ADVANCES IN PHOTOCHEMISTRY Volume 14
ADVANCES IN PHOTOCHEMISTRY Volume 14 Editors
DAVID H. VOLMAN Department of Chemistry, University of California, Davis, California
GEORGE S. HAMMOND Allied-Signal, Inc., Morristown, New Jersey
KLAUS GOLLNICK Institut fur OrganischeChemie, Universitat Miinchen, Miinchen, West Germany
A Wiley-Interscience Publication
JOHN WILEY & SONS New York
Chichester
Brisbane
Toronto
Singapore
Copyright 0 1988 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc.
L i b w of Congress C&&g
in Pub&a&wi Data:
Library of Congress Catalog Card Number: 63-13592 ISBN 0-471-81524-1 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
CONTRIBUTORS
Beauford W. Atwater Department of Chemistry The Florida State University Talahassee, Florida 32306 Giinther von Biinau Institut fur Physikalische Chemie der Universitiit Siegen Postfach 21 02 09 D-5900 Siegen 21, West Germany Guy J. CoUi DCparment des Sciences Fondementales Universitk du Qutbec B Chicoutimi Chicoutimi, Quebec, Canada G7H 2B 1
Julian P. Heicklen Department of Chemistry and
Center for Air Environment Studies The Pennsylvania State University University Park, Pennsylvania 16802
Jack Saltiel Department of Chemistry
The Florida State University Tallahassee, Florida 32306
Thomas WOE
Institut f~ Physikalische Chemie der Universitiit Siegen Postfach 21 02 09 D-5900 Siegen 21, West Germany
James Guillet Department of Chemistry University of Toronto Toronto, Canada MSS 1Al
V
PREFACE
Volume 1 of Advances in Photochemistry appeared in 1963. The stated purpose of the series was to explore the frontiers of photochemistry through the medium of chapters written by pioneers who are experts. As editors we have solicited articles from scientists who have strong personal points of view, while encouraging critical discussions and evaluations of existing data. In no sense have the articles been simple literature surveys, although in some cases they may have also fulfilled that purpose. This volume initiates the second quarter-century of the existence of Advances in Photochemistry. In the introduction to Volume 1 of the series, the editors noted the developments in a brief span of prior years that were important for progress in photochemistry: flash photolysis, nuclear magnetic resonance, and electron spin resonance. In the past quarter century, two developments have been of prime significance: the emergence of the laser from an esoteric possibi!ity to an important light source; the evolution of computers to microcomputers in common laboratory use for data acquisition. These developments have strongly influenced research on the dynamic behavior of excited states and other transients. With an increased sophisticationin experiment and interpretation, photochemists have made substantial progress in achieving the fundamental objective of photochemistry: elucidation of the detailed history of a molecule which absorbs radiation. The scope of this objective is so broad and the systems to be studied are so many that there is little danger of exhausting the subject. We hope that the series will reflect the frontiers of photochemistry as they develop in the next quarter century. Davis, California Morristown, New Jersey Miinchen, Federal Republic of Germany October 1987
D A V I D H . VOLMAN
GEORGE S . HAMMOND KLAUSGOLLNICK
CONTENTS
Spin-StatisticalFactors in Diffusion-ControlledReactions JACKSALTIEL BEAUFORD W. ATWATER,Department of Chemistry, The Florida State University, Tallahassee, Florida Photochemistry and Molecular Motion in Solid Amorphous Polymers JAMESGUILLET,Department of Chemistry, University of Toronto, Toronto, Ontario, Canada Photochemistry of Simple Olefins: Chemistry of Electronic Excited States or Hot Ground States? GUYJ. COLLIN,Dtfpartement des Sciences Fondementales, Universittfdu Qukbec a Chicoutimi, Chicoutimi, Quebec, Canada The Decomposition of Akyl Nitrites and the Reactions of Akoxyl Radicals JULIAN P. HEICKLEN, Department of Chemistry and Centerfor Air EnvironmentStudies, The Pennsylvania State University, University Park, Pennsylvania
1
91
135
177
Photochemistry in Surfactant Solutions G~NTHER VON BUNAUAND THOMAS WOLFF,Znstitut fur Physikalische Chemie der Universitat Siegen, Siegen, West Germany
273
Index
333
Cumulative Index, Volumes 1-14
337
Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.
SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS Jack Saltiel and Beauford W.Atwater Department of Chemistry, The Florida State University, Tallahassee, Florida 32306
CONTENTS I. 11. III. IV.
Introduction Diffusion-controlled reactions Electronic spin multiplicity Excited-state interactionswith 3 0 2 A. Singlet excited states B. Triplet excited states C. Oq('Ag)yields V. Radical self-termination VI. Triplet excitation transfer VII. Triplet-triplet annihilation Appendix A. A+B-P B. A+A-P Acknowledgments References
I.
INTRODUCTION
The highly energetic species produced from molecules by absorption of electromagnetic radiation in the UV and visible region include singlet and triplet electronicallyexcited states and neutral and ionic radicals derived from them, e.g.,
2
SPIN-STATISTICALFACTORS IN DIFFUSION-CDNTROLLEDREACTIONS
Despite their short lifetimes, they undergo efficient bimolecular physical and chemical interactionsin solution with each other and with a host of other suitable quenchers or reactants. Consequences of these interactions form a large part of photochemistry (1). This work reviews the fastest of these processes, namely those that are diffusion-controlled with an emphasis on the influence of electronic spin of encounter partners on the outcome of the interactionsin solution. Specific topics considered will include the quenching of electronicallyexcited molecules by ground state 02,triplet-triplet excitation transfer, radical self-termination reactions, and triplet-triplet annihilation.
II. DIFFUSION-CONTROLLED REACTIONS Fast bimolecular reactions between different species A and B in solution are usually expressed in terms of formation and reaction of an encounter complex,
(W,
where kdir and k-, are the rate constants for diffusion of A and B together and apart, and k, is the rate constant for reaction of the encounter complex (2). The overall observed rate constant is given by
The reaction is said to be fully diffusion-controlled when k, >> Ldfapplies leading to kobsd = kw If the reacting species are identical, i.e., A = B in Eq. 2, multiplication of the rate constant by the factor ?4prevents counting the same reacting partner twice (3). For a diffusion-controlled A A reaction
+
where kdif is defined in Eq. 2. When transient terms can be neglected owing to long reactant lifetimes, T~ > s-', the rate constant in M-' s-l for a reaction which occurs upon every encounter can be based approximately on a theoretical model (see Appendix) by Smoluchowski (43)
kdif = 41rNpDlO-~
47rNpD
k
+k
DIFNSION-CONTROLJ.,ED REACI'IONS
3
where N is Avogadro's number, p is the reaction distance (i.e., the sum of radii of the reactants, rA rB). D is the diffusion coefficient for relative diffiision of the reacting molecules (taken as the sum of the individualdiffusion coefficients: D = DA + DB),and k is the rate constant for infinitely fast translatory diffusion. Under conditions where k >> 41rNpD Eq. 5 reduces to
+
kdif = 41rNpD
(6)
which is the form most often used. The individual diffusion coefficients are inversely related to friction coefficients 5:
DA =-
kT
(7)
5A
where k is the Boltzmann constant. For a spherical species of radius rA, the Stokes equation
cA
where 6, the coefficient of sliding friction, relates to the macroscopic medium viscosity q. Two limiting cases for 5 are usually considered (5). The stick or no-slippage (p = 01) limit, assumed to apply for systems composed of large solutes moving among relatively small solvent molecules, gives 5 = 6 1 ~ q rIt. corresponds to the Stokes-Einstein equation for the diffusion coefficient, DsE, on which the standard Debye equation
is based (a = 3,000, assuming rA = rB).At the other extreme, the free-slippage (p = 0) limit gives 5 = 4.rrqr, which leads to the modified Debye equation, Eq.8 with 01 = 2,000, and is supposed to apply for small solutes moving among large solvent molecules when free spaces between solvent molecules are large compared to the size of solute molecules. For either limiting case, mlT and kdimlT are predicted to be constant, independent of solvent or viscosity. This prediction has been shown to fail for several supposedly diffusion-controlled reactions of electronically excited molecules (5) and for radical self-termination reactions (6), especially when high-molecular-weight alkanes or alcohols are employed as solvents. But even in such cases, rate constants for reactions considered to be diffusion-controlled mirror the behavior of empirical diffusion coefficients, which, if not known, can be calculated from available empirical or semiempirical formulas (6).
4
SPIN-STATISTICAL. FACTORS IN DIFRISION-CONTROLLEDREACTIONS
Recommended for nonhydroxylic solvents (5,6) is the empirical formula of Spernol and Wirtz (7), which relates deviations of empirical D s from DsE’sto solute (r) and solvent (rd molecular-radius ratios:
ft
= 0.16
+ 0.4-rLr
where ft is the empirical microfriction factor for translation. Molecular radii are estimated from molar volumes, V in cm’, using r =
3000vx
”’
(T)
where x = 0.74 is the space-filling factor for closest-packed spheres. The procedure is justified in part by the microfriction theory of Gierer and WiaZ (8). Systematic solvent- and solute-specific deviations between experimental (Eq. 10) and calculated, (Eq. 11) ft’s were related to reduced solvent and solute temperatures, TrL and T,, respectively:
where T is the experimental temperature and Tbpand Tmpare the melting point and boiling point of the solute or solvent(7).Inclusion of the reduced-temperature term modifies Q. 11 to
ft
=
(0.16 +
0.4-
‘1
rL
(0.9
+ O.4TrL - 0.25TJ
(14)
and renders ft more solvent- and solute-independent. Microfriction factors obtained from Eqs. 11 and 14 are referred to as full and truncated, respectively.
III. ELECTRONIC SPIN MULTIPLICITY Empirically, the multiplicity M of a molecular or atomic electronic state indicates the number of distinct states (sublevels)into which a beam of molecules or atoms in that state is resolved on passing through a strong magnetic field one (singlet),
ELECTROMC SPIN MULTIPLICITY
5
two (doublet), three (triplet), and so on (1). Quantum mechanics associates this phenomenon with the state's total spin quantum number, S, which is the magnitude of the vector sum of the spins (+Yi or %) of the individual electrons. Since electrons occupying the same orbital are spin-paired (Pauli principle), S > 0 requires the presence of electrons in singly occupied orbitals as a necessary but insufficient condition. The multiplicity, given by
-
M = 2 S + 1
115)
is indicated numerically as a superscript preceding the symbol for the species; e.g., if A were a radical, 2A would specify its doublet multiplicity. Transitions between states of different multiplicity [spin isomers (l)], or even between sublevel states of a specific multiplet, q u i r e a magnetic perturbation and can be relatively slow (k = lo6 - 10" s-') processes. They are said to be multiplicity-forbidden. Since most ground-state reactions of organic molecules occur adiabatically on singlet ground-state surfaces (S = 0 throughout), they are multiplicity-allowed processes. Accordingly, the singlet multiplicity designations of the reactants, the encounter complex, and the products in Q. 2, though understood, are generally left out. We are concerned here with very fast bimolecular reactions in which at least one of the partners has S > 0. Written for the general case, Fiq. 2 becomes
where the product mn gives the number of possible encounter-pair spin states. Since in the absence of external magnetic fields the sublevel states of each multiplet are essentially degenerate, they are equally populated under equilibrium conditions at ordinary temperatures. It follows that the probability of formation of each encounter spin state is given by the spin-statistical factor (mn)-'.For example, interaction of two radicals
is expected to give four encounter-pair spin states with equal probability, three of which are sublevels of the encounter pair with triplet multiplicity and the
fourth is the singlet encounter pair. Similarly, when two triplet states interact,
6
SPIN-STATISTICALFACTORS IN DIFFUSIONCONTROLLED REACTIONS
they give nine encounter pair spin states which constitute the sublevels of encounter pairs with quintet, triplet, and singlet multiplicities. Since encounter-pair lifetimes are generally too short to allow appreciable interconversion between spin states of different multiplicity, and since, furthermore, reactions are dfision-controlled only when k, >> k-&f (i.e., k, > 10" s-'), it follows that only those encounterpairs which conservemultiplicity in going to products are expected to react. For example, if the product in Eq. 18 were formed only with triplet multiplicity, the maximum expected experimental rate constant would be given by
where the spin-statistical factor u = ?4 would reflect the fact that only those encounters resulting in the three triplet sublevels proceed to product, the rest being dissociative. In the following sections, several reactions will be discussed which illustrate the applicability of Q. 19.
IV. EXCITED-STATE INTERACTIONS WITH
302
The ground state of molecular oxygen involves assignment of the two highestenergy electrons to degenerate molecular orbitals and, in agreement with Hund's rule, is a triplet state (3&J, Occupation of the same orbitals by the two highestenergy electrons gives in addition two singlet states which conform to Pauli's principle (9). These are the lowest excited states of O2 and are located at 22.5 ('Ag) and 37.5 kcaVmol('2~)above the ground state (10). The triplet multiplicity of the ground state and the availabilityof low-lying excited states are responsible for the functioning of O2 as a very efficient quencher of electronically excited molecules in solution. Quenching is often associated with 02('Ag) formation. O2('Z;), when formed in solution, is thought to be much shorter-lived due to very rapid decay to 02('Ag).
A.
Singlet Excited States
Most extensively studied has been the interaction of excited singlet states of aromatic hydrocarbons with 0,(11,12). In nonpolar organic solvents the process
EXCITED-STATE INTERACTIONS
w m 302
7
is thought to give the triplet state of the hydrocarbon with unit efficiency and is known as oxygen-induced intersystem crossing (13,14). The efficiency of the quenching remains unchanged when the SI-T, energy gap of the hydrocarbon drops below 22.5 kcal/mol, indicating that formation of singlet oxygen is not an essential condition (15). Most observations are summarized well by askd
I-+
3M*
+ Oz('Ag)
Since both decay channels shown for the triplet encounter pair are multiplicityallowed, u = 1 is expected for Eq. 20. Experimental rate constants for a large number of molecules have been obtained from Stern-Volmer plots of the effect of [O,] on the fluorescence intensity and by measuring the fluorescence lifetime in the absence and presence of 02:
1 1 = T + ex[o,l Trn 7, Some variation in rate constants obtained by different research groups can be attributed to use of different references for the solubility of 0, in the solvents employed, or even to incorrect application of Bunsen or Ostwald coefficients in the calculation of [O,]. Since the atmospheric pressure, the temperature, and the degree of humidity when measurements were made in the presence of air are usually not reported, correction of the rate constants by application of uniform 0, concentrations is difficult. It will nonetheless be attempted when necessary, using a recently published critical and comprehensivecompilation of O2 solubility data (16). Very large Stern-Volmer constants for fluorescence quenching of aromatic hydrocarbons by oxygen have long been known (17,18). Ware's singlet-excitedstate lifetime measurements yielded k:x values which were shown to be diffusioncontrolled by comparison with calculated values from Eq. 6 using empirical D's and p = 6 8, (11). Rate constants obtained from steady-state fluorescence measurements (Eq. 21) were on the average -7% larger than those based on decay rates (Eq. 22) (1 1). Since the diffusion coefficients of 02,Dox, are 2.5 to 4 times greater than those of aromatic hydrocarbons, D,,, their large contribution to D in Eq. 5 has a (11). This accounts for Berlman's successful correlation leveling effect on of (Zdr), with T, for a large number of aromatic molecules (12), as shown in
ex
8
SPIN-STATISTICALFACIDRS IN DIFFUSION-CONTROLLEDREAcnoNS
-t-a
L
W
\ 0 H
Y
o.oh
0
[
20
1
40
r,, ns-
[
60
I
00
[
100
Figure 1. I,JIaiairvs. 7, in cyclohexane. See Table 1; data from Ref. 12.
Table 1 and Fig. 1. Since I, was obtained by bubbling N2through cyclohexane solutions, the (Zdr), values in Table 1 should be regarded as lower limits. The values in the table were calculated using [O,] = 2.10 x M ,which assumes 20°C as "room temperature" (20).* The points plotted in Fig. 1 correspond to a k,, range of (2.5-3.2) x 10" M-' s-'; the least-squares line with unit intercept gives = (2.81 -+ 0.09) X 10" M-' s-'. This value can be compared with k,", = (2.79 2 0.05) X 10" M-' s-l obtained from the lifetime measurements of Patterson et al. in cyclohexane at 25°C (19) for polycyclic aromatic hydrocarbons, using Eq. 22 and [O,] = 2.10 X M (20), by averaging the five largest kzx values from Ref. 19, Table 1. Though the range of values in the latter study, (2.27-2.84) X 10" M-' s-', is lower than that used in Fig. 1, this is somewhat deceiving, since where the two studies overlap, Berlman's k z values are significantly smaller (Table 1). Several nitrogen-containing compounds in Berlman's study exhibited much larger rate constants than those listed in Table 1. They are not considered here, since they may include static-quenchingcontributionsreflecting the presence of ground-state (IWO,) charge-transfer complexes (2 1,22). Experimental evidence for the formation of O,(lA,) as a result of singletexcited-state quenching by 0,(@. 20, as > 0) exists and will be presented in a later section. The energeticconsiderationsof the quenching events are illustrated by the two cases in Figure 2. In case I, Us+, > 22.5 kcallmol and formation of O2(lAg) is energetically feasible. This case, exemplified by anthracene and
ex
gx
*At 25°C. [02J = 2.17 x lo-' M is obtained. However, since in Ref. 19 the use of dry air was not specified, a somewhat lower value was used.
TABLE 1. Selected Rate Constants for 'M* Quenching by O2 in Cyclohexane" sc
Compound (AES~.T,)~ Benzene (24.9) Benzene-d, Fluombenzene Toluene Ethylbenzene 2-Pheny lbutane Diphenylmethane Methoxybenzene Diphenyl ether p-Xylene m-Xylene 0-Xylene p-Ethyltoluene p-Methoxytoluene p-Dimethoxybenzene 1,2,4-Trimethylbenzene 1,3,5-Trimethylbenzene 1,3,5-Triethylbenzene Biphenyl pBenzylbipheny1 p-Methoxybiphenyl p-Phenoxybiphenyl Dibenzofuran p,p"-Dihexahydrofarnesoxy-p-terphenyl Naphthalene (30.0) Naphthalene-d, 1-Methylnaphthalene 2-Methylnaphthalene 2.3-Dimethylnapthalene 2,6-Dimethylnaphthalene Acenaphthene 1-Phenylnaphthalene 1&diphenylnaphthalene 1,5-diphenylnaphthalene 1,l '-Dinaphthyl 2,2'-Dinaphthyl hthracene (34.3) 9-Meth ylanthracene Phenanthrene (20.6) Chrysene (22.0) Naphthacene (31.O) Triphenylene (15.3)
(b/I)air
7,
(ns)
2.4 2.63 1.47 3 .O 2.53 2.32 2.55 1.54 1.13 2.84 2.67 2.75 2.7 1.48 1.19 2.77 3.O 2.48 1.95 1.86 1.66 1.32 1.44
29.0 26.6 7.6 34.0 31.0 25 .O 25.3 8.3 2.0 30.0 30.8 32.2 30.8 8.7 2.9 27.2 36.5 24.0 16.0 13.9 9.4 4.8 7.3
1.06 6.4 6.8 5.5 4.1 5.83 3.2 3.54 1.65 1.07 1.12 1.21 2.90 1.25 1.29 3.8 3.18 1.26 2.53
0.95 96.4 96.0 67.O 59.0 78.4 38.4 46.0 13.0 1.25 2.0 3.O 35.2 4.9(4.9) 4.6 57.5 44.7(44.7) 6.4 36.6
k:: (lo~oM-~s-')
2.30 2.92 2.94 2.80 2.35 2.51 2.92 3.10 3.10 2.92 2.58 2.59 2.63 2.63 3.1 3.10 2.61 2.94 2.83 2.95 3.34 3.17 2.87
-
-
e _
3.O -
2.61 2.88 3.20
2.50 2.93 2.73 2.63 __
2.38 2.1 2.9 3.3 2.57 2.43(2.81) 3.oo 2.32 2.32(2.75) 1.93 1.99 _L
10
SPIN-STATISTICAL FACTORS IN DIFFUSIONCONTROLLEDRJ3MTIONS
TABLE 1. (Continued) Compound (AEs,-T,)b
~W)air
Triphenylene-d12 Perylene (28.3)
3.17 1.30
1,2,5,6-Dibenzanthracene 1,2-Benzanthracene 1,2,3,4-Dibenzanthracene 3,4,9,10-Dibenzpyrene Fluoranthene(18) 3.4-Benz~wne
1.49
SC
7,
(ns)
38.0 6.4 (37.5) (49.4) (53.5) (143.0) 53.0 (57.5)
::k
(loloM-l s-l) 2.72 -
2.23 (2.70) (2.84) (2.44) (2.55)
0.44
(2.83)
M was employed: see text. "Data from Ref. 12, unless otherwise indicated, [OJ = 2.1 X bFrom Ref. 14, except for last entry, which is from Ref. 12; in kcal/mol. 'Values in parentheses determined from Eq. 22 using T'S in Ref. 19, 25"C, [Od = 2.10 X lod3 M,underlined values correspond to points in Fig. 1 .
many of its derivatives (23), has the added feature of the availability of a higher triplet state, T2, nearly isoenergeticwith S1. In such systems S, --* T2intersystem crossing is favored over S1 +T1 in the absence of 02,and it has been suggested that it may also be enhanced by 0,(23). The functioning of such a quenching event may diminish aseven in those cases for which formation of 02( 'Ag)would be exoergonic. Case I1 illustrates the absence of a higher triplet quenching < 22.5 kcaYmol. For such systems as = 0 is expected. pathway, and Consideration of the entries in Table 1 has led to the conclusion that availability of the O2(lAg)formation channel is not essential in determining the
t
lu
%--
so-
Figure 2. Energetics for 'M*quenching by 02(3S;>.
EXCITED-STATEINTERACI?ONS m 3
11
4
magnitude of k,", (14). Actually, the rate constants for phenanthrene and triphenylene, from which no 02('Ag) formation should be expected, are somewhat smaller and may reflect less than diffusion-controlled quenching. Especially small k", values have also been observed for several fluoranthenes (12,24),as illustrated for the parent compound in the last entry of Table 1. Here, too, formation of 02('Ag) would be exoergonic, and it has been suggested as a possible reason for the quenching inefficiency (12). Another example of less than diffusion-controlledquenching is provided by 9,10-dichloroanthracene,for values in several solvents are consistently about 30% smaller than which those for anthracene (1 1,25). Equation 21 has been applied to data for several aromatic hydrocarbons in benzene for O2 concentrations ranging from air to one atmosphere of O2 (26). Assuming that the work was done at 760-Torr pressure, the [O,] values employed M S [O,] =s7.32 X M in are about 10% low (the range of 1.49 X Ref. 26 would correspond to an atmospheric pressure of 692 Torr (27);expected M). The M* s [o,]s 7.93 x for 760 TOIT is a range of 1.66 x rate constants from this study adjusted to the higher [O,] values are shown in Table 2, along with a few values obtained in other laboratories. Excluding the lowest two values (rubrene and perylene), an average kix = (2.83 2 0.24) X 10" M-' s-l is obtained for benzene at * 25°C.
ex
TABLE 2. Rate Constants for 'M* Quenching by 0, in Benzene
ex(%.
