peroxide (Yeliseyeva et al., 1976), as can be observed from rate versus conversion curves for polymerization of MA, EA, and BA initiated by benzoyl peroxide in the presence of two emulsifiers (SDDS and AAOES). Figure 18 shows that the end of the constant rate period for both emulsifiers corresponds to 15.8% conversion for MA, 26.6 for EA, and 32.4% for BA, which coincides approximately with the moment of disappearance of the monomer phase. Therefore, continuation of the constant rate period after the disappearance of the monomer phase is typical only of persulfate initiation. When using a poor1y soluble initiator this inconsistency is not observed, and the polymerization of alkyl acrylates obeys in this respect the regularities of c1assical kinetics. A possible explanation for the observed difference in duration of the constant rate period is concerned with the differences in structure and formation mechanism of partic1es. In the case of a poor1y water soluble initiator the process begins in emulsifier micelles from which PMP are formed, the latter being stabilized from the very beginning. With an increase in conversion and partic1e size the surface of partic1es is protected by the
(In
.
(8)
i:I:t 0.5
20
50
20
80
C07!Versio7! (%) Fig. 18. Rate (R %/min) versus conversion dependence during polymerization of (1) methyl acrylate; (2) ethyl acrylate; and (3) butyl acrylate in the presence of SDDS (A) and AAOES (B). The graphs are plotted from the kinetic curves in Fig. 9. Initiator benzoyl peroxide.
282
V. 1. Yeliseyeva
adsorption of emulsifier and the rate of attainment of equilibrium adsorption value is sufficiently high for protection of partic1es from flocculation. The protection is also enhanced by the absence in the surface layer of negatively charged S04' groups. Therefore, the probable ratio between living and dead partic1es is retained at 1: 1 as required by the Smith-Ewart (1948) theory, and the duration of the constant rate period approximately coincides with the period of the existence of the monomer phase. Because of the considerable solubility of ethyl acrylate in water in the case of persulfate initiation, the process begins in the aqueous phase with the formation of charged polymer radicals which, after reaching a certain critical size, precipitate forming primary PMP. Establishment of equilibrium adsorption of the emulsifier, which ensures stability of the partic1es, is preceded by the flocculation of partic1es with other primary PMP which at the beginning is accomplished by interpartic1e termination of radicals. Thus, a new termination factor appears which is not considered in the above theory and which leads to a higher relative content of d¡;:adpartic1es. This is confirmed by data on the average number of radicals per partic1e which drops to 0.07 for persulfate ibitiation of ethyl acrylate polymerization (Mamadaliev, 1978). The large number of equilibrium monomer-swollen partic1es creates, after the disappearance of the monomer phase, a reserve of monomer in the system which, being redistributed via the aqueous phase into the growing partic1es, facilitates maintenance of equilibrium monomer concentration and thus continuation of the constant rate period after disappearance of the monomer phase. This may also be facilitated by the complex structure of partic1es and the existence of a monomer concentration gradient. The logarithmic dependence of the ethyl acrylate polymerization rate on concentration of emulsifiers of various chemical structure is shown in Fig. 19 (Yeliseyeva et al., 1976). Polymerization was carried out in a dilatometer
f.O
2.0
- i¡.+ Lg Cc (mol/dm3) Fig. 19. Dependence of ethyl acrylate polymerization rate (R moljdm3sec) on concentration (moljdm3) of (1) SDDS; (2)sulfated polyoxyethylated (10) octadecyl alcohol; and (3) oxyethylated (30) cetyl alcohol.
7.
Polymerization of Polar Monomers
283
at 45°C at a phase ratio of 1: 9, at an ammonium persulfate concentration of 2.2 x 10-3 moljdm3 in the aqueous phase. The polymerization rate was determined during the constant rate periodo As can be seen, the rate increases only up to a certain value of emulsifier.concentration, after which the rate remains constant. The dependence is strongly affected by the nature of the emulsifier: for the emulsifiers studied the reaction order is 0.4 for C-30 [oxyethylated (30) cetyl alcohol], 0.25 for sulfatized oxyethylated (10) octadecyl alcohol, 0.21 for sodium dodecylsulfate. On the basis of the data presented the kinetic equation forethyl acrylate polymerization in the presence of various emulsifiers may be written as foIlows: (7) where x is the reaction order with respect to emulsifier which varies from 0.2 to 0.4 depending on the chemical structure of the emulsifier. Such dependence must be associated with the energy of adsorption of the latter at the interface.
IX.
Relationship between Polymerization Kinetics and Adsorption Characteristic of the Interface
In order to establish whether Eq. (7) may be extended to other polymerization systems (Yeliseyeva and Zuikov, 1977; Yeliseyeva et al., 1976, 1978) a study was conducted on the dependence of.the polymerization rate on the concentration of dodecylsulfate and its homologs in the polymerization of other homologs of alkyl acrylates. The logarithmic dependences of polymerization rate of alkyl acrylates on sodium dodecylsulfate concentration is presented in Fig. 20. With the shortening of the alkyl chain, the slope of the straight line is regularIy decreasing, indicating a weakening of the rate dependence on emulsifier concentration. A similar dependence for a wide range of monomers differing in water solubility was earlier observed by Gershberg (1965). Data presented in Fig. 20 indicates the general trend of the established dependence. This is further confirmed by the graph for styrene which also conforms to this regularity. The value of x determined from the slopes of the straight lines regularIy increase from MA to hexyl acrylate (HA) to styrene (from 0.13 to 0.46 to 0.5, respective1y) and from dedecylsulfate to hexadecylsulfate (from 0.29 to 0.33 respectively) (Table IX). In order to establish the correlation between the value of x and emulsifier adsorption characteristics in the given reaction system in latexes prepared according to the same recipes, as was used in determination of ~eaction order, the adsorption areas of emulsifier molecules in the saturated
284
V. 1. Yeliseyeva
2.0
1.8
1.6
~gCe'.l11oZ /dmJ) Fig. 20. Dependence of the polymerization rate (R mol/dm3 sec) of (1) methyl acrylate; (2) ethyl acrylate; (3) butyl acrylate; (4) hexyl acrylate; and (5) styrene on sodium dodecylsulfate concentration. Ammonium persulfate 0.025% in aqueous phase; phase ratio 1:4; T, 60%.
adsorption layer (ASlim)were determined (Yeliseyeva et al., 1978). As follows from Table IX there is a relationship between these values and the energy of emulsifier adsorption on the initial monomer-water interface, as determined from adsorption isotherms. As can be seen from Table IX the product X. ASlim
=K
(8)
is approximately constant for most polymerization systems. Deviation from the constant value toward lower values is observed for the two lower alkyl acrylates and SDDS, Le., in systems characterized by the lowest adsorption energy of emulsifier. In these systems an increase nf the real dynamic value ASdynas compared with its equilibrium value ASlim(p. 263) is most probable. As shown even for polymerization of EA in the presenC'e of SDDS, the overall partic1e surface does not vary up to 60% conversion (Fig. 21) (Mamadaliev, 1978) except for a smallleap at the earliest stage. This may be considered as eV;idence in favor of the partic1e surface being the main polymerization site. Since from Eq. (8) the value of the overall interface is
s = K 1 . ASlim
(9)
285
7. Polymerizationof Polar Monomers TABLEIX
Adsorption and Kinetic Characteristics of PolymerizationSystems Based on AlkylAcrylates, Styrene, and VariousAlkylSulfates Monomer MA EA EA EA BA HA Sty
Emulsifier
x
Ead. (kJ/mol)
Asum (nm2)
K (nm2)"
20.0 22.1 23.3 24.6 25.6 -
1.51 0.92 0.82 0.74 0.67 0.52 0.48
0.197 0.198 0.238 0.244 0.222 0.240 0.240
0.13 0.21 0.29 0.33 0.33 0.46 0.50
C12H2SS04Na C12H2SS04Na C14H29S04Na C16H31S04Na C12H2SS04Na C12H2SS04Na C12H2SS04Na
-
" K = x . Asum.
it follows that x
= K2/S.
Thus the role of emulsifier
in polymerization
kinetics decreases with decrease in its participation in the creating of the overall interface area. This supports Med.vedev's theory that the main zone of emulsion polymerization is the surface of the forming particIes. The shortcoming of his scheme [Eq. (2)] is the assumption that the magnitude of this zone is determined by the concentration of the emulsifier, whereas in reality it also depends on the polarity of the polymer-monomer phase itself. Summing up the results presented here it may be concIuded that in the polymerization rate equation the reaction o,rder with respect to emulsifier is a variable and a function of the area occupied by the emulsifier molecule in the saturated adsórption layer on particIes of the resultant latex x = f(Aslim). The basic difference of this equation from the equations proposed earlier [Eqs. (1) and (2)] is the presence of a parameter that characterizes the properties of the interface (adsorption capacity), which is necessary for a kinetic equation of polymerization occurring in a colloidal
o
o
6 20
o
5/.
'+0
o 60
Converston (0/0> Fig. 21. Dependence of overall surface of particles (5) on conversion during polymerization of ethyl acrylate. SDDS 1.04 x 10-3 mol/dm3; ammonium persulfate 0.44 x 10- 3 mol/dm3; phase ratio, 1: 9; T, 45°C.
286
V. 1. Yeliseyeva
system. Both characteristics of the interface discussed-the energy of the emulsifier adsorption on the water-monomer interface and the degree of protection of partic1e surface-are important for processes of partic1e flocculation and mass transfer between phases. The kinetic scheme of emulsion polymerization of polar monomers initiated by persulfate which follows from the experimental data described above is presented in Table X in comparison with the c1assicalscheme. TABLEX Kinetic Se heme of Emulsion Polymerization during the Constant Rata Perioda Classical (for hydrophobic
N = const Am = ASlim
For polar monomers (of the type of acryl acrylates)
monomers)
N = ((Ead"t) S = const
= const
.
R = KC~_6C?_4
ASlim= I(Ead,) R = kC~ . C?-5[X = ",(Ead,) =
tr.con~1 =
K/Aslim = K'/AsdyoJ tr'con~1> !m'ph
t'm'ph
aAbbreviations: N, number of particles during the constant rate period; Amand ASlim,areas occupied by emulsifier molecule in the micelle and saturated particle surface; "-C0051 and 'm-ph' duration of the constant rate period and polyrnerization period up to disappearance of the monomer phase; t, polyrnerization period; S, overall partlcle surface.
Nomenclature Am As ASlim C. C¡
D Ead' I:1G
K
area of emulsifier molecule in a micelle calculated value of the area occupied by emulsifier molecule on the particle surface of resultant latex assuming that all the emulsifier is adsorbed adsorption area of emulsifier molecule at saturation of the adsorption layer ernulsifier concentration initiator concentration¡ diarneter of latex particles overall free energy of adsorption free energy of adsorption per CH2 group particle monodispersity coefficient
K
= DJD = w
kp N
propagation rate constant number of particles
p¡ R
(ASlim!As}-degree of adsorption polymerization rate
n-D~
1/3
"~ n-D~
-1/3
~¿ni ) (LniD~) ~
of particles
of resultant
latex
7. . Polymerization of Polar Monomers
s x
287
overall particle surface polymerization period reaction order in emulsifier
1'12 interfacial tension at the boundary of the first and second phases I'¡ surface tension at the ith phase 1'1,1'~2 surface or interfacial tension due to dispersion interaction I'f, I'Y2 surface or interfacial tension due to polar interaction
r adsorption value 'm.ph duration of monomer phase existence 'r'consl duration of the constant rate period
References Bagdasar'yan, Kh. S. (1966). "Theory of Radical Polymerization," p. 102. Nauka, Moscow. Bakaeva, T. V., Yeliseyeva, V. 1., and Zubov, P. 1. (1966). Vysokomol Soedin. 8, 1073. Breitenbach, J. W., Kuchner, K., Fritze, H., and Tarkowsky, H. (1970). Dr. Polym. J. 2, 13. Davis, J. T., Higuchi, T., and Rytting, J. H. (1972). J. Pharm. Pharmacol. 24, 30. Dunn, A. S., and Chong, Z. C-H. (1970). Dr. Polym. J. 2, 49. Fitch, R. M., and Tsai, C. H. (1971). "PolymerColloids" (R. M. Fitch, ed.), pp. 73,103. Plenum Press, New York. Fowkes, F. M. (1964). Ind. Eng. Chem. 56, 40. Gerrens, H. (1964). DECHEMA Monogr., Frankfurt a/M 49, (859), 346. Gershberg, D. (1965). J. Chem. Eng. Symp. Ser. Inst. Chem. Eng. N3, 3. Granzhan, V. A. (1969). Zh. Vses. Khim. Obshch. 14, 223. Gritsenko, G. M., and Medvedev, S. S. (1956). Dokl. Akad. Nauk SSSR 11, 235. Harkins, W. D. (1947). J. Am. Chem. Soco 69, 522. Jacobie, E. (1960). Electron Microsc. 1. Kaeble, D. H. (1971). "Physical Chemistry of Adhesion," pp. 153-170. Wiley (Interscience), New York. Kiselev, M. R., Evko, E. t.. and Luk'yanovich, V. M. (1966). Zavodskaya Lab. 32, 201.
Klein,A.,Kuist,C. H., and Stannett,V.T. (1973).J. Polym.Sci. 11,211I. Kudryavtseva, N. M., and Deryagin, B. V. (1963). Kolloid. Zh. 25, 739. Mamadaliev, A. (1978). Candidates Dissertation. Institute of Physical Chemistry Akad. Nauk SSSR, Moscow. Medvedev, S. S. (1968). "Kinetics and Mechanism of Formation and Conversion of Macromolecules," pp. 5-24. Nauka, Moscow. Nikitina,S. A., Konstantinova,V.V.,Zakieva,S. Kh., and Taubman,A. B.(1961).Zh. Pricklad. Khim. 34, 2658. Okamura, S., and Motoyama, T. (1953). Kyoto Univ. 15, (4), 242. Paxton, T. R. (1969).J. ColloidInterface Sci. 31, 19. Piirma, l., and Chen, S-R. (1980). J. Colloid Interface Sci. 74, 90. Rhebinder, P. A. (1927). Z. Phys. Chem. 129, 161. Smith, W. V., and Ewart, R. H. (1948). J. Phys. Chem. 16,592. Snuparek, 1., and Tutalkova, A. (1978). Int. Symp. Polydispersionen, Dresden, Kurtzreferate N3. Staudinger, H., and Trommsdorff, E. (1933). Ann. Ed. 502, 201. Sütterlin, N., Kurth, H. J., and Markert, G. (1976). Makromol. Chem. 177, 1549. van der Hoff, B. M. E., (1960).J. Polym. Sci. 48,175. Vijayendran, B. R. (1979). J. Appl. Polym. Sci. 23, 733.
288
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Wolfram, E. (1966). Kolloid Z. Po/ym. 211, 84. Wu, S. (1974). J. Macromo/. Sci. C. 10, l. Yakovlev, Y. M., Lebedev, A. V., and Fermor, N. A. (1971). "Prob1ems
ofSynthesis,
Study of
Properties and Treatment of Latexes," pp. 148-158. TSNITE Neftekhim., Moscow. Ye1iseyeva, V. 1. (1966). USSR Patent No. 203899. Yeliseyeva, V. l. (1972). Acta Chim. Acad. Sci. Hungar. 71, 465. Yeliseyeva, V. 1., and Bakaeva, T. V. (1968). Vysokomo/. Soedin. Ser. A 11,2186. Yeliseyeva, V. 1., and Petrova, S. A. (1970). Vysokomo/. Soedin. Ser. A 12, 162l. Yeliseyeva, V. 1., and Petrova, S. A. (1972). Dok/. Akad. Nauk.SSSR 202 N(2), 374. Yeliseyeva, V. l., and ZiJikov, A. V. (1976). Am. Chem. Soco Ser. 24, 62-82. Yeliseyeva, V. l., and Zuikov, A. V. (1977). Vysokomo/. Soedin. Ser. A 19, 2617. Yeliseyeva, V. l., Zaides, A. L., and Zubaryan, K. M. (1965). Dok/. Akad. Nauk. SSSR 162, 1085. Yeliseyeva, V. l., Zharkova, N. G., and Evko, E. 1. (1967). Vysokomo/. Soedin. Ser. A 9, 2478. Yeliseyeva, V. l., Zharkova, 178, 1113. Yeliseyeva, Ye1iseyeva, Yeliseyeva, Yeliseyeva,
V. V. V. V.
l., 1., l., l.,
N. G., and Luk'yanovich,
V. M. (1968). Dok/. Akad. Nauk SSSR
Petrova, S. A., and Zuikov, A. V. (1973). J. Po/ym. Sci. Part C 63. Zuikov, A. V., and Kalnin'sh, B. Ya. (1975a). Kolloid. Zh. 37, 152. Zuikov, A. V., and Mamadaliev, A. (1975b). Zh. Fiz. Khim. 49, 1044. Mamada1iev, A., and Zuikov, A. V. (1976a). Vyso.komo/. Soedin. Ser. A 18,
114l. Yeliseyeva, V. 1., Zuikov, A. V., and Lavrov, S. V. (1976b). Vysokomo/. Soedin. Ser. A 18,648. Yeliseyeva, V. 1., Zuikov, A. l., Vasilenko, A. l., and Shehepetil'nikov, B. V. (1978). Int. Symp. Macromol. Chem. Tashkent 89-90. Yuzenko, V. l., and Mints, S. M. (1945). Dokl. Akad. Nauk SSSR 47(2),106. Zuikov, A. V., and Soloviev, J. V. (1979). Acta Polym. 30, 503. Zuikov, A. V., and Vasilenko, A. 1. (1975). Kolloid. Zh. 37, 640. Zuikov, A. V., Vasi1enko, A. l., and Yeliseyeva, V. l. (1976). Vysokomol Soedin. Ser. A 18,707.
CON/\.CYT PROYECTO
8 Recent Developments and Trends in the Industrial Use of Latex Carlton G. Force
1. Introduction . 11. Factors in Adhesion . A. Physical Adsorption B. Diffusion. C. Electrical Charge Distribution
.
D. Chemisorption . E. Tack . 111. Bonding Applications . A. Adhesives B. Fiber Bonding C. Tufted Carpet Applications D. Paints and Industrial Coatings E. Paper Coatings . .' IV. Construction Applications . V. Rubber Goods VI. Properties of Various Latexes References
l.
289 291 291 296 297 298 298 300 300 302 306 309 310 312 313 314 316
Introduction
A uniqueness common to latexes which is advantageous in many of their applications is the small size of the polymer particles (0.050.5 J.lm)suspended in the aqueous medium. Among the advantages of such small particle size is easy penetration into the smallest crevices of the substrates ~eing treated with thf; polymer, maximum efficiencyin deposition of thin films of the polymer, and optimum optical control of the films produced from the polymer particles because of the light scattering characteristics that occur over the particle size ranges available. The intense Brownian motion of such small particles maintains the colloidal stability of 289 EMULSION POLYMERIZATION
Copyright«:> 1982by AeademiePress. Ine. Al! rights of reproduetion in any forro reserved. ISBN 0-12-556420-1
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Carlton G. Force
latexes for very long periods even when there is a considerable discrepancy between the density of the polymer and that of the aqueous medium. This small particle size is a characteristic necessity of the emulsion polymerization reaction permitting good heat control through the aqueous medium at rapid polymerization rates. However, technology is emerging (Vanderhoff et al., 1979) which permits the preparation of emulsions in the latex particle size range from polymers that have previously been unavailable as latexes primarily because of sensitivity to water in their synthesis. This technology is expected to expand rather rapidly as the understanding of methods for producing microemulsions in the latex particle size range is transferred from monomeric systems, such as those being dealt with in tertiary oil recovery research (Shah and Chan, 1980), to polymeric applications. This type of technology has already been used commercially for more than a decade for the preparation of polyethylene emulsions by the indirect pressure method (von Bramer and McGillen, 1966). Availability of such a universally convenient me~ium of application permits optimization of product properties through polymer designo The most fundamental property of polymers deposited from latexes is their glass transition temperature. This dictates the temperature conditions under which they form continuous films and the degree of softness or flexibility imparted to the item containing the latex polymer. The glass transition temperature is characterized by the monomer making up the backbone of the polymer molecule. However, it can be modified without overwhelming other desirable characteristics by the copolymerization of such comonomers as low glass transition temperature acrylic esters with high glass transition temperature vinyl chloride to produce copolymers incorporating the advantages of poly(vinyl chloride) (PVC) but with glass transition temperatures down to below room temperature. Comparable technology is used in the production of many plastics and elastomers, for example, poly(vinyl acetate) and styrene-butadiene (S-BR). Flexibility can also be imparted to films developed through the fusion of high glass transition temperature polymers when a phase inversion takes place in the polymer melt to incorporate thoroughly the plasticizer in which the polymer had been previously suspended. Again, this is common practice in the utilization of poly(vinyl chloride) produced by the emulsion polymerization process (e.g., plastisols and organosols). In the utilization of emulsion polymers many specific characteristics are imparted by the specific polymer to the product. Although cost is always a factor in producing any commodity, achieving optimum characteristics for end use at an acceptable price is of course the ultimate aim. Latexes have found many of their opportunities through permitting achievement of this goal by unique designs producing equal or better utility more cost ef-
8. Recent Developments and Trends in the Industrial Use of Latex
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ficiently than the products they replace. Thus, the versatility permitted with latexes for the ingenious incorporation of the proper polymer into a construction allows tremendous latitude, with the price of the polymer often being a minor consideration compared to the properties imparted. This chapter is organized around current applications of latexes. The specific properties imparted by the various latexes utilized for each application will be pointed out. New and emerging technology in each field will be emphasized. However, the main objective will be to pro vide sufficient background and stimulation to enable the reader to begin synthesizing innovative emulsion polymers. 11. Factors in Adhesion Regardless of the end use, factors that have been recognized as important in adhesion are usually involved to some extent. Therefore, an outline of these factors is desirable. An excellent comprehensive review of this subject was recently published by Wake (1978). The factors responsible for adhesion can be subdivided into four categories: (i) physical adsorption, (ii) diffusion, (iii) electrical charge distribution, and (iv) chemisorption, all of which i~teract to some degree in every adhesive bond. A fifth characteristic relating primarily to the adhesive polymer is tack. A.
Physical Adsorption
Physical adsorption is a universal phenomena, producing some, if not the major, contribution t.o almost every adhesive contact. It is dependent for its strength upon the van der Waals attraction between individual molecules of the adhesive and those of the substrate. Van der Waals attraction quantitatively expresses the London dispersion force between molecules that is brought about by the rapidly fluctuating dipole moment within an individual molecule polarizing, and thus attracting, other molecules. Grimley '(1973) has treated the current quantum mechanical theories involved in simplified mathematical terms as they apply to adhesive interactions. For qualitative purposes, it is instructive to look at the equation developed by Hamaker (1937) for calculating the van der Waals force of attraction between materials. FA = A/6nd" (1) From this equation, it is seen that the force of attraction FA is proportional to a constant A commonly called the Hamaker constant. This constant is dependent upon the molecular composition of the materials. For example,
292
Carlton G. Force
the Hamaker constants of metals and their oxides suspended in water generally fall in the 1O-13-erg range. Organic polymers suspended in water usually have Hamaker constants in the 10-16 to 1O-14-erg region, with the lower surface energy materials, such as tluorinated hydrocarbons, having the smaller values (Visser, 1972). Experimentally, polystyrene in latex has been found to have a Hamaker constant on the order of 10-14 to 10-13 erg (Ottewill and Shaw, 1966; Watillon and Joseph-Petit, 1963). In the author's doctoral thesis work utilizing a commercial styrene-butadiene latex, the Hamaker constant for this polymer was established, in water medium, to be about 3 x 10-14 erg (Force and Matijevic, 1968). This value has since been confirmed using a better defined latex (Green and Saunders, 1970) and by theoretical calculations (Fowkes, 1967). In the denominator of Eq. (1) is inc1uded the distance of separation of the surfaces from each other d raised to a power n. Since the van der Waals attraction is an inverse function of distance of separation d, the c10ser the molecules are together, the greater the force of attraction. This effect is accentuated even more by the power n to which d is raised; n also decreases as the distance of separation becomes less. From a distance d of about 800 A separation between surfaces, n gradually decreases from 3 to 2 at about 80 A separution (Brisco and Tabor, 1972). This points out dramatically why, for good adhesion, there must be intimate contact between the adhesive and the substract. Initimate contact is also necessary for the diffusion and chemisorption mechanisms whereas electrical charge distribution assists the van der Waals forces in assuring this contact. Promotion of contact by methods such as applying pressure is important in insuring optimum bond strength. In fact, application of sufficient pressure sometimes enhances bonding even more than can be predicted from these surface force interactions because deformation of the adhesive into the micro roughness present on the surface of any solid substrate produces an increased area of contact. This dynamic phenomena is virtually impossible to calculate accurately, or even measure, because of the minute distances and small forces involved. Therefore, theoreticians have found it necessary to formulate their models on thermodynamic considerations involving the equilibrium situations of liquids adhering to solids and to ignore the kinetic happenings involved in placing a solid in contact with, and then separating it from, another solido The primary thermodynamic consideration involved is that of wetting or spreading. For the adhesive to achieve the molecular c10seness to the substrate required for strong van der Waals forces to develop, it must wet the substrate. In order for this to happen, the spreading coefficient S (Harkins, 1941)as defined by the equation (2) S = Ysv - (YSL+ YLv)
8. Recent Developments and Trends in the Industrial Use of Latex
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must be positive. In Eq. (2), Ysvrefers to the surface free energy of surface tension of the solid, YLv is the surface tension of the liquid, and YSLis the interfacial tension between the solid and liquido In other words, the surface free energy of the solid must be decreased by the combination of the surface free energy of the liquid plus the interfacial free energy between the solid and the liquid for spontaneous spreading and wetting of the solid by the liquid to take place. For solids, neither Ysvnor YSLis directIy measurable. However, two methods have been developed which permit determination of whether this condition of wetting of the substrate by a proposed adhesive is likely to be met. A strictIy experimental method deveIoped by Zisman and co-workers (1968) at the Naval Research Laboratory is based on a value Ye, defined as the critical surface tension of the surface. Ye is the surface tension of the liquid which will just, and only just, wet the surface of the solido In order to determine this value experimentalIy, use is made of the concepts developed by Young. The Young equation is the mathematical expression of the vector diagram of a drop (shown in Fig. 1) which only partialIy wets a solid surface: Ysv
=
(3)
YSL+ YLv cos (J
In Eq. (3), the angle (Jis the contact angle made by the liquid on the flat solid surface. It is dependent on the surface tension of the liquido The lower the surface tension, the greater the tendency to wet the solid, and the smalIer the angle (J.Ye is the value obtained by extrapolating to zero contact angle the results of contact angle measurements made with a series of liquids having different surface tensions on tQe solid in question. The Naval Research Laboratory group has actively pursued this approach for welI over a decade and has recentIy published (Shafrin, 1977) Ye values covering some 150 synthetic and naturalIy occurring polymers. The values for some of the materials of interest to the emulsion polymers industry are shown in Table 1. A more theoretical approach to determining whether an adhesive can be expected to wet the surface of a solid has been developed and promoted by Girifalco and Good (1957) and Fowkes (1964). Utilizing the geometric mean
Fig.1.
Vector diagram
of a liquid drop which partially
wets a so lid surface.
Carlton G. Force
294 TABLEI Critical Surface Tensions of Polymer Materials
Critical surface tension (y c)
Polymer Phenol/resocrinol adhesive Resorcinol adhesive Wool Cellulose (regenerated) Nylon 2 Polyacrylonitrile Casein Nylon 7,7 Poly(ethylene oxide) Poly(ethylene terephthalate) Nylon 6,6 Nylon 11 Nylon 6 , Cellulose, from cotton linters Nylon Poly(methyl acrylate) Polyoxyphenylene Polysulfone Poly(vinylidene chloride) Cellulose acetate Poly(methyl methacrylate) Poly(vinyl chloride) Starch Chloroprene Polyisoprene, chlorinated Poly(vinyl acetate) Poly(vinyl alcohol) Nylon 9,9 Poly(vinyl ethyl ether) Rubber (natural)/rosin adhesive Cellulose, from wood pulp Polyacrylamide Polyacrylate Polyepichlorohydrin Nylon 8,8 Polyisoprene, cyclized Poly(ethyl methacrylate) Polystyrene Nylon 10,10 cis- Poly-1,3-butadiene Polyoxypropylene trans- Poly-1 ,3,-butadiene
(dynecm-I) 52.0 51.0 45.0 44.0 44.0 44.0 43.0 43.0 43.0 43.0 42.5 '42.0 42.0 41.5 41.0 41.0 41.0 41.0 40.0 39.0 39.0 39.0 39.0 38.0 37.0 37.0 37.0 36.0 36.0 (36.0 35.5 3540 35.0 35.0 34.0 34.0 33.0 32.8 32.0 32.0 32.0 31.0 (continued)
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TABlE I (continuad) Critical surface tension (Yc) (dyne cm -1)
Polymer
31.0 31.0 30.0 29.0 29.0 29.0 28.0 28.0 27.0 27.0 25.0 22.0
Polyethylene cis- Polyisoprene trans- Polyisoprene Poly-4-tert- butylstyrene Polyurethane Poly(vinyl methyl ether) Poly(butyl acrylate) Poly(vinyl butyal) Butyl rubber Polyisobutene Poly-l,2-butadiene Silicone rubber a
Adapted from Skeist (1977). Reprinted by permission of
Van Nostrand
Reinhold
Co.
to take into account the London dispersion forces between molecules across the interface, the interfacial tension between two immiscible liquids, such as mercury or water and a hydrocarbon, can be expressed by Y12= Yl + Y2
-
2{r1Y1)1/2
(4)
Mercury itself is capable of interacting by two main interatomic forces, the metallic bond and London dispersion forces. Similarly, water has the potential for both hydrogen bond and London dispersion force interactions. However, hydrocarbons cannot interact with either the metallic bond, in the case of mercury, or hydrogen bonds, in the case of water. Therefore, the only primary interatomic force within hydrocarbons and across the interface is due to the London dispersion interaction, and Y2 = Y1
(5)
for the hydrocarbon. Various hydrocarbons have surface tensions covering the range from 18.to 30 ergjcm2. From the interfacial tensions between several of them and water, the London dispersion force field of water has been found to be 21.8 :!: 0.7 ergjcm2. Since water, for example, only partially wets most polymeric materials, yd of the polymer can be calculated from the contact angle water makes with it. Having established yd for the solid, Fowkes (1964) has shown that not only can the strength of an adhesive bond be predicted, but several other thermodynamic properties of
296
Carlton G. Force
the polymer can also be calculated, such as the heat and free energy of adsorption. The van der Waals attractive constant A can also be calculated from yd, as was done for S-BR latex mentioned earlier. These dispersion force interactions are quite strong, being approximately equal in strength to hydrogen bonds. In cases, where solid and liquid systems can interact only by London dispersion forces, Fowkes has demonstrated that for wetting to occur yty~ > 2YL
(6)
From Eq. (6), it can be determined that y~ must exceed 243 dynejcm for water to wet a solid surface. From this, it can be seen why meticulously clean surfaces are usually necessary for good adhesion. Although the contaminant may wet and thus coat the substrate, the contaminant will often have sufficiently low surface free energy so that the adhesive in turn cannot wet it. It should be noted, however, that contaminants do not always lead to poor adhesion. In some cases, a contaminant can improve adhesion, for example, by providing improved wetting on one constituent and adhesion by another mechanism, such as chemisorption or hydrogen bonding, to the other constituent.
B. Diffusion This mechanism of adhesion advanced and originally promoted by the Soviets (1963) is of the greatest importance to applications where a material is being adhered to itself, such as in the self tack of rubber. Another familiar example is the application of the same adhesive to two different surfaces from a solvent system, allowing the solvent to dry partially or totally, and then combining the treated surfaces, such as in the use of "contact cement" or self-se¡llingenvelopes. In the theory of diffusion it is postulated that high molecular weight polymer molecules interdiffuse with each other across the interface. The term "autohesion" is often applied to this process in the adhering of portions of the same plastic material together. Since molecules of the same material diffuse across the interface, making the two layers one, the original joint disappears. Once the joint is completely healed, there is little chance that adhesive failure will occur at the original interface. For autohesion to occur, the polymer must be well above its glass transition temperature. It is the primary mechanism operating in the heat sealing of plastics and the coalescence of droplets from emulsions of the film-forming plastics such as S-BR rubber during drying.
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Those who are familiar with the difficulties in formulating polymer blends will quickly recognize, however, that care must be taken in trying to apply this mechanism to the bonding of two different polymers. Very few polymers exhibit good compatibility with each other. The concept of solubility parameters (Hildebrand and Scott, 1950) is often utilized to help predict the degree of compatibility to be expected. Voyutskii (1971) has presented data that he interpreted as evidence that molecules of one polymer, poly(vinyl chloride), can diffuse into another, poly(butyl methacrylate), having a solubility parameter nearly three units lower. In this case, there was no indication that poly(butyl methacrylate) molecules had diffused back into the PVC. With poly(methyl methacrylate), whose solubility parameter is within 0.8 units of PVC, an interfacial zone of nearly 4000 A was shown by UV luminescence, where intermingling of the molecules presumably existed. There is data relating peel strength to thermodynamic compatibility, but further studies are necessary before quantitative predictions can be made on the contribution of diffusion to adhesion in relation to polymer compatibility. The order of strength demonstrated could also be contributed primarily by physical adsorption. C.
Electrical Charge Distribution
Fowkes (1973) has recentIy provided an explanation for the electrostatic theory of adhesion based on donor-acceptor relationships across the interface that seems quite plausible. This type of acid-base interaction is responsible for the improved adhesion of carboxylated polymers to inorganic fillers, such as calcium carbonate, al~minum hydroxide, and other familiar metal oxides' and hydroxides. The polymer surface is predominantIy negative in charge, whereas the metallic compound has a positively charged surface. In more general terms, common polymer electron-donor groups are oxygen atoms, amides, and double bonds. Chlorine atoms in poly(vinyl chloride) and fluorine atoms in fluorinated polymers are potential electron acceptors. In addition to the every present van der Waals attractive force, carboxyl groups on rubber also pro vide a potential for hydrogen bonding to strengthen adhesion to oxygen-containing substrates such as cellulosic materials. . In inorganic systems, ionic bonds across interfaces must also be considered as electrostatic adhesion. In a number of instances, oxide or other films are deliberately created on metal surfaces to promote adhesion with other systems, such as polymers. The bond between the metal oxide and the metal itself. is primarily electrostatic and is usually stronger than the cohesive strength of the metal oxide.
298
Carlton G. Force
D. Chemisorption Whereas the electrical charge distribution mechanism described in the preceding section postulates a relatively nonspecific electrostatic attraction or donor-acceptor interaction across the interface, chemisorption is considered to involve the formation of covalent or donor-acceptor bonds between specific molecules on opposite sides of the interface. One of the more popular current applications of this theory is the siloxane coupling agents used for bonding glass or hydrated metal oxides to polymeric adhesives. These coupling agents are provided with appropriately reactive terminal groups on one of the organic linkages to the silicon atom. The reactive group could be a double bond, for reaction with unsaturated polyester resins dissolved in styrene; an amine or carboxyl group, for reaction with epoxy resins; or a mercaptan, to interact in the vu1canization reaction with rubber. Some materials which are blended with elastomers for the purpose of reacting with the substrate, the elastomer, or both, to produce chemisorptive adhesion, include isocyanates and resorcinolformaldehyde resins in the familiar RFL, or resorcinol, formaldehyde, vinyl pyridine latexes used for tire cord dips. Patterson (1969) has written a good survey of the technical and patent literature of fiber adhesion. Chemisorption is strongly emphasized in this survey, although not to the exclusion of other mechanisms.
E. Tack Closely associated with the factors responsible for adhesion is the tackiness of the polymer. An adhesive is said to possess tack if, under the conditions of application, only light pressure is required to produce a bond sufficiently strong to require work to restore the interfjlce to its original separated state. This differs from the preceeding four factors in that the objective in those four cases was to produce a sufficiently strong bond so that failure would be cohesive in the substrate or adhesive, but not at the original interface. Tack is generally measured by the energy required to separate the bond after contact has been made, under carefully controlled conditions, which should include pressure, time, and temperature. Two primary factors are involved in such a measurement. First, the adhesive' surface must readily wet the surface of the material with which it is brought into contact in order to bond quickly with minimum pressure. Second, the bulk of the adhesive should generally be capable of absorbing, through deformation, a portion of the energy applied to separate the bond. Thus, the viscoelastic properties of the adhesive are extremely important in
8.
Recent Developments and Trends in the Industrial Use of Latex
299
obtaining optimum strength without producing a bond that cannot be separated when desired. Certain materials, such as natural rubber, possess considerable tack without modification. Many synthetic rubbers, such as S-BR, do not show much tack in the dry state, although their latexes may be quite tacky while water is still present during drying. Dry tack can be improved by blending these polymers with other materials. The mechanism by which tackifiers, such as rosin, terpenes and their esters, and phenolic and hydrocarbon resins, operate is complex and obscure. However, they possess a sufficient degree of incompatibility with the adhesive so that they migrate, to some degree, to the air or substrate-adhesive interface. Here they may carry out a number of functions, such as forcing low molecular weight polymer, which is sometimes generated on or exuded to the surface, back into the bulk so it will not produce weak bonds. The tackifier will also tend to separate entangled polymer chains near the surface by virtue of its prescnce in the area. Since there is a degree of incompatibility, some of these separated chain heads may prefer to be at the air-tackifier interface for good bonding while their tails remain firmly imbedded in the bulk polymer. AIso, the effect the tackifier-adhesive combination has on wetting characteristics toward the substrate cannot be ignored. Materials generally considered to be tackifying resins for pressuresensitive applications have one characteristic in common, a softening point well above room temperature. The glass transition temperature of the PARTS RESIN PER HUNDRED PARTS RUBBER
;;-¡ ID o a: CL
30
10
1400
50 70
200
100
400
900
1200 1000
<{
i5
800
'", S
600
a:
UJ CL
'" '-' ¡:!
400 200
I
I
I
20
O
I
I
40
I
I
60
I
'Q
80
I 100
PERCENT TACKIFYING RESIN IN NATURAL RUBBER
Fig. 2.
Variation of taek with proportion of taekifyingresin in the elastomer (from
Skeist, 1977, eourtesy, Hereules, Nostrand Reinhold Co.).
Ine., Wilmington,
Delaware.
Reprinted
by permission
of Van
Carlton G. Force
300
adhesive elastomer is considerably below room temperature. Apparently, in some manner, this incongruity of properties synergizes tack benefits to produce a large maximum in the work of separation at somewhere near equal blends of resin and elastomer. A typical tack curve is depicted in Fig. 2. As the region of maximum tack is reached, it has been demonstrated by a variety of measurements that two phases actually exist on the surface. Such a remarkable increase in strength, however, must be the result of a combination of substrate bonding and viscoelastic changes in the bulk polymer.
III.
Bonding Applications
The polymer particle size in latexes is far too small to be effective for adhesive applications. Therefore, many of these very tiny building blocks must coalesce through the diffusion adhesion mechanism to provide an optimum sized critical mass of polymer for the particular adhesive requirement. Methods of bringing the crucial number of particles together at the proper point of intersection for optimum bonding represents much of the ingenuity and skill involved in the utilization of emulsion polymers in adhesive applications. Equally important is having the correct emulsion polymer for the physical conditions available to create the bond. This involves such factors as glass transition temperature of the specific polymer and molecular weight of the polymer molecules. Too low a molecular weight do es not provide sufficient chain length for adequate entanglement and diffusion across particle boundaries. Too high a molecular weight makes the polymer so viscous it cannot flow readily enough to pro vide maximum intimate contact with the optimum amount of substrate during the time provided for bonding under application conditions (Mallon et al., 1980). In emulsion polymerization,molecular weight is generallycontrolled by the quantity of chain-transfer agent (often an alkyl mercaptan) used in the recipe.
A.
Adhesives
The ever increasing emphasis on reducing air pollution and on health
considerations emphasized by OSHA has provided a strong impetus for adhesive manufacturers to develop water-based emulsion polymer systems
to replace the organic solvent-based systems on which the industry was fou!lded.This has been a difficultprocess.
8. Recent Developments and Trends in the Industrial Use of Latex
301
First, latex polymers had to be optimized for the specific adhesion characteristics required in their primary areas of utility: pressure sensitive and contact adhesives. Second, there had to be developed suitable aqueous dispersions of auxiliary ingredients; most notable in this category are tackifiers. Finally, there has been economic resistance on the part of those who apply the adhesives because of the greater difficulty in evaporating water compared to organic solvents. Thus, most adhesive manufacturers have found it expedient to install solvent recovery equipment to meet air quality standards. The problems to be solved include minimization of adjuncts such as surfactants in the latexes and auxiliary agents which interfere with adhesion. Application to water-sensitive substrates also presented a problem now being solved by transferring a film of the adhesive to the substrate from a continuous low-surface-energy belt such as mylar on which the latex system was deposited and dried. Latex manufacturers are rising to these challenges by designing additional properties into the polymer molecules and developing systems which give both the desired adhesive characteristics and a savings in application energy through higher solids and optimized temperatures in suitably designed drying ovens (Mallon et al., 1980; Lee, 1980). The rapidly rising costs of energy and petroleum solvents is bound to catalyze the utilization of emulsion polymers throughout the rapidly growing adhesives industry. Because of the speed and ease of utilization, pressure-sensitive adhesives have become an integral part of a multitude of items utilized in both home and industry over the last generation. They can be designed to provide either permanent or removable bonds and are applied to cloth, plastics, aluminum, paper, and numerous other substrates for tapes, labels, wall covering, packaging, and many other uses. Pressure-sensitive adhesives require good tack and wetting properties for the substrate to which they will be attached. Elasticity is also desirable, particularly for removables. These properties are generally obtained from rubbery polymers such as natural rubber and S-BR. For more demanding performance, such as light stability and solvent resistance, acrylics, nitrile rubber, polychloroprene, and other high-performance polymers may be required. These so-called elastomers are characterized by low glass transition temperatures and a coiled or folded molecular chain configuration capable of great extension. Similar performance flexibility available from latex is required in a broad variety of applications where adhesives are utilized in manufacturing processes. Latexes are also finding wide application in foil laminating for food and other types of packaging. In short, there are very few items which a consumer purchases where adhesives have not been used at some time in their manufacture and packaging. For example, ther~ are
Carlton G. Force
302
on the order of 10 different adhesive operations in producing a carton of filter tip cigarettes. Contact adhesives are another large market where rapid penetration is being achieved by latexes. Most generally in this high technology application two types of material each, coated with a dried layer of the adhesive, are brought together to form the bond. Often a requirement of the adhesive is to allow some movement to permit redistribution of stresses in use due to physical differences such as thermal expansion coefficients between the materials being bonded. Examples where these types' of adhesives are utilized include shoe manufacture, automotive product assembly, adhering Formica to furniture, various construction applications, and do-it-yourself home repair. The rapidly increasing cost of solvents as well as the emphasis on environmental and health regulations are quickly phasing the solventbased contact adhesive systems previously used out of this market worldwide. . Government
regulations regarding flame spread. in construction ma-
terials have shaped another trend in latex adhesives. Suitably compounded polychloroprene latex has Underwriter Laboratory approval for the bonding of fiberglass batting to its facing for home insulation. It is also used for adhering insulation to the inside of heating and air conditioning ductwork in commercial buildings. Not all solvent adhesives will be replaced with latexes per se. For some applications, hot melt adhesive systems are being developed. However, just as ethylene-vinyl acetate copolymers produced by emulsion polymerization are a major component of many hot melt systems, suitably designed emulsion polymers to meet specific requirements will probably be present in these systems, too.
