Advances in Photochemistry (Volume 14)

ADVANCES IN PHOTOCHEMISTRY Volume 14

ADVANCES IN PHOTOCHEMISTRY Volume 14 Editors

DAVID H. VOLMAN Department of Chemistry, University of California, Davis, California

GEORGE S. HAMMOND Allied-Signal, Inc., Morristown, New Jersey

KLAUS GOLLNICK Institut fur OrganischeChemie, Universitat Miinchen, Miinchen, West Germany

A Wiley-Interscience Publication

JOHN WILEY & SONS New York

Chichester

Brisbane

Toronto

Singapore

Copyright 0 1988 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc.

L i b w of Congress C&&g

in Pub&a&wi Data:

Library of Congress Catalog Card Number: 63-13592 ISBN 0-471-81524-1 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1

CONTRIBUTORS

Beauford W. Atwater Department of Chemistry The Florida State University Talahassee, Florida 32306 Giinther von Biinau Institut fur Physikalische Chemie der Universitiit Siegen Postfach 21 02 09 D-5900 Siegen 21, West Germany Guy J. CoUi DCparment des Sciences Fondementales Universitk du Qutbec B Chicoutimi Chicoutimi, Quebec, Canada G7H 2B 1

Julian P. Heicklen Department of Chemistry and

Center for Air Environment Studies The Pennsylvania State University University Park, Pennsylvania 16802

Jack Saltiel Department of Chemistry

The Florida State University Tallahassee, Florida 32306

Thomas WOE

Institut f~ Physikalische Chemie der Universitiit Siegen Postfach 21 02 09 D-5900 Siegen 21, West Germany

James Guillet Department of Chemistry University of Toronto Toronto, Canada MSS 1Al

V

PREFACE

Volume 1 of Advances in Photochemistry appeared in 1963. The stated purpose of the series was to explore the frontiers of photochemistry through the medium of chapters written by pioneers who are experts. As editors we have solicited articles from scientists who have strong personal points of view, while encouraging critical discussions and evaluations of existing data. In no sense have the articles been simple literature surveys, although in some cases they may have also fulfilled that purpose. This volume initiates the second quarter-century of the existence of Advances in Photochemistry. In the introduction to Volume 1 of the series, the editors noted the developments in a brief span of prior years that were important for progress in photochemistry: flash photolysis, nuclear magnetic resonance, and electron spin resonance. In the past quarter century, two developments have been of prime significance: the emergence of the laser from an esoteric possibi!ity to an important light source; the evolution of computers to microcomputers in common laboratory use for data acquisition. These developments have strongly influenced research on the dynamic behavior of excited states and other transients. With an increased sophisticationin experiment and interpretation, photochemists have made substantial progress in achieving the fundamental objective of photochemistry: elucidation of the detailed history of a molecule which absorbs radiation. The scope of this objective is so broad and the systems to be studied are so many that there is little danger of exhausting the subject. We hope that the series will reflect the frontiers of photochemistry as they develop in the next quarter century. Davis, California Morristown, New Jersey Miinchen, Federal Republic of Germany October 1987

D A V I D H . VOLMAN

GEORGE S . HAMMOND KLAUSGOLLNICK

CONTENTS

Spin-StatisticalFactors in Diffusion-ControlledReactions JACKSALTIEL BEAUFORD W. ATWATER,Department of Chemistry, The Florida State University, Tallahassee, Florida Photochemistry and Molecular Motion in Solid Amorphous Polymers JAMESGUILLET,Department of Chemistry, University of Toronto, Toronto, Ontario, Canada Photochemistry of Simple Olefins: Chemistry of Electronic Excited States or Hot Ground States? GUYJ. COLLIN,Dtfpartement des Sciences Fondementales, Universittfdu Qukbec a Chicoutimi, Chicoutimi, Quebec, Canada The Decomposition of Akyl Nitrites and the Reactions of Akoxyl Radicals JULIAN P. HEICKLEN, Department of Chemistry and Centerfor Air EnvironmentStudies, The Pennsylvania State University, University Park, Pennsylvania

1

91

135

177

Photochemistry in Surfactant Solutions G~NTHER VON BUNAUAND THOMAS WOLFF,Znstitut fur Physikalische Chemie der Universitat Siegen, Siegen, West Germany

273

Index

333

Cumulative Index, Volumes 1-14

337

Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.

SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS Jack Saltiel and Beauford W.Atwater Department of Chemistry, The Florida State University, Tallahassee, Florida 32306

CONTENTS I. 11. III. IV.

Introduction Diffusion-controlled reactions Electronic spin multiplicity Excited-state interactionswith 3 0 2 A. Singlet excited states B. Triplet excited states C. Oq('Ag)yields V. Radical self-termination VI. Triplet excitation transfer VII. Triplet-triplet annihilation Appendix A. A+B-P B. A+A-P Acknowledgments References

I.

INTRODUCTION

The highly energetic species produced from molecules by absorption of electromagnetic radiation in the UV and visible region include singlet and triplet electronicallyexcited states and neutral and ionic radicals derived from them, e.g.,

2

SPIN-STATISTICALFACTORS IN DIFFUSION-CDNTROLLEDREACTIONS

Despite their short lifetimes, they undergo efficient bimolecular physical and chemical interactionsin solution with each other and with a host of other suitable quenchers or reactants. Consequences of these interactions form a large part of photochemistry (1). This work reviews the fastest of these processes, namely those that are diffusion-controlled with an emphasis on the influence of electronic spin of encounter partners on the outcome of the interactionsin solution. Specific topics considered will include the quenching of electronicallyexcited molecules by ground state 02,triplet-triplet excitation transfer, radical self-termination reactions, and triplet-triplet annihilation.

II. DIFFUSION-CONTROLLED REACTIONS Fast bimolecular reactions between different species A and B in solution are usually expressed in terms of formation and reaction of an encounter complex,

(W,

where kdir and k-, are the rate constants for diffusion of A and B together and apart, and k, is the rate constant for reaction of the encounter complex (2). The overall observed rate constant is given by

The reaction is said to be fully diffusion-controlled when k, >> Ldfapplies leading to kobsd = kw If the reacting species are identical, i.e., A = B in Eq. 2, multiplication of the rate constant by the factor ?4prevents counting the same reacting partner twice (3). For a diffusion-controlled A A reaction

+

where kdif is defined in Eq. 2. When transient terms can be neglected owing to long reactant lifetimes, T~ > s-', the rate constant in M-' s-l for a reaction which occurs upon every encounter can be based approximately on a theoretical model (see Appendix) by Smoluchowski (43)

kdif = 41rNpDlO-~

47rNpD

k

+k

DIFNSION-CONTROLJ.,ED REACI'IONS

3

where N is Avogadro's number, p is the reaction distance (i.e., the sum of radii of the reactants, rA rB). D is the diffusion coefficient for relative diffiision of the reacting molecules (taken as the sum of the individualdiffusion coefficients: D = DA + DB),and k is the rate constant for infinitely fast translatory diffusion. Under conditions where k >> 41rNpD Eq. 5 reduces to

+

kdif = 41rNpD

(6)

which is the form most often used. The individual diffusion coefficients are inversely related to friction coefficients 5:

DA =-

kT

(7)

5A

where k is the Boltzmann constant. For a spherical species of radius rA, the Stokes equation

cA

where 6, the coefficient of sliding friction, relates to the macroscopic medium viscosity q. Two limiting cases for 5 are usually considered (5). The stick or no-slippage (p = 01) limit, assumed to apply for systems composed of large solutes moving among relatively small solvent molecules, gives 5 = 6 1 ~ q rIt. corresponds to the Stokes-Einstein equation for the diffusion coefficient, DsE, on which the standard Debye equation

is based (a = 3,000, assuming rA = rB).At the other extreme, the free-slippage (p = 0) limit gives 5 = 4.rrqr, which leads to the modified Debye equation, Eq.8 with 01 = 2,000, and is supposed to apply for small solutes moving among large solvent molecules when free spaces between solvent molecules are large compared to the size of solute molecules. For either limiting case, mlT and kdimlT are predicted to be constant, independent of solvent or viscosity. This prediction has been shown to fail for several supposedly diffusion-controlled reactions of electronically excited molecules (5) and for radical self-termination reactions (6), especially when high-molecular-weight alkanes or alcohols are employed as solvents. But even in such cases, rate constants for reactions considered to be diffusion-controlled mirror the behavior of empirical diffusion coefficients, which, if not known, can be calculated from available empirical or semiempirical formulas (6).

4

SPIN-STATISTICAL. FACTORS IN DIFRISION-CONTROLLEDREACTIONS

Recommended for nonhydroxylic solvents (5,6) is the empirical formula of Spernol and Wirtz (7), which relates deviations of empirical D s from DsE’sto solute (r) and solvent (rd molecular-radius ratios:

ft

= 0.16

+ 0.4-rLr

where ft is the empirical microfriction factor for translation. Molecular radii are estimated from molar volumes, V in cm’, using r =

3000vx

”’

(T)

where x = 0.74 is the space-filling factor for closest-packed spheres. The procedure is justified in part by the microfriction theory of Gierer and WiaZ (8). Systematic solvent- and solute-specific deviations between experimental (Eq. 10) and calculated, (Eq. 11) ft’s were related to reduced solvent and solute temperatures, TrL and T,, respectively:

where T is the experimental temperature and Tbpand Tmpare the melting point and boiling point of the solute or solvent(7).Inclusion of the reduced-temperature term modifies Q. 11 to

ft

=

(0.16 +

0.4-

‘1

rL

(0.9

+ O.4TrL - 0.25TJ

(14)

and renders ft more solvent- and solute-independent. Microfriction factors obtained from Eqs. 11 and 14 are referred to as full and truncated, respectively.

III. ELECTRONIC SPIN MULTIPLICITY Empirically, the multiplicity M of a molecular or atomic electronic state indicates the number of distinct states (sublevels)into which a beam of molecules or atoms in that state is resolved on passing through a strong magnetic field one (singlet),

ELECTROMC SPIN MULTIPLICITY

5

two (doublet), three (triplet), and so on (1). Quantum mechanics associates this phenomenon with the state's total spin quantum number, S, which is the magnitude of the vector sum of the spins (+Yi or %) of the individual electrons. Since electrons occupying the same orbital are spin-paired (Pauli principle), S > 0 requires the presence of electrons in singly occupied orbitals as a necessary but insufficient condition. The multiplicity, given by

-

M = 2 S + 1

115)

is indicated numerically as a superscript preceding the symbol for the species; e.g., if A were a radical, 2A would specify its doublet multiplicity. Transitions between states of different multiplicity [spin isomers (l)], or even between sublevel states of a specific multiplet, q u i r e a magnetic perturbation and can be relatively slow (k = lo6 - 10" s-') processes. They are said to be multiplicity-forbidden. Since most ground-state reactions of organic molecules occur adiabatically on singlet ground-state surfaces (S = 0 throughout), they are multiplicity-allowed processes. Accordingly, the singlet multiplicity designations of the reactants, the encounter complex, and the products in Q. 2, though understood, are generally left out. We are concerned here with very fast bimolecular reactions in which at least one of the partners has S > 0. Written for the general case, Fiq. 2 becomes

where the product mn gives the number of possible encounter-pair spin states. Since in the absence of external magnetic fields the sublevel states of each multiplet are essentially degenerate, they are equally populated under equilibrium conditions at ordinary temperatures. It follows that the probability of formation of each encounter spin state is given by the spin-statistical factor (mn)-'.For example, interaction of two radicals

is expected to give four encounter-pair spin states with equal probability, three of which are sublevels of the encounter pair with triplet multiplicity and the

fourth is the singlet encounter pair. Similarly, when two triplet states interact,

6

SPIN-STATISTICALFACTORS IN DIFFUSIONCONTROLLED REACTIONS

they give nine encounter pair spin states which constitute the sublevels of encounter pairs with quintet, triplet, and singlet multiplicities. Since encounter-pair lifetimes are generally too short to allow appreciable interconversion between spin states of different multiplicity, and since, furthermore, reactions are dfision-controlled only when k, >> k-&f (i.e., k, > 10" s-'), it follows that only those encounterpairs which conservemultiplicity in going to products are expected to react. For example, if the product in Eq. 18 were formed only with triplet multiplicity, the maximum expected experimental rate constant would be given by

where the spin-statistical factor u = ?4 would reflect the fact that only those encounters resulting in the three triplet sublevels proceed to product, the rest being dissociative. In the following sections, several reactions will be discussed which illustrate the applicability of Q. 19.

IV. EXCITED-STATE INTERACTIONS WITH

302

The ground state of molecular oxygen involves assignment of the two highestenergy electrons to degenerate molecular orbitals and, in agreement with Hund's rule, is a triplet state (3&J, Occupation of the same orbitals by the two highestenergy electrons gives in addition two singlet states which conform to Pauli's principle (9). These are the lowest excited states of O2 and are located at 22.5 ('Ag) and 37.5 kcaVmol('2~)above the ground state (10). The triplet multiplicity of the ground state and the availabilityof low-lying excited states are responsible for the functioning of O2 as a very efficient quencher of electronically excited molecules in solution. Quenching is often associated with 02('Ag) formation. O2('Z;), when formed in solution, is thought to be much shorter-lived due to very rapid decay to 02('Ag).

A.

Singlet Excited States

Most extensively studied has been the interaction of excited singlet states of aromatic hydrocarbons with 0,(11,12). In nonpolar organic solvents the process

EXCITED-STATE INTERACTIONS

w m 302

7

is thought to give the triplet state of the hydrocarbon with unit efficiency and is known as oxygen-induced intersystem crossing (13,14). The efficiency of the quenching remains unchanged when the SI-T, energy gap of the hydrocarbon drops below 22.5 kcal/mol, indicating that formation of singlet oxygen is not an essential condition (15). Most observations are summarized well by askd

I-+

3M*

+ Oz('Ag)

Since both decay channels shown for the triplet encounter pair are multiplicityallowed, u = 1 is expected for Eq. 20. Experimental rate constants for a large number of molecules have been obtained from Stern-Volmer plots of the effect of [O,] on the fluorescence intensity and by measuring the fluorescence lifetime in the absence and presence of 02:

1 1 = T + ex[o,l Trn 7, Some variation in rate constants obtained by different research groups can be attributed to use of different references for the solubility of 0, in the solvents employed, or even to incorrect application of Bunsen or Ostwald coefficients in the calculation of [O,]. Since the atmospheric pressure, the temperature, and the degree of humidity when measurements were made in the presence of air are usually not reported, correction of the rate constants by application of uniform 0, concentrations is difficult. It will nonetheless be attempted when necessary, using a recently published critical and comprehensivecompilation of O2 solubility data (16). Very large Stern-Volmer constants for fluorescence quenching of aromatic hydrocarbons by oxygen have long been known (17,18). Ware's singlet-excitedstate lifetime measurements yielded k:x values which were shown to be diffusioncontrolled by comparison with calculated values from Eq. 6 using empirical D's and p = 6 8, (11). Rate constants obtained from steady-state fluorescence measurements (Eq. 21) were on the average -7% larger than those based on decay rates (Eq. 22) (1 1). Since the diffusion coefficients of 02,Dox, are 2.5 to 4 times greater than those of aromatic hydrocarbons, D,,, their large contribution to D in Eq. 5 has a (11). This accounts for Berlman's successful correlation leveling effect on of (Zdr), with T, for a large number of aromatic molecules (12), as shown in

ex

8

SPIN-STATISTICALFACIDRS IN DIFFUSION-CONTROLLEDREAcnoNS

-t-a

L

W

\ 0 H

Y

o.oh

0

[

20

1

40

r,, ns-

[

60

I

00

[

100

Figure 1. I,JIaiairvs. 7, in cyclohexane. See Table 1; data from Ref. 12.

Table 1 and Fig. 1. Since I, was obtained by bubbling N2through cyclohexane solutions, the (Zdr), values in Table 1 should be regarded as lower limits. The values in the table were calculated using [O,] = 2.10 x M ,which assumes 20°C as "room temperature" (20).* The points plotted in Fig. 1 correspond to a k,, range of (2.5-3.2) x 10" M-' s-'; the least-squares line with unit intercept gives = (2.81 -+ 0.09) X 10" M-' s-'. This value can be compared with k,", = (2.79 2 0.05) X 10" M-' s-l obtained from the lifetime measurements of Patterson et al. in cyclohexane at 25°C (19) for polycyclic aromatic hydrocarbons, using Eq. 22 and [O,] = 2.10 X M (20), by averaging the five largest kzx values from Ref. 19, Table 1. Though the range of values in the latter study, (2.27-2.84) X 10" M-' s-', is lower than that used in Fig. 1, this is somewhat deceiving, since where the two studies overlap, Berlman's k z values are significantly smaller (Table 1). Several nitrogen-containing compounds in Berlman's study exhibited much larger rate constants than those listed in Table 1. They are not considered here, since they may include static-quenchingcontributionsreflecting the presence of ground-state (IWO,) charge-transfer complexes (2 1,22). Experimental evidence for the formation of O,(lA,) as a result of singletexcited-state quenching by 0,(@. 20, as > 0) exists and will be presented in a later section. The energeticconsiderationsof the quenching events are illustrated by the two cases in Figure 2. In case I, Us+, > 22.5 kcallmol and formation of O2(lAg) is energetically feasible. This case, exemplified by anthracene and

ex

gx

*At 25°C. [02J = 2.17 x lo-' M is obtained. However, since in Ref. 19 the use of dry air was not specified, a somewhat lower value was used.

TABLE 1. Selected Rate Constants for 'M* Quenching by O2 in Cyclohexane" sc

Compound (AES~.T,)~ Benzene (24.9) Benzene-d, Fluombenzene Toluene Ethylbenzene 2-Pheny lbutane Diphenylmethane Methoxybenzene Diphenyl ether p-Xylene m-Xylene 0-Xylene p-Ethyltoluene p-Methoxytoluene p-Dimethoxybenzene 1,2,4-Trimethylbenzene 1,3,5-Trimethylbenzene 1,3,5-Triethylbenzene Biphenyl pBenzylbipheny1 p-Methoxybiphenyl p-Phenoxybiphenyl Dibenzofuran p,p"-Dihexahydrofarnesoxy-p-terphenyl Naphthalene (30.0) Naphthalene-d, 1-Methylnaphthalene 2-Methylnaphthalene 2.3-Dimethylnapthalene 2,6-Dimethylnaphthalene Acenaphthene 1-Phenylnaphthalene 1&diphenylnaphthalene 1,5-diphenylnaphthalene 1,l '-Dinaphthyl 2,2'-Dinaphthyl hthracene (34.3) 9-Meth ylanthracene Phenanthrene (20.6) Chrysene (22.0) Naphthacene (31.O) Triphenylene (15.3)

(b/I)air

7,

(ns)

2.4 2.63 1.47 3 .O 2.53 2.32 2.55 1.54 1.13 2.84 2.67 2.75 2.7 1.48 1.19 2.77 3.O 2.48 1.95 1.86 1.66 1.32 1.44

29.0 26.6 7.6 34.0 31.0 25 .O 25.3 8.3 2.0 30.0 30.8 32.2 30.8 8.7 2.9 27.2 36.5 24.0 16.0 13.9 9.4 4.8 7.3

1.06 6.4 6.8 5.5 4.1 5.83 3.2 3.54 1.65 1.07 1.12 1.21 2.90 1.25 1.29 3.8 3.18 1.26 2.53

0.95 96.4 96.0 67.O 59.0 78.4 38.4 46.0 13.0 1.25 2.0 3.O 35.2 4.9(4.9) 4.6 57.5 44.7(44.7) 6.4 36.6

k:: (lo~oM-~s-')

2.30 2.92 2.94 2.80 2.35 2.51 2.92 3.10 3.10 2.92 2.58 2.59 2.63 2.63 3.1 3.10 2.61 2.94 2.83 2.95 3.34 3.17 2.87

-

-

e _

3.O -

2.61 2.88 3.20

2.50 2.93 2.73 2.63 __

2.38 2.1 2.9 3.3 2.57 2.43(2.81) 3.oo 2.32 2.32(2.75) 1.93 1.99 _L

10

SPIN-STATISTICAL FACTORS IN DIFFUSIONCONTROLLEDRJ3MTIONS

TABLE 1. (Continued) Compound (AEs,-T,)b

~W)air

Triphenylene-d12 Perylene (28.3)

3.17 1.30

1,2,5,6-Dibenzanthracene 1,2-Benzanthracene 1,2,3,4-Dibenzanthracene 3,4,9,10-Dibenzpyrene Fluoranthene(18) 3.4-Benz~wne

1.49

SC

7,

(ns)

38.0 6.4 (37.5) (49.4) (53.5) (143.0) 53.0 (57.5)

::k

(loloM-l s-l) 2.72 -

2.23 (2.70) (2.84) (2.44) (2.55)

0.44

(2.83)

M was employed: see text. "Data from Ref. 12, unless otherwise indicated, [OJ = 2.1 X bFrom Ref. 14, except for last entry, which is from Ref. 12; in kcal/mol. 'Values in parentheses determined from Eq. 22 using T'S in Ref. 19, 25"C, [Od = 2.10 X lod3 M,underlined values correspond to points in Fig. 1 .

many of its derivatives (23), has the added feature of the availability of a higher triplet state, T2, nearly isoenergeticwith S1. In such systems S, --* T2intersystem crossing is favored over S1 +T1 in the absence of 02,and it has been suggested that it may also be enhanced by 0,(23). The functioning of such a quenching event may diminish aseven in those cases for which formation of 02( 'Ag)would be exoergonic. Case I1 illustrates the absence of a higher triplet quenching < 22.5 kcaYmol. For such systems as = 0 is expected. pathway, and Consideration of the entries in Table 1 has led to the conclusion that availability of the O2(lAg)formation channel is not essential in determining the

t

lu

%--

so-

Figure 2. Energetics for 'M*quenching by 02(3S;>.

EXCITED-STATEINTERACI?ONS m 3

11

4

magnitude of k,", (14). Actually, the rate constants for phenanthrene and triphenylene, from which no 02('Ag) formation should be expected, are somewhat smaller and may reflect less than diffusion-controlled quenching. Especially small k", values have also been observed for several fluoranthenes (12,24),as illustrated for the parent compound in the last entry of Table 1. Here, too, formation of 02('Ag) would be exoergonic, and it has been suggested as a possible reason for the quenching inefficiency (12). Another example of less than diffusion-controlledquenching is provided by 9,10-dichloroanthracene,for values in several solvents are consistently about 30% smaller than which those for anthracene (1 1,25). Equation 21 has been applied to data for several aromatic hydrocarbons in benzene for O2 concentrations ranging from air to one atmosphere of O2 (26). Assuming that the work was done at 760-Torr pressure, the [O,] values employed M S [O,] =s7.32 X M in are about 10% low (the range of 1.49 X Ref. 26 would correspond to an atmospheric pressure of 692 Torr (27);expected M). The M* s [o,]s 7.93 x for 760 TOIT is a range of 1.66 x rate constants from this study adjusted to the higher [O,] values are shown in Table 2, along with a few values obtained in other laboratories. Excluding the lowest two values (rubrene and perylene), an average kix = (2.83 2 0.24) X 10" M-' s-l is obtained for benzene at * 25°C.

ex

TABLE 2. Rate Constants for 'M* Quenching by 0, in Benzene

ex(%.

21)" (101OM-l s-I)

Comuound 9,lO-Dimethylanthracene 9,lO-Diphenylanthracene 9,lO-Dimethyl-1,Zbenzanthracene Naphthacene Rubrene Perylene Anthantiuene Anthracene 1.2-Benzanthracene 1,2-Benzanthracene-7-d "From Ref. 26, %om Ref. 11, 'From Ref. 21, dFrom Ref. 28,

*I021

2.87 f 0.18 3.30 f 0.23 2.51 -+ 0.15 2.17 -+ 0.16 1.07 k 0.07 2.47 f 0.27 3.23 k 0.55 2.67' 2.61d 2.8od

ex(a. Wb

( 101OM-l s- l)

2.8

3.2

3.1 2.47d 2.74d

25 2 2°C. unless otherwise indicated. 25/26"C, unless otherwise indicated. 24 f 1°C. 22.5"C for Eq. 21, 25 +- 1°C for Eq. 22.

= 1.61 X

M

at 25°C

was used to account for atmospheric moisture.

12

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS

B. Triplet Excited States Similar rate constants for the quenching of the lowest triplet states of a series of rigid polycyclic aromatic hydrocarbons, kzx, have been measured in cyclohexane (19). in benzene (29), and in n-hexane (29). Since triplet lifetimes are generally long in the absence of 02,the rate constants were based on the triplet lifetimes in &-equilibrated solutions:

Rate constants for cyclohexane and benzene are shown in Table 3. Also shown in Table 3 are the triplet energies of the aromatic hydrocarbons. The importance of overall spin conservation in the quenching of triplet states by paramagnetic species via an encounter complex was considered generally by Porter and Wright (30), and the spin-statistical consequences for the specific case of oxygen quenching were proposed by Stevens and Algar to account for steady-state observations with 9,lO-dimethylanthracene which suggested that (kTx/ex)= 9'9 (31):

,

\ M a-'(MO2)*

k.,'M

+ 02('Ag)

Since only one of the nine encounter-pair spin states has singlet multiplicity, only one of the encounters can lead to quenching by electronic excitation transfer in a process which is overall multiplicity-allowed. Strict adherence to the spinstatistical factor of % for the quenching rate constant, kzx = % kdif, is most simply explained if (a) intersystem crossing to the singlet encounter pair from spin states of different multiplicities are slow relative to diffusion apart of the encounter partners, and if (b) all singlet encounter pairs give quenching (31). The results of Porter and coworkers (19,29) for planar aromatic hydrocarbons (Table 3) indicate strongly that these conditions are fulfilled at least for molecules for which falls in the 29-42-kcdm01 range. Within this triplet energy range, kzx's in benzene plateau at a nearly constant maximum value of (3.50 +0.05) x lo9 M-' s-', whereas in the somewhat more viscous solvent cyclohexane, a value of 2.80 X lo9 M-' s-' is suggested by the more limited data (19,29). The triplet quenching mechanism in Eq. 24 is entirely consistent with the singlet quenching mechanism in JZq. 20, since in both, encounter pairs with triplet multiplicity are shown as completely dissociative with respect to 3M* formation. It is gratifying therefore that when limiting maximum values in Tables 1-3 are employed, the condition = is adhered to nicely

ex %ex

EXCITED-STATE INTERACIIONS WITH 3oz

13

TABLE 3. Rate Constants for O2 Quenching of Planar Aromatic Hydrocarbon Triplets Compound Pentacene Naphthacene

6,12-DimethyIanthanthrene lO-Methyl-3,48,9-dibenzpyrene 3,4:8,9-Dibenzpyrene 3,4:9,10-Dibenzpyrene Anthracene 3,CBenzpyrene 1,2-Benzanthracene Pyrene 1,2:3,4-Dibenzanthrwene 1,2:5,6-Dibenzanthracene Chrysene Picene 3,4-Benzphenanthrene Phenanthrene 1,3,5-Triphenylbenzene Coronene Tripheny lene

k:Xa (109K's-')

k;f, (109K's-')

AET,-SoC

(kcaVmol)

2.07 3.88 3.45

22.9 29.5 32.3

3.55 3.45 3.55 3.45 3.45 2.82 2.70 2.26 1.97 1.73 1.75

33.5 34.3

2.48

2.80 2.80 2.51 1.83 1.54 1.40 1.22 0.99

42.0 42.3 47.2 48.3 50.9 52.3 57.2 57.4 58.9d 61.8 64.6 54.3 66.6

0.97

1.38

0.52 1.38

"From Ref. 29, benzene solvent, 25°C assumed, adjusted to [O,] = 1.61 %om Ref. 19, cyclohexane solvent, 25"C, adjusted to [O,] = 2.10 X 'From Ref. 29. %om Ref. 19.

X

M (27). M (20).

(19,29,31). It is important to note that the spin-statistical factor is obtained here values provide an without having to rely on a theoretical value for kdiP The empirical measure of kdif in an ideal reference system, since diffusion coefficients ratio. and encounter distances must cancel in the The decrease of kTx for pentacene, whose triplet energy is expected to be within 1.5 kcal/mol of the energy of Oz('Ag), is not surprising, since similar inefficiencieshave long been known in triplet-triplet excitation transfer processes (see Section VI) when the net reaction is less than 3 kcdmol exothermic (1,32). The values show a general inverse dependence on the triplet energy of the aromatic molecules for AET,-% > 42 kcdmol (19,29) (Fig. 3). For these molecules the inequality k,, >> k-dif does not hold (19,29) and kz. is given by

ex

ex

14

-log

kdif

t

0

20

40

AET,+so, itcat/mol-

60

Figure 3. kzx vs. AET,-soin benzene; see text.

For the specific case chrysene (A&,+, = 57.2 kcallmol), the expected increase of k', with increasing solvent viscosity was established experimentally (29). It was also shown that kzx for chrysene increases with increasing solvent polarity (29). The theoretical implications of the dependence of on AET,-s,have been discussed in Ref. 29. A theoretical treatment of triplet quenching by O2 had predicted that excitation transfer via the singlet encounter pair would be the dominant quenching pathway (33). In addition, it was pointed out that the large transitions for ' 2, + 'A, and '2; -+ Franck-Condon factors for the (0) '2; excitation of oxygen meant that the Franck-Condon overlap integrals controlling the size of ket should be determined primarily by the aromatic molecules (33). A general inverse relationship of ket on AET+, is then expected, since the Franck-Condon factor of the donor triplet state decreaseswith increasing > 38 kcaymol less excess triplet energy (33,34). Furthermore, since for energy need be accommodated by the ground state of the aromatic hydrocarbon as vibrational excitation when 02( '2;) rather than 02( 'A,) is formed, the former process was predicted to be more efficient: ket = 1 0 e (33). This conclusion is inconsistent with the experimental k;f, values (29). When the donor's triplet energy falls comfortably between 22.6 and 37.5 kcallmol, the excitation energies of 02('Ag) and 02('8:), >> is expected. It can be seen that k:x retains its limiting value in this energy region, so that >> k--dif even when the excitation transfer process is 15 kcallmol exothermic. On the other hand, kzx

ex

et

EXCITED-STATEINTERACTIONS

w m 302

15

starts to decrease soon after the energy of O2('Z;) is exceeded, indicating that, decreases much more rapidly than k$ if the O2('X;) pathway is operative, as the exothermicity of the process increases (see below, however). Preferential formation of 02('Ag) over O2('2;) when a high-triplet-energy donor is quenched has been rationalized by a theory which includes orbital symmetry restrictions in the transfer process (29,35). The aromatic molecules considered thus far are relatively rigid and have well-defined TI-So energy gaps. We turn now to flexible molecules whose relaxation in the triplet state may lead to substantiaIly different equiIibrium geometries, relative to the ground state, corresponding to significantly smaller T l S o energy gaps. The So and T1potential energy curves for twisting about the central bond in stilbene (Figure 4) illustrate this situation in a particularly well-studied example (36). The triplet curve is based on spectroscopic data (37) for the transoid (3t*) and cisoid (3c*) limits and on the functioning of the stilbenes as acceptors and donors of triplet excitation (38,39,40) for twisted configurations. The steeper T, potential-energy curve on the cis side of the relaxed triplet, 3p*, accounts nicely for the fact that acceptors with triplet energies as low as ~ 2 2 kcaVmol (@-carotene) deactivate stilbene triplets only on the trans side by excitation transfer (41). This process,

I

0

HI2

7T

Figure 4. Potential-energy curves for central-bond twisting in So and T,of the stilbenes. From Ref. 36, reprinted with permission from J . Phys. Chern. (1987) 91,2755. Copyright 1987, American Chemical Society.

16

SPIN-STATISTICALFACTORS IN DIFFUSIONCONTROLLEDREACTIONS

P*

+

'A

%

(3p*A)

c

e

(3t*A) &'It

km

+ 3A*

(26)

is modestly activated, since it requires sufficientdistortion towards 3t*to produce the So-T, electronic energy gap required for the excitation of the acceptor, A, to its triplet state (39,40). It is an example of triplet-triplet excitation transfer (see Section VI) for which a spin-statistical factor of unity is expected, since overall triplet multiplicity is maintained throughout. Substitution on the phenyl group of stilbene, or replacement of phenyl with other aryl groups, can change the relative energies of 3p* and 3t*in olefins so that 3t*can be thermodynamically favored. Generally, however, excitation transfer occurs from transoid triplet geometries, whereas cis-trans photoisomerization occurs by radiationless decay from nearly perpendicular geometries, 3p* (37): 3p*

-

6't

+ (1 - 6)'c

(27)

Consequently, ([t]/[c]),, the photostationary composition ratios for the triplet sensitized photoisomerization of such olefins, increase linearly with acceptor concentration. Schemes 1 and 2 have been shown to account for such observations (39). The first applies to stilbene, for which most triplets have the 3p* geometry

Scheme 1. The Common Triplet Mechanism

Scheme 2. Transoid and Twisted Stilbene Triplets in Equilibrium

.

EXCITED-STATE INTERACI~ONSWITH 3

17

4

at room temperature, and the second applies to olefins, for which a substantial fraction of the triplets at equilibrium have a transoid geometry. In view of the well-documented ability of 0, to function generally as an acceptor of triplet energy, it had been expected that its presence should also increase ([t]/[c]), ratios for the triplet sensitized photoisomerization of stilbenelike olefins. However, as was first noted for nitrostilbenes, the quenching of the olefin triplets by 0,does not alter ([t]/[c]), (42,43). For the parent stilbene it was shown that when azulene is used as a quencher of stilbene triplets the slope of the ([t]/[~])~-vs.-[Az]plot is strongly attenuated by 0,; see Figure 5 (41$4). Since the intercept of the azulene plot .was not influenced by 0,. it was reasoned that O2 deactivates 3p* without changing the decay fraction 6 as predicted by Schemes 1 and 2 (44).To account for stilbene triplet deactivation by 0, without change in 6 two possibilities were considered

3p*

+ 02(32i)+s3(p02)*

k,

6' 't

+ (1

- 6') 't

+ 02(3z,)

If 02('Ag) were produced efficiently, then the 22.5-kcaYmol energy gap required would be achieved with equal efficiency by torsional displacement of the 3p* partner of the singlet encounter pair toward either cisoid or transoid geometries. If, on the other hand, excitation transfer does not usually accompany the quenching process, then quenching could occur from the triplet encounter complex by a spin-exchange mechanism (45)-a process that should come into play because the energetic proximity of So and TI at twisted geometries allows quenching to occur without the usual requirement for simultaneous removal of electronic energy. This quenching is effectively enhanced intersystem crossing (33) and should give similar transkis ratios to those for natural 3p* decay. Verification of the spin-exchange mechanism as the dominant quenching pathway was accomplished by substituting p-carotene for O2as a co-quencher with azulene for stilbene triplets (41). As can be seen in Figure 5 , the effects of azulene and p-carotene are strictly additive. Thus, when stilbene triplet quenching is by electronic excitation transfer, it occurs on the trans side exclusively. Based on Scheme 1, the following steady-state expression can be derived:

where k,[Az] and k,[C] are the azulene and p-carotene contributions of Eq. 26, in accord with the experimental observations. p-Carotene was selected because

SPIN-STATISTICAL FAClQR.9 IN DIFFUSIONCONTROLLEDREACTIONS

18

its triplet energy must be very close to the energy of 02('Ag), as evidenced by its functioning as an acceptor of triplet excitation from low-triplet-energy donors (46) and specifically from O,('A ) (47,48,49) with a nearly diffusion-controlled rate constant, (1.1 2 0.1) x lOg10 M-1 s-1 in benzene (49). A precedent to the spin-exchange quenching mechanism of olefin triplets by oxygen is provided by the interaction of stilbene triplets with the stable free radical di-ferf-butyl nitroxide, ,N (50). In this case hiplet-sensitized ([t]/[c]),

-€

,(pN)* --+ 6' 't

3p*

+ (1 - 8') 'C + 2N

+ 2N

(30)

t 4(PN)*

ratios become more cis-rich as tbe concentration of [,N] is increased (50). Analysis of the data assuming quenching of 'p* only gives 6/6' = I. 11 and kN/kd = 110 +- 20 M-' in benzene (50,51). From the latter value kN = 1.8 X lo9 M-' s-' can be estimated using the known stilbene triplet lifetime (38). Since no electronic excitation transfer is expected for spin-exchange quenching of 3p*, only the doublet encounter pair provides a multiplicity-allowed pathway, so that the limiting value of kN should be %kcif. Clearly the observed value is not far from this limit. Rate constants for quenching of planar aromatic triplets with large So-Tl energy gaps are generally smaller than kN for stilbene; e.g., for naphthalene, AET,s, = 61 kcdmol, kN = 6.3 x 10' M-' S-' (50). If only the spin-exchange mechanism for O2 quenching of stilbene triplets were operative, then k:x = ?L3kdifwould be the maximum rate constant expected and no 02('Ag) would be formed. Actually, 13-18% of the quenchinginteractions have been shown to give 02(lAg) (52,53), indicating that both the k,, and k, channels in Q. 28 are important. By analogy with B-carotene, excitation transfer from 3p* to 0, should occur only on the trans side. It appears therefore that 6=6' is coincidental for O,, reflecting a balance between energy-transfer deactivation on the trans side and spin-exchange preference on the cis side (53). Inclusion of the energy-transfer pathway increases the maximum limiting k,'x in this case to 4/gkdif. Indeed, the experimental value, = 9.0 X lo9 M-' s-' (38), though not quite as large as 4/9kdif, is significantly larger than the rate constants in Table 3, which reflect only singlet encounter-pair quenching (see also below). Rate constants for O2 quenching in benzene of several olefin triplets and a few rigid analogs are listed in Table 4. The first three entries are stilbene analogs with little structural freedom for torsion about the olefinic bond. They exhibit kzx values indistinguishablefrom those for planar aromatic hydrocarbons in the 29.5-42.3-kcaVmol A&,+ range (Table 3). Since the triplet energy of the ?runs-stilbene analog indeno[2,1-u]indene is 47.6kcal/mol(69), and that of the

ex

TABLE4. Rate Constants for O2Quenchingof Olefin Triplets and Rigid Analogs in Benzene, 25°C

Indeno[2,l-a]indene 2-Phen ylindene 1,2-Diphenylcyclobutene Stilbened 4-Nitrostilbened tran~-4,4'-Dinitrostilbene

4-Nitro-4'-methoxystilbened 4-Nitro-4'-dimethylaminostilttened 1,l-Diphenylethene

Triphenylethene Tetraphenylethene trans, trans-1.4-Diphenyl1,3-butadiene All-trans-1,6-diphenyl1,3,5-hexatriene All-trans- 1,&diphenyl1,3,5,7-0ctatetraene trans-1-Phenyl-2-(2naphthyl) ethene 3.3-Dimethyl- 1-(Znaphthyl)1-buteneg 3,4-Dihydrophenanthrene 2-( 1-Naphthyl)propene 1-(1-Naphthyl)cyclopentene 1-(1-Naphthyl)cyclohexene 1-(1-Naphthyl)cycloheptene 1-(1-Naphthyl)cyclooctene 1-Phenyl-1-(1-naphthyl)-2methylpropene 1-(1-Naphthy1)indene 1-(l-Naphtyl)3,4-dihydronaphthalene 1,l-Di-( 1-naphthy1)ethene 1-Phenylcyclohexene All-trans-P-carotene' Retinal* Retinolk

2

1.5msc 0.10 ms 0.20 ms 62 ns 74 ns 102 ns 130n5 77 ns

38 38 38 38 42 42 42 55

5.3 9.0 11.0 4.8 2.4

2PS 41 ns 41 ns 105ns 18011s

42 56 57h 56 56

3.7

10 ps

58

5.5

100 ps

58

6.0

100 ps

58

5.6

15011s

59

3.4 3.8 3.4 9.0 7.0 6.0 6.8 5.9'

= 130ns

5.3 5.1

120n5

60 59 60 57h 57 57 57 57

6.1 2.7

100ns 4.5 p,S

57 57

3.0 4.4 9.0 2.5 2.8k 1.9 4.7

4.5 ps 220 ns 3 65 nsi 9 FS 7P S 9 PS 13 ps

57 57 57 62 62 62 62

2.4-4.7 5.2 2.1 4.4

3.0 2.8

80 IIS 1.2 ps 550 ns 3.6p5 2 CLS

53 ns

19

20

TABLE 4.

SPIN-STATISTICAL. FACTORS IN DIFFUSION-CONTROLLED REACTIONS

(Continued)

2-Cyclohexenone'