21)" (101OM-l s-I)
Comuound 9,lO-Dimethylanthracene 9,lO-Diphenylanthracene 9,lO-Dimethyl-1,Zbenzanthracene Naphthacene Rubrene Perylene Anthantiuene Anthracene 1.2-Benzanthracene 1,2-Benzanthracene-7-d "From Ref. 26, %om Ref. 11, 'From Ref. 21, dFrom Ref. 28,
*I021
2.87 f 0.18 3.30 f 0.23 2.51 -+ 0.15 2.17 -+ 0.16 1.07 k 0.07 2.47 f 0.27 3.23 k 0.55 2.67' 2.61d 2.8od
ex(a. Wb
( 101OM-l s- l)
2.8
3.2
3.1 2.47d 2.74d
25 2 2°C. unless otherwise indicated. 25/26"C, unless otherwise indicated. 24 f 1°C. 22.5"C for Eq. 21, 25 +- 1°C for Eq. 22.
= 1.61 X
M
at 25°C
was used to account for atmospheric moisture.
12
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS
B. Triplet Excited States Similar rate constants for the quenching of the lowest triplet states of a series of rigid polycyclic aromatic hydrocarbons, kzx, have been measured in cyclohexane (19). in benzene (29), and in n-hexane (29). Since triplet lifetimes are generally long in the absence of 02,the rate constants were based on the triplet lifetimes in &-equilibrated solutions:
Rate constants for cyclohexane and benzene are shown in Table 3. Also shown in Table 3 are the triplet energies of the aromatic hydrocarbons. The importance of overall spin conservation in the quenching of triplet states by paramagnetic species via an encounter complex was considered generally by Porter and Wright (30), and the spin-statistical consequences for the specific case of oxygen quenching were proposed by Stevens and Algar to account for steady-state observations with 9,lO-dimethylanthracene which suggested that (kTx/ex)= 9'9 (31):
,
\ M a-'(MO2)*
k.,'M
+ 02('Ag)
Since only one of the nine encounter-pair spin states has singlet multiplicity, only one of the encounters can lead to quenching by electronic excitation transfer in a process which is overall multiplicity-allowed. Strict adherence to the spinstatistical factor of % for the quenching rate constant, kzx = % kdif, is most simply explained if (a) intersystem crossing to the singlet encounter pair from spin states of different multiplicities are slow relative to diffusion apart of the encounter partners, and if (b) all singlet encounter pairs give quenching (31). The results of Porter and coworkers (19,29) for planar aromatic hydrocarbons (Table 3) indicate strongly that these conditions are fulfilled at least for molecules for which falls in the 29-42-kcdm01 range. Within this triplet energy range, kzx's in benzene plateau at a nearly constant maximum value of (3.50 +0.05) x lo9 M-' s-', whereas in the somewhat more viscous solvent cyclohexane, a value of 2.80 X lo9 M-' s-' is suggested by the more limited data (19,29). The triplet quenching mechanism in Eq. 24 is entirely consistent with the singlet quenching mechanism in JZq. 20, since in both, encounter pairs with triplet multiplicity are shown as completely dissociative with respect to 3M* formation. It is gratifying therefore that when limiting maximum values in Tables 1-3 are employed, the condition = is adhered to nicely
ex %ex
EXCITED-STATE INTERACIIONS WITH 3oz
13
TABLE 3. Rate Constants for O2 Quenching of Planar Aromatic Hydrocarbon Triplets Compound Pentacene Naphthacene
6,12-DimethyIanthanthrene lO-Methyl-3,48,9-dibenzpyrene 3,4:8,9-Dibenzpyrene 3,4:9,10-Dibenzpyrene Anthracene 3,CBenzpyrene 1,2-Benzanthracene Pyrene 1,2:3,4-Dibenzanthrwene 1,2:5,6-Dibenzanthracene Chrysene Picene 3,4-Benzphenanthrene Phenanthrene 1,3,5-Triphenylbenzene Coronene Tripheny lene
k:Xa (109K's-')
k;f, (109K's-')
AET,-SoC
(kcaVmol)
2.07 3.88 3.45
22.9 29.5 32.3
3.55 3.45 3.55 3.45 3.45 2.82 2.70 2.26 1.97 1.73 1.75
33.5 34.3
2.48
2.80 2.80 2.51 1.83 1.54 1.40 1.22 0.99
42.0 42.3 47.2 48.3 50.9 52.3 57.2 57.4 58.9d 61.8 64.6 54.3 66.6
0.97
1.38
0.52 1.38
"From Ref. 29, benzene solvent, 25°C assumed, adjusted to [O,] = 1.61 %om Ref. 19, cyclohexane solvent, 25"C, adjusted to [O,] = 2.10 X 'From Ref. 29. %om Ref. 19.
X
M (27). M (20).
(19,29,31). It is important to note that the spin-statistical factor is obtained here values provide an without having to rely on a theoretical value for kdiP The empirical measure of kdif in an ideal reference system, since diffusion coefficients ratio. and encounter distances must cancel in the The decrease of kTx for pentacene, whose triplet energy is expected to be within 1.5 kcal/mol of the energy of Oz('Ag), is not surprising, since similar inefficiencieshave long been known in triplet-triplet excitation transfer processes (see Section VI) when the net reaction is less than 3 kcdmol exothermic (1,32). The values show a general inverse dependence on the triplet energy of the aromatic molecules for AET,-% > 42 kcdmol (19,29) (Fig. 3). For these molecules the inequality k,, >> k-dif does not hold (19,29) and kz. is given by
ex
ex
14
-log
kdif
t
0
20
40
AET,+so, itcat/mol-
60
Figure 3. kzx vs. AET,-soin benzene; see text.
For the specific case chrysene (A&,+, = 57.2 kcallmol), the expected increase of k', with increasing solvent viscosity was established experimentally (29). It was also shown that kzx for chrysene increases with increasing solvent polarity (29). The theoretical implications of the dependence of on AET,-s,have been discussed in Ref. 29. A theoretical treatment of triplet quenching by O2 had predicted that excitation transfer via the singlet encounter pair would be the dominant quenching pathway (33). In addition, it was pointed out that the large transitions for ' 2, + 'A, and '2; -+ Franck-Condon factors for the (0) '2; excitation of oxygen meant that the Franck-Condon overlap integrals controlling the size of ket should be determined primarily by the aromatic molecules (33). A general inverse relationship of ket on AET+, is then expected, since the Franck-Condon factor of the donor triplet state decreaseswith increasing > 38 kcaymol less excess triplet energy (33,34). Furthermore, since for energy need be accommodated by the ground state of the aromatic hydrocarbon as vibrational excitation when 02( '2;) rather than 02( 'A,) is formed, the former process was predicted to be more efficient: ket = 1 0 e (33). This conclusion is inconsistent with the experimental k;f, values (29). When the donor's triplet energy falls comfortably between 22.6 and 37.5 kcallmol, the excitation energies of 02('Ag) and 02('8:), >> is expected. It can be seen that k:x retains its limiting value in this energy region, so that >> k--dif even when the excitation transfer process is 15 kcallmol exothermic. On the other hand, kzx
ex
et
EXCITED-STATEINTERACTIONS
w m 302
15
starts to decrease soon after the energy of O2('Z;) is exceeded, indicating that, decreases much more rapidly than k$ if the O2('X;) pathway is operative, as the exothermicity of the process increases (see below, however). Preferential formation of 02('Ag) over O2('2;) when a high-triplet-energy donor is quenched has been rationalized by a theory which includes orbital symmetry restrictions in the transfer process (29,35). The aromatic molecules considered thus far are relatively rigid and have well-defined TI-So energy gaps. We turn now to flexible molecules whose relaxation in the triplet state may lead to substantiaIly different equiIibrium geometries, relative to the ground state, corresponding to significantly smaller T l S o energy gaps. The So and T1potential energy curves for twisting about the central bond in stilbene (Figure 4) illustrate this situation in a particularly well-studied example (36). The triplet curve is based on spectroscopic data (37) for the transoid (3t*) and cisoid (3c*) limits and on the functioning of the stilbenes as acceptors and donors of triplet excitation (38,39,40) for twisted configurations. The steeper T, potential-energy curve on the cis side of the relaxed triplet, 3p*, accounts nicely for the fact that acceptors with triplet energies as low as ~ 2 2 kcaVmol (@-carotene) deactivate stilbene triplets only on the trans side by excitation transfer (41). This process,
I
0
HI2
7T
Figure 4. Potential-energy curves for central-bond twisting in So and T,of the stilbenes. From Ref. 36, reprinted with permission from J . Phys. Chern. (1987) 91,2755. Copyright 1987, American Chemical Society.
16
SPIN-STATISTICALFACTORS IN DIFFUSIONCONTROLLEDREACTIONS
P*
+
'A
%
(3p*A)
c
e
(3t*A) &'It
km
+ 3A*
(26)
is modestly activated, since it requires sufficientdistortion towards 3t*to produce the So-T, electronic energy gap required for the excitation of the acceptor, A, to its triplet state (39,40). It is an example of triplet-triplet excitation transfer (see Section VI) for which a spin-statistical factor of unity is expected, since overall triplet multiplicity is maintained throughout. Substitution on the phenyl group of stilbene, or replacement of phenyl with other aryl groups, can change the relative energies of 3p* and 3t*in olefins so that 3t*can be thermodynamically favored. Generally, however, excitation transfer occurs from transoid triplet geometries, whereas cis-trans photoisomerization occurs by radiationless decay from nearly perpendicular geometries, 3p* (37): 3p*
-
6't
+ (1 - 6)'c
(27)
Consequently, ([t]/[c]),, the photostationary composition ratios for the triplet sensitized photoisomerization of such olefins, increase linearly with acceptor concentration. Schemes 1 and 2 have been shown to account for such observations (39). The first applies to stilbene, for which most triplets have the 3p* geometry
Scheme 1. The Common Triplet Mechanism
Scheme 2. Transoid and Twisted Stilbene Triplets in Equilibrium
.
EXCITED-STATE INTERACI~ONSWITH 3
17
4
at room temperature, and the second applies to olefins, for which a substantial fraction of the triplets at equilibrium have a transoid geometry. In view of the well-documented ability of 0, to function generally as an acceptor of triplet energy, it had been expected that its presence should also increase ([t]/[c]), ratios for the triplet sensitized photoisomerization of stilbenelike olefins. However, as was first noted for nitrostilbenes, the quenching of the olefin triplets by 0,does not alter ([t]/[c]), (42,43). For the parent stilbene it was shown that when azulene is used as a quencher of stilbene triplets the slope of the ([t]/[~])~-vs.-[Az]plot is strongly attenuated by 0,; see Figure 5 (41$4). Since the intercept of the azulene plot .was not influenced by 0,. it was reasoned that O2 deactivates 3p* without changing the decay fraction 6 as predicted by Schemes 1 and 2 (44).To account for stilbene triplet deactivation by 0, without change in 6 two possibilities were considered
3p*
+ 02(32i)+s3(p02)*
k,
6' 't
+ (1
- 6') 't
+ 02(3z,)
If 02('Ag) were produced efficiently, then the 22.5-kcaYmol energy gap required would be achieved with equal efficiency by torsional displacement of the 3p* partner of the singlet encounter pair toward either cisoid or transoid geometries. If, on the other hand, excitation transfer does not usually accompany the quenching process, then quenching could occur from the triplet encounter complex by a spin-exchange mechanism (45)-a process that should come into play because the energetic proximity of So and TI at twisted geometries allows quenching to occur without the usual requirement for simultaneous removal of electronic energy. This quenching is effectively enhanced intersystem crossing (33) and should give similar transkis ratios to those for natural 3p* decay. Verification of the spin-exchange mechanism as the dominant quenching pathway was accomplished by substituting p-carotene for O2as a co-quencher with azulene for stilbene triplets (41). As can be seen in Figure 5 , the effects of azulene and p-carotene are strictly additive. Thus, when stilbene triplet quenching is by electronic excitation transfer, it occurs on the trans side exclusively. Based on Scheme 1, the following steady-state expression can be derived:
where k,[Az] and k,[C] are the azulene and p-carotene contributions of Eq. 26, in accord with the experimental observations. p-Carotene was selected because
SPIN-STATISTICAL FAClQR.9 IN DIFFUSIONCONTROLLEDREACTIONS
18
its triplet energy must be very close to the energy of 02('Ag), as evidenced by its functioning as an acceptor of triplet excitation from low-triplet-energy donors (46) and specifically from O,('A ) (47,48,49) with a nearly diffusion-controlled rate constant, (1.1 2 0.1) x lOg10 M-1 s-1 in benzene (49). A precedent to the spin-exchange quenching mechanism of olefin triplets by oxygen is provided by the interaction of stilbene triplets with the stable free radical di-ferf-butyl nitroxide, ,N (50). In this case hiplet-sensitized ([t]/[c]),
-€
,(pN)* --+ 6' 't
3p*
+ (1 - 8') 'C + 2N
+ 2N
(30)
t 4(PN)*
ratios become more cis-rich as tbe concentration of [,N] is increased (50). Analysis of the data assuming quenching of 'p* only gives 6/6' = I. 11 and kN/kd = 110 +- 20 M-' in benzene (50,51). From the latter value kN = 1.8 X lo9 M-' s-' can be estimated using the known stilbene triplet lifetime (38). Since no electronic excitation transfer is expected for spin-exchange quenching of 3p*, only the doublet encounter pair provides a multiplicity-allowed pathway, so that the limiting value of kN should be %kcif. Clearly the observed value is not far from this limit. Rate constants for quenching of planar aromatic triplets with large So-Tl energy gaps are generally smaller than kN for stilbene; e.g., for naphthalene, AET,s, = 61 kcdmol, kN = 6.3 x 10' M-' S-' (50). If only the spin-exchange mechanism for O2 quenching of stilbene triplets were operative, then k:x = ?L3kdifwould be the maximum rate constant expected and no 02('Ag) would be formed. Actually, 13-18% of the quenchinginteractions have been shown to give 02(lAg) (52,53), indicating that both the k,, and k, channels in Q. 28 are important. By analogy with B-carotene, excitation transfer from 3p* to 0, should occur only on the trans side. It appears therefore that 6=6' is coincidental for O,, reflecting a balance between energy-transfer deactivation on the trans side and spin-exchange preference on the cis side (53). Inclusion of the energy-transfer pathway increases the maximum limiting k,'x in this case to 4/gkdif. Indeed, the experimental value, = 9.0 X lo9 M-' s-' (38), though not quite as large as 4/9kdif, is significantly larger than the rate constants in Table 3, which reflect only singlet encounter-pair quenching (see also below). Rate constants for O2 quenching in benzene of several olefin triplets and a few rigid analogs are listed in Table 4. The first three entries are stilbene analogs with little structural freedom for torsion about the olefinic bond. They exhibit kzx values indistinguishablefrom those for planar aromatic hydrocarbons in the 29.5-42.3-kcaVmol A&,+ range (Table 3). Since the triplet energy of the ?runs-stilbene analog indeno[2,1-u]indene is 47.6kcal/mol(69), and that of the
ex
TABLE4. Rate Constants for O2Quenchingof Olefin Triplets and Rigid Analogs in Benzene, 25°C
Indeno[2,l-a]indene 2-Phen ylindene 1,2-Diphenylcyclobutene Stilbened 4-Nitrostilbened tran~-4,4'-Dinitrostilbene
4-Nitro-4'-methoxystilbened 4-Nitro-4'-dimethylaminostilttened 1,l-Diphenylethene
Triphenylethene Tetraphenylethene trans, trans-1.4-Diphenyl1,3-butadiene All-trans-1,6-diphenyl1,3,5-hexatriene All-trans- 1,&diphenyl1,3,5,7-0ctatetraene trans-1-Phenyl-2-(2naphthyl) ethene 3.3-Dimethyl- 1-(Znaphthyl)1-buteneg 3,4-Dihydrophenanthrene 2-( 1-Naphthyl)propene 1-(1-Naphthyl)cyclopentene 1-(1-Naphthyl)cyclohexene 1-(1-Naphthyl)cycloheptene 1-(1-Naphthyl)cyclooctene 1-Phenyl-1-(1-naphthyl)-2methylpropene 1-(1-Naphthy1)indene 1-(l-Naphtyl)3,4-dihydronaphthalene 1,l-Di-( 1-naphthy1)ethene 1-Phenylcyclohexene All-trans-P-carotene' Retinal* Retinolk
2
1.5msc 0.10 ms 0.20 ms 62 ns 74 ns 102 ns 130n5 77 ns
38 38 38 38 42 42 42 55
5.3 9.0 11.0 4.8 2.4
2PS 41 ns 41 ns 105ns 18011s
42 56 57h 56 56
3.7
10 ps
58
5.5
100 ps
58
6.0
100 ps
58
5.6
15011s
59
3.4 3.8 3.4 9.0 7.0 6.0 6.8 5.9'
= 130ns
5.3 5.1
120n5
60 59 60 57h 57 57 57 57
6.1 2.7
100ns 4.5 p,S
57 57
3.0 4.4 9.0 2.5 2.8k 1.9 4.7
4.5 ps 220 ns 3 65 nsi 9 FS 7P S 9 PS 13 ps
57 57 57 62 62 62 62
2.4-4.7 5.2 2.1 4.4
3.0 2.8
80 IIS 1.2 ps 550 ns 3.6p5 2 CLS
53 ns
19
20
TABLE 4.
SPIN-STATISTICAL. FACTORS IN DIFFUSION-CONTROLLED REACTIONS
(Continued)
2-Cyclohexenone'
4,4-Dimethyl-2-c yclohexen~ne~
Testosteronee
cis-Thioindigo
6,6'-Dietho~ythioindigo~ h-ans-N,N'-Diacetylindigo p-Ionone' A6-Testosteronem
25 ns 25 ns
7 7.5
2.2 3.2 2.9
63,64 63 64 65 65 66 67 68
440 ns
279 ns 143ns llns 140ns
5.7
5.1
1.7
lops ~
~~~
"Unless otherwise indicated, triplets produced using benzophenone, xanthone, or other carbonyl triplet energy donor. kifetimes in ws time scale are minimum values, since in most cases outgassed instead of rigorously degassed solutions were employed. 'From Ref. 54 in toluene, degassed; Ref. 38 gives > 5 p s , outgassed. qdentical results starting from cis or trans isomer. Tyclohexane, [O,] adjusted to agree with ref. 16. &ate constants depend on wavelength region of triplethiplet absorption. gSimilar rate constants for cis and trans isomers, but results depend on triplet sensitizer. "[O,]adjusted to 1.61 X M for air-equilibrated solutions (16) for all ko,'s from ref. 57. 'From Ref. 61. '21.3"C; [O,] adjusted to agree with ref. 16; anthracene-sensitized, pulse radiolysis. 'n-Hexane, 21.3"C. 'Toluene.
"'Ethanol.
cis-stilbene analog 1,2-diphenylcyclobutenemust surely exceed this value (Figure values do not show the decrease observed for the planar aromatic hydrocarbons with increasing exothermicity (Table 3, Figure 3). Similarly notable are the relatively low Exvalues that correspond to the other rigid molecules in which the double bond is constrained to be nearly planar: 1-(1-naphthyl)cyclopentene, 3.0 x lo9 M-' s-'; 1-(1-naphthyl)indene, 2.7 x lo9 M-' s-'; l-(l-naphthyl)-3,4-dihydronaphthalene,3.0 X lo9 M-' s-'; 3,4dihydrophenanthrene, 2.1 x lo9 M-' s-'; testosterone, 2.2 X lo9 M-' s-' (cyclohexane). Of special interest are the large values, e.g., stilbene (9 X lo9M-' s-I), 1,l-diphenylethene (9-1 1 X lo9 M-' s-'), l-phenylcyclohexene (9 X lo9 M-' s-I), which approach the %kdif to %kdif limits and must surely reflect spin-exchange quenching at 3p* geometries. Most of the remaining rate constants are intermediate in magnitude and probably represent different combinations of the spin-exchange and energy-transfer channels. Since the former mechanism usually applies when So +TI energy gaps are small at substantially twisted geometries, whereas the latter requires So + TI energy gaps exceeding
4) (70), these
ex
ex
EXCITED-STATEINTERACTIONS WITH 3
4
21
-22 kcaUmol which are achieved at more nearly planar geometries, the size of
ko', has been used as a criterion in establishing the equilibrium geometries of
olefin triplets (41,44,55,57,58). It must be used cautiously, however, because if the encounter pair is sufficiently long-lived and/or if the triplet potential-energy curve of the olefin is sufficiently flat, the triplet olefin partner may explore several geometries prior to quenching. Thus just as a triplet acceptor such as azulene may quench twisted triplets because the lifetime of the encounter is sufficiently long for them to undergo torsional excursion towards transoid geometries, so might 3(t02)* encounter pairs undergo spin-exchange quenching if the olefin partner has time to approach or reach 3p* geometries. It is perhaps relevant that direct determinations of for stilbene (38) and l-phenyl-2(2-naphthy1)ethene (59) based on triplet transient-decay measurements give significantly smaller values ('0.6 factor) than inferred from 0,'s attenuation of the azulene effect on ([t]/[cJ), (38,39,41,59). Though the differences may reflect large experimental errors, they might also provide evidence for cooperative quenching of olefin triplets by 0, and azulene. The latter possibility would require exciplex intermediates between the olefin triplets and either or both quenchers having much longer lifetimes than expected for simple encounter complexes. Fortunately, other experimental parameters are sensitive to olefin triplet geometry and assist in the evaluation of the They include (1) the triplet lifetime, which (see Table 4) is long for nearly planar triplets (ms-ps) and short for nearly perpendicular triplets (ns), (2) the magnitude of triplet-triplet excitation-transfer rate constants, e.g. k, which is large for planar and small for perpendicular triplets, (3) the shape of the triplet-triplet absorption spectrum and its dependence on structural or medium constraints to torsion about the olefinic double bond, (4) the fraction of quenching interactions which give 02('Ag), and ( 5 ) where applicable, the trandcis decay ratio, 8'/(1 - a'), associated with the O2 quenching interaction. Stilbene, for which several of the above criteria have been applied, has already been considered. Examination of some of the other cases is instructive. We start with a comparison of the behavior of I-phenylcyclohexene (PC) with that of 1-(1-naphthyl)cyclohexene ( 1-NC). PC triplets are short-lived (263 ns) , are not quenched by low-triplet-energy acceptors, decay to give cis and trans isomers = 9 X lo9 M-' s-'). Taken (71), and are quenched very efficiently by 0, together, all these observations indicate strongly that the relaxed PC triplet has a nearly perpendicular geometry. On the other hand, 1-NC triplets are almost as long-lived (2 ps) as those of the rigid analog 1-(1-naphthy1)indene (4.5 ks), are quenched efficiently by low-triplet-excitation acceptors [ferrocene, 5 40 kcaUmol (46), kf, = 3.0 X lo9 M-' s-' (56)], do not give trans isomer upon decay, and are relatively inefficientlyquenched by 02(&= 2.8 X 1 0 9 K 's-'). Accordingly 1-NP has been assigned a nearly planar relaxed triplet geometry. The effect of the naphthyl for phenyl substitution in shifting the equilibrium
ex<
ex's.