B.
Fiher Bonding
Another area where emulsion polymers have found broad acceptance is in the bonding of fibers. These fibers can all be of the same material, as in nonwoven-type structures or of different materials, such as in the woven and nonwoven composites utilized in tufted carpets. Optimized deposition of the polmer at fiber intersections rather than overall fiber coating and in some instances the copious use of inert fillers represent the art involved in developing properties at minimum cost. The earliest of these applications was natural rubber latex bonded paper. This was patented in England in 1926 and commercially developed in the United States before 1930 to produce products which effectively replaced leather in applications such as shoe insoles and midsoles. Latex was
8. Recent Developments and Trends in the Industrial Use of Latex
303
incorporated into the fibrous stock before formation of the paper (beateradd) in this initial development. Arter World War n, synthetic rubber latexes provided the smaIler partiele size, versatility, and broader range of properties which permitted expansion of the industry into new methods of rubber addition to pre-formed sheets (dry web and wet web saturation). Applications also expanded to inelude replacement of eloth as weIl as leather. The uniqueness of the products often developed their own special applications, such as in asbestos and fiber reinforced gasketing. The area has now expanded to inelude nonwoven synthetic fiber composites prepared from both water and air layed structures. Those bonded by latexes are primarily dry web saturated in one manner or another. There has been considerable development over the last few years in methods for saturating these nonwoven structures. Additional new methods would be expected to emerge periodicaIly to provide the physical and aesthetic properties required to broaden the rapid expansion of this industry into different applications characteristic of its growth. Among the saturating techniques presently used for synthetic fiber nonwovens are print bonding (the desired amount of latex is transferred by a patterned gravure roIl of a two roIl nip to the web), saturation bonding (the synthetic web, often supported, is saturated in latex bath and excess squeezed out in passing through a two-roIl nip), impregnation bonding (the desired amount of latex is transferred to the unsupported web by the lower roIl of a two-roIl nip the bottom of which, is rotating in a latex bath), foam bonding (the foamed latex is metered onto the fibrous web with a knife coater and sucked into the structure by passing the web ov.er a vacuum box), and spray bonding (the latex is sprayed onto a high bulk to weight ratio web for end uses such as fiber-fiIl'insulation while a vacuum box below the web control s penetration) (Brooks, 1979). The synthetic fiber nonwoven industry developed around air lay fiber substrates. The hydrophobic character of synthetic fibers in water makes them difficult to disperse satisfactorily to produce suitable substrate using the more rapid water lay papermaking technology. However, this has been overcome by developing synthetic fibers having tiny hairlike protrusions (fibrils) extending, verticaIly from their surfaces in water. These fibrils keep the fibers physicaIly separated from each other and in good dispersion for substrate formation on papermaking equipment. In order to provide adequate strength in the substrate for drying on paper machine drying drums or other unsupported drying systems, it is often desirable to incorporate some latex prior to sheet formation to assist the fibrils in fiber bonding until the sheet is finaIly saturated. The primar"y advantage imparted to fibrous structures by latex bonding is toughness in the form of very good hand tear strength along a smooth cut
304
Carlton G. Force
edge. This is provided by low viscosity chewing gum-like polymers which stretch to distribute tear stresses over many fiber rubber junetions. Sueh soft polymers are also useful in providing the drape or "hand" eharaeteristies of the leather and c10th substrates often imitated by latex bonded fiber products. Other strength properties (e.g., tensile) whieh are dependent on firmer bonding are sometimes poorer in latex bonded sheets than ordinary kraft paper (Sweeney, 1958). Less dramatie but often as useful eharaeteristies provided by. latex bonding for specifie applieations are inereased elongation, better internal bond, improved eompress¡"on reeovery, solvent resistanee, wet abrasion resistanee and folding or flex enduranee (Heiser et al., 1962). Mueh teehnology has developed around methods for produeing efficient latex bonding of fibers. Only that latex deposited within or around a fiber junetion to pro vide a sufficient volume of rubber to allow adequate extension before breaking eontributes to optimum efficiency. Therefore, in addition to the requirements of good wetting and adhesion to the fibers of the substrate, the rubber needs the proper viseoelastic charaeteristics and the latex must coagulate andlor eoalesce to an adequate partic1e size. In addition, its efficieney is governed by how much of the total rubber actually deposits within or surrounding fiber junctions. In the beater addition of rubber, the latex is coagulated in a eontrolled manner by some means such as addition of multivalent counterions, ehange in pH, or reduction in colloidal charge by other methods to produce rubber partic1es of a charaeteristie and optimized size for deposition in the forming sheet. Ir the charge on the partic1es is of the same sign as that of the fibers, the rubber will be deposited within the fiber strueture primarily by filtration. Bonding efficiency is improved by both wet and dry pressing of the sheet providing the rubber possesses sufficient tack to bond to the fibers that are pressed into contaet with it. The Dow Chemical Company (Heiser et al., 1962) and the Rohm and Haas Company (Sweeney, 1958) have reported on the development of experimental latexes with positively charged functional groups bound into their polymer structure. Such cationic latexes are attracted to the normally anionic charge sites on eellulose and synthetic fibers in aqueous medium to create an eleetrostatic bond. Again, it is necessary for an optimum number of latex partic1es to eoagulate at the bonding sites to develop satisfactory end use properties. Work has recently been published (Alinee et al., 1978) demonstrating various methods whereby cationic latex deposits on eellulose fiber furnish. This type of e1ectrostatie deposition should pro vide greatly improved rubber bonding efficiency because of the e1ectrical attraction between deposited rubber and neighboring fibers. To aehieve such effieieney, methods must be developed for agglomerating cationie latexes to optimal bonding partic1e size before introduction into the
8. Recent Developments and Trends in the Industrial Use of Latex
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anionic fiber furnish. Dow points out that the many previous attempts to utilize cationic latexes in fiber furnishes ha ve shown no pronounced advantage because the latexes were stabilized with migratable monomeric cationic emulsifiers (Heiser et al., 1962; Wessling, 1979). In aqueous solution, sufficient of these emulsifier molecules quickly migrate to the negative charge sites on the fibers making them neutral before the bulkier rubber particles can travel and attach to these sites. In this same vein, care must be taken not to add materials such as alum to the fiber furnish which will make it cationic (Goring and Mason, 1950; Goring et al., 1950) before addition of the cationic latex. In latex saturation processes of preformed fiber webs, the predominant force responsible for drawing the rubber particles to fiber crossings and coagulating these particles into a coherent mass is the surface tension of the evaporating water medium. Current trends are to develop latexes whose surface tension is close to water by utilizing oligomeric emulsifiers (White, 1976) or emulsifiers polymerized into the polymer chain (Sweeney, 1958) to maximize the surface tension forces. This industry has remained highly technological, producing on relatively slow equipment and employing a disproportionately large technical staff compared to other areas of papermaking primarily because of cost considerations involved in the relatively inefficient utilization of rubber. With the possible exception of optimized systems in which the latex is of opposite charge to the fiber at the time of addition, paper products with suitable tear strength ordinarily contain from 20 to 40% rubber. Inefficiency in anionic latex beater-add sheet s is due to the frac.tion of filtered rubber particles attached to only one fiber. In saturated, preformed webs most fiber junctions are encapsulated with rubber, whereas much less would be required if the rubber were located only between the fiber crossings. Again considerable rubber is deposited on only one fiber. Fiber bonding is a market strongly dependent on latex properties. The tear strength is dependent on the viscoelastic properties of the rubber. Adhesive strength of the rubber to the fiber must only be greater than the tensile strength of the rubber itself. Thus, the low viscosity rubber will string out and break near the center between two fibers before the attachment to either fiber separates. This may welI be why carboxylated latexes show little or no advantage in properties over uncarboxylated versions in these products. The additional bond strength provided by carboxylation in many applications is simply not required in fiber bonding. Rubber cure can also be undesirable in some latexes in that it shortens the stretchability of the rubber. Any degree of sulfur cure of S-BR bonded fibers drasticalIy reduces tear strength of the product. However, slight sulfur cure of a natural rubberbonded product is desirable for improving the rubber oxidative stability
Carlton G. Force
306
without harming tear strength. Cure of other polymers such as the metal oxide-catalyzed cure of neoprene or the heat cure of acrylics is desirable to improve properties such as solvent resistance and often develops the optimum degree of stretchability for tear strength (Sweeney, 1958). A myriad of opportunities exist for the latex producer to design specific properties into new latexes that will allow the bonded fiber manufacturers to develop new products. These can be based on polymer properties such as solvent resistance,' flexibility characteristics, and stre~gth. New developments can also be based on the colloidal characteristics 'of the latex. The cationic latexes of Dow and Rohm and Haas are examples. Another opportunity is in the development of methods for reducing the tendency of latex particles to migrate with the evaporating water from the center of saturated products to the hotter surfaces during drying. Unique colloid stability characteristics might also permit the development of new beater addition and saturation techniques for improved latex efficiency and properties. C.
Tufted Carpet Applications
Another area of fiber bonding where latex is the key ingredient is in the m~nufacture of tufted carpets. In this process, the yarn tufts making up the surface of the carpet are needle punched through a fabric known as the primary backing. This was originally jute fabric (burlap). However, it has been replaced by nylon nonwoven fabric which in turn is currently being displaced in many grades of carpeting by a coarse woven ribbon-like polypropylene fabrico Another backing that will sit on the underlay pad or floor is then attached to this basic carpet structure. This secondary backing is often fabric (Klein, 1979). Jute, the secondary fabric workhorse until the fall Qf 1979, is presently being replaced by woven polypropylene and spunbonded polypropylene because of economics and the uncertainty of jute supply from the Far East. Roughly one-fifth of tufted carpeting in the United States and almost all tufted carpeting in Europe has, as the secondary backing, attached foam rubber made from latex. A latex adhesive is necessary to bond the tufts into the primary backing, adhere the individual fiber strands in the yarn tufts together so they don't separate and "pill" at the carpet surface, and attach the secondary backing to this primary structure. This is accomplished almost exclusively by carboxylated styrene-butadiene latex containing 400 or more parts per hundred parts of rubber of a mineral filler. In addition to economics, this filler helps pro vide density and stiffness to the carpet structure for the desired "hand." Feldspar used to be the filler of choice, but less expensive calcium carbonate has replaced it in most instances.
8. Recent Developments and Trends in the Industrrnl Use of Latex
307
It is desirable to have a minimum of water to evaporate in carpet manufacture for the obvious energy savings. Therefore, the dry filler makes it possible to compound a 50% solids latex to about 85% solids. In current practice for viscosity control purposes, it is necessary to reduce this to about 82% solids with a small amount of water. Current trends aim to eliminate the need for this dilution. In this application, it is necessary for the adhesive to pro vide a quick, strong bond to both the carpet components and the mineral filler. Carboxylated latex is desirable because of the enhanced adhesion provided, particularIy to the filler, by enactment of the e1ectrical charge distribution mechanism. Permanent grab earIy in the adhesive drying cyc1e is necessary when applying a fabric secondary backing because any place it separates from the primary carpet structure during drying will not readhere with adequate strength unless additional adhesive is applied. This requires hand slitting of the fabric in the defective area, application of the adhesive and sale of the carpet as a "second." In order to achieve this so-called green tack, the rubber partic1es must coagulate into a large enough mass to pro vide adhesion between components as soon as possible after drying begins. This coagulation is brought about by the surface tension forces in the reducing volume created by evaporation of the water. The more rapidly the water evaporates, the more quickly the partic1es are brought into intimate contact by the surface tension of the aqueous phase. The poorer the stability of the adhesive system the lower the solids at which the desired degree of coagulation will occur. Many factors are'involved in providing the optimum degree of stability to the adhesive system. The carboxylated latexes generally have a sufficiently low concentration of monomeric emulsifier so that their surface tension is no lower than the mid-forties in dynes per centimeter (White, 1976; Klein, 1979) (pure water has a surface tension of 72 dynejcm). The filler competes with the latex rubber partic1e surface for this monomeric emulsifier. Therefore, the more finely ground the filler, the more surface area it has available to adsorb emulsifier. However, fineness of the grind can also affect other properties of the adhesive such as its viscosity characteristics (Klein, 1979). Finally, a development that has moved rapidly through the industry recently is frothing the adhesive to volumes of from half again to more than twice its unfrothed volume just before application. This produces at least three effects. Each bubble wall containing the solids has two large interfaces with air (inside and outside) which strongly compete with the rubber partic1es and filler for emulsifier, thus destabilizing the latex. Second, this large surface area provided by the bubbles produces
308
Carlton G. Force
more rapid remo val of the water. Third, the thinner films of rubber within the bubble walls assure thorough coverage of the two substrate surfaces with a lower quantity of adhesive if other characteristics such as bond are adequate. Adhesive frothing, which has now expanded to over 90% of United States industry, has reduced green tack adhesion problems considerably allowing acceptable properties to be achieved without the excess of adhesive often applied to insure good early bonding. Frothed latex application has been important in the drapery and furniture fabric industries for at least a decade to provide strength, the adhesive for fIock coating and desired "hand" properties to the fabrics utilized. Westvaco has recently introduced a water-dispersed tackifier to the carpet industry which improves both green tack and final adhesion. Since these properties are currentIy adequate, it is possible to reduce the amount of rubber in the adhesive compound by substituting this tackifier and still maintain the required properties in the carpe1. Good success is achieved replacing up to 15% of the rubber in fabric backed carpets and 20% of the rubber in the precoat upon which latex foam backing is to be applied. Because of the difficult wetting characteristics of polypropylene, opportunities exist to provide latexes and ingredients that stimulate better adherence between substrates made from this polymer. The current no-gel process of applying foam rubber to carpet tuft bonded with a precoat that might contain 700 or more parts of mineral filler per hundred parts of rubber became predominant in 1975. Prior to that, and still used for applications such as waffie-designed carpet backing and underlay, the more technically demanding gel system was utilized. Gel foam is compounded with ammonium acetate which is decomposed to acetic acid and ammonia gas by infrared heat just beyond the foam coat metering bar. This acidifies the system sufficientIy so that zinc ions present enter a pH region where they are hydrolyzed to a + 3 species which then electrolytically coagulates the rubber (Force, 1971). In the no-gel system, a frothing agent (tallow amine sulfosuccinamate) produces a foam of sufficient stability that the water can be dried from it without foam collapse. This simpler technique has permitted the carpet milis to reduce costs by compounding their own products for foam backing instead of relying on technical experts who supplied the gel formulation. However, they have accepted some disadvantages in doing this. One is a reduction in coating speed to permit sufficient drying before the first turn roll in multipass ovens so the coating will not fall off the carpe1. The second is greater carpet drying difficulty after water spills in use because of the more hydrophilic character of the surfactant used in the no-gelsystem. Finally, tallow amine sulfosuccinamate does not produce as firm a rubber foam structure as the gel system. This softer resiliance provides a less cushiony feel under foo1. In spite of these
8. Recent Developments and Trends in the Industrial Use of Latex
-309
deficiencies, economics dictate that no process much more costly than the no-gel system can gain prominence in this industry. However, the deficiencies also provide opportunities for latex producers and chemical suppliers to develop new products and new processes for this application. The predominant latex used for backing foam carpet is S-BR made by the cold redox-initiated system. Smaller amounts of specialty latexes such as poly(vinyl chloride) and polychloroprene are sometimes used for meeting specific flame spread requirements where chlorine-containing polymers compounded with suitable catalysts such as antimony salts pro vide distinct advantages. A fraction of hydrated alumina in the filler portion of both the adhesive and foam coating allow S-BR to meet government regulations for flame spread for most applications. Urethane foam is making small inroads into this market. A number of suppliers are currently developing urethane foam systems. The cost and availability of natural gas normally used for carpet drying will probably be the factor governing how quickly this development matures. Materials that permit compounding of higher solids latex foam systems should help deter penetration of urethane into this industry. Systems that permit application of foam backing of greater thickness than the roughly i in. limit currently practical could also expand the United States market beyond the one-fifth of carpeting which it now enjoys and utilize more latex per carpet. D.
Paints and Industrial Coatings
Another large-scale application of latexes as adhesives is in the bonding to continuous substrates of pigments, clays, ~mdmineral particles in coatings that produce specific end use advantages. Major among these are paints and paper coatings. There are also many functional coatings applied to a variety of substrates to pro vide solvent resistance, to retard vapor and liquid permeability, or pro vide a host of other benefits. Following World War n, synthetic latexes made possible the development of a new concept in coating technology with the introduction of water-based paints. Their first use was interior home walls where hiding and color were qf primary importance. Such paints are formulated to cure over a period of time to provide wa.shability and scrubability. A particularly challenging problem has been the development of suitable viscosity characteristics to achieve good leveling to smooth out brush marks while maintaining sufficient body so the paint do es not splatter easily under application conditions or "run" on the surface. This has been achieved by additives that pro vide optimized thixatropy to the paints so they thin sufficiently under the shear conditions of roller or brush application for quick leveling but remain sufficiently thick before and soon after application
310
Carlton G. Force
to prevent splattering and running. The capacity of latex polymer to adhere quickly in the wet state to the substrate and to coalesce into a continuous film during drying in order to maintain the hiding and color pigments welI dispersed over the surface makes synthetic latexes welI suited for paint purposes. From their beginning with S-BR latex paints on interior walIs, continual performance improvement through additive and polymer development has expanded the markets to gloss woodwork coatings, durable chalking and mildew-resistant exterior coatings, and currently to a degree of penetration into the more demanding industrial coatings market. In industrial and maintenance coatings, chemical resistance is of primary concern in many applications. It is also necessary that industrial coatings form a continuous film and cure to acceptable rust and chemical resistance quickly after application. Mechanical and flexibility characteristics of the film that pro vide durability against cracking are also of primary importance in many industrial uses (Bierwagen, 1979). Storage stability is a special problem with paints., The pressures de- . veloped by the formation of ice crystals quickly coagulate latex particles. Therefore, additives must be incorporated such as specific nonionic type emulsifiers to pro vide good freeze-thaw stability. Maintaining adequate dispersion of the pigments and other ingredients over long storage periods so they can be easily reblended uniformly at their original particle size is also a necessity. Specific opportunities always available for improvement by unique formulating ingredients and advanced latexes are water sensitivity of the film, viscosity stability and shear stability of the paint in storage, and in general the whole realm of application characteristics involving leveling, flow, and viscosity. As these are advanced for specific applications, latexbased products will gain larger shares of industrial and maintenance coatings markets. Increasing cost of solvents and governmental restrictions on their use pro vide a strong incentive for market penetration as quickly as suitable properties are available.
E.
Paper Coatings
Paper and paperboard for printing are coated to improve both printability and appearance. The coating consists primarily of mineral pigments bound to the celIulose surface with synthetic and natural polymers. A variety of additives may also be incorporated into the coating such as lubricants, antifoams, pigment dispersants, flow modifiers, and dyes. The binder level is generalIy in the range of lOto 20% of the quantity of pigment and is composed of a combination of synthetic latex and a natural polymer such as starch, protein, or casein. In addition to bonding the pigment to the substrate, each binder pro vides other desirable properties to the coating.
8. Recent Developments and Trends in the Industrial Use of Latex
311
For example, carboxylated S-BR helps produce gloss in the coating and seal the surface for good ink hold out. In offset printing both water and inks are applied to the paper. Therefore, the coating must be hydrophilic and porous enough for the paper to absorb the water during drying. Starch for hydrophilicity and poly(vinyl acetate) which pro vides strong pigment bonding but is nonfilm forming to maintain porosity is the binder combination of preference for coating offset printing paper. For gravure printing, which is currently gaining in popularity, the ink used is of sufficiently low viscosity that surface bond strength of the coating is of little importance whereas surface smoothness is of greater significance. Thus, film-forming synthetic latex is often the exclusive binder (Heiser, 1979). Pigment and binder help fill in voids between the surface fibers. The pigments main purposes, however, are to reflect more light back to the eye for improved brightness of the surface and to help scatter light passing through the sheet for better opacity to prevent show-through of the printing. Because of its high refractive index, titanium dioxide is an extremely effective light scatterer for opacity improvement. Small particle size clays, calcium carbonate, and hydrated alumina make good brightnessimproving pigments. Dow has introduced some synthetic polymer pigments in the form of latex-like water dispersions. Just as polystyrene latex binder pro vides high gloss in supercalendered paper, these 0.4 to 0.5 Jlm pigment particles provide gloss, optimized scattering for opacity due to the specific particle size, good brightness, and ink holdout. Economics will be important in determining how much penetration plastic pigments make into this market. Carboxylated latexes made with a small fraction of polymerizable fatty acid in the monom'er mix pro vide many advantages as coating binders. These improvements include better adhesion to both the mineral pigment and cellulose through the bound carboxyls enhancement of the electrical charge distribution mechanism and hydrogen bonding mechanism, respectively. This provides advantages in gluability and wet rub. Other advantages include improved compatibility with starch and better coating blade performance. Among current trends is the compounding of paper coatings to higher solids for faster drying at lower energy requirements. Future opportunities in which the latex manufacturer can participate include providing better ink holdout and more uniform ink adsorption, enhancing easier finishing (or even elimination of the need for finishing), providing specific latexes for low, medium, or high gloss coatings, enhancing faster ink drying, providing improved basestock reinforcing and better coverage at faster coating speeds, and improving coating blade runability (Heiser, 1979). These challenges will be met through both polymer design and colloid chemistry of the latex and coating systems.
Carlton G. Force
312
IV.
ConstructionApplications
A relatively new opportunity for latexes is in providing special benefits to various types of pavement. Probably the fastest growing market worIdwide in this respect is coatings for recreational and athletic surfaces. Here, a top coat consisting of ground rubber scrap is bonded with latex to make a i-in. surface over an asphalt or concrete subsurface. Its resiliency, durability, and elasticity pro vide a. maintenance-free playing surface. Such surfaces have been medically demonstrated to create fewer imfirmities to joints and other parts of the body jolted in athletic endeavor, to help prevent playground injuries, and to produce a lower degree of fatigue than the subsurfaces alone or most other surfaces. These surfaces have required no repair in all types of weather over the ll-year history since they were first introduced in 1969. Thus, the additional cost of application is now recognized to be more than compensated for by their minimal maintenance. Small amounts of S-BR or the more oxidation-resistant polychloroprene latex ih asphaltic concretes are beneficial in bonding crushed aggregate firmly while leaving a sufficieritly open structure around the aggregate particle for rain water to penetrate below the pavement surface. This effective method for eliminating hydroplaning is being utilized for airport runway construction in some of the western United States. However, because of the additional cost imparted by the latex,"broaq penetration into airport construction and carryover to general road construction has not yet developed. Currently, in the more dangerous stretches, grooves are mechanically impressed into pavement surfaces to help pro vide the drainage required to overcome the hydroplaning problem. Another paving system in which latexes provide unique properties is alumina hydraulic cement. Here, 10 to 15% latex (based on the cement fraction) produces a flex modulus which greatly reduces fatigue for persons who work on concrete floors. Latexes such as polychloroprene also help produce chemical resistance and nonporous structure in concrete. As a result, latex is used in Terezo-type flooring in shower stalls and for hospitals and dairies where sterilization is important. Along this same line, latex in concrete pavement prevents fizzures from developing due to the expansion of absorbed water upon freezing. In climates where icing is common in winter, concrete bridges are particularIy vulnerable. Water rapidly penetrates the concrete sufficiently to rust the reinforcing rods requiring costly bridge repair in a relatively short periodo This problem is especially evident through the northern half of the United States on the interstate road system .which is now about 20 years old. Unfortunately, latex is still not sufficiently cost effective to be utilized in much of this first round of bridge surface replacement. However, it is finding appli-
8. Recent Developments and Trends in the Industrial Use of Latex
313
cation in parking garages, recreational are as, and industrial areas where the resiliency property is also of prime importance. A large application of latex is in blends with asphalt to produce a waterproof membrane on cinder block and concrete walls. Here, as well as when incorporated into concrete mortars, the rubber fraction produces better adhesion, durability, and temperature expansion tolerance than the asphalt or mortar base alone. With the decreasing availability and increasing price of petroleum, methods are being implemented to convert more of it to higher value distilled fractions. As a result, the residual asphalt fraction, is changing in properties. There are also vast differences in asphalt properties depending upon the section of the world from which the crude oil is obtained. An active program is just beginning among petroleum refiners to investigate the potential for achieving and retaining optimum properties in asphalt through the incorporation of a fraction of latex in their products.
v.
RubberGoods
A large proportion of solid polymers are made by emulsion polymerization covering the entire range from tire rubber to high technology thermoplastic resins such as ABS. However, these solid polymers and their production is too vast a subject for a single chapter. Thus, this section will be confined to a couple of product applications whose production technology is dependent on the colloid chemistry of latexes, in addition to being a convenient medium for production of the .rubber. Elastic thread used in many garments such as pajama waists and sock tops is made either by cutting from solid rubber or extruding from latex. Cut thread has the disadvantage in some applications of having square edges. Extruded thread is produced by running a continuous stream of latex into a coagulation bath through a circular hole that pro vides cylindrical thread of the proper diameter. For natural rubber latex, the coagulant is usually acetic acid whose density is adjusted to allow the thread to remain suspended whilt: being drawn through the bath. The rubber thread thus formed is then drawn through a leach bath to remo ve salts and passed through an oyen for drying and curing of the rubber. This method of elastic thread production is less costly than cut thread. However, the dry heat resistance, particularly under tension, of this extruded thread is not as good as cut thread. Development of better rubber cure technology in the extruded thread process should allow latex to take over the majority of this market. Synthetic latexes can provide special properties to the thread (e.g., polychloroprene can pro vide good solvent resistance under stress). In such
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Carlton G. Force
cases,the coagulation bath density must be balanced to the density of the polymer. The second area utilizing latexes for production is dipped goods products. These include articles such as toy balloons, rubber gloves, finger cots, and automotive floor gear shift rubber boots dipped onto a metal support. The form on which the article is to be produced can be coated by straight dip where the latex is simply allowed to dry or a coagulation dip as dictated by processing and application requirements including e!!-seof removal from the formo In coagulation dipping, the form is often first dipped in a coagulant bath of 20 to 35% calcium nitrate dissolved in water, then into the latex bath and sometimes back into a coagulant bath to set the outer surface. Dipped goods articles can be either unsupported or supported such as the gear shift boot or a rubber coated textile glove, respectively. Often such a textile article. first is straight dipped followed by one or more coagulation dips. After deposition of the proper thickness of rubber from a latex bath of suitable viscosity to maintain uniform films for the item being manufactured, the articles are leached to remove residual salts, dried, and cured in appropriate apparatus. . The latexes upon which this industry developed were natural rubber and polychloroprene for solvent resistance. However, technology is advancing to permit penetration of carboxylated nitrile latex for optimized solvent resistance and tougher abrasion resistance. Among the competition to latexes in this field are poly(vinyl chloride) plastisols. As technology develops in producing small particle size latexes from polymers whose synthesis is too water-sensitive for emulsion polymerization, the dipped goods industry will quickly convert to their utilization from the solvent-based cements of these polymers now employed. Prime candidates include butyl rubber, EPDM, hypalon, and viton.
VI.
Properties of Various Latexes
In Table 11,common characteristics of a variety of polymer latexes are listed. Throughout the text, the more important requirements for each application were alluded to. Initial work on a specific problem should quickly establish the properties needed in both the polymer and its latex. The table is organized to permit easy determination of the capability of different classes of latexes to satisfy property requirements. Latex producer's specific product literature should be consulted to determine which of the many products within a polymer class would be most likely to satisfy the desired application. Although this book is devoted to emulsion polymerization, natural rubber latex has been included in this chapter for two
TABLE
Application
Natural rubber Styrene-butadiene Nitrile Polychloroprene Poly(vinyl chloride) Poly(vinyl acetate) Acrylic resin Adapted
Properties of Commonly
Used Latexes8,b
Glass Typical transition Uncured Organic Price cohesive Polymer Oxidative Color solvent Water temp Compounding Specific Gravity (0C) requirements latex solids ranking strength Resiliency tack stability stability resistance resistance
Latex
a
11
E F S E G G G
E S E E G F F
from Industrial Adhesives
E F P-G P-G P-G' F
F F G G-Ed G-E E E
F F F F . S E E
P P E S-Ed
G-S F-G F-G
edited by G. W. Koehn. Courtesy,
E E E E E F G-S
Armstrong
-67 -48 -25 -40 78' 30 -55 to 451
Extensive Extensive Average Extensive Minimal Minimal Minimal
Cork Co., Lancaster,
0.95 1.00 1.00 1.12 1.17 1.09 1.06
Pennsylvania.
b Code: E, excellent; S, superior; G, good; F, fair, P, poor. , Partial hydrolysis to poly(vinyl alcohol) produces good tack.
. d
Cured systems.
Copolymerized with acrylate or vinylidene chloride 1 Depending on acrylate monomers utilized.
monomers;
glass transition
temperature
may be as low as -25°C.
Major markets (by topic outline)
0.91 High B-I,3,D 0.99 Moderate B-l,2,3,4,5,C 1.00 High B-l,2,3,5,D 1.23 High B-l,2,3,C,D 1.41 Low B-2,3,4,5,C,D 1.18 Low B-l,2,4,5,C 1.10 Moderate B-l,2,3,4,C
316
reasons. Many of latex and natural uncured cohesive synthetic emulsion
Carlton G. Force the industries were developed utilizing natural rubber rubber possesses a few important properties such as strength and tack that have yet to be matched by polymers.
Acknowledgment The author wishes to express his appreciation to the following persons who graciously provided information on the subjects dealt with in this chapter: William de Vry and David Weaver of B. F. Goodrich Chemical Company; B. R. Vijayendran of Celanese Polymer Specialities Company; Evans Townsend of the Norton Company; and J. J. Gorman, C. H. Gilbert, and J. C. Fitch of E. I. duPont de Nemours and Co. Appreciation is also expressed to Westvaco Corporation for permission to publish this chapter and to numerous colleagues at Westvaco for their suggestions and assistance.
References Alinee, B., Robertson, A. A., and Inoue, M. (1978). J. Co/loid Interface Sci. 65, 98. Bierwagen, G. P. (1979). Adv. Emul. Polym. Latex Technol., Ann. Short Course Papers, 10th, Vol. n. Lehigh Univ., Bethlehem, Pennsylvania. Briscoe, B. J., and Tabor, D. (1972). Faraday Special Discussion, "Solid/Solid Interfaces," Chem. Soco No. 2, p. 7. Chemical Society, London. Brooks, B. A. (1979). Adv. Emul: Polym. Latex Technol., Ann. Short Course Papers. 10th, Vol. n. Lehigh Univ., Bethlehem, Pennsylvania. Force, C. G. (1971). Paper presented at American Chemical Society, Rubber Div., Southern Rubber Group Meeting, Memphis, Tennessee, October. Force, C. G., and Matijevié, E. (1968). Ko/loid Z. Z. Polym. 224, 51-62. Fowkes, F. M. (1964). 1nd. Eng. Chem. 56, (12) 40-52. Fowkes, F. M. (1967). "Surface and Interfaces" (J. J. Burke, ed.), Vol. 1,p. 199. Syracuse Univ. Press, Syracuse, New York. Fowkes, F. M. (1973). "Recent Advances in Adhesion" (L. H. Lee, ed.), pp. 39-43, Gordon and Breach, New York. Girifalco, L. A., and Good, R. J. (1957). J. Phys. Chem. 61, 904. Goring, D. A. l., Biefer, G. J., and Mason, S. G. (1950). Can. J. Res. 288, 339-344. Goring, D. A. l., and Mason, S. G. (l950a). Can. J. Res. 288, 307-322. Goring, D. A. l., and Mason, S. G. (l950b). Can. J. Res. 288,.323-338. Green, B. W., and Saunders, F. L (1970). J. Co/loid Inte~race Sci. 33, 393-404. Grimley, H. (1973). "Aspects of Adhesion" (D. H. Alner and K. W. Allen, eds.), Vol. 7, p. 11. Transcripta Books, London. Hamaker, A. C. (1937). Physica 4, 1058. Harkins, W. D. (1941). J. Chem. Phys. 9, 552. Heiser, E. J. (1979). Adv. Emul. Polym. Latex Technol., Ann. Short Course Papers, 10th, Vol. n. Lehigh Univ., Bethlehem, Pennsylvania. Heiser, E. J., Morgan, R. W., and Reder, A. S. (1962). TAPPI 45,588. Hildebrand, J. H., and Scott, R. L. (1950). "Solubility of Non-Electrolytes," 3rd ed. Van Nostrand-Reinhold, Princeton, New Jersey.
8. Recent Developments and Trends in the Industrial Use of Latex
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Klein, A. (1979). Adv. Emul. Polym. Latex Technol., Ann. Short Course Papers, 10th, Vo!. 11. Lehigh Univ., Bethlehem, Pennsylvania. Lee, Y. S. (1980). Polym. Con! Polym. Improved Energy Efficiency, 11th, Akron, Ohio. Mallon, C. B., Hagan, J. W., and Hamer, A. D. (1980). Polym. Con[ Polym. Improved Energy Efficiency, 11th, Akron. Ottewill, R. H., and Shaw, J. N. (1966). Discuss. Faraday Soco 42, 154. Patterson, H. T. (1969). "Treatise on Adhesion and Adhesives," (R. L. Patrick, ed.), Vol. 2, Chapter 6. Dekker, New York. Shafrin, E. G. (1977). "Handbook of Adhesives" (l. Skeist, ed.), 2nd ed., pp. 67-71. Van Nostrand-Reinhold, Princeton, New Jersey. Shah, D. O., andChan, K. S. (1980). J. Dispersion Sci. Technol. 1, 55. Skiest, 1. (ed.) (1977). "Handbook of Adhesives," 2nd ed. Van Nostrand-Reinhold (Litton Educational Pub!.), Princeton, New Jersey. Sweeney, E. J. (1958). TAPPI 41,304. Vanderhoff, J. W., EI-Asser, M. S., and Ugelstad, J. (1979). U.S. Patent 4,177,177, December 4. Visser, J. (1972). Adv. Colloid Interface Sci. 3, 331. von Bramer, P. T., and McGillen, W. D. (1966). Soap Chem. Spec. 42(12), 123. Voyutskii, S. S. (1963). "Autohesion and Adhesion of High Polymers" (S. Kaganoff, Translator), (lnterscience), Wiley, New York. Voyutskii, S. S. (1971). J. Adhes. 3, 69. Wake, W. C. (1978). Polymer 19, 29. Watillon, A., and Joseph-Petit, A. M. (1963). Am. Chem. Soco Div. Water and Waste Preprints 61-65. Wessling, R. A. (1979). Adv. Emul. Polym. Latex Technol.. Ann. Short Course Papers, 10th, Vol. 11. Lehigh Univ., Bethlehem, Pennsylvania. White, W. W. (1976). J. Elastomer. Plast. 8, 475. Zisman, W. A. (1968). "Contact Angel, Wettability and Adhesion" (R. F. Gould, ed.), Adv. Chem. Ser. No. 43. American Chemical Society, Washington, D.C.
9 Latex Reactor PrincipIes: Design, Operation, and Control A. E. Hamielec and J. F. MacGregor
1. Introduction . 11. Batch Reactors . A. Introduction . B. Monomer Consumption Rate . C. Polymer Quality . D. Initiation Systems . E. Heat Removal 111. Continuous Stirred-Tank Reactors: Steady-State Operation . A. Introduction . B. Polymer Quality . C. Optimal Reactor Type and Operation for Continuous Emulsion Polymerization IV. Continuous Stirred-Tank Reactors: Dynamic .. Behavior . A. Introduction . B. A Dynamic Model Based on Age Distribution Functions. C. Consideration of Dynamics in Reactor Design . V. On-Une Control of Continuous Latex Reactors A. Introduction . B. On-line Instrumentation C. On-line Estimation . D. On-line Control. VI. Summary. Nomenclature References
319 320 320 322 325 329 330 333 333 334 338 339 339 340 344 345 345 346 348 349 351 351 353
l. Introduction The principIes of latex reactor design, operation, and control will be illustrated by a consideration of the homopolymerization of styrene and vinyl acetate. Emulsion polymerization of vinyl acetate follows Case 1 319 EMULSION
POLYMERIZATION
Copyright ~ 1982 by Aeademie Press, Ine. AIl rights of reproduetion in any form reserved. ISBN 0-12-556420-1
320
A. E. Hamielec and J. F. MacGregor
kinetics with the production of polymer with long-chain branching, and styrene follows Case 2 kinetics forming linear polymer chains. The choice of these systems will permit a consideration of the control of long chain branching as well as polymer particle number and size distribution, all of which are important characteristics of paints, adhesives, and rubber products. Another consideration, of course, is the considerable number of experimental and theoretical investigations published on the emulsion polymerization of styrene and vinyl acetate. The principIes of latex reactor design, operation, and control illustrated here with eniulsion homopolymerization should largely be applicable to copolymerizations. ll.
Batch Reactors
A. lntroduction* We consider a polymerizing system with Np polymer particles per unit volume of latex. Np is usually of the order 1016-1018 particles per liter of latex. Early in their life when polymer particles are relatively small (1001000 Á).and when the polymer concentration is relatively low, termination with an entering radical will be effectivelyinstantaneous. Thus, particles will contain either zero or one radical. Later in the polymerization particles may contain two or more radicals. The polymerization rate in a single particle with n free radicals is given by
= kp[Mp]n
R pp
(1)
NA
The total polymerization rate is obtained by summation over all polymer particles <1J
Rp
-
"
(2)
kp[Mp] '--' nNn NA n=1
The average number of radicals per particle is given by <1J
¿
= n=1 n;np
(3)
= kp[Mp]Npñ
(4)
ñ and finally Rp
* Symbols are defined on pages 351-353 in the Nomenclature
section.
9. Latex Reactor Principies: Design, Operation, and Control
321
The conversion of monomer X is defined as (5) and therefore dX dt
= VRp
(6)
NMn
To get a feel for a typical polymer production rate, let us employ reasonable numerical values for the parameters in Eqs. (4) and (6). These follow: kp [Mp] Np
= 103 liter/Gmol
v=
sec
= 5 Gmol/liter
= 1017 partic1es/liter
latex
1 liter
NMn= 5 Gmol ñ = 0.5 (Case 2 kinetics)
from which Eq. (6) yields dX/dt '" 30%/hr. This is certainly a desirable rate of polymerization for commercial production. The production rate in practice would likely be limited by the heat removal capacity of the reactor. The number of partic1es Np is a function of emulsifier type and concentration and initiator level, although for monomers that obey Case 1 kinetics such as vinyl chloride and vinyl acetate, Np is almost independent of initiator level (Ugelstad et al., 1969; Friis and Nyhagen, 1973). The calculation of Np for various reactor operations will be discussed later. The monomer concentration in the polymer partic1e [Mp] can be obtained using a simple mas s balance. Assuming the monómer and polymer volumes are additive, one obtains. the following relationship for the conversion interval, Xc :<::: X :<::: 1.0 where Xc is the monomer conversion at the end of Stage 11. (7) To calculate
[Mp] in Stages 1 and 11 set X
= Xc
in Eq. (7). The deter-
mination of ñ requires, in general, solution of the Smith-Ewart recurrence formulas (O'Toole, 1965; Ugelstad et al., 1967). The general solution for the case of negligible water-phase termination (Y = O)is shown graphically in Fig. f. The parameters are given by a = p1 V/(Npk,P) a' = R.V(Npk,P) m = kdeV/k,P
(8)
Y = 2Npk,pk'w/(k; V)
For most emulsion polymerizations, water-phase termination can be neglected (Y = O) (Ugelstad et al., 1969). However, when an active chain-transfer
322
A. E. Hamielec and J. F. MacGregor
y=o
o
-3 L..L -8
-6
-4
-2
o
2
log a' Fig. 1.
General solution of tbe Smitb-Ewart recurrence equations. Negligiblewater-
pbase termination (adapted from Ugelstad et al., 1967).
agent is employed, higher rates of radical desorption may result giving significant water-phase termination and lower polymerization rates. It has also been shown that at high initiator levels the free radical capture efficiency may be appreciably less than 100%, presumably due to significant water-phase termination (Gilbert et al., 1980). B.