4,4-Dimethyl-2-c yclohexen~ne~

Testosteronee

cis-Thioindigo

6,6'-Dietho~ythioindigo~ h-ans-N,N'-Diacetylindigo p-Ionone' A6-Testosteronem

25 ns 25 ns

7 7.5

2.2 3.2 2.9

63,64 63 64 65 65 66 67 68

440 ns

279 ns 143ns llns 140ns

5.7

5.1

1.7

lops ~

~~~

"Unless otherwise indicated, triplets produced using benzophenone, xanthone, or other carbonyl triplet energy donor. kifetimes in ws time scale are minimum values, since in most cases outgassed instead of rigorously degassed solutions were employed. 'From Ref. 54 in toluene, degassed; Ref. 38 gives > 5 p s , outgassed. qdentical results starting from cis or trans isomer. Tyclohexane, [O,] adjusted to agree with ref. 16. &ate constants depend on wavelength region of triplethiplet absorption. gSimilar rate constants for cis and trans isomers, but results depend on triplet sensitizer. "[O,]adjusted to 1.61 X M for air-equilibrated solutions (16) for all ko,'s from ref. 57. 'From Ref. 61. '21.3"C; [O,] adjusted to agree with ref. 16; anthracene-sensitized, pulse radiolysis. 'n-Hexane, 21.3"C. 'Toluene.

"'Ethanol.

cis-stilbene analog 1,2-diphenylcyclobutenemust surely exceed this value (Figure values do not show the decrease observed for the planar aromatic hydrocarbons with increasing exothermicity (Table 3, Figure 3). Similarly notable are the relatively low Exvalues that correspond to the other rigid molecules in which the double bond is constrained to be nearly planar: 1-(1-naphthyl)cyclopentene, 3.0 x lo9 M-' s-'; 1-(1-naphthyl)indene, 2.7 x lo9 M-' s-'; l-(l-naphthyl)-3,4-dihydronaphthalene,3.0 X lo9 M-' s-'; 3,4dihydrophenanthrene, 2.1 x lo9 M-' s-'; testosterone, 2.2 X lo9 M-' s-' (cyclohexane). Of special interest are the large values, e.g., stilbene (9 X lo9M-' s-I), 1,l-diphenylethene (9-1 1 X lo9 M-' s-'), l-phenylcyclohexene (9 X lo9 M-' s-I), which approach the %kdif to %kdif limits and must surely reflect spin-exchange quenching at 3p* geometries. Most of the remaining rate constants are intermediate in magnitude and probably represent different combinations of the spin-exchange and energy-transfer channels. Since the former mechanism usually applies when So +TI energy gaps are small at substantially twisted geometries, whereas the latter requires So + TI energy gaps exceeding

4) (70), these

ex

ex

EXCITED-STATEINTERACTIONS WITH 3

4

21

-22 kcaUmol which are achieved at more nearly planar geometries, the size of

ko', has been used as a criterion in establishing the equilibrium geometries of

olefin triplets (41,44,55,57,58). It must be used cautiously, however, because if the encounter pair is sufficiently long-lived and/or if the triplet potential-energy curve of the olefin is sufficiently flat, the triplet olefin partner may explore several geometries prior to quenching. Thus just as a triplet acceptor such as azulene may quench twisted triplets because the lifetime of the encounter is sufficiently long for them to undergo torsional excursion towards transoid geometries, so might 3(t02)* encounter pairs undergo spin-exchange quenching if the olefin partner has time to approach or reach 3p* geometries. It is perhaps relevant that direct determinations of for stilbene (38) and l-phenyl-2(2-naphthy1)ethene (59) based on triplet transient-decay measurements give significantly smaller values ('0.6 factor) than inferred from 0,'s attenuation of the azulene effect on ([t]/[cJ), (38,39,41,59). Though the differences may reflect large experimental errors, they might also provide evidence for cooperative quenching of olefin triplets by 0, and azulene. The latter possibility would require exciplex intermediates between the olefin triplets and either or both quenchers having much longer lifetimes than expected for simple encounter complexes. Fortunately, other experimental parameters are sensitive to olefin triplet geometry and assist in the evaluation of the They include (1) the triplet lifetime, which (see Table 4) is long for nearly planar triplets (ms-ps) and short for nearly perpendicular triplets (ns), (2) the magnitude of triplet-triplet excitation-transfer rate constants, e.g. k, which is large for planar and small for perpendicular triplets, (3) the shape of the triplet-triplet absorption spectrum and its dependence on structural or medium constraints to torsion about the olefinic double bond, (4) the fraction of quenching interactions which give 02('Ag), and ( 5 ) where applicable, the trandcis decay ratio, 8'/(1 - a'), associated with the O2 quenching interaction. Stilbene, for which several of the above criteria have been applied, has already been considered. Examination of some of the other cases is instructive. We start with a comparison of the behavior of I-phenylcyclohexene (PC) with that of 1-(1-naphthyl)cyclohexene ( 1-NC). PC triplets are short-lived (263 ns) , are not quenched by low-triplet-energy acceptors, decay to give cis and trans isomers = 9 X lo9 M-' s-'). Taken (71), and are quenched very efficiently by 0, together, all these observations indicate strongly that the relaxed PC triplet has a nearly perpendicular geometry. On the other hand, 1-NC triplets are almost as long-lived (2 ps) as those of the rigid analog 1-(1-naphthy1)indene (4.5 ks), are quenched efficiently by low-triplet-excitation acceptors [ferrocene, 5 40 kcaUmol (46), kf, = 3.0 X lo9 M-' s-' (56)], do not give trans isomer upon decay, and are relatively inefficientlyquenched by 02(&= 2.8 X 1 0 9 K 's-'). Accordingly 1-NP has been assigned a nearly planar relaxed triplet geometry. The effect of the naphthyl for phenyl substitution in shifting the equilibrium

ex<

ex's.

(ex

22

SPIN-STATISTICALFACTORS IN DIFNSION-CONTROLLEDREACTIONS

triplet geometry towards planarity is clearly electronic, since the cyclohexene ring should experience no greater structural constraints to twisting in 31-NC* than in 3PC*. Furthermore, even the acyclic 2-(l-naphthyl)propene appears to have a nearly planar triplet state (56); 2-naphthyl substitution on the olefinic double bond as in 3,3-dimethyl- 1-(2-naphthyl)-l-butenealso appears to shift the equilibrium geometry towards planarity (60). This is reflected in the effect of 0, on the ([t]/[c]),-vs.-[Az] plots. In contrast to stilbene (Fig. 5), in this case 0,increases the intercept of the plot in addition to attenuating the slope-a clear indication that the excitation-transferquenching pathway is strongly contributing (72). Interestingly, O2 does not alter the intercept of the azulene plot for the l-phenyl-2-(2-naphthyl)ethenes (73), which appear to behave more like the stilbenes. A pronounced effect of substitution of the phenyl group with a more extended .rr-system (lower AET,.+, for substituent) is probably responsible for the interesting 3c* --* 3t* one-way photoisomerization of 2-anthryl olefins, to which transoid equilibrium triplet geometries have been assigned (74,75). The 4-nitrostilbenes represent an interesting class of compounds (37). For several of these, the optical density of the triplet-triplet absorption is independent of temperature and medium viscosity, indicating efficient triplet population under all conditions studied (76). For the same solvent the triplet-triplet absorption spectra are also temperature-independent, though the trans-xis quantum yield drops sharply as the temperature is decreased and the medium viscosity is increased (74). These results indicate a transoid equilibrium geometry for the triplets at all temperatures studied (76), consistent with large ferrocene (4.7 X lo9 M-' s-', cyclohexane) and azulene (4.4 X lo9 M-l s-', cyclohexane) quenching rate constants at least for 4-nitro-4'-methoxystilbene (55). Nonetheless, they exhibit short triplet lifetimes and large gxvalues (Table 4), indicating that the 3p* geometry is readily accessible from 3t*. Furthermore, 0, quenching, though it attenuates the ferrocene effects on ([t]/[c]),. does not alter the decay fraction, i.e., 6 = 6' (55). It appears that the following quenching sequence may apply:

Derivatives of indigo and thioindigo represent a related case. A transoid relaxed triplet geometry has been assigned to a number of them on the basis of triplet-triplet absorption behavior analogous to that of the 4-nitrostilbenes (65,77). In this case, however, 0,decreases+t+ for the direct photoisomerization

EXCITED-STATE INTERACTIONS WITH 3 0 2

23

4'0

Figure 5. Azulene effecton the benzophenone-sensitized stilbene photoisomerization in benzene: line 1 , degassed; line 2, 0, atmosphere; line 3, degassed with 2.90 X M p-C. From Ref. 41, with permission of North-Holland Publishing.

and increases ([t]/[c]), for both the direct and triplet sensitizedphotoisomerizations (78). Deactivation of thioindigo (78) and N,N'-diacetylindigo (65) triplets exclusively to trans isomers with concomitant formation of 02('Ag), at least for the former (78), suggests triplet excitation transfer from 3t* to O2 rather than spin-exchange quenching of 'p*. Thus, in these cases, only the singlet encounterpair channel in Eq.31 leads to products, though 3p* should be readily accessible from 3t*, since decay to cis occurs and short triplet lifetimes are involved. Also noteworthy is that compounds related to indigo are unique in that their excited singlet states are immune to O2 quenching at normal O2 concentrations. Neither +f nor Tf varies with [O,] despite the large T: values (up to 13.5 ns!) (65,66,78). We are not aware of any other examples of this type, nor can we offer an explanation for these interesting results, unless they represent severe cases of orbital symmetry restrictions (35). Comparison of the enone and dienone data in Table 4 again leads to the conclusion that in the absence of structural constraints a 3p*-type geometry is attained which undergoes spin-exchange quenching by O2 (62,63,64,67,68). Extended conjugation as in diphenylhexatriene and diphenyloctatetraene(58) and in @-carotene,retinal, and retinol (62) appears to favor planar geometries. In all of these, relatively long triplet lifetimes are involved and the kzx values

24

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS

are near the l/gkdif limit. That these criteria can be misleading is exemplified by p-carotene (C), for which a considerablebody of additionalexperimentalevidence is available. Excitation transfer from Oz('Ag) to p-carotene occurs at roughly %kdif, gives 3C*, and has allowed the use of p-carotene as a probe for 02('Ag) yields for a variety of triplet energy donors (49). A triplet excitation energy of 21-25 kcallmol for C, nearly equal to the energy of 02('Ag), has been based on rate constants of triplet excitation transfer from a series of aromatic hydrocarbons to C (Sandros plot) which fall to = 1h their maximum value at donor A E T , a , = 23 kcaVmol (pentacene) (46). Since ex's for C and pentacene (Tables 3 and 4) are also very similar, it is tempting to conclude that well-matched energy gaps in the C-02 pair have resulted in reversible excitation transfer:

This conclusion is, however, inconsistent with Foote and Denny's demonstration 'Ag) reactivity (47). The lifetimes of that p-carotene strongly suppresses 02( Oz('Ag), -30 ps (79,81), and of 3C*, 9 ps (62), in benzene solution are sufficiently long for the equilibrium in Eq. 32 to be substantially established at moderate O2 and 'C concentrations:

Since in Foote and Denny's experiments [02] exceeded the ['Cl's by more than one order of magnitude (47), the concentration of 02('Ag) would not have been = 0.21 (52,62), and little or no quenching greatly diminished (Eq. 33), would have occurred if the transfer were reversible. Since, in contrast to this prediction, pronounced quenching was observed at all ['Cl's, the notion of reversible excitation transfer must be rejected. The absence of chemical consumption of 'C (47) then suggests that the process is best described as spin-exchange quenching:

gx/@

+

Accordingly, kox = %k&fkse/(kse k-,if). The failure of the singlet encounter pair to provide an effective deactivation channel and the small energy gap implied by the efficiency of the spin-exchange path suggest that thermally equilibrated

25

=CITED-STATE I N T E R A ~ O N SWITH 3 0 2

3C* has lost some of its initial energy, possibly through significant geometric adjustments. values than Y9kdf have been reported for several molecules with Larger n,T* lowest triplet states (Table 5 ) . Since these generally do not exceed %kdif, combinations of quenching via the singlet and triplet encounter pairs have been proposed (52,8248). In view of the high A&,+, values involved, even the kTx value of benzophenone, which is nearly equal to %kdjf (compare with value for anthracene in Tables 3 and 5 ) , can be regarded as anomalously high if only the

ex

TABLE 5. Rate Constants for Oz Quenching of n,T* Triplets Compound Acetoneb Xanthone' Acetophenone' 4.2 Benzophenone' Anthraquinonec P-AcetonaphthoneCsd Carbazole' Tripheny laminee N-Methy lindole' N-Methylthioacridond

e x a

(109K's-') 9.2 5.9 74.1 5. l b 3.O 3.2 2.3 1.5 1.5 2.0 1.9 6.0 15 17 15 12.3B 15Sh 2.3 1.9

Acridine'

3.2 3.1 2.2

&,so

(kcaUmo1)

=78

74.1 52,84 69.5 62.9 58.9 70.4 70.1 69.2 42.6 60.9

Ref. 82 52.83 82 52 84 85 84 86 84 85 84 87 52 84 88 88 84 85

42.0

84 85 85

"Rate constants in benzene at room temperature, by pulse radiolysis and/or flash photolysis unless otherwise stated. M for air-equilibrated cyclohexane solution, 20°C (16). bAdjusted to [O,] = 2.10 X 'Adjusted to [O,]= 1.61 X M for air-equilibrated solution (16). &?r,m* state, included for comparison with Table 3. Wethylcyclohexane. f3-Methylpentane, phosphorescence. s ~ & vs. [O,]. hWI vs. [O,].

26

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS

singlet encounter pair leads to quenching. The k;f, values of N-methylindole, N-methylthioacridone, and triphenylamine are especially notable in that they are, within experimental uncertainty, equal to 4/kdif(89). The possibility that chargetransfer interactionsin the encountercomplexes increase the quenching efficiency has also been stressed (29,33,84,90,91). III the case of chrysene, the kTx/kdif ratio increases generally as the polarity of the solvent is increased (29). A large increase in this ratio has also been reported for rose bengal, methylene blue, thionene, and erythrosin as the solvent is changed from methanol or cyclohexanol to the more viscous solvent ethylene glycol or to water (92). Whereas k;f, = ?hkdif in cyclohexanol, it is very close to Y9kdifin ethylene glycol and water (92). The triplet states of phenol, p-cresol, anisole, and tyrosine are quenched by O2 in water at 25°C with rate constants in the (4.84.3) X lo9 M-'s-' range (90); kdif = (5.3 & 1.1) X lo9 M-' s-' in water has been estimated from k,, values (92). With some of the phenols, transient absorptions have been assigned to phenoxy and superoxide radicals, and the quenching has been attributed to electron transfer (90):

3ArOH*

+ O2

4

573.'(ArOH/02)*--t A I O + G2-

+ H+

(35)

Similarly, large kzx values ('5 X lo9 M-' s-', 25°C) have been obtained in water for quenching the triplet states of nitrogen-containing molecules, including indole, tryptophan, and tryptamine (90). Thus far we have assumed that encounter pairs of different multiplicities do not interconvert. This requires that for %kdif S kOx S 4/9kdif the yields of 02('Ag) per encounter, aT, should be given by 1 2 aT 3 0.25, in the same order. An alternative mechanism that would also give the same k,, range includes interconversion of singlet and triplet encounter pairs through stronger spin-orbit and spin-spin interactions than those applicable to aromatic hydrocarbons (52,84,88). Since charge-transfer interactions are also postulated, the encounter pairs

'(M02)* k,_ 'M

+ 02('Ag)

can be viewed as exciplexes of different multiplicity. This mechanism will accommodate any aTin the range 0 S cxT S 1 , independent of the value of k;,. Clearly, then, determination of quantum yields for sensitized 02( 'A,) formation is crucial for evaluation of the importance of the energy transfer relative to all

27

EXCITED-STATE INTERACTIONSWITH 3 0 2

other quenching channels, and for differentiation between noninterconverting and interconverting encounter pairs, at least in limiting cases.

C. Oz(*Ag)Yields An expression for +A in terms of the kinetic parameters can be based on

+ 02(3&J53M* + o'O~(~A,) + (1 (37) 3M* + 02(3X;) 5 'M + aT02('A,) + (1 - CX~)O,(~Z,) (38) 'M*

as)02(3X,)

which are more general forms of Eqs. 20, 24, 31, 34, and 36. The singlet contribution to the quantum yield, given by

+,:

is not expected to be large, even if as is significant, because of incomplete 'M* quenching (Table 1) (93-95). On the other hand, since in the presence of O2 Eq.38 usually accounts for all triplet decay, the triplet contribution +A is given by

where +is and 4: are intersystem crossing yields of 'M* in the presence and in the absence of 02.respectively. Combining Eqs. 39 and 40 gives

which can be combined further with Eq. 21 to give

+

It can be seen that +A + aT as as -+ 0 . Both indirect and direct approaches for the determination of +A have been applied. Early methods employed the highly reactive substrates tetramethylethylene ( W E )(96), 2,5-dimethylfuran (DMF) (96,97), and 1,3-diphenylisobenzofuran (DPBF) (48,67,85,93,94) to trap 02('Ag):

28

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLED REACTIONS

Studies of the photooxidation of these substrates have established chemical reaction with 02( 'Ah,) as the only significant quenching interaction; essentially no physical quenching of 02('Ag) is involved (48,85,93,94,96-100). A related set of studies is based on the photoperoxidation of anthracenes, e.g., rubrene, and 9,lO-dimethylanthracene(DMA) as the 02('Ag) trapping reaction (95,101). 02('Ag) sensitizer molecules for which +A values were determined in this way were excited directly or, when small +is values were involved, indirectly via a triplet energy donor, using both pulsed (flash photolysis and/or radiolysis) and steady-state irradiation conditions. Chemical and physical measurements have included monitoring 0,consumption, substrate depletion (bleaching), and/or oxidation product formation. To illustrate the kinetics for the steady-state excitation case we need only consider

'A

+ OZ('Ag)

'A02

(43)

where 'A represents a completely effective chemical trapping agent [02('Ag) acceptor]. The oxidation product quantum yield, +Ao2, is then given by

which can be inverted to the more useful form

from the intercepts, and Plots of (+Ao2)-1 vs. [A]-' allow calculation of aT asvalues can be generated using Eq. 41 or 42. A second indirect approach to the determination of +A, based on the absorption of the p-carotene triplet generated by excitation transfer from 02('Ag) (52), has already been mentioned. Transient decay of the p-carotene mplet absorption is monitored, and the long series of excitation-transfer steps which precede its formation lead to rather complex kinetic expressions (52). Two direct methods for the determination of

+

EXCITED-STATE INTERACTIONS WITH

29

3 4

+A

have been employed. The first is based on monitoring the sensitized 02('Ag) infrared-luminescence (IR-L) intensity, (55,102-104,107),and the second is based on time-resolved thermal-lensing (TL) calorimetric measurements (10 1). Listed in Table 6 are +A values obtained with air- andor oxygen-saturated solutions. Minimum values for aT + as and maximum values for aT have been calculated for the limiting cases aT = 1 and as = 0, respectively. The quantity aT as is obtained by rearrangement of Eq. 42:

+

and the aT is obtained from Eqs. 40 and 41: aT =

+A

- 4: <-4A +is

+is

(48)

+A (+is

- l)(Z110)

+

1

The equality in J2q. 49 applies when as # 0, provided that the singlet states involved are too short-lived to be quenched at the oxygen concentrationsnormally employed, :T s 1 ns. Several of the carbonyl compounds in Table 6 fall in this category. Agreement between measurements of +A by different groups is satisfactory provided that the same type of probe was utilized. This can be seen by examining the results obtained for rubrene, aT as >, 1.4, with several chemical traps for 02('Ag). However, +A and aT values obtained by direct methods (IR-L or TL) are usually smaller than those based on indirect methods. For example, in the case of anthracene, chemical-trapping data have given variously aT as 3 1.46 with as = 0.46for aT = 1.00 (95) and aT = 1.00, as = 0 (106),whereas direct measurements based on 02( 'Ag) luminescence (107)and thermal-lensing calorimetry (105) indicate that orT = 0.8 2 0.1 and as = 0. The general picture which emerges for aromatic hydrocarbons is that aT must be close to, if not exactly, unity in several instances, whereas as appears to be much smaller than unity and may be close to zero even in cases where > 22.6 kcalhol, e.g., naphthalene, pyrene, 9,10-dimethyl-l,2-benzanthracene, and perhaps anthracene. For molecules in which T2 lies below S , a small as value can be rationalized (93)in terms of

+

+

Since this process is nearly energy-neutral, multiplicity-allowed spin-exchange should be favored by relatively large Franck-Condon overlap factors. Some evidence that this pathway contributes in the case of anthracenehas been presented (23).This explanation cannot be applied to molecules for which T2 lies well

TABLE 6. Efficiencies of 02(1$) Formation" Compound

Naphthalene

Fluorene Biphenyl Anthracene

9-Methylanthracene 9-Phenylanthracene 9,lO-Dimethylanthracene

9,lO-Diphenylanthracene Rubrene

+*

aT'

Aromatic Hydrocarbons 0.14 20.02' 1.05 0.97 0.53 0.0920.02' 0.57 0.88 50.07 1.12 1.51 (1.12 2 0.09) 1.28 1.46 0.73' 1.o 1.o 0.72 0.8' 0.61 20.06 0.79 k O . l

Probe

Ref.

TME,DMF P-CIAPf p-CM DPBFIPR~ TME,DMF DPBFIPR~ DMA DMA

96 52 52 85

96 85

DPBFIPR~ IR-L TL

95 95 106 85 107 105

DTBP

(0.97 20.03)';

1.1520.2

1.1820.2

DMF

97

(1.09 2 0.05)k

1.35 k0.2

1.41k0.2

DMF

97

0.52 20.03 (1.0220.06) (1.14 20.05)k

1.29 2 0.1 1.34 20.1 1.41 20.2

2.050.4 Self(DMA) 1.30 k 0.1 Self 1.3520.1 Self 1.4220.2 DMF

(1.20 2 0.06)'; (0.82 2 0.05)

1.4620.2

(0.91 20.05) (1.20 2 0.02)'

1.47 2 0.2

0.3020.06 (0.88 20.07) (0.89)

1.21 e0.2 1.4920.2

1.920.4 1.235 0.2 1.50 2 0.2

0.6820.04

0.9820.2 1.0420.2

1.220.2 0.9220.2 1.07e0.2

(0.85 20.05)

9,10-Dimethyl-l,2benzanthracene Pyrene 0.61 50.04' (0.7920.04)k Perylene (1.27 k 0.06)k Terphenyl

1.47 20.2 1.32 20.2 1.2 5 0.2' 1.47 50.2 1.54zt0.2

Naphthacene

30

aT+asd

1.050.2

0.8020.2 1.6420.2 0.94

DMF DPBF DPBF DPBF DPBF Self Self Self TME Self DPBF DPBF

Self TME,DMF 0.8020.2 DMF 1.6420.2 DMF DPBFPR~

101 95 95 97 97 94,97 93 94 97 101

95 95 112 101 93 93 101 96 97 97 85

TABLE 6. (Continued) Compound

2-Pentanonem 3-Pentanone"' Xanthone Acetophenone

4a

(0.03) (0.04) 0.58?0.02' 0.17 & 0.02'

m-Methoxyacetophenone Benzophenone

0.50 20.04' 0.24 2 0.0 le 0.17'." 0.54" (0.39k0.08)

Benzaldehyde P-Acetonaphthone

0.60 & 0.04e

p-Ionone Fluorenone

0.25 0.06 &0.01' 0.03 k0.01'

Pyrene- 1aldehyde All-transretinal trans-Stilbene 1, I-Diphenyl-

ethylene 1-Phenylcyclohexene 1-Methyl-2-phenylcyclohexene

aT

Carbonyls 0.03 0.04 0.53 0.65 0.58 0.17 0.29'

aT+asd

Probe

Ref.

DPBF DPBF

108 108 52 52 96 96 113

P-c P-c

DMF TME IR-L

0.27' 0 S O 2 0.04 0.2420.01 0.17 0.54 0.56 0.29' 0.39+0.08 0.43 0.60-CO.04 0.70' 0.53 0.50 0.07 0.03 0.8'

IR-L DMF TME DTBF DPBF,DMA

LF

113 96 96 106 95 P-c 52 IR-L 102,107 DPBF 109 DPBFPR~ 85 TME,DMF 96 IR-L 102,107 85 DPBFPR~ 110 DPBF 96 DMF 96 TME 170 IR-L

(0.87)p (0.68)

1.2

DPBF DPBF

109 109

(0.66)p

1 k0.3

DPBF

109

Olefins 0.13 k0.08 0.18 k 0.05 0.1620.03'

p-CIPRh IR-Lq IR-L

52 53 104

0.16t 0.04'

IR-L

104

0.41 20.03'(67)

IR-L

104

0.2720.03'(91)

IR-L

104

31

TABLE 6. (Continued) Compound

4%

aTc

aT+asd

Probe

Ref.

IR-L

104

IR-L

104

IR-L

104

DMF DPBFIT"

97 111

IR-L IR-L

103 103

IR-L

103

1,ZDiphenylcyclohexene 0.06 -C 0. O r (168) 1-Phenyl-&methylcyclohexene 0.45 +0.03'(93) 1,&Diphenyl0.46 ~0.02'(111) cyclohexene 1,6-Diphenyl-1,3,5hexatriene (1 -0220.05)' 1.162 0.02 1.1820.2 0.25 20.05' All-trans-retinol Psoralen Pseudopsoralen 5-Methoxypsoralen 8-Methoxy psoralen 5,8-Dimethoxypsoralen 4,5',8-Trimethoxypsoralen 3-carbethoxypsoralen 3-carbethoxypseudopsoralen

(0.o 12) (0.026)

FurocowMtins'*' 0.34 0.57

(0.021)

0.32

(O.O@w

0.40

IR-L

103

(O.OO40)

0.10

IR-L

103

(0.084)

0.41

IR-L

103

IR-L

103 103

(0.30)

1.o

(0.49)

0.96

IR-L

Other 0.75

DPBFPR~

85

P-CIAPf

52

P-CW

52

Self Self

95 95

Acndine

N-Methylindole 3,5-DiphenylisobenZ0furan Tetraphenylporphine Zinc tetraphenylporphine Hematoporphyrine Tris-(bipyridene) mthenium(I1) Methylene blue Rose bengd

32

0.32

1.o

0.56

0.40 0.28 +0.02 (0.78k0.05)

1.29 1.51

(0.89) 0.58 & 0.06

1.o 0.71 20.1

TME

0.73 20.07

0.8320.1

TL

105

0.65

0.78"

DPBF

114

(0.83) 0.50" 0.7Y

0.9 1.o 1.o

DPBF TME

109 112 112

1.39 1.54

TL

TME

112 105

EXCITED-STATE INTERACTIONS WITH

TABLE 6. (Continued)

+*

Compound Emin

Chlorophyll a

0.42x 0.60

aTc

aT+asd

1.o >1.0

33

3 4

Probe

TME TME

Ref. 112 112

?n benzene, unless otherwise stated. *Air-saturated solution, oxygen-saturated solution in parentheses. 'Upper limit from Q. 48. dLower limit from 4 . 4 7 . I n methanol.

fAcetophenone-sensitized.

gXanthone-sensitized. *Pulse radiolysis. 'Assuming aT = 1.00for acridine. '2,s-di-t-Butylfuran. 'In n-hexane. 'From data for three [O,] values. "Neat ketone solvent; acetone, 2-butanone, 2-hexanone, 3-heptanone, and 4-heptanone all gave similar +A's (within a factor of 3) in methanol using DMF as probe (108). "Neglecting OZ(lAg)quenching by benzophenone (97). in oxygen-saturated solution is not included because it predicts too low T', "A higher value for for benzophenone (104,109). PCyclohexane. Qenzophenone-sensitized. 'n-Heptane, assuming aT = 1.00 for naphthalene; T; in parentheses in ns. Triphenylene-sensitized, assuming aT = 1.OO for anthracene. '+A and aT estimated correct to ?S% and t 1096, respectively. "In methanoVD,O, 9 1. Xelative to methylene blue standard in Ref. 112; methanol, see Ref. 115.

above S , . For such molecules high fluorescence quantum yields are not uncommon, and 0, quenching must proceed directly via T,. Small as values could then be due to the following spin-allowed exothermic sequence (93):

The new step in the sequence represents internal conversion within the triplet

34

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTR0LLF.DREACTIONS

encounter-pair manifold and could be faster than the rate constant for diffusion apart of the M(T,), 02('Ag) pair. A more elaborate mechanism involving reencounter quenching of solvent-separated M(Tl), O2(*Ag)has been proposed for the case of anthracene (95,115). This mechanism distinguishesbetween 'A; and 'Ag components of the lowest singlet state of oxygen (116) and is based on state-symmetry considerations(116,118). It is kinetically indistinguishable from q.50. Singlet quenching, Q. 38, is negligible for most ketones and aldehydes due to subnanosecond singlet lifetimes. Accordingly, Q. 42 reduces to +A = aT+)s, from which aT values are readily calculated. Generally, rather small aT values are obtained for carbonyl compounds with n,n* lowest triplet states (Table 6) consistent with the large k;f; values associated with the quenching process. Since aT > 0.25 appears to apply for several of the aromatic carbonyl compounds (e.g., benzophenone and benzaldehyde) despite the large triplet excitation energies involved, some interconversion of triplet and singlet encounter complexes, as shown in Eq. 37, is implied. The large fractions of quenching events which do not give OZ('Ag) (see especially the aliphatic ketones) have been attributed to charge-transfer quenching via the triplet encounter pair (52). Recently, the notion that the small efficienciesof O,( 'Ag) formation are caused by competing photophysical events has been challenged (1 13). The proposal that a chemical entity, X,forms from the interaction of some ketone triplets, 3K*, with O2('Z,) is based on the observation that, for relatively high excitation pulse energies, the decay of the emission of Oz('Ag) deviates from strictly first-orderkinetics (113). Formation of 02(lAg) sensitized by acetophenone (AP), rn-methoxyacetophenone (MAP), benzophenone (BP), and P-acetonaphthone (AN) was examined in aerated benzene and acetonitrile solutions. Cleanly firstorder decay of OZ('Ag)luminescence was observed for AN, though the highest 02('Ag) concentrations were achieved with this sensitizer (aTlargest, Table 6). The importance of this finding is that it shows that self-annihilation of 02('Ag) (10) does not provide a second-order decay contribution (1 13). Similar results were obtained for BP in benzene. In contrast, the decay of the IR luminescence generated with AP, MAP, or BP as sensitizers in acetonimle and with AP or MAP in benzene showed a faster initial decay and could be analyzed as a combination of first- and second-order components. Since the second-order portion can be observed to contribute over tens of ps, well after the decay of the ketone triplets (7 = (k;f,[O,])-' 6 0.3 ps), reencounter quenching of 3K* and 02('Ag) (95,115) must also be ruled out as a potential explanation. In addition, experiments with benzoquinone, an OZt trap, eliminated electron transfer as a competing 3K*quenching process and 0 , ' as a viable O,('A,) quencher (1 13). It was therefore concluded that reaction of 3K*with 02(3X,) gives singlet and triplet bnadicals in competition with the physical quenching interactions considered thus far, and that these biradicals-or, more likely, the trioxetane which may form from them-deactivate 02('Ag) and are responsible

35

EXCITEDSTATE INTERA~~~ONS WITH 30,

for the apparent second-order decay component, Eqs. 51, 52 (113). Since no permanent photoreaction was observed, all transients must eventually regenerate 'K and 02(3Z;) (1 13):

3K*

f

+ 02(32,)

-

'602)*

xFoT 1K

R

+ 02(3z;) (51)

1

'K

02('Ag)

R

3(~~2)*-+

+ 02('Ag)

+ XRx:;o R

?

-

O~(~Z;)+

?

In this scheme, the apparent second-order component arises only because of the transient nature of X and not because the initial concentrations of 02(lAg) and X are similar, as has been proposed (1 13). Therefore, the lifetime of X under the conditions of these experiments must be in the 10-30-ps range. Sensitizer-O;?biradical intermediates were proposed long ago by Schenck as key intermediates in sensitized photooxidations (1 19-121). Elucidation of the role of 02('A,) in such photooxidations (122,123) and its wide acceptance as the active agent (1 15,124,125) had rendered biradical species superfluous, except as intermediates in the photoxidations of menthone (126), benzil(127,128), and other diketones (128). It is important, therefore, that kinetic evidence for their formation with specific ketone sensitizers appears to have been found (1 13). As pointed out earlier, k:x values for several of the ketones exceed I/gkdif (Table 5 ) , implicating the triplet encounter pair in the deactivation. However, the possible involvement of the biradical quenching route and the likely interconversion of singlet and triplet biradicals prevents a straightforwardinterpretationof aTvalues. AN, for which k;fxis very similar to that of naphthalene and for which no kinetic evidence for biradical formation could be found (103), probably utilizes mainly the singlet encounter pair route as indicated by its relatively high aTvalue. Pyrene-1-aldehyde with its low T,T* triplet state probably behaves similarly. On the other hand, dialkyl ketones with high kzx values (see acetone, Table 5 ) and very low aT's are probably quenched via the triplet biradical route shown in Eq.5 1. The enormous 02('Ag) lifetime increase on changing the solvent from acetone (65.3 2 5.3 ps) to perdeuterioacetone (838 f 119 ps) (80) suggests strongly that addition of 02('Ag) to the carbonyl group of ground-state ketone is not a significant reaction.

36

SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLEDREACTIONS

Values of aT well below unity for the olefins in Table 6, 1,6-diphenyl-l,3,5hexatriene excepted, are consistent with variable contributions of the spinexchange mechanism described above for the stilbenes. The relatively large kzx values and the short triplet lifetimes,=40-180 ns, observed for the diphenylethylenes and the cyclohexenes clearly reflect the involvement of 3p* conformations in both 02-assisted and -unassisted triplet decay. Since the excitation-transfer pathway also contributes, nearly planar conformations must play a significant role in the quenching process. These conclusions point to rather shallow triplet potential-energy curves along the double-bond torsional coordinate, twisted to cisoid and/or transoid, for most of the olefins in Table 6. A complex spectrum of olefin mplet-0, interactions can thus be imagined, variations of which are described in Schemes 1 and 2 and Eqs. 28 and 31, which include equilibration among geometriesof the olefin in the encounter pairs, e .g .,Eq . 3 1. If, in addition, singlet and triplet encounter pairs interconvert,as shown in Eq. 36, the description of 0,quenching will be complicated further. Selection of a likely mechanism for a specific olefin is greatly facilitated when the fate of the olefin triplets involved in the quenching process is known. We showed earlier how the effects of O2in photostationary states and isomerizationquantum yields could be utilized in proposing mechanismsfor stilbenesand for indigoid dyes. As a further example we consider the case of all-trans-retinol, for which the effect of [O,] on +t -,c has been measured (1 11). Though its large triplet lifetime, 100 ps (Table 5), suggests that transoid triplets predominate in solution, the large k;f; and low aT values implicate 3p* in quenching and indicate a shallow triplet potential-energy curve in this case also. Since no special spin-orbit coupling mechanisms for the equilibration of encounter-pair spin states are expected for retinol, we assume that they maintain their integrity. With this condition, quenching via singlet and triplet encounter pairs is shown for the general case in Scheme 3 (for the cyclohexenes,substitute c for t) which represents an expanded version of Eq. 28. ‘t

+ OZ(lAg)

K,

‘(to2)*

‘(p02)*

Thus, a complete description requires knowledge of the rate constants for formation and dissociation of four exciplexes, three equilibrium constants for conformational equilibration, and the rate constants ket and k,. We can avoid

EXCKEBSTATE INTERACITONS m30,

37

this kinetic nightmare by not specifying the geometry of the triplet state in the scheme. The simplest mechanism which will account for the observations for retinol (1 11) is

'Tr ?r*

-b

+

3R*2

'Tr*-% ?r* 't 'Tr + %* 6 't

-+ (1 - 8) 'c

+ 02(32;) 5I t + O ~ ( ~ A J 3R* + 02(32;) -%6' 't + (1 - 6') 'c + 02(3Z,) 3 ~ *

(56)

(57)

where Tr and R represent the sensitizer triphenylene and retinol, respectively. Quenching of ?r* by oxygen can be neglected at the oxygen concentrations employed, s 1.4 x M, and neglecting quenching of 'Tr* (Table 1) introduces less than a 10%error in the analysis. Application of the steady-state approximation in excited species gives

where r = &'-,&is the ratio of initial isomerization rates in the absence and in the presence of 02.8 = (1 - 6')/(1 - a), and 7 = 1kd. Figure 6 , a

[ O ~ I - ~1, 0 4 ~ - 4 '

F

w 6. The effect of 0,on the rate of triphenylene-sensitized t +c photoisomerization of all-trans-retinol, Eq.58. From Ref. 111 with permissionof Royal Society of Chemistry.

38

SPIN-STATISTICALFACTORS D l DIFFUSIONCONTROUED REACTIONS

reproduction of Fig. 1 in Ref. 111, shows that the data adhere nicely to Eq.58, intercept 20.08, slope = 1.56 X K'. Using kzx = k& + =5 X lo9 M-' s-l (Table 5 ) and aT = = 0.25 (Table 6)gives 1.25 X lo9 M-' s-' and 3.75 x lo9 M-' s-l for and respectively. These rate constants and the intercept from Figure 6 give 8 = 0.10 and together with the slope give kd = 7.2 X lo4 s-', in excellent agreement with the observed value of 7.9 x lo4 s-' (Ref. 103 and Table 5). In contrast to the results for stilbene, which indicate that spin-exchange quenching of 3p* by O2 favors the cis side more than does natural decay, i.e., 8 > 1.0, the results for retinol require that quenching of 3p*favor the trans ground state substantially more than does natural decay. Since k;f, is smaller than 4hkc, by more than a factor of 2, an ctT value consistent with = 3 is no more than a coincidence. However, if the equilibrations shown in Scheme 3 are fast relative to "exciplex" dissociation or decay, the coincidence could be that k&, kdis) = ke& k&) 1 0.4. The above interpretation of the retinol data differs from that in Ref. 111 (129). The kinetic analysis in Ref. 111, based on Scheme 2, can be readily shown to be flawed. Though an equation of the same form as Eq. 58 was derived, it was assumed that the quenching efficiencies are governed by the equilibrium populations of 3t* and 3p* rather than by the spin states of the encounter pairs. Also, 8 = 1 was assumed, and the observed decay rate constant of 3R* was incorrectly set equal to kd in Scheme 2 instead of to kd&,/(l Ktp) (38,57,58). The behavior of all-rrarzs-retinol is very different from that of all-trans-retinal. In the latter case an aT value close to unity (Table 6) and a small k;f, value (Table 4) suggest that only the singlet encounter pair leads to quenching by 02. 1,6-Diphenyl-1,3,5-hexatriene with aT5 1 and k:x = 5.5 X lo9M-' s-l does not appear to fulfill expectations based on Scheme 3. Unless triplet and singlet encounter pairs interconvert in this case, either aTor k;f, is too large. For several of the other compounds listed in Table 6charge-transfer quenching via the triplet encounter pair may contribute. Most of the aTvalues, though smaller than unity, are larger than 0.25, indicating either that the energy-transfer pathway is more efficient, or that there is interconversion between encounter pairs of different multiplicity. N-Methylindole, for which aT > 0.25 but k:x 2 4/kdiif(Tables 5 and 6), appears to fall in the latter category.

ex

+ ex)

ex ex,

+

+

+

V. RADICAL SELF-TERMINATION Conclusions concerningthe role of spin-statistical factors in the preceding section are based on the well-founded assumption that singlet-excited-statequenching by 02(3Z;) provides an empirical measure of the magnitude of fully diffusioncontrolled rate constants. Singlet quenching provides a nearly perfect dynamic model for kdif in triplet quenching. Differences in D (Eqs. 5 and 6)should be negligible, since in both interactions D is dominated by the large diffusion

RADICAL SELF-TERMINATION

39

coefficients of 02,and differences in p should also be negligible, especially for excited singlet and triplet states of the same molecule. Thus, as we have seen, cancellation of kdif allows calculation of u from k;f,/kzxin limiting cases. This approach can be extended to reactions between organic molecules of similar size only if appropriate empirically based diffusion-controlled rate constants can be found. In this section we consider recent results on radical-termination rate constants which show that termination is a suitable reference reaction. Radical self-termination is the reaction of two identical free radicals, R*, with each other. For simple alkyl radicals with @-hydrogenstwo highly exothermic reaction channels are available: disproportionation to alkane R(+H) and alkene R(-H) by transfer of the @-hydrogenatom and combination to dimer alkane R-R:

We start with the extensive and rigorous study of Schuh and Fischer on r-butyl radical self-termination (6). Earlier work on this reaction, reviewed in Ref. 6, had yielded 4 values in the 109-10'0 M-' s-l range with poor agreement among different research groups even in cases for which identical radical sources and reaction conditions were employed. Schuh and Fischer used the photolysis of di-r-butyl ketone in solution as the source of r-butyl radicals. Consideration of some of the details of this reaction is instructive, especially since it was the inefficiency of radical formation from the photolysis of acetone in solution which first led to the postulation of solvent cage effects in radical reactions, i.e., the competition of reactions of geminate radical pairs with their diffusion apart (129). Excitation in the n,m* region of di-f-butyl ketone gives a relatively long-lived excited singlet state, T = 5 ns (130), which intersystem-crosses and undergoes cleavage to pivaloyl and t-butyl radicals, & = 0.71 (130), predominantly from its triplet state (131; cf. however 130). Chemically induced dynamic nuclear polarization of the starting ketone measured relative to that of pivaloyl aldehyde, which is formed in low yield by disproportionation of the geminate radical pair, shows that 3~ 96% of the radicals escape the cage (13 1). The virtual absence of a cage effect is readily explained by postulating that multiplicity-allowed triplet ketone cleavage gives triplet radical pairs whose relatively slow T +S intersystem crossing prevents the formation of singlet cage products. Since decarbonylation of pivaloyl radicals is fast, k = 2.5 x lo5 s-l at 40°C (132,133), the overall quantum yield of t-butyl radical formation is 1.4. The inferred slow intersystem crossing of triplet radical pairs is consistent with slow radical spin-relaxation rate constants obtained using dynamic-polarization recovery rates; see Table 7

292

0.2

290

0.6

CH3CHOH

29 1

1.3

(Ch&;OH

290

2.7

CHZOH 0

r;'

"Spin-lattice relaxation time,R( 1 )-E( *Selected values from Ref. 134.

).

TABLE 8. Triplet Biradical L&ifhnes" Solvent

Biradical

T (K)

k

Ref.

(s-')

Ph 295

1.07 X lo7

136

215.9 293.2 357.5

0.98 X lo7 1.06 X lo7 1.09 x 10'

137

295 295

4.13 X lo6 1.45 X lo7

138

!Benzene

293

3.3

X

lo6

139

CH3CN

295

4.5

X

lo6

140

Ph CH30H

$0.

Ph

Ph

40

TABLE 8. (Continued) Biradical

Solvent

k

T (K)

Ref.

(s-l)

n-C7H 16

295

2.04 X lo7

141

n-C7H16

295

1.78 X lo7

141

(CD3)zSO/DzO(4:lw/w)

303

5.3

lo6

142

n-C7H,6

295

5.9 X 108

136

n-C7H16

295

1.6 X 10’

136

CH3CN

295

6.3 X lo8

143

CH,CN/HzO

295

8.3 X

lo5

144

CH,CN/H,O

295

1.67

lo5

144

0

X

Ph &OH

OPh YH

J O H

o Ph fph

P

0

X

“Selected values from Ref. 135. 41

SPIN-STATISTICAL FAcIylRs IN DIFFUSION-CONTROLLEDREAcIloNS

42

(134). Recent measurements of relatively long triplet biradical lifetimes, T = lo-’ s (Table 8) also show that only singlet encounter pairs will contribute to the reactivity of freeradicals in solution. Accordingly, Eq.(59) can be rewritten as

(60) 2R*

-k 2 R * 1 5 , 1 ( 2 R * ) +R-R

+ R(+H) + R(-H)

which requires that the rate constants of diffusion-controlledradical self-reactions be attenuated by a spin-statistical factor of cr = %. =

=$kg

The disappearanceof t-butyl radicals, followed by ESR spectroscopyin twelve solvents over a wide range of temperatures, obeyed second-order kinetics and gave experimental rate constants 2k, in very good agreement with rate constants obtained independently from product yields (6). Linear Arrhenius plots are obtained for n-alkane solvents (n-heptane through n-hexadecane), benzene, acetonitrile (T < 325 K),and octamethylcyclotetrasiloxane,but not for the protic solvents t-butyl alcohol, 3-methyl-3-pentano1, and a 1:2 mixture of t-butyl alcohol:pinacol. Arrhenius parameters for nonhydroxylic solvents, In 2 4 = In 2At - E,/RT, are shown in Table 9 together with corresponding parameters for the Andrade equation, In q = In tly) + E?/RT (6). The agreement between activation energies for self-reaction and activation energies for viscous flow is generally very good, E, - E,, S 0.5 kcdmol. Especially revealing are plots of 24 vs. T/q (Fig. 7,8), which generate a family of at least seven lines with slopes increasing with solvent molecular weight (alkanes) and solvent association (alcohols). Moreover, linearity is not observed in hydroxylic solvents. The slopes are larger than predicted by the stick and slip limits of the Stokes equation (Eqs. 9 and 61), showing that neither can be applied generally for calculation of diffusion coefficients (the dashed lines in Figs. 7 and 8 are based on Eqs. 9 and 61 with OL = 3,000). At the very least diffusion coefficients must be corrected in a solvent-specific way. A direct test of the Smoluchowski equation for kdif (J3q. 6) in predicting 2k, was hampered by the lack of empirical DA’s for t-butyl radicals. Using isobutane as the model for the radical, Schuh and Fischer initially evaluated nine empirical or semiempirical methods for the calculation of D, (6). Calculated D,’s were checked for internal consistency by using them together with the experimental 2kt’s to calculate reaction distances p from Eq. 61 and 6 with D = 20,:

TABLE 9. Arrhenius and Andrade Parametersfor the Self-termination of t-Butyl Radicals Termination Rate Constants 2k, Solvent n-C7H,, n-CsH1, n-C1oH*2 n-C 1 2H26 n-C14H30

Gdi,

CH&N Benzene

( 1 0 " 2 ' ~ - ~ ) (kcaVmo1) Ezk,

Dynamic Viscosities q

2.44 2.45 2.70 2.80 3.31 3.71 2.01 2.46

4.9 3.9 5.0 4.3 8.2 13.9

2.0 3.1

-5@as)

(10

1.51 1.41 1.62 1.29 0.81 0.93' 2.42 1.63

Ell (kcaVm01)

- Ell

&I"

(kcaYmo1)

1.94 2.15 2.35 2.74 3.28 3.39" 1.60 2.12 ~~~~

0.50 0.30 0.35 0.06 0.03 0.32 0.41 0.34 ~~~

Source: Ref. 6 . "Strictly valid for temperature >35OC.

r/qx

10-4, KP-I-

Figure 7. 2k, vs. T/qfor 1-butyl radical self-termination in (0)n-heptane, (0) n-octane, (m) n-decane, and (A)n-hexadecane. The dashed line is based on Eqs. 9 and 61. From Ref. 6 with permission of Helvetica Chimica Acta.

43

44

SPIN-STATISTICALFACTORS IN DIFRISION-CONTROLLEDREACTIONS

Figure 8. 2k, vs. T/qfor r-butyl radical self-termination in (0)acetonitrile, (0) benzene, (m) t-butanol, (0) 3-methyl-3-pentanol. The dashed line is based on Eqs. 9 and 61. From Ref. 6 with permission of Helvetica Chimica Acta.

Resulting p’s are strikingly independent of solvent and temperature when DA’s are obtained by interpolation from closely related experimental diffusion coefficients (alkanes). They also agree very well with the theoretical value of p based on calculated radii of t-butyl radicals, pth = 2rA = 5.6 -+ 0.8 8, (6). The successful prediction of p by the Smoluchowski equation in the less viscous media lends credence to the assumption that, subject to (T = ‘A, t-butyl radical self-reaction is diffusion-controlled. It was concluded that among the semiempirical methods, the formula of Spemol and Wirtz (7)gives reliable DAIS for low-viscosity nonassaciating solvents, whereas for alcohols the formula of Gainer and Metzner (145) is best (6). These two methods modify the Stokes-Einstein relationship for DA (see Eqs. 10-14) by accounting for (1) the molecular sizes of solute and solvent and (2) the effects of different solute-solvent and solventsolvent interactions (6). A comparison of the experimental 2kt’s with theoretical 2kp’s based on Eqs. 6 and 61 with p = 5.6 A and the “best” calculated D ( = 2DA) is given in Fig. 9 (6). The points cluster about a line with slope one, as expected for the mechanism shown in Eq. 60. The same conclusion can be reached by plotting the experimental termination rate constants, 2kt, against the calculated diffusion coefficientsD,. This is done in Fig. 10, for two representative solvents. Taking p = 5.6 A, the slopes for the lines, 8 ~ p N l O - ~ ugive , u =

Figure 9. Experimental vs. calculated termination rate constants for t-butyl radicals in (0)n-heptane, (0) n-octane, (m) n-decane, (0) n-dodecane, (A) n-tetradecane,

n-hexadecane, Ref. 6.

(v)acetonitrile, and

benzene; see text. The line has unit slope. From

Figure 10. 2k, vs. D, for t-butyl radical self-teenation in (0)n-heptane and acetonitde (6);see text. The line is based on Eqs. 6 and 61 with p = 5.6 A and u = !A.

(0)

45

46

SPIN-STATISTICALF A m R S IN DIFRISION-CONTROLLEDREACTIONS

0.24 and 0.22 for n-heptane and acetonitrile, respectively, in excellent agreement with the expected spin-statistical factor of %. Reasonable agreement between results of several independent measurements of the rate constant for benzyl radical self-reaction (146-148) have led Fischer and coworkers (148) to recommend that this reaction be used for calibration purposes. In a study which parallels closely that described for the r-butyl radicals, Lehni, Schuh, and Fischer used the photolysis of dibenzyl ketone as the source of benzyl radicals and monitored their decay by kinetic ESR (148). Dibenzyl ketone undergoes very efficient a-cleavage from its triplet state (149, 150) to yield a triplet pair of phenylacetyl and benzyl radicals. Reformation of ketone from this pair in various media, though inefficient, has been the subject of elegant recent studies (151-154). In ordinary solvents T --f S intersystem crossing is too slow to compete with radical separation, most geminate pairs [<95% (149)] escape the cage, and phenylacetyl radicals decarbonylate (155, 156). A quantitative yield of CO, &, 3:0.7, is obtained (149,157), and benzyl radicals, the only radicals observed by ESR at T > -50°C (158), give bibenzyl either directly by a,acoupling (155,157,159) or by rearrangement from initially formed semibenzenes (12-25% a,o and a,p coupling for -18°C =sT S 62°C) ( 1 0 ) . Self-reaction rate constants were determined as a function of T in toluene, in cyclohexane, and at 298 K in mixtures of the two, because experimental diffusion coefficients for toluene are available in these solvents; see Table 10 (148). Since it is reasonable to expect identical DA values for benzyl radicals and toluene molecules, the data in Table 10 afford an excellent test of the Smoluchowski

Figure 11. 24 vs. DA for benzyl radical self-termination in (0)toluene and (0) cyclohexane; see text. The line is based on Eqs. 6 and 61 with p = 5.8 8, and u = %.

From Ref. 148.

TABLE 10. Empirical and Semiemperical Dtrusion Coef€icients ~~

Solvent Solure: i-C,H,," n-C7H16

n-C8H18

n-C12H26

294 307 325 342 349 365

7.9 9.0 11.8 13.9 15.5 17.0

4.2 4.9 5.9 6.8 7.3 8.3

4.0 4.7 5.8 7.0 7.4 8.6

0.95 0.96 0.98 1.03 1.01 1.04

297 308 325 34 1 345 368

6.8 7.9 8.8 11.6 11.4 14.4

3.6 4.2 5.1 6.1 6.3 7.8

3.5 4.1 5 .O 6.0 6.2 7.8

0.97 0.98 0.98 0.98 0.98 1.oo

295 312 328 343 354

5.6 6.8 8.7 10.2 11.8

2.5 3.2 3.9 4.7 5.3

2.4 3.1 3.8 4.6 5.2

0.96 0.97 0.97 0.98 0.98

297 308 327 346 369

4.2 4.6 6.1 7.4 10.5

1.8 2.2 2.9 3.7 4.9

1.8 2.2 2.9 3.8 5 .O

1.oo 1.oo 1.oo 1.03 1.02

297 308 326 343 369

3.4 3.9 6.6 9.8

1.5 1.7 2.3 3.0 4.1

1.2 I .5 2.2 2.9 4.3

0.80 0.88 0.96 0.97 1.05

299 305 308 31 1 318 323 330 343 356 366

2.9 3.2 3.8 3.4 4.4 4.6 5.2 6.3 7.8 9.1

1.2 1.3 1.4 1.5 1.7 1.7 2.0 2.5 3.O 3.4

0.94 1.1 1.2 1.3 1.5 I .6 1.8 2.4 2.9 3.4

0.78 0.85 0.86 0.87 0.88 0.94 0.90 0.96 0.97 1.oo

5.5

47

TABLE 10. (Continued) T

2k,

CH&N

266 280 290 293 306 320 337 349

4.7 5.4 6.4 6.7 7.7 8.8 11.4 13.6

2.6 3.1 3.4 3.5 4.0 4.5 5.2 5.7

Benzene

28 1 293 295 302 305 314 325 336 345 35 1

4.6 5.8 6.1 6.6 6.9 7.3 8.7 9.5 11.0 11.2

2.6 2.9 3.0 3.2 3.3 3.6 3.9 4.2 4.5 4.7

Toluene

222 229 235 240 248 256 262 269 277 283 293 298 304 314 326 331

Solvent

c-C6H 12

48

(K) (109M-' s-')

283 29 1 298 305 312

Dexp (lo+ cm2s-')

Solute: Tolueneb 0.98 0.449 0.544 1.1 1.2 0.635 0.72 1.5 0.87 1.9 1.04 2.4 1.18 2.7 1.35 3.0 1.57 3.4 1.76 4.4 2.08 5.1 2.26 5.2 2.48 5.4 2.87 6.4 7.6 3.40 3.63 9.0

3.5 4.1 4.1 4.3 5.0

1.29 1.45 1.58 1.75 1.95

(

Dsw

cm2s-') DsJDcxp

1.01 1.18 1.33 1.53 1.78 1.94 2.29 2.47 2.64 3.17 3.58 3.66 1.34 1.52 1.73 1.90 2.08

1.16 1.14 1.13 1.13 1.13 1.10 1.10 1.09 1.06 1.11 1.05

1.01 1 .# 1.05

1.09 1.08 1.07

~

TABLE 10. (Continued) Solvent

T

(K)

322 332

2k Dexp Dsw ( I O ~ M - ’s - ~ ) (10-’crn~s-’) (10-’crn2s-’) 5.3 5.9

2.19 2.47

Solute: n-C3HsC 8.7 5.4 9.9 6.0 9.9 6.6 10.8 7.2 11.1 7.8

D,J

D

2.45 2.73

1.12 1.11

6.0 6.8 7.5 8.3 9.2

1.11 1.13 1.14 1.15 1.18

n-C7H16

313 323 333 343 353

n-C16H34

313 323 333 343 353

3.1 3.7 4.0 4.6 5.2

1.5 1.8 2.1 2.4 2.7

1.5 1.8 2.2 2.6 3.1

1.oo 1.oo 1.05 1.08 1.15

(Et0)4Si

313 323 333 343 353

6.2 7.1 8.0 8.2 8.0

3.5 3.9 4.3 4.8 5.2

4.5 5.1 5.7 6.4 7.1

1.29 1.30 1.33 1.33 1.37

(Et),CHOH

313 323 333 343 353

3.3 4.5 5.2

I .5 1.9 2.3 2.8 3.3

1.O 1.5 2.2 3.2 4.6

0.67 0.79 0.96 1.14 1.39

CH,COCH, in (EtO),Si

5.4

5.9

143 158 180 208 232

Solute: n-C3H/ 1.5 2.3 4.3 4.8 7.6

2.4 4.4 6.3

255 292 30 1 303 307 311 313 32 1

Solute: CH3COCH,e 1.7 3.8 4.4 4.6 4.8 5.2 5.2 6.1

0.84 1.76 2.06 2.13 2.27 2.43 2.50 2.94

0.97 1.2

49

~

~

~

50

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEJ3REACTIONS

TABLE 10. (Continued) T 2k, (K) (109M-' s-I)

Solvent

(

Dexp

cm2s-I) (

CH,COCH3 in (EtO),Si

255 292 301 303 307 311 313 321

Solute: (EtO),Sic 1.3 2.5 3.0 3.0 3.1 3.4 3.4 3.8

CH,OH

208 216 226 248 265 288

Solute: C H 3 0 H 1.85 0.36 1.1 0.48 1.4 0.66 2.5 1.22 3.6 1.83 4.9 2.93

"From Ref. 6. Trom Ref. 168.

%om Ref. 148. %om fFrom Ref. 169.

Ref. 166.

Dsw cm2s-') D,JDexp

0.46 0.96 1.12 1.16 1.24 1.32 1.37 1.61 0.33 0.44 0.60 1.10 1.65 2.66

0.92 0.92 0.91 0.90 0.90 0.91

dFrom Ref. 167.

equation: see Fig. 11. Estimates of p ranged from 6.30 A based on Eq. 12 to 5.64 A based on the volume-increment method (165). Employing p = 5.8 A (148), which is close to the average of values calculated from empirical formulas, and the slope in Fig. 11 gives u = 0.27. The agreement with the expected spin-statistical factor of Y4 (Eq.60)is again astounding in view of estimated errors of ~fr25% in 2kt and 5 30% in D , (148). The conclusion that the benzyl radical self-reaction is diffusion-controlled is further strengthened by the fact that in both solvents Et 'c E,, (Table 9). Measurements of 2k, values for i-propyl(166), ally1 (167), (CH&COH (168), (Et0)3SiOCHCH3 (168), and .CH20H (169) radicals in a variety of solvents provide further tests of the applicability of the Smoluchowski equation (Eq. 6) in defining l$$ in Eq. 61 (Table 10). These equations require that as radical systems and the solvents in which they react are changed 2 4 should remain That this expectation is admirably proportional to pD, with slope 8amN fulfilled in all cases but one is shown in Fig. 12. Not only are the points for the t-butyl and benzyl radicals collinear within experimental error, but radicals with substantially different p's, 4.3 S p S 7.2 (Table 1l), also fall on the same line. The correlation achieved in Fig. 12 is particularly satisfying in light of the great range of experimental solvents (n-heptane to methanol) and the use of the Spernol0

RADICAL SELF-TERMINATION

2k, x

D-p

10-9, MV

for

51

@&

10': 0tn3;'-

Figure 12. 2k, vs. both Dp (bottom) and 2k, for benzyl radicals in toluene (top), for the self-termination of (0)r-butyl radicals in various solvents, (0)i-propyl radical in Rheptane, i-propyl radical in n-hzxadecane, (H) i-propanolyl radical in acetone and tetraethoxysilane, (0) (EtO),SiOCHCH, in acetone and tetraethoxysilane, (A) hydroxymethyl radial in methanol; from Table 10 (see text). The line is based on Eqs. 6 and 61 with u = 'A.

(a)

Wirtz formula (Eq. 14) in calculating D,'s when empirical values were not available. As can be seen from Table 10, the Dsw values are nearly idential to the experimental values D , in hydrocarbon solvents. Spin-statistical factors calculated from the individual slopes in Fig. 12 are all very close to the expected value of % (Table 11). Of the radicals in Table 10, only the i-propyl radical shows systematicdeviations from the theoretical line (166). Since these deviations are outside of the estimated experimental uncertainty (166), and this behavior was not expectedapriori, the results for the i-propyl radical are treated in detail below. Lipscher and Fischer used di-i-propyl ketone photolysis to generate i-propyl radicals (166). As with the other ketones, the mechanism for i-propyl radical formation involves a-cleavage from the triplet state followed by activated decarbonylation of 2-methylpropanoyl radicals, with log A (s-') = 14.0 -+ 0.5, Et = 13.0 2 0.5 kcaVmol(l66). At T > 35°C the decarbonylation is sufficiently fast to allow clean bimolecular self-reaction, monitored by ESR, of the i-propyl radicals to give coupling and disproportionation products (Eq.59). Below this temperature the longer lifetime of the 2-methylpropanoyl radicals introduces

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS

52

TABLE 11. Spin-StatisticalFactors Determined from Experimental 2kt Values"

Radical

Pb (lO-'crn)

Solvent

5.6 5.6 5.6 5.6 5.6 5.6 5.6 5.6 5.8 5.8 5.2 5.2 5.3

n-C7H16 n-C8H I 8

n-C1d22 n-C12H26 n-C14H30 n-C16H34

CH3CN Benzene Toluene c-C6H 12 n-C7H16 n-C16H34 n-C3H16

5.d

(EtO),Si (EtO)$i CH3OH

~

~

7.2' 4.3

UC

0.24 0.22 0.26 0.25 0.27 0.31 0.22d 0.26d 0.26 0.29 0.27e 0.27e 0.21d.e 0.28g 0.24gsh 0.29h

Ref. 6 6 6 6 6 6 6 6 148 148 166 166 167 168 168 169

~

"Calculated from plots of 2 4 vs. D; slope = 8 r p u N b2rA, estimated using molar volumes and van der Waals volume increments (165). %alculated with empirical diffusion coefficients unless otherwise noted. dDiffusion coefficients were calculated using the Spernol-Wirtz treatment, Eq. 14. Talculated from plots of (2kJ-I vs. D-I. 'Estimated by using the van der Waals volume increments only (165). 8Adjusted with Spemol-Wim values based on empirical values for (MeO),Si. 'Based on low-diffusivity points; values at high diffusivities deviated from linearity (see text)

cross-disproportionation to 2-methylpropanal and propene as a significant reaction pathway for i-propyl radicals (166). Diffusion coefficients for i-propyl radicals were narrowly defined by averaging experimental DAISfor propane and propene (Table 10). The downward curvature in the i-propyl plot in Fig. 12 can be accounted for if either the condition k, >> k-dif in Eq. 3, or the condition kAB >> 4aNpD in Eq. 5, or both,cease to apply. It should be noted that the latter condition is equivalent to PA>> 2mNpD in Eq. A. 15 because kAA = YzkAB. The physical distinction between the failures of these two conditions is that in the first instance the reaction of singlet radical pairs deviates from being fully diffusion-controlled at high D's, while in the second it remains fully diffusioncontrolled at all D's. To appreciate the interplay of these two conditions, Eqs. 3 and A. 15 can be combined to give

RADICAL, SELF-TERMINATION

53

e,/G

where [ = (note that = Id!&)).The plot of (2k)-' vs. DA-' for the i-propyl radical is linear as predicted by Eq. 63 (Fig. 13), and u = 0.26 can be calculated from its slope. In the general case for which neither the holds, the intercept condition k,>> kdif nor the condition kAA >> 2rrNpD is assumed, then the of the line gives (l/u)('/2kAA + u p ) .If only k, >> Ldif intercept reduces to ( 2 P u ) - ' . This approximation was applied by Lipscher and Fischer to the data for the four solvents and gives 2 p = 1.7 X 10" M-' s-'. If on the other hand, only PA >> 2~rNpD is assumed, the intercept reduces to 5/a p. There has been no unanimity in the literature concerning 5. However, an equation for 5 derived by Eigen, 5 = 3000/(4dVp3) (170), which gives 5 = 1.8 M for p = 6 A, has often been employed, and an expression for 5 twice that value has been attributed to random-walk theory (171). For example, Eigen's equation has been useful in accounting for exciplex dissociation rate constants (172) and has been applied to estimate Ldif of encounter complexes involved in triplet excitation transfer (173). An empirical expression for exciplex dissociation in polar solvents has also been developed which predicts k-&f = 2.3 x 109/q for systems lacking coulombic interaction (174). We have favored an evaluation of 5 based on thermodynamics (40,54). Assuming that the enthalpy change for encounter-pair formation is zero, 5 is determined by the entropy change (cratic), ASc, for bringing two solutes together. For a net change of one solute molecule ASc = - R ln[M], where [MI is the molarity of the solvent, i.e., 5 = [MI (175). Relative to the Eigen equation, in which 5 is independent of solvent, the cratic-

0;'

10-4 SCm'2

-

Figure 13. 2k;' vs. DA' for the self-tennination of i-propyl radical in (0)n-heptane and (0) n-hexadecane; see text.

54

SPIN-STATISTICAL. FACTORS IN DIFFUSION-CONTROLLED REACI?ONS

entropy approach, being solvent-specific, gives 2-10 times larger 5 values (54). Assuming an intercept of & u p for the plot in Fig. 13 and treating the data for the n-alkanes separately gives u = 0.29 2 0.03 and 0.27 2 0.02 for n-heptane and n-hexadecane, respectively, and kpA = (6.6 2.1) X 10" s-l and (4.1 & 2.2) X 10" s-' with 5 = 6.8 M and 3.4 M in the same order. In the absence of additional information, distinguishing between the two extreme interpretations of the intercept in Fig. 13 is difficult. Intuitively we prefer interpreting it as & u p , because the chemical significance of k in Eq. 5 (2kAA in Eq. 62) is unclear. The magnitude of k has been estimated by assuming it equal to a gas-phase collision rate constant (4), and it has variously been called the rate constant that would pertain if the equilibrium concentration of encounter pairs were maintained (176) and a radiation boundary constant (166). On the other hand, it is clear that as the stability of the radicals is increased by appropriate substitution, k, decreases relative to k-&f (177) even to the point of resulting in persistent radicals. Whatever the cause of the curvature in Fig. 12, it is not at all obvious why i-propyl radicals should behave differently from t-butyl radicals. The difference may reflect the lower precision of the r-butyl radical 2ktvalues. In conclusion, it appears that Eq. 6 can be used with confidence to calculate rate constants for fully diffusion-controlled processes when empirical diffusion coefficients for the reactants in the solvents of interest are known. The recipe for calculating the reaction distance p may vary from reaction to reaction, but if we rely on radical self-termination as a guide, it may be taken as the sum of reactant radii estimated by averaging values obtained from molar volumes (Eq. 12) and from volumes based on van der Waals volume increments (165). When empirical diffusion coefficients Dexprare not available, they may be estimated from the Stokes-Einstein equation using the Spernol-Wirtz microfriction factor (Eqs. 10-14). When applied to nonassociating hydrocarbon solvents, as recommended (6), Dsw values are generally within f 10% of empirical values and seldom deviate by as much as & 25% (Tables 10, 11). This procedure will probably be best when applied to liquid solutes in fairly nonviscous solvents, i.e., to systems similar to those used in generating Eqs. 11-14. Furthermore, since the reduced-temperature term in Eq. 14 compensates marginally for rather small deviations from Eq. 11 (s25%), its use with higher-molecular-weight solvents and solutes is not recommended. Finally, when diffusion-controlled 2kt values are available in a specific solvent for radicals with D close to that for an A + B reaction, kdif for that reaction can be taken as 8k.

*

VI. TRIPLET EXCITATION TRANSFER Triplet excitation transfer involves a multiplicity-allowed electron exchange interaction in an encounter pair (178).

-

55

TRIPLET EXCITATION TRANSFER

3D*

+

'A

e kdd

k-d#

'(D*A)

ken k-cn

3(DA*)

k-dd

'D

+ 3A*

(64)

When, based on spectroscopic triplet excitation energies, the process is at least 3 kcal/mol exothermic, it has been found to attain a maximum rate constant (1, 5, 179-181) and has often been considered to occur upon every solution encounter. In such cases ken does not significantly contribute, and kobsd = kdifken/(ken k-,& Accordingly, the limiting condition kObd = kdifis expected to be especially valid in solvents of high viscosity in which solution encounters last longer, i.e. k-dif << ken (182,183). Wagner and Kochevar first recognized that in the low-viscosity solvents usually employed in photochemical studies, diffusion apart of donor-accceptor pairs competes with triplet-excitation transfer-even when, due to high exothermicity, the limiting rate constant kobsd has been attained (171). They showed that in a series of hydrocarbon solvents (q = 0.233 - 3.15 cP), kobsd values for the quenching of valerophenone triplets by 2,5-dimethyl-2,4-hexadieneare up to three times smaller than predicted by Eq. 9, (Y = 2,000, but approach predicted values in the highest-viscosity solvents (171). They reasoned that limiting kobsd values of (5 ? 1) X lo9 M-' s-l obtained earlier for a variety of donor-acceptor pairs in benzene (179,180) were not fully diffusion-controlled as had been supposed previously. The treatment of kobsdTD values for the quenching of triplet valerophenone photoelimination by 2,5-dimethyl-2,4-hexadienewas based on the assumptions that (a) the valerophenone triplet lifetime rDis solvent-independent, (b) kdif is given by the slip limit of the Debye equation (Eq. 9), OL = 2000, and (c) ken& is solventindependent (171). In light of the radical self-reaction results, assumption (b) is untenable (6),and, to the extent that cratic entropy controls 5, so is assumption (c) (54). A more satisfactory treatment of the results can be based on

+

where 5 is the molarity of the solvent, kdif is obtained from Eq. 6 with p = r, + r, = 7.1 A (radii based on molar volumes), and the D's are based on the Spernol-Wirtz formula (Eqs. 10-14); see Table 12. The plot of the data according to Eq. 65 (Fig. 14) shows that n-alkane and cycloalkane points fall on somewhat different lines. Treating the data separately gives TD = 4.35 ns and ken = 2.52 X 10" s-' for the n-alkanes, and TD = 6.9 ns and ken = 1.3 X 10" s-' for the cycloalkanes. These conclusions are not entirely satisfactory, because though 713%which is determined by the dynamics of y-Habstraction, may show a small solvent dependence, it is unlikely that ken should be that sensitive to subtle solvent changes. Despite the difference in treatments, efficiencies of tripletexcitation transfer, p , based on ken = 2.52 x 10" s-l are remarkably close to those obtained in Ref. 171 (see Table 12) and are consistent with the original conclusions. Experimental estimates of ken 3 9 x 10" s-' and ken 2 10" s-'

TABLE 12. The Quenching of Valerophenone Triplets by 2,5-Dimethyl-2,4hexadiene

36 95 79 72 63 56 51 32.5 48 39 30.5

11.2 8.7 7.6 6.9 6.2 5.6 5.1 3.4 9.3 8.2 7.5

1.85 4.70 3.56 2.97 2.48 1.93 1 .so 0.82d 1.32 0.93 0.59

0.54 0.38 0.48 0.55 0.62 0.70 0.77 0.90 0.67 0.77 0.85

"From Ref. 171. bMolar volumes at 20°C. Lange's Huna'book of Chemisrry, 9th Ed., Handbook Publishers, Inc., Sandusky, Ohio, 1956. %om Eqs. 6 and 10-14. qruncated form off, was employed. ' p = ken/(ken + skf)with kn = 2.52 x 10" s-'; see text.

I ( I /
1

2 ~

-

x 10". i'

I

3

Figure 14. Treatmentof thedatain Ref. 171 using&. 65: (0)alkanes, (e)cycloalkanes, (0)benzene.

56

TRIPLET EXCITATION TRANSFER

57

have been based on the quenching of y-phenylbutyrophenone triplets by neat cis-l,3-pentadiene (17 1) and on transient measurements of benzophenone triplet decay in neat 1,3-pentadienes (184). Flash kinetic spectroscopy has been used to determine rate constants for triplet energy transfer from indeno[2,l-a]indene to azulene as a function of temperature in n-pentane (228-290 K), toluene (228-309 K), acetonitrile (233-308 K), and r-butyl alcohol (309-342 K)(54). The adherenceof kobsd to the Arrheniusequation is satisfactory in all four solvents (Figure 15), and activation energies for excitation transfer are close to those for r-butyl radical self-reaction and to activation energies for viscous flow (Table 13). The variation of kobsd with Tlq parallels closely that found for 2kt for r-butyl radicals, as is demonstrated more directly by plots of kobsd vs. kt in Fig. 16 (54). Based on the fact that the range of k,bsd/k[ ratios, 3.14.5, is close to the reciprocal of the spin-statistical factor for radical self-reaction, a-' = 4, it was erroneously concluded that the excitation-transferprocess is fully diffusion-controlled (54). Not appreciated was the fact that since rate constants for an A + B reaction were being compared with those for an A + A reaction, the slopes in Fig. 16 should have been (2a)-' = 8 if both reactions were diffusion-controlled.Correction for differences in D and p in Eq. 6 for the two reactions can be based on Spernol-Wirtz microfriction factors for the nonhydroxylic solvents,

T-' x

to3. K

-

(A),

(o),

Figure 15. Arrhenius treatment of kObd in n-pentane acetonitrile (a),toluene and r-butyl alcohol (0) from Ref. 54. Reprinted with permission from J . Am. Chem. Soc. (1980) 102 6799. Copyright 1980, American Chemical Society.

TABLE 13. Arrhenius Parmeters for Triplet Excitation Transfer from Indeno[2,1-u]indene to Azulene" Solvent n-Pentane Toluene Acetonitrile t-BUtyl alcohol

T(K) 233-273 273-303 203-253 253-323 232-305 302-321 321-347

log A,,

E$ ~

-3.63 -3.67 -4.33 -3.85 -3.66 -7.45 -6.43

1.35 1.40 2.73 2.17 1.63 8.27 6.77

log Aobsd

E:bsd

~

12.0720.05 2.1920.05 11.9820.2 2.7220.10" 11.45-CO.2 1.7220.3 13.1720.1 4.7020.4

Source: Table VEI in Ref. 54; A,, in poise, AoM in M-' s-', E's in kcal/mol. "E,'s for benzyl radical self-reaction in toluene (148) and for r-butyl radical in acetonitrile and r-butyl alcohol (6) are 2.99 2 0.72, 2.03 f 0.2, and 5.36 f 0.2, respectively.

Figure 16. Plots of kObd for 31n*-'Az energy transfer vs. k, for t-butyl radicals; lines 1-4 are for t-butyl alcohol, n-pentaneln-heptane, toluenehnzene, and acetonitrile, respectively. The dashed line is drawn with 0 intercept and slope 4. From Ref. 54, reprinted with permission from J . Am. Chern. Soc. (1980), 102,6799. Copyright 1980, American Chemical Society.

58

TRIPLET EXCITATION TRANSFER

59

where t-Bu, Az, and In designate the solutes. Employing truncatedh's for Az and In (Eq. 11) and fullf,'s for r-Bu increases the apparent ( 2 0 ) ~ values ' from 3.6-3.9 to 4.3-4.5 in n-pentane, from 3.1-3.4 to 4.3-4.6 in toluene (185), and from 4.5 20.1 to 6.3 -+O. 1 in acetonitrile (54). The deviations of these values from the expected value of 8 suggest strongly that in this case also triplet excitation transfer, though exothermic by = 8 kcal/mol and though T,T*triplet states in both donor and acceptor are involved (1 86), is nor fully diffusion-controlled. It follows that kobsd = &,if, where p = ken/ke, + k-& '/2 in n-pentane and toluene and p = 34' in acetonitrile. Since p is insensitive to temperature in all solvents employed, it appears that the activation energies of ken and k-dif must be similar. A more quantitative demonstration of this fact can be based on a comparison of rate constants for benzyl radical termination with rate constants for In-Az triplet excitation transfer in toluene (Table 14). Values of p in Table 14, based on the assumption that kdif = 8kt, are probably underestimated by

-

TABLE 14. Comparison of Rate Constants for Benzyl Radical Termination with Rate Constants for In-Az Triplet-Excitation Transfer in Toluene

331 326 3 14 304 298 293 283 277 269 262 256 248 240 235 229 222

33.8 31.4 26.3 22.5 20.4 18.7 15.6 13.9 11.8 10.2 8.9 7.4 6.0 5.3 4.5 3.6

15.3 14.3 12.2 10.6 9.7 8.9 7.6 6.8 5.9 5.1 4.6 3.8 3.2 2.8 2.4 2.0

0.44, 0.44, 0.452 0.45, 0.462 0.466 0.472 0.47, 0.48, 0.49, 0.49, 0.50, 0.51, 0.52, 0.53, 0.54,

9.01 9.06 9.19 9.29 9.35 9.40 9.50 9.56 9.64 9.71 9.77 9.85 9.93 9.98 10.05 10.12

"Based on Arrhenius parameters from data in Ref. 148. bBased on Arrhenius parameters from data in Ref. 54. 'Molar volumes of toluene based on densities from Inrernarional Crirical Tables, McGraw-Hill, New York, 1930, Vol. VII, pp. 29-31.

60

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLED REACTIONS

<15%. since p for benzyl radicals is somewhat larger than p for t-butyl radicals: see Eq. 66 and (185). Basing p on the molar volume of toluene gives In- kdif ken

-=

= In 1-P

P5

In- Adif 4 n

+

Een-Edif

RT

The data are plotted according to Eq. 67 in Fig. 17. As expected, a linear relationship is obtained (2 = 0.9999) which gives (Adif/Aen) = 0.392 M-' and Een - Edif = -0.68 kcaymol. These values, together with the activation parameters for 84, give A,, N 1.28 X lo'* s-l and E,, = 2.31 kcaymol. In view of the 8-kcdm01 exothermicity associated with k,,, this large activation energy was not expected. In the past inefficiencies in exothermic triplet-excitation transfer rate constants, inferred from data at room temperature, have been assigned to the transmission coefficient K,, (173). We stress that the present analysis depends on the assumption that, as in radical self-termination, the encounter distance pet for electronic energy transfer by the exchange mechanism can be approximated as the sum of the radii of the donor and acceptor. If this approximation overestimated petby a factor of 2, then the deviation of the slopes in Fig. 16 from the expected value of 8 would be accounted for, the treatment in Fig. 17 would be invalidated, and the conclusion (54) that triplet-excitation transfer from In to Az is fully diffusion-controlled would stand. In either case, triplet-excitation transfer would not provide a suitable model reaction on which to base kdif values.

-L

9

V

Figure 17. Treatment of the data in Table 14 using Eq. 67.

61

TRIPLET EXCITATION TRANSFER

A very pretty study which illustrates the functioning of spin-statistical factors even though a large fraction of encounter pairs of the proper spin state are dissociative has been described by Wilkinson and Tsiamis (187). It concerns the rate constants for the quenching of the triplet states of a series of organic compounds by chromium (HI) P-diketonates with formulas

R2

Symbol

C6H, CH, t-Bu CF,

Cr(bzac), Cr(acac), Cr(dpm), Cr(hfac),

R, Cr 3

CH, CH3 r-Bu CF,

in benzene. The observed variation of kq with the triplet excitation energy of the donor is shown in Table 15 and Fig. 18, (187). Also shown on the abscissa of Fig. 18 are the energies of the lowest available excited states of the acceptors

TABLE 15. Quenching Rate Constants of Donor Triplet States by Chromium (III) P-Diketonates in Benzene (187)" Dono? Benzophenone Triphenylene Phenanthrene Naphthalene P-Acetonaphthone Chrysene Coronene 1,2,3,4-Dibenzanthracene Pyrene Acridine Anthracene Perylene Tetracene Pentacene @-Carotene "At room temperature. %om Ref. 1 87. 'From Ref. 187a. dFrom Ref. 187b. 'From Ref. 187c.

k,"(109 M - ~ s - ~ )

b

*&I+,

(kcal/mol) Cr(bzac),

Cr(acac),

69.5 66.6 61.8 60.9 58.9 57.2 55.5

4.95k0.20 3.10k0.20

50.9 48.0 45.2 42.0 35.5 29.5 22.9 18.0

1.3220.07 1.80k0.11 1 5 7 2 0.09 1.4820.05 0.23k0.01

Cr(dpm)3

Cr(hfac),

0.89k0.04 0.9220.05

4.52k0.02 8.2k0.4

0.52k0.04 0.38k0.04 0.38k0.04 0.09k0.01

8.220.4 5.220.3 8.2k0.3 8.2k0.4

4.5620.20 2.50k0.15 3.3620.14 1.80k0.13 2.6520.11 1.54k0.09 2.3020.07 1.64kO.10

<0.001 <0.001

1.22 k 0 . 12 1.34k0.11 0.080+0.009 8.2k0.4 1.28 k 0.13 0.075 k 0.009 1.20 k 0.08 1.2520.04 0.075k0.007 4.50k0.2 <0.005 3.95k0.2 0.047k0.01
62

SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS

7.0 10

20

30

40

A +FTIzsO, k c a l l mol-

50

60

7C

(o),

Cr(acac), (m), Cr(dpm),, (O), and Cr(hfac), (0)quenching rate constants on the triplet energies of the donors. Information from Ref. 187. Reprinted with permission from J . Am. Chem. Soc. (1983) 105,767 and J . Phys. Chem. (1981)85,4153. Copyright 1983 and 1981, AmericanChemicalSociety. Figure 18. The dependence of Cxfbzac),

(187). The correlation of quenching constants with donor triplet energy indicates that at least for Cr(bzac),, Cr(acac),, and Cr(dpm), electronic energy transfer is the quenching mechanism. Furthermore, for Cr(bzac), and C r ( a ~ a c the ) ~ ratio of the maximum rate constants attained to those definicg the plateaus in Fig. 18 at 41 s s 52 kcaYmol is very close to three. Since quartet quencher ground states are involved, this observation has been accounted for (187) by

5'D + 4Cr(L)$

3D* -!- 4 C r ( L ) 3 ~ , ~'/.kbr4 ( D C r ( L ) 3 ) * -41

(68)

For donors with triplet energies below 52 kcaVmol only doublet acceptor states are energetically accessible; hence only the doublet encounter pair provides a spin-allowed excitation-transfer channel with a maximum rate constant of 1/6kdif. At higher donor energies excitation to a quartet excited state of the acceptor is also possible and both quartet and doublet encounter pairs can lead to excitation transfer. The combined maximum quenching rate constant when both doublet

TRIPLET-TRIPLET ANNIHILATION

63

and quartet channels are fully functional is (% -t 1/6)kdif= ?hkdif and accounts nicely for the factor-of-three change between the fnst plateau and the beginning of the second. If we base our estimate of kdifon the radical self-reaction rate constants, it is clear that even the kq’s for Cr(bzac), are not fully diffusioncontrolled when corrected for the appropriate spin-.tatistical factor. But even if they were, we can be certain that the rate constants for Cxfacac), and Cr(dpm), do not represent diffusion-controlled processes and are given by kq = ukdip. The differences in quenching efficiencies p between the three quenchers have been attributed to differences in the transmission coefficients for excitation transfer (187). Larger K, values for Cr(bzac), can be associated with the nephelauxetic (e--cloud-expanding) effect of the phenyl group, while the smaller K, values for Cr(dpm), are attributed to the steric effect of the t-Bu groups, which reduces the overlap of orbitals on the triplet donor with orbitals centered on the Cr of the acceptor (187b). It is possible that the initial sharp rise of kq for Cr(dpm), at 56-57 kcaYmol is associated with an increase of 2 ~ , , , the transmission coefficient for formation of doublet excited acceptor due to the presence of the %2g in that energy region as an additional exit channel from the doublet encounter pair (187b). The larger kq values associated with quenching by the much better electron acceptor Cr(hfac), are apparently due to quenching via ion radical pairs (187~).Supporting this proposal is the fact that the dips in the Cr(hfac), curve in Fig. 18 occur when the organic triplet states being quenched are poor electron donors. Apparently in such cases, quenching by exchange energy transfer again predominates (187c). A parallel study with iron (111) 6diketonates as quenchers has also been carried out (188).

VII. TRIPLET-TRIPLET ANNIHILATION Interaction of two excited triplet states of the same molecule in solution is known as triplet-triplet annihilation (TTA) because it provides an important triplet decay pathway. It often gives rise to monomer and excimer delayed fluorescence (189,190). Rate constants for TTA are usually obtained indirectly from the analysis of the second-order component of the decay of triplet-triplet absorption following flash excitation (191-196). Such analyses are generally based on

--d[,A*] dt

= kl[,A*]

+

k2[,~*12

and yield experimental values of K = k&, where et is the molar absorptivity for 3A*, the triplets being investigated, at the monitoring wavelength, and 1 is the path length of sample probed by the monitoring beam (191-196). Since I is known, extraction of k2 from K depends on accurate independent measurements of E,. Unfortunately, the K’S are often obtained using unspecified broad-band

SPIN-STATISTICALFACTORS IN DIFNSIONCONTROLLED REACTIONS

64

probing beams which, though centered at &- for triplet-triplet absorption, represent a range of wavelengths and lead to the replacement of E, in K by an unknown smaller effective absorptivity, T, (196). Nonetheless, early measurements by Livingston and Ware of the temperature and viscosity dependence of K had established that TTA is a diffusion-controlled process (192c). In a study of anthracene triplet decay (3A*), k , , which was apparently controlled entirely by pseudounimolecular diffusion-controlled quenching by residual O,, was shown to be proportional to K over a wide range of temperatures in several solvents (192c). In addition, the slopes of Arrhenius plots of K were found to correspond closely to the activation energies for viscous flow (192c). The calculation of k2 values for 3A* in toluene has been based (196) on the triplet-triplet absorption spectrum of 3A* in benzene (197b). Effective absorptivities7;were determined by integration over the monitoring band profile. represents )* the singlet excimer and the other Use of Scheme 4, where '(a symbols are self-explanatory, gives = k,(2 - pt - ps+is)rwhere p , = (2k, + kgMkt + k g + ksg + kgg + k) andps = k S g K k , + kg + ksg + kgg + k) are the probabilities that the paired triplets, (3A*3A*), will give directly 3A* and 'A*, respectively, and +is = kis/(k, kf ki, +k,[ 'A]) is the intersystem crossing yield of 'A*(196).

+ +

'A

+ hv

'A

3A*

+ 3A*

3A*

+

'A

DIMER Scbeme 4. Kinetics for Triplet Formation apd Decay

To obtain 2 - p , - ps+is,k, was plotted vs. kobd for triplet-excitation transfer from In to Az. It should now be clear that this procedure was based on compensating erroneous assumptions. The two assumptions, namely that (a) triplet-excitation transfer from In to Az is fully diffusion-controlled and (b) it can be taken as an empirical measure of k,, the rate constant for triplet-triplet association, are summarized by koM = kdir = k, (196). However, since TTA is an A A reaction, the proper relationship is k, = Y e .As discussed in the previous section, appreciation of this subtlety also leads to the conclusion Y for the ~n-Az system, and hence a fortunate cancellation of that kob& = & =. k,. errors occurs: kob& =

+

YG

65

TRIPLET-TRIPLET ANNIHILATION

The quantitative treatment of the k2 values for 3A* in toluene can be based on the empirical benzyl-radical termination rate constants. Justification for this assertion is provided by the diffusion coefficients for anthracene (DA)and for toluene, (&), listed in Table 16. As expected, truncated Spernol-Wirtz diffusion coefficients are in satisfactoryagreementwith experimentalvalues for anthracene, whereas full Spernol-Wirtz coefficients agree well with experimental values for toluene (assumed the same as for benzyl radicals). The choice of the value of pB = 5.8 A for benzyl radicals was discussed above; see Table 11 (148). For anthracene Eq. 12 gives r, = 3.47 A and the Van der Waals volume increment method gives rA = 3.41 A (165), leading to an average value of pA = 6.88 A. It can now be seen that due to compensation in the relative magnitudes of the D's and p's, the Dp products predict nearly identical kdif values for these two solutes. The temperature dependence of k2 (196) and kdif, based on 8k, for benzyl radicals (148), in toluene is shown in Table 17. The ratio of k2 to %kdif is relatively insensitive to temperature, decreasing from 0.62 to 0.50 as the temperature is increased from 207 to 318 K. The plot of k2 vs. Y2kdif, Fig. 19, gives 2 - p t = 0.53 +- 0.02 as the slope of the best line through the origin. This value is also obtained directly from the 2k2/kdifratios in the 292-308K range. The results of several determinations give +f = 0.27 & 0.02 (199) = 0.73 f 0.02 (200), independent of solvent, for the fluorescence and and intersystem crossing yields of anthracene at room temperature. Three independent determinations of Pdf = paka/k2, the efficiency of delayed fluorescence of anthracene, have yielded values of 0.077 (201a), 0.08 (201b), and 0.080 (201c) in ethanol. Since Parker has reported that delayed-fluorescence results for

TABLE 16. Diffusion Coefficients for Anthracene and Toluene in Hydrocarbon Solvents, 25OC

Hexane Octane Cyclohexane Methylcyclohexane Benzene Toluene

3.16 2.00 (1.24) 1.61 (1.72) (2.02)

3.54 2.28 1.18 1.62 1.68 1.93

(3.22) 1.58 (2.19) 2.26

3.93 2.83 1.61 1.84 2.28 2.27

"Measured for 'A* (198), except values in parentheses, which are interpolated from plots of Dexp vs. rlrL in Ref. I, ?Based on truncatedA, 4. 11. 'From Ref. 148; for values in parentheses, see footnote a. dBased on fullf,, Eq. 14.

TABLE 17. The Temperature Dependence of k2 for Anthracene in Toluene Set 1

258.2 263.2 268.2 278.2 288.2 298.2 308.2 318.2

2.74 3.09 3.58 4.10 5.04

5.37 6.53 6.93

Set 2

9.55 10.7 11.9 14.5 17.5 20.9 24.6 28.7

207.3 218.1 235.1 246.7 262.1 279.6 292.3

0.71 1.01 1S O 2.19 2.90 3.99 4.97

2.28 3.27 5.38 7.27 10.4 14.9 18.9

“From Ref. 196. % a d on Arrhenius parameters for 8k,for benzyl radicals (148). ‘Adjusted values from Ref. 192c (196).

Figure 19. The dependence of k2 for anthracene triplets on the rate constant for diffusion (44 for benzyl radicals).

66

67

TRIPLET-TRIPLET ANNIHILATION

anthracene in cyclohexane are similar to those obtained in ethanol ( lw c ) , pdf = 0.080 was assumed to apply in toluene; with k21k, = 0.53 it gives p s = 0.042. Substitution of p s and +is into 2 - pt - ps+is = 0.53 then gives pt = 1.44. These revised p s and pt values differ only slightly from those in Ref. 196 and thus do not significantly alter the spin-statistical mechanism presented in that paper. As in the case of triplet quenching by ground-state oxygen, triplet-triplet encounters produce with equal probabilities nine spin states, except that in this case double asterisks indicate that initially these states are doubly excited, having the energy content of two monomer triplets, = 85 kcaymol. The following simple mechanism predicts exactly pt = 1.44: W)k.

'A*

+ 'A*-+,

r (%Via

*(AA)** I no 'A* directly 3(AA)** 4 3(AA)* __* 'A*

+

(70)

'A

It is assumed that all quintet sublevels are completely dissociative giving back both monomer triplets; that the triplet doubly excited pairs undergo internal conversion to dissociativetriplet excimers, thus regenerating one triplet monomer per pair; and that the singlet doubly excited state regenerates no 3A* directly. The overall probability of triplet regeneration according to Q. 70 isp, = 2(%) + 2(%)('/2) = 1.44, which is identical to the experimental value. The dissociative nature of the triplet excimer follows from the fact that only one in lo5encounters of 'A* with 'A leads to quenching (202). From a photochemical point of view, more interesting is the fate of the singlet encounter pairs. Both photodimer formation and anthracene momomer delayed fluorescence could be accounted for as multiplicity-allowed channels from these intermediates. Anthracene photodimerization as a consequence of TTA was first reported by Backstrom and Sandros, who used triplet biacetyl as sensitizer (203,204). The role of 'TTA in dianthracene (A2) formation following direct excitation of anthracene was quantitatively revealed by the strong dependence of +Az on light intensity in degassed, but not in air-saturated benzene solutions (205). Kinetic expressions describing the dependence of +A2 on the concentration of 'A on the steady-state concentration of 3A* and on the light intensity were derived using Scheme 4. An excellent fit of more than 50 +Az values over wide concentration and intensity ranges was obtained to these expressions, employing computer assistance and mainly literature rate constants (205). The fraction of triplet-triplet encounter pairs that give the precursor of the dimer, p: = k2(k, + ktg ksg kgg k:),

-

+

+

+

68

SPIN-STATISTICALFAffORS IN DIFFUSION-CONTROLLEDREACTIONS

was the single derived parameter: ps = 0.115 & 0.007. This value, being indistinguishablefrom the spin-statistical factor of '/9 for formation of the singlet 'IT encounter pair, was taken as strong evidence for associating the singlet pair state exclusively with photodimerization (205). This conclusion appeared to be strengthened by the fact that the rate constant for 'AA* formation directly from 'A* and 'A, k,, inferred from photodimerization quantum yields (206,207) and steady-state (208) and transient (209) 'A* fluorescence measurements in benzene and toluene is nearly identical to rate constants for triplet energy transfer from 31n* to Az (54). Since the latter process was thought to be fully diffusioncontrolled, it was reasoned that anthracene excimer formation was irreversible (196,205,206) and that 'A* was generated by intersystem crossing from 5(AA)* to a dissociative excited excimer state '(AA)*' as had been discussed in a theoretical paper by Krishna (210). The argument, of course, is faulty because it is based on underestimation of the magnitude of as described in detail in Section VI. The conclusion that k, is at most implies that '(AA)* formation is reversible. Since '(AA)* may form from the singlet l T encounter pair '(AG)**, the latter must now be considered as a possible source of 'A*, providing an explanation for delayed monomer fluorescence which does not require intersystem crossing. Before reevaluating the photodimerization data using better estimates of rate constants, a few remarks concerning the mechanism of this reaction are in order. Theoretical treatments of allowed concerted photocycloadditions have predicted that the path to adducts requires crossing from the singly excited excimer into a doubly excited state which correlates with the ground states of addends and adducts (211,212). Avoided crossing between appropriatecorrelationlines creates a pericyclic minimum on the doubly excited surface. This minimum is thought to represent the "funnel" or "hole" through which return to ground state addends and formation of adducts occurs. It is also thought to be the intermediate through which photocycloreversion of adducts to addends occurs. On the addend side the doubly excited state can be represented as arising through interaction of the lowest triplet states of the addends (211,213,214). The complete photodimerization mechanism is shown for anthracene in Fig. 20, and possible sequences of steps summarized in Scheme 5 , where '(AA)&f represents the relaxed doubly excited state at the pericyclic minimum. In terms of Scheme 5, the effective rate constant for singlet-excimer formation, k, in Scheme 4 , becomes k, = k,A(k, + kf, kFdif)/kC k,&kdkC]-' which reduces to the familiar k, = k,&J(k, + k-dif) when ke and k, are small. In the latter case generation of 'A* from the initially formed doubly excited singlet'IT pair could still occur by direct relaxation of '(AA)** to '(AA)*.

+

+

TRIPLET-TRIPLET ANNMILATlON

69

r

REACTION COOROINATE

Figure 20. Potential-energy diagrams showing the two paths for anthracene photodimerization. From Ref. 205, reprinted with permission from J . Am. Chem. SOC. (1983) 105,3413. Copyright 1983, American Chemical Society.

Scheme 5. The Two Pathways to Anthracene Photodimerization

The first column of parameters in Table 18 was the set employed in Ref. 205 in fitting photodimerization quantum yields to the mechanism in Scheme 4. The last, p: = 0.115 & 0.007, was the only derived parameter. Given in the second column are improved estimates of the fixed parameters. As can be seen, the adjustments to pt and p s based on the new analysis of the k2 values are rather small. The value of k, = Y e is based on the benzyl-radical termination rate constant adjusted for the toluene-to-benzene solvent change using the viscosity ratio. Values of k, obtained in benzene at room temperatureare 8.5 X lo9M-' sfrom the dependence of +A on ['A] at high ['A] and low light intensity (207), and more directly, 7.3 x lo4M-' s-' from fluorescence-intensityself-quenching

70

SPIN-STATISTICAL FACTORS IN DIFFUSIONCONTROLLEDREACTIONS

TABLE 18. Parameters Used in Computing Dimer Quantum Yields in Benzene, 30°C

Parameter

Ref. 205

Pt PS PfA k, (M-'s-')

1.40 0.046 0.22 9.6 x 109 9.6 x 109 6.43 x 107 1.74 X lo8 0 49 3.73 x 105 0.115 2 0.007

ke (M-'S - 1 )

kds-')

kis(s-l) kds k:t(s-') k (M-ls-') "p Pe

CIOHIOLl

1.44 0.042 0.22-0.24 1.06 X 10" 8.5 x 109 6.43 x 107 1.74 X lo8 0 2849 3.09 x 105 0.081-0.102

CIODlO(216) 1.44 0.042 0.22-0.24 1.06 X 10" 8.5 x 109 6.43 x 107 2.00 x 108 0 8.549 3.09 x 105 0.053-0.076

This work; see text.

(208), and 7.4 x lo9 M-' s-' from the dependence of 7, on ['A] (209). Since all these values must be adjusted upward for the temperature increase to 30"C, the choice of 8.5 x lo9 M-' s-' is a good compromise. The lower value of k,, is bas9d on new measurements in our laboratory (215) adjusted to 30°C using the activation parameters in Ref. 202. The range of 2 8 4 9 s-l for kzt is established by the lowest values observed in a glassy hydrocarbon medium (216) and in dilute 'A solutions (192c,202,217) respectively. The probability &d that the singlet excimer gives dimer was set at 0.22 or 0.24, literature values for benzene (207) and toluene (206), respectively. The best-fit value of p: is substantially coupled to the choices ofk:, andpd; the lowest value,pL = 0.081, corresponding to kzt = 28 s-' andp, = 0.24, and the highest, p: = 0.102, corresponding to k;, = 49 s-l andp, = 0.22. The range of ps + pe = 0.1234.144 is no doubt within experimental error of % and thus suggests that most, if not all, monomer fluorescence and photodimerization come from '(AA)**. The possible contribution of electron-nuclear hyperfine coupling (HFC) as a mechanism for intersystem crossing between TI' encounter pairs of different multiplicity was strongly suggested by recent resonance-Raman-spectroscopic determinations of k2 = 5.3 X lo9 M-' s-' and 2.1 x lo9 M-' s-' (Eq. 67) for perhydro- (A-h,,) and perdeuterioanthracene (Adlo), respectively, in cyclohexane or ethanol at room temperature (218).* Such a large deuterium isotope effect on k2 implies that the protons in perhydroanthracene enhance the efficiency of triplet destruction by providing a mechanism (HFC?) for intersystem crossing between T f encounter pairs of different multiplicity. Such interconversion would *It is not clear which of the two solvents indicated was employed for these measurements.

71

TRIPLET-TRIPLET ANNIHILATION

invalidate the simple spin-statistical mechanism for A-h,, TTA in Eq. 70, and would suggest that the near-equality of the sum of the derived parameters p i and p , to '/9 may be fortuitous. Fortunately, our own independent measurements of K = k21d in benzene for A-hlo and A-dlo under identical conditions show no deuterium isotope effect on this quantity (219). Since no deuterium effect is expected on et or k,, it follows that there is no deuterium isotope effect on 2 - pt p&. Since the deviation of the latter quantity from 2 is primarily due to pt, the spin-statistical mechanism in Eq. 70 is left intact. We have also shown that there is no deuterium isotope effect on k,, (219). Furthermore, the dependence of A-dIo photodimerization quantum yields on light intensity and ['A-d,,,] is accounted for nicely by Scheme 4 and gives p i = 0.0534.076 (Fig. 21). In

1

Y

0 I

N

7 4

-8

I .o

1;

0.01

I

0

/ /

I 10

[A]-'

0

I

20

I

30

x lo-*, M -

I

40

I

50

I

60

Figure 21. The dependence of A-d,, dimer quantum yields on intensity and [A-d,,]. Points are from independent runs, and lines are drawn through calculated values: (A) I, = 12.0 X einstein s-', I, = 4.5 X einstein s-', (0) I, = 1.9 x lop9 einstein s - ' , (0) I, = 0.31 X einstein s-', (0)in the presence of air. From Ref. 219.

w)

72

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS

deriving p l , the values in the last column of Table 18 were employed for the other parameters. These are identical to those for A-hlo except that for ki,, which was adjusted upward to account for the lower fluorescence quantum yield of A-dlo in benzene (219,220), and k:t, which is substantially lower at 77 K (216). Assuming that p s is unaffected by perdeuteration gives pl p s = 0.10-0.12, in excellent agreement with the expected value of %. It is not clear at this time whether the small difference in p; values for A-hlo and A-dlo is outside experimental uncertainty. If it were, it would allow for a small contribution of HFC induced interstate mixing. A theoretical treatment of the effect of coupling a particle with a nuclear spin of '/z to one of two lightly coupled spin-1 particles predicts that, to the extent that HFC contributes, interstate mixing should be induced between quintet and triplet and between triplet and singlet, but not between quintet and singlet encounter pairs (219). We suspect that as in the case of radical pairs, such intersystem crossing steps will contribute only when structural or medium constraints increase the time of interaction at short distances. However, in the case of biradicals it has been established that at short end-to-end distances spin+rbit coupling dominates over HFC as the intersystem crossing mechanism (22 1). A great deal of TTA work on other arenes has been carried out in ethanol, for which good estimates of kdif are not available. The reader should consult Ref. 196 for a brief review of some of the key papers. In most of the early work a common error is the assumption that k, in Scheme 4 is equivalent to @ instead of Gf.In polar solvents l T A may also produce cation-anion radical pairs. This process should certainly be energetically possible in systems where even the singlet excimer undergoes dissociation to ion radicals. A pertinent example is provided by transient absorption spectra obtained on the picosecond time scale from excited bis(9-anthry1)methane and bis(9-anthry1)carbinol (222). It appears that the intramolecular interaction of 'A* with 'A in these molecules has a strong charge-transfer component leading to full electron transfer in acetonitrile and ethanol (222). The same ion-pair intermediates are obtained by photocleavage of the corresponding intramolecular cycloadducts in these solvents (222). The possibility that quintet encounter pairs may give a quintet monomer excited state and the ground state of the other partner has also been considered (223). However, theoretical calculations suggest that for most arenes quintet monomer states are not energetically accessible from TT encounters involving the same partners (224). A comprehensive study of 1,Zbenzanthracene TTA in n-hexane at 23°C has been reported (225), which allows the calculation of p s and pt and at first glance suggests that the spin-statistical mechanism given for anthracene in Eq. 70 does not apply generally. Algebraic manipulation of Eq. 10 in Ref. 225 shows it to be equivalent to our k2 = (2 pt p,&,)k,, since k, = e / 2 . The value of k2 = 2.03 X 10'' M-' s-' was set equal to the slope of the plot of = kl + k2 r3BA*]) using all but the next to the last set of values in Table 1 of Ref. 225.

+

- -

r(

73

TRIPLET-TRIPLET ANNIHILATION

The value k, = 2.09 X 10" M-' s-' was based on 4k, for t-butyl radicals by adjusting the value obtained in n-heptane to n-hexane using the ratio of solvent viscosities; k, may be 10-20% high due to imperfect Dp compensation in Eq. 6. Together with k2 it gives 2 - p , - ps+is = 0.97. The parameter p , (y, in Ref. 225) can be calculated directly from Eq. 12 in Ref. 225 using the estimated k, value, the experimentally measured value of = 0.72, and the appropriate quantities in Table 1 of Ref. 225. An average value of p s = 0.138 is obtained, the range of seven independent values being 0.,125-0.147. Use of p s = 0.138 and +is = 0.72 gives pr = 0.93. While the p s value is acceptably close to %, p , is too small and if correct would require that, in contrast to anthracene, quintet pair states participate in the destruction of triplets. Such quintet involvement has in fact been suggested to account for a small but significant decrease in k2 as the strength of an applied external magnetic field is increased (223). If, for example, the process

$% 3BA*

+ 3BA*

'(BA*BA)* 3(BAeBA)*

-

'BA*

+

'BA

3BA*

+

'BA

J.

(71)

applied, p , = 0.111 and p , = 0.89 would be predicted and inhibition of the quintet - triplet interconversion for either the pair state or the monomer could account for the magnetic-field effect. Unfortunately, the analysis of the data in Ref. 225 and our own above reinterpretation (factor-of-2 errors aside) suffers from the use of an anomalously high value E, = 4.36 X lo4 M-' cm-' (226) for the 'IT absorption of BA to calculate ,C and Q,,the absorbed incident intensity (Q, = ['BA*]). It also suffers from the assumption that at the two lowest C, values used in this work the k has attained the limiting kl value. As it turns out, all these shortcomings of the treatment of the data in Ref. 215 can be overcome. The 2, value employed, which was based on the estimation of cT by ESR at 77 K in 2-methyltetrahydrof~ran~ has been shown to fail statistical tests when compared with many other E, determinations in the literature (227). On the other hand, E, = 2S6 X lo4 M-' cm-', measured using rotating-sector excitation and singlet depletion in n-hexane at 27°C (228)-conditions nearly identical to those used in Ref. 225-is in excellent agreement with independently measured values in other hydrocarbon solvents (227). Use of this lower E, and Eqs. 6 and 7 in Ref. 225 with +is = 0.72 (228) gives c, = 3.77 x lo-', where the ratio of the voltages is the empirical measure of the steady-state triplet concentration. It is now possible to use the steady-state condition directly:

74

SPIN-STATISTICALFACTORS IN DIFNSION-CONTROLLED REACTIONS

together with the relationship Q, = asN, (where 6, are the transmission factors of the attenuation filters used to alter incident intensity), to obtain least-squares fit parameters of the experimental data. Again excluding the sixth set of data from the analysis because the reported value is anomalously low, we have a = 3.06 X M, k , = 347 s-', and k2 = 1.11 X 10" M-' s-'. Using k, = 2.09 X 10" M-' s-' (see above) gives 2 - pt - ps+is = 0.529, and with k,, our derived parameters, and the appropriate experimental quantities of Table 1, Eq. 12 in Ref. 225 gives p , = 0.0785 & 0.0015. With +is = 0.72 (228), it follows that pt = 1.41. The new pt and p s values are in remarkable agreement with the spin-statistical mechanism proposed for anthracene in Eq. 70. As with anthracene, no delayed excimer fluorescence is observed for 1,2benzanthracene under these conditions (225), and the deviation of p , from % may well be due to decay from the relaxed doubly excited singlet pair state as shown in Scheme 5. A relatively smallp, = 0.092 value for 1,Zbenzanthracene has been estimated from photodimerization results in cyclohexane (229). The 1,2-benzanthracene case illustrates some of the difficulties associated with the evaluation of published TTA data. Undoubtedly, depending upon the availability of quintet, triplet, and excited singlet monomer states at or below the energy of initially formed triplet encounter pairs, exceptions to Eq. 70 and Scheme 5 will be found. The details of the mechanism proposed here may also need to be modified even for anthracene and 1,Zbenzanthracene. A careful study of the spectral distribution of the delayed fluorescence of several arenes (including BA) at -80°C in methylcyclohexane has uncovered significant S, + So (n > 1) components in the emission and has led to the conclusion that population of the highest energetically accessible monomer singlet state is the dominant process occurring from the singlet encounter pair (230). If this were also the prevailing initial step at higher temperatures and lower viscosities, relaxation directly into the doubly excited (pericyclic) minimum would be precluded, as would be the hope of observing enhanced efficiency of TTA-induced photodimerization. Departures from the mechanism in Eq. 70 and Scheme 5 could also be caused when intersystem crossing allows interconversion between encounter pairs of different multiplicity, e.g. Eq. 71. Though the above reevaluation of the 1,Zbenzanthracene data suggests strongly that, at least in n-hexane at room temperature, TTA conforms largely with Eq. 70, a role for intersystem crossing pathways is indicated by significant magnetic-field effects on k2 (223). The higher efficiency of delayed fluorescence from naphthalene TI'A in cyclohexane at room temperature is worth mentioning in this connection (201b). Independent measurements of E, for naphthalene in cyclohexane are in very good agreement (227). Using E, = 2.4 x lo4 M-' cm-' at 414 nm and the flash-kinetically determined K gives k2 = 3.3 X lo9 M-' s-' (201b), from which 2 - pt - ps+is = 0.40 is obtained by assuming k, = 4kt = 8.2 X lo9 M-' s-' from termination of benzyl radicals in cyclohexane at 25°C (148). From the determination of the efficiency of monomer delayed fluorescence (no

75

TRIPLET-TIUPLET ANNIHILATION

excimer fluorescence was observed), pdf = pska/k2 = 0.52, it follows that p, = 0.21. The value of +is for naphthalene is in the range of 0.684.82 in various solvents (200a,231). Using +is = 1 - +f = 0.77 in cyclohexane (12) givesp, = 1.44. Though the mechanism in Eq. 70 predicts p , exactly, it fails to account for ap, value which, being nearly Y9, is twice its predicted maximum. It appears that intersystem crossing at the triplet pair andor monomer stage(s) play(s) an important role in this case. Assuming that all quintet pair states are fully dissociative, the following is one of several mechanisms which would account for the results:

3N*

+ 3N*

3(NN)**

--

3N*

+

'N

(73)

Dimerizations of reactive intermediates such as diarylcarbenes and trimethylenemethanes which have triplet ground states are subject to the spin-statistical considerations which are applicable to TTA. An early example is the formation of tetramesitylethylene from triplet dimesitylcarbene, which was explained as arising from the interaction of two carbenes, one having two a spins and the other two p spins (232). That such reactions can be diffusion-controlledor nearly so was demonstrated by flash-kinetics spectroscopy (233). The disappearance of diarylcarbenes in benzene solution at 25"C, accounted for by Eq. 69, gives k2 = (5.4 k 1.6) x lo9, (3.5 k 1.1) X lo9, and (1.1 I+- 0.3) X lo9 M-' s-' for diphenylcarbene, p,p'-dibromodiphenylcarbene and p,p'-dimethyldiphenylcarbene, respectively, employing 3.0 X lo4M-' cm-' for the molar absorptivity of dibromodiphenylcarbene and 2.5 X lo4 M-' cm-' for the other two (234). To account for the deviation of these rate constants from kdif, it was suggested that quintet encounter pairs are unproductive, triplet encounter pairs may give triplet olefin, and singlet encounter pairs give ground-state olefin (233):

(2Ar2C:)

-

Ar2C=CAr2

Basing k, = 4k, = 9.7 x lo9 M-' s-' on benzyl radical termination in toluene (148), adjustedfor T/q,givesp, = 1.44 +- 0.17, 1.64 f 0.11, and 1.89 2 0.03 for the three carbenes in the same order. The pt's predicted by Eq. 74 range from 1.11, if all triplet pairs gave triplet olefin, to 1.78, if all triplet pairs were

76

SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLEDREACTIONS

unproductive. While two of the pt values fall comfortably within this range, the pt value for the methyl derivative deviates significantly from the others. It is not clear at this time why methyl substitution at a position remote from the reaction site should have such a profound effect on pt. However, the fact that S, -+ TI intersystem crossing for diphenylcarbene in hydrocarbon solvents is a very fast [ki, = 1.05 X 10" s-l(235)], possibly reversible, process may imply substituent dependent interconversion between triplet and singlet carbene pairs in Q. 74. It is of interest to note that the ESR spectra of several triplet carbenes in rigid media at low temperatures (T < 40 K) exhibit weak lines which have been assigned to quintet states arising from spin correlation of nearest-neighbor carbenes (236). The decline of the ESR signal of the trimethylenemethane triplet

3TMM in a 3 :2 mixture of isopropyl and n-propyl alcohols at 143.5 K is cleanly secondorder [ k , = 0, k2 = (2 & 0.8) X lo3M-' s-', Eq. 691 and is associated with the formation of several dimers (237). A very high viscosity, q = 2 x lo3 P, applies under these conditions. Though a good empirical value for kdif in this medium is lacking, k, = 4 4 = 1.9 x lo4 M-' s-' can be based roughly on the termination of hydroxymethyl radicals in methanol (169). It follows that 2 - pt = 0.11 2 0.05,which gives pt = 1.89 4 0.05.If dimers formed only from singlet encounter pairs and if all of these were fully productive, 2 - pt = 0.22 and pt = 1.78 would be expected.

APPENDIX The derivation of a theoretical expression for the rate constant of diffusion along a concentration gradient has been described in a straightforward manner by Collins (238) and Noyes (3), for the reaction A

+B

L

P

(A. 1)

The model assumes that when the two molecules react, the concomitant depletion of their concentration in the vicinity of the reaction leads to a concentration imbalance which is corrected by diffusion of molecules toward the reaction site. This reestablishes a uniform distribution of reactants in solution. The time delay in attaining equilibrium is a function of the diffusivities of the molecules and

APPENDIX

77

their distance from the reaction site. The motion of molecules toward the reaction site is the diffusional flux and has units of number of molecules diffusing per unit of time. If, for example, as in Eq. A. 1 , one molecule of product is formed, then one molecule each of A and B must diffuse into the reaction site for an equilibrium once again to be attained. The applicable relationship, known as Fick’s law, is given for a spherically symmetrical system by 4 d D -dc dr

=

dn dt

where D represents the diffusion coefficients of the reactants, 47r3 is the area of a spherical surface of radius r through which the reactants must pass to reach the reaction site, dnldr or a, the diffusional flux, is the number of molecules crossing the surface of the sphere per unit time, and dcldr is the change in reactant concentration along the radius r . To apply the gradient-flux model it is generally assumed that the reactive center, in this case the molecule A, remains reactive as molecules of B diffuse toward it. It has been pointed out that this assumption requires no leap of faith, since, for example, it applies exactly in the catalytic conversion of B to products

Nonetheless, for the general case represented by Eq. A . l , the condition is not valid, and as Collins states, “After such a reaction there is no longer an A particle at the center, and the concentration gradient so formed seems to have lost its interest” (238). To circumvent this and other difficulties with the model, Collins resorts to a sophisticated mathematical treatment which distinguishes between “reacted” and “unreacted” A and B molecules. Since both simple and sophisticated treatments give the same result, the initial simple model has generally been adopted. Confusion arises when the model is extended to the reaction

Since for both Eqs. A . l and A.4 the model designates A as a permanently reactive center, one B species for Eq. A.l and one A species for Eq. A.4 are assumed to be destroyed for each reactive event. This leads to the conclusion that the diffusional flux for B in Eq. A.l is identical to the diffusional flux for A in Eq. A.4. However, in real reactions where both reactants are destroyed, it is clear that the diffusional flux for A in Eq. A.4 should be twice as large as the flux for B in Eq. A.1.

78

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS

We suggest that the designation of a permanently reactive A center is unnecessary for the derivation. It appears to arise from an attempt to ascribe chemical significance to a coordinate translation which facilitates the mathematical solution. Instead of the permanently reactive A center we assume that a random encounter between the reactantss A and B leads to their concomitant concentration depletion, which initiates a diffusional flux for each toward the reaction site. The origin of our coordinate system is now a concentration hole toward which A and B species diffuse radially. If we shift the origin of our coordinate system from the concentration hole to the nearest A, the resulting mathematical description is identical to that of the older model. The difference is that it is now conceptually clear that the concentration gradient for A in Eq. A.4 will be twice as large as the concentration gradient for B in J3q. A. 1.

The crossing of a molecule B of the sphere with r = p, where p is the sum of the two molecular radii rA and r,, is equivalent to a collision between A and B and is assumed as a necessary and sufficient condition for a reaction to occur. Integration of Eq. A.2 with the boundary conditions r = p and r = w gives

c, - cp =

a) 47FpD

where cp is the concentration of B molecules within the reaction sphere and c, is the concentration of B in the bulk solution, [BJ. The relationship of the diffusional flux to the microscopic reaction rate, i.e. for one reactive center, is given by

where k is the microscopic rate constant. Substitution of Eq. A.6 into Eq. A.5 gives cp =

C,

1

+ (k/41~pD)

The overall observed rate, Robsd,for product formation is given by the loss of B molecules:

where kobsd is the observed rate constant, cA is the concentration of reactive centers, and c, = [B] is, again, the concentration of B in the bulk solution. In

79

APPENDIX

a steady-state system, the flux is just maintained, so that the concentration gradient remains unchanged. In such a situation the flux created by all of the microscopic reaction centers is given by

From Eqs. A.6, A.7, and A.9, a value for kobsd as a function of k and 47rpD is obtained: =

1

+

k (kI47rpD)

47rpDk 47rpD k

+

(A. 10)

Since all collisions are reactive, kobsd is kdif. The term 47rpD is the rate constant for diffusion resulting from the concentration gradient. The microscopic rate constant k is the limiting rate constant for infinitely fast translatory diffusion D = w. In practice k has been assumed to be no greater than the rate constant for collisions in the vapor phase (4). = kdif = 47rpD. If the term 47rpD << k, then Eq. A.10 reduces to This condition applies to most organic solvents in which the diffusivity of the reactants is low. At low viscositiesEq. A. 10 must be used for diffusion-controlled rate constants.

B. A + A + P The major departure from the previous case is that with two A molecules reacting at the reactive center, the diffusionalflux of A molecules toward the concentration hole is twice the microscopic rate of reaction: @ = 2kcp

(A. 11)

Substitution of Eq. A. 11 into Eq. A S yields c,

-

2k cp cp --47rpD

k cp 27rpD

(A. 12)

The observed rate of product formation is half that of reactant loss, (A. 13) Assuming a system at steady state, the flux of A molecules toward the reaction center is twice the rate of product formation:

80

SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED MACTlONS

(A. 14) By combining Eqs. A. 11-A. 14 the observed rate constant can be expressed as a function of 2 ~ p D and k: ed

=

1

+

k (k/2.rrpD)

k

+

2.rrpDk 2npD

=

k$

(A.15)

+

As can be seen, for a system of A A + P the rate constant for diffusion is half that for the A B case, Gt = 1/2kdif, Eq. 4.

+

ACKNOWLEDGMENTS Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of the preparation of this article. Additional support was received through NSF Grant CHE 84-00706.

REFERENCES 1. N. J. Turro, Modern Molecular Photochemistry, Benjamin, Menlo Park, California, 1978. 2. A. M. North, Quart. Rev. 18, 421 (1964). 3. D. M. Bishop and K. J. Laidler, J . Chem. Phys. 42, 1688 (1965). 4. (a) R. M. Noyes, in Progress in Reaction Kinetics, Vol. 1, G . Porter, Ed., Pergamon Press, Oxford, 1961, p. 129. (b) R. M. Noyes, J . Am. Chem. Soc. 86, 4529 (1964). 5 . A. H. Alwattar, M. D. Lumb, and J. B. Birks, in Organic Molecular Photophysics, Vol. 1, J. B. Birks, Ed., Wiley, London, 1973, p. 403. 6. H.-H. Schuh and H. Fischer, Helv. Chim. Acta 61, 2130 (1978) and references cited. 7. A. Spernol and K. Wirtz, 2. Nafurforsch. A 8, 522 (1953). 8. A. Gierer and K. Wirtz, 2. Naturjorsch. A 8, 532 (1953). 9. F. Wilkinson, in Singlet Oxygen, B. Ranby and J. F. Rabek, Eds., Wiley, New York, 1978, p. 27. 10. A. U. Khan, in Singlet Oxygen, Vol. 1, A. A. Frimer, Ed., CRC Press, Boca Raton, Florida, 1985, p. 39. 11. W. R. Ware, J. Phys. Chem. 66, 455 (1962).

REFERENCES

81

12. I. B. Berlman, Handbook of Fluorescence Spectra of Aromatic Molecules, 2nd ed., Academic Press, New York, 1971. 13. R. Potashnik, C. R. Goldschmidt, and M. Ottolenghi, Chem. Phys. Lett. 9 404 (1971). 14. B. E. Algar and B. Stevens, J. Phys. Chem. 74, 3029 (1970). 15. C. S. Parmenter and J. D. Rau, J. Chem. Phys. 51, 2242 (1969). 16. IUPAC Analytical Chemistry Division, Commission on Solubility Data, “Oxygen and Ozone,” in Solubility Data Series, R. Battino, Ed., Vol. 7, Pergamon, Oxford, 1981. 17. P. Pringsheim, Fluorescence and Phosphorescence, Interscience, New York, 1949, p. 333. 18. E. J. Bowen, Trans. Faruday SOC. 50, 97 (1954). 19. L. K. Patterson, G. Porter, and M. R. Topp, Chem. Phys. Lett. 7, 612 (1970). 20. Reference 16, p. 142. 21. J. Saltiel, D. E. Townsend, B. D. Watson, P. Shannon, and S. L. Finson, J. Am. Chem. SOC. 99, 884 (1977). 22. (a) D. F. Evans, J. Chem. SOC. 345 (1953). (b) H. Tsubomura and R. S. Mulliken, J. Am. Chem. SOC.82, 5966 (1960). 23, J. Saltiel, D. E. Townsend, and A. Sykes, J. Am. Chem. SOC. 105,2530 (1983) and references cited. 24. I. B. Berlman, H. 0. Wirth, and 0. J. Steingraber, J. Am. Chem. SOC. 90, 566 (1968). 25. J. Saltiel, D. E. Townsend, B. D. Watson, andP. Shannon, J . Am. Chem. SOC. 97,5688 (1975). 26. B. Stevens and B. E. Algar, J. Phys. Chem. 72, 2582 (1968). 27. Reference 16, p. 150. 28. J. L. Charlton, D. E. Townsend, B. D. Watson, P. Shannon, J. Kowalewska, and J. Saltiel, J . Am. Chem. SOC. 99, 5992 (1977). 29. 0. L. J. Gijzeman, F. Kaufman, and G. Porter, J . Chem. Soc., Faraduy Trans. 2 69, 708 (1973). 30. G. Porter and M. R. Wright, Discussions Faraday SOC. 27, 18 (1959). 31. B. Stevens and B. E. Algar, Ann. N.Y. Acad. Sci. 171, 50 (1970). 32. A. A. Lamola, in Energy Transfer and Organic Photochemistry, A. A. LamolaandN. J. Turro, Eds., Wiley-Interscience,New York, 1969, p. 17. 33. K. Kawaoka, A. U. Khan, and D. R. Kearns, J . Chem. Phys. 46, 1842 (1967); 47, 1842 (1968). 34. W. Siebrand, J. Chem. Phys. 44, 4055 (1966). 35. 0. L. J. Gijzeman and F. Kaufman, J. Chem. SOC., Faraday Trans. 2 69, 721 (1973).

82

SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS

36. J. Saltiel, S. Ganapathy, andC. Werking, J. Phys.Chem. 91,2755 (1987). 37. For a review see J. Saltiel and J. L. Charlton, in Rearrangements in Ground and Excited States, Vol. 3 , P. de Mayo, Ed., Academic Press, New York, 1980, p. 25. 38. H. Gomer and D. Schulte-Frohlinde, J. Phys. Chem. 85, 1835 (1981). 39. J. Saltiel, A. D. Rousseau, and B. Thomas, J. Am. Chem. SOC. 105,7631 (1983). 40. J. Saltiel, G. R. Marchand, E. Kirkor-Kaminska, W. K. Smothers, W. B. Mueller, and J. L. Charlton, J. Am. Chem. SOC. 106, 3144 (1984). 41. J. Saltiel and B. Thomas, Chem. Phys. Lett. 37, 147 (1976). 42. D. V. Bent and D. Schulte-Frohlinde, J. Phys. Chem. 78, 446 (1974). 43. D. V. Bent and D. Schulte-Frohlinde, J. Phys. Chem. 78, 451 (1974). 44. J. Saltiel and B. Thomas, J. Am. Chem. SOC. 96, 5660 (1974). 45. G. J. Hoytink, Accounts Chem. Res. 2 , 114 (1969). 46. W. G. Herkstroeter, J. Am. Chem. SOC.97, 4161 (1975). 47. C. S. Foote and R. W. Denny, J. Am. Chem. SOC. 90, 6233 (1968). 48. P. B. Merckel and D. R. Keams, J. Am. Chem. SOC. 94, 7244 (1972). 49. A. Farmilo and F. Wilkinson, Photochem. Photobiol. 18, 447 (1973). 50. R. A. Caldwell and R. E. Schwerzel, J. Am. Chem. SOC.94, 1035 (1972); 95, 1382 (1973). 51. J. Saltiel, D. W. L. Chang, E. D. Megarity, A. D. Rousseau, P. T. Shannon, B. Thomas, and A. K. Uriarte, J. Pure Appl. Chem. 41, 559 (1975). 52. A. Gamer and F. Wilkinson, in Singlet Oxygen, B. Ranby and J. F. Rabek, Eds., Wiley, New York, 1978, p. 48. 53. A. A. Gorman and M.A. J. Rodgers, Chem. Phys. Lett. 120,523 (1985). 54. J. Saltiel, P. T. Shannon, 0. C. Zafiriou, and A. K. Uriarte, J . Am. Chem. SOC. 102, 6799 (1980). 55. H. Gomer and D. Schulte-Frohlinde, Ber. Bunsenges. Phys. Chem. 81, 713 (1977). 56. H. Gomer, J. Phys. Chem. 86, 2028 (1982). 57. S. Lazare, R. Bonneau, and R. Lapouyade, J. Phys. Chem. 88,18 (1984). 58. H. Gorner, D. W. Eaker, and J. Salliel, J. Am. Chem. SOC. 103, 7164 (1981). 59. H. Gomer, J. Photochem. 19, 343 (1982). 60. T. Arai, H. Sakuragi, K. Tokumaru, Y.Sakaguchi, J. Nakamura, and H. Hayashi, Chem. Phys. Lett. 98, 40 (1983). 61. R. Bonneau, J. Am. Chem. SOC. 104, 2921 (1982). 62. T. G. Truscott, E. J. Land, and A. Sykes, Photochem. Photobiol. 17,43 (1973).

REFERENCES

63. 64. 65. 66. 67.

68. 69. 70. 71.

72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86.

83

R. Bonneau, J. Am. Chem. SOC. 102, 3816 (1980). J. H. Rao, R. Bonneau, and D. I. Schuster, private communication. K. H. Grellmann and P. Hentzschel, Chem. Phys. J A t . 53, 545 (1978). D. Schulte-Frohlinde, H. Herrmann, and G. M. Wyman, Z . Phys. Chem. Neue Folge 101, 115 (1976). S. K. Chattopadhyay, C. V. Kumar, and P. K. Das, Photochem. Photobiol. 42, 17 (1985). D. I. Schuster, D. A. Dunn, and R. Bonneau, J. Photochem. 28, 413 (1985). J. Saltiel, G.-E. Khalil, and K. Schanze, Chem.Phys. Lett. 70,233 (1980). W. G. Herkstroeter, D. P. Specht, and S. Farid, J. Photochem. 21, 325 (1983). (a) R. Bonneau, J. Jousot-Dubien, L. Salem, and A. J. Yarwood, J. Am. Chem. SOC. 98, 4329 (1976). (b) W. G. Dauben, H. C. H. A. van Riel, C. Hauw, F. Leroy, J. Jossot-Dubien, and R. Bonneau, J. Am. Chem. SOC. 101, 1901 (1979). (c) W. G. Dauben, H. C. H. A. van Riel, J. D. Robbins, and G. J. Wagner, J. Am. Chem. SOC. 101, 6363 (1979). T. Arai, H. Sakuragi, and K. Tokumaru, Chem. Lett. 1335 (1980). J. Saltiel and D. W. Eaker, Chem. Phys. Left. 75, 209 (1980). T. Arai, T. Karatsu, H. Sakuragi, and K. Tokumaru, Tetrahedron Lett. 24, 2873 (1983). T. Karatsu, T. Arai, H. Sakuragi, and K. Tokumaru, Chem. Phys. Lett. 115, 9 (1985). H. Gomer and D. Schulte-Frohlinde, Ber. Bunsenges. Phys. Chem. 82, 1102 (1978). H. GornerandD. Schulte-Frohlinde, Chem.Phys. Lett. 66,363 (1979). A. D. Kirsch and G. M. Wyman, J. Phys. Chem. 81, 413 (1977); 79, 543 (1975). J. R. Hurst, J. D. McDonald, and G. B. Schuster, J. Am. Chem. Sac. 104, 2065 (1982). 3. G. Parker and W. D. Stanbro, J . Am. Chem. Soc. 104, 2067 (1982). P. R. Ogilby and C. S. Foote, J. Am. Chem. SOC.104, 2069 (1982). T. Wilson and A. M. Halpem, J. Am. Chem. SOC.102, 7279 (1980). A. Gamer and F. Wilkinson, J. Chem. SOC., Faraday Trans. 2 72, 1010 (1976). A. Gamer and F. WiUcinson, Chem. Phys. Lett. 45, 432 (1977). A. A. Gorman, G. Lovering, and M. A. J. Rodgers, J. Am. Chem. SOC. 100, 4527 (1978). B. E. Holme, E. J. Land, and G. 0. Phillips, J. Chem. Soc., Faraday Trans. Z68, 2003 (1972).

84

SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLEDREACTIONS

87. E. W. Forster and K. M. Grellman, Chem. Phys. Lett. 14, 536 (1972). 88. A. Safarzadeh-Amiri, D. A. Condirston, R. E. Verrall, and R. P. Steer, Chem. Phys. Lett. 77, 99 (1981). 89. See Ref. 12. The quenching of the fluorescence of several indoles in cyclohexane is normal (kzx = k,J and does not reveal any static-quenching contributions. 90. D. V. Bent and E. Hayon, J.Am. Chem. SOC.!37,2599,2606,2612 (1975). 91. H. Ishida and H. Tsubomura, J. Photochem. 2, 285 (1974). 92. R. H. Young and D. R. Brewer, in Singlet Oxygen, B. Ranby and J. F. Rabek, Eds., Wiley, New York, 1978, p. 36. 93. P. B. Merkel and W. G. Herkstroeter, Chem. Phys. Lett. 53,350 (1978). 94. K. C. Wu and A. M. Trozzolo, J. Phys. Chem. 83, 2823 (1979). 95. B. Stevens, K. L. Marsh, and J. A. Barltrop, J. Phys. Chem. 85, 3079 (1981). 96. K. Gollnick, T. Franken, G. Schade, and G. Dorhofer, Ann. N.Y.Acud. Sci. 171, 89 (1970). 97. K. C. Wu and A. M. Trozzolo, J. Phys. Chem. 83, 3180 (1979). 98. P. B. Merkel and D. R. Kearns, J. Am. Chem. SOC. 97, 462 (1975). 99. C. S. Foote and T.-N. Ching, J. Am. Chem. SOC. 97, 6209 (1975). 100. D. F. Evans and J. N. Tucker, J. Chem. Soc., Faraday Trans. 2 72, 1661 (1976). 101. B. Stevens and J. A. Ors, J. Phys. Chem. 80, 2164 (1976). 102. A. A. Gorman, I. Hamblett, and M. A. J. Rodgers, J. Am. Chem. SOC. 106, 4679 (1984). 103. C. N. Knox, E. J. Land, andT. G. Truscott, Photochem. Photobiol. 43, 359 (1986). 104. R. D. Caldwell and H. Misawa, private communication. 105. G. Rossbroich, N. A. Garcia, and S. E. Braslavsky, 1. Photochem. 31, 37 (1985). 106. A. A. Gorman, I. R. Gould, and I. Hamblett, Tetruhedron Left. 21, 1087 (1980). 107. A. A. Gorman, I. Hamblett, and M. A. Rodgers, J. Photochem. 25, 1 15 (1984). 108. K. C. Wu and A. M. Trozzolo, J. Photochem. 10, 407 (1979). 109. S. K. Chattopadhyay, C. V. Kumar, andP. K. Das, Photochem. Photobiol. 24, 1 (1984). 110. S . K. Chattopadhyay, C. V. Kumar, and P. K. Das, Photochem. Photobiol. 42, 17 (1985). 111. G. J. Smith, J. Chem. SOC., Faraday Trans. 2 79, 1 (1983).

REFERENCES

85

112. C. Tanielian, L. Golder, and C. Wolff, J . Photochem. 25, 117 (1984) and 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134.

135.

136. 137. 138.

references cited. A.A.GormanandM.A. J.Rodgers, J.Am. Chem.Soc. 108,5074(1986). E. Reddi, G. Jori, M. A. J. Rodgers, and J. D. Spikes, Photochem. Photobiol. 38, 639 (1983). K. Gollnick, Adv. Photochem. 6, 1 (1968). B. Stevens, J . Phys. Chem. 85, 3555 (1981). D. R. Kearns, J . Am. Chem. SOC.91, 6554 (1969). B. Stevens, J . Photochem. 3, 393 (1974/5). G. 0. Schenck, Naturwiss. 35, 28 (1948); 40,205, 229 (1953). G. 0. Schenck, Angew. Chem. 69, 579 (1957). K. Gollnick and G. 0. Schenck, Pure Appl. Chem. 9, 507 (1964). C. S. Foote and S. Wexler, J. Am. Chem. SOC.86, 3879, 3880 (1964). E. J. Corey and W. C. Taylor, J . Am. Chem. SOC.86, 3881 (1964). C. S. Foote, Acc. Chem. Res. 1, 104 (1968). B. Stevens, Acc. Chem. Res. 6, 90 (1973). G. Quinkert, Pure Appl. Chem. 9, 607 (1964). J. Saltiel and H. C. Curtis, Mol. Photochem. 1, 239 (1969). Y. Sawaki and C. S. Foote, J . Org. Chem. 48,4934 (1983) and references cited. J. Franck and E. Rabinowitch, Trans. Faraday SOC.30, 120 (1934). N. C. Yang, E. D. Feit, M. H. Hui, N. J. Turro, and J. C. Dalton, J . Am. Chem. SOC.92, 6974 (1970). B. Blank, A. Henne, and H. Fischer, Helv. Chim. Acta 57, 920 (1974). H. Schuh, E. J. Hamilton, Jr., H. Paul, and H. Fischer, Helv. Chim. Acta 57, 2011 (1974). M. J. Perkins and B. P. Roberts, J . Chem. SOC. Perkin Trans. II, 297 (1974); 77 (1975). D. M. Bartels, R. G. Lawler, and A. D. Trifunac, J . Chem. Phys. 83, 2686 (1985). J. C. Scaiano, in Landolt 1 Bornstein, Numerical Data and Functional Relationships in Science and Technology, New Series 11, 13e, Radical Reaction Rates in Liquids, Ed. H . Fischer, Springer-Verlag, New York, 1985, p. 294. R. A. Caldwell, T. Majima, and C. Pac, J . Am. Chem. SOC. 104, 629 (1982). J. C. Scaiano, Tetrahedron 38, 819 (1982). R. A. Caldwell, S. N. Ohawan, and T. Majima, J. Am. Chem. SOC. 106, 6454 (1984).

86

SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS

139. H. Kobashi, R. Kondo, H. Ikowa, andT. Morita, Bull. Chem. Soc. Jpn. 57, 1197 (1984). 140. S. Takamuku and W. Schnabel, Chem. Phys. Lett. 69, 399 (1980). 141. R. A. Caldwell, H. Sakuragi, and T. Majima, J . Am. Chem. Soc. 106, 2471 (1984). 142. G. L. Closs and R. J. Miller J. Am. Chem. SOC.103, 3586 (1981). 143. S. C. Frelich and K. S. Peters, J . Am. Chem. Soc. 103, 6255 (1981). 144. M. V. Encinas and J. C. Scaiano, J. Chem. Soc. Perkin Trans. ZZ, 56 (1980). 145. J. L. Gainer and A. B. Metzner, AZCHE-I. Chem. Symp. Ser., No. 6, 74 ( 1965). 146. R. J. Hogemann and H. A. Schwartz, J. Phys. Chem. 71, 2694 (1967). 147. R. D. Burkhart, J. Am. Chem. Soc. 90, 273 (1968); J. Phys. Chem. 7 3 , 2703 (1969). 148. M. Lehni, H. Schuh, and H. Fischer, J. Chem. Kin. 11, 705 (1979) and references cited. 149. P. S. Engel, J. Am. Chem. Soc. 92, 6074 (1970). 150. H. Fischer, B. Blank, and P. G. Mennitt, IUPAC Spec. Lect., 23rd Congress Pure Appl. Chem. 4, 1 (1971). 151. N. J. Turro, M-F. Chow, C-J. Chung, and B. Kraeutler. J. Am. Chem. Soc. 103, 3886 (1981). 152. N. J. TUITO, M-F. Chow, C-J. Chung, Y. Tanimoto, and G. Weed, J . Am. Chem. SOC.103, 4574 (1981). 153. N. J. Turro, C-J. Chung, G. Jones, 11, and W. G. Becker, J. Phys. Chem. 86, 3677 (1982). 154. M. B. Zimmt, C. Doubleday, Jr., and N. J. Turro, J . Am. Chem. SOC. 106, 3363 (1984). 155. W. K. Robbins and R. H. Eastman, J. Am. Chem. Soc. 92, 6076, 6077 (1970). 156. G. Brunton, H. C. McBay, and K. U. Ingold, J. Am. Chem. SOC. 99, 4447 (1977). 157. G. Quinkert, K. Opitz, W. W. Wiersdrorff, and J. Weinlich, Tetrahedron Lett., 1863 (1963). 158. H. Paul and H. Fischer, Helv. Chim. Acra 56, 1575 (1973). 159. T. 0. Meiggs, L. I. Grossweiner, and S. I. Miller, J. Am. Chem. SOC. 94, 7981, 7986 (1972). 160. H. Langhals and H. Fischer, Chem. Ber. 111, 543 (1978). 161. G. J. Kruger and R. Weiss, Z. Naturforsch. A. 25, 777 (1970). 162. D. E. O’Reilly and E. M. Peterson, J. Chem. Phys. 56, 2262 (1972). 163. S. A. Sanni, C. J. D. Fell, and H. P. Hutchinson, J. Chem. Eng. Data 16, 424 (1971).

REFERENCES

87

164. I. Kamal and E. McLaughlin, in Proceedings of the N Symposium on Thermophysicul Properties, Vol. 4, J . R. Moszynski, Ed., American Society of Mechanical Engineers, New York, 1968, p. 278. 165. J. T. Edward, J. Chem. Ed. 47, 261 (1970). 166. J. Lipscher and H. Fischer, J. Phys. Chem. 88, 2555 (1984). 167. H. J. Hefter, C-H. S. Wu, and G. S. Hammond, J. Am. Chem. SOC.95, 851 (1973). 168. (a) H. Paul and C. Segaud, J. Chem. Kin. 12, 637 (1980). (b) H. Paul, Chem. Phys. 15, 115 (1975). 169. H. S . Sandhu, J. Mag. Res. 17, 34 (1975). 170. M. Eigen, Z. Phys. Chem. (Frankjkrt am Main) 1, 176 (1954). 171. P. J. Wagner and I. Kochevar, J. Am. Chem. SOC.90, 2232 (1968). 172. D. Rehm and A. Weller, Ber. Bunsenges. Phys. Chem. 73, 834 (1969); Zsr. J . Chem. 8, 259 (1970). 173. V. Balzani, F. Bolletta, and F. Scandola, J. Am. Chem. SOC. 102, 2152 (1980). 174. A. Weller, Z . Phys. Chem. (Wiesbaden) 130, 129 (1982). 175. R. W. Gurney, Ionic Processes in Solution, McGraw-Hill, New York, 1953. 176. W. R. Ware and J. S. Novros, J. Phys. Chem. 70, 3246 (1966). 177. A. Burshtein, I. V. Khudyakov, and B. I. Yakobson, Prog. Reaction Kinetics 13, 221 (1984). 178. D. L. Dexter, J . Chem. Phys. 21, 836 (1953). 179. K. Sandros, Acta Chem. S c a d . 18, 2355 (1964). 180. W. G. Herkstroeter and G. S. Hammond, J. Am. Chem. SOC.88, 4769 (1966). 181. W. G. Herkstroeter, J. Am. Chem. SOC. 97, 3090. 4161 (1975). 182. A. D. Osborne andG. Porter, Proc. Roy. Soc. London, Ser. A 284,9 (1965). 183. F. S. Dainton, M. S. Henry, M. J. Pilling, and P. C. Spencer, J. Chem. Soc., Faraday Trans. 1, 73, 257 (1977). 184. R. W. Anderson, Jr., R. M. Hochstrasser, H. Lutz, and G. W. Scott, J. Chem. Phys. 61,2500 (1974). 185. A range of 3.6-3.9 is obtained if interpolated& values from the plot of Dexpvs. rlrL in Ref. 7 are employed (54). 186. M. R. Mirbach, V. Ramamurthy, M. J. Mirbach, N. J. Turro, and P. J. Wagner, Nouv. J. Chem. 4, 471 (1980). 187. (a) F. Wilkinson and C. Tsiamis, J. Chem. SOC., Faraday Trans. 11, 77, 1681 (1981). (b) J. Phys. Chem. 85, 4153 (1981). (c) J . Am. Chem. SOC. 105, 767 (1983). 188. F. Wilkinson and C . Tsiamis, Znorg. Chem. 23, 3571 (1984).

88

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS

189. B. Stevens and E. Hutton, Nature (London) 186, 1045 (1960). 190. (a) C. A. Parker and C. G. Hatchard, Proc. Chem. Soc., 147 (1962). (b) Trans. Faraday SOC. 59, 284 (1963). (c) C. A. Parker, Adv. Photochem. 2, 305 (1964). 191. (a) H. Linschitz and K. Sarkanen, J . Am. Chem. SOC. 80, 4826 (1958). (b) H. Linschitz and L. Pekkarinen, J. Am. Chem. SOC.82,2411 (1960). (c) H. Linschitz, C. Steel, and J. A. Bell, J. Phys. Chem. 66,2574 (1962). 192. (a) G. Jackson, R. Livingston, and A. Pugh, Trans. Faraday SOC.56, 1635 (1960). (b) G. Jackson and R. Livingston, J. Chem. Phys. 35, 2182 (1961). (c)R. Livingston and W. R. Ware, J. Chem. Phys. 39,2593 (1963). 193. G. Porter and M. Wright, J . Chim. Phys. 705, 2593 (1958). (b) Discuss. Faraday SOC.27, 18, 94 (1959). 194. A. R. Watkins, 2. Phys. Chem. (Frankfurt am Main)96, 125 (1975). 195. K. H. Grellmann and H.-G. Scholz, Chem. Phys. ktt. 62, 64 (1979). 196. J. Saltiel, G. R. Marchand, W. K. Smothers, S. A. Stout, and J. L. Charlton, J. Am. Chem. SOC.103, 7159 (1981). 197. (a) R. Bensasson and E. J. Land, J. Chem. Soc., Trans. Faraday SOC. 67, 1904 (1971). (b) M. B. Ledger and M. B. Salmon, J. Chem. SOC., Faraday Trans. 2, 72, 883 (1976). 198. E. G. Meyer and B. Nickel, 2. Naturforsch. 35a, 503 (1980). 199. (a) W. R. Dawson and M. W. Windsor, J. Phys. Chem. 72, 3251 (1968). (b) J. B. Birks and D. J. Dyson, Proc. R. SOC.London, Ser. A 275, 135 (1963). (c) G. Weber and F. W. J. Teale, J . Chem. Soc., Trans. Faraday SOC.53,646 (1957). (d) W. H. Melhuish, J. Phys. Chem. 65,229 (1961). 200. (a) A. R. Horrocks and F. Wilkinson, Proc. R. SOC.London, Ser. A 306, 257 (1968). (b) 7’.Medinger and F. Wilkinson, Trans. Faraaky SOC. 61, 620 (1965). (c) R. P. DeToma and D. 0. Cowan, J. Am. Chem. SOC. 97, 3283 (1975). 201. (a) K. Kikuchi, H. Kokubun, and M. Koizumi, Bull. Chem. SOC.Jpn. 41, 1545 (1968). (b) F. Tfibel and L. Lindqvist, Chem. Phys. 10,471 (1975). (c) D. K. K. Liu and L. R. Faulkner, J. Am. Chem. SOC.100,2635 (1978). 202. J. Saltiel, G. R. Marchand, R. Dabestani, and J. M. Pecha, Chem. Phys. Lett. 100, 219 (1983). 203. H. L. J. Backstrom andK. Sandros, Acra Chem. Scad. 12,823 (1958). 204. J. Saltiel, Sum. Prog. Chem., 2 , 239 (1964). 205. J. L. Charlton, R. Dabestani, and J. Saltiel, J. Am. Chem. SOC. 105, 3473 (1983). 206. T. Vember, T. V. Vaselova, I. E. Obyknovennaya, A. Cherkasov, and V, Shirokov, Izv. Akad. Nauk SSSR, Ser. Fiz. 37, 837 (1973). 207. J. Saltiel, D. E. Townsend, B. D. Watson, P. Shannon, and S. L. Finson, J . Am. Chem. SOC. 99, 884 (1977).

REFERENCES

208. 209. 210. 21 1. 212.

213. 214. 215. 216. 217. 218. 219. 220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233.

89

E. J. Bowen, Trans. Faraday SOC. 50, 97 (1954). W. R. Ware, J. Am. Chem. SOC.83, 4374 (1961). V. G. Krishna, J. Chem. Phys. 46, 1735 (1967). (a) J. Michl, Pure Appl. Chem. 41,507 (1975). (b) Photochem. Photobiol. 25, 141 (1977) and references cited. For early work see especially: (a) H. C. Longuet-Higgins and E. W. Abrahamson, J. Am. Chem. SOC.87,2045 (1965). (b) H. E. Zimmerman, J. Am. Chem. SOC. 88, 1566 (1966). (c) W. Th. A. M. van der Lugt and L. J. Oosterhoff, J. Am. Chem. SOC.91, 6042 (1969). B. Stevens, Chem. SOC. Ann. Reports A , 29 (1974). R. A. Caldwell, J. Am. Chem. Soc., 102, 4004 (1980). J. Saltiel, S. Ganapathy, and B. W. Atwater, J. Am. Chem. SOC. 109, 1209 (1987). B. R. Henry and J. L. Charlton, J. Am. Chem. SOC.95, 2782 (1973). K. H. Grellmann and H.-G. Scholz, Chem. Phys. Lett. 62, 64 (1979). G. N. R. TripathiandM. R. Fisher, Chem. Phys. Lett. 104,297 (1984). J. Saltiel, B. W. Atwater, R. Dabestani, and R. Northup, unpublished results. E. C. Lim and H. R. Bhattacharjee, Chem. Phys. Lett. 9, 249 (1971). E. C. Lim and H. R. Bhattacharjee, J. Chem. Phys. 55, 5126 (1971). M. B. Zimmt, C. Doubleday, Jr., and N. J. Turro, J. Am. Chem. SOC. 108, 3618 (1986), and references cited. L. E. Manring, K. S. Peters, G. Jones, 11, and W. R. Bergmark, J. Am. Chem. SOC.107, 1485 (1985). See, e.g.: J. Spichtig, H. Bulska, and H. Labhart, Chem. Phys. 15, 279 (1976). K. Lendi, P. Gerber, and H. Labhart, Chem. Phys. 18,449 (1976); 20, 145 (1977). B. Dick and B. Nickel, Chem. Phys. 78, 1 (1983). H. Staerk, J . Lumin. 11, 413 (1976). J. S. Brinen, J. Chem. Phys., 49, 586 (1968). I. Carmichael and G. L. Hug, J. Phys. Chem. Ref. Data 15, 1 (1986). W. Heinzelmann and H. Labhart, Chem. Phys. Lett. 4, 20 (1969). A. Costellan, Ph.D. Dissertation, University of Bordeaux I, Bordeaux, France, 1974. B. Nickel, Hetv. Chim. Acta 61, 198 (1978). F. Wilkinson, in Organic Molecular Photophysics, Vol. 2, J. B. Birks, Ed., Wiley, London, 1975, p. 95. H. E. Zimmerman and D. H. Paskovich, J. Am. Chem. SOC.86, 2149 (1964). G. L. Closs and B. E. Rabinow, J. Am. Chem. SOC.98, 8190 (1976).

90

SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS

234. A. M. Trozzoloand W. A. Gibbons, J . Am. Chem. SOC.89,239(1967). 235. (a) K. B. Eisenthal, N. J. Turro, M. Aikawa, J. A. Butcher, Jr., C. DuPuy, G. Hefferon, W. Hetherington, and M. J. McAuliffe, J . Am. Chem. SOC. 102, 6563 (1980). (b) E. V. Sitzmann, J. Langan, and K. B. Eisenthal. J . Am. Chem. SOC.106, 1868 (1984). 236. H. Murai, J. R i b , M. Torres, and 0. P. Strausz, J . Am. Chem. SOC. 103, 6422 (198 1) and references cited. 237. M. S. Platz and J. A. Berson, J . Am. Chem. SOC.98, 6743 (1976). J. A. Berson, Acc. Chem. Res. 11, 446 (1978). 238. F. C. Collins and G. E. Kimball, J . Colloid Sci. 4, 425 (1949).

Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS James Guillet Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 1Al

CONTENTS I. Introduction II. Molecular motion in polymeric solids 111. Diffusionin polymericsolids Iv. Theory of diffusionand permeabilityin polymers V. Solubilityand diffusion VI . Temperature coefficientsfor diffusion VII. Cage reactions VIII. The internal viscosity of polymeric solids Ix. Studiesof cage reactions in polymers X. Photochemistryof polymerscontainingketone groups XI. Polymersfor photolithography XII. Sy nchrotron-radiationstudies xIII. Polyacrylophenones XIV . The photo-Fries reaction xv. Cis-trans isomerization XVI. Photocyclization XVII . Conclusions References 91

Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.

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I. INTRODUCTION The purpose of this chapter is to review the kinetics and mechanisms of photochemical reactions in amorphous polymer solids. The classical view for describing the kinetics of reactions of small molecules in the gas phase or in solution, which involves thermally activated collisions between molecules of approximately equivalent size, can no longer be applied when one or more of the molecules involved is a polymer, which may be thousands of times more massive. Furthermore, the completely random motion of the spherical molecules illustrated in Fig. la, which is characteristic of chemically reactive species in both gas and liquid phase, must be replaced by more coordinated motion' when a macromolecule is dissolved or swollen in solvent (Fig. lb). Furthermore, a much greater reduction in independent motions must occur when one considers a solid polymer matrix illustrated in Fig. lc. According to the classical theory of thermal reactions the collisional energy available in the encounter must be sufficient to transfer at least one of the reacting species to some excited-state complex from which the reaction products are derived, The random thermal motion thus acts as an energy source to drive chemical reactions. The restrictions on motion described in Fig. 1 will not alter the average thermal energy of the system, but may result in a different distribution of energy between colliding partners. For example, it may require more collisional energy to induce the excited state in a large polymer molecule which has many degrees of freedom than in a small molecule which has fewer alternative modes of dissipating the energy. Another factor which affects the reactivity of polymer molecules is that the reactants must be expected to achieve a particular geometrical relationship with respect to each other in order to form the excited complex from which reaction occurs. If mobility is severely restricted, this geometry may not be achievable within the lifetime of the excitation, and chemists not familiar with macromolecular reactions might assume that the restrictions of motion in the solid state would be so great that reaction would not occur at all. In fact, this is not the case, and there are many examples of photochemical reactions which are just as efficient in solid polymers as they are in dilute solutions of small-

(a1

(b)

(C)

Figure 1. Restrictions on mobility caused by polymer structure: (a) solution; (b)polymer solution; (c) polymer bulk.

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93

molecule analogs. On the other hand, as we will see, there are a number of reactions which are completely inhibited in the solid phase. The key to understanding these effects is to determine how much movement of atoms is required in order to form the geometry of the excited or transition state and to allow separation of products. Reactions differ in these respects, and so one can expect to observe different effects when we study chemical reactions in polymeric systems. To answer these questions we must first understand the kinds of motions which occur in polymeric solids.

11. MOLECULAR MOTION IN POLYMERIC SOLIDS Polyatomic molecules in the gas phase undergo three types of motion: translation, vibration, and rotation. The latter two are quantized, giving rise to spectra; those corresponding to vibration are usually observed in the infrared, whereas those for rotation are normally observed in the microwave region. Electronic spectra, when carefully analyzed, also contain information about both the vibration and rotation of small molecules. Extensive studies of the infrared spectra of polymeric materials in both solution and the solid phase have shown that, in general, the vibration of small groups such as the bending and stretching modes of C=O, and stretching of C-H, C-Cl and C f N are almost unaffected by the presence of the polymer environment. For this reason, infrared spectra can be used to analyze polymer structures and composition because the location of the bands is usually much the same as in small-molecule analogs. However, the rotation spectra of polymeric molecules are much more complex, since they will include rotations not only of the very large polymer itself but also of segments of the molecule and side chains. The rate of these processes will depend very much on the molecular architecture and the flexibility of the polymer chain as well as the viscosity of the medium. For flexible chains in solution, rotation is primarily due to sequential movements of segments of the chain (Fig. 2). These segments are not necessarily defined by the monomer unit from which the polymer is derived, but in hydrocarbon polymers often consist of segmentsof 20 to 50 carbon atoms in length. Segment motion occurs both in dilute solution and in the solid amorphous phase, provided the polymer is above its glass transition, Tg.This characteristic temperature of all amorphous polymers will be considered later. It can be defined for our purposes as the temperature below which this type of coordinated segment motion can no longer occur. An important kinetic difference between a polymer molecule in solution and the same molecule in an amorphous solid phase is that in dilute solution there can be a net translational motion of the center of mass of the polymer as in Fig. 2u, whereas in the solid the rate of this process is exceedingly slow.

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PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

(a1 <-

(C

Figure 2. Types of motion in polymer molecules: (a)translational; (b) segmental rotation; (c) group rotation. Reprinted, with permission, from J. E. Guillet, Polymer Physics and Photochemistry, Cambridge University Press, Cambridge, England, 1985, p. 2.

In the amorphous phase of macromolecules having some degree of chain flexibility we can consider that the solid consists of a large number of interpenetrating flexible chains that approximate a random coil configuration. If such a polymer were cooled slowly to absolute zero, it would be expected that it would achieve its most stable geometry in closest packing corresponding to the lowest-free-energy state. However, because of the large macroscopic viscosity of the solid polymer, it seldom achieves this packing density in finite times unless it undergoes crystallization at a relatively high temperature. As a result, even at absolute zero, the polymer matrix will contain some “free volume.” Free volume in this context could be defined as the space unoccupied by atoms because the maximum packing density cannot be achieved. At 0 K, of course, this free volume will be relatively small, and because there is no energy to activate the molecules, they will not occupy the space. However, as the temperature is increased, thermal motion will begin and the solid will expand. This expansion creates additional free volume and allows small-scale rotations or oscillations of atoms or groups of atoms. The change in specific volume of an amorphous polymer as a function of temperature is shown in Fig. 3. As the free volume increases, the motion of particular groups of polymers is observed at various temperatures which are known as “transition temperatures.” Such solid phase transition temperatures

MOLuluLAR MOTION IN POLYMERlC SOLIDS

I

0

I

150

L

,

I

300

T (K)

t

I

1

450

95

I

600

Figure 3. Specific volume and “free volume” of a polymeric solid.

can be detected by a variety of physical measurements on the polymer, including dielectric relaxation and thermal or mechanical deformation (1). The point designated by Ty in Fig. 3 represents the temperature at which sufficient free volume is available in polystyrene, for example, to observe the motion of phenyl rings at a fkquency of about 10 Hz.As the temperature is raised still further, additional free volume becomes available. At a point indicated by Tg a change in the slope of the specific-volume-temperature curve is observed, which is due to the beginning of the motion of the very long segments of the polymer chain referred to previously. Motion observable below Tg in solid polymers will vary with the chemical nature of the polymer. Specific motions which have been identified in polymer systems, including rotations of phenyl, methyl, carboxyl, carboxylicester, nitrile, and keto groups, as well as conformational transformations. At temperatures above Tgthe motion of flexible chains becomes very rapid and the conformational mobility appears to be nearly as great as if they were dissolved at high dilution in good solvent (2). However, not all transitionsin solid polymers can be identified with specific groups in the chain, for example, those relating to coordinated motion of the backbone atoms such as the so-called “crankshaft motion” in polyethylene. A number of flexible polymer chains can crystallize with a high degree of order and if properly annealed can actually form single crystals. The regular packing of the polymer chain in the crystal and the strength of the lattice interactions are such that penetration of the crystalline region by other molecules is drastically reduced and the free volume required for chemical reaction is usually not available. As a result, chemical reactions in semicrystallinepolymers such as polyethylene will occur primarily in the amorphous phase or at crystal boundaries where sufficient free volume is available. Exceptions to this general rule are photochemical reactions such as those studied by Wegner (3), in which the lattice dimensions of the product are almost identical to that of the reagent crystal, and hence only very small amounts of free volume are required for the transformation to occur.

96

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

A number of important chemical reactions occur in polymer gels, which can be part of membranes or swollen crosslinked polymers. In a typical gel the polymer may represent only 10 or 20% of the total weight of the material, the remainder being made up of solvent molecules. However the gel may appear to be completely solid. In gels it is important to remember that much of mobility and molecular motion is imparted by the solvent rather than by the polymer, and reactions in gels containing a major amount of solvent usually occur with nearly the same velocity as in the pure solvent alone.

III. DIFFUSION IN POLYMERIC SOLIDS The kinetics of many photoprocesses in solid polymers will depend on the rate of diffusion of one or more molecular species. The theory of diffusion-controlled processes has been well developed for reactions in gases and conventional liquids. However, the special nature of polymer solutions requires further consideration. Diffusion in solid polymers occurs as a result of molecular motion under a chemical or physical potential. Whereas in simple liquids diffusion occurs primarily as a result of translational displacements of small molecules, the situation is much more complex in a solid polymer matrix. All of the motions in a polymer chain and its side groups referred to in the previous section will be involved in the diffusion of small molecules through the polymer. With small diffusant molecules such as the permanent gases (e.g.. oxygen, nitrogen, hydrogen, carbon dioxide, and argon) diffusion can occur in solid polymers at temperatures well below the glass transition temperature. It is believed that the translational motion of these molecules in the polymer matrix is assisted by the formation of thermally activated packets of free volume that are caused by small-scale motion of polymer segments or the librational movement of groups attached to the side chains. Bueche (4) has proposed a theory which relates the diffusion constant D to a frequency by the jump distance 6 through

It is expected that the jump distance 6 will be relatively constant from one polymer to the next, and that variations in the diffusion constant are caused primarily by differences in the jump frequency This frequency depends on the probability of collecting a sufficient number of packets of free volume to give a hole of volume v* of sufficient size that the diffusing molecule can move into it. The creation of a hole in the polymer requires the expenditure of a certain quantity of energy Eh, and the probability of forming such a hole can be calculated from Boltzmann statistics to be proportional to exp( -Eh/RT). Application of this theory to both polymeric and small-molecule liquids has given jump distances 6 which correspond roughly to the dimensions of small molecules (i.e., 2-20

+.

97

DIFFUSION IN POLYMERIC SOLIDS

A) and typical jump frequencies ranging from lo4 to lo6 per second. These and

other free-volume theories are described in more detail in Crank and Park (5). The important concept that is central to all free-volume theories is that diffusion occurs in polymers through free volume obtained by minor displacements of side groups or segments of the chain but without net translational displacement of the center of mass of the polymer. As discussed previously, the larger-scale segmental motions which occur above the glass transition impart relatively large amounts of free volume to the system, and the activation energy for diffusion in polymers is significantlyhigher than for conventional small-molecule liquids. As a result of these two factors, the rates of diffusion of small molecules in polymeric solids above the glass transition are often only one or two orders of magnitude below those in ordinary liquids. Amorphous polymers are thus not viscous media in the conventional sense, because the diffusing penetrants are not affected by the motions of the center of mass but only by segment mobility. For example, measurements of the diffusion of naphthalene in polyethylene at 80°C by Heskins and Guillet (6) show an effective viscosity (q,& of about 1 poise, which is slightly higher than that of ethylene glycol but lower than that of glycerin (Table 1). This so-called microviscosity of polymer systems is many orders of magnitude lower than that which would be predicted from the macroscopic properties of the polymeric solid. For example, in solid polyethylene the macroscopic viscosity (q) would be of the order of 10" poise. This important principle has gone unrecognized in many studies of polymer photophysics and photochemistry. As a polymer chain is crosslinked, the coordinated segment motion available for the permeation is reduced, with a consequent reduction in the diffusion constant. However, the macroscopic properties of the polymer are affected more than diffusion. Crosslinking has very little effect on diffusion until the crosslink density exceeds about 3% (7).

TABLE 1. Internal Viscosities qht and kaurforReaction in Various Media at 20°C" kdiff

(L mol-' s-')

Medium

q,,t(piSe)

Hexane Benzene Toluene Ethylene glycol Polyethylene Glycerin

3.1 x 6.5 x 10-3 5.9 x 10-3 0.2 lob

2x 1x 1 x 4x 1x

1o'O 1o'O 10'0

11

6

lo6

%om Ref. 6. bExtrapolated from data at 80°C.

X

108

107

98

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

IV. THEORY OF DIFFUSION AND PERMEABILITY IN POLYMERS The simplesttheory of diffusion in isotropic substances is based on the assumption that the rate of transfer between diffusing molecules through unit cross-section area is proportional to the concentration gradient:

where F is the flux (i.e., the rate of transfer per unit area cross section), c is the concentrationof diffusing substance, and x is the space coordinate measured normal to the section. D is known as the diffusion coefficient, and in the simplest case (Fickian diffusion) is independent of c. If F and c are expressed in the same units, D has dimensions of t2/rand is usually expressed in units of cm2/s. In the case of three-dimensional diffusion through a volume element where D is constant, the fundamental differential equation for diffusion is given by ac

a2c

a2c

- at= D ( T + T

+

A) a2

(3)

Where D is not independent of c, the most general form of the fundamental equation becomes

-= at

div(grad c)

(4)

For diffusion across films or membranes the concentration gradient can often be treated as unidirectional (Le., along the x-axis), in which case Eq. 3 becomes -ac= at

This is known as Fick’s second law.

DS

For a plane sheet or membrane of thickness C whose surfaces are exposed to constant concentrations c1 and c2 of penetrant, a steady state will be reached where the rate of transfer F across all sections is constant and given by

SOLUBILITY AND DIFFUSION

99

In some cases in which a gas or vapor diffuses through a membrane, the surface concentrations may not be known, but provided that Henry’s law is obeyed, c will be proportional to the partial pressure of the gas; thus c =

sp

(7)

where p is the partial pressure and S is called the “solubility” or “solubility coefficient.” The flux under these conditions is given by

where Pis called the permeability, or permeabilitycoefficient,and is given by

P = DS

(9)

V. SOLUBILITY AND DIFFUSION It is important to note that the rates of reactions in solid polymers will be controlled not only by the rate of diffusion but also by the solubility of the permeant in the polymer. For example, the diffusion constant for oxygen is quite large in many polymers, but usually the solubility is very low, and as a result, rates of oxidation tend to be quite small. Experimentalvalues of the permeability P and diffusion constant D for various organic permeants and oxygen in lowdensity polyethylene (8) illustrate this point (see Table 2). The concentration of diffusant, c, is given by c =

P g p

Thus at a given partial pressure p of the diffusing species, one can calculate that the concentration of benzene in polyethylene, for example, would be approximately 3 x lo4 times as great as that of oxygen, thus giving rise to a permeability some two orders of magnitude greater for benzene than for oxygen, in spite of its larger molecular volume. It is possible to determine the diffusion constants and solubilities for organic compounds in polymers by a number of physical methods. Classical methods are well reviewed by Crank and Park (5). More recent methods involving luminescence and inverse gas-liquid chromatography have been reviewed by Guillet (9).

100

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

TABLE 2. Diffusion Constants (0)and Permeabilities (P)for Small Molecules in Low-Density Polyethylenea

Permeant Oxygen Decane Benzene Hexane Carbontetrachloride Ethyl alcohol Ethyl acetate

D X lo6 (cm2s-') 460

3.5 8.2

P x 1010 [cm3(STP)cm

cm-2

s- 1 cmHg-'1

2.9

&W

-

5300 2910 3810

-

513

-

56

Source: Ref. 8.

VI. TEMPERATURE COEFFICIENTS FOR DIFFUSION Since diffusion is a thermally activated process involving small scale translational motions in the penetrant or segment motion in the polymeric medium, the diffusion constant can be expressed in Arrhenius form:

where D, and Ed are the preexponential factor and the activation energy of diffusion, respectively. Typical values for the activation energy Ed for the selfdiffusion of small solvent molecules in conventional liquids are 8-12 kJ/mol, while diffusion in polymeric solids usually shows higher values, ranging from about 20 to 80 kJ/mol. This seems to be related to the greater energy required to displace large polymer segments to provide holes for the diffusing penetrant. Typical values for diffusion constants and activation energies for gases in natural rubber, polyethylene, and polystyrene are shown in Table 3. It can be seen that as the size of the penetrant increases, the diffusion constant decreases but the activation energy increases. As a result, at high temperatures, the rate of diffusion of gases in molten polymers will not be very different from that for conventional liquids. At ambient temperature (25"C), however, values for the rates of gaseous diffusion in ordinary liquids are typically about two orders of magnitude greater than in polymers. For example, for oxygen in cyclohexane, D = 5.3 X cm2/s at 30 "C, as compared with 4.6 x lo-' in low-density polyethylene at the same temperature.

101

CAGE REACTIONS

TABLE 3. Diffusion Constants and Activation Energies for Gases in Polymers at 25°C

Polymer

Gas

Natural rubber (cis-polyisoprene) (amorphous) T = -60°C Polyethylene (semicrystalline) T = -40°C

T = 80°C

DA

(tdmol-’)

216 15.8 11.0 8.9

0.031 1.94 3.7 1.97

18 35 37 36

68 4.6 3.7 1.9

(d = 0.914)

Polystyrene (glassy)

D x 10’ (cm2s-‘)

He

0 2

co2

104 1.1 0.58

0.13 4.48 1.85 17.2 0.0019 0.125 0.128

Ed

25

40

38 46

13 35 36

Source: Reprinted, with permission, from J. E. Guillet, Polymer Physics and Phorochemistry, Cambridge University Press, Cambridge, England, 1985, p. 55.

Luminescence procedures present a powerful method for the determination of diffusion constants for a variety of penetrants in polymer systems, and have been reviewed recently (9).

VII. CAGE REACTIONS The concept of the “cage reaction” is often invoked in polymer chemistry to explain observed differences in reactivity between polymers and small molecules. It is proposed that restrictions on mobility in the solid phase prevent the separation of reactive species, thus causing them to recombine to form the original reactant. The result is a reduction in the efficiency or quantum yield of the process in question. The original concept of cage processes, due to Franck and Rabinowitsch (lo), was invoked to explain the reduction in quantum yields which occur on the photolysis of simple molecules like acetone and iodine when carried out in solution as compared to the gas phase. Extensive studies were carried out by Noyes (11) during the 1950s and 1960s to develop a theoretical understanding,

102

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

Rinwry cage

recombhotion

(a)

Secondary cage recombination (b)

Figure 4. Scheme showing (a) primary and (b) secondary cage recombination.

but it was not until the development of picosecond lasers that the early stages of the processes of separation could be probed experimentally. It is now known that in the dissociation of two radical species, for example, recombination will occur in the primary cage in times from 10 to 100 ps (12). The situation is shown schematically in Fig. 4. The primary radical pair separates with a velocity dependent on the amount of excess energy partitioned into translational velocity along the axis defined by their centers of mass. This translational energy is exchanged by momentum transfer with the surrounding solvent molecules. If, as a result of these first collisions, they rebound to a position where they are within a distance of u of each other, where u is the radius for reactive collision of the species, they will recombine to reform the initial reactant. In iodine atom dissociation this process occurs in about 50 ps. If, on the other hand, their energy is great enough to displace one or more solvent molecules to produce a pair of radicals separated by at least one solvent molecule, then a random diffusion will occur. Because the local concentration is high, there is still a good possibility (> 50%) that the two particles will diffuse to adjacent sites and recombine. This is called “secondary cage recombination,” even though it has nothing to do with restriction of motion by a solvent cage, but is primarily an effect due to the nonuniform distribution of radical species. The probability of reaction depends on the rate of diffusion of the radicals in the medium, the concentration of radicals from other dissociating molecules, and alternative reaction paths, such as H-atom abstraction from the solvent. Many authors have assumed that because of restrictions in mobility in solid polymers, dissociating radicals would undergo efficient recombination in the primary cage. Recently, Moore and Guillet (13) studied the quantum yield for photolysis of benzoyl peroxide in two solvents, benzene and toluene, and in solid polyethylene and polystyrene films:

THE INTERNAL VISCOSITY OF POLYMERIC SOLIDS 0 @ ! ! O O - ! ~

0

103

0

k> 2 W o ->

Products

(12)

In both the solids and in liquid solution the quantum yields were uniformly high ( S 0.8). indicating that primary cage recombination represented at most 20% of the total and did not depend on either the bulk or the microviscosity of the medium. Presumably the separating radicals exchange momentum only with small segments of the polymer chain, and the motion which can occur in the short time scale of the primary cage recombination (10-100 ps) cannot be influenced by the polymeric nature of the solvent. There was also no difference between the quantum yield in polyethylene, which is above its glass transition at 25”C, and in polystyrene, which is well below its Tg, so the glassy nature of the medium also showed little effect. For this reason, any specific “polymer effects,” if indeed they do occur, must be attributed to processes occurring outside the primary cage. Secondary cage recombination, on the other hand, will be affected by the slower rate of diffusion in the polymer matrix. This might be expected to reduce the number of radicals which can escape the region associated their primary partners, thus increasing recombination. Estimates of the probability of escape of radical pairs in solution in conventional solvents have been made by product analysis of the decomposition of diacyl peroxides. For example, Braun et al. (14) estimated that 60 to 80% of the methyl radicals produced in the thermolysisof acetyl peroxide escapegeminate cage recombination. However, Guillet and Gilmer (15) showed that for longer chain C9 and C,, radicals the probability was much lower, ranging from 5% at 76°C to 16% at 262°C. The lower escape probabilities in this case can be attributed to the greater mass of the C9 and C,, radicals and the greater internal viscosity of the mineral-oil solvent.

Vm. THE INTERNAL VISCOSITY OF POLYMERIC SOLIDS Any treatment of diffusion processes in polymers must include estimates of the “internal viscosity” qint of the solid polymer matrix. For example, for recombination of active free radicals which occur at every collision, one can write the rate expression in the form Rate = k&R*I2

(13)

104

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

The simplified form of the Einstein-Smoluchowskiequation gives for radicals land2

where p’ is some collision radius for reaction, dv is Avogadro’s number, and

D 1and D2are the diffusion constants for species 1 and 2, respectively.

We can consider three limiting cases, depending on the relative size of the radical species. Case 1. Two small radicals of equal size. Then Eq. 14 reduces to the Debye equation: kdiff

=

mT

ooorlint

= 2.2 x 105-

T rl

where qintis the “internal” viscosity of the medium. Case 2. One small radical and one large polymer radical. In this case D2 = 0 and

The rate is only one-half that for two small radicals. Case 3. Two polymer radicals. Then

It is not possible to estimate the value of kdiE in this case, but it will remain proportional to T/qint.In concentrated polymer solutions and in solid polymers, diffusion will almost certainly involve movement by reptation and will be very slow. Values for kdiffand qintfor various solvents and polyethylene are also included in Table 1. The average distance a particle can diffuse in time t can be shown to be x = J m

The Stokes equation relates the diffusion constant for a spherical particle of radius r to the internal viscosity qintby

THE INTERNAL VISCOSITY OF POLYMERIC SOLIDS

105

TABLE 4. Diffusion Distance x = -for Spherical Particles of Radius 3 A in Media of Differing Internal Viscosities llht Time of Observation

D

'lint

(PI

(cm2s-')

1 .o 10-1 10-2 10-3 10-4 6X

7x 7x 7x 7x 7x 1.2 x

10-8 10-7 10-5

10-4 10-5

1 ns

10 ns

100ns

1 ms

0.12 0.38 1.2 3.9 13 1.6

0.38 1.3 3.9 13

1.2 3.9 13

3.9 13 40 128 412 52

40

5.3

40

128 16

"Average value for toluene and benzene.

This allows the calculation of diffusion distances n for particles in media with varying internal viscosities qht. Table 4 shows values calculated for particles of radius 3 A-somewhat larger than methyl radicals, but smaller than phenyl groups. It should be noted that these are for thermalized particles, which have lost all the excess kinetic energy imparted to them in the initial dissociation process. The calculations are thus only applicable to secondary cage recombination, not the process occurring in the primary cage. Clearly the threeorder-of-magnitude difference in qintbetween polyethylene and solvents such as benzene or toluene should have important effects on the probability of secondary cage recombination, even for relatively small radical fragments. As the size of the separating radical increases, its probability of escape should also decrease. However, for spherical particles, the effect is not a strong function of the molecular weight. If one assumes that the particle is spherical, then

D where M

=

CX(-$-)''~

molecular weight, and thus the distance diffused in time t is

x

a( + ) " 6

Thus a ten-fold increase in the mass of a spherical particle would only reduce x by a factor of 0.68.

Once the particle becomes a linear polymer, it will diffuse by reptation in a polymer matrix. In this case the scaling law proposed by de Gennes indicates that x would vary as

106

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

X K -

1

M

M. STUDIES OF CAGE REACTIONS IN POLYMERS Because of the relatively slow rates of radical diffusion in polymer matrices, it seems likely that the probability of secondary recombination will depend very much on the separation achieved while the particles are moving apart with the original excess kinetic energy imparted in the primary dissociation step. This, in turn, should depend on the energy of the exciting photon. There is some evidence for this, even in small molecules in solution. For example, Slivinskas and Guillet (16) report a one-hundred-fold increase in the relative yields of Nomsh type I radical products from simple aliphatic ketones, when the reaction is initiated by y-rays rather than ultraviolet light (Table 5). Similar increases were observed in polymeric systems such as in ethylene40 copolymers (17). Early studies by Hartley and Guillet (18) on the photochemical quantum yields for type-I reaction in model ketones of structure R-C(=O)-R showed that the quantum yield in solution at 120°C in p d i n oil decreased continuously from 0.02,when R = 4, to a limiting value of 0.012 at R = 12 (Fig. 5 ) . Model compounds where R > 12 gave values nearly identical with that for R = 12, as did copolymers of ethylene with carbon monoxide. Furthermore, the result was independent of solvent viscosity, being nearly identical in heptane (0.28 cP), dodecane (0.73cP), and parain oil (9.2 CP at 60 "C).The viscosity of paraffin oil is 2.1 CP at 120"C,which is comparable to that of typical organic TABLE 5. Comparison of G-Values for Photolysis (313 nm) and Radiolysis of Symmetrical Aliphatic Ketones at 35°C G (Radiolysis)

G (Photolysis)

CO (1)

Ketone ~~

Methyl Ketone

~~

~~

4-Heptanone 5-Nonanone 6-Undecanone 7-Tndecanone 8-Pentadecanone 12-Tncosanone

~

0.44

0.025 0.020 0.017 0.015 0.012

3.8 2.8 2.4 2.0 1.7 1.5

Ratio GdGn

Alkane/;?

0.12 0.0090 0.0083 0.0085 0.0088 0.0080

0.71 0.43 0.28 0.18 0.065

(1)

0.040

Methyl Ketone (11)

Ratio GI&

0.49 0.51 0.45 0.26 0.092 0.081

1.45 0.88 0.62 0.69 0.71 0.69

Source: Reprinted with permission from J. A. Slivinskas and J. E. Guillet, y-Radiolysis of ketone polymers, Journal of Polymer Science, Polym. Chem. Ed. 11, 3053 (1973). Copyright 1973 John Wiley & Sons, Inc.

STUDIES OF CAGE REACTIONS IN POLYMERS

0

10

20

30

107

40

Chain length

Figure 5. Quantum yield for carbon monoxide evolution ($co) as a function of chain length: temperature, 120°C; solvent, paraffin oil. Reprinted with permission from G. H. Hartley and J. E. Guillet, Photochemistry of Ketone Polymers 11. Studies of Model Compounds, Macromolecules, 1, 415 (1968).

solvents such as toluene and benzene at 20°C. The apparent activation energy for the type-I quantum yield is quite large, namely 4.8 kcal mol-’, whereas the usual E, for a diffusion-controlled process is =2-3 kcal. Both of these considerationssuggest that these quantum yields reflect the effect of the molecular weight of the radical on its escapefrom the primary cage, rather than on secondary diffusive recombination. In our concept of primary-cage recombination, escape should depend on the momentum imparted in the primary dissociation step. The distance reached in the escape trajectory will be proportional to the velocities (v) of the particles. Since the exciting wavelength was the same (313 nm), the total kinetic energy should be very similar for each ketone. From simple kinetic theory the velocity (v) should be proportional to (l/M)”*, where M is the molecular weight of the fragment. If +I is a measure of the probability of escape from the cage, then one might expect that

On the other hand, for secondary diffusiverecombination, Eq.21 would predict

As shown in Table 6, the data of Hartley and Guillet are fitted quite well by Eq. 23 for values of M up to M,.One must conclude that for longer chain flexible

108

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

0 II TABLE6. QuantumYieldsforModel AlkanonesR-C-Rat 120°C inParaffhOi1

(4,)rn

41

R

n-C,H,

0.021 0.024 0.022 0.021 0.021 0.028

0.0212 0.0191 0.0181 0.0154 0.0127 0.0123

n-C5H1 1 n-C6H13

n-C7H,4 n-C11H23 n-C2 lH43

segments, escape must involve indepenent motions of chain segments approximately 12 carbon atoms in length. Additional information regarding structural effects in model polymer ketones was reported by Plooard and Guillet (19), who compared the photochemical quantum yields in solution for the methyl esters of ketone diacids with polyesters containing the same structure:

0

0 II

0 II

II

MeO- C -(CH,), -C-(CH,), -C -OMe (a) n = 2; (b) n = 3; (c) n = 4

0 0 II II COCH2CH2CH2CH2O-C -(CH2),-C- (CH2),-

---

(d) n = 2; (e) n = 3; ( f ) n = 4 TABLE 7. Quantum Yields for Keto Esters and Polyesters Methyl Esters

(a) (b) (c)

n

M

Type I

2 3 4

202 230 258

0.20 0 0.01

Type 0 0.29 0.20

II

Polyesters

4s Other

Total

A0.2 0.12 0

G0.4 0.41 0.23

"Based on reduction in type-I or type4 yields.

M

4s

R~uction Factof

15,000

0.014 0.012 0.013

1/14 1/24 1/15

9,900 6,900

109

PHOTOCHEMISTRY OF POLYMERS CONTAINING KETONE GROUPS

Their results are summarized in Table 7. It is clear that by including the carbonyl in the backbone of a polymer chain a substantial reduction in quantum yield can be expected, even when the photolysis is carried out in solution. For the type-I process this probably results from cage effects, while in the type-I1 it is the reduction in conformational mobility which prevents the formation of the cyclic six-membered intermediate known to be involved in this reaction:

OH

0 II R-C-CH3

<-

I

R-C=CH2

+ CH2=CH-R

This conformational factor will Se discussed further in later sections.

X. PHOTOCHEMISTRY OF POLYMERS CONTAININGKETONEGROUPS The largest body of experimental work on the photochemistry of solid polymers relates to the study of the photolysis of homo- and copolymers of vinyl ketones. In early work, Guillet and Norrish (20) and Wissbrun (21) showed that polymeric ketones such as poly(methylviny1 ketone) and poly(methylisopropeny1ketone) underwent the same classical photochemical reactions as their low-molecularweight analogs. The photophysical and photochemical processes which occur are summarized below:

*

R

R

I

I

c=o

->

(S')

->

(T1 1

->

&

(27) (SO) + hv

110

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMOFU'HOUS POLYMERS

& R I

h" &c - oH

R I

RH'

R R I

R

OH R

I

I

c=o* ic

(32)

This work has been reviewed recently (22). For our present purposes, only

a few of these studieswill be included to illustratespecificpoints about solid-phase

photochemistry. As with simple small-molecule ketones, there are strong effects due to the structure of the ketone and the nature of its substituents on both the quantum yields and the nature of the products. These same structural features are usually reflected in the analogous polymeric molecules. The ketone group is a useful model because it can be excited selectively in the presence of other groups commonly contained in polymer chains, such as the phenyl rings in polystyrene, and so the locus of excitation is well defined. Furthermore, there is a great deal known about the photochemistry of aromatic and aliphaticketones, and one can draw on this body of information in interpreting the results. A further advantage of the ketone chromophore is that it exhibits a number of photochemical processes from the same excited state. Thus one has a probe of the effects of the polymer matrix on these processes by determination of the quantum yields. The competing processes include (1) fluorescence (Eq. 26), (2) phosphorescence (Eq. 27), (3) the Nomsh type-I reaction (Eq. 28), (4) the Nomsh type-I1 reaction (Eq. 29), (5) photoreduction (Eq.30), (6) the

PHOTOCHEMISTRY OF POLYMERS CONTAINING KETONE GROUPS

111

formation of cyclobutanol (Eq.311, and (7) intersystem crossing to the ground state (Eq.32). The polymers discussed here will generally be polymers of ethylene or styrene copolymerized with monomers capable of introducing ketone groups with a variety of structural features. Some of these copolymer structures are shown in Table 8. When a thin film of solid polymer containing a ketone group is cooled to 0 K, no motion of the groups or chain constituents of the polymer is possible. If the film is gradually warmed to room temperature in air and irradiated with UV light, phosphorescence emission is observed. Since this is a strictly electronic transition, no molecular motion is required and the intensity of the emission remains relatively high until certain transition points are observed. If one plots the phosphorescence intensity from thin films of polystyrene or polyethylene in the form of an Arrhenius plot, these transitions are identified by intersections of straight-line portions of the response curve shown in Fig. 6u.As the temperature is increased from 0 K the specific volume of the polymer increases in a manner shown schematically in Fig. 3. As the free volume in the polymer increases, various types of molecular motion begin to occur, and these are identified by the transitions associated with the motion of various subgroups in the polymer. The important ones observable by this experiment (Fig. 6u)are the crankshaft motion of polyethylene at about -85°C and the transition associated with movement of the phenyl ring in polystyrene at about -77°C (Fig. 6b).The minor transition in PE-CO at - 150°C may be related to some form of coordinated motion of the carbonyl group itself.

12 10

10 8

8

a

-

I-!

-

6 2 C

c 6 4

4

2

2

'

4

6

8

10

4

6

8

1

0

0

IOOO/OK

Figure 6. Arrhenius plots for phosphorescence intensity for (a) poly(ethy1ene-1% CO) and (b)poly(styrene-5% PVK),showing transition temperatures and activation energies.

TABLE 8. Structures of Ketone Copolymers Studied Copolymer

Structure

Structure Number

Poly(ethylene-co-carbon monoxide) (PE-CO)

Poly(ethy1ene-co-methyl vinyl ketone) (PE-MVK)

Poly(ethylene-co-methyl isopropenyl ketone) (PE-MIPK)

* c=o I

CH 3

Poly(styrene-co-methyl vinyl ketone) (PS-MVK)

isopropenyl ketone) (PS-MIPK)

Poly(styrene-co-rerrbutyl vinyl ketone) (PS-tBVK)

rn

112

v

CH 3

n 3 C - cI CH3

3

vinyl ketone) (PS-PVK)

IV

VI

PHOTOCHEMISTRY OF POLYMERS CONTAINING KETONE GROUPS

113

TABLE 8 (Continued) Copolymer

Structure

Structure Number

Poly(styrene-co-phenyl isopropenyl ketone) (PS-PIPK)

The straight-line portion of the Arrhenius curve above about 100 K observed in both cases is attributed to quenching of the phosphorescence emission by oxygen, and the slope of this curve accurately reflects the activation energy associated with the permeability of the oxygen quencher. This effect can be used (23,24) as a means of measuring the rates of oxygen diffusion in a variety of polymers. As a general rule, the activation energy for a given process in a solid matrix can be related to the amount of free volume required for that process (9), so that small-scale motions requiring small amounts of free volume adjacent to the moving group will have low activation energies, whereas those requiring larger packets of free volume will have large activation energies. Typically, the activation energies for diffusion of oxygen in polymers range from 7 to 10 kcal mol-' , whereas those for small-scale rotations or methyl and methoxy groups are of the order of 1 to 3 kcal mol-'. In early work, Hartley and Guillet (25) associated the reduction in c$= in PE-CO at about -40°C with restrictions in conformational mobility associated with the glass transition, Tg. However, measurable values of c$ll were observed down to about -100°C due to the Occurrence of a crankshaft motion of the polyethylene backbone chains which permitted the formation of the cyclic intermediate (Eq.25) required for reaction within the lifetime of the n-T* excited state of the carbonyl (I 20 ns). The activation energy for $n below -40°C was 2 2 kcal mol-', which is similar to that of the crankshaft motion. Below - 100°C this motion is frozen out and no further photochemistry is observed. On the other hand, in the absence of quencher the photophysical processes of fluorescence and phosphorescence may be quite efficient. In early photochemical studies it was shown (26) that the quantum efficiency for the type-I processes in polymers containing ketone groups is highly sensitize

114

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

to the location of the ketone group with respect to polymer chain, as shown in structures A and B below:

When the ketone is in the backbone of the polymer, the excitation of the ketone produces two polymeric radicals which must separate from each other within a short period of time in order to produce chemical products. If, however, the ketone group is in a side chain, as in structure B, then a polymeric radical is formed simultaneously with a small radical fragment. This second fragment can diffuse relatively rapidly through the polymer solid, and the quantum yields are increased by at least one order of magnitude (26-28). In a previous section it was demonstrated that a substantial reduction in quantum yields was observed when the ketone group was included in the backbone of a polyester chain. A similar variation in the quantum yield of the Norrish type-I process is illustrated in Fig. 7 for solid copolymers of ethylene containing

lrrodiotion time (hours)

Figure 7. Relative rates for carbonyl loss (type I) in films of ethylene-ketone copolymers under nitrogen at constant light intensity (26). Reprinted with permission from F. Sitek, J. E. Guillet, and M. Heskins, Some aspects of the photolysis and photochemistry of PE containing ketone groups, Journal of Polymer Science-Polymer Symposia, 57,35 1 (1976). Copyright 1976, John Wiiey & Sons, Inc.

PHOTOCHEMISTRY OF POLYMERS CONTAINING KETONE GROUPS

115

three different ketone structures. The ketone groups in the backbone of the polymer chain in PE-CO copolymer show much lower quantum yields than those from the secondary or tertiary structures induced by copolymerization of methyl vinyl ketone (MVK) and methyl isopropenyl ketone (MIPK) with ethylene. In the latter two cases, the Nomsh type-I cleavage produces a small radical and a polymer radical, and the small radical has a much greater probability of escaping the cage. The quantum yields for type-I and type-I1 processes at various temperatures are summarized in Table 9. The significant increase in type-I quantum yields in structures I1 (PE-MVK, PE-MIPK) and 111appears to occur with a concomitant reduction in type 11,indicatingthat the two reactions are indeed in competition. Further confirmation of the important effect of solid-phase transitions in polymer photochemistry was reported by Dan and Guillet (29). They studied the quantum yields of chain scission, as a function of temperature in thin solid films of vinyl ketone homo- and copolymers. For polymers where the Nonish type-I1 mechanism was possible, large increases in were observed at and above the glass transition Tg. Figure 8 shows this effect in a styrene copolymer containing about 5% phenyl vinyl ketone (PVK). Below Tg,& is about 0.07, but at Tg it rises to about 0.3, a value similar to that observed for photolysis in solution at 25°C. A similar effect was observed with poly(methy1 methacrylateco-methylvinyl ketone) (PMMA-MVK) and PVK homopolymer. The generality of this effect suggests that even in the solid phase above Tg, the conformational freedom of large segments of the polymer chain is comparable to that in solution, and consequently one should expect equivalent chemical reactivity. When this effect was first discovered, it was important to determine whether or not it was a general phenomenon applicable to all photochemical reactions in solid polymer systems. Fortunately this is not the case, and only those reactions requiring relatively large amounts of free volume, such as the Nomsh type 11, will show this strong effect at the glass transition temperature. For example, Table 10 shows data on the type-I quantum yield (loss of

+,,

+=

TABLE 9. Quantum Yields for Ketone Ethylene Copolymers Polymers

1%CO

2% MVK

2% MIPK

T("C)

+I

+n

+I

+U

+I

23 35 54.5 69.5

0.073 0.065 0.074 0.054

0.074 0.099 0.065 0.057

0.22 0.23 0.15 0.12

0.044 0.034 0.016 0.014

0.25 0.23 0.15 0.11