(ex
22
SPIN-STATISTICALFACTORS IN DIFNSION-CONTROLLEDREACTIONS
triplet geometry towards planarity is clearly electronic, since the cyclohexene ring should experience no greater structural constraints to twisting in 31-NC* than in 3PC*. Furthermore, even the acyclic 2-(l-naphthyl)propene appears to have a nearly planar triplet state (56); 2-naphthyl substitution on the olefinic double bond as in 3,3-dimethyl- 1-(2-naphthyl)-l-butenealso appears to shift the equilibrium geometry towards planarity (60). This is reflected in the effect of 0, on the ([t]/[c]),-vs.-[Az] plots. In contrast to stilbene (Fig. 5), in this case 0,increases the intercept of the plot in addition to attenuating the slope-a clear indication that the excitation-transferquenching pathway is strongly contributing (72). Interestingly, O2 does not alter the intercept of the azulene plot for the l-phenyl-2-(2-naphthyl)ethenes (73), which appear to behave more like the stilbenes. A pronounced effect of substitution of the phenyl group with a more extended .rr-system (lower AET,.+, for substituent) is probably responsible for the interesting 3c* --* 3t* one-way photoisomerization of 2-anthryl olefins, to which transoid equilibrium triplet geometries have been assigned (74,75). The 4-nitrostilbenes represent an interesting class of compounds (37). For several of these, the optical density of the triplet-triplet absorption is independent of temperature and medium viscosity, indicating efficient triplet population under all conditions studied (76). For the same solvent the triplet-triplet absorption spectra are also temperature-independent, though the trans-xis quantum yield drops sharply as the temperature is decreased and the medium viscosity is increased (74). These results indicate a transoid equilibrium geometry for the triplets at all temperatures studied (76), consistent with large ferrocene (4.7 X lo9 M-' s-', cyclohexane) and azulene (4.4 X lo9 M-l s-', cyclohexane) quenching rate constants at least for 4-nitro-4'-methoxystilbene (55). Nonetheless, they exhibit short triplet lifetimes and large gxvalues (Table 4), indicating that the 3p* geometry is readily accessible from 3t*. Furthermore, 0, quenching, though it attenuates the ferrocene effects on ([t]/[c]),. does not alter the decay fraction, i.e., 6 = 6' (55). It appears that the following quenching sequence may apply:
Derivatives of indigo and thioindigo represent a related case. A transoid relaxed triplet geometry has been assigned to a number of them on the basis of triplet-triplet absorption behavior analogous to that of the 4-nitrostilbenes (65,77). In this case, however, 0,decreases+t+ for the direct photoisomerization
EXCITED-STATE INTERACTIONS WITH 3 0 2
23
4'0
Figure 5. Azulene effecton the benzophenone-sensitized stilbene photoisomerization in benzene: line 1 , degassed; line 2, 0, atmosphere; line 3, degassed with 2.90 X M p-C. From Ref. 41, with permission of North-Holland Publishing.
and increases ([t]/[c]), for both the direct and triplet sensitizedphotoisomerizations (78). Deactivation of thioindigo (78) and N,N'-diacetylindigo (65) triplets exclusively to trans isomers with concomitant formation of 02('Ag), at least for the former (78), suggests triplet excitation transfer from 3t* to O2 rather than spin-exchange quenching of 'p*. Thus, in these cases, only the singlet encounterpair channel in Eq.31 leads to products, though 3p* should be readily accessible from 3t*, since decay to cis occurs and short triplet lifetimes are involved. Also noteworthy is that compounds related to indigo are unique in that their excited singlet states are immune to O2 quenching at normal O2 concentrations. Neither +f nor Tf varies with [O,] despite the large T: values (up to 13.5 ns!) (65,66,78). We are not aware of any other examples of this type, nor can we offer an explanation for these interesting results, unless they represent severe cases of orbital symmetry restrictions (35). Comparison of the enone and dienone data in Table 4 again leads to the conclusion that in the absence of structural constraints a 3p*-type geometry is attained which undergoes spin-exchange quenching by O2 (62,63,64,67,68). Extended conjugation as in diphenylhexatriene and diphenyloctatetraene(58) and in @-carotene,retinal, and retinol (62) appears to favor planar geometries. In all of these, relatively long triplet lifetimes are involved and the kzx values
24
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS
are near the l/gkdif limit. That these criteria can be misleading is exemplified by p-carotene (C), for which a considerablebody of additionalexperimentalevidence is available. Excitation transfer from Oz('Ag) to p-carotene occurs at roughly %kdif, gives 3C*, and has allowed the use of p-carotene as a probe for 02('Ag) yields for a variety of triplet energy donors (49). A triplet excitation energy of 21-25 kcallmol for C, nearly equal to the energy of 02('Ag), has been based on rate constants of triplet excitation transfer from a series of aromatic hydrocarbons to C (Sandros plot) which fall to = 1h their maximum value at donor A E T , a , = 23 kcaVmol (pentacene) (46). Since ex's for C and pentacene (Tables 3 and 4) are also very similar, it is tempting to conclude that well-matched energy gaps in the C-02 pair have resulted in reversible excitation transfer:
This conclusion is, however, inconsistent with Foote and Denny's demonstration 'Ag) reactivity (47). The lifetimes of that p-carotene strongly suppresses 02( Oz('Ag), -30 ps (79,81), and of 3C*, 9 ps (62), in benzene solution are sufficiently long for the equilibrium in Eq. 32 to be substantially established at moderate O2 and 'C concentrations:
Since in Foote and Denny's experiments [02] exceeded the ['Cl's by more than one order of magnitude (47), the concentration of 02('Ag) would not have been = 0.21 (52,62), and little or no quenching greatly diminished (Eq. 33), would have occurred if the transfer were reversible. Since, in contrast to this prediction, pronounced quenching was observed at all ['Cl's, the notion of reversible excitation transfer must be rejected. The absence of chemical consumption of 'C (47) then suggests that the process is best described as spin-exchange quenching:
gx/@
+
Accordingly, kox = %k&fkse/(kse k-,if). The failure of the singlet encounter pair to provide an effective deactivation channel and the small energy gap implied by the efficiency of the spin-exchange path suggest that thermally equilibrated
25
=CITED-STATE I N T E R A ~ O N SWITH 3 0 2
3C* has lost some of its initial energy, possibly through significant geometric adjustments. values than Y9kdf have been reported for several molecules with Larger n,T* lowest triplet states (Table 5 ) . Since these generally do not exceed %kdif, combinations of quenching via the singlet and triplet encounter pairs have been proposed (52,8248). In view of the high A&,+, values involved, even the kTx value of benzophenone, which is nearly equal to %kdjf (compare with value for anthracene in Tables 3 and 5 ) , can be regarded as anomalously high if only the
ex
TABLE 5. Rate Constants for Oz Quenching of n,T* Triplets Compound Acetoneb Xanthone' Acetophenone' 4.2 Benzophenone' Anthraquinonec P-AcetonaphthoneCsd Carbazole' Tripheny laminee N-Methy lindole' N-Methylthioacridond
e x a
(109K's-') 9.2 5.9 74.1 5. l b 3.O 3.2 2.3 1.5 1.5 2.0 1.9 6.0 15 17 15 12.3B 15Sh 2.3 1.9
Acridine'
3.2 3.1 2.2
&,so
(kcaUmo1)
=78
74.1 52,84 69.5 62.9 58.9 70.4 70.1 69.2 42.6 60.9
Ref. 82 52.83 82 52 84 85 84 86 84 85 84 87 52 84 88 88 84 85
42.0
84 85 85
"Rate constants in benzene at room temperature, by pulse radiolysis and/or flash photolysis unless otherwise stated. M for air-equilibrated cyclohexane solution, 20°C (16). bAdjusted to [O,] = 2.10 X 'Adjusted to [O,]= 1.61 X M for air-equilibrated solution (16). &?r,m* state, included for comparison with Table 3. Wethylcyclohexane. f3-Methylpentane, phosphorescence. s ~ & vs. [O,]. hWI vs. [O,].
26
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS
singlet encounter pair leads to quenching. The k;f, values of N-methylindole, N-methylthioacridone, and triphenylamine are especially notable in that they are, within experimental uncertainty, equal to 4/kdif(89). The possibility that chargetransfer interactionsin the encountercomplexes increase the quenching efficiency has also been stressed (29,33,84,90,91). III the case of chrysene, the kTx/kdif ratio increases generally as the polarity of the solvent is increased (29). A large increase in this ratio has also been reported for rose bengal, methylene blue, thionene, and erythrosin as the solvent is changed from methanol or cyclohexanol to the more viscous solvent ethylene glycol or to water (92). Whereas k;f, = ?hkdif in cyclohexanol, it is very close to Y9kdifin ethylene glycol and water (92). The triplet states of phenol, p-cresol, anisole, and tyrosine are quenched by O2 in water at 25°C with rate constants in the (4.84.3) X lo9 M-'s-' range (90); kdif = (5.3 & 1.1) X lo9 M-' s-' in water has been estimated from k,, values (92). With some of the phenols, transient absorptions have been assigned to phenoxy and superoxide radicals, and the quenching has been attributed to electron transfer (90):
3ArOH*
+ O2
4
573.'(ArOH/02)*--t A I O + G2-
+ H+
(35)
Similarly, large kzx values ('5 X lo9 M-' s-', 25°C) have been obtained in water for quenching the triplet states of nitrogen-containing molecules, including indole, tryptophan, and tryptamine (90). Thus far we have assumed that encounter pairs of different multiplicities do not interconvert. This requires that for %kdif S kOx S 4/9kdif the yields of 02('Ag) per encounter, aT, should be given by 1 2 aT 3 0.25, in the same order. An alternative mechanism that would also give the same k,, range includes interconversion of singlet and triplet encounter pairs through stronger spin-orbit and spin-spin interactions than those applicable to aromatic hydrocarbons (52,84,88). Since charge-transfer interactions are also postulated, the encounter pairs
'(M02)* k,_ 'M
+ 02('Ag)
can be viewed as exciplexes of different multiplicity. This mechanism will accommodate any aTin the range 0 S cxT S 1 , independent of the value of k;,. Clearly, then, determination of quantum yields for sensitized 02( 'A,) formation is crucial for evaluation of the importance of the energy transfer relative to all
27
EXCITED-STATE INTERACTIONSWITH 3 0 2
other quenching channels, and for differentiation between noninterconverting and interconverting encounter pairs, at least in limiting cases.
C. Oz(*Ag)Yields An expression for +A in terms of the kinetic parameters can be based on
+ 02(3&J53M* + o'O~(~A,) + (1 (37) 3M* + 02(3X;) 5 'M + aT02('A,) + (1 - CX~)O,(~Z,) (38) 'M*
as)02(3X,)
which are more general forms of Eqs. 20, 24, 31, 34, and 36. The singlet contribution to the quantum yield, given by
+,:
is not expected to be large, even if as is significant, because of incomplete 'M* quenching (Table 1) (93-95). On the other hand, since in the presence of O2 Eq.38 usually accounts for all triplet decay, the triplet contribution +A is given by
where +is and 4: are intersystem crossing yields of 'M* in the presence and in the absence of 02.respectively. Combining Eqs. 39 and 40 gives
which can be combined further with Eq. 21 to give
+
It can be seen that +A + aT as as -+ 0 . Both indirect and direct approaches for the determination of +A have been applied. Early methods employed the highly reactive substrates tetramethylethylene ( W E )(96), 2,5-dimethylfuran (DMF) (96,97), and 1,3-diphenylisobenzofuran (DPBF) (48,67,85,93,94) to trap 02('Ag):
28
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLED REACTIONS
Studies of the photooxidation of these substrates have established chemical reaction with 02( 'Ah,) as the only significant quenching interaction; essentially no physical quenching of 02('Ag) is involved (48,85,93,94,96-100). A related set of studies is based on the photoperoxidation of anthracenes, e.g., rubrene, and 9,lO-dimethylanthracene(DMA) as the 02('Ag) trapping reaction (95,101). 02('Ag) sensitizer molecules for which +A values were determined in this way were excited directly or, when small +is values were involved, indirectly via a triplet energy donor, using both pulsed (flash photolysis and/or radiolysis) and steady-state irradiation conditions. Chemical and physical measurements have included monitoring 0,consumption, substrate depletion (bleaching), and/or oxidation product formation. To illustrate the kinetics for the steady-state excitation case we need only consider
'A
+ OZ('Ag)
'A02
(43)
where 'A represents a completely effective chemical trapping agent [02('Ag) acceptor]. The oxidation product quantum yield, +Ao2, is then given by
which can be inverted to the more useful form
from the intercepts, and Plots of (+Ao2)-1 vs. [A]-' allow calculation of aT asvalues can be generated using Eq. 41 or 42. A second indirect approach to the determination of +A, based on the absorption of the p-carotene triplet generated by excitation transfer from 02('Ag) (52), has already been mentioned. Transient decay of the p-carotene mplet absorption is monitored, and the long series of excitation-transfer steps which precede its formation lead to rather complex kinetic expressions (52). Two direct methods for the determination of
+
EXCITED-STATE INTERACTIONS WITH
29
3 4
+A
have been employed. The first is based on monitoring the sensitized 02('Ag) infrared-luminescence (IR-L) intensity, (55,102-104,107),and the second is based on time-resolved thermal-lensing (TL) calorimetric measurements (10 1). Listed in Table 6 are +A values obtained with air- andor oxygen-saturated solutions. Minimum values for aT + as and maximum values for aT have been calculated for the limiting cases aT = 1 and as = 0, respectively. The quantity aT as is obtained by rearrangement of Eq. 42:
+
and the aT is obtained from Eqs. 40 and 41: aT =
+A
- 4: <-4A +is
+is
(48)
+A (+is
- l)(Z110)
+
1
The equality in J2q. 49 applies when as # 0, provided that the singlet states involved are too short-lived to be quenched at the oxygen concentrationsnormally employed, :T s 1 ns. Several of the carbonyl compounds in Table 6 fall in this category. Agreement between measurements of +A by different groups is satisfactory provided that the same type of probe was utilized. This can be seen by examining the results obtained for rubrene, aT as >, 1.4, with several chemical traps for 02('Ag). However, +A and aT values obtained by direct methods (IR-L or TL) are usually smaller than those based on indirect methods. For example, in the case of anthracene, chemical-trapping data have given variously aT as 3 1.46 with as = 0.46for aT = 1.00 (95) and aT = 1.00, as = 0 (106),whereas direct measurements based on 02( 'Ag) luminescence (107)and thermal-lensing calorimetry (105) indicate that orT = 0.8 2 0.1 and as = 0. The general picture which emerges for aromatic hydrocarbons is that aT must be close to, if not exactly, unity in several instances, whereas as appears to be much smaller than unity and may be close to zero even in cases where > 22.6 kcalhol, e.g., naphthalene, pyrene, 9,10-dimethyl-l,2-benzanthracene, and perhaps anthracene. For molecules in which T2 lies below S , a small as value can be rationalized (93)in terms of
+
+
Since this process is nearly energy-neutral, multiplicity-allowed spin-exchange should be favored by relatively large Franck-Condon overlap factors. Some evidence that this pathway contributes in the case of anthracenehas been presented (23).This explanation cannot be applied to molecules for which T2 lies well
TABLE 6. Efficiencies of 02(1$) Formation" Compound
Naphthalene
Fluorene Biphenyl Anthracene
9-Methylanthracene 9-Phenylanthracene 9,lO-Dimethylanthracene
9,lO-Diphenylanthracene Rubrene
+*
aT'
Aromatic Hydrocarbons 0.14 20.02' 1.05 0.97 0.53 0.0920.02' 0.57 0.88 50.07 1.12 1.51 (1.12 2 0.09) 1.28 1.46 0.73' 1.o 1.o 0.72 0.8' 0.61 20.06 0.79 k O . l
Probe
Ref.
TME,DMF P-CIAPf p-CM DPBFIPR~ TME,DMF DPBFIPR~ DMA DMA
96 52 52 85
96 85
DPBFIPR~ IR-L TL
95 95 106 85 107 105
DTBP
(0.97 20.03)';
1.1520.2
1.1820.2
DMF
97
(1.09 2 0.05)k
1.35 k0.2
1.41k0.2
DMF
97
0.52 20.03 (1.0220.06) (1.14 20.05)k
1.29 2 0.1 1.34 20.1 1.41 20.2
2.050.4 Self(DMA) 1.30 k 0.1 Self 1.3520.1 Self 1.4220.2 DMF
(1.20 2 0.06)'; (0.82 2 0.05)
1.4620.2
(0.91 20.05) (1.20 2 0.02)'
1.47 2 0.2
0.3020.06 (0.88 20.07) (0.89)
1.21 e0.2 1.4920.2
1.920.4 1.235 0.2 1.50 2 0.2
0.6820.04
0.9820.2 1.0420.2
1.220.2 0.9220.2 1.07e0.2
(0.85 20.05)
9,10-Dimethyl-l,2benzanthracene Pyrene 0.61 50.04' (0.7920.04)k Perylene (1.27 k 0.06)k Terphenyl
1.47 20.2 1.32 20.2 1.2 5 0.2' 1.47 50.2 1.54zt0.2
Naphthacene
30
aT+asd
1.050.2
0.8020.2 1.6420.2 0.94
DMF DPBF DPBF DPBF DPBF Self Self Self TME Self DPBF DPBF
Self TME,DMF 0.8020.2 DMF 1.6420.2 DMF DPBFPR~
101 95 95 97 97 94,97 93 94 97 101
95 95 112 101 93 93 101 96 97 97 85
TABLE 6. (Continued) Compound
2-Pentanonem 3-Pentanone"' Xanthone Acetophenone
4a
(0.03) (0.04) 0.58?0.02' 0.17 & 0.02'
m-Methoxyacetophenone Benzophenone
0.50 20.04' 0.24 2 0.0 le 0.17'." 0.54" (0.39k0.08)
Benzaldehyde P-Acetonaphthone
0.60 & 0.04e
p-Ionone Fluorenone
0.25 0.06 &0.01' 0.03 k0.01'
Pyrene- 1aldehyde All-transretinal trans-Stilbene 1, I-Diphenyl-
ethylene 1-Phenylcyclohexene 1-Methyl-2-phenylcyclohexene
aT
Carbonyls 0.03 0.04 0.53 0.65 0.58 0.17 0.29'
aT+asd
Probe
Ref.
DPBF DPBF
108 108 52 52 96 96 113
P-c P-c
DMF TME IR-L
0.27' 0 S O 2 0.04 0.2420.01 0.17 0.54 0.56 0.29' 0.39+0.08 0.43 0.60-CO.04 0.70' 0.53 0.50 0.07 0.03 0.8'
IR-L DMF TME DTBF DPBF,DMA
LF
113 96 96 106 95 P-c 52 IR-L 102,107 DPBF 109 DPBFPR~ 85 TME,DMF 96 IR-L 102,107 85 DPBFPR~ 110 DPBF 96 DMF 96 TME 170 IR-L
(0.87)p (0.68)
1.2
DPBF DPBF
109 109
(0.66)p
1 k0.3
DPBF
109
Olefins 0.13 k0.08 0.18 k 0.05 0.1620.03'
p-CIPRh IR-Lq IR-L
52 53 104
0.16t 0.04'
IR-L
104
0.41 20.03'(67)
IR-L
104
0.2720.03'(91)
IR-L
104
31
TABLE 6. (Continued) Compound
4%
aTc
aT+asd
Probe
Ref.
IR-L
104
IR-L
104
IR-L
104
DMF DPBFIT"
97 111
IR-L IR-L
103 103
IR-L
103
1,ZDiphenylcyclohexene 0.06 -C 0. O r (168) 1-Phenyl-&methylcyclohexene 0.45 +0.03'(93) 1,&Diphenyl0.46 ~0.02'(111) cyclohexene 1,6-Diphenyl-1,3,5hexatriene (1 -0220.05)' 1.162 0.02 1.1820.2 0.25 20.05' All-trans-retinol Psoralen Pseudopsoralen 5-Methoxypsoralen 8-Methoxy psoralen 5,8-Dimethoxypsoralen 4,5',8-Trimethoxypsoralen 3-carbethoxypsoralen 3-carbethoxypseudopsoralen
(0.o 12) (0.026)
FurocowMtins'*' 0.34 0.57
(0.021)
0.32
(O.O@w
0.40
IR-L
103
(O.OO40)
0.10
IR-L
103
(0.084)
0.41
IR-L
103
IR-L
103 103
(0.30)
1.o
(0.49)
0.96
IR-L
Other 0.75
DPBFPR~
85
P-CIAPf
52
P-CW
52
Self Self
95 95
Acndine
N-Methylindole 3,5-DiphenylisobenZ0furan Tetraphenylporphine Zinc tetraphenylporphine Hematoporphyrine Tris-(bipyridene) mthenium(I1) Methylene blue Rose bengd
32
0.32
1.o
0.56
0.40 0.28 +0.02 (0.78k0.05)
1.29 1.51
(0.89) 0.58 & 0.06
1.o 0.71 20.1
TME
0.73 20.07
0.8320.1
TL
105
0.65
0.78"
DPBF
114
(0.83) 0.50" 0.7Y
0.9 1.o 1.o
DPBF TME
109 112 112
1.39 1.54
TL
TME
112 105
EXCITED-STATE INTERACTIONS WITH
TABLE 6. (Continued)
+*
Compound Emin
Chlorophyll a
0.42x 0.60
aTc
aT+asd
1.o >1.0
33
3 4
Probe
TME TME
Ref. 112 112
?n benzene, unless otherwise stated. *Air-saturated solution, oxygen-saturated solution in parentheses. 'Upper limit from Q. 48. dLower limit from 4 . 4 7 . I n methanol.
fAcetophenone-sensitized.
gXanthone-sensitized. *Pulse radiolysis. 'Assuming aT = 1.00for acridine. '2,s-di-t-Butylfuran. 'In n-hexane. 'From data for three [O,] values. "Neat ketone solvent; acetone, 2-butanone, 2-hexanone, 3-heptanone, and 4-heptanone all gave similar +A's (within a factor of 3) in methanol using DMF as probe (108). "Neglecting OZ(lAg)quenching by benzophenone (97). in oxygen-saturated solution is not included because it predicts too low T', "A higher value for for benzophenone (104,109). PCyclohexane. Qenzophenone-sensitized. 'n-Heptane, assuming aT = 1.00 for naphthalene; T; in parentheses in ns. Triphenylene-sensitized, assuming aT = 1.OO for anthracene. '+A and aT estimated correct to ?S% and t 1096, respectively. "In methanoVD,O, 9 1. Xelative to methylene blue standard in Ref. 112; methanol, see Ref. 115.
above S , . For such molecules high fluorescence quantum yields are not uncommon, and 0, quenching must proceed directly via T,. Small as values could then be due to the following spin-allowed exothermic sequence (93):
The new step in the sequence represents internal conversion within the triplet
34
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTR0LLF.DREACTIONS
encounter-pair manifold and could be faster than the rate constant for diffusion apart of the M(T,), 02('Ag) pair. A more elaborate mechanism involving reencounter quenching of solvent-separated M(Tl), O2(*Ag)has been proposed for the case of anthracene (95,115). This mechanism distinguishesbetween 'A; and 'Ag components of the lowest singlet state of oxygen (116) and is based on state-symmetry considerations(116,118). It is kinetically indistinguishable from q.50. Singlet quenching, Q. 38, is negligible for most ketones and aldehydes due to subnanosecond singlet lifetimes. Accordingly, Q. 42 reduces to +A = aT+)s, from which aT values are readily calculated. Generally, rather small aT values are obtained for carbonyl compounds with n,n* lowest triplet states (Table 6) consistent with the large k;f; values associated with the quenching process. Since aT > 0.25 appears to apply for several of the aromatic carbonyl compounds (e.g., benzophenone and benzaldehyde) despite the large triplet excitation energies involved, some interconversion of triplet and singlet encounter complexes, as shown in Eq. 37, is implied. The large fractions of quenching events which do not give OZ('Ag) (see especially the aliphatic ketones) have been attributed to charge-transfer quenching via the triplet encounter pair (52). Recently, the notion that the small efficienciesof O,( 'Ag) formation are caused by competing photophysical events has been challenged (1 13). The proposal that a chemical entity, X,forms from the interaction of some ketone triplets, 3K*, with O2('Z,) is based on the observation that, for relatively high excitation pulse energies, the decay of the emission of Oz('Ag) deviates from strictly first-orderkinetics (113). Formation of 02(lAg) sensitized by acetophenone (AP), rn-methoxyacetophenone (MAP), benzophenone (BP), and P-acetonaphthone (AN) was examined in aerated benzene and acetonitrile solutions. Cleanly firstorder decay of OZ('Ag)luminescence was observed for AN, though the highest 02('Ag) concentrations were achieved with this sensitizer (aTlargest, Table 6). The importance of this finding is that it shows that self-annihilation of 02('Ag) (10) does not provide a second-order decay contribution (1 13). Similar results were obtained for BP in benzene. In contrast, the decay of the IR luminescence generated with AP, MAP, or BP as sensitizers in acetonimle and with AP or MAP in benzene showed a faster initial decay and could be analyzed as a combination of first- and second-order components. Since the second-order portion can be observed to contribute over tens of ps, well after the decay of the ketone triplets (7 = (k;f,[O,])-' 6 0.3 ps), reencounter quenching of 3K* and 02('Ag) (95,115) must also be ruled out as a potential explanation. In addition, experiments with benzoquinone, an OZt trap, eliminated electron transfer as a competing 3K*quenching process and 0 , ' as a viable O,('A,) quencher (1 13). It was therefore concluded that reaction of 3K*with 02(3X,) gives singlet and triplet bnadicals in competition with the physical quenching interactions considered thus far, and that these biradicals-or, more likely, the trioxetane which may form from them-deactivate 02('Ag) and are responsible
35
EXCITEDSTATE INTERA~~~ONS WITH 30,
for the apparent second-order decay component, Eqs. 51, 52 (113). Since no permanent photoreaction was observed, all transients must eventually regenerate 'K and 02(3Z;) (1 13):
3K*
f
+ 02(32,)
-
'602)*
xFoT 1K
R
+ 02(3z;) (51)
1
'K
02('Ag)
R
3(~~2)*-+
+ 02('Ag)
+ XRx:;o R
?
