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
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 [ -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

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

{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 0.16. 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 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 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.

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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 > [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