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 Organische Chemie, Universitat Miinchen, Miinchen, West Germany

A Wiley-Interscience Publication

JOHN WILEY & SONS

New York Chichester Brisbane Toronto Singapore

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 Organische Chemie, 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

Postfach 21 02 09 D-5900 Siegen 21, West Germany

der Universitiit Siegen

Guy J. CoUi DCparment des Sciences

Universitk du Qutbec B Chicoutimi Chicoutimi, Quebec, Canada G7H 2B 1

Fondementales

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

Postfach 21 02 09 D-5900 Siegen 21, West Germany

der Universitiit Siegen

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 sophistication in experiment and interpretation, photochem- ists 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

DAVIDH. VOLMAN GEORGE S . HAMMOND KLAUS GOLLNICK

CONTENTS

Spin-Statistical Factors in Diffusion-Controlled Reactions 1 JACK SALTIEL Chemistry, The Florida State University, Tallahassee, Florida

BEAUFORD W. ATWATER, Department of

Photochemistry and Molecular Motion in Solid Amorphous Polymers 91 JAMES GUILLET, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada

Photochemistry of Simple Olefins: Chemistry of Electronic Excited States or Hot Ground States?

GUY J. COLLIN, Dtfpartement des Sciences Fondementales, Universittf du 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 Environment Studies, The Pennsylvania State University, University Park, Pennsylvania

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

Index

Cumulative Index, Volumes 1-14

135

177

273

333

337

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. Introduction 11. Diffusion-controlled reactions

III. Electronic spin multiplicity IV. Excited-state interactions with 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 electronically excited states and neutral and ionic radicals derived from them, e.g.,

2 SPIN-STATISTICAL FACTORS IN DIFFUSION-CDNTROLLED REACTIONS

Despite their short lifetimes, they undergo efficient bimolecular physical and chemical interactions in 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 interactions in solution. Specific topics considered will include the quenching of electronically excited 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, >> Ldf applies 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 ?4 prevents 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)

k 47rNpD + k

kdif = 41rNpDlO-~

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 individual diffusion 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:

kT 5A

DA =-

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

(7)

where 6, the coefficient of sliding friction, relates cA 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 r . It 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-CONTROLLED REACTIONS

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

r ft = 0.16 + 0.4- rL

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

3000vx ”’ r = (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 Tbp and Tmp are 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- (0.9 + O.4TrL - 0.25TJ (14)

and renders ft more solvent- and solute-independent. Microfriction factors obtained from Eqs. 1 1 and 14 are referred to as full and truncated, respectively.

( rL ‘1

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-STATISTICAL FACTORS 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 encounter pairs which conserve multiplicity 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 highest- energy 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 highest- energy 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 availability of 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, (1 1,12). In nonpolar organic solvents the process

EXCITED-STATE INTERACTIONS w m 3 0 2 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 multiplicity- allowed, 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 Trn 7, - = T + ex[o,l

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 comprehensive compilation 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-excited- state lifetime measurements yielded k:x values which were shown to be diffusion- controlled 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 leveling effect on ex (1 1). This accounts for Berlman's successful correlation of (Zdr), with T, for a large number of aromatic molecules (12), as shown in

8 SPIN-STATISTICAL FACIDRS IN DIFFUSION-CONTROLLED REAcnoNS

t - L -- a

0

W \

H Y

o.oh [ 1 [ I [ 0 20 40 60 00 100

r,, ns-

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

Table 1 and Fig. 1. Since I, was obtained by bubbling N2 through cyclohexane solutions, the (Zdr), values in Table 1 should be regarded as lower limits. The ex 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 gx = (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-quenching contributions reflecting the presence of ground-state (IWO,) charge-transfer complexes (2 1,22).

Experimental evidence for the formation of O,(lA,) as a result of singlet- excited-state quenching by 0, (@. 20, as > 0) exists and will be presented in a later section. The energetic considerations of 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

*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"

k:: s c

7, Compound (AES~.T,)~ (b/I)air (ns) ( l o ~ o M - ~ s - ' )

Benzene (24.9) Benzene-d, Fluombenzene Toluene Ethylbenzene 2-Pheny lbutane Diphenylmethane Methoxybenzene Diphenyl ether p-Xylene m-X ylene 0-Xy lene p-Ethyltoluene p-Methoxytoluene p-Dimethox ybenzene 1,2,4-Trimethylbenzene 1,3,5-Trimethylbenzene 1,3,5-Triethylbenzene Biphenyl pBenzylbipheny1 p-Methoxybiphenyl p-Phenoxybiphenyl Dibenzofuran p,p"-Dihexahydro-

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 (3 1 .O) Triphenylene (15.3)

farnesoxy -p-terphenyl

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

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

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

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

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

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

- - -

-

-

e_

- - - - - - - __

_L

10 SPIN-STATISTICAL FACTORS IN DIFFUSIONCONTROLLED RJ3MTIONS

TABLE 1. (Continued)

k:: SC 7,

Compound (AEs,-T,)b ~W)air (ns) (loloM-l s-l)

2.72 Triphenylene-d 12 3.17 38.0 Perylene (28.3) 1.30 6.4 2.23 1,2,5,6-Dibenzanthracene (37.5) (2.70)

-

1,2-Benzanthracene (49.4) (2.84) 1,2,3,4-Dibenzanthracene (53.5) (2.44)

Fluoranthene ( 18) 1.49 53.0 0.44 3,4,9,10-Dibenzpyrene (143.0) (2.55)

3.4-Benz~wne (57.5) (2.83)

"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 .