-
O~(~Z;)+
?
In this scheme, the apparent second-order component arises only because of the transient nature of X and not because the initial concentrations of 02(lAg) and X are similar, as has been proposed (1 13). Therefore, the lifetime of X under the conditions of these experiments must be in the 10-30-ps range. Sensitizer-O;?biradical intermediates were proposed long ago by Schenck as key intermediates in sensitized photooxidations (1 19-121). Elucidation of the role of 02('A,) in such photooxidations (122,123) and its wide acceptance as the active agent (1 15,124,125) had rendered biradical species superfluous, except as intermediates in the photoxidations of menthone (126), benzil(127,128), and other diketones (128). It is important, therefore, that kinetic evidence for their formation with specific ketone sensitizers appears to have been found (1 13). As pointed out earlier, k:x values for several of the ketones exceed I/gkdif (Table 5 ) , implicating the triplet encounter pair in the deactivation. However, the possible involvement of the biradical quenching route and the likely interconversion of singlet and triplet biradicals prevents a straightforwardinterpretationof aTvalues. AN, for which k;fxis very similar to that of naphthalene and for which no kinetic evidence for biradical formation could be found (103), probably utilizes mainly the singlet encounter pair route as indicated by its relatively high aTvalue. Pyrene-1-aldehyde with its low T,T* triplet state probably behaves similarly. On the other hand, dialkyl ketones with high kzx values (see acetone, Table 5 ) and very low aT's are probably quenched via the triplet biradical route shown in Eq.5 1. The enormous 02('Ag) lifetime increase on changing the solvent from acetone (65.3 2 5.3 ps) to perdeuterioacetone (838 f 119 ps) (80) suggests strongly that addition of 02('Ag) to the carbonyl group of ground-state ketone is not a significant reaction.
36
SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLEDREACTIONS
Values of aT well below unity for the olefins in Table 6, 1,6-diphenyl-l,3,5hexatriene excepted, are consistent with variable contributions of the spinexchange mechanism described above for the stilbenes. The relatively large kzx values and the short triplet lifetimes,=40-180 ns, observed for the diphenylethylenes and the cyclohexenes clearly reflect the involvement of 3p* conformations in both 02-assisted and -unassisted triplet decay. Since the excitation-transfer pathway also contributes, nearly planar conformations must play a significant role in the quenching process. These conclusions point to rather shallow triplet potential-energy curves along the double-bond torsional coordinate, twisted to cisoid and/or transoid, for most of the olefins in Table 6. A complex spectrum of olefin mplet-0, interactions can thus be imagined, variations of which are described in Schemes 1 and 2 and Eqs. 28 and 31, which include equilibration among geometriesof the olefin in the encounter pairs, e .g .,Eq . 3 1. If, in addition, singlet and triplet encounter pairs interconvert,as shown in Eq. 36, the description of 0,quenching will be complicated further. Selection of a likely mechanism for a specific olefin is greatly facilitated when the fate of the olefin triplets involved in the quenching process is known. We showed earlier how the effects of O2in photostationary states and isomerizationquantum yields could be utilized in proposing mechanismsfor stilbenesand for indigoid dyes. As a further example we consider the case of all-trans-retinol, for which the effect of [O,] on +t -,c has been measured (1 11). Though its large triplet lifetime, 100 ps (Table 5), suggests that transoid triplets predominate in solution, the large k;f; and low aT values implicate 3p* in quenching and indicate a shallow triplet potential-energy curve in this case also. Since no special spin-orbit coupling mechanisms for the equilibration of encounter-pair spin states are expected for retinol, we assume that they maintain their integrity. With this condition, quenching via singlet and triplet encounter pairs is shown for the general case in Scheme 3 (for the cyclohexenes,substitute c for t) which represents an expanded version of Eq. 28. ‘t
+ OZ(lAg)
K,
‘(to2)*
‘(p02)*
Thus, a complete description requires knowledge of the rate constants for formation and dissociation of four exciplexes, three equilibrium constants for conformational equilibration, and the rate constants ket and k,. We can avoid
EXCKEBSTATE INTERACITONS m30,
37
this kinetic nightmare by not specifying the geometry of the triplet state in the scheme. The simplest mechanism which will account for the observations for retinol (1 11) is
'Tr ?r*
-b
+
3R*2
'Tr*-% ?r* 't 'Tr + %* 6 't
-+ (1 - 8) 'c
+ 02(32;) 5I t + O ~ ( ~ A J 3R* + 02(32;) -%6' 't + (1 - 6') 'c + 02(3Z,) 3 ~ *
(56)
(57)
where Tr and R represent the sensitizer triphenylene and retinol, respectively. Quenching of ?r* by oxygen can be neglected at the oxygen concentrations employed, s 1.4 x M, and neglecting quenching of 'Tr* (Table 1) introduces less than a 10%error in the analysis. Application of the steady-state approximation in excited species gives
where r = &'-,&is the ratio of initial isomerization rates in the absence and in the presence of 02.8 = (1 - 6')/(1 - a), and 7 = 1kd. Figure 6 , a
[ O ~ I - ~1, 0 4 ~ - 4 '
F
w 6. The effect of 0,on the rate of triphenylene-sensitized t +c photoisomerization of all-trans-retinol, Eq.58. From Ref. 111 with permissionof Royal Society of Chemistry.
38
SPIN-STATISTICALFACTORS D l DIFFUSIONCONTROUED REACTIONS
reproduction of Fig. 1 in Ref. 111, shows that the data adhere nicely to Eq.58, intercept 20.08, slope = 1.56 X K'. Using kzx = k& + =5 X lo9 M-' s-l (Table 5 ) and aT = = 0.25 (Table 6)gives 1.25 X lo9 M-' s-' and 3.75 x lo9 M-' s-l for and respectively. These rate constants and the intercept from Figure 6 give 8 = 0.10 and together with the slope give kd = 7.2 X lo4 s-', in excellent agreement with the observed value of 7.9 x lo4 s-' (Ref. 103 and Table 5). In contrast to the results for stilbene, which indicate that spin-exchange quenching of 3p* by O2 favors the cis side more than does natural decay, i.e., 8 > 1.0, the results for retinol require that quenching of 3p*favor the trans ground state substantially more than does natural decay. Since k;f, is smaller than 4hkc, by more than a factor of 2, an ctT value consistent with = 3 is no more than a coincidence. However, if the equilibrations shown in Scheme 3 are fast relative to "exciplex" dissociation or decay, the coincidence could be that k&, kdis) = ke& k&) 1 0.4. The above interpretation of the retinol data differs from that in Ref. 111 (129). The kinetic analysis in Ref. 111, based on Scheme 2, can be readily shown to be flawed. Though an equation of the same form as Eq. 58 was derived, it was assumed that the quenching efficiencies are governed by the equilibrium populations of 3t* and 3p* rather than by the spin states of the encounter pairs. Also, 8 = 1 was assumed, and the observed decay rate constant of 3R* was incorrectly set equal to kd in Scheme 2 instead of to kd&,/(l Ktp) (38,57,58). The behavior of all-rrarzs-retinol is very different from that of all-trans-retinal. In the latter case an aT value close to unity (Table 6) and a small k;f, value (Table 4) suggest that only the singlet encounter pair leads to quenching by 02. 1,6-Diphenyl-1,3,5-hexatriene with aT5 1 and k:x = 5.5 X lo9M-' s-l does not appear to fulfill expectations based on Scheme 3. Unless triplet and singlet encounter pairs interconvert in this case, either aTor k;f, is too large. For several of the other compounds listed in Table 6charge-transfer quenching via the triplet encounter pair may contribute. Most of the aTvalues, though smaller than unity, are larger than 0.25, indicating either that the energy-transfer pathway is more efficient, or that there is interconversion between encounter pairs of different multiplicity. N-Methylindole, for which aT > 0.25 but k:x 2 4/kdiif(Tables 5 and 6), appears to fall in the latter category.
ex
+ ex)
ex ex,
+
+
+
V. RADICAL SELF-TERMINATION Conclusions concerningthe role of spin-statistical factors in the preceding section are based on the well-founded assumption that singlet-excited-statequenching by 02(3Z;) provides an empirical measure of the magnitude of fully diffusioncontrolled rate constants. Singlet quenching provides a nearly perfect dynamic model for kdif in triplet quenching. Differences in D (Eqs. 5 and 6)should be negligible, since in both interactions D is dominated by the large diffusion
RADICAL SELF-TERMINATION
39
coefficients of 02,and differences in p should also be negligible, especially for excited singlet and triplet states of the same molecule. Thus, as we have seen, cancellation of kdif allows calculation of u from k;f,/kzxin limiting cases. This approach can be extended to reactions between organic molecules of similar size only if appropriate empirically based diffusion-controlled rate constants can be found. In this section we consider recent results on radical-termination rate constants which show that termination is a suitable reference reaction. Radical self-termination is the reaction of two identical free radicals, R*, with each other. For simple alkyl radicals with @-hydrogenstwo highly exothermic reaction channels are available: disproportionation to alkane R(+H) and alkene R(-H) by transfer of the @-hydrogenatom and combination to dimer alkane R-R:
We start with the extensive and rigorous study of Schuh and Fischer on r-butyl radical self-termination (6). Earlier work on this reaction, reviewed in Ref. 6, had yielded 4 values in the 109-10'0 M-' s-l range with poor agreement among different research groups even in cases for which identical radical sources and reaction conditions were employed. Schuh and Fischer used the photolysis of di-r-butyl ketone in solution as the source of r-butyl radicals. Consideration of some of the details of this reaction is instructive, especially since it was the inefficiency of radical formation from the photolysis of acetone in solution which first led to the postulation of solvent cage effects in radical reactions, i.e., the competition of reactions of geminate radical pairs with their diffusion apart (129). Excitation in the n,m* region of di-f-butyl ketone gives a relatively long-lived excited singlet state, T = 5 ns (130), which intersystem-crosses and undergoes cleavage to pivaloyl and t-butyl radicals, & = 0.71 (130), predominantly from its triplet state (131; cf. however 130). Chemically induced dynamic nuclear polarization of the starting ketone measured relative to that of pivaloyl aldehyde, which is formed in low yield by disproportionation of the geminate radical pair, shows that 3~ 96% of the radicals escape the cage (13 1). The virtual absence of a cage effect is readily explained by postulating that multiplicity-allowed triplet ketone cleavage gives triplet radical pairs whose relatively slow T +S intersystem crossing prevents the formation of singlet cage products. Since decarbonylation of pivaloyl radicals is fast, k = 2.5 x lo5 s-l at 40°C (132,133), the overall quantum yield of t-butyl radical formation is 1.4. The inferred slow intersystem crossing of triplet radical pairs is consistent with slow radical spin-relaxation rate constants obtained using dynamic-polarization recovery rates; see Table 7
292
0.2
290
0.6
CH3CHOH
29 1
1.3
(Ch&;OH
290
2.7
CHZOH 0
r;'
"Spin-lattice relaxation time,R( 1 )-E( *Selected values from Ref. 134.
).
TABLE 8. Triplet Biradical L&ifhnes" Solvent
Biradical
T (K)
k
Ref.
(s-')
Ph 295
1.07 X lo7
136
215.9 293.2 357.5
0.98 X lo7 1.06 X lo7 1.09 x 10'
137
295 295
4.13 X lo6 1.45 X lo7
138
!Benzene
293
3.3
X
lo6
139
CH3CN
295
4.5
X
lo6
140
Ph CH30H
$0.
Ph
Ph
40
TABLE 8. (Continued) Biradical
Solvent
k
T (K)
Ref.
(s-l)
n-C7H 16
295
2.04 X lo7
141
n-C7H16
295
1.78 X lo7
141
(CD3)zSO/DzO(4:lw/w)
303
5.3
lo6
142
n-C7H,6
295
5.9 X 108
136
n-C7H16
295
1.6 X 10’
136
CH3CN
295
6.3 X lo8
143
CH,CN/HzO
295
8.3 X
lo5
144
CH,CN/H,O
295
1.67
lo5
144
0
X
Ph &OH
OPh YH
J O H
o Ph fph
P
0
X
“Selected values from Ref. 135. 41
SPIN-STATISTICAL FAcIylRs IN DIFFUSION-CONTROLLEDREAcIloNS
42
(134). Recent measurements of relatively long triplet biradical lifetimes, T = lo-’ s (Table 8) also show that only singlet encounter pairs will contribute to the reactivity of freeradicals in solution. Accordingly, Eq.(59) can be rewritten as
(60) 2R*
-k 2 R * 1 5 , 1 ( 2 R * ) +R-R
+ R(+H) + R(-H)
which requires that the rate constants of diffusion-controlledradical self-reactions be attenuated by a spin-statistical factor of cr = %. =
=$kg
The disappearanceof t-butyl radicals, followed by ESR spectroscopyin twelve solvents over a wide range of temperatures, obeyed second-order kinetics and gave experimental rate constants 2k, in very good agreement with rate constants obtained independently from product yields (6). Linear Arrhenius plots are obtained for n-alkane solvents (n-heptane through n-hexadecane), benzene, acetonitrile (T < 325 K),and octamethylcyclotetrasiloxane,but not for the protic solvents t-butyl alcohol, 3-methyl-3-pentano1, and a 1:2 mixture of t-butyl alcohol:pinacol. Arrhenius parameters for nonhydroxylic solvents, In 2 4 = In 2At - E,/RT, are shown in Table 9 together with corresponding parameters for the Andrade equation, In q = In tly) + E?/RT (6). The agreement between activation energies for self-reaction and activation energies for viscous flow is generally very good, E, - E,, S 0.5 kcdmol. Especially revealing are plots of 24 vs. T/q (Fig. 7,8), which generate a family of at least seven lines with slopes increasing with solvent molecular weight (alkanes) and solvent association (alcohols). Moreover, linearity is not observed in hydroxylic solvents. The slopes are larger than predicted by the stick and slip limits of the Stokes equation (Eqs. 9 and 61), showing that neither can be applied generally for calculation of diffusion coefficients (the dashed lines in Figs. 7 and 8 are based on Eqs. 9 and 61 with OL = 3,000). At the very least diffusion coefficients must be corrected in a solvent-specific way. A direct test of the Smoluchowski equation for kdif (J3q. 6) in predicting 2k, was hampered by the lack of empirical DA’s for t-butyl radicals. Using isobutane as the model for the radical, Schuh and Fischer initially evaluated nine empirical or semiempirical methods for the calculation of D, (6). Calculated D,’s were checked for internal consistency by using them together with the experimental 2kt’s to calculate reaction distances p from Eq. 61 and 6 with D = 20,:
TABLE 9. Arrhenius and Andrade Parametersfor the Self-termination of t-Butyl Radicals Termination Rate Constants 2k, Solvent n-C7H,, n-CsH1, n-C1oH*2 n-C 1 2H26 n-C14H30
Gdi,
CH&N Benzene
( 1 0 " 2 ' ~ - ~ ) (kcaVmo1) Ezk,
Dynamic Viscosities q
2.44 2.45 2.70 2.80 3.31 3.71 2.01 2.46
4.9 3.9 5.0 4.3 8.2 13.9
2.0 3.1
-5@as)
(10
1.51 1.41 1.62 1.29 0.81 0.93' 2.42 1.63
Ell (kcaVm01)
- Ell
&I"
(kcaYmo1)
1.94 2.15 2.35 2.74 3.28 3.39" 1.60 2.12 ~~~~
0.50 0.30 0.35 0.06 0.03 0.32 0.41 0.34 ~~~
Source: Ref. 6 . "Strictly valid for temperature >35OC.
r/qx
10-4, KP-I-
Figure 7. 2k, vs. T/qfor 1-butyl radical self-termination in (0)n-heptane, (0) n-octane, (m) n-decane, and (A)n-hexadecane. The dashed line is based on Eqs. 9 and 61. From Ref. 6 with permission of Helvetica Chimica Acta.
43
44
SPIN-STATISTICALFACTORS IN DIFRISION-CONTROLLEDREACTIONS
Figure 8. 2k, vs. T/qfor r-butyl radical self-termination in (0)acetonitrile, (0) benzene, (m) t-butanol, (0) 3-methyl-3-pentanol. The dashed line is based on Eqs. 9 and 61. From Ref. 6 with permission of Helvetica Chimica Acta.
Resulting p’s are strikingly independent of solvent and temperature when DA’s are obtained by interpolation from closely related experimental diffusion coefficients (alkanes). They also agree very well with the theoretical value of p based on calculated radii of t-butyl radicals, pth = 2rA = 5.6 -+ 0.8 8, (6). The successful prediction of p by the Smoluchowski equation in the less viscous media lends credence to the assumption that, subject to (T = ‘A, t-butyl radical self-reaction is diffusion-controlled. It was concluded that among the semiempirical methods, the formula of Spemol and Wirtz (7)gives reliable DAIS for low-viscosity nonassaciating solvents, whereas for alcohols the formula of Gainer and Metzner (145) is best (6). These two methods modify the Stokes-Einstein relationship for DA (see Eqs. 10-14) by accounting for (1) the molecular sizes of solute and solvent and (2) the effects of different solute-solvent and solventsolvent interactions (6). A comparison of the experimental 2kt’s with theoretical 2kp’s based on Eqs. 6 and 61 with p = 5.6 A and the “best” calculated D ( = 2DA) is given in Fig. 9 (6). The points cluster about a line with slope one, as expected for the mechanism shown in Eq. 60. The same conclusion can be reached by plotting the experimental termination rate constants, 2kt, against the calculated diffusion coefficientsD,. This is done in Fig. 10, for two representative solvents. Taking p = 5.6 A, the slopes for the lines, 8 ~ p N l O - ~ ugive , u =
Figure 9. Experimental vs. calculated termination rate constants for t-butyl radicals in (0)n-heptane, (0) n-octane, (m) n-decane, (0) n-dodecane, (A) n-tetradecane,
n-hexadecane, Ref. 6.
(v)acetonitrile, and
benzene; see text. The line has unit slope. From
Figure 10. 2k, vs. D, for t-butyl radical self-teenation in (0)n-heptane and acetonitde (6);see text. The line is based on Eqs. 6 and 61 with p = 5.6 A and u = !A.
(0)
45
46
SPIN-STATISTICALF A m R S IN DIFRISION-CONTROLLEDREACTIONS
0.24 and 0.22 for n-heptane and acetonitrile, respectively, in excellent agreement with the expected spin-statistical factor of %. Reasonable agreement between results of several independent measurements of the rate constant for benzyl radical self-reaction (146-148) have led Fischer and coworkers (148) to recommend that this reaction be used for calibration purposes. In a study which parallels closely that described for the r-butyl radicals, Lehni, Schuh, and Fischer used the photolysis of dibenzyl ketone as the source of benzyl radicals and monitored their decay by kinetic ESR (148). Dibenzyl ketone undergoes very efficient a-cleavage from its triplet state (149, 150) to yield a triplet pair of phenylacetyl and benzyl radicals. Reformation of ketone from this pair in various media, though inefficient, has been the subject of elegant recent studies (151-154). In ordinary solvents T --f S intersystem crossing is too slow to compete with radical separation, most geminate pairs [<95% (149)] escape the cage, and phenylacetyl radicals decarbonylate (155, 156). A quantitative yield of CO, &, 3:0.7, is obtained (149,157), and benzyl radicals, the only radicals observed by ESR at T > -50°C (158), give bibenzyl either directly by a,acoupling (155,157,159) or by rearrangement from initially formed semibenzenes (12-25% a,o and a,p coupling for -18°C =sT S 62°C) ( 1 0 ) . Self-reaction rate constants were determined as a function of T in toluene, in cyclohexane, and at 298 K in mixtures of the two, because experimental diffusion coefficients for toluene are available in these solvents; see Table 10 (148). Since it is reasonable to expect identical DA values for benzyl radicals and toluene molecules, the data in Table 10 afford an excellent test of the Smoluchowski
Figure 11. 24 vs. DA for benzyl radical self-termination in (0)toluene and (0) cyclohexane; see text. The line is based on Eqs. 6 and 61 with p = 5.8 8, and u = %.
From Ref. 148.