~~~~~

Source: Ref. 28.

+ll

0.048 0.039 0.019 0.004

0.32

-

1

I

I

-

0.24

-

-

0.16

-

-

In

a"

-

TABLE 10. Temperature Effects for Type4 Reaction in PS-MIPK Copolymer Films at 313 nm in N, +-co 23 64 89 104

0.26 0.26 0.30 0.32

Source: Ref. 30.

TABLE 11. Quantum Yields for the Irradiationof Poly(styrene-co-vinyl Aromatic Ket0nes)s at 313 nm in N, Co-monomer

PVK PVK PVK PVK PIPK

(")

T

@-CO

Film

Film

Film

Solution

1.1 3.6 7.6 7.6 6.1

23 23 23 55 23

0.20 0.21 0.22 0.23 0.32

0.19 0.18 0.20

0.043 0.054 0.072

0.08

-

0.13 0.15 0.42 0.53 0.36

@OH

-

@S

-

Source: Ref. 30. "Determined by W spectropbotometry with the homopolymers as standards.

116

+;

M01-8~

POLYMERS FOR PHOTOLITHOGRAPHY

117

carbonyl) in films of poly(styrene-co-methyl isopropenyl ketone) irradiated at 313 nm in nitrogen (30). There is a small but continuous increase in the quantum yield from 23 to 104"C, but no discontinuous change is observed in the region of Tg, which is around 98°C for these polymers. The total loss of carbonyl is considered to be the sum of the type-I and photoreduction (Eq.30) processes, both of which apparently require very small volumes of activation in order to occur. It is interesting to note that in many cases the efficiency of radical reactions in solid glassy polymers appears to be unaffected by the polymer matrix. In the case of type-I reactions in solid polystyrene we have observed that the efficiency of radical escape when at least one of the radicals is a small molecule is similar in polymeric glasses to that observed in solution. One can deduce from this that polymeric glasses are not particularly good at trapping radical species unless they are cooled to very low temperatures. As shown in Table 11, the photoreduction process is quite efficient in phenyl vinyl ketone copolymers with styrene. Because of the rapid intersystem crossing in the phenyl ketone chromophore, it seems likely that both the reduction and chain scission processes proceed via the intermediacy of the triplet state. An interesting feature shown in Table 11 is that, with PVK copolymers (structure VII), +-co corresponds almost exactly to +OH, suggesting that photoreduction (or cyclization) is the major route for loss of carbonyl in these polymers. However, with PIPK copolymers, +-co is four times as great as We suggest that in this case, because of the greater stability of the tertiary radical formed, the major loss of carbonyl in these polymers (structure VIH) is by the Nomsh type-I reaction. Because of mobility restrictions for the type-I1 process in the solid phase, the quantum yield +I appears to be significantlyhigher than in solution.

XI. POLYMERS FOR PHOTOLITHOGRAPHY The development of microlithography for the production of microcircuits has created new interest in obtaining polymers which undergo efficient chain scission when exposed to UV or other patterning radiation, including electron beams and soft x-rays. Ketone-containing polymers have been used commercially for such purposes, but are also of interest in establishing the mechanism of photochemical reactions in solid polymers. Whereas in ethylene40 copolymers and their structural analogs (type A), both type4 and type-I1 processes can lead to chain scission in the primary photochemical act, it was assumed in early studies that in structures containing pendant carbonyl, only the type-I1 process would lead to chain scission and have a reduction in molecular weight via

11% PHOTocHEMlSTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

Norrisb type Il

More recently it has been shown (30) that efficient chain scission can occur also from the type-I process followed by p-scission: hv

(34) + 3-scission

>

Norrish type I, followed by fhcission

Extensive studies have been reported on copolymers of styrene with a variery of ketone functional groups introduced by copolymerization with substituted vinyl ketone monomers. The copolymer structures are shown schematically in Table 8. The quantum yields in the styrene ketone copolymers are highly dependent on the structure of the ketone group included in the polymer. For example, the quantum yield for the type-I process is 0.09 in MVK copolymers where the substituent on the ketone group is a methyl group, but increases to 0.45 where the substituent is tertiary butyl (30):

-I -

HJC

C

CH3

CH3

-'

(36) +

'k-CH3 I CH3

+

C=O

Depending on the fate of the secondary polymer radical produced, this could lead to either chain scission or crosslinking in the solid phase. Similartrends were observed when the same films were exposed to synchrotron and electron-beamradiation (31). The higher efficiency of the type-I reaction in these structures is attributed to the formation of more stable radicals from the tertiary butyl than from the methyl ketone. Adding an additional substituent to

POLYMERS FOR PHOTOLITHOGRAPHY

119

the carbon a to the carbonyl group creates still further stability in the radical formed by type I and still higher sensitivity to both light and y-rays. For example, poly(t-butyl isopropenyl ketone) (structure IX) is one of the most sensitive polymers yet developed, both as a near-UV and as an electron-beamresist (32):

M

Studies were also made of the photochemistry of styrene copolymers containing minor amounts (2-7%) of the ketone monomers to minimize the effects of energy transfer and migration. The polymers were photolyzed in thin (-0.1 mm) solution-cast films and in solution. In the latter case the rates could be followed by automatic viscometry using the procedure described by Kilp et al. (33,34) and by Nemzek and Guillet (35). Chemical changes in the solid state were followed by FTIR spectroscopy. The major chemical changes which occur are the loss of ketone carbonyl function (+-co), the formation of hydroxyl (+OH), and changes in molecular weight (&). In solution the major change in molecular weight is due to chain scission by the Norrish type-I1 process (Eq.29). There is some contribution due to p-scission of the akyl radical formed by the type-I process, particularly in the MIPK and t-BVK polymers. Loss of carbonyl occurs from photoreduction or the formation of cyclobutanolrings, and also from vaporization of the aldehyde formed by hydrogen abstraction by acyl radicals formed in the Norrish type-I process. As in the case of the corresponding ethylene copolymers, the quantum yields of carbonyl loss are substantiallydifferent for the copolymers, being fastest for t-BVK, slower for MIPK, and least efficient for MVK copolymers. These polymers are of potential interest as photoresists, and their photochemistry was also studied in very thin (1-4 pm) films which were spun cast on polished salt plates. After irradiation in a standard xenon arc photoilluminator, the loss of carbonyl could be determined from FTIR measurements. Experiments were carried out both at 254 nm (deep UV) and 313 nm (near UV). Typical rate curves are shown in Fig. 9. The results at 254 and 313 nm are qualitatively similar, in that the same order of relative sensitivity is observed. Microelectronic devises are now manufactured using a variety of photosensitive polymers (photoresists) to define the geometry of the circuits and to construct

120

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

I 0.5

-

I

I

I

I

Irradiation time (min)

Figure 9. Irradiation of ketone copolymers at 254 nm: 1, = 0.024 mW cm-2.

circuit elements such as transistors, resistors, capacitors, etc. Current manufacturing practice has now reached a level of precision at which the number of such devices which can be placed on a silicon chip is limited by the wavelength of the light used in the patterning step. For this reason it is now important to develop polymers which are sensitive to raadiation having shorter effective wavelengths, such as electron beams and soft x-rays. With both of these high-energy radiations, the primary events induced are the formation of high-energy ions and electrons, whose recombination yields showers of secondary electrons with lower energy. After both elastic and inelastic scattering by the medium, ultimately these electrons reach energies where they can interact with valence electrons to produce secondary ions. In polar media, ions may have appreciable lifetimes and can generate chemical products via well-known ionic reaction mechanisms. However, in relatively nonpolar polymeric solids such as polyethylene and polystyrene, most of the chemical products seem to arise from recombinations of the ions with each other or with low-energy electrons to provide molecules or groups in highly excited electronic states. These will lose energy by collisional processes, and in the absence of alternative energy-dissipatingpathways may eventually populate the lowest-energy singlet and triplet states of the molecule or chromphore. Experimental evidence for this is derived, for example, from product studies on the y-irradiation of ketones which show that the predominant reactions are the Nomsh types I and 11, which are known to result from direct excitation of these states via the absorption of UV photons. Furthermore, polystyrene emits fluorescence from excimer states whose spectra are nearly identical to those observed when excited by W radiation. Recently it has been shown (36) that electron-beam irradiation of styrene-vinyl ketone copolymers show higher yields of type-I radicals than expected from UV photolysis measurements. It seems clear that some part of the excess energy of high-energy photons and electrons is imparted to the translation kinetic energy

SYNCHROTRON-RADIATIONSTUDIES

121

of the separating radical fragments, thus carrying them farther apart before they start their “thermalized” random diffusion. For example, Noyes (11) has calculated that for methyl radicals separation of the primary pair by a critical distance = 5 A reduces the probability of reencounter to 50%. This probability drops off rapidly as the distance exceeds 5 A. These considerations should apply generally to cases where at least one of the separating fragments is small enough to diffuse like a spherical particle. However, when the two fragments are both polymeric, diffusion becomes much more restricted.

XII. SYNCHROTRON-RADIATION STUDIES The use of soft x-radiation from a synchrotron source has certain advantages for the production of microcircuitry. In particular, the short wavelength of the x-ray photons (1-50 A) should provide higher pattern resolution in production devices, thereby increasing the density of circuit elements on the chips, with a concomitant improvement in speed. It was therefore of interest to see if the same chemical selectivity observed in the photoresponse of these styrene-ketone polymers in the near and deep W extended to processes induced by the absorption of soft x-ray photons with energies two to three orders of magnitude greater than those in the UV region. Earlier experiments by Slivinskas and Guillet (37) on poly(styrene-co-methyl vinyl ketone) using y-radiation suggested that this might indeed be the case. The relationships between processes induced by high-energy radiation in polymers and photochemistry has been reviewed recently by Guillet (22). The Stanford Synchrotron source was used for exposure of film samples to synchrotron radiation. The window size on this instrument was 2 mm X 12 mm. The small size of the window severely restricted the amount of material which could be exposed, but there was enough to measure changes in the ZR spectrum by FTIR. After this measurement the molecular-weight changes were estimated by highpressure liquid-exclusionchromatography (GPC) using polystyrene standards for calibration. Measurements of the sensitivity were made in two ways: 1. Loss of ketone carbonyl was determined by FI’IR on the exposed samples

by measuring the relative absorbance A at 1700 cm-’. The ratio (MA)17oo was adjusted for film thickness using the styrene bands at 1600, 1495, and 1455 cm-’. This value is proportional to the rates of the Nomsh type-I and photoreduction processes in the copolymer. 2. Changes in molecular weight result from scission in the backbone of the polymer chain.

122

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

A measure Z of the sensitivityto main-chain scission can be derived as follows. The number of photons absorbed is

n = ZAb

(37)

where Z is incident intensity per unit area. A is the absorption coefficient, C is the film thickness, and a is the area exposed. a is the same for all films irradiated, and kz = w , the weight of film exposed. Therefore

n = iAw

(38)

The quantum yield 4 is the number of bond scissions S which occur per photon absorbed. From stoichiometric considerations (35)

where @ and Mnare the original and final number-average molecular weight of the polymer. Therefore

We can define a response function

which is related to the quantum yield 4 by

4

=- z

ZA

Since the x-ray absorbance A is likely to be identical for the styrene copolymer films used in this experiment, Z will be proportional to the quantum yield when the films are exposed to equal intensities Z of radiation. Representative values (31) for the carbonyl loss and molecular-weight change for three styrene-vinyl ketone copolymers are summarized in Table 12. It is clear from the carbonyl-loss data that the relative sensitivity of these films to synchrotron radiation is the same as for UV exposure. This has important implications for the design of photoresists for soft x-ray patterning.

123

FOLYACRYLOPHENOhFS

TABLE 12. Relative Sensitivity of Styrene-Vinyl Ketone Copolymers to Synchrotron Radiation

CarbonylLoss

Copolymers PS-3% MVK P S d % MIPK PS-7% tBVK

Chain Scission

Z (TYFI + Type 11)

(8) (Type 1)

5

2.1

13 25

4.8 4.9

Xm. POLYACRYLOPHENOIWS The polyacrylophenones represent another important category of photosensitive polymers. Substitution on the phenyl ring can alter both the efficiency and mechanistic pathway to reaction products (38). Early work (39) showed that the photochemistry could be related to that of small-molecule analogs. Work at the Slovak Academy of Sciences (40) has extended to a very large number of substituted derivatives. In common with other ketone systems, the quantum yields for chain scision are reduced significantly in the solid phase. Some of this is due to the restrictions on molecular mobility, which reduce the quantum yields of type-II photoprocesses. Another important factor is the extensive triplet migration, which, in the solid phase, leads to quenching by reaction products (41). such as the olefin produced by the type-11 photoprocess. Recently, studies have been reported (42) on the solid-phase photochemistry of para-substituted poly(acry1ophenone)s which degrade primarily by t y p e 4 processes:

R

R

i

The results are summarized in Table 13. Substitution with fluorine gives values comparable to the unsubstituted polymer, but C1 and ethyl substituents reduce the sensitivity and the para-methoxy compound has a very low quantum yield, probably because of a long-lived triplet state (7 G 4.6 ms) (43) which is easily quenched by oxygen or other impurities in the film.

124

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

TABLE 13.

Quantum Yields for Chain Scission (+& for Substituted Poly(acry1ophenone)s in the Solid Phase at 313 nm

TgCC)

R

H

F -c1 -c2H5

4%

73.5

0.14 0.15

89 51.5

0.05

--OCH,

0.06 0.001

Source: Ref. 42.

XIV.

THE PHOTO-FRIES REACTION

The photo-Fries reaction occurs readily in solid polymers and is observable in phenyl esters, particularly in poly(pheny1acrylate)and poly(pheny1methacrylate) and their derivatives. The course of the reaction can be followed very easily by ultraviolet spectroscopy, since the product hydroxy ketones have strong absorbance at 260 and 320 nm (Fig. 10). Reaction occurs with equal efficiency in small model compounds in solution and in the polymers in the solid phase (44). An Arrhenius plot of the quantum yield for the para product (Fig. 11) shows a linear increase up to 294 K, above which no further change in quantum efficiency is observed, either above or below the glass transition temperature.

200

300 350 400 Wavelength (nm)

250

figure 10. Absorption spectra of a PPA film after different periods of irradiation at room temperature, using light of wavelengths between 220 and 340 nm from an AEI mediumpressure mercury lamp. Reprinted with permission from s. K. L. Li and J. E. Guillet, Studies of the photo-Fries reaction in solid poly(phenylacrylate), Macromolecules, 10, 840 (1977). Copyright 1977, American Chemical Society.

CISTRANS ISOMERIZATION

125

I 03/TOK

Feure 11. Arrhenius plot of the formation ofp-hydroxyphenonegroups as measured by absorbance changes at 265 nm. The transition temperatures of the polymer are also included. Reprinted with permission from S. K. L. Li and J. E. Guillet, Studies of the photo-Fries reaction in solid poly(phenylacry1ate). Macromolecules, 10, 840 (I 977). Copyright 1977, American Chemical Society.

The linear portion of the curve has an activation energy of 1.8 kcal mol-' and is believed to be associated with the activated process involving small motions of the phenyl ring on the ester group. The positions of the transitions were determined by the phosphorescence method (23) and are shown in the figure. The activation energy for the ortho product is 1.2 kcal mol-', which presumably reflects the smaller amount of motion required to move to the ortho than to the para position. The small value of the activation energy is presumably associated with the very small volume required for the rotation of the phenoxy radical before it recombines to form the hydroxy ketone.

XV. CIS-TRANS ISOMERIZATION One of the simplest photochemical processes which can be observed in solid polymers is the photoisomerization of a double bond in olefins such as stilbene. The reaction can be followed easily by spectrophotometric methods, and the irradiation can take place in thin polymer films. The amount of free volume required is relatively small, but will obviously depend on the substituentsattached to the double bond. In early studies, Gegiou et al. (45) showed that the quantum

126 PHOTOCHEMISTRY AND

MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

yield of cis-trans isomerization of stilbene itself decreased with increasing viscosity of the medium. It was also shown that a polymer matrix such as poly(isobuty1ene)did not inhibit the photoisomerizationas long as the temperature was above the glass transition temperature Tg.Above Tgthe photoisomerization followed first-order kinetics, but below that temperature the kinetics were very complex and suggest the occurrence of a multiplicity of different first-order processes. It was postulated that an increase in free volume was necessary for the transforma5on of trans to cis stilbene:

H\

,

c=c

/

/c6H5~~pitive

'

H

H

\

c=c

/

c6H5

H

\ c6H5

and that restrictions on the rotation of the phenyl groups in the polymer matrices reduced the quantum yield of the process. It was suggested that stilbenemolecules were located in a range of different guest sites associated with differing amounts of free volume. The situation is equivalent to having a spectrum of microscopic viscosities, each determining the rate constant for the observed process. This phenomenon now has been observed in a wide variety of similarphotocyclizations and reaarrangements in polymer matrices, and it now seems to be a general phenomenon. Modem theories of glassy polymers propose that submicroscopic voids exist in the polymer matrix with a range of surface free energies associated with their distribution and size. Location of the probe molecule at or near one of these voids would provide a variety of environments which would give rise to the spectrum of rate constants.

XM. PHOTOCYCLIZATION Photocyclization is a particularly valuable route to the formation of cyclic compounds. There is a wide variety of photocyclization reactions reported in the literature of organic photochemistry, but relatively few of these have been carried out in solid polymers. The earliest reports concern the photodimerization of cinnamic acid derivatives, leading to crosslinking in solid polymers. These polymers have important applications as commercial photoresists. The chemistry has been reviewed by Delzenne (46)and Williams (47). Other similar photoreactive groups such as chalcones (48), coumarins (49). and dibenzazepines (50) have been proposed for similar applications. Photocyclodimerization is now considered to be a major factor in mutagenesis in DNA and polynucleotides. The reaction involves the photoinduced dimerization of pyrimidine bases such as thymine. The crosslinkingwhich results causes a defect in the coding sequence and can cause other cell damage.

127

PHOTOCYCLEATION

Meador and Wagner (5 1) have reported that a-(0-toly1)acetophenone undergoes a photocyclization reaction via the intramolecular abstraction of the yhydrogen, with a quantum yield close to unity: H hv

3 1 3 nm’ benzene

(45)

The ketone absorbs available solar energy in the 280-360-nm region, but the product 2-phenyl-2-indanol is transparent above 280 nm. This is of particular value because the reaction can be run to a high degree of conversion with no interference by light absorption by the product. Guillet et al. (52)have shown that solar photochemicalreactions can be carried out using crosslinked poly(ethyleneviny1acetate) (EVA) beads as a solvent. The beads can be exposed in solar ponds and the products recovered by extraction. Figure 12 shows data on the rate of photolytic conversion of the a-(0-toly1)acetophenone when exposed in the solid bead and in benzene solution. Identical rates and quantum yields were observed in both media, showing that the rate of cyclizationsof this type are independentof the internal viscosity of the medium. Bimolecular cyclizations, as might be expected, are more sensitive to the nature of the polymeric medium. Several studies have been reported of examples of the cycloaddition reaction

60

I

0

45

-

I

I

1

1

-

Solution

Beads

0 C

Joules/cm*

Figure 12. Photoconversion of a-(o-toly1)acetophenone as a function of absorbed dose in benzene solution and in solid EVA beads. Reprinted with permission from J. E. Guillet, W. K. MacInnis, and A. E. Redpath, Prospects for solar synthesis. 11. Study of the photocyclization of a-(0-toly1)acetophenone in solution and in crosslinked ethylene-vinyl acetate beads. Canadian Journal of Chemistry, 63, 1333 (1985).

128

PHOTCKHEhUSTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

R' fwvCRXR.nrr

R' + 'C-X R.f

I

hv>

R'--C-X

I

-CR---CR-

(46)

I

An early example is the photo reaction of benzophenone with cis-polyisoprene

(53). This reaction occurs readily in both the solid phase and solution to give polymers of unusual structure:

The inclusion of the large ring system into the polymer backbone increases the chain stiffness, and hence the glass transition temperature Tg also increases. Table 14 shows the rapid rise in Tg with irradiaation time. In the solid state, complete conversion is inhibited above about 70%, presumably because of restrictions on the diffusion of benzophenone to the remaining double bonds in the polymer. Holden and Guillet (54) have reported the photoaddition of a variety of olefins to thin films of poly(viny1benzophenone):

>

6

-CCH2-CH-CH2-CHO'C

b

g

R

z

R3

R4

(47)

Conversions of up to about 80% oxetane were observed (Table 15), and quantum yields in the solid phase were independent of temperature between 23 and 65°C and relativey low (0.012). No change was observed at the glass transition temperature (Tg = 40°C). Such a result agrees with a number of studies of diffusion coefficientsand equilibrium solubilitiesof gases in amorphous polymer, which show that there is often no abrupt change in diffusivity or solubility at Tg for gases that are small in relation to the polymer repeating unit. A summary of the processes involved in the solid-phase cycloaddition is proposed ir. the following:

129

PHOTOCYCLIZATION

TABLE 14. Glass Transition Temperature of Polyisoprene and Its PhotochemicalAdduct with RenzophenoneDetermined by DSC Irradiation Time (min)

Conversion

0

15 30 45

60

120

Tg

(%)

("C)

0 29.6 38.2 42.0 48.5 57.4

-64.9 31 37.8 37.6 41.2 45.8

TABLE 15. Properties of Cycloadducts between Poly(styrene-coVinylbenzophenone)a and Various Olefins Olefins

h1

Conversion to Oxetane (%)

unreacted Ketone (%)

(dLg-9

79 72 82 61

2 7 1 11

0.44 1.49 1.09 0.50

Isobutene ZMethyl-2-butene 2-Methyl-2-hexene 2,3-Dimethyl-2-butene

"[q] = 1.43 dL g-', in benzene at 3O.O"C. q n benzene at 30.0"C.

42C=0 2(b2C=O* (TI) Excitation hu

T,

-

A 42C=0 TI

t

+ hv'

4,C=O

I

4

(48)

Phosphorescence

(49)

Nonradiative decay

(50)

1%

PHoTocHEMlsTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS

T1 + (CH&C=CH,

+26-OH

+

CH3 * I CH2-C=CH,

(52)

The quantum yield of oxetane formation is then equal to the rate of photocycloaddition divided by the sum of rates of all processes which deactivate the ketone triplet (Eq. 54):

where a = k2/(k2 + k3), and [I] and [RH] are the effective concentrations of isobutene and of polymer hydrogen, respectively. It is clear from Eq. 54 that , , , , ,$ is a function not only of the rate of photocycloaddition but of the rates of all other triplet deactivating processes. It is possible that changes in kl may be offset by changes in one or more terms in the denominator of Eq. 54, which would lead to a quantum yield of oxetane formation apparently independent of temperature.

XVII.

CONCLUSIONS

What can be seen from the foregoing examples is that one can use the photochemistry of small model compounds to predict the photochemistry of a polymeric material provided that certain structural features are included and that one has some idea of the free volume required for the conformational changes or molecular motions necessary for the formation of the excited state and rearrangement or disproportionation into products. It can be concluded that reactions which require very little change in the geometry of the excited state from that of the reactants should proceed as well in solid glassy polymer matrices as in solution. Dissociation of free radical pairs will be relatively efficient in the solid state if one of the components is a small free radical, but will be significantly inhibited if both components are polymer radicals. Reactions which can be considered to be associated with caged radicals, such as the photo-Fries and certain internal cyclizations, will require very little free volume and can be expected to be quite efficient in solid polymers, even below the glass transition, whereas photochemical processes like the Norrish type-11process will be expected to be substantially reduced in glassy polymers below Tgunless the geometry of the cyclic six-membered ring is particularly favored by steric factors in the chain, so that the most stable conformation corresponds to that required for reaction. And finally, bimolecular reactions which require the diffusion of a small-molecule

REFERENCES

131

reagent to a species in a polymer matrix will depend on both the diffusion constant and the solubility of the material in the matrix. However, it should be noted that diffusion in solid glassy matrices, particularly of small molecules, is much higher than would be predicted from the bulk viscosity of the medium. Solid polymers generally have internal viscosities only two to three orders of magnitude less than those for simple liquids such as b e m n e or hexane, so that under suitable conditions quite efficient bimolecular reaction can be induced to occur by diffusional processes in polymeric materials.

REFERENCES 1. R. Haward, in Molecular Behavior and the Development of Polymer Materials, A. Ledwith and A. M. North, Eds., Chapman and Hall, London, 1975. 2. E. Dan and J. E. Guillet, Macromolecules 6 , 230 (1973). 3. G. Wegner, Pure Appl. Chem. 49, 443 (1977). 4. F. Bueche, Physical Properties of Polymers, Interscience, New York, 1%2. 5. J. Crank and G. S . Park, Dimsion in Polymers, Academic Press, London, 1968. 6. M. Heskins and J. E. Guillet, Macromolecules 3, 224 (1970). 7, R. M. Barrer and G. Skirrow, J. Polym. Sci. 3 , 549 (1948). 8. J. Brandrup and E. H. Immergut, Eds., Polymer Handbook, 2nd ed., Wiley, New York, 1975. 9. J. E. Guillet, in Photophysical and Photochemical Tools in Polymer Science, M. A. Winnik, Ed., Reidel, Dordrecht, 1986. 10. J. Franck and E. Rabinowitsch, Trans. Faraday SOC.30, 120 (1934). 11. R. M. Noyes, Progr. React. Kinet. 1, 128 (1961). 12. T. J. Chuang, G. W. Hoffman, and K. B. Eisenthal, Chem. Phys. Lett. 25, 201 (1974). 13. J. W. Moore and J. E. Guillet, manuscript in preparation. 14. W. Braun, L. Rajbenback, andF. R. Eirich, J . Phys. Chem. 66,1951 (1962). 15. J. E. Guillet and J. C. Gilmer, Can. J. Chem. 47, 4405 (1969). 16. J. A. Slivinskas and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 11, 3043 (1973). 17. J. A. Slivinskas and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 12, 1469 (1974). 18. G. H. Hartley and J. E. Guillet, Macromolecules 1, 413 (1968). 19. P. I. Plooard and J. E. Guillet, Macromolecules 5 , 405 (1972).

132

PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORF'HOUS WLYMERS

20. J. E. Guillet and R. G. W. Nomsh, Proc. R. SOC.London, Ser. A 233, 153 (1955). 21. K. F. Wissbrun, J. Am. Chem. Soc. 81, 58 (1959). 22. J. E. Guillet, Polymer Photophysics and Photochemistry, CambridgeUniversity Press, Cambridge, 1985, Ch. 10. 23. A. C. Somersall, E. Dan, and J. E . Guillet, Macromolecules 7,233 (1974). 24. J. E. Guillet and M. Andrews, manuscript in preparation. 25, G. H. Hartley and J. E. Guillet, Macromolecules 1 , 165 (1968). 26. F. Sitek, J. E. Guillet, andM. Heskins, J. Polym. Sci. SymposiumNo. 57, 343 (1976). 27. J. E . Guillet, Naturwissenschafien 59, 503 (1972). 28. S. K. L. Li and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 18, 2221 (1980). 29. E. Dan and J. E. Guillet, Macromolecules, 6 , 230 (1973). 30. J. E. Guillet, S. K.L. Li, and H. C. Ng, in Materials for Microlithography, L. F. Thompson, C. G. Willson, and J. M. J. Frechet, Eds., ACS Symp. Ser. No. 266, 1984, p. 165. 31. J. E. Guillet, S. K.L. Li, S. A. MacDonald, and C. G. Willson, in Materials for Microlithography, L. F. Thompson, C. G. Willson and J. M. J. Frechet, Eds., ACS Symp. Ser. No. 266, 1984, p. 389. 32. S. A. MacDonald, H. Ito, C. G. Willson, J. W. Moore, H. M. Gharapetian, and J. E. Guillet, in Materialsfor Microlithography, L. F. Thompson, C. G. Willson, and J. M. J. Frechet, Eds., ACS Symp. Ser. No. 266, 1984, p. 179. 33. T. Kilp, B. Houvenaghel-Defoort, W. Panning, and J. E. Guillet, Rev. Sci. Instrum. 47, 1496 (1976). 34. T. Kilp and J. E. Guillet, Macromolecules 10,90 (1977). 35. T. L. Nemzek and J. E. Guillet, Macromolecules 10, 94 (1977). 36. S. A. M. Hesp, M.Sc. Thesis, University of Toronto, 1987; S. A. M. Hesp and J. E. Guillet, manuscript in preparation. 37. J. A. Slivinskas and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 11, 3057 (1973). 38. P. Hrdlovic and I. Lukac, in Developments in Polymer Degradation 4 , N. Grassie, Ed., Applied Science, London, 1982. 39. F. J. Golemba and J. E. Guillet, Macromolecules 5 , 212 (1972). 40. I. Lukac and P. Hrdlovic, Polym. Photochem. 2, 277 (1982). 41. T. Kilp and J. E. Guillet, Macromolecules 14, 1680 (1981). 42. P. Hrdlovic and J. E. Guillet, Polym. Photochem. 7, 423 (1986). 43. P. Hrdlovic, J. C. Scaiano, I. Lukac, and J. E. Guillet, Macromolecules 19, 1637 (1986).

REFERENCES

133

44. S. K. L. Li and J. E. Guillet, Mucromlecules 10, 840 (1977). 45. D. Gegiou, K. A. Muszkat, and E. Fischer, J. Am. Chem. SOC.W,12 (1968). 46. G. A. Delzenne, Znd. Chim. Belg. 34, 249 (1974). 47. J. L. R. Williams, Fortschr. Chem. Forsch. 13, 227 (1969). 48. K. S. Lyalikov, G. L. Gaeva, and N. A. Evlasheva, Tr. Leningrad Znsr. Kinoinzh. 16, 42 (1970). 49. R. Anet, Can. J. Chem. 40, 1249 (1962). 50. P. Hyde, L. J. Kricka and A. Ledwith, J. Polym. Sci., Polym. Lett. Ed. 11, 415 (1973). 51. M. A. Meador and P. J. Wagner, J. Am. Chem. SOC. 105, 4484 (1983). 52. J. E. Guillet, W. K. MacInnis, and A. E. Redpath, Can. J. Chem. 63, 1333 (1985). 53. H. C. Ng and J. E. Guillet, Mucromlecules 10, 866 (1977). 54. D. A. Holden and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 18, 565 (1980).

Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.

PHOTOCHEMISTRY OF SIMPLE OLEFINS: CHEMISTRY OF ELECTRONIC EXCITED STATES OR HOT GROUND STATE? Guy J. Collin apartement des Sciences Fondamentales, Universit6 du Qukbec B Chicoutimi, Chicoutimi, Qudbec, Canada G7H 2B1

CONTENTS

I. Introduction II. The ethylene case III. The methyl substitutedethylenes A. Propene B . Other methylated ethylenes IV. The other acyclic olefins A. The p(C-C) bond rupture B . The excess energy distribution C. Photosensitization D. The isomerizationof acyclic alkenes E. Conclusion V. The cyclic monoolefins A. The fragmentationprocesses in direct photolysis B . Fragmentation in photosensitizedexperiments C. Isomerizationprocesses D. Conclusion VI . Conclusion Acknowledgments References 135

136

PHOTOCHEMISTRY OF SIMPLE OLEFINS

I. INTRODUCTION The very far UV and vacuum UV photochemistry of gaseous alkenes has been studied for more than 25 years. Several laboratories have looked at the stability of the photoexcited molecules at various wavelengths. The absorption threshold for alkenes is located between 200 and 230 nm, depending on the number of alkyl substituents attached to the double bond (1,2). Of course, the use of the true resonance line or mercury (A = 184.9 nm) was very easy. However, wavelengths as short as 104.2 nm have been used, i.e. at energies much higher than the ionization onset of these molecules: 10.51 3 I.P.(alkenes) B 8.4 eV (3). Much of this work has been performed at 147.0 nm (8.4 eV). At this point it must be mentioned that the 1980s have seen the availability of rare gas-halide excimer lasers that produce light in this spectrum region. Thus, the variety of experimental conditions is large. In all cases, fragmentation processes have been observed. In some of these studies, the geometric cis-trans isomerization process as well as different structural ones have been reported. Conversely, photoexcited ethylenic compounds are not known to fluoresce very efficiently (4). On the other hand, spectroscopy has undergone many developments. Through the use of supercomputers, ab inifio calculations are more and more powerful. Although many details are still lacking or are even controversial, the nature and energetics of various electronic excited states for this group of molecules are better understood (2,5). Since the absorption of a photon will create an electronically excited molecule, it is tempting to look at the properties of each of thesse states in order to get a better insight into the different reaction pathways leading to products (6). It is the aim of this review to update the links between the photochemical behavior of ethylenic molecules and their electronic properties. In the past 20 years, several studies have been published (7). In order to keep the length of this review as short as possible. we shall avoid making a systematic review of all the earlier references.

II. THE ETHYLENE CASE Of course, ethylene is the first and the simplest molecule of this group. Its direct photochemistry has been studied for many years; several laboratorieshave looked at various aspects of its behavior under various photon beams. One of the first studies, if not the first, appeared in 1961 (8): it identified two main fragmentation channels involving the 147.0 nm photoexcited molecule:

THE E"XYLENE CASE

137

with +2 z +3. One year later, by photolyzing CH2CD2, Okabe and McNesby showed that the terminal elimination of hydrogen dominates the 1,2-elimination (9), giving rise to the formation of a vinylydene intermediate:

Moreover, both works agree that it is not necessary to call upon the formation of vinyl radical intermediates. If transient vinyl radicals are formed in the process in Eq. 3, they must have sufficient internal energy to decompose in a very short time before collision. In fact, at a longer wavelength, it was later observed that part of the acetyleneformation involves energized vinyl radicals (1Oa). Moreover, the observed decomposition rate constant is in good agreement with what can be calculated by using Rice-Ramsperger-Kassel-Marcus (RRKM) assumptions (lob):

C2H2

+

H

(8)

The 184.9 nm photolysis of C2H4 was studied by Borrell et al. (1 1) and Glasgow et al. (12). The latter group undertook a systematic study between 147.0 and 193.1 (a carbon lamp) nm and made the following remarks: (1) the process in Eq. 2-the molecular elimination of hydrogen-is independent of various parameters tested (pressure, temperature, wavelength), and 42 0.42 between 147.0 and 184.9 nm and between 0.1 and 100 Tom; (2) the process in Eq. 3 decreases with increasing pressure and increases with increasing photon energy; (3) the processs in Eq.6 decreases with an increase in photon energy. Hara and Tanaka, one year later, arrived at somewhat different conclusions and values, although the latter are in the same range (1Oa). The photochemistry of liquid and solid ethylene at 184.9 nm shows that the ratio of the free radical to the molecular decomposition is about 0.03 in the liquid at - 160°C (14). The same work indicatesthat there was isotopic scrambling in the various unreacted dideuterioethylenes. This scrambling was assumed to involve the relaxation of excited ethylene to ethylidene and may be followed by the molecular elimination of H2:

PHOTOCHEMISTRY OF SIMPLE OLEFINS

138

in agreement with the isotopic scrambling reported in the acetylene product formed in the 147.0 nm solid phase photolysis of CH2CD2 (15). It was also proposed that the formation of methylcyclopropane involves the reaction of excited ethylidene with ethylene in the solid phase (16). Finally, the study of ethylene photosensitization (A = 253.7 nm) involving a triplet excited state shows similar processes leading to fragmentation (H2 + C2H2)in competition with pressure quenching, cis-trans isomerization, and isotopic scrambling (17). Decomposition of ethylene into acetylene and hydrogen was scarcely observed for the Cd(3P1)-photosensitizedreaction over the 275-350°C range: A = 326.1 nm (17a). The mechanism involved in the direct photochemistry of ethylene has been recently questioned by Laufer (18). He observed by absorption spectroscopy (A = 137.4 nm( the formation of a triplet (3B2)vinylidene with a quite high quantum yield, probably in a secondary process (18b). Thus, no one can preclude the involvement of triplet intermediates, although they are generally ignored. More disturbing is the fact that at the shortest delay times attainable with his system, i.e. 4 ps after the flash, he was unable to observe acetylene (Fig. 1). Since it is admitted that the singlet vinylidene radical has a very short lifetime (T < lo-" s with respect to rearrangement to acetylene), he concluded that there is no evidence of the formation of ground state 'A, vinylidene.

I

I

10

8 In

c c 3

6

.,

/-x

,'

'

I

I

x; I

/.

I

'

/=/',

'\

\

x

\ \ \

.

\

1 . 7

.l_i

.... .

.

0

Time ( p s )

X,

Figure 1. Time profdes for acetylene (0)and vinylidene (3B2)( x ) in the flash photolysis of ethylene (arbitrary units and different y-scales). Reprinted with permission from Ref. 18a and 18b. Copyright Elsevier Sequoia SA.

THE ETHYLENE CASE 205

c

>

139

X/nm

185

180

170

160

1.2

ln

2

W

n

0.0

48.10

54.58 Frequency

55.56

/

cm-'

59.61 Y

lo3

63.66

Figure 2. The absorption spectrum of ethylene. Broken line: nitrogen pressurized (104 am) spectrum. From Ref. 13 with kind permission of the authors.

The absorption threshold for ethylene is located at 200 nm (Fig. 2). Its spectrum consists of diffuse bands which become a continuum at shorter wavelengths. The diffuse bands as well as the continuum are ascribed to the IT* + IT transition (1,2,5). The first singlet Rydberg band is superimposed on the V +N transition: h = 174 nm. Upon addition of a high pressure of nitrogen, there is an important broadening of the Rydberg bands on the high energy side of the spectrum, while the V +- N transition is not affected (2). This relative simplicity in the absorption spectrum does not reveal all the available excited states, and it is a very difficult or even impossible task to link the photochemical processes and the different known excited states (5,19) (see Fig. 3) - or the calculated one (20) (see Table 1). It must be emphasized that there is a tremendous need for more experimental and theoretical information to get a better insight into the spectroscopy of ethylene (5). In fact, several recent studies from various laboratories have shown how complex and fascinating is the field of excited states of ethylene (5). Different techniques or approaches are used: absorption spectroscopy (2 1-23), magnetic circular dichroism (24), photoelectron spectroscopy (25,26), electron (27) and ion impact (28), multiphoton ionization (29), ab inifio calculations (30,31), etc. At this point, it is relevant to note that theoretical work using ab initio MO-CZ methods indicates that the reactions of twisted singlet excited ethylene, to give directly either the lowest singlet state of vinylidene+H2 or ethylidene, are easy pathways that have relatively low computed activation energies, in partial contradiction with Laufer's observation reported above. The fragmentation of

140

PHOTOCHEMISTRY OF SIMPLE OLEFINS

I*.

‘E

Figure 3. Schematic potential energy diagram for ethylene.

+

the singlet ethylidene, giving rise to acetylene H2formation, is also calculated not to be difficult (32). Finally, the authors add that they are far from a complete knowledge of the photochemical processes, although “it would be best not to describethe product-forming processes as arising from a conceptually hot groundstate molecule” (32). In short, the photochemistry of ethylene seems better explained in terms of undefined electronic excited state(s) where vinylidene as well as ethylidene transient species may be involved and molecular as well as atomic hydrogen species are formed.

III. THE METHYL SUBSTITUTED ETHYLENES A.

Propene

The simplest alkene of this subgroup is propylene. Its first vacuum UV photochemistry study was published in 1965 (33) and was followed by several others (34-36). For example, at 147.0 nm, many products were identified. From partially deuterated material, as well as from the effect of added nitric oxide, the molecular formation of hydrogen and methane was observed as well as those of hydrogen

141

THE METHYL SUBSTITUTED ETHYLENES

TABLE 1. Excited States of Ethylene-h, Upper State Configuration 3

Symmetry

Frequency, (cm- I)

eV

*B,,

1B3"

35,200 53,720 57,338 61,300 62,790 62,905 65,735 66,875 69,080 69,531 71,813

B3u B1u

75,250

vert., 4.36 advert., 6.66 advert., 7.1 1 vert., 7.60 advert., 7.78 advert.,7.80 advert., 8.15 advert., 8.29 advert., 8.56 advert., 8.62 advert., 8.90 advert.,8.98 advert.,9.33

(.rr,.rr*)

3(.rr,3s)

*BSU

'(.rr,3S)

lB3u

'(a,.rr*)

lBlU

3(a

.3PY) (.rr,3PY) 3(.rr93px) '(a93px) 3(.rr,3do) '(?r,3do) '(.rr,3dS) '(.rrr,4s) (.rr,3dxz) '(.rr94P)

3B1,

1

lB1,

3Ag 3B3u lB3u 1

'

B2,

Source: Refs. 5 , 19, 31.

atoms and methyl radicals. Although there was no indicationof measured quantum yields, a rough estimate indicates that many more methyl radicals appear than methane molecules:

W(iso-C4HIo)

+

Q'(CH4) 2 @'(C2H6)

+ CPr(l-C4Hs)

= 0.114

(1)

In this equation isobutane, ethane, and 1-butene are supposed to be formed in the appropriate combination reactions of methyl radicals plus a suitable radical. Since methane is partly formed in disproportionationreactions of methyl radical with other radical species, the abovementioned ratio is an upper value of the relative importance of the molecular elimination of methane. The relative importance of the moleculm elimination of hydrogen is not so obvious, although, at most, it counts for less than 20% of the acetylene yield. The 163.3 nm (37) and 184.9 nm photolysis (38,39) were documented much more, and a very good knowledge of the photoexcited molecule was attained. At 184.9 nm, the molecular elimination of either methane (@ = 0.04) or hydrogen (a = 0.02) is of less importance than the primary p (C-H) and (Y (C-C) bond ruptures: CP = 0.63 and 0.36, respectively (39). It appears from Table 2 that the elimination of molecular products increases with increasing photon energy at the expense of the simple rupture of the C-C or C-H bonds (36):

142

PHOTWHEh%lSTRYOF SIMPLE OLEFINS

+ CH4 , C3H$* C3H4 + H2 , C3Hg* C3H3 + H , C3HZ* +C2Hg + CH3.