M was employed: see text.

many of its derivatives (23), has the added feature of the availability of a higher triplet state, T2, nearly isoenergetic with S1. In such systems S, --* T2 intersystem 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 as even in those cases for which formation of 02( 'Ag) would be exoergonic. Case I1 illustrates the absence of a higher triplet quenching pathway, and < 22.5 kcaYmol. For such systems as = 0 is expected. 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-STATE INTERACI?ONS m 3 4 11

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-controlled quenching is provided by 9,10-dichloroanthracene, for which ex values in several solvents are consistently about 30% smaller than 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 are about 10% low (the range of 1.49 X M in Ref. 26 would correspond to an atmospheric pressure of 692 Torr (27); expected for 760 TOIT is a range of 1.66 x M). The 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.

M S [O,] =s 7.32 X

M* s [o,] s 7.93 x

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

ex(%. 21)" ex (a. Wb Comuound (101OM-l s-I) ( 101OM-l s- l)

9,lO-Dimethylanthracene 2.87 f 0.18 9,lO-Diphenylanthracene 3.30 f 0.23 2.8 9,lO-Dimethyl-1 ,Zbenzanthracene 2.51 -+ 0.15 Naphthacene 2.17 -+ 0.16 Rubrene 1.07 k 0.07 Perylene 2.47 f 0.27 3.2 Anthantiuene 3.23 k 0.55 Anthracene 2.67' 3.1 1.2-Benzanthracene 2.61d 2.47d 1,2-Benzanthracene-7-d 2.8od 2. 74d

"From Ref. 26, 25 2 2°C. unless otherwise indicated. %om Ref. 11, 25/26"C, unless otherwise indicated. 'From Ref. 21, 24 f 1°C. dFrom Ref. 28, 22.5"C for Eq. 21, 25 +- 1°C for Eq. 22.

*I021 = 1.61 X M at 25°C was used to account for atmospheric moisture.

12 SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS

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 spin- statistical 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 ex = %ex is adhered to nicely

13 EXCITED-STATE INTERACIIONS WITH 3oz

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

k:Xa k;f, AET,-SoC Compound (109K's- ') (109K's- ') (kcaVmol)

Pentacene 2.07 22.9 Naphthacene 3.88 29.5 6,12-DimethyIanthanthrene 3.45 32.3 lO-Methyl-3,48,9-di-

benzpyrene 3.55 33.5 3,4:8,9-Dibenzpyrene 3.45 34.3 3,4:9,10-Dibenzpyrene 3.55 2.80 Anthracene 3.45 2.80 42.0 3 ,CBenzpyrene 3.45 2.51 42.3 1,2-Benzanthracene 2.82 1.83 47.2 Pyrene 2.70 1.54 48.3 1,2:3,4-Dibenzanthrwene 2.26 1.40 50.9 1,2:5,6-Dibenzanthracene 1.97 1.22 52.3 Chrysene 1.73 0.99 57.2 Picene 1.75 57.4 3,4-Benzphenanthrene 0.97 58.9d P h e n an thre n e 2.48 61.8 1,3,5-Triphenylbenzene 1.38 64.6 Coronene 0.52 54.3 Triphen y lene 1.38 66.6

"From Ref. 29, benzene solvent, 25°C assumed, adjusted to [O,] = 1.61 X

%om Ref. 19, cyclohexane solvent, 25"C, adjusted to [O,] = 2.10 X

'From Ref. 29. %om Ref. 19.

M (27). M (20).

(19,29,31). It is important to note that the spin-statistical factor is obtained here without having to rely on a theoretical value for kdiP The ex values provide an empirical measure of kdif in an ideal reference system, since diffusion coefficients 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 inefficiencies have 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 ex 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

ratio.

14

-log kdif

t

0 20 40 60 AET, +so, itcat/mol-

Figure 3. kzx vs. AET,-so in 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 ex 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 Franck-Condon factors for the (0) transitions for '2, + 'A, and '2; -+

'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 decreases with increasing triplet energy (33,34). Furthermore, since for > 38 kcaymol less excess 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 = 10e (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:), >> et 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

EXCITED-STATE INTERACTIONS w m 302 15

starts to decrease soon after the energy of O2('Z;) is exceeded, indicating that, if the O2('X;) pathway is operative, decreases much more rapidly than k$ 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 T1 potential 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-STATISTICAL FACTORS IN DIFFUSIONCONTROLLED REACTIONS

c km

* + 'A % (3p *A) e (3t*A) &'It + 3A* (26) P

is modestly activated, since it requires sufficient distortion 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~ONS WITH 3 4 17

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 stilbene- like 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 O2 as 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

18 SPIN-STATISTICAL FAClQR.9 IN DIFFUSIONCONTROLLED REACTIONS

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

3p* + 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 = ?L3kdif would be the maximum rate constant expected and no 02('Ag) would be formed. Actually, 13-18% of the quenching interactions 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, ex = 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 indistinguishable from 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 47.6 kcal/mol(69), and that of the