TABLE 10. Empirical and Semiemperical Dtrusion Coef€icients ~~
Solvent Solure: i-C,H,," n-C7H16
n-C8H18
n-C12H26
294 307 325 342 349 365
7.9 9.0 11.8 13.9 15.5 17.0
4.2 4.9 5.9 6.8 7.3 8.3
4.0 4.7 5.8 7.0 7.4 8.6
0.95 0.96 0.98 1.03 1.01 1.04
297 308 325 34 1 345 368
6.8 7.9 8.8 11.6 11.4 14.4
3.6 4.2 5.1 6.1 6.3 7.8
3.5 4.1 5 .O 6.0 6.2 7.8
0.97 0.98 0.98 0.98 0.98 1.oo
295 312 328 343 354
5.6 6.8 8.7 10.2 11.8
2.5 3.2 3.9 4.7 5.3
2.4 3.1 3.8 4.6 5.2
0.96 0.97 0.97 0.98 0.98
297 308 327 346 369
4.2 4.6 6.1 7.4 10.5
1.8 2.2 2.9 3.7 4.9
1.8 2.2 2.9 3.8 5 .O
1.oo 1.oo 1.oo 1.03 1.02
297 308 326 343 369
3.4 3.9 6.6 9.8
1.5 1.7 2.3 3.0 4.1
1.2 I .5 2.2 2.9 4.3
0.80 0.88 0.96 0.97 1.05
299 305 308 31 1 318 323 330 343 356 366
2.9 3.2 3.8 3.4 4.4 4.6 5.2 6.3 7.8 9.1
1.2 1.3 1.4 1.5 1.7 1.7 2.0 2.5 3.O 3.4
0.94 1.1 1.2 1.3 1.5 I .6 1.8 2.4 2.9 3.4
0.78 0.85 0.86 0.87 0.88 0.94 0.90 0.96 0.97 1.oo
5.5
47
TABLE 10. (Continued) T
2k,
CH&N
266 280 290 293 306 320 337 349
4.7 5.4 6.4 6.7 7.7 8.8 11.4 13.6
2.6 3.1 3.4 3.5 4.0 4.5 5.2 5.7
Benzene
28 1 293 295 302 305 314 325 336 345 35 1
4.6 5.8 6.1 6.6 6.9 7.3 8.7 9.5 11.0 11.2
2.6 2.9 3.0 3.2 3.3 3.6 3.9 4.2 4.5 4.7
Toluene
222 229 235 240 248 256 262 269 277 283 293 298 304 314 326 331
Solvent
c-C6H 12
48
(K) (109M-' s-')
283 29 1 298 305 312
Dexp (lo+ cm2s-')
Solute: Tolueneb 0.98 0.449 0.544 1.1 1.2 0.635 0.72 1.5 0.87 1.9 1.04 2.4 1.18 2.7 1.35 3.0 1.57 3.4 1.76 4.4 2.08 5.1 2.26 5.2 2.48 5.4 2.87 6.4 7.6 3.40 3.63 9.0
3.5 4.1 4.1 4.3 5.0
1.29 1.45 1.58 1.75 1.95
(
Dsw
cm2s-') DsJDcxp
1.01 1.18 1.33 1.53 1.78 1.94 2.29 2.47 2.64 3.17 3.58 3.66 1.34 1.52 1.73 1.90 2.08
1.16 1.14 1.13 1.13 1.13 1.10 1.10 1.09 1.06 1.11 1.05
1.01 1 .# 1.05
1.09 1.08 1.07
~
TABLE 10. (Continued) Solvent
T
(K)
322 332
2k Dexp Dsw ( I O ~ M - ’s - ~ ) (10-’crn~s-’) (10-’crn2s-’) 5.3 5.9
2.19 2.47
Solute: n-C3HsC 8.7 5.4 9.9 6.0 9.9 6.6 10.8 7.2 11.1 7.8
D,J
D
2.45 2.73
1.12 1.11
6.0 6.8 7.5 8.3 9.2
1.11 1.13 1.14 1.15 1.18
n-C7H16
313 323 333 343 353
n-C16H34
313 323 333 343 353
3.1 3.7 4.0 4.6 5.2
1.5 1.8 2.1 2.4 2.7
1.5 1.8 2.2 2.6 3.1
1.oo 1.oo 1.05 1.08 1.15
(Et0)4Si
313 323 333 343 353
6.2 7.1 8.0 8.2 8.0
3.5 3.9 4.3 4.8 5.2
4.5 5.1 5.7 6.4 7.1
1.29 1.30 1.33 1.33 1.37
(Et),CHOH
313 323 333 343 353
3.3 4.5 5.2
I .5 1.9 2.3 2.8 3.3
1.O 1.5 2.2 3.2 4.6
0.67 0.79 0.96 1.14 1.39
CH,COCH, in (EtO),Si
5.4
5.9
143 158 180 208 232
Solute: n-C3H/ 1.5 2.3 4.3 4.8 7.6
2.4 4.4 6.3
255 292 30 1 303 307 311 313 32 1
Solute: CH3COCH,e 1.7 3.8 4.4 4.6 4.8 5.2 5.2 6.1
0.84 1.76 2.06 2.13 2.27 2.43 2.50 2.94
0.97 1.2
49
~
~
~
50
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEJ3REACTIONS
TABLE 10. (Continued) T 2k, (K) (109M-' s-I)
Solvent
(
Dexp
cm2s-I) (
CH,COCH3 in (EtO),Si
255 292 301 303 307 311 313 321
Solute: (EtO),Sic 1.3 2.5 3.0 3.0 3.1 3.4 3.4 3.8
CH,OH
208 216 226 248 265 288
Solute: C H 3 0 H 1.85 0.36 1.1 0.48 1.4 0.66 2.5 1.22 3.6 1.83 4.9 2.93
"From Ref. 6. Trom Ref. 168.
%om Ref. 148. %om fFrom Ref. 169.
Ref. 166.
Dsw cm2s-') D,JDexp
0.46 0.96 1.12 1.16 1.24 1.32 1.37 1.61 0.33 0.44 0.60 1.10 1.65 2.66
0.92 0.92 0.91 0.90 0.90 0.91
dFrom Ref. 167.
equation: see Fig. 11. Estimates of p ranged from 6.30 A based on Eq. 12 to 5.64 A based on the volume-increment method (165). Employing p = 5.8 A (148), which is close to the average of values calculated from empirical formulas, and the slope in Fig. 11 gives u = 0.27. The agreement with the expected spin-statistical factor of Y4 (Eq.60)is again astounding in view of estimated errors of ~fr25% in 2kt and 5 30% in D , (148). The conclusion that the benzyl radical self-reaction is diffusion-controlled is further strengthened by the fact that in both solvents Et 'c E,, (Table 9). Measurements of 2k, values for i-propyl(166), ally1 (167), (CH&COH (168), (Et0)3SiOCHCH3 (168), and .CH20H (169) radicals in a variety of solvents provide further tests of the applicability of the Smoluchowski equation (Eq. 6) in defining l$$ in Eq. 61 (Table 10). These equations require that as radical systems and the solvents in which they react are changed 2 4 should remain That this expectation is admirably proportional to pD, with slope 8amN fulfilled in all cases but one is shown in Fig. 12. Not only are the points for the t-butyl and benzyl radicals collinear within experimental error, but radicals with substantially different p's, 4.3 S p S 7.2 (Table 1l), also fall on the same line. The correlation achieved in Fig. 12 is particularly satisfying in light of the great range of experimental solvents (n-heptane to methanol) and the use of the Spernol0
RADICAL SELF-TERMINATION
2k, x
D-p
10-9, MV
for
51
@&
10': 0tn3;'-
Figure 12. 2k, vs. both Dp (bottom) and 2k, for benzyl radicals in toluene (top), for the self-termination of (0)r-butyl radicals in various solvents, (0)i-propyl radical in Rheptane, i-propyl radical in n-hzxadecane, (H) i-propanolyl radical in acetone and tetraethoxysilane, (0) (EtO),SiOCHCH, in acetone and tetraethoxysilane, (A) hydroxymethyl radial in methanol; from Table 10 (see text). The line is based on Eqs. 6 and 61 with u = 'A.
(a)
Wirtz formula (Eq. 14) in calculating D,'s when empirical values were not available. As can be seen from Table 10, the Dsw values are nearly idential to the experimental values D , in hydrocarbon solvents. Spin-statistical factors calculated from the individual slopes in Fig. 12 are all very close to the expected value of % (Table 11). Of the radicals in Table 10, only the i-propyl radical shows systematicdeviations from the theoretical line (166). Since these deviations are outside of the estimated experimental uncertainty (166), and this behavior was not expectedapriori, the results for the i-propyl radical are treated in detail below. Lipscher and Fischer used di-i-propyl ketone photolysis to generate i-propyl radicals (166). As with the other ketones, the mechanism for i-propyl radical formation involves a-cleavage from the triplet state followed by activated decarbonylation of 2-methylpropanoyl radicals, with log A (s-') = 14.0 -+ 0.5, Et = 13.0 2 0.5 kcaVmol(l66). At T > 35°C the decarbonylation is sufficiently fast to allow clean bimolecular self-reaction, monitored by ESR, of the i-propyl radicals to give coupling and disproportionation products (Eq.59). Below this temperature the longer lifetime of the 2-methylpropanoyl radicals introduces
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS
52
TABLE 11. Spin-StatisticalFactors Determined from Experimental 2kt Values"
Radical
Pb (lO-'crn)
Solvent
5.6 5.6 5.6 5.6 5.6 5.6 5.6 5.6 5.8 5.8 5.2 5.2 5.3
n-C7H16 n-C8H I 8
n-C1d22 n-C12H26 n-C14H30 n-C16H34
CH3CN Benzene Toluene c-C6H 12 n-C7H16 n-C16H34 n-C3H16
5.d
(EtO),Si (EtO)$i CH3OH
~
~
7.2' 4.3
UC
0.24 0.22 0.26 0.25 0.27 0.31 0.22d 0.26d 0.26 0.29 0.27e 0.27e 0.21d.e 0.28g 0.24gsh 0.29h
Ref. 6 6 6 6 6 6 6 6 148 148 166 166 167 168 168 169
~
"Calculated from plots of 2 4 vs. D; slope = 8 r p u N b2rA, estimated using molar volumes and van der Waals volume increments (165). %alculated with empirical diffusion coefficients unless otherwise noted. dDiffusion coefficients were calculated using the Spernol-Wirtz treatment, Eq. 14. Talculated from plots of (2kJ-I vs. D-I. 'Estimated by using the van der Waals volume increments only (165). 8Adjusted with Spemol-Wim values based on empirical values for (MeO),Si. 'Based on low-diffusivity points; values at high diffusivities deviated from linearity (see text)
cross-disproportionation to 2-methylpropanal and propene as a significant reaction pathway for i-propyl radicals (166). Diffusion coefficients for i-propyl radicals were narrowly defined by averaging experimental DAISfor propane and propene (Table 10). The downward curvature in the i-propyl plot in Fig. 12 can be accounted for if either the condition k, >> k-dif in Eq. 3, or the condition kAB >> 4aNpD in Eq. 5, or both,cease to apply. It should be noted that the latter condition is equivalent to PA>> 2mNpD in Eq. A. 15 because kAA = YzkAB. The physical distinction between the failures of these two conditions is that in the first instance the reaction of singlet radical pairs deviates from being fully diffusion-controlled at high D's, while in the second it remains fully diffusioncontrolled at all D's. To appreciate the interplay of these two conditions, Eqs. 3 and A. 15 can be combined to give
RADICAL, SELF-TERMINATION
53
e,/G
where [ = (note that = Id!&)).The plot of (2k)-' vs. DA-' for the i-propyl radical is linear as predicted by Eq. 63 (Fig. 13), and u = 0.26 can be calculated from its slope. In the general case for which neither the holds, the intercept condition k,>> kdif nor the condition kAA >> 2rrNpD is assumed, then the of the line gives (l/u)('/2kAA + u p ) .If only k, >> Ldif intercept reduces to ( 2 P u ) - ' . This approximation was applied by Lipscher and Fischer to the data for the four solvents and gives 2 p = 1.7 X 10" M-' s-'. If on the other hand, only PA >> 2~rNpD is assumed, the intercept reduces to 5/a p. There has been no unanimity in the literature concerning 5. However, an equation for 5 derived by Eigen, 5 = 3000/(4dVp3) (170), which gives 5 = 1.8 M for p = 6 A, has often been employed, and an expression for 5 twice that value has been attributed to random-walk theory (171). For example, Eigen's equation has been useful in accounting for exciplex dissociation rate constants (172) and has been applied to estimate Ldif of encounter complexes involved in triplet excitation transfer (173). An empirical expression for exciplex dissociation in polar solvents has also been developed which predicts k-&f = 2.3 x 109/q for systems lacking coulombic interaction (174). We have favored an evaluation of 5 based on thermodynamics (40,54). Assuming that the enthalpy change for encounter-pair formation is zero, 5 is determined by the entropy change (cratic), ASc, for bringing two solutes together. For a net change of one solute molecule ASc = - R ln[M], where [MI is the molarity of the solvent, i.e., 5 = [MI (175). Relative to the Eigen equation, in which 5 is independent of solvent, the cratic-
0;'
10-4 SCm'2
-
Figure 13. 2k;' vs. DA' for the self-tennination of i-propyl radical in (0)n-heptane and (0) n-hexadecane; see text.
54
SPIN-STATISTICAL. FACTORS IN DIFFUSION-CONTROLLED REACI?ONS
entropy approach, being solvent-specific, gives 2-10 times larger 5 values (54). Assuming an intercept of & u p for the plot in Fig. 13 and treating the data for the n-alkanes separately gives u = 0.29 2 0.03 and 0.27 2 0.02 for n-heptane and n-hexadecane, respectively, and kpA = (6.6 2.1) X 10" s-l and (4.1 & 2.2) X 10" s-' with 5 = 6.8 M and 3.4 M in the same order. In the absence of additional information, distinguishing between the two extreme interpretations of the intercept in Fig. 13 is difficult. Intuitively we prefer interpreting it as & u p , because the chemical significance of k in Eq. 5 (2kAA in Eq. 62) is unclear. The magnitude of k has been estimated by assuming it equal to a gas-phase collision rate constant (4), and it has variously been called the rate constant that would pertain if the equilibrium concentration of encounter pairs were maintained (176) and a radiation boundary constant (166). On the other hand, it is clear that as the stability of the radicals is increased by appropriate substitution, k, decreases relative to k-&f (177) even to the point of resulting in persistent radicals. Whatever the cause of the curvature in Fig. 12, it is not at all obvious why i-propyl radicals should behave differently from t-butyl radicals. The difference may reflect the lower precision of the r-butyl radical 2ktvalues. In conclusion, it appears that Eq. 6 can be used with confidence to calculate rate constants for fully diffusion-controlled processes when empirical diffusion coefficients for the reactants in the solvents of interest are known. The recipe for calculating the reaction distance p may vary from reaction to reaction, but if we rely on radical self-termination as a guide, it may be taken as the sum of reactant radii estimated by averaging values obtained from molar volumes (Eq. 12) and from volumes based on van der Waals volume increments (165). When empirical diffusion coefficients Dexprare not available, they may be estimated from the Stokes-Einstein equation using the Spernol-Wirtz microfriction factor (Eqs. 10-14). When applied to nonassociating hydrocarbon solvents, as recommended (6), Dsw values are generally within f 10% of empirical values and seldom deviate by as much as & 25% (Tables 10, 11). This procedure will probably be best when applied to liquid solutes in fairly nonviscous solvents, i.e., to systems similar to those used in generating Eqs. 11-14. Furthermore, since the reduced-temperature term in Eq. 14 compensates marginally for rather small deviations from Eq. 11 (s25%), its use with higher-molecular-weight solvents and solutes is not recommended. Finally, when diffusion-controlled 2kt values are available in a specific solvent for radicals with D close to that for an A + B reaction, kdif for that reaction can be taken as 8k.
*
VI. TRIPLET EXCITATION TRANSFER Triplet excitation transfer involves a multiplicity-allowed electron exchange interaction in an encounter pair (178).
-
55
TRIPLET EXCITATION TRANSFER
3D*
+
'A
e kdd
k-d#
'(D*A)
ken k-cn
3(DA*)
k-dd
'D
+ 3A*
(64)
When, based on spectroscopic triplet excitation energies, the process is at least 3 kcal/mol exothermic, it has been found to attain a maximum rate constant (1, 5, 179-181) and has often been considered to occur upon every solution encounter. In such cases ken does not significantly contribute, and kobsd = kdifken/(ken k-,& Accordingly, the limiting condition kObd = kdifis expected to be especially valid in solvents of high viscosity in which solution encounters last longer, i.e. k-dif << ken (182,183). Wagner and Kochevar first recognized that in the low-viscosity solvents usually employed in photochemical studies, diffusion apart of donor-accceptor pairs competes with triplet-excitation transfer-even when, due to high exothermicity, the limiting rate constant kobsd has been attained (171). They showed that in a series of hydrocarbon solvents (q = 0.233 - 3.15 cP), kobsd values for the quenching of valerophenone triplets by 2,5-dimethyl-2,4-hexadieneare up to three times smaller than predicted by Eq. 9, (Y = 2,000, but approach predicted values in the highest-viscosity solvents (171). They reasoned that limiting kobsd values of (5 ? 1) X lo9 M-' s-l obtained earlier for a variety of donor-acceptor pairs in benzene (179,180) were not fully diffusion-controlled as had been supposed previously. The treatment of kobsdTD values for the quenching of triplet valerophenone photoelimination by 2,5-dimethyl-2,4-hexadienewas based on the assumptions that (a) the valerophenone triplet lifetime rDis solvent-independent, (b) kdif is given by the slip limit of the Debye equation (Eq. 9), OL = 2000, and (c) ken& is solventindependent (171). In light of the radical self-reaction results, assumption (b) is untenable (6),and, to the extent that cratic entropy controls 5, so is assumption (c) (54). A more satisfactory treatment of the results can be based on
+
where 5 is the molarity of the solvent, kdif is obtained from Eq. 6 with p = r, + r, = 7.1 A (radii based on molar volumes), and the D's are based on the Spernol-Wirtz formula (Eqs. 10-14); see Table 12. The plot of the data according to Eq. 65 (Fig. 14) shows that n-alkane and cycloalkane points fall on somewhat different lines. Treating the data separately gives TD = 4.35 ns and ken = 2.52 X 10" s-' for the n-alkanes, and TD = 6.9 ns and ken = 1.3 X 10" s-' for the cycloalkanes. These conclusions are not entirely satisfactory, because though 713%which is determined by the dynamics of y-Habstraction, may show a small solvent dependence, it is unlikely that ken should be that sensitive to subtle solvent changes. Despite the difference in treatments, efficiencies of tripletexcitation transfer, p , based on ken = 2.52 x 10" s-l are remarkably close to those obtained in Ref. 171 (see Table 12) and are consistent with the original conclusions. Experimental estimates of ken 3 9 x 10" s-' and ken 2 10" s-'
TABLE 12. The Quenching of Valerophenone Triplets by 2,5-Dimethyl-2,4hexadiene
36 95 79 72 63 56 51 32.5 48 39 30.5
11.2 8.7 7.6 6.9 6.2 5.6 5.1 3.4 9.3 8.2 7.5
1.85 4.70 3.56 2.97 2.48 1.93 1 .so 0.82d 1.32 0.93 0.59
0.54 0.38 0.48 0.55 0.62 0.70 0.77 0.90 0.67 0.77 0.85
"From Ref. 171. bMolar volumes at 20°C. Lange's Huna'book of Chemisrry, 9th Ed., Handbook Publishers, Inc., Sandusky, Ohio, 1956. %om Eqs. 6 and 10-14. qruncated form off, was employed. ' p = ken/(ken + skf)with kn = 2.52 x 10" s-'; see text.
I ( I /
1
2 ~
-
x 10". i'
I
3
Figure 14. Treatmentof thedatain Ref. 171 using&. 65: (0)alkanes, (e)cycloalkanes, (0)benzene.
56
TRIPLET EXCITATION TRANSFER
57
have been based on the quenching of y-phenylbutyrophenone triplets by neat cis-l,3-pentadiene (17 1) and on transient measurements of benzophenone triplet decay in neat 1,3-pentadienes (184). Flash kinetic spectroscopy has been used to determine rate constants for triplet energy transfer from indeno[2,l-a]indene to azulene as a function of temperature in n-pentane (228-290 K), toluene (228-309 K), acetonitrile (233-308 K), and r-butyl alcohol (309-342 K)(54). The adherenceof kobsd to the Arrheniusequation is satisfactory in all four solvents (Figure 15), and activation energies for excitation transfer are close to those for r-butyl radical self-reaction and to activation energies for viscous flow (Table 13). The variation of kobsd with Tlq parallels closely that found for 2kt for r-butyl radicals, as is demonstrated more directly by plots of kobsd vs. kt in Fig. 16 (54). Based on the fact that the range of k,bsd/k[ ratios, 3.14.5, is close to the reciprocal of the spin-statistical factor for radical self-reaction, a-' = 4, it was erroneously concluded that the excitation-transferprocess is fully diffusion-controlled (54). Not appreciated was the fact that since rate constants for an A + B reaction were being compared with those for an A + A reaction, the slopes in Fig. 16 should have been (2a)-' = 8 if both reactions were diffusion-controlled.Correction for differences in D and p in Eq. 6 for the two reactions can be based on Spernol-Wirtz microfriction factors for the nonhydroxylic solvents,
T-' x
to3. K
-
(A),
(o),
Figure 15. Arrhenius treatment of kObd in n-pentane acetonitrile (a),toluene and r-butyl alcohol (0) from Ref. 54. Reprinted with permission from J . Am. Chem. Soc. (1980) 102 6799. Copyright 1980, American Chemical Society.
TABLE 13. Arrhenius Parmeters for Triplet Excitation Transfer from Indeno[2,1-u]indene to Azulene" Solvent n-Pentane Toluene Acetonitrile t-BUtyl alcohol
T(K) 233-273 273-303 203-253 253-323 232-305 302-321 321-347
log A,,
E$ ~
-3.63 -3.67 -4.33 -3.85 -3.66 -7.45 -6.43
1.35 1.40 2.73 2.17 1.63 8.27 6.77
log Aobsd
E:bsd
~
12.0720.05 2.1920.05 11.9820.2 2.7220.10" 11.45-CO.2 1.7220.3 13.1720.1 4.7020.4
Source: Table VEI in Ref. 54; A,, in poise, AoM in M-' s-', E's in kcal/mol. "E,'s for benzyl radical self-reaction in toluene (148) and for r-butyl radical in acetonitrile and r-butyl alcohol (6) are 2.99 2 0.72, 2.03 f 0.2, and 5.36 f 0.2, respectively.
Figure 16. Plots of kObd for 31n*-'Az energy transfer vs. k, for t-butyl radicals; lines 1-4 are for t-butyl alcohol, n-pentaneln-heptane, toluenehnzene, and acetonitrile, respectively. The dashed line is drawn with 0 intercept and slope 4. From Ref. 54, reprinted with permission from J . Am. Chern. Soc. (1980), 102,6799. Copyright 1980, American Chemical Society.
58
TRIPLET EXCITATION TRANSFER
59
where t-Bu, Az, and In designate the solutes. Employing truncatedh's for Az and In (Eq. 11) and fullf,'s for r-Bu increases the apparent ( 2 0 ) ~ values ' from 3.6-3.9 to 4.3-4.5 in n-pentane, from 3.1-3.4 to 4.3-4.6 in toluene (185), and from 4.5 20.1 to 6.3 -+O. 1 in acetonitrile (54). The deviations of these values from the expected value of 8 suggest strongly that in this case also triplet excitation transfer, though exothermic by = 8 kcal/mol and though T,T*triplet states in both donor and acceptor are involved (1 86), is nor fully diffusion-controlled. It follows that kobsd = &,if, where p = ken/ke, + k-& '/2 in n-pentane and toluene and p = 34' in acetonitrile. Since p is insensitive to temperature in all solvents employed, it appears that the activation energies of ken and k-dif must be similar. A more quantitative demonstration of this fact can be based on a comparison of rate constants for benzyl radical termination with rate constants for In-Az triplet excitation transfer in toluene (Table 14). Values of p in Table 14, based on the assumption that kdif = 8kt, are probably underestimated by
-
TABLE 14. Comparison of Rate Constants for Benzyl Radical Termination with Rate Constants for In-Az Triplet-Excitation Transfer in Toluene
331 326 3 14 304 298 293 283 277 269 262 256 248 240 235 229 222
33.8 31.4 26.3 22.5 20.4 18.7 15.6 13.9 11.8 10.2 8.9 7.4 6.0 5.3 4.5 3.6
15.3 14.3 12.2 10.6 9.7 8.9 7.6 6.8 5.9 5.1 4.6 3.8 3.2 2.8 2.4 2.0
0.44, 0.44, 0.452 0.45, 0.462 0.466 0.472 0.47, 0.48, 0.49, 0.49, 0.50, 0.51, 0.52, 0.53, 0.54,
9.01 9.06 9.19 9.29 9.35 9.40 9.50 9.56 9.64 9.71 9.77 9.85 9.93 9.98 10.05 10.12
"Based on Arrhenius parameters from data in Ref. 148. bBased on Arrhenius parameters from data in Ref. 54. 'Molar volumes of toluene based on densities from Inrernarional Crirical Tables, McGraw-Hill, New York, 1930, Vol. VII, pp. 29-31.