Monomer Consumption Rate
1. Case 1 Kinetics Consider a monodispersed latex, where water-phase termination is pegligible and termination is instantaneous when a radical enters a polymer particle containing one radical. By definition, N2 = N3 = ... = O and the total radical entry rate per liter of latex equals pl. Application of the stationary-state hypothesis gives R)
= 2pl(N¡/Np)
(9)
In the limit of very rapid radical desorption (10) and therefore (11) and (12)
9. Latex Reactor Principies: Design, Operation, and Control
323
Ugelstad et al. (1967, 1969) have derived a more general expression which accounts for the possibility that two radicals can coexist in a polymer particle:
=
R p
kp[Mp]
(N ) ( A
1/2
)
RI12 VpNi + Np 2k.p 2kde
(13)
A useful expression for the radical desorption coefficient fo11ows(Nomura et al., 1976). kde = (12~w/mD;(;)(kf.Jkp) (; = (1 + ~w/m~p)
(14a) (14b)
In Stage III, the reduction in Dp and increase in (; lead to a reduction in desorption coefficient with an increase in polymer-phase viscosity. For vinyl chloride emulsion polymerization the separate monomer phase disappears at about 70% conversion (Xc = 0.7). Therefore, as soon as Np reaches a constant value, the only parameter that changes for X < Xc is Vp.In fact, it is mainly the increase in Vpthat causes the acceleration in rateo For X > Xc the situation is more complex, with both k.p and kde fa11ingas polymer concentration increases. For vinyl acetate, the separate monomer phase already disappears at 20% conversion. For X > Xc, Vpis almost constant; however [Mp], k.p, and kdea11decrease with conversion. These effects will be discussed in more detaillater. 2. Case 2 Kinetics Consider a monodispersed latex, where water-phase termination and radical desorption are negligible and termination is instantaneous when a radical enters a polymer particle containing one radical. By definition, N2 = N3 = ... = O and the total radical entry rate per liter of latex equals R" the rate of radical generation per liter of latex via initiator decomposition. The rate of radical termination per liter of latex is equal to twice the rate at which radicals enter polymer particles containing one radical (two radicals are consumed per radical entry). Application of the stationarystate hypothesis gives R, = 2R,NdNp
(15)
= No = tNp
(16)
In other words NI
and ñ-1. -2
(17)
324
A. E. Hamielec and J. F. MacGregor
One normally assumes that systems such as styrene and methyl methacrylate, where transfer to monomer is not prominent, follow Case 2 kinetics when latex particles are small and termination in polymer particles is instantaneous. It has recently been shown that at low initiation rates radical desorption can be significant relative to radical absorption, and as a consequence ñ values appreciably smaller than 0.5 were found (Gilbert et al., 1980).At higher initiation rates ñ = 0.5 was approached. The use of chain-transfer agents would of course increase the desorption rate and lower ñ. For Case 2 kinetics the rate of polymerization is given by Rp
= kp[Mp]Np/2NA
(18)
with the rate independent of initiator concentration for fixed Np. Ir the initiation rate is reduced to a great extent, ñ will fall below 0.5 as radical desorption becomessignificant. 3. Stage III PolymerizatiolJs In Stage III, the polymer concentration in the polymer particles increases with ever increasing chain entanglements, and if the polymerization tem-: perature is below the glass-transition temperature of the polymer being syntht;sized, a glass-state transition will occur with the diffusion coefficients of small molecules falling by several orders of magnitude. The pro paga tion reaction becomes diffusion-controlled and a limiting conversion of less than 100% is reached where the rate of polymerization is effectively zero (Friis and Hamielec, 1976). Marten and Hamielec (1978) pro po sed the following models for the effect of polymer molecular weight and free volume on the termination and propagation constants. k ~=
M:
2a
1 ---
1
VF
VFcrl
( ) [ ( ~ = exp[- B(~ - ~ )] k,o
kpo
a exp(b/RT)
~C
exp -A
Mw
VF
)]
(20)
VFcr2
(21)
= M~c:' exp(A/VFcr.)
VF = [0.025 + Cip(T-
(19)
Tgp)]p
+ [0.025 + Cim(T- Tgm)]m
(22)
where a, b, Ci,A, B, VFcr!'and VFcr2are adjustable parameters found by fitting rate and molecular weight data.
9.
325
Latex Reactor Principies: Design, Operation, and Control
TABlEI Diffusion-ControlledTermination and Propagation Model Parameters Polyrner PMMA PS PVC
Tgp(0C)
A
B
ex
110 95 85
1.05 0.48 0.25
1.0 0.7 0.2
1.75 1.75 1.75
VFcr1
0.066 0.043 0.085
a
b
0.563 0.926
8900 3830
Parameters for three homopolymer systems are tabulated in Table 1. Using Eq. (20), Sundberg et al. (1980) observed values of B = 0.6 and VFcr2= 0.061 for the emulsion polymerization of both styrene and methyl methacrylate. The volume fraction of monomer in the polymer partic1e for X > Xccan be ca\culated using (23) To ca\culate m for X < Xc set X
= Xc in Eq. (23).
C. Polymer Quality 1. Molecular Weight Polymer can be produced via the followjng reactions: transfer to monomer to chain transfer agent and to polymer, termination reactions, and terminal double bona reactions. Transfer to polymer and terminal double bond reactions produce long-chain branches. Transfer to small molecules and termination reactions produce linear polymer chains. A major simplifiGation in the modeling of molecular weight and branching development results when it can be assumed that a negligible amount of polymer is produced via termination reactions. Fortunately, in most emulsion polymerizations, transfer reactions are relatively more important than termination reactions in the production of polymer. This is a direct consequence of the compartmentalization of radical s in polymer partic1es which permits commercial polymerization rates at relatively low radical initiation rates. When the amount of polymer produced by termination reactions is negligible, molecular weight and branching development is independent of initiator and emulsifier levels (or number and size of the polymer partic1es). The appropriate equations that describe molecular weight and branching development, which have been proved valid for the emulsion polymerization
326
, A. E. Hamielec and J. F. MacGregor
of vinyl chloride and vinyl acetate in a batch reactor, follow (Friis and Hamielec, 1975). For X < Xc
-
MR KXc 1+CM 1 - Xc
(
) 2MR 1 + KXc ( ) CM+-1+1 - Xc (1 - Xc)( 1 - XC) EN= ~ ( - )( + K)
MN=-
(25)
2
M=
l-Xc'
w
1
Xc
CM = krm/kp,
KXc
2CpXc
CpXc
CpMn MR
Cp = kr~/kp,
K = k;/kp
(26)
(27) (28)
For X > Xc dQo = CM- KQo dX 1- X
(29)
dQl = 1 dX
(30) 1
dQ2 =2 dX
(
1
KX + 1- X
)(
d(QoEN) - CpX + KQo dX 1- X IN = 1000MREN/MN MN
= MRQdQo
Mw = MRQ2/Ql
CpQ2
KX
+1=X+1=X C
CpX M+I-X
(31)
) (32) (33) (34) (35)
Equations (29-32) can be solved using standard numerical techniques. The initial conditions may be found using Eqs. (25-27). When polymer produced by termination reactions is appreciable, molecular weight and branching development depend on the initiation rate and emulsifier concentration (number of particles and their size distribution). This more general problem has never been solved and is perhaps intractable because of the long-chain branching reactions. Solutions have been obtained for the case where long-chain branching reactions are neglected;
..
9. Latex Reactor Principies: Design. Operation. and Control
327
these involved the use of population balance equations and sophisticated numerical solution techniques. The most general model that predicts particle size and molecular weight distributions was developed by Min and Ray (1974). Work of a more fundamental nature on the details of the microscopic events that control particle size and molecular weight development is being done by Lichti et al. (1977; Lichti, 1980). 2.
Particle Number and Size Distribution
The prediction of particle number and size distribution has been far less successful than the prediction of conversion time histories and molecular weight development, given these parameters as initial conditions. The nucleation and early growth of polymer particles is even today, after the comprehensive investigations of Ugelstad and Hansen (1976), not. well understood. There are several reasons for this. First, the measurement of number
and size of polymer
particles
smaller than
100
A presents
rather
difficult experimental problems. Many complex processes occur simultaneously including radical capture by micelles and polymer particles, precipitation of growing radicals from the aqueous phase, and finally particle flocculation and coagulation. To illustrate how certain variables such as initiation rate and emulsifier concentra tion might affect particle number, we will refer to a highly idealized model for particle number after Smith and Ewart (1948). To simplify the analysis, let us assume that the area occupied by an emulsifier molecule is the same on the micelle as on the polymer particle. In other words (36) For typical emulsifiers, as has values of 30-100 A2jmolecule or 1.8-6 x 107 dm2jGmol. The detailed derivation may be found in the original reference and the final result has the form (37) where (X= 0.53 when radical capture by polymer particles is neglectedand = 0.37 when micelles and polymer particles both capture radicals and assuming surface area on both kinds of particles are equally effective in the capture process. The diffusion theory of radical capture would predict that the micelles, being smaller, would provide more effective surface area for radical capture and thus give an exvalue greater than 0.37. According to Ugelstad and Hansen (1976), the capture process is more complex with the possibility of both collision and diffusion theories of radical capture applying under different limiting conditions. To develop effective control strategies for polymer particle concentration, it is of considerable importance to (X
328
A. E, Hamielec and J. F. MacGregor
establish the time scale for micellar nucleation of polymer particles. The effectiveness of any control scheme would of course depend on the nucleation time. Np is given by Np
= NAR.tr
(38)
where tr is the nucleation time (time to end of Stage 1). A value of 2fkd
=
10-6 sec-1 (K2S208
=6
at 50°C) and [/]
X 10-3
Gmol/liter
gives
an initiation rate' of 6 x 10- 9 Gmol/sec liter latex. The time required to nucleate 1018 particles per liter of latex is thus only abou't 5 mino It is clear that manipulation of initiator and emulsifier concentrations to control polymer particle nucleation would not be an easy task. Equation (37) has been shown to be valid for the emulsion polymerization of styrene (Gerrens, 1959). It does not apply to Case 1 systems such as vinyl chloride and vinyl acetate where in fact Np is independent of initiator concentration. This disagreement is not unexpected as ¡.J.is a function of initiation rate and the total radical entry rate into micelles and polymer particles is much greater than the initiation rateo Parti~le nucleation has been successfully modeled for vinyl chloride polymerization by Min and Gostin (1979). The particle size distribution (PSD) of a fully converted latex depends on the conditions in both Stages 1 and 11. It depends on the original PSD at time tr (end of Stage 1) and the subsequent growth rates of various sized particles in Stage 11.Gerrens (1959) has shown that the cumulative PSD at time tr is, for Case 2 kinetics, given by
v cum F(v) =
¡.J.tr
v = O.53¡.J.2/5(as[S]/R.NA)3/5
(39)
It is clear that the PSD at time tr narrows with increasing initiation rate and broadens with increasing emulsifier concentration. Ir the original PSD at tr is very narrow, then all particles will grow at the same rate in Stage 11 and the fully converted latex will have a narrow PSD. On the other hand, if the original PSD is broad, the final PSD will be broad. Data on the final PSD after Gerrens (1959) showing the effect of initiator concentration on the breadth of the PSD are shown in Fig. 2. As anticipated by Eq. (39), the distribution broadens with decrease in initiator concentration. To predict the PSD to the end of Stage 11 for a broad distribution requires a knowledge of the radical capture mechanism. According to the collision theory, surface area on a small particle is equally effective in capturing radicals to that on a large particle. On the other hand, according to the diffusion theory surface area on a small particle is more effective.
.
9.
Latex Reactor Principies: Design, Operation, and Control
329
1.0
0.8
A
~ 0.6 IL
E ::J () 0.4
0.2
1.0
0.5
1.5
2.0
V (LlTERS X 1016)
Fig. 2. Cumulative partic1e size distributions for styrene emulsion polymerization at different initiator concentrations [1]0 (in g/liter of water) (adapted from Gerrens, 1959): A, 5.41; B; 2.88; C, 1.80; D, 1.08; E, 0.541; F, 0.361.
D. lnitiation Systems Hydrophilic initiators such as the persulfates and hydrogen peroxide and initiators with varying solubilities in the polymer particles such as the hydroperoxides with 'or without reducing agents are employed in emulsion polymerization. A recent review of redox systems in emulsion polymerization was published by Warson (1976). The most efficient manner of adding the components of a redox system is gradually in stages or by adding the peroxide at the start and then the reducing agent gradually (Warson, 1976). A typical redox system for cold SBR production employs sodium formaldehyde sulfoxylate (reducing agent), a hydroperoxide (oxidant), and ferrous sulfate, plus' a chelating agent or a chelated irol) salt. A simplified kinetic mechanism for this redox couple follows (Wright and Tucker, 1977). ROOH + FeH Fe3+ + XH
--
RO'+M-
ROM'
330
A. E. Hamielec and J. F. MacGregor
The function of the chelator is to complexthe ferrousion and thus limit the concentration of free iron. Redox systems appear very versatile, permitting polymerization at ambient temperatures and the possibility of control of the rate of radical initiation versus polymerization time. This would thus permit control of heat generation and the minimization of reaction time. The use of the redox system ammonium persulfate (2 mmol) together with sodium pyrosulfite (Na2S20S 2.5 mmol) together with copper sulfate (0.002 mmol) buffered with sodium bicarbonate in 1 liter of water form an effective redox system for vinyl acetate emulsion polymerization. The reaction was started at 25°C and run nonisothermally to 70°C. The time to almost complete conversion was 30 min (Warson, 1976; and Edelhauser, 1975). The rational for the use of finishing initiators that have appreciable solubility in the polymer particJe follows. At high conversions, the concentration of monomer in the aqueous phase is very low and water-phase termination of hydophilic radical s becomes excessive. The rate of radical entry into polymer particJes is thus greatly reduced an,d the polymerization rate falls to a very low level prematurely.
E. Heat Removal
1. Techniquesfor Heat Removal An energy balance for a batch reactor may be written as V( - LlHp)Rp = UAw(T - Te)+ QE (40) As reactors are increased in size it is usually necessary to add supplemental heat removal capacity since the heat transfer area of the jacket only increases with reactor volume to the 0.67 power whereas heat generation rate increase is proportional to volume. Internal cooling coils and baffies are often used to increase heat transfer and in this way heat transfer area may be increased 40-50%. In some processes external heat exchangers are used where the reaction mixture is continuously pumped through the heat exchanger cooled and ret.urned. Reflux cooling is very effective in increasing heat removal capacity and is extensively used with large latex reactors. It is of interest to investigate the effect of reactor size on the magnitude of QE' The results of sample calculations indicate that for reactor volumes greater than 5000 gal additional cooling capacity would likely be required to achieve commercial production rates. 2.
Techniquesfor the Reduction of Reaction Time
To minimize the polymerization time, it is necessary that full utilization of the heat removal capacity of the reactor be made at all times during the
331
9. Latex Reactor Principies: Design. Operation. and Control
batch. In other words, the polymerization rate and associated heat generation rate should equal the heat removal capacity at all times during the batch. For an isothermal polymerization this can best be done by controlling the initiation rate using a redox system. Of course, the sinallest reaction time occurs with adiabatic polymerization. The temperature rise can be reduced by controlled heat removal to moderate the spread in molecular weights. Typical conversion and heat generation rate profiles for an isothermal polymerization with constant radical initiation are shown in Fig. 3. The heat generation rate over the batch is far from optimal as the maximum heat remo val capacity of the reactor is about 220 arbitrary units. The polymerization time could be significantly reduced by employing a higher initiation rate early in the polymerization and by letting it fall with time so as not to exceed a heat generation rate of 220 arbitrary units. A similar reduction in polymerization time could be achieved with semibatch monomer feed using monomer starvation to give a polymerization rate equal to Rpmax'A cold monomer feed would also assist in heat removal. The shortest batch time would be obtained using semibatch monomer feed giving Rpmaxand permitting the temperature to rise. In semibatch emulsion polymerizations the polymer particles are kept monomer-starved to obtain higher rates of polymerization and to permit easier control of the rate and particle size distribution. There are two aspects to the control of PSD. The controlled addition of emulsifier during particle growth stabilizes the particles without further particle nucleation. The second aspect is related to the particle sticky stage which often occurs 1.0
2.5
0.8
1.5 ~
0.6
"el. :J: <1 1.0 I
X 0.4
0.5
2
3
4
5
6
7
8
t (hrl
Fig. 3. Conversion and instantaneous heat generation rate for a typical isothermal batch emulsion polymerization.
332
A. E. Hamielec and J. F. MacGregor 5
.O
-
-
4
>C U Q) lit I
.. Q) ::
3
......
o E
2
Q. Q:
o
1.0
. 2.0
3.0
4.0
ff4] mol/ 1Iter 100
50 Conversion
Fig. 4. semibatch
J o
(%)
Polymerizationrate curve showingstable and unstable operating points for a
emulsion polymerization.
at intermediate conversion levels and certain polymerjmonomer concentrations. During the sticky stage wall fouling and formation of coagulum often occur. The use of semibatch operation under monomer-starved conditions effectively eliminates the sticky stage. To illustrate that it is easier to control a semibatch emulsion polymerization under monomerstarved conditions, consider the rate curve shown in Fig. 4. Point P1 at low monomer concentration is a stable operating point for semibatch feed of monomer, whereas P2 is unstable. A consideration of perturbations in monomer feed rate clearly illustrates this fact. Semibatch operations are commonly employed in copolymerizations to maintain a more uniform copolymer composition. The monomers are fed at rates equal to their consumption rates in the reactor.
9. Latex Reactor PrincipIes: Design, Operation, and Control
333
111. Continuous Stirred-Tank Reactors: Steady-State Operation
A. lntroduction In this section, emulsion polymerization in continous stirred-tank reactor(s) (CSTRs) operating at steady state will be treated, with emphasis on polymer quality, Le., molecular weight, long-chain branching, and polymer particle number and size distribution. The commercially important problems associated with oscillations in conversion (Le., particle number and size, weight average molecular weight, and long-chain branching) and their control will be considered in following sections. A single CSTR or a train of CSTRs may offer several advantages over batch reactors both with regard to production rate and polymer quality. The copolymer composition distribution obtained in a CSTR is generally narrower than that for a batch reactor. To obtain fairly narrow copolymer composition distributions without appreciable loss in productivity, one has the flexibility to increase the number of CSTRs in series to approach plug flow. Because of diffusion-controlled termination and propagation with concomitant Rpmaxat a particular conversion, it is possible to operate a CSTR at considerably higher production rates. Because of the additional beneficial effects of cold monomer and water feeds on heat removal, much higher production rates are possible than with a batch reactor of the same volume. It should be remembered that polymer production rates are usually limited by heat removal capacity. Quality variations in the polymer produced in batch reactors are often caused by slight vaI:iations in the reactor start up procedure. Furthermore, the polymerization rate may change considerably during the batch and this may give temperature variations that are difficult to reproduce causing batch-to-batch variations in quality. These problems would be minimized with CSTRs if the continuous reactor system could be operated for at least several weeks before wall fouling and coagulum build up become critical and require reactor shutdown for cIeanup. Ir an effective start-up procedure for a continuous reactor train is not available, the costs associated with offspec material' could make continuous operation uneconomical. In addition, with a continuous reactor system one loses the flexibility of batch reactors when a multiproduct operation, with its short productions runs, is involved. During start-up and operation of CSTRs there is a potential safety hazard created by the possibility of more than one stable steady-state
334
A. E. Hamielec and J. F. MacGregor
operating point (Ley and Gerrens, 1974). The start-up procedure should ensure that the desired steady state is reached.
B. Po/ymer Qua/ity 1. Particle Number and Size Distribution The frequency distribution of partic1e radius F(R) is. related to the exit age distribution E(t) with the identity F(R) dR
= E(t) dt
(41a)
which states that the number fraction of polymer partic1es in the exit stream of a CSTR train with radius in the range R to R + dR equals the fraction of fluid in the exit stream with age in the range t to t + dt. For a single CSTR F(R) dR
= rr1 exp( -
tlO) dt
(41b)
Equation (41b) is valid when there are no polymer partic1es flowing into the reactor with aIl the partic1es nudeated within the reactor. lt is assumed thar density changes can be neglected and that partic1es foIlow the streamlines. These are reasonable assumptions in view of the smaIl size of partic1es and the smaIl density difference between particIe and water. When two or more CSTRs are employed in series, however, one must remember that the total residence time of a polymer partic1e is made up of different times in each reactor in the train. The relative amounts of time spent in each reactor wilI not matter when the volumetric growth rate of a partic1e is the same in each. This would require that the temperature, monomer concentration, and average number of radicals per partic1e be the same for each reactor, an unlikely possibility. This idealization is useful, however, when ilIustrating the effect of increasing the number of CSTRs in series on the breadth of the partic1e size distribution. The exit age distribution function for N tanks in series is given by E(t) =
(~)((N ~ 1)!)(~r-1 exp(-tIO)
(42)
The change in partic1e radius with time is obtained as dRldt
= KñlR2
(43a)
where K = kp[Mp]MR/4nNAdp
(43b)
To solve Eq. (43a), a relationship between ñ and time or partic1e radius is required. The simplest situation is to treat Case 2 kinetics where ñ is
I
9.
335
Latex Reactor Principies: Design, Operation, and Control
independent of t and R and equals 1- Using ñ = 1, integrating Eq. (43a) and then substituting for t in Eq. (41b) for a single CSTR, one obtains the differential frequency distribution. F(R)
= (2R2/K()
(44a)
exp[ -(2/3K()R3J
and the cumulative frequency distribution cum F(R)
= 1-
(44b)
exp[ -(2/3K()R3J
In a similar manner the following PSD may be derived for Case 1 kinetics for a single CSTR (Friis and Hamie1ec, 1976). (45a) F(R) = K~() exp[ -(2~1() )R2 J cum F(R)
=
K 1
(45b)
= 1 - exp[ -C~I()
[
(4/3n)2/3 R,
kp[MpJMR
dp
)R2 J 1/2
(45c)
J[ 16n2NANpkáe J
The cumulative distribution for Case 2 kinetics [Eq. (44b)] is shown in Fig. 5 plotted for different values of the parameter K(). It is c1ear that the
0.8
~0.6
E
=' 0.4 u
4
8
R ( Al( Fig.5.
Cumulative
16
12
partic1e size distributions
20
24
10-3) for a single CSTR. Case 2 kinetics.
.
336
A. E. Hamielec and J. F. MacGregor
PSD broadens with increasing K(). For situations where a separate monomer phase exists, [Mp] is a constant independent of (/ and perhaps varying slightly with temperature. K will therefore depend on temperature alone and increase with an increase in kp. Thus, increase in temperature and () broaden the PSD. The PSD from a single CSTR is excessively broad for most applications and it is thus desirable to add additional CSTRs in the train to narrow the PSD. Eq. (42) shows the effect of increasing the number of CSTRs on the .exit age distribution which also narrows and approaches that of a plug flow reactor (PFR) (or a batch reactor). The narrowest PSD would be obtained in a PFR. The use of 5-6 CSTRs in series should give a PSD which is insignificantly narrower than that for a PFR. The total number of polymer particles per liter of emulsion (Np) in a single CSTR may be calculated by [S]o
-
[S]
Np
(4nNp/as) Loo R2F(R)
= ()R¡NA
(
as[S]
Ap
dR
(46)
=O
)
[S]
+ aseS] = ()R¡NA [S]o
(47)
The last term in Eq. (46) gives the amount of emulsifier covering the polymer particles in the exit stream. Equation (47) is obtained by equating the rate of particle outflow to the rate of particle nucleation within thé
reactor employingthe collisiontheory. For Case 2 kinetics N p is givenby ()R¡NA Np
(48)
= 1 + NAR¡(4n/as[S]0)(3K/2)2/3()S/3r(5/3)
This equation is identical to the one derived by Gershberg and Longfield (1961). Equation (48) is shown graphically in Fig. 6. It appears that for a
Q. Z
10 81hrl
Fig. 6.
Number of polymer particles as a function of emulsifier and initiator levels for a
single CSTR. Case 2 kinetics.
9.
Latex Reactor Principies: Design, Operation, and Control
337
given set of operating conditions there is a O which gives a maximum Np. Npm.xhas been observed experimentally by Veda et al. (1971) and Nomura et al. (1971) for continuous styrene emulsion polymerization. Gerrens and Kuchner (1970) have furthermore confirmed the zero-order dependence on initiator, the first-order dependence on emulsifier at long residence times, and that Np oc 0-2.3 at large O. The mechanisms of particle nucleation for commercial monomer systems such as vinyl acetate, vinyl chloride, methyl acrylate, and chloroprene have not been as extensive1y studied experimentally as has styrene. It is likely, however, that an Npmaxwould occur with these more complex systems and this fact should be considered when designing a reactor train with high volumetric efficiency (Nomura, 1980). 2.
Molecular Weight and Long-Chain Branching
For the calculation of molecular weights in CSTR emulsion reactors, a useful classification comes to mind. This includes those monomer systems whose molecular weight and branching development depends on particle size and those that do no1. Styrene falls into the former class and vinyl chloride and vinyl acetate into the latter class. Thus, in vinyl chloride emulsion polymerization where LCB is neglected, the instantaneous molecular weight distribution is given by W(M)
= (MjM~)
exp(-MjMN)
(49) -1
=
M N
1.fJ: 2
W
=M
(
krm + krx[xJ
R kp.
kp[M]
)
It should be noted that at high conversions some branched PVC may form and it may therefore be necessary to consider the transfer to polymer reaction (Hamielec et al., 1980b). When transfer reactions control molecular weight development, all polymer particles in the first CSTR in the train will have the same molecular weight distribution (MWD) (neglecting inflow of polymer particles) given by Eq. (49). It there is no CTA and each reactor in the train is at the same temperature then the MWD will be the same in all the reactors in the train. Ir a CT A is employed for an isothermal train, the contribution from the CT A will increase in downstream reactors as the monomer concentration falls, and therefore molecular weight averages will fall. Of course, the MWD in each reactor will be of the same form and given by Eq. (49), but the final whole polymer will be a composite of the polymer produced in each reactor. This can be easily calculated if the conversion in each reactor is known. It should be remembered that less than one CTA molecule is consumed per polymer chain and therefore the CT A consumption by reaction can often be neglected.
338
A. E. Hamielec and J. F. MacGregor
With vinyl acetate the situation is more complex since transfer to polymer and terminal double bond reactions are significant at all conversion levels. If one calculates the MN, Mw, and BNfor a nucleated polymer particle with different lifetimes in a single CSTR, it is found that these quantities are independent of the particle age and are given by
M = MR N.
Mw
CM
where
~
1
KWp
(50)
p
2
KW 2MR 1 + 1 -
-
( = ~ (c
BN
( + 1- W ) (
1
~)
M+1-W
Wp
)(
p
1-W
CpMn
+K
MR
(51)
p
CpWp- 2CpWp 1 p
)(
K~
+l-W
p
)
)
(52)
is the weight fraction of polymer in the polymer particle. Friis et
al. (1974) have measured the following parameters for vinyl acetate using batch emulsion polymerization. kp = 1.89 x 107 exp(- 5650/R T) krm= 3.55 x 106exp(-9950/RT) krp = 1.430 x 106exp(-9020/RT) (k:)o = 1.07 x 107 exp(-5650/RT)
liter/mol sec liter/mol sec liter/mol sec liter/mol sec
(53)
For Wp> 0.2, a decrease in k: was observed and this decrease is given by
k: = (k:)o - (l69.6~ + 479.9W; + 1014.0W;)
(54)
At 60°C with a conversion of 60% in a single CSTR, BN= 4.86 long branches per polymer molecule. Increasing the number of equal-sized CSTRs in series so as to approach plug ftow (or batch reactor) behavior, one would obtain a BNof about 1.5 long branches per polymer molecule. In other words the long-chain branching frequency can be greatly reduced by increasing the number of CSTRs in a train. This is clearly the strategy that is used for the production of SBR and polychloroprene. Even with a CSTR train it is necessary to limit the conversion to keep branching at a low level. C.
Optima/ Reactor Type and Operation lor Continuous Emu/sion Po/ymerization
This section is a review of a recent paper by Nomura (1980) who has made some interesting suggestions about the design and operation of
9. Latex Reactor Principies: Design, Operation, and Control
339
continuous latex reactors with stable operation at steady-state conditions. The conventional CSTR train is operated with a11the recipe ingredients being fed into the first reactor and the product latex removed from the last reactor in the train. For a given production rate, the size and cost of the CSTR train can be reduced by maximizing the nuc1eation of polymer partic1es in reactor one. This can be done by increasing the emulsifier and initiator concentrations in the feed stream and by lowering the temperature of the first reactor. The use of higher emulsifier levels may have deleterious effects on the polymer product, however, Other techniques of maximizing the number of polymer partic1es in the first reactor are given. The optimal choice of mean residence time will give Npm.xas already discussed earlier in this chapter. Another approach to increasing the number of polymer partic1es early in the train is to use a plug flow type reactor (PFR) as reactor one. A larger number of polymer partic1es can be produced in a PFR than in a CSTR at the optimal value of (J.The volume of the PFR could then be reduced substantia11y by reducing monomer in feed and feeding rest of the monomer into reactor two. It is also c1aimed that a PFR as first reactor in the train would substantia11y reduce oscillations and thus increase the stability of operation of a CSTR train. These design and operation suggestions by Nomura are based on calculations performed with a steady-state model. More realistica11ythe design, operation, and control of a CSTR train of latex reactors should be based on calculations with a transient CSTR model. This subject will be considered in the fo11owingsections.
IV.
Continuous S~rred-Tank Reactors: Dynamic Behavior
A. lntroduction Continuous emulsion polymerization is one of the few chemical processes in which major design considerations require the use of dynamic or unsteady-state models of the process. This need arises because of important problems associated with sustained oscillations or limit cyc1es in conversion, partic1e'nlJmber and size, and molecular weight. These oscillations can occur in almost a11commercial continuous emulsion polymerization processes such as styrene (Brooks et al., 1978), styrene-butadiene and vinyl acetate (Greene et al., 1976; Kiparissides et al., 1980a), methyl methacrylate, and chloropene. In addition to the undesirable variations in the polymer and partic1e properties that will occur, these oscillations can lead to emulsifier concentrations too low to cover adequately the polymer partic1es, with the result that excessive agglomeration and fouling can occur. Furthermore, excursions to high conversions in polymer like vinyl acetate
340
A. E. Hamielec and J. F. MacGregor
and styrene-butadiene where transfer to polymer reactions are important can lead to excessive long-chain branching and thereby result in poor processability of the rubber. Although these oscillations can be avoided by operating at sufficiently high emulsifier concentrations, the concentrations needed are often high for most commercial processes. Even if, under the conditions used, a nonoscillatory steady-state exists, it is not unusual that during start-up or other disturbance transients an oscillation is induced which qamps out only very slowly (20 or more residence times). Furthermore, oné is never certain whether steady-state models actually apply in any given situation unless one either has experimental confirmation or verifies it by first solving a dynamic model.
B.
A Dynamic Model Based on Age Distribution Functions
In this section we consider a model for the continuous emulsion polymerization of vinyl acetate based on one presented by Kiparissides et al. (1978). Latex properties such as average particle size, number of particles, total particle surface area and volume, molecular weight averages, and average number of long-chain branches per molecule will be considered. The approach is similar to that used by Dickinson (1976) and focuses on the residence time or age distribution of particles in the reactor rather than on the size distribution. The latter approach (Min and Ray, 1974) has recently been used successfully by Min and Gostin (1979) to model the semibatch emulsion polymerization of poly(vinyl chloride)~ However this approach could lead to difficulties in modeling reactors where the growth rate of a particle is not only dependent on its current size and . the current conditions in the reactor but also on the conditions prevailing during its previous history. Using an age distribution approach if we define the function n(t, -r)d-r to be the number of particles in the reactor at time t that were born in the time interval (-r,-r+ d-r),and p(t, -r)tobe a property of the latex associated with this cIass of particles, then the total property P(t) = J~ p(t, -r)n(t,-r)d-rfor all particles in a CSTR reactor will be given by dP(t) -=--+ dt
P(t) ()
1 op(t, -r) ) ( t) + f( tpt -nt ( -r) d-r , ' 1o ot
(55)
where () is the reactor residence time and f(t) is the net rate of particle generation in the reactor. Using this equation, property balances for the total number of particles, the total diameter, the area and volume of
9.
341
Latex Reactor Principies: Design, Operation, and Control
partic1es,and the conversion can be written as follows (Kiparissides et al., 1978; Chiang and Thompson, 1979): dN(t) = - N(t) + f(t) dt ()
(56)
dD (t) --f¡-
(57)
D (t)
= ---t-
+ 2~(t)N(t) + dp(t,t)f(t)
dAp(t) + 4nW)Dp(t) + tIp(t,t)f(t) dt = - A~(t) (7 dVit) dt
=-
dX(t) -¡¡¡-
= (1 - e-I/6){
V~t) (7
(58)
(59)
+ ~(t)Ap(t) + vp(t,t)f(t)
1
- X(t) ()
+ Rp(t)
(60)
[MFJ }
The exponential term in the conversion equation arises from the assumed start-up condition of a reactor filled only with degased water and then fed at time zero with a stream having monomer concentration [MFJ. Assuming both micellar and homogeneous nuc1eation the partic1e generation ratef(t) can be written as (61) and following Fitch and Tsai (1971), the homogeneous rate constant is assumed to decrease with partic1e area as k.h= kho(1- ApL/4). Applying the stationary-state hypothesis to the radical balance gives the radical concentration in the wáter phase as (62) where the rate of appearance p(t) of free radicals in the water phase is given by
(63) Assuming that radical termination takes place exc1usively in the polymer partic1e,the average number of radicals in a partic1eof volume vp(t,-r)can be obtained as (Ugelstad and Hansen, 1976) q(t, -r) =
[
R
1 2kde(t, -r)n(t,-r)d-rJ
1/2
a (t -r) n(t -r) d-r
[
p"
Ap(t)
J
1/2
(64)
342
A. E. Hamielec and J. F. MacGregor
Using Eq. (14) the desorption rate constant can be expressed as kde(t, ,) = kge/ap(t, ,) which when substituted
into Eq. (64) yields
-
q(t,,)
-
-
R,
1/2
[
2kodeJ
1/2
a;(t,')
[
A p(t)
J
(65)
Substituting these i~to Eq. (63) and integrating gives p(t) = R,(t) + (!kgeR,)1/2(N(t)/A~/2(t))
(66)
The partic1e generation rate f(t) can now be evaluated using Eqs. (61), (62), and (66),in conjunction with the property balance equations (56-60). The rate of polymerization Rp [see Eq. (2)] can be expressed here as Rp(t) = (kp[Mp]/NA) LtJ(t,,)n(t,,) d, = (kp[Mp]/NA)(RJ2kge)1/2 A~/2(Ó
(67) (68)
The time function ~(t) in the property balance equations (57-59) is given by kpdm R, ~(t) = NAdp 2kge
1/2
( )
1
cI>m(t)
A~/2(t) 1 - cI>m(t)
(69)
where cI>m(t) is the monomer volume fraction in the polymer partic1es given earlier in Eq. (23). The property balances must be coupled with the balances for the initiator and emulsifier given, respectively, by d[1]/dt
= e-1([1F]- [1]) - R,
(70)
where R, = 2fkd[1], and
d[S]/dt = e-1([SF] - [S])
(71)
The micellar area Am(t) needed in Eqs. (61) and (62) can then be obtained as Am(t) = ([S]
-
[Scmc])as- Ap(t)
(72)
where as is the coverage area of 1 mole of emulsifier.
The set of simultaneous nonlinear differentialequations defined by Eqs. (56-60) and Eqs. (70)and (71)therefore provides a dynamic model for the total latex properties of PV Ac being produced in a single eSTRo This model has been shown to provide an excellent representation of the conversion-time experimental data of Greene et al. (1976) under conditions of sustained oscillations (see Fig. 7) and of the extensive data of Kiparissides et al. (1980a,b) under both steady-state and sustained-oscillation conditions
343
9. Latex Reactor Principies: Design, Operation, and Control
30
t520 ¡¡;
Q: ILI
~ 15 o
<..>
10 1]= 0.005
2
4
6 8 10 12 14 DIMENSIONLESS TIME (t / e)
16
18
20
Fig. 7. CSTR conversion transients. Comparison between experimental results of Greene et al. (1976) and model predictions. Model (---): Greene's experimental results (-0-0-).
using sodium lauryl sulfate as an emulsifier and potassium persulfate as initiator. Figure 8 illustrates the behavior of the number of particles, the particle area, and the free soap or micellar area predicted by the model for one of Greene's runs. The reasons for the s4stained oscillation phenomenon are quite apparent from these figures. In periods where kmAm or khO(1 - ApL/4) are greater than zero, rapid generation of particles occurs leading to a large surface area and the subsequent depletion of free emulsifier. Micellar particle nucleation therefore stops and, with the explosive increase in particle are a (Ap), so does homogeneous nucleation. There follows a long period, the duration of which depends on the emulsifier feedrate and residence time of the reactor, in which particles are not generated. However, as the washout of existing particles continues, the emulsifier concentration builds up again to exceed the CMC, and a new .generation of partÍcles is formed. This periodic nucleation leads to the formation of discrete particle populations with concomitant oscillations in polymerization rate, conversion, and latex properties. In other situations where the emulsifier feedrate to the reactor is sufficient to produce a steady-state concentration in the CSTR that is above the CMC, one observes damped oscillations upon start-up followed by an eventual attainment of a steady-state, nonoscillatory condition (Kiparissides
et al., 1980a,b).
344
A. E. Hamielec and J. F. MacGregor
2.0 re TQ .. ..... .. ...
= 1.5 ...... C/) UI
.J o ~
~
1.0
el. la. O a: UI m :!! 0.5 :) z .J
~ O
1-
O O
2
4
6 8 10 12 14 DIMENSIONLESSTIME (tIa)
16
18
Fig. 8. CSTR transients.Model predictions for number of particles, free emulsifier concentration and total particle surface area. 6 = 30min, 1 = 0.01molJliter,S = 0.01molJliter, MjW = 0.43.
C.
Cons;derat;on 01 Dynam;cs ;n Reactor Des;gn
These unsteady-state experiments and the dynamic models developed to explain the observed behavior ha ve a number of important implications for the design of continuous emulsion polymerization reactor trains. In order to avoid this oscillation phenomenon and the varying latex quality that results from it, one should not design continuous flow stirred-tank reactor. trains along previous lines, namely with a number of equal or nearly equalsized CSTRs in series with all the feed streams of the receipe entering the first reactor. Most continuous industrial systems designed in this manner exhibit oscillations in the early reactors of a magnitude comparable to those shown in Fig. 7. Although the oscillations may be largely damped out by the later reactors in the train certain inhomogeneities will exist in the latex. A common industrial practice used to avoid oscillations is to seed the first reactor with small-diameter seed particles produced earlier in batch reactors. By then keeping the emulsifier concentration below the CMC one avoids further micellar generation and simply grows the seed particles. Although in some cases this may introduce additional flexibility in that a
9.
Latex Reactor Principies: Design, Operation, and Control
345
cheaper or otherwise more desirable polymer may be used for the seed partic1es, it usually results in costlier operations resulting from the need for batch reactors to produce the seed partic1es. This oscillation phenomenon, however, can be avoided quite easily without the need for seeding. By employing as the first reactor in the train a small, optimally sized CSTR reactor and splitting the emulsifier, initiator, water, and monomer feeds to enter at various points along the train it is quite possible to ensure that all partic1e generation occurs in the first small reactor under nonoscillatory or steady-state conditions, followed only by growth of these partic1es in the subsequent reactors (Pollock, 1981; Nomura, 1980). As a simple illustration one could feed most of the emulsifier to the small first CSTR "seeding" reactor along with part of the initiator and part of the water and monomer, thereby ensuring continuous partic1e generation in condition of excessemulsifier. By feeding much of the remaining water and monomer to the second reactor, the emulsifier is diluted to a value below the CMC at which partic1e generation is avoided and partic1e growth only is promoted. A good dynamic model is the key to sizing the reactors determining an optimal split of the feed streams. As will be discussed later, the dynamic model is also the key to designing an on-line monitoring and control system that will ensure that the desired conditions of latex quality and quantity are maintained. It is also possible, and in some cases more desirable,to use a continuous
tubular reactor as the first "seeding" reactor (Nomura, 1980). Oscillations should not be a problem in such a reactor, but reactor fouling might be a more important consideration.
V. On-Line Control of Continuous Latex Reactors
A. Introduct;on As indicated above a number of fundamental control problems with cOQtinuous emulsion polymerization reactors are associated with the initial .
reactor systemdesign,and such problems should, therefore,be solved at the design stage. However, even with an efficient design some on-line monitoring and control are needed to ensure that the design conditions are indeed being maintained in the face of numerous disturbances which can affectthe system.In this section we first consider some of the on-line instrumentation and techniquesfor monitoring reactor condition, and then we look at some of the techniques that are being used fOr"the control of polymer latex properties in these reactors.
346 B.
A. E. Hamielec and J. F. MacGregor
On-Line Instrumentation
The most useful on-line instruments would be those capable of measUfing the latex properties given in Eqs. (56-60), the free soap concentration (Am), and some molecular weight characteristics. In this section we will not attempt on exhaustive survey, but will only concentrate on a few of the more rugged and more promising on-line measurements that have been used.
1. Reactor Heat Balances One of the earliest attempts at monitoring the progress of emulsion polymerization reactors was to perform an on-line enthalphy balance around the reactor or the reactor cooling jacket in order to monitor the heat release by reaction. Using temperature measurements in the reactor, in the cooling jacket entrance and exit, and at any ~ther essential points, together with relevant cooling water flows one can perform steady-state or unsteady-state enthalpy balances using an on-line minicomputer. From the computed rate of heat release, the rate of reaction can be evaluated, and the conversion in the reactor can be followed using Eq. (60). A major problem in successfully implementing this scheme is to overcome the effects of the numerous measurement errors that propagate into the ca1culated reaction rate and conversion. For any given situation a simple propagation of error analysis will reveal the precision possible. Usually, significant filtering of the measurements is necessary in order to obtain worthwhile results. Two approaches are possible, both requiring an on-line mini- or microcomputer. In the first approach instantaneous steadystate balances can be performed over short periods using averaged or filtered values of many measurements. Alternatively, less-frequent measurements can be utilized with the unsteady-state balance equations in the form of a Kalman Filter (Astrom, 1970; Jazwinski, 1970). 2. Density A number of fairly rugged on-line instruments are available to follow the emulsion density variations. Examples include nuclear instruments and instruments based on mechanicaloscillator techniques(Kratky et al., 1973). By utilizing the density difference between the unreacted monomer and the polymer (providing a reasonable difference exists) the reactor conversion ca,n then be ca1culated via
x = (Pe- p~)/(p:oo- p~)
,
9.
347
Latex Reactor Principies: Design, Operation, and Control
where the emulsion densities at O and 100% conversion (p~ and be approximated
P:OO)
may
by the weighted averages
o_
Pe
{' - 1.mPm + JwPw
100 _ Pe - 1.mPp
{'
+ JwPw
Here fm and fw are the feed stream weight fractions of monomer and water, and Pm, Pw, and Pp are the densities of, respectively, monomer, water, and polymer. Using the new on-line densitometers which rely on vibrational frequencies, a precision of approximately :t 0.5% on conversion can be reasonably attained in the polymerization of methyl methacrylate (Schork and Ray, 1980) or vinyl acetate (Pollock, 1981).
3. Turbidity Spectra Light transmission has been a standard method for the measurement of the size of spherical particles for many years. Mie and Rayleigh scattering theories show how the measured turbidity can be related to particle diameter and number. In the Mie regime (1 < nD/Am < 10) information on the number of particles and the size distribution could be obtained, particularly if used in conjunction with other instruments such as a densitometer (Maxim et al., 1969). In the Rayleigh regime (nD/Am< 1) only a turbidity-average particle diameter is easily obtained. From the point of view of on-line process measurements, turbidity instruments are rugged and have been demonstrated to follow easily the oscillations in average particle diameter in continuous emulsion polymerizations (Kiparissides et al., 1980a). For example, Fig. 9 shows a plot ofthe absorbance at 350 nm and the 0.4 o~ o o
10 0.31<')
o;t 3000 a:
~
IIJ 1IIJ ~ 2000 ~ iS IIJ ..J U ¡: 1000 a: ~ Q.
w u 0.2~ al a: o 0.1
2
4
6
e
10
12
14
(f) al ~
o 16
DIMENSIONLESS TIME (t181
Fig. 9.