-

C3H$* 4 C*H, __*

Ab initio SCF-MO calculations have been reported on the fundamental electronic state of propylene (42). They reveal that an internal 1,3-sigmatropic hydrogen shift may be in competition with the fragmentation of the excited molecule. In other words, this rearrangement may occur before the fragmentation takes place. From symmetry considerations, one can say that the ground state forbidden suprafacial reaction is allowed in the singlet excited state. Conversely, the antarafacial process, which is allowed in the ground state, is forbidden in the excited state. It must be added that from geometric consideration this antarafacial transfer is of very low probability (43). In the condensed phase photochemistry of propylene, the major primary processes occumng in the 149.5-174.5 nm range are the molecular detachment of methane acetylene and to a smaller extent hydrogen C3H4 (44).These observations are rather in contradictionwith the above reported gas phase results. However, these results can be explained on the basis of a fast stabilizing process in the matrix, involving either the electronic excited molecule or the hot electronic ground state or both. Recombination of radical fragments in the cage may also be part of the explanation. No quantum yields are available, so that further discussion is risky. Let us say only that the molecular products are similar to those observed in the gas phase at 184.9 nm. The triplet photochemistry of propylene has also been studied by several laboratories and in different conditions (40). Cis-trans isomerization is the main process and is observed in the presence of various sensitizers. As far as fragmentation is concerned, the C-C and C-H bond ruptures are observed in a 0.125h.O ratio (40a). In the case of the Hg(3P,) photosensitization of transpropylene-l,3,3,3-d4, no isomerization to propylene-2,3,3,3-d4 was observed. This is in marked contrast to the observation of the internal 1,2-hydrogen atom transfer observed in ethylene (4Oc). There is also formation of tiny amounts of cyclopropane and molecular methane and hydrogen (40). Coming back to the a(C-C)/P(C-H) primary split ratio (Table 3), it would be valuable to compare these values with that obtained either in the thermal pyrolysis of propene or in chemical activated systems. For example, in shock tube experiments (1650-2300 K), the dominant bimolecular initiation reaction leads to the C-C bond rupture, although a possible contribution of the p(C-H) bond rupture cannot be excluded (50). This is also observed in the decomposition of hot propene formed from ethylcarbene [(E)(C3H$) Z 414 kJ/mol]: a(C-C)/ P(C-H) 22 (51). Conversely, hot propene formed by the addition of singlet methylene to ethylene [(E)(C3Ha) % 464492 kJ/mol) gives rise to C-H bond

+

+

40a

~~~~~~~~~~~~~

-

0.2

-

11

89

40b

-

-

-

1-1.4 1-1.4 80-86 10-17

253.7+184.9a

"Photosensitization,relative yields only. 9onization potential: I.P.(propene) = 9.73 eV (41).

Total Ref.

+

C2H2 + CH4 C3H4 + H2 C3H5 H CzH3 + CH3 CzH4 + CH2 CYCIO-C~H~ [C3W1+ + e-

253.7a

0.90 38

-

-

0.03

0.40

0.04 0.02(?) 0.41

184.9

39

1.05

-

0.00

-

0.04 0.02 0.63 0.36

Quantum Yields for Sensitized and Direct Photochemistry of Propene

ProcessC,H$*

TABLE 2.

0.97 37

-

0.565 0.335 0.02

0.05(?)

163.3

20.68 36

-

-

0.21 0.06

0.27 0.04

20.68 36

0.30'

-

20.05

20.34

123.6

a0.03 20.34

147.O

144

PHOTOCHEMISTRY OF SIMPLE OLEFINS

TABLE 3. Relative Importance of the or(C-C) and p(C-H) Primary Splits in the Photolysis of Some Olefins Olefin

Ref.

Propene

163.3 184.9 253.7 174 184.9 174 184.9 202.6-206.2 253.7 184.9 >200

Isobutene cis-2-Butene

trans-2-Butene 2-Methyl-1-butene

0.59 0.571 (0=0.054) 0.11,0.12 0.90 0.95 (0=0.10) 1.02 0.96 2 0.13 1.45 0.4 1.35 2 0.20 0.73

37 39 40 39 39 45 46 47 48 46 49

rupture with a rate twice that of the C-C (52). One must add that the propene system is not an easy one, since in many cases it involves a chain mechanism and, as is known, vinyl radicals react with propene. If the C-C bond rupture is the main primary process occurring in the thermal system, this would suggest that the fragmentation of the photoexcited molecule does not involve the fundamental state. Another alternative proposal resides in the dependence of the a(C-C)/P(C-H) ratio on the energy content of the propene molecule. Unfortunately, there is some controversy about RRKM results (53).

B.

Other Methylated Ethylene

Other methylated ethylenes have been studied by different laboratories. One of the fust studies involved the irradiation of cis-2-butene at 202.6-206.2 nm at pressures between 20 adn 500 Ton (47). The collisional stabilization of the trans isomer competes with the first order decomposition reactions: cis-2-C4Hg*

-

C3H5 + CH3,

c~s-~-C~HZ* +C4H7

+

H,

k

k

2

5.0 lo8 s-'

(15)

3.5 lo8 s-1

(16)

It is concluded that the cleavage reactions occur after rapid internal conversion to the ground electronic state. Moreover, the cis-trans isomerization and isomerization to 1-butene(5% of the total reaction) occur in a short time compared to the time between deactivating collisions even at 500 Torr (47). This model can be reasonably extended to the other methylated ethylenes from their absorption

THE m

n SUBSTITUTED ETHYLENES

145

threshold to, and including, 147.0 nm. For example, the photolysis of isobutene is known to produce mainly allene and propyne plus methyl radicals and hydrogen atoms at all wavelengths (3934). The problem arises from the identification of the products coming from either the primary p(C-H) or the a(C-C) bond ruptures. This problem has recently been solved: the a(C-C)/p(C-H) ratio is in the 0 . W 0.95 range at 184.9 and 174.0 nm (39). This value must be compared with those observed in different systems (Table 3). A very interesting and intriguing effect appears to be attached to the number and location of the methyl substituents: this effect may be due to the electrophilic property of the methyl groups. Of course, the experimental a(C-C)/p(C-H) primary split ratio is very dependent on how correct and accurate the active mechanism is. Taking the recently calculated values from our own experiments (39,46), we were unable to link the increase in this ratio (going from 0.57 in propene to 1.35 in trans-2-butene) to any simple property of these molecules (39). In fact, it is likely that the a(C-C)/ p(C-H) ratio is not dependent on only one parameter. The variation of this ratio may be discussed in terms of spectroscopy. Both Rydberg and valence states are populated at 184.9 nm. Do the two fragmentation pathways result from the same excited state or different ones? If each exit channel is linked to one electronic state, the a(C-C)/p(C-H) ratio can be explained in terms of differences in the absorption process. Another possibility resides in the above mechanism itself. It is consistent with the view that the internal conversion of electronic excitation energy to vibrational energy preceeded the bond cleavage process. However, it cannot be precluded that bond cleavage is part of the conversion process itself.

150

170

Wavelength

/

nm

190

Figure 4. The UV absorption spectrum of I-butene. Reprinted with permission from Ref. 41. Copyright (1962) American Institute of Physics.

146

PHOTOCHEMISTRY OF SIMPLE OLEFINS

In that case, the geometry of the molecule may play a role in the redistribution of energy. In all cases, the quantum yield of the molecular elimination of either methane or hydrogen is considered to be smaller than 0.05. Thus, the main primary processes involve either the a(C-C) or the B(C-H) bond ruptures. This observation differs from that made for ethylene, where at least 40% of the fragmentation involves the molecular elimination of hydrogen. May this behavior be linked to the differences observed in the absorption spectra? At least, it may be said that well-defined absorption bands, one of which is probably Rydberg in nature, are observed in the ethylene spectrum. Conversely, the spectra of methyl substituted ethylenes are rather unstructured (1). The W absorption spectrum of l-butene is shown in Figure 4. We shall come back later to this pint. One interestingreport must be mentioned here. On direct excitation in solution at 228.8-214.4 or 213.9 nm, cis-trans isomerization is the major reaction path observed both in cis- and tram-2-butene. Moreover, dimers-tetramethylcyclobutanes-are formed, and this formation is stereospecific (55):

Thus, it seems possible that these products arise from an excited 2-butene molecule originally having either the cis or the trans structure. From the known structures of the electronic excited states of ethylene, this excited molecule may be the Rydberg excited state, whose structure is not far from the original planar structure (Fig. 3). The involvement of either the ‘V and 3R states-which have a skew structure-will lead to nonstereospecific cyclobutane derivatives. A theoretical study of the addition process has shown from the localized state correlation diagram that the ?r,R(3s)Rydberg singlet state of ethylene can interact with the ground state of another ethylene molecule (56). Moreover, a very rapid reduction in the extent of photochemical cyclodimerization of liquid 2-butene as a result of dilution was observed. It was tentatively suggested that bimolecular diffusional kinetics are not adequate for description of B* B +-dimer reactions and that something like a solvent cage effect is operative. It seems possible that the excitationprocess itself involves pairs of adjacent molecules which are directly excited to excimers. Similar explanation was also proposed for the formation of dimeric compounds in the irradiation of 1,3-~yclohexadieneat long wavelength (57).

+

THE OTHER ACYCLIC OLEFINS

147

The direct or sensitized cis-trans photoisomerization has been described by many authors (58). The Hg$Pr) photoisomerizationwas explained on the basis of vibrationally excited triplet molecules. In the case of the Cd(3Pl), the photosensitization of unsaturated hydrocarbons mainly results in the cis-trans process. The main difference between mercury and cadmium sensitization resides in the lower energy content delivered in cadmium experiments: 366.4 in comparison with 469.4 kllmol (59). A very recent study of the zinc photosensitization of 2butene concludes with the cis-trans isomerization process as the main process (60).

IV. THE OTHER ACYCLIC OLEFINS A.

The p(C-C) Bond Rupture

In this category appear all the alkenes having at least one p(C-C) bond. The Occurrenceof the primary P(C-C) bond rupture in acyclic olefins was first shown to be the main process by Callear and Lee. Using a flash photolytic system (A > 160 nm), they generated various allylic radicals and were thus able to measure the electronic spectrum of these radicals in the 210-250 nm region (61). The quantum yields of the rupture of this bond is @ 2 0.8 (47,49,62). For example, the 147.0 and 163.3 nm photolysis of n-1-hexene leads to the primary p(C-C) bond rupture with a high quantum value (63):

This simple mechanism leads to the well-known Stern-Volmer equation: the ethylene quantum yield is linked to the total pressure through the following expression (66):

where the @-values are the quantum yields measured at any pressure and the @,-value is the quantum yield obtained by extrapolation to zero pressure. Figure

PHOTOCHEMISTRY OF SIMPLE OLEFINS

148

x lo3 Nm-*

a

12

12

0

20

LO

Pressure / Torr

80

60

100

Figure 5. The reciprocals of the ethylene quantum yields in th3 photolysis of n-l-hexene at various wavelengths versus the pressure. From Ref. 63b.

5 shows the good linearity obtained from the Stern-Volmer plot. From the @,-value, @&,H4) 2 0.9, the relative importance of the processes in Eqs. 20-21 may be seen. Thus, more than 80% of the absorption of photon leads to the ethylene formation through the primary p(C-C) bond rupture, followed by the secondary fragmentation of the energized n-propyl intermediate (Table 4). The 184.9 nm photolysis of 2,3- and 3,3-dimethyl-l-butene has also been recently studied. As in the previous case, the p(C-C) bond rupture is the main primary process observed. In fact, the @o(CH3)-valuesmeasured at zero pressure are close to unity (67a). This situation was also observed in cis-3-hexene and 4methyl-cis-2-pentene (67b). From the slope/interceptratios, the kJkd-values may be obtained. These Stern-Volmer plots are shown in Fig. 6:

[@(CH,)]-' =

4-l

+ $-I 5 [MI kd

x103 4

Alkene

Nm-2

a

12

16

pressure / Torr

Figure 6. The reciprocals of the primary methyl radical quantum yields in the 184.9 nm photolysis of 2,3(0) and 3,3-dimethyl-l-butene (a),cis-3-hexene (a),and 4-methyl-cis2-pentene (0) versus the pressure. From Ref. 67.

TABLE 4. Quantum Yields for Direct and SensitizedPhotochemistry of 1-Hexene ~

Direct

~~~~~~~

Sensitized"

Process n-1-C6€€@-+

147.0

163.3

184.9

253.7

C3H-T + C3H5 CZH3 + C4H9 2C3H6 C2H5 + C4H7 (CH,)2-CyClO-C,H6 CH~-CYC~O-C~H~ cyclo-C& * 2

0.80 0.05 0.06 0.15

0.65 0.10 0.04 0.10

0.75

Not observed

0.03, 0.13

Total Ref.

1.06 63b

0.89 63a

0.995 63b

0.08

Z0.14

Z0.07 0.01 0.005 0.225" 75

"1-hexene is also among the products: recyclization of 1,&hexanediyl radicals.

149

150

PHOTOCHEMISTRY OF SIMPLE OLEFINS

TABLE 5. Quantum Yield Valuesof the Major Processes in the Photofragmentation of n-Butene and n-1-Penteneat Various Wavelengths

Quantum Yield

n-Butene Wavelength (nm) 184.9 174.0 147.0 123.6

Energy (eV) 6.4 7.1

8.4

10.0

Ref. 62 68a 69a 69b

n-Pentene

PW-C) (C-W Cleavage Cleavage 0.71 0.66 0.51 0.29

0.12 0.22 0.26 20.23

Ref. 62 68b 70a 70b

C-C

C-H

-

-

0.64

0.08

0.47

0.26

0.16 0.24

The importance of the p(C-C) bond cleavage seems to be sensitive to the incident wavelength. For example, Table 5 shows the quantum yields of the p(C-C) and the C-H bond ruptures. Obviously, the importance of the p(C-C) bond rupture decreases with a decrease in the wavelength or, better said, an increase in the incident energy. Conversely, the C-H cleavage becomes more and more important at greater energy. These results are in agreement with a fragmentation taking place from the hot ground state, where it is well known that the p(C-C) bond is the weakest one (64).Moreover, from the Stern-Volmer plot of the methyl radical quantum yield, the ks/kd ratio may be obtained (Eq.111). By assuming that k, is the rate constant for the stabilizing collision process (obtained from the gas kinetic theory), or using the process in Eq. 22b as an internal clock, kd may be estimated. From these values, the lifetimes of the photoexcited molecules may be obtained: they are shown in Table 6. Taking advantage of the general P(C-C) bond cleavage shown above, recent studies involving an excimer ArF laser have been published. The 193.2 nm ArF laser line pumps an electronic excited state of various substituted alkenes, and the absorption spectra of transient substituted ally1 radicals were observed with time. From these results, the formation rates of allylic radicals have been observed. The lifetimes of the photoexcited molecules so calculated are reported in Table 6 (71), as well as those measured from the Stern-Volmer plots of the methyl radical quantum yields described above. First, it must be said that the results agree fairly well, if one takes into account the two diffeient families of experiments: see, for example, the n-I-hexene values. Moreover, in the C6 family, the lessening of the lifetime of the vibrationally excited molecule is probably a direct consequence of the number of available reaction channels (1 in 1-hexene, 2 in 2,3-dimethyl-l-butene, and 3 in 3,3-dimethyl-l-butene) and also a slight decrease of activation energy with an increase of the ramification of the parent molecule (67).

THE OTHER ACYCLiC OLEFINS

151

TABLE 6. Lifetimes of the Far UV Photoexcited Unsaturated Akenes Alkene 2,fDimethyl2-butene n-1-Hexene n-1-Hexene cis-3-Hexene 4-Methyl-2-pentene 2.3-Dimethyl1-butene 3,3-DimethylI-butene 1-Heptene 2,3-Dirnethyl2-pentene 2,3,3-Trimethyl1-butene

A (nm)

~(ns)

Origin"

Ref.

193.2

70

Abs. sp.

71b

184.9 193.2 184.9 184.9 184.9

2 5 r 2 2 3

s.-v.

s.-v. s.-v. s.-v.

67 71b 67b 67b 67a

S.-V.

67a

184.9

1

0.35

Abs. sp.

193.2 193.2

33 37

Abs. sp. Abs. sp.

71b 71a

193.2

17.9

Abs. sp.

71a

"S.-V.: Results from Stern-Volmer plots of one of the primary fragmentation processes; Abs. sp.: results from the absorption spectra of the primary ally1 fragments.

More recently, N. Nakashima et al. made a systematic study of the 2-methyl-lalkene family

H,C=C(CH3)CH2),CH$*

CH,C(CH,)CH,

+ (CHz),CH3

(23)

m = 0 , . . . ,5 They confirmed the trend reported above: the bigger the molecule is, the longer is its lifetime and the smaller is its dissociationrate constant (Table 7). Moreover, the dissociation rate constants so measured are in good agreement with RRKM calculations (Fig. 7) (72). All these results may be rationalized on the grounds of the following mechanism:

TABLE 7. Dissociation Rate"kdof Various 2-Methyl-1-alkenesat 193.2 nm (Eq. 23) m

Olefm 2-Methyl-1-butene 2-Methyl-1-pentene 2-Methyl-1-hexene 2-Methyl-1-heptene 2-Methyl-1-0ctene 2-Methyl-1 -nonene

kd(106s-') >300 150 19 4.5 1.25 < 0.5

"Obtained from absorption spectroscopy: Ref. 72.

m : see

process 23

Figure 7. The relation between observed (0)and RRKM (0) calculated rate constants for the decomposition of various photoexcited 2-methyl-1-alkene molecules at 193.2 nm. From Ref. 72 with kind permission of the authors.

152

THE OTHER ACYCLIC OLEFINS

153

B. The Excess Energy Distribution Coming back to the n-1-hexene system (Eqs. 20-21), the k& ratio for the excited n-C3Hq intermediates can be extracted from either the Stern-Volmer intercept with the pressure axis or the slopehtercept ratio. For example, in n-1-hexene and in terms of pressure, the k& value is 160 Torr at 147.0 nm. Using the RRKM calculations made by Rabinovitch and Setser (73), this value leads to an excess internal energy of 87.8 kJ/mol for the n-propyl precursor. By taking into account the energy needed for the reaction in Eq. 21a one can attribute an internal energy of 217 kJ/mol to the n-propyl radicals (62) formed in the process in Eq. 20. The photon energy is 811 kJ/einstein at 147.0 nm. Since an energy of 297 kJ/mol is required for the primary p(C-C) bond rupture (Eq.20), 8 11 - 297 = 5 14 kJ/mol must be distributed among the fragments. If the n-propyl fragment has 217 kJ/mol, the ally1 species will have the difference, i.e. = 514 - 217 = 297 kJ/mol. Since the splitting of the photoexcited molecule results from the transformation of vibrational energy, a large amount of translational energy is not expected in the fragments, although some energy may be released in relative motions (66). If this is true, then on neglecting this translational energy, the smaller fragment C3H5carries more energy (58%) than the larger fragment C3H7,which has 42%. The fragmentation of the photoexcited molecule probably occurs for long enough after its formation to allow an internal redistribution of the energy in the vibrational framework of the molecule, but not long enough for a complete randomization of this internal energy. This deduction agrees very well with Chesick’s earlier statement in that the cleavage occurs after rapid internal conversion to the ground electronic state (47). It must be recalled at this point that various RRKM calculations may be used (step ladder model, exponential model, etc.). Each of them involves various assumptions and several adjusted parameters. If vibration frequencies of the starting alkenes are relatively well known, those of the excited complex must be approximated and some of them are chosen to fit experimental values. Thus, the observed agreement may be fortuitous and cannot preclude the possibility that bond cleavage is actually part of the internal conversion process itself. Other vibrations might be “coreceiver” modes. Although the primary C-H bond rupture has a low quantum yield in the photolysis of 1-akene, Niedzielski et al. have confrmed the possibility that hydrogen atoms formed in the 8.4 and 10.0 eV photolysis of 1-butene may be hot (74). In their experiments, the addition of a hydrogen atom to the double bond gives rise to a vibrationally hot butyl radical. This hot butyl radical may eventually decompose, leading to the formation of propene. From kinetic treatment and using a plot of the rate constant for dissociation versus excess

PHOTOCHEMISTRY OF SIMPLE OLEFINS

154

energy reported by Rabonivotch and Setser (73), the energy of these hot atoms can be estimated to be 0.26 eV (25 kJ/mol) and 0.6 eV (58 kJ/mol) at 147.0 and 123.6 nm, respectively. Unfortunately, in this system, hydrogen atoms are formed in the primary as well as secondary fragmentation processes. Thus, the process leading to these hot atoms is not obvious, although on thermodynamic grounds, it can be reasonably assumed that they are formed in the primary fragmentation processes.

C. Photosensitization The H S ( ~ Pphotosensitization ~) of alkenes gives rise to the cis-trans isomerization, [1,3J-sigmatropic hydrogen shift, and cyclization of a triplet biradical, after internal hydrogen atom shifts. The vibrationally excited triplet states of 1-hexene and 2-octene were proposed to be involved in an olefinic type I1 reactions consisting of an intramolecular 1,Shydrogen abstraction through a six membered transition states and subsequent reaction of the resulting radicals. This was shown to be in sharp contrast to the well-established allylic C-C and C-H bond cleavage of alkenes without y-hydrogen (75). The results are also very different from those observed in direct photolysis (Table 4). For example, in the case of 1pentene, at pressure around 100 Tom, k26&6&2&k2a = 100:35:7: 1 (76):

-

1.s-shin

3(

1-C5H10) * CH2CH2CH2tHCH3__* methylcyclobutane I ,CshiH

3( 1-C5H10) 3(

l-C5HI0)

3( l-C5Hlo)

I .3-sbift

1.4-shift

CH3tHCH26HCH34 cis-dimethylcyclopropane 0

.

-

CH,CH2CHCHCH3 4 cis-

CH2CH2CH2CH2tH2

+

+ trans-2-pentene

cyclopentane

(264 (26b) (26~) (264

More recently, a detailed study of the Hg(3Pl) photosensitization of 3-methyl1-butene was published (77): ethane is a major product (@ S 0.07) as well as olefinic and methyl substituted cyclopropane isomers (CP S 0.08). The addition of molecular oxygen removes the 2-pentene formation (@ = 0.06). Thus, it may be assumed that the Hg (3P1) photosensitization of 3-methyl-1-butenemainly results in the primary p(C-C) bond rupture. Conversely, the dimethylcyclopropane yield decreases slightly in the presence of oxygen. A mechanism mainly involving both vibrationally excited and thermalized triplet 2-methylbuta-1,3-diyl radicals was proposed. These radicals are formed from the excited triplet 3methyl-1-butene through an internal hydrogen atom shift. A similar mechanism was also proposed in the case of the Hg(3PI)photosensitization of 3,3-dimethyl-1butene (78):

THE OTHER ACYCLIC OLEFINS

3A* ,A*

Hg('Pi)

-

3M1B

__*

,(3MlB)*

CH,

(M)

__f

,(A)

3A* 4 '(A*)

+

-+

3[cH2CH(CH3)6HCH3]*

155

(27)

(3A*> CH3CHCHCH2

(28)

-

__*

dimethyl-1,2-cyclopropane

dimethyl-l,2-cyclopropane

(29) (30)

D. The Isomerization of Acyclic Alkenes The photoisomerization of acyclic alkenes is well documented in both the direct and the photosensitized experiments (79). Of course, the cis-trans process does not need to be discussed here: see above and (58). Let us only recall that in direct photochemistry it has been linked to the skew structure of the '(n,n*) excited state (80). The internal methyl shift was attributed to the Rydberg '[n,R(3s)] electronic state. This process is particularly efficient in the gaseous and liquid phase photoirradiation of tetramethylethylene (81-83):

(CH,),C=C(CH3)2 [(CH3)3C-C-CH3] [(CH3)&-C-CH31

(C6H12)Ry

-

[(CH3)3C-C-CH3]

(CH3)3CCH=CH2 (DMB) (CH,),C

CH2 / - kHCH, (TMC)

(31)

(32) (33)

The ratio (b(DMB)/(b(TMC) is independent of wavelength between 184.9 and 228.8 nm (82,83) and temperature between 10 and 70°C (82), and is equal to 1.5 +- 0.15. These reactions are believed to involve the formation of a carbene transient intermediate(80). This carbene intermediateundergoes either an internal hydrogen atom transfer with the formation of 3,3-dimethyl-l-butene (Eq.32) or an insertion of the carbene center in a C-H bond of the remote methyl groups with the formation of trimethylcyclopropane (Eq. 33). The importance of this methyl shift (Eq.31) increases with the number of alkyl substituents around the double bond (83). It is known that this number has a stronger effect on the energy of the singlet Rydberg '(n,3s) excited state than on the 'V(n,n*) state (20,80).Both transitions are lowered in energy, but the Rydberg states are much more affected. Figure 3 gives the vertical excitation for the pertinent processes. As far as the absorption spectrum of tetramethylethylene is concerned, it shows a strong V + N absorption band with its maximum centered at 185 nm. Another band, well separated from the previous one, is located between 210 and 240 nm (48000 - 42000 cm-'). In a thin polycrystalline film (T = 23 K), this band is

I

I

I

L _ _ -

Cd

4.0

4.4

Wovenumber

I

Zn

4.8

I' I' 1 Hg

ArF

/

52

I

-

5.6

cm-'

Figure 8. The absorption spectrum of tetramethylethylene in the gas phase. From Ref. 83 with kind. permission of the authors.

000

BOO

-

I

E

7

x

600

500

Figure 9. Effects of the number of methyl substituents on energy levels in ethylenic compounds.

156

THE OTHER ACYCLIC OLEFINS

157

severely perturbed (2) and it corresponds to a IT --5, R(3s) transition: this is shown in Fig. 8. Unfortunately, the values for the 0,O transition are not so well known. This is important, since the minimum energy for the V(IT,IT*)excited state may be lowered by as much as 2.2 eV in ethylene (25). The energy minima of the 'R(IT,~s)and the 'V(~,P*)of ethylene are 6.8 and 5.42 eV, respectively (2,5). In tetramethylethylene,the same minima may be located in the 5 .O-5.2 eV range (2). Then, the photoexcited molecules, by internal conversion, may pass from one excited hypersurface to the other, and the relative energy of the two states has a strong effect on both populations. In other words, Fig. 9 gives strong support to the involvement of the Rydberg excited states in the methyl shift processes. The internal 1,Zdouble bond shift, or in other words the sigmatropic [1,3]hydrogen atom shift, was also observed in many cases. For example, 1-pentene is formed upon direct photoirradiation of gaseous cis-2-pentene: 4 = 0.02, (84); and cis- and trans-2-octene are formed in the pentane solutions of I-octene (85). This transfer was also observed in more substituted acyclic alkenes (82): see Table 8. Again, the quantum yield for the 1,3-H transfer increases with the number of alkyl substituents around the double bond. On the other hand, the 2,3-dimethyl-l-butene/3,3-dimethyl-1-butene ratio decreases with an increase in the wavelength from 184.9 to 228.8 nm (82b). It is possible that at the lower wavelength, a relatively high energy carbene is produced which leads to the formation of the terminal alkene. Kropp has retained the T,U* excited state as one of the candidates for this process (81). Conversely, Inoue et al. have rather proposed the u,,(CH2) +a*(C=C), or the IT(C=C) ---* o$(CH,) charge transfer excitation as an alternative (82a,b). Unfortunately, ub initio calculations on electronic statess of monoolefins are rather uncommon. One very interesting paper by Bouman and Hansen appeared recently (20). They used a random phase approximation including an extended basis set and well-chosen geometries. They got good agreement with experimental values of vertical excitation energies for ethylene, propene, and the two 2-butenes. They showed that successive methylation results in roughly additive red shift for the Rydberg excitations. Conversely, the two valence excitations, m + m* and or --* IT*, are notably less sensitive to methylation. Finally, the cry +IT*transition lies at much higher energies, 9.2-9.5 eV, than the energy available at 184.9 nm, in disagreement with the above mechanism. Recently, we have studied the infrared multiphoton irradiation of cis-2-pentene. In this kind of experiment, it is hoped that the photoexcited molecule will not accumulate too much energy, so that it will stay on the electronic ground state. Provided that the fluence of the photon beam is higher than 4 J/cm2, there is a large amount of fragmentation among the heated molecules as well as some 1-pentene formation (86). Thus, although it is not very efficient, the 1,3-hydrogen shift is an open channel from the hot ground

=

0.045 0.017 0.02 0.028 0.18

Not observed 1-Pentene 4-Methyl-1-pentene

2-Methyl-I-butene 3-Methyl-1-butene 3-Methyl-1-pentene 2-Ethyl-1-butene 2.3-Dimethyl- 1-butene

1 -Alkene cis-2-Pentene 4-Methy l-cis2-pentene 2-Methyl2-butene 3-Meth yl-cis2-pentene 2,3-Dimethyl2-butene

‘Quantum values measured in the presence of 3-5 a m of added propane (82b).

0.025 0.04

Product

Alkenes

1,3-HTransfer

TABLE 8. PbotoisOmeriZation of Gaseous Alkenes at 184.9 nm

0.017

0.03 0.05 3,3-Dimethyl-l-butene Trimethyl- 1,1,2-~yclopropane

0.009

0.01

0.015 0.01

+a

Dimethyl-1.1-cyclopropane 2,3-Dimethyl-1 -butene

cis- 1,2-Dimethylcyclopropane

Not observed 2-Methyl-1-butene Iwpropylcyclopropane

Product

CH3Transfer

THE OTHER ACYCLIC OLERNS

159

state. Of course, this result does not preclude the involvement of an electronic excited state in the UV photoinitiated 1,3-hydrogen shift. At this point it is relevant to recall the very low fluorescence quantum yields measured in olefinic systems (the more substitued the double bone is, the higher the quantum yield is): +(fluorescence) = in tetramethylethylene when it is excited in the 184.9-228.8 nm region in either the gas or the solution phase. The lifetime of the emitter was measured in the picosecond range, and it was proposed that this emitter is a Rydberg singlet excited state (4). It was reported very recently that the lifetime of a fluorescent excited state in tetramethylethylene vapor when excited at 235 nm is 20.8 & 0.9 ns (87),a rather long lifetime for a singlet state. This suggests a very drastic wavelength effect. We have also noticed that the 184.9 nm photosiomerization of gaseous tetramethylethylene gives rise to the formation of trimethyl-l,1,2-cyclopropane,and the electronic precursor- probably a Rydberg singlet state-of this cyclopropane derivative might be responsible for the observed fluorescence (83). The structural isomerization of olefins through triplet electronic excited states has already been recalled: see Eqs. 23-26.

E. Conclusion The conclusion to this review on the photochemical behavior of acyclic alkenes is that it is not easy to establish clearly the fate of various electronic excited states. First, it seems that ethylene is a very specific case. The formation of its photoproducts is better explained in terms of electronic excited states. Proofs are however needed to confirm this assumption. The fragmentation products of the other acyclic alkenes can be reasonably explained on the basis of the fragmentation of the hot ground states formed after internal conversion from singlet electronic excited states. Isomerization processes involving an internal methyl shift are reasonably linked to the Rydberg electronic singlet state. This process is particularly efficient in tetramethylethylene. Finally, the origin of the internal 1,3-hydrogen shift is still a matter of debate. This process may involve either a very hot ground state or an electronic singlet excited state. Figure 10 shows a schematic potential energy diagram of a photoexcited substituted ethylene molecule. It is assumed that the absorption of a photon is made through the V -+ N transition, and that triplet states are ignored as well as the decomposition of the electronic excited state into electronic excited fragments. The left hand side of the graph is highly speculative as far as the 1,3-hydrogen atom shift is concerned. The right hand side includes the cis-trans isomerization process, bond rupture, internal 1,2-alkyl shift, and reference to infrared multiphoton photochemistry.

PHOTOCHEMISTRY OF SIMPLE O E F h %

160

Figure 10. Schematic behavior of various electronic states of substituted ethylenic compounds.

V. THE CYCLIC MONOOLEFINS A.

The Fragmentation Processes in Direct Photolysis

Reports of the photofragmentation of various cyclic monoolefins were published at the beginning of the seventies. Particularly, Doepker et al. made a systematic study of different C4H6 isomers illuminated in the 104.2-147.0 nm range. In this range of energy (E > 8.4 eV, 811 kJ/mol), all the studied photoexcited molecules undergo fragmentation. This is obviously true for cyclobutene (89a) and methylenecyclopropane(89b). In both cases, the main fragmentation process gives rise to the formation of ethylene and acetylene. Vinylacetylene is also a major product. Two hydrogen atoms rather than one molecule of hydrogen are formed in the same process: C4H$* --*CZH, C4HZ* +C4H4

+

CZH,

+ 2H

At 184.9 nm, the fragmentation as well as the isomerization of substituted cyclobutenes, namely bicyclo[3.2 .O]hept-6-ene and bicyclo[4.2 .O]oct-7-ene, were studied in pentane solutions. Acetylene and cycloalkenes are the major photoproducts, whereas the Woodward-Hoffmann allowed ring opening gives rise to 1,3-cyclodienes with lower quantum yields (90).

THE CYCLIC MONOOLEFINS

161

The 147.0 nm photofragmentation of methylenecyclobutane was also important (91). An important molecular fragmentation process has been identified it leads to the formation of allene and ethylene, probably in one step. However, due to the high energy content, the primary products are relatively unstable and suffer further fragmentation. Thus, excited allene molecules further decompose and, among secondary products, C3H3radicals appear. These radicals were observed through the formation of 1-butyne-4,4,4-d3 and 1,Zbutadiene4,4,4-d3 when a mixture of methylenecyclobutaneand CD31 is photolyzed. It is known thtt the C 3 5 species may exist in two different electronic structures: CH=C-CH, and CH=C=CH2 (92). However, it was very difficult to measure the quantum value for this species because of its high reactivity towards monomer. Thus, the fragmentation pattern of the photoexcited molecule was hardly established. A little bit later, the photolysis of vinylcyclopropane was studied in the same energy range. In this case, the fragmentation is dependent on the cyclopropane ring and gives rise to an important methylene elimination process: CP = 0.20 ? 0.04 at 147.0 nm. This process was shown to be of general occurrence in various alkylated cyclopropanes (93). R-cyclo-C,HT*

__*

'CH,

+ RCH=CH2

(36)

The 8.4 eV photodecomposition of cyclopentene was also studied in the same laboratory. Ethylene, acetylene, and cyclopentadiene are the major products, although a high yield of hydrogen atoms was also observed (94). On the other hand, methylenecyclobutane (a= 0.04) and bicyclo[2.1 .O]pentane (a= 0.03) were the only primary products observed in the 184.9 nm photochemistry of n-heptane solution of cyclopentene (95). The formation of 1,4-pentadiene (CP = 0.01) was ascribed to secondary processes. Very recently we have undertaken a systematic study of the 184.9 nm gas phase photochemistry of cyclopentene at pressures from 1 Torr to 6 atm of added propane. Again at low pressure, ethylene (0 = 0.12), acetylene (CP = 0.03), allene (CP = 0.06), and cyclopentadiene (0= 0.22) are the main products (96). About 80% of the formation of cyclopentadiene involves the elimination of a hydrogen molecule in agreement with the Woodward-Hoffmann allowed 1,4 concerted molecular elimination process (97). Moreover, several isomers are also formed provided

162

PHOTOCHEMISTRY OF SIMF'LE OLEFINS

+

the total pressure is raised to appropriate values. For example, the (cis trans) 1,3-pentadienequantum yield increases from 0.00 at a pressure of 1 Torr to 2 0.33 at a pressure of 100 Torr of added propane, and it eventually decreases with a further increase in the propane pressure. Similar behavior is also observed for the quantum yields of 1,Cpentadiene and vinylcyclopropane, although the pressure scales must be shifted at higher pressure: Qmm(1,Cpentadiene) = 0.22 at 300 Ton and @-(vinylcyclopropane) = 0.21 at 3 atm. Similar results were observed at 213.8 nm, although the maxima for the quantum yields are observed at somewhat lower pressures. This effect may reasonably be attached to the lower energy content of the photoexcited molecules formed at 213.8 nm. These results are included in Figures 11 and 12. The formation of these isomers was assumed to involve the primary fragmentationof s(C-C) bond in the photoexcited molecule. The so-formed allyl-alkyl radical is allowed to recyclize (cyclopentene and vinylcyclopropane are the products) and to rearrange through internal hydrogen atom shifts (1,Cpentadiene and 1,3-pentadiene are among the products). Although these products are isomers of the starting material, their formation is explained in terms of fragmentation rather than isomerization processes (96). This mechanism is in agreement with the fragmentation of hot vinylcyclopropane molecules formed through the addition of a singlet methylene radical on 1.3-butadiene (98). The photolysis of cyclohexene is particularly well documented in the 105184.9 nm wavelength (99-101). The main products are ethylene and 1,3-

1o3

1 oo

N m-2

1 0' 1 o2 Propane pressure

/

1D6

1o3 Torr

1 o4

Figure 11. The 213.8 nm photoirradiationof cyclopentene. The quantum yields of various products at different pressures of added propane.

THE CYCLIC MONOOLEFINS

163

2 Nm-2

Propane

pressure

/ Torr

Figure 12. The 213.8 nm photoirradiation of cyclopentene.The quantum yields of various products at different pressures of added propane. butadiene: they are formed from a molecular elimination process-a retro-DielsAlder reaction-in agreement with Woodward-Hoffmann rules: = 0.8 at 184.9 nm (102):

This process has also been observed in cis- and nuns-3,4-dimethylcyclohexene. The 2-butene formed retains the originid cis or trans structure:

Conversely, the direct 184.9 nm photolysis of the cyclic C,, C8, and C9 monomers leads to the formation of a,w-dienes and vinylcycloalkanes (100,103) through

164

PHOTOCHEMISTRY OF SIMPLE OLEFINS

B. Fragmentation in the Photosensitized Experiments The fragmentation of H S ( ~ Pphotosensitized ~) cis-4,5-dimethylcyclohexenedoes not conserve the original cis structure in 2-butene (104). In this case the mechanism is thought to involve a triplet allyl-alkyl radical. This intermediate may decompose at low pressure or may recombine, giving rise to the original alkene or vinylcyclobutane (105):

+d=‘

[i] *

=

+=\=/

b+d

A review of various processes occumng in the Hg 6(3P1)photosensitization of cyloolefins was published by De M a d et al. (106); see Table 9. Vinylcycloalkanes were the major product observed in cyclopentene and l-methylcyclopentene. From extrapolation of the quantum yields of cyclopropanes to zero pressure and by combining these values with the estimated quantum efficiencies of other proceses, they calculated that “two-thirds of the triplet cyclopentene molecules always return to the ground state without requiring collisional stabilization” (106). They concluded that the occurrence of such an intersystem crossing to the ground state is a general phenomenon in mercury photosensitization of cyclic olefins. However, cyclooctene (107) and cyclononene (103) do not seem to follow this pattern completely. The formation of various bicycloalkanes is now important, as well as that of a,o-dienes. The former products are the result of an internal hydrogen atom transfer from an appropriate methylene group to the olefinic double bond with a subsequent or simultaneous C-C bond formation (Table 10). It is not clear if these bicyclocompounds are the result of the hot ground state or the triplet excited state. On the other hand, the am-diene

TABLE 9. Comparison of the Quantum Yields of Various Processes in the Hg 6@,) Photosensitization of Gaseous Cycloolefins Cycloolefin Cyclopentene 1-Methylcyclopentene Cyclohexene 3-Methylcyclohexene Cycloheptene Cyclooctene Cyclononeneb Methylenecyclopropane Methylenecyclobutane Methylenecyclopentane

RetroDiels-Alders

Intersystem Crossing

Ring Contraction to Vinylcycloalkanes

-

0.6 0.6

0.35 0.3

0.2 0.04

0.7

0.06 0.05

-

c0.83 0.9

-

-

?

-

-

0.85

?

>0.9

<0.05, ZO

0.0

-

Source: Ref. 106. “From Ref. 103.

TABLE 10. Formation of Bicycloalkanes and a,o-Dienes in the Hg 6(’P1) Photosensitizationof Cycloalkenes

Yield (wmol)

Cycloolefin Bicyclo [4.1.O]heptane [4.2.O]octane [3.3 .O]octane [4.3.0]nonane [5.2.0lnonane [6.1 .O]nonane a,o-Dienes

Cycloheptene (Ref. 108) 0.088”

0.025“

Cyclooctene (Ref. 107)

0.98 0.17

0.97

cis-

Cyclononene (Ref. 103)

60.23 20.54 1.18 0.07

“Quantum values.

165

166

PHOTOCHEMISTRY OF SIMPLE OLEFINS

formation seems to involve a similar p(C-C) bond rupture, as is reported above, in the direct photolysis of cyclopentene, cycloheptene, cyclooctene, etc. :

C. Isomerhation Processes Very recently, a good review of the 184.9 nm photoisomerization of olefins and strained cycloolefins was published by Adam andd Oppenllinder (109). For the smallest members of this group, one of the more important studies comes from Fields and Kropp (110): they observed tht the liquid or solution photochemistry of C5-C, monocyclic monoolefins gives rise to a variety of mono- and bicyclic isomers, whose formationmay be explained in terms of a carbeneintermediate:

These reactions were also reported by Inoue et al. (100). Later Srinivasan and Brown reinterpretedthe mechanism in terms of two different intermediates(1 11): the first one is that just reported above; the second is included in the following reaction:

The total quantum yields of the isomeric products are generally in the 0.02-0.10 range at 184.9 nm (112). The [1,3]-sigmatropic shift was also observed (113):

THE CYCLIC MONOOLEFINS

83 '/*

167

10%

In the same work, the shift was observed in molecules where the cycle was attached in the 1,l position of an ethylenic molecule: the process in Eq. 49. The formation of the cyclopentene molecule is much favored over the other isomer: the shift seemed to be favored by the a-strain of the cyclopentene ring. Thus, it was concluded that the migration may be due in part to the emergence of the P,U* state as the lowest-lying excited state (1 12). Very recently we have restudied the 184.9 nm photochemistry of cyclohexene. At high pressure, there is formation of methylenecyclopentane and bicyclo[3.1 .O]hexane. The Stern-Volmer plots for the quantum yields of these isomers appear in Figs. 13 and 14. It is clear from these results that these isomers do not involve the same precursor. In the same manner, in the 184.9 nm photochemistry of cyclopentene, the methylenecyclobutanequantum yield increases with an increase in the pressure of added propane. Conversely, we have not seen any formation of bicyclo[2.l.O]pentane. At 213.8 nm (that is at a lower energy), the formation of methylenecyclobutaneand bicyclo[2.1.O]pentane was observed at high pressure of added propane (Fig. 11). Clearly, both products are formed in somewhat different pressure scales (1 14). Thus, it is also fakly safe to assume that two different precursors are involved in such formations. More particularly, from the Stern-Volmer plots of methylenecyclobutane and ethylene, the lifetime of an excited methylenecyclobutanemolecule can be estimated:

c

L, 100

8 Y

50

0

0.01

[Pmssurel-'

/

(Torr1-l

0.02

Figure 13. The reciprocals of the bicyclo[3.1 .O]hexane quantum yields versus the recip rocal of the pressure of added propane in the 184.9nm photoirradiationof cyclohexene.

PHOTOCHEMISTRY OF SIMPLE OLEFINS

168

Y

B

Y

0 [Propane

0.25 pressure]-'

/

0.5 (Torrl-'

1

Figure 14. The reciprocals of the methylenecyclopentane quantum yields versus the reciprocals of the pressure of addedairin the 184.9 nm photoirradiationof cyclohexene.

The following Stern-Volmer equations apply to this mechanism:

=

From Figs. 15 and 16, the following kgk: values were estimated to be 11.5 atm from both Stem-Volmer plots at 184.9 nm. By assuming kl as being the rate constant of the physical collision process, the lifetime of the very excited precursor is around 10 picoseconds. One interesting approach to synthesize trans-cycloalkene must be recalled here. It was developed by using the singlet photosensitization of cis-cycloalkene. This isomerization takes place via a singlet mechanism, which involves a nonvertical energy transfer from an excited aromatic ester to the cycloalkenes (1 15). For example, it has been shown that the direct and sensitized photolysis gave quite different photostationary wanskis ratios after prolonged irradiation of cyclooctene. The ratios are 1.0 and 0.05 in the direct 184.9 nm and the sensitized liquid singlet, respectively (116).

=

THE CYCLIC MONOOLEFB'S

0.5

80

x lo-'

N-' m

169

1

Figure 15. The Stern-Volmer plot for the methylenecyclobutane quantum yields measured in the 184.9 nm photoirradiation of cyclopentene.

D. Conclusion First, it seems reasonable to link the fragmentationprocesses, mainly the p(C-C) bond rupture as well as the rectro-Diels-Alder process, to the hot ground state formed through either the internal conversion of the excited singlet state or the intersystem crossing from the triplet excited state. On the other hand, part of the isomers are formed from electronic excited states. Methylene cycloalkane and bicyclo[n.l.O]alkane are probably the results of the isomerization of the Rydberg electronic singlet state, at least in cyclopentene and cyclohexene. The a,o-dienes formed in the triplet photochemistry of the higher members of the cycloalkene series probably involve an internal hydrogen atom transfer in the

6

0

2 Propane

4

pressure

/

Atm

6

Figure 16. The Stern-Volmer plot for the ethylene quantum yields measured in the 184.9 nm photoirradiation of cyclopentene.

170

PHOTOCHEMISTRY OF SIMPLE OLEFINS

hot ground state of the allyl-alkyl radicals. Conversely, it is likely that the formation of bicyclocompoundsis the result of internal hydrogen atom migration in the triplet excited states (117).

M. CONCLUSION The above material seems a little bit confusing, and a simple trend in the fate of photoexcited molecules is not obvious. Ethylene seems to be a special case, although it is tempting to l i t h e molecular elimination from photoexcited acyclic olefins to the electronic excited state. Similarly, some of the isomerization products observed in either the high pressure or the liquid phase experimentson both acyclic and cyclic olefins are very likely linked to electronic excited state(s). The singlet Rydberg excited state is very often suggested to be involved in these processes. Conversely, it seems more appropriate to retain the fundamental and very hot ground state as an intermediate leading to the primary fragmentation processes, involving a bond rupture. In short, there is an obvious need for more research both at the theoretical and experimental levels.

ACKNOWLEDGMENTS The author would like very much to thank Professors C. Sandorfy (Universite de Montdal), G. R. De Mar6 (Universitk Libre de Bruxelles), and E. Evleth (Universitk de Paris VI) for many helpful discussions. We would like also very much to thank Professor N. Nakashima (Institutefor Molecular Science, Okazaki) for providing us with very recent results, and particularly Fig. 9. Financial help from the Natural Sciences and Engineering Research Council of Canada was much appreciated. Note added on proof: Recently, a review of the photochemistry of allyl-, vinyl-, and alkylidenecyclopropaneswas published (118). It adds very interesting mechanistic details as well as relative importance of cleavage, fragmentation, and isomerization pathways for these compounds in pentane solutions.

REFERENCES 1. A. J. Merer and R. S. Mulliken, Chem. Reviews 69, 639 (1968), and references cited therein. 2. M. B. Robin, in Higher Excited States of Polyatomic Molecules, Vol. 11, Academic Press, New York, 1975, and references cited therein.

REFERENCES

171

3. H. M. Rosenstock, K. Draxl, B. W. Steiner, and J. T. Herron, J. Phys. Chem. Ref. Data 6 , Suppl. 1 (1977), and references cited therein. 4. F. Hirayama and S. Lipsky, J. Chem. Phys. 62, 576 (1975).

5. M. B. Robin, in Higher Excited States of Polyatomic Molecules, Vol. 111, Academic Press, New York, 1985, pp. 213/236, and references cited therein. 6. (a) L. Salem, Zsr. J. Chem., 14, 89 (1975); (b) L. Salem, Science, 191, 822 (1976). 7. See for example: (a) K. J. Crowley and P. H. Mazzocchi, in The Chemistry ofAlkenes, Vol. 2, J. Zabicky, Ed., Wiley-Interscience,New York, 1970, pp. 267-325; (b) J. D. Coyle, Chem. SOC. Rev. 3, 329 (1974); (c) G. Kaupp, Angew. Chem. Int. Ed. Engl. 17, 150 (1978); (d) Yu. I. Dorofeev and V. E. Skurat, Russ. Chem. Rev. 51, 527 (1982). 8. M. C. Sauer, Jr. and L. M. Dorfman, J. Chem. Phys. 35, 497 (1961). 9. H. Okabe and J. R. McNesby, J . Chem. Phys. 36, 601 (1962). 10. (a) H. Hara and I. Tanaka, Bull. Chem. SOC. Japan 46, 3012 (1973); (b) H. Hara and I. Tanaka, Bull Chem. SOC.Japan 47, 1543 (1974). 11. P. Borrell, P. Cashmore, and A. E. Plan, J . Chem. SOC.A , 3063 (1968). 12. (a) L. C. Glasgow and P. Potzinger, J . Phys. Chem. 76, 138 (1972); (b) P. Potzinger, L. C. Glasgow, and G. von Biinau, 2. Nuturf. 27a, 628 (1972). 13. M. B. Robin and N. A. Kuebler, J. Mol. Spectr. 33, 274 (1970). 14. S.-I. Hirokami and R. J. Cvetanovii, J. Phys. Chem. 78, 1254 (1974). 15. R. Gorden, Jr. andP. Ausloos, J. Res. Natl. Bur. Stand. 75A,141(1971). 16. E. Tschuikow-Roux, J. R. McNesby, W. M. Jackson, and J. L. Faris, J. Phys. Chem. 71, 1531 (1967). 17. (a) S. Tsunashima, S.-I. Hirokami, and S. Sato, Can. J. Chem. 46, 995 (1968), and references cited therein; (b) S. Sato, Znt. Un. Pure Appl. Chem., Org. Phatochem. 2, 87 (1967) (Int. Symp. Enschede). 18. (a) A. H. Laufer, J. Photochem. 27, 267 (1984); (b) A. Fahr and A. H. Laufer, J. Photochem. 34, 261 (1986). 19. Y.-P. Lee and G. C. Pimentel, J. Chem. Phys. 75, 4241 (1981). 20. T. D. Bouman and A. E. Hansen, Chem. Phys. Lett. 117, 461 (1985), and references cited therein. 21. R. S. Mulliken, 1. Chem. Phys. 71, 556 (1979). 22. R. McDiarmid, J. Phys. Chem. 84, 64 (1980). 23. E. T. Nelson and C. K. N. Patel, Proc. Natl. Acud. Sci. U.S.A. 78, 702 (1981). 24. P. 'A. Snyder, P. N. Schatz, and E. M. Rowe, Chem. Phys. Lett. 110, 508 (1984).

172

PH~OCHEMISTRYOF SIMPLE OLEFINS

25. D. M. Mintz and A. Kuppermann, J . Chem. Phys. 71, 3499 (1979). 26. J. CarlierandR. Botter, J . ElectronSpectr. Rel. Phenom. 17,91(1979). 27. D. G. Wilden and J. Comer, J . Phys. B: Atom. Mofec. Phys. 12, L371 (1979). 28. Y. Sato, K. Satake, and H. Inouye, Bull. Chem. SOC.Japan 55, 1290 (1982). 29. A. Gedanken, N. A. Kuebler, and M. B. Robin, J . Chem. Phys. 76,46 (1982). 30. C. Petrogonlo, R. J. Buenker, and S. D. Peyerimhoff, J . Chem. Phys. 76, 3655 (1982). 31. M. H. Palmer, A. J. Beveridge, I. C. Walker, and T. Abuain, Chem. Phys. 102, 63 (1986). 32. (a) E. M. Evleth and A. Sevin, J . Am. Chem. SOC. 103, 7414 (1981); (b) J. D. Goddard, Chem. Phys. LRtt. 83, 312 (1981). 33. D. A. Becker, H. Okabe, and J. R. McNesby, J . Phys. Chem. 69, 538 (1965). 34. S. Arai, S . Shida, and T. Nishikawa, Bull. Chem. Soc. Japan 39, 2548 (1966). 35. E. Tschuikow-Roux, J . Phys. Chem. 71, 2355 (1967). 36. J. Niedzielski, W. Makulski, and J. Gawlowski, J . Photochem. 19, 123 (1982). 37. G. J. Collin, H. Deslauriers, and J. DeschCnes, Can. J . Chem. 57, 870 (1979). 38. P. Borrell, A. Cervenka, andJ. W. Turner,J. Chem. SOC.B , 2293 (1971). 39. H. Deslauriers and G. J. Collin, J . Chim. Phys. 82, 1033 (1985). 40. (a) M. Avrahami and P. Kebarle, J. Phys. Chem. 67, 354 (1963); (b) C. A. Heller and A. S. Gordon, J . Chem. Phys. 42, 1262 (1965); (c) S . 4 . Hirokami and S. Sato, Bull. Chem. SOC. Japan 43, 2389 (1970). 42. W. R. Rodwell, W. J. Bouma, and L. Radom, Znt. J . Quunt. Chem. 18, 107 (1980). 42. W. R. Rodwell, W. J. Bouma, andL. Radom, Int. J. Quant. Chem. 18, 107 (1980). 43. (a) J. A. Hush, in Concepts in Theoretical Organic Chemisrry, Allyn & Bacon, Boston, 1974, pp. 67 ff.; (b) R. G. Pearson, in Symmetry Rules for Chemical Reactions, Wiley-Interscience, New York, 1976, pp. 95-96, 469-470. 44. W. A. Guillory and S. G. Thomas, Jr., J . Phys. Chem. 79,692 (1975). 45. A. Wieckowski and G. J. Collin, J. Phys. Chem. 81, 2592 (1977). 46. H. Deslauriers, W. Makulski, and G. J. Collin, Can. J. Chem. 65, 1631 (1987).

REFERENCES

173

47. J. P. Chesick, J. Chem. Phys. 45, 3934 (1966). 48. P. Kebarle and M. Avrahami, J. Chem. Phys. 38, 700 (1963). 49. F. Bayrakceken, J. H. Brophy, R. D. Fink, and J. E. Nicholas, J . Chem. SOC.,Faraahy Trans. 169, 228 (1973). 50. J. H. Kiefer, M. Z. Al-Alami, and K. A. Budach, J. Phys. Chem. 86, 808 (1982). 51. J. M. Figuera, E. Fernandez, and M. J. Avila, J. Phys. Chem. 78, 1348 ( 1974). 52. J. W. Simons, B. S. Rabinovitch, and F. H. Dorer, J. Phys. Chem. 70, 1076 (1966). 53. (a) A. U. Acuiia, J. M. Figuera, and V. Menendez, Anal. Real SOC.ESP. Fis, Quim. 67, 181 (1973); (b) W. Makulski, J. Gawlowski, and J. Niedzielski, J. Phys. Chem. 85, 2950 (1981). 54. (a) P. Borrell and P. Cashmore, Trans. Faraday Sac. 65, 558 (1969); (b) J. Herman, K. Herman, and P. Ausloos, J. Chem. Phys. 52, 28 (1970). 55. H. Yamazaki, R. J. CvetanoviC, and R. S. Irwin, J. Am. Chem. SOC.98, 2198 (1976). 56. E. M. Evleth and E. Kassab, Can. J. Chem. 61, 306 (1983). 57. (a) G. 0. Schenck, S.-P. Mannsfeld, G. Schomburg, and C. H. Krauch, 2. Narurforsch., B 19, 18 (1964); (b) Y. L. Bahurel, D. J. MacGregor, T. L. Penner, and G. S. Hammond, J. Am. Chem. SOC.94,637 (1972). 58. J. Saltiel, J. D’Agostino, E. D. Megatity, L. Metts, K. R. Neuberger, M. Wrighton, and 0. C. Zafirious, Org. Phorochem. 3, 1 (1973), and references cited therein. 59. (a) R. S. Konar and B. DeB. Darwent, J. Indian Chem. SOC. 53, 891 (1976); (b) S. Tsunashima and S. Sato, Rev. Chem. Int. 4, 201 (1979). 60. S. Yamamoto, N. Nobusada, Y. Sueishi, and N. Nishimura, Chem. Lett., 723 (1985). 61. (a) A. B. Callear and H. K. Lee, Nature 213, 693 (1967); (b) A. B. Callear and H. K. Lee, Trans. Faraduy SOC.64, 308 (1968); (c) A. B. Callear and H. K. Lee, Trans. Faraday SOC.64, 2017 (1968). 62. P. Borrell, P. Cashmore, A. Cervenka, and F. C. James, J. Chim. Phys., 229 (1970). 63. (a) H. Deslauriers and G. J. Collin, J. Photochem. 12, 249 (1980); (b) H. Deslauriers, G. J. Collin, andB. Simard, J. Phorochem. 21, 19(1983). 64. (a) W. Tsang, Int. J. Chem. Kiner. 1, 245 (1969); (b) W. Tsang, Znr. J. Chem. Kinet. 10, 1199 (1978). 65. W. E. Falconer, B. S. Rabinovitch, and R.J. CvetanoviC, J. Chem. Phys. 39, 40 (1963).

174

PHOTOCHEMISTRY OF SIMPLE OLEFlNS

66. W. Forst, in Theory of Unimolecular Reactions, Academic Press, New York, 1973, pp. 235 ff. 67. (a) H.Deslauriers and G. J. Collin, Can. J. Chem. 63,62 (1985); (b) G. J. Collin and H. Deslauriers, Can. J. Chem. 63,944 (1985). 68. (a) G. J. Collin and A. Wiqckowski, J. Photochem. 8, 103 (1978); (b) A. Wiqckowski and G. J. Collin, Can. J. Chem. 56, 1435 (1978). 69. (a) J. Niedzielski, W. Makulski, and J. Gawlowski, J. Photochem. 9, 519 (1978); (b) J. Niedzielski, P. Geblewicz, and J. Gawlowski, J. Photochem. 10, 287 (1979). 70. (a) J. Gawlowski, J. Niedzielski, and A. Wiqckowski, J. Photochem. 12, 321 (1980); (b) J. Niedzielski and J. Gawlowski, J. Photochem. 14, 323 (1980). 71. (a) N. Nakashima, N. Shimo, N. Ikeda, and K. Yoshihara, J . Chem. Phys. 81, 3738 (1984); (b) N. Shimo, N. Nakashima, N. Ikeda, and K. Yoshihara, J. Photochem. 32, 279 (1986). 72. N. Nakashima, N. Ikeda, N. Shimo, and K. Yoshihara, presented at XIIth Int. Conf. Photochem., Tokyo, 1985; and private communication. 73. B. S. Rabinovitch and D. W. Setser, Adv. Photochem. 3, 1 (1964). 74. J. Gawlowski and G. J. Collin, J. Photochem. 23, 241 (1983). 75. Y. Inoue, S. Takamuku, andH. Sakurai, Can. J. Chem. 54,3117 (1976). 76. D. W. Placzek and B. S. Rabinovitch, Can. J . Chem. 43, 820 (1964), 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87.

and references cited therein. (a) D. C. Montague, J. Chem. SOC., Faraday Trans. 1 7 7 , 262 (1977); (b) D. C. Montague, J. Chem. SOC., Faraday Trans. Z 77, 277 (1977). D. C. Montague, J. Chem. SOC., Faraday Trans. Z 75, 398 (1975). See, for example, N. J. Turro, in Modern Molecular Photochemistry, BenjamidCummings, Menlo Park, Calif. 1978. P. J. Kropp, Molecular Photochem. 9, 39 (1978-79). P. J. Kropp, E. J. Reardon, Jr., Z. 1. F. Gaibel, K. F. Williard, and J. H. Hattaway, Jr., J. Am. Chem. SOC. 95, 7058 (1973). (a) Y. Inoue, T. Mukai, and T. Hakushi, Chem. Lett., 1665 (1983); (b) G. J. Collin and H. Deslauriers, Can. J. Chem. 63, 1424 (1985). F. H. Watson, Jr. and S. P. McGlynn, Theoret. Chim. Acta 21,309 (197 1). G. R. De Mark, G. J. Collin, H. Deslauriers, and J. Gawlowski, J. Photochem. 30,407 (1985). Y. Inoue, T. Mukai, and T. Hakushi, Chem. Lett., 1725 (1984). (a) R. H. Back and G. J. Collin, J. Phys. Chem. 90, 5684 (1986); (b) F. D. Lewis, P. Teng, and E. Weitz, J. Am. Chem. SOC.108,2818 (1986). M. A. Wickramaaratchi, J. M. Preses, and R. E. Weston, Jr., Chem. Phys. Lett. 120, 491 (1985).

REFERENCES

175

88. P. J. Kropp, Org. Photochem. 4, 1 (1979). 89. (a) A. DeLeon and R. D. Doepker, J. Phys. Chem. 75, 3656 (1971); (b) K. L. Hill and R. D. Doepker, J. Phys. Chem. 76, 3153 (1972).

90. Y. Inoue, M. Sakae, and T. Hakushi, Chem. Lett., 1495 (1983). 91. C.-K. Tu and R. D. Doepker, J. Photochem. 1, 271 (1972-73). 92. P. Kebarle, J. Chem. Phys. 39, 2218 (1963). 93. (a) G. J. Collin, J. Chim. Phys. 74, 302 (1977), Table 2; (b) E. Lopez and R. D. Doepker, J. Phys. Chem. 83, 573 (1979). 94. C.-K. Tu and R. D. Doepker, J . Photochem. 3, 13 (1974). 95. W. Adam and T. Oppenltinder, J. Am. Chem. SOC. 107, 3924 (1985). 96. (a) W. Makulski and G. J. Collin, J. Phys. Chem. 91,708 (1987); (b) G. J. Collin, H. Deslauriers, and W. Makulski, J. Photochem. 39, 1(1987). 97. K. G. Kosnik and S. W. Benson, J. Phys. Chem. 87, 2790 (1983). 98. P. M. Crane and L. T. Rose, J. Phys. Chem. 79, 403 (1975). 99. (a) M. D. Sevilla and R. A. Holroyd, J. Phys. Chem. 74, 2459 (1970); (b) R. Lesclaux, S. Searles, L. W. Sieck, and P. Ausloos, J. Chem. Phys. 100. 101.

102. 103. 104. 105.

106. 107. 108. 109.

53, 3336 (1970). Y. Inoue, S. Takamuku, and H. Sakurai, J. Chem. Soc., Perkin Trans. ZZ, 1635 (1977). G. J. Collin and H. Deslauriers, Can. J. Chem. 61, 1970 (1983). R. B. Woodward and R. Hoffman, in The Conservation of Orbital Symmetry, Verlag Chemie, Weinhein, 1970. Y. Inoue, S . Takamuku, and H. Sakurai, Bull. Chem. SOC. Japan 49, 1147 (1976). Y. Inoue, S. Takamuku, and H. Sakurai, Bull. Chem. SOC. Japan 48, 3101 (1975). (a) G. R. De Mar& 0. P. Strausz, and H. E. Gunning, Can. J. Chem. 43, 1329 (1965); (b) G . R. De Mark, Bull. Chem. Soc. Belges 81, 459 (1972). G. R. De Mark, N. Antheunis, J. Olbregts, and M. Termonia, J. Phorochem. 4, 299 (1975), and references cited therein. S. Takamuku, K. Moritsugu, and H. Sakurai, Bull. Chem. SOC.Japan 44, 2562 (1971). Y. Inoue, M. Kadohira, S. Takamuku, and H. Sakurai, Tetrah. Lett. 5 , 459 (1974). W. Adam and T. Oppenlhder, Angew. Chem. 25, 661 (1986).

110. T. R. Fields and P. J. Kropp, J. Am. Chem. SOC. 96, 7559 (1974). 111. R. Srinivasan and K. H. Brown, J. Am. Chem. SOC. 100, 4602 (1978).

176

PHoTocHEMlSTRY OF SIMPLE OLEFINS

112. H.-P. Schuchmann, C. Von Sonntag, and R. Srinivasan, J . Phorochem. 15, 159 (1981). 113. P. J. Kropp, H. G . Fravel, Jr., and T. R. Fields, J . Am. Chem. Soc. 98, 840 (1976). 114. G. J. Collin, H. Deslauriers, and W. Makulski, J . Photochem., 39, 1 (1987). 115. Y . Inoue, S. Takamuku, Y. Kunitomi, and H. Sakurai, J . Chem. SOC. Perkin Trans. ZZ, 1672 (1980). 116. Y. Inoue, S. Takamuku, and H. Sakurai, J . Chem. SOC.Chem. Comm., 423 (1976). 1 17. G . J. Collin and G . R. De Mar& J . Phorochem. 38, 205 (1987). 118. W. J. Leigh and R. Srinivaszn, Acc. Chem. Res., 20, 107 (1987).

Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.

THE DECOMPOSITION OF ALKYL NITRITES AND THE REACTIONS OF ALKOXYL RADICALS Julian Heicklen Department of Chemistry and Center for Air Environment Studies, The Pennsylvania State University, University Park, Pennsylvania 16802

Dedicated to Yuri Tarnopolsky, chemist and soviet Jew, who served in a labor camp in Chita, Siberia because of his desire to emigrate.

CONTENTS 1. Introduction 11. Photolysis of alkyl nitrites A. Ultraviolet absorption B . Photodecomposition C . Primary process quantum yield D. Formation of excited products E. Summary 111. Thermal decomposition of alkyl nitrites A. Earlywork B. Mechanism C. Modem studies IV. Reactions of alkoxyl radicals with NO, ratio A. RO NO disproportionation-to-combination B . RO + NO2disproportionation-to-combinationratio C. Relative rate of RO with NO and NO, D . Rate coefficient for RO + NO

+

177

THE DECOMPOSI'IION OF ALKm NITRITES

178

+

E. Rate coefficient for RO NO2 V. Decomposition and isomerization of alkoxyl radicals A. Decomposition 1. CH30 2. C2H.30 3. i-C3H70 4. n-C3H70 and i-C4&0 5. S-C4H90 6. t-C4HgO 7. 2-C5Hl,O 8. t-Amoxyl 9. (CF3)2C(O)CH3 and CF3C(O)(CH& 10. Phenoxyl 11. summary B Isomerization VI. Reactions of alkoxyl radicals with O2 A. Early work B CH30and CD30 C. C*H,O, i-C,H,O, n-C3H70, and i-C4H90 D . n-C&O and s-C4H90 E. Comparison of results for simple alkoxy radicals F. Other radicals VII. Other reactions of alkoxyl radicals A. Reactions with radicals B . Abstraction of H atoms from molecules 1. CH30 2. CZHSO 3. i-C3H70 4. t-C4H90

. .

5.

s-C4&0

C. Addition reactions D. Reaction with O3 Acknowledgements References

I. INTRODUCTION The reactions of akoxyl radicals are important in combustion and in polluted atmospheres. Therefore there has been considerable interest in studying their reactions. Overall reviews of the field were made from 1959 to 1972 (Gray and

PHOTOLYSIS OF ALKYL NlTRlTEs

179

Williams, 1959; Gray et al., 1967; Heicklen, 1968; Howard, 1972), but no general update seems to have appeared. However, Ban (1979) has reviewed the thermochemistry and thermal-decomposition kinetics for alkoxyl radicals and alkyl nitrites. It is the purpose of the present review to report all work through June, 1986 (and some later) on the reactions of alkoxy radicals. In addition, since alkoxyl radicals often are produced in laboratory experiments from alkyl nitrites, the photochemical and thermal decomposition of these species will also be reviewed. The units used for rate coefficients will be molar and seconds. Activation energies will be given in kcavmole. The symbol 8 represents RT In 10 where R is 1.987 x kcdmole-K. For reactants which give more than one set of products, the reaction channels are split into a, b, c, etc. Thus the overall reaction 2 has two channels, reactions 2a and 2b, with k2 = k2= k2b. Prefix abbreviations are: n, normal; i, iso; c, cyclo; s, secondary; t, tertiary.

+

11. PHOTOLYSIS OF ALKYL NITRITES

A. Ultraviolet Absorption The absorption spectrum of gaseous methyl nitrite at 25°C is shown in Fig. 1. The first band has structure in the region 290-380 nm. At higher wavelengths the absorption is very weak and drops rapidly with increasing wavelength, though some absorption exists to 435 nm. Below 290 nm, the absorption rises sharply and reaches a maximum at 214 nm. An enlarged absorption spectrum of the region >280 nm is given in Fig. 2. The absorption of HONO results from a singlet n+vr* electronic transition (King and Moule, 1962). Presumably the same is true of alkyl nitrites. The absorption is complicated because it is a composite of cis and trans isomers (Elkins and Kuhn, 1935;Tarte, 1952). This causes a change in relative intensities with wavelength as the temperature, and thus the relative abundance, of the isomers changes. The absorption of alkyl nitrites in the region from 25000-30000 cm-' was studied by Elkins and Kuhn (1935), who found evidence for two different electronic transitions, based on the variation of the circular dichroism and anisotropic factor of alkyl nitrites. According to Sidman (1958), the major part of the absorption should be due to the n--yTT*transition involving oxygen nonbonding electrons. However, Calvert and Pins (1966) believe the n%* transition involves a lone-pair electron on the nitrogen atom. The photoabsorption cross section at 366 nm is (1.79 2 0.03) X cm2, independent of temperature from 25 to 150°C (Wiebe and Heicklen, 1973). Other results at cm2 cm2 (Pate et al., 1974) and (1.74 ? 0.16) X 25°C are 1.84 X (Taylor et al., 1980).

180

THE DECOMPOSITTON OF ALKYL

WAVELENGTH. nm

Figure 1. Photoabsorption spectrum of gaseous CH,ONO 91980) with permission of John Wiley and Sons, Inc.

at

298 K. From Taylor et al.

The photoabsorption cross sections in Figs. 1 and 2 are in good agreement. The cross section at the wavelengths of maximum absorption in the two bands (339 and 214 nm) are: at 339 nm, 3.1 x cm2 (Calvert and Pitts, 1966), 3.4 X cm2 (Napier and Nomsh, 1967), and (3.24 2 0.16) X cm2 (Taylor et al., 1980); and at 214 nm, 4.97 x lo-'* cm2 (Napier and Nomsh, 1967), 4.2 x cm2 (Calvert and Pitts, 1966), (4.59 & 0.58) X lo-'* cm2 (Taylor et al., 1980), and (4.2 +- 0.4) X cm2 (Lahmani et al., 1980a). Lahmani et al. (1980a) have shown that below 190 nm, the absorption of CH30N0 continues to decrease to a minimum at 2168 nm. It then increases to a maximum at 139 nm, which has an extinction cross section of (3.33 & 0.08)

PHOTOLYSIS OF ALKYL NITRlTES

181

Wavelength, A

Figure 2. Absorption spectra at 25°C of: (1) CH,ONO(g), (2) (CH,)CONO(g). From Calvert and Pitts (1966) with permission of Drs. Jack Calvert and James Pitts, Jr.

X cm2,considerablylarger than the maximum of (4.6 f 0.4) x cm2 at 215 nm. The ultraviolet absorption spectra of t-C4H90N0, C2H,0N0, i-C3H70N0, n-C3H70N0, i-C4H90N0, and n-C4H90N0 are shown in Figs. 2-7, respectively. These spectra are similar to that for CH30N0. They have a banded structure from 310 to 400 nm and a very strong continuum below 300 nm. However, the peak absorption in the banded region is at 339 nm for CH30N0 and -380 nm for t-C,H,ONO. For the other compounds the spectra are almost identical and the peak absorptions occur at 3: 358 nm. The absorption cross sections are listed in Table 1 . At 366 nm, they are all about 1.3 X cm2 independent of temperature, except for CH30N0, where it is 1.8 x cm2 independent of temperature. The band spacings in the absorption spectrum were first given by Thompson and Purkis (1936) and Purkis and Thompson (1936) for CH30N0, C2H50N0, s-C4H90N0, and isoamyl nitrite. Their results are shown in Fig. 8.

B. Photodecomposition The photodecomposition pathways of alkyl nitrites have been reviewed by Calvert and Pitts (1966). Earlier a review of the photolysis of complex organic nitrites in solution was given by Akhtar (1964). Since the review of Calvert and Pitts

0.00

,

260

I

280

I

300

I

320

340

I

3€Q

WAVELENGTH

I

380

I

400

I

420

I

440

( nm )

Figure 3. The utraviolet absorption spectrum of C2H50NO(g) (0.012%C2H50N0 in N,) at 25°C. From Morabito (1985) with permission.

Figure 4. The ultraviolet absorption spectrum of CC,H,ONO vapor at 25°C. From McMillan et al. (1971) with permission of American Elsevier Publishing C o . , Inc. 182

4.00-

'

I

I

I

I

I

I

I

Yz

3

K

v) 0

m

a

I

_

-

3.503.00-

I

n-C,H,ONO

. I

-

2.50-/ 2.00-

-

1.50-

-

1.00-

-

0.50-

-

0.00-

I

I

I

I

I

I

I

1

I

I

I

000-

I

I

I

I

I

I

280

300

320

340

360

380

I

I

- C&ONO

I

400

I

I

420

440

WAVELENGTH (nm)

Figure 6. The ultraviolet absorption spectrum of i-C4H90N0 in n-hexane solution at 25°C. From Morabito (1985) with permission.

183

THE DECOMPOSITION OF ALKYL NITRlTEs

184

260

200

300

320

340

360

WAVELENGTH

380

400

420

440

(nml

Figure 7. The ultraviolet absorption spectrum of n-C4&ON0 in n-hexane solution 25°C. From Morabito (1985) with permission.

at

(1966), Heicklen (1973) has briefly reviewed the photochemistry of CH,ONO. However there appears to have been no comprehensive review in 20 years. Apparently the first study of the photodecomposition of alkyl nitrites was performed by Purkis and Thompson (1936), who used irradiation from a full mercury arc. They photolyzed CH30N0 and C2H,0N0. In the case of CH,ONO, gaseous products consisted mainly of N2 and N20. Also found was a white solid believed to be parafomaldehyde. With C2H50N0, they found N2, N20, CH,, and CO as gaseous products and a liquid which gave a positive identification for aldehydes. They concluded that the primary process was direct molecular decomposition to HNO plus the aldehyde, with the HNO subsequentlydisproportionating to H 2 0 N20. Thompson and Dainton (1937) extended these studies to n-C3H70N0, i-C3H70N0, s-C4&ON0, and t-C4H90N0 and reached the same conclusion. However a number of years later Gray and Style (1952) investigated the photodecomposition of CH30N0 at 366 nm from 30 to 156°C. They explained their results in terms of primary rupture of the CH,O-NO bond,

+

RON0

+ hu

-

RO

+ NO

(14

since they found NO as a product. The formation of NO and CH20 as products was confmed by Tarte (1953), who photolyzed CH30N0 with a full arc. He

PHOTOLYSIS OF ALKYL "WTES

185

TABLE 1. Photoabsorption Cross Section IJ of RON0 A

iemp.

m

nm

"C

U

cm*/molecule

Reference

CH30N0

366

25 to 150

339

25

214

25

1.79 x 10-19 1.84 x 1 0 - l ~ 1.74 x 10-19 3.1 x 10-19 3.4 x 10-19 3.24 x 10-19 4.2 X lo-'* 4.97 x 10-'8 4.59 x 10-'8 4.2 X lo-''

Wiebe and Heicklen (1973) Pate et al. (1974) Tayloret al. (1980) Calvert and Pitts (1966) Napier and Nomsh (1967) Tayloretal. (1980) Calvert and Pitts (1966) Napier and Norrish (1967) Taylor et al. (1980) Lahmani et al. (1980a)

C,H,ONO

366

-148t0120

1.20 x 10-19

Zabarnick and Heicklen (1985a)

n-C3H,0N0 Zabamick and Heicklen (1985b) 1.25 x

366

-26 to 120

366

-8to 120

1.30 x

366

-8 to 120

1.37 x

i-C4H90N0

Zabamick and Heicklen (1985~)

n-C4H90N0

Morabito andHeicklen(1987)

also found NO in the photolysis of n-C,H,ONO and n-C4H90N0, but not in a number of other C3-C5 alkyl nitrites. A major advance was made by Brown and Pimentel(1958), who found CH20 and HNO as the initial photoprcducts in a solid Ar matrix at 20 K with photolysis of CH30N0 between 240 and 360 nm from a mercury arc. They identified these products by low-temperature infrared spectroscopy. Confirmation that HNO was produced was given by Dalby (1958), who observed its absorption spectrum in the wavelength region 650-770 nm in the flash photolysis of isa-amyl nitrite. McGraw and Johnston (1969) also observed HNO by its infrared absorption at 3300 cm-'. Hanst and Calvert (1959) showed from product analysis that the primary process in CH30N0 photolysis at wavelengths >310 nm from a mercury lamp could be explained by 0-N bond cleavage, Eq. la. By doing experiments in the absence and presence of large amounts of Oz, they were able to show that there was no formation of CH, NO,, CH, NO 0, or CH30N 0. This was deduced from the fact that the products expected from these free radicals

+

+

+

+

THE DECOMPOSITION OF mcnm

186 Y.

cm-'

34OOo.

-

-

33000.

-

-

32000 . 320727 '4 939

t

31000 -

311331

3oooo -

30139-7 959 V 291mIT 1011

290002800027000 2600025000 -

V

2816931039 V 27130-pj 1068 26062=p

894 33784=, 882 3 3 1 % ~ 8 b 32082 32788"; 32734N3 795 9 32257-1.b 31939" A 890 8$5 3 1 3 6 7 - d 31104=C A - 9k6 30441-A 33680- b

-

31776-P 87 !

V

34518-1

-

'v6

8 b 30148--b 30120=r4 923 994 t 29197;29154-d~ 1020

q5

2 8 1 7 7 - r n 2816971040 1069 27137*)

c

27100-)

t

1163

1

-1

,3200

b

- 3400

-

1116

4 I

- 3600

c

- 3800

990 28498--1 27382-

1708

2567q

(b) Ethyl

(c) sec-Butyl

,3000

-

294481

1518

25582(d) Amy1

- 913

x, A

(a)Methyl

4Ooo

Figure 8. Band spacing in the absorption spectra of (a) CH,ONO, (b) C2H50N0, (c)sC,H,ONO, and (d) iso-my1 nitrite. From Purkis and Thompson (1936) with permission of The Royal Chemical Society.

were absent. The products observed by Brown and Pimentel (1958) could then be explainedby the reaction of CH30 NO, which could proceed by two paths,

+

+ NOM.,CH,ONO

CH~O

-CH2O

-I-HNO

At room temperature the HNO disappears by disproportionation 2HNO -N2O

+ H20

(3)

which accounts for the N,O observedby the early workers (Purkis and Thompson, 1936; Thompson and Dainton, 1937; Gray and Style, 1952). Kabaskalian and Townley (1962a) also showed that the primary process gave RO + NO in a series of alkyl nitrites photolyzed in benzene solution. They deduced this from the products formed which were aldehydes and alcohols, the products expected from the disproportionation of RO radicals. For RO radicals

187

PHOTOLYSIS OF ALKYL IWlUTES

larger than C2H50, they also saw the decomposition products (aldehydes or ketones) expected from these radicals. This conclusion was supported by the work of McGarvey and McGrath (1964), who found that NO absorption reached a maximum within 50 psec after the flash photolysis of a whole series of alkyl nitrites. In the case of CH30N0 the W absorption spectrum of CH30 was also seen (McGrath and McGarvey, 1964; McGarvey and McGrath, 1964). Free radicals also were detected by electron paramagnetic resonance in CH30N0 photolysis at 77 K from a mercury arc by Bielski and Timmons (1964). Further confirmation came from Ohbayashi et al. (1977), who observed emission spectra of CH30, C2H50.i-C3H70,and NO in the photolysis of the corresponding alkyl nitrites by iodine, mercury, xenon, and krypton lamps; and by Sanders et al. (1980), who measured the laser-induced fluorescence from CH30 produced in the 266-nm photolysis of CH,ONO. During the 1960sthe photochemistry of t-C4H90N0was studiedby McMillan and his coworkers. Earlier Coe and Doumani (1948) had shown the products to be CH3N0 + acetone in the vapor-phase photolysis at 25°C with aquartz mercury lamp. Coe and Doumani had concluded that these products probably were formed by a molecular elimination. However in his fust study, McMillan (1962) photolyzed t-C4&ON0 at 253.7 nm and found that the quantum yield of acetone was pressure dependent. He interpreted his results via the mechanism t-C$&ONO

+ hv

-

t-C4H90t

t-C4H90t -CH3 t-C4&Ot CH, t-C4&0

+

+ NO

acetone

+ M t-C4H90 + M + NO -CH,NO + NO t-C4H90N0 4

(la) (4) (5)

(6)

(24

where the superscript refers to excess energy. From his results, McMillan concluded that the quantum efficiency +la 20.84 at 26°C and 20.97 2 0.04 at 99°C. In a similar analysis of the photolysis of C2H5(CH3)2CON0(amyl nitrite), McMillan et al. (1971) concluded that = 1.O at 253.7 nm and 25”C, and Durant and McMillan (1966)concluded that +la = 1.O at 366 nm and 114°C. McMillan (1963) photolyzed t-C&ONO at 366 nm and 25°C in the presence of 15N0 to measure the exchange via the back reaction of t-C,H90 with I5NO. Under these conditions he found that “hot” radical production was small, since wacetone} = 0.04. He found wr-C4&0 ”NO} tobe0.99 0.03 andconcluded that +la was 1.0. However, in his experiments the 15N0 pressure was at least 14.5 TOK,so that exchange could have occurred with electronically excited t-C4&ON0. Thus the primary quantum yield in t-C4&ON0 photolysis at 366 nm is still unknown. However, if +la is <1.0, then the ”NO exchange with the excited CH30N0 would have to be 100% efficient.

THE DECOMPOSITION OF ALKYL MTRITEs

188

McMillan et al. (1964) confirmed the formation of CH3N0 in the gas-phase photolysis of t-C,qONO with a full arc (-75% of the radiation absorbed was below 255 nm) by using in sinc infrared absorption spectroscopy. In the presence of small amounts of O2 (which scavenge CH3 radicals) the CH3N0 production occurred with an induction period, thus indicating that it was coming from a precursor that reacts competitivelywith NO and 0,(presumably CH3radicals).

C. Primary Process Quantum Yield The first indication that the quantum yield for photodecomposition of CH30N0 was <1.O was given by Napier and Norrish (1967). When they flashed photolyzed CH30N0 in a large excess of N2, the long-wavelength bands of the spectrum almost disappeared, then returned to near the initial intensity at long delays. Coincident with the disappearance of bands, a short-wavelength continuum appeared at 290-300 nm and then decayed over the same period during which the nitrite bands returned. The minimum in the CH30N0 absorption and maximum in the new continuum occurred at 34 psec after the flash. The presence of excess NO had no effect on the time delay. The investigators interpreted their results in terms of formationof a thermal isomer in equilibriumwith CH30N0. Schuck and Stephens (1967) photolyzed C2H50N0in a 60-Lreaction vessel at concentrations of 0.58-62 mTorr at room temperature with peak energy at 350 nm and a distribution such that 85% of the energy was between 330 and 375 nm. They found that the initial quantum yield of C2H,0N0 disappearance dropped from 0.99 at their lowest pressure to <0.089 as the pressure was raised to 1 atm of N,. Increasing the pressure of C2H50N0 or NO also decreased the quantum yield. They interpreted these results in terms of both a direct cleavage reaction (la) and the formation of an excited molecule RONO* which could decompose directly to acetaldehyde + HNO at low pressure, but which could be collisionally stabilized at pressures > 15 mTorr C,H,ONO. This was deduced from the fact that C2H50N0 disappearance shifted from second-order decay below 15 mTorr to first-order decay above 15 mTorr. Ludwig and McMillan (1969) photolyzed i-C3H70N0at several wavelengths and temperatures. They found CH3CH0 and CH3COCH3 as products, which they interpreted as coming from CC3H70N0

+ hv

__*

gi-C3H,0t

-

i-C3H70t -CH3CH0 i-C3H70 + NO

+M

+ (1 - c)i-C3H70 + NO + CH3

i-C3H70N0

----*CH3COCH3

+ HNO

(la) (4)

189

PHOTOLYSIS OF ALKYL NITRITES

This mechanism predicts that +la

= @{CH3CHO}

+

k2b

cP{CH3COCH3}

Ludwig and McMillan adopted the value of kZdkz = 0.18 given by Hughes and Phillips (1967), and obtained the values of +la listed in Table 2. The value of +la is considerably less than unity. It increases slightly with temperature and is independent of wavelength. for C2H,0N0 was first The question of the value of the magnitude of addressed by McMillan et al. (1971). The rate law predicts

TABLE 2. Primary Quantum Yield for RO Production in RON0 Photolysis

R

CH3 C2H@

i-C3H70

X,(nm)

366 366 366 366 366 366 366

T,"C

= 25 25 25

'ha

c1.0 c0.75 0.33

50 c0.58 -48 to 120 0.29O 23 0.28 26 0.32-0.36 85

t-CaH90

327 39 1 253.7

n -C H 0

366

i-C4H90 n-C4H90 t-C,H 11 0

366 366 253.7 366

125 26

0.33 0.31 26 20.84 99 a0.97 23 0.37 +- O.Olb 50 0.36 & O.Olb -26 to 120 0.38 2 0.04b -8to 120 0.19 +- 0.02' -8t0 120 0.19 5 0.04 25 1.o 114 1.o

Reference

Napier and Nomsh (1967) Wiebeetal. (1973) This work McMillanetal. (1971) Zabarnick and Heicklen (1985a) Morabito and Heicklen (1985a) Ludwig and McMillan (1969)

McMillan (1962) McMillanetal. (1971) Zabarnick and Heicklen (1985b) Zabarnick and Heicklen (1985~) Morabito and Heicklen (1987) McMillanetal. (1971) Durant and McMillan ( 1966)

"Quantumyield is <0.003 for CH3CH0 + HNO productionand <0.002 for C,H, See text. %ese quantum yields are based on different values of kZ&. 'As corrected by Morabito and Heicklen (1985b).

+ NOz production.

190

THE DECOMPOSITION OF A L K n NITRlTEs

where CzH50

+ NO

C2H50N0 -CH3CHO

+ HNO

(2a) (2b)

With the value of k2dk2 = 0.23 reported by Arden et al. (1964), and the values of @{CH3CHO}measured by McMillan et al. (1971), they computed +la to be 0.59 2 0.01 at 23°C and 0.58 2 0.01 at 50°C. However, these measurements were made in the Torr pressure range of reactants, so that reaction 2a was not in the high-pressure regime. Thus their estimates are too high. A more accurate estimate was made by the same method by Zabarnick and Heicklen (1985a), who found that at higher total pressures (>lo0 Torr), WCH3CHO} = 0.070 -t 0.006, independent of temperature from -48 to 120°C. They used this value along with the average value of k2dk2 = 0.24 found by Phillips and coworkers in three separate studies (Arden et al., 1964; Livermore and Phillips, 1966; East et al., 1968) to deduce from Eq. b that +la = 0.29 & 0.03 independent of temperature from -48 to 120°C with 366-nm radiation. for n-C3H,0N0 McMillan et al. (1971) used the same analysis to estimate at 366 nm. They assumed 5 = 0.00 and k2dk2 = 0.23, the same value as for C2H50 radicals. With these values they deduced +,a = 0.37 2 0.01 at 23°C and 0.36 2 0.01 at 50°C. Zabarnick and Heicklen (1985b) used the same analysis and computed +la = 0.38 -+ 0.04 independent of temperature from -26 to 120"C, using a value of k d k 2 = 0.30 measured by East and Phillips (1970). Thus McMillan et al. and Zabarnick and Heicklen obtained the same value for +,a, but this is fortuitous (and inexplicable), since they used different values for k2dk2. Unfortunately, McMillan et al. (1971) did not list their values of WC2H5CHO}, so it is not clear whether there is a real discrepancy in the data or a computational error. For the sake of consistency, we will assume a computational error. In an analogous manner, Zabarnick and Heicklen (1985a) deduced that +la = 0.24 -+ 0.02 independent of temperature from -8 to 120°C in the photolysis of i-C4H90N0 at 366 nm using k2dk2 = 0.27, which is the average of the values found for C2H50and n-C3H70radicals. Since then Morabito and Heicklen (1985b) have measured k&k2 = 0.33 k 0.03, so that +,a becomes 0.19 ? 0.02. Likewise Morabito and Heicklen (1987) deduced +la = 0.19 -+ 0.04 independent of temperature from -8 to 120°C in the photolysis of n-C4H90N0 at 366 nm, using k2dk2 = 0.29 -C 0.05 (Morabito and Heicklen, 1985b). The question of the value of the primary quantum yield to produce CH30 + NO was addressed by Wiebe et al. (1973). They photolyzed CH30N0 at 366 nm and 25°C in the presence of "NO so that they could measure the CH301'N0 formed in reaction 2a as well as the N20 produced from the HNO formed in should be given by 2 ~ 3 o N Z 0 } that of reaction 2b. The primary quantum yield, ala. + @{CH3015NO}.This sum was found to be 0.75 2 0.01 at high pressure; thus

PHOTOLYSIS OF ALKYL, NllWTES

191

Wiebe et al. (1973) concluded that it represented +la. However, subsequent work with higher alkyl nitrites (Morabito and Heicklen, 1985a) has shown that 15N0 can exchange with the photoexcited alkyl nitrite, which does not undergo decomposition. Thus +la might be less than 0.75. Cox et al. (1980) photolyzed CH30N0 with homogeneous radiation from 310 to 410 nm with peak intensity at 350 nm and measured the quantum yield for CH30N0 removal to be 1.0 at a total pressure of 1 a m of N2 or N2 + 02.This is difficult to believe in the absence of 02,since some CH30N0 must be re-formed from the reaction of CH30 with NO. Another way to obtain the primary quantum yield +la is from a knowledge of k 4 k 2 = 0.33 at 174°C obtained from thermal sources of CH30 radicals by Arden et al. (1964), since at low NO pressures but high total pressure

and k2Jk2 is temperature independent (see Section IV-A). Both McGraw and Johnston (1969) and Wiebe and Heicklen (1973) obtained a value of 0.055 for wN20} at low NO pressures and high total pressure. Likewise Zellner (1986) flash-photolyzed CH30N0 at 351 nm and found Q>{CH20}= 0.12. Thus $la = 0.33 at 366 nm, and most of the absorbed light does not lead to products: CH3ONO

+ h~

CH30NO*

(1b)

where the asterisk (*) indicates electronic excitation. There is an incompatibility between the direct measurements for +la and that obtained from k2,,/k2.This is a problem that still needs to be resolved. However, in view of the results of Napier and Norrish (1967), we tentatively favor the value for +la = 0.33. Tuck (1977) photolyzed C2H50N0 with the polarized output of a lser at 347 nm and observed the angular dependence of the photofragments. His conclusion was that the photodissociation process occurs in less than the time for one rotation, thus implying the absence of a long-lived excited state at 347 nm, which is in a valley between two absorption bands. However, 366 nm is at a band peak where both a long-lived excited state and a continuum could overlap. Morabito and Heicklen (1985a) have shown that for the alkyl nitrites RONO* exchanges with "NO via the competition RONO*

+

-

15~0

RO

-

15~0

-RONO RONO*

RON0

+

+ NO

(7a)

15~0

(7b) (8)

THE DECOMPOSmON OF ALKYL NKRITES

192

This mechanism leads to the rate law

where it is assumed that [l4N0] is sufficiently low not to quench RONO* or react with RO to any significant extent. Since for CH30N0 photolysis at 366 nm, one has qCH3015NO}+ 2 q N 2 0 } = 0.75 2 0.01, +la = 0.33, and +la = 0.67, the left-hand side of Eq. a can be evaluated. The experiments of Wiebe et al. (1973) were done with [l5N0] = 5.6 +- 2.9 Torr.The value of k7a/k7 is not known for CH30NO*, but it is close to 1.0 for C2H50NO*and decreases towards 0.50 as the complexity of the alkyl nitrite increases (Morabito and Heicklen, 1985a). Thus we can assume that k7a/k7 * 1.0. With this assumption, k8/k7 = 1.8 X M. Jacox and Rook (1982) photolyzed CH30N0 at 14 K in a solid Ar matrix and observed the products by infrared spectroscopy. They found that the threshold for photodecomposition lies near 370 nm (77.3 kcdmole), with no evidence for photoisomerization at longer wavelengths. Thus the photodissociation threshold is at a very much greater energy than the dissociation energy of 684 nm (41.8 kcdmole) reported by Batt et al. (1974). The possibility of other primary photodecomposition processes was investigated by Zabarnick and Heicklen (1985a). They photolyzed C,H50N0 at 366 nm in the presence of either C3H6or i-C4H10 to scavenge the C2H50 radicals. They found that (P{N,O} dropped to zero, and concluded that the quantum yield HNO was for the direct photodecomposition of C2H50N0 to CH30N0 C0.003. Additional experiments with added NO2 showed that @{C2H5N0J <0.002, thus ruling out the possibility of a direct photodecompositionto C2H5 + NO2. The value of the magnitude of +la was thrown into doubt by the work of Rose (1979), working in McMillan’s laboratory. He photolyzed C2H50N0 at 366 nm and 296 K in the presence of excess NO2 and measured @{C2H50N02} and @{CH,CHO}. He assumed that these products resulted from

+

C2H50

+ NO2 %C2H50N02 + HN02 -CH3CHO

Corrections for the CH3CH0 produced resulting from photodecomposition of NO, followed by 0-atom attack on C2H50N0 were made. He found (P{C2H50NOJ = 0.93 -t 0.05, and from his results concluded that bJba= 0.09 +- 0.01. Thus +la should be 1.0. found by Rose can be explained if NO, exchanges The high value for with C,H,ONO* formed by absorption of the radiation:

193

PHOTOLYSIS OF ALKYL,

Since the sum @{C2H50NOJ + @{CH3CHO} found by Rose was 1.02 f 0.05, then reactions 10b and 8 could be of no importance under their conditions. This is consistent with the fact that there was no dependence of the quantum yields with NO2 pressure from 0.10 to 0.85 Torr. Thus klo&lo <0.03 and kslklo <2 X loM6 M.With the value of +la = 0.28 reported by Morabito and Heicklen (1985a), bdk, becomes 0.29 2 0.03. In a similar fashion, Rose (1979) photolyzed n-C3H70N0 and s-C4H90N0 in the presence of NO2 at 366 nm and 2 3 T , and came to the same conclusion for s-CH4H90N0 is not known, but that +la = 1.0. The actual value for that for n-C3H70N0 is 0.38 ? 0.04. Since Q>(n-C3H70N02} was measured to be 0.89 ? 0.04, we can estimate kgdk, = 0.26 2 0.03. Morabito and Heicklen (1985a) showed that the fraction of light absorbed that did not lead to photodissociation gave an electronically excited state that could exchange with "NO. They studied the photolysis of C2H50N0, nC3H70N0, n-C,H,ONO, and i-C4H,0N0 at 366 nm and 23°C in the presence of I5NO. The indicated mechanism from their result was

-

RONO -t hv -+ RO

+ NO

(la)

RONO*

RONO*

+

1 5 ~ 0-+

RO

1 5 ~ 0

+ NO-RON0

-

+ NO

(74

+ 15~0 + NO

--RONO RONO*

(1b)

(7b) (7)

RONO* -RON0 RO

+

1 5 ~ 0

RO

(8)

__*aldehyde RO

+ NO

(2a 15N)

1 5 ~ 0

+

Hi5N0

RONO

-aldehyde

(2b "N) (2a 14N)

+

HNO

(2b I4N)

RO +decomposition or isomerization

( I 1)

194

THE DECOMPOSlTION OF ALKn

where the rate coeffiients h ( l 5 N ) = k,(14N) = k, k2b(15N) = k~b('~N) = k2b, and k7 = k7a + km if the small kinetic isotope effect is ignored. They envisioned the isotope exchange reaction to proceed as follows:

RONO*

+

15~0

RO15N0

+ NO

RONO

+1

5 ~ 0

In the case where 14N0 is used, the two paths given by reactions 7a and 7b are indistinguishable. The steady-state rate law based on the above mechanism is

+

[l4N0]. Values of = 1.0 - + l a y +l,,k2,4 where [NO]= = [l5N0] k2, and kll/k2 were available from other studies, where k2 = k2a + k2,,. Thus the left-hand side of the equation could be computed and plotted versus [I5NO]-'. For C2H50NOya better straight-line plot was obtained with + l b = 0.28 rather than the 0.29 adopted by Zabarnick and Heicklen (1985a), and this value was used in the computations. The plot for n-C,H70N0 is shown in Fig. 9, and it is linear. From the least-squares values for the slopes k8/(k7a+la) and intercepts k,[NO],/ (+lak7a['5NO])yvalues of k8/k, and k7$k7 could be computed, and they are also listed in Table 3. From an inspection of the results in Table 3, we can conclude that kg/k7 = (2.7 & 0.5) x (3.4 +- 1.1) x (1.30 & 0.16) x and (2.3 & 0.3) X M, and that k7a/k7 = 1.0, 1.0,0.56 & 0.03, and0.64 k 0.04, respectively, for C2H50N0, n-C,H70N0, CC4HgON0,and n-C4H90N0. The uncertainties represent estimated absolute errors. There is no apparent trend in the values for kg/k7. However, k7Jk7 decreases as the molecular complexity increases. Perhaps this reflects the possibility that the intermediate RO(N0h can have more transient stability for more complex molecules and let k7a/k7approach the statistically expected value of 0.50. Finally we comment on the fact that Schuck and Stephens (1967) found quantum yields of 1.O for C2H50N0 photodecomposition at =350 nm and very

0 0

I

125

I

250

I

375

1 5.m

I

625 I"NOI-',

I

750

I

875

I

I

la00 1125

I

I

12.50 13.75

Tor,-'

I

ISM)

Figure 9. Plot of

versus [15NO]-1 for n-CSH70NO with +lb = 0.38, &,k4,,/k4 = 0.115, and k,,/k, = 0.0032 Tom. [15NO]/[NO]T = 0.887. From Morabito and Heicklen (1985a) with permission of John W.iley & Sons.