60
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLED REACTIONS
<15%. since p for benzyl radicals is somewhat larger than p for t-butyl radicals: see Eq. 66 and (185). Basing p on the molar volume of toluene gives In- kdif ken
-=
= In 1-P
P5
In- Adif 4 n
+
Een-Edif
RT
The data are plotted according to Eq. 67 in Fig. 17. As expected, a linear relationship is obtained (2 = 0.9999) which gives (Adif/Aen) = 0.392 M-' and Een - Edif = -0.68 kcaymol. These values, together with the activation parameters for 84, give A,, N 1.28 X lo'* s-l and E,, = 2.31 kcaymol. In view of the 8-kcdm01 exothermicity associated with k,,, this large activation energy was not expected. In the past inefficiencies in exothermic triplet-excitation transfer rate constants, inferred from data at room temperature, have been assigned to the transmission coefficient K,, (173). We stress that the present analysis depends on the assumption that, as in radical self-termination, the encounter distance pet for electronic energy transfer by the exchange mechanism can be approximated as the sum of the radii of the donor and acceptor. If this approximation overestimated petby a factor of 2, then the deviation of the slopes in Fig. 16 from the expected value of 8 would be accounted for, the treatment in Fig. 17 would be invalidated, and the conclusion (54) that triplet-excitation transfer from In to Az is fully diffusion-controlled would stand. In either case, triplet-excitation transfer would not provide a suitable model reaction on which to base kdif values.
-L
9
V
Figure 17. Treatment of the data in Table 14 using Eq. 67.
61
TRIPLET EXCITATION TRANSFER
A very pretty study which illustrates the functioning of spin-statistical factors even though a large fraction of encounter pairs of the proper spin state are dissociative has been described by Wilkinson and Tsiamis (187). It concerns the rate constants for the quenching of the triplet states of a series of organic compounds by chromium (HI) P-diketonates with formulas
R2
Symbol
C6H, CH, t-Bu CF,
Cr(bzac), Cr(acac), Cr(dpm), Cr(hfac),
R, Cr 3
CH, CH3 r-Bu CF,
in benzene. The observed variation of kq with the triplet excitation energy of the donor is shown in Table 15 and Fig. 18, (187). Also shown on the abscissa of Fig. 18 are the energies of the lowest available excited states of the acceptors
TABLE 15. Quenching Rate Constants of Donor Triplet States by Chromium (III) P-Diketonates in Benzene (187)" Dono? Benzophenone Triphenylene Phenanthrene Naphthalene P-Acetonaphthone Chrysene Coronene 1,2,3,4-Dibenzanthracene Pyrene Acridine Anthracene Perylene Tetracene Pentacene @-Carotene "At room temperature. %om Ref. 1 87. 'From Ref. 187a. dFrom Ref. 187b. 'From Ref. 187c.
k,"(109 M - ~ s - ~ )
b
*&I+,
(kcal/mol) Cr(bzac),
Cr(acac),
69.5 66.6 61.8 60.9 58.9 57.2 55.5
4.95k0.20 3.10k0.20
50.9 48.0 45.2 42.0 35.5 29.5 22.9 18.0
1.3220.07 1.80k0.11 1 5 7 2 0.09 1.4820.05 0.23k0.01
Cr(dpm)3
Cr(hfac),
0.89k0.04 0.9220.05
4.52k0.02 8.2k0.4
0.52k0.04 0.38k0.04 0.38k0.04 0.09k0.01
8.220.4 5.220.3 8.2k0.3 8.2k0.4
4.5620.20 2.50k0.15 3.3620.14 1.80k0.13 2.6520.11 1.54k0.09 2.3020.07 1.64kO.10
<0.001 <0.001
1.22 k 0 . 12 1.34k0.11 0.080+0.009 8.2k0.4 1.28 k 0.13 0.075 k 0.009 1.20 k 0.08 1.2520.04 0.075k0.007 4.50k0.2 <0.005 3.95k0.2 0.047k0.01
62
SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS
7.0 10
20
30
40
A +FTIzsO, k c a l l mol-
50
60
7C
(o),
Cr(acac), (m), Cr(dpm),, (O), and Cr(hfac), (0)quenching rate constants on the triplet energies of the donors. Information from Ref. 187. Reprinted with permission from J . Am. Chem. Soc. (1983) 105,767 and J . Phys. Chem. (1981)85,4153. Copyright 1983 and 1981, AmericanChemicalSociety. Figure 18. The dependence of Cxfbzac),
(187). The correlation of quenching constants with donor triplet energy indicates that at least for Cr(bzac),, Cr(acac),, and Cr(dpm), electronic energy transfer is the quenching mechanism. Furthermore, for Cr(bzac), and C r ( a ~ a c the ) ~ ratio of the maximum rate constants attained to those definicg the plateaus in Fig. 18 at 41 s s 52 kcaYmol is very close to three. Since quartet quencher ground states are involved, this observation has been accounted for (187) by
5'D + 4Cr(L)$
3D* -!- 4 C r ( L ) 3 ~ , ~'/.kbr4 ( D C r ( L ) 3 ) * -41
(68)
For donors with triplet energies below 52 kcaVmol only doublet acceptor states are energetically accessible; hence only the doublet encounter pair provides a spin-allowed excitation-transfer channel with a maximum rate constant of 1/6kdif. At higher donor energies excitation to a quartet excited state of the acceptor is also possible and both quartet and doublet encounter pairs can lead to excitation transfer. The combined maximum quenching rate constant when both doublet
TRIPLET-TRIPLET ANNIHILATION
63
and quartet channels are fully functional is (% -t 1/6)kdif= ?hkdif and accounts nicely for the factor-of-three change between the fnst plateau and the beginning of the second. If we base our estimate of kdifon the radical self-reaction rate constants, it is clear that even the kq’s for Cr(bzac), are not fully diffusioncontrolled when corrected for the appropriate spin-.tatistical factor. But even if they were, we can be certain that the rate constants for Cxfacac), and Cr(dpm), do not represent diffusion-controlled processes and are given by kq = ukdip. The differences in quenching efficiencies p between the three quenchers have been attributed to differences in the transmission coefficients for excitation transfer (187). Larger K, values for Cr(bzac), can be associated with the nephelauxetic (e--cloud-expanding) effect of the phenyl group, while the smaller K, values for Cr(dpm), are attributed to the steric effect of the t-Bu groups, which reduces the overlap of orbitals on the triplet donor with orbitals centered on the Cr of the acceptor (187b). It is possible that the initial sharp rise of kq for Cr(dpm), at 56-57 kcaYmol is associated with an increase of 2 ~ , , , the transmission coefficient for formation of doublet excited acceptor due to the presence of the %2g in that energy region as an additional exit channel from the doublet encounter pair (187b). The larger kq values associated with quenching by the much better electron acceptor Cr(hfac), are apparently due to quenching via ion radical pairs (187~).Supporting this proposal is the fact that the dips in the Cr(hfac), curve in Fig. 18 occur when the organic triplet states being quenched are poor electron donors. Apparently in such cases, quenching by exchange energy transfer again predominates (187c). A parallel study with iron (111) 6diketonates as quenchers has also been carried out (188).
VII. TRIPLET-TRIPLET ANNIHILATION Interaction of two excited triplet states of the same molecule in solution is known as triplet-triplet annihilation (TTA) because it provides an important triplet decay pathway. It often gives rise to monomer and excimer delayed fluorescence (189,190). Rate constants for TTA are usually obtained indirectly from the analysis of the second-order component of the decay of triplet-triplet absorption following flash excitation (191-196). Such analyses are generally based on
--d[,A*] dt
= kl[,A*]
+
k2[,~*12
and yield experimental values of K = k&, where et is the molar absorptivity for 3A*, the triplets being investigated, at the monitoring wavelength, and 1 is the path length of sample probed by the monitoring beam (191-196). Since I is known, extraction of k2 from K depends on accurate independent measurements of E,. Unfortunately, the K’S are often obtained using unspecified broad-band
SPIN-STATISTICALFACTORS IN DIFNSIONCONTROLLED REACTIONS
64
probing beams which, though centered at &- for triplet-triplet absorption, represent a range of wavelengths and lead to the replacement of E, in K by an unknown smaller effective absorptivity, T, (196). Nonetheless, early measurements by Livingston and Ware of the temperature and viscosity dependence of K had established that TTA is a diffusion-controlled process (192c). In a study of anthracene triplet decay (3A*), k , , which was apparently controlled entirely by pseudounimolecular diffusion-controlled quenching by residual O,, was shown to be proportional to K over a wide range of temperatures in several solvents (192c). In addition, the slopes of Arrhenius plots of K were found to correspond closely to the activation energies for viscous flow (192c). The calculation of k2 values for 3A* in toluene has been based (196) on the triplet-triplet absorption spectrum of 3A* in benzene (197b). Effective absorptivities7;were determined by integration over the monitoring band profile. represents )* the singlet excimer and the other Use of Scheme 4, where '(a symbols are self-explanatory, gives = k,(2 - pt - ps+is)rwhere p , = (2k, + kgMkt + k g + ksg + kgg + k) andps = k S g K k , + kg + ksg + kgg + k) are the probabilities that the paired triplets, (3A*3A*), will give directly 3A* and 'A*, respectively, and +is = kis/(k, kf ki, +k,[ 'A]) is the intersystem crossing yield of 'A*(196).
+ +
'A
+ hv
'A
3A*
+ 3A*
3A*
+
'A
DIMER Scbeme 4. Kinetics for Triplet Formation apd Decay
To obtain 2 - p , - ps+is,k, was plotted vs. kobd for triplet-excitation transfer from In to Az. It should now be clear that this procedure was based on compensating erroneous assumptions. The two assumptions, namely that (a) triplet-excitation transfer from In to Az is fully diffusion-controlled and (b) it can be taken as an empirical measure of k,, the rate constant for triplet-triplet association, are summarized by koM = kdir = k, (196). However, since TTA is an A A reaction, the proper relationship is k, = Y e .As discussed in the previous section, appreciation of this subtlety also leads to the conclusion Y for the ~n-Az system, and hence a fortunate cancellation of that kob& = & =. k,. errors occurs: kob& =
+
YG
65
TRIPLET-TRIPLET ANNIHILATION
The quantitative treatment of the k2 values for 3A* in toluene can be based on the empirical benzyl-radical termination rate constants. Justification for this assertion is provided by the diffusion coefficients for anthracene (DA)and for toluene, (&), listed in Table 16. As expected, truncated Spernol-Wirtz diffusion coefficients are in satisfactoryagreementwith experimentalvalues for anthracene, whereas full Spernol-Wirtz coefficients agree well with experimental values for toluene (assumed the same as for benzyl radicals). The choice of the value of pB = 5.8 A for benzyl radicals was discussed above; see Table 11 (148). For anthracene Eq. 12 gives r, = 3.47 A and the Van der Waals volume increment method gives rA = 3.41 A (165), leading to an average value of pA = 6.88 A. It can now be seen that due to compensation in the relative magnitudes of the D's and p's, the Dp products predict nearly identical kdif values for these two solutes. The temperature dependence of k2 (196) and kdif, based on 8k, for benzyl radicals (148), in toluene is shown in Table 17. The ratio of k2 to %kdif is relatively insensitive to temperature, decreasing from 0.62 to 0.50 as the temperature is increased from 207 to 318 K. The plot of k2 vs. Y2kdif, Fig. 19, gives 2 - p t = 0.53 +- 0.02 as the slope of the best line through the origin. This value is also obtained directly from the 2k2/kdifratios in the 292-308K range. The results of several determinations give +f = 0.27 & 0.02 (199) = 0.73 f 0.02 (200), independent of solvent, for the fluorescence and and intersystem crossing yields of anthracene at room temperature. Three independent determinations of Pdf = paka/k2, the efficiency of delayed fluorescence of anthracene, have yielded values of 0.077 (201a), 0.08 (201b), and 0.080 (201c) in ethanol. Since Parker has reported that delayed-fluorescence results for
TABLE 16. Diffusion Coefficients for Anthracene and Toluene in Hydrocarbon Solvents, 25OC
Hexane Octane Cyclohexane Methylcyclohexane Benzene Toluene
3.16 2.00 (1.24) 1.61 (1.72) (2.02)
3.54 2.28 1.18 1.62 1.68 1.93
(3.22) 1.58 (2.19) 2.26
3.93 2.83 1.61 1.84 2.28 2.27
"Measured for 'A* (198), except values in parentheses, which are interpolated from plots of Dexp vs. rlrL in Ref. I, ?Based on truncatedA, 4. 11. 'From Ref. 148; for values in parentheses, see footnote a. dBased on fullf,, Eq. 14.
TABLE 17. The Temperature Dependence of k2 for Anthracene in Toluene Set 1
258.2 263.2 268.2 278.2 288.2 298.2 308.2 318.2
2.74 3.09 3.58 4.10 5.04
5.37 6.53 6.93
Set 2
9.55 10.7 11.9 14.5 17.5 20.9 24.6 28.7
207.3 218.1 235.1 246.7 262.1 279.6 292.3
0.71 1.01 1S O 2.19 2.90 3.99 4.97
2.28 3.27 5.38 7.27 10.4 14.9 18.9
“From Ref. 196. % a d on Arrhenius parameters for 8k,for benzyl radicals (148). ‘Adjusted values from Ref. 192c (196).
Figure 19. The dependence of k2 for anthracene triplets on the rate constant for diffusion (44 for benzyl radicals).
66
67
TRIPLET-TRIPLET ANNIHILATION
anthracene in cyclohexane are similar to those obtained in ethanol ( lw c ) , pdf = 0.080 was assumed to apply in toluene; with k21k, = 0.53 it gives p s = 0.042. Substitution of p s and +is into 2 - pt - ps+is = 0.53 then gives pt = 1.44. These revised p s and pt values differ only slightly from those in Ref. 196 and thus do not significantly alter the spin-statistical mechanism presented in that paper. As in the case of triplet quenching by ground-state oxygen, triplet-triplet encounters produce with equal probabilities nine spin states, except that in this case double asterisks indicate that initially these states are doubly excited, having the energy content of two monomer triplets, = 85 kcaymol. The following simple mechanism predicts exactly pt = 1.44: W)k.
'A*
+ 'A*-+,
r (%Via
*(AA)** I no 'A* directly 3(AA)** 4 3(AA)* __* 'A*
+
(70)
'A
It is assumed that all quintet sublevels are completely dissociative giving back both monomer triplets; that the triplet doubly excited pairs undergo internal conversion to dissociativetriplet excimers, thus regenerating one triplet monomer per pair; and that the singlet doubly excited state regenerates no 3A* directly. The overall probability of triplet regeneration according to Q. 70 isp, = 2(%) + 2(%)('/2) = 1.44, which is identical to the experimental value. The dissociative nature of the triplet excimer follows from the fact that only one in lo5encounters of 'A* with 'A leads to quenching (202). From a photochemical point of view, more interesting is the fate of the singlet encounter pairs. Both photodimer formation and anthracene momomer delayed fluorescence could be accounted for as multiplicity-allowed channels from these intermediates. Anthracene photodimerization as a consequence of TTA was first reported by Backstrom and Sandros, who used triplet biacetyl as sensitizer (203,204). The role of 'TTA in dianthracene (A2) formation following direct excitation of anthracene was quantitatively revealed by the strong dependence of +Az on light intensity in degassed, but not in air-saturated benzene solutions (205). Kinetic expressions describing the dependence of +A2 on the concentration of 'A on the steady-state concentration of 3A* and on the light intensity were derived using Scheme 4. An excellent fit of more than 50 +Az values over wide concentration and intensity ranges was obtained to these expressions, employing computer assistance and mainly literature rate constants (205). The fraction of triplet-triplet encounter pairs that give the precursor of the dimer, p: = k2(k, + ktg ksg kgg k:),
-
+
+
+
68
SPIN-STATISTICALFAffORS IN DIFFUSION-CONTROLLEDREACTIONS
was the single derived parameter: ps = 0.115 & 0.007. This value, being indistinguishablefrom the spin-statistical factor of '/9 for formation of the singlet 'IT encounter pair, was taken as strong evidence for associating the singlet pair state exclusively with photodimerization (205). This conclusion appeared to be strengthened by the fact that the rate constant for 'AA* formation directly from 'A* and 'A, k,, inferred from photodimerization quantum yields (206,207) and steady-state (208) and transient (209) 'A* fluorescence measurements in benzene and toluene is nearly identical to rate constants for triplet energy transfer from 31n* to Az (54). Since the latter process was thought to be fully diffusioncontrolled, it was reasoned that anthracene excimer formation was irreversible (196,205,206) and that 'A* was generated by intersystem crossing from 5(AA)* to a dissociative excited excimer state '(AA)*' as had been discussed in a theoretical paper by Krishna (210). The argument, of course, is faulty because it is based on underestimation of the magnitude of as described in detail in Section VI. The conclusion that k, is at most implies that '(AA)* formation is reversible. Since '(AA)* may form from the singlet l T encounter pair '(AG)**, the latter must now be considered as a possible source of 'A*, providing an explanation for delayed monomer fluorescence which does not require intersystem crossing. Before reevaluating the photodimerization data using better estimates of rate constants, a few remarks concerning the mechanism of this reaction are in order. Theoretical treatments of allowed concerted photocycloadditions have predicted that the path to adducts requires crossing from the singly excited excimer into a doubly excited state which correlates with the ground states of addends and adducts (211,212). Avoided crossing between appropriatecorrelationlines creates a pericyclic minimum on the doubly excited surface. This minimum is thought to represent the "funnel" or "hole" through which return to ground state addends and formation of adducts occurs. It is also thought to be the intermediate through which photocycloreversion of adducts to addends occurs. On the addend side the doubly excited state can be represented as arising through interaction of the lowest triplet states of the addends (211,213,214). The complete photodimerization mechanism is shown for anthracene in Fig. 20, and possible sequences of steps summarized in Scheme 5 , where '(AA)&f represents the relaxed doubly excited state at the pericyclic minimum. In terms of Scheme 5, the effective rate constant for singlet-excimer formation, k, in Scheme 4 , becomes k, = k,A(k, + kf, kFdif)/kC k,&kdkC]-' which reduces to the familiar k, = k,&J(k, + k-dif) when ke and k, are small. In the latter case generation of 'A* from the initially formed doubly excited singlet'IT pair could still occur by direct relaxation of '(AA)** to '(AA)*.
+
+
TRIPLET-TRIPLET ANNMILATlON
69
r
REACTION COOROINATE
Figure 20. Potential-energy diagrams showing the two paths for anthracene photodimerization. From Ref. 205, reprinted with permission from J . Am. Chem. SOC. (1983) 105,3413. Copyright 1983, American Chemical Society.
Scheme 5. The Two Pathways to Anthracene Photodimerization
The first column of parameters in Table 18 was the set employed in Ref. 205 in fitting photodimerization quantum yields to the mechanism in Scheme 4. The last, p: = 0.115 & 0.007, was the only derived parameter. Given in the second column are improved estimates of the fixed parameters. As can be seen, the adjustments to pt and p s based on the new analysis of the k2 values are rather small. The value of k, = Y e is based on the benzyl-radical termination rate constant adjusted for the toluene-to-benzene solvent change using the viscosity ratio. Values of k, obtained in benzene at room temperatureare 8.5 X lo9M-' sfrom the dependence of +A on ['A] at high ['A] and low light intensity (207), and more directly, 7.3 x lo4M-' s-' from fluorescence-intensityself-quenching
70
SPIN-STATISTICAL FACTORS IN DIFFUSIONCONTROLLEDREACTIONS
TABLE 18. Parameters Used in Computing Dimer Quantum Yields in Benzene, 30°C
Parameter
Ref. 205
Pt PS PfA k, (M-'s-')
1.40 0.046 0.22 9.6 x 109 9.6 x 109 6.43 x 107 1.74 X lo8 0 49 3.73 x 105 0.115 2 0.007
ke (M-'S - 1 )
kds-')
kis(s-l) kds k:t(s-') k (M-ls-') "p Pe
CIOHIOLl
1.44 0.042 0.22-0.24 1.06 X 10" 8.5 x 109 6.43 x 107 1.74 X lo8 0 2849 3.09 x 105 0.081-0.102
CIODlO(216) 1.44 0.042 0.22-0.24 1.06 X 10" 8.5 x 109 6.43 x 107 2.00 x 108 0 8.549 3.09 x 105 0.053-0.076
This work; see text.
(208), and 7.4 x lo9 M-' s-' from the dependence of 7, on ['A] (209). Since all these values must be adjusted upward for the temperature increase to 30"C, the choice of 8.5 x lo9 M-' s-' is a good compromise. The lower value of k,, is bas9d on new measurements in our laboratory (215) adjusted to 30°C using the activation parameters in Ref. 202. The range of 2 8 4 9 s-l for kzt is established by the lowest values observed in a glassy hydrocarbon medium (216) and in dilute 'A solutions (192c,202,217) respectively. The probability &d that the singlet excimer gives dimer was set at 0.22 or 0.24, literature values for benzene (207) and toluene (206), respectively. The best-fit value of p: is substantially coupled to the choices ofk:, andpd; the lowest value,pL = 0.081, corresponding to kzt = 28 s-' andp, = 0.24, and the highest, p: = 0.102, corresponding to k;, = 49 s-l andp, = 0.22. The range of ps + pe = 0.1234.144 is no doubt within experimental error of % and thus suggests that most, if not all, monomer fluorescence and photodimerization come from '(AA)**. The possible contribution of electron-nuclear hyperfine coupling (HFC) as a mechanism for intersystem crossing between TI' encounter pairs of different multiplicity was strongly suggested by recent resonance-Raman-spectroscopic determinations of k2 = 5.3 X lo9 M-' s-' and 2.1 x lo9 M-' s-' (Eq. 67) for perhydro- (A-h,,) and perdeuterioanthracene (Adlo), respectively, in cyclohexane or ethanol at room temperature (218).* Such a large deuterium isotope effect on k2 implies that the protons in perhydroanthracene enhance the efficiency of triplet destruction by providing a mechanism (HFC?) for intersystem crossing between T f encounter pairs of different multiplicity. Such interconversion would *It is not clear which of the two solvents indicated was employed for these measurements.