Particlediameterand absorbancemeasuredduring the production of poly(vinyl
acetate) in a eSTRo O = 20 min; 1
= 0.01
mol/liter;
S
= 0.01
moljliter.
348
A. E. Hamielec and J. F. MacGregor
average particle diameter as determined by size-exclusion chromatography measured on poly(vinyl acetate) latices being produced under conditions of sustained oscillations in a single eSTRo 4.
Surface Tension
Recently, Schork and Ray (1980) developed an on-line tensiometer based on the maximum blibble pressure technique and demonstrated its usefulness in following surface tension in methyl methacrylate batch-emulsion polymerization. The value of this surface tension measure for monitoring emulsion polymerization reactors lies in being able to combine it with a measure or knowledge of the monomer concentration in the water phase to give a measure of the free emulsifier concentration (Am) in the water phase. As discussed previously (Sections IV,B and C), the free emulsifier concentration Am is of the utmost importance in the dynamics of particle generation in continuous emulsion polymerizations, and being able to monitor it on-line would be a very important step ip.the control of these reactors. C.
On-Line Estimation
Realistically, one could never hope to have on-line measurements of all tge major properties of lnterest but would have to rely perhaps on one or two of the above. However, herein líes the utility of a good dynamic model for the process, in that, by using the measurements that are available, the remaining properties or states of the system can be inferred froIDthe on-line solution of the model equations. Such state estimation can be accomplished by using an extended Kalman Filter (Jazwinski, 1970), which essentially combines the model equations with the measurements to yield a set of recursive equations providing estimates of all the states. The state measurements that are made serve to keep the model tracking those particular states closely, thereby forcing reasonable estimates of the other states, providing the model is good. Using an earlier version of the dynamic model given in Section IV,B, Kiparissides et al. (1980b) illustrated the use of such an extended Kalman Filter to infer N(t), Vp(t),Ap(t), and X(t) from measurements taken only on conversion [X(t)] using UV turbidity spectra. Jo and Bankoff (1976) used these filters to track some of the moments of the MWD of PVAc in a solution polymerization process using measurements made on refractive index and viscosity.
9. Latex Reactor Principies: Design. Operation. and Control D.
349
On-Line Control
A number of different approaches to the computer control of emulsion polymerization reactors can be taken, depending on the level of modeling and control theory sophistication one wishes to use. Most batch or semibatch emulsion polymerization control systems consist of a preprogrammed recipe addition, a start-up and shut-down scheduler, temperature and pressure controls, and perhaps a heat balance control for reaction rate (Amrehn, 1977), but no feedback control on the latex properties. ExactIy what can be done in the way of feedback control in these systems is an area of current research. One is essentiaIly limited by the fact that most of the particIe generation occurs in the first 5 to 15 min and there is very little one can do over the remainder of the batch to compensate for things that went wrong at this stage. In continuous reactor trains particIe generation is continuous, or at least periodic, and it can be monitored and adjustments can be made in the recipe ingredient ftows to the system and in their splits between the various reactors of the train. Two possible approaches are discussed below. 1. Advanced Control Based on Theoretical Dynamic Models To ilIustrate this approach we consider the emulsion polymerization of vinyl acetate in a single eSTRo The dynamic model given by Eqs. (56-60), and Eqs. (69) and (70) can be represented more concisely by the set of nonlinear differential equations
. dx(t)/dt
= f[x(t), u(t)] + w(t)
(73)
where the vector of states x = (N, Dp, Ap, Vp,X, 1, S)Tand the vector of manipulatable variables u = (IF, SF)' The vector of measurements can be expressed generaIly as y(t) = f[x(t), u(t)] + v(t)
(74)
where the vector y(t) and the function f[x(t), u(t)] wilI depend upon which on-line instruments are available. The vectors x(t) and w(t) represent, respectively, measurement noise and process disturbances arising from other variations in the process not accounted for in the modeI. The variance-covariance structure of these noise sources can be identified from process data taken from the system. Using this model of the reactor system, usuaIly discretized for some sampling interval, near-optimal control algorithms can be formulated which
350
A. E. Hamielec and J. F. MacGregor
will manipulate the input vector at time instant (UI)'in such a way as to try to optimize some performance index involving the system states (XI)and the manipulations (UI)over some interval of time. The most commonly chosen performance index is the quadratic one N
J(x,u)= E
L [(XI 1=1
Xdes)TQl(XI
-
xdes)
+ (UI-l- Udes)TQiul-l- Udes)]
where E denotes the expectation, xdes and Udesare the desired operating levels, and Ql and Q2 are positive semidefinite matrices. For example, this would inelude the case where it is desired to minimize a weighted sum of the mean squared errors of the states about their desired values subject to a constraint on the magnitude mean squared errors of the manipulated variables about their target values. Kiparissides et al. (1980b) illustrated the use of this approach, using a simulation of their single CSTR for the emulsion polymerization of VAc. They looked at control during reactor start-up, during switching from one operating condition to another, and at trying to reduce the magnitude of the oscillations in partiGR: properties while operating in the oscillation region (i.e., at low emulsifier concentrations). Note that in the latter situation one cannot entirely eliminate the oscillations since partieles must be generated sometime. To implement such near optimal control algorithms would require considerable space and time on a process minicomputer because of the severe nonlinearities in the process, and therefore it is probably impractical in most situations. However, off-line simulations of this control policy shows some upper-limits as to what could possibly be accomplished and the nature and magnitudes of the feedrate manipulations that are necessary. This can then lead to the development of simpler heuristic-type control algorithms which capture the important aspects of the optimal control but are more easily implemented on-line. Some simpler approaches to conversion control using material and energy balances on a train of CSTRs are described by Amrehn (1977).
2. Control Based on ldentified Empirical Models In some situations where one or more of the latex properties are measured either directly or indirectly through their correlation with sur. rogate variables and where extreme nonlinearities such as the periodic generation of polymer partieles does not occur, one can use much simpler modeling and control techniques. Linear transfer function-type models can be identified directly from the plant reactor data. Conventional control devices such as PID controllers or PID controllers with dead-time compensation can then be designed. If process data is also used to identify
9. Latex Reactor Principies: Design, Operation, and Control
351
models for the disturbances in the system, optimal controllers can also be developed (Box and Jenkins, 1970; Astrom, 1970). MacGregor and Tidwell (1979) iIIustrate some of the steps involved in running plant experimentation, building these process and disturbance models, and implementing simple optimal controllers on some continuous condensation polymerization processes. A number of similar applications to continuous emulsion polymerization processes have also been made. VI.
Summary
In this chapter an attempt has been made to review the state of the art of the design, operation, and control of latex reactors and to introduce some promising new approaches to the design of latex reactor trains using dynamic models. Highly sophisticated dynamic models which can accurately predict particIe number and size distribution and also molecular weight averages and long-chain branching frequency are being developed. These dynamic models should permit the design of a new generation of commerciallatex reactor systems. Nomenclature as ap(t,T) Ap, Ap(t) Am Aw A,B a,b BN CM,Cp, K dM dp dp(t,T) !?)w !?)p DpDp(t) E E(t) F(R) fm.!", f(t) [l] [/]0 [/F]
area occupied by an emulsifier molecule area of polymer particles born at time T arid present at time t total area of polymer particles per liter of latex total area of micelles per liter of latex jacket heaf transfer area parameters in Eqs. (19) and (20) parameters in Eq. (21) number average number of long branches
per polymer molecule
kinetic parameters defined by Eq. (28) monomer density polymer density diameter of polymer particles born at time T and present at time t diffusion coefficient of monomer transfer radicals in the water phase diffusfon coefficient of monomer transfer radicals in polymer particles total diameter of polymer particles per liter of latex éxpectation operator exit age distribution function frequency distribution of polymer particle radius weight fractions of monomer and water in feed stream particle nucleation rate initiator concentration initial initiator concentration initiator concentration in feed
352 K KI kp k,p k,w krm kfx krp k*p
.
k,o k. k~. kd. km kv kh L m M MR MN Mw Mw., [MpJ [MFJ Np NA Nn NMo NM
N,N(t) n ñ . n(t, t) dt p{t, t) P(t)
A. E. Hamielec and J. F. MacGregor defined in Eq. (43b) defined in Eq. (45b) propagation constant in the polymer particles termination constant in the polymer particles termination constant in the water phase rate constant for transfer to monomer rate constant for transfer to chain transfer agent rate constant for tran~fer to polymer rate constant for terminal double bond reaction terminatÍon constant when reaction is chemically controlled rate constant
for radical
absorption
into
a particle
of radius
v
defined in text kd.(t, t) is the.rate constant for radical desorption from a particle of volume v (or born at time t and present time t) rate constant for micellar particle generation volume of particle phase over volume of water phase rate constant for homogeneous particle generation distance a radical will dilfuse before precipitating partition coefficient in Eq. (14) molecular weight monomer molecular weight number average molecular weight weight average molecular weight weight average molecular weight when termination
becomes dilfusion controlled
monomer concentration in the polymer particles in GmolJliter monomer concentration in the feed number of polymer particles per liter of latex Avogadro's number number of polymer particles containing n radicals(n ~ O) initial moles of monomer moles of monomer at time t number of polymer particles per liter of latex number of radicals average number of radicals per particle number of particles born at time t and present at time t property associatedwiththe n(t,,) d, total property
class of
particles
Qo, Ql' Q2 Ql'Q2 QE ij(t, t)
zeroeth, first, and second moments of the molecular weight distribution are positive semidefinite matrices in the control performance index heat removed by coils, condenser or other device
Rpp RI
monomer
Rp Rpma. R
[8]0
polymerization rate in Gmoljsec liter latex maximum polymerization rate polymer particle radius and gas constant radical concentration in water phase concentration of emulsifier initial concentration of emulsifier
[SmJ
concentration of emulsifier present as micelles
[KJw [8]
average number of radicals in particles born at time, present at time t consumption
rate in Gmoljsec
particle
rate of initiation of radicals in the water phase in Gmolejsec liter latex
9. Latex Reactor Principies: Design, Operation, and Control [Sp] [SCMcJ T T. t tr Tam,1'.p U u" u(t) Vp VF VFe" VF.., Vp(t,T) V V(t)
concentration concentration
of emulsifier adsorbed of emulsifier at CMC
353
on polymer partic1es
absolute temperature, polymerization temperature coolant temperature polymerization time time to the end of Stage I are glass transition temperatures for pure monomer overall heat transfer coeffici¿nt
and polymer
vector of manipulatable variables (Ud.. is desired operating level) volume of polymer partic1es per liter of latex free volume fraction free volume fraction when termination becomes diffusion controlled
-
~ W(M) W(t) X X. [X] x"x(t) y(t) c<,o:l,m,Y
Cl «1>m,«1>m(t) «1>p, «1>p(t)
S(t) f1 T lJ
P., p~, p:OO p' p(t) -ÓHp IN
free volume fraction when propagation becomes diffusion controlled volume of latex partic1es generated time T and present at time t volume of latex, reactor volume vector of measurement noise weight fraction polymer in polymer partic1es weight fraction of polymer of molecular weight M vector of process disturbances monomel' conversion monomer
conversion
at the end of Stage 11
concentration of chain-transfer agent in polymer partic1es vector of states (xd.. is the desired operating level) vector of measurements kinetic parameters defined in Eq. (8) differences between coefficients of volumetric expansion above (polymer and monomer) exponent in model for diffusion-controlled termination [Eq. (19)] volume fraction monomer in polymer partic1es volume fraction polymer in polymer partic1es. defined in text
and
below
1'.
volumetric growth rate time of birth of a polymer partic1e defined by. Eq. (14a) emulsion densities (defined in text) is the total radical entry rate into polymer partic1es of volume v per liter of latex rate of appearance of radicals in the water phase heat of polymerization is the number average number oflong branches per 1000 monomer units
References Amrehn, H. (1977). Automatica 13, 533-545. Astrom, K. J. (1970). "Introduction to Stochastic Control Theory." Academic Press, New York. Box, G. E. P., and Jenkins, G. M. (1970). "Time Series Analysis, Forecasting and Contro1." Holden Day, San Francisco. Brooks, B. W., Kropholler, H. W., and Purt, S. N. (1978). Polymer 19, 193-196.
354
A. E. Hamielec and J. F. MacGregor
Chiang, A., and Thompson, R. W. (1979). Am. Inst. Chem. Eng. J. 25, 552-554. Dickinson, R. F. (1976). Ph.D. Thesis, Univ. ofWaterloo. Edelhauser, H. (1975). In "Polymer Norway.
Colloids."
NATO Advanced
Fitch, R. M., and Tsai, C. H. (1971). In "Polymer Plenum Press, New York. Friis, N., and Nyhagen, Friis, N., and Hamielec,
Colloids"
Study lnstitute,
Trondheim,
(R. M. Fitch, ed.), pp. 103-115.
L. (1973). J. Appl. Polym. Sci. 17, 2311-2327. A. E. (1975). J. Appl. Polym. Sei. 19,97-113.
Friis, N., ap.d Hamielec, A. E. (1976). In Polymer Reaction Engineering-Principles ofPolyrner Reactor Design. McMaster Univ. Professional Development Course. Friis, N., and Hamielec, A. E. (1976). In" Emulsion Polymerization" (l. p¡irma and J. L. Gardon. eds.), (Am. Chem. Soco Symp. Ser.) Vol. 24. pp. 82-91. Friis, N., Goosney, D., Wright, J. D., and Hamielec, A. E. (1974). J. Appl. Polym. Sci. 18, 1247-1259. Gerrens, Gerrens,
H. (1959). Fortschr. Hochpolym. Forsch. 1, 234-246. H., and Kuchner, K. (1970). Br. Polym. J. 2, 18-30.
Gershberg, AIChE Gilbert,
D. B., and Longfield, Preprims.
R. G., Napper,
J. E. (1961). In Polymerization
Kinetics and Catalyst
D. H., Lichti, G., Ballard, M., and Sangsterr
Systems.
D. F. (1980). In Emulsion
Polymerization, pp. 527-530. Am. Chem. Soco Preprints, Las Vegas. Greene, R. K., Conzalez, R. A., and PQehlein, G. W. (1976). In "Emulsion Polyrnerization" (l. Piirma and J. L. Gardon, eds.), pp. 341-358. Am. Chem. Soco Ser. 24, Washington, D.C. Hamielec, A. E., and Marten, L. (1980a). In "Emulsion Polyrnerization," pp. 515-519. Am. Chem. Soco Preprints, Las Vegas. Hamielec, A. E., Gomez-Vaillard, R., and Marten, L. (1980). Diffusion-controlled free radical polyrnerization-effect on polymerization Symp., 3rd, Cleveland, Ohio. Jazwinski, York.
A. H. (1970). "Stochastic
rate and molecular
Processes
and Filtering
properties
Theory."
of PVC, 1m. PVC
Academic
Press, New
Jo, J. H., and Bankoff, S. G. (1976). Am. Inst. Chem. Eng. J. 22, 361-369. Kiparissides,
c., MacGregor,
J. F., and Hamielec, A. E. (1978). J. Appl. Polym. Sci. 23, 401-418.
Kiparissides, C., MacGregor, J. F., and Hamielec, A. E. H. (1980a). Can. J. Chem. Eng. 58,48-71. Kiparissides, (5).
c., MacGregor,
J. F., and Hamielec,
A. E. H. (l980b).
Am. Inst. Chem. Eng. J. 26,
Kratky, O., Leopold, H., and Stabinger, H. (1973). Methdds Enzymol. 27, 98-110. Ley, G., and Gerrens, H. (1974). Makromol. Chem. 175, 563-575. Lichti, G., Gilbert, R. G., and Napper, D. H. (1977). J. Polym. Sci. 15, 1957-1969. Lichti, G. (1980). PhD Thesis, Univ. of Sydney.
MacGregor, J. F., and Tidwell, P. W. (1980). In "Computer Application to Chemical Engineering" (1. Squires and l. Reblaitis, eds.), pp. 251-268. Am. Chem. SocoSymp. Ser. 124. Marten, L., and Hamielec, A. E. (1978). In "Polymerization Reactors and Processes" (J. N. Hendersonand T. C. Bouton, eds.), pp. 43-70. Am. Chem. Soco Soco Ser. 104. Maxim, L. D., Klein, A., Mayer, M. E., and Kuist, C. H. (1969). J. Polym. Sci. Part C 27, 195-207. Min, K. W., and Gostin, H. 1. (1979). Ind. Eng. Chem.-Prod. Res. Dev. 18,272-284. Min, K. W., and Ray, W. H. (1974). J. Macromol. Sci.-Rev. Macromol, Chem. Cll, 177-255. Nomura,
M. (1980). In "Emulsion
Polyrnerization,"
pp. 822-823. Am. Chem. Soco Preprints,
Las
Vegas. Nomura, M., Kojima, H., Harada, M., Eguchi, W., and Nagata, S.(1971).J. Appl. Poly~. Sci.15, 675-695.
9. Latex Reactor Principies: Design, Operation, and Control
355
Nomura, M., Harada, M., Eguchi, W., and Nagats, S. (1976). In "Emulsion Polymerization" (1. Piirma and J. L. Gardon, eds.), pp. 102-121. Am. Chem. Soco Symp. Ser. 24. O'Toole, J. T. (1965). J. Appl. Polym. Sci. 9, 1291-1302. Pollock, M. (1981). PhD Thesis, McMaster Univ. Schork, F. J., and Ray, W. H. (1980). In "Emulsion Polymerization," pp. 823-828. Am. Chem. Soco Preprints, Las Vegas. . Smith, W. V., and Ewart, R. H. (1948). J. Chem. Phys. 16, 592-606. Sundberg, D. c., Soh, S. K., and Hsieh, J. Y. (1980). In" Emulsion Polymerization," pp. 520-525. Am. Chem. Soco Preprints, Las Vegas. Ueda, T., Omi, S., and Kubota, H. (1971). J. Chem. Eng. Jpn. 4, 50-63. Ugelstad, J., and Hansen, F. K. (1976). Rubber Chem. Technol. 49, 536-561. Ugelstad, J., M0rk, P. C., and Aasen, J. E. (1967). J. Polym. Sci. A-I 5, 2281-2296. Ugelstad, J., M0rk, P. c., Dahl, P., and Rangnes, P. (1969). J. Polym. Sci. C 27,49-60. Warson, H. (1976). In "Emulsion Polymerization" (1. Piirma and J. L. Gardon, eds.), pp. 228-235. Am. Chem. Soco Symp. Ser. 24. Wright, D. E., and Tucker, H. (1977). In Polymer Reaction Engineering-Process TechnologySynthetic Elastomers. McMaster Univ. Professional Development Course.
10 Emulsion Polymerization in Continuous Reactors Gary W. Poehlein
1. Introduction . A. Background Information . B. Reactor Configurations and Flow Possibilities . C. Differencesbetween CSTRsand BatchReactors D. Scope of This Chapter . 11. Smith-Ewart Case 2 Model for a CSTR . A. Particle Formation . B. Particle Growth . C. ParticleAge and Size Distributions . D. Number of Particles and PolymerizationRate . E. Comparison with a Batch Reactor F. Effect of Inhibitors in Feed Streams . G. Use of a Seed-Particle Feed Stream . 111. Deviations from Smith-Ewart Case 2. A. Large Particles or Slow Termination Rates . B. Radical Desorption . .. . C. Other Particle Formation Mechanisms . D. ExperimentalResults IV. Transient Behavior of CSTR Systems. A. ExperimentalObservations. B. Physicochemical Mechanisms C. Control Methods . V. Strategies for Process and Product Development . A. Reactor Design Considerations . B. Product Development Considerations VI. Summary. References
357 357 358 359 361 361 361 362 363 363 366 367 367 367 368 369 370 374 375 375 375 378 378 378 380 381 381
l. Introduction
A.
Background lnformation
Three major types of chemical reactor systems are used to produce emulsion polymers; batch, semicontinuous, and continuous. Batch reactors usually consist of stirred tanks with various forms of heat removal 357 EMULSION POLYMERIZATION Copyrigbt ~.1982 by Aeademie Pres" Ine. All rigbts of reproduetion in any form rescrved. ISBN 0-12-556420-1
358
Gary W. Poehlein
devices such as jackets, reflux condensers, internal cooling surfaces, and/or external heat exchanger loops. All of the recipe ingredients are added at or near the beginning of the batch cycle, the reaction is carried out to the target conversion, and the reactor contents are discharged for further processing. Most kinetic studies and models are based on batch reactor data and batch operation. Semicontinuous (semibatch is probably a better name) reactors are designed like batch reactors, but with the former Qot all of the recipe ingredients are added at the beginning of the reaction 'cycle. Part of the monomer, and sometimes other ingredients as well, are added in a programmed manner after the reaction has started. Semicontinuous operation can be used to control reaction rate, copolymer composition drift, particle size distribution, particle morphology, and perhaps other product propertieso Semicontinuous reactors are widely used for coatings and adhesive products. Continuous reactors are operated with continuous, and it is hoped, steady input flows of reagents and output flows of products. Such reactors are generally economically advantageous when high production rates of closely related products are required. Continuous systems are not used if rather long run times cannot be achieved. Thus, latexes that foul badly and cause frequent shutdowns are usually produced in batch or semicontinuous reactors. Likewise, continuous reactors are not practical for product distributions which require frequent, significant recipe changes. Commercial continuous processes have been reported for synthetic rubbers [SBR: Wolk, 1959; Owen et al., 1947; Lundrie and McCann, 1949; Feldon et al., 1953 and CR (Chloroprene Rubber): Calcott and Starkweather, 1954; Aho, 1958] and a number of other polymers (Poehlein and Dougherty, 1977). As sales volumes have increased a number of industrial organizations have become interested in continuous processes and current activity in this area is significant. B.
Reactor Configurations and F/ow Possibilities
Commercial continuous reactor systems generally consist of a number of continuous stirred-tank reactors (CSTRs) connected in series. The reagents are pumped into the first reactor and the product is removed from the last. Heat is exchanged through reactor jackets and internal cooling surfaces. Commercial SBR systems sometimes consist of as many as 12-15 equalsized reactors connected in series. Reactor sizes are 2500-3500 gal with total mean residence times of about 8 hr. More recent SBR systems consist of fewer reactors and some commercial systems contain CSTRs that are not all the same size.
10. Emulsion Polymerization in Continuous Reactors
359
Continuous tubular reactors can also be used to produce emulsion polymers. Such reactors have been used in series with CSTRs (Gonzalez, 1974), as flow-through reactors (Rollins et al., 1979; Ghosh and Forsyth, 1976) and in a continuous loop process (Lanthier, 1970) in which material is fed and removed from a tubular loop with a circulating flow greater than the throughput. A tubular prereactor, in series with CSTR system, can offer stability advantages, which will be discussed later. A number of other flow alternatives are also possible with a CSTR-series system but these alternates are not widely utilized. An obvious flow alternative for a reactor system consisting of a series of CSTRs would be to introduce some portion of the total recipe at places other than the front end of the reactor train. These intermediate feeds would, in many respects, be analogous to semicontinuous operation of batch reactors. Intermediate feeds of monomer, water, emulsifier, etc., could be used to control particle generation, copolymer composition, particle morphology, particle size distribution, and molecular structure. The use of intermediate feed streams andjor recycle streams has not been studied extensively. This is an area in which process advances might be made. C.
Differences hetween CSTRs and Batch Reactors
The performance of a single CSTR can be quite different from that of a batch reactor for a number of reasons. First, the distribution of reactor residence times in a CSTR is quite broad. This leads to broad size and age distributions of the latex particles. By contnist, the polymer particles in a batch reactor are usually all formed near the beginning of the reaction and the particle size and age distributions of the product latex are narrow. A second important difference concerns reactor behavior in response to inhibitors andjor retarders in the feed streams. In a batch reactor these compounds react near the beginning of the cycle and then the polymerization proceeds in a near normal manner. In a CSTR, inhibitors in the feed streams are continuously added to the reactor and serve to reduce the rate of initiation of poly,mer molecules. Copolymer compósition is a third area of contrast. Copolymer composition in a batch reactor tends to change with time. The first polymer formed is rich in the more reactive monomer and the final polymer contains more of the least reactive monomer. This drift in composition can lead to polymer particles with nonuniform composition in the radial dimension. The copolymer product formed in a single CSTR, however, should be relatively uniform in composition if the reactor is operated at steady state. Ir several CSTRs are connected in series, polymers of several different
360
Gary W. Poehlein
compositions can be formed. Sincemost partic1eswould be nuc1eatedin the first reactor, the final partic1esfrom a multireactor system would also be nonuniform in composition. The consumption of chain-transfer agents can be influenced by the same phenomena that effect comonomers. Thus, their performance may differ with reactor type. A fourth concern in operating a CSTR involvesthe addition of the feed streams. All ingredients are added near the beginning of a batch reaction cyc1e,before the partic1es are formed. Recipe ingredients are usually divided among séveral feed streams in continuous systems. In this case the mixing should be sufficient to blend these streams rapidly with the polymerizing mixture in the reactor. The addition of the initiator stream can be especially critical. The water-soluble initiation systems normally used for emulsion polymerizations are electrolytes, and they can cause significant flocculation if they are highly concentrated andjor if they are not introduced to the reactor in a proper manner and mixed quickly. Monomer and monomer emulsion streams must also be added and mixed properly in order to prevent situations in which mass transfer factors may control the polymerization rateo A fifth, and commercially important difference between CSTRs and batch reactors is heat removal. Heat generation in a batch polymerization can be highly nonuniform. Sometimes the reactor productivity is dependent entirely on the capacity to remove heat during the peak reaction periodo Heat removal in steady-state, continuous systems is uniform and, for this among other reasons, higher productivity can often be achieved. Reactor fouling is a sixth area wherein continuous systems can perform differently. The batch cyc1e involves filling and emptying the reactor frequently. A disadvantage of this operation is that the latex can dry or stick to the walls and initiate the formation of wall polymer. The fact that the reactor is emptied frequently, however, does provide an opportunity for c1eaning. A properly designed continuous reactor system should operate full of latex, without a vapor space. This helps to prevent or retard the formation of wall polymer. In fact the absence of a liquid-vapor interface may slow the formation of coagulum in the latex. Heller and Peters (1970a,b, 1971; Heller and De Lauder, 1971a,b) have c1early demonstrated that interfacial flocculation can be significant. One disadvantage of a continuous system is that operation in a particular reactor must be stopped for c1eaning.If frequent disruptions are required continuous reactor systems will probably not be economically feasible. A seventh difference between batch reactors and CSTRs is concerned with molecular weight, branching, and cross-linking characteristics. In general, branching, cross-linking, and gel-effect phenomena become more significant at higher conversions. The final product from a batch reactor
10.
Emulsion Polymerization in Continuous Reactors
361
consists of molecules formed over a rather broad range of conversion; this is less true in emulsion polymerization than in bulk or solution polymerization since the conversion at the reaction site in the polymer particles may be quite high even through the overall reaction conversion is low. In a CSTR, however, the polymer is formed at a constant conversion, that existing under the state of operation. Usually this will be higher than the average conversion over a batch reactor cycle. Thus, branching and crosslinking reactions are normally more pronounced in CSTR systems.
D.
Scope of This Chapter
Other parts of this book contain detailed discussions of emulsion polymerization mechanisms, kinetics, and reaction engineering. Thus, the intent of this chapter is to introduce the reader to some of the basic conceptsof continuous reactor systems.A rather simplesteady-state reactor model will be presented for a single CSTR system. This model will be compared with a batch reactor model for the same reaction mechanism and the model differences highlighted. Deviations from the simple model will be reviewed and transient reactor behavior will be discussed. Possible methods for control of continuous reactors will be suggested and strategies for process and product development will be considered.
II. Smith-Ewart Case 2 Model Cora CSTR Models for emulsÍon polymerization reactors must account for particle formation and particle growth. Ir these two phenomena can be handled in a satisfactorymanner one can predict the polymerizationrate, the number of particles formed, and the particle size distribution. The model presented below was first developed by Gershberg and Longfield (1961). It is based on the concepts developed for batch reactors by Smith and Ewart (1948) in their "Case 2" modelo A.
Particle Formation
Free radical s, initiated in the aqueous phase, can form polymer particles by a number of mechanisms. Smith and Ewart (1948) considered two quantitative models for predicting the number of particles formed. One of these models is shown as Eq. (1) below. (1)
362
Gary W. Poehlein
where N is partic1e concentration in number per volume of aqueous phase, t is time, R¡ is the rate of initiation of polymer oligom~rs in the aqueous phase (assuming no aqueous phase termination), NAis Avogadro's number, Af is the area that could be covered by the emulsifier that is not adsorbed on the surface of the polymer partic1es, as is the area occupied by one molecule of adsorbed emulsifier, and S is the total emulsifier concentration. Note that the term (asSNA) represents the total surface covering capability of the emulsifier charged. Thus, Eq. (1) is based on the assumption that the partic1e formation rate is directiy proportional to the fraction of emulsifier not adsorbed on the surface of the polymer partic1es. Since no polymer partic1es exist at the beginning of the reaction, the rate of formation is dN/dt = R¡NA. Partic1e formation stops when AF = O,that point where the total partic1e surface is (asSNA). In a single CSTR the number partic1es does not change with time and the partic1e number equation analogous to Eq. (1) is N
= R¡fJNA[Arf(asSNA)]
(2)
where () is the mean residence time of the reactor, the working volume divided by the volumetric effluent flow rateo In order to calculate N one needs to determine Af from equations for partic1e size distributions. These equations in turn, come from partic1e growth and reactor residence time relationships. B.
Particle Growth
The basic tenet of the Smith-Ewart Case 2 partic1e growth model is that each partic1e will contain an active free radical one half of the time. Thus, the average number of free radicals per partic1e ñ is 0.5. The rate of polymerization Rp is given by Rp
= kp[M][R.] = kp[M](ñN/NA)
(3)
where kp is the propagation rate constant and [R -J is the total radical concentration at the reaction site in the polymer partic1es. The polymerization rate per partic1e Rpp is (4) Rpp = kp[M](ñ/NJ If excess monomer is available in the form of monomer drops the monomer concentration in the partic1es remains relatively constant. Thus, particle growth occurs when monomer is converted to polymer, and additional monomer for swelling the polymer diffuses into the partic1e from the
10.
Emulsion Polymerization in Continuous Reactors
363
monomer droplets. Under these conditions the particIe growth relationship is given by
dv/d7:= 4nr2 dr/d7: = K1[M]ñ
(5)
where K 1 is a constant dependenton the monomer swelling of the latex particIe and on the propagation rate constant. Ir ñ = 0.5, Eq. (5) can be integrated to yield the following relationships for particIe size as a function of age 7:.
v=
Vo +
0.SK1[M]7:
(6a)
r3 = r~ + 3K¡[M]7:/Sn
(6b)
where ro and Voare the radius and volume respectively, of the particIe at nucIeation.
C. Particle Age and Size Distrihutions The particIe age distribution in a single CSTR is given by f(7:)
= 0-1 exp(-7:/0)
(7)
The particIe size density function U(r) is obtained by combining the growth equation with the age distribution. U(r)
= f(1:)/(dr/dt)
U(r)
= [Snr2/(K
The cumulative distribution
U(r)
(Sa)
I[M] O)] exp[
-
Sn(r3 - r~)/(3K 1 [M] O)]
(Sb)
function is given by Eq. (9).
= J: U(r) dr = 1.0 - exp[-'Snr3/3Kl[M]0]
(9)
The last equation has been derived by assuming that ro, the nucIeation particIe radius, is equal to zero. Ir the conversion in the reactor is modest and the particIe sizes are not too large, Eq. (9) can be used for accurate predictions of particIe size distributions in styrene latexes. Figure 1 is a typical comparison of Eq. (9) with experimental data. D.
Numher 01 Particles and Polymerization Rate
Equation (2) for the number of particIes per unit volume of aqueous phase has one undetermined parameter Af which is the difference between the surfactant charged and the surfactant adsorbed on the surface of the polymer particIes. (10)
364
Gary W. Poehlein 1.0
~
¡;: => al
/
0.8
,~ ~,,/
~ 0.6 (J)
15
eI '
ILI
~ 0.4
~ ~
=> :::!:
e'I I
a 0.2
I
/
,,
e,' ,
,I
" ,/ .,,,,,¿;€I
O
O
200
400
600
PARTlCLE
800
1000
DIAMETER
(Al
1200
1400
Fig. 1. Particle size distribution for a styrene latex (Poehlein and De Graff, 1971). T = 70oC: 0= 15min; (S)= 2.79g/lOOg H20; (/) = 0.35g/IOOg H20. ---, Dn ($-E Case 2) = 690 Á; -, Dn(De Graaf) = 700Á: O, Dn(Exper.) = 720Á.
Combining Eqs. (10), (8b), and (2) yields the following relationship for N (R¡fJNAfN) = 1 + (C
-
C(1[M])]2/3
(11)
or 1t1 = 1
+ 1t2
where the 1t1 and 1t2 are the groups indicated, c(o= 3.85(MoVp)2/3, C(l= (MoVrnx 10-3), Mo is the monomer molecular weight, and Vp and Vrn are specific vqlumes of polymer and monomer, respectively. Equation (11) is written in dimensionless formo The second term on the right hand side 1t2 represents the ratio of surfactant adsorbed on the polymer particIes to the free surfactant Ar. This ratio is normally much greater than 1 and Eq. (11) reduces to
(12) Combining Eqs. (3) and (11) permits the calculation of polymerization rateo (13) or 1t3
= 1+ 1t2
Figures 2 and 3 show a comparison of Eqs. (11) and (13) with data for styrene emulsion polymerization over a wide range of experimental conditions. The rate data fit the theory quite well and the particIe number data
10.
Emulsion Polymerization
o
in Continuous
DEGRAFF
"
GERSHBERG a
o
GERRENSa KUCHNER
.
365
Reactors
LONGFIELD
CALCULATED FROM R~ ASSUMING
1\
.
1/2
F
STYRENE
1
1
lO'
102 I
Fig.2. 1971).
103 + lf2
Particle number: Theory-experimental
o
'" o
comparisons (Poehlein and De Graff,
DEGRAFF GERSHBERG a LONGFIELD GERRENS a KUCHNER
STYRENE
101
I
Fig.3. 1971).
loS
102 + 1T2
Po1ymerization rate: Theory-experiment
comparisons (Poehlein and De Graff,
Gary W. Poehlein
366
also tit in a reasonable manner. The particle number data are usually somewhat lower than model predictions. There are at least two reasons that the pro po sed theoretical model would predict more particles than actually measured. First, the procedures used for counting particles would normally error on the small side. Second, the model equations are based on the assumption that the particle nucleate size ro is zero. Thus, the model would overestimate the number of particles. E.
Comparison with a Batch Reactor
The Smith-Ewart Case 2 model for the number of particles formed in a batch reaction is given by N
= kR?4(asSNA)0.6
(14)
where k is a constant. The polymerization rate relationship given by Eq. (3) is also valid for the batch reactor when N is given by Eq. (14). The important point here is that the same physicochemical mechanisms yield model equations for the two reactor types in which even the exponents on the important recipe parameters are different (see Table 1). In such cases the use of batch data for design of continuous reactor systems would involve considerable risk. A second important difference between the batch reactor model and the CSTR model is the prediction of a maximum number of particles for the CSTR as a function of mean residence time. This maximum is readily determined by setting the derivative (dN/dO),obtained from Eq. (11), equal to zero and solving for N. The result of this computation is NCSTR'MAXIMUM
=
(15)
O.577NBATCH
Thus, fewer particles will be produced from the same recipe in a eSTRo The particle concentration in a eSTR can be increased by increasing the emulsitier concentration or by using seed particles in the feed streams. TABLEI Model Equation Exponents for Smith-Ewart Case 2 Models Equation exponents
Parameter R; S
e
Batch reactor
0.4 0.6 NA
CSTR O 1.0 -0.67
10. Emulsion Polymerization in Continuous Reactors F.
367
Effect ollnhibitors in Feed Streams
Inhibitors are normally present in stored monomers and sometimes in other feed streams. In batch reactors inhibitors delay the start-of polymerization, but in a CSTR they cause a reduction in the rate of initiation. The effective initiation rate for the first CSTR in a series system is given by (16) where f is the initiator efficiency factor, kd is the decomposition rate constant, [/]0 and [H]o are the concentrations of initiator and inhibitor, respectively, in the combined feed streams, and fH is the number of free radicals consumed per inhibitor molecule. Equation (16) is valid only if the quantity within the brackets is positive. If this term is zero or negative no polymerization will take place in the first reactor. The rate of initiation in the second CSTR in a series system is (17) where e2 is the mean residence time in reactor 2. R¡.2 can be larger than R¡.l and this fact can sometimes cause problems with heat removal and temperature control in the second reactor. This effect can be strong enough in some situations to require that additional inhibitor be added to the second reactor. G.
Use 01 a Particle Feed Stream
Emulsion polymerization reactions are sometimes carried out with small seed particles formed in another reaction system. A number of advantages can be derived from using seed particles. In a batch reactor seed latex can be helpful in controlling particle concentration, polymerization rate, particle morphology, and particle size characteristics. In a CSTR the use of a feed stream containing seed particles can also help to prevent conversion andjor surface tension oscillations, which are caused by particle formation phenomena. This factor will be discussed in more detaillater in this chapter. III.
Deviations from Smith-Ewart Case 2
The key assumption in the Smith-Ewart Case 2 theory can be stated mathematically by the simple expression ñ = 0.5. The physicalbasis for this assumption involves several phenomena. First is the fact that free radicals react with one another to terminate polymerization very rapidly. Second, the latex particles, which are the reaction sites, are very small. Third, the
368
Gary W. Poehlein
mobility of free radicals within the polymerizing partic1es is considered to be high. Fourth, the free radical oligomers within the partic1es are assumed to be incapable of escaping from the partic1es. Factors that alter any of these phenomena will cause deviations from Smith-Ewart Case 2 kinetics. A.
Large Particles or Slow Termination
Stockmayer (1957) was the first to present a genera) solution to the Smith-Ewart recursion equation for ñ. This solution is reproduced below for the case in which free radical escape from partic1es is not possible. ñ
= (a/4) (Io[a]/l
(18)
l[a])
where a = (Pa/N)(v/kt), lo and 11 are Bessel Functions, and kt is the termination rate constant in the latex partic1es. Figure 4 is a plot of Eq. (18). Higher values of a can be caused by large partic1es (large v), slow termination reactions (low kt), or a high radical flúx per partic1e (large pJN). When ñ becomesgreater.than 0.5 the larger partic1esgrow faster,in a volumetric sense, than the 'smaller partic1es. This causes the partic1e size. 1.5
1.0
0.5
IC: O>
O
!2
-0.5
- 1.0
-4
-3
-2
-1 log 01
-
O
2
3
Fig. 4. Stockmayer's equation plotted as logn as a function of logO( (Ugelstad and Hansen, 1976). m = O; O(= Pav/Nk,.
10.
369
Emulsion Polymerization in Continuous Reactors 1.0
08
z 0.6 o ¡:: :o ID ¡¡: ....
'" o 0.4 "' > ¡::
a
0.2.
/ 0/ / / / /
O
o
500
1000 PARTICLE
1500
2000
2500
3000
3500
4000
OIAMETER (A)
Fig. 5. Particle size distribution for a styrene latex made at a mean residence time of 59min (Poehlein and De Graff, 1971). T=50°C: O=59min; (S)=0.6g/100g H20; (1) = 1.5 g/100 g H20. ---, Dn (S-E Case 2) = 858 Á; -, Dn (De Graaf) = 1018 Á; 0, Dn (Exper.) = 1090 Á. .
distribution to become broader. Figure 5 shows this effect for a styrene emulsion polymerization. The dashed curve is based on the Smith-Ewart Case 2 model and th~ solid curve includes the Stockmayer correction. B.
Radical Desorption
Ugelstad and co-workers (1967, 1976) presented a more general solution to the problem of computing ñ. Their work was presented in the form of a series of graphs based on the parameters listed below (X'= (RJNkt/v)
(19)
m = k~v/kt
(20)
y = 2Nktktw/k;v
(21)
where k~ is the rate constant for radical desorption from particles, ktw is a termination rate constant for the water phase, and ka is arate constant for radical absorption. Ugelstad's theory allowed for the reabsorption of previously desorped radials; a factor not handled properly by Stockmayer.
370
Gary W. Poehlein 2
IC
'" .2
o
-1
-2
-6
-8
-o
-2
-4
2
4
logo'-
Fig. 6.
Average number
of radicals
per partic1e as a function of el and m for Y
= 10-2
(Ugelstad el al., 1967).
Ugelstad's results were presented as a series of graphs such as shown by Figure 6. The parameters defined by Eqs. (19-21) need to be defined differently when dealing with particle populations that are not monodisperse. The basic result, however for a system where ñ #- 0.5, is that particle growth is a positive function of particle size, i.e., dv/dt = k'vr
r>O
(22)
This causes particle size distributions in the latex from a CSTR to be broader. Rate of polymerization is directly proportional to (ñN). Since ñ can decrease as N increases the rate of polymerization may not depend strongly on N. C.
Other Particle Formation Mechanisms
Smith and Ewart (1948) assumed that particles are formed when free radical s diffuse into monomer-swollen micelles. Roe (1968) demonstrated later that the S-E Model, in a mathematical sense, did not depend on the concept of a micelle. Roe referred simply to the stabilizing capability of the
10.
371
Emulsion Polymerization in Continuous Reactors
HYDROPHILlC
-S04'
!
+M
---
-S 04M
SURFACE ACTIVE
--
I I +M
t
,-
-S04Mn
HYDROPHOBIC I HOMOGENOUS I+M NUCLEATION
ADSORPTION ONEXISTING R\RTICLES OR MONOMERDROPS CAPTUREBY MICELLES
so; FLOCCULA
FLOCCULATION OF PRIMARY R\RTICLES
TION
ONTO MATURE R\RTICLES
+MaS POLYMERIZATION GROWTH
CONTINUED GROWTH BY
POLYMERIZATION I FLOCCULATION, OR
Fig.7.