TABLE 3. Values of Rate Coefficient Ratios Involving RONO* at 23°C ~

R CH3 C2H5

n-C3H,ONO i-C4H90NO n-CdHgONO

k7$k7a

1 .ob 1 .oo 1 .oO 0.56 2 0.03 0.64 2 0.04

"For "NO. bAssumed.

105k8/k7,M 18.0 2.7 2 0.5 3 . 4 2 1.1 1.30 k 0.16 2.3 0.3

*

~~~~

Reference

I

From data of Wiebe et al. (1973) Morabito and Heicklen ( 1985)

195

1%

THE DECOMPOSITION OF ALKYL. IWRITES

low pressures. This suggests that RONO* may be formed with sufficient vibrational energy to photodissociate unless stabilized by collision. The photodecomposition of the higher nitrites lead to the formation of hydroxynitroso compounds. The overall reaction is

,7i-

\F -7-

,"",p 4

0

This reaction was first shown to proceed by Barton et al. (1960,1961). However, this reaction does not proceed as written, but through the usual C-O cleavage reaction. The alkoxyl radicals formed can transfer an H atom,

to yield a radical which adds to NO to give 1 1 1 1 HOC-C-C-CNO

1

1

1

1

Kabasakalian et al. (1962a. 1962b) and Kabasakalian and Townley (1962a, 1962b) showed that for this reaction to proceed the nitrite needed a chain of at least four carbon atoms. Lower nitrites did not show this reaction. A review of these reactions was given by Nussbaum and Robinson (1962) and by Akhtar (1964).

D. Formation of Excited Products McMillan (1962) photolyzed r-butyl nitrite at 253.7 and 313.0 nm and found that acetone was the major product, with CH30N02 and N2 as minor products. He noticed that the acetone quantum yield decreased with increasing pressure. Therefore he interpreted the acetone as coming from decompositionof an excited r-butoxyl radical, which could be stabilized by collision. Thus the primary process is

PHOTOLYSIS OF ALKYL NllWlES

RON0

+

&Rot + (1 - &)RO

h~

197

+ NO

-

(14

where 5 is the fraction of radicals with sufficient energy to decompose f-C4H90t

CH3COCH3

(4)

if not collisionally stabilized f-C4€&,0t

+M

__*

t-C4H90

+M

(5)

The collisionally stabilized alkoxyl radicals are removed by NO. From a study of the competition between reactions 4 and 5 , the following rate law is found:

@{acetone)-' =

(1 + k4 k5[M1 )

Values of the parameters 5+la and k5/k4 are listed in Table 4. The work was extended to 366 nm (McMillan, 1963), using the same techniques. These results are also in Table 4. It can be seen that the fraction of excited radicals, increases with temperature and incident wavelength from 0.04 at 366 nm and 25°C to 0.97 at 253.7 nm and 99°C. From these latter results, +la must be close to unity at 253.7 tun. It also can be seen from Table 4 that k5/k4 for C2H6 as a quenching gas increases from 253.7 to 313.0 n-n. This indicates that not only is the excited radical yield changed, but the degree of excitation increases with incident energy. The photodecomposition of t-C5H,,ON0 (C,H,C(CH,),ONO) was studied by Durant and McMillan (1966). The t-C5Hl10 radical produced in the primary process can decompose in two ways:

The sum of the quantum yields of formation of the two ketones was found to be unity at both 366 and 253.7 nm;thus +la = 1.O at both wavelengths. However the ratio of the quantum yields for the two ketones changed with pressure. The high-pressure ratio is that expected for thermal t-C5H,,O radical decomposition. Thus from the shift in ratio as a function of temperature the fractions of excited radicals produced could be deduced (McMillan et al., 1971), and they are listed in Table 4. Likewise Ludwig and McMillan (1969)deduced the fraction of excited radicals produced in the photolysis of i-C3H,0N0 from @{CH3CHO},since the CH3CH0 comes from

~

CZHSONO

r-C4H,0N0

RON0

~~

-

-

C2H6

-

t-C4&ON0

N2

C2H6

r-C,H,ONO NO

M

26 26 26

253.7 327.0 366.0 366.0 366.0 39 1.O 253.7

253.7

26 26

253.7 366

25

125 26 25

85

26 26 26 26 79 99 26 25 25

Temp., "C

253.7 253.7 253.7 253.7 253.7 253.7 313.0 366.0 253.7

A, nm

-

1.o 0.05

0.45

0.86 0.122 0.029 0.080 0.095 0.013 0.67

-

Christie and Hetherington (1977)

-

Ludwig and McMillan ( 1969)

McMillanetal. (1971)

McMillanetal. (1971)

McMillan (1963) Christie and Hetherington ( 1977)

Reference

Christie and Hetherington (1977)

}

}

'

-

-

-

-

36.1

7.2

0.87 0.87 0.87 0.87 0.94 20.97 0.2 0.04 0.87

ksfk4, hf-

TABLE 4. Parameters for Excited Alkoxyl Radical Production in Alkyl Nitrite Photolysis

PHOTOLYSIS OF A L K n

199

The values for qCH3CHO} = are listed in Table 4 for a variety of wavelengths and temperatures. Wiebe and Heicklen (1973) argued that the pressure dependence that they saw on (P{N20}in the photolysis of CH30N0 at 366 nm probably was due to decay of energetic CH30 produced in the primary process. However, a more likely explanation is that the pressure effect seen in their studies was due to the chaperone effect in the recombination of CH30 and NO. There is no evidence that hot CH30 radicals are formed with 366-nm photolysis. Christie and Hetherington (1977) photodecomposed t-butyl, isopropyl, and ethyl nitrites at 253.7 nm. They found respective values for t+laof 0.87,0.67, and 0.45. Their result agrees exactly with that of McMillan (1962) for tC,H,ONO, but is somewhat lower than the value 0.86 reported for i-C3H70N0 (McMillan et al., 1971). A few studies have investigated the energy in the NO fragment. Lahmani et al. (1980a, 1980b) photodissociated CH30N0 at wavelengths from 110 to 160 nm, where CH30N0 shows a diffuse absorption spectrum. The formation of NO in the A 'X+ (v'=0,1,2), C 211(v'=O), and D '2 (v'=O) states has been observed. The quantum yields for formation of the three states are, respectively, 0.18 & 0.03 at 144 nm, 0.07 2 0.02 at 138 nm, and 0.05 r 0.02 at 120 nm. The experimental energy threshold to produce each NO excited state is in agreement with the bond dissociation energy D(CH30-NO} = 1.8 eV. The total quantum yield of detected excited fragments was 0.4 at 120-125 nm. The vibrational energy in the NO (A 2s+)state was very nearly statistical. From this it was deduced that an important part of the excess energy went into the CH30 radical. Lahmani et al. (1986) examined alignment effects in highly rotating NO in the fnst excitedvibrationallevel produced from the photodissociationof CH30N0 at 355 nm. From polarization experiments, the rotational angular momentum of the NO was shown to be aligned preferentially along the transition moment of the parent molecule. The results were consistent with an impulsive dissociation with fragments recoiling close to the initial molecular plane. Radhakrishnan and Estler (1983) photolyzed CH30N0, C2H50N0, and nC,H,ONO at 382-383 nm under collision-free conditions. They found very large and nonthermal NO rotational excitation (Emt > 2100 cm-') from CH30N0. However, for C2H50N0 and n-C,H,ONO, the rotational temperature could be characterized by temperatures of 350 and 250 K, respectively. Keller et al. (1986) measured the photofragment time-of-flight mass spectra of the photodecomposition of CH30N0 at 248 and 350 nm. They found the respective translational energies in the NO to be 6940 & 180 and 4070 & 180 cm-'. and in the CH30 to be 6710 -C 170 and 3930 & 170 cm-I.

200

THE DE€OMPOSlTION OF ALKYL NKRITES

E. Summary The photodecomposition of alkyl nitrites proceeds exclusively by 0-N bond NO at all wavelengths. However, the quantum yield scission to give RO appears to be considerably less than one at 366 nm and possibly at other wavelengths where absorption is into a band of the absorption spectrum. At 366 nm, most of the alkoxyl radicals are produced without enough excess energy to enhance the unimolecular radical decomposition rates. However, the energetic radical yield increases with incident photon energy. The NO produced is highly rotationaly excited at 355 and 382 nm. Electronically excited NO has been observed for photolysis at 110-160 nm.

+

III. THERMAL DECOMPOSITION OF ALKYL NITRITES A. Early Work The thermal decomposition of alkyl nitrites was first studied by Steacie and Shaw (1934a). They showed that the decomposition of CH30N0 was homogeneous and unimolecular from 33.3 to 5 13.5 Torr and 190 to 24 1"C with a rate coefficient of 1.84 X 1013exp(-36.4/Rn sec-'. The overall stoichiometry of the decomposition was CH30NO __* NO

+

'/2CH20

+

'/2CH30H

(13)

which suggests that the initial reaction is cleavage of the CH30-N0 bond. At lower pressures (0.05 to 50 Torr) at 210-240°C, the rate coefficient fell with decreasing pressure as shown in Fig. 10 (Steacie and Calder, 1936). The solid lines are fitted with RRK theory assuming 13degrees of freedom and a molecular diameter of 5.0 X lo-' cm. Steacie and Rosenberg (1936) extended the data at 217.5"C from 650 Torr to 39 atm and found no further increase in rate coefficient. Carter and Travers (1937) examined at 200°C in a complex experiment referred to as the "method of detailed analyses." They concluded (erroneously) that there was no justification for first-order kinetics. However, they were the first to report N20 as a product, which we now know comes from HNO formed in the reaction of CH,O with NO. Steacie and his coworkers examined the thermal decomposition of several other simple alkyl nitrites. Steacie and Shaw (1934b) studied C2HSON0 at 190-24O"C. They found the reaction to be homogeneous and first-order with a rate coefficient of 1.39 X 1014 exp(-37.7/RT) sec-'. There was no falloff in the rate constant for pressures down to 55 Torr. Steacie and Shaw also examined the thermal decomposition of n-C3H70N0 (Steacie and Shaw, 1935a) and GC3H,0N0 (Steacie and Shaw, 1935b) from

THERMAL DECOMPOSITION OF ALKYL NITRITES

201

0

d c

i

d.

0

V."

-2.4

-1.8

-1.2

-0.6 0.0 0.6 Log P

1.2

1.8

Figure 10. Effect of pressure on time to 40% decomposition of CH30N0. C w e : (1) 514.4 K; (2) 504.4 K; (3) 494.3 K, (4) 484.3 K. Full circles from Steacie and Calder

(1936); open circles from Steacie and Shaw (1934a). From Steacie and Calder (1936)

with permission of the American Institute of Physics.

170 to 210°C. In both cases, the reactions were homogeneous and first-order, the respective rate coefficients being 2.75 x 1014 exp(-37.65/RT) sec-' and 1.26 X 1014exd-37.OIRn sec-'. There was no falloff in rate coefficients at any pressures used, which went down to 60.8 Ton for n-C3H70N0 and 33.3 Torr for i-C3H70N0. n-C4H90N0 pyrolysis was studied by Steacie and Smith (1936) from 50 to 400 TOK pressure and 170 to 212°C. The reaction was also homogeneous and first-order, but they were not able to obtain an accurate Anhenius expression for the rate coefficient. However, at 189.9"C the rate coefficient was 8.88 X sec-'. This confiied the trend in increasing rate coefficient with complexity of the molecule as shown in Table 5. Steacie and Katz (1937) examined the thermal decomposition of C,H,ONO and n-C3H70N0at low pressures to study the falloff in rate coefficient at reduced pressure! (down to 0.02 Tom for C2H50NO). They found their results to be in complete accord with Kassel's theory. The pressures for a factor-of-2 decrease in rate coefficient, P ~ , are ~ , about 0.4 TOK for C2H50N0 at 484-505 K and

TABLE 5. Rate Coefficients for Alkyl Nitrite Decomposition at 189.9"C RON0

CH30NO CzHsONO i-C3H,ONO wC~H~ONO n-CdHQONO

1o4k_,,, sec-' 0.97 1.89 3.70 3.95 8.88

Reference

Steacie and Shaw (1934a) Steacieand Shaw (1934b) Steacie and Shaw (1935b) Steacieand Shaw (1935a) Steacie and Smith (1936)

THE DECOMPOSITION OF unNITWITS

202

about 0.2 TOITfor n-C,H,ONO at 484 K. These can be compared with values of about 4 TOITfor CH30N0 at 484-514 K (Steacie and Calder, 1936). Rice and Rodowskas (1935) examined the decomposition of C2H50N0. At low pressures of C,H,ONO diluted in an inert gas at 425°C. they showed with the use of tellurium mirrors that CH, radicals were produced, and that they were the only radicals to react with tellurium in their system. These results were explained in terms of the mechanism C2HsONO *CZHSO

-

C2H50-CH3

CH3

+ NO

+ CHZO + CH3CHO + NO

+ C,H5ONO---*CH4 2CH3 + Te (CH3)*Te

(-24 (4) (14) (15)

The activation energy of the reaction was found to be 34.3 703 to 803 K.

&

3 kcallmole from

B. Mechanism There appear to have been no further studies on the thermal decomposition of alkyl nitrites until 1949. Then two more complex nitrites were studied. Kornblum and Oliveto (1949) examined the thermal decompositionof optically active 2-octyl nitrite in the liquid phase at 100°C. Optically pure d-2-octanol was obtained in excellent yield, thus showing that 2-octoxyl radicals were produced, and that these did not racetnize. Kuhn and DeAngelis (1954) looked at the thermal decomposition of vicinal dinitrites. The vapor-phase decompositions of propane-l,2-dinitrite, butane-2,3dinitrite, and cis- and trans-cyclohexane-1,2-dinitrite all proceed via the overall reaction RCH(ON0)-CH(ON0)R

2NO

+ 2RCHO

(16)

Thus the reaction appears to proceed via elimination of the two NO groups accompanied by C-C bond scission. However, in the liquid phase the products of decomposition of butane-2,3-dinitrite were mainly RC(0) -C(O)R and (RCHOH), as well as NO. This suggests that the initially formed free radical is stable long enough to abstract an H atom from the parent compound. This sequence would be repeated by both reactants, so that the initially formed radical would become the dialcohol, and the secondary radical, which had lost an H atom, would become the diketone.

THERMAL DECOMPOSITION OF ALKYL. NITWTES

203

Adler et al. (1955) examined the pyrolysis of n-C3H70N0, i-C3H70N0, n-C4&ON0, i-C4H90N0, and s-C4H90N0 at 230-240°C. They found that the akoxyl radical formed in pyrolysis decomposed as follows:

where the split occurs more easily the larger the R group. Gowenlock and Trotman (1956) have shown that the alkyl radicals can then react with NO to produce nitrosoalkanes, RNO . Yoffe (1954) studied the thermal decomposition of t-C4H90N0 both in the vapor phase at 340°C in a flow system and in isopropylbenzene solution under a N2 atmosphere at 80°C. In both cases the products were consistent with bond cleavage to give t-C4H90 + NO as the initial step. Gray (1954) observed chemiluminescence from the decomposition of CH30N0 and C2H50N0 from 290 to 400°C. The chemiluminescence, which was attributed to RO radicals, is facilitated by increasing the temperature, by adding inert gases, and by decreasing the surface/volume ratio. In the presence of O2 or NO,, luminescence occurs readily and explosive ignition could also occur. For C2H50N0, the reciprocal initial concentration for luminescence has an activation energy of 30 kcal/mole. For CH30N0, the activation energy varies with temperature. Nagiev et al. (1956a, 1956b) studied the thermal decomposition of nC3H70N0 and n-C4H90N0. They found the respective rate coefficients to be 1.6 X 1013 exp(-34.7/RT) and 4.53 X 1013 exd-36.2IRT) sec-'. Levy (1956a) reported on the thermal decomposition of C2H50N0 at 10-50 Ton and temperatures of 161, 181, and 201°C. The addition of large amounts of NO did not materially affect the reaction rate, but increased both the CH,CHO and N20 yields. In the presence of CH3CH0, the rate increased sharply but N20 was not produced. These results were explained by the mechanism

-

C2HSONO C ; C 2 H 5 0 C2HSO

+ NO

2HNO

C2H5O

+

__*

HNO

N20

HNO-C2HSOH

+ NO

+ CH3CH0

+ H2O

+ NO

(-2a,2a) (2b) (3) (17)

The fact that NO additions did not reduce the rate of reaction indicated that C~HSO was not reacting to any significant extent with CzHSONOor with itself. Furthermore, since increasing NO increased CH3CH0 and N20, reaction 17 was becoming less important. Finally, the results in the presence of CH3CH0 could be explained by

THE DJXOMPOSmON OF ALKYL NTnUTES

204

C2H50

+ CH3CH0 -C2H50H

+ CH3C0

(18)

Thus the rate went up and N20 went down because reactions 2a and 2b were reduced in importance, since the C2H50radicalswere being scavengedby reaction 18. This mechanism leads to the limiting rate laws at low [NO] and [CH3CHO], where reaction 17 is dominant in removing HNO, of

-d[C,H,ONO]

dt

-

2k2&2,[RONO] k2

= 2R{CH3CHO} = 2R{C2H50H} (g)

and

For high values of [NO] or [CH,CHO], where reaction 17 is negligible, the rate law is

As we shall see later, k2,4k2, = 0.30, so that the effective rate coefficient is 0.46k-,, at low [NO] and [CH3CHO], 0.23k-,, at high [NO] and low [CH3CHO], and k2,at high [CH,CHO]/[NO]. Since NO is produced in reaction -2a, there are no experiments at truly low [NO], so the rate coefficient -0.3kF2, at all NO pressures, but increases to k - , at high [CH3CHO]/[NO]. Furthermore, in the absence of added CH,CHO, R{N,O} is near zero at low [NO], rises toward 0.12k-2,[RONO] as [NO] is increased, and then drops back toward zero as [CH3CHO]/[NO] is increased. Meanwhile R{CH,CHO} is near 0.23k-,,[CH30NO] at low [NO] and [CH3CHO], rises toward 0.23k-2,[CH30NO] as [NO] increases, and drops back toward zero as [CH,CHO]/[NO] increases. R{N20}/R{CH3CHO} goes from near zero at low [NO] toward 0.5 as the [NO] is raised, independent of the added CH3CH0 pressure. These conclusions are all in accord with Levy’s results, and f i n n y establishedthe mechanism of reaction as given above. From Levy’s data kVza = 6.1 x 1013 exp(-(37.5 2 0.5)/ RT) sec-’. Levy (1956b) extended his studies to i-C3H70N0, n-C3H70N0, and tC4H90N0. He found that the rates of thermal decomposition of these nitrites were sharply decelerated by the addition of NO. The NO reduced the importance of alkoxyl radical decomposition reactions but increased the N 2 0 produced. Thus

THERMALDEColMpoSITION OF ALKYl. NlTRITEs

205

these results supported the mechanism developed by Levy (1956a) for C2HSON0 decomposition. Gray and Williams (1960) reexamined the pyrolysis of CH30N0 at 178-3 15°C in static and flow systems. They found an activation energy of 36.4 kcal/mole. The N 2 0 yield was always about 0.13 mole N 2 0 per mole CH30N0 decomposed, which supported Levy's mechanism (reactions 2, 3, 17, and 18 above). The pyrolysis of CH30N0 also was reexamined by Phillips (1961) between 150 and 240°C. He found that the reaction was frrst-order and proceeded by

-

CH30N0 A CH30 CH30

+ NO

2CH30

NO

CH30N0

-CH20

2HNO

+

H20

f

HNO

+ NZO

CHzO

+ CH30H

However his rate coefficients,like those of Shaw and Trotman-Dickenson (1960), were about half those given by Steacie and Shaw (1934a). The free-radical nature of the reaction was shown by adding cyclohexene, a free-radical scavenger. This increased the yields of CH30H and NO, and almost eliminated N20. The rate coefficient found by Phillips for CH30N0disappearance was 10'2.2exp{-34.3/ R n sec-'. Napier and Nomsh (1967) spectroscopically observed HNO in the pyrolysis of CH,ONO, and showed that its concentration increased with added NO. This confirmed that HNO was an intermediate, and that it was formed by reaction of NO with CH30. Ferguson and Phillips (1965) examined the pyrolysis of i-C3H70N0at 175200°C and 35 Torr pressure. Their results confirmed the presence of HNO as an intermediate. Likewise Marta and Seres (1966) studied the thermal decomposition of CzHSONO at 200-230°C and 20-200 Torr. Their results substantiated the mechanism of Levy (1956a). Marta and Sees found k-2a = 4.58 x 1013expi-36.69IRT) sec-'. The thermal decomposition of CH30N0 in shock waves was studied at 7801OOO"K and 0.35-1.6 atm (Zaslonko et al., 1970). The rate coefficient was found to be 10'2.9 exp(-34.O/RT} sec-' by measuring the absolute intensity of the light emission from electronically excited CH20 and HNO produced in the reaction. Their rate-coefficient expression gives rate coefficients a factor of 1.5-2.0 higher than obtained by extrapolation of the results of Steacie and Shaw (1934a) and a factor of 5.8-6.1 higher than obtained by extrapolation of the results of Phillips (1961). This is because the back reaction is not important at the higher temperatures, since the CH30 radical decomposesbefore recombining with the NO produced. The thermal decompositionof aromatic nitrites was investigated by Gray and

THE DECOMPOSlTION OF ALKYL NlTRlTH

206

coworkers. Gray et al. (1960) studied the thermal decompositionof benzyl nitrite at 100-215°C in liquid, gas, and solution. Decomposition occurs by 0-N bond cleavage in a unimolecdar reaction to give C&CH20 and NO. The decomposition of 1-phenylethyl nitrite was studied by Gray et al. (1961) in solution and as the pure liquid from 80 to 140OC. Again decomposition occurs by 0-N bond cleavage in a unimolecular reaction. Gray et al. (1961) showed that alicyclic alkoxyl radicals were produced in the thermal decomposition of cyclohexyl- and 1-methylcyclohexylnitrite.

C. ModernStudies In the 1970s. a substantial effort was made by Batt and his coworkers to obtain accurate Arrhenius parameters for the thermal decomposition of simple alkyl nitrites in the gas phase. Batt et al. (1974) used bomb calorimetry to obtain the heats of combustion of several alkyl nitrites. From these they obtained the enthalpies of formation, and these are listed in Table 6. Also listed in Table 6 are the enthalpies of formation of the corresponding alkoxyl radicals obtained from the pyrolysis of dialkyl peroxides. When these data were combined with AH'&8 {NO} = 21.6 k 0.3 kcal/mole, values for D(Ro-NO} could be obtained. These are listed in Table 6 and are all about 4 1.5 k c d m l e .They are considerably higher than the activation energies for decompositionreported by earlier workers. Thus Batt's laboratory started on a program to redetennine the Arrhenius parameters for RONO decomposition. Batt and Milne remeasured the decay rates of CH30N0 (Batt et al., 1977), C2H50N0(Batt and Milne, 1977b), i-C3H,0N0 (Batt and Milne, 1977a). and

TABLE 6. Thennochemical Data for RONO" kcallmole, A@{RONO>, kcaVmole

R

- 16.0 f 0.2'

Me Et n-Pr i-Pr n-Bu i-Bu S-BU t-Bu

-24.5' -28.4 -31.9 -34.8 -36.1 -36.5 -41.0 ~~

f1 5 1 2 1

f1 f1 2 1

(298" K)

Af$CRO>, kcaVmole 4.2 -4.1 -9.9 -12.5 -13.9 -15.7 -17.0 -21.7

2 0.7 f 0.7 2 1.5 f 0.7 f1 2 1 2 1 +- 0.7

~

"From Ban et al. (1974) with permission of John Wiley and Sons, Inc. %om Silverwood and Thomas (1%7). 'From Benson et al. (1%9).

WRO-NOI, kcahole 41.8 2 0.9 42.0 2 1.3 40.1 2 1.8 41.0 t 1.3 42.5 f 1.5 42.0 f 1.5 41.1 4 1.5 41.1 2 1.3

THERMAL DECOMPOSlTfON OF ALKYL NITRITES

207

t-C45ONO (Baa and Milne, 1976). They obtained larger Arrhenius parameters than previous workers by studying the decompositions in the presence of additives which either scavenged the alkoxyl radical (i-C4Hlo) or aided their thermal decomposition (CF, at = 0.9 atm). Their values are more in agreement with the thermochemical data and RRKM theory. These values, as well as those found in earlier studies, are listed in Table 7. For the t-C,H,ONO decay, they also found a direct molecular path to give i-C4H8 + HONO which could not be quenched by free-radical scavengers: t-C,H,ONO

-

i-C4Hs

+ HONO

(20)

with log{A, sec-’} = 12.9 +- 0.4 and an activation energy of 33.6 2 0.8 kcal/mole (Batt and Milne, 1974). Likewise traces of olefin were found in the decomposition of C,H,ONO and i-C3H70N0, and these were attributed to reaction paths analogous to Eq. 20. For the CH30N0, C2HsON0, and i-C3H70N0 decays Batt and his coworkers suggested that some aldehyde 4- HNO was produced by direct 4-center elimination to explain the “excess” aldehyde expected based on ratios k2dk2. In light of more recent work (Batt et al., 1978b), there appears to be no reason to include the 4-center elimnination mechanism in a homogeneous process. However, there was evidence that a heterogeneous process may be operative for i-C3H70N0 (Batt and Milne, 1977a). Mendenhall et al. (1975) studied the thermal decomposition of f-C4H90N0 using the very-low-pressure pyrolysis technique from 525 to 765 K. The highpressure first-order Arrhenius parameters were log{A, sec-’} = 15.8 with an activation energy of 39.3 kcal/mole. Mendenhall et al. (1975) also obtained evidence for the molecular elimination process in t-C,H90N0 from the excess decomposition at low temperatures over that predicted from RRKM theory as shown in Fig. 11. They attributed this process to heterogeneous decay to give i-C4H, a d HONO. However, an analogous process for i-C3H70N0, i-C3H70N0

-

C3H6 + HONO

(20)

was seen by Batt et al. (1978b) with log{A, sec-’} = 12.7 and an activation energy of 37.9 kcal/mole. These Arrhenius parameters, as well as those obtained by Batt and Milne (1976), are reasonable values for a homogeneous 6-center elimination reaction. Batt et al. (1978b) also ascertained that no HNO was produced by molecular elimination from C,HSONO or i-C3H70N0, but that it came entirely from disproportionation of NO with alkoxyl radicals. Other studies from Batt’s laboratory concerned the decomposition of sC4H90N0(Batt and McCulloch, 1976b) and t-CSH,lONO (Batt et al., 1978a). In the case of s-C4H,0N0, a molecular elimination to produce CH3COC2HS+

THE DECOMPOSITION OF ALKYL NITRlTEs

208 10'

I

I

700

800

102

1

10-1

500

600 TPK

Figure 11. First-order reaction rate coefficients for the very-low-pressure pyrolysis of t-C,H,ONO for collision numbers of 11200, 2,470 (0); 387 From Mendenhall et al. (1975) with permission of John Wiley and Sons, Inc.

a);

(a).

HNO was reported. However, in lieu of the later conclusion of Batt et al. (1978b) that no HNO is formed by a homogeneous molecular elimination in the lower alkyl nitrites, it is not likely to occur in s-C4H90N0 either. The Arrhenius parameters for alkyl nitrite decomposition are listed in Table 7. All of these results have been summarized by Batt (1979). The homogeneous decompositionsproceed by 0-N bond cleavage to give RO + NO with activation energies of -41 kcal/mole and Arrhenius preexponential factors of about 1 x 1OI6sec-'. There does not appear to be any direct elimination to give aldehydes plus HNO. However both r-C4H,0N0 and i-C3N70N0 do give alkenes plus HONO in a molecularelimination,though thismay be in a heterogeneousprocess.

RW\CI?ONS OF ALKOXYL RADICALS WlTH NO,

TABLE 7.

209

Rate Coefficients for the Thermal Decomposition of RONO E-b, kCaYmole

References

36.4 36.4 34.3" 34.0 41.2 f 1.2

Steacie and Shaw (1934a) Gray and Williams (1960) Phillips (1961) Zaslonko et al . (1970) Battetal. (1974)

13.79 13.66 16.0 f 0.4

37.7 34.3 2 0.3 37.5 2 0.5 36.7 41.8 2 0.9

Steacie and Shaw (1934b) Rice and Rodowskas (1935) Levy ( I956a) Marta and Seres ( 1966) Batt and Milne (1977b)

170-210 = 227

14.44 13.20

37.7 34.7

Steacie and Shaw (1935a) Nagievetal. (1956a, 1956b)

i-Pr

170-210 130-160

14.10 16.2 f 0.4

37.0 41.0 2 0.8

Steacie and Shaw (1935b) Batt and Milne (1977a)

n-Bu

170-212

13.66

36 36.2

Steacie and Smith (1936) Nagiev et al. (1956a)

Temp. Range, "C

log{A-z,, sec-'}

190-241 178-315 150-240 507-727 170-200

13.26

190-240 430-530 161-20 1 200-230 162-2 18

14.14

n-Pr

R Me

Et

-

-

12.2 12.9 15.8 % 0.6

-

-

S-BU

130-200

16.2 f 0.4

40.9 2 0.8

Batt and McCulloch (1976b)

t-Bu

377492 120-160

15.8 16.3 f 0.4

39.3 40.3 f 0.8

Mendenhall et al. (1975) Batt and Milne (1976)

?-Am

120-190

16.3 f 0.1

40.3 f 0.1

Batt el al. (1978a)

"Corrected by Batt el al. (1974) to 38.9 kcal/mole.

IV. REACTIONS OF ALKOXYL RADICALS WITH NO, A.

RO

+ NO Disproportionation-to-CombinationRatio

It has been known since the 1950s that alkoxyl radicals add to NO and NO2. This early work has been reviewed by Gray et al. (1967) and by Heicklen and Cohen (1968), and all of it will not be discussed here. It was shown by Levy (1953) that C2H50 radicals could add to NO, and later inferred by him (Levy, 1956a, 1956b) that alkoxyl radicals could aansfer an H atom to NO to give HNO, which could then form H20 N20 by self-annihilation:

+

RO.

+ NO,

RONO,

(24

210

THE DECOMPOSITION OF ALKYL

RlRzCHO

+ NO,

RlR2CO

+ HNOx

(2b)

The first study of the disproportionation-to-combination ratio of alkoxyl radicals with NO was made by McMillan (1961), who photolyzed diisopropyl peroxide at 230-290 nm in the presence of NO. From the ratio of (CH,),CO to i-C3H70N0produced he could deduce kidk,.His values are given in Table 8. In the 1960sa series of studies was undertaken by Phillips and his collaborators to measure the relative rate coefficientsfor addition and disproportionation.They thermally decomposed dialkyl peroxides in the presence of NO and measured the amounts of RONO and aldehyde produced. From these data they could from which k2&3 can be deduced, and these values are listed deduce k&, in Table 8. Estimates of k2, could be made from the equilibrium constant and rate coefficients for the thermal decomposition of RONO. These also are listed in Table 8. Livermore and Phillips (1966) also studied the thermal decomposition of C2H50 in the presence of NO at 200°C at very low pressures in a flow system. They found reaction 2a to be pressure dependent and follow a Lindemann mechanism with a half-reaction pressure of 0.08-1.6 Torr of (C2H5O), as a chaperone. This agrees exactly with the results of Steacie and Calder (1936), who found a similar half-reaction pressure for the reverse reaction. Rebbert (1963) photolyzed C2H50N0 at 366 nm and 25°C to produce C2H50 radicals. In the presence of NO, he measured C2H50N0and CH3CH0 to obtain kalk2b -3.3. Baker and Shaw (1965) pyrolyzed (CH30)2,(C2H5O)2, and (r-C&0)2 at 130°C in the presence of NO and NO2. They measured CH20 as CO and CH3CH0 as C02 produced in further oxidation. From these compounds and the amounts of RONO, formed, relative rate coefficients could be obtained, and they are given in Table 8. Ludwig and McMillan (1967) pyrolyzed (CC,H,O), in the presence of 200 Torr N2 from 120 to 180°C. The ratio [(CH,),CO]/[(CH,),CHONO] produced in the reaction was temperature dependent below 160°C, but temperature independent at 0.17 above 160°C. The temperature-dependentportion was shown to be due to a surface reaction which gave excess (CH3)2C0.This heterogeneous process was overwhelmed at the higher temperatures, and k2dkz, was taken to be 0.17 at 160-18OoC, exactly the same as found by McMillan (1961) at lower temperatures. Yee Quee and Thynne (1968) studied the thermal decomposition of (i-C&0)2 in the presence of NO. They obtained k2dk, = 0.15 & 0.02 independent of temperature at 121.5-158.7"C from the ratio of CH3COCH3and i-C3H70N0 produced. Four studies employed the photolysis of CH30N0 in order to obtain k2,/k2 (McGraw and Johnston, 1969; Wiebe and Heicklen, 1973; Wiebe et al., 1973; Glasson, 1975). However, in all cases high values for the primary photodecompo-

REACTTONS OF ALKOXYL RADICALS WITH NO,

211

sition quantum yield were used. Thus these studies were really suited to determine this yield rather than W k , . Additional values of k2dk2 were obtained by Morabito and Heicklen (1985b). They examined the thermal decomposition of several alkyl nitrites in the presence of 15N0. By measuring the RO'%JO and aldehyde produced they had a direct determination of k d k Z b .Their results also are given in Table 8. Single determinations exist for k2dk2 for CH30, n-C4H90, i-C&o, and S-C&O of 0.33, 0.29 & 0.05, 0.33 2 0.03, and 0.21 0.02, respectively. Three determinations for CzH50radicals give 0.23,0.23, and 0.25; and another gives >0.16. For i-C3H70, five values range from 0.13 to 0.18. Two values for n-C3H70 are 0.30 f 0.01 and 0.26 & 0.03. Thus for those systems with more than one determination good agreement is achieved. For t-C4H90, which has no abstractable a-H atoms, the ratio is zero. Table 9 summarizes the values of k2Jk2 as a function of the number of H atoms on the a carbon atom. For those radicals with no a H atoms, no abstraction occurs and k24k2 = 0. The methoxyl radical, which has three a H atoms, has the largest value of k2Jk2 = 0.33. The value for k,dk2 is less for radicals with two a H atoms, and even less for radicals with one a H atom. However within each group, the ratio k2dk2 increases with the complexity of the radical. Thus k, = 0.16 for i-C&o, but 0.21 for s-C4H90. It increases from 0.23 to 0.33 as RO goes from C2H50 to n-C3H70to n-C4H90to i-C4H90. If only the number of a H atoms were responsible for the value of k2dkz, we would expect the values to be in the ratios of 0, 1, 2, and 3 for k2dkb. Taking k2dk2a = 0.50 for CH30 would give 0.17 and 0.33 for radicals with one and two OL H atoms. These values are approximately what is observed, but, except for C2H50,the observed values are slightly larger than expected from this simple prediction. Since neither reaction 2a nor 2b has an activation energy, we must look for other reasons for the radical complexity effect. Presumably the stronger van der Waals attractive forces in the bulkier radical tend to pull the incoming NO group more toward the hydrocarbon end and away from the oxygen-atom end of the radical. Thus the relative collision frequency of the NO with an H atom is enhanced compared to that with the oxygen atom.

*

B. RO

+ NOz Disproportionation-to-CombinationRatio

Measurement of the ratio kgdk, has been made for CH30, C2H50, and n-C3H70, and attempted for S-C4H90 radicals. In the case of CH30 radicals, there is considerable uncertainty in the results, though all studies agree that k9dk9 zs 0.1. For C,H50, Baker and Shaw (1965) pyrolyzed (C2H5O)Z at 130°C in the presence of NO2 and reported k&, = 0.31 2 0.02. Rose (1979), who photolyzed alkyl nitrites at 366 nm in the presence of NO2 at 25"C, reported k9dk9, = 0.09 & 0.01 from the acetaldehyde produced, assuming a primary quantum

N -+

-53 to + 200 25

27

167198 119148 22

25

110

"0.013f

e

-

9.92

-0.036 20.007f

eo.1

e

9.9=.b

-

9.92 ~k0.03~

-

20.6'

10.1

-

-

772

61-

740 k0.03" ~9.85"

90

-

25

-

-

kO.01

0.09

k9dk9

167-

log{ba. M-l-sec-'}

+ HONO (9b)

55-

R'O

9.57 +0.03" 9.73

k2dk2

+ NOz

-

bdkz,, W'-sec-'}

RONOz (9a); RO

Press, Tom

4

>80

+ NO,

130

174

Temp. Range, "C

(2b); RO

+

CHJ + hv + NO CH30N0 + hw(366 nm) CH30N0 pyrolysis (CH30)2 pyrolysis CH30NO hv(266 nm) F + CH30H

+

(CH30)2 pyrolysis (CH3Oh pyrolysis CH3 NO2

Source of RO

+ HNO

Zellner (1986)

(1985)

McCaully et al.

Batt and Rattray (1979) Sanders et al. (1980) Fortuno (1982)

Battet al. (1977)

Shaw (1 965) Phillips and Shaw (1965) Johnston and Heicklen ( 1966) Wiebe et al. (1973)

Baker and

Ardenetal. (1964)

Reference

TABLE 8. Rate Coeilicientsfor Reactions of Alkoxyl Radicalswith NO and NO2: RO + NO +RON0 ( 2 ~ ) RO ; + NO +R'O

2

200682

13-32

80 = 680 (CF4) 2-760

150 (N2)

30-63

35-57

>200

95135 130

200

25 162197 25

175

26

77

160180 105149 121159 128158

(CF4)

= 680

-

30155

(Nz)

>80

25-37

28

-

0.18 r0.02 0.13 r0.02

0.16 20.02 0.15

-

-

-

-

-

-

0.13 kO.01

-

-

-

k 0 .03B

9.80

-

0.22 20.02

-

0.25 k0.03 >O. 16

-

2 0.03

0.23

-

0.29 %0.03h

-

0.31 50.02

-

(i'C3H7°)2 pyrolysis (i'C3H70)z pyrolysis (i-C3H70)2 pyrolysis (i-C3H70NO) pyrolysis

+

Morabito and Heicklen (1985b)

Arden et al. ( 1964) Baker and Shaw ( 1965) Livemore and Phillips (1966) East et al. (1968) Batt and Milne (1977b) Rose ( 1979)

Rebbert (1963)

Ludwig and McMillan (1967) Hughes and Phillips (1967) Yee Quee and Thynne (1968) Batt and Milne (1977a)

(i-C3Wh McMiIIan ( 1 961) hv(230-290 nm)

C,HSONO, + hv(366 nm) (CzH5O)z pyrolysis (C2H50)2 pyrolysis (CZHSO), pyrolysis C2H5 + NO, CZHSONO pyrolysis CZHSONO + hv(366 nm) C,H,ONO pyrolysis

N

G

2281

100150 300540 25

150 (NZ)

25139

175

100140

(N2)

= 10.1 0.21 20.02

0.33 20.03

0.29 20.05

175

0.30 20.01

0.26 20.03

150

10.8

-

31

10.16 2 0.40'

175

2-760

-

1-50

22111

TABLE 8. (Continued)

-

-

-

-

9 3

10.28

2 0.08i

-

RO = s-C.,H90

-

RO = i-C4H90

-

RO = n-C4H90

0.26 +0.03h

-

RO = n-C3H,0

-

i-C4H90N0 pyrolysis

n-C4H90N0 pyrolysis

+ hv(366 nm) n-C3H70N0 pyrolysis

(n-C&0)2 pyrolysis nC3H70NO2 pyrolysis n-C3H70N0

i-C3H70NO + hv(366 nm)

Walker and Phillips (1968)

Morabito and Heicklen (198513)

Morabito and Heicklen (1985b)

Morabito and Heicklen (1985b)

East and Phillips (1970) Mendenhall et al. (1975) Rose ( 1979)

Ballaet al. (1985)

-

-

10.4,

1

2-

22"

10.5 -C 0.2'

-

-

0

= t-CdHpO

I

RO = t-amoxyl

RO

-

t-amylONO pyrolysis

(t-C&@h pyrolysis t-C,&ONO py ro1y si s t-C,H&NO pyrolysis

S-C,H,ONO pyrolysis

"Based on log{k2,, M-'-sec-'} = 10.00. bBased on k2dk2 = 0.33, k&, = 0.1, and k2/k9 = 1.3 'Equilibrium calculation from reverse rate coefficient. = 0.33. dBased on k,&, 'At low pressure k2s = (8.0k 1.1) x 10" M-2-sec-' (Fortuno, 1982) or 9.4 X 10" M-*-sec-' (25°C)(McCaully et al., 1985). based on log{ba, M-'-sec-'} = 9.82 8Based on log{k,,, M-'-sec-'} = 10.2and kZa/k9,,= 2.5 'Corrected for +h = 0.28 and 0.38,respectively, for CzHSONOand n-C,H,ONO. 'Assumes kzdkz = 0.16. Value for log#+} = Iog{b, + hb}. 'Assuming log{kJ = 10.3. 'Pressure not given. Experiments done in excess CF,. '"i-C,H,,or CF,.

155

120-

0.4'

I

-

-

9.8'

-

-

10.07 rtrO.O$

-

-

>77

130150 377492 119158

-

0.4'

10.4-C -

I

131160

Batt et al. (1978a)

Baker and Shaw, (1965) Mendenhall et al. (1975) Batt andMilne ( 1976)

Batt and McCulloch (1 976b)

3

2

1

0

No. of ci HAtoms

n-C3H70 n-C4H90 i-C4H90 CH30

C2H50

t-C4H90 t-amyl i-C3H70 s-C~H~O

RO

0 0 0.16 2 0.02 0.21 k 0.02 0.23 f 0.02 0.28 f 0.03 0.29 f 0.05 0.33 f 0.03 0.33

k2dk2 0 0 0.19 0.26 0.30 0.39 0.41 0.50 0.50

k2dk2a

1.5 2 0.5 1.5 k 0.5 1.5 2 0.5 1.5 f 0.5 1.5 k0.5 1.5 20.5 1.5 2 0.5 1.5 2 0.5 1.5 -t 0.5

k2dk9a

0.05 k 0.05

-

r0.33 ~0.26

-

0 0

k9dkg

log{k,,*

10.3 k 0.2 10.3 k 0.2 10.3 2 0.2 10.3 k0.2 10.2 k0.2 10.3 f 0.2 10.3 f 0.2 10.3 f 0.2 10.0 5 0.1

M - '-sec-'}

TABLE 9. Recommended Values for Reactions of Alkoxyl Radicals with NO and NOz

REACTIONS OF ALKOXYL RADICALS WITH NO,

217

yield for alkyl nitrite photodecomposition of 1.O. In an analogous manner, Rose found k9dk9, = 0.11 -C 0.01 and 0.08 & 0.08 for n-C3H70 and s-C4H90 radicals, respectively. However, as discussed in Section 11-C, the primary quantum yields for photodecomposition of C2H50N0 and n-C3H70N0 are, respectively, 0.28 and 0.38. Thus kdka = 0.41 +- 0.04 for C2H50 and 0.35 ? 0.03 for n-C&O. The primary quantum yield for s-C4H90N0 photolysis is not known, so bdkafor S-C4H9O cannot be computed. It is difficult to see why the ratio k9dk9 is so much smaller for CH30 radicals than for larger alkoxyl radicals. More verification is needed before any of these values can be accepted.

C. Relative Rate of RO with NO and NOz Phillips and Shaw (1965) heated mixtures of CH3CH0, NO, NO2, and neopentane to 55 or 90°C.The CH3CH0 decomposed to give CH, radicals, which reacted with NO2 to give CH30 radicals: CH3

CH30NOt CH30NOt

CH30 CH30

-

+ N02+CH30NOt +

M -+

+ NO CH30N0 + M CH30

+ NO-CH30N0

+

NO2 -CH,0N02

This mechanism leads to the rate law

Phillips and Shaw found that the ratio [CH30NO]/[CH30N02] did not depend on the total pressure, but only on [NO]/[NO,]. Thus they concluded that the reaction in Eq. 23 was negligible under their conditions. From their data kZa/k9, = 1.86 t 0.14 at 90°C. The conclusion that Eiq. 23 is negligible is in agreement with the theoretical prediction of Gray (1955). However, Patsevich et al. (1958) reported that C2H5radicals could react with NO2 at - 15 to 96°C to give C2H50N0 directly. Now C2H50N0is more complex than CH30N0, so that lower pressures would be required to stabilize it, and there may be no conflict between the conclusions of Phillips and Shaw and of Patsevich et al. However, if some CH30N0 is formed in reaction 23, then k2a/k9a will be (1.86.

THE DECOMPOSlTlON OF ALKYL IWRlTES

218

Johnston and Heicklen (1966) photolyzed CH31 in an excess of NO at room temperature to produce CH30 and NO2. From the CH,ONO and CH30N02 produced they obtained an approximate value for = 1.4. Wiebe et al. (1973) photolyzed CH30N0 at 366 nm and 25°C in the presence of NO and NOz. They measured the quantum yield of CH30N02. The rate law for CH30N02 formation is

wba

where +,a is the quantum yield of CH30 production. Their analysis was based on their measured value of 0.76 for +la, which may be only 0.33. Their data are replotted in Fig. 12. The best fit of the data gives an intercept less than 3.0, which is not possible if
28

I

I

I

I

I

I

I

0

REAcIlONS OF ALKOXYL RADICALS WITH NO,

219

CH30N02 produced, they deduced kdb,. Both rate coefficients are pressure dependent, but they reach their high-pressure limiting value in the presence of >500 Torr CF4. Under these conditions k&ba = 2.03 & 0.47 independent of temperature from 119 to 148°C if the surface-to-volume ratio was sufficiently low. (Reaction 2a appeared to have some heterogeneous component.)

D. Rate Coeficient for RO

+ NO

Mendenhall et al. (1975) studied the very-low-pressurepyrolysis of t-C4H,0N0 and measured the rate coefficient for decomposition from 377 to 492°C. From this value and the estimated equilibrium constant they computed log{k2,, W 1 sec-'} = 9.8. In a series of papers from Baa's laboratory, the kinetics of the thermal decomposition of RONO were studied (see Section III-C). From these data and thermochemical data for RONO, RO, and NO, the reverse reaction rate coefficients could be determined: RO

+ NO

-

RONO

(2a)

These values are listed in Table 8. For all the compounds studied, k2a = 1010.1-'0.5 W'-sec-' independent of temperature. Sanders et al. (1980) produced CH,O from the flash photolysis of CH30N0 at 266 nm and measured its rate coefficient of reaction with NO to be (1.25 f 0.07) x 10" M-'-sec-', using laser-induced fluorescence to monitor CH30 removal and HNO appearance. This result is in exact agreement with that of Baa et al. (1977). Choo and Benson (1981) have argued that the values for the RO NO rate coefficients for all alkoxyl radicals reported by Baa's group are too large by a factor of 5 . However, Ban and Robinson (1982) have responded to Choo and Benson and reported that their most recent measurements on the gas-phase decomposition of t-C,H,O radicals support their earlier reported values for the RO NO rate coefficients. Further information on the rate coefficients for the reactions in Eqs. 2a and 2b is given in some recent papers. Gutman and Nelson (1983) used laser-induced fluorescence to study the addition reactions of the C2H30 radical with O2 and NO. The bimolecular rate coefficients for the reaction with NO were observed over the major portion of the transition region from the low- to high-pressure limits and give at room temperature ko = (2.36 f 0.31) X lOI3 W2-sec-' with N2 as a chaperone and k" = (1.51 f 0.18) X 10" M-'-sec-'. However the C2H30 radical has two resonance forms,

+

+

220

THE DECOMPOSITION OF ALKYL NITRITES

Ab in& theoretical considerations indicate that the ground electronic state is essentially the carbon-centered radical, and the first excited electronic state is the oxygen-centered radical (Dupuis et al., 1982). Thus the measured rate coefficient is probably for the carbon-centered radical, and need not correlate with information on alkoxyl radical reactions. Balla et al. (1985) have used the flash photolysis of i-C3H70N0at 355 nm to measure the rate coefficients for the reactions of i-C3H70with NO, NO,, and O,, by monitoring i-C3H70decay using laser-induced fluorescence. They found k2 = (7.3 f 1.7) X lo9 exp((+ 0.62 2 0.14)/0} M-'-sec-' at 22-105°C and 1-50 Torr pressure. This expression gives an average value over their temperature range of 1.8 X 10" M-'-sec-', which is somewhat smaller than that of = 3 X 10" M-l-sec-' reported by Batt and Milne (1977a), though the two values are well within the reported uncertainties. Zellner (1986) reported on the pressure dependence of the CH30 NO reaction in the presence of 5-300 Torr He. From the data obtained in his laboratory at 298 K, he deduced that k,, = 8.4 X lo9 M-l-sec-' in the high-pressure limit and 1.1 X 1014Md2-sec-' in the low-pressure limit for He as a chaperone. The low-pressure value is based on a long extrapolation of the data and is about 12 times as large as reported by Fortuno (1982) or McCaully et al. (1985). The values of k2, increase slightly with the complexity of the molecule. The computed values from Batt's group increase from 10g{k2,, M-'-sec-'} = 10.1 for CH30 to 10.5 for more complex alkoxyl radicals. The direct measurements in McDonald's laboratory give 10g{k2,, M-'-sec-'} = 9.92 for CH30 and 10.16 for i-C3H70. Zellner (1986) also finds kza = 9.92 for CH30. Based on these data we recommend log{k,,, M-l-sec-'} = 10.0 for CH30, 10.2 for C2H50, and 10.3 for C3-C5 alkoxyl radicals.

+

E. Rate Coefficient for RO

+ NOz

Mendenhall et al. (1975) studied the very-low-pressurepyrolysis of n-C3H70N02 and measured the rate coefficient for decomposition from 300 to 540°C. From this value and the estimated equilibrium constant they computed 10g{k9,, Msec-'} = 9.5. McCaulley et al. (1985) studied the reactions of CH30 with NOz by using laser-induced fluorescence to monitor CH,O produced by direct IR laser dissociation of C&OCH3 in a flow tube. Downstream NO, was added in large excess to convert the CH3radicals produced to CH30 radicals in a rapid reaction. The reaction of CH30 with NO, was of mixed order under their conditions. By assuming that reaction 9a was third-order and reaction 9b was second-order, they deduced rate coefficients of k9, = (9.4-2-5) +3.3 x 10'2(T/300)-4.5't:3 K 2 sec-' and kSb = (5.t?T;t5) x lo9 exp((-ll50;:~)fT} M-'-sec-'. These give room-temperature values of ba= 9.4 x 10" M-'-sec-' and k9,, = (1.2 2

'-

DECOMPOSITION AND ISOMERlZAnON OF ALKOXYL RADICALS

221

10') M-'-sec-'. Another direct measurement of haand kSbwas done by Fortuno (1982), who used laser magnetic resonance to monitor CH30 decay in the presence of NO, and obtained k9b = (2.5 2 0.5) X 10' M-l-sec-' at room temperature by extrapolating the pressure dependence of k9 to zero pressure. He also obtained = (8.0 2 1.1) X lo', K2-sec-' at 300 K. In their study of the reaction of i-C3H70 with NO,, Balla et al. (1985) found the results to be slightly dependent on laser power. However, their results extrapolated to zero laser power give an average value of h = (1.9 4 0.3) X 10" M-l-sec-' from 295 to 384 K, the same value that they found for k2. All other studies have determined the ratio h,/k2,. From the data of Wiebe et al. (1973), we get a ratio of 1.3 for CH30 radicals. However, the other competitive studies give ratios of k2a/k9a = 2.7 (Baker and Shaw, 1965) and 2.03 ? 0.47 (Batt and Rattray, 1979) for CH,O, 2.5 (Baker and Shaw, 1965) for C2H50, and 1.7 (Baker and Shaw, 1965) for r-C4H90. Thus there is some uncertainty regarding the values of ha.Until further information becomes available we recommend using k2a/k9a = 1.5 2 0.5.

V. DECOMPOSITION AND ISOMERIZATION OF ALKOXYL RADICALS A. Decomposition Early reviews of the thermochemistry and reactivity of alkoxyl radicals were given by Gray and Williams (1959), Hershenson and Benson (1962), Gray et al. (1967), Heicklen (1968), and Kerr and Lloyd (1968). The work discussed in those reviews was mostly qualitative and will not be discussed here. The Arrhenius expressions that were reported are included in Table 10. 1. CH30. From their data on @{CH30} = 3.8 & 0.2 kcawmole, Batt and McCulloch (1976a) estimated that = 21.3 kcallmole for the reaction

ale

Furthermore if AGIe is taken to be 25.4 cam-mole, and if the rate of the reverse reaction is the same as that for H + C,H,, then log{klle, sec-'} was estimated by them to be 14.2 - 25/9. 2. C2H50.Leggett and Thynne (1970) studied the thermal decomposition of the C2H50 radical from 149 to 176°C by using the pyrolysis of (C,HSO), a; a radical source. They foundtheratecoefficient tobe 10'2.'5exp{-22. URT) sec- .

h2

w

+

CH304 CH20 H CzH50 + M -+ CH3 + CH2O + M C2H50--* CH, + CH2O C2HSO --* CH, + CH20 C2H50 + CH3 + CH,O C2H5O + CH3CHO + H i-C,H,O + CH3 + CH3CHO i-C3H,0 -+ CH, + CH3CHO i-C,H,O + M -+ CH3 + CH3CHO + M i-C3H,O --* CHg + CH3CHO

Reaction

20-230 20-230

160-200

160-200

-

14.36

35

175-200

-

13.21

-

-

16.5

12.65

14.4

15.0

-

-

12.15

=10

12.6

=14.2

log@)

23-63 (C-CrjH,,)

-

5.3-30

-

Torr

Ress.,

149-176

-

15-195

-

Temp. "C E, kcaYmole

11.8

8.3

17.2

16.0

23.4

21.6

22.1

17

25 13

-

TABLE 10. Rate Coeffkients for Decomposition of Akoxyl RadieaEP

+hv

-

iX3H70NO pyrolysis i-C3H70N0 pyrolysis i-C3H,ONO pyrolysis

Estimate

(CzHsOh pyrolysis Estimate

-

C2H5C(0)OC2HS

-

Source of RO

~~~~

Gray e t d . (1967)'

Coxetal. (1966)

Leggett and Thyme (1970) Batt and Milne (1977b) Batt and Milne (1977b) Ferguson and Phillips (1965) Coxetal. (1966)

Gray et al. (1967)'

McCulloch (1976a) Wijnen (1960)*

Batt and

Reference

+

+

CC3H,0 -+ CH3 + CH3CHO S-CdHgo --* CH3CHO + C2H5 S-C&go M + CH3CHO f C2H5 + M s - C ~ H ~+ O CH$HO f C2H5 t+C4Hg-+ CH3 + (CH3)zCO t-C4H90 -+ CH3 + (CH3,ZCO t-C4H90 --f CH3 + (CH3)zCO t-C4H,0 M +, CH3 + (CH3)zCO + M r-C4Hg0+ CH3 + (CH,),CO t-C&gO CH3 + (CH,),CO t-C,H,O -+ CH3 + (CH,)-/ZO

130-170

25-1500

14.5 & 0.6

15.9

17.0

15.4

119-158

13.4 12

15.5 11.2

10-60

-

125-163

22.8

17.5

125-163 10-60

16.5

15.5

-

17.1

15.6

-

15,3

10.6

14.8

14.26

167-197

12-200

17.5

16.11

12-200

150-190

150-190

17.3

14.6

20-760

333-373

* 1.2

t-CdHgONO pyrolysis t-C,GONO pyrolysis

-

2,2’-Azopmpane + hu S-C~H~ONO pyrolysis s-C~H~ONO pyrolysis S-C~H~ONO pyrolysis

Banand Milne (1976) Batt and Robinson ( I 982)

Yee Quee and Thynne (1967) Yee Quee and Thynne (1967) Heicklen (1968)‘

A1 k e e l and Waddington (1984) East and Phillips (1967) East and Phillips ( 1967) Batt and McCulloch (1976b) Hershenson and Benson (1962p Gray et al. (1967)‘

C*HS+ co (Ar)

1307

(Ar]

304-684

0.2

0.20

11.4Ok

k

43.9 & 0.9

47.7 & 1.4

12.0

7371157 727-

380-684

18.7

13.8 r 0.8

14.8

0.4

E, kcal/mole

160

_t

'Units of A are sec-' for first-order reaction; K ' - s e c - ' for second-order reactions. bAs analyzed by Heicklen (1968). 'Xeview of earlier data. dAs recalculated by Batt and Milne (1976).

Phenoxyl-+ C& + co

+ CH3

14.1

logI4

14.3 ? 1

160-190

t-Am0 (C&&CO + t-Am0 += CH,COC,HS PhenoxyI +

>I500

Tom

press.,

14.5 5 0.2

90-140

"C

Temp.

2-pentoxyl --f CH3CH0 + n-C3H7

Reaction

TABLE 10. ( C o n h u e 4

pyrolysis

C6H5@33

pyrolysis

C6H5mH3

2-Pentyl peroxide pyrolysis r-AmONO pyrolysis t- AmONO pyrolysis

Source ofRO

( 1978a)

Lin and Lin (1985) Lin and Lin (1986)

Batt et al. (1978a) Battetal.

D6N et al. ( 1986)

Reference

DECOMPOSITION AND ISOMERIZATIONOF ALKOXYL RADICALS

225

Estimates of the thermal-decomposition rate coefficients of C2HS0 radicals have been made by Batt and Milne (1977b) based on thermochemical data and comparisons with similar reactions. Their results are listed in Table 10.

3. i-C&O. Ferguson and Phillips (1965) examined the pyrolysis of iC3H70N0 at 175-200°C and 35 Torr pressure. By measuring the ratio of CH3CH0 to (CH3),C0 produced they could measure the relative ratio k, IJk2b:

Their results give kl 1c/k2b = I O ~ . ~ ~ ~16.0IRT) X P ( - M. Based on a value of k2b - 109.58M-1-sec-1(see SectionIV-D), kllc = 10'3.21e x d - 16.O/RT}sec-'. The results of Ferguson and Phillips are in the pressure falloff region. Thus Cox et al. (1966) measured the rate coefficient from 160 to 200°C and from 20 to 230 Torr to obtain high- and low-pressure limiting values of kl1,/kzb. They obtained log{A,dA~,,, M-'} = -4.78 and log{A2dAyl,} = -3.07 with E~~ = 17.2 and - E~~ = 8.3 kcaUmole. With kZb = 109.58M-'-sec-', exp(-8.3/RT} one has k;,, = 10'4.36 exp(-17.2/RT) sec-' and kyle = 1012.65 sec-I. The photooxidation of trans-2,2'-azopropane has been studied by A1 k e e l and Waddington (1984) between 333 and 434 K. The whole system was computer modeled. From the CH3CH0 yield, the pressure falloff behavior was determined for

-

(CH3)2CH0%CH3

+ CH3CH0

(1 1c)

The results at four temperatures are shown in Fig. 13. These data are well fitted by RRK theory using log{A;l,, sec-'} = 14.6 and ETlc = 17.3 kcaUmole. Balla et al. (1985) made direct measurements of i-C&O radical decomposition from 2 to 296 Torr N2at 378 and 406 K. They found the reaction to be in the pressure falloff regime at all pressures studied. Their results are shown in Fig. 14, where they have included the high-pressure limiting rate coefficientscomputed from Batt's (1979) Arrheniusexpression of log{k71,, sec-I} = 14.6 0.5 - (17.2 & I)/€). This expression gives k;,, = 2.2 X lo5 and 4.5 X lo4 sec-I, respectively, at 406 and 378 K. The data of Balla et al. suggest larger high-pressure limits. The results of A1 k e e l and Waddington (1984) are in good agreement with those of Cox et al. (1966). The Arrhenius parameters of Ferguson and Phillips (1965) are lower and lead to rate coefficients about 22% of those from the other studies at 180°C.

*

226

1.5

s

1.0

c) l

0

200 lG00 600 Total pressure (Torr)

Figure 13. Effect of total pressure on the rate coefficient for the decomposition of (CH,),CHO radical: 0,333 K; 343 K; 0 , 353 K;0, 373 K. From A1 Akeel and Waddington (1984) with permission of the Royal Society of Chemistry. n-C&,O and i-C4€&0. Zabarnick and Heicklen (1985b, 1985c) photolyzed n-C3H70N0 and i-C,H,ONO at 366 nm to produce the alkoxyl radicals. Decomposition of the alkoxyl radicals was studied relative to their reaction with NO. At 150 Torr total pressure of N,, the relative rate coefficients k11/k2were (3.3 & 0.3) x lo-', (5.1 f 1.0) x lo-', and (2.3 f 0.2) X M at 55, 88, and 120°C, respectively, for n-C3H70, and (4.6 f 1.0) X (2.8 tr 0.3) x and (5.8 tr 2.2) x M at 23, 55, and 88"C, respectively, for i-C41-L,0 radicals. These results are all in the pressure-dependent regime and cannot be compared directly with either kY1/k2or kyI/k2.

4.

5. s-C4&0. East and Phillips (1967) used a similar technique to measure the decomposition of s-C4H90 to C,H, + CH,CHO at 150-190"C and 12-200 Torr '} = -6.39 and lOg{A2dA:lb} = -4.54 pressure. They found lOg{A2dA:1br With q 1 b - E2b = 17.5 and q l b - &, = 10.6 kcallmole. with k2b =

i 8 DECOMPOSITION AND ISOMERlzAnoN OF ALKOXYL RADICALS

A

A

A

227

a+

A

t

A

A

A=406K

0 =378K

I o3

TOTAL 10 PRESSURE ( T O R R I

1

100

Figure 14. Pressure dependence of the rate coefficient for the thermal decomposition of i-C3H,0 radicals. The high-pressure limit values are from Batt (1979). From Balla et al. (1985) with permission of Elsevier Science Publishers.

lo9.', M-'-sec-', one has kylb = 1 0 ' 6 ~ ' 1 e x ~ - 1 7 . 5 / RSeC-' ~ and kylb = 10'4.26exp(-10.6/RT) M-'-sec-'. Ban and McCulloch (1976b) measured the decompositionof s-C4&0 relative to its rate of addition with NO in the pyrolysis of s-C4H90N0 at 167-197°C:

They found a rate coefficient of 10'4.9-15.3'esec-' at about 1 atm pressure (mostly NO) based on k2, = M-l-sec-' and k2& = 0.26. With our adopted value of k,, = 10lO.~M-l-sec-', their rate coefficient k,,, becomes 10'4.8-'5.3'e sec-'. This rate coefficient should be close to the high-pressure limiting value. They also estimated kllc = 10'4.9-i9/esec-', for the decomposition to form CzHSCHO CH3.

+

228

THE DECOMPOSITION OF ALKYL NKRllES

Drew et al. (1985) studied the thermal decomposition of S-C&o radicals generated from the reaction of F atoms with s-C4H90H. They found CH3CH0 and C2H5CH0 as products, which they assumed came from

No CH3COC2H5was found, so that the reactions in Eqs. 1l b and 1lc accounted for all the decomposition. From 398.6 to 493.3 K they found E l , , - E l l c = -2.68 -+ 0.19 kcaVmole andA,,~A,,, = 0.59 & 0.14, independent of pressure from 80 to 600 Ton.

6. t-C,&O. The pyrolysis of (t-C4&O)2 was studied in the presence of NO at 398-436 K and at 10-60 Tom pressure by Yee Quee and Thynne (1967). The decompositionof the t-C4H90radical was studied in competition with its reaction with NO. The relative rate was pressure dependent. Extrapolation through a Lindemann mechanism gave log{k&lc} = -5.17 f 0.81 + (13.4 & 1.7)/8 and log{k&~,,, M - I } = -7.17 k 0.77 + (22.8 1.6)/8. With log{k,,, M-'-sec-'} = 10.3, one haslog{k~,,,M-'-sec-'} = 15.5 - 13.4/8 and log{kyl,, sec-'} = 17.5 - 22.8/8. Batt and Milne (1976) studied the thermal decay of the t-C4H90radical in comparison with its reaction with NO in the pyrolysis of t-C4H90N0. This reaction was pressure dependent at 0.025-0.9 atm and 160°C. Over the temperaturerange of 119-158"C, the high-pressurelimiting rate coefficient for

*

t-C4&0 d C H 3

+

(CH3),C0

(11C)

was 10'5.5exd-17.0/Rn sec-' based on a value of k2, = M-'-sec-'. M-'-sec-', then k l l c = If we use our adopted value of k2a = exd- 17.0/Rn sec-'. Fuke et al. (1981) used a thermal-lensingstudy in the photolysis of (t-C,H,O), to determine the rate coefficient for r-C4&0 in solution at 27 2 1°C. The rate coefficient was found to be (9 f 1) x lo4 M-'-sec-' in acetonitrile and (5.3 -C 0.5) X lo4 M-'-sec-' in benzene. The difference in the two values probably is caused by differences in the cage effect in the two solutions. Batt and Robinson (1982) made a detailed study of the pressure dependence for the decomposition of t-C4H90 radicals at 130-170°C and 25-1500 Tom pressure. Their data at 402.6 K are shown in Fig. 15. With their data and the treatment recommended by Oref and Rabinovitch (1968), they concluded that their results extrapolated to a value for log{k~lc,sec-'} = 14.6 -t 0.6 - (15.9 ? 1.2)/8 based on log{k,, M-'-sec-'} = 10.3.

DECOMPOSITION AND ISOMERJZATION OF ALKOXYL. RADICALS

229

a

I

f ,

1.5

I

I

2.0 2.5 log iPITorr)

0

1

3.0

Figure 15. log{k,,,} vs log(pressure of added gas} for the decomposition of the t-BuO radical at 402.6 K. X , CF,; 0 , SF,. Computed curves: solid, CF,; dot-dash, SF,; dashed, N,. From Batt and Robinson (1982) with permission of John Wiley and Sons.

7. 2-CsHll0. D6bi et al. (1986) studied the decomposition of 2-pentoxyl radicals obtained from the pyrolysis of 2-pentyl peroxide, C3H7CH(6)CH3__* CH,CHO

+ n-C,H,

(1 10

relative to its combination with NO at pressures above 1500 Torr and temperatures of 363-413 K. They found log{kllflkza, M} = 3.8 & 0.4 - (13.8 0.8)/8. With our recommended value of kza = 10.3, one has log{kllf, sec-'} = 14.1 & 0.4 (13.8 0.8ye.

*

-

8. t-Amoxyl. Batt et al. (1978a) examined the gas-phase pyrolysis of r-amyl nitrite in the presence of NO at 160-190"C. In this way they studied the competition between

230

-

THE DECOMPOSITION OF ALKYL IWlUTES

&Am0

+ NO

t-AmONO

and

From the variation in the acetone yield with NO pressure, klldk2, could be measured. Baa et al. (1977) obtained log{k,,,, sec-'} = 14.7 f 0.2 (14.3 -t l)/0 using their measured value for kza = 10'0.520.2M-'-sec-'. With our recommended value of kz, = M-'-sec-', one has log{kll,, sec-'} = 14.5 2 0.2 - (14.3 f 1)/0. Batt et al. (1978a) also found that at 160°C, k l , ~ k l l , = 80 where reaction l l c is

-

?-Am0

-

C2HSCOCH3 + CH,

(11c)

From this result they concluded that log{kll,, sec-'} = 15.0 - 18.718, which we correct to 14.8 - 18.7/0.

9. (CF3)2C(6)CH3and CF3C(b)C(CH3)2.Drew and Kerr (1983) prepared hexafluoro-t-butoxyl radicals from the reaction

F

+ (CF,),C(OH)CH,

__*

HF

+ (CF,hC(6)CH3

(24)

Over the temperature range 40WjOO K, the radical decomposes exclusively by loss of CF, rather than CH,, the ratio of rate coefficients being 2 8 0 . Likcwise Ken and Wright (1984) examined the decomposition of CF,C(O)(CH,), prepared from the reaction of F atoms with CF,C(OH)(CH3)2. They found that at 361-600 K,decomposition occurred exclusively by loss of the CF, groups, the ratio of CF, to CH3 loss being 275. 10. Phenoxyl. The decomposition of phenoxyl radicals was first studied by Colussi et al. (1977), who found the rate coefficient to be 10 -+ 5 sec-' at lo00 K:

This reaction was studied over the temperature range 1010-1430 K by Lin and Lin (1985), who prepared the radicals from the shock-tube decomposition of C&150CH3in Ar at 0.5-0.9 atm total pressure. They monitored the CO produced as a function of reaction time and determinedkll, = * 0-2exp((-24,000 2 690)/nsec-'. The low preexponential factor supported a tight cyclic activation complex as suggested by Colussi et al. (1977):

DECOMPOSITION AND ISOMEREATIONOF ALKOXYL RADICALS

231

In a subsequent study Lin and Lin (1986) studied the decomposition of methyl phenyl ether (anisole) in incident shock waves in Ar at 1000-1580 K and 0.4-0.9 atm. Some runs were also done with ally1 phenyl ether as the source of phenoxyl radicals. They deduced k,,, = 1011.40*o.20exp((-22,100 450)/T) sec-' from kinetic modeling of the CO formed.

*

11. Summary. Batt (1979) reviewed all the data and gave recommended values for the high-pressure limiting rate coefficients. These are given in Table 11. The Arrhenius parameters in some cases are estimated and in other cases are based on extrapolation from data in the pressure falloff regime. Furthermore the Arrhenius preexponential factors are based on knowledge of the rate coefficients of competitive reactions used to obtain the data. TABLE 11. Thermochemical and Kinetic Data for Alkoxyl Radicals log{A, sec-'}

Reaction

E, kcallmole-'

hH" (298) kcdmole-'

-

r-Am0 fMEK + Me b M , K Et 14.8

+

-

r-BuO+M2K sBuO

+ Me

,MEK+Me EtCHO+Me \ACH + Et

seC-1

4.4 13.8

1.4

4.8 x 104

17.0

5.6

1.08 x 103 -

-

-

14.9 14.9

19 15.3

11.7 6.0 2.6

9.3 4.8 x i d 3.4 x 10-2

,MzK

+H

14.3

21.5

12.2

\AcH

+Me

14.6

17.2

7.0

14.4

23.4

16.5

1.7 x 1 0 - ~

CH,O+Me

(15.0)

21.6

12.9

0.14

+H

14.2

27.5

22.3

1.1 x 10-6

i-PI0

,

AcH+H

EtO

15.5

k(298 K},

Me0 --t CH,O

Source: Batt (1979), with permission of John Witey and Sons, Inc.

97

THE DECOMFOSlTION OF ALKYL NITRlTEs

232

TABLE 12. Estimated ArrheniuS Parameters of Akoxyl Radical Decomposition Reactions

Reaction (CH3)3CO +CH3 + (CH3)2CO (CH3)2CHO +CH3 CHSCHO CH3CH2O +CH3 + CH2O (CH~)~(C~HS)CO +C2H, + ( C H W O +CH3 CH3(C,H,)CO C2HS(CH3)CHO +C2H5 CH3CHO

E,

hH0,

log {A, sec-'}

kcdmole

kcdmole

14.1 13.8 13.6 13.6 13.8 13.6

15.3 16.8 20.0 12.4 (10.7) 16.1 13.5 (11.8) 15.6

5.8 8.4 13.2 1.2 4.7 4.7

9.7

0.2 2.1 8.1

~~

+

+ +

+

CH20 C2HSCH20+C2H5 i-C3H7(CH3)2CO +K 3 H 7 (CH3)ZCO i-C3H7(CH3)CH0+i-C3H7 CH3CH0 CC3H7CH20-+ K 3 H 7 + CH20

+ +

13.7 13.6 13.7 13.7

10.3 12.4

9.0

Source: Choo and Benson (1981), with permission of John Wiley and Sons, Inc.

Choo and Benson (1981) estimated the preexponential factors for the rate coefficients of alkoxyl radical decay by comparison with similar reactions. With these values and measured rate coefficients, they computed activation energies. Their results are listed in Table 12. The preexponential factors are all given by log{A, sec-'} = 13.6-14.1, considerably lower than the measured values. Drew and Kerr (1983) pointed out that the values of Choo and Benson are about 10 times lower than predicted from equilibrium constants at 423 K. An examination of all the data shows that the high-pressure limiting decompositions which give H atoms have log{A,,,, sec-'} = 14.3, whereas those that give alkyl radicals have log{A, ,sec- '} = 15.O. Therefore these values are taken as universal A factors for these reactions, and, where necessary, the activation energies have been recomputed to fit the data using these preexponential factors. The recommended recalculated values for the high-pressure limiting activation energies are given in Table 13. For those decomposition reactions which give H atoms, the activation energies lie in the range of 21-25 kcallmole, with the activation energy decreasing as the molecular complexity increases. If the radical decomposes to give CH, radicals, and it contains no higher alkyl groups, then the activation energy decreases from about 21.6 to 16.5 kcallmole as the complexity increases. If the radical is capable of decomposing to give an akyl radical larger than CH,, but still decomposes to give a CH, radical, the activation energies are in the same range (16.5-21.5 kcaVmole), and the activation energy also decreases with increasing complexity. For alkoxyl radicals that decompose to give alkyl radials larger than CH3, the

,

233

DECOMPOSITION AND ISOMERJZATION OF ALKOXK RADICALS

TABLE 13. Recommended Limiting High-Pressure Arrhenius Parameters for Akoxyl Radical Decomposition

Reaction

E, kcal/mole

Reaction Giving H Atoms (log(A, sec-'} = 14.3) CH30+CH,O H C2H50 CH3CH0 H i-C3H70+(CH3)2C0+ H

+

+

= 25

23.3 21.5

Radicals That Can Only Give CH, (or H ) (log(Asec-'} = 15.0) 21.6 C2H5O +CH20 + CH3 i-C3H,0 +CH3CH0 CH, 17.5 16.5 t-C,H,O -+ (CH3)2CO+ CH,

+

Other Radicals That Can Give CH3 (log(A, sec-'} = 15.0) s-C,H,O +C2H5CH0 + CH, t-Am0+C2H5COCH3+ CH,

19.1 18.7

Reactions That Give C2H, or C3H7 (log{A,sec-'} = 15.0) s-C~H,) CH3CHO C2H5 t-Am0-(CH,),CO + C2H5 2-C5H,,O+CH3CH0 + n-C,H7

15.4 15.3 15.4

+

activation energy is lowest of all and is about 15.4 kcal/mole. There is less information on the low-pressure limiting rate coefficient for alkoxyl decomposition. However the limited data that do exist suggest that the preexponential factors drop to 1.8% or less of their high-pressure values. The activation energies are lower by =50% in their low-pressure limits.

B. Isomerization The isomerization of allcoxyl radicals by the shift of a hydrogen atom from a carbon atom to the oxygen atom to give a hydroxyalkyl radical has been suggested in hydrocarbon combustion. These suggestions have been reviewed by Fish (1964). Chow et al. (1970) have shown that such reactions can occur in the room temperature photolysis of 1-pentylnitrite and menthyl nitrite,

ON0

menthyl nitrite

234

THE DECOMRXITION OF ALKYL NlTRrES

Likewise Carter et al. (1976) and Baldwin et al. (1977) have suggested that such reactions could explain the formation of some products in photochemical smog. However, there is no evidence that such reactions occur in akoxyl radicals except for those which contain a hydrogen atom on the &carbon position:

I 1

H I

a-C-7-L-C I a $ ? $

-

1 1 1 .

HO-C-C-C-CI I I I

This isomerization occurs through a six-membered ring intermediate and thus has minimal strain-energy contribution to the activation energy. In particular Batt et al. (1981) have estimated that Iog{klla, sec-'} = 13.05 f 0.5 - (5680 & 5Oo)lT for H-atom migration in CH30 radicals to form CH20H radicals. This estimate gives a value of 485 sec-' for klla at 548 K, which is larger than the upper limit of 70 sec-' at 548 K measured by Fortuno (1982). The first experimental evidence that reaction l l a could occur was given by Baldwin and Golden (1978) in the low-pressure pyrolysis of n-butyl nitrite at 590-750 K. In the presence of DI, both CH3CH2CH2CH,0D and CH2DCH2CH2CH20Hwere observed. Their results suggested a value of klla = 9.2 X lo8 sec-' at 690 K. Both Carter et al. (1976) and Baldwin and Golden (1978) estimated kllafor exp(-7.7/RT) sec-', n-C4&0 radicals to be lo".' expC-8.9/RT) and respectively. In the photolysis of n-C4H90N0 at 366 nm and 25"C, Rose (1979) found that isomerization of n-C4H90 occurred in competition with reaction with NO2. He reported kllJkg, = (2.8 2 0.5) x M at 25°C. Taking ks, = 1.34 X 10" M-'-sec-' gives klla= 3.74 X lo5 sec-'. However, the only measurements over a temperature range were made by Morabito and Heicklen (1987), who studied the reaction from -8 to 120°C in the photolysis of nC4H90N0. From @{n-C3H,CHO}, they were able to deduce 1n{kllJk2, M} = 1.92 k 1.60 - (4014 & 509)/T.With a value of k2 = 2.8 x 10" M-l-sec-', one has log{klla, sec-'} = 11.28 f 0.69 - (8.0 & l.O)/e, in reasonable agreement with the earlier estimates. This expression gives a room-temperature rate coefficient klla= 2.47 x Id sec-', which is about 66% of the value given by Rose and 79% of the value actually found by Morabito and Heicklen at 23°C. The isomerization of 2-pentoxyl radicals was studied by D6M et al. (1986), who prepared the radical, either by pyrolysis or photolysis of 2-pentyl peroxide or by photolysis of 2-pentyl nitrite. The isomerization reaction was studied in competition with the decompositionreaction, which was measured independently in the same study. The isomerized radical was trapped by addition of CH3radicals to give 2-hexanol. From 279 to 385 K, one has log{k,,$kllf} = -(3.1 f 0.2) + (4.0 & 0.4)/0 where reaction l l a is

-

RJZACllONS OF A L K O X n RADICALS WlTH O2

C3H,CH(6)CH3

CH3CHOHC2H4CH2*

235

(1la)

With log{kl1, M-'-sec-'} = 14.1 - 13.818, one has log{klla,M-'-sec-'} = 0.7) - (9.8 2 o.s)/e. (11.0 At 279 and 301 K, the CH3 radicals can also react directly with 2-pentoxyl, CH3CH(6)C3H7 + CH3

as well as with themselves,

CH3CH(OCH,)C3H,

(25)

so that klla/k;k2/k2, could be evaluated. Since k25 and k26 have no activation energy, the activation energy for the ratecoefficient ratio is that for klla. This was found to be 9.0 2 1.6 kcal/mole. Since this value was lower than that found by the other method, the value recommended by D6M et al. (1986) for Ella was 9.5 2 1.1 kcallmole. The rate coefficients for alkoxyl radical isomerization are given in Table 14. The direct measurements for n-C,&O and 2-C5H, both give a preexponential factor of log{A, la, sec-'} 2 11.1. However, the activation energy for 2-pentoxyl isomerization appears to be larger than that for n-C4H90 radicals, though the values all lie within the experimental uncertainties.

M. REACTIONS OF ALKOXYL RADICALS WITH 0 2

A. Early Work The early work on this reaction was reviewed by McMillan and Calvert (1965) and by Heicklen (1968). Most of this work was qualitative, and led to the inference that alkoxyl radicaals could react with O2by H-atom transfer. However, as pointed out by Heicklen (1968), two studies led to estimates for the rate coefficients. Cerfontain and Kutschke (1962), in the photolysis of (C2H5),N2, estimated the relative importance between C2H50 + and

0 2 +CH3CHO f

HO2

(27)

400

3113

6-112

-

Press., Tom

-8-120

-

"C -

Temp.,

11.020.7

11.8 11.4 11.2820.69

13.0520.5

sec - '1

log{A,,,,

b(2-C5H1,O), pyrolysis or 2-CSHl10NOphotolysis.

"As reported by Carter et al. (1979).

2-Pentoxyl

n-C4H90

CH30

Radical

9.521.1

8.9 7.7 8.0k1.0

11.3+- 1.0

Eilal

kcallmole

Severalb

Estimate Estimate n-C4H,0N0

Estimate

+ hu

Sourceof RO

References

D6bC et al. (1986)

Carter et al. (1976)" Baldwin andGolden (1978) Mortabito and Heicklen (1987)

Battetal. (1981)

TABLE 14. Rate Coefkients for Isomerization of Alkoxyl Radicals by H-Atom Migration

REACTIONS OF ALKOXYL RADICALS WITH O2

237

Their computations showed that k27 was roughly equal to k28 at both 118 and 152°C. However, their system was complex, and they made a number of assumptions. For example, they neglected the reactions of H02 radicals, which almost surely must be incorrect. Nevertheless, k28 can be assumed equal to the rate coefficient for H abstraction by C2H50 from C2H5C02C2H5by analogy. Thus, if Cerfontain and Kutschke's conclusion is correct, then k28 C= k27 N- lo8.' exd- 5.5JRn M- '-set- . The competition

'

+ O2 -H02

+ aldehyde 2RO +ROH + aldehyde

RO

(27) (19a)

was studied by Heicklen and Johnston (1962a, 1962b) in the photooxidation of alkyl iodides at 25°C. They found k27/ki/t = 1.97 X and 4 X M-'12 - sec-'12, respectively, for R = CH, and C2H5.Since kI9, is C= M-'-sec-', respectively, at 25°C. M-'-sec-', k27 becomes 103.4and Both of these early studies established the importanceof the reaction of alkoxyl radicals with 02.HovGever, as we shall see, the estimates of the rate coefficients were much too low. A further study which indicated that &C&O reacted with O2 was done by Milne and Steel (1968), who photooxidized azoisopropane at 25 and -27°C. Recent work (Zellner, 1986) in which both CH30 and CH20 were measured by laser-induced fluorescence gave a yield of 0.85 f 0.15 for CH20 from the O2 + CH30 reaction.

B. CH30 a d CD30 In the 1970s, after it became clear that the alk0xyl-0~reaction was important in photochemical smog chemistry, an effort was made to determine the rate coefficient for the CH,O + O2 reaction. Wiebe et al. (1973) examined the reaction at 25°C in the photooxidation of CH30N0 at 366 nm in the presence of NO2. They monitored the CH30N02 produced in the competitive reaction CH30

+ NO,

-

CH30N02

(94

From this reaction and the competition between NO and 0, for CH,O, they determined k271k2 = 4.7 x CH30 CH30

-

+ O2 -CH20

+ NO

+

CH,ONO

-CH20

H02

+ HNO

238

THE DECOMPOSITION OF ALKYL NITRlTEs

where the NO2 was produced from the reaction of H02 with NO. They used their measured primary quantum yield +la = 0.76 in their analysis. However, since their values for @{CH30NOJ in the absence of 0,were compatible with this value, their reported value for k27/k2 should be correct. With our recommended value of k2 = 1.5 X 10" M-'-sec-', k27 becomes 7.0 X 10' M-'-sec-'. In a similar experiment Glasson (1975) obtained k27/k2 = (4.5 ? 0.6) X With k2 = 1.5 X 10" M-'-sec-', k27 becomes 6.8 X lo5 M-l-sec-'. Alcock and Mile (1975) studied the photolysis of azomethane in the presence of O2 and 2,3-dimethylbutane. In order to interpret their data, they found it necessary to incorporate reaction 27. From model calculations of their data they deduced that k27 = 1.2 X lo6 M-l-sec-' at 100°C. They also reinterpreted the data of Home and Whytock (1967) and obtained k27 = (0.46-1.8) X lo6 M-l-sec-' at 1 0 0 " ~ . The reaction was studied at higher temperaturesby Barker et al. (1977). They examined the thermal decomposition of (CH30)2 at 396-442 K in the presence of NO, and 0,.From the competition between reactions 9a and 27 they obtained log{k2,, M-'-sec-'} = (8.5 ? 1.5) - (4.0 -+ 2.8)/0 for ha= 109.8*0.5 M-'-sec-'. In a similar experiment at 110-16OoC, Batt zkd Robinson (1979) obtained log{kz7, M-I-sec-'} = 9.0 ? 0.6 - (4.8 & l.l)/fJ. This expression gives a value of 105.6M-'-sec-' at 298 K. Cox et al. (1980) also used the same competitive reactions, but used the photolysis of CH30N0 at 299-423 K as the source of CH30. Their photolysis radiation was homogeneous from 310 to 410 nm with a peak intensity at 350 nm. Their results were based on their measured primary quantum yield for CH30-radicalproduction of 1.O. They combined their data with all previous data to get an Arrhenius expression for log(k27, M-'-sec-'} = 7.9 & 0.2 - (2.7 2 0.7)/0. Direct measurements were made for the reactions of CH30 with 0,by monitoring the radical concentrations (Gutman et al., 1982). The CH30 radicals were produced by the 266-nm photolysis of CH30N0. The rate coefficient for the CH30 + 0, reaction from their study along with the results of several other studies was fitted by the expression k27 = 6.3 X lo7 exp(-2.6/RT} M-l-sec-' from 140 to 355"C, in excellent agreement with the composite value reported by Cox et al. (1980). Fortuno (1982) measured the decay of CH,O by laser magnetic resonance in the presence of 0,in a flow-tube experiment. The CH30 radicals were generated by the reaction of F atoms with CH30H. This system also produces CH20H, which reacts rapidly with 0,to produce HO,, which in turn reacts with CH30. Fortuno's analysis attempted to sort out the various paths for CH30 removal, andhedete~minedk,~ = (3.65 & 0.41) X 1O8K'-sec-'from 100to275"C. Lorenz et al. (1985) measured the rate coefficients for the reaction of CH30 with 0,at 300-500 K using laser flash photolysis of CH30N0 at 248 nm. The CH30 radicals were monitored by laser-inducedfluorescence. The rate coefficient

REACI'IONS OF ALKOXYL RADICALS WITH 0, lo7,

u,

I

0

I

239

I

I

I

2.60

285

3.10

I

0

-

-

106

-

0

-

1.60

I 1.85

2.10

2.35

lo3I T ,

OK-'

3.35

0

Figure 16. Anhenius plot for the CH30/02 reaction rate coefficient: , Wiebe et al. (1973); 0,Glasson (1975); 4,Alcock and Mile (1975); V, Mendenhall et al. (1975); 0 ,Barker et al. (1977); 0,Batt and Robinson (1979); 0,Cox et al. (1981); H, Gutman et al. (1982); A, Lorenz et al. (1985); 0, Fortuno (1982).

for the CH30 + O2reaction was reported to be (3.3 -t 1.2) X 107exp{- lOOO/T} M-l-sec-'. A composite Arrhenius plot of all the data is shown in Fig. 16. The data obtained from relative rate measurements have been corrected to be consistent with our recommended values for k2a = 1.O X 10" M-'-sec-' and ha= 6.67 x lo9M-'-sec-'. With these corrections, the data fit a least-squares expression of log{kZ7,M-l-sec-'} = 7.71 f 0.13 - (2.57 f 0.22)/8. Fortuno's data are much higher than those of the other investigators and were omitted from the regression analysis. The reaction of CD30 with 0, was studied by Weaver et al. (1975), who prepared CD,O from the photolysis of CD3N2CD3at 25°C. They found kZ7/k&; = 9.7 X lo-, (M-sec)-'" for the reactions

240

-

THE DECOMPOSlTION OF ALKm NERITFS

CD30

+ O2

CD,O

2CD30 -CD30D

+ DO2 + CD20

(27) (19a)

The rate coefficient for reaction 19ais probably similar to that for its hydrogenated analog, i.e. kI9, 2 2 x 10" M-I-sec-'. Thus kZ7 1: 1.4 >no4 M-'-sec-', about 0.020 times as large at 298 K as the rate coefficient for the reaction of its hydrogen analog. With the assumption that the C-H stretching frequency is 3200 cm-' , the expected shift in zero-point energies between CH30 and CD30 would be 465 cm-', which would predict an 89% reduction, compared to the observed 5.5 times as large as the reduction of 98%. Thus the predicted value is measured value. Further work needs to be done on this system to resolve the discrepancy.