71
TRIPLET-TRIPLET ANNIHILATION
invalidate the simple spin-statistical mechanism for A-h,, TTA in Eq. 70, and would suggest that the near-equality of the sum of the derived parameters p i and p , to '/9 may be fortuitous. Fortunately, our own independent measurements of K = k21d in benzene for A-hlo and A-dlo under identical conditions show no deuterium isotope effect on this quantity (219). Since no deuterium effect is expected on et or k,, it follows that there is no deuterium isotope effect on 2 - pt p&. Since the deviation of the latter quantity from 2 is primarily due to pt, the spin-statistical mechanism in Eq. 70 is left intact. We have also shown that there is no deuterium isotope effect on k,, (219). Furthermore, the dependence of A-dIo photodimerization quantum yields on light intensity and ['A-d,,,] is accounted for nicely by Scheme 4 and gives p i = 0.0534.076 (Fig. 21). In
1
Y
0 I
N
7 4
-8
I .o
1;
0.01
I
0
/ /
I 10
[A]-'
0
I
20
I
30
x lo-*, M -
I
40
I
50
I
60
Figure 21. The dependence of A-d,, dimer quantum yields on intensity and [A-d,,]. Points are from independent runs, and lines are drawn through calculated values: (A) I, = 12.0 X einstein s-', I, = 4.5 X einstein s-', (0) I, = 1.9 x lop9 einstein s - ' , (0) I, = 0.31 X einstein s-', (0)in the presence of air. From Ref. 219.
w)
72
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS
deriving p l , the values in the last column of Table 18 were employed for the other parameters. These are identical to those for A-hlo except that for ki,, which was adjusted upward to account for the lower fluorescence quantum yield of A-dlo in benzene (219,220), and k:t, which is substantially lower at 77 K (216). Assuming that p s is unaffected by perdeuteration gives pl p s = 0.10-0.12, in excellent agreement with the expected value of %. It is not clear at this time whether the small difference in p; values for A-hlo and A-dlo is outside experimental uncertainty. If it were, it would allow for a small contribution of HFC induced interstate mixing. A theoretical treatment of the effect of coupling a particle with a nuclear spin of '/z to one of two lightly coupled spin-1 particles predicts that, to the extent that HFC contributes, interstate mixing should be induced between quintet and triplet and between triplet and singlet, but not between quintet and singlet encounter pairs (219). We suspect that as in the case of radical pairs, such intersystem crossing steps will contribute only when structural or medium constraints increase the time of interaction at short distances. However, in the case of biradicals it has been established that at short end-to-end distances spin+rbit coupling dominates over HFC as the intersystem crossing mechanism (22 1). A great deal of TTA work on other arenes has been carried out in ethanol, for which good estimates of kdif are not available. The reader should consult Ref. 196 for a brief review of some of the key papers. In most of the early work a common error is the assumption that k, in Scheme 4 is equivalent to @ instead of Gf.In polar solvents l T A may also produce cation-anion radical pairs. This process should certainly be energetically possible in systems where even the singlet excimer undergoes dissociation to ion radicals. A pertinent example is provided by transient absorption spectra obtained on the picosecond time scale from excited bis(9-anthry1)methane and bis(9-anthry1)carbinol (222). It appears that the intramolecular interaction of 'A* with 'A in these molecules has a strong charge-transfer component leading to full electron transfer in acetonitrile and ethanol (222). The same ion-pair intermediates are obtained by photocleavage of the corresponding intramolecular cycloadducts in these solvents (222). The possibility that quintet encounter pairs may give a quintet monomer excited state and the ground state of the other partner has also been considered (223). However, theoretical calculations suggest that for most arenes quintet monomer states are not energetically accessible from TT encounters involving the same partners (224). A comprehensive study of 1,Zbenzanthracene TTA in n-hexane at 23°C has been reported (225), which allows the calculation of p s and pt and at first glance suggests that the spin-statistical mechanism given for anthracene in Eq. 70 does not apply generally. Algebraic manipulation of Eq. 10 in Ref. 225 shows it to be equivalent to our k2 = (2 pt p,&,)k,, since k, = e / 2 . The value of k2 = 2.03 X 10'' M-' s-' was set equal to the slope of the plot of = kl + k2 r3BA*]) using all but the next to the last set of values in Table 1 of Ref. 225.
+
- -
r(
73
TRIPLET-TRIPLET ANNIHILATION
The value k, = 2.09 X 10" M-' s-' was based on 4k, for t-butyl radicals by adjusting the value obtained in n-heptane to n-hexane using the ratio of solvent viscosities; k, may be 10-20% high due to imperfect Dp compensation in Eq. 6. Together with k2 it gives 2 - p , - ps+is = 0.97. The parameter p , (y, in Ref. 225) can be calculated directly from Eq. 12 in Ref. 225 using the estimated k, value, the experimentally measured value of = 0.72, and the appropriate quantities in Table 1 of Ref. 225. An average value of p s = 0.138 is obtained, the range of seven independent values being 0.,125-0.147. Use of p s = 0.138 and +is = 0.72 gives pr = 0.93. While the p s value is acceptably close to %, p , is too small and if correct would require that, in contrast to anthracene, quintet pair states participate in the destruction of triplets. Such quintet involvement has in fact been suggested to account for a small but significant decrease in k2 as the strength of an applied external magnetic field is increased (223). If, for example, the process
$% 3BA*
+ 3BA*
'(BA*BA)* 3(BAeBA)*
-
'BA*
+
'BA
3BA*
+
'BA
J.
(71)
applied, p , = 0.111 and p , = 0.89 would be predicted and inhibition of the quintet - triplet interconversion for either the pair state or the monomer could account for the magnetic-field effect. Unfortunately, the analysis of the data in Ref. 225 and our own above reinterpretation (factor-of-2 errors aside) suffers from the use of an anomalously high value E, = 4.36 X lo4 M-' cm-' (226) for the 'IT absorption of BA to calculate ,C and Q,,the absorbed incident intensity (Q, = ['BA*]). It also suffers from the assumption that at the two lowest C, values used in this work the k has attained the limiting kl value. As it turns out, all these shortcomings of the treatment of the data in Ref. 215 can be overcome. The 2, value employed, which was based on the estimation of cT by ESR at 77 K in 2-methyltetrahydrof~ran~ has been shown to fail statistical tests when compared with many other E, determinations in the literature (227). On the other hand, E, = 2S6 X lo4 M-' cm-', measured using rotating-sector excitation and singlet depletion in n-hexane at 27°C (228)-conditions nearly identical to those used in Ref. 225-is in excellent agreement with independently measured values in other hydrocarbon solvents (227). Use of this lower E, and Eqs. 6 and 7 in Ref. 225 with +is = 0.72 (228) gives c, = 3.77 x lo-', where the ratio of the voltages is the empirical measure of the steady-state triplet concentration. It is now possible to use the steady-state condition directly:
74
SPIN-STATISTICALFACTORS IN DIFNSION-CONTROLLED REACTIONS
together with the relationship Q, = asN, (where 6, are the transmission factors of the attenuation filters used to alter incident intensity), to obtain least-squares fit parameters of the experimental data. Again excluding the sixth set of data from the analysis because the reported value is anomalously low, we have a = 3.06 X M, k , = 347 s-', and k2 = 1.11 X 10" M-' s-'. Using k, = 2.09 X 10" M-' s-' (see above) gives 2 - pt - ps+is = 0.529, and with k,, our derived parameters, and the appropriate experimental quantities of Table 1, Eq. 12 in Ref. 225 gives p , = 0.0785 & 0.0015. With +is = 0.72 (228), it follows that pt = 1.41. The new pt and p s values are in remarkable agreement with the spin-statistical mechanism proposed for anthracene in Eq. 70. As with anthracene, no delayed excimer fluorescence is observed for 1,2benzanthracene under these conditions (225), and the deviation of p , from % may well be due to decay from the relaxed doubly excited singlet pair state as shown in Scheme 5. A relatively smallp, = 0.092 value for 1,Zbenzanthracene has been estimated from photodimerization results in cyclohexane (229). The 1,2-benzanthracene case illustrates some of the difficulties associated with the evaluation of published TTA data. Undoubtedly, depending upon the availability of quintet, triplet, and excited singlet monomer states at or below the energy of initially formed triplet encounter pairs, exceptions to Eq. 70 and Scheme 5 will be found. The details of the mechanism proposed here may also need to be modified even for anthracene and 1,Zbenzanthracene. A careful study of the spectral distribution of the delayed fluorescence of several arenes (including BA) at -80°C in methylcyclohexane has uncovered significant S, + So (n > 1) components in the emission and has led to the conclusion that population of the highest energetically accessible monomer singlet state is the dominant process occurring from the singlet encounter pair (230). If this were also the prevailing initial step at higher temperatures and lower viscosities, relaxation directly into the doubly excited (pericyclic) minimum would be precluded, as would be the hope of observing enhanced efficiency of TTA-induced photodimerization. Departures from the mechanism in Eq. 70 and Scheme 5 could also be caused when intersystem crossing allows interconversion between encounter pairs of different multiplicity, e.g. Eq. 71. Though the above reevaluation of the 1,Zbenzanthracene data suggests strongly that, at least in n-hexane at room temperature, TTA conforms largely with Eq. 70, a role for intersystem crossing pathways is indicated by significant magnetic-field effects on k2 (223). The higher efficiency of delayed fluorescence from naphthalene TI'A in cyclohexane at room temperature is worth mentioning in this connection (201b). Independent measurements of E, for naphthalene in cyclohexane are in very good agreement (227). Using E, = 2.4 x lo4 M-' cm-' at 414 nm and the flash-kinetically determined K gives k2 = 3.3 X lo9 M-' s-' (201b), from which 2 - pt - ps+is = 0.40 is obtained by assuming k, = 4kt = 8.2 X lo9 M-' s-' from termination of benzyl radicals in cyclohexane at 25°C (148). From the determination of the efficiency of monomer delayed fluorescence (no
75
TRIPLET-TIUPLET ANNIHILATION
excimer fluorescence was observed), pdf = pska/k2 = 0.52, it follows that p, = 0.21. The value of +is for naphthalene is in the range of 0.684.82 in various solvents (200a,231). Using +is = 1 - +f = 0.77 in cyclohexane (12) givesp, = 1.44. Though the mechanism in Eq. 70 predicts p , exactly, it fails to account for ap, value which, being nearly Y9, is twice its predicted maximum. It appears that intersystem crossing at the triplet pair andor monomer stage(s) play(s) an important role in this case. Assuming that all quintet pair states are fully dissociative, the following is one of several mechanisms which would account for the results:
3N*
+ 3N*
3(NN)**
--
3N*
+
'N
(73)
Dimerizations of reactive intermediates such as diarylcarbenes and trimethylenemethanes which have triplet ground states are subject to the spin-statistical considerations which are applicable to TTA. An early example is the formation of tetramesitylethylene from triplet dimesitylcarbene, which was explained as arising from the interaction of two carbenes, one having two a spins and the other two p spins (232). That such reactions can be diffusion-controlledor nearly so was demonstrated by flash-kinetics spectroscopy (233). The disappearance of diarylcarbenes in benzene solution at 25"C, accounted for by Eq. 69, gives k2 = (5.4 k 1.6) x lo9, (3.5 k 1.1) X lo9, and (1.1 I+- 0.3) X lo9 M-' s-' for diphenylcarbene, p,p'-dibromodiphenylcarbene and p,p'-dimethyldiphenylcarbene, respectively, employing 3.0 X lo4M-' cm-' for the molar absorptivity of dibromodiphenylcarbene and 2.5 X lo4 M-' cm-' for the other two (234). To account for the deviation of these rate constants from kdif, it was suggested that quintet encounter pairs are unproductive, triplet encounter pairs may give triplet olefin, and singlet encounter pairs give ground-state olefin (233):
(2Ar2C:)
-
Ar2C=CAr2
Basing k, = 4k, = 9.7 x lo9 M-' s-' on benzyl radical termination in toluene (148), adjustedfor T/q,givesp, = 1.44 +- 0.17, 1.64 f 0.11, and 1.89 2 0.03 for the three carbenes in the same order. The pt's predicted by Eq. 74 range from 1.11, if all triplet pairs gave triplet olefin, to 1.78, if all triplet pairs were
76
SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLEDREACTIONS
unproductive. While two of the pt values fall comfortably within this range, the pt value for the methyl derivative deviates significantly from the others. It is not clear at this time why methyl substitution at a position remote from the reaction site should have such a profound effect on pt. However, the fact that S, -+ TI intersystem crossing for diphenylcarbene in hydrocarbon solvents is a very fast [ki, = 1.05 X 10" s-l(235)], possibly reversible, process may imply substituent dependent interconversion between triplet and singlet carbene pairs in Q. 74. It is of interest to note that the ESR spectra of several triplet carbenes in rigid media at low temperatures (T < 40 K) exhibit weak lines which have been assigned to quintet states arising from spin correlation of nearest-neighbor carbenes (236). The decline of the ESR signal of the trimethylenemethane triplet
3TMM in a 3 :2 mixture of isopropyl and n-propyl alcohols at 143.5 K is cleanly secondorder [ k , = 0, k2 = (2 & 0.8) X lo3M-' s-', Eq. 691 and is associated with the formation of several dimers (237). A very high viscosity, q = 2 x lo3 P, applies under these conditions. Though a good empirical value for kdif in this medium is lacking, k, = 4 4 = 1.9 x lo4 M-' s-' can be based roughly on the termination of hydroxymethyl radicals in methanol (169). It follows that 2 - pt = 0.11 2 0.05,which gives pt = 1.89 4 0.05.If dimers formed only from singlet encounter pairs and if all of these were fully productive, 2 - pt = 0.22 and pt = 1.78 would be expected.
APPENDIX The derivation of a theoretical expression for the rate constant of diffusion along a concentration gradient has been described in a straightforward manner by Collins (238) and Noyes (3), for the reaction A
+B
L
P
(A. 1)
The model assumes that when the two molecules react, the concomitant depletion of their concentration in the vicinity of the reaction leads to a concentration imbalance which is corrected by diffusion of molecules toward the reaction site. This reestablishes a uniform distribution of reactants in solution. The time delay in attaining equilibrium is a function of the diffusivities of the molecules and
APPENDIX
77
their distance from the reaction site. The motion of molecules toward the reaction site is the diffusional flux and has units of number of molecules diffusing per unit of time. If, for example, as in Eq. A. 1 , one molecule of product is formed, then one molecule each of A and B must diffuse into the reaction site for an equilibrium once again to be attained. The applicable relationship, known as Fick’s law, is given for a spherically symmetrical system by 4 d D -dc dr
=
dn dt
where D represents the diffusion coefficients of the reactants, 47r3 is the area of a spherical surface of radius r through which the reactants must pass to reach the reaction site, dnldr or a, the diffusional flux, is the number of molecules crossing the surface of the sphere per unit time, and dcldr is the change in reactant concentration along the radius r . To apply the gradient-flux model it is generally assumed that the reactive center, in this case the molecule A, remains reactive as molecules of B diffuse toward it. It has been pointed out that this assumption requires no leap of faith, since, for example, it applies exactly in the catalytic conversion of B to products
Nonetheless, for the general case represented by Eq. A . l , the condition is not valid, and as Collins states, “After such a reaction there is no longer an A particle at the center, and the concentration gradient so formed seems to have lost its interest” (238). To circumvent this and other difficulties with the model, Collins resorts to a sophisticated mathematical treatment which distinguishes between “reacted” and “unreacted” A and B molecules. Since both simple and sophisticated treatments give the same result, the initial simple model has generally been adopted. Confusion arises when the model is extended to the reaction
Since for both Eqs. A . l and A.4 the model designates A as a permanently reactive center, one B species for Eq. A.l and one A species for Eq. A.4 are assumed to be destroyed for each reactive event. This leads to the conclusion that the diffusional flux for B in Eq. A.l is identical to the diffusional flux for A in Eq. A.4. However, in real reactions where both reactants are destroyed, it is clear that the diffusional flux for A in Eq. A.4 should be twice as large as the flux for B in Eq. A.1.
78
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS
We suggest that the designation of a permanently reactive A center is unnecessary for the derivation. It appears to arise from an attempt to ascribe chemical significance to a coordinate translation which facilitates the mathematical solution. Instead of the permanently reactive A center we assume that a random encounter between the reactantss A and B leads to their concomitant concentration depletion, which initiates a diffusional flux for each toward the reaction site. The origin of our coordinate system is now a concentration hole toward which A and B species diffuse radially. If we shift the origin of our coordinate system from the concentration hole to the nearest A, the resulting mathematical description is identical to that of the older model. The difference is that it is now conceptually clear that the concentration gradient for A in Eq. A.4 will be twice as large as the concentration gradient for B in J3q. A. 1.
The crossing of a molecule B of the sphere with r = p, where p is the sum of the two molecular radii rA and r,, is equivalent to a collision between A and B and is assumed as a necessary and sufficient condition for a reaction to occur. Integration of Eq. A.2 with the boundary conditions r = p and r = w gives
c, - cp =
a) 47FpD
where cp is the concentration of B molecules within the reaction sphere and c, is the concentration of B in the bulk solution, [BJ. The relationship of the diffusional flux to the microscopic reaction rate, i.e. for one reactive center, is given by
where k is the microscopic rate constant. Substitution of Eq. A.6 into Eq. A.5 gives cp =
C,
1
+ (k/41~pD)
The overall observed rate, Robsd,for product formation is given by the loss of B molecules:
where kobsd is the observed rate constant, cA is the concentration of reactive centers, and c, = [B] is, again, the concentration of B in the bulk solution. In
79
APPENDIX
a steady-state system, the flux is just maintained, so that the concentration gradient remains unchanged. In such a situation the flux created by all of the microscopic reaction centers is given by
From Eqs. A.6, A.7, and A.9, a value for kobsd as a function of k and 47rpD is obtained: =
1
+
k (kI47rpD)
47rpDk 47rpD k
+
(A. 10)
Since all collisions are reactive, kobsd is kdif. The term 47rpD is the rate constant for diffusion resulting from the concentration gradient. The microscopic rate constant k is the limiting rate constant for infinitely fast translatory diffusion D = w. In practice k has been assumed to be no greater than the rate constant for collisions in the vapor phase (4). = kdif = 47rpD. If the term 47rpD << k, then Eq. A.10 reduces to This condition applies to most organic solvents in which the diffusivity of the reactants is low. At low viscositiesEq. A. 10 must be used for diffusion-controlled rate constants.
B. A + A + P The major departure from the previous case is that with two A molecules reacting at the reactive center, the diffusionalflux of A molecules toward the concentration hole is twice the microscopic rate of reaction: @ = 2kcp
(A. 11)
Substitution of Eq. A. 11 into Eq. A S yields c,
-
2k cp cp --47rpD
k cp 27rpD
(A. 12)
The observed rate of product formation is half that of reactant loss, (A. 13) Assuming a system at steady state, the flux of A molecules toward the reaction center is twice the rate of product formation:
80
SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED MACTlONS
(A. 14) By combining Eqs. A. 11-A. 14 the observed rate constant can be expressed as a function of 2 ~ p D and k: ed
=
1
+
k (k/2.rrpD)
k
+
2.rrpDk 2npD
=
k$
(A.15)
+
As can be seen, for a system of A A + P the rate constant for diffusion is half that for the A B case, Gt = 1/2kdif, Eq. 4.
+
ACKNOWLEDGMENTS Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of the preparation of this article. Additional support was received through NSF Grant CHE 84-00706.
REFERENCES 1. N. J. Turro, Modern Molecular Photochemistry, Benjamin, Menlo Park, California, 1978. 2. A. M. North, Quart. Rev. 18, 421 (1964). 3. D. M. Bishop and K. J. Laidler, J . Chem. Phys. 42, 1688 (1965). 4. (a) R. M. Noyes, in Progress in Reaction Kinetics, Vol. 1, G . Porter, Ed., Pergamon Press, Oxford, 1961, p. 129. (b) R. M. Noyes, J . Am. Chem. Soc. 86, 4529 (1964). 5 . A. H. Alwattar, M. D. Lumb, and J. B. Birks, in Organic Molecular Photophysics, Vol. 1, J. B. Birks, Ed., Wiley, London, 1973, p. 403. 6. H.-H. Schuh and H. Fischer, Helv. Chim. Acta 61, 2130 (1978) and references cited. 7. A. Spernol and K. Wirtz, 2. Nafurforsch. A 8, 522 (1953). 8. A. Gierer and K. Wirtz, 2. Naturjorsch. A 8, 532 (1953). 9. F. Wilkinson, in Singlet Oxygen, B. Ranby and J. F. Rabek, Eds., Wiley, New York, 1978, p. 27. 10. A. U. Khan, in Singlet Oxygen, Vol. 1, A. A. Frimer, Ed., CRC Press, Boca Raton, Florida, 1985, p. 39. 11. W. R. Ware, J. Phys. Chem. 66, 455 (1962).
REFERENCES
81
12. I. B. Berlman, Handbook of Fluorescence Spectra of Aromatic Molecules, 2nd ed., Academic Press, New York, 1971. 13. R. Potashnik, C. R. Goldschmidt, and M. Ottolenghi, Chem. Phys. Lett. 9 404 (1971). 14. B. E. Algar and B. Stevens, J. Phys. Chem. 74, 3029 (1970). 15. C. S. Parmenter and J. D. Rau, J. Chem. Phys. 51, 2242 (1969). 16. IUPAC Analytical Chemistry Division, Commission on Solubility Data, “Oxygen and Ozone,” in Solubility Data Series, R. Battino, Ed., Vol. 7, Pergamon, Oxford, 1981. 17. P. Pringsheim, Fluorescence and Phosphorescence, Interscience, New York, 1949, p. 333. 18. E. J. Bowen, Trans. Faruday SOC. 50, 97 (1954). 19. L. K. Patterson, G. Porter, and M. R. Topp, Chem. Phys. Lett. 7, 612 (1970). 20. Reference 16, p. 142. 21. J. Saltiel, D. E. Townsend, B. D. Watson, P. Shannon, and S. L. Finson, J. Am. Chem. SOC. 99, 884 (1977). 22. (a) D. F. Evans, J. Chem. SOC. 345 (1953). (b) H. Tsubomura and R. S. Mulliken, J. Am. Chem. SOC.82, 5966 (1960). 23, J. Saltiel, D. E. Townsend, and A. Sykes, J. Am. Chem. SOC. 105,2530 (1983) and references cited. 24. I. B. Berlman, H. 0. Wirth, and 0. J. Steingraber, J. Am. Chem. SOC. 90, 566 (1968). 25. J. Saltiel, D. E. Townsend, B. D. Watson, andP. Shannon, J . Am. Chem. SOC. 97,5688 (1975). 26. B. Stevens and B. E. Algar, J. Phys. Chem. 72, 2582 (1968). 27. Reference 16, p. 150. 28. J. L. Charlton, D. E. Townsend, B. D. Watson, P. Shannon, J. Kowalewska, and J. Saltiel, J . Am. Chem. SOC. 99, 5992 (1977). 29. 0. L. J. Gijzeman, F. Kaufman, and G. Porter, J . Chem. Soc., Faraduy Trans. 2 69, 708 (1973). 30. G. Porter and M. R. Wright, Discussions Faraday SOC. 27, 18 (1959). 31. B. Stevens and B. E. Algar, Ann. N.Y. Acad. Sci. 171, 50 (1970). 32. A. A. Lamola, in Energy Transfer and Organic Photochemistry, A. A. LamolaandN. J. Turro, Eds., Wiley-Interscience,New York, 1969, p. 17. 33. K. Kawaoka, A. U. Khan, and D. R. Kearns, J . Chem. Phys. 46, 1842 (1967); 47, 1842 (1968). 34. W. Siebrand, J. Chem. Phys. 44, 4055 (1966). 35. 0. L. J. Gijzeman and F. Kaufman, J. Chem. SOC., Faraday Trans. 2 69, 721 (1973).