BOTH
Paths for free radicals initiated
in the aqueous
phase.
system or the free emulsifier concentration. We know that particles can be formed by a number of mechanisms. Figurs: 7 shows some potential ways in which a sulfate ion-radical might become associated with a latex particle. The rate at which 'various mechanisms proceed depends on a number of factors, including those listed below: 1. Monomer solubility in water. 2. Propagation rate of the polymerization reaction in the aqueous and organic phases. 3. Size and concentration ofmonomer drops. 4. Size and concentration of micelles if any are present. 5. Size and 'concentration of polymer particles. 6. Solubility of the growing polymer oligomers in the water phase. 7. Concentration of free emulsifiers in the water phase. 8. Concentration of electrolyte in the water phase. The monomer solubility in the water phase, discounting that located in any swollen micelles, will influence the rate at which the oligomer chains grow. Monomer solubility will, of course, also be related to oligomer solubility, or more precisely to how long the oligomer chains might grow
372
Gary W. Poehlein TABLE
11
Solubility of Monomer in Water and Polymer Concentration in (M):
Monomer
Water
Styren"e Butadiene Vinylidene chloride Vinyl chloride Methyl methacrylate Vinyl acetate Ethylene Acrylonitrile Acrolein
0.005 0.015 0.066 0.11 0.15 0.3 0.3-0.6 1.75 3.1
Polymer partic1es
5.4 6.5 . 1.1 6.0 7.0 7.6 5.0
before they precipitate. Table 11gives monomer solubilities in water and in the polymer particles for several common monomers. It should be noted that in copolymer systems the oligomers formed in the water phase would be expected to have a higher concentration of the more soluble monomer if the reaction rates are of the same order. The size and number of monomer droplets are usually ignored in emulsion polymerization kinetic stud~es. The basis for this comes from several observations. First, in CIassical recipes the monomer is located in a relatively few, large monomer droplets that represent a small total surface area when compared to the micelles or free emulsifier. Second, large particles are not usually seen in electronmicrographs of latex particles. Ir one or two are found they can be conveniently forgotten. Ugelstad et al. (1973) cIearly demonstrated that if the monomer droplets can be made small enough, they can efTectivelycompete for free radicals and form particles. Considerable work has been published (see Ugelstad and Hansen, 1976, for other references) on the preparation of finely dispersed monomer droplets for the formation of latex particles by direct polymerization. Recently,Durbin et al. (1979)have shown that a few large particles are formed by monomer droplet polymerization in cIassical styrene recipes. Their work showed that the number of oversized particles increased with increased intensity of preemulsification. Thus, in some circumstances the installation of preemulsification systems may be counterproductive. The size and number of micelles and particles will influence the path taken by free radicals in the water phase. As sizes andjor numbers increase the probability for absorption increases.
10. Emulsion Polymerization in Continuous Reactors
373
PRIMARY PARTICLE Fig. 8.
Schematic representation of the growth and precipitation of an oligomeric
radical (Fitch and Tsai, 1971).
The vertical path shown in Fig. 7 iIIustrates a rnechanisrn of particle formation which Fitch and Tsai (1971) have called "hornogeneous nucleation." Figure 8 shows this process of diffusion and addition of rnonorner units schernatically. As the oligorneric radical grows it becornes strongly hydrophobic. In this state, it rnay precipitate to forrn a prirnary particle or deposit on an existing particle, micelle, or rnonorner drop. Estirnates of the degree of polymerization necessary to cause precipitation have been given as 54 for vinyl acetate (Priest, 1952),65 for methyl rnethacrylate (Fitch and Tsai, 1971), and 30 for styrene (Peppard, 1974). Another rnechanisrn for particle forrnation involves the scheme shown in Fig.7, but it oCGurslater in sorne batch polyrnerizations. This secondary nucleation is caused by free ernulsifier which is libenited from the particle surface. Figure 9 shows sorne data of Gerrens for a batch ernulsion polyrnerization of MMA. These data were successfully modeled by Ray and Min (1976). The population of srnaller particles was forrned late in the reaction because ernulsifier was desorped beca use of the crowding of radical end groups on the surface and because of particle shrinkage caused by . rnonorner conversion to polyrner.
374
Gary W. Poehlein .30
'"
Q
"
.20
>1¡¡j Z LrJ o .J ~ ~ a: o z
.10.
o
O
40
80
DIAMETER
120 (nm)
Fig. 9. Experimental and predictedparticle sizedistribution for a MMA latex (Ray and Min, 1976).0,Gerren'sdata: -, Model prediction (97.8%conversion).
D.
Experimental Results
The model based on S-E Case 2 kinetics has been quite successful in handling steady-state data for styrene emulsion polymerizations in a CSTR. One or more of the mechanisms described above, however, generally cause other monomer systems to deviate from this simple model. The nature of these deviations varies among the different monomers. Ir published literature data are fitted to equations of the type listed below one can obtain values for the exponents a, b, and c. Rp = kRRf[S]bOc
(23)
= kNRf[S]bOC
(24)
N
Table III gives the results of this fitting for styrene, methyl acrylate, methyl methacrylate, vinyl acetate, vinyl chloride, and ethylene. Only the styrene data agree with the simple theory. The exponents on R¡ are usually greater than 0.0 (the theory prediction). This can be explained by radical desorption from the particles, by slow t.erminatiop in the particles, or by a combination of these factors. Data on the other variables ([S] and O)are incomplete but scattered results show significant deviations from the S-E Case 2 Model. More complete models, such as those presented in this book by Hamielec, have been successful with nonstyrene monomers.
10.
375
Emulsion Polymerization in Continuous Reactors TABLE
Steady-State
111
Behavior of CSTRs Approximate exponents
a Theory (Rp and N) Styrene (Rp and N) MA(N) MA(Rp) MMA (Rp) VA (Rp) VC(Rp) Ethylene (Rp)
IV. A.
0.0 0.0 0.0 0.65 0.8 0.8 0.5 or less 0.5
b
e
1.0 1.0 0.85 0.0 0.9 SmaIl ? 0-0.3
-0.67 -0.67 -0.67 +0.43 ? 0.0 SmaIl Small
Transient Behavior of CSTR Systems Experimental Observations
An understanding of the transient behavior. of continuous reactors is important for start-up and reactor control considerations. Continuous oscillations have been observed by a number of workers. Figures 10 and 11 show data for styrene and methyl methacrylate. Gerrens and Ley (1974) reported continuous, undamped oscillations in surface tension during a styrene emulsion polymerization run which lasted for more than 50 mean residence times. Nearly five complete cycles were observed during this run. Berens (1974) conducted experiments with vinyl chloride in which the measured particIe size changed with time. No steady state was achieved with the data shown in Fig. 12.
B.
Physicochemical Mechanisms
The reason for oscillations in conversion and surface tension become clear when one considers particle formation and growth phenomena. If a single CSTR is started empty or by adding initiator to a full vessel of inactive emulsion, a conversion overshoot occurs. The first free radicals generated are almost entirely utilized to form new particles. Since these particles do not grow rapidly to the steady-state size distribution, radical
376
Gary W. Poehlein 70 60
STYRENE 40 z O Cñ a: 30 UJ
> Z O u
-
-~ - -
-
-~
80
120 RUN
Fig. 10.
Conversion transients
160 TIME
at
start-up
200
7O'C
_STAGE2 - ~ 7O'C
¿.: STAGEI .100'C
20
10 O
StAGE 3
240
280
{min} for
styrene
emulsion
polymerization
(Gershfield and Longfield, 1961).
50
40
30
z 020 Cñ a: UJ >
~
U
10 METHYL
METHACRYLATE
O O
2
4
Fig. 11.
TIME
10
12
14
(t le)
MMA conversion transíent (Greene, Gonzalez, and Poehlein, 1976). T
40°C: IJ= 20 min: (NaHC03)
8
6
DIMENSIONLESS
(S) = 0.01molj\iter;
= O.OL (NaCI)
= 0.02.
(1) = 0.01molfliter; Monomer:H20
=
= 0.43;
377
10. Emulsion Polymerization in Continuous Reactors 30 i 10
/
-,
í',
,1 \
"'
3
"
\
"
-,
¡
,
'1
/
I
/
\ \ \
\,
,
z
\
I
\,
" i, I
::>
\
i I
\'
11 11
Q: 1.0 w ID
\
I I I
"-
/
1Z w <.) Q: W a.
/'.,
I
/
I
'
I
\
'Y..
'
I "
'-
'-
" '-. '-
' I I
\
\",
\ \
,
0.3
/
/ /
/-..
\
0.1 O
500
1000
1500
2000
2500
3000
~RTICLE DIAMETER (A) Fig. 12. PVC particle size distribution transients (Berens,1974).-, '-, t = 120mins;---, t = 240mino
t = 60 min; -
efficiency in particle formation rema ins high and the particle concentration pass es its steady-state value. As these parti~les grow they genera te too much surface to be saturated by the emulsifier and the particle formation rate become much smaller, perhaps zero. The effiuent from the reactor carries some of this unsaturated surface and new emulsifier is being continuously added with the feed. Eventually, the surface will be saturated and free emulsifier will be available to stabilize new particles. If the particle formation and growth rates are appropriate, continuous limit-cycle oscillations can be observed. The particle formation rate depends on the rate of production of free radicals and on the relative rates of the various mechanisms in which these free radicals participate. A high rate of particle formation in the presence of small amounts offree emulsifier will contribute to unstable cyclic behavior. The rate of growth of particles depends on the concentration of the reagents in the particles, radicals and monomer, and on the propagation rate constant. The gel effect, which causes the termination rate constant to be lower at higher conversions, can cause higher free radical concentrations in the particles and thus higher particle growth rates. This effect also contributes to conversion oscillations.
378
Gary W. Poehlein
C. Control Methods A number of methods have been considered for controlling transients in eSTRs. One simple method for trying to handle transients involves the use of a smalI eSTR as a prereactor. The natural oscilIations and transients from this reactor are damped by backmixing in the larger reactors that folIow. Greene el al. (1976) demonstrated that strong initial overshoots and conversion oscilIatiQns could, in some cases, be avoided by careful start-up. The reactor was started either with a seed latex from a previous run or fuIl of distilIed water. Both procedures were successful in achieving steady operation in some cases. In other cases, however, significant transients were obse!ved after a smooth start-up. Hamielec el al. (1980) and Ray and Schork (1980) have worked on potential feedback control schemes. Hamielec and co-workers have developed an on-line light scattering device that dilutes the latex and measures scattering at several waveIengths. This data is then used to predict changes in particIe concentrations and size characteristics. . Ray and Schork (1980) have developed an on-line device for measuring surface tension. A bubble rise technique is used. Ir this method or the light scattering technique of Hamielec were used in a control system one could presumably alter the feed rate of a key ingredient, probably emulsifier, to prevent undesired transients. More work is needed to demonstrate the potential of these methods. Berens (1974) and Gonzalez (1974) have shown that the use of a seed latex in the feed stream can prevent oscilIatory behavior. Berens used a latex seed generated in a separate reactor. He demonstrated that the particIe size distribution reached a constant state in a pve polymerization. Steady states were not observed in unseeded reactions. Gonzalez placed a continuous tubular reactor in front (upstream) of the eSTRo In this case the particIe seed was formed in the tube from a recipe that did not contain seed. Gonzalez found the tube-CSTR system to be quite stable so long as the conversion in the tu be was adequate to prevent significant particIe formation in the eSTRo The use of a particIe seed has the added advantage of aIlowing more careful control of particIe concentration and reaction rate in the eSTRo
v.
Strategies for Process and Product Development
A.
Reactor Design Considerations
A continuous emulsion polymerization system needs to operate for significant periods between shut-downs. Thus, the reactor system should be designed and operated to prevent, as much as possible, the formation of waIl polymer. The causes of and cures for waIl polymer are not completeIy
1 ~ ~ 1
10.
Emulsion Polymerization in Continuous Reactors
379
understood. The factors listed below need to be considered to help minimize the wall polymer problem.
1. Liquid level: The reactor should be operated full. A vapor space almost always causes problems. Latex can dry on the wall and present a site for growth, sometimes accelerated, of more deposits. 2. Nozzle locations: The location of the feed and effiuent nozzles should insure rapid mixing of the feed streams and prevent short circuiting between feed and effiuent. Electrolyte streams should be as dilute as feasible to prevent electrolyte flocculation of the latex. 3. Reactor surface: The internal surface of the reactor should be smooth. Rough places pro vide sites for polymer nucleation andjor deposition. Glass and polished stainless steel surfaces are common. Stainless . steel is preferable if it can be used because the glass coatings reduce heat transfer capability. 4. Agitation: The agitation needs to be designed to provide adequate mixing of the feed streams and adequate heat transfer. Good mixing usually involves a balance between flow and turbulence. Since turbulence or high shear can sometimes cause coagulation this balance usually involves more flow and less turbulence. Good mixing normally requires internal baffies in the reactor. These baffies, however, represent potential sites for wall polymer and thus should be minimized or, if possible, eliminated. Good mixing can be achieved in unbaffied reactors with axial flow impellers mounted at an angle to the vertical. Such reactors are described in G~rman Patent 2,520,891 assigned to Bayer, A. G. 5. Operationjsurface tension: The reactor should be operated in such a manner that large transients in surface tension are avoided. Conversion and surface tension oscillations will tend to contribute to wall polymer formation. Start-up policies, system design, and control procedures should be selected to insure steady, free emulsifier levels in the particle formation reactor. In some cases it may also be desirable to add more emulsifier to downstream reactors. 6. Operationjcleaning: The reactor should be cleaned very well. The growth of polymér deposits are usually non-linear functions of time in which the size of deposits increase rapidly. During cleaning one must also avoid damaging the surface. Cracks, roughness, and surface imperfections represent potential nucleation sites for wall polymer buiidup. 7. Wall temperatures:Some practitioners of the art and science of emulsion polymerization believe that nonuniform wall temperatures can playa role in wall polymer formation. The reaction in any deposit could be faster if the temperature is higher. Thus, some reactors are designed with cooling jackets that cover as much of the reactor as possible, including the reactor topo
380
Gary W. Poehlein
I
Other reactor design considerations may be necessary in special cases. Monomer mass transfer, not normally a problem, can be important if the monomer-aqueous phase interface is small. This is more likely in systems involving gaseous monomers in which the large surface area of the monomer emulsion is not presento In such cases special attention must be paid to gas dispersion and transporto Other factors that can have a significant effect on reactor design include latex viscosity, heat transfer rates, reaction pressure, and control mechanisms.
I
I
;;
~ ~ ~ ~ ~ ~
~
I
B.
Product Development Considerations
A number of factors need to be considered when developing a product that will be produced in a continuous reactor system. The initial development work on most new products is carried out in batch reactors. Bottle polymerizers are often used for this purpose because a large number of experiments can be completed quickly. These early experiments provide a product that can be tested against fundamental standards (molecular weight, particle size, rheology, etc.) and in proposed applications. Preliminary recipes evolve from such tests. Further development of any product usually involves more specialized reactors and product testing. The results of these tests include more refined recipes, reactor operation procedures, and engineering data for use in design of the final commercial process. Ir a continuous process is to be used for commercial production, a similar small-scale reactor system should be utilized in this second stage of product development. There are a number of reasons for this recom.mend~tion. The earlier discussion of the difference between batch reactors and CSTRs lists some of these reasons. If, for example, engineering data are to be obtained for design of a commercial unit, the variable relationships might be quite different for the different reactors. The Smith-Ewart CSTR model predicts a linear relationship between Rp or N and the surfactant concentration [S]. The same mechanistic model for a batch reactor predicts a 0.6 power relationship between Rp or N and [S]. Products from continuous, batch, and semicontinuous reactors can differ in a number of ways. Some of the more obvious characteristics that might be influenced are listed below: 1. Particle characteristics: particle number, average size, and size distribution. 2. Distribution of the composition of molecules in copolymer products. 3. Particle morphology or the distribution of copolymer composition as a function of radius. '
I
1
10. Emulsion Polymerizationin Continuous Reactors
381
4. Molecular weight averages and distributions. 5. Frequency and distribution of branching andjor grafting sites on the molecules. Batch, semicontinuous, and continuous reactors that are designed intelligently can be utilized to manipulate almost any fundamental andjor application property. Suitable products for most applications can usually be manufactured in several different reactor systems. One may be required, however, to adjust the latex recipe and reaction conditions to produce a satisfactory product in one reactor type if that produce has been developed in another reactor system. Thus, if a reactor system has been chosen for the commercial unit one should plan on some, and in most cases considerable, product development work in a similar, small-scale system.
VI. Summary Some of the fundamentals of reactor systems have been presented and discussed in this chapter. This material should assist the reactor engineer in planning appropriate pilot studies for a new or revised process. Equally important, the concepts reviewed should help the product development personnel in devising reactor systems and operating procedures that will produce satisfactory products. More complete discussions of polymerization kinetics and reactor modeling are contained in other chapters of this book. These factors will also be of great value to the reactor engineer and the development chemist. As the kinetic mechanisms and reaction models become better developed we can look forward to more efficient research and development programs for new products and processes.
Acknowledgment This material is based, in part, upon work supported by the National Science Foundation under Grant No. CPE-8011455.
References Aho, C. E. (1958). U.S. Patent 2,831,842 (to E. 1. duPont de Nemours and Co., Wilmington, Delaware), April 22. Berens, A. (1974). J. Appl. Polym. Sci. 18,2379. Calcott, W. S., and Starkweather, H. W. (1954). U. S. Patent 2,384,277 (to E. l. duPontde Nemours and Co., Wilmington, Delaware), September 4.
382
Gary W. Poehlein
Durbin, D. P., EI-Aasser, M. S., Poehlein, G. W., and Vanderhoff, J. W. (1979). J. App/. Po/ym. Sci. 24, 703. Feldon, M., McCann, R. F., and Lundrie, R. W. (1953). Indian Rubber Wor/d 128(1), 51. Fitch, R. M., and Tsai, C. H. (1971). In "Polymer Colloids" (R. M. Fitch, ed.), Chapters 5 and 6. Plenum Press, New York. Gerrens, H., and Ley, G. (1974). Private cornmunication. Gershberg, D. B., and Longfield, J. E. (1961). Symp. Po/ym. Kinet. Cata/o Syst., 45th AIChE Meeting, New York Preprint 10. Ghosh, M., and Forsyth, T. H. (1976). In "Emulsion Polymerization" (1. Piirma and J. L. Gardon, eds.), pp. 367-378. American Chemical Society Symp. Series 24, Washington, D.C. Gonzalez, P. R. A. (1974). M.S. Thesis, Chem. Eng. Dept., Lehigh Univ., Bethlehem,
Pennsylvania.
.
Greene, R. K., Gonzales, R. A., and Poehlein, G. W. (1976). In "Emulsion Polymerization" (1. Piirma and J. L. Gardon, eds.), pp. 341-358. American Chemical Society Symp. Series 24, Washington, D.C. Hamielec, A. E., Kiparissides, G., and MacGregor, J. F. (1980). In "Polymer Colloids 11"(R. M. Fitch, ed.), pp. 555-582. Plenum Press, New York. HelIer, W., and De Lauder, W. B. (197Ia). J. Col/oid Interface Sci. 35(2), 300--307. Heller, W., and De Lauder. W. B. (197Ib). J. Col/oid Interface Sci. 35(2), 308-313. Heller, W., and Peters, J. (1970a). J. Col/oid Interface Sci. 32(4), 592-605. Heller, W., and Peters, J. (1970b). J. C9l/oid Interface Sci. 33(4), 578-585. Heller, W., and Peters, J. (1971). J. Col/oid Interface Sci. 35(2), 300--307. Lanthier, R. (1970). U.S. Patent 3,551,396 (to Gulf Oil Canada, Ltd.), December 29. Lundrie, R. W., and McCann, R. F. (1949). Ind. Eng. Chem. 41, 1568. Owen, J. J., Steele, C. T., Parker, P. T., and Carrier, E. W. (1947). Ind. Eng. Chem. 39, 110. Peppard, B. D. (1974). PhD Dissertation, Chem. Eng. Dept., Iowa State Univ., Ames, Iowa. Poehlein, G. W., and DeGraff, A. W. (1971). J. Po/ym. Sci. Part A-2 9, 1955-1976. Poehlein, G. W., and Dougherty, D. J. (1977). Rubber Chem. Techno/. 50(3), 601. Priest, W. J. (1952). J. Phys. Chem. 56, 1077. Ray, W. H., and Min, K. W. (1976). In "Emulsion Polymerization" (1. PiirmaandJ. L. Gardon, eds.), pp. 359-366. American Chemical Society Symp. Ser. 24, Washington, D.C. Ray, W. H., and Schork, F. J. (1980). News artic1e, Chem. Eng. News. 58(37), 44-46. Roe, C. P. (1968). Ind. Eng. Chem. 60, 20. Rollins, A. L., Patterson, W. l., Archambault, J., and Bataille, B. (1979). In "Polymerization Reactors and Processes" (J. N. Henderson and T. C. Bouton, eds.), pp. 113-136. American Chemical Society Symp. Ser. 104. Washington. D.C. Smith, W. V., and Ewart, R. H. (1948). J. Chem. Phys. 16,592. Stockmayer, W. H. (1957). J. Po/ym. Sci. 24, 314. Ugelstad, J., EI-Aasser, M. S., and VanderholT, J. W. (1973). J. Po/ym. Sci. Po/ym. Leu. Ed. 11, 505. Ugelstad, Ugelstad,
J., and Hansen, F. K. (1976). Rubber Chem. Techno/. 49(3), 536-609. J., Mork, P. c., and Aasen, J. O. (1967). J. Po/ym. Sci. Part A-I 5. 2281.
Wolk, l. L. (1959). U.S. Patent
2,458,456 (to Phillips Petroleum
Co.), January
4.
11 Effect of Additives on theFormation of M onomer Emulsions and Polymer Dispersions J. Ugelstad, P. C. M0rk, A. Berge. T. Ellingsen, and A.A. Khan
1. Introduction . 11. Thermodynamic Treatment of Swelling and Phase Distributions 111. Rate of Interphase Transport . IV. Preparation of Polymer Dispersions . A. Polymerization with Initiation in Monomer Droplets Formed by the Diffusion Process . B. Emulsificationof PolymerSolutions . V. Effectof Addition of Water-Insoluble Compounds to the Monomer Phase . VI. Emulsificationwith Mixed EmulsifierSystems . List of Symbols . References
383 384 392 396 396 399 401 408 411 412
l. Introduction* Quite recently, new methods for the preparation of emulsions by diffusion processes have been described in a number of papers. The methods in volved the diffusion of slightly soluble compounds' (ZI) through the continuous phase to become absorbed into droplets of relatively low molecular weight; highly insoluble compounds (Z2) or into particles consisting of polymer and highly insoluble compounds (Z2)' The swelling capacity of such systems was in several cases shown to exceed that of pure polymer particles by a factor of more than 1000. * For an explanation
of symbols see p. 411.
383 EMULSION POLYMERIZATION Copyright @ 1982 by Academic Preso. loc. All righto of reproductioo io aoy forro reserved. ISBN 0-12-556420-1
384
J.Ugelstad et al.
A section of the present chapter is devoted to a rather detailed description of the basic thermodynamic and kinetic principIes involved in the various swelling procedures. This seems justified in view of the present, and potential, applications of these principIes to the preparation of emulsions and polymer dispersions. The swelling procedures developed so far have led to the first successful methods for preparation of large, monodisperse partic1es. Addition of small amounts of Z2 to solutions of polymers has been shown to facilitate formation of aqueous emulsions of 'such solutions. A very recent application involves the addition of Z2 to the monomer phase in an ordinary emulsion polymerization. This resuIts in a decrease in the concentration of monomer in the polymer partic1es and thereby in a change in the kinetics of polymerization. Another, more specific method for the preparation of emulsions of ZI involves the addition of ZI to a preformed mixture of an ionic emulsifier, a long-chain fatty alcohol, and water. In this way, the. rapid formation of a stable emulsion may be obtained at ordinary stirring with relatively modest amounts of emulsifier. The mechanism of this process is still not satisfactorily explained. AIso, subsequent polymerization (in the case where ZI is a monomer) may lead to polymerization with initiation in monomer droplets. The present chapter reviews the most recent work on the abovementioned topics and inc1udes some hitherto unpublished theoretical and experimental material. 11. Thermodynamic Treatment of Swelling and Phase Distributions The formation of emulsions and the swelling of polymer-oligomer partic1es involve the mixing of amorphous substances of different molecular weights. These processes will be discussed in terms of the original FloryHuggins theory for the free energy of mixing. For a mixture consisting of n components, the free energy of mixing may be expressed as n
I1G/RT
=
n- 1
n
" N In +" "
L... i=1
t
A.. 'rt
~ ¿ i=lj=i+1
~. J.NA.. I ro/) Xt,)
(1)
where X:,j is the interaction parameter per segment of component i with component j, Ji is the number of segments in component i, Ni is the number of moles and
I1G/RTV =
L
i=1
(
+ (1/Y.)(
+
+
+
(2)
11. The Formation of Monomer Emulsions and Polymer Dispersions
385
where V¡.Mis the partial molar volume of component i and V. is the volume of one segment. According to Eq. (2) the terms representing the combinatorial entropy are inversely proportional to V¡.M' Therefore, with large values of V¡.M,as in the case of the mixing of two polymer compounds, the combinatorial entropy makes a very small contribution to the free energy of mixing. Expressing the interaction energy in terms of Hildebrand solubility parameters (Hildebrand, 1964),one obtains Xl.)~. = Vs (é>.I
2 é>. J)
/RT
(3)
Accordingly, polymers will only be miscible when they have almost equal values of 'é>,or if specific interactions between the two types of polymer chains are present, in which case the values of xi.j may be negative. In practice it turns out that the value of xi.j is not only a function of temperature but also varies with the composition. More recent treatments applying the lattice theory of Flory-Huggins have taken this into account. AIso, the original Hildebrand approach has been refined to take into account the contribution of polar groups and hydrogen bonds to the solubility parameters. These modifications of the Flory-Huggins theory and of the solubility parameter concept have made these methods an even more useful tool in the description of solutions, especially of mixtures containing polymer compounds. A comprehensive treatment of these extensions of Flory-Huggins' and Hildebrand's theories, as well as the new "equation of state" approach of Flory (1965), has recently been published (Shinoda, 1978; Olabisi et al., 1979). . The systems considered in the present context may consist of several phases, some or all of which may be present as droplets. The differential molar free energy f9r an n-component system is given by n
dG
= V dP - S dT + L GndNn +
y dA
(4)
where Gn js the partial molar free energy for component n, y is the interfacial tension, and A is the surface area. Assuming monodisperse droplets and subst"ituting dA = 2 dV/r, it follows from Eq. (4) that the partial molar free energy of mixing for any component i when pure i in bulk (plane surface) is used as the reference state is (5) where LlGr is the partial molar free energy of mixing of component i for the case that one operates with aplane surface (r = ct:.»and r is the droplet radius.
386
J. Ugelstad el al.
The condition for equilibrium in the system is that the activity of any component i is the same in all phases. Choosing the pure component in bulk as the reference state, the equilibrium conditions may be written l:1G ia
= l:1G
ib
= l:1G ic = ...
(6)
where a, b, c oo.refer to the phases that make up the system. In practice, the equilibrium state of one or several of the components may be so slowly established that a semiequilibrium state is reached. In this state, the compounds that are more easily transferred between the' phases will have attained their semiequilibrium distribution. Throughout the following discussion, the low molecular weight compounds that are equilibrated between the phases will be denoted by Zl, the relatively low molecular weight compounds which are effectively hindered from being transferred between the phases are denoted by Z2, and the polymer by Z3' Emulsions of Zl that are slightly soluble in the continuous phase may be stabilized toward degradation by diffusion by the presence in the droplets of Zl of a small amount of a Z2 that is insoluble in the continuous phase. This idea was first suggested by Higuchi and Misra (1962). Later, a more general thermodynamic discussion was presented by Ugelstad (1978) and Ugelstad et a/. (1977, 1978a, 1980a,b; Ugelstad and Hansen, 1976). At the instant the droplets in such a system are formed, their composition, with respect to Zl and Z2, is identical. Consider two droplet sizes raoand rg where rao> rg. The initial driving force for the diffusion of Zt from b to a droplets expressed as (l:1GlbO - l:1G1ao)is then given by l:1G tbO
-
l:1G taO
= 2yV1M(l/rg-
l/raO)
(7)
As it is assumed that Z2 is almost completely insoluble in the continuous phase, the transport of Zl from the smaller to the larger droplets leads to an increase in the volume fraction CP2bin the b droplets and a corresponding decrease in CP2a'A concentration potential working in the direction opposite the interfacial free energy difference in Eq. (7) will thus build up. At equilibrium, the activity of component i is the same in the a and b droplets, and furthermore equal to the activity in the continuous phase. The semiequilibrium distribution of component i is therefore determined by l:1Gra
+ 2YV¡Mlra = l:1Grb + 2YV¡Mlrb= RTlnaiw
(8)
where the values of the interfacial tension and radii are those at equilibrium (see note on p. 413). The index w is used to denote the continuous phase, most commonly water. It should however be noted that it mayas well be a mixture of water and nonaqueous compounds or pure nonaqueous solvents. The partial molar free energy differences may be obtained from
11. The Formation of Monomer Emulsions and Polymer Dispersions
Flory-Huggins expression. Substituting semiequilibrium state discussed above In(4)la/4>lb)+ (1 - J¡jJ2)(4)2a
-
387
in Eq. (8) one obtains for the
4>2b)
+ 2V1My(1/ra - 1/rb)/RT = O
+ (4)1a -
4>1b)x12
(9)
where X12 = J1X~2is the interaction parameter per mole of Zl' Calculations based on Eq. (9) show that even minor quantities (-1%) of Z2 may prevent degradation by diffusion to the extent that the size of the resulting emulsion droplets deviate only slightly from their "instantaneous" values. As Eq. (9) describes a semiequilibrium situation, the emulsion is subject to further degradation by diffusion. The rate of this "secondary" degradation process is however determined by the rate of transport of Z2 from b to a droplets. For many practical purposes, this rate may be almost negligible. In systems that are stabilized toward coalescence by means of conventional emulsifiers, the capability of small amounts of Z2 to prevent degradation by diffusion has been demonstrated by several authors (Higuchi and Misra, 1962; Hallworth and Carless, 1974; Davies and Smith, 1974). It has also been demonstrated that the stabilizing effect of different compounds is independent of the chemical structure and determined only by those compound's solubility in the continuous phase (U gelstad et al., 1980a). Thus, the effect of straight- and branched-chain alkanes was found to be the same for compounds with equal solubility. Long-chain alcohols also stabilize aqueous emulsions toward degradation by diffusion to an extent determined mainly by their water sólubility. This observation seems to contradict the suggestion by Hallworth and Carless (1974) that the formation of a condensed layer of emulsifier and fatty alcohol at the droplet surface plays a significant stabilizing role. The effect of relatively water-insoluble additives has been utilized by Ugelstad (1978) and Ugelstad et al. (1978a,b, 1979a, 1980a,b) for the preparation of emulsions by diffusion. The main principIe of these methods is that particles that consist wholly or partly of low molecular weight, insoluble Z2 are .capable of absorbing much larger quantities of Zl than are pure polymer partitles of comparable size. In practice, tbe preparation of an emulsion by diffusional swelling is carried out by first producing an aqueous dispersion of the water-insoluble compounds. This dispersed phase may consist either of pure Z2 or of polymer particles into which Z2 has been introduced in a first step. During the subsequent swelling of these preformed dispersions with a slightly water-soluble Zl, conditions are such that the only transport process possible is the diffusion of Zl through the aqueous phase to become absorbed into the preformed droplets or particles.
388
J. Ugelstad el al.
Any diffusion of Z2 from the particles to the original phase of Z1 is hindered by the low solubility of Z2' The swelling capacity of such particles may be calculated from Eq. (8). Since in this case Zl is present as apure phase, the appropriate equation describing the semiequilibrium state is In cPla+ (1 - J¡jJ2)cP2a+ (1 - J¡jJ3)cP3a+ cPiaX12+ cPiaX13 + (X12 + X13 - X23J¡jJ2)cP2acP3a + 2V1My(1/ra
-
l/rb)/RT
=O
(10)
where raand rb are the radii of the swollen particles and the droplets of Zl at equilibrium. In case no polymer is present, the terms '1Vithindex 3 should be omitted. Figure 1 shows the volume (V1)of Z1 which, according to Eq. (10), may be absorbed per unit volume of polymer (V3)+ Z2 (V2)for different values of J2fJ1 as a function of y/ro. Here, y is the interfacial tension at equilibrium and ro is the radius of the polymer-oligomer particles prior to swelling with Zl' The values of the interaction parameters are arbitrarily chosen to be X12 = X13 = 0.5 and X23 = O. Furthermore, l/rb is considered negligible when compared to l/ra.
o 3
5
4 Lag I ~/ro)
6
(nm-2)
Fig. 1. Swelling capacity of polyrner-oligomer partic1es as a function of 'Ilrofor various values of J2fJ. as ca1culated fram Eq. (10): ro = radius of polymer-oligomer partic1e prior to swelling with ZI, V2 = V3= 0.5, X12= XI3= 0.5, X23= O, V.M= 10-4 m3/mol, T = 323 K.
11. The Formation of Monomer Emulsions and Polymer Dispersions
389
Figure 1 reveals that the swelling capacity of polymer particles containing 50% of a relatively low molecular weight, water-insoluble compound is drastically increased compared to the case with pure polymer particles of the same size (J2fJI = 00). It also appears that the swelling capacity of
polymer-Z2 particles is far more dependent on the value of y/re than is the case for pure polymer particles. This has been verified experimentally by Ugelstad et al. (1978b).Calculations of the swellingof pure droplets of Z2 with ZI give similar curves (Ugelstad et al., 1980a). Figure 2 illustrates the swelling capacity dependence on V2 at a constant value of J2fJI = 5. It appears that even low amounts of Z2 should give a substantial increasein swellingcapacity at low values of y/re. This effecthas been verified experimentally (Ugeistad et al., 1979a). In the course of the swelling process, LlGlasteadily increases. This means that
the driving
force, LlGlb
-
LlGla
--
LlGla (in case rb =
00), steadily
decreases. Figure 3 gives LlGla/RT as a function of the swelling ratio V¡/(V2+ V3)for different values of y/re. It is seen that LlGla/RT is close to zero even at values of VI that are far from the equilibrium value. This means 6 5
l
V¡:1.0 0.67 0.50
0.20
f'r 3
0.10 0.05 0.02
o ..J
21
0.01 O
o 3
t.
5
6
Log(~/ro) Fig. 2. Swellingcapacity of polymer-oligomerparticles versus y/ro for different values of v2: ro = radius of polymer-oligomer particles prior to swelling with Zt> V2+ V3 = 1, J2/J, = 5, X12= X13= 0.5, X23= O, V1M= 10-4 m3/mol, T = 323 K.
390
J. Ugelstad et al.
0.002 0.000
- 0.002 - O.OO~
1~:;:-0.006 -0.008
I
¡
-0.010 -0.012 -0.014 10
1000
10,000
VI/IV2>V3)
Fig. 3. Partialmolar free energy of ZI in swelling partic1es versus swelling ratio, for various values of "t/ro: XI2 = XI3 = 0.5, X23= O, J2/J1= 5, V2= 2/3, V3= 1/3, V1M= 10-4 m3/mol,T= 323K.
that the maximum obtainable swelling is very sensitive to factors that would cause a deviation in the entropy of mixing from that given by the Flory-Huggins expressions. At equilibrium the activity of Zl in the continuous phase is equal to its activity in the a and b droplets. Ir an excess of pure Zl is present and if the radius of the b droplets is considered to be infinite, as in the case discussed above, this activity is equal to unity. The swelling equilibrium is in this case the same as the one that would be obtained for swollen particles in equilibrium with a saturated solution of Zl in the continuous phase. Ir Zl is present .as droplets of finite size, its activity at equilibrium (equal in all phases) is larger than unity because of the interfacial free energy of the b droplets. This in turn may lead to an increase in the degree of swelling. Ir the b droplets are smaller than the a droplets, or become smaller during the swelling, one may in principie obtain "infinite" swelling of the a droplets. Finally, it may be desirable to emphasize some points regarding the general application of Eq. (8) for calculations of swelling and equilibrium distribution of Zl between the various phases. 1. Ir one operates with an excess of Zl, the swelling of each phase may be treated independently of the other phases. Ir there is a shortage of Zl,
11. The Formation of Monomer Emulsions and Polymer Dispersions
391
several cases of competitive swelling may be encountered in practice. They may easily be dealt with by applying the correct expression for dGl to the various phases. A typical example is the swelling of polydisperse droplets of Z2' The final distribution is determined by the initial droplet sizes only. The swelling of a mixture of monodisperse droplets of various Z2 cO'nstitutes another example. In this case the final size distribution will be determined by the value of J2 for the various compounds. A third possibility is the swelling of a system consisting of two types of monodisperse polymer particIes containing different amounts of the same Z2' The appropriate equilibrium equation in this case is In
+ (1 - J¡jJ2)(
+ (
+ 2yV1M(1/raIn this equation,
-
-
X23JlfJ2)
1/rb)/RT= O
(11)
a and b denote the two different particIe sizes. Combining
Eq. (11) with a material balance for Zl allows the caIculation of the radius of the two types of particIes as a function of the total amount of Zl absorbed. Excellent agreement between caIculated and experimental results has been obtained for such systems (Ugelstad et al., 1979b, 1980a). 2. Every compound that may be transferred between the phases within the time scale of the experiment will equilibrate between the various phases. This means that if for instance one type of Zl has been incorporated in a polymer particIe in a first step, and another type of Zl is added in a second step, the equilibrium' swelling of the particIe will not deviate noticeably from the one obtained in the presence of either Zl' The reason for this is that the type of Zl first absorbed will diffuse out of the particIes and become mixed with the second type of Zb with the concomitant gain in entropy that this mixing process involves. Similarly, if the system consists of droplets of the insoluble Z2, or of polymer particIes containing Z2, and if a mixture of two types of Zl with similar J values is added, the resulting swelling will be approximately the ~ame as that obtained with either of the two types of Zl' 3. Equation (10) may easily be extended to incIude the swelling of particIes containing any number of different Z2' Again it should be noted that for a given particIe size, the presence of a mixture of two or more types of Z2 will not in crease the degree of swelling beyond that obtained with the same amount of one type of Z2 as long as the various types have similar J2
values. Points 2 and 3 (above) emphasize the fact that the driving force for the swelling process is mainly the gain in entropy obtained by mixing of the various components of the system.
392
J. Ugelstad el al.
111. Rate of Interphase
Transport
The rate of transport of ZI from phase b to another phase a may in principie be governed by one of several mass transfer steps. These inc1ude diffusion from the interior of b to the interface, transport across the interface of phase b, diffusion through the continuous phase, transport across the interface of phase a, and finally diffusion inside phase a. Transport within a phase may be rate determining where a polymer constitutes a major part of the phase and the temperature.is below the glass transition point. Diffusion across the interfaces may be rate determining in cases where polymeric emulsifiers are applied (Netschey el al., 1969; Napper et al., 1971), whereas conventional surfactants probably do not constitute any interfacial barrier to micron-sized droplet systems (Higuchi and Misra, 1962). For such a case, these authors derived an expression for the rate of degradation of emulsions by molecular diffusion. Several papers on the mechanisms of interphase transport (Goldberg el al.,. 1967; Goldberg and Higuchi, 1969) and on the effect of interfacial barriers on interphase transport (Ghanem et al., 1969; 1970a,b) have appeared. For the present purpose, discussions will be restricted to cases where the transport of ZI through the continuous phase is the rate-determining step. The rate of transport from the bulk of the continuous phase to the surface of the swelling partic1es (phase a) is 'then given by (Smoluchowski, 1918) R
la
= 4nraNaDw(CI- Clas)
(12)
where CI is the concentration of ZI in the bulk of the continuous phase, Clas is the concentration at the partic1e interface, Dw is the diffusion constant of ZI in the continuous phase, and Na is the number of partic1es with radius ra, Assuming that Henry's law may be applied, one has for low values of CI Clas
= Clooexp(AGla/RT)
(13)
where Cloo is the concentration in the continuous phase when this is equilibrated with pure ZI in bulk (plane surface), Substituting for Clas in Eq. (12),one obtains for the rate of swelling of a partic1es dVIJdt
= Rla = 4nDwraNa[CI -
Cloo exp(AGla/RT)]
(14)
where the concentrations are given in v/v units. In the case where the solution is saturated with ZI (relative to pure ZI in bulk), Eq. (14) may be written dVla/dl
= 4nDwraNaCloo[1- exp(AGIJRT)]
(15)
-
11. The Formation of Monomer Emulsions and Polymer Dispersions
393
If the swelling system consists of a solution of Zl and a number of a
particles, then C1 will decrease as the swellingproceeds unless a very large excess of the solution of Zl is employed, in which case Cl may remain approximately constant. Usually, however, Zl is dispersed as droplets (phase b) and the rate of transport from the droplets to the bulk of the continuous phase (Rlb) must be taken into account. Setting Rla = Rlb, the followinggeneral expression for the rate of swelling is obtained (Ugelstad et al., 1980a). dVla/dt = 4nfaNafbNbDwClOO [exp(dGlb/RT) faNa
+
fbNb
- exp(dGla/RT)]
(16)
The values of dGla and dGlb may be calculated using the appropriate forms of Eq. (5). Two limiting cases of Eq. (16) will now be treated. Case 1 Equation (16) is then simplified to dVlJdt
= 4nfaNaClooDw[exp(dGlb/RT)
-
exp(dGla/RT)]
(17)
This implies that the concentration of Zl in the continuous phase is kept constant, equal to the solubility of ZI from the b droplets. Even if fb > fa this sitnation may be realized if the swelling is carried out with a very large excess of ZI' If f~ > 10 f.1.m,Eq. (17) is for all practical purposes equal to Eq. (15). Case 2
(faNa ~ fbNb)
This condition is \.1sually fulfilled for fa ~ fb when a moderate excess of phase b is applied. In many cases the magnitude of fb is such that
-
exp(dGlb/RT) may be set equal to unity (with dGlb 4 x 10- 5J/mol. Equation (16) may then be written dVla/dt = 4nfbNbClct:,Dw[1- exp(dGla/RT)]
fb = 10 f.1.m, (18)
Equation (18) illustrates the importance of subdividing phase b in order to obtain high rates.of swelling. Since fbNb = 3Vb/4nf;, therate is proportional to the volume of monomer and inversely proportional to the square of the droplet radius. Figure 4 shows the results of some calculations of the degree of swelling, expressed as V1alv.°,as a function of time for some selected.cases. The general Eq. (16) was used with Dw = 10-10 m2/sec and Cloo = 6 X 10-4 m3/m3, Le., values that approximately would be applicable to styrene in water. It was further assumed that the radius of the b droplets f~ remained constant during the swelling, as this seems to be the more
394
J. Ugelstad el al.
180 160 140
o. >
.