-

C. C2H50, CC3H70, n-C3H70, and i-C4H90 The first quantitative study of the reaction of C2H50 with 0,was made by Gutman et al. (1982). They measured the rate coefficient directly by monitoring the concentration of C2H5O radicals, which were produced in the 266-nm photolysis of C2H,0N0. They found the rate coefficient to be 4.8 x lo6 M-'sec-' at 23°C and 5.9 x lo6 M-'-sec-' at 80°C. In a series of papers, Zabarnick and Heicklen (1985a, 1985b, 198%) measured the rate coefficients for the reactions of CZHSO, n-C3H70, and i-C4H90radicals with 0,.They prepared the radicals from the photolysis of the corresponding alkyl nitrite at 366 nm and studied the competition between NO and 0, for the radical. They found the relative rate coefficients to fit the expressions l ~ g { k ~ ~ / k ~ } = -2.17 f 0.14- (1.84 & 0.19)/8forC2H50from--48to+120"C,log{k2,/k2} = -2.17 -+ 0.20 - (1.75 -+ 0.23)/8 for n-C&70 from -26 to +88"C, and log{k2,/k2} = -2.15 & 0.22 - (1.66 & 0.32)/8 for i-C4H90 from -8 to 120°C. With the adopted values for k2 for the corresponding reactions, namely log k2 = 10.31, 10.46, and 10.46, one obtains log k27 = 8.14 - 1.84/8, 8.29 1.75/6, and 8.31 - 1.66/8, respectively. Balla et al. (1985) measured the rate coefficient for the i-C3H70 0,reaction by directly monitoring the i-C3H70 radicals produced in the flash photolysis of i-C3H70N0 at 355 nm. They found the rate coefficient to be (9.1 f 4.22) X lo6 exd-0.39 -t 0.28/RT) M-l-sec-' at 25-110°C and 1-50 Torr pressure. This expression gives a room-temperature rate coefficient similar to those of other C,-C4 alkoxyl radical (except for s-C4H90)reactions with 0,.However, the Arrhenius parameters are very much smaller for the i-CsH70 + O2 reaction. It is difficult to understand why this should be.

+

REACTIONS OF ALKOXYL RADICALS WITH 0,

241

Morabito and Heicklen (1987) used the same technique as Zabarnick and Heicklen to measure the rate coefficient for the n-C&O + O2 reaction. They found ln{k,,/k,} = -4.09 2 0.54 -(1178 2 176)IT from 23 to 88°C. With log{k,, M-I-sec-'} = 10.46 this gives l ~ g { k M-'-sec-'} ~~, = 8.68 - (1178 5 176)/ 2.3031: This expression gives a similar room-temperaturerate coefficient to that obtained from the C2H50 0, and n-C3H70 0, reactions. However, the Arrhenius parameters are considerably higher for the n-C4H90 reaction. This may reflect experimental uncertainty, both because the experimental temperature range was small and because the analysis was complicated by the presence of the reaction of Eq. 1la, which occurs only in the n-C4H90 system. The photooxidation of n-C4H90N0 in air at 298 5 2 K was studied by Niki et al. (1981b). They studied the competition between

+

n-C&@

+

+ 02-H02

and n-C4H90

-

+ nC3H7CH0

HOCH2CH2CH2CH2

(27)

(1 la)

by measuring the quantum yield of n-C3H7CH0 production. They assumed that reaction 1l a leads to no further formation of n-C3H7CH0, which conflicts with the later findings of Morabito and Heicklen (1987). Nevertheless, based on their analysis, they reported k27[02]/klla= 0.23 2 0.03 at 700 Torr of air. If we take log{klla, sec-I} to be 11.28 5 0.69 - (4014 2 509)/2.3033, then kZ7 = 7.9 x lo6 M-l-sec-' at 298 K, in good agreement with the finding of Morabito and Heicklen (1987). Another study of the reaction of n-C4H90 and S-C&@ radicals with 0, was made by Cox et al. (1981). They produced their radicals from the reaction of HO with n-C4HIoin N2-02 mixtures. For the n-C4H90 system they monitored the n-C3H7CH0 yield to obtain klla/kZ7= (2.5 2 0.8) x lo-' M at 1 atm pressure and 293 K. Based on log{k,,,, sec-'] = 11.28 & 0.69 - (8.0 2 l.O)/e, one has k27 = 1.04 x lo7 M-'-sec-', again in good agreement with the findings of the other studies. For the s-C4H90 radical, Cox et al. (1981) found klldk27 = (4.32 +- 0.58) x M at 1 atm pressure and 296 K, where sec-C4H90

-

+ 0, -C2H5COCH3

sec-C4H90

CH3CH0

+ HO,

+ CzH5

(27) (1 1b)

C2H50

CD30

CH,O

Radical

?

6.68 6.79

-

1.84 0.19 -48-+ 120 _+

-

-

118-152

8.14

5.5

= 8.0

-

c

C2HsONO + hv C2HSONO + ~ I J

(C2H&N2 + hv

+ hv

+

CDjNZCD3

-

-

3.4 5.85 5.83 5.57 5.6 5.9 5.89 6.07 6.06

-

System

24.1

Temp., "C

8.5 f 1.5 9.050.6 7.9 f 0.2 7.8 8.0420.04 7.52k0.20

'CI

E27

kcdmole CH31 + hv CHSONO + hv CH3ONO + hv (CH,O), pyrolysis (CH,O), pyrolysis CH3ONO + hv CH3ONO hv F + CH3 CH30H CHSONO + hv

l-sec- I}

lOdA279

M-

25 25 23 4.0 2 2.8 123-1 69 4.8+ 1.1 110-160 2.7 + 0.7 26-150 2.6 140-355 2.68 k 0.06 100-275 2.0 27-227

lOg{k&5"C), M-1-sec-1)

TABLE 15. Reaction of Alkoxyl Radicals with O2

Cerfontain and Kutschke (1962)" Gutmanet al. ( 1982)b Zabarnick and Heicklen (1985a)

Weaver et al. (1975)

Heicklen and Johnston (1962a) Wiebe et al. (1973) Glasson (1975) Barkeretal. (1977) Batt and Robinson (1979) Cox et al. (1980) Gutmanet al. (1982) Fortuno (1982) Lorenzetal. (1985)

Reference

7.00

7.09

6.90 7.02 6.94

6.04 7.84-8.17' 8.19d

n-C3H70

i-C4H90

n-C4h90

s-C~H~O

aAs evaluated by Heicklen (1968). blog k = 6.77 at 80°C. Trom 1.5 to 100 Torr N, dHigh-pressure limit.

C2H30

6.67

i-C3H70

-8-+120

1.66 k0.32

-

22-200 27-227

-

12.36 k 0.35 23-88

8.68

-

-

-

-23- +88

1.75 2 0.23

0.39 2 0.28 25-1 10

-

8.31

8.29

6.9620.28

i-C4H90N0 + hu

n-C3H70NO + hv

i-C3H70N0 + hv

Lorenz et al. (1985)

Gutmanand Nelson (1983)

Coxetal. (1981)

Niki et al. (1981b) Cox et al. (1981) Morabito and Heicklen (1987)

Zabarnick and Heicklen (198%)

Zabarnick and Heicklen (1985b)

Ballaet al. (1985)

244

THE DECOMPOSITION OF A L K n NITRlTEs

The ratio kl,dk2, wass found from the ratio of the yields of CH3CH0 and C2H,COCH3. If we take k,,, = 4.8 x lo3 sec-', then k27 = 1.11 X lo6 M-'-sec-'. This value is surprisingly low compared to that for n-C4H,O. We would expect log k27 to be reduced by 0.3 because there is only one abstractable H atom, rather than two. However, the activation energy for abstraction should be no lower for the sec-C4Hg0 radical than for the n-C4H@ radical. Thus we would expect log k27 to be at least 6.4. Perhaps the value used for kllb is too low by a factor of -2.5.

E. Comparison of Results for Simple Alkoxyl Radicals A summary of results for the reactions of simple alkoxyl radicals with O2 is given in Table 15. The activation energy for the CH30 O2 reaction is greater than that for the reactions involving larger radical analogs. Consequently, the rate coefficient for the CH30 + O2 reaction is the lowest at any temperature. For C2H50, i-C3H70, n-C&O, i-C41&0, and n-C4H90 the room-temperature rate coefficients are all nearly the same. Thus the reactions should all have similar Arrhenius factors, except for i-C3&0, which has only one, rather than two, abstractable H atoms. Here a reduction in A factor by 50% from that of the other radicals would be expected. Figure 17 is an Arrhenius plot for the rate coefficients for the reactions of O2 with C2H50, i-C3H70, n-C3H70, I'-C&@, and n-C&@ radicals. In the case of i-C3H70, twice the rate coefficient is plotted to compensate for the fact that this radical has only one, rather than two, abstractable H atoms. For the other radicals, whose rate coefficients were determined by comparison with their corresponding reaction with NO, our recommended rate coefficient of 2.04 X 10" M-l-sec-' was used for the overall reaction of C2H50 with NO (k2a k2J, and a value of 2.86 X 10" M-'-sec-' was used for the larger radicals. The data show that k{C2H,0 + 0,) and 2k{i-C3H70}lie on the same line whose least-squares Arrhenius expression is log{&, M-I-sec-'} = 7.99 4 0.19 (1.59 2 0.26)/8, where n = 1 for C2H50 and 2 for i-C3H70. The data for n-C&O, i-C4H,0 and n-C4H90 can all be fitted by one line whose least-squares Arrheniusexpressionis log{k, M-'-sec-'} = 8.47 -t 0.12 - (1.98 2 0.17)6. The recommended values for the Arrhenius parameters for simple alkoxy radicals are listed in Table 16. It can be seen that log A27 increases as the radicals become more complex. The activation energy for the CH30 radical reaction is considerably greater than for the other radicals.

+

+

F. Other Radicals Niki et al. (1981a) generated HOCH2CH20radicals from the addition of HO to C2H4 in the presence of 0, and NO via

-

4x10'-

lo'/

T

,

+,

OK-'

Figure 17. Arrhenius plots for the RO + 0, reaction rate coefficients: k{C,H,O + 02}, Gutman et al. (1982); M, k{C2H50 + 03, Zabamick and Heicklen (1985a); 0 , 2k{i-C3H70 + O,}, Balla et al. (1985);A. k{n-C&O + O,}, Zabarnick and Heicklen (1985b); 0,k{i-C4H90 + O,}, Zabamick and Heicklen (198%); k{n-C&@ + O,}, Morabito and Heicklen (1987).

v,

TABLE 16. Recommended Arrhenius Parameters for Reactions of Alkoxyl Radicals with O2 Radical

E27, kcal/mole"

log{A2,, M-'-sec-')"

CH3O

2.57 2 0.26 1.59 f 0.26 1.59 & 0.26 1.98 0.17 1.98 f 0.17 1.98 & 0.17

7.71 ? 0.13 7.99 & 0.19 7.69 2 0.19 8.29 ? 0.12 8.29 & 0.12 8.29 2 0.12

C2H50

i-C3H70 n-C3H70 i-C4H90 n-C4H90

*

"Uncertainites are one standard deviation.

245

THE DE€OMFOSITION OF ALKYL NTIWTES

246

HO

+ C2H4

HOC2H4 HOC2H402

4

HOC2H4

+ 0 2 +HOC2H402

+ NO----*HOC2&0

They found that at mom temperature and 700 Torr pressure ([N2]/[02] = Y3), the HOC,&O radical decomposed to HOCH, CH20 about 79% of the time, but reacted with 0, as follows about 21% of the time:

+

HOCH2CH20

+ 02-HOCH2CHO

+

H02

(32)

Sahetchian et al. (1982) have shown that n-C7H150reacts with 0, to give H 0 2 at 160-240"C and 180 Torr pressure. Gutman and Nelson (1983) measured the rate of the reaction of C2H30 02.The C2H30 radicals were generated from the 193-nm flash photolysis of CH30C2H3, and the C2H30 radicals were monitored by laser-induced fluorescence. The rate coefficients increased with pressure, but decreased slightly with increasing temperature, suggesting a second-order addition reaction in its pressure falloff regime. The rate coefficients were (0.5-1.8) x lo8 M-l-sec-' at 295-473 K and 1.5-100 Torr (N2 or SF,) pressure. The room-temperature data are shown in Fig. 18. Lorenz et al. (1985) measured the rate coefficient for the reaction of C2H,0 with O2 at 300-500 K using the laser flash photolysis of CH30C2H3at 193 nm. The C2H30 radials were monitored by laser-induced fluorescence. The rate coefficient was found to be pressure dependent as shown in Fig. 18. AT 298 K, the limiting rate coefficients were

+

k"

= (1.6 & 0.3) x

lo8 M-'-sec-'

and

ko = ( 7 3 x 10" M-*-sec-'

with He as a chaperone. A negative temperature coefficient was obtained, the rate constant at [He] = 1.7 x M being (1.6 k 0.9) x lo7 exp{+668/T} M - l-sec-

'.

VII. OTHER REACTIONS OF ALKOXYL RADICALS A. Reactions with Radicals Radical-radical reactions involving alkoxyl radicals have been reviewed by Gray and Williams (1959), Gray et al. (1967), and Heicklen (1968). The early works referenced therein showed that simple alkoxyl radicals could react with alkyl or

OTHER REACTIONS OF ALKOXYL RADICALS

- -125 -

247

I

9 I

zoo

100

p/-r

I

300

-

Figure 18. Pressure dependence of the rate constants for CH2CH0 + O2 at 298 K: 0, = SF,, N2); 0 , Lorenz et al. (1985). From Lorenz et al. (1985) with permission of VHC Verlagsgesellschaft.

A, Gutman and Nelson (1983) (M

other alkoxyl radicals, either by combination or disproportionation, and that the ratio of these processes was independent of temperature. For the self-reaction of alkoxyl radicals disproportionation was about 10 times as important as combination. For reactions of alkoxyl radicals with alkyl radicals, disproportionation was still favored, but only by factors of 1.3-3.4. In both cases the overall rate coefficients were about 10'°K'-sec-', independentof temperature. Surprisingly little work has occurred since then. The rate coefficient for the disproportionation of CH30 radicals was measured in a shock decomposition of CH30N0 by monitoring the electronically excited CH,O produced by the disproportionation of CH30 radicals (Eremin et al., 1970). The rate coefficient was found to be 7.4 X 10'oTo.28M-l-sec-' from 790 to 1070 K. At 298 K, this would give a rate coefficient of 1.50 X 10" M-'-sec-'. Shortridge and Heicklen (1973) produced CH30 radicals from the steady-state photolysis of CH3N2CH3in O2 at 25°C. They interpreted their results with the same mechanism as used by Heicklen and Johnston (1962a): CH3N2CH3 + hv CH3

+ 0,

-

2CH3

+

N2

-

CH302

+ 0, CH30H + CH,O

2CH302-2CH30 2CH30

+CH302CH3

+ CH30-CH300H + CH2O CH20 + HO, CH30 + 0, HO, + CH302 -CH302H +02

CH302

__*

THE DECOMPOSITION OF ALKYL

248

From an analysis of product ratios they obtained k3d(k35k19)'/2= 0.31, k19Jk19b = 8.9, and k2&? = 0.021 M-'"-sec-'". These values can be compared with the respective values of Heicklen and Johnston (1962a), which were 0.14,9-12, and 0.020 M-1n-sec-''2, where the CH302 radicals were prepared from the steady-state photolysis of CH31-02 mixtures. However, in Heicklen and Johnston's work no direct calibrationwas made for CH300H. This could account for the factor-of-2 discrepancy in the two reported values for k3&35k19)"2. Presumably the later study, in which CH300H was calibrated, gives a more reliable value for this rate-coefficient ratio. Weaver et al. (1975) produced CD30 radicals from the steady-statephotolysis of CD,N2CD, in 0,at 25°C. They used the above mechanism to interpret their data, but also included the reactions 2CH302

-

CH30H

-CH,O2CH,

+ CH20 + O2 +02

(35b) (35c)

Based on their own work and a reinterpretation of the earlier work, they obtained 0.20 for the protonated system and 0.22 for the deuterated system. They also found k27/k:k2 = 6.3 X 10-?W'n-sec-1/2 and 9.7 X M-'/2-sec-'/2 respectively for the two systems. Since for the protonated system k27 = 6.71 x lo5 M-'-sec-', then k19 = 1.15 X 1014M-1-sec-1,animpossibly large value. The reason for this discrepancy is not known. Furthermore Weaver et al. (1975) showed that all of the peroxide could be explained by reaction 35c in both systems. Of course reaction 19b must occur, since it is the reverse reaction for the decomposition of alkyl peroxides. However, its estimated rate coefficient is only about 6 x lo8 M-l-sec-' (Heicklen, 1968), so that the reaction could be unimportant in these systems. Hassinen et al. (1985) examined the flash photolysis of dimethyl oxalate in the gas phase to produce CH,, CH30, and COOCH3. They determined rate coefficients from product analysis for the reactions k3d(k35k19)1/2 =

and found them to be k3ga = (2.1 f 0.2) X 10" M-I-sec-' and k3gb = (2.3 2 0.1) X 10" M-'-sec-' at 298-448 K. Zellner (1987) and Rhasa and Zellner (1986) have reported on the flash photolysis of CH,0NO-03-N2 mixtures at 248 nm to produce both CH,O radicals and 0 atoms. The CH,O was monitored by laser-induced fluorescence to determine the rate coefficient for the CH30-0 reaction to be (1.3 4 0.4) x 10" M-l-sec-' at 25°C. The products of the reaction were = 80% CH, O2 and =20% HO CH20.

+

+

OTHER REACTIONS OF WKOXYL RADICALS

249

Wong (1981) studied the competition between the self-reaction of r-C4H,0 radicals and the reaction of r-C4H,0 with several hydrocarbons in solution at 293 K. He used a flash-photolysissystem with electron-spin-resonancedetection of the radicals to measure the competitive reactions. Based on his earlier results for the hydrocarbon rate coefficients (Wong, 1979), he deduced the rate coefficient for the self-reaction to be (1.3 5 0.5) X lo9 M-l-sec-' at 293 K. The hydrocarbons used in the competitive experiments were cyclo-pentane, anisole, methyl-rerr-butylether, and methanol, with respective rate coefficients for reaction with &C4H,O of 3.4 X lo5, 7.2 x lo4, 2.43 x lo5, and 1.29 X lo5 M-l-sec-'. Lin and Lin (1986) studied the decomposition of methyl phenyl ether (anisole) in incident shock waves at 1000-1580 K and 0.4-0.9 atm. The CO formed could be accounted for by a four-reaction mechanism:

Kinetic modeling of the CO gave k4 = (5.5 ? 2.0) X lo8 M-l-sec-'. Francisco et al. (1981) showed that CF,O could be produced in the multiple infrared photolysis of (CF30),. Zhang et al. (1982) used this technique to generate CF30 radicals. By measuring the amount of CF30 produced, they studied the reaction

in competition with HI

+ F -HF

+I

(42)

At 300 K, k41 was found to be (3.5 2 0.5) x 10" M-'-sec-', using k4* = 2.5 x 10" M-l-sec-' (Wurzberg and Houston, 1980). A list of recommended rate coefficients is given in Table 17. This list is based on the work discussed here and that by Gray et al. (1967) and Heicklen ( 1968).

B. Abstraction of H Atoms from Molecules The abstraction of H atoms from molecules by alkoxyl radicals was reviewed by Gray and Williams (1959). by Ingold (1967), by Gray et al. (1967), by Heicklen (1968), and by Howard (1972). The studies discussed there will not

250

THE DECOMPOSITION OF ALKYL NITRlTEs

TABLE 17. Recommended Values of Rate Coefficients for RadicaliRadical Reactions in the Gas Phase

log(overal1k,M-'-sec-'}

Reaction

CH,O + CH30 CH,O + CH, CH,O + CH302 CH,O + CH,C(O)O CH,O + 0 CD,O + CH, CD,O + CH3 C2H50 + C2H50 C2HSO + CZH, i-C,H,O + i-C3H70 i-C,H,O + CH, t-C,H,O + r-C,H,O CF,O + F

kd/kca 10-70 1.1.9

9.9-10.7 10.20 39.2 10.64 10.11

m

1.1 m

1.4 1.8 1 2-70 1.3'0r2.3' 10-70 3.4 0

9.11 10.54

0

"Disproportionation-to-combinationratio. %or disproportionation products of C,& + CH,CHO. Tor disproportionation products of C,H, + C,H,OH.

be reviewed again here in any detail. A more recent review was given by Howard and Scaiano (1984).

1. CH30. The rate coefficients recommended by Gray et al. (1967) and by Heicklen (1968), based on their reviews of the early literature, are given in Table 18 for the abstraction of H atoms by CH30. The rate-coefficient parameters reported by Gray et al. (1967) were obtained from the rate coefficients of the reverse reaction and the equilibrium constants. Those reported by Heicklen (1968) were obtained from the ratio k28klf/k43for the reactions 2CH3

CH30 CH,O

-

C2H6

+ RH -CH,OH

+ CH3

__*

+R

CH30CH3

(26)

(28) (43)

The values used for log kZ6and log k43 were 10.3 and 9.8, respectively, where the rate coefficients are in units of M-l-sec-'. The activation energies recommended by the two reviews are in excellent agreement. However the A factors recommended by Heicklen are in general 0.3 log units (a factor of 2) higher than those of Gray et al. This discrepancy is certainly within the uncertainty of the analyses, especially since k43 is not well established.

OTHER REACTIONS OF ALKOXn RADICALS

251

TABLE 18. Arrhenius Parameters for the Gas-Phase Reaction CH,O CH30 + R GS?"

CH4

8.8 8.4 9.1 8.2 7.4 7.9 8.7 9.2 7.6 8'

C2H6

c-C~H, C3H8

n-C4H10 i-C4Hlo neo-C,H,, HCOOCH, CH3COOCH3 CHZO CH3OC02CH3 CH3OH CH300CH3 CH3OCH3

--*

E, kcaUmoIe

log{A, M-'-sec-'}

RH

+ RH

Hb

GST"

-

11.0 7.1 9.7 5.2 2.9 4.1 7.3 8.2 6.6 3 .O

8.1 8.8 7.9 7.1 7.6 8.4 8.8 7.9 7.1 7.85

Hb

7.1 9.7 5.2 2.9 4.1 7.3 8.2 7.1 3 .O 5.9

6.0 5.8 15-20

"From Gray et al. (1967). based on a review of earlier work. %om Heicklen (1968). based on a review of earlier work. 'Assumed.

Hoare and Whytock (1967) studied the steady-state photooxidation of acetone at 100-250°C and at 3 13 nm. From a product analysis, they were able to measure the competition between 0,(k27) and CH3COCH3(kZ8)for CH30 radicals from 100 to 200°C. From their data a least-squares analysis gives log(k27lk2,) = -3.23 f 0.76 (1962 & 322)/T. With l ~ g { AM-'-sec-'} ~~, = 7.71 and E27 = 2.57 kcdmole, one obtains l~g{k,~,M-'-sec-'} = 10.94 - 11.54/8. Undoubtedly the Arrhenius preexponential factor and activation energy are actually smaller. Kelly and Heicklen (1978) studied the competition between CH3CH0 and O2 for CH30 generated from the steady-state photolysis of azomethane at 25°C. Their analysis involved a complex mechanism, from which they found that CH30 reacted about 14 times as fast with CH3CH0 as with O2 at 25°C. The latter rate coefficient is 6.7 X lo5 M-'-sec-', so that the rate coefficient for CH30 CH3CH0 becomes 9.4 X lo6 M-l-sec-'. Nangia and Benson (1980), using the data of Bercts and Trotman-Dickenson (1961), deduced that the rate coefficient for the reaction of CH30 with i-C4Hlo is given by log{k, M-l-sec-'} = 8.3 - 4.1/8. Both primary and tertiary H atoms can be abstracted, the specific expression for abstraction of tertiary H atom k i n g log{k, M-'-sec-'} = 8.0 - 3.7/8.

+

+

252

THE DECOMPOSITION OF ALKYL IWlUTES

2. C2Hs0.The activation energy for the abstraction of an H atom from C2H5C02C2H5by C2H50 was found to be 5.5 kcallmole by Wijnen (1960). Heicklen (1968) estimated the preexponential factor to be r l X lo8 M-l-sec-'. There appears to be no further quantitative work on C2H50 abstraction reactions since then.

3. i-C,H,O. Only very limited data exist on the abstraction of H atoms by i-C3H70 radicals. Batt and Milne (1977a), in their study of the thermal decomposition of i-C3H70radicals, found that at 16O"C, i-C4H,o at M could remove -25% of the radicals. If we take our recommended value for the decompositionrate coefficient of 10'5.0exp(- 17.YRZ') sec-', then the abstraction rate coefficient is 2.0 x lo7 M-l-sec-' at 160"~. Balla et al. (1985) monitored i-C3H70 radicals directly in the presence of several added gases. Because of experimental limitations they could only find upper limits of rate coefficients for i-C3H70reactions with i-C4Hlo,C2H4, and (CH3)&=CHCH3. At 25°C these were 1.3 X lo7, 1.2 X lo7, and 1.4 X lo7 M-l-sec-', respectively. They also reported a provisional value for the rate coefficient for the i-C3H70 CH3CH0 reaction of (1.1 & 0.3) X lo8 K 1 sec-'.

+

4. t-C,%O. Early work on t-C4H90 radicals was reviewed by Gray et al. (1967) and Howard (1972). This included work in both the gas phase and solution. A summary of the rate coefficients obtained in the earlier work is given in Table 19. Only the more recent work will be reviewed here. The reactions of r-C4b0 radicals were studied in solution in Walling's laboratory and reviewed by him (Walling, 1967). Walling and Jacknow (1960) used r-butylhypochloriteas a source of f-C4H90radicals and measured its relative reactivity with a number of hydrocarbons in aromatic solvents at room temperature. They found that t-C4H90 abstracted H atoms with increasing ease for primary, secondary, and tertiary H atoms at 40°C. Walling and Wagner (1963) studied the reactivity of f-C4H90 radicals with cyclohexane compared to its decomposition. They found that the rate coefficient varied by a factor of 40 at 0°C in various solvents. At 100°C the effect was very much smaller. This work was extended to the reactions of t-C4H90with toluene and r-butylbenzene by Walling and Kurkov (1966). Walling and McGuinness (1969) examined the reaction of t-C4H90 with toluene in CC14 solution at 70°C compared to decomposition and found a relative rate coefficient of 2.0-2.5 for abstraction relative to decomposition. In all the studies the source of r-C4H90 was principally the decomposition of the hypochlorite. In the last study decompositions of the hyponitrite and hypobromite were also used. The reactions of r-C4H90 radicals have also been studied in Ingold's laboratory. Kennedy and Ingold (1966) measured the relative rates of H-atom abstraction from ten substituted toluenes in CC14 solution at 40°C. In the study

c:w

8.12 24.7 16.9 16.4 39.0 14.2 9.12 2.84 52.8 625 (40°C)

40°C

k28/k,lc,M-’

’

Source: Gray et al. (1967) with permission of Pergamon Press. “Reactions: (CH,),CO. CH3*+ CH3COCH3(1 lc) (CH,),CO. + RH + (CH,),COH + R (28).

Gas phase

c2c13F3

C2H2CIz (trans) C2H2C12(cis) CH3COOH

c2c14

C,H,CN C6H5CI

--f

0.68 2.82 1.90 2.65 4.14 2.26 1.57 0.65 4.29 203 (60°C)

CH$N

C6H6

l0o”C

Solvent 81.9 207 109 91.7 293 98.9 52.2 12.4 487 1040(30°C)

0°C

- E28,

9.54 8.66 8.28 7.21 8.72 7.69 7.04 5.80 9.65 10.8

{kcal-mole-’}

ELlC

TABLE 19. Relative Reactivity of f-C,H,O Radicals with H-containing Compounds“

5.73 4.63 4.58 3.82 4.16 4.16 3.92 3.64 5.04 4.77

log{A,,JA,,, M}

254

THE DECOMPOSITION OF A L K n NlTRITEs

of the kinetics of the r-butyl hypochlorite chlorination of toluene in solution, Carlsson and Ingold (1967a) found k28/(2k19a)'l2 = 0.36 (M-sec)-'12 at 24°C and 0.42 (M-sec)-'" at 30°C, which compares with an extrapolated value of 1.1 (M-sec)-'I2 at 30°C from Walling and Kurkov's (1966) results. Carlsson and Ingold (1967b) extended their work to other compounds. Their results are shown in Table 20. Furthermore, if 2k1, = 2.1 x lo8M-l-sec-' for r-C4H,0 self-removal, then k28 for the abstraction of H from toluene by r-C4H,0 is 6.7 X lo7 exp(-5.6/RT} M-'-sec-'. Zavitsas and Pinto (1972) extended the results of Carlsson and Ingold to substituted toluenes. Their results are shown in Table 21. These and other data showed that the relative reactivity decreased exponentially with an increase in C-H bond dissociation energy. Stoddart et al. (1974) studied the gas-phase reactions of r-C,H90 radicals with 1-substitutedbutanes, the radicals being generated from the decomposition of r-butyl hypochlorite. The relative reactivities for abstraction of H atoms from the various positions are given in Table 22. The reactions of r-C4H,0 radicals with several substrates were studied in solutions of 1:2 benzene-(r-C,H,O), at 22°C in Scaiano's laboratory (Small and Scaiano, 1978; Paul et al., 1978). The radicals were generated from the nanosecond laser flash photolysis of (GC~H,O)~. The resultant rate coefficients are listed in Table 23. Wong (1979) studied the reactions of t-C&o with several substrates in solution from 253 to 303 K. The radicals were produced from the flash photolysis TABLE 20. Relative Reactivities toward the t-Butoxyl Radical" Relative Reactivity Reactant Toluene p-Xylene m-Chlorotoluene t-Butylbenzene Triphenylmethane Cyclohexane Chloroform

W

K

1 2.3 0.3

0.3 1.6 5.8

a

"

k*8"

1

2.4 0.4

0.3

Competition lb

2.9' 0.6'

0.3d

0.7

3.2d

5.7

6.0d 1 .O"

-

Source: Carlsson and Ingold (196%) with permission of the American Chemical Society. "At 24" in CCI, or C2C13F3. bAssumed. 'At 40" in CCI,: Kennedy and Ingold (1%). dAt 40"in reactants: Walling and Jacknow (1960).

Toluene 1-Octene 1-0ctene Toluene Toluene Toluene Toluene Toluene Toluene Toluene p -Xy 1ene p-Xylene p-Xylene

None' Noneb None' 0.11b.' 0.04' 0.35' 0.04' 0.04' 0.04' 0.04' 0.22' 0.224 0.22'f 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 13.3 31.0 50.0

2.50 2 0.20 0.565 2 0.011 0.183 k 0.013d 3.28 k 0.08 3.31 2 0.06 3.18 f 0.04 1.96 ? 0.03 2.35 2 0.03 0.699 2 0.004 0.822 2 0.006 2.58 2 0.01 2.57 2 O.0ls 2.56 f 0.028

Source: From Zavitsas and Pinto (1972) with permission of the American Chemical Society. "Per molecule; two determinations, each analyzed in triplicate. *Solvent, CCI,. 'Solvent, CF,CICFCI,. dFive determinations. '1 -0ctene. fThe concentration of trichloroethylene did not decrease during the run, within experimental error. 8Tnree determinations.

Ethylbenzene Ethylbenzene Toluene Ethylbenzene Ethylbenzene Ethylbenzene m-Xylene p-Xylene m-Chlorotoluene p-Chlorotoluene Cyclohexane Cyclohexane Cyclohexane

TABLE 21. Relative Reactivities of Hydrocarbons toward tert-Butyl Hypochlorite by Direct Competition

TABLE 22. Relative Selectivities for the Attack by t-C4E190 on Butane and 1-Fluoro-, 1-Chloro-, and 1-Cyanobutaneat -90°C in the Gas Phase ~~~

Position of H Atom Abstracted ci

P

Y 6

Relative Selectivity

H

F

c1

CN

1 8.0 8.0 1

6.8 3.3 8.0 1

6.4 3.6 8.0 1

2.8 2.5 8.0 1

Source: Stoddart et al. (1974), with permission of the Royal Society of Chemistry.

TABLE 23. Rate Coeffieients for Hydrogen Abstraction by t-C4H,0 in 1:2 CJ&(t-C4&0), solution^ Substrate Toluene Ethylbenzene Cumene Mesitylene Cyclopentane Cyclohexene 1,7-0ctadiene 1,3-Cyclohexadiene 1,4-Cyclohexadiene Methanol Ethanol 2-Propanol

2-Propanol-d, 1-Phenylethanol Diphenylmethanol Diisopropyl ether Tetrahdrofuran Tetrahydrofuran-d, t-buty1hydroperoxide

kRH.

lo5M-l-sec-' 2.3 10.5 8.7 8.3 8.8 57 23 420 540 2.9 11.0 18

5.5 188 69 12.0 83 30 25Wh

kRH4Ol"elle

Paulet al. (1978) Others 1.o

4.5

3.8 3.6 3.8 25 10 18 23 1.3 4.8 7.8 2.4 7.8 30 5.2 36 13 109

Source: Paul et al. (1978), with permission of the American Chemical Society. Walling (1967). %gold ( 1967). Walling and Jacknow (1960). dTaken as 6'7 of the cyclohexane reactivity. 'Zavitsas and Pinto (1972) 'Taken as twice the reactivity of I-octene. BExtrapoiated to zero substrate concentration. *Based on only one substrate concentration.

256

1.o 2.3" ,3.2' 2.8",6.8' 4.0c,d 5.O",4Sb 37' 1led

52"

OTHER REACIlONS OF ALKOXYL RADICALS

257

of (t-C4H90), and measured by ESR spectroscopy. For cyclopentane, anisole, f-C4H,0CH3, and CH30H, log(A, M-'-sec-') = 9.1, 8.8, 8.8, and 8.6, respectively, per active H atom, and E = 6.1, 5.9, 5.2, and 5.3 kcallmole, respectively. The corresponding room-temperature rate coefficients were 3.4 x lo5, 7.2 X lo4, 2.43 X lo5, and 1.29 X lo5 M-l-sec-'. These are 50% higher than previous indirect estimates, but only one-half the values of Paul et al. (1978). Fuke et al. (198 1) studied the laser photolysis of di-r-butyl peroxide to produce r-C4&0 radicals. They then measured the heat given off by reactions of these radicals by a thermal-lensing technique. In this way they deduced that the rate coefficients for r-C4H,0 reactions with di-r-butyl peroxide, toluene, and cyclohexane were, respectively, 6 5 X lo3, (7 2 1) x lo4, and (3.6 f 0.4) x lo5 M-'-sec-' at 27 f 1°C in 1:4 (t-C4H,0)2--benzene solutions. Lissi et al.'(1985) measured the reactivity of t-C4H90radicals with a number of methyl-substituted aromatic compounds in benzene solution at 120°C. Their results are given in Table 24. They found that the reactivity depended almost exclusively on the aromatic moiety and was almost independent of the methylgroup position. Encina and Lissi (1978) studied the gas-phase abstraction of H atoms from various amines by f-C4H90 radicals in competition with t-C4H,0 decay:

Taking kllc as 5.5 X lo4 M-l-sec-', they obtained rate coefficients for reaction 28 at 115°C of 25.0 x lo6, 6.6 X lo6, 3.8 x lo6, 2.2 X lo6, 0.2 x lo6, and 0.14 x lo6 M-l-sec-', respectively for RH = N-methyl aniline, triethylamine,diethyl amine, n-butyl amine, tert-butyl amine, and cyclohexane. The absolute reactivity of t-C4H,0 with a series of amines in 1 :2 benzene+C4H90)2 solutions was studied by Griller et al. (1981) at room temperature, where the radical was produced from the flash photolysis of di-ferf-butyl peroxide and monitored directly. The rate coefficients were large and varied from 3.3 x lo6 M-'-sec-' for f-Bum2 to 1.8 X lo8 M-l-sec-' for (C2H5)3N.They are listed in Table 25. The H/Disotope effect for hydrogen abstraction was measured by using the EPR competition technique. From -93 to +15"C, log{k,lk,} = -0.14 0.07 + (0.36 & 0.7)/0. Encina et al. (1981) found that the reactivity depended on the amine ionization potential and the solvent; in general the rate coefficient decreased with increasing ionization potential. Arrhenius parameters for the hydrogen-abstraction reaction of t-C4H90 radicals with (CH3),SiH and GC4HlO were measured at 4345°C in the gas phase by Park et al. (1982). These reactions were measured by competition with the decomposition of r-C4H90,whose Arrhenius parameters were taken to be log{A, sec-'} = 14.1 and E, = 15.3 kcal/mole. For the reaction

*

258

THE DECOMPOSITION OF ALKYL NITRITES

TABLE 24. Rate Constantsfor f-C4&0 Abstraction Reaction in Benzeneat 120°C Compound Toluene 1-Methylnaphthalene 2-Methylnaphthalene 1+Dimethylnaphthalene 2,3-Dimethylnaphthalene 2,6-Dimethylnaphthalene 1-Methylanthracene 9-Meth ylanthracene 9,lO-Dimethylanthracene 1-Methylphenanthrene 1-Ethylbenzene 2-Ethylnaphthalene Benzyl alcohol 1-Naphthalenemethanol 2-Napthalenemethanol Benzaldehyde 2-Naphthaldehyde 1-Pyrenecarboxaldehyde Phenanthrene-9-carboxaldehyde p-Cresol p-Methoxyphenol Hydroquinone

0.17 0.37 0.38 1.10 1.o 0.67 1.13

1.05

2.25 0.40 0.62 0.66 2.7 2.7 3.0 13 16 19 17 202 383 803

1.24 2.7 2.8 4.0

3.5 1.8 8.1 7.7 8.1 2.9 6.6 7.1 29 22 32 280 330 410 370 4.3 x 103 8.4 x 103 8.5 x 103

2.2 2.3 3.2 2.9 2.0 6.6 6.2 6.6(22)b 2.3 5.3 5.8 24 18 26 230 270 330 300 3.5 x 103 6.8 x lo3 7 x 103

Source: Lissi et al. (1985). with permission of John Wiley and Sons, Inc. "Estimated emr: k 15%. bAt 70" in bromobenzene. From Tanner et al. (1980)

-

+ (CH3)Si (28) = 8.5 - 3.7/9. Likewise for f-C&O + i-C4Hloone has

f-C4H90

+ (CH3)3SiH

f-C4H90H

1og{kZ8,M-I-sec-'} 10g{kz8,M-'-sec-'} = 8.4 - 4.3/8. A general rule for the rate coefficient for H-atom abstraction by t-C,&O was found to be log{A,,, M-l-sec-'} = 8.4 2 0.5 per H atom and E28 = 0.42 AH 8.7 (+_0.7)kcdmole, where AH is the enthalpy of reaction. This work was extended by Lee and Choo (1986) to GeH, and PH3 as well as (CH3)3SiHat 403-458 K.The respective values for E,, were 1.9, 1.4 and 2.1 kcaymole, and for log{A2,, M-I-sec-'} were 9.1, 9.0, and 8.5. With our recommended values for the Arrhenius parameters for t-C4H90 decomposition of log{Allc, sec-I} = 15.0 and E l l c = 16.5 kcaVmole, these rate coefficientsare changed, and the recomputed values are listed in Table 26.

+

TABLE 25. Rate Constants for the Reaction of t-Butoxyl with Amines at 22" Compound

k,M-s-'

Me3N

1.1 x lo8

Et3N

1.8

n

N-LN

W

X

lo8

2.8 x

107

1.3 X lo8

-Cm

7.9 x

lo7

9.5 x 107 n-PrNH2

1.7 x lo7

t-BuNH,

3.3 x lo6

Source: Griller et al. (1981), with permission of the American Chemical Society.

TABLE 26. Rate Coefficients for Abstraction Reactions of t-C4H90 in the Gas

Phase" RH

i-C4HI0 (CH,),SiH (CH3)3SiH GeH, PH3

log{A,,, M-'-sec- '}

Ez8, kcaUmole

9.3 9.4 9.4 10.0 9.9

3.3

"Based on the competition with t-C.&O

Reference Parketal. (1982)

2.6

Lee and Choo (1986)

decomposition of log{A,,,, sec-I} = 15.0 and El,, =

16.5 kcallmole.

259

THE DECOMFOSITIONOF ALKYL NllWTES

260

The gas-phase reactions of r-C4H90 radicals with CH20, CH3CH0, CH3COCH3, and CD3COCD3 were studied at 399434 K by A1 Akeel et al. (1981). The t-C4H90 was generated from pyrolysis of ( G C ~ H ~ Oand ) ~ ,the abstractionreactions of r-C4H90with the substrateswere measured in competition with the unimolecular decomposition of t-C4H90 radicals. Likewise Sway and Waddington (1984) studied the reactions of r-C4H90with 2,2-dimethylpropane, butane, 2-methylpropane, cyclohexane, propne, 2-methylpropene, cis- and trans-butene-2, 2-methylbutene-2, and 2,3-dimethylbutene-2 from 399 to 434 K. In order to determine the absolute rate coefficients, the rate coefficient for the f-C4H90 radical decomposition must be known. This unimolecular decomposition was in its pressure falloff regime, and its rate coefficients as a function of pressure were estimated from RRK theory together with various estimates of the limiting high-pressure rate coefficient. For all the abstraction reactions, log(A2,, M-l-sec-') = 9.9-10.5 and the activation energies were 4.5-7.7 kcallmole. s-C4H90. East and Phillips (1967) found that S-C.&o, produced from the thermal decomposition of s-C4H90N0, abstracted an H atom from s-C4H90N0 with a rate coefficient of 4 X 10' exd-3.91Rq M-l-sec-' from 150 to 190°C. This rate coefficient was found from the competition with 5.

s-C4H90 + NO

-

+ HNO

C,H,COCH,

(2b)

whose rate coefficient was taken to be 1 x 10'' cm3/mole-sec. (Presumably, they meant M-'-sec-'.) With our recommended value of 5.2 X lo9 M-l-sec-' for this rate coefficient, the rate coefficient for the abstraction reaction becomes 2.1 X 10' exd-3.9lR7) M-l-sec-'.

C. Addition Reactions Thynne (1964) found that C2H50 radicals could add to C2H4 at 70 and 160°C. Heicklen (1968) estimated that the rate coefficient should be -108.5exp(-6.0/RT} M - -sec-' . Lissi et al. (1973) produced CH30 from the thermal decomposition of CH300CH3 at 123-153°C. They found that CH30 could oxidize CO:

'

CH30

+ CO

__*

CH,

+

COz

(44)

They studied this reaction in competition with 2CH,0-CH30H

+ CH20

(19a)

OTHER REACTIONS OF ALKOXYL RADICALS

261

by measuring the CO, formed. Taking k19, = 1.0 x 10'' M-l-sec-', Lissi et al. (1973) obtained k4 = 10'o.2'o.6 exp((-11.8 & 1.5)/RT) M-l-sec-'. They then added C& and other olefins to their system (Lissi et al., 1975). They studied the competition between reaction 44 and CH30

+ CZH4 -CH,OC,H4

(45)

At 127°C they found that k45 = (3.7 2 0.8) x lo4 M-'-see-'. For the other olefins, the rate coefficients were given relative to that for CZH4. They are listed in Table 27. The value for CH30 addition to C2H4 is only 22% of that predicted by Heicklen's estimate for the addition of C2H,0 to C 2 b , indicating either that the preexponentialfactor is <108.5or that the activationenergy is >6.0 kcavmole. In a system similar to their study of CH30 with CO, Lissi et al. (1971) studied the reaction of t-C4H90with CO and obtained a rate coefficient of log{k, M-lsec-'} = 7.0 ? 1.8 - (10.4 2 3.4)/8 from 371 to 421 K. Alkoxyl radicals have been shown to add to phosphites, phosphines, and boranes (Pobedimskii et al., 1972; Griller et al., 1979). The adduct radical is unstable and loses an alkyl group, either the one in the original akoxyl radical or one of those attached to the substrate. The oxidation in solution (usually cyclopentane as solvent) of trialkyl phosphites by t-C4H90 radicals was studied by Davies et al. (1971a, 1972b) using ESR spectroscopy to detect the radicals. The reactions of interest for triethyl phosphite were TABLE 27. Relative Rate Coefficients for the Gas-PhaseAddition of CH,O to Olefm at 127°C Olefin C2H2 CH3CCH CH,CHF

CFZCF,

cis-CHClCHCl tram-CHClCHCl CC1,CHCl

CC12CC1, CH2CCH2

CH2CHCHCH2 c-CsHKl

Relative k a

*

1.7 0.3 2.5 2 0.4 3.3 f 0.4 2.2 & 0.4 1.3 ? 0.3 0.95 f 0.30 0.40 f 0.15 0.2 2 0.1 5.2 2 0 . 8 27 19

Source: Lissi et al. (1975). with permission of John Wiley and Sons, Inc. "Relative to C,H+

262

THE DECOMPOSlTION OF ALKX NKRlTES

with rate coefficients from 204 to 245 K given by log{ka, M-'-sec-'} = 9.83 - 2.24/8 and log{k4,, sec-'} = 12.95 - 10.34/8. For the reaction of r-C4H90 with (C2H5),P, Davies et al. (1972~)found the overall rate coefficient for the displacement of a C2H5 group by r-C4&0 to be log{k, M-'-sec-'} = 9.34 1.34/8 from -42 to +34"C in cyclopentane solution based on a rate coefficient of log&, M-'-sec-'} = 9.83 2.2418 for the competitive reaction of r-C4H90 with P(OC2H5)3. They also found that f-C4H90added to C2H50P(C2H5)2,and that the adduct decomposed to give C2H5 t-C4&0P(C2H5)OC2H5with a rate coefficient log{k, sec-'} = 10.91 - 8.16/8 from - 128 to -37°C in isopentane solution. Davies et al. (1971b) also studied the reactions of r-C4H90, prepared from (t-C4H90), photolysis, with boron compounds in competition with the reaction with cyclopentanein peroxide or isooctane solutions. They monitored the radicals produced from the respective reactions by electron spin resonance. The reactions of r-C4H90 with boron compounds had rate coefficients of 2 X lo5 3 X lo7 M-'-sec-' at 30°C. This work was extended by Davies et al. (1972a), who used t-butylhypochlorite as the source of f-C4H90radicals and measured the amount of alkyl chlorides produced from the akyl radical products at 40°C. Rate coefficients for the akoxyl radical attack on the phosphorus and boron centers are in Table 28. For phosphites some additional relaative rate coefficients are listed in Table 29. The decay of the phosphoranyl and boranyl radicals initially produced in the reaction have been measured by Griller et al. (1979), and their results are listed in Table 30. In a study of the reaction of CF30F with C3F6 at 20-75°C Afonso and Schumacher (1984) proposed CF30 as an intermediate and suggested that it could add to C3F6.

-

+

-

D. Reaction with 0, Attempts to measure the rate coefficient for the reaction of CH30 with 0,have shown that the reaction is immeasureably slow at room temperature. Simonaitis and Heicklen (1975) prepared CH30 from the reactions of O('D) with CH, and the subsequent oxidation of the CH3radical produced in the reaction. They found no reaction at 25°C and estimated the upper limit to be 1.2 X lo6M- l-sec-' . Fortuno (1982) produced CH30 radicals in a flow tube from the reaction of F atoms with CH30H. He monitored the CH30 directly by laser magnetic resonance and could see no reaction of CH30 with 03.His upper limit for the reaction was 3.0 x lo7 M-'-sec-'.

Ph3P Ph3P P(OEt)3 PEt3 Ph3B n-Bu3B i-Bu3B s-Bu~B (MeB0)3

t-BuO. Me0 t-BuO. t-BuO. t-BuO. t-BuO. t-BuO. t-BuO. t-BuO.

1.9 x lo9 5.1 x 109 8.1 X 10' 1.2 x 109 1.0 x 10' 1.5 X 10' 5.1 X lo6 1.5 X lo6 1.0 x 10'

Laser photolysis Pulse radiolysis ESR competition with cyclopentanenpb ESR competition with P(OEt), ' Laser photolysis ESR competition with cyclopetanea*d ESR competition with cyclopentaneaed ESR competition with cyclopentane",d ESR competition with cyclopentane'*d

Source

Source: Griller et al. (1979), with permission of the American Chemical Society. "Competitive rate measurements from the original publication combined with the rate for cyclopentane from laser photolysis measurements (Paul et al., 1978). The analysis usually assumes that the intermediate decays solely to give scission products, a condition which is met at low readical concentrations. %om Davies et al. (1971a. 1972b). 'From Davies et al. (1972~). dFrom Davies et al. (1971b).

X3M

Radical

TABLE28. Representative Rate Constantsfor AlkoxylRadical Attack at the Phosphorus and Boron Centers at Room Temperature

THE DECOMPOSTlPON OF ALKn NKTUTES

264

TABLE 29. Ratiosof the Rate Constantsfor theReactions of t-BuO Radicals with Triethyl Phosphh and Triphenylpbospine (wO"C, Hydrocarbon) SlhlkRH

Hydrocarbon Cyclohexane Cyclohexene Cyclopentene Cumene 2.3-Dimethylbutam

(EtO),P

Ph3P

610 2 10

7.0 f 0.2

440 2 10 610 2 10 730 2 10 llook loo

7.4 f 0.2 7.4 f 0.2 10.3 f 0.5 9.8 2 0.7

Sources: Pobedimskii et al. .0972),with pamision of the 3ritish Library document Supply Centre.

TABLE 30. Rate Ckstanb for Decay of Phosphoranyl and Boranyl Radicals Radical"

Temp, K

1

295

2

293 272 263 253

1 1 1 I

1 1 1

3

2441 239 232

225 295

k, sec-'

Solvent and Methods

1110 750 87.7

Benzene-t-BuOOBu-t, flash photolysis Methanol, pulse radiolysis Toluene, ESR Toluene, ESR Toluene, ESR Toluene, ESR Toluene, ESR Toluene, ESR Toluene, ESR Benzene-t-BuOOBu-t, laser photolysis

39.6 12.9 5.59 4.18 2.17 1.28 66,OOo

Source: Griller.et al. (1979). wi? permission of the.American Chemical Society. al = t-C4HgOPPh,; 2 = CH,OPPh,; 3 = t-C&OBPh,.

ACKNOWLEDGMENTS The author thanks R. J. Balla, P. Gray, D. Waddington, S. Zabarnick, and R. Zellner for helpful comments and corrections.

REFERENCES Adler, D. G., M. W. T. Ratt, and P. Gray (1955) Chem. & I d . , 1517. Afonso, M. dos S. andH. J. Schumacher(1984) In!. J . Chem. Kinetics 16 103.

REFERENCES

265

Akhtar, M. (1964) Adv. Photochem. 2, 263. A1 Akeel, N. Y. and D. J. Waddington (1984) J. Chem. SOC., Perkin Trans. ZZ, 1575. A1 Akeel, N . Y, K. Selby, and D. J. Waddington (1981) J. Chem. SOC., Perkin Trans. ZZ, 1036. Alcock, W. G. and B. Mile (1975) Combustion and Flame 24, 125. Arden, E. A., L. Phillips, and R. Shaw (1964) J. Chem. SOC.,5126. Baker, G. and R. Shaw (1965) J. Chem. SOC., 6965. Baldwin, A. C. and D. M. Golden (1978) Chem. Phys. Lett. 60, 108. Baldwin, A. C., 3. R. Barker, D. M. Golden, and D. G. Hendry (1977), J . Phys. Chem. 81, 2483. Balla, R. J., H. H. Nelson, and J. R. McDonald (1985) Chem. Phys. 99,323. Barker, J. R., S. W. Benson, and D. M. Golden (1977) Znt. J. Chem. Kinetics 9, 31. Barton, D. H. R., J. M. Beaton, L. E. Geller, and M. M. Pecket (1960) J. Am. Chem. SOC. 82, 2640. Barton, D. H. R., J. M. Beaton, L. E. Geller, and M. M. Pechet (1961) J . Am. Chem. SOC. 83,4076. Batt, L. (1979) Znt. J. Chem. Kinetics 11, 977. Batt, L. and R. D. McCulloch (1976a) Znr. J. Chem. Kinetics 8, 491. Batt, L. and R. D. McCulloch (1976b) Znt. J. Chem. Kinetics 8, 911. Batt, L. and R. T. Milne (1974) Znt. J. Chem. Kinetics 6 , 945. Batt, L. and R. T. Milne (1976) Znt. J. Chem. Kinetics 8, 59. Batt, L. and R. T. Milne (1977a) Znt. J . Chem. Kinetics 9, 141. Batt, L. and R. T. Milne (1977b) Znt. J . Chem. Kinetics 9, 549. Batt, L. and G. N. Rattray (1979) Znt. J. Chem. Kinetics 11, 1183. Batt, L. and G. N. Robinson (1979) Znt. J. Chern. Kinetics 11, 1045. Batt, L. and G. N. Robinson (1982) Znt. J. Chem. Kinetics 14, 1053. Batt, L., K. Christie, R. T. Milne, and A. J. Summers (1974) Znt. J. Chem. Kinetics 6 , 877. Batt, L., R. T. Milne, and R. D. McCulloch (1977) Znt. J. Chem. Kinetics 9,567. Batt, L.,T. S . A. Islam, and G. N. Rattray (1978a) Znt. J. Chern. Kinetics 10,93 I . Batt, L., T. S . A. Islam, and H. Scott (1978b) Znt. J . Chem. Kinetics 10,1195. Batt, L., J. P. Burrows, andG. N. Robinson(l981) Chem. Phys. Lett. 78,467. Benson, S. W., F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O’Neal, A. S. Rodgers, R. Shaw, and R. Walsh (1969) Chem. Rev. 69, 279. BercCs, T. and A. F. Trotman-Dickenson (1961) J. Chem. Soc., 348. Bielski, B. H. J. and R. B. Timmons (1964) J . Phys. Chem. 68, 347.

266

THE DECOMPOSlTlON OF ALKYL NlTRlTEs

Brown, H.W. and G. C. pimentel(l958) J. Chem. Phys. 29, 883. Calvert, J. G. and J. N. Pitts, Jr. (1966) Photochemistry, John Wiley and Sons, Inc., New York, pp. 452-455, 480-485. Carlsson, D. J. and K. U. Ingold (1967a) J. Am. Chem.SOC. 89,4885. Carlsson, D. J. and K. U. Ingold (1967b) J. Am. Chem. SOC. 89,4891. Carter, A. G. and M.W. Travers (1937) Proc. Roy. Soc. London Ser. A 158,495. Carter, W. P. L., K. R. Damell, A. C. Lloyd, A. M.Winer, and J. N. Pitts, Jr. (1976) Chem. Phys. Lett. 42, 22. Carter, W. P. L., A. C. Lloyd, J. L. Sprung, and J. N. Pitts, Jr. (1979) Znt. J . Chem. Kinetics 11, 45. Cerfontain, H.and K. 0. Kutschke (1962) J. Am. Chem.SOC.84,4017. Christie, M. I. and P. M.Hetherington (1977) J. Photochem. 6 , 285. Choo, K. Y. and S. W. Benson (1981) Znt. J. Chem. Kinetics 13, 833. Chow, Y. L., T. Hayasaka, and J. N. S . Tam (1970) Can. J. Chem. 48,508. Coe, C. S. and T. F. Doumani (1948) J. Am. Chem. SOC. 70, 1516. Colussi, A. J., F. Zabel, and S.W. Benson (1977) Znr. J. Chem. Kinerics 9,161. Cox, D. L., R. A. Livermore, and L. Phillips (1966) J. Chem. SOC.(B), 245. Cox, R. A., R. G. Derwent, S . V. Kearsey, L. Batt, and K. G. Patrick (1980) J . Photochem. 13, 149. Cox, R. A., K. F. Patrick, and S. A. Chant (1981) Environ. Sci. Tech. 15,587. Dalby, F. W. (1958) Can. J. Phys. 36, 1336. Davies, A. G., D. Griller, and B. P. Roberts (1971a) Angew. Chem., Int. Ed. Engl., 10, 738. Davies, A. G., D. Griller, andB. P. Roberts (1971b)J. Chem. SOC.(B), 1823. Davies, A. G., T. Malci, and B. P. Roberts (1972a) J. Chem. SOC.Perkin Trans. zz, 744. Davies, A. G . , D. Griller, and B. P. Roberts (1972b) J. Chem. SOC. Perkin Trans. ZZ, 993. Davies, A. G., R. W. Dennis, D. Griller, and B. P. Roberts (1972~)J. Organomet. Chem. 42, C47. D6M, S . , T. Bkrces, and F. M h (1986) Znt. J. Chem. Kinetics 18, 329. Drew, R. M.and J. A. Kerr (1983) Znt. J. Chem. Kinetics 15. 293. Drew,R. M., J. A. Kerr, andJ. Olive (1985)Znr. J . Chem. Kinetics 17,167. Dupuis, M., J. J. Wendoloski, and W. A. Lester, Jr. (1982) J. Chem. Phys. 76,488. Durant, D. and G. R. McMillan (1966) J. Phys. Chem. 70, 2709. East, R. L. and L. Phillips (1967) J. Chem. SOC. (A), 1939. East, R. L. and L. Phillips (1970) J. Chem. SOC. (A), 331.

REFERENCES

267

East, R. L., J. R. Gilbert, and L. Phillips (1968) J. Chem. SOC.(A), 1673. Elkins, H. B. and W. Kuhn (1935) J. Am. Chem. SOC.57,296. Encina, M. V. and E. A. Lissi (1978) Znt. J . Chem. Kinetics 10, 653. Encina, M. V.,S. Dim, and E. Lissi (1981) Znr. J. Chem. Kinetics 13, 119. Eremin, A. V.,I. S. Zaslonko, S. N. Kogarko, E. V. Mozzhukhin, and Yu. P. Petrov (1970) Kinetika i Kataliz 11, 869; Engl. transl., 717. Ferguson, J. M. and L. Phillips (1965) J. Chem.Soc., 4416. Fish, A. (1964) Quart. Rev., 18, 243. Fortuno, G. (1982) Ph.D. Thesis, Dept. of Physics, Harvard University, Cambridge, MA. Francisco, J. S., M. A. Findeis, and J. I. Steinfeld (1981) Znt. J. Chem. Kinetics,

13, 627. Fuke, K., A. Hasegawa, M. Ueda, and M. Itoh (1981), Chem. Phys. Lett. 84, 176. Glasson, W. A. (1975) Environ. Sci. Tech. 9, 1048. Gowenlock, B. G. and J. Trotman (1956) J. Chem.Soc., 1670. Gray, J. A. and D. W. G. Style (1952) Trans. Faraday SOC. 48, 1137. Gray, P. (1954) Proc. Roy. SOC. London Ser. A 221, 462. Gray, P. (1955) Trans. Faraday SOC. 51, 1367. Gray, P. and A. Williams (1959) Chem. Rev. 59, 239. Gray, P. and A. Williams (1960) Nature 188, 56. Gray, P., P. Rathbone, and A. Williams (1960) J. Chem. SOC., 3932. Gray, P., M. J. Pearson, and P. Rathbone (1961) J. Chem. SOC., 4006. Gray, P., P. Rathbone, and A. Williams (1961) J. Chem. SOC.,2620. Gray, P.,R. Shaw,and J. C. J. Thynne (1967) Progress Reaction Kinetics 4,63.

Griller, D . , K. U. Ingold, L. K. Patterson, J. C. Scaiano, and R. D. Small, Jr. (1979) J . Am. Chem. Soc. 101, 3780. Griller, D., J. A. Howard, P. R. Marriott, and J. C. Scaiano (1981) J . Am. Chem. Soc. 103, 619. Gutman, D. and H. H. Nelson (1983) J . Phys. Chem. 87, 3902. Gutman, D., N. Sanders, and J. E. Butler (1982) J . Phys. Chem. 86, 66. Hanst, P. L. and J. G. Calvert (1959) J. Phys. Chem. 63, 2071. Hassinen, E., P. Riepponen, K. Blomqvist, K. Kalliorinne, A. M. Evseev, and J. Koskikallio (1985) Znt. J. Chem. Kinetics 17, 1125. Heicklen, J. (1968) Oxidation of Organic Compounds-11 Adv. Chem. Series No. 76, p. 23. Heicklen, J. (1973) Chemical Kinetics Data Survey V . Sixty-six Contributed Rate and Photochemical Data Evaluations on Ninety-four Reactions, National Bureau of Standards Interim Report 73-206, D. Garvin, Ed.

268

THE DECOMPOSlTIONOF ALKYL NITRITES

Heicklen, J. and N. Cohen (1968) Adv. Photochem. 5, 157. ’ Heicklen, J. and H. S. Johnston (1962a) J. Am. Chem. SOC.84, 4030. Heicklen, J. and H. S. Johnston (1962b) J . Am. Chem. SOC.84, 4394. Hershenson, H. and S. W. Benson (1962) J. Chem. Phys. 37, 1889. Hoare, D. E. and Whytock, D. A. (1967) Can. J. Chem. 45, 865. Howard, J. A. (1972) in Adv. Free Radical Chem. 4, (G. H. Williams, Ed.), Logan Press, London, p. 49. Howard, J. A. and J. C. Scaiano (1984) Numerical Data and Functional Relationships in Science and TechnologyZI, Atomic and Nuclear Physics 13, 1. Hughes, G. A. and L. Phillips (1967) J. Chem. SOC.(A),894. Ingold, K. U. (1967) Pure and Applied Chem. 15, 49. Jacox, M. E. and F. L. Rook (1982) J. Phys. Chem. 86, 2899. Johnston, T. and J. Heicklen (1966) J. Phys. Chem. 70, 3088. Kabaskalian, P. and E. R. Townley (1962a) J. Am. Chem. SOC.84, 2723. Kabaskalian, P. and E. R. Townley (1962b) J. Am. Chem. SOC.84, 2724. Kabaskalian, P., E. R. Townley, and M. D. Yudis (1962a) J. Am. Chem. SOC. 84, 2716. Kabaskalian, P., E. R. Townley, and M. D. Yudis (1962b) J. Am. Chem. SOC. 84, 2718. Keller, B. A., P. Felder, and J. R. Huber (1986) Chem. Phys. Lett., 124, 135. Kelly, N. and J. Heicklen (1978) J. Photochem. 8, 83. Kennedy, B. R. and K. U. Ingold (1966) Can. J. Chem. 44, 2381. Kerr, J. A. and A. C. Lloyd (1968) Quarterly Rev. 4, 549. Kerr, J. A. and J. P. Wright (1984) Znt. J . Chem. Kinetics 16, 1321. King, G. W. and D. Mode (1962) Can. J. Chem. 40,2057. Kornblum, N. and E. P. Oliveto (1949) J . Am. Chem. Suc. 71, 226. Kuhn, L. P. and L. DeAngelis (1954) J. Am. Chem. SOC. 76, 328. Lahmani, F., C. Lmdeux, M. Lavoll&, and D.Solgadi (1980a) J. Chem. Phys. 73, 1187. Lahmani, F., C. Lardeux, and D. Solgadi (1980b) J. Chem. Phys. 73, 4433. Lahmani, F., C. Lardeux, and D. Solgadi (1986) Chem. Phys. Lett. 129, 24. Leggett, C. and J. C. J. Thynne (1970) J . Chem. SOC. (A), 1188. Lee, Y.-E. and K. Y. Choo (1986) Znt. J.Chem. Kinetics 18, 267. Levy, J. B. (1953)J. Am. Chem. SOC.75, 1801. Levy, J. B. (1956a) J . Am. Chem. SOC.78, 1780. Levy, J. B. (1956b) Ind. Eng. Chem. 48, 762. Lin. C.-Y. and M. C. Lin (1985) Int. J. Chem. Kinetics 17, 1025. Lin, C.-Y. and M. C. Lin (1986) J. Phys. Chem. 90, 425.

REFERENCES

269

Lissi, E. A., J. C. Scaiano, and A. E. Villa (1971) Chem. Commun., 457. Lissi, E. A., G. Massiff, and A. E. Villa (1973) J . Chem. Sm. Furuday Trans. 169, 346. Lissi, E. A., G. Massiff, and A. Villa (1975) Znt. J. Chem. Kinetics 7 , 625. Lissi, E. A., J. Collados, and A. Olea (1985) Znt. J. Chem. Kinetics 17, 265. Livermore, R. A. and L. Phillips (1966) J . Chem. SOC. (B), 640. Lorenz, K., D. Rhasa, R. Zellner, and B. Fritz (1985) Ber Bunsenges. Phys. Chem. 89, 341. Ludwig, B. E. and G. R. McMillan (1967) J. Phys. Chem. 71, 762. Ludwig, B. E. and G. R. McMillan (1969) J. Am. Chem. SOC.91, 1085. Marta, F. and L. Seres (1966) Ber. Bunsenges. Phys. Chem. 70, 921. McCaulley, J. A., S. M. Anderson, J. B. Jeffiies, and F. Kaufman (1985) Chem. Phys. Lett. 115, 180. McGarvey, J. J. and W. D. McGrath (1964) Trans. Furuduy SOC. 60, 2196. McGrath, W. D. and J. J. McGarvey (1964) Nature 201, 991. McGraw, G. E. and H. S. Johnston (1969) Znt. J. Chem. Kinetics 1, 89. McMillan, G. R. (1961) J. Am. Chem. SOC.83, 3018. McMillan, G. R. (1962) J. Am. Chem. SOC. 84,4007. McMillan, G. R. (1963) J. Phys. Chem. 67, 931. McMillan, G. R. and J. G. Calvert (1965) Oxidation Combust. Rev. 1, 83. McMillan, G. R., J. G. Calvert, and S. S. Thomas (1964)J. Phys. Chem. 68,116. McMillan, G . R., J. Kumari, and D. L. Snyder (1971) in Chemical Reactions in Urban Atmospheres, C . S. Tuesday, Ed., American Elsevier, New York, p. 35. Mendenhall, G. D., D. M. Golden, and S. W. Benson (1975) Znt. J. Chem. Kinetics 7 , 725. Milne, G. S . and C. Steel (1968) J . Phys. Chem. 72, 3754. Morabito, P. L., Jr. (1985) Ph.D. Thesis, The Pennsylvania State University. Morabito, P. and J. Heicklen (1985a) Znt. J . Chem. Kinetics 17, 535. Morabito, P. and J. Heicklen (1985b) J. Phys. Chem. 89, 2914. Morabito, P. and J. Heicklen (1987) Bull. Chem. SOC.Japan, 60,2641. Nagiev, M. F., Z. G. Petrova, and A. I. Sultanova (1956a) Zzv. Akud. Nuuk Azerb. SSR 2, 1 1 . Nagiev, M. F., Z. G. Petrova, and A. I. Sultanova (1956b) Dokl. Akad. Nuuk SSSR 109, 573; Chem. Abstr. 51, 9271h (1957). Nangia, P. S . and S. W. Benson (1980) Znt. J . Chem. Kinetics 12, 169. Napier, I. M. and R. G. W. Norrish (1967) Proc. Roy. SOC. London Ser. A 299, 317.

270

THE DECOMPOSITTON OF ALKYL NITRITES

Niki,H., P. D. Maker, C. M. Savage, and L. P. Breitenbach (1981a) Chem.

Phys. Lett. 80, 499. Niki, H., P. D. Maker, C. M.Savage, and L. P. Breitenbach (1981b) J . Phys. Chem. 85, 2698. Nussbaum, A. L. and C. H. Robinson (1962) Tetrahedron 17, 35. Ohbayashi, K., H. Akimoto, and I. Tanaka (1977) J. Phys. Chem. 81, 798. Oref, I. and B. S. Rabinovitch, (1968) J. Phys. Chem. 72, 4488. Park, C. R., S. A. Song, Y. E. Lee, and K. Y.Choo (1982) J. Am. Chem. SOC. 104,6445. Pate, C. T., B. J. Finlayson, and J. N.Pitts, Jr. (1974) J. Am. Chem. SOC.96, 6554. Patsevich, I. V., A. P. Topchiev, and V. I. Shtern (1958) Doklady Akud. Nuuk SSSR 123, 696; English transl., Proc. Acud. Sci. USSR 123, 913. Paul, H . , R. D. Small, Jr., and J. C. Scaiano (1978) J. Am. Chem. SOC., 100, 4520. Phillips, L. (1961) J. Chem. SOC., 3082. Phillips, L. and R. Shaw (1965), Proc. 10th Int. Symp. Combustion, p. 453. Pobedimskii, D. G., N. A. Mukmeneva, and P. A. Kirpichnikov (1972) Russ. Chem. Rev. 41, 555. Purkis, C. H. and H. W. Thompson (1936) Trans. Furuduy SOC.32, 1466. Radhakrishnan, G. and R. C. Estler (1983) Chem. Phys. Lett. 100, 403. Rebbert, R. E. (1963) J. Phys. Chem. 67, 1923. Rhasa, D. and R. Zellner (1986) Chem. Phys. Lett., 132, 474. Rice, F. 0. and E. L. Rodowskas (1935) J. Am. Chem. SOC.57, 350. Rose, M. (1979), Ph.D. Thesis, Department of Chemistry, Case-Westem Reserve University, Cleveland, OH. Sahetchian, K. A., R. Rigny, A. Heiss, and R.I. Ben-Aim (1982) Chem. Phys. Lett. 87, 333. Sanders, N . , J. E. Butler, L. R. Pasternack, and J. R. McDonald (1980) Chem. Phys. 48, 203. Schuck, E. A. and E. R. Stephens (1967) Environ. Sci. Tech. 1, 138. Shaw, R. and A. F. Trotman-Dickenson (1960) J. Chem. SOC., 3210. Shortridge, R. and J. Heicklen (1973) Can. J. Chem. 51, 2251. Sidman, J. W. (1958) Chem. Rev. 58, 689. Silverwood, R. and J. H. Thomas (1967) Trans. Furuduy SOC. 63, 2476. Simonaitis, R. and J. Heicklen (1975) J. Phys. Chem. 79, 298. Small, R. D. Jr. and J. C. Scaiano (1978) J. Am. Chem. SOC. 100, 296. Steacie, E. W. R. and D. S. Calder (1936) J. Chem. Phys. 4, 96.

REFERENCES

271

Steacie, E. W. R. and S. Katz (1937) J. Chem. Phys. 5 , 125. Steacie, E. W. R. and S. Rosenberg (1936) J. Chem. Phys. 4, 223. Steacie, E. W. R. and G. T. Shaw (1934a) Proc. Roy. SOC. London Ser. A 146, 388. Steacie, E. W. R. and G. T. Shaw (1934b) J. Chem. Phys. 2, 345. Steacie, E. W. R. and G. T. Shaw (1935a) J. Chem. Phys. 3, 344. Steacie, E. W. R. and G. T. Shaw (1935b) Proc. Roy. SOC. London Ser. A 151, 685. Steacie, E. W. R. and W. McF. Smith (1936) J. Chem. Phys. 4, 504. Stoddart, I. K., A. Nechvatal, and J. M. Tedder (1974) J. Chem. SOC.Perkin Trans. 11, 473. Sway, M. I. and D. J. Waddington (1984) J. Chem. SOC.Perkin Trans.II,63. Tanner, D. D., E. V. Blackburn, D. W. Reed, and B. P. Setiloane (1980) J. Org. Chem. 45, 5183. Tarte, P. (1952) J. Chem. Phys. 20, 1570. Tarte, P. (1953) Bull. SOC.Roy. Liege 22, 226. Taylor, W. D., T. D. Allston, M. J. Moscato, G. B. Fazekas, R. Kozlowski, and G. A. Takacs (1980) Int. J. Chem. Kinetics 12, 231. Thompson, H. W. and F. S. Dainton (1937) Trans. Faraday SOC. 33, 1546. Thompson, H. W. and C. H. Purkis (1936) Trans. Faraday SOC. 32, 674. Thynne, J. C.J. (1964) J. Chem. SOC., Suppl. I , 5882. Tuck, A. F. (1977) J. Chem. SOC. Farad. Trans. I I 7 3 , 689. Walker, R. F. and L. Phillips (1968) J. Chem. SOC. (A), 2103. Walling, C . (1967) Pure Applied Chem. 15, 69. Walling, C. and B. B. Jacknow (1960) J. Am. Chem. SOC. 82, 6108. Walling, C. and V. Kurkov (1966) J. Am. Chem. SOC. 88, 4727. Walling, C. and J. A. McGuinness (1969) J. Am. Chem. SOC. 91, 2053. Walling, C. and P. Wagner (1963) J. Am. Chem. SOC.85, 2333. Weaver, J., R. Shortridge, J. Meagher, and J. Heicklen (1975) J. Photochem. 4, 109. Wiebe, H. A. and J. Heicklen (1973) J. Am. Chem. SOC. 95, 1. Wiebe, H. A., A. Villa, T. M. Hellman, and J. Heicklen (1973) J. Am. Chem. SOC.

95, 7.

Wijnen, M. H. J. (1960) J . Am. Chem. SOC. 82, 3034. Wong, S. K. (1979) J. Am. Chem. SOC. 101, 1235. Wong, S. K. (1981) Int. J. Chem. Kinetics 13, 433. Wurzberg, E. and P. L. Houston (1980) J. Chem. Phys. 72, 5915. Yee Quee, M. J. and J. C. J. Thynne (1967) Trans. Faraday SOC. 63, 2970.

272

THE DECOMPOSITION OF ALKYL NIlWTES

Yee Quee, M. J. and J. C. J. Thynne (1968) Trans. Faraday SOC. 64, 1296. Yoffe, A. D. (1954) Research 7, S44. Zabarnick, S. and J. Heicklen (1985a) Znr. J . Chem. Kinetics 17,455. Zabarnick, S. and J. Heicklen (1985b) Znt. J . Chem. Kinetics 17,477. Zabarnick, S. and J. Heicklen (1985~)Znt. J . Chem. Kinetics 17,503. Zaslonko, I. S., S. M. Kogarko, E. V. Mozzhukhin, Yu. P. Petrov, and A. A. Borisov (1970) Kinetika i Karaliz 11, 296; Engl. transl., 249. Zavitsas, A. A. and J. A. Pinto (1972) J . Am. Chem. SOC. 94, 7390. Zellner, R. (1987) J . Chim. Phys., 84, 403. Zhang, F., J . S . Francisco, and J . I . Sreinfeld (1982)J . Phys. Chem. 86,2402.

Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS Gunther von Biinau and Thomas Wol€f Institut f i r Physikalische Chemie der Universitat Siegen, Siegen, West Germany

CONTENTS

I. Introduction 11. Structureof surfactantsolutions III. Distribution of solutes in microheterogeneoussystems IV. Elementary photochemical processes in micellar systems V. Photochemicaleffects A. Effects of the solution structure on photochemical reactions 1. Effects due to local concentration and cage effects 2. Preorientation of reactants B. Effects of photochemical reactions on the solution structure: Photorheologicaleffects VI. Spectroscopicprobes A. Critical micelle concentrations B . Micellar occupation statistics C. Micellar size and aggregation numbers D. Counterionbinding E. Polarity and polarizability F . Microfluidity G. Solubilizationsites H. Frozen micelles I. Intermicellarprocesses VII. Conclusions Acknowledgement References 213

274

PHOTOCHEMISTRY IN SURFAffANT SOLUTIONS

I. INTRODUCTION Aqueous solutions of surfactants, such as the ionic and nonionic tensides, are often highly dispersed colloidal systems. Apart from their widespread use as detergents and emulsifiers, they are receiving growing attention from photochemists exploiting and exploring the unique properties of these solutions. The “microheterogeneous” structureof surfactant solutions provides a high local concentration of substrate molecules, keeping their overall concentration low. This situation has a drastic influence on the selectivity of bimolecular photoreactions and on rates of recombinations involving the products of unimolecular decay processes. Photochemical reactions in surfactant solutions were first studied by Forster and Selinger (1) in their pioneering work on the formation of excimers of pyrene and of 2-methylnaphthalene in aqueous solutions containing cetyldimethylbenzylammonium chloride. Several years later the kinetics of related reactions were investigated in great detail and used for probing the structure of surfactant solutions containing substrate molecules (2-16). These studies have opened the way to a proliferation of photochemical work on various other colloidal systems, which have recently been reviewed (17-19). Related subjects include the photochemical cleavage of water (20), artificial photosynthesis (21), and the photochemistry in zeolithes (22). In this article we shall focus on recent work involving dilute aqueous surfactant solutions. As a background the thermodynamics and statistics of these solutions will be discussed first (Section II). The distribution of substrate molecules in microheterogeneous solution is considered in Section III. It is decisive for the kinetics of elementary photochemical reactions (Section IV), which depend on the peculiar colloidal solution structure. Effects of the microscopic environments on photochemical reactions are treated in Section V. Finally, the use of known photochemical systems as probes for studying details of the structureof surfactant solutions will be considered in Section VI.

II. STRUCTURE OF SURFACTANT SOLUTIONS Surfactants are characterized by solubility in water and by their ability to lower the surface tension of water. (The term “surfactant” was coined in 1950 (23) as an acronym of “surface active agent.”) Surfactantmolecules are amphiphilic, i.e., they consist of hydrophobic and hydrophilic parts. They form monolayers on surfaces and aggregates of widely different shapes, i.e. micelles, in solutions. Surfactants are classified as anionic, e.g. R-0SO3- Na+, R-COO- Na+,

STRUCTURE OF SURFACrANT SOLUTIONS

275

cationic, e.g. R-NH3+ Br-, R2N(CH3)2+C1-, zwitterionic or amphoteric, e.g. R-NH2+-CH2CH2-COO-, nonionic, e.g. R-(O-CH2CH2), -OH. Here R represents a long hydrophobic chain, e.g. a paraffin chain with 10 to 20 C atoms. Highly dilute aqueous solutions contain monomeric surfactant molecules (or dissociated ion pairs). These entities aggregate spontaneously when the concentration is raised beyond a certain specific, rather sharply defined critical surfactant concentration, usually and misleadingly called the “critical micelle concentration” (cmc). The appearance of micellar aggregates manifests itself by a change of solution properties, such as conductivity and light absorption and scattering, around the cmc (24,25). Further increase of the overall concentration leads to an increase of the number of micelles while the concentration of the molecular surfactant entities changes so little that it may be considered to retain the constant value of the cmc. This is a consequence of the law of mass action governing spontaneous aggregation. Light scattering data reveal that micelles are often spherical at low surfactant concentration. At higher concentrations a transition to rodlike and disclike micelles is observed. Many surfactants depart from this scheme in a manner which is dictated by the molecular properties of the aggregating units. For example, amphiphile molecules with two hydrocarbon chains R’ and R”, such as dioctadecyldimethylammonium bromide DODAB or chloride DODAC as well as the biologically important phosphoglycerides CH*-OPO,X

1

YH-o-Co-R’

CH2-O -CO-R" [X = H, CH,CH2N(CH3)3+, etc.] form bilayers at the cmc which may rearrange to spherical shells enclosing water-filled cavities. These ‘‘vesicles” are highly interestingobjects because they provide a means to separate hydrophilicreactants. A popular representation of spherical micelles was devised by Hartley (26). As indicated in Fig. 1, the Hartley model of, e.g., an anionic micelle exhibits a spherical electric double layer composed of bulky, hydrated anionic “heads” of surfactant molecules and their counterions in the aqueous phase, while the hydrophobic “tails,” visualized as sticks, form a hydrocarbon-like micellar interior. Because of the high surface charge density of the micelle, there is only little electrolytic dissociation of counterions. The Hartley model explains the low conductivity of micellar solutions and the way surfactants work as detergents by solubilizing (i.e. incorporating) hydrophobic substrates. The model fails to explain certain N M R and fluorescence data that demonstrate some contact of

276

PHoTocHEMlSTRY IN SURFACTANT SOLUTIONS

Figure 1. Hartley model of an anionic micelle.

the hydrocarbon chains with the surrounding water phase (27). Furthermore, as was pointed out by Fromherz (28), there is the difficulty of crowding in the center of the micelle when straight hydrocarbon tails are packed in an essentially radial arrangement. Both difficulties were resolved by Dill and Flory (29), who emphasized that neighboring segments in a hydrocarbon chain may have a local gauche and not only a trans conformation with respect to each other: see Fig. 2. According to their model, parts of some chains may be located on the surface of the micelle, and crowding is avoided, since segments can only occupy one lattice site within the volume of the micelle. As a consequence of the Dill-Flory model, the molecular order, i.e. rigidity, at the center of the micelle is higher than near its surface. The Dill-Flory model may be considered as a more rigorous version of the Hartley model (30). Both models are readily applied to other shapes of micelles, such as rods, discs, bilayers, and vesicles. Also, it follows that diameters of spherical, rodlike, and disclike micelles cannot exceed the total length of two hydrocarbon chains in all-trans conformation. The number of entities in one micelle, i.e. the aggregation number s, is therefore readily estimated for any given chain length r. Assuming equal densities p ( = 0.777 g/cm3) for micelles and solid n-alkanes, r may be obtained from the volume v and the constant cross section A ( = 2.385 X cm2) of alkane chains:

r =

A V

where v = mlp and m represents the mass of the alkane molecule. For a chain of n C atoms connected in an all-trans conformation at a constant C-C bond distance b (= 0.154 nm), r is also given by

STRUCTURE OF SURFACTANT SOLUTIONS

277

0 Figure 2. Dill-Flory model of an anionic micelle.

where a’ takes account of the space occupied by the chain ends. A different value, a, must be chosen to allow for the larger space requirements of polar head groups, so that the aggregation number can be written as

Values of s are given in Table 1 using a = 2.2 in order to match experimental results. Light scattering experiments provide information on micelle masses m,. For globular micelles m, = p s v = 4~ p r3/3. Since r is given by Eq. 1 for given surfactant molecules of mass rn = p v, the quantity (= 1 for spherical micelles)

(4)

contains only experimentally known quantities and may be taken as a test for sphericity of micelles. When aggregation leads to other micelle shapes, r has still the value given by Eq. 1. In the case of rodlike micelles having the shape of a spherocylinder of radius r and length 1+2r we have

PHoTocHEMlsTRY IN SIJRFACTANT SOLUTIONS

278

TABLE 1. Aggregation Numbers of Surfactant Molecules with Paraffhic Chains0 No. of C Atoms in Chain

Aggregation Number 56 73 92 113 137

12 14 16 18 20 “Calculated from Eq. 3.

3 1 q = l + - 4 r and for discs

(cf. Table 2). An important quantity to consider is the area per head group, A,, on the micelle surface (24). It may be deduced from the surface/volume ratio, which is 3/r for spheres; in this case A, = 3v/r = 3A. Further expressions for A, are given in Table 2. It is seen that transitions sphere +rod +disc are accompanied by decreasing values of A,, i.e. increasing head group repulsion in ionic micelles, which must be overcompensated by the hydrophobic effect favoring association. Consequently, surfactants with two hydrophobic chains per head group, such as the phosphoglycerides, prefer the formation of large disclike micelles (bilayers), which may rearrange into spherical vesicles ( 31). More sophisticated considerations are, of course, required when hydrophobic chains are branched or contain aromatic rings, functional groups, etc., or when additives affect head group repulsion. Apart from thermodynamic issues, the general packing problem and the determination of average cross sections A of hydrophobic chains is difficult so that Eqs. 4-6 are in general not readily applicable. Because of their size, micelles diffuse only slowly. According to the StokesEinstein relation the diffusion constant D of spherical objects of radius r in a medium of viscosity q is given by

D =

kT 6mqr

(7)

~3

n r3

+

Volume

"A = cross section of hydrophobic chain ( = 23.85 x bSpherocylinderof total length I 2 r . 'Generated by rotating cross sections of spherocylinders.

Disc'

Rodb

Sphere

Shape

cm2 for alkane chains).

4nr2

Surface

TABLE 2. Geometric Relations Concerning Micelles of Different Shapes

3A

Area per Head Group on the Micelle Surface"

280

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

where T is the temperature and k is Boltzmann’s constant. Neighboring micelles, being present at a molar concentration c,, are separated by an average distance d = (L c , ) - ~ ’ ~

(8)

(Lis Avogadro’s constant). Therefore, the time f required for diffusion through this distance may be estimated from r = - =d2 2 0

3.rrqrd2

kT

(9)

For spherical micelles at c, = loF3M with an aggregation number of 80, the orders of magnitude are r = 2.3 nm,D = lo-’’ m2/s, d = 12nm, r = s. From a thermodynamic point of view aggregation of amphiphilic entities may be envisaged as a phase separation process (32). Alternatively, aggregation can be described by the law of mass action. Rusanov (33) has shown that these two approaches are equivalent, since the separation of a microscopic phase which is bounded by a curved surface does not take place at a sharp transition point on the concentration scale as is characteristic for macroscopic phases. Let x1 denote the’ mole fraction of free monomer surfactant molecules, and xJs the mole fraction of micellar aggregates of size s. Equilibrium between aggregates and monomers is defined by a constant

where R is the gas constant,& is the activity coefficient of free monomers, and p! and p! are standard values of the chemical potential; p! refers to free monomers and I.,” to monomers aggregated in micelles of size s. (Activity coefficients of the micelles are assumed to be unity). Eq. 10 represents the distribution of micelle sizes explicitly if the dependence of k! on s is known. Since the overall surfactant concentration i s given by xo =

XI

+

c m

x,

s=2

we obtain for the number average of micelle sizes m

s, =

STRUCI'URE OF SURFACTANT SOLUTIONS

281

and for the weight average

c c m

,s

sxs

s=2

=

P

s=2

xs

Furthermore, the most probable micelle size S i s calculated from the maximum of the distribution function by taking logarithms of both sides of Eq. 10, rearranging, and differentiating:

i.e. ape RT RT (s) = - + T as s2 S

InX,fi

+ I4 S

I2

Tanford (2,9,10) has considered explicitly the dependence on s of the quantity -. F :, which is supposed to be the sum of a hydrophobic and an electrostatic contribution. The hydrophobic part is represented as a linear function of the area per chain, which decreases with increasing micelle size s. The electrostatic part depends on the area per head group on the micelle surface; it is given as a three-term series of negative powers of this quantity. Empirically, size distributions are often approximated by p!

where b is a measure of the width of the distributionfunction (34).Size distribution functions of globular micelles are often quite narrow, so that T = s, = s,. However, rodlike and disclike micelles may have broad and asymmetric distributions (35). In an interesting, more rigorous statistical treatment of the aggregation process Rusanov (33) has connected the concentration c, of aggregates containing s monomers with the surface tension u at a micelle-water interface of area A. Introducing a function

282

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

the size distribution is given by

where c1 is the concentration of free monomers and the standard value of the concentration is defined by ce =

[

]

2nmkT h2

2 ' 3

(19)

At low surfactant concentration, c, is a monotonically decreasing function of s. Above the cmc the distribution function exhibits a maximum corresponding to the most probable micelle size T.Further information, including expressions for calculatingTfor rod- and disclike micelles and for transitionsbetween the various micellar shapes, may be taken from Rusanov's article. The size and shape of micelles are determined by a delicate balance between various factors, such as chemical constitution, electricalrepulsion of head groups, amphiphile and solute concentration, and temperature. The addition of electrolytes will in general raise aggregation numbers of ionic micelles and may even induce sphere-rod transitions. Temperature has an enormous influence on aggregation numbers of nonionic micelles, but only a little effect on those of ionic and amphoteric micelles. There is a vast literature covering the subject (24,25,36). Experimentally, size distributions have been obtained from relaxation times measured after the equilibrium between monomer amphiphiles and aggregates are subjected to a sudden change (in T-jump, p-jump, and shock tube studies). Relaxation was found to take place in two time regimes: a fast process (10-4-10-3 s) assigned to the exchange of monomers between micelles and the surrounding aqueous phase, and a slow process (0.014.1 s) ascribed to the formation and dissolution of micelles (37,38). Both relaxation times depend on micelle concentration, aggregation number, and width of the distribution function. Explicit expressions were derived by Aniansson et al. (38), assuming the distribution to be Gaussian.

HI. DISTRIBUTION OF SOLUTES IN MICROHETEROGENEOUS SYSTEMS

The addition of solutes to micellar solutions of surfactants in water may give rise to different phenomena depending on the chemical nature of the additive. Ionic solutes carrying the same charge as the head groups of an ionic micelle

DISTRIBUTION OF SOLUTES IN MICROHETEROGENEOUS SYSTEMS

283

will be repelled. Oppositely charged ions, however, may replace counterions at the micelle surface and thus be concentrated. Hydrophobic solutes are concentrated by incorporation (“solubilization”) in the micelle interior. The capacity of a micelle for solubilizing hydrophobic additives depends on specific properties of the solute. It may be so large that an “oil in water” ( O W )emulsion is formed which is thermodynamically stabilized by only a few surfactantentities. Likewise, stable “water in oil” (W/O) emulsions are obtained by adding surfactants to a dispersion of aqueous solutions in some hydrophobic liquid. In these microheterogeneous systems so-called “reversed micelles” are assumed, i.e. small globular droplets constituting the aqueous phase. The size of reversed micelles is readily controlled by changing the water content of the W/O emulsion. While this feature is of some interest to photochemists, we shall be primarily concerned with ordinary micelles in an aqueous surrounding. In general, the chemical potential of the solution in the micellar phase must equal that in the surrounding aqueous medium when thermodynamic equilibrium is established. Nonpolar solutes, such as the permanent gases, which do not interact strongly with either phase may be distributed rather evenly over the whole microheterogeneous system (39). On the other hand, typical electrolytes are practically restricted to the aqueous medium, while molecules of hydrophobic substances, e.g. hydrocarbons, are almost totally sequestered in the micelles. Following Infelta and W t z e l (M),we consider the transfer of a single solute molecule S, from the aqueous phase to a micelle Mi-l already occupied by i-1 solute molecules so that a micelle Mi is obtained:

Here K‘ and k, represent rate constants. The following assumptions are made: 1. K’ is independent of i ; 2. k, = i k’ is proportional to i.