....
120 100
->
80 60 40 20
10
20
30
40
50
80
10 Tim_1
10
10
100
110
120
130
minI
Fig. 4; Volume of 21 absorbed per unit volume of polymer-oligomer (v.O) versus time, calculated from Eq. (16): Dw = \O-10 m2jsec, CI", = 6 X \0-4 m3jm3, r~ = 2 x \0-7 m, V2a = V3a = 0.5 V.o, Ya= Yb= 5 mNjm, X12 = X23 = 0.5, X23 = O, J2fJI = 3, VIM= \0-4 m3jmol, T=
323 K, rg and Vb°¡v.° as indicated.
realistic approximation when the b droplets consist of 21 only. The decrease in the size of the b droplets, which might be expected to result from transport of 21 from b to a droplets, is probably counteracted by coalescence and by diffusion among the b droplets. In practice, a given stirring intensity will tend to give the same average droplet size independent of "conversion." Curve A in Fig. 4 illustrates a case where a large excess of small b droplets
are assumed
to be present (r~
=
1 jlm). This would correspond
to
the case exemplified by Eq. (17). Curve B is caIculated for a case where the concentration of 21 in the aqueous phase is constant, equal to the saturation concentration relative to aplane phase (CI",). In curve C, a large excess (Vb°;v..°= 105) of lO-jlm droplets
of 21 is
assumed to be present. The higher rate of swelling obtained in the case A as compared to B and C is due to the interfacial free energy term which, because of the lower value of r~ in case A, gives a higher value of L\Glb, i.e.
395
11. The Formation of Monomer Emulsions and Polymer Dispersions
a higher solubility of Zl in the aqueous phase. Curve B corresponds to the case leading to Eq. (15), and as is seen from a comparison of curves B and C in Fig.4, this equation is a good approximation when rg> 10 p.m and a large excessof b droplets is present. Curves F and D illustrate the effect of decreasing the diameter of the b droplets at constant value of VbO fV..0(= 100). Comparison of curves C, E, and F shows the effect of decreasing the volume of the b phase at a constant value of rg (= 10 p.m). For curve E, the general Eq. (16) must be applied, although the term exp(LlG1b/RT) may approximately be set equal to unity. Curve F may be described by the limiting case given by Eq. (18). Figure 5 shows some experimental results (Mfutakamba et al., 1979) of the swelling of 2.3-p.m polystyrene-dioctyladipate particles (V3afV2a= 0.5) with chlorobenzene at 308 K. When the swelling is carried out with ordinary stirring and an excess of chlorobenzene corresponding to 16
D 14
12
e
E
.=
10
...
..
B
.. 8 E 111 e 6
A
4
2
2
3
5
6
7
8
Time (hrl
Fig. 5. Swelling of polystyrene/dioctyladipate particles with chlorobenzene: r~=1.l5xl0-6m, V2.JV3a=0.5, T=308K. (A): V¡,°¡v.°=49, ordinary stirring (140rpm); (B): V¡,0/V.o = 49, Ultraturrax; (C): V¡,0¡v.0 = 290, ordinary stirring (140 rpm); (D): Vb°¡v.°= 290, Ultraturrax.
396
J. Ugelstad el al.
VbO/Ya0 = 49, curve A is obtained. If the mixture of chlorobenzene, water, and emulsifier is treated with a high-speed mixer (Ultraturrax) droplets of chlorobenzene in the micron-size range are formed. When the polystyrenedioctyladipate particIes are added to this dispersion, curve B is obtained. As expected, the reduction in droplet size leads to a substantial increase in the rate of swelling. Curves C and D are obtained with a chlorobenzene-particIe volume ratio of 290: 1, the other conditions being the same as for curves A and B, respectively. A comparison of curves A and C or of curv~s B and D cIearly shows the effect of increasing the total volume of the b phase, in accordance with what would be expected from Eq. (18),which should apply to this case. It thus seems quite evident that in this case, the rate-determining step in the swelling process is the mass transfer from the droplets of Zl to the water phase.
IV. A.
Preparation of Polymer Dispersions Polymerization with lnitiation in Monomer Droplets Formed by the Diffusion Process
Monomer emulsions prepared by the methods described above have been applied to the preparation of polymer dispersions. The crucial point in such applications is to establish conditions that ensure that the initiation takes place in the monomer droplets. In practice, this requires that the concentration of emulsifier in the aqueous phase during polymerization be as low as possible and certainly below the CMC (Hansen and Ugelstad, 1979). Polydisperse PVC latexes with particIe sizes in the range of 0.3-1.5 ,um have been prepared by homogenization of different Z2 with water and emulsifier to give stable emulsions of Z2 with droplet sizes from 0.050.3 ,um. When water and monomer are added to t~is preemulsion, a monomer emulsion is formed by rapid diffusion of vinyl chloride into the preformed droplets of Z2' Polymerization may be carried out by using either water- or oil-soluble initiators (Ugelstad et al., 1978a, 1980a,b). A similar method has been applied to produce acrylate latexes of very low particIe size (Ugelstad et al., 1978a). Another interesting application of this method is the preparation of large, monodisperse polymer particIes. In this case the starting point is small, monodisperse particIes (seed) in the size range of 0.3-1 ,um, produced by ordinary emulsion polymerization according to procedures known to give mono disperse particIes (Vanderhoff et al.,1956, 1970; Goodwin et al.,
11. The Formation of Monomer Emulsions and Polymer Dispersions
397
1973, 1976, 1978). Low molecular weight, water-insoluble compounds (oligomers) may be incorporated into the partic1es during their preparation by addition of a chain-transfer agent during polymerization (Ugelstad, 1978; Ugelstad et al., 1978b), or may alternatively be introduced into the preformed polymer partic1es. One way of doing this is to swell the polymer particles with monomer and initiator and carry out the subsequent polymerization under conditions that lead to the formation of oligomers. Another procedure requires the seed in a first step to be swollen with a low molecular weight, water-insoluble Z2' (Ugelstad et al., 1978a,b, 1979a,
Fig.6.
Scanning
electron micrograph
of monodisperse
5.3-Jlm polystyrene
particles.
398
J. Ugelstad el al.
1980a.) One way of facilitating this process is to add a water-soluble solvent to increase the solubility of Z2 and thereby make possible its diffusion through the continuous phase to become absorbed in the seed particIes. In a next step the monomer is added to the dispersion of polymer-oligomer or polymer-Z2 particIes. The experimental conditions in this second step are adjusted so that no transport of oligomer or Z2 out of the particIes is possible during the swelling with monomer. The mono disperse monomer droplets formed by this procedure are subsequently polymerized, preferably with an oil-soluble initiator. Figure (6) shows a scanning electron micrograph of mono disperse 5.3-j.lm polystyrene particIes produced according to this method. ParticIes up to about 15 j.lm have been prepared with a standard deviation of about 0.6% (measurements performed by Becton and Dickinson with an "Ultra-Flow" high resolution particIe analyzer). Monodisperse particIes may also be produced with a cross-linked structure, and monodisperse porous particIes may be obtained (Ugelstad el al., 1980a) by applying methods known from suspe,nsion polymerization. ParticIes with functional surface groups have been prepared by chemical modification of the surface' of cross-linked monodisperse particIes of styrene-di.vinylbenzene or by copolymerization with monomers containing the desired functional groups. In principIe, the two-step swelling procedure discussed above may be applied to swell polymer particIes with a quite different type of monomer to
Fig. 7. Electron micrograph of particles resulting from polymerization of a polystyrene seed (500 nm) swollen with a mixture of acrylic monomers (magnification 4080 x ).
11. The Formation of Monomer Emulsions and Polymer Dispersions
399
obtain a homogeneousmixture of polymer Z2 and the second monomer. By the subsequent polymerization, however, a phase separation will normally take place. The reason for this, as was discussed in connection with Eq. (2), is the low entropy of mixing in the case of two polymer substances. Most interesting in this context is the fact that the original polymer particle may be restored as a separate phase in the course of the polymerization. This particle may be partly expelled from the final particle which consists mainly of the polymer formed from the second monomer. The phenomenon has been observed in the case of polystyrene swollen with a mixture of styrene and methacrylic acid and even more so when polystyrene is swollen with methyl methacrylate or mixtures of methyl methacrylate and hydrophilic acrylates. An example of this phenomenon is shown in Fig. 7. Applying the two-step swelling procedure, a monodisperse polystyrene seed was swollen with a mixture of acrylate monomers. The droplets formed appeared to consist of a homogeneous mixture of the monomers, Z2 and polystyrene. After polymerization the original polystyrene particle is almost completely expelled from the acrylic polymer particle. B.
Emulsification of Polymer Solutions
The recent trend to avoid organic solvents has led to substantial elforts to prepare aqueous dispersions of polymers that cannot be prepared directly by emulsion polymerization. This includes such important polymers as epoxy resins, polyurethanes, and silicones. One method. to achieve this is by emulsifying solutions of the polym~r by homogenization, followed by evaporation of the solvent. Most often this method gives particles in the range of 1 to 211m. 1'his may be a disadvantage in that the dispersion is unstable toward settling of the particles on storage, and furthermore, large particles tend to give inferior film properties. Vanderholf et al. (1979) showed that addition of small amounts of Z2 to the solution of a polymer before homogenization led to much more finely dispersed droplets of the polymer solution. A number of dilferent polymer dispersions have since been prepared (EI-Asser et al., 1977a,b; Vanderholf et al., 1978; Miscra et al., 1978). Ugelstad (1978) and Ugelstad et al. (1978a) have explained the elfect of adding small amounts of Z2, along the same lines as the thermodynamic treatment above. In the present discussion the previous explanation of the effect of Z2 is somewhat extended. The solvents applied in practice are all slightly water soluble, i.e., Zl types. At a given composition of the solution of polymer (Z3) and solvent (Zl) there is a theoretical minimum in the droplet size that may be obtained before phase separation should occur. A droplet of this minimum size
400
J. Ugelstad el al.
contains a given amount of polymer. The minimum droplet size corresponds to the swelling capacity of a partic1e consisting of this amount of polymer. Therefore, the minimum droplet size will in crease with increasing amount of solvent (ZI)' If a small amount of Z2 is added before homogenization, the droplets formed contain a small amount of Z2 in addition to Z3' The swelling capacity of a partic1e in which even a small amount of Z3 is replaced by Z2 is considerably higher than that of pure Z3' Therefore, in the presence of Z2 the. minimum diameter that may be obtained with a given amount of solvent (ZI) may be drastically reduced. 'Calculation of this minimum diameter may be carried out by applying Eq. (10). An example of such a calculation is given in Table 1. It appears from the table -that the minimum diameter in creases with increasing amounts of ZI' It also appears that even with small amounts of Z2 it is possible to obtain small partic1es. This is also the case where without Z2 one gets phase separation even at infinite diameters of the partic1es. During homogenization of a solution of polymer (Z3)' solvent (Z¡), and water, droplets of different sizes are formed. Becaúse of the interfacial energy difference, a transport of ZI from the smaller to the larger droplets will take place. If droplets smaller than the critical size are formed, these droplets, especially, will rapidly lose ZI to the surrounding larger droplets. The viscosity within these small droplets will increase and a further degradation may be mechanically hindered. In the presence of Z2, two effects that will facilitate subdivision of the emulsion may be encountered. 1. The degree of diffusion between small and large droplets will be reduced because the presence of Z2 means that a counteracting concentration potential is more rapidly established. TABLEI The Minimum Diameter That May Be Obtained by Homogenization of a Polymer Dissolved in a Solvent (Z,) as a function of Volume V, of the Solvent and Volume V2 of a Z28.b
X
X = 0.5
= 0.3
O 0.01 0.02 0.10
.
2
5
10
2
5
10
2
21 20 19 16
110 103 96 66
415 370 334 190
48 44 40 24
454 338 269 105
2980 1500 1005 280
147 108 85 32
From
Ugelstad
b XI2 =
O, XI3
T= 300 K.
X =0.6
(1978)
= X23
with
5
10
2545 3 x 105 146 356
permission.
= X, V2+ V3= 1, J2fJI = 5, V1M= 10-4 m3/mol, y.= 5X10-3 N/m,
11. The Formation of Monomer Emulsions and Polymer Dispersions
401
2. The presence of Z2 tends to decrease the critical minimum size. In practice this means that the formation of droplets with a higher viscosity, due to transport of ZI from small to large droplets, is reduced. The presence of Z2 makes possible the formation of small droplets with relatively high amounts of ZI, and therefore low viscosity, without getting below the critical value of the droplet size.
V.
Effect of Addition ofWater-Insoluble Compoundsto the MonomerPhase
If in an ordinary emulsion polymerization, a water-insoluble Z2 is added to the monomer phase, the etfect will obviously be to decrease the activity of the monomer in this phase and accordingly to decrease the concentration of the monomer in the partic1es (Azad et al., 1980; Ugelstad et al., 1980b,c). The appropriate form of the equilibrium equation for the case in which one has ZI equilibrated between Z3 partic1es and monomer droplets containing Z2 will be In 4>13 + 4>33
+
4>f3X13
= In 4>lb + (1 -
+ 2V¡My/r3RT J¡jJ2)4>2b
+
4>ibXl2
+ 2V1My/rbRT
(19)
where index a and b refer to polymer partic1es and monomer droplets, respectively, and J3 is set equal to infinity. If the monomer droplet radius (rb)is very large the last term may be neglected. It appears that if y/r3is assumed to be constant, any equilibrium value-of 4>2b will correspond to a value of 4>13 that is independent of the initial monomer-polymer nitio. Such a situation was considered by Azad el al. (1980) in their discussion of the etfect of additives to the monomer phase on the degree of swelling and on the kinetics of polymerization. A more relevant approach to this problem might be to consider the etfect of a given amount of Z2, V2, or a
given initial volume fraction of Z2, 4>Rb' in the monomer phase on 4>13/4>13 (V2= O)(Le.,the ratio of the volume fractions of monomer in the partic1es with and without addition of Z2 to the monomer phase) for various values of vNV30,the initial.ratio of monomer to polymer. In order to illustrate the etfects one may expect and the problems in interpretation of experimental results, some ca1culationsshowing the etfect of addition of Z2 to the monomer phase have been carried out using Eq. (19). In Figures 8 and 9, 4>13/4>13 (V2= O)is given as a function of VIO/V30for various values of 4>fb = V2/(V2+ VIO)and V2, respectively.In these ca1culations, the radius of the polymer partic1es is assumed to be r~ = 5 x 10- 8 m
400
J. Ugelstad el al.
contains a given amount of polymer. The minimum droplet size corresponds to the sweIling capacity of a particIe consisting of this amount of polymer. Therefore, the minimum droplet size wiII increase with increasing amount of solvent (21), If a smaIl amount of 22 is added before homogenization, the droplets formed contain a smaIl amount of 22 in addition to 23' The sweIling capacity of a particIe in which even a smaIl amount of 23 is replaced by 22 is considerably higher than that of pure 23' Therefore, in the presence of 22 the minimum diameter that may be obtained with a given amount of solvent (21) may be drasticaIly reduced. Calculation of this minimum diameter may be carried out by applying Eg. (lO). An example of such a caIculation is given in Table 1. It appears from the table 'that the minimum diameter increases with increasing amounts of 21, It also appears that even with smaIl amounts of 22 it is possible to obtain smaIl particIes. This is also the case where without 22 one gets phase separation even at infinite diameters of the particIes. During homogenization of a solution of polymer (23), solvent (21), and water, droplets of different sizes are formed. Because of the interfacial energy difference, a transport of 21 from the smaIler to the larger droplets wiII take place. If droplets smaIler than the critical size are formed, these droplets, especiaIly, wiII rapidly lose 21 to the surrounding larger droplets. The viscosity within these smaIl droplets wiII increase and a further degradation may be mechanicaIly hindered. In the presence of 22, two effects that wiIIfacilitate subdivision of the emulsion may be encountered. 1. The degree of diffusion between smaIl and large droplets wiII be reduced because the presence of 22 means that a counteracting concentration potential is more rapidly established. TABLEI The Minimum Diameter That May Be Obtained by Homogenization of a Polymer Dissolved in a Solvent (Z1) as a function of Volume V1 of the Solvent and Volume V2 of a Z2a.b X = 0.3
x = 0.5
x = 0.6
>\'
2
5
10
2
5
10
2
O 0.01 0.02 0.10
21 20 19 16
110 103 96 66
415 370 334 190
48 44 40 24
454 338 269 105
2980 1500 1005 280
147 108 85 32
a
From Ugelstad
b X12
5
10
2545 3 x 105 146 356
(1978) with permission.
= O, XI3= X23= X, V2+ V3= 1, J2/11= 5, VIM= 10-4 m3/mol, y = SX10-3 N/m,
T= 300 K.
11. The Formation of Monomer Emulsions and Polymer Dispersions
401
2. The presence of Z2 tends to decrease the critical minimum size. In practice this means that the formation of droplets with a higher viscosity, due to transport of ZI from small to large droplets, is reduced. The presence of Z2 makes possible the formation of small droplets with relatively high amounts of ZI, and therefore low viscosity, without getting below the critical value of the droplet size.
v.
Effect of Addition ofWater-Insoluble Compoundsto the MonomerPhase
If in an ordinary emulsion polymerization, a water-insoluble Z2 is added to the monomer phase, the effect will obviously be to decrease the activity of the monomer in this phase and accordingly to decrease the concentration of the monomer in the partic1es (Azad et al., 1980; Ugelstad et al., 1980b,c). The appropriate form of the equilibrium equation for the case in which one has ZI equilibrated between Z3 partic1es and monomer droplets containing Z2 will be In I/Jla
+ 1/J3a +
I/Jfax13+ 2VIMy/raRT
= In I/Jlb+ (1 - J¡jJ2)1/J2b+ l/JibX12+ 2VIMy/rbRT
(19)
where index a and b refer to polymer partic1es and monomer droplets, respectively, and J3 is set equal to infinity. If the monomer droplet radius (rb) is very large the last term may be neglected. It appears that if y/ra is assumed to be constant, any equilibrium value-of 1/J2bwill correspond to a value of I/Jla that is independent of the initial monomer-polymer ratio. Such a situation was considered by Azad et al. (1980) in their discussion of the effect of additives to the monomer phase on the degree of swelling and on the kinetics of polymerization. A more relevant approach to this problem might be to consider the effect of a given amount of Z2, V2, or a given initial volume fraction of Z2, I/J~b'in the monomer phase on I/JIJI/JIa (V2 = O) (Le., the ratio of the volume fractions of monomer in the partic1es with and without addition of Z2 to the monomer phase) for various values of vNv30, the initiaf ratio ofmonomer to polymer. In order to ilIustrate the effects one may expect and the problems in interpretation of experimental results, some ca1culations showing the effect of addition of Z2 to the monomer phase ha ve been carried out using Eq. (19). In Figures 8 and 9, I/JlaNla (V2= O) is given as a function of VI°IV30for various values of I/Jfb = V2/(V2 + VIO)and V2, respectively. In these ca1culations, the radius of the polymer partic1es is assumed to be r~ = 5 x 10-8 m
402
J. Ugelstad et al.
1.0 0.9 0.8
-o
0.7
N >
0.6
"
o 02b
" 61 ..... !! 61
=
0.2 o 02b =0.3
0.5
0.1,
0.3
0.2
0.1
1.0
2.0
5.0
3.0 VI/V3
Fig. 8.
Ratio of volume fraction of ZI in a partic1es to the same volume fraction when
=
V2 O versus initial ratio of ZI to Z3 for various values of the initial volume fraction of Z2 in the b phase: r~ = 5 x 10-8 m, X12 = X13 = 0.5, V1M= 10-4 m3/mol, V2M= 3 X 10-4 m3jmol,
y = 5 mNjm,J2jJ¡ = 3, T = 323K.
and the monomer droplet radius is set equal to infinity. The values of X12 and X13are arbitrarily chosen to be 0.5 and the molar volumes of 21 and 22 are set equal to 10-4 and 3 x 10-4 m3/mol, respectively. The interfacial tension at equilibrium is assumed to be 5 mN/m and T = 323 K. It would
appear
from Fig. 8 that
(V2
= O)
passes
through
a
minimum as VIo/V3oincreases. This minimum occurs at a value of VIO /V30 corresponding to that of maximum swelling of the polymer particles in the absence of 22 and is less pronounced as the value of
11. The Formation of Monomer Emulsions and Polymer Dispersions
0.9
V2=0.S V2=1.0
0.8
-
403
0.7
o
11 N
0.6 ni SI -ni SI
o.S 0.4 03
0.2 01 2
¿
6
e
IC
1,
14
16 18 20
v / V3 Fig. 9. cP.Jc/>1a (V2= 0.)versus vNvJoat various 'values of the volume (V2) of Z2 in the b phase. V~ = 1. Parameter~ equal to those in Fig. 8.
reduced. AIso in Fig. 9 a minimum in the volume fraction ratio is observed at low values of V2. As expected, the minimum disappears as V2increases. When the etTect of Z2 on the rate of polymerization is determined experimentally, it should be kept in mind that with a given value of
+ (VIO -
ra = r~[(V3a VI
= V1a+
Vlb)(d¡jd3)
+ Vla)/V30]
1/3
V1b
where di and d3 are the densities ofmonomer and polymer, respectively.
404
J. Ugelstad el al. 8 7 6
-... E S 't:I ...
o E 4 .. u 3
2
0.1
0.2
0.3
0.4
0.5
Q6
0.7
0.8
0.9
10
Fig. 10. Concentration of monomer in the polymer particJes during polymerization as a function of conversion when Z2 is present in the monomer phase: V2= 0.1, V30= 1, VIOas
indicated, r~= 5 x 10-8 m, VIM= 10-4 m3/mol, J2/JI = 3, X12= X13= 0.5, y = 5 mN/m, T= 323K.
Figure 10 gives CIa as a function of the conversion of monomer, defined VI)/VIO for V2 = 0.1 and V30= 1 at variousvaluesof vt The ratio d¡/d3 is set equal to 0.82, the other parameters being the same as those used in Figs. 8 and 9. It would appear that the value of CI. also decreases in Interval n, even in the case where y is kept constant. In the case where y/r. remains constant, the decrease in CI. will be more pronounced. The effect of the additive on the rate will of course depend upon whether we operate in Interval n or In, and moreover on whether Smith-Ewart Case 1, 2, or 3 is operating. Figure 11 gives an example of experiments with seeded styrene polymerization with different amounts of hexadecane
as 1J= (V? -
added. The value of VIO/V30 is in this case
-
20, the value of 4>fbis 0.08 and
0.16, respectively. It would appear that the initial rate is lower the higher the value of 4>fb' as would be expected under Smith- Ewart n conditions from the lowering of the concentration of monomer in the particles. At increasing conversions it
405
11. The Formation of Monomer Emulsions and Polymer Dispersions 195,- -
- -
- -
-
150 o'"
I
J: .... E
~
I 100
DI
i
-~
50
.::.
0.6g K2S20a/dm3 H20
H20
10"10Hexadecane O
I
0.6 g K2S20a/dm3 20"10 Hexadecane
H20
Seed: 10g /dm3 H~ N
10
O
~--3 0.6 g K2S20a/ dm
3.010'6 part.l dm3H20
~-l 60
120
lao
21,0
300
360 TIME
420
I,ao
51,0
600
(min)
Fig. 11. Conversion versus time curves for seeded emulsion polymerizations with hexadecane present in the monomer phase. T = 333 K.
of sty~ene
turns out that when hexadecaneis present, the rate of polymerization increasesand becomeshigher than in the casewithout hexadecane.This is most probably due to a Trommsdortf etfect. In the caseof vinyl chloride, the additiori of Z2 to the monomer phase leads to an increase in rate from low conversions on (Fig. 12). This result is in accordance with the results of Ugelstad et al. (1967)who found that the rate of polymerization of vinyl chloride, at constant particle number, increased when the reaction was carried out at subsaturation pressures. In the above calculations we ha ve assumed that the monomer is evenly distributed in the polymer particles. In this case oÍle finds that at low values of V?fV30 the value of fb' From Fig. 8 it is seen that at a value of V,ojV30= 0.05, the value of
= O) is
0.95 at
is
added continuously, Le., semicontinuous or continuous polymerization, one has "starving" conditions with respect to monomer concentration. It has been suggested that in such cases, polymerization may take place in an outer shell of the particles. Figure 13 gives the result of a calculation of the swelling in an outer shell of thickness 50 A, expressed as 4>la/4J'a(V2 = O), versus the initial monomer-polymer volume ratio for various values of
406
J. Ugelstad et al.
300
oN
:x: PI
e ~ 200 (.)
> o. el
100
100 Fíg. 12. chloride
200 TIME (min)
300
Conversions versus time curves for seeded emulsion polymerization of vinyl
with hexadecane
present
in the monomer
H20. Seed: 3.6x 1016 particles/dm3 H20, hexadecane.
phase.
[K2S20SJ
= 2.7
x 10-3 moljdm3
T= 323 K. A: without hexadecane: B: 20%
reduced by a factor that decreases as the particle radius increases. In the present example (r~ = 0.05 Jlm) this factor is initially 0.27. The relevant equation for calculating the curves in Fig. 13 is obtained from Eq. (19) by inserting the following relationships r.
= raO[(V3o + V1s)fV30] 1/3
Vs = V30(3r;c5
- 3rac52 + c53)/(r~)3
= V1sIVs
where VIS is the volume of monomer in the shell of thickness c5and total volume Vs. The other parameters used in calculating the curves in Fig. 13 are the same as in Fig. 8. Comparing Fig. 13 with Fig. 8 it appears that in this case one may expect a considerably larger effect of the additive. Thus, for VIO fV30= 0.05 and
11.
The Formation of Monomer Emulsions and Polymer Dispersions
1.0
407
..
I
0.9 0.8 a7
o
-o
" N > ..'"
ii .....
02b
=
0.2
0.6
0.5
SI 0.4 0.3
02
0.1
05
1S
10
2.0
V~/V3
Fig. 13.
Swellingof a 50-Á outer shell of a
Ratio of volume fraction of monomer
polymer particle with radius 5 x 10- 8 m. in the shell with and without Z2 present in the monomer
phase versus initial volume ratio of monomer given in Fig. 8.
to polymer.
Other parameters
are equal to those
limited to a sheIl of thickness 50 A, as compared to 0.95 when the monomer is evenly distributed in the polymer particIe. Azad et al. (1980) applied a ratio of VNV30 3.5 and measured the rate of polymerization with different additives in the monomer phase. With addition of octadecane in an amount corresponding to
408
J. Ugelstad el al.
This will tend to counteract the effect of an increasing CP2b.AIso, as they pass into Interval III they may have had a Trommsdorff effect counteracting the decrease in the concentration of monomer.
VI.
Emulsification with Mixed Emulsifier Systems
One of the metl¡.ods described above for preparing stable emulsions of ZI involved homogenization of Z2 with water and emulsifier. to produce small droplets of Z2 which served as loci for the subsequent preparation of an emulsion of ZI by diffusion. A different method which makes the use of a homogenization process unnecessary involves the use of a mixture of ionic emulsifier and long-chain fatty alcohols. This procedure seems to have been known industrially for quite a long time. The first paper that clearly demonstrated that this method could be used to prepare stable emulsions of monomer and that the subsequent polymeri~ zation might take place with initiation in monomer di-oplets was presented by Ugelstad el al. (1973a). Since then a number of papers on this subject have been published (Ugelstad el al., 1973b, 1974; Hansen et al., 1973, 1974; Lange et al., 1974; Azad et al., 1975). The process is carried out by mixing water, fatty alcohol, and emulsifier at a temperature above the melting point of the fatty alcohol. ZI is then added at ordinary stirring and within a few minutes, afine emulsion with droplet sizes in the range of 0.2 to 1.5 11m is obtained. In the case where ZI is a monomer, subsequent polymerization may lead to initiation in the monomer droplets. A typical recipe may consist of 0.2-0.5 g ionic emulsifier, 0.2-1 g fatty alcohol, 50-100 g monomer, and 100 g water. The following points should be noted: 1. The fatty alcohol and the ionic emulsifier should be mixed with water at a temperature above the melting point of the fatty alcohol before addition of monomer. If such small amounts of fatty alcohol are dissolved in the monomer before addition to a mixture of water and ionie emulsifier, only very coarse and unstable emulsions are formed. 2. The fatty alcohol that is to be used should have a chain length of at least 16 carbon atoms. 3. The ratio of fatty alcohol to ionie emulsifier should be approximately in the range of 1:1 to 4: 1 on a molar basis. 4. If fatty alcohol s with chain length equal to or less than 16 carbon atoms are applied, the emulsion formed is relatively unstable. In order to get initiation in monomer droplets, the polymerization should then be carried out immediately after preparation of the monomer emulsion. This emulsification process thus exhibits the interesting phenomenon of a rapid and easy formation of an emulsion that is relatively unstable toward
11. The Formation of Monomer Emulsions and Polymer Dispersions
409
degradation by diffusion. The fact that with fatty alcohols below a certain chain length one gets very unstable emulsions indicates that also in this case the degradation by diffusion is a major cause of instability and that a fatty alcohol may act as a "Z2" whose stabilizing effect is determined by its solubility in the continuous phase. This does not exc1ude the possibility that a condensed layer of emulsifier and fatty alcohol is formed at the interface. Such a complex will in crease the stability toward coalescence and may also decrease the rate of degradation by diffusion by forming a barrier to transport of Z¡ through the interface (HalIworth and Carless, 1974). Such a hindered transport through the interface was also suggested as an explanation for the decrease in the rate observed in the seeded polymerization of vinyl chloride when mixtures of ionic emulsifier and fatty alcohols were applied (Ugelstad el al., 1973b). The ease of formation of these emulsions is still not satisfactorily explained. When an ionic emulsifier and a fatty alcohol are dissolved in water, mixed micelIes, liquid crystals, and crystalline, rodlike partic1es (1-2 ¡.¡.mlength, 0.1-0.2 ¡.¡.mdiameter) are formed (Chou el a/., 1980). Chou el a/. carried out an extensive study of the formation of emulsions with mixed emulsifiers. The emulsifier systems were prepared by heating water with fatty alcohol and cationic emulsifier. To this mixture styrene was added gradualIy, and the resulting emulsion was examined spectroscopicalIy and by mesurement of the electrical conductivity. The conductivity of the mixed emulsifier system was found to be considerably lower than that of an equimolar solution of pure ionic emulsifier, and more so the higher the fatty alcohol-emulsifier ratio. This result is expected since the complexation of the emulsifier with the fatty alcohol leads to a reduction in the amount of free emulsifier in the' aqueous phase. When styrene was added, the conductivity at first decreased and then increased on further addition of styrene before the curve leveled off or started to decrease slightly. With high fatty alcohol-ionic surfactant ratios, when the conductivity before addition of styrene was at its lowest, the conductivity increased from the start when styrene was added. The most stable emulsions were formed with a molar ratio of fatty alcohol to ionic emulsifier of about 3: 1, whereas higher ratios gave more unstable emulsions. Similar results were obtained using systems with anionic emulsifier (Hansen et a/., 1973). Chou el al. observed that addition of relatively smalI amounts of styrene caused the rodlike crystals to disappear. They did not come to any conc1usion about the mechanism of the emulsification process but suggested that the droplets may have been formed by diffusion of styrene into the crystalline, rodlike partic1es. Chou el al. ascribed the stability of the emulsions to the formation of an emulsifier-fatty alcohol complex at the surface of the droplets. As discussed
410
J. Ugelstad el al.
above, it seems plausible that even if such a complex may be formed and even if it increases stability toward coalescence, the major stabilizing effect is the prevention of degradation by diffusion, caused by the fact that a longchain fatty alcohol may act as a Z2' Another explanation that has been advanced by Azad et al. (1975) implies that when stirring the mixture, the mixed micelles collide with droplets of Zt with the result that fatty alcohol is transferred to the droplets. During this process, a transient high concentration of fatty alcohol in the outer layer of the droplets of Zt may cause a spontaneous emulsification of parts of the droplet. It is well known that spontaneous emulsification may be obtained with 20-30% fatty alcohol (Schulman et al., 1940). Another explanation that has more recently been advanced by Ugelstad and Fitch (to be published) is based on the principIe of formation of emulsions by diffusion. During stirring, droplets of Zt with fresh surface and therefore a high interfacial tension are formed. Diffusion of Zt from the surface of these droplets into neighboring mixed micelles takes place rapidly. The swelling of the mixed micelle is determined by its fatty alcohol content, acting as a Z2' As the mixed micelles are very small (10-20 nm) the initial swelling must be very limited. To be able to absorb more of Zt, the initial small droplets must be furnished with more emulsifier, and even more importantly, with more fatty alcohol (Z2)' This may be achieved by coalescence of initial droplets or by absorbtion of mixed micelles from the surroundings. The assumption that the emulsification takes place by a diffusion process seems to be supported by experiments with mixed systems of ionic emulsifier and fatty alcohol and various dispersed phases, showing that a necessary condition for a rapid emulsification is that the compound to be emulsified have slight water solubility. Furthermore, it has been observed that if even small amounts of Z2 are added to Zt before addition to the water-mixed emulslfier system, the extent of emulsification is reduced and the resulting emulsion becomes less stable. Another interesting phenomenon is that post-addition of small amounts of a highly insoluble compound to an emulsion leads to a rapid degradation of the emulsion (J. Ugelstad, unpublished results). It has also been observed that if the molar ratio of fatty alcohol to emulsifier is increased above four, at a constant concentration of emulsifier, the stability of the emulsions decrease (Lange et al., 1973; Chou et al., 1980). In all these cases, a bulk phase containing Z2 will be present, even if an emulsion of Zt is formed. Thus, the emulsion may degrade by diffusion of Zt from the emulsion droplets to the bulk phase containing Z2' The increase in conductivity observed by Chou et al. at increasing
411
11. The Formation of Monomer Emulsions and Polymer Dispersions
additions of styrene may be explained as resulting from a dissolution of fatty alcohol in the interior of the styrene droplets, leading to a liberation of free emulsifier.
List oí Symbols ZI Z2
a¡w a and b A CI Cta. Clo:> di Dw dG t:.G t:.Gi
low molecular weight compound(s) that are equilibrated between phases relatively low molecular weight compound(s) that may be effectively hindered being transferred between phases polymer(s) insoluble in the continuous phase activity of component i in the continuous phase type of phases or partic1es surface area of partic1es or droplets concentration of ZI in the bulk of the continuous phase concentration of Z. in the continuous phase at the droplet interface of phase a concentration of Z. in the continuous bulk (plane surface)
phase when this is equilibrated
density of component i diffusion constant of Z. in the continuous phase differential molar free energy free energy of mixing partial molar free energy of mixing for any component surface) as reference state partial molar surface
free energy of mixing of component
from
with pure ZI in
i, with pure i in bulk (plane
i when the mixture
has aplane
t:.Gix t:.G¡xO i j Ji N. Nb Ni P
type of number number number number pressure
rO x R
partic1e or droplet radius partic1e or droplet radius indexed (x = a or b) to distinguish between two different sizes andjor partic1e compositions initial rx befQre any mass transport has taken place in or out of the partic1es gas constant .
Rix
(dV;Jdt)
S t T V; "Ix "1M
V;~
t:.Gi in phase x (x = a or b) initial t:.Gix before any mass transport type of component component of segments of partic1es of partic1es of moles of
=
rate
has occurred
between phases
in component i with radius r. with radius rb component i
of transport
ZI from
the bulk
of the continuous
phase
of the swelling partic1es entropy time absolute
temperature
volume of component i volume of component i in phase x partial molar volume of component initial "Ix before any mass transport
i has taken place between phases
to the
surface
412 v.
J. Ugelstad et al.
Vs
segment volume total volume of outer shell (of thickness
vIS i' b
volume of compound interfacial tension shell thickness
bi r¡ rPi rPix
Hildebrand solubility parameter for component i degree of conversion of monomer, defined by (V.o V¡)!V¡o volume fraction of component i volume fraction of component i in phase or particle type x
b) of a particle
21 in outer shell of particle
-
rPi~
initial
Xi.;
interaction parameter per mole of component i with component j
xi.;
Xi)Ji
rPix
before any mass transport
= interaction
parameter
has taken place between t~e phases
per segment of component
i with component
j
References Azad, A. R. M., Ugelstad, J., Fitch, R. M., and Hansen, F. K., (1975). Paper presented at Symp. Emul. Polym. Philadelphia, Pennsylvania Vol. 1. American Chemical Society Ser. 24, Washington, D.C. Azad,A. R. M., Nomura, M, and Fitch, R. M. (1980). Org. Coat. Plast. Chem. Preprints43, 537. Chou, Y. J., EI-Asser, M. S., and Vanderhoff, J. W. (1978). Paper presented at Symp. Phys. Chem. Properties Colloidal Partides, Miami. Chou, Y. J., EI-Asser, M. S., and Vanderhoff, J. W. (1980). "Polymer Colloids" (R. M. Fitch, ed.), Vol. 11.Plenum Press, New York. Davies, S. S., and Smith, A. (1974). Paper presented at Symp. Theory Practice Emul. Technol. Brunel Univ. p. 325. Academic Press, New York. EI-Asser, M. S., Vanderhoff, J. W., and Poehlein, G. W. (1977a). Preprints Am. Chem. Soc. Div. Organ Coating Plast. Chem. 37, 92. EI-Asser, M. S., Miscra, S. C., Vanderhoff, J. W., and Manson, T. A. (1977b). J. Coatings Technol. 49, 71. Flory, P. J. (1965). J. Am. Chem. Soco 86, 1833. Ghanem, A. H., Higuchi, W. l., and Simonelli, A. P. (1969). J. Pharm. Sci. 58, 165. Ghanem, A. H., Higuchi, W. l., and Simonelli, A. P. (1970a). J. Pharm. Sci. 59, 232. Ghanem, A. H., Higuchi, W. l., and Simonelli, A. P. (1970b). J. Pharm. Sci. 59, 659. Goodwin, J. W., Hearn, J., Ho, C. C., and Ottewill, R. H. (1975). Br. Po/ym. J. 5, 347. Goodwin, J. W., Hearn, J., Ho, C. C., and Ottewill, R. H. (1976). Colloid Po/ym. Sci. 60,173. Goldberg, A. H., and Higuchi, W. 1. (1967). J. Pharm. Sci. 56, 1432. Goldberg, A. H., Higuchi, W.I., Ho, N. F. H., and Zografi, G. (1969). J. Pharm. Sei. 58,1341. Hallworth, G. W., and Charles, J. E. (1974). Paper presented Symp. Theory Practice Emul. Technol., Brunel Univ. p. 305. Academic Press, New York. Hansen, F. K., Ugelstad, J., and Lange, S. (1973). Abstr. Seand. Symp. Surface Chem., 5th, Abo. Fin/and. Hansen, F. K., Bauman Ofstad, E., and Ugelstad, J. (1974). Paper presented at Symp. Theory Practice Emul. Techno/., Brunel Univ. p. 1. Academic Press, New York. Hansen, F. K., and Ugelstad, J. (1979). J. Po/ym. Sci. Po/ym. Chem. Ed. 17, 3069. Higuchi, W. J., and Misra, J. (1962). J. Pharm. Sci. 51, 459. Hildebrand, J. H. (1964). In "The Solubility of Non Electrolytes" Dover, New York. Lange, S., Ugelstad, J., and Hansen, F. K. (1973). Abstr. Scand. Symp. Surface Chem., 5th, Abo, Fin/and. Mfutakamba, H., Mork, P. C., and Ugelstad, J. (1979). Unpublished results.
11. The Formation of Monomer Emulsionsand Polymer Dispersions .
413
Miscra, S. c., Manson,J. A.,and Vanderhoff,J. W (1978). Preprints Am. Chem. SocoDiv. Organ. Coatings Plast. Chem. 38(1), 213. Napper, D. H., Netschey, Netschey, A., Napper, D. Olabisi, O., Robeson, L. Academic Press, New
A, and Alexander, A. E. (1971). J. Polym. Sei. Part A-I 9, 81. H., and Alexander, A E. (1969). J. Polym. Sci. Polym. Lett. 7, 829. M., and Shaw, M. T. (1979). In "Polymer-Polymer Miscibility." York.
Schulman, J. A., and Cockbain, E. G. (1940). Trans. Faraday Soco 36, 651. Shinoda, K. (1978). In "Principies of Solutions and Solubility." Decker, New York. Smoluchowski, M. V. (1918). Z. Phys. Chem. 92, 129. Ugelstad, J., Merk, P. c., Dahl, P., and Rangnes, P. (1967). J. Polym. Sci. Part C 27,49. Ugelstad, J., EI-Asser, M. S., and Vanderhoff, J. W. (1973a). J. Polym. Sei. Polym. Letl. Ed. 11, 505. Ugelstad, J., Flegstad, H., Hansen, F. K., and Ellingsen, T. (1973b). J. Polym. Sei. Part C42, 473. Ugelstad, J., Hansen, F. K., and Lange, S. (1974). Makromol. Chem. 175,507. Ugelstad, J., and Hansen, F. K. (1976). Rubber Chem. Technol. 44(3), 536. Ugelstad, J., Hansen, F. K., and Kaggerud, K. H. (1977). Faserforsch. Textiltech.-Z. Polym. Forsch. 28, 309. Ugelstad, J. (1978). Makromol. Chem. 179, 815. Ugelstad, J., ElIingsen, T., and Kaggerud, K. H. (1978a). Int. Conf Organ. Coatings Sci. Technol. Preprillts, p. 425. Ugelstad, J., Kaggerud, K. H., and Fitch, R. M. (1978b). Symp. Phys. Chem. Properties Colloidal Particles. Miami. Ugelstad, J., Kaggerud, K. H., Hansen, F. K., and Berge, A (1979a). Makromol. Chem. 180,737. Ugelstad, J., Merk, P. C., and Kaggerud, K. H. (1979b). Paper presented at Int. Conf Surface Co/loid Sci. 3rd. Stockholm Abstracts, p. 344. Uge1stad, J., Merk, P. C., Kaggerud, K. H., ElIingsen, T., and Berge, A. (1980a). Adv. Co/loid Interface Sci. 13, 101. Ugelstad, J., Merk, P. C., Hansen, F. K., Kaggerud, K. H., and Ellingsen, T (1980b). J. Pure Appl. Chem. (in press.) Ugelstad, J., Merk, P. c., and Khan,
A. A. (1980c). Organ. Coatings Plast. Chem. Preprints
43,514. Ugelstad, J., Ellingsen, T., and Kaggerud, K. H. (1980). Adv. Organ. Coatings 2, 1. Ugelstad, J., Kaggerud, K. H., and Fitch, R. M. (1980). "Polymer Colloids" (R. M. Fitch, ed.), Vol. n. Plenum Press, New York. Vanderhoff, J. W., Vitkuske, J. F., Bradford, E. B., and Alfrey, T. (1956). J. Polym. Sei 20,225. Vanderhoff, J. W., van den Hui, H. J., Tausk, R. J. M., and Overbeck, J. Th. G. (1970). In "Clean Surfaces. Their Preparation and Characterization for Interfacial Studies" (G. Goldfinger, ed.), Dekker, New York. Vanderhoff,
J. W., EI-Asser,
M. S., and Hoffman,
J. D. (1978). U.S. Patent 4,070.323.
Vanderhoff,
J. W., EI-Asser,
M. S., and Ugelstad,
J. (1979). U.S. Patent 4,177.177.
Note Added in Proof In equations describing rates of transport and equilibria between two phases (a and b) (see page 386), it has been assumed that the interfacial tension between them and water is the same for the two phases. In so me cases this assumption may not hold, for instance, if the two phases have different compositions. In these cases it would be more appropriate to inelude separate terms for the two phases, for example, Yaand ')lbfor the interfacial tensions.
12 Radiation- lnduced Emulsion Polymerization Vivian T. Stannett
415 1. Introduction . 418 11. LaboratoryResults with Different Monomers 418 A. Styrene 424 B. Acrylonitrile . 425 C. Methyl Methacrylate 428 D. VinylAcetate. 429 E. VinylChloride 431 F. Miscellaneous Monomers . 433 111. Copolymerizations . 433 A. Random Copolymers . 434 B. Block and Graft Copolymers . IV. Radiation-Induced Emulsion Polymerization Using 436 Electron Accelerators 437 V. Pilot Plant and Related Studies 437 A. Introduction . 437 B. VinylAcetate. 440 C. Ett¡ylene . 442 D. Tetrafluorethylene . E. Tetrafluorethylene-Propylene and Other 444 Copolymers . 447 References
l. Introduction The fitst.reported work on the radiation-inducedpolymerization of a vinyl monomer in emulsion appears to be that of Ballantine (1954) at Brookhaven National Laboratory in 1953. This work was confined to styrene and utilized a tantalum y source with a dose rate of only 60,000 radjhr. Smooth conversions at high rates and high molecular weights to more than 90% were obtained at 25°C with about 2 Mrad. Soap concentration, monomer to water ratio, and temperature were varied. These and other results obtained with styrene, the classical monomer for such studies, wil\ be described later. The motivation for the work was the considerable industrial 415 EMULSION POLYMERIZATION Copyright ~ 1982 by Aeademie Pros,. Ine. An right, or reproduetion in any form reserved. ISBN 0-12-556420-1
416
Vivian T. Stannett
interest in emulsion polymerization and the high yield of free radical s from the radiolysis of water. This latter feature in addition to the high kinetic chain lengths associated with emulsion po!ymerization kinetics has led to a continued interest in radiation as the initiator for a number of monomers. There are a number of other practica! advantages associated with the use of radiation-induced emulsion polymerization. These will be described in the next few paragraphs. Radiation, particularly using isotopes such as 60Co, can give an essentially unlimited range of radical fluxes from zero to those equivalent to many moles per liter of chemical initiators, which would c1early be impracti. cal. Associated with this range is the ease with which the fluxes can be monitored during the course of the polymerization reaction as the kinetics and other considerations demando The fluxes can be programmed and built into modern process control techniques leading in principIe to the orderly control of molecular weight and partical size distributions and to the elimination of residual monomer. Alternatively, there need be no change in the radical flux during the reaction, Le., no initiator exhaustion, and the initiation process can be started and stopped at will by simply dropping away or raising the radiation source. This could be useful for changes in the feed in copolymerizations and, in principIe, for block and graft polymerization in emulsion. Initiation with radiation is essentially temperature independent. This leads to comparatively low temperature dependencies for the overall reaction, the activation energy dropping from about 20 for chemical initiation to only about 7 kcaljmol. This difference, especially when coupled with the ease of removing the initiation source, makes the possibility of exothermic, runaway reactions extremely low indeed. Furthermore, initiation is not a function of polymerization temperature and hence is completely uncoupled, in direct contrast to chemical initiation. The lack of any activation energy with the initiation reaction has already been emphasized. This also means that polymerizations can be conducted at will at any temperature and at any initiation rateo In principIe, this can be, and is indeed, accomplished with chemical initiation inc1uding redox systems. In practice, however, especially low-temperature initiation is not easy to achieve and control, particularly with polar monomers. The lowtemperature polymerization of vinyl acetate is of particular interest. It is well known that monomers such as vinyl chloride and vinyl acetate, whose degree of polymerization is mainly governed by chain transfer to monomer, have a negative dependence of molecular weight on temperature. To achieve high molecular weights, therefore, low-temperature polymerizations are necessary. The radicals produced by the radiolysis of water are hydrogen atoms and, mainly, hydroxyl radicals. These are neutral and highly reactive
1-2. Radiation-Induced Emulsion Polymerization
417
radicals which lead to efficient initiation and there are no electrolytes such as arise from most chemical systems; this leads to somewhat higher surface tension latices with lower ionic strengths and higher pH values, often eliminating the need for adding buffers as, for example, is the case with potassium persulfate initiation. No contamination with residual initiator frag~ents occurs. Another advantage that could conceivably become of considerable importance is that radiation is ideal for initiating the polymerization of systems using cationic soaps. which often interact with chemical systems. This feature was pointed out and investigated many years ago in Japan by Inagaki et al. (1960a,b,c); such cationic lattices were found to be quite stable. There are disadvantages to the use of radiation; for example, there are no ionic end groups such as arise from persulfate initiation. These could, in principie, lead to some stabilization of the resulting latex. In addition, the radiation attacks all the components including the emulsifier and the polymer as it is formed. The former could lead to a very small amount of grafting but is probably a negligible factor. The latter, however, leads to branching and a very small loss of acetate groups. It is doubtful, however, under the conditions that would prevail in an industrial process where low total doses would be used, that any of these problems could cause difficulties. A more important problem, which could arise in flow reactors or even kettle systems, is possible build-up of polymer on the walls of the reaction vessel caused by diminishing flow rate approaching the walls. This could also arise because the radiation is at its most intense near the radiation elements. However, with suitable reactor designs this problem could also be eliminated, as well as the general coating problems that can arise with chemical initiation. In fact, with kettle reactors these effects have not been observed, at least over the limited time periods involved in pilot plant studies. With wide-tube flow reactors some coating of the walls has been observed, but again it is probably not a major problem, at least over reasonable time periods. In general, for most investigations, 60Co }' radiation has been used because of its high degree of penetration and the comparative ease of estimating dose-depth characteristics and because radical fluxes comparable to those used witr. chemical initiation can easily be achieved. There have also been a few, comparatively brief, studies using electr.on accelerators to initiate emulsion polymerization in emulsion. These have mainly been conducted in Japanese laboratories. From a fundamental point of view it is interesting to speculate on the differences that could exist between the kinetics of emulsion polymerization initiated by }' radiation and those of a conventional chemical initiator with, for example, potassium persulfate. At dose rates giving a free radical flux comparable to those achieved with chemical initiation any differences
418
Vivian T. Stannett
should be minoro The aqueous radicals produced by the radiolysis of the water are essentially hydrogen atoms and hydroxyl radical s, both of which are neutral, fast moving, and efficient compared with the sulfate ion radical s produced by persulfate ions or various redox systems. In addition, however, radiation can attack the surfactant, the monomer, and the polymer being produced, causing some additional differences. The surfactant is usually present in small amounts and should not cause too much perturbation of normal kinetics. Radiolysis of the monomer and polymer could lead to more significant changes, particularly with polar materials such as vinyl acetate, vinyl chloride, and the acrylates and methacrylates. In these cases, the radical yields can approach those of water itself, Le., 5-7 radicals per 100 eV of absorbed radiation. Unfortunately, this group of monomers has extremely complex and large unresolved kinetics and it is difficult to make a clear differentiation between radiation and chemical initiation. The polymers, as they are produced, however, should be attacked to varying degrees by the radiation, leading to branching and even cross-linking and other changes in the resulting polymers. Styrene and pólystyrene have very low radical yields, (~0.7) compared to water and should be relatively immune to such differences. The dienes such as butadiene and isoprene have low radical yields but could be subject to branching and cross-linking because of the residual double bonds in the polymer. It is pro po sed to discuss some of the various monomers that have been studied on a laboratory scale with radiation. Since styrene should be the least subject to special effects introduced by the use of radiation, it will be the first monomer to be discussed.
11. Laboratory Results with DitIerent Monomers
A. Styrene In his early work, Ballantine (1954) used 1% of an amine long-chain alcohol sulfate (Duponol G) as the emulsifier and monomer to water ratios of 1:7 and 1:9 at 25, 35, and 45°C. The overall activation energy for the rate was found to be 3.7 kcaljmol. The molecular weights decreased slightly with conversion but were very high, close to or more than one million. The rates were quite high reaching, for example, 54% per hr at 45°C with molecular weights up to 2 million. Abkin et al. (1959) presented the next published work, followed closely by Inagaki et al. (1960a,b,c) and Bradford et al. (1961). Hummel et al. (1962) conducted a long series of studies with styrene and other monomers beginning in 1962. There was an interesting paper by Acres and Dalton in 1963. The present author and his -colleagues began
12. Radiation-Induced Emulsion Polymerization
419
work on the radiation-induced polymerization of styrene and other monomers in 1964, with the first published report in 1967. Styrene is one of the best-behaved of monomers in that it tends to follow most closely classical Ewart and Smith (1948) kinetics. There are many exceptions, however, even with potassium persulfate, the standard chemical initiator. The best agreement was found with potassium persulfate as the initiator and sodium lauryl sulfate as the emulsifier. Until recentIy (Garreau et al., 1979), the various studies were mainly conducted with other systems and for reasons other than to check whether there are, indeed, any real differences between radiation and chemieal initiation in such an ideal system. Abkin et al. (1959) found the dependence of rate on the dose rate to be close to 0.4, the Classical Smith-Ewart (1948) Case 2 value. The molecular weights wc-reclose to those caIculated from the chain transfer to monomer values. However, they found close to zero activation energy for the rates and substantial post-irradiation polymerization. It was pointed out that the radiation could also generate hydrogen peroxide as an additional initiation source. One cationic and three anionic emulsifiers were studied, and the cationic emulsifier gave a very low rateo Inagaki et al. (1960a,b,c) concentrated their studies on the elfect of different emulsifiers: anionic, nonionie, alld cationie. In all cases the rate increased with increasing emulsifier concentration. The rate, in general, was greatest with anionic emulsifiers and least with cationic. The rate and molecular weight dependencies (on the soap concentrations) were in the range 0.14-0.40. Cationie lattices are not easy to prepare with chemical initiators, and this earIy work pioneered the use of y irradiation for their production. Stable lattiees with up to 50% solids content were made with an overall activation energy of 6.2 kcaljmoI. Bradford et al. (1961) conducted a detailed study using the dihexyl ester of sodium sulfosuccinate as the emulsifier. Their main emphasis was on the competitive growth of particles using seeded systems and was related to their development of highly uniform particle size polystyrene lattices (e.g., Bradford and Vanderhoff, 1955). The paper also included, however, a rather detailed kinetic study leading to values of the termination rate constant kl' the average nUII).berof radieals per particle ñ, and the activation energy associated with die molecular weights produced (7.2 kcaljmol). Rather similar results were obtained with 60Co y radiation as with potassium persulfate initiation. However, the number of particles decreased with temperature using radiation but increased with potassium persulfate. This was attributed to the increase in the rate of initiation with temperature in the case of persulfate initiation. In general, their values for the activation energy, the efficiencies of initiation, and the rate constants for termination werein good agreementwith those obtained later by Garreau et al. (1979).
420
Vivian T. Stannett
The work of Hummel et al. (1962,1967; Hummel, 1963) was fundamental in character involving not only styrene but methyl methacrylate, methyl acrylate, ethyl acrylate, vinyl acetate, and a number of other monomers. Unique dilatometer systems were developed which enabled both continuous and intermittent determination of rates, with sodium lauryl sulfate as the emulsifier. The molecular weight was found to decrease with increasing dose rateo In general, in the case of styrene, standard Smith-Ewart Case 2 kinetics approximated the experimental findings. The rate-conversion curves showed an initial increase in rate followed by a c'onstant period and an eventual decline. In some cases there was an increase in rate at high conversions, presumably due to a small gel effect. These results are in agreement with results obtained with potassium persulfate initiation and the Case 2 Smith-Ewart picture. Acres and Oalton (1963a), using the dioctyl ester of sodium sulfosuccinate as the emulsifier, found the intensity exponent of the rate to vary with the monomer to water ratio from 0.22 to 0.34 but to reach the classical Smith-Ewart value of 0.4 when extrapolated back' to zero monomer concentration. They interpreted this result in terms of the special role of the hydrogen atoms arising from the radiolysis of water. Araki et al. (1967, 1969) conducted some rather straightforward polymerizations of styrene, and the properties of the resulting latices using 60Co y radiation were determined in a simple dilatometer. Again smooth, rapid polymerizations to high conversions were observed. A typical conversion curve is shown in Fig. 1. The shape of the conversion curves agreed with those observed by Hummel et al. (1962, 1967) and were similar to those found with potassium persulfate under normal Case 2 Smith-Ewart conditions. The overall activation energy was 3.6 kcal/mol, in excellent agreement with the results of Ballantine (1954). The viscosity average molecular weight decreased with decreasing temperature in agreement with Ballantine and consistent with a constant rate of initiation and a reduced rate of propagation with temperature lowering. Compara tive studies indicated that the molecular weight distribution was somewhat sharper with radiation than with potassium persulfate initiation. Radiation Mw/Mn values, for example were about 3 as compared with 6 for persulfate. Some other properties are presented in Table 1 for both radiation and chemical initiation. The surface tensions are somewhat higher with radiation and the pH values much higher, 8-9 compared with 3.8 with persulfate. Low pH values are typical with initiation by persulfate ion decomposition and, as discussed in the introduction to this chapter, indica te an advantage offered by radiation. The particles sizes and molecular weights are similar at 60°C. As with molecular weight, particle size distribution is narrower with radiation, some typical differential distributions are shown in Fig. 2.
12.
Radiation-Induced
421
Emulsion Polymerization
100
75 c: .o Q)
> c: o Ü
50
eQ) (,)
...
,f
25
Fig. 1. Typical styrene conversion curve at 30°C (dilatometer trace). Dose rate 0.02 Mradjhr, 25%solids, 6.7%sodium lauryl sulfateon total volume.
Recently, Garreau et al. (1979) reported a careful and rather detailed study of the kinetics of the radiation-induced polymerization of styrene in emulsion with sodium lauryl sulfate under conditions found earlier to lead to c10se agreement with simple Case 2 Smith-Ewart kinetics (Smith, 1948). Most of the normal reaction variables were studied, and the rates of polymerization were found to be independent of the monomer-to-water TABLE I Chemical and Radiation Polymerization
of Styrene in Emulsion Preparation y-Radiation
Property pH Surface tension (dyne/cm) Particle size (J¡m) Molecular weight (viscosity)
K2S20S at 600C. 3.8 61.1 0.13 2,700,000
9.2 68.9 0.10 1,664,000
7.9 69.0 0.07 413,000
.25% solids and 6.7% sodium lauryl sulfate based on water content
(Araki el al., 1969).
422
Vivian T. Stannett B
24.... 22 20 18L
A
16 14 e
:o
12
10 o Cñ 8 6,
:1
O
250
-Diameter
2000
(,.\.)
Fig. 2 Differential particle size distribution of polystyrene lattices initiated by: A, radiation O°C; B, radiation 600C; C, potassium persulfate 60°C (Araki et al., 1967).
ratio and to the 0.4 power of the dose rate (Fig. 3). The activation energy (Fig.4) associated both with the rate and the molecular weight was 7.9 :t 0.6, in good agreement with Van der Hoff et al. (1958) and with the literature values for Ekp' This is reasonable since little or no activation energy is involved in the initiation and termination steps. The dependence of the rate and the molecular weight on the emulsifier concentration was about 0.7, in reasonable agreement with the Smith-Ewart value of 0.6. The number of particles, however, was of the correct order of 0.6 with respect to the emulsifier concentration. The termination rate constants were caIculated using the method of Van der Hoff (1958). The values found were in excellent agreement with those of Van der Hoff for persulfate initiation and Bradford et al. (1961) for y initiation. The propagation rate constant kp was caIculated from Case 2 Smith-Ewart kinetics and found to vary between 32 and
68 M- 1 sec- 1, well within the range of the reported literature values at 30°C. The caIculated efficiencies of initiation were low, about 40%, but similar to those discussed by Bradford et al. with y irradiation and determined by Van der Hoff (1958) with persulfate initiation. No seeded polymerizations were conducted but the above results indicate clearly that the
423
12. Radiation-Induced Emulsion Polymerization ~ .s::.
~
90 80 70 60
~
.~
20
E >-
o a. 10
.2
.3
.4 .5.67.8.9
1
2
3
4 5 6 789
Dose Rate (mradjhr x10) Fig. 3. Dependence of the rate of polymerization of styrene on the dose rate at 300C and 2.0% sodium lauryl sulfate concentration (Garreau et al., 1979; reproduced with permission of Journal of Colloid amI Interface Science.)
radiation-induced polymerization of styrene under the correct conditions cIosely approximate the kinetics found with potassium persulfate. Karpov et al. (1968) reported a number of experiments concerning the post polymerization of styrene in emulsion using y irradiation. The polymerization' continued long after the removal of the source, reaching cIose to 100% conversion and very high viscosity average molecular weights (1528 x 106) in about 20 hr at 22°C. The conversion curves were similar to those normally found with continuous irradiation, Le., linear until the separa te monomer phase disappeared and then tapering off. The molecular weight continued to increase during post-polymerization. It was demonstrated experimentally that very few radical s disappeared during the process. The polymer had about 85% of narrow molecular weight distribution. The half-life times of the propagating radical s were determined in a large number ofmonomer systems by Hummel et al. (1969). Styrene had the highest value, up to 80 min in some cases. Karpov et al. (1969) determined the kinetic parameters of the radiation polymerization of styrene with potassium laurate as the emulsifier. The rates were found to be of approximate orders of 0.5~with respect to dose rate and emulsifier concentration. The number of particles was proportional to the dose rate to the 0.4-0.6 power and the emulsifier to the 0.6 power. The activation energies were 4.6 and 3.9 kcaljmol with respect to the rates and number of particles, respectively. Cetyl trimethyl ammonium chloride gave slower rates and an activation energy of 7.7 kcaljmol for the rateo The same group (Karpov et al., 1973a) found the rate of polymerization to be independent of the number of particles up to 1016particlesjper milliliter. This is contrary to the resuIts found with chemical initiation and is attributed to chain transfer to
424
VivíanT. Stannett
':"
2
le
I
f" 20 'ol-e
'-..§)
G .. I
-
O
t.
v
lO
lO 9 8 7 6
o 9 -E 8 7 Z 6 O e
. ... N
5
5
4
4
Z O e N ...
.
! ... O
A. ... O
... ... 111:
o ... Q
...
O A. 3 ... O ... e
2
111:
3.1
3.2
3.3
3.4
3.5
3.6
Fig. 4. Temperature dependenceof the rates and degreesof polymerization for the radiation induced polymerization of styrene. Dose rate 0.093MradJhr (Garreau et al., 1979; reproducedwith permissionof Journal of Col/oid and Interface Science.)
the initiator. There was considerable activity by this group of Soviet workers and additional references may be found in the articIes quoted in this chapter.
B. Acrylonitrile The emulsion polymerization of acrylonitrile is quite complex because of the high solubility of the monomer in water (7.4% at 25°C) and the insolubility of the polymer in the monomer. Hummel et al. (1967), using a sophisticated recording dilatometer, showed that the rate-conversion curves
12. Radiation-Induced Emulsion Polymerization
425
were very complex, with an initial rise followed by two periods of almost constant, but different rates, and finally a first-order reaction rate at high conversions. Partic1e formation in the aqueous phase was assumed. A few studies reported by Glazkova et al. (1971) were conducted below the critical micelle concentration of the emulsifier used. Karpov et al. (1974) reported a rather thorough study using three different emulsifiers: potassium laurate, sodium alkyl sulfonate, and a cationic emulsifier, cetyl pyridinium chloride. Contrary to the general experience with styrene, vinyl acetate, and methyl methacrylate, the rates were markedly higher with the cationic emulsifier. True latices were formed when the monomer concentration was below the solubility limit, Le., no monomer droplets were present. With potassium laurate, however, only coagulum was formed in every case. The number of partic1es formed in the latex systems were found to be independent of the dose rate but proportional to the emulsifier concentration to about the 0.6 power. With high concentrations (0.5%) of cationic emulsifier the number of partic1es increased linearly with conversion, but at lower concentrations and always with the sulfonate the number remained constant. The molecular weight did not vary more than about twofold over a wide range of emulsifier, with monomer concentration and dose rate being of the order of 106 viscosity average. There is much useful practical data in the paper but the results are confounded by the presence of heavy concentrations of coagulum. O'Neill and Stannett (1974) also found, with sodium lauryl sulfate as the emulsifier, that when a separate monomer phase was present a milky slurry that was 100% filterable was formed even ~t low conversions. However, in the water-soluble regio n low solid latices were obtained. The initial rates were much higher than in the absence of emulsifiers as was previously reported by Karpov et al. A plot of the initial rates versus the monomer concentration is shown in Fig. 5. A first-order dependence on monomer concentration was found. Again, as with Karpov et al., considerable useful data is presented for systems where a separate monomer phase is present. Since these are not truly emulsion polymerizations, further details will not be discussed in this chapter. The molecular weights were essentially independent of the emulsifier concentration and in the same range, about 106,as found by Karpov et al. Izumi et al. (1967; Izumi, 1967) obtained similar results with ammonium persulfate as the initiator. C.
Methyl Methacrylate
Methyl methacrylate is a monomer that behaved "nonideally" with conventional initiators (Zimmt, 1959). This is due mainly to the larger size partic1es which lead to a larger average number of radical s per partic1e than
426
Vivian T. Stannett 400
200
e .2100 '" Q;
~
O u
~
80
60
w
'< IX 40 .....
~
20
10 0.1
/8 0.2
0.4
0.6 0.8 1.0
2.0
[M]c!ml-') Fig. 5. Dependenee of the rate of the radiation-indueed polymerization of aerylonitrile in aqueous solution, linear portions of rate eurves, on the monomer eoneentration at 25°C 8 in the absenee of sodium lauryl sulfate, O with 0.21% (O'Neill and Stannett, 1974: reprodueed with permission of Journa/ of Macromo/ecu/ar Science-Chemistry AS, p. 949, by eourtesy of Mareel Dekker, Ine.)
the ideal value (Smith-Ewart Case 2) of one-half and to the prevalence of the gel effect at comparatively low conversions. The first published report of the radiation polymerization of this monomer was by Abkin et al. (1959). Very high rates, up to 6% per minute at room temperature were observed with high molecular weights. Inagaki et al. (1960a,b,c) polymerized with 'Y radiation methyl methacrylate and anionic, nonionic, and cationic emulsifiers, and as with styrene the rates were highest with anionic and lowest with cationic emulsifiers. The molecular weights were similar with anionic and nonionic and somewhat lower with cationic emulsifiers. Both the rate and the molecular weight increased with increasing emulsifier concentration in all cases. The order of reaction for the rate and the molecular weight was
12.
Radiation-Induced
Emulsion Polymerization
427
found to be 0.3, 0.4, and 0.2 for anionic, nonionic and cationic, respectively. The dose rate dependence of the rate was 0.3 with the cationic emulsifier, stearyl trimethyl ammonium chloride, and the activation energy was 6.7 kcal/mol. Allen et al. (1962) conducted a few experiments in connection with their work on block and graft polymer synthesis in emulsion. An estimate of 92 M-1 sec-1 at 25°C for the rate constant for propagation was obtained, in reasonable agreement with the published solution and bulk values. As with Abkin et al. the possible contribution to the initiation step from peroxides arising from the irradiation was stressed and some supporting evidence presented. A more detailed fundamental study was reported by Hummel et al. (1962; Hummel, 1963). Using a sensitive recording dilatometer of their own design they could follow the variation of the rate of polymerization with time and conversion. There was an abrupt rise in the rate for the first few percent conversion attributed to particle formation. There followed a constant rate period up to about 30% when the free monomer phase disappeared. An increase in rate to a maximum was then observed, ascribed to the gel effect, followed by a steady decrease in rate due to monomer depletion and slower diffusion of the monomer to the active sites in the highly viscous particles.
The particle sizes were rather small, about 500
A
diameter, compared with those often obtained with chemical initiation (e.g., Zimmt, 1959). This presumably explains the comparatively close adherence to the simple Smith-Ewart picture up to the appearance of the gel effect. Acres and Dalton (1963a) also studied the emulsion polymerization of methyl methacrylate initiated by 60Co y raqiation using a recording dilatometer. Only the conversion-time curves were measured with constant dose rate, varying monomer concentration, and with constant monomer concentration at different dose rates. Except at the lowest monomer concentration a clear gel effect was observed, with linear rates up to that point. The linear rates increased with increasing monomer concentration up to .
about 0.4 mol/liter and then leveledoff. The dependenceof the rate, before the gel effect, on the dose rate was 0.4 and, unlike their findings with styrene, not dependent on the monomer concentration. Their results w~re consistent with those of Hummel et al. that methyl methacrylate follows, with y radiation, the generally accepted Smith-Ewart Case 2 kinetics except for the marked gel effect. Hoigné and O'Neil (1972) studied several features of the y radiationinitiated polymerization in emulsion. Sodium lauryl sulfate, dioctyl and dibutyl sodium sulfosuccinates, and two nonionic, polyoxyethylene-type emulsifiers were used. Sodium lauryl sulfate gave, by far, the highest rates and most stable lattices and was used for all of the results reported. The rates were found to be 0.43 order on the dose rate and 0.53 on the
428
VivianT. Stannett
emulsifier, above the critical micelle concentration. The activation energy was 4.8 kcal/mol. Molecular weights of about one million were obtained at 22°C, but no systematic study of this property was made.
D.
Vinyl Acetate
Vinyl acetate, in marked contrast to styrene, has a most complex mechanism (Klein et al., 1975). This monomer was among the earliest investigated with y-radiation initiation in emulsion (Allen.et al., 1956, 1960, 1962; and Inagaki et al., 1960a,b,c). Rapid rates to high conversions were obtained, and the curves were linear from about 20 to 70% conversion, similar to chemically initiated systems. Molecular weights as high as one million were obtained. The rates, although high, were far less than those calculated with conventional Smith-Ewart theory and the accepted values for the propagation rate constant. This was correctly ascribed to the possibility that the number of radicals per particle averaged less than 0.5 and that perhaps the Smith-Ewart Case 1 would be a 'better description. As with styrene and methyl methacrylate, Inagaki et al. (1960a,b,c) studied anionic, nonionic, and cationic emulsifiers. The relative rates, as with the other two; were found to be anionic > nonionic > cationic. The principIe additional findings were that the activation energy for the rates of polymerization was 5.7 kcal/mol, the rates increased with increasing dose rate but with an unspecified dependency. The dependence of the rate and molecular weight on the emulsifier concentrations was found to be between 0.14 and 0.40 order. Stable cationic lattices up to 50% by weight were obtained. A more thorough investigation of the stability of radiation-initiated poly(vinyl acetate) lattices has also been reported by Ohdan et al. (1970; Ohdan and Okamura, 1969) and by Kamiyama et al. (1970). Araki et al. (1967, 1969) carried out a more systematic study of the kinetics and other features of the y-initiated emulsion polymerization of vinyl acetate using sodium lauryl sulfate as the emulsifier. This system had been thoroughly investigated with potassium persulfate as the initiator (Litt et al., 1960, 1970). Some post effects have been observed with vinyl acetate, particularly above 50% conversion (Friis, 1973; Sunardi, 1979). These effects had been used by Allen et al. (1960, 1962)for the possible synthesis of block and graft polymers and will be described later in this chapter. The half-life of the radicals in a vinyl acetate latex polymerization was determined by Humme! et al. (1969) as 0.8 min at 53.8% conversion. Araki et al. (1967, 1969) determined all the normal rate dependencies and included some seeded latex studies. Their results and those of other investigators are summarized in Table II together with those found with potassium persulfate initiation and those predicted by the Smith-Ewart Case 2 theory. The
429
12. Radiation-Induced Emulsion Polymerization TABLE IJ
Orders ot Reaction tor the Rates with Potassium Persultate and Radiation Polymerizationot VinylAcetatea Order Variable Initiator
or dose rate
Ditto with seeded system Number of partic1es Monomer-water ratio Emulsifier (sodium lauryl sulfate) a
0.5- 1.0 0.8 0.2 0.35 0.1-0.3
Radiation
Smith-Ewart 2
0.5-0.9 0.26 0.7 0.2 0.3-1.0
0.4 O 1.0 O 0.6
Data taken from various sources.
radiation results tend to approach the Smith-Ewart theory more dosely than the persulfate-initiated polymerizations. As indicated by the ranges reported in Table n, there are considerable variations in the literature results with both radiation and chemical initiation. In particular, there is a wide range of dependence of the rate on the dose rate, the initiator concentration, and the emulsifier concentration. The molecular weight, in general, was found to be insensitive to dose rate and emulsifier concentration, consistent with the determining factor being chain transfer to monomer. The radiation-produced poly(vinyl acetate) had a somewhat higher molecular weight even at the same temperature, perhaps due to branching initiated by direct radiolysis of the polymer chains.
E.
Vinyl Chloride
Wang (1962) was the first to report studies on the y-radiation initiated polymerization of vinyl chloride in emulsion at room temperature. Rapid rates to high conversions were obtained after rather long induction periods of 1 to 3 hr. The degrees of polymerization were constant within experimental error at ab0l!t 2000, in keeping with termination being dominated by chain transfer to monomer. Little or no dependence .of the rate on the emulsifier concentration or the monomer concentration was observed. However, the rates were proportional to the 1.22 power of the dose rateo Some preliminary results were presented by Barriac et al. (1969) and followed by a more detailed report (Barriac et al., 1976) wherein two emulsifiers were used. Again at 25°C, for example, the degree of polymerization was essentially independent of the dose rate or the emulsifier concentration and similar to that obtained by Wang. A strong post effect
430
VivianT. Stannett
was observed, and even at low conversions these effects were eliminated experimentally by freezing in liquid nitrogen immediately after irradiation. The conversion curves were linear up to about 80% conversion with a small gel effect apparent at the lowest emulsifier, Le., largest size particles, concentration. The rates of polymerization and the number of particles were proportional to the 0.4 power of the dose rateo The rate was dependent on the 0.3 power, and the number of particles on the 1.0-1.3 power of the emuls.ifier concentration and independent of the monomer to water ratio. The activation energy for the rate for both emulsifiers was 4.0 kcal/mol and for the number of particles the unusualIy high value of 17.0 kcal/mol. A detailed kinetic analysis of these and the other results was made. The mechanism and kinetics were in accord with those derived by Gardinovacki et al. (1971) and Hansen and Ugelstad (1976), modified somewhat due to the very smalI particles obtained with y initiation. The smalI size and correspondingly larger number of particles is often found to be a feature of radiation initiation. It has been explained by the lower ionic strength of the aqueous phase leading to. the stabilization of more and smalIer particles in addition to the faster diffusing and neutral hydroxyl radicals and hydrogen atoms compared with the negatively charged, larger sulfate-type radicals. Karpov et al. (1977) studied the polymerization in the presence of a number of anionic emulsifiers below the critical micelIe concentration. High molecular weight polymers with low concentrations of impurities were obtained at high rates. The overalI rate was found to be about 0.5 order with resp~t to the dose rate with an activation energy of 5 kcal/mol, in reasonableagreementwith those reported by Barriac et al. (1976). A number of interesting and unusual phenomena were reported by the same group of workers. With cationic emulsifiers suspensions rather than latices were obtained although similar systems gave stable latices with chemical or UV initiation (Karpov et al., 1971). It was hypothesized that the radiation conferred some negative charges on the particles, reducing their stability. Karpov et al. (1972)reported that higher rates were obtained with cationic emulsifiers below their critical micelIe concentration but that the reverse was true with hydrogen peroxide. With anionic sulfonate emulsifiers, Karpov et al. (1973b) found that with monomer concentrations below 35% stable lattices were obtained but that above 35% free flow suspensions were obtained. Latex inversion was suggested as the explanation. Kinetics similar to those found with anionic emulsifiers was reported by Karpov et al. (1973c) when cationic emulsifiers below the critical micelIe concentration were used.
12. Radiation-Induced Emulsion Polymerization F.
431
Miscellaneous Monomers
1. Vinylidene Chloride Panajkar and Rao (1979) have reported a rather extensive study of the y radiation-initiated polymerization of vinylidene chloride in emulsion. With sodium lauryl sulfate as the emulsifier smooth polymerization-time curves at high rates were obtained, up to more than 90% conversion. Between 45 and 60% conversion, the linear region, the rate was 0.3 order with respect to the emulsifier concentration. The molecular weights were found to increase with conversion and values up to 79,000 were obtained. Some reasons for the departure from Smith-Ewart behavior were suggested. Earlier, Hummel et al. (1967) had presented some interesting data on a closely related system, a similar rate-time behavior was observed and a tentative explanation proposed. Both discussions were based on the insolubility of the polymer in its own monomer. 2.
Butadiene
This monomer has been investigated by Ishigure et al. (1974) using sodium lauryl sulfate as the emulsifier. The polymerizations were found to proceed slowly in the initial stages with rates increasing gradually with conversion. Diffusion of the monomer appeared to be an important factor, higher agitation rates giving higher rates. Four different anionic emulsifiers gave essentially the same rate at the same molar concentrations. Since the conversion plots were curving for most of the polymerization, it was difficult to get a clear picture of the order of the réaction. The rates were very low with maximum G (Q1onomer)values of less than 4000 at 40°C. The addition of n-dodecyl mercaptan caused increases in the rates but only by 20-30%. An interesting
feature was the small particle sizes, ranging from 122-537
A
in diameter, obtained with radiation. This was partly due, however, to the rate of radical production at the dose rates used since styrene under similar conditions had only about double the diameters. 3.
Methyl Acrylate
Methyl acrylate behaves differently from the other acrylates because of its comparatively high solubility in water, 5.2% at 30°C. This monomer has been extensively studied by Hummel et al. (1962,1967; Hummel, 1963). The rate first rises steeply and then drops off as the conversion proceeds, with two roughly linear slopes. Rapid polymerization to stable latices was obtained and the molecular weights were high, greater than one million.
432
Vivian T. Stannett
"Cross-linking" occurred in some experiments; this could be partially due to entanglements. There was little temperature effect on the rate, molecular weight, rate-time slope, or number of particles. The dose rate dependences of the linear portions and the maximum rates were about 0.55. It was suggested that a strong gel effect was present and that prolonged particle formation in the aqueous phase was occurring. The work of Hummel et al. appears to be the most detailed study of the radiation-induced polymerization of methyl acrylate and the original references should be consulted for further details. Ohdan and Okamura (1969) reported some further details including the stability and other properties of the resulting latices. 4.
Ethyl Acrylate
This monomer also appears to have been studied only by Hummel et al. (1962, 1967; Hummel, 1963). The rate-time curve shows an initial sharp rise followed by a slow decline, with no zero-order portion.. The curve can be adequately explained by the assumption of a strong gel effect and the high solubility of the polymer in the monomer; presumably the separate monomer phase disappears early in the reaction whereas the creation of new particles continues longer than, for example, in the case of styrene because of the comparatively high solubility of the monomer in water, 1.8 compared with 0.012% with styrene. 5. n-Butyl Acrylate Hummel et al. (1967) reported a brief study of this monomer with sodium lauryl sulfate as the emulsifier. Behavior similar to ethyl acrylate was observed. The rate increased rapidly during the first 10% conversion, presumably because of particle formation. There followed a long first-order decline in the rateo This behavior, like ethyl acrylate, was ascribed to the high degree of swelling of the polymer by the monomer leading to the early (-15% conversion) disappearance of the separate monomer phase. A more detailed study with the same emulsifier has been described by Hoigné and O'Neill (1972). The overall activation energy of the rate was very low, only 0.5 kcaljmol; that of the molecular weight, however, was 3.9 kcaljmol. The dependence of the rate was about 0.7 order with respect to dose rate and 0.48 with respect to the emulsifier concentration. The molecular weight was essentially independent of the emulsifier concentration and the dose rateo The values were high, 2.6-6.2 million, viscosity average, but they could be systematically reduced by the addition of n-butyl mercaptan. The rate dependencies are similar to those found with potassium persulfate initiation.
12. Radiation-Induced Emulsion Polymerization
433
6. Other Monomers Hummel et al. (1967) also conducted brief studies of a number of other monomers. Chloroprene behaved similarly to styrene. Methacrylonitrile behaved somewhat like methyl methacrylate with a detinite gel effect. Butyl methacrylate behaved somewhat like styrene but with two small maxima in the rate-conversion curves; the reasons for this are unknown but the second small peak could arise from the gel effect. Decyl methacrylate showed only one maximum rate at about 50% conversion. Again the reasons for this behavior are unclear. Isoprene did not polymerize in emulsion at either low or high dose rates. Kalyadin et al. (1975) have presented a study of the radiation-induced polymerization of vinyl fluoride in emulsion.
111. Copolymerizations
There have been a few reports on the use of .radiation to initiate copolymerization in emulsion. Earlier than the conventional random copolymerization work there were a number of studies on the formation of block and graft copolymers in latex formo
A.o Random Copo/ymers Butadiene has been successfully copoly¡perized with styrene (Ishigure et al., 1974) and with acrylonitrile (Ishigure and Stannett, 1974). In addition, vinyl acetate has been successfully copolymerized in a few experiments with dibutyl maleate and with methyl, n-butyl, and 2-ethylhexyl acrylates (Araki et al., 1969); all the copolymerizations proceeded smoothly with good yields. The butadiene-styrene system polymerized slowly but with the rate increasing with increased styrene content. They were considerably slower, however, than comparable polymerizations using potassium persulfate as the initiator, whereas styrene behaved normally. G(-M) values ranged from only 1,000 for 21.5 mol
% styrene
to 3,800 with 60% styrene, compared
with
87,000 for pure styrene under similar conditions. The reasons for the low rates, as with butadiene itself, are not clear. Acrylonitrile, however, as the comonomer with butadiene behaved normally with easy copolymerizations at rapid rates. G(-M) values reached 100,000 with 90% acrylonitrile. In the range used for nitrile rubbers G values were still around 25,000, a quite practical yield from the industrial viewpoint. The copolymer reactivity ratios were normal. Strong post effects were observed showing a clear tirstorder termination process. Kamiyama and Okamura (1969) copolymerized
VivianT. Stannett
434
styrene and acrylonitrile in emulsion using y radiation. two nonionic emulsifiers were used. A maximum in the close to a 50: 50 molar proportion of the two monomers nonionic emulsifiers, in contrast to bulk and chemically polymerizations. Explanations based on the mechanism presented.
B.
One anionic and rate was observed in the case of the initiated emulsion of initiation were
Block and Graft Copolymers
Block and graft copolymer formation in latices using radiation as the means of initiation have been studied since early times. The basic idea, first apparentIy suggested by Allen et al.{1956, 1958),is to use the trapped radicals in the latex particles either during the polymerization ofthe first monomer or by irradiation of a completed latex and adding an additional different monomer. The former procedure should lead to block polymers an~ the latter to either blocks or grafts. Hummel et al. (1969) have measured the half-lives of the propagating radicals using intermittent 60Co irradiation. Such values depend to various extents on the conversion and were found to vary from 20 min for styrene at 28.8% conversion to 0.8 min for vinyl acetate at 53.8% conversion. The early work of Allen et al. involved adding methyl methacrylate to poly(vinyl acetate) at 70% conversion. It was clearly shown that block formation did indeed occur. More detailed reports of similar systems were published in subsequent papers (Allenet al., 1960,1962).It was shown that graff copolymers were also formed by transfer reactions. Styrene radicals which have a low transfer activity did not yield graft polymers, showing the great importance of such reactions in the overall reaction. Mukoyama and Toriaki (1962) successfully grafted vinyl acetate to polypropylene latices by irradiation, followed by the addition of monomer. The effect of monomer concentration, monomer purity, and type of emulsifier were studied. Ito and Watanabe grafted methyl methacrylate to polyethylene latices and a number of details of the reaction were ellucidated in their 1965 publication. Acres and Dalton (1963b) studied the graft andjor block copolymerization of methyl methacrylate onto irradiated polystyrene latex and styrene onto irradiated poly{methyl methacrylate) latex. A number of experimental variables and conditions that give good yields were investigated. It was difficult to separa te the copolymers from the homopolymers but it was clear that good yields of nonrandom copolymers were indeed obtained. The direct radiation grafting of vinyl monomers to natural rubber latex was studied by two groups of workers. Cockbain et al. (l958, 1959) grafted methyl methacrylate using both y radiation and a chemical redox system.
12. Radiation-Induced Emulsion Polymerization
435
The grafting efficiencies and molecular weights of the side chains were both much higher with radiation initiation. An interesting observation was that the y-grafted latices formed strong continuous films on drying whereas the redox grafts gave cracked or crazed films. This difference was attributed to the chemical grafts being located mainly on or near the rubber particIe surfaces, producing a heterogeneous polymer system. Evidence to support this idea was provided by adding oil- and water-soluble retarders in the radiation grafting experiments. The oil-soluble ones also gave cracked films since they presumably reduced the amount of homogeneous grafting whereas excellent films were obtained in the presence of water-soluble retarders. Cooper et al. (1959a-c; Cooper and Vaughan, 1959) also carried out extensive studies of the direct radiation grafting of methyl methacrylate. A general kinetic scheme was developed for the grafting system and the activation energy determined as 3.1 kcal/mol for the rate, whereas the molecular weight of the grafted side chains was little affected by temperature. A number of other interesting and useful observations were reported in these papers. More recentIy, Ishigure et al. (1973) and Garreau et al. (1980) reported rather detailed investigations of the direct radiation grafting of styrene to polybutadiene latices. The motivation for the work was for the possible synthesis of such latices for use in the production of high-impact polystyrene. Both papers described direct comparisons between radiation- and potassium persulfate-initiated systems. The earlier paper used gel-free smallparticle-size latices whereas the second used a larger particle-size crosslinked latex of the type used commercial~y for high-impact polystyrene production. The former types of polybutadiene latex yielded propagation rate constants and activation energies in good agreement with the literature values for styrene. The grafting efficiencies decreased with conversion but were similar in both radiation and chemical initiation. A simple model was presented of the basis for the grafting efficiencies, and it gave a cIearer picture of the various reactions involved. The second paper (Garreau et al., 1980) with the larger cross-linked polybutadiene latex gave a much more complicated pattern of behavior with significant departures from the simple Smith-Ewart picture. It was shown that the extracted homopolystyrene had molecular weights similar to the grafted side chains after destruction of the polybutadiene backbone polymer. Radiation was found to lead to more grafted side chains of lower molecular weight than was observed for persulfate initiation. This was explained by the higher rate of initiation in the former case and led to somewhat lower grafting efficiencies. Nevertheless, under proper conditions up to 80% efficiency was obtainable. The conversions also produced
436
Vivían T. Stannett
economically favorable yields. These results, when coupled with the ease of control and other radiation features described in the introduction, make radiation a viable and effective alterna tive to chemical initiation for grafting processes on an industrial scale.