When equilibrium is reached, we have

Setting

284

PHOTOCHEMISTRY IN SiJRFAmANT SOLUTIONS

it follows from Eq. 21 that [Mil

=

2

NIT

The total concentration of micelles is

i=O

i=O

and the probability for a micelle to be occupied by i solute molecules is

i.e., the distribution of solute molecules among micelles is described by Poisson statistics. The mean occupancy number (i) of micelles is readily identified as the quantity introduced in Eq. 22:

It may also be noted from Eq. 22 that the ratio

corresponds to the Nernst distribution law.

The Poisson distribution of solute molecules among micelles has, therefore, a high degree of plausibility and is widely used (4147). It has also been derived by purely statisticalreasoning (42). Its main difficultyis the infinite sum appearing in Eq. 24. It is known that some types of micelles can only accommodate a limited number k of solute molecules. In this case a binomial distribution is more appropriate (45):

In the limit k -+ Eqs. 25 and 28 become identical. Also at low average concentration the probability of unoccupied micelles, i.e. Po(z) or P&k> respectively, is nearly identical for all values of k; the same holds for the probability of singly occupied micelles, P l ( z ) and P,(z,k) respectively as long as z << 1 . Some of

DISTRIBUTION OF SOLUTES IN MICROHETEROGENEOUS SYSTEMS

Figure 3. Poisson distribution Pi(z) and binomial distribution P,(z,k) for i andzS3.

285

2, k =z 3 ,

these probability functions are illustrated in Fig. 3 for k CQ and for a few low values of k. Distribution statistics do not differentiate between different sizes and shapes of micelles and different locations of solute molecules with respect to the center of the micelle. The occupancy of a micelle by a solute molecule may lead to its incorporation in the micellar core, such as may be expected for hydrophobic solutes. Substrate ions, on the other hand, may replace given counterions of ionic micelles and may be firmly bound by their surface charge. For our purposes we shall only be concerned with systems in which the overall solute concentration c is large compared to [SJ,the concentration of solute molecules in the aqueous phase (c >> [S,]), i.e., practically all solute molecules are somehow attached to micelles. The concentration of micelles c, is obtained from the overall surfactant concentration c,, the aggregation number F, and the surfactant concentration in the aqueous phase. It follows from the law of mass action, Eq. 10, that the latter quantity is almost identical with the critical micelle concentration when s is reasonably large, i.e. c1 = cmc; therefore

286

PHOTOCHEMISTRY IN S W A C T A N T SOLUTIONS

Under these conditions micelles will be occupied by an average number

of solute molecules. It is more difficult to establish the preferred location and orientation of solute molecules within micelles. This information is required for the interpretation of kinetic results that may depend on these parameters (Section V). Often photochemical probes are used in attemptsto analyze relevant data (Section VI).

IV. ELEMENTARY PHOTOCHEMICAL PROCESSES IN MICELLAR SYSTEMS

The remarkable capability of micelles to solubilize hydrophobic substances in water and locally to concentrate ions has a decisive influence on the course of elementary photochemical processes. In this respect micelles are sometimes referred to as “supercages” and as “microscopic reactors” which favor bimolecular processes (17,18). Also the term “micellar catalysis” is used to describe the higher rate at which bimolecular photochemical reactions proceed. Moreover, ionic micelles, being surrounded by an electric double layer, may promote or inhibit unimolecular processes involvingionization as well as electron transfer. Bimolecular reactions of excited species A* with substrate molecules B (which may be identical with A) may be classified as energy transfer reactions leaving the A-molecule intact and photoreactions leading to chemically different reaction products. B-molecules act as quenchers when radiative transitions A* --f A hv compete with the bimolecular process. Since the emission can also be studied in the absence of quenchers, it may be used as a probe for investigating the bimolecular reaction. Photoreactions require a contact between A*- and Bmolecules, i.e. diffusion; energy transfer of the Forster type (48-52) can be fast in comparison with relevant diffusion times. The time scale T for energy transfer depends on the natural lifetime T~ of the excited donor molecule A*, on the distance r between donor and acceptor, and on the distance & for which energy transfer and radiative transition have equal probability:

+

T = T o [ % ]

6

Typical values are q, = 1 ns, r = 2.5 nm (representing a typical micellar radius), & = 5 nm, and T = 16 ps. Assuming a diffusion constant of D =

ELEMENTARY PHOTOCHEMICAL PROCESSES IN MICEZLAR SYSTEMS

287

m2/s, we may estimate the average distancz d through which a molecule within the micelle will diffuse during the time T :

d =

fiT

= 0.2

nm

Presumably, this is an upper limit, since the assumed value of D is typical for ordinary solvents and not for the more rigid medium of a micellar interior. Therefore the rate of energy transfer between molecules in micelles or in the double layer surrounding a micelle depends on the quasistatic distribution of distances between A*- and B-molecules in micelles (“static quenching”). As an example, we consider the fluorescencedecay of A*-molecules following pulse excitation. Initially (at time 7 = 0) the system contains a total number No of excited species distributed over micelles which contain an average number z of quencher molecules B. Using Poisson statistics, the probability that a micelle contains no quencher molecule at all is given by e-‘. A*-molecules in these micelles decay with the fluorescence rate constant $. In all other tnicellesoccumng with probability 1 - e-‘-fluorescence and energy transfer compete. Assuming an average energy transfer rate constant k (= I/?), the total decay rate constant of A*-molecules in micelles containing at least one quencher molecule B is

(33)

k , = k , + k

The total number N of excited A*-molecules (at time t > 0) is therefore a sum of two contributions:

In general, the measured fluorescence intensities I, I, are proportional to the numbers N , No of excited species, so that Eq. (34) can be written as In

I 10

=

-z -

t

+

In 11

+ (e‘

- I)e-k’]

(35)

In the limit z << 1 EIq. 35 takes the form

while for t -+ co In

I I0

=

-z -

$t

(37)

288

PHOTOCHEMISTRYIN SURFACTANT SOLUTIONS

and for r --* 0

It should be noted that the derivation of Eq. 35 rests upon the simplifying assumption that the energy transfer rate constant k is independent of the number of quencher molecules occupying the same micelle as a given excited species A*. Howeve:, in view of Eq. 31, k should be a complicated increasing function of the mean occupation number z. Various models have been discussed in the literature to treat this problem (9,13,53-56). Rodgers and Da Silva e Wheeler (9) have assumed that k is proportional to the number of quencher molecules actually present in micelles containing an excited species A*. This leads to 36. Recently, Berberan-Santos and Prieto (55) have treated a more detailed model according to which A- and B-molecules occupy specific locations a and r within a globular micelle of radius r (see Fig. 4). Let x designate the distance between a given pair of A*- and B-molecules in a micelle they define a quantity

a.

and obtain the result

In

I I0

= z(J

-

1)

- br

Experimental tests of these models require highly accurate time-resolved quenching data. Calculated results are plotted in Fig. 5 for z = 2 and time units Ilk = l/b.The graphs of Eqs. 36 and 40 are seen to be virtually identical, while that of Eq. 35 represents slightly higher quenching efficiencies.

Figure 4. Definition of the quantities used in Eq. (39).

ELEMENTARY PHOTOCHEMlCAL PROCESSES IN MICELLAR SYSTEMS

289

t

Figure 5. Typical fluorescence quenching curves in time-resolved studies. Solid line: Eqs. 36 and 39 (coinciding). Dotted line: Eq. 35. Broken line: ln(I,,/Z) = -k, t (for reference).

A further test is provided by steady state measurements. Assuming an average quenching rate constant k would lead to a constant fluorescence probability kdk, in micelles occupied by an arbitrary number of quencher molecules; the total time-independent fluorescence probability would then be given by

More realistically, k is assumed to increase with the number i of quencher molecules present in a given micelle containing an excited A*-molecule. Taking (9757)

k = ik’

we obtain instead of Eq. 41

(42)

290

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

i= 1

i k’

+ k0

(43)

i!

A Stern-Volmer plot of ZJZvs. z , given inFig. 6, shows that positive deviations from Stern-Volmer kinetics are expected when quenching is efficient, i.e. for large quencher concentrations (or large mean micellar occupation numbers z) and also for large values of the quenching constant k. Comparing Eqs. 41 and 43 by plotting ln(ZJZ) vs. z as in Fig. 7, it is seen that these curves coincide at low values of z and are identical when k0 << k. In this case z may be obtained directly when ln(Zdr) is plotted vs. the analytical quencher concentration (58,59); cf. Section III, Eq. 30. There is a vast body of experimental data on fluorescence quenching in micellar solutions. Most authors have used Eq. 36 or its analogues for the interpretation of their data (59-75). Results from steady state measurements are adequately represented by Eq. 43 or its limiting cases (76-87). An extension of the static quenching models is required when diffusion cannot be neglected, i.e. when “dynamic quenching” is operative. Diffusion is necessarily involved in photoreactions. It must be considered when micelle sizes are particularly large, as in reversed micelles (70,81). Diffusion also becomes

I 1

z

I 2

I

3

Figure 6. Steady state fluorescence quenching data: fluorescence intensity in the absence (lo)and presence (0of quenchers. z = mean occupation number of quencher molecules per micelle (proportional to analytical quencher concentration). Curve a: k’ = b,Eq. 43; curve b: k = b, Eq.41; curve c: IdZ = 1 + d2 (Stern-Volmer reference line).

ELEMENTARY PHOTOCHEMICAL PROCESSES IN MICELLAR SYSTEMS

291

z

Figure 7. Steady state fluorescence quenching as a function of the relative magnitudes of the rate constants for quenching, k’ (or k) and for radiative transition, k,. Solid lines: Eq. 43, broken lines: Eq. 41. Curve a: k‘ = 100 k, (k = 100 k,). Curve b: k‘ = 10 k, (k = 10 k,). Curve c: k’ = k, ( k = k,).

important when the Forster radius R,, is small and when emission lifetimes are long. Both criteria are fulfilled when triplet states are involved (88). Several authors have treated various aspects of dynamic quenching in detail (89-102). Infelta et al. (89) have considered the escape of quencher molecules from micelles as a competing process. Assuming the rate constant of escape, k: = i k,, to be proportional to the number i of quencher molecules in a micelle, they derived the expression In

I I0

=[ + k

k,

1’

* Z

kp[-(k

+ k,)t] -

11

- bf

ke --kk + k,

2

(In the limit k, << k Eqs. 44 and 36 become identical.) Diffusion was explicitly considered by Hatlee et al. (97), who solved the diffusion equation for the three different situations illustrated in Fig. 8. The fist of these topologically distinct situations (Fig. 8a) refers to reactions of excited donor (or reactant) molecules D*with acceptors A being confined to the micelle surface, as may be expected for ionic reactants. The micelle interior was treated as a homogeneous phase. In the second case (Fig. 8b) excited donor and acceptor molecules occupy the same (homogeneous)micelle interior. Diffusion was treated

292

00“0. PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

A

A

Figure 8. Dynamic quenching situations: (a)excited donor molecule D* inside a micelle, acceptor molecules A on the surface; (b) both donor and acceptor within the micelle; (c) both donor and acceptor on the surface.

as a three dimensional random walk in a sphere with “reflecting” barriers. The third case (Fig. 8c) deals with reactants that are restricted to diffusion within the micelle surface. In all cases explicit solutions of diffusion kinetic differential equations were derived and expressed as sums of infinite series. Graphs of calculated concentrations c(t) of the excited donor resemble Fig. 5 (ln[c(r)lc(O)] vs. t). A distinction between static and dynamic quenching is therefore difficult to make from decay curves only, but must rely on additional information such as spectroscopic, thermodynamic, and statistical data and on product analyses.

V. PHOTOCHEMICAL EFFECTS A.

Effects of the Solution Structure on Photochemical Reactions

Three principally different effects influence the kinetics of photoreactions in microheterogeneous solvents: (i) effects due to locally different concentrations, (ii) cage effects, and (iii) effects due to preorientation of reactant molecules. In contrast to these effects we will not recognize it as a specific micellar effect when other solvent properties like polarity, polarizability,availability of protons, viscosity, etc., which are displayed by a microheterogeneous solvent at some sites are responsible for observed results. 1. Effects Due to Local Concentration and Cage Effects The rates or efficienciesof bimolecular photoreactions such as excimer formation, photodimerization, and photoaddition can be strongly affected by using micellar solvents when the reactants associate with the micelles: When low concentrations of reactants are solubilized in solutions of high concentrations of micelles, the reactants will be separated by association to different micelles and the reaction will be inhibited. Under opposite conditions high local concentrationswill cause an increase of quantum yields compared to homogeneous solutions of equal analytical concentration. Thus in micellar solution the efficiency of bimolecular

293

PHOTOCHEMICAL EFFECTS

photoreactions depends on occupancy numbers z defined by Eq. 30. The effect was first observed by Forster and Selinger (1) and used for investigating excimer formation of several aromatic compounds. Examples for enhanced yields were reported for the photodimerization of acenaphthylene ( 103)

trans

and of anthracene derivatives (104,105)

0hl

Ohh

A

for the photocycloaddition of acrylonitrile to acenaphthylene (106)

and of isobutylene to cyclohexenone (107)

8hv

H3C

+

(48)

H3C

CH3

Quantum yields of the photodimerization of some anthracene derivates A in ionic surfactant solutions are given in Table 3 as functions of the micelle concen-

TABLE 3. Dimerization Quantum Yields QD and Ratios @W,/'BDhh of Head-to-Tail vs. Head-to-Head Photodimerization of 9-Methyhthracene, 9-Hydroxymethylanthracene, 9-Anthracene Propionic Acid, and 9-Anthracene Carboxylic Acid (Concentration c,J in Several Homogeneous and Micellar Solutions at 25°C" Solvent

z

cm,

CA.

~ o - ~ M ~ o - ~ M 10%~

@Dhf

PMethylanthracene 1.40 2.95 9.27

10.8 18.3 46.7

1.01 1.01 1.02

1.01 10.51

10.0 50.5

1.60 1.43

Diethyl ethe?

1.44 2.45

11.2 20.8

1.51 1s o

Methanol

0.98

8.8

2.01

Cyclohexane

Benzene

CTAB

0.36 0.44 0.89 1.23 1.76 1.81 2.05

3.0 3.0 1.5 3.O 0.75 3.0 3.0

1.08 1.33 1.33 3.70 1.32 5.43 6.15

6.1 9.2 11.9 21.6 16.7 28.5 29.7

1.4 2.0 1.5 2.0 2.3 2.0 2.5

CTAC

0.29 0.34 0.42 0.85 1.02 1.23 1.71 1.81

4.5 3.0 3.O 1.5

1.30 1.02 1.27 1.21

10.3 8.3 12.1 15.7

1.7 1.9 2.0 1.8

3.O 0.75 3.0

3.O

3.06

3.70 1.28 5.43

29.7 22.6 38.4

2.0 1.8 2.0

0.29 0.35 0.41 1.44 1.63

4.5 3.0 3.O 0.75 3.0

1.29 1.05 1.24 1.08

11.4 11.2 16.2 22.0 63.0

1.7 2.0 2.0

SDS

Cyclohexane

Benzene

294

4.90

9-Hydroxymethylanthracene 1.40 1.31

2s .o

2.7 4.5

1.9

4.0 4.0 >15

2.9

TABLE 3. (Continued) Solvent

Z

cm, 10-~w

CA*

~ o - ~ M lo3@,

QDht

Diethyl ethe?

1S O 1.15

6.2 3.8

1.2 1.2

Methanol

1.25

3.3

3.2

CTAB

0.45 0.91 1.79

3.0 1.5 0.75

1.34 1.36 1.34

2.2 3.1 6.5

0.96 0.76 0.70

CTAC

0.89

1.5

1.34

6.3

0.76

SDS

0.44

3.O 1.5 0.75

1.31 1.27 i .30

4.3 7.9 13.0

1.06 0.67 0.62

Diethyl ethe? Methanol CTAB CTAC SDS

9-Anthracene Propionic Acid 1.51 1.47 1.19 1.5 1.26 1.20 1.5 1.25 1.17 1.5 1.28

3.1 4.6 3.4 3.7 5.8

3.5 8.9 1.9 1.2 0.91

Diethyl ethe?

9-Anthracene Carboxylic Acid 2.18

13.9

4.9

Methanol

2.01 12.38

4.2 23.2

6.5 4.8

Ethanol

31.2 47.1 2.1 3.9

>15 >15 5.2 >15

CTAB

SDS

0.85 1.73

0.67 1.41

3.0 1.5

9.21 14.01 2.01 2.11

2.81

0.75

2.11

5.2

0.57 1.25 2.00

3.0 1.5 0.75

1.72 1.87 1S O

1.2 1.8 2.3

15

6.8 2.3 1.4

ac,,, = concentration of micelles; z = occupancy number. bAt 20°C.

295

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

296

tration c, and the mean number z of A-molecules per micelle. Yields are seen to be of the order of lo-*. It follows that the time scale of dimerization is two orders of magnitude longer than that of the competing unimolecular decay. According to Eq. 9 the time required for diffusion of micelles through intermicellar separations is about s at the micelle concentrations given in Table 3. Therefore, the observed dependence of the yields on c, indicates a small contribution of intermicellar reaction to the total yield of dimerization. The probability of dimerization by intermicellarreaction is proportional to [A]*. That of the intramicellarreaction depends on z. Provided the aggregation number s is a constant, the probability of micelles being occupied by one excited and i-1 ground state A-molecules is proportional to iPj where Pi may be taken from Poisson statistics (Eq.25). Assuming the probability of dimerization to be given by (i-l)k, we may express the intramicellar reaction probability of excited Amolecules by a quantity proportional to iPi[k, (i-l)k], where k,is the probability of the unimolecular decay processes. The total reaction probability is proportional to

+

i Pi i= 1

[b +

Since [A] = z c,

(i - l)k]

+ k,

[A]’ = k+z

+ k 2 + k,[A]’

(49)

the dimerization quantum yield may be written as

Plotting l/QD vs. l/z, a straight line is expected for constant c,:

Experimental results (Table 3) are in reasonable agreement with Eq. 51; cf. Fig. 9. It should be noticed, however, that the assumed constancy of aggregation number and applicability of Poisson statistics may be quite unrealistic for high values of z; cf. Section V.B. In the reactions mentioned so far hydrophobic solubilizates are sequestered by the lipophilic part of micelles or microemulsions. Also, hydrophilic substrates may be gathered in the water pools of reversed micelles, or products of electron transfer reactions may be separated by solubilization of the donor (or acceptor) in the hydrophobic parts of the microheterogeneous solvent and the acceptor (or donor) in hydrophilic regions, generally bulk water. This kind of charge separation is being investigated in numerous laboratoriesin order to design systems capable of storing light (solar) via photocatalytic water splitting. Solutions of micelles (108), microemulsions (109), and synthetic vesicles (110) have been used for

297

0

1

2

1 z

3

Figure 9. Quantum yields of photodimerization of 9-methylanthracene in micellar solutions of CTAB (0) and CTAC &7) as a function of mean occupation numbers z. Straight lines drawn according to Eq. 51 using c, = 0.003 M,k/k,, = 0.01 1 and 0.016, k,/k,, = 730 and 1080 for CTAB and CTAC, respectively.

these purposes. For instance, Ford et al. (111) used an aqueous solution of anionic vesicles with methylviologene cations (MV2+) adsorbed at the surface (see Fig. lo), a hydrophobic dye ([R~(bpy)~]~') solubilized in the lipophilic membrane, and an electron donor ethylene diamine tetraacetic acid (EDTA) in the waterpool inside the vesicles. Electronic excitation of the dye leads to electron transfer to M Y 2 + , which can be regenerated by reduction of water (evolution of hydrogen). The oxidized dye may be reduced by EDTA, which is consumed in this system. Great stability of the vesicles is desirable and can be achieved via polymerization of the lipophilic area of the vesicles (1 10). About 80% of the countefions of ionic micelles are bound to the micelle surface, so that a high local counterion concentration is achieved. Therefore any interaction of counterions with excited molecules associated with the micelles will be favored in comparison with homogeneous solutions that contain these ions. For instance, heavy atom interactions were observed in micellar solutions containing heavy anionic counterions (104,112-1 14) as well as cationic ones (115-118). The heavy atom effect of bromide counterions was proven by comparing the yields of excited singlet and triplet molecules after flash irradiation of aromatic molecules (112): the observed decrease of the singlet yield (fluorescence) was shown to reappear as an increase in the triplet yield (see Table 4). Using this effect in the photodimerization of acenaphthylenes, the stereoselectivity of the reaction may be directed: Mayer and Sauer as well as Ramesh and Ramamurthy found increasing amounts of triplet products in the photodimerization of acenaphthylene (trans dimer, Eq. 45) and its isomers

298

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

Figure 10. Microscopic detail of a solution of anionic surfactant vesicles used for photochemical reduction of methylviologene (MV). EDTA ethylenediamine tetraacetate; [R~(bpy)~]*+: mbidiumtrisbipyridylium complex.

(113,114) when the counterionswere changed from chlorideto bromide or iodide. Enhanced triplet state formationof aromatic and haloaromaticcompounds-partly leading to phosphorescence observable at room temperature- was found by several authors (115-1 18). The nucleophilic substitution by CN- in nitronaphthalenes

was studied by Hautala and Letsinger (119). They found increases of the quantum yields up to 6800-fold when the reaction was performed in cetyltrimethylammoniumchloride (CTAC) micelles, while in sodium dodecylsulfate (SDS) micelles decreases of the quantum yields were observed. The effects were only partly due to the high local concentration of CN' at the surface of the cationic CTAC micelles and to the repulsion of CN- by the anionic SDS micelles, since the excited state properties of the aromatic substrates are sensitive to solvent polarity. Similarly, despite high local concentrations of OH- ions at the surface of cationic tetradecyltrimethylaonium chloride W A C ) micelles, the quantum yield of the bimolecular alkaline photohydrolysis of 2 ,Cdinitroanisoles

0.66 0.95 0.72

0.85

0.33 0.69 0.68

-

0.33'

0.89' 0.68"

0.85C,d

0.26

CTAC

0.29

Ethanol

0.30"

Ethanol (Ref.)

-

0.15

0.01 0.36

0.03b 0.32"

0.91 0.39 0.69

0.34

0.74

CTAC

0.67'

0.72"

Ethanol (Ref.)

Triplet (@,)

0.54

0.08

CTAB

'A. R. Horrocks and F. Wilkinson, Proc. R . Sac. London Ser. A306, 257 (1968). bC. A. Parker, Photoluminescence of Solutions, Elsevier, Amsterdam, 1968. 'S. C. Shim and J. S . Chae, Bull. Chem. SOC. Japan 55, 1310 (1980). 'In diethyl ether.

Anthracene 9-Methylanthracene 9, 10-Dimethylanthracene Fluorene Indeno[2,l-a-]indene

Compound

Fluorescence (af)

Quantum Yield

-

0.92' 1.00"

0.02 0.60 0.29

1.00'

1.02"

Ethanol

0.41

1.01

CTAB (Ref.)

+

@,

0.93 0.99 0.98

1.oo

0.95

1.00 0.96 1.08

1.09

CTAB 1.oo

CTAC

@f

TABLE 4. Fluorescence and Triplet Quantum Yields of Aromatic Compounds in Ethanol and Aqueous Solutions of Cetyltrimethylammonium Bromide and Chloride (CTAB and CTAC) Measured at (24 2 2)"C

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

decreased compared to aqueous solutions.This result was explainedby a reduction of the triplet state lifetime of 2,4-diNtroanisoles in the micellar environment (120). Quantum yields of the monomolecular photohydrolysis of mmethoxybenzyl acetates

are increased in solutions of cationic and anionic micelles (121) in comparison with water-dioxane mixtures. In this case, the effect is simply due to the higher light transmission of the micellar solvents. The term “cage effect” was originally applied to geminate radical pairs held together within a cage of solvent molecules prior to diffusion. This situation favors recombination of singlet radical pairs. Triplet radical pairs can recombine only after their spin correlation has been removed by hyperfine interactions. Therefore they usually live longer than singlet radical pairs and have a greater chance to escape the solvent cages. Similarly, in surfactant solutions the micellar ‘‘cage effect” prevents intermediates of photochemical (and thermal) reactions from leaving the micelle within which they are formed, so that a preferred formation of (re)combination products is observed. T m o and Cherry (122) irradiated unsymmetrically substituted dibenzylketones benzene

CTAC

in micellar and homogeneous solutions: They found 50% cage products compared to a statistical distribution of possible products in homogeneous solutions. Turro and Mattay (123) as well as Turro and Weed (124) successfully used the cage

301

PHOTOCHEMICAL EFFECTS

effect for investigating magnetic field effects on the kinetics of radical pair reactions. Influences of the size of micelles cannot be expected in these reactions, since benzyl radicals are relatively long-lived and not reactive with respect to solvent molecules. However, such effects are observed when phenyl radicals are formed within micelles. Phenyl radicals in hydrocarbon solvents always give benzene as a product formed by abstraction of hydrogen from the solvent. This is also the case in large micelles of polyoxyethylene (n = 23) dodecylether (Brij-35) after intermediategeneration of phenyl radicals by irradiation of diphenylmercury (125) (see Table 5): CTAB. SDS

hexane

*98%

(56)

-

=

1%

However, in the smaller micelles of cetyltrimethylammoniumbromide (CTAB) and of SDS significant amounts of the combination product biphenyl were found, increasing with decreasing micellar volume. These experiments also show the difference from ordinary cage effects, which increase with solvent viscosity: the “microviscosity” of SDS micelles is smaller than that of CTAB micelles (measured by several spectroscopic probes; see Section VI), so that opposite results (if any) should be excepted from ordinary cage effects. TABLE 5. Product Yields of the Photolysisof Diphenylmercuryin Various Solvents Solvent

Benzene: %

Biphenyl: %

Micellar Weight, g mol-’

-

n-Hexane Methanol

100 100

-

0.1 MBrij-35 0.1 Mcetyltrimethylammonium

100

-

61700‘

96 98

>0.5

30000 17800

bromide

0.1 M sodium dodecylsulfate

1.5

Source: Ref. 125. Values were determined by a W detector after liquid chromatography. Because of the 100 times higher extinction coefficient of biphenyl, the determination of both the products with the same accuracy was possible. q n 0.4 M NaCl.

302

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

The variation of the micelles can be carried out more easily in reversed micelles, simply by varying the water content. This technique was used elegantly by Ulrich and Steiner (126), who investigated the magnetic field dependence of the recombination kinetics of geminate radical pairs. They generated radical pairs via electron transfer from aniline to excited thionine within the water pools of reversed micellar solutions and found a decrease of intramicellar recombination rate constants with increasing magnetic field strength and a reduction of the effect when the micelle radius was increased. Photoionizations of hydrophobic solutes are studied in many investigations dealing with charge separation in biological and artificial photosyntheses (127,128). Microheterogeneous solutions provide advantages in these studies: electrons ejected from solutes residing in the hydrophobic regions of micelles, microemulsions, etc. may be solvated in the aqueous phase and prevented from recombination by the charge on the surface of these entities (129). Gauduel et al. (130), using femtosecond light pulses, have investigated the first steps of the photoionization process of phenothiazine solubilized in SDS micelles and in reversed micelles of (bis-Zethylhexyl) sodium sulfosuccinate (aerosol-OT, AOT). Photoejection and solvation of electrons in the aqueous phase were shown to take place within 500 fs, and no decay of the hydrated electron is observed within 100 ps, indicating very low geminate recombination. Hautecloque et al. (131) measured photoionization yields of perylene in SDS solutions as functions of added salts. The quantum yields of hydrated electrons decreases exponentially to a limiting value as the salt concentration is increased. Most efficient in this respect are tetraethylammonium ions, which are bound to the micellar surface and reduce the electricpotential of this surface, which is responsible for preventing geminate recombination. Similar additive effects were observed in a series of recent studies (132-135) in which Kevan et al. investigated the photoionization of tetramethylbenzidine in solutions of SDS and dodecyltrimethylammonium chloride (DTAC) micelles, at room temperature and in a frozen state at 77 K in which the micellar structure is retained. The authors used electron spin resonance and electron spin echo modulation techniques for monitoring the photogenerated cations of tetramethylbenzidine (TMB+). Upon 337 nm excitation in DTAC at room temperature the TMB+ yield is only 0.002, but can be increased to 0.03 in the presence of anionic electron scavengers, i.e. NO; adsorbed at the cationic DTAC surface; in solutions of the anionic SDS micelles the TMB+ quantum yield is about 0.1 without any additional scavenger. 2. Preorientation of Reactants Preorientation (alignment) effects on photoreactions were first reported in photodimerizations and photoadditions of enones (107,136-140). Substrates like

303

PHOTOCHEMICAL EFFECTS

cyclopentenones ( 136,137)

0

0

isophorone (107,139)

cycrohexane

microemulsion

90 %

0

head- tohead (anti) 0

%

95%

0

and 2-pyridones (140) (Q. 59).

were found to form two isomeric dimers on irradiation: head-to-tail and head-tohead photodimers, differing in the direction of the carbonyl group in the products. While in certain organic media the formation of head-to-tail products prevails, in micellar and microemulsion solutions high yields of head-to-head photodimers were obtained. The authors explained their observations by assuming an orientation of the reactants within the micellar aggregates: the polar carbonyl

304

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS ethanoi

CTAB

100%

2

0

b

(59)

trans syn

65%

cis anti

35%

group directed towards the polar region of the micelle-water interface, and the less polar moieties of the molecules directed towards the less polar micellar interior, an orientation that might lead to preferred formation of head-to-head products. However, the regioselectivity of these reactions is sensible to solvent polarity, too. For instance, isophorone photodimerization yields head-to-tail photodimers mainly in nonpolar solvents while in polar solvents the amount of head-to-head dimers is proportionally larger. Therefore it is not easy in these cases to discriminate between micellar and polarity effects, since microheterogeneous solvents offer sites of different polarity to solubilizates. Moreover, Muthuramu et al. (141) failed in detecting an analogous alignment

305

PHOTOCHEMICAL EFFE€TS

effect in the photodimerization of coumarins

RwR 0

0

although the authors synthesized “surfactant-like” coumarins bearing alkane chains of various lengths in order to achieve an improved alignment of reactants. They concluded that in this case the polarity influence exceeds possible micelle effects. Similarly, Sauer et al. (113,142,143) discussed their results on the regioselectivity of the photodimerization of polar substituted acenaphthylenes (cf. Eq. 45) and of several (4+2)-photoadditions exclusively in terms of polarity effects in micellar solutions. Hence in order to prove the preorientation unequivocally, it is desirable to compare reactions of polar aligning compounds with reactions of nonpolar reference substances for which no alignment is to be expected. This was possible in the photodimerization of 9-substituted anthracenes (104,105). Two isomeric photodimers are formed, of which the head-to-tail dimer (Dht in Eq. 46) is the thermodynamically more stable one, and the head-to-head dimer (Dhh in Eq. 46) the one to be favored by preorientation in micellar environments when a polar substituent is directed towards the interfacial region of the micelle and the aromatic moiety of the anthracene towards the nonpolar micellar core. In Table 3 ratios of quantum yields of head-to-tail vs. head-to-head dimerization are listed for the nonpolar reference substance 9-methylanthracene and for the polar substituted compounds 9-hydroxymethylanthracene and 9-anthracenepropionic acid in SDS, CTAB, and CTAC solutions as well as in several homogeneous solvents. It can be seen that in 9-methylanthracene head-to-tail photodimerization prevails in homogeneous and in micellar solvents, particularly at high occupancy numbers. The polar compounds, 9-hydroxymethylanthracene and 9anthracene propionic acid, show a more pronounced predominance of head-to-tail photodimerization in homogeneous solvents, while in micellar solutions head-tohead dimerization increases and can exceed head-to-tail dimerization, which clearly demonstrates the preorientation effect.

306

PHOTOCHEMISTRY IN SURFA‘XAIYT SOLUTIONS

Influences of micellar size, of occupancy numbers, and of the spacing between the polar substituent and the anthracene moiety of the molecules turned out to be small. It seems that increased occupancy numbers improve the alignment (cf. Table 3). In the case of another polar compound, 9-anthracene carboxylic acid, different results were obtained (103, as the factors governing the regioselectivity are controlled by dissociationof the acid and electrostaticrepulsion of the anionic carboxylic groups.

B.

Effects of Photochemical Reactions on the Solution Structure: Photorheological Effects

Due to the dynamic nature and to the small micellization enthalpies (25), micelles and other aggregates of amphiphilic molecules are sensitive in shape and size to various additives. It has been known for a long time that the addition of salt to solutions of ionic sphericalmicelles induces the formation of rodlike aggregates ( l a ) , but also the solubilization of alcohols, alkanes, and aromatic liquids (36,145-147) has consequences on aggregation numbers and on shapes of micelles. Conformational changes of the aggregates change the flow behavior of micellar solutions: CTAB solutions in the concentration range of spherical micelles show a constant relative viscosity (q/cam). while the growing of rodlike micelles is accompanied by an increase of relative viscosity (148) and may give rise to non-Newtonian flow behavior. The addition of KBr andor aromatic compounds bearing hydroxylic groups (benzoic acids, naphthol) is known to induce viscoelasticity in CTAB solutions (149-153). However, not all solubilizates change the micellar structure and the flow behavior of the solution. Figure 11 shows the viscosity of an aqueous 0.25 M solution of spherical CTAB micelles as a function of several anthracene derivatives. It can be seen that anthracene and 9,lO-dimethylanthracenedo not affect the viscosity, while in the presence of several 9-substituted anthracenes the viscosity increases strongly with the concentration of the solubilizates. We call this class of solubilizates “rheologically active” and the former class “rheologically inactive.” Interestingly, in situ irradiation of solutions containing rheologically active anthracenes at a wavelength of 366 nm causes a decrease of viscosity (154,155); see Fig. 11. On irradiation photodimers of the anthracenes (Eq.46) and-in the presence of oxygen-also endoperoxides

307

PHOTOCHEMICAL EFFECTS

& o mp 59 'C

A mp 1.7 'C

+ mp 99 'C

&

mp 216 'C

n mp 211. 'C

mp 19L 'C

x

"0 A

mp 111 'C

10

20

30

Concentration of solubilizate, rnrnol/drn3

Figure 11. Dynamic viscosity q of aqueous solutions of CTAB (0.25 M) as a function of the concentration of various solubilizates. Curves are for methyl-, ethyl-, and butylanthracene; horizontal straight line for anthracene and 9,lO-dirnethylanthracene.

are formed which obviously belong to the rheologically inactive compounds, so that the decrease of viscosity can be ascribed to removal of monomeric anthracene derivatives. Photodimers (104-156) and endoperoxids (157,158) can be cleaved thermally and photochemically at a shorter wavelength. Thereby monomers may be regained in part, accompanied by an increase of viscosity. However, because of the low solubility of photodimers only a small fraction of monomers can be converted prior to precipitation of dimers, narrowing the range of photochemically induced viscosity modulations in these systems. More easily to handle are systems containingCTAB and substitutedstilbenes

R, ,R, = OH,COOH

308

PHOTOCHEMISTRY IN SURFACT+NT SOLUTIONS

which are accessible to photochemical trans-cis and cis-trans isomerizations (159) and to thermal cis-trans isomerization. Cis isomers are rheologically more active than trans isomers, so that the viscosity may be changed photochemically in both directions. Figure 12 displays some photochemical and thermal experiments of this kind using 4-hydroxystilbene as a solubilizate (160). Also tested were 4- and 3-stilbene carboxylic acid, in which much larger amplitudes of the photorheological effects can be achieved. Similar experiments performed at higher CTAB concentrationsnear the phase transition from isotropic solution to lyotropic liquid crystals show that the phase transition temperature is affected by the presence of rheologically active compounds (155,161). Figure 13 demonstrates that the phase transition temperature increases when small amounts of 9-anthracene carboxylic acid are solubilized. Irradiation at A = 366 nm, i.e. photodimerization, removes the effect, and reirradiationat X = 254 nm (splittingof the dimers)causes a reincrease of the phase transition temperature. Low angle light scattering experiments performed in these systems (162) prove that the photorheological effects described above are connected with changes of size and shape of the micelles in the isotropic concentration region: in the presence of nonpolar rheologically active anthracenes and of the stilbene

4

6

8

CHS. mmol/dm3

Figure 12. Photochemically and thermally induced viscosity changes of 0.25 M aqueous CTAB at various concentrations of 4-hydroxystilbene (cHs).Solid and broken lines and the symbols H, X refer to the trans isomer and to a cis-rich mixture, respectively; hv to irradiations at 313 and 254 nm, A to storage of the sample at 25°C for 1 week; A,

0 to values reached after irradiation and thermal reaction, respectively. The dotted line corresponds to the viscosity reached after exhausting irradiation at 313 nm.

309

PHOTOCHEMICAL EFFECTS

366 nrn

X-A

A-0

% CTAB by weight

--f

Figure 13. Phase transition temperature of the system of isotropic solution and hexagonal liquid crystal. Pure CTAB-H,O, 0;CTAB-H,O + 0.62%9-anthracene carboxylic acid before irradiation, X ; after irradiation at 366 nm, A; after reirradiation at 280 nm, 0. From Ref. 155 with the permission of VCH Verlagsgesellschaft.

derivatives, globular micelles are formed which exceed the size of ordinary spherical micelles. The radii of these globular micelles change upon irradiation. In these systems only Newtonian flow is observed. Differently, the solubilization of 9-anthracene carboxylic acid induces the formation and growth of rodlike micelles the length of which varies upon irradiation. In this system non-Newtonian flow behavior such as thixotropy, rheopexy, and viscoelasticityoccurs, depending on the concentration ratio of CTAB and anthracene carboxylic acid. Rodlike aggregates are a prerequisite for viscoelastic solutions (153). Variation of rod lengths is a likely reason for the photochemically induced phase transition in more concentrated CTAB solutions. A few further photochemically induced changes of properties of solutions containing amphiphilic aggregates are reported in the literature: Balasubramanian et al. (163) as well as Kano et al. (164) found changes in the electrical resistance and in the light transmission of microemulsions and membrane systems on photochemical cis-trans isomerization of azobenzene derivatives:

R

R

Photochemically induced morphological changes of bilayer vesicles were described by Kunitake et al. (165). When a solution of spherical vesicles formed from a surfactant bearing a tram-azobenzene chromophore within its aliphatic

310

PHOTOCHEMISTRYIN SURFACTANT SOLUTIONS

chain was irradiated (trans-cis isomerization), rodlike aggregates of approximately the same weight were observed which regained the spherical shape on photochemical or thermal back reaction. Sunamoto et al. (166) were able to mediate the transport of phenylalanine across liposomal bilayers after transforming a benzopyranindole derivative into its intermediate zwitterionic form:

VI. SPECTROSCOPIC PROBES A number of properties of amphiphilic aggregates are accessible to more or less direct measurements, i.e. size and shape via light or X-ray scattering; counterion binding, diffusion coefficients, and solubilization sites via NMR spectroscopy; some structural details of single aggregates via neutron scattering; and macroscopic properties of the solutions via viscometry. However, certain properties (such as “microfluidity,” i.e. the fluidity of the micelle interior) cannot be investigated by direct methods, but can be studied in a more simple manner by optically excited spectroscopic probes incorporated at a specific site of the aggregates. Therefore a wealth of information obtained by use of spectroscopic probes has been accumulated in the literature with respect to critical micelle concentrations, premicellar aggregates, micellar size and aggregation numbers, intermicellar processes, “micropolarity” and microfluidity, solubilization sites and occupation numbers, water penetration into micelles, and properties of frozen micelles. As to the large number of papers concerned with spectroscopic probes we refer to a recent review by Singer (19). Spectroscopic probes should fulfill certain requirements such as minimal perturbation of the medium, specific location within the aggregate to be probed, and specific sensitivity to the property under investigation. These and other requirements have been discussed in detail by Zachariasse (167).

A.

Critical Micelle Concentrations

Compared to an aqueous solution, nearly all aromatic substances show small spectral changes of several nanometers in the absorption and emission spectra when they are solubilized by micelles. These shifts are mostly similar to shifts that occur when the solvent polarity is decreased. In principle all shifts can be used for the determination of critical micelle concentrations when spectral changes

311

SPECTROSCOPIC PROBES

are measured as a function of surfactant concentration (see for instance Refs. 168,169). Particularly sensitive are probes that show a dual fluorescence. For instance, Khalil and Sonnessa (170) used p-N,N-dimethylanilinobenzonitril, which shows a short wavelength emission at -360 nm and a long wavelength emission around 520 nm. The relative intensities of the two fluorescences depend on solvent properties. The intensity of the latter emission is strongly increased when the probe is solubilized by micelles.

TABLE 6. Critical Micelle Concentrations determined by the Acridine Fluorescence Method in Comparison with Other Methods Cmc, 1 0 - ~ ~ 4 SurfactanP CTAC CTAB

HFC 'ITAC DTAC SDS

Acridine 12.8 7.1 9.3

46

190

46

Other

Other Method

13 9 8.5 9.2 9 45 200 80 95

Conductivity Fluorescence Fluorescence Conductivity Solubility Conductivity Conductivity Fluorescence Conductivity Absorption Fluorescence Fluorescence Absorption Fluorescence Melting point depr. Adsorption

60 46

Triton X-100

3.3

90 2.4 2.7 9

2

Source b c

d e

f B

h c e

i d

i k

i I rn

'CTAC, CTAB: cetyltrimethylammoniumchloride, bromide; HPC: hexadecylpyridinium chloride; 'ITAC, DTAC: tetradecyltrimethyl ammonium chloride, dodecyltrimethylammonium chloride; SDS: sodium dodecylsulfate; Triton X-100: polyoxyethylene (n=9.5) isooctylphenylether. bA. W. Ralston et al., J . Am. Chem. SOC., 69, 2095 (1947). %ef. (170). dC. David et al., Ber. Bunsenges. Phys. Chem., 86, 710 (1982). %. J. Fendler and J. H. Fendler. Adv. Phys. Chem. 8 , 271 (1970). rG. S. Hartley, J. Chem. SOC., 1968 (1938). 8H. W. Hoyer and A. Marmo, J . Phys. Chem., 65, 1807 (1961). hJ. Osugi et al., Rev. Phys. Chem. Japan, 35, 32 (1965). 'M. Comn and D. W. Harkins, 1. Am. Chem. SOC., 69, 683 (1947). 'R. C. Mast and L. V. Haynes, J . Colloid Interface Sci., 53,35 (1975). kA. Ray and G. Nkmethy, J. Phys. Chem., 75, 809 (1971). 'E. Gonick and J. W. McBain, J. Am. Chem. Soc., 69, 334 (1947). "S. Ross and J. P. Olivier, J . Phys. Chem. 63, 1671 (1959).

312

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

A large sensitivity for probing micellization can be attained using the fluorescence of acridine (171), which is only emitted in protic solvents. Consequently the solubilization within micelles protects the probe from the aqueous protic environment, so that the fluorescence quantum yield in aqueous solution decreases dramatically at surfactant concentrations above the cmc . This method can be used in anionic, cationic, and nonionic micelles. A similar but less pronounced effect was found with 7-alkoxycoumarins (172). Table 6 shows that critical micelle concentrationsdeterminedusing the acridinemethod generally agree well with values determined by other methods. However, it is noted that the value found for SDS (cmc = 4.6 mM) is among the lowest literature values. Therefore a possible effect of the acridine probe on the cmc was tested independently by the surface tension method. Only in the case of SDS was a M acridine decrease of the cmc from 8 to 4.6 mM in the presence of 1.2 x found (see Fig. 14). This example shows clearly that in any application one has to check carefully any possible perturbation of the system by the probe molecule. Especially SDS solutions tend to form “premicellar aggregates” in the presence of certain additives such as the cyanine or the acridine orange dyes investigated by Sat0 et al. (6042,173).

B. Micellar Occupation Statistics In quantitative studies requiring more than one probe molecule per micelle, a valid assumption on the distribution of probe molecules among micelles is needed.

h

Without acridine

10-~

10-2

cs, M

Figure 14. Surface tension u of aqueous solutions of SDS (concentration C,) in the presence of 0.012 mM acridine and without acridine.

SPECTROSCOPIC PROBES

313

Most authors assume that the distribution follows Poisson statistics (Eq.25). Some attempts have been made to prove the Poisson distribution experimentally: Miller et al. (45) found that the Poisson distribution describes the results of a pyrene excimer study well. Also, Yekta et al. (174) concluded the applicability of Poisson statistics from static and dynamic fluorescencequenchingexperiments. Nevertheless, any such assumption is based on constancy of aggregation numbers in the presence of solubilizates, which at least in special cases is definitely wrong (see Section V.B and Refs. 145,146,175).

C. Micellar Size and Aggregation Numbers Calculations of micelle sizes and aggregation numbers have been made from static and time-resolved quenching experiments in which deviations from the behavior in homogeneous solutions due to compartmentalizationof the reactants in micelles (cage effect) were quantitatively exploited (cf. Section IV). It is assumed that the number of quenchers per micelle follows Poisson statistics, and it must be guaranteed that the time which donors and acceptors spend in a micelle is long compared to fluorescence lifetimes of donors and that quenching by the acceptors is the main deactivation process of the donors. In their pyrene excimer study Miller et al. (45) determined SDS aggregation numbers as a function of temperature and of added salt (see Fig. 15). Koglin et

200

I\ i

10

30

50

70

T,“C

Figure 15. Aggregation number 7 of SDS as a function of Na,SO, concentration and temperature (redrawn after Ref. 45).

314

PHoTocHEMlSTRY IN SURFACTANT SOLUTIONS

al. (176) found a Forster energy transfer system (diphenylacetylene-pyrene) which gave correct aggregation numbers for SDS micelles, as did the study of quenching the fluorescence of tris(2,2-bipyridyl)~thenium(II) by 9-methylanthracene performed by Almgren and Ufroth (79). Roelants et al. (177) studied mean aggregation numbers Sof CTAC and TTAC micelles using fluorescence 3 was found to quenching of 1-methylpyrene by N-methyl-N-decylaniline; decrease with increasing temperature. The same tendency was found for a variety of anionic, cationic, and nonionic micelles by Malliaris et al. (178) in a pyrene excimer study. Ltifroth and Almgren tested nonionic micelles of ethylene glycol mono-n-dodecyl ether, applying the system pyrene-N,N-dibutylaniline (179). For data evaluationthey used a model taking micellar polydispersity into account. The results indicate that micelles grow with temperature when the cloud point is approached-a problem discussed in the literature (180,181). Gelad6 and De Schryver determined aggregation numbers of SDS micelles at different ionic strengths and also of reverse micelles in dodecylammonium propionate (DAP) and Aerosol-OT systems (71,182). They used pyrene and indole derivatives as donors and cyan0 benzenes as quenchers in the SDS micelles, while in the reverse micellar systems naphthalene derivatives and inorganic ions were donors and quenchers, respectively. Although in many cases good agreement has been found between aggregation numbers obtained by fluorescence quenching techniques and by other methods (light scattering, etc.) in other cases the results differ greatly (i.e. in big and polydisperse micelles and at high concentrations). These differences must be due to: (i) uncertainties or polydispersity of aggregation numbers and (ii) the influence of probe molecules on the structure of micelles (see Section V.B), as comparatively high solute concentrations are necessary to ensure measurable quenching. At any rate, “the utmost care must be taken when aggregation numbers are derived from quenching experiments,” as was pointed out by Infelta (183).

D. Counterion Binding Fluorescence probes associated with micelles are sensitive to changes of counterions bound to the micellar surface when the counterions differ in capability of quenching. This effect has been exploited in anionic as well as cationic micelles. Ziemiecki and Cherry (86) investigated the quenching of pyrene fluorescence by metal ions in SDS solutions. In all cases nonlinear upward-bent Stern-Volmer plots were obtained on adding increasing amounts of salts of the metal ions to a given SDS concentration. Binding constants of the metal ions to SDS micelles were calculated to decrease in the series Eu3+, Mn2+,T1+, Co2+, Cu*+, C?’. The authors interpreted the results, consideringthat not only electrostatic interactions but also the specific chemistry of the metal ions (solvatization,

SPECTROSCOPIC PROBES

315

crystal field stabilization, etc.) contribute to the binding constants. In our view the influence of added salt on cmc and aggregation numbers-known to change under such conditions (184)-deserves further scrutiny. This complication can be circumventedwhen mixtures of SDS and dodecyl sulfates of the metals under investigation are used. Abdel-Kaderet al. (185) proceeded in this way and found that Ni2+is bound much more strongly than Na+. Repetition of the experiments at constant ionic strength reduced the quenching efficiency and lead to a linear Stern-Volmer plot. Previously, mixtures of CTAB and CTAC were investigated by means of time-resolved ( 186) and static fluorescence measurements ( 187) using the probe anthracene quenched by bromide ions. It was found that relatively more bromide ions and less chloride ions are adsorbed on the micelles than expected from the CTABKTAC ratio in the surfactantconcentration(c,)range 0.01 M < c, < 0.3 M. The excess of adsorbed bromide was about 1.6, a value that was derived from nonlinear Stern-Volmer plots as displayed in Fig. 16 (crosses). Additionally, at higher surfactant conentrations (c, > 0.3 M ) more efficient quenching at high molar fractions of CTAB was obtained (open circles in Fig. 16) due to formation of larger rodlike micelles that bear more adsorbed bromide. Interestingly, within a narrow concentrationrange just above the cmc, Stern-Volmer analysis resulted in a straight line (filled circles in Fig. €6). which points to a statistical distribution of chloride and bromide ions. At this concentration spherical micelles are present

XCTAB

Figure 16. Fluorescence intensity ratio ZdZ (I, = intensity in the absence of CTAB) of anthracene (0.02 mM) in aqueous CTAB-CTAC mixtures as a function of the molar fraction of CTAB, Xmm. Total surfactant concentrations:0.01 M (0); 0.3 M ( X ); 0.3 M (0). From Ref. 187 with the permission of VCH Verlagsgesellschaft.

316

PHOTOCHEMISTRYIN SURFACTANT SOLUTIONS

in the solution with strongly hydrated head groups that attract the counterions only because of electrostatic forces not differing for bromide and chloride. In the region of higher surfactant concentration the spherical micelles shrink, lose water of hydration from the head groups, and then contain partially undissociated ion pairs, thereby making preferential binding of bromide ions possible. These two states of sphericalmicelles are also revealed by measurementsof the viscosity (148). Analogous quenching experiments were performed in solutions of sonicated artificial vesicles formed from mixtures of the surfactants dioctadecyldimethylammonium bromide (DODAB)and dioctadecyldimethylammonium chloride (DODAC) using anthracene and pyrene as fluorescenceprobes. At all surfactant concentrations investigated (1.2 mM to 0.48 M) linear Stem-Volmer plots as shown in Fig. 17 were found, corresponding to a ratio of bromide to chloride ions at the surface coinciding with that of DODAB to DODAC (188). This result is not easily rationalized, as one might have expected that the vesicles, being more rigid than micelles, would offer a more specific surface for adsorbing counterions. However, due to the high aggregation numbers (-lo5), the concentrations of aggregates is much smaller than in CTAB-CTAC micelles, so that interactions of vesicles leading to dehydration of head groups do not necessarily occur.

0 0 Anthracene

+ O 0

f

l

+Pyrene

0.5

1

XDODAS

Figure 17. Fluorescence intensity ratio ZdZ (Zo = intensity in the absence of DODAB) of anthracene and pyrene (both at 0.02 mM) as a function of the molar fraction of DODAB in aqueous mixtures of DODAC and DODAB vesicles. Surfactantconcentration: 9.6 mM.

SPECTROSCOPIC PROBES

317

E. Polarity and Polarizability The local polarity of microheterogeneoussolutions can be examined by studying the emission of intramolecular heteroexcimers with little charge separation (sometimescalled “mixed excimers”). These show measurable emission in polar solvents, in contrast to heteroexcimers of high dipole moment (i.e. more than 14 D). Zachariasse et al. (167) investigated a series of micelles, microemulsions, and phosphatidylcholine bilayers using the probe 1-(4-biphenylyl)-3-(pentamethy1)propane:

It can be seen from Table 7 that the emission maximum shifts to higher frequencies when the polarity of the solvent is decreased and that microemulsions and phospholipid bilayers provide a less polar environment to the hydrophobic probe TABLE 7. Data for Intramolecular Exciplex Formation with 1-(4-Biphenylyl)-3(pentamethy1phenyl)propane in Aqueous Micellar Solutions, Microemulsions, and PhosphatidylcholineBilayers ~~~~

~

~

Exciplex Emission hu,,, lo3cm-I Surfactant’or Solvent ~~~~~

~

SDS

STS SHS ‘ITAC CTAC SDS(M)‘ SHS(M)‘ Hexadecane (E = 2.06) 1-Pentan01 (E = 13.9)

DMPC

DPPC ~~~

I’ll

Conc., M

30°C

50°C

30°C

50°C

0.1 0.1 0.1 0.05 0.05

27.5 27.8

27.3 27.7 28.0 27.2 27.3 28.3 28.3 28.7 28.1 (28.1) 28.2

0.83 0.81

1.22 1.55 1.05 1.35 1.17

~

-

27.2 27.3 28.3 28.2 28.6 28.0 28.3 (28.4)

-

0.73 0.64 1.22 1.10 0.90 1.26 0.42

1.46

1.28 0.99 1.47

-

0.66

~

Source: Ref. 167 “SDS: sodium dodecyl sulfate; STS: sodium tetradecyl sulfate; SHS: sodium hexadecyl sulfate; TTAC: tetradecyltrimethylaonium chloride; CTAC: hexadecyltrimethylammonium chloride; DMPC: dimyristoyl phosphatidylcholine; DPPC: dipalmitoyl phosphatidylcholine. bExciplex/monomerfluorescence intensity ratio, measured at the exciplex emission maximum (1’) and at 310 nm (I). ’Microemulsion prepared by mixing the surfactant SDS or SHS (1.25 g), 3.4 ml 1-pentanol, 0.6 ml hexadecane, and 13.5 ml water.

318

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

than smaller micellar aggregates. Saito and Sat0 (189) define an “inner polarity” of nonionic micelles formed by polyoxyethylenecetyl ethers that can be monitored by the degree of enolization of benzoylacetoanilide. This compound is known to enolize in the core of the micelle. A decrease of the enolic absorption at 310 nm is observed when the polyoxyethylene chain length is increased. This result was interpreted as an increase in polarity due to hydration of polyoxyethylene chains. The vibrational structure of the fluorescence of aromatic molecules is also sensitive to solvent polarity. Particularly the ratio of the intensity of the fust over the fourth peak of the pyrene monomer fluorescence increases with the polarity of the solvent (Ham effect). This was used by Nakajima (190) and by Kalyanasundaram and Thomas (191) to probe the environment of pyrene in SDS and CTAC micelles, which turned out to be similar to short chain alcohols. This polarity must be attributed to the surface region of the micelles, since it was concluded from NMR investigationsthat pyrene in these micelles is solubilized in the surface region (192). Another probe used to investigate interface regions in surfactant solutions is pyridinium N-phenolbetain,

in which the spectral position of an intramolecular charge transfer band senses

polarity. With this probe Zachariasse et al. confirmed the surface region of small

micelles to be more polar than that of phospholipid bilayers (193). Kano et al. (68) used dansyldodecylamine (5-dimethylaminonaphthalene-1sulfonic acid n-dodecylamide) as a probe in which the energy of the emission maximum decreases with the polarity of the environment. The results show that Triton X-100micelles provide a less polar environment to the probe than SDS and CTAC micelles. This was discussed in terms of a more rigid structure of the Trition X-100 micelles. More quantitively,Fernandez and Fromhen investigated the interfacialregion of SDS, CTAB, and Triton X-100 micelles (194). They used fluorescent pH indicators, hydroxycoumarin and aminocoumarin dyes substituted by alkane chains, and measured shifts of the PIC-values. The authors attributed these shifts partly to the dielectric constant at the micelle-water interface and partly to the electrical potential at the surface of charged micelles. In this way they calculated

319

SPU-TROSCOPIC PROBES

electrical potentials of -134 mV for SDS and 148 mV for CTAB micelles (vs. normal hydrogen electrode). Information about the polarizability of a solvent or of a solubilization site in a microheterogeneous solvent can be obtained from absorption or excitation spectra of probe molecules, since the spectral position of an absorption band depends more on the polarizability of the medium, i.e. on the refractive index n, than on the polarity represented by the dielectric constant e. The spectral shift Av that occurs when a molecule is transferred from vacuum to a refracting medium can be expressed as (195) Av = 10.71 x 109 f . vu3

n2-1 2n2 - 1

where f i s the oscillator strength, v the energy of the transition in cm-’, and a the radius of the spherical volume that a probe molecule requires in the solubilized state. Zachariasse et al. (196) made use of the effect in studying absorption spectra of di(1-pyrenylmethyl) ether solubilized in SDS micelles and some membrane systems. The latter aggregates were found to exhibit higher refractive indices than the micellar system.

F. Microfluidity The fluidity in the neighborhood of probe molecules can be tested by use of probes capable of intramolecularexcimer formation. The probe molecules contain the two excimer-forming moieties linked by an alkyl chain. The extent of excimer formation depends on the viscosity of the environment and can be monitored by measuring the excimer/monomer fluorescence intensity ratio. The dependence of this ratio on reciprocal viscosity for the probe molecule dipyrenylpropane is shown in Fig. 18, in which the obtained microfluidities for surfactant systems are indicated. The fluidities decrease in the order SHS microemulsion, SDS, CTAC, Triton X-100; cf. Ref. 167 (for abbreviations see Tables 6 and 7). The same sequence order was found by Kano et al. (68). In systems containing heavy counterions the method leads to data that must be evaluated carefully, since heavy atom interactions may be different with excited monomers and excimers. The intramolecular excimer technique is also useful in biological studies. For instance, Almeida et al. investigated the sarcoplasmic reticulum membrane in which the activity of the Ca2+-pumpingenzyme is modulated by the membrane fluidity (197). The quantum yield of the cis-trans isomerization of stilbene derivatives, in particular “surfactant stilbenes,” depends on the fluidity of the environment,

320

PHOTOCHEMISTRY IN SURFACXANT SOLUTIONS

“’k/ Triton X-100

0

0

0.1

0.4

0.2

0.3

Figure 18. Excimer/monomer fluorescence intensity ratio Z’lZ at 30°C of 1,3-di(1pyreny1)propane [Py(3)Py] as a function of the reciprocal viscosity for a series of hexadecane-liquid paraffin mixtures (curve). The I’lZ ratios obtained with Py(3)Py in aqueous micellar solutions of sodium dodecyl sulfate (SDS, 0.1 M), cetyltrimethylammonium chloride (CTAC, 0.05 M), and Triton X-100 (0.004 M), and in the microemulsion SHS(M) (see Table 7) are indicated. The fluidities determined were: 3.1 mPa s [SHS(M)], 11 mPa s [SDS] 37 mPa s [CTAC], and 105 mPa s [Triton X-1001. Redrawn after Ref. 167.

i.e., it is lower in less fluid solvents. Using this effect, Suddaby et al. investigated homogeneoushydrocarbon, micellar, and vesicle systems. The fluidity was found to decrease in this order (198).

G. Solubilization Sites Working with spectroscopic probes, one needs to know the solubilization site of the probe, which should be determined independently on the spectroscopic effect to be exploited. However, when micelles of a homologous series of surfactants are investigated, information on variation of solubilization sites may be obtained. Roelants et al. (177) concluded from activation energiesof quenching processes that the quencher molecule N-methyl-N-decylaniline resides a little “deeper” in ‘ITAC micelles than in CTAC micelles. The preferred location of aromatic solutes in micelles cannot be learned unequivocally from the literature. Evidence has been presented for solubilization in the micelle core, at the surface, or at both these sites, depending on the concentration (43,199-204). Therefore the solubilization site of aromatic compounds seems to depend on details of the respective systems. In the case of the probe acridine, site information can be derived from relative quantum yields

321

SPECTROSCOPICPROBES

of its blue fluorescence, which is only emitted when a water molecule as a protic complex partner is available for an excited acridine molecule within its lifetime (205). When acridine is solubilized by various surfactant solutions in the concentration range of spherical micelles, the quantum yields of the blue acridine fluorescence decrease in the series dodecyl-, tetradecyl-, hexadecylammonium chloride (DTAC, Tl'AC, CTAC) (206), i.e., they decrease with increasing micellar radius as shown in Table 8. This result is expected when random movement of acridine molecules inside the micellar core takes place, since the encounter probability of acridine and water molecules in the surface region will also decrease with increasing micelle size.

H. Frozen Micelles When aqueous micellar solutions are cooled quickly to 77 K, the micellar structure is found to be retained (210). Thereby methods become applicable that cannot be used at room temperature in fluid solutions but may give some insight into the micelle structure and into interactions with solubilizates. Petrin et al. (21 1) investigated heavy atom effects on excited naphthalene in frozen SDS solutions containing either AgDS or TlDS by means of optically detected magnetic resonance. They found that selectivity and degree of spin-orbit coupling differ between Ag+ and T1+ ions, indicating the formation of a Ag+-naphthalene complex in the ground state which is absent in the T1+ system. Also, electron spin resonance (ESR) investigations of probe molecules in the excited triplet state are possible in frozen micellar solutions. Time-resolved ESR measurements allow one to observe triplet lifetimes at various temperatures of nonemitting probes in such nontransparent systems (212). These investigations may provide information on solubilization sites of probe molecules. TABLE 8. Relative Quantum Yields (mn)of the Blue Fluorescence of Acridine (0.12mM) in Solutions of Spherical Micellesof Dodecyltrimethylammonium Chloride (DTAC), Tetradecylammonium Chloride (TTAC), and Cetyltrimethylammonium Chloride (CTAC) at pH = 12" Surfactant

DTAC TTAC CTAC

@fl

0.10 0.09 0.08

S

50'

ad 82'

r, nm 2.2' 2.5' 2.8'

W ' , = 1 in water at pH = 12. Values are related to aggregation numbers s a n d micellar radius r. v a l u e for DTAB (207). which should not differ much from DTAC. 'Calculated using Eq. 4. dFrom Ref. 208. 'From Ref. 209.

322

PHOTOCHEMISTRYIN SURFAmANT SOLUTIONS

I. Intermicellar Processes In time-resolved or static quenching experiments with probes in long-lived excited states, sometimes the involvement of intermicellarprocesses cannot be excluded and complicates the evalution of data and the interpretation of results. In particular, two possible mechanisms must be considered: (i) probe molecules leaving micelles and entering others (exit-entrance processes); (ii) intermolecular collisions making the exchange of solubilizates possible. Although exit and entrance rates in some cases may be determined independently (43),it is generally difficult to discriminatebetween the two mechanisms, as intermicellar collisions could only be identified unambiguously by using probes that cannot possibly escape the micelles. Glkle et al. investigated 1-bromonaphthalenein the excited triplet state quenched by pyrene, having solubilized donor and acceptor molecules in different SDS micelles; the quenching process was found to be governed by exit and entrance rates (88). In a fluorescence quenching study in dodecylammonium propionate micelles, Gelad6 and De Schryver found that the two possible mechanisms could not be distinguished (70).

VII. CONCLUSIONS The photochemistry of surfactant solutions is a rapidly expanding field of active research. It is closely related to the photochemistryof other heterogeneous systems such as membranes and colloidal dispersions of semiconductors that are being investigated with respect to their potential use for solar energy conversion. Indeed, the particular electrochemical structure of micellar surfactant solutions provides a way to separate charge carriers generated by light absorption. Back reactions reducing the efficiencies of light-induced reactions are thus impeded. However, irreversible processes are not excluded, and a practicable route to the direct generation of electrical energy has not emerged from such studies, nor is it likely that it will. On the other hand, the kind of irreversible (i.e. chemical) processes that is favored by the micellar solution structure deserves scrutiny. There is a growing body of information on the regioselectivity of photoreactions in surfactant solutions. Selectivity i s intimately connected with details of the micelle structure that are mostly unknown. Over 50 years after Hartley’s work [26],the structure of micelles is still in debate. Micelles are known to have a fleeting existence which renders it difficult to predict the stereochemistry of intramicellar photoreactions. Many ingenious probes have been devised in order to measure relevant macroscopic quantities pertaining to the interior of micelles. The results obtained are very interesting but difficult to interpret, and often reflect properties of the probe rather than those of the micelle. Further work on probes should concentrate

REFERENCES

323

on the existing connection between packing statistics and photochemical properties of micellar aggregates. Because of the subtle thermodynamic balance responsible for the existence of micelles, there is always the problem of probemicelle interactions which may influence aggregation statistics. Obviously, much basic research needs to be done to acquire a deeper insight into the structure of micelles occupied by solubilizates. Apart from these subtleties, the preparative potential of the photochemistry in surfactant solutions should be explored further. There is a fundamental interest in the scaling up of micellar reactions which emanates from two salient features of surfactant solutions: high local concentrations of reactants giving rise to higher quantum yields, and aqueous micellar systems replacing organic solvents, which are often poisonous and have high vapor pressures. Both advantages concur in photochemical conversions that require dilute solutions for extended penetration of light quanta into the system.

ACNOWLEDGMENT We thank Mrs. Christian for preparing some of the drawings. We are further indebted to Firma Henkel, Diisseldorf, who supplied surfactants for most of our own work. Support by the Deutsche Forschungsgemeinschaft, the Minister f i b Wissenschaft und Forschung des Landes Nordrhein-Westfalen, and the Fonds der Chemischen Industrie is gratefully acknowledged.

REFERENCES 1. T. Forster and B. Selinger, 2. Nururforschg. 19a, 38 (1964). 2. M. Hauser and U. Klein, 2. Phys. Chem. 78, 32 (1972). 3. R. C. Dorrance and T. F. Hunter, J. Chem. Soc. Furuday Trans. Z68, 1312 (1972). 4. R. R. Hautala and N. J. Tuno, Mol. Phofochem. 4 , 545 (1972). 5. M. Gratzel and J. K. Thomas, J . Am. Chem. Soc. 95, 6885 (1973). 6. M. Gratzel, A. Henglein, and E. Janata, Ber. Bunsenges. Phys. Chem. 79, 475, 541 (1975). 7. W. Schnecke, M. Gratzel, and A. Henglein, Ber. Bunsenges. Phys. Chem. 81, 821 (1977). 8 . N. Roessler and G. von Biinau, J . Phorochem. 9, 307 (1978). 9. M. A. J. Rodgers and M. F. Da Silva e Wheeler, Chem. Phys. Lett. 53, 165 (1978). 10. B. K. Selinger and A. R . Watkins, Chem. Phys. Lerr. 56, 99 (1978).

324

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

11. Y. Waka, K. Hamamoto, and N. Mataga, Chem. Phys. Let?. 53, 242 (1978). 12. K. Zachariasse, Chem. Phys. Let?. 57, 429 (1978). 13. S. S. Atik, M. Nam, andL. A. Singer, Chem. Phys. Let?.67,75 (1979). 14. D. J. Miller, Ber. Bunsenges. Phys. Chem. 85, 337 (1981). 15. C. N. Henderson, B. K. Selinger, and A. R. Watkins, J . Photochem. 16, 215 (1981). 16. B. K. Selinger and A. R. Watkins, J. Photochem. 17, 319 (1982). 17. N. J. Turro, M. Graml, and A. M. Braun, Angew.Chem. 92,712 (1980). 18. N. J. T w o , G. S. Cox, and M. A. Paczkowski, Top. Curr. Chem. 129, 57 (1985). 19. L. A. Singer, in Solution Behavior of Su~actants:Theoretical and Applied Aspects, K. L. Mittal and E. J . Fendler, Eds., Plenum Press, New York, 1982, pp. 73-112. 20. M. Graml, Acc. Chem. Res. 14, 376 (1981.) 21. M. Griitzel, Biochem. Biophys. Actu 683, 221 (1982). 22. N. J. Turro, Pure Appl. Chem. 58, 1219 (1986). 23. Kirk-Othmer, Encyclopedia of Chemical Technology, 2nd ed., Vol. 19, Wiley, New York 1969, p. 507. 24. C. Tanford, The Hydrophobic Effect, 2nd ed., Wiley-Interscience, New York, 1980, p. 63. 25. B. Lindman and H. Wennerstrom, Top. Curr. Chem., 87, 1 (1980). 26. J. Malsch and G. S. Hartley, Z. Phys. Chem. A170, 321 (1934). 27. N. Ramnath, V. Ramesch, and V. Ramamurthy, J. Sci. Znd. Res. 44, 199 (1985). 28. P. Fromherz, Chem. Phys. Len. 77, 460 (1981). 29. K. A. DillandP. J. Rory, Proc. Narl. Acad. Sci. U.S.A. 78,676(1981). 30. D. W. R. Gruen, J. Phys. Chern. 89, 146, 153 (1985). 31. P. Fromherz, C. Rticker, and D. Ruppel, Faraduy Disc. Chem. SOC. 81, 39 (1986). 32. E. M. Wooley and T. E. Burchfield, J. Phys. Chem. 89, 714 (1985). 33. A. I. Rusanov, J. Coll. Znter$ace Sci. 85, 157 (1982). 34. C.Tanford, Proc. Nut. Acad. Sci. U.S.A. 71,181 1 (1974);J. Phys. Chem. 78, 2469 (1974). 35. P. Mukerjee, J. Phys. Chem. 76, 565 (1972). 36. H. W. Offen, D. R. Dawson, and D. F. Nicoli, J . Coll. Znterjiace Sci. 80, 118 (1981). 37. E. A. G. Aniansson and S. Wall, J. Phys. Chem. 78, 1024 (1974); 79, 857 (1975). 38. E. A. G. Aniansson, S. N. Wall, M. Almgren, H. Hoffmann, I. Kielmann, W. Ulbricht, R. Zana, J. Lang, and C. Tondre, J. Phys. Chem. 80, 905 (1976). 39. N. Roessler and T. Wolff, Photochem. Photobiol. 31, 547 (1980).

REFERENCES

325

40. P. Infelta and M. Gratzel, J. Chem. Phys. 70, 179 (1979). 41. M. Almgren, Photochem. Photobiol. 15, 297 (1972). 42. R. C. Dorrance and T. F. Hunter, J. Chem. SOC.Faraday Trans. Z70, 1572 (1974). 43. M. Almgren, F. Grieser, and J. K. Thomas, J. Am. Chem. SOC.101, 279 (1979). 44. D. J. Miller, J. Chem. Educ. 55, 776 (1978). 45. D. J. Miller, U. K. A. Klein, and M. Hauser, Ber. Bunsenges. Phys. Chem. 84, 1135 (1980). 46. G. Rothenberger, P. P. Infelta, and M. Gratzel, J. Phys. Chem. 83, 1871 (1979). 47. M. Almgren and J. E. Lofroth, J . Chem. Phys. 76, 2734 (1982). 48. T.Forster, Z.Naturforsch. 4a, 321 (1949);Ann. Physik 2 , 55 (1948). 49. K. B. Eisenthal and S. Siegel, J. Chem. Phys. 41, 652 (1964);42, 814 (1965). 50. R. A. Cellarius, Photochem. Photobiol. 6 , 91 (1967). 51. M. Hauser, U.K. A. Klein, and U. Gosele, 2. Phys. Chem. (N.F.)101, 255 (1976). 52. A. Blumen, Nuovo Cimento 63B,50 (1981). 53. T. Marszalek, A. Baczynski, W. Orzeszko, and A. Rozploch, 2. Naturforsch. 35a, 85 (1980). 54. M. D. Ediger, R. P. Domingue, and M. D. Fayer, J . Chem. Phys. 80, 1246 (1984). 55. M. N. Berberan-Santos and M. J. E. Prieto, XI IUPAC Symp. Photochem. Lisboa 1986, Abstracts, p. 496. 56. M. Tachiya, Chem. Phys. Lett. 33, 289 (1975). 57. P. Infelta, Chem. Phys. Len. 61, 88 (1979). 58. N. J. Turro and A. Yekta, J. Am. Chem. SOC. 100, 5951 (1978). 59. A. Henglein and R. Scheerer, Ber. Bunsenges. Phys. Chem. 82, 1107 (1978). 60. T. Ban., K. Kasatani, M. Kawasaki, and H. Sato, Photochem. Photobiol. 37, 131 (1983). 61. H. Sato, M. Kawasaki, K. Kasatani, N. Nakashima, and K. Yoshihara, Bull. Chem. SOC.Japan 56, 3588 (1983). 62. H. Sato, M.Kawasaki, K. Kasatani, N. Kusumoto, N. Nakashima, and K. Yoshihara, Chem. Lett. Japan 1980, 1529. 63. H. Sato, Y. Kusomoto, N. Nakashima, and K. Yoshihara, Chem. Phys. Lett. 71,326 (1980). 64. J.H.BaxendaleandM.A. J.Rodgers,Chem. Phys.Lett.72,424(1980). 65. M. P.Pileni, B. Lerebours, P. Brochette, andY. Chevalier, J. Photochem. 28,273 (1985). 66. T. Miyashita, T. Murakata, Y. Yamaguchi, and M. Matsuda, J. Phys. Chem. 89,497 (1985).

326

PHOTOCHEMISTRY IN SURFAffANT SOLUTIONS

67. T. Miyashita, T. Murakata, and M. Matsuda, J . Phys. Chem. 87, 4529 (1983). 68. K. Kano, Y. Ueno, andS. Hashimoto, J . Phys. Chem. 89,3161 (1985). 69. M. Van der Auweraer, J. C. Dederen, E. Geladd, and F. C. De Schryver, J . Chem. Phys. 74, 1140 (1981). 70. E. Geladd and F. C. De Schryver, J . Photochem. 18, 223 (1982). 71. F. C. De Schryver, Y. Croonen, E. Gelad6, M. Van der Auweraer, J. C. Dederen, E. Roelants, N. Boens, and K. U. Leuven, in Sur$actants in Solution, K . L. MittalandB. Lindmun, Eds., Vol. 1, Plenum, 1984, p. 663. 72. A. Malliaris, J. Lang, and R. Zana, J . Phys. Chem. 90, 655 (1986). 73. A. Malliaris, J. Lang, and R. Zana, J . Chem. SOC.Faraday Trans. Z82, 109 (1986). 74. A. Malliaris, J. Lang, andR. Zana, J . Coll. ZnterfaceSci. 110,237 (1986). 75. P. Lianos, M. Dinh-cao, J. Lang, and R. &a, J . Chim. Phys. 78, 497 (1981). 76. G. S . Singhal, E. Rabinowitch, J. Hevesi, and V. Srinivasan, Pho:ochem. Phorobiol. 11, 531 (1970). 77. Y. Usui and A. Gotou, Photochem. Photobiol. 29, 165 (1979). 78. S. S. Atik and J. K. Thomas, J . Am. Chem. SOC. 103,4367 (1981). 79. M. Almgren and J. E. Lcifroth, J . Coll. Interface Sci. 81, 486 (1981). 80. S. M. B. Costa and A. L. Macanita, J . Phys. Chem. 84, 2408 (1980). 81. S. M. B. Costa, M. R. Aires de Barros, and J. P. Conde, J . Photochem. 28, 153 (1985). 82. Y. Waka, K. Hamamoto, and N. Mataga; Chem. Phys. Lett. 53, 242 (1978). 83. J. A. Delaire, M. A. J. Rodgers, and S. E. Webber, J . Phys. Chem. 88, 6219 (1984). 84. M. Mitsuzuka, K. Kikuchi, H. Kokubun, and Y. Usui, J . Phorochem. 29, 363 (1985). 85. T. MiyashitaandM. Matsuda, Bull. Chem. SOC.Japan58,3031(1985). 86. H. Ziemiecki and W. R. Cheny, J . Am. Chem. SOC. 103, 4479 (1981). 87. A. M. Braun, M. Krieg, N. J. Turro, M. Aikawa, I. R. Gould, G. A. Graf, and P. C. C. Lee, J . Am. Chem. SOC. 103,7312 (1981). 88. K. Glasle, U. K. A. Klein, and M. Hauser, J . MoZ. Srrucr. 84,353 (1982). 89. P. P. Infelta, M. Gratzel, and J. K. Thomas, J . Phys. Chem. 78,190 (1974). 90. M. Almgren, P. Stilbs, J. Alsins, P. Linse, and N. Kamenka, J . Phys. Chem. 89, 2666 (1985). 91. M. Almgren, P. Linse, M. Van der Auweraer, F. C. De Schryver, E. Geladd, and Y. Croonen, J . Phys. Chem. 88, 289 (1984). 92. M. Almgren, G. Gunnarsson, and P. Linse, Chem. Phys. Lett. 85, 451 (1982). 93. J. E. Liifmth and M. Almgren, J . Phys. Chem. 86, 1636 (1982). 94. M. Almgren, S. Swamp, and J. E. Lofroth, J . Phys. Chem. 89, 4621 (1985).

REFERENCES

327

95. Y. Croonen, E. Geladk, M. Van der Zegel, M. Van der Auweraer, H. Vanderdriessche, F. C. De Schryver, and M. Almgren, J. Phys. Chem. 87, 1426 (1983). 96. G. Rothenberger, P. P. Infelta, and M. Graml, J. Phys. Chem. 85, 1850 (1981). 97. M. D. Hatlee, J. J. Kozak, G. Rothenberger, P. P. Infelta, andM. Gratzel, J . Phys. Chem. 84, 1508 (1980). 98. P. P. Infelta and M. Griitzel, J. Chem. Phys. 78, 5280 (1983). 99. C. K. Gratzel and M. Gratzel, J , Phys. Chem. 86, 2710 (1982). 100. M. P. Pileni and M. Gratzel, J . Phys. Chem. 84, 1822 (1980). 101. P. Hall and B. Selinger, J. Phys. Chem. 85, 2941 (1981). 102. P. Hall and B. Selinger, 2.Phys. Chem. N.F. 141, 77 (1984). 103. Y. Nakamura, Y. Imakura, T. Kato, and Y. Morita, J. Chem. SOC., Chem. Commun., 887 (1977). 104. T. Wolff, N. Miiller, and G. von Biinau, J. Photochem. 22, 61 (1983). 105. T. Wolff, N. Miiller, J. Photochem. 23, 131 (1983). 106. Y. Nakamura, Y. Imakura, and Y. Morita, Chem. Lett. 965 (1978). 107. R. Fargues, M. T. Maurette, E. Oliveros, M. Rivi2re, and A. Lattes, Nouv. J . Chim. 3, 487 (1979). 108. J. K. Thomas, Chem. Rev. 80, 283 (1980). 109. I. Willner, W. E. Ford, J. W. Otvos, and M. Calvin, Nature 280, 823 (1979). 110. J. H. Fendler and P. Tundo, Acc. Chem. Res. 17, 3 (1984). 111. W. E. Ford, J. W. Otvos, and M. Calvin, Proc. Nufl. Acud. Sci. U.S.A. 76, 3590 (1979). 112. T. Wolff, Ber. Bunsenges. Phys. Chem. 86, 1132 (1982). 113. H. Mayer and J. Sauer, Tetruh. Letr. 24, 4091, 4095 (1983). 114. V. Ramesh and V. Ramamurthy, J . Photochem. 24, 395 (1984). 115. K. Kalyanasundaram, F. Grieser, and J. K. Thomas, Chem. Phys. Lett. 51, 501 (1977). 116. N. J. Turro, K.-C. Liu, M.-F. Chow, and P. Lee, Photochem. Photobiol. 27, 523 (1978). 117. N. J. Turro and M. Aikawa, J. Am. Chem. SOC. 102, 4866 (1980). 118. M. Scrilec and L. J. C. Love, J. Phys. Chern. 85, 2047 (1981). 119. R. R. Hautala and R. L. Letsinger, J. Org. Chem. 36, 3762 (1971). 120. J. B. S. Bonilha, H. Chaimovich, V. G. Toscano, and F. Quina, J. Phys. Chem. 83, 2463 (1979). 121. T. Wolff, J. Phafochem. 18, 285 (1982). 122. N. J. Turro and W. R. Cherry, J. Am. Chem. SOC. 100, 7431 (1978). 123. N. J. Turro and J. Mattay, J. Am. Chem. Soc. 103, 4200 (1981). 124. N. J. Turro and G. C. Weed, J. Am. Chem. SOC. 105, 1861 (1983). 125. T. Wolff, J. Photochem. 18, 265 (1982). 126. T. Ulrich and U. E. Steiner, Chem. Phys. Lett. 112, 365 (1984).

328

PHOTOCHEMISTRY IN SURFACTANT SOLUTIONS

127. P. P.Infelta, M. Gratzel, and J. H. Fendler, J. Am. Chem. SOC. 102, 1479 (1980). 128. J. H.Fendler, Acc. Chem. Res. 13, 7 (1980). 129. M. Gram1 and J. K . Thomas, J. Phys. Chem. 7 8 , 2248 (1974). 130. Y. Gauduel, A. Migus, J. L. Martin, Y. L e c q n t i e r , and A. Antonetti, Ber. Bunsenges. Phys. Chem. 89, 218 (1985). 131. S.Hautecloque,D.Grand,andA.Bernas,J.Phys. Chem.89,2705(1985). 132. R.ArceandL.Kevan, J.Chem.Soc., Furu&yTruns.ISl, 1025(1985). 133. R.ArceandL.Kevan,J. Chem.Soc., FaruduyTruns.I81,1669(1985). 134. A. Plonka and L. Kevan, J. Phys. Chem. 89,2087 (1985). 135. E. Szajdzinska-Pietek, R. Maldonado, L. Kevan, and R. R. M. Jones, J. Am. Chem. SOC. 107, 6467 (1985). 136. K. H.Lee and P. de Mayo, J. Chem. Soc., Chem. Commun., 493 (1979). 137. P.de Mayo and L.K. Sydnes, J . Chem. SOC.,Chem. Commun., 994(1 980). 138. N. Berenjian, P.de Mayo, M. Sturgeon, L. K. Sydnes, and A. C. Weedon, Can. J . Chem. 60,426 (1982). 139. R. Fargues, M. T. Maurette, E. Oliveros, M. Rivihre, and A. Lattes, J . Photochem. 18, 101 (1982). 140. Y. Nakamura, T.Kato, and Y. Morita, Tetruh. Len. 22, 1025 (1981). 141. K. Muthuramu, N. Ramnath, and V. Ramamurthy, J. Org. Chem. 48, 1872 (1983). 142. H. Mayer, F. Schuster, and J. Sauer, Tetruh. Lett. 27, 1289 (1986). 143. R. Braun, F. Schuster, and J. Sauer, Tefruh. Len. 27, 1285 (1986). 144. K. Kalyanasundaram, M. Griitzel, and J. K. Thomas, J. Am. Chem. SOC. 97,3915 (1975). 145. M. Almgren and S. Swarup, J. Phys. Chem. 86, 4212 (1982). 146. M. Almgren and S. Swarup, J. Coll. Interface Sci. 91, 256 (1983). 147. P. Stilbs, J. Coll. Interface Sci. 89,547 (1982). 148. P. Ekwdl, L. Mandell, and P. Solyom, J. ColZ. Interface Sci. 35, 519 (1971). 149. T.Nash, J. Coll. Interjiuce Sci. 13, 134 (1958). 150. L. S. C. Wan, J. Pharm. Sci. 55, 1395 (1966). 151. A. J.HydeandD. W.M. Johnstone, J. Coll.InrerfaceSci.53,349(1975). 152. S . Gravsholt, J. Coll. Interface Sci. 57, 575 (1976). 153. M. Angel, H. Hoffmann, M. Lobl, K. Reizlein, H. Thurn, and I. Wunderlich, Progr. Coll. Polymer Sci. 69, 12 (1984). 154. N. Miiller, T.Wolff, and G. von Biinau, J . Photochem. 24, 37 (1984). 155. T.WolffandG. vonBiinau, Ber. Bunsenges. Phys. Chem. 88,1098(1984). 156. S. Yamamoto and K.-H. Grellmann, Chem. Phys. Lett. 85,73 (1982). 157. W. Bergmann and M. J. McLean, Chem. Rev. 28, 367 (1941). 158. S.-Y. Hou, C. G. Dupuy, M. J. McAuliffe, D. A. Hrovat, and K. B. Eisenthal, J. Am. Chem. SOC. 103, 6982 (1981). 159. J. Saltiel and J. L. Charlton, in Rearrangements in Ground and Excited

REFERENCES

329

States, P. de Mayo, Ed., Vol. 3, Academic Press, New York, 1980, pp. 25-89. 160. T.Wolff and G. von Bunau, J. Phorochem. 35, 239 (1986). 161. T. Wolff and G. von Bunau, J. Coll. Zntegace Sci. 99, 299 (1984). 162. T. Wolff, T. A. Suck, C.-S. Emming, and G. von Bunau, Progr. Coll. Polym. Sci. 73, 18 (1987). 163. D. Balasubramanian, S. Subramani, and C. Kumar, Nature 254, 252 (1975). 164. K. Kano, Y. Tanaka, T. Ogawa, M. Shimomura, Y. Okahata, and T. Kunitake, Chem. Lett., 421 (1980). 165. T.Kunitake, N. Nakashima, M. Shimomura, Y. Okahata, K. Kano, and T.Ogawa, J . Am. Chem. SOC. 102, 6642 (1980). 166. J. Sunamoto, K. Iwamoto, Y. Mohri, and T. Kominato, J . Am. Chem. Soc. 104, 5502 (1982). 167. K. A. Zachariasse, “Polarity and Viscosity Probes in Lipids,” in Excited State Probes in Biochemistry and Biology, A. Szabo, Ed., Plenum Press, New York, 1985. 168. N. E. Schore and N. J. Turro, J . Am. Chem. SOC. %, 306 (1974). 169. T.-H. Lin, W. R. Cherry, and W. L. Mattice, Polym. Commun. 27, 37 (1986). 170. 0. S. Khalil and A. J. Sonnessa, Mol. Photochem. 8, 399 (1977). 171. T. Wolff, J. Coll. Zntegace Sci. 83, 658 (1981). 172. K. Muthuramu and V. Ramamurthy, J. Phorochem. 26, 57 (1984). 173. M. Katsumata, K. Kasatani, M. Kawasaki, andH. Sato, Bull. Chem. SOC. Jupun 55, 717 (1982). 174. A. Yekta, M. Aikawa, andN. J. TUKO,Chem. Phys. Lett.63,543 (1979). 175. M. Almgren and S. Swarup, J. Phys. Chem. 87, 876 (1983). 176. P. K. F. Koglin, D. J. Miller, J. Steinwandel, and M. Hauser, J. Phys. Chem. 85, 2363 (1981). 177. E. Roelants, E. Gelade, J. Smid, and F. C. De Schryver, J. Coll. Interface Sci. 107, 337 (1986). 178. A. Malliaris, J. Le Moigne, J. Sturm, and R. Zana, J . Phys. Chem. 89, 2709 (1985). 179. J.-E. Lofroth and M. Almgren, “Fluorescence Quenching Aggregation Numbers in a non-Ionic Micelle Solution,” in Sugactants in Solution, K. L. Mittal and B. Lindman, Eds., Plenum, New York, 1984, Vol. 1, pp. 627-643. 180. M. Corti and V. Degiorgio, J. Phys. Chem. 85, 1442 (1981). 181. P.-G. Nilsson, H. Wennerstrom, and B. Lindman, Chem. Scr. 25, 96 (1985). 182. E. Geladt? and F. C. De Schryver: “Fluorescence: A Method to Obtain Information about Reverse Micelles,” in Reverse Micelles, P. L. Luisi and B. E. Straub, Eds., Plenum, New York, 1984, pp. 143-164.

330

PHOTOCHEMISTRY IN SURFACrANT SOLUTIONS

183. P. P. Infelta, Chem. Phys. Lett. 61, 88 (1979). 184. K. J. Mysels and L. H. Princen, J. Phys. Chem. 63, 1696 (1959). 185. M. H. Abdel-Kader, A. M. Braun, and N. Paillous, J . Chem. SOC.,Furuduy Trans. Z 81,245 (1985). 186. L. K. Patterson and E. Vieil, J. Phys. Chem. 77, 1191 (1973). 187. T. WolffandG. vonBiinau, Ber. Bunsenges. Phys. Chem. 86,225(1982). 188. T. WOW.Photochemische Untersuchungen in mikroheterogenen Liisungen, Habilitationsschrift, Siegen, 1983. 189. Y. Saito and T. Sato, J. Phys. Chem. 89, 2110 (1985). 190. A. Nakajima, Bull. Chem. SOC.Jupun 46, 2602 (1973). 191. K. Kalyanasundaram and J. K. Thomas, J. Am. Chem. SOC. 99, 2039 (1977). 192. K. A. Zachariasse, B. Kozankiewicz, and W. Kuhnle, in Surfuctunts in Solurions, Vol. 1, K. L. Mittal and B. Lindman, Eds., Plenum Press, New York, 1984, p. 565. 193. K. A. Zachariasse, N. van Phuc, and B. Kozankiewicz, J . Phys. Chem. 85, 2676 (1981). 194. M. S. Fernandez and P. Fromherz, J. Phys. Chem. 81, 1755 (1977). 195. S . Bayliss, J. Chem.Phys. 18, 292 (1950). 196. K. A. Zachariasse, W. L. C. Vaz, C. Sotomayor, and W. Kiihnle, Biochem. Biophys. Actu 688, 323 (1982). 197. L. M. Almeida, W. L. C. Vaz, K. A. Zachariasse, and V. M. C. Madeira, Biochem. 23, 4714 (1984). 198. B. R. Suddaby, P. E. Brown, J. C. Russel, and D. G. Whitten, J. Am. Chem. SOC. 107, 5609 (1985). 199. J. C. Eriksson and G. Gillberg, Acru Chem. S c u d . 24, 2019 (1966).

200. P. Mukerjee, J. R. Cardinal, and N. R. Desai, in Micellization, Solubilizution, and Microemulsions, K. L. Mittal, Ed., Vol. 1, Plenum Press, New York, 1977, p. 171. 201. J. R. Cardinal and P. Mukerjee, J. Phys. Chem. 82, 1614 (1978). 202. P. Mukerjee and J. R. Cardinal, J. Phys. Chem. 82, 1620 (1978). 203. P. Mukerjee, Ber. Bunsenges. Phys. Chem. 82, 931 (1978). 204. J. Ulmius, B. Lindman, G. Lindbloom, and T. Drakenberg, J. Coll. Interface Sci. 65, 88 (1978). 205. E. J. Bowen, N. J. Holder, and G. B. Woodger, J. Phys. Chem. 66,2491 206. 207. 208. 209. 210.