IV. Radiation-InducedEmulsionPolymerizationUsing ElectronAccelerators There have been a number of brief reports, all Japanese, of the use of electron accelerators to affect radiation initiation in emulsions. Vinyl acetate has been studied in most detail although brief reports on other monomer polymerization, inc1uding styrene in emulsion, have been published. Kamiyama (1974) used pulsed electrons (6 MeV) from a linear and continuous 3-MeV electro n Van de Graaff accelerator for the emulsion polymerization of vinyl acetate using sodium lauryl sulfate as the emulsifier. Close to 90% conversions were obtained in a few secopds with degrees of polymerization of about 2500, almost independent of the dose rateo The latter observation could be due to termination by chain transfer to monomero The resulting latices had a semitransparent appearance suggesting very small partic1e sizes. The rates were proportional to about the 0.5 power of the dose rateo The continuous irradiations were several times slower than the pulsed experiments with a weak dependence on the pulse frequency. Kamiyama and Saito (1975) extended these studies to methyl and ethyl acrylates and styrene. The conversions leveled off at about 90 %. The latices were less turbid than those obtained by y radiation. Again, those obtained at the highest dose rates were almost transparent, with partic1e sizes as low as 23 nm in diameter. In the case of styrene, the rates were almost independent of the dose rate but were found to be to the 0.3, 0.5, and 0.7 powers for methyl and ethyl acrylates and vinyl acetate, respectively. At dose rates higher than 2000 rad/sec the dependency dropped to 0.2. The acrylates were so reactive that limiting conversions were reacted in a few seconds. Kamiyama and Shimizu (1975) also studied vinyl propionate and vinyl nbutyrate. The dose rate dependencies were 0.55 and 0.46, respectively, even at the maximum dose rates. The rate-determining process at the high dose rates associated with electron accelerators was suggested as being the rate of diffusion of the monomer from the droplets to the aqueous phase in the case of styrene, whereas with vinyl acetate the competition between polymer nuc1eation and radical recombination of radicals in the aqueous phase could be important. A further brief study of the vinyl acetate system was presented by Kamiyama (1975).
12. Radiation-Induced Emulsion Polymerization
437
Finally, a very recent study (Hayashi and Okamura, 1980) was conducted in a flow system with electro n beam irradiation. Styrene gave very low rates with broad distribution molecular weights (mn) averaging about 1000. Vinyl acetate, on the other hand, polymerized at much higher rates reaching 60% conversion in 200 sec, in some cases at a dose rate of 0.1 Mradjsec at 40°C. Trimodal molecular weight distributions were obtained at peak s of about 400, 40,000, and 400,000. The highest peak may have been cross-linked or highly branched. Further studies of emulsion polymerization at high dose rates could be quite rewarding and possibly of industrial interest in certain cases. V. Pilot Plant and Related Studies
A. lntroduction The previous sections discussed the results of a large number of laboratory experiments concerning radiation-induced emulsion polymerization. In this section the results obtained from a number of investigations using small-scale pilot plant type equipment will be described. A full discussion of these, more engineering oriented experiments, is beyond the scope of this chapter. It was considered important, however, to summarize these studies and to inelude those references which present the full details of the work. Engineering flow systems and small scale autoelaves, designed largely for batch experiments were developed for these investigations. Experiments of this kind are necessary preludes to the eventuallarge-scale use of radiation for industriallatex production. .
B.
Vinyl Acetate
The basic laboratory studies described earlier were with batch systems; in addition, one larger size and two micro pilot plants have been constructed and operated. AII were based on the general principIe of recirculation from a stirred vessel away from the radiation source. The emulsions were ~ontinuously circulated through tubing to an in-so urce "plug-flow" reactor and back to the kettle. The two micro pilot plants were largely based on the originally designed and operated pilot plant described by Stahel and Stannett (1969, 1971). The larger pilot plant, constructed by Neutron Products, Inc., was designed and constructed simultaneously but quite independently of the micro plants (Allen et al., 1969). The radiation emulsion pilot plants described by Stahel et al. were investigated for styrene, vinyl chloride-vinyl acetate copolymers (Stahel et al., 1979), and for grafting to latex (Memetea et al., 1977).
438
VivianT. Stannett
The first micro pilot plant for vinyl acetate to be described was that of Hoigné el al. (1972), which was essentially an all glass apparatus. The semicontinuous equipment consisted of a stirred, constant temperature 3000-ml glass reservo ir from which the emulsion was pumped through a double helix 240 mI-reactor situated within the radiation cavity. On leaving the reactor the emulsion flowed through a cooler and back into the reservoir. The reservoir has inlets for monomer, soap solution, and the pure nitrogen with which the apparatus was purged prior to and during the run. The conversion curves were found to be linear between 1,5 and 60%. No post effects were observed although this could have been caused by traces of oxygen in the system beca use of the diffusion of air through the thin-walled polyethylene transfer lines. Increasing the flow rate decreased the rate of polymerization, and at very rapid rates of flow the polymerization ceased entirely. This effect again was attributed to traces of oxygen in the equipment since the residence time in the oxygen-free reactor itself became too short for the oxygen to be consumed. The dependence of the rates was found to be about 0.3 and 0.5 order on the emulsifier' concentration and dose rate, respectively. An experimental flow equipment was also built by Friis (1973). There were two important differences from the Hoigné el al. system. First, after initial purging of the system with nitrogen the polymerizations were conducted in the absence of any gas phase, and second the conversion-time curves were measured by means of a dilatometer rather than sampling. In the absence of any oxygen, increasing the flow rate increased the rate of polymerization, confirming perhaps the explanation of Hoigné el al. by the opposite effect of the flow rateo A very small post effect was found. A large-scale pilot plant constructed by Neutron Products, Inc., (Allen el al., 1969) was built as a model for a commercial-scale facility, i.e., it had features that would be important in an industrial process such as heat exchangers and pumps capable of handling high-viscosity polymeric emulsions, multiple-stage processing, and the capability for continuous operation. Furthermore, all materials used in the latex formulations were of commercial grade with no purification prior to reaction. The pilot plant consisted of four complete reactor loops. The reactors varied in total volume from 3 to 35 gal and were all interconnected to permit multistage processing. The reactants were pumped from the surge tank through a heat exchanger embedded in a 6 ft concrete floor that separated the radiation zone from the rest of the pilot plant. The reactants were then circulated around the source in a specified configuration, through another heat exchanger, then back to the surge tank. All or part of the emulsion returning from the radiation zone could be drawn off for continuous operation.
12. Radiation-Induced Emulsion Polymerization
439
The majority of the efforts of AlIen et al. at the Neutron products facility were directed toward producing a poly(vinyl acetate) latex suitable for production of high-quality paints. They employed a practical commercial formulation containing a comonomer, a complex emulsifier system, a stabilizer, and a buffer. The highest quality latexes were produced with a two-stage batch or semibatch process. The first stage, for initiation and propagation, was operated on either a batch or semibatch basis with continuous monomer addition. Generally, the first stage was operated to about 12% residual monomer content at which time the product was transferred to the second stage for finishing under different conditions. The second stage was operated in either a batch or a continuous manner. Experiments were also performed with the plant óperating on an entirely continuous basis and a good quality latex was obtained. The properties of the latices and the paints produced from them were evaluated by several commercial firms. The latex properties varied somewhat from sample to sample but, in general, the paints produced from the latexes were comparable to those produced from high-grade commercial latexes made by conventional means. One property of the paint produced from the radiation-catalyzed latex, enamel holdout, which is one measure of the capability of a paint to serve as a primer for enamel on unpainted wood, was superior to that of paint made from conventionally produced latex. The results showed that production of latices by radiation catalysis is a commercially feasible process. However, the authors did not appear to have resolved two process-development problems: the reduction of residual monomer to commercially acceptable levels and the eIimination of polymer build-up inside the process lines. The authors noted, however, that these are problems of formulation and operation rather than of the basic process itself. Using the data obtained in the pilot plant, a conceptual design and cost analysis was made for a commercial-scale radiation catalysis plant (AlIen et al., 1969, 1971). The conceptual design was based on a two-stage semicontinuous process. The first stage is operated on a semibatch basis with continuous monomer addition and intermittent feed to the second stage which is operated on a batch basis. Economic analysis indicated that capital and operating costs for radiation catalysis and conventional catalysis plants would be about the same; but the authors felt that the greater enamel holdout of the radiation-initiated product would justify the use of a radiation catalysis plant. In addition, the early work of Araki et al. (1969) showed that better wet-scrub resistance was obtained with paints formulated with high molecular weight radiation-produced homovinyl acetate latices compared with their conventional commercial counterparts.
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The results of the laboratory and pilot plant studies show clearIy that a radiation-induced emulsion polymerization process for vinyl acetate is of considerable interest. In addition to the general advantages discussed in the introduction, the smooth and easy polymerization at low temperatures is of special interest for vinyl acetate and its copolymers since it leads to very high molecular weight products. High molecular weight-polymerized acetate latices are known to lead to paints and coatings with better ink and enamel holdout and superior wet-scrub resistance. C.
Ethylene Polymerization in Emulsion
These investigation s were all conducted, using 60Co y radiation, in the laboratories of the Japan Atomic Energy Research Institute in Takasaki (Konishi et al., 1974). The flow sheet of the apparatus used is shown in Fig.6. The polymerization vessel was a 500-ml stainless steel autoclave equipped with a variable motor speed driven propeller. The effect of the reaction conditions on the rate of polymerization was studied using a number of emulsifiers. The potassium salts of a number of fatty acids gave the highest rates, potassium stearate being the best. The rate was found to be linearIy proportional to the ethylene pressure. Oxygen was found to inhibit the reaction in the sense that an induction period was introduced. After this the steady-states rates were not affected. Increasing the rate of stirring first increased th~ reaction rate which then levelled off aboye about 600 rpm. No effect of the monomer to water ratio was found. Both the rate and the number average molecular weight were
Fig. 6. Flow sheet of apparatus: (1) ethylene cylinder, (2) air-operated automatic intensifier, (3) autoclave, (4) temperature-controlled oi! bath, (5) 60Co radiation source, (6) buret for flushing of medium, (7) sampling line, (8) shielded room (Senrui et al., 1974a: reproduced with permission of Journal of Polymer Science.)
12.
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Emulsion Polymerization
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found to follow Arrhenius law with an activation energy of 4.6 kcal/mol up to 80°C but to become negative at -4.5 kcal/mol after this maximum temperature. The change was attributed to a near melting of the polyethylene particIes causing an increase in the rate of termination by the increased mobility of the growing radicals. Chain transfer to the emulsifiers was found and carboxylic acid groups were introduced in this way to the polyethylene. The transferred radicals were thought to escape from the particIes to the aqueous phase. A more detailed kinetic study (Senrui et al., 1974a) with potassium myristate as the emulsifier showed that the rate increased only slightIy with increasing emulsifier concentration and was proportional to the 0.5 power of the dose rateo Seeded polymerizations showed an increasing rate with increasing seed volumes but only to a small extent. The solubility of ethylene in water at the pressures used (200 kg/cm2) is comparatively high ( 0.5 mol/liter) compared with 5 mol/liter in the particIes themselves. In some ways, therefore, the polymerization mechanism could be compared to that of vinyl acetate polymerization. An elaborate kinetic scheme for the polymerization was presented. A further study substituted ammonium perfluorooctanoate as the emulsifier (Senrui et al., 1974b). This was to avoid the complications introduced by the chain transfer of the growing polyethylene chains to the emulsifier. Indeed, no fluorine could be detected in the polyethylene produced using this emulsifier. The rate of polymerization was proportional to the 0.6 power of the emulsifier concentration, in marked contrast to the fatty acid saIts which had a very low dependence, reminiscent of vinyl acetate emulsion polymerizations. This tends to confirm the mechanisms proposed for the fatty acid saIt systems. The number of particIes was found to be approximately proportional to the 0.6 power on the emulsifier concentration. The dose rate dependence of the rate was 0.5, similar to that found with the hydrocarbon emulsifiers. No post polymerization was observed, even at room temperature. This was confirmed by two separate types of two-stage experiments. It was postulated that any remaining radicals soon transferred to monomer and escaped and terminated in the aqueous phase. The resuIt is in marked contrast to the long-lived radicals found with the radÜltion-induced bulk polymerization of ethylene at room temperature (Gotoda et al., 1965). Seeded polymerizations showed arate dependence on the number of seeds to be about 0.4 and on the dose rate to be 0.35. A kinetic scheme was developed that was in reasonable agreement with the experimental results. The effect of pressure and temperature on the rate of polymerization was studied in more detail by using a seeded system developed by Senrui and Takehisa (1974) and by considering the effect of added alcohols and
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VivianT. Stannett
electrolytes. With seeded polymerization the rate was found to be proportional to the 1.8 power of the ethylene pressure and to the 2.5 power of the fugacity. The temperature dependence again slowed a maximum in the rate, but at 87° rather than at 800C. Mixed emulsifiers showed that the overall rate was close to the sum of the separate rates. It was believed that the two, very different emulsifiers, behaved independently due to the big difference in the solubility parameters of n-dodecane and nperfluoroheptane (7.8 and 5.6, respectively). Alcohols depressed the rate, presumably because of chain transfer since they should increase the solubility of the ethylene in the aqueous phase. The addition of salts increased the rate of polymerization, and this effect was shown to be attributable to an increase in the number of particles. Experiments using no emulsifier were conducted in the same stainless steel autoclave equipment described above (Machi et al., 1975). Stable latices were obtained, believed to be achieved by hydroxyl end groups and adsorbed hydroxyl ions. As with a number of the experiments with emulsifiers the polyethylene had a considerable cross-linked gel contento Finally, the same group of workers studied the radiation-induced emulsion polymerization of ethylene in a ftow system (Kodama et al., 1974). Both potassium myristate and ammonium perfluorooctanoate were used as emulsifiers. At longer residence times (above 0.2 hr) the rate of polymerization was essentially constant. As with the batch system it was assumed that the number of particles remained constant. In this region the rate was found to be proportional to the 0.3 power of the potassium myristate concentration and the 0.5 power of the dose rate, not too different from the batch systems. The kinetics was developed and estimates of the propagation rate constants obtained. Despite other similarities between the two systems, these were quite different, however, from those extracted from the batch experimento These extensive and important studies of ethylene polymerization have only been summarized in this review. The original papers should be consulted for the full details.
D. Tetrafluoroethylene Machi et al. (1974) first reported an investigation of the radiationinduced emulsion polymerization of tetraftuoroethylene, with ammonium perfluorooctanoate as the emulsifier. A 200-ml stainless steel autoclave, equipped with a magnetically driven propeller-type stirrer, was used. The standard recipe used was 28 gm of monomer in 150 mI of water with 1% emulsifier (based on the water). n-Hexadecane (2.0 mI) was added to inhibit any gas-phase polymerization. The polymerizations were conducted at
12. Radiation-Induced Emulsion Polymerization
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25°C. The rate of stirring had a considerable effect on the reaction rateo The dose rate exponent of the reaction rate was found to be 0.8, with little effect on the molecular weights. The emulsifier concentration hardly affected the rates but greatIy changed the molecular weights, which increased with decreasing emulsifier concentration. The particIe shapes were also affected, being spherical at less than 0.5% and rod-like and eventually fibrillar above this concentration. There was considerable post-irradiation polymerization with increasing molecular weight. Molecular weights were in the 105-106 range. In the absence of emulsifier much higher molecular weights were obtained, presumably due to lower chain-transfer reactions. There followed a very important series of papers concerning the emulsifier-free system (Machi et al., 1978, 1979a-d). The equipment used was a modification of that used earlier, but the tetrafluoroethylene pressure was continuously recorded with the use of a strain gauge. In the first paper of the series (Machi et al., 1978) the rate of polymerization was shown to be proportional to the 1.0 and 1.3 powers of the dose rate and the initial pressure, respectively. The activation energies were 0.8 above and - 5.2 kcal/mol below 70°C. There was a maximum in the molecular weights at about the same temperature. This behavior is reminiscent of the behavior of ethylene and was again attributed to the increased mobility of the growing chains above the maximum temperature. The very low mobility would also account for the first-order dependence of the rate on the dose rate below 70°C. As before, n-hexadecane pro ved to be an excellent inhibitor of polymerization in the gas phase. ParticIe sizes in the range of 0.1-0.2 microns were obtained. A detailed study of the size, distribution, and number of particIes was presented in the secorid part (Machi et al., 1979a). It was found that the particIes grow faster at higher dose rates in concert with the higher reaction rates. At the higher dose rates the particIe size levels off with reaction time but continues to grow at the lower dose rates. The size and number of particIes are essentially independent of the temperature from 30-100oC. The effect of pressure was complex but the particIe size tends to increase and the number of partic1es to decrease with increasing pressure. The partic1e size distribution also becomes broader, perhaps due to increased flocculation effects at higher pressures. It was concIuded that after the 'generation of the particIes, which tends to be in the first five minutes, they grow by propagation at the surfaces. The particIes are believed to be stabilized by hydroxyl and carboxyl end groups and possibly by adsorption of ions. A discussion of the mechanism of particIe formation and .the loci of the polymerization was also presented. Machi et al. (1979b) also investigated the concurrent formation of hydrofluoric acid during the polymerization due to the radiolysis of the
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Vivian T. Stannett
monomer. It was found to be unaffected by the agitation rate or the presence of n-hexadecane. G values varied from 27 to 180, being larger at high pressures and increasing with increasing dose rateo Possible mechanisms for the formation of the acid were discussed. The molecular weights were normally in the 105--106range but a few samples from the emulsifier-free grade were higher than 107. This was in the conventional molding powder grade region and therefore of considerable interest. A number of particles to decrease with increasing pressu~e. The particle size control the molecular weights. Oxygen was found to decrease the rate and the molecular weight; this was attributed to its capacity to inhibit radical s in the aqueous phase and to diffuse into the particles to retard the growing chains. A number of additives were studied but the conventional radical scavengers were the most effective. Hydroquinone and benzoquinone are highly soluble in water but barely soluble in the polymer particles. Their effect was, therefore, to inhibit the rate of polymerization but to increase the molecular weight. Molecular weights of 2 x 107 were obtained in the presence of hydroquinone. Ethylenediamine and triethylamine were both found to retard the rate, but the molecular weight was decreased by the latter and increased by the former additive. The decrease was ascribed to the power of triethylamine to absorb on the particles inhibiting the chain growth. Further details of these and other additives were described, including their effect on particle size and distribution. In the final paper of this important series (Machi et al., 1979d) the effect of the reaction conditions on the stability of the tetrafluoroethylene latices was studied. The stabilization was believed to be due to either carboxyl end groups or to the adsorbed hydrofluoric acid formed by radiolysis of the monomer or to both. The surface charge densities, electrophoretic mobilities, and infrared spectra were all measured. The storage stability of the latices, measured by the appearance of coagulum, was found to be proportional to the total dose and the polymer concentration and not to depend on the dose rateo Since the stabilization results from the radiolysis of the monomer and water this is quite reasonable as is the effect of concentration. The presence of monomer was necessary in the sense that irradiation of the latex in the absence of monomer did not improve the storage stability.
E. Tetrajluorethylene-Propylene and Other Copolymers Ishigure et al. (1964) reported that the radiation-induced polymerization of tetrafluoroethylene and propylene in the liquid phase produced an essentially alternating rubbery copolymer. Ito et al. (1974a) and Matsuda et al. (1974a) studied the same system in emulsion using a variety of mixed and pure emulsifiers. The experiments were conducted in a stirred 200-ml
12. Radiation-lnducedEmulsion Polymerization
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stainless steel autoclave with 60Co radiation. Ammonium perfluorooctanoate gave the highest rates and molecular weights and was therefore chosen for the detailed investigation. Increasing the stirring speed first increased the rates and stability but then essentially leveled off. The emulsion system gave a higher rate and molecular weight than the corresponding polymerizations in bulk. Increasing the temperature slightly decreased the rate and increased the molecular weight. The copolymers were essentially alternating, as were the bulk copolymerizations previously mentioned. Oxygen caused a small induction period which was followed by a resumption of the normal rates. The effect of the emulsifier concentration was to cause an increase in the rate and molecular weight above 1% and then to have little further effect. The number average molecular weight ranged from 3 to 8 X104. Matsuda et al. (1974b) continued their detailed studies using ammonium perfluorooctanoate as the emulsifier. The rate of polymerization was found to be 0.9 order and 0.26 order with respect to the dose rate and the emulsifier concentration, respectively. Both the rate and the molecular weight increased with increasing tetrafluoroethylene content of the feed. The copolymer composition, however, remained alternating over a very wide range of compositions. The dose rate dependence indicated that most of the termination was by degradative chain transfer to the propylene monomer. Danno et al. (1974) presented additional work showing that above the critical micelle concentration (CMC) of the emulsifier the dose rate dependence of the rate was actually 0.7 and below the CMC as 0.6. The molecular weight was higher above the critical micelle concentration and independent of the dose rate and lower below the CMC and decreasing with increasing dose rateo These and other details of the polymerization reaction were discussed further in terms of the particle sizes, which are larger and less numerous at zero or low-emulsifier contents and at lower dose rates and degradative chain transfer to propylene monomer. Okamoto and Suzuki (1974) presented the results of a brief study of the effects of a number of additives on the polymerization. Hexachlorethane and carbon tetrachloride were found to decrease markedly the molecular weight; the former had no effect whereas .the latter decreased the rateo 1,1,2-Trichloro-l,2,2trifluoroethane had no effect on either the rate or 'molecular weight. Alcohols reduced the rate in the order isopropyl > ethyl > methyl, in the same order as the ease of hydrogen abstraction but had no effect on the molecular weight. This indicated that the primary radical s were reacting with the alcohols in the aqueous phase but not in the particles themselves. Diphenyl picrylhydrazyl and p-benzoquinone, as expected, completely inhibited the polymerizations above 3 x 10- 3 molar concentration. Okamoto and Suzuki (1975) also investigated the hydrofluoric acid yields during the polymerization. The yields were first order with the dose rateo The presence
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Vivian T. Stannett
ve mor.omer
VA monomer
Metering
pump
Metering
pump
Soap
solution
tank
Solvent tank
Liquid level gauge
EmuHifying tank
Sample
Temperature bath
Metedng pump
Vent
Rotameters
Off produc.t drum
Fig. 7. Schematic diagram for radiation-induced copolymerization pilot plant (Stahel et al., 1979; reproduced with permission of Journal 01 Applied Polymer Science.)
. 12. Radiation-Induced Emulsion Polymerization
447
of oxygen increased the yield, but was decreased greatly when more than 1% of emulsifier was used. G values were much lower than with pure tetrafluoroethylene emulsion polymerization. Some tentative explanations were presented. Ito et al. (1974b) also studied the copolymerization of ethylene and hexafluoropropylene with the same autoclave batch system used with ethylene and with ammonium perfluorooctanoate as the emulsifier. The rate of polymerization was found to be proportional to the 1.6 power of the ethylene fugacity. The ratio of ethylene units in the copolymer increased linearly with the reaction rate, extrapolating to zero at zero rateo This agrees with the fact that hexafluoropropylene does not homopolymerize. A number of thermal and other properties of the copolymers were determined. Properties varied from semicrystalline polyethylene types to amorphous rubbers. Memetea et al. (1977) attempted to graft styrene to a previously radiation prepared, poly(vinyl chloride) latex. A recirculating flow system was used, very similar to those used earlier by Stahel et al. (1969) and others and shown schematically in Fig. 7. In contrast to earlier results published by Wang (1963) very little grafting occurred if the correct extraction procedures for the homopolystyrene were used. Interestingly, the polymerization of styrene on the poly(vinyl chloride) seeds ciosely approximated Smith-Ewart Case 2 behavior. The less than 3 %grafting was attributed to the low total dose needed to effect the essentially complete polymerization of the styrene, only about 0.1 Mrad. Parallel experiments with styreneswollen films and the literature results did give reasonable grafting yields at higher doses (e.g., 33% with 3.6 Mrad). Finally, Stahel et al. (1979) studied the radiation-induced emulsion copolymerization of vinyl chloride and vinyl acetate in an engineering flow system with a l-gallon reactor, shown schematically in Fig. 7. The copolymerization proceeded smoothly to high conversions. The rate was found to be proportional to the 0.17 power of the emulsifier concentration, within the range reported for the individual monomers. The activation energies were 5.5 and -2.0 kca1/mol for the rate and molecular weight, respectively, in good agreement with literature results for similar, chemically initiated systems. The res.ults showed that radiation does represent a viable and practical method for producing stable lattices with high conversions and solids content in engineering systems'. References Abkin, A. D., Mezhirova, L. P., Iakovleva, M. K., Matveeva, A. V., Khomikovskii, P. M., and Medvedev, S. S. (1959). Vysokomo/. Soedin. 1, 68. Acres, G. J. K., and DaIton, F. L. (I963a). J. Po/ym. Sci. A 1, 3009.
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Acres, G. J. K., and Dalton, F. L. (1963b). J. Po/ym. Sci. A 1,2419. AIIen, P. E. M., Downer, J. M., Hastings, G. W., MelviIle, H. W., Molyneux, P., and Urwin, J. R. (1956). Nalure (London) 177,910. Allen, P. E. M., Bumett, G. M., Downer, J. M., Hardy, R., and Melville, H. W. (1958). Nalure (London) 182, 245. AIIen, P. E. M., Bumett, G. M., Downer, l. M., and Melville, H. W. (1960). Makromo/. Chem. 38,72. AIIen, P. E. M., Burnett, G. M., Downer, J. M., and Majer, J. R. (1962). Makromo/. Chem. 58, 169. AIIen, R. S., RansohotT,. l. A., and Woodard, D. G. (1969). USAEC Rep. ORO 673 (October 1969); See also Proc. Jpn. Conf Radioisolopes 9, 598. AIIen, R. S., RansohotT, J. A., and Woodard, D. G. (1971). Isolopes and Radial. Techno/. 9, 92. Araki, K., Stannett, V., Gervasi, J. J., and Keamey, J. J. (1967). USAEC Rep. TID-24281, December l. Araki, K., Stannett, V., Gervasi, J. A., and Keamey, J. J. (1969). J. App/. Po/ym. Sci. 13, 1175. BaIlantine, D. S. (1954). Brookhaven National Laboratory, New York, Rep. BNL-294 (T-50), March. Barriac, J., Oda, E., Russo, S., Stahel, E. P., and Stannett, V. (1969). Proe. Jpn. Conf. Radioisolopes 9, 605. Barriac, l., Knorr, R., Stahel, E. P., and Stannett, V. (1976). Adv. Chem. Ser. 24, 142. Bradford, E. B., and VanderhotT, J. W. (1955). J. App/. Phys. 26, 864. Bradford, E. B., VanderhotT, J. W., Tarkowski, H. L., and Wilkinson! B. W. (1961). J. Po/ym. Sci. 50, 265. Cockbain, E. G., Pendle, T. D., and Turner, D. T. (1958). Chem. Ind. (London) 759. Cockbain, E. G., Pendle, T. D., and Tumer, D. T. (1959). J. Po/ym. Sci. 39, 419. Cooper, W., and Vaughan, G. (1959). J. Po/ym. Sci. 37, 241. Cooper, W., Vaughan, G., Miller, S., and Fielden, M. (1959a). J. Po/ym. Sci. 34, 651. Cooper, W., Vaughan, G., and Madden, R. W. (1959b). J. App/. Po/ym. Sei. 1, 329. Cooper, W., Sewell, P. R., and Vaughan, G. (l959c). J. Po/ym. Sci. 41, 167. Danno, A., Matsuda, O., Okamoto, J., Suzuki, N., and Ito, M. (1974). J. Po/ym. Sci.-Chem. Ed. 12, 1871. Ewart, R. H., and Smith, W. V. (1948). J. Chem. Phys. 16,592. Friis, N. (1973). Danish A.E.C. Riso Rep. 282. Gardinovacki, B., Lervik, H., Ugelstad, J., and Sund, E. (1971). Pure App/. Chem. 26, 121. Garreau, H., Stannett, V., Shiota, H., and Williams, J. L. (1979). J. Co/loid Interface Sci. 71,130. Garreau, H., Yoshida, K., Ishigure, K., and Stannett, V. (1980). J. Maeromo/. Sci.-Chem. A14, 739. Glazkova, K. G. el al. (1971). Vysokomo/. Soedin. BI3, 173. Gotoda, M., Machi, S., Hagiwara, M., and Kagiya, T. (1965). J. Po/ym. Sci. A 3, 2931. Hansen, F. K., and Ugelstad, J. (1976). Ruúber Chem. Teehno/.49, 537. Hayashi, K., and Okamura, S. (1980). Ann. Rep. Osaka Lob. JAERl M-9214, 113. Hoigné, J., and O'Neill, T. (1972). J. Po/ym. Sei. A-110, 581. Hoigné, J., O'Neill, T., and Pinkava, J. (1972). Proe. Tihany Symp. Radial. Chem., 3rd, Tihany, Hungary. 1971 1, 713. Hummel, D. (1963). Agnew. Chem. In l. Ed. 2, 295. Hummel, D., Ley, G., and Schneider, C. (1962). Adv. Chem. Ser. 34, 60. Hummel, D., Ley, G. J. M., and Schneider, C. (1967). Adv. Chem. Ser. 66, 184. Hummel, D., Ley, G. J. M., and Schneider, C. (1969). J. Po/ym. C 27, 119. Inagaki, H., Okamura, S., Motoyama, T., and Manabe, T. (1960a). .. Large Radiation Sources in Industry," Vol. I. pp. 368-373. IAEA, Vienna.
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Inagaki, H., Yagi, K., Saeki, S., and Okamura, S. (1960b). Chem. High Polym. (Jpn.) 17,37. Inagaki, H., Yagi, K., Saeki, S., and Okamura, S. (l960c). Chem. High Polym. (Jpn.) 17, 135. Ishigure, K., and Stannett, V. (1974). J. Macromol. Sci. Chem. AS, 337. Ishigure, K., Tabata, Y., and Sobue, H. (1964). J. Polym. Sci. A2, 2235. Ishigure, K., Yoshida. K., and Stannett, V. (1973). J. Macromol. Sci. A7, 813. Ishigure, K., O'Neill, T., Stahel, E. P., and Stannett, V. (1974). J. Macromol. Sci.-Chem. AS, 353. Ito, l., and Watanabe, T. (1965). J. Chem. Soc. Jpn.-/nd. Chem. Sect. 68, 552. Ito, M., Matsuda, O., Okamoto, J., Suzuki, N., and Tabata, Y. (1974a). J. Macromol. Sci.-Chem. AS, 775. Ito, M., Senrui, S., and Takehisa, M. (1974b). J. Polym. Sci. 12, 627. Izumi, Z. (1967). J. Polym. Sci. A-l 5, 469. Izumi, Z., Kuichi, H., and Watanabe, M. (1967). J. Polym. Sci. A-l 5, 455. Kalyadin, V. G., Sirlibaev, T. S., and Tirkashev, 1. (1975). Nauch Tr. Tashkent Un-T (462) 100; (1974) CHAB. 83, 193858f. Kamiyama, H. (1974). Ann. Rep. Osaka Lab. JAER15029, 33. Kamiyama, H. (1975). Ann. Rep. Osaka Lab. JAER/ M-6260, 23. Kamiyama, H., and Okamura, S. (1969). Ann. Rep. Osaka Lab. JAER/5022, 33. Kamiyama, H., and Saito, K. (1975). Ann. Rep. Osaka Lab. JAERI 5030, 147. Kamiyama, H., and Shimizu, Y. (1975). Ann. Rep. Osaka Lab. JAER/503O, 148. Kamiyama, H., Kitayama, M., and Okamura, S. (1970). Ann. Rep. Osaka Lab. JAER/5026(3), 26. Karpov, V. L., Lukhovitskii, V. l., Polikarpov, V. V., Lebedeva, A. M., and Lagucheva, R. M. (1968). Vysokomol. Soedin. AI0, 835. Karpov, V. L., Lukhovitskii, V. l., Polikarpov, V. V., Lebedeva, A. M., and Lagucheva, R. M. (1969). Khim. Vys. Energ. 4, 173. Karpov, V. L., Smirnov, A. M., and Lukhovitskii, V. 1. (1971). Khim. Vys. Energ. 5, 470. Karpov, V. L., Smirnov, A. M., and Lukhovitskii, V. 1. (1972). Vysokomol. Soedin. B-l 4, 6. Karpov, V. L., Lukhovitskii, V. l., and Lebedeva, A. M. (1973a). Vysokomol. Soedin. A15, 2465. Karpov, V. L., Smirnov, A. M., and Lukhovitskii, V. 1. (1973b). Vysokomol. Soedin. B15, 726. Karpov, V. L., Lukhovitskii, V. l., and Pozdeeva, R. M. (1973c). Vysokomol. Soedin. B15, 907. Karpov, V. L., Polikarpov, V. V., Lukhovitskii, V. l., and Pozdeeva, R. M. (1974). Vysokomol. Soedin. A16, 2207. Karpov, V. L., Smirnov, A., Lukhovitskii, V. l., and Pozdeeva, R. M. (1977). Plast. Massy (USSR) 3, 18. Klein, A., Stannett, V., and Litt, M. (1975). Br. Polym. J. 7, 139. Kodama, A., Senrui, S., and Takehisa, M. (1974). J. Polym. Sci. 12, 2403. Konishi, K., Senrui, S., Suwa, T., and Takehisa, M. (1974). J. Polym. Sci. 12,83. Litt, M., Patsiga, R., and Stannett, V. (1960). J. Phys. Chem. 64, 801. Litt, M., Patsiga, R., and Stannett, V. (1970). J. Polym. Sci. A-l S, 3607. Machi, S., Suwa, T., and Takehisa, M. (1974). J. Appl. Polym. Sci. lS, 2249. Machi, S., Suwa, T., N'akajima, H., and Takehisa, M. (1975). J. Polym. Sci. Polym. Lett, Ed. 13, 369. . Machi, S., Suwa, T., Watanabe, T., and Okamoto, J. (1978). J. Polym. Sci. Chem. Ed..16, 2931. Machi, S., Suwa, T., Watanabe, T., Seguchi, T., and Okamoto, J. (1979a). J. Polym. Sci. Chem.
Ed. 17, 111.
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Machi, S., Suwa, T., Watanabe, T., and Okamoto, J. (1979b). J. Polym. Sci. Chem. Ed. 17, 129. Machi, S., Watanabe, T., Suwa, T., and Okamoto, J. (1979c). J. Appl. Polym. Sci. 23, 967. Machi, S., Suwa, T., Watanabe, T., and Okamoto, J. (l979d). J. Polym. Sci. Chem. Ed. 17,503. Matsuda, O., Suzuki, N., and Okamoto, J. (1974a). J. Macromol. Sci.-Chem. AS, 793. Matsuda, O., Suzuki, N., and Okamoto, J. (l974b). J. Polym. Sci. Chem. Ed. 12, 2045.
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lndex D
A Diffusion, 296
Acrylonitrile, 372, 424 Adhesion, 291 Adhesives, 300
Dispersion interaction, 250 DLVO theory, 8, 17,85
tufted carpet applications,
306
Adsorption, 250, 253, 291 of anion-active emulsifiers, 267 area, 232, 254 characteristics of surfactants, 256
E Electrostatic Electrostatic
isotherms, 251, 254 kinetics, 253, 268 Application properties of latexes, 315 Attractive interactions of particles, 8, 12
Electrostatic repulsion, Emulsification
8
with mixed emulsifier systems, 408 of polymer solutions, Emulsifier
B Butadiene,
effects, 6 forces, 3
399
adsorption, 250, 252, 268 anionic and nonionic, mixtures of, 227 area occupied by saturated monolayer, 231-233
372, 431
tran~fer, 242
e
Emulsion polymerization choice of emulsifier, effect of, 221 distribution of components and phases, 53 emulsifier-free, 257 initiatibn mechanisms, 51
Chemisorption, 298 Coagulation, 2, 7, 24 with aluminum salts, 19-22
with ionic emulsifiers, 230-233 kinetics~ 51, 145, 191,278,283,319,357 with nonionic emulsifiers, 229
as kinetic process, 14 measurements of rate, 15 Colloidal behavior of polymerization 261 Colloidal characteristics
systems,
particle stability, 45 radiation-induced, 415
of latexes, 264
Ethylene, 440
Colloidal stability definition, 2
F
theory, 8 Constant rate period, 286 Copolymerization block and graft, 434 random, 433
Fiber bonding, 302 . FIocculation, 2, 7, 24 of particles, 262
Critical coagulation concentration, 15 determination of values, 17-19 Critical micelle concentration, 51, 63
H
Critical surface tensions of polymeric materials, 294
Hamaker constant,
451
10
452
Index
Hamaker equation, 291 Heterocoagulation, 36 Hydrophile-lipophile balance, 225
Molecular weiglit distributions, in bulk, 116
concepts in emulsion, 118, 183 experimental deterrninations, 139-141 generaltheory, 120-124, 183 polydispersity ratio, 132-133 Monodisperse latexes, 228 Monomers
1 Initiation emulsifier-induced decomposition, in monomer droplets, 396 radiation-induced, 415 systems, 329 Interface characteristics, 249 liquid-liquid, 251 liquid-polymer, 254 Interfacial tension, 249, 251 monomer-water, 256 Ions
115
239
concentration within reaction loci, 151 emulsification, 224 polarity effects, 258
.
solubility in water and polymer, stabilization, 237
372
water insoluble compounds, effect of addition of, 401
N
interaction with water, 19 Nonionic surfactants, Nucleation
organic, 26
31
homogeneous, 52, 73 micellar, 54, 63
L
in monomer droplets, Latex application properties, Latex particles . colloidal behavior, 2
86
315
effect of electrolyte on, 6-8 formation mechanisms, 51 nature of, 2 nucleation, 51 sterically stabilized, 5 surface charge, 3 Lyophobic colloids, 8, 14 theory of stability, 8
M Macromolecules, oligomeric, 53 adsorbed on particles, 5, 42, 43 grafted on particles, 5, 42, 43 Micellar nucleation newer methods, 63 Smith'- Ewart theory, 54 Micellar size, 234 effect of polymerization, 235 Mixed electrolyte systems, 35 Molecular weight, 325 of styrene, 421 theoretical predictions, 93
o Oligomeric radicals, 53
P Paints and industrial coatings, 309 Paper coatings, 310 Particle generation homogeneous nucleation, 73 mechanisms, 51, 257, 270, 370 micellar, 54, 63 in monomer droplets, 86 Particle number, 327, 334, 363 effect of emulsifier, 233 initial emulsifier concentration, of,69 rate of initiator decomposition, 70
as function as function of,
in styrene emulsion polymerization, Particle size, 93, 258 Particle size distribution 363 approximate
90
(PSD), 258, 327, 334,
approaches,
95
453
Index in batch polymerization, 99 in continuous polymerization, cumulative, 335 experimental investigations, functions, 102
mechanisms,
56
reabsorption, 199 Radical desorption, 191, 199, 204, 369
105 109-114
monodispersity index, 260 population balance model, 96 of radiation-induced polystyrene, 422 theoretical predictions, 93 Partic1e stability, 1-48 in absence of added emulsifier, 45 Peptization, 40 Poly(alkyl acrylates), 265 adsorption of C12H2SS04Na, 285 colloidal characteristics of latexes, 264 structural characteristics of latexes, 277
Radical number per locus theoretical prediction, 181 theory for generation of pairs, 185 Rate of interphase transport, 392 Reactors batch, 320, 359 continuous stirred-tank,
latex ccc values, 19,31 partic1e number dependence concentration
on emulsifier
experimental, 90 theoretical, 69
Secondary minimum effects, 9, 22 Smith-Ewart theory, 54 Case 1, 322 Case 2, 248, 323, 361,419-425 derivations, 156-160, 194-198 deviations from Case 2, 367 solution of nonsteady state, 167-176 solution of steady-state, 164-167 solutions of equation, 160-164 Sodium dodecyl sulfate, 82, 261 adsorption area, 256, 264
energy characteristics, Solvation effects, 6
polymerization,
Poly(vinyl acetate), 428, 437 Potential energy coagulation versus repeptization, diagrams, 9-13,16 ' primary minimum, 9 secondary minimum, 9, 22 effects, 22-26
R Radical absorption inverse absorption efficiency,
s
energy, 252 kinetics, 268
partic1e size distributions experimental, 110 theoretical, 1l1 radiation-induced
of, 344
Rubber goods, 313
Poly(butyl acrylate), 42, 281, 432 Poly(butyl methacrylate), 262 Poly(ethyl acrylate), 42, 279, 432 Polymer colloids, definition, 2 Polymer dispersions, preparation, 396 Poly(methyl acrylate), 42, 259, 261,431 Poly(methyl methacrylate), 82, 259, 425 PSDs, experimental and theoretical, comparison of, 112 Polystyrene, 259 adsorption of C12H2SS04Na, 285 coagulation by lanthanium nitrate, 34 colloidal characteristics of latexes, 264
333, 339, 359
design considerations, 378 dynamics in design, consideration heat-removal techniques, 330 on-line control, 345, 349 reaction time, reduction of, 330
61
418
41
252, 253
Stability of Iyophobic colloids, 8 adsorbed or grafted macromolecules, of,42 Steric effects, 6 Steric stabilization, 4 Surface coagulation, 39' Surface groupings, 3 Surface potential, 3 Surface properties of latex partic1es. 2 Surfactants adsorption characteristics, 252- 256 Swelling of outer shell of partic1e, 407 and phase distributions, 384
effect
.
454
Index T
Taek, 298 Tetrafluoroethylene,
442
polymer latex cee values, 27, 31
v Vinyl ehloride, 429 latex panicle size distribution, Vinylidene ehloride, 431
377