(1962). T. Wolff, Ber. Bunsenges. Phys. Chem. 85, 145 (1981). H. V. Tartar and A. L. M. Lelong, J. Phys. Chem. 59, 1185 (1955). W. Philippoff, Disc. Furuduy SOC. 11, 96 (1951). F. Reiss-Husson and V. Luzzati, J . Phys. Chem. 68, 3504 (1964). P. A. Narayama, A. S. W. Li, and L. Kevan, J. Am. Chem. SOC. 103, 3603 (1981).

REFERENCES

331

21 1 . M. Petrin, A. H. Maki, and S. Ghosh, Chern.Phys. Lett. 128,425 (1986). 212. G. von Biinau, H. Meling, and T. Wolff, in preparation.

Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.

Acyclic olefin photochemistry, 147 p(C-C) bond rupture in, 147 excited state lifetimes, 150, 159 fragmentation in, 150, 159 hot ground states, 159 Alkoxy radical-radical reactions, 246 methoxy disproportionation, 247 perdeuteromethoxy disproportionation, 248 perfluoromethoxy,249 phenoxy, 249 Alkoxy radicals, 178 abstraction of hydrogen atoms from molecules by, 249 s-butoxy, 260 t-butoxy, 252 ethoxy, 252 isopropoxy, 252 methoxy, 250 addition of,260 to boranes, 261 to boron compounds, 262 t-butoxy to carbon monoxide, 261 ethoxy to ethylene, 260 methoxy to carbon monoxide, 260 methoxy to ethylene, 261 perfluoromethoxy to perfluoropropene, 262 to phosphines, 261 to phosphates, 261 decomposition of, 221 r-amoxy, 229

s-butoxy, 226 t-butoxy, 226 ethoxy, 221 hexafluoro-t-butoxy,230 isobutoxy, 226 isopropoxy, 225 methoxy, 221 2-pentoxy, 228 phenoxy, 230 triluoro-t-butoxy, 230 isomerization of, 233 n-butoxy, 234 methoxy, 234 2-pentoxy, 234 Alkoxy radical reactions with nitric oxide, 209 disproportionation to combination ratio, 209 rate constants, 219 Alkoxyl radical reactions with nitrogen dixoide, 211 disproportionation to combination ratio, 211 rate constants, 220 Alkoxyl radical reactions with oxygen, 235 n-butoxy, 241 s-butoxy, 241 ethoxy, 235,240,244,246 n-heptoxy, 246 hydroxylmethoxy, 244 isobutoxy, 240, 244 isopropoxy, 240,244

333

334 Alkoxyl radical reactions with oxygen (Continued) methoxy, 237,238, 244 n-propoxy, 240, 244 trideuteromethoxy, 237, 239 Alkoxyl radical reactions with ozone, 262 methoxy, 262 Alkyl nitrites, 179 absorption spectrum, 179 photodemposition, 179, 1% t-butyl nitrite, 187 electronic excited radicals, 196, 200 electronic excited state, 191, 193 ethyl nitrite, 192, 194 excited products, 1% isopropyl nitrite, 188 methyl nitrite, 185, 188 primary process, 186, 192 n-propyl nitrite, 190 thermal decomposition, 200 aromatic nitrites, 205 n-butyl nitrite, 203 s-butyl nitrite, 207 t-butyl nitrite, 203,206,207 ethyl nitrite, 200, 203, 206 isopropyl nitrite, 204,205, 206 methyl nitrite, 200,205, 206 Zoctyl nitrite, 202 n-propyl nitrite, 200, 203,204 vicinyl dinitrites, 202 Amorphous polymer, 92 specific volume of, 94 Biradicals: quenching route for, 35 singlet and triplet, 34 Bueche theory, 96 ck-2-Butene, 144 absorption spectrum, 145 excited states, 145 redistribution of energy in, 145 photoisomerization, 144, 146 photolysis, 144 tram-2-Butene photoisomerization, 146 1-Butene photolysis, 153 hot hydrogen atoms in, 153 n-Butene photolysis, 150 Cage reactions in polymers, 101 diffusion effect in, 103

INDEX

primary recombination in, 102, 107 secondary recombination in, 102 Crankshaft motion, 111 Cycloaddition reactions in polymers, 127 Cyclic monoolefin photolysis, 160 fragmentation in, 160 cyclic C,, C, and C, monomers, 163 cyclobutene isomers, 160 cyclohexene, 162 cyclopentene, 161 rnethylenecyclobutane, 161 substituted cyclobutenes, 160 vinylcyclopropane, 161 photoisomerization in, 166 cis-cycloalkenes, 168 cyclohexene, 167 De Gennes scaling law, 105 Diffusion: activation energy for, 100 coefficients of, 3, 13, 65,99 empirical calculation of, 3 oxygen, 7 Stokes-Einstein equation for, 3, 54 crosslinking effect on, 97 Fickian, 98 internal Viscosity effect on, 103 rate of, 97, 99 Debye equation for, 3 oxygen, 7, 113 Stokes equation for, 104 rate constant for, 2, 5 Smoluchowski model of, 2 theoretical derivation of expression for, 76 reptation and, 104 theory of, 98 Diffusion-controlled processes, 96, 98 in simple liquids, 96 theory of, 98 Dimerization of reactive intermediates, 75 3,3-Dimethyl-l-butene photolysis, 148 Doubly excited surface, pericyclic minimum on, 68 Electron-nuclear hyerfine coupling, 70 Electron spin resonance spectra, 76 Encounter complex, 2, 24 charge-transfer interactions in, 26, 38, 75,76

INDEX

singlet and triplet interconversion, 26, 34, 36 spin states of 5, 12, 23, 62, 67, 74 Ethylene absorption spectrum, 139 Ethylene photolysis, 136 condensed state, 137 excited states in, 138 fragmentation channels, 136 sensitized, 138 vinyl radical in, 137 theory of, 139 Exciplexes, 36, 38 Eigen’s equation and dissociation of, 53 Eximers, 64,66 singlet, 64,71 triplet, 67

335

Ketone group containing polymers, photochemistry of, 109 effect of location on, 114 effect of structure on, 110, 118

Micellar systems photochemical effects, 292 local concentration and cage, 292 heavy atom, 297 intermicellar and intramicellar, 296 micellar cage effect, 300 nucleophilic substitution, 298 photocycloaddition, 293 photodimerization, 293 photohydrolysis, 298 photoionization, 302 preonentation of reactants, 303 photoadditions, 303 photodimerizations, 303 solution structure affected by, 306 electrical resistance, 309 light transmission, 309 morphological, 309 rheological, 306 Micellar systems spectroscopic probes, 310 aggregation numbers, 313 countenon bonding, 314 critical micelle concentrations, 310 frozen micelles, 321 intermicellular processes, 322 micellar size, 313 microfluidity, 310, 319 occupation statistics, 312 polarity and polarizability, 317 premicellar aggregates, 312 solubilization sites, 320 Microheterogeneous systems, 282 solute distribution in, 282 binomial, 284 critical micelle concentrations, 285 Poisson statistics for, 284 Multiplicity, 4 electron spin, 4 total quantum number for, 5 spin isomers and, 5

2-Methyl-1-alkene photochemistry, 151 Methyl substituted ethylenes, 140 photolysis of, 140, 144 spectrum of, 145 Micellar systems elementary photochemical processes, 286 energy transfer, 286 fluorescence dynamic quenching, 290 fluorescence static quenching, 287 Stern-Volmer kinetics, 290

Oxygen: acceptor of triplet energy by, 17 isomerization of stilbene analogs, 17 diffusion coefficient of, 7 fluorescence in presence of, 7 intensity of, 7 Stern-Volmer plots for, 7 lifetime of, 7 quenching interactions with, 21 diffusion controlled or less, 11

Franck-Condon factors, 14,29 Free volume, 94, 96 Friction coefficients, 3 Eigen equation for, 53 Stokes’ equation for, 3 Glass transition temperature, 94 n-1-Hexene photolysis, 147 intermediates in, 153 excess energy distribution for, 153 RRKM calculations on, 153 Internal viscosity of polymers, 103 Interstate mixing, 72 Intersystem crossing, 70 enhanced, 17

336

INDEX

Oxygen (Continued) solubility of, 7 Oxygen singlet state, 6, 8, 15, 23, 24 formation of by high-triplet-energy donor, 15 formation of by singlet state quenching, 8 photooxidation, role of, 28 quenching and, 8 Oxygen triplet state, 6, 12 n-1-Pentene photolysis, 150 Photocyclization, 164 Photo-Fries reaction, 124 Photoisomerization of acyclic alkenes, 155 alkyl substituents effect on, 157 calculation of electronic states of, 157 fluorescence related to, 159 ck-2-pentene, 157 tetramethyl ethylene, 155 Photoisomerization in polymers, 125 Photolithography polymers, 117 chain scission by irradiation of, 117 Photoreduction of polymers, 117 Photoresists, cinnamic acid derivatives, 126 Photosensitization, 154 acyclic alkenes isomerization by, 155 cyclic monoolefins fragmentation by, 164 Polyacrylophenones, 123 Polymer gels, 96 Polymer structures, infrared spectra determination of, 93 Propene, 140 electronic state of, 142 photolysis of, 140 condensed phase, 142

ethylcarbene derived, 142 pathways in, 141 sensitized, 142 triplet photochemistry of, 142 Quantum yields for polymers, 113 ketone group location and, 114 significance of, 110 Quenching: reencounter, 34 singlet, 34 aldehydes and ketones, 34 valerophene triplets, 55 Radical pairs: singlet, 42

triplet, 39 Radical self-termination, 38 as reference reaction, 39 solvent cage effects in, 39, 46 Reptation movement in polymers, 104 Rotation spectra of polymers, 93 Sandros plot, 24 Scaling law, de Gennes, 105 Semicrystalline polymers, 95 Singlet excited states, 6 oxygen, 6 quenching and, 7 Soft X-rays, 121 synchotron as source of, 121 Spin-exchange quenching, 24, 35, 38 olefin triplets, 17, 18 cooperative by oxygen and azulene, 21 stilbene triplets, 18 oxygen mechanism for, 18 Spin-statistical factor, 5 , 12, 13, 16, 42, 46, 57, 58, 68 Stokes-Einstein equation, 3, 54, 278 Stokes equation, 104 Surfactant solutions, 274 classification of, 274 micelles in, 275 diffusion of, 278 Dill-Flory model of anionic, 276 Hartley model of anionic, 275 size distribution of, 280 Temperature: glass transition, T,, 93 motion relative to, 95 reactivity relative to, 115 solid phase transition, T,, 95 Translation: microfriction factor for, 4 Spernol-Wirtz, 54 Transmission coefficient, 60,63 Triplet states: p-carotene absorption from, 28 excitation transfer from, 24, 59 quintet pair states in destruction of, 73 spin conservation in quenching of, 12 Triplet-triplet: annihilation, 63 doubly excited pairs, 67 encounters, 67 excitation transfer, 13, 16

Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.

CUMULATIVE INDEX, VOLUMES 1-14

Addition of Atoms to Olefins, in Gas Phase (Cvetanovic) . . . . . . . . . . . . Alcohols, Ethers, and Amines, Photolysis of Saturated (von Sonntag and Schuchmann) . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . , . . . Alkanes and Alkyl Radicals, Unimolecular Decomposition and Isotope Effects of (Rabinovitch and Setser) .. . .. .. .... . .. . . .. . . . .. .. .. . Alkyl Nitrites, Decomposition of and the Reactions of Alkoxyl Radicals (Heicklen) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aromatic Hydrocarbon Solutions, Photochemistry of (Bower) . . . . . . . . Benzene, Excitation and Deexcitation of (Cundall, Robinson and Pereira) . . . .. . . . . . . . . . . . . . . . . . .. . . . . . .. . . . .. .. . . . .. . . . . . . . . . Bichromophoric Systems, Excited State Behavior of Some (De Schryver, Boens and Put) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carbonyl Compounds, The Photocycloaddition of, to Unsaturated Systems: The Syntheses of Oxetanes (Arnold) . . . . . . . . . . . . . . . . . . Cobalt (111) and Chromium (111) Complexes, the Photochemistry of, in Solution (Valentine, Jr.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cyclic Ketones, Photochemistry of (Srinivasan) . .. . . . .. . . . . . .. .. . . . . Cyclobutanones, Solution Phase Photochemistry of (Morton and Turro) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . a-Dicarbonyl Compounds, The Photochemistry of (Monroe) . . . . . . . . . Diffusion-Controlled Reactions, Spin-Statistical Factors in (Saltiel and Atwater) ............... ........ ............................ Electron Energy Transfer between Organic Molecules in Solution (Wilkinson) . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . , . . . . . . .. . . . . . .. .. Electronically Excited Halogen Atoms (Husain and Donovan) . . . . . . . . Electron Spin Resonance Spectroscopy, Application of to Photochemistry (Wan) .......................................

VOL. 1

PAGE 115

10

59

3

1

14 1

177 23

10

147

10

359

6

301

6 1

123 83

9

197

8

77

14

1

3 8

24 1

9

1

1

337

338

INDEX

Electron Transfer, Photoinduced in Organic Systems, Control of Back Electron Transfer of (Fox) ................................... Electron Transfer Luminescence in Solution (Zweig) ................ Excimers, What’s New in (Yakhot, Cohen, and Ludmer) ............ Free Radical and Molecule Reactions in Gas Phase, Problems of Structure and Reactivity (Benson) ............................. Gas Phase, Addition of Atoms of Olefins in (Cvetanovic) ............ Gas Phase Reactions, Photochemical, in Hydrogen-Oxygen System (Volman) .................................................. Gas Phase Reactions Involving Hydroxyl and Oxygen Atoms, Mechanisms and Rate Constants of (Avramenko and Kolesnika) Halogenated Compounds, Photochemical Processes in (Majer and Simons) .................................................... Hydrogen-Oxygen Systems, Photochemical Gas Phase Reactions in (Volman) .................................................. Hydroxyl and Oxygen Atoms, Mechanisms and Rate Constants of Elementary Gas Phase Reactions Involving (Avramenko and Kolesnikova) ............................................... Hydroxyl Radical with Organic Compounds in the Gas Phase, Kinetics and Mechanisms of the Reactions of (Atkinson, Darnall, Winer, Lloyd and Pitts) ............................................. Hypophalites, Developments in Photochemistry of (Akhtar) .......... Imaging Systems, Organic Photochemical (Delzenne) ................ Intramolecular Proton Transfer in Electronically Excited Molecules (Klopffer) .................................................. Ionic States, in Solid Saturated Hydrocarbons, Chemistry of (Kevan and Libby) ................................................. Isotopic Effects, in Mercury Photosensitization (Gunning and Strausz) Mechanism of Energy Transfer, in Mercury Photosensitization (Gunning and Strausz) ....................................... Mechanistic Organic Photochemistry, A New Approach to (Zimmerman) .............................................. Mercury Photosensitization, Isotopic Effects and the Mechanism of Energy Transfer in (Gunning and Strausz) ..................... Metallocenes, Photochemistry in the (Bozak) ....................... Methylene, Preparation, Properties, and Reactivities of (De More and Benson) .................................................... Neutral Oxides and Sulfides of Carbon, Vapor Phase Photochemistry of the (Filseth) .............................................. Nitric Oxide, Role in Photochemistry (Heicklen and Cohen) ......... Noyes, W.A., Jr., A Tribute (Heicklen) ........................... Nucleic Acid Derivatives, Advances in the Photochemistry of (Burr) . .

13 6 11

237 425 489

2

1 115

43 2

25

2

137

1

43

2

25

11 2

375 263

11

1

10

311

2 1

183 209

1

209

1

183

1 8

209 227

2

219

10

1 157 vii 193

5

13 6

INDEX

Olefins. Photolysis of Simple. Chemistry of Electronic Excited States or Hot Ground States? (Collin) ............................... Organic Molecules. Photochemical Rearrangements of (Chapman) .... Organic Molecules in Adsorbed or Other Perturbing Polar Environments. Photochemical and Spectroscopic Properties of (Nicholls and Leermakers) ................................... Organic Molecules in their Triplet States. Properties and Reactions of (Wagner and Hammond) ..................................... Organic Nitrites. Developments in Photochemistry of (Akhtar) ....... Organic Photochemical Refractive-Index Image Recording Systems (Tomlinson and Chandross) .................................. Organo-Transition Metal Compounds. Primary Photoprocesses of (Bock and von Gustorf) ...................................... Perhalocarbons. Gas Phase Oxidation of (Heicklen) ................. Phosphorescence and Delayed Fluorescence from Solutions (Parker) . . Phosphorescence-Microwave Multiple Resonance Spectroscopy (ElSayed) ..................................................... Photoassociation in Aromatic Systems (Stevens) .................... Photochemical Mechanisms. Highly Complex (Johnston and Cramarossa) ................................................ Photochemical Oxidation of Aldehydes by Molecular Oxygen. Kinetics and Mechanism of (Niclause. Lemaire. and Letort) ............. Photochemical Reactivity. Reflections on (Hammond) ............... Photochemical Rearrangements of Conjugated Cyclic Ketones: The Present State of Investigations (Schaffner)...................... Photochemical Transformations of Polyenic Compounds (Mousseron) Photochemistry of Conjugated Dienes and Trienes (Srinivasan) ....... Photochemistry of Rhodopsins. The (Ottolenghi) ................... Photochemistry of Simple Aldehydes and Ketones in the Gas Phase (Lee and Lewis) ............................................ Photochemistry of the Troposphere (Levy) ......................... Photochemistry of Vitamin D and Its Isomers and of Simple Trienes (Jacobs and Havinga) ........................................ Photochemistry. Vocabulary of (Pitts. Wilkinson. Hammond) ........ Photochromism (Dessauer and Paris) .............................. Photo-Fries Rearrangement and Related Photochemical (1.j) Shifts of (j =3.5.7) of Carbonyl and Sulfonyl Groups (Bellus) ............ Photography. Silver Halide. Chemical Sensitization. Spectral .. Sensitization. Latent Image Formation (James) ......... Photoionization and Photodissociation of Aromatic Molecules. by Ultraviolet Radiation (Terenin and Vilessov) ................... Photoluminescence Methods in Polymer Science (Beavan. Hargreaves and Phillips) ................................................ Photolysis of the Diazirines (Frey) ................................ Photooxidation Reactions. Gaseous (Hoare and Pearson) ............ Photooxygenation Reactions. Type 11. in Solution (Gollnick) ......... Photopolymerization. Dye Sensitized (Eaton) . . Photosensitized Reactions. Complications in (Engel and Monroe) .....

14 1

135 323

8

315

5 2

21 263

12

201

10

221

7 2

57 305

9 8

311 161

4

1

4 7

25 373

4 4 4 12

81 195 113 97

12 9

1 369

11 1 1

305 1 275

8

109

13

329

2

385

11

207 225 83

4

3 6 8

1

427 245

340

INDEX

Polymers. Photochemistry and Molecular Motion in Solid Amorphous (Guillet) ................................................... Primary Processes and Energy Transfer: Consistent Terms and Definitions (Porter. Balzani and Moggi) .......................

14

91

9

147

...

13

95

Radiationless Transitions. Isomerization as a Route for (Phillips. Lemaire. Burton and Noyes. Jr.) .............................. Radiationless Transitions in Photochemistry (Jortner and Rice) .......

5

329 149

7 11

311 105

4 13

49 1

2 7 13 4

183 1 165 143

2 14

63 273

12 5

283 1

3

157

2

385

Quantum Theory of Polyatomic Photodissociation (Kresin and Lester)

Singlet Molecular Oxygen (Wayne) ................................ Singlet Molecular Oxygen. Physical Quenchers of (Bellus) ........... Singlet and Triplet States: Benzene and Simple Aromatic Compounds (Noyes and Unger) .......................................... Small Molecules. Photodissociation of (Jackson and Okabe) .......... Solid Saturated Hydrocarbons. Chemistry of Ionic States in (Kevan and Libby) ................................................. Spin Conservation (Matsen and Klein) ............................. Stilbenes. Bimolecular Photochemical Reactions of (Lewis) .......... Sulfur Atoms. Reactions of (Gunning and Strausz) .................. Sulfur and Nitrogen Heteroatomic Organic Compounds. Photochemical Reactions of (Mustafa) ...................................... Surfactant Solutions. Photochemistry in (von Biinau and Wolff) ...... Theory and Applications of Chemically Induced Magnetic Polarization in Photochemistry (Wan) ..................................... Triatomic Free Radicals. Spectra and Structures of (Herzberg) ....... Ultraviolet Photochemistry. Vacuum (McNesby and Okabe) .......... Ultraviolet Radiation. Photoionization and Photodissociation of Aromatic Molecules by (Terenin and Vilessov) .................

7

THE NATURE OF LIVING SYSTEMS by James G.Miller President, University of Louisville

General living systems theory is concerned with seven levels of living systems-cell, organ, organism, group, organization, society, and supranational system. An exposition of the basic concepts in this theory appeared in “Living Systems: Basic Concepts,” Behavioral Science, 1965, 10, 193-237. (See also “Living Systems: Structure and Process,” and “Living Systems: Cross-Level Hypotheses,” Behavioral Science, 1965,lO.337-411.) A condensation of the basic concepts also appeared in “The Nature of Living Systems,” Behavioral Science, 1971,16,277-301,which is reprinted beginning on the next page. Following that i s a n analysis in terms of this conceptual system of present knowledge concerning one level of living system-the society. I n order to emphasize the cross-level formal identities among levels of living systems, this article follows exactly the same outline a s other articles written by the author on the cell (“Living Systems. 11. The Cell,” Currents in Modern Biology, 1971,4,78-206),the organ (“Living Systems. 111.The Organ,” Currents in Modern Biology. 1971,4.207-256). the organism (“Living Systems. 11. The Organism,” Quarierly Review of Biology, 1973.48: 1 (Pt 2). 92-276).the group (“Living Systems: The Group,” Behavioral Science, 1971,16,302-358),and the organization (“Living Systems: The Organization,” Behavioral Science, 1972 17.1-182). Their subheadings and section numbers are identical. All these articles will also be published as chapters of the author’s forthcoming book Living Systems (New York: McGraw-Hill, 1976). Another chapter in that book, also following the same outline. will analyze current knowledge about the highest level of living systems-the supranational system. Since anatomists and physiologists are usually laymen i n organization theory or international relations, psychologists are commonly laymen in economics, and social scientists are ordinarily laymen in cellular biology, all parts of the book, including the article published here, are necessarily written for intelligent laymen rather than experts, even though the articles deal with many technical topics. Some statements in them will seem to experts to be too elementary to be worth repeating. If a fact is fundamental and may not be known to specialists in other fields, it is stated here, even if it is elementary to the experts. The complex division of labor of modern science, often characterized by pluralistic insularity, requires this. The multitude of detailed and specialized experiments and studies that have been carried out provide the substance of the scientific investigation of organizations. Their findings constitute the trees. But a n overview of these results and of the relationships among them-a view of the forest-is also essential. Such a telescopic rather than a microscopic view may suggest the proper balance for research on various aspects of society and clarify the priorities for future efforts. Many ideas presented here are not original with the author, though the arrangement is. Unless several persons have wrestled with an idea it i s often not fundamental. The author has necessarily selected only a few researches to discuss out of the vast published repertoire, and so his selection has necessarily been arbitrary. Experts in each special field might agree on other studies as more important. Some of the author’s statements may be wrong and his analysis ill advised. If so he would appreciate corrections-it i s hard to cover such a wide range and still make no errors. The discussion of the processes of each subsystem ends with a number of examples of the variables of that subsystem which can be observed and measured. These variables make concrete the content of science a t this level. They appear also to be common for a particular subsystem a t multiple levels of living systems. Measurement of these variables, therefore, can be one way to determine whether crosslevel formal identities exist. Throughout the text there are numerous references to cross-level hypotheses. These are mentioned for a similar purpose-to show that propositions possibly valid a t other levels may also apply to societies. These hypotheses, numbered to indicate the section of the article to which they apply, appear on pages 366-368 of the article on the society. Many of them have been shown in other articles to be relevant to other levels of living systems as well. At each level there are scientists who apply systems theory in their investigations. They are system theorists but not necessarily general systems theorists. They are general systems theorists only if they accept the more daring and controversial position that-though every living system and every level is obviously unique-there are important formal identities of large generality across levels. These can potentially be evaluated quantitatively, applying the same model to data collected a t two or more levels. This possibility is the chief reason why the author has used the same outline with identically numbered sections to analyze the present knowledge about each of the seven levels of living systems. The following survey of what i s known about societies as systems, therefore, is to be read as a single segment of a larger, integrated whole. 343

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systems theory is a set of re- pull on each other. (e) Solid objects moving lated definitions, assumptions, and in such space cannot pass through one propositions which deal with reality as an another. (f) Solid objects moving in such integrated hierarchy of organizations of space are subject to friction when they matter and energy. General living systems contact another object. The characteristics and constraints of theory is concerned with a special subset of physical space affect the action of all conall systems, the living ones. Even more basic to this presentation crete systems, living and nonliving. The than the concept of “system” are the con- following are some examples: (a) On the cepts of “space,” “time,” “matter,” “en- average, people interact more with persons ergy,” and “information,” because the liv- who live near to them in a housing project ing systems discussed here exist in space than with persons who live far away in the and are made of matter and energy organ- project. (b) The diameter of the fuel supply lines laid down behind General Patton’s adized by information. vancing American Third Army in World 1. SPACE AND TIME War I1 determined the amount of friction In the most general mathematical sense, the lines exerted upon the fuel pumped a space is a set of elements which conform through them, and therefore the rate at to certain postulates. The conceptual spaces which fuel could flow through them to supof mathematics may have any number of ply Patton’s tanks. This wm one physical dimensions. constraint which limited the rate at which Physical space is the extension surround- the army could advance, because they had ing a point. Classically the three-dimen- to halt when they ran out of fuel. (c) Today sional geometry of Euclid was considered information can flow worldwide almost into describe accurately all regions in physi- stantly by telegraph, radio, and television. cal space. The modern general theory of In the Seventeenth Century it took weeks relativity has shown that physical space- for messages to cross an ocean. A governtime is more accurately described by a ment could not send messages so quickly to geometry of four dimensions, three of space its ambassadors then as it can now because of the constraints on the rate of movement and one of time. This presentation of a general theory of of the marker bearing the information. Conliving systems will employ two sorts of sequently ambassadors of that century had spaces in which they may exist, physical much more freedom of decision than they or geographical space and conceptual or do now. Physical space is a common space, for the abstracted spaces. reason that it is the only space in which all 1.1 Physical or geographical space concrete systems, living and nonliving, exist This will be considered as Euclidean space, (though some may exist in other spaces which is adequate for the study of all aspects simultaneously). Physical space is shared by of living systems as we now know them. all scientific observers, and all scientific Among the characteristics and constraints data must be collected in it. This is equally of physical space are the following: (a) true for natural science and behavioral From point A to point B is the same dis- science. Most people learn that physical tance as from point B to point A . (b) Mat- space exists, which is not true of many ter or energy moving on a straight or curved spaces I shall mention in the next section. path from point A to point B must pass They can give the location of objects in it. through every intervening point on the path. 1.2 Conceptual or abstracted spaces This is true also of markers bearing inforScientific observers often view living mation. (c) In such space there is a maxi- systems as existing in spaces which they conmum speed of movement for matter, en- ceptualiie or abstract from the phenomena ergy, and markers bearing information. (d) with which they deal. Examples of such Objects in such space exert gravitational spaces are: (a) Peck order in birds or other ENERAL

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THE NATUREOF LIVINGSYSTEMS animals. (b) Social class space (lower lower, upper lower, lower middle, upper middle, lower upper, and upper upper classes). (c) Social distance among ethnic or racial groups. (d) Political distance among political parties of the right and the left. (e) Sociometric space, e.g., the rating on a scale of leadership ability of each member of a group by every other member. (f) A space of time costs of various modes of transportation, e.g., travel taking longer on foot than by air, longer upstream than down. These conceptual and abstracted spaces do not have the same characteristics and are not subject to the same constraints as physical space. Each has characteristics and constraints of its own. These spaces may be either conceived of by a human being or learned about from others. Interpreting the meaning of such spaces, observing relations, and measuring distances in them ordinarily require human observers. Consequently the biases of individual human beings color these observations. Social and some biological scientists find conceptual or abstracted spaces useful because they recognize that physical space is not a major determinant of certain processes in the living systems they study. E.g., no matter where they enter the body, most of the iodine atoms in the body accumulate in the thyroid gland. The most frequent interpersonal relations occur among persons of like interest or like attitudes rather than among geographical neighbors. Families frequently come together for holidays no matter how far apart their members are. Allies like England and Australia are often more distant from each other in physical space than they are from their enemies. It is desirable that scientists who make observations and measurements in any space other than physical space should attempt to indicate precisely what are the transformations from their space to physical space. Other spaces are definitely useful to science, but physical space is the only common space in which all concrete systems exist. 1.3 Time

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T i m is the particular instant at which a structure exists or a process occurs, or the measured or measurable period over which a structure endures or a process continues. For the study of all aspects of living systems as we know them, for the measurement of durations, speeds, rates, and accelerations, the usual absolute scales of time-seconds, minutes, days, years-are adequate. A concrete system can move in any direction on the spatial dimensions, but only forwardnever backward-on the temporal dimension. 2. MATTER AND ENERGY

Matter is anything which has mass (m) and occupies physical space. Energy ( E ) is defined in physics as the ability to do work. The principle of the conservation of energy states that energy can be neither created nor destroyed in the universe, but it may be converted from one form to another, including the energy equivalent of rest-mass. Matter may have (a) kinelk energy, when it is moving and exerts a force on other matter; (b) potential energy, because of its position in a gravitational field; or (c) rest-muss energy, which is the energy that would be released if mass were converted into energy. Mass and energy are equivalent. One can be converted into the other in accordance with the relation that rest-mass energy is equal to the mass times the square of the velocity of light. Because of the known relationship between matter and energy, throughout this article the joint term matterenergy is used except where one or the other is specifically intended. Living systems require matter-energy, needing specific types of it, in adequate amounts. Heat, light, water, minerals, vitamins, foods, fuels, and raw materials of various kinds, for instance, may be required. Energy for the processes of living systems is derived from the breakdown of molecules (and, in a few recent cases, of atoms as well). Any change of state of matter-energy or its movement over space, from one point to another, is action. It is one form of process. 3. INFORMATION

Throughout this presentation informatioii ( H ) will be used in the technical sense first

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suggested by Hartley in 1928.1 Later it was developed by Shannon in his mathematical theory of communication.2 It is not the same thing as meaning or quite the =me as information as we usually understand it. Meaning is the significance of information to a system which processes it: it constitutes a change in that system’s processes elicited by the information, often resulting from associations made to it on previous experience with it. Information is a simpler concept: the degrees of freedom that exist in a given situation to choose among signals, symbols, messages, or patterns to be transmitted. The total of all these possible categories (the alphabet) is called the ensemble. The amount of information is measured by the binary digit, or bit, of information. It is the amount of information which relieves the uncertainty when the outcome of a situation with two equally likely alternatives is known. Legend says the American Revolution was begun by a signal to Paul Revere from Old North Church steeple. It could have been either one or two lights, “one if by land or two if by sea.” If the alternatives were equally probable, the signal conveyed only one bit of information, resolving the uncertainty in a binary choice. But it carried a vast amount of meaning, meaning which must be measured by other sorts of units than bits. The term marker refers to those observable bundles, units, or changes of matterenergy whose patterning bears or conveys the informational symbols from the ensemble or repertoire.a These might be the stones of Hammurabi’s day which bore cuneiform writing, parchments, writing paper, Indians’ smoke signals, a door key with notches, punched cards, paper or magnetic tape, a computer’s magnetized ferrite core memory, an arrangement of nucleotides in a DNA molecule, the molecular structure of a hormone, pulses on a telegraph wire, or waves emanating from a radio station. The marker may be static, as in a book or in a computer’s memory. Communication of any sort, however, requires that the marker move in space, from the transmitting system to the receiving system, and this movement follows the same physical laws as the

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movement of any other sort of matterenergy. The advance of communication technology over the years has been in the direction of decreasing the matter-energy costs of storing and transmitting the markers which bear information. The efliciency of information processing can be increased by lessening the mass of the markers, making them smaller so they can be stored more compactly and transmitted more rapidly and cheaply. Over the centuries engineering progress has altered the mode in markers from stones bearing cuneiform to magnetic tape bearing electrons, and clearly some limit is being approached. I n recent years systems theorists have been fascinated by the new ways to study and measure information flows, but matterenergy flows are equally important. Systems theory deals both with information theory and with energetics-such matters as the muscular movements of people, the flow of raw materials through societies, or the utilization of energy by brain cells. It was noted above that the movement of matter-energy over space, action, is one form of process. Another form of process is information processing or communication, which is the change of information from one state to another or its movement from one point to another over space. Communications, while being processed, are often shifted from one matter-energy state to another, from one sort of marker t o another. If the form or pattern of the signal remains relatively constant during these changes, the information is not lost. For instance, it is now possible to take a chest X ray, storing the information on photographic film; then a photoscanner can pass over the film line by line, from top to bottom, converting the signals to pulses in an electrical current which represent bits; then those bits can be stored in the core memory of a computer; then those bits can be processed by the computer so that contrasts in the picture pattern can be systematically increased; then the resultant altered patterns can be printed out on a cathode ray tube and photographed. The pattern of the chest structures, the information, modified for easier interpretation, has remained largely invariant

THE NATURE

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throughout all this processing from one sort of marker to another. Similar transformations go on in living systems. One basic reason why communication is of fundamental importance is that informational patterns can be processed over space and the local matter-energy a t the receiving point can be organized to conform to, or comply with, this information. As already stated, if the information is conveyed on a relatively small, light, and compact marker, little energy is required for this process. Thus it is a much more efficient way to accomplish the result than to move the entire amount of matter-energy, organized as desired, from the location of the transmitter to that of the receiver. This is the secret of success of the delivery of “flowers by telegraph.” It takes much less time and human effort to send a telegram from London to Paris requesting a florist in the latter place to deliver flowers locally, than it would to drive or fly with the flowers from the former city to the latter. Shannon was concerned with mathematical statements describing the transmission of information in the form of signals or messages from a sender to a receiver over a channel such as a telephone wire or a radio band.4 These channels always contain a certain amount of noise. In order to convey a message, signals in channels must be patterned and must stand out recognizably above the background noise. Matter-energy and information always flow together. Information is always borne on a marker. Conversely there is no regular movement in a system unless there is a difference in potential between two points, which is negative entropy or information. Which aspect of the transmission is most important depends upon how it is handled by the receiver. If the receiver responds primarily to the material or energic aspect, it is a matter-energy transmission; if the response is primarily to the information, it is an information transmission. For example, the banana eaten by a monkey is a nonrandom arrangement of specific molecules, and thus has its informational aspect, but its use to the monkey is chiefly to increase the energy available to him. So it is an

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energy transmission. The energetic character of the signal light that tells him to depress the lever which will give him a banana is less important than the fact that the light is part of a nonrandom, patterned organization which conveys information to him. So it is an information transmission. Moreover, just as living systems must have specific forms of matter-energy, so they must have specific patterns of information. For example, some species of animals do not develop normally unless they have appropriate informatiori inputs in infancy. As Harlow showed, for instance, monkeys cannot make proper social adjustments unless they interact with other monkeys during a period between the third and sixth months of their lives? 4. SYSTEM

The term system has a number of meanings. There are systems of numbers and of equations, systems of value and of thought, systems of law, solar systems, organic systems, management systems, command and control systems, electronic systems, even the Union Pacific Railroad system. The meanings of ‘(system” are often confused. The most general, however, is: A system is a set of interacting units with relationships among them.6 The word (‘set” implies that the units have some common properties, which is essential if they are to interact or have relationships. The state of each unit is constrained by, conditioned by, or dependent on the state of other units.’ The units are coupled.

4.1 Conceptual systems 4.1.1 Units. Units of a conceptual system are terms, such as words (commonly nouns, pronouns, and their modifiers), numbers, or other symbols, including those in computer simulations and programs. 4.1.2 Relationships. A relationship of a conceptual system is a set of pairs of units, each pair being ordered in a similar way. E.g., the set of all pairs consisting of a number and its cube is the cubing relationship. Relationships are expressed by words (eommonly verbs and their modifiers), or by logical or mathematical symbols, including

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system is all there is going to be. The energy gradually is used up and the matter gradually becomes disorganized. A body in a hermetically sealed casket, for instance, slowly crumbles and its component molecules become intermingled. Separate layers of liquid or gas in a container move toward random distribution. Gravity may prevent entirely random arrangement. 4.2.5 Nonliving system. Every concrete 4.2 Concrete system system which does not have the characA concrete systewa is a nonrandom accumu- teristics of a living system is a nonliving lation of matter-energy, in a region in phys- system. ical space-time, which is organized into 4.2.6 Living systems. The living systems interacting, interrelated subsystems or com- are a special subset of the set of all possible ponents. concrete systems, composed of the plants 4.2.1 Units. The units (subsystems, com- and the animals. They all have the followponents, parts, or members) of these systems ing characteristics: are also concrete systems.* (a) They are open systems. 4.2.2 Relationships. Relationships in con(b) They use inputs of foods or fuels to crete systems are of various s o h , including restore their own energy and repair breakspatial, temporal, spatiotemporal, and cau- downs in their own organized structure. (c) They have more than a certain minisal. Both units and relationships in concrete mum degree of complexity. systems are empirically determinable by (d) They contain genetic material comsome operation carried out by an observer. posed of deoxyribonucleic acid (DNA), I n theoretical verbal statements about con- presumably descended from some primordial crete systems, nouns, pronouns, and their DNA common to all life, or have a charter, modifiers typically refer to concrete systems, or both. One or both of these is the temoriginal “blueprint” or “prosubsystems, or components; verbs and their plate-the modifiers usually refer to the relationships gram”-of their structure and process from among them. There are numerous examples, the moment of their origin. however, in which this usage is reversed (e) They are largely composed of protoand nouns refer to pat,terns of relationships plasm including proteins and other characor processw, such as “nerve impulse,” teristic organic compounds. “reflex,” “action,” “vote,” or “annexation.” (f) They have a decider, the essential 4.2.3 Open system. Most concrete sys- critical subsystem which controls the entire tems have boundaries which are at least system, causing its subsystems and compartially permeable, permitting sizeable ponents to interact. magnitudes of a t least certain sorts of mat(g) They also have certain other specific ter-energy or information transmissions to critical subsystems or they have symbiotic cross them. Such a system is an open sys- or parasitic relationships with other living tem. Such inputs can repair system compo- or nonliving systems which carry out the nents that break down and replace energy processes of any such subsystem they lack. (h) Their subsystems are integrated tothat is used up. 4.2.4 Closed system. A concrete system gether to form actively self-regulating, dewith impermeable boundaries through which veloping, reproducing unitary systems, with no matter-energy or information transmis- purposes and goals. (i) They can exist only in a certain ensions of any sort can occur is a closed system. No actual concrete system is completely vironment. Any change in their environclosed, so concrete systems are either rela- ment of such variables as temperature, air tively open or relatively closed. Whatever pressure, hydration, oxygen content of the matter-energy happens to be within the atmosphere, or intensity of radiation, out-

those in computer simulations and programs, which represent operations, e.g., inclusion, exclusion, identity, implication, equivalence, addition, subtraction, multiplication, or division. The language, symbols, or computer programs are all concepts and always exist in one or more concrete systems, living or nonliving, like a scientist, a textbook, or a computer.

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THE NATURE OF LIVINGSYSTEMS side a relatively narrow range which occurs on the surface of the earth, produces stresses to which they cannot adjust. Under such stresses they cannot survive. 4.3 Abstracted system

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system is abstracted from this, being the set of relationships which are the form of organization. To him the important units are classes of input-output relationships of subsystems rather than the subsystems themselves.

4.3.1 Units. The units of abstracted systems are relationships abstracted or selected 4.4 Abstracted vs. concrete systems by an observer in the light of his interests, One fundamental distinction between abtheoretical viewpoint, or philosophical bias. stracted and concrete systems is that the Some relationships may be empirically de- boundaries of abstracted systems may at terminable by some operation carried out times be conceptually established a t regions by the observer, but others are not, being which cut through the units and relationonly his concepts. ships in the physical space occupied by con4.3.2 Relationships. The relationships men- crete systems, but the boundaries of these tioned above are observed to inhere and latter systems are always set at regions interact in concrete, usually living, systems. which include within them all the units In a sense then, these concrete systems are and internal relationships of each system. the relationships of abstracted systems. A science of abstracted systems certhhly The verbal usages of theoretical statements is possible and under some conditions may concerning abstracted systems are often be useful. When Euclid was developing the reverse of those concerning concrete geometry, with its practical applications to systems: the nouns and their modifiers typ- the arrangement of Egyptian real estate, it ically refer to relationships and the verbs is probable that the solid lines in his figures and their modifiers (including predicates) to were originally conceived to represent the the concrete systems in which these relation- borders of land areas or objects. Sometimes, ships inhere and interact. These concrete as in Fig. 1 , he would use dotted “consystems are empirically determinable by struction lines” to help conceptualize a some operation carried out by the observer. geometric proof. The dotted line did not A theoretical statement oriented to con- correspond to any actual border in space. crete systems typically would say “Lincoln Triangle ABD could be shown to be conwas President,” but one oriented to ab- gruent to Triangle CBD, and therefore the stracted systems, concentrating on relation- angle BAD was equal to the angle BCD. ships or roles, would very likely be phrased After the proof was completed, the dotted “The Presidency was occupied by Linc~ln.”~line might well be erased, since it did not An abstracted system differs from an correspond to anything real and was useful abstraction, which is a concept (like those only for the proof. Such construction lines, that make up conceptual systems) repre- representing relationships among real lines, senting a class of phenomena all of which are considered to have some similar “class characteristic.” The members of such a class are not thought to interact or be interrelated, as are the relationships in an abstracted system. Abstracted systems are much more common in social science theory than in natural science. Parsons has attempted to develop general behavior theory using abstracted systems. To some a social system is something concrete in space-time, observable and presumably measurable by techniques like those of natural science. To Parsons the FIG.1. A Euclidean Figure. Behavioral Science, Volume 20, 1975

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were used in the creation of early forms of abstracted systems. If the diverse fields of science are to be unified, it would help if all disciplines were oriented either to concrete or to abstracted systems. It is of paramount importance for scientists to distinguish clearly between them. To use both kinds of systems in theory leads to unnecessary problems. It would be best if one type of system or the other were generally used in all disciplines. All three meanings of “system” are useful in science, but confusion results when they are not differentiated. A scientific endeavor may appropriately begin with a conceptual system and evaluate it by collecting data on a concrete or on an abstracted system, or it may equally well first collect the data and then determine what conceptual system it fits. Throughout this article and the next the single word “system,” for brevity, will always mean “concrete system.” The other sorts of systems will always be explicitly distinguished as either “conceptual system” or “abstracted system.” 5. STRUCTURE

The structure of a system is the arrangement of its subsystems and components in three-dimensional space at a given moment of time. This always changes over time.’O It may remain relatively fixed for a long period or may change from moment to moment, depending upon the characteristics of the process in the system. This process halted at any given moment, as when motion is frozen by a high-speed photograph, reveals the three-dimensional spatial arrangement of the system’s components as of that instant. 6. PROCESS

All change over time of matter-energy or information in a system is process. If the equation describing a process is the same no matter whether the temporal variable is positive or negative, it is a reversible process; otherwise it is irreversible. Process includes the ongoing function of a system, reversible actions succeeding each other from moment to moment. Process also includes history, less readily reversed changes like mutations, birth, growth, development, Behavioral Science, Volume 20, 1975

aging, and death; changes which commonly follow trauma or disease; and the changes resulting from learning which are not later forgotten. Historical processes alter both the structure and the function of the system. The statement “less readily reversed” has been used instead of “irreversibleJJ(although many such changes are in fact irreversible) because structural changes sometimes can be reversed. E.g., a component which has developed and functioned may atrophy and finally disappear with disuse; a functioning part, like the tentacle of a hydra, may be chopped off of the animal and regrow. History, then, is more than the passage of time. It involves also accumulation in the system of residues or effects of past events (structural changes, memories, and learned habits). A living system carries its history with it in the form of altered structure, and consequently of altered function also. So there is a circular relation among the three primary aspects of systems-structure changes momentarily with functioning, but when such change is so great that it is essentially irreversible, a historical process has occurred, giving rise to a new structure. 7. TYPE

If a number of individual living systems are observed to have similar characteristics, they often are classed together as a type. Types are abstractions. Nature presents an apparently endless variety of living things which man, from his earliest days, has observed and classified-first, probably, on the basis of their threat to him, their susceptibility to capture, or their edibility, but eventually according to categories which are scientifically more useful. Classification by species is applied to organisms, plants or animals, or to free-living cells, because of their obvious relationships by reproduction. These systems are classified together by taxonomists on the basis of likeness of structure and process, genetic similarity and ability to interbreed, and local interaction, often including, in animals, ability to respond appropriately to each other’s signs. There are various types of systems at other levels of the hierarchy of living systems besides the cell and organism levels,

THENATUREOF LIVINGSYSTEMS each classed according to different structural and process taxonomic differentia. There are, for instance, primitive societies, agricultural societies, and industrial societies. There are epithelial cells, fibroblasts, red blood cells, and white blood cells, as well as free-living cells. 8. LEVEL

The universe contains a hierarchy of systems, each higher level of system being composed of systems of lower levels.11Almns are composed of particles; molecules, of atoms; crystals and organelles, of molecules. About a t the level of crystallizing viruses, like the tobacco mosaic virus, the subset of living systems begins. Viruses are necessarily parasitic on cells, so cells are the lowest level of living systems. Cells are composed of atoms, molecules, and multimolecular organelles; organs are composed of cells aggregated into tissues; organisms, of organs; groups (e.g., herds, flocks, families, teams, tribes), of organisms; organizations, of groups (and sometimes single individual organisms) ;societies, of organizations, groups and individual persons or organisms; and supranationul systems, of societies and organizations. Highrr levels of systems may be of mixed composition, living and nonliving. They include planets, solar systems, galaxies, and so forth. It is beyond the scope of this paper t o deal with the characteristicswhatever they may be-of systems below and above thoscl levels which include the various forms of life, although others have done so.12 The subset of living systems includes cells, organs, organisms, groups, organizations, societies, and supranational systems. It would be convenient for theorists if the hierarchical levels of living systems fitted neatly into each other like Chinese boxes. The facts are more complicated. No one can argue that there are exactly these seven levels, no more and no less. For example, one might conceivably separate tissue and organ into two separate levels. Or one might maintain that the organ is not a level, since no known organ, except perhaps some mcsozoans which are composed of a few cells and are usually considered organisms, exist independent of other organs. What arc the criteria for distinguishing Behavioral Science, Volume 20. 1975

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any one level from the others? They are derived from a long scientific tradition of empirical observation of the entire gamut of living systems. This extensive experience of the community of scientific observers has led to a consensus that there are certain fundamental forms of organization of living matter-energy . Indeed the classical division of subject-matter among the various disciplines of the life or behavioral sciences is implicitly or explicitly based upon this consensus. It is important to follow one procedural rule in systems theory, in order to avoid confusion. Every discussion should begin with an identification of the level of reference, and the discourse should not change to another level without a specific statement that this is occurring.ls Systems a t the indicated level are called systems. Those a t the level above are suprasystems, and a t the next higher level, suprasuprasystems. Below the level of reference are subsystems, and below them subsubsystems. For example, if one is studying a cell, its organelles are the subsystems, and the tissue or organ is its suprasystem, unless it is a free-living cell whose suprasystem includes other living systems with which it interacts.I4 8.1 Intersystem generalization

A fundamental procedure in science is to make generalizations from one system to another on the basis of some similarity between the systems, which the observer sees and which permits him to class them together. For example, since the Nineteenth Century, the field of “individual differences” has been expanded, following the tradition of scientists like Galton in anthropometry and Binet in psychometrics. I n Fig. 2, states of separate specific individual systems on a specific structural or process variable are represented by I1 to I, . For differences among such individuals to be observed and measured, of course, a variable common to the type, along which there are individual I,

.... I,, 7’1 .... T n ‘h# L1 .... L,

-

c . -

FIG.2. Individual, Type, Level

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variations, must be recognized (TI). Physiology depends heavily, for instance, upon the fact that individuals of the type (or species) of living organisms called cats are fundamentally alike, even though minor variations from one individual to the next are well recognized. Scientists may also generalize from one type to another (TI to Tn).An example is cross-species generalization, which has been commonly accepted only since Darwin. It is the justification for the labors of the white rat in the cause of man’s understanding of himself. Rats and cats, cats and chimpanzees, chimpanzees and human beings are similar in structure, as comparative anatomists know, and in function, as comparative physiologists and psychologists demonstrate. The amount of variance among species is greater than among individuals within a species. If the learning behavior of cat Felix is compared with that of mouse Mickey, we would expect not only the sort of individual differences which are found between Mickey and Minnie Mouse, but also greater species differences. Cross-species generalizations are common, and many have good scientific acceptability, but in making them interindividual and interspecies differences must be kept in mind. The learning rate of men is not identical to that of white rats, and no man learns at exactly the same rate as another. The third type of scientific generalization indicated in Fig. 2 is from one level to another. The basis for such generalization is the assumption that each of the levels of life, from cell to society, is composed of systems of the previous lower level. These crosslevel generalizations or hypotheses which may apply to two or more levels will, ordinarily, have greater variance than the other sorts of generalizations, since they include variance among types and among individuals. But they can be made, and they can have greater conceptual significance. That there are important uniformities, which can be generalized about, across all levels of living systems is not surprising. All are composed of comparable carbonhydrogen-nitrogen constituents, most importantly a score of amino acids organized Behavioral Science. Volume 20.1975

into similar proteins, which are produced in nature only in living systems. All are equipped to live in a water-oxygen world rather than, for example, on the methane and ammonia planets so dear to science fiction. Also they are all adapted only to environments in which the physical variables, l i e temperature, hydration, pressure, and radiation, remain within relatively narrow ranges.16 Moreover, they all presumably have arisen from the same primordial genes or template, diversified by evolutionary change. Perhaps the most convincing argument for the plausibility of cross-level generalization derives from analysis of this evolutionary development of living systems. Although increasingly complex types of living systems have evolved a t a given level, followed by higher levels with even greater complexity, certain basic necessities did not change. AU these systems, if they were to survive in their environment, had, by some means or other, to carry out the same vital subsystem processes. While free-living cells, like protozoans, carry these out with relative simplicity, the corresponding processes are more complex in multicellular organisms like mammals and even more complex at higher levels. The same processes are “shredded out” to multiple components in a more complex system, by the sort of division of labor which Parkinson has made famous as a law.l6 This results in formal identities across levels of systems, more complex subsystems at higher levels carrying out the same fundamental processes as simpler subsystems at lower levels. A formal identity among concrete systems is demonstrated by a procedure composed of three logically independent steps: (a) recognizing an aspect of two or more systems which has comparable status in those systems; (b) hypothesizing a quantitative identity between them; and ( c ) demonstrating that identity within a certain range of error by collecting data on a similar aspect of each of the two or more systems being compared. It may be possible to formulate some useful generalizations which apply to all living systems at all levels. A comparison of systems is complete only when statements of their formal identities

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9. ECHELON arc associated with specific statements of their interlevel, intertype, and interinThis concept may seem superficially simdividual formal disidentities. The confirma- ilar to the concept of level, but is distinctly tion of formal identities and disidentities is different. Many complex living systems, at done by research. various levels, are organized into two or What makes interindividual, intertype, or more echelons (in the military sense of a interlevel formal identities among systems step in the “chain of command,” not in the important and of absorbing interest is that other military sense of arrangement of troops very different structures may well carry out in rows in physical space). In living systems acts so much alike that they can be quite pre- with echelons the components of the decider, cisely described by the same formal model. the decision making subsystem, are hierConversely, it may perhaps be shown as a archically arranged so that usually certain general principle that subsystems with com- types of decisions are made by one comparable structures but quite diff erent proc- ponent of that subsystem and others by esses may have quantitative similarities as another. Each is an echelon. All echelons are well. within the boundary of the decider subsystem. Ordinarily each echelon is made up 8.2 Emergents of components of the same level as those The more complex systems a t higher levels which make up every other echelon in that manifest characteristics, more than the sum system. Characteristically the decider comof the characteristics of the units, not ob- ponent a t one echelon gets information from served a t lower levels. These characteristics a source or sources which process information have been called emergenis. Significant as- primarily or exclusively to and from that pects of living systems a t higher levels will echelon. It may be that at some levels of be neglected if they are described only in living systems-e.g., cells-there are no cases terms and dimensions used for their lower- in which the decider is organized in echelon structure. level subsystems and components. After a decision is made at one echelon A clear-cut illustration of emergents can be found in a comparison of three electronic on the basis of the information received, it systems. One of these-a wire connecting the is transmitted, often through a single subpoles of a battery-can only conduct elec- component which may or may not be the tricity, which heats the wire. Add several same as the decider, but possibly through tubes, condensers, resistors, and controls, more than one subcomponent, upward to the and the new system can become a radio, next higher echelon, which goes through a capable of receiving sound messages. Add similar process, and so on t o the top echelon. dozens of other components, including a Here a final decision is made and then compicture tube and several more controls, and mand information is transmitted downward the system becomes a television set which to lower echelons. Characteristically incan receive sound and a picture. And this is formation is abstracted or made more not just more of the same. The third system general as it proceeds upward from echelon has emergent capabilities the second system to echelon and it is made more specific or did not have, emergent from its special de- detailed as it proceeds downward. If a given sign of much greater complexity, just as the component does not decide but only passes second has capabilities the first lacked. But on information, it is not functioning as an there is nothing mystical about the colored echelon. I n some cases of decentralized merry-go-ground and racing children on the decision making, certain types of decisions television screen-it is the output of a sys- are made at lower echelons and not transtem which can be completely described by mitted to higher echelons in any form, while complicated differential equations such as information relevant to other types of electrical engineers write, including terms decisions is transmitted upward. If there are representing the characteristics of each of multiple parallel deciders, without a hierthe television set’s components. archy that has subordinate and super-

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ordinate deciders, there is not one system but multiple ones. 10. SUPRASYSTEM

10.1 Suprasystem and environment The suprasystem of any living system is the next higher system in which it is a component or subsystem. For example, the suprasystem of a cell or tissue is the organ it is in; the suprasystem of an organism is the group it is in at the time. Presumably every system has a suprasystem except the “universe.” The suprasystem is differentiated from the environment. The immediate environment is the suprasystem minus the system itself. The entire environment includes this plus the suprasuprasystem and the systems a t all higher levels which contain it. In order to survive the system must interact with and adjust to its environment, the other parts of the suprasystem. These processes alter both the system and its environment. Living systems adapt to their environments, and in return mold it. The result is that, after some period of interaction, each in some sense becomes a mirror of the other. 10.2 Territory

The region of physical space occupied by a living system, and frequently protected by it from an invader, is its territory.’’ Examples are a bowerbird’s stage, a dog’s yard, a family’s property, a nation’s land. A N D COMPONENT In every system it is possible to identify one sort of unit, each of which carries out a distinct and separate process, and another sort of unit, each of which is a discrete, separate structure. The totality of all the structures in a system which carry out a particular process is a subsystem. A subsystem, thus, is identified by the process it carries out. It exists in one or more identifiable structural units of the system. These specific, local, distinguishable structural units are called components or members or parts. Reference has been made to these components in the definition of a concrete system as “a nonrandom accumulation of matter-energy, in a region in physical space11. SUBSYSTEM

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time, which is organized into interacting, interrelated subsystems or components.” There is no one-to-one relationship betwem process and structure. One or more processes may be carried out by two or more components. Every system is a component, but not necessarily a subsystem of its suprasystem. Every component that has its own decider is a system at the next lower level, but many subsystems are not systems a t the next lower level, being dispersed to several components. The concept of subsystem process is related to the concept of role used in social science.’* Organization theory usually emphasizes the functional requirements of the system which the subsystem fulfills, rather than the specific characteristics of the component or components that make up the subsystem. The typical view is that an organization specifies clearly defined roles (or component processes) and human beings “fill them.”1g But it is a mistake not to recognize that characteristics of the component-in this case the person carrying out the role-also influence what occurs. A role is more than simple “social position,” a position in some social space which is “occupied.” It involves interaction, adjustments between the component and the system. It is a multiple concept, referring to the demands upon the component by the system, to the internal adjustment processes of the component, and to how the component functions in meeting the system’s requirements. The adjustments it makes are frequently compromises between the requirements of the component and the requirements of the system. The way living systems develop does not always result in a neat distribution of exactly one subsystem to each component. The natural arrangement would appear to be for a system to depend on one structure for one process. But there is not always such a one-to-one relationship. Sometimes the boundaries of a subsystem and a component exactly overlap, are congruent. Sometimes they are not congruent. There can be (a) a single subsystem in a single component; (b) multiple subsystems in a single component; (c) a single subsystem in multiple com-

THE NATURE OF LIVINGSYSTEMS TABLE I THECRITICAL SUBSYSTEMS .-

;MatterEnergy Processmg Subsystems

Subsystems Which Procl Both Matter-Energy and Information

Informafion Processing Subsystems

Reproducer Boundary Ingeetor Diatributor Converter Producer MatterEnerw Storage

Input Transducer Internal Transducer Channel and Net Decoder Amciator Memory Decider Encoder

Motor Supporter

Output Tranaducer

nents; or (d) multiple subsystems in multiple components. Systems differ markedly from level to level, type to type, and perhaps somewhat even from individual to individual, in their patterns of allocation of various subsystem processes to different structures. Such process may be (a) localized in a single component; (b) combined with others in a single component; (c) dispersed laterally to other components in the system; (d) dispersed upwardly to the suprasystem or above; (e) dispersed downwardly to subsubsystems or below; or (f) dispersed outwardly to other systems outside the hierarchy it is in. Which allocation pattern is employed is a fundamental aspect of any given system. For a specific subsystem function in a specific system one strategy results in more efficient process than another. One can be better than another in maximizing effectiveness and minimizing costs. Valuable studies can be made a t each level on optimal patterns of allocation of processes to structures. I n all probability there are general systems principles which are relevant to such matters. Possible examples are: (a) Structures which minimize the distance over which matterenergy must be transported or information transmitted are the most efficient. (b) If multiple components carry out a process, the process is more difficult to control and less efficient than if a single component does it. Behavioral Science, Volume 20, 1975

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(c) If one or more components which carry out a process are outside the system, the process is more difficult to integrate than if they are all in the system. (d) Or if there are duplicate components capable of performing the same process, the system is less vulnerable to stress and therefore is more likely to survive longer, because if one Component is inactivated, the other can carry out the process alone. 11.1 Critical subsystem

Certain processes are necessary for life and must be carried out by all living systems that survive or be performed for them by some other system. They are carried out by the following critical subsystems listed in Table 1. The definitions of the critical subsyetems are as follows: 11.1.1 Subsystems which process both matter-energy and information. Reproducer, the subsystem which is capable of giving rise to other systems similar to the one it is in. Boundary, the subsystem at the perimeter of a system that holds together the components which make up the system, protects them from environmental stresses, and excludes or permits entry to various sorts of matter-energy and information. 11.1.2 Matter-energy processing subsystems. Ingester, the subsystem which brings matter-energy across the system boundary from the environment. Distributor, the subsystem which carries inputs from outside the system or outputs from its subsystems around the system to each component. Converter, the subsystem which changes certain inputs to the system into forms more useful for the special processes of that particular system. ProduEucEr, the subsystem which forms stable associations that endure for significant periods among matter-energy inputs to the system or outputs from its converter, the materials synthesized being for growth, damage repair, or replacement of compo-

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nents of the system, or for providing energy for moving or constituting the system’s outputs of products or information markers to its suprasystem. Matter-energy storage, the subsystem which retains in the system, for different periods of time, deposits of various sorts of matterenergy. Extruder, the subsystem which transmits matter-energy out of the system in the forms of products and wastes. Motor, the subsystem which moves the system or parts of it in relation to part or all of its environment or moves components of its environment in relation to each other. Supporter, the subsystem which maintains the proper spatial relationships among components of the system, so that they can interact without weighting each other down or crowding each other. 11.13 Information processingsubsystems.

Input transducer, the sensory subsystem which brings markers bearing information into the system, changing them to other matter-energy forms suitable for transmission within it. Internal transducer, the sensory subsystem which receives, from all subsystems or components within the system, markers bearing information about si@;nificantalterations in those subsystems or components, changing them to other matter-energy forms of a sort which can be transmitted within it. Channel and net, the subsystem composed of a single route in physical space, or multiple interconnected routes, by which markers bearing information are transmitted to all parts of the system. Decoder, the subsystem which alters the code of information input to it through the input transducer or the internal transducer into a “private” code that can be used internally by the system. Associator, the subsystem which carries out the first stage of the learning process, forming enduring associations among items of information in the system. Memory, the subsystem which carries out the second stage of the learning process, storing various sorts of information in the system for different periods of time. Behavioral Science, Volume 20, 1975

Decider, the executive subsystem which receives information inputs from all other subsystems and transmits to them information outputs that control the entire system. Encoder, the subsystem which alters the code of information inputs to it from other information processing subsystems, from a “private” code used internally by the system into a “public” code which can be interpreted by other systems in its environment. Output transducer, the subsystem which puts out markers bearing information from the system, changing markers within the system into other matter-energy forms which can be transmitted over channels in the system’s environment. Of these critical subsystems only the decider is essential, in the sense that a system cannot be dependent on another system for its deciding. A living system does not exist if the decider is dispersed upwardly, downwardly, or outwardly. Since all living systems are genetically related, have similar constituents, live in closely comparable environments, and process matter-energy and information, it is not surprising that they should have comparable subsystems and relationships among them. All systems do not have all possible kinds of subsystems. They differ individually, among types, and across levels, as to which subsystems they have and the structures of those subsystems. But all living systems either have a complement of the critical subsystems carrying out the functions essential to life or are intimately associated with and effectively interacting with systems which carry out the missing life functions for them. 11.2 Inclusion Sometimes a part of the environment is surrounded by a system and totally included within its boundary. Any such thing not a part of the system’s own living structure is an inclusion. Any living system at any level may include living or nonliving components. The amoeba, for example, ipgests both inorganic and organic matter and may retain particles of iron or dye in its cytoplasm for many hours. A surgeon may replace an arteriosclerotic aorta with a plastic one and

THE NATUREOF LIVINGSYSTEMS that patient may live comfortably with it for years. To the two-member group of one dog and one cat an important plant component is often added-one tree. An airline firm may have as an integral component a computerized mechanical system for making reservations which extends into all its offices. A nation includes many sorts of vegetables, minerals, buildings, and machines, as well as its land. The inclusion is a component or subsystem of the system if it carries out or helps in carrying out a critical process of the system; otherwise it is part of the environment. Either way the system, to survive, must adjust to its characteristics. If it is harmless or inert it can often be left undisturbed. But if it is potentially harmfullike a pathogenic bacterium in a dog or a Greek in the giant gift horse within the gates of Troy-it must be rendered harmless or walled off or extruded from the system or killed. Because it moves with the system in a way the rest of the environment does not, it constitutes a special problem. Being inside the system it may be a more serious or more immediate stress than it would be outside the system’s protective boundary. But also, the system that surrounds it can control its physical actions and all routes of access to it. For this reason international law has developed the concept of extraterritoriality to provide freedom of action to ambassadors and embassies, nations’ inclusions within foreign countries. 11.3 Artifact

An artifact is an inclusion in some system, made by animals or man. Spider webs, bird nests, beaver dams, houses, books, machines, music, paintings, and language are artifacts. They may or may not be prosthses, inventions which carry out some critical process essential to a living system. An artificial pacemaker for a human heart is an example of an artifact which can replace a pathological process with a healthy one. Insulin and thyroxine are replacement drugs which are human artifacts. Chemical, mechanical, or electronic artifacts have been constructed which carry out some functions of all levels of living systems. Behavioral Science. Volume 20, 1975

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Living systems create and live among their artifacts. Beginning presumably with the hut and the arrowhead, the pot and the vase, the plow and the wheel, mankind has constructed tools and devised machines. The Industrial Revolution of the Nineteenth Century, capped by the recent harnessing of atomic energy, represents the extension of man’s matter-energy processing ability, his muscles. A new Industrial Revolution, of even greater potential, is just beginning in the Twentieth Century, with the development of information and logic-processing machines, adjuncts to man’s brain. These artifacts are increasingly becoming prostheses, relied on to carry out critical subsystem processes. A chimpanzee may extend his reach with a stick; a man may extend his cognitive skills with a computer. Today’s prostheses include input transducers which sense the type of blood cells that pass before them and identify missiles that approach a nation’s shores; photographic, mechanical, and electronic memories which can store masses of information over time; computers which can solve problems, carry out logical and mathematical calculations, make decisions, and control other machines; electric typewriters, high speed printers, cathode ray tubes, and photographic equipment which can output information. An analysis of many modern systems must take into account the novel problems which arise at man-machine interfaces. Music is a special sort of human artifact, an information processing artifact.20So are the other arts and cognitive systems which people share. So is language. Whether it be a natural language or the machine language of some computer system, it is essential to information processing. Often stored only in human brains and expressed only by human lips, it can also be recorded on nonliving artifacts like stones, books, and magnetic tapes. It is not of itself a concrete system. It changes only when man changes it. As long as it is used it is in flux,because it must remain compatible with the ever-changing living systems that use it. But the change emanates from the users, and without their impact the language is inert. The artifactual language used in any information transmis-

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sion in a system determines many essential aspects of that system’s structure and process.2l 12. TRANSMISSIONS I N CONCRETE

SYSTEMS

All process involves some sort of transmission among subsystems within a system, or among systems. There are inputs across the boundary into a system, internal processes within it, and outputs from it. Each of these sorts of transmissions may consist of either (a) some particular form of matter; (b) energy, in the form of light, radiant energy, heat, or chemical energy; or (c) some particular pattern of information. 13. STEADY STATE

When opposing variables in a system are in balance, that system is in equilibrium with regard to them. The equilibrium may be static and unchanging or it may be maintained in the midst of dynamic change. Since living systems are open systems, with continually altering fluxes of matter-energy and information, many of their equilibria are dynamic and are often referred to as JEux equilibra or steady states. These may be unstable, in which a slight disturbance elicits progressive change from the equilibrium state-like a ball standing on an inverted bowl; or stable, in which a slight disturbance is counteracted so as to restore the previous state-like a ball in a cup; or neutral, in which a slight disturbance makes a change, but without cumulative effects of any sortlike a ball on a flat surface with friction. All living systems tend to maintain steady states (or homeostasis) of many variables, keeping an orderly balance among subsystems which process matter-energy or information. Not only are subsystems usually kept in equilibrium, but systems also ordinarily maintain steady states with their environments and suprasystems, which have outputs to the systems and inputs from them. This prevents variations in the environment from destroying systems. The variables of living systems are constantly fluctuating, however. A moderate change in one variable may produce greater or lesser alterations in other related ones. These alterations may or may not be reversible.

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13.1 Stress, strain, and threat There is a range of stability for each of numerous variables in all living systems. It is that range within which the rate of correction of deviations is minimal or Bero, and beyond which correction occurs. An input or output of either matter-energy or information which, by lack or excess of some characteristic, forces the variables beyond the range of stability, constitutes stress and produces a strain (or strains) within the system. Input lack and output excess both produce the same strain-diminished amounts in the system. Input excess and output lack both produce the opposite strain-increased amounts. Strains may or may not be capable of being reduced, depending upon their intensity and the resources of the system. The totality of the strains within a system resulting from its template program and from variations in the inputs from its environment can be referred to as its values. The relative urgency of reducing each of these specific strains represents its hierarchy of values. Stress may be anticipated. Information that a stress is imminent constitutes a threat to the system. A threat can create a strain. Recognition of the meaning of the information of such a threat must be based on previously stored (usually learned) information about such situations. A pattern of input information is a threat when-like the odor of the hunter on the wind; a change in the acidity of fluids around a cell; a whirling cloud approaching the city-it is capable of eliciting processes which can counteract the stress it presages. Processes-actions or communications-occur in systems only when a stress or a threat has created a strain which pushes a variable beyond its range of stability. A system is a constantly changing cameo and its environment is a similarly changing intaglio, and the two at all times fit each other. That is, outside stresses or threats are mirrored by inside strains. Matter-energy storage and memory also mirror the past environment, but with certain alterations. 13.1.1 Matter-energy stress. There are various ways for systems to be stressed. One class of stresses is the matter-energy stresses,

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including: (a) matter-energy input lack or as it becomes greater, first nearby links and or inadequate fuel then those farther and farther away, take underload-starvation input; (b) input of an excess or overload of up part of the load. Thus a heavy weight matter-energy; and (c) restraint of the sys- which would break any of the component tem, binding it physically. [This may be the wires alone can be sustained. I n a living equivalent of (a) or (b).] system, if one component cannot handle a 13.1.2 Information stress. Also there are stress, more and more others are recruited information stresses, including: (a) informa- to help. Eventually the entire capacity of tion input lack or underload, resulting from the system may be involved in coping with a dearth of information in the environment the situation. or from improper function of the external 13.2.1 Feedback. The term feedback means sense organs or input transducers; (b) injec- that there exist two channels carrying intion of noise into the system, which has an formation, such that Channel B loops back effect of information cutoff, much like the from the output to the input of Channel A previous stress; and (c) information input and transmits some portion of the signals excess or overload. Informational stresses emitted by Channel A (see Fig. 3).23These may involve changes in the rate of informa- are tell-tales or monitors of the outputs of tion input or in its meaning. Channel A. The transmitter on Channel A is a device with two inputs, formally repre13.2 Adjustment processes sented by a function with two independent Those processes of subsystems which variables, one the signal to be transmitted on maintain steady states in systems, keeping Channel A and the other a previously transvariables within their ranges of stability mitted signal fed back on Channel B.The new despite stresses, are adjustment processes. In signal transmitted on Channel A is selected some systems a single variable may be in- to decrease the strain resulting from any fluenced by multiple adjustment processes. error or deviation in the feedback signal from As Ashby has pointed out, a living system’s a criterion or comparison reference signal inadjustment processes are so coupled that dicating the state of the output of Channel the system is ultrastable.22 This character- A which the system seeks t o maintain steady. istic can be illustrated by the example of an This provides control of the output of Chanarmy cot. It is made of wires, each of which nel A on the basis of actual rather than exwould break under a 300-pound weight, yet pected performance. When the signals are fed back over the it can easily support a sleeper of that weight. The weight is applied to certain wires, and feedback channel in such a manner that they

FIG.3. Negative Feedback.

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increase the deviation of the output from a steady state, positwe feedback exists. When the signals are reversed, so that they decrease the deviation of the output from a steady state, it is negative feedback. Positive feedback alters variables and destroys their steady states. Thus it can initiate system changes. Unless limited, it can alter variables enough to destroy systems. At every level of living systems numerous variables are kept in a steady state, within a range of stability, by negative feedback controls. When these fail, the structure and process of the system alter markedly-perhaps to the extent that the system does not survive. Feedback control always exhibits some oscillation and always has some lag. When the organism maintains its balance in space, this lag is caused by the slowness of transmissions in the nervous system, but is only of the order of hundredths of seconds. An organization, like a corporation, may take hours to correct a breakdown in an assembly line, days or weeks to correct a bad management decision. I n a society the lag can sometimes be so great that, in effect, it comes too late. General staffs often plan for the last war rather than the next. Governments receive rather slow official feedbacks from the society at periodic elections. They can, however, get faster feedbacks from the press, other mass media, picketers, or demonstrators. Public opinion surveys can accelerate the social feedback process. The speed and accuracy of feedback have much to do with the effectiveness of the adjustment processes they mobilize. 13.2.2 Power. In relation to energy processing, power is the rate at which work is performed, work being calculated as the product of a force and the distance through which it acts. The term also has another quite different meaning. I n relation to information processing, power is control, the ability of one system to elicit compliance from another, at the same or a different level. A system transmits a command signal or message to a given address with a signature identifying the transmitter as a legitimate source of command information. The message is often in the imperative mode, specifying an action the receiver is expected Behavioral Science. Volume 20. 1975

to carry out. It elicits compliance a t the lower levels because the electrical or chemical form of the signal sets off a specific reaction. At higher levels the receiving system is likely to comply because it has learned that the transmitter is capable of evoking rewards or punishments from the suprasystem, depending on how the receiver responds. 13.2.3 Purpose and goal. By the information input of its charter or genetic input, or by changes in behavior brought about by rewards and punishments from its suprasystem, a system develops a preferential hierarchy of values that gives rise to decision rules which determine its preference for one internal steady state value rather than another. This is its purpose. It is the comparison value which it matches to information received by negative feedback in order to determine whether the variable is being maintained a t the appropriate steady state value. In this sense it is normative. The system then takes one alternative action rather than another because it appears most likely to maintain the steady state. When disturbed, this state is restored by the system by successive approximations, in order to relieve the strain of the disparity recognized internally between the feedback signal and the comparson signal. Any system may have multiple purposes simultaneously. A system may also have an external goal, such as reaching a target in space, or developing a relationship with any other systein in the environment. Or it may have several goals a t the same time. Just as there is r o question that a guided missile is zeroing in on a target, so there is no question that a rat in a maze is searching for the goal of food a t its end or that the Greek people under Alexander the Great were seeking the goal of world conquest. As Ashby notes, natural selection permits only those systems to continue which have goals that enable them to survive in their particular environment^.^^ The external goal may change constantly, as when a hunter chases a moving fox or a man searches for a wife by dating one girl after mother, while the internal purpose remains the same. A system’s hierarchy of values determines

THE NATUREOF LIVINQSYSTEMS its purposes as well as its goals. It is not difficult to distinguish purposes from goals, aa the terms have been used: an amoeba haa the purpose of maintaining adequate energy levels and therefore it has the goal of ingesting a bacterium; a boy has the purpose of keeping his body temperature in the proper range and so he has the goal of finding and putting on his sweater; Poland had the purpose in March 1939 of remaining uninvaded and autonomous and so she sought the goal of a political alliance with Britain and France in order to have assistance in keeping both Germany and Russia from crossing her borders. 13.2.4 Costs and efficiency. All adjustment processes have their costs, in energy of nonliving or living systems, in material resources, in information (including in social systems a special form of information often conveyed on a marker of metal or paper money), or in time required for an action. Any of these may be scarce. (Time is a scarcity for mortal living system.) Any of these is valued if it is essential for reducing Itrains. The coats of adjustment processes differ from one to another and from time to time. They may be immediate or delayed, short term or long term. How successfullysystems accomplish their purposes can be determined if those purposes are known. A system’s e&iemy, then, can be determined as the ratio of the success of its performance to the costs involved. A system constantly makes economic decisions directed toward increasing its efficiency by improving performance and decreasing costs. How efficiently a system adjusts to its environment is determined by what strategies it employs in selecting adjustment processes and whether they satisfactorily reduce strains without being too costly. This decision process can be analyzed by game theory, a mathematical approach to economic decisions. This is a general theory concerning the best strategies for weighing “plays” against Lrpay-offs,” for selecting actions which will increase profits while decreasing losses, increase rewards while decreasing punishments, improve adjustments of variables to appropriate steady state values, or attain goals while diminishing Beharioril Sdeace. Volume 20, 1975

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costs. Relevant information available to the decider can improve such decisions. Consequently such information is valuable. But there are costs to obtaining such information. A mathematical theory on how to calculate the value of relevant information in such decisions was developed by Hurley.2b This depends on such considerations as whether it is tactical (about a specific act) or strategic (about a policy for action); whether it is reliable or unreliable, overtly or secretly obtained, accurate, distorted, or erroneous. 14. CONCLUSIONS

This analysis of living systems use8 concepts of thermodynamics, information theory, cybernetics, and systems engineering, as well aa the classical concepts appropriate to each level. The purpose is to produce a description of living structure and process in terms of input and output, flows through systems, steady states, and feedbacks, which will clarify and unify the facts of life. The approach generates hypotheses relevant to single individuals, types, and levels of living systems, or relevant across individuals, types, and levels. These hypotheses can be confirmed, disconflrmed, or evaluated by experiments and other empirical evidence. REFERENCES AND NOTES 1. Hartley, R. V. L. Trammission of information. Bell Sys. tech. J . , 1928,7,535. 2 . Shannon, C. E. A mathematical theory of communication. Bell Sya. k h . J . , 1948, 27, 379423 and 623-866. 3. von Neumann, J. The computcr and the brain. New Haven, Conn.: Yale Univ. Press, 1958, 6-7. NOTE:Christie, Luce, and Macy (Christie, L. S., Luce, R. D., & Macy, J., Jr. Communication and learning i n iaak-oriented groupa. Cambridge, Mass.: Research Lab. of Electronics, MIT, Tech. Rep. No. 231, May 13, 1952) call the physical form which the communication takes the “symbol design,” and the information itself the “symbol contents.” 4. Shannon, C. E. Op. cit., 380-382. 5. Harlow, H. F. &Harlow,M. I(.Social deprivation in monkeys. Sci. Amer., 1982, 207(5), 137-146. 6 . Bertalanffy, L. v. General systems theory. Yearb. Soc. Gen. Sya. Res., 1956,1,3. NOTE:Bertalanffy suggests that systems can

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be defined much aa I define them, as “set8 of elements standing in interaction.” And he says that this definition is not so vague and general aa to be valueless. He believes these system can be specified by families of differential equations. 7. NOTE:Rothstein, J. Communication, organization, and science. Indian Hills, Colo.: Falcon’s Wing Press, 1958, 34-36, deals with the constraints among units of organized systems in terms of entropy and communication aa information processing: Ha, “What do we mean by an organization? First of all an organization presupposes the existence of parts, which, considered in their totality, constitute the organization. The parts must interact. Were there no communication between them there would be no organization, for we would merely have a collection of individual elements isolated from each other. Each element must be associated with its own set of alternatives. Were there no freedom to choose from a set of alternatives, the corresponding element would be a static, passive cog rather than an active unit. We suggest the following general characterization of organization. Consider a set of elements, each sssociated with its own set of alternatives. We now define a complexion aa a particular set of alternatives. There are, of course, as many complexions ss there are ways of selecting a representative from each set of alternatives. The set of complexions then has an entropy which is merely the sum of the entropies of the individual sets of alternatives so long aa the 8. elements do not interact. Complexion entropy is a maximum for independent elements. Maximal entropy, i.e., zero coupling, will be 9. said to constitute the condition of zero organization.” h h b y [Ashby, W. R. Principles of the self-organizing system. I n H. von Foerster & G. W. Zopf (Eds.). Principles of self-organizalion. New York: Pergamon Press, 1982, 2552571 also deals with this. He says, speaking of what “organization” meam as applied to syst e m , “The hard core of the concept is, in my opinion, that of ‘conditionality.’ As soon as the relation between two entities A and B 10. become conditional on C’s value or state then a necessary component of ‘organization’ is present. Thus the theory of organization i s partly co-eztensiue with the theory of functions of more than one variable.” He goes on to ask when a system is not a system or is not organized: “The converse of ‘conditional on,’ is ‘not conditional on,’ so the converse of ‘organization’ must therefore be, as the mathematical theory shows aa clearly, the concept of ‘reducibility.’ (It is aleo called ‘separability.’) This occurs, in mathematical forms,

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when what looks like a function of several variables (perhaps very many) proves on closer examination to have parts whose actions are not conditional on the values of the other parts. It occum in mechanical forms, in hardware, when what looks like one machine proves to be composed of two (or more) sub-machines, each of which is acting independently of the others. . . . “The treatment of ‘conditionality’ (whether by functions of many variables, by correlation analysis, by uncertainty analysis, or by other ways) makes us realize that the essential idea is that there is first a product space-that of the possibilities-within which some sub-set of points indicates the actualities. This way of looking a t ‘conditionality’ makes us realize that it is related to that of ‘communication,’ and it is, of course, quite plausible that we should define parts aa being ‘organized’ when ‘communication’ (in some generalized sense) occurs between them. (Again the natural converse is that of independence, which represents non-communication.) “Now ‘communication’ from A to B necessarily implies some constraint, some correlation between what happens a t A and what a t B. If, for a given event at A , all possible events may occur at B, then there is no communication from A to B and no constraint over the possible ( A , B ) couples that caa occur. Thus the presence of ‘organization’ between variables is equivalent to the existence of a constraint in product-space of the posbilities.” See Hall, A. D. & Fagan, R. E. Definition of system. Yearb. SOC.G‘en. Sys. Res., 1956, 1, 18. NOTE:In Cervinka, V., A dimensional theory of groups, Sociometq, 1948, 11, 100-107, the author very precisely distinguishes, at the group level, between a concrete system, which he calls a “socius,” that is a single person in a group together with all his relationships, and a “groupoid,” an abstracted system, which is a pattern of attachments of a single kind of relation selected by an observer, which interrelates a set of people. NOTE: This definition is consistent with the usage of Weiss [Weiss, P. A. In R. W. Gerard (Ed.). Concepts of biology. Behau. Sci., 1958, 3 , 1401. Murray [Murray. H. A. Preparations for the scaffold of a comprehensive system. In S. Koch (Ed.). Psychology: A study of a science, Vol. 3. New York: McGraw-Hill, 1959, 241 prefers the word “configuration” for an instantaneous spatial arrangement of subsystems or components of a system (or “entity,” in his terms) and “structure” for an enduring arrangement. He distinguishes these clearly from an “in-

THENATURE OF LIVINGSYSTEMS tegration” of recurrent temporal relations of component processes, a patterning of temporal variables. 11. NOTE:This concept is not a product of our times. It developed long ago. For instance, in the middle of the Nineteenth Century, Virchow (Virchow, R. Atome und Individuen, Vier Reden ilber Leben und Krankstein. Berlin, 1862. Trans. by L. J. Rather as: Atoms and individuals. In Disease, life, and man, selected essays by Rudolph Virchow. Stanford, Calif.: Stanford Univ. Press. 1958, 120-141) wrote that the scope of the life sciences must include the cellular, tissue, organism, and social levels of living organization. In modern times the concept of hierarchical levels of systems is, of course, basic to the thought of Bertaladfy and other general systems theorists (see Bertalanffy, L. v. Op. cit., 7). Even some scientists not explicitly of such persuasion, who have perhaps been skeptical in the past (see Simon, H. A. The architecture of complexity. Proc. Amer. Phil. SOC.,1962, 106, 467), recognize value in such an approach. For example, Simon (Ibid., 467-468) writes: “A number of proposals have been advanced in recent years for the development of ‘general systems theory’ which, abstracting from properties peculiar to physical, biological, or social systems, would be applicable to all of them. We might well feel that, while the goal is laudable, systems of such diverse kinds could hardly be expected to have any nontrivial properties in common. Metaphor and analogy can be helpful, or they can be misleading. All depends on whether the similarities the metaphor captures are significant or superficial. “It may not be entirely vain, however, to search for common properties among diverse kinds of complex systems. The ideas that go by the name of cybernetics constitute, if not a theory, a t least a point of view that has been proving fruitful over a wide range of applications. It has been useful to look a t the behavior of adaptive systems in terms of the concepts of feedback and homeostasis, and to analyze adaptiveness in terms of the theory of selective information. The ideas of feedback and information provide a frame of reference for viewing a wide range of situations, just as do the ideas of evolution, of relativism, of axiomatic method, and of operationalism.” He goes on to assert that “hierarchic systems have some common properties that are independent of their specific content. . . “By a hierarchic system, or hierarchy, I mean a system that is composed of interrelated subsystems, each of the latter being, in turn, hierarchic in structure until we reach some

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lowest level of elementary subsystem. I n most system in nature, it is somewhat arbitrary as to where we leave off the partitioning, and what subsystems we take aa elementary. Physics makes much use of the concept of ‘elementary particle’ although particles have a disconcerting tendency not to remain elementary very long. Only a couple of generations ago, the atoms themselves were elementary particles; today, to the nuclear physicist they are complex systems. For certain purposes of astronomy, whole stars, or even galaxies, can be regarded aa elementary subsystems. In one kind of biological research, a cell may be treated as an elementary subsystem; in another, a protein molecule; in still another, an amino acid residue. “Just why a scientist has a right to treat aa elementary a subsystem that is in fact exceedingly complex is one of the questions we shall take up. For the moment, we shall accept the fact that scientists do this all the time, and that if they are careful scientists they usually get away with it.” Leake sees value in the concept of levels for contemporary theory about biological organization (see Leake, C. D. The scientific status of pharmacology. Science, 1961, 134, 2076). He writes: “Life begins with complex macromolecules such aa genes and viruses, and here the principles of physics and chemistry directly apply. Macromolecules may be organized and integrated with many other chemical materials to form cells, which at Virchow’s time were thought to be the basic units of life. Cells, however, may be organized into tissues or organs, with specific integrations serving their specific functions. These tissues and organs may further be integrated into organisms, constituting individuals such as human beings. Human beings, and indeed many other organisms, are capable of further integration and organization into societies. These societies in turn may be integrated with a more or less limited ecological environment.” The view is also well stated by de Chardin (de Chardin, P. T. The phenomenon of man. New York: Harper, 1959,4344) : “The existence of ‘system’ in the world is a t once obvious to every observer of nature, no matter whom. “The arrangement of the parts of the universe has always been a source of amazement to men. But this disposition proves itself more and more astonishing as, every day, our science is able to make a more precise and penetrating study of the facts. The farther and more deeply we penetrate into matter, by means of increasingly powerful methods, the more we are confounded by the interdependence of its parts. Each element of the cosmos is positively woven from all the others; from beneath itself by the mysterious phenomenon

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of ‘composition,’ which makes it subsistent popular implicit recognition of hierarchical throughout the apex of an organized whole; levels of living systems. As one instance out of and from above through the influence of many, six banners in one of the halls of the unities of a higher order which incorporate United Nations Palais des Nations in Geneva and dominate it from their own ends. depict six levels of social organization. They “ I t is impossible to cut into this netsay: Family, Village, Clan, Medieval State, work, to isolate a portion without i t becoming Nation, and Federation. frayed and unravelled at all its edges. 12. Newman, J. & Scott, E. L. On a mathematical “All around us, as far as the eye can see, theory of populations conceived as conthe universe holds together, and only one way glomerations of clusters. Yearb. SOC. of considering it is really possible, that is, to Gen. Sys. Res., 1958,3,180-192. take it aa a whole, in one piece.” Also Newman, J., Scott, E. L., & Shane, C. D. Kaplan (Kaplan, M. A. System and Statistics of images of galaxies with parprocess i n international politics. New York: ticular reference to clustering. Yeurb. Wiley, 1957, 12) has applied the concept of a SOC.Gen. Sys. Res., 1958,3,193-219. hierarchy of systems to international rela- 13. Cf. Herbst, P.G. Situation dynamics and the tions: theory of behavior systems. Behav. Sci., “The same variables will be used at dif 1957,2, 28. Herbert makes it clear that ferent system levels. The international system one should make the level of reference is the most inclusive system treated by this explicit. He says that often, in writing book. National and supranational systems are on group research, for instance, an subsystems of the international system. They author will change his level of reference may, however, be treated separately aa sysfrom the leader (organism) to the group tems, in which case inputs from the interand back to a group member (organism) national system would function as parameters. again without explicitly referring to the This holds also for subsystems of nation states change. This produces confusing conand even for personality systems.” ceptual ambiguity. The Panel on Basic Research and Grad- 14. NOTE:Illustrative of the similarities between uate Education of the President’s Science the approach outlined here and current thinking about electronic system design Advisory Committee of the United States in is the following statement by Goode 1960 appeared also to recognize value in a (Goode, H. H. Intracompany systems general systems approach [see Seaborg, G. T., management. IRE Trans. engng. Mgmt. (Chairman) Panel on Basic Research and EM-7, 1960, 15) concerning the need to Graduate Education of the President’s Science identify the level of reference: Advisory Committee. Scientific progress and “Confusion . . . arises from considerathe federal government. Science, 1960, 132, tion of the level of design. System design may 18lOl.They wrote “. . .we suggest that there is be done: great promise in such an emerging subject aa “1) At the set level: that is, a radar, an a general study of complex systems in action, ignition system, a navigation set. Any of within which such very large questions as the these may be designed on a system engineering communication sciences, cognition, and large basis, given a need and the necessary analysis parts of biology itself might conceivably be of requirements. treated as special cases.” “2) A t the set of sets level: thus an airA textbook of psychology has been writplane, a telephone exchange, a missile system, ten which embodies a conceptualization of a each is itself a set of sets and is subject to hierarchy of living systems like that I advance system design. in the present work (see Coleman, J. C. Per“3) At the set of sets of sets level: thus sonality dynamics and effective behavior. Chian over-all weapon system, a telephone syscago: Scott-Foresman, 1960). tem, an air traffic system, represent such sets A presidential address of the Asof sets of sets.” sociation of American Medical Colleges inIn a similar analysis Malcolm [Malcolm, cluded a passage emphasizing the desirability D. G. Reliability maturity index (RM1)-an of synthesizing the medical curriculum around extension of PERT into reliability managethe concept of the relations among levels of living systems. Hubbard (Hubbard, W. N., ment. J. industr. Engng., 1963, 14, 4-51 disJr. Janus revisited. J. med. Educ., 1967, 42, tinguishes eight hierarchical levels in a large 1079) wrote: “For the medical student . . . the weapon system: system, subsystem, composignificance of descriptions at the molecular nent, assembly, subassembly, unit, unit comand submolecular level must be presented in ponent, and part. the context of their relationship to the more complex organizations of these same living 15. Henderson, L. J. The fitness of the environment: An inquiry into the biological sigsystems a t the level of the organ, the innificance of the properties of mutter. dividual, and the family group.” Boston: Beacon, 1958. And there is widespread scientific and

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THENATURE OF LIVINGSYSTEMS 16. Parkinson, C. N. Parkinson’s law. Boston: Houghton M a i n , 1957,2-13. 17. See Ardrey, R. The territorial imperative. New York: Atheneum, 1966. 18. See Levinson, D. J. Role, personality, and social structure in the organizationel setting. J. abnorm. soc. Psychol., 1959, 58, 170-180. 19. Weber, M. The theory of social and economic organization. (Trans. by A. M. Henderson & T. Parsons.) New York: Oxford Univ. Press, 1947. 20. See Meyer, L. B. Meaning in music and information theory. J . Aesthet. art. Crit., 1957, 15,412-424. Also J. E. Cohen. Information theory and music. Behav. Sci., 1962, 7, 137-163. 21. See Whorf, B. L. Language, thought, and re-

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ality. Cambridge, Mass. : Technology Press, 1956. 22. Ashby, W. R. Design f o r a brain. (2nd ed. rev.) New York: Wiley, 1960,153-158,210-211. 23. Roeenblueth, A., Wiener, N., & Bigelow, J. Behavior, purpose and teleology. PhiZos. s c i . , 1943, 10, 19. 24. Ashby, W.R. Cybernetics today and its future contribution to the engineering-sciences. New York: Foundation for Instrumentation, Engineering and Research, 1961,

6-7. 25. Hurley, W. V. A mathematical theory of the value of information. Report 633. New York: Port of New York Authority, Engineering Department, Research and Development Division, May, 1963.