82
SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS
36. J. Saltiel, S. Ganapathy, andC. Werking, J. Phys.Chem. 91,2755 (1987). 37. For a review see J. Saltiel and J. L. Charlton, in Rearrangements in Ground and Excited States, Vol. 3 , P. de Mayo, Ed., Academic Press, New York, 1980, p. 25. 38. H. Gomer and D. Schulte-Frohlinde, J. Phys. Chem. 85, 1835 (1981). 39. J. Saltiel, A. D. Rousseau, and B. Thomas, J. Am. Chem. SOC. 105,7631 (1983). 40. J. Saltiel, G. R. Marchand, E. Kirkor-Kaminska, W. K. Smothers, W. B. Mueller, and J. L. Charlton, J. Am. Chem. SOC. 106, 3144 (1984). 41. J. Saltiel and B. Thomas, Chem. Phys. Lett. 37, 147 (1976). 42. D. V. Bent and D. Schulte-Frohlinde, J. Phys. Chem. 78, 446 (1974). 43. D. V. Bent and D. Schulte-Frohlinde, J. Phys. Chem. 78, 451 (1974). 44. J. Saltiel and B. Thomas, J. Am. Chem. SOC. 96, 5660 (1974). 45. G. J. Hoytink, Accounts Chem. Res. 2 , 114 (1969). 46. W. G. Herkstroeter, J. Am. Chem. SOC.97, 4161 (1975). 47. C. S. Foote and R. W. Denny, J. Am. Chem. SOC. 90, 6233 (1968). 48. P. B. Merckel and D. R. Keams, J. Am. Chem. SOC. 94, 7244 (1972). 49. A. Farmilo and F. Wilkinson, Photochem. Photobiol. 18, 447 (1973). 50. R. A. Caldwell and R. E. Schwerzel, J. Am. Chem. SOC.94, 1035 (1972); 95, 1382 (1973). 51. J. Saltiel, D. W. L. Chang, E. D. Megarity, A. D. Rousseau, P. T. Shannon, B. Thomas, and A. K. Uriarte, J. Pure Appl. Chem. 41, 559 (1975). 52. A. Gamer and F. Wilkinson, in Singlet Oxygen, B. Ranby and J. F. Rabek, Eds., Wiley, New York, 1978, p. 48. 53. A. A. Gorman and M.A. J. Rodgers, Chem. Phys. Lett. 120,523 (1985). 54. J. Saltiel, P. T. Shannon, 0. C. Zafiriou, and A. K. Uriarte, J . Am. Chem. SOC. 102, 6799 (1980). 55. H. Gomer and D. Schulte-Frohlinde, Ber. Bunsenges. Phys. Chem. 81, 713 (1977). 56. H. Gomer, J. Phys. Chem. 86, 2028 (1982). 57. S. Lazare, R. Bonneau, and R. Lapouyade, J. Phys. Chem. 88,18 (1984). 58. H. Gorner, D. W. Eaker, and J. Salliel, J. Am. Chem. SOC. 103, 7164 (1981). 59. H. Gomer, J. Photochem. 19, 343 (1982). 60. T. Arai, H. Sakuragi, K. Tokumaru, Y.Sakaguchi, J. Nakamura, and H. Hayashi, Chem. Phys. Lett. 98, 40 (1983). 61. R. Bonneau, J. Am. Chem. SOC. 104, 2921 (1982). 62. T. G. Truscott, E. J. Land, and A. Sykes, Photochem. Photobiol. 17,43 (1973).
REFERENCES
63. 64. 65. 66. 67.
68. 69. 70. 71.
72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86.
83
R. Bonneau, J. Am. Chem. SOC. 102, 3816 (1980). J. H. Rao, R. Bonneau, and D. I. Schuster, private communication. K. H. Grellmann and P. Hentzschel, Chem. Phys. J A t . 53, 545 (1978). D. Schulte-Frohlinde, H. Herrmann, and G. M. Wyman, Z . Phys. Chem. Neue Folge 101, 115 (1976). S. K. Chattopadhyay, C. V. Kumar, and P. K. Das, Photochem. Photobiol. 42, 17 (1985). D. I. Schuster, D. A. Dunn, and R. Bonneau, J. Photochem. 28, 413 (1985). J. Saltiel, G.-E. Khalil, and K. Schanze, Chem.Phys. Lett. 70,233 (1980). W. G. Herkstroeter, D. P. Specht, and S. Farid, J. Photochem. 21, 325 (1983). (a) R. Bonneau, J. Jousot-Dubien, L. Salem, and A. J. Yarwood, J. Am. Chem. SOC. 98, 4329 (1976). (b) W. G. Dauben, H. C. H. A. van Riel, C. Hauw, F. Leroy, J. Jossot-Dubien, and R. Bonneau, J. Am. Chem. SOC. 101, 1901 (1979). (c) W. G. Dauben, H. C. H. A. van Riel, J. D. Robbins, and G. J. Wagner, J. Am. Chem. SOC. 101, 6363 (1979). T. Arai, H. Sakuragi, and K. Tokumaru, Chem. Lett. 1335 (1980). J. Saltiel and D. W. Eaker, Chem. Phys. Left. 75, 209 (1980). T. Arai, T. Karatsu, H. Sakuragi, and K. Tokumaru, Tetrahedron Lett. 24, 2873 (1983). T. Karatsu, T. Arai, H. Sakuragi, and K. Tokumaru, Chem. Phys. Lett. 115, 9 (1985). H. Gomer and D. Schulte-Frohlinde, Ber. Bunsenges. Phys. Chem. 82, 1102 (1978). H. GornerandD. Schulte-Frohlinde, Chem.Phys. Lett. 66,363 (1979). A. D. Kirsch and G. M. Wyman, J. Phys. Chem. 81, 413 (1977); 79, 543 (1975). J. R. Hurst, J. D. McDonald, and G. B. Schuster, J. Am. Chem. Sac. 104, 2065 (1982). 3. G. Parker and W. D. Stanbro, J . Am. Chem. Soc. 104, 2067 (1982). P. R. Ogilby and C. S. Foote, J. Am. Chem. SOC.104, 2069 (1982). T. Wilson and A. M. Halpem, J. Am. Chem. SOC.102, 7279 (1980). A. Gamer and F. Wilkinson, J. Chem. SOC., Faraday Trans. 2 72, 1010 (1976). A. Gamer and F. WiUcinson, Chem. Phys. Lett. 45, 432 (1977). A. A. Gorman, G. Lovering, and M. A. J. Rodgers, J. Am. Chem. SOC. 100, 4527 (1978). B. E. Holme, E. J. Land, and G. 0. Phillips, J. Chem. Soc., Faraday Trans. Z68, 2003 (1972).
84
SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLEDREACTIONS
87. E. W. Forster and K. M. Grellman, Chem. Phys. Lett. 14, 536 (1972). 88. A. Safarzadeh-Amiri, D. A. Condirston, R. E. Verrall, and R. P. Steer, Chem. Phys. Lett. 77, 99 (1981). 89. See Ref. 12. The quenching of the fluorescence of several indoles in cyclohexane is normal (kzx = k,J and does not reveal any static-quenching contributions. 90. D. V. Bent and E. Hayon, J.Am. Chem. SOC.!37,2599,2606,2612 (1975). 91. H. Ishida and H. Tsubomura, J. Photochem. 2, 285 (1974). 92. R. H. Young and D. R. Brewer, in Singlet Oxygen, B. Ranby and J. F. Rabek, Eds., Wiley, New York, 1978, p. 36. 93. P. B. Merkel and W. G. Herkstroeter, Chem. Phys. Lett. 53,350 (1978). 94. K. C. Wu and A. M. Trozzolo, J. Phys. Chem. 83, 2823 (1979). 95. B. Stevens, K. L. Marsh, and J. A. Barltrop, J. Phys. Chem. 85, 3079 (1981). 96. K. Gollnick, T. Franken, G. Schade, and G. Dorhofer, Ann. N.Y.Acud. Sci. 171, 89 (1970). 97. K. C. Wu and A. M. Trozzolo, J. Phys. Chem. 83, 3180 (1979). 98. P. B. Merkel and D. R. Kearns, J. Am. Chem. SOC. 97, 462 (1975). 99. C. S. Foote and T.-N. Ching, J. Am. Chem. SOC. 97, 6209 (1975). 100. D. F. Evans and J. N. Tucker, J. Chem. Soc., Faraday Trans. 2 72, 1661 (1976). 101. B. Stevens and J. A. Ors, J. Phys. Chem. 80, 2164 (1976). 102. A. A. Gorman, I. Hamblett, and M. A. J. Rodgers, J. Am. Chem. SOC. 106, 4679 (1984). 103. C. N. Knox, E. J. Land, andT. G. Truscott, Photochem. Photobiol. 43, 359 (1986). 104. R. D. Caldwell and H. Misawa, private communication. 105. G. Rossbroich, N. A. Garcia, and S. E. Braslavsky, 1. Photochem. 31, 37 (1985). 106. A. A. Gorman, I. R. Gould, and I. Hamblett, Tetruhedron Left. 21, 1087 (1980). 107. A. A. Gorman, I. Hamblett, and M. A. Rodgers, J. Photochem. 25, 1 15 (1984). 108. K. C. Wu and A. M. Trozzolo, J. Photochem. 10, 407 (1979). 109. S. K. Chattopadhyay, C. V. Kumar, andP. K. Das, Photochem. Photobiol. 24, 1 (1984). 110. S . K. Chattopadhyay, C. V. Kumar, and P. K. Das, Photochem. Photobiol. 42, 17 (1985). 111. G. J. Smith, J. Chem. SOC., Faraday Trans. 2 79, 1 (1983).
REFERENCES
85
112. C. Tanielian, L. Golder, and C. Wolff, J . Photochem. 25, 117 (1984) and 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134.
135.
136. 137. 138.
references cited. A.A.GormanandM.A. J.Rodgers, J.Am. Chem.Soc. 108,5074(1986). E. Reddi, G. Jori, M. A. J. Rodgers, and J. D. Spikes, Photochem. Photobiol. 38, 639 (1983). K. Gollnick, Adv. Photochem. 6, 1 (1968). B. Stevens, J . Phys. Chem. 85, 3555 (1981). D. R. Kearns, J . Am. Chem. SOC.91, 6554 (1969). B. Stevens, J . Photochem. 3, 393 (1974/5). G. 0. Schenck, Naturwiss. 35, 28 (1948); 40,205, 229 (1953). G. 0. Schenck, Angew. Chem. 69, 579 (1957). K. Gollnick and G. 0. Schenck, Pure Appl. Chem. 9, 507 (1964). C. S. Foote and S. Wexler, J. Am. Chem. SOC.86, 3879, 3880 (1964). E. J. Corey and W. C. Taylor, J . Am. Chem. SOC.86, 3881 (1964). C. S. Foote, Acc. Chem. Res. 1, 104 (1968). B. Stevens, Acc. Chem. Res. 6, 90 (1973). G. Quinkert, Pure Appl. Chem. 9, 607 (1964). J. Saltiel and H. C. Curtis, Mol. Photochem. 1, 239 (1969). Y. Sawaki and C. S. Foote, J . Org. Chem. 48,4934 (1983) and references cited. J. Franck and E. Rabinowitch, Trans. Faraday SOC.30, 120 (1934). N. C. Yang, E. D. Feit, M. H. Hui, N. J. Turro, and J. C. Dalton, J . Am. Chem. SOC.92, 6974 (1970). B. Blank, A. Henne, and H. Fischer, Helv. Chim. Acta 57, 920 (1974). H. Schuh, E. J. Hamilton, Jr., H. Paul, and H. Fischer, Helv. Chim. Acta 57, 2011 (1974). M. J. Perkins and B. P. Roberts, J . Chem. SOC. Perkin Trans. II, 297 (1974); 77 (1975). D. M. Bartels, R. G. Lawler, and A. D. Trifunac, J . Chem. Phys. 83, 2686 (1985). J. C. Scaiano, in Landolt 1 Bornstein, Numerical Data and Functional Relationships in Science and Technology, New Series 11, 13e, Radical Reaction Rates in Liquids, Ed. H . Fischer, Springer-Verlag, New York, 1985, p. 294. R. A. Caldwell, T. Majima, and C. Pac, J . Am. Chem. SOC. 104, 629 (1982). J. C. Scaiano, Tetrahedron 38, 819 (1982). R. A. Caldwell, S. N. Ohawan, and T. Majima, J. Am. Chem. SOC. 106, 6454 (1984).
86
SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS
139. H. Kobashi, R. Kondo, H. Ikowa, andT. Morita, Bull. Chem. Soc. Jpn. 57, 1197 (1984). 140. S. Takamuku and W. Schnabel, Chem. Phys. Lett. 69, 399 (1980). 141. R. A. Caldwell, H. Sakuragi, and T. Majima, J . Am. Chem. Soc. 106, 2471 (1984). 142. G. L. Closs and R. J. Miller J. Am. Chem. SOC.103, 3586 (1981). 143. S. C. Frelich and K. S. Peters, J . Am. Chem. Soc. 103, 6255 (1981). 144. M. V. Encinas and J. C. Scaiano, J. Chem. Soc. Perkin Trans. ZZ, 56 (1980). 145. J. L. Gainer and A. B. Metzner, AZCHE-I. Chem. Symp. Ser., No. 6, 74 ( 1965). 146. R. J. Hogemann and H. A. Schwartz, J. Phys. Chem. 71, 2694 (1967). 147. R. D. Burkhart, J. Am. Chem. Soc. 90, 273 (1968); J. Phys. Chem. 7 3 , 2703 (1969). 148. M. Lehni, H. Schuh, and H. Fischer, J. Chem. Kin. 11, 705 (1979) and references cited. 149. P. S. Engel, J. Am. Chem. Soc. 92, 6074 (1970). 150. H. Fischer, B. Blank, and P. G. Mennitt, IUPAC Spec. Lect., 23rd Congress Pure Appl. Chem. 4, 1 (1971). 151. N. J. Turro, M-F. Chow, C-J. Chung, and B. Kraeutler. J. Am. Chem. Soc. 103, 3886 (1981). 152. N. J. TUITO, M-F. Chow, C-J. Chung, Y. Tanimoto, and G. Weed, J . Am. Chem. SOC.103, 4574 (1981). 153. N. J. Turro, C-J. Chung, G. Jones, 11, and W. G. Becker, J. Phys. Chem. 86, 3677 (1982). 154. M. B. Zimmt, C. Doubleday, Jr., and N. J. Turro, J . Am. Chem. SOC. 106, 3363 (1984). 155. W. K. Robbins and R. H. Eastman, J. Am. Chem. Soc. 92, 6076, 6077 (1970). 156. G. Brunton, H. C. McBay, and K. U. Ingold, J. Am. Chem. SOC. 99, 4447 (1977). 157. G. Quinkert, K. Opitz, W. W. Wiersdrorff, and J. Weinlich, Tetrahedron Lett., 1863 (1963). 158. H. Paul and H. Fischer, Helv. Chim. Acra 56, 1575 (1973). 159. T. 0. Meiggs, L. I. Grossweiner, and S. I. Miller, J. Am. Chem. SOC. 94, 7981, 7986 (1972). 160. H. Langhals and H. Fischer, Chem. Ber. 111, 543 (1978). 161. G. J. Kruger and R. Weiss, Z. Naturforsch. A. 25, 777 (1970). 162. D. E. O’Reilly and E. M. Peterson, J. Chem. Phys. 56, 2262 (1972). 163. S. A. Sanni, C. J. D. Fell, and H. P. Hutchinson, J. Chem. Eng. Data 16, 424 (1971).
REFERENCES
87
164. I. Kamal and E. McLaughlin, in Proceedings of the N Symposium on Thermophysicul Properties, Vol. 4, J . R. Moszynski, Ed., American Society of Mechanical Engineers, New York, 1968, p. 278. 165. J. T. Edward, J. Chem. Ed. 47, 261 (1970). 166. J. Lipscher and H. Fischer, J. Phys. Chem. 88, 2555 (1984). 167. H. J. Hefter, C-H. S. Wu, and G. S. Hammond, J. Am. Chem. SOC.95, 851 (1973). 168. (a) H. Paul and C. Segaud, J. Chem. Kin. 12, 637 (1980). (b) H. Paul, Chem. Phys. 15, 115 (1975). 169. H. S . Sandhu, J. Mag. Res. 17, 34 (1975). 170. M. Eigen, Z. Phys. Chem. (Frankjkrt am Main) 1, 176 (1954). 171. P. J. Wagner and I. Kochevar, J. Am. Chem. SOC.90, 2232 (1968). 172. D. Rehm and A. Weller, Ber. Bunsenges. Phys. Chem. 73, 834 (1969); Zsr. J . Chem. 8, 259 (1970). 173. V. Balzani, F. Bolletta, and F. Scandola, J. Am. Chem. SOC. 102, 2152 (1980). 174. A. Weller, Z . Phys. Chem. (Wiesbaden) 130, 129 (1982). 175. R. W. Gurney, Ionic Processes in Solution, McGraw-Hill, New York, 1953. 176. W. R. Ware and J. S. Novros, J. Phys. Chem. 70, 3246 (1966). 177. A. Burshtein, I. V. Khudyakov, and B. I. Yakobson, Prog. Reaction Kinetics 13, 221 (1984). 178. D. L. Dexter, J . Chem. Phys. 21, 836 (1953). 179. K. Sandros, Acta Chem. S c a d . 18, 2355 (1964). 180. W. G. Herkstroeter and G. S. Hammond, J. Am. Chem. SOC.88, 4769 (1966). 181. W. G. Herkstroeter, J. Am. Chem. SOC. 97, 3090. 4161 (1975). 182. A. D. Osborne andG. Porter, Proc. Roy. Soc. London, Ser. A 284,9 (1965). 183. F. S. Dainton, M. S. Henry, M. J. Pilling, and P. C. Spencer, J. Chem. Soc., Faraday Trans. 1, 73, 257 (1977). 184. R. W. Anderson, Jr., R. M. Hochstrasser, H. Lutz, and G. W. Scott, J. Chem. Phys. 61,2500 (1974). 185. A range of 3.6-3.9 is obtained if interpolated& values from the plot of Dexpvs. rlrL in Ref. 7 are employed (54). 186. M. R. Mirbach, V. Ramamurthy, M. J. Mirbach, N. J. Turro, and P. J. Wagner, Nouv. J. Chem. 4, 471 (1980). 187. (a) F. Wilkinson and C. Tsiamis, J. Chem. SOC., Faraday Trans. 11, 77, 1681 (1981). (b) J. Phys. Chem. 85, 4153 (1981). (c) J . Am. Chem. SOC. 105, 767 (1983). 188. F. Wilkinson and C . Tsiamis, Znorg. Chem. 23, 3571 (1984).
88
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS
189. B. Stevens and E. Hutton, Nature (London) 186, 1045 (1960). 190. (a) C. A. Parker and C. G. Hatchard, Proc. Chem. Soc., 147 (1962). (b) Trans. Faraday SOC. 59, 284 (1963). (c) C. A. Parker, Adv. Photochem. 2, 305 (1964). 191. (a) H. Linschitz and K. Sarkanen, J . Am. Chem. SOC. 80, 4826 (1958). (b) H. Linschitz and L. Pekkarinen, J. Am. Chem. SOC.82,2411 (1960). (c) H. Linschitz, C. Steel, and J. A. Bell, J. Phys. Chem. 66,2574 (1962). 192. (a) G. Jackson, R. Livingston, and A. Pugh, Trans. Faraday SOC.56, 1635 (1960). (b) G. Jackson and R. Livingston, J. Chem. Phys. 35, 2182 (1961). (c)R. Livingston and W. R. Ware, J. Chem. Phys. 39,2593 (1963). 193. G. Porter and M. Wright, J . Chim. Phys. 705, 2593 (1958). (b) Discuss. Faraday SOC.27, 18, 94 (1959). 194. A. R. Watkins, 2. Phys. Chem. (Frankfurt am Main)96, 125 (1975). 195. K. H. Grellmann and H.-G. Scholz, Chem. Phys. ktt. 62, 64 (1979). 196. J. Saltiel, G. R. Marchand, W. K. Smothers, S. A. Stout, and J. L. Charlton, J. Am. Chem. SOC.103, 7159 (1981). 197. (a) R. Bensasson and E. J. Land, J. Chem. Soc., Trans. Faraday SOC. 67, 1904 (1971). (b) M. B. Ledger and M. B. Salmon, J. Chem. SOC., Faraday Trans. 2, 72, 883 (1976). 198. E. G. Meyer and B. Nickel, 2. Naturforsch. 35a, 503 (1980). 199. (a) W. R. Dawson and M. W. Windsor, J. Phys. Chem. 72, 3251 (1968). (b) J. B. Birks and D. J. Dyson, Proc. R. SOC.London, Ser. A 275, 135 (1963). (c) G. Weber and F. W. J. Teale, J . Chem. Soc., Trans. Faraday SOC.53,646 (1957). (d) W. H. Melhuish, J. Phys. Chem. 65,229 (1961). 200. (a) A. R. Horrocks and F. Wilkinson, Proc. R. SOC.London, Ser. A 306, 257 (1968). (b) 7’.Medinger and F. Wilkinson, Trans. Faraaky SOC. 61, 620 (1965). (c) R. P. DeToma and D. 0. Cowan, J. Am. Chem. SOC. 97, 3283 (1975). 201. (a) K. Kikuchi, H. Kokubun, and M. Koizumi, Bull. Chem. SOC.Jpn. 41, 1545 (1968). (b) F. Tfibel and L. Lindqvist, Chem. Phys. 10,471 (1975). (c) D. K. K. Liu and L. R. Faulkner, J. Am. Chem. SOC.100,2635 (1978). 202. J. Saltiel, G. R. Marchand, R. Dabestani, and J. M. Pecha, Chem. Phys. Lett. 100, 219 (1983). 203. H. L. J. Backstrom andK. Sandros, Acra Chem. Scad. 12,823 (1958). 204. J. Saltiel, Sum. Prog. Chem., 2 , 239 (1964). 205. J. L. Charlton, R. Dabestani, and J. Saltiel, J. Am. Chem. SOC. 105, 3473 (1983). 206. T. Vember, T. V. Vaselova, I. E. Obyknovennaya, A. Cherkasov, and V, Shirokov, Izv. Akad. Nauk SSSR, Ser. Fiz. 37, 837 (1973). 207. J. Saltiel, D. E. Townsend, B. D. Watson, P. Shannon, and S. L. Finson, J . Am. Chem. SOC. 99, 884 (1977).
REFERENCES
208. 209. 210. 21 1. 212.
213. 214. 215. 216. 217. 218. 219. 220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233.
89
E. J. Bowen, Trans. Faraday SOC. 50, 97 (1954). W. R. Ware, J. Am. Chem. SOC.83, 4374 (1961). V. G. Krishna, J. Chem. Phys. 46, 1735 (1967). (a) J. Michl, Pure Appl. Chem. 41,507 (1975). (b) Photochem. Photobiol. 25, 141 (1977) and references cited. For early work see especially: (a) H. C. Longuet-Higgins and E. W. Abrahamson, J. Am. Chem. SOC.87,2045 (1965). (b) H. E. Zimmerman, J. Am. Chem. SOC. 88, 1566 (1966). (c) W. Th. A. M. van der Lugt and L. J. Oosterhoff, J. Am. Chem. SOC.91, 6042 (1969). B. Stevens, Chem. SOC. Ann. Reports A , 29 (1974). R. A. Caldwell, J. Am. Chem. Soc., 102, 4004 (1980). J. Saltiel, S. Ganapathy, and B. W. Atwater, J. Am. Chem. SOC. 109, 1209 (1987). B. R. Henry and J. L. Charlton, J. Am. Chem. SOC.95, 2782 (1973). K. H. Grellmann and H.-G. Scholz, Chem. Phys. Lett. 62, 64 (1979). G. N. R. TripathiandM. R. Fisher, Chem. Phys. Lett. 104,297 (1984). J. Saltiel, B. W. Atwater, R. Dabestani, and R. Northup, unpublished results. E. C. Lim and H. R. Bhattacharjee, Chem. Phys. Lett. 9, 249 (1971). E. C. Lim and H. R. Bhattacharjee, J. Chem. Phys. 55, 5126 (1971). M. B. Zimmt, C. Doubleday, Jr., and N. J. Turro, J. Am. Chem. SOC. 108, 3618 (1986), and references cited. L. E. Manring, K. S. Peters, G. Jones, 11, and W. R. Bergmark, J. Am. Chem. SOC.107, 1485 (1985). See, e.g.: J. Spichtig, H. Bulska, and H. Labhart, Chem. Phys. 15, 279 (1976). K. Lendi, P. Gerber, and H. Labhart, Chem. Phys. 18,449 (1976); 20, 145 (1977). B. Dick and B. Nickel, Chem. Phys. 78, 1 (1983). H. Staerk, J . Lumin. 11, 413 (1976). J. S. Brinen, J. Chem. Phys., 49, 586 (1968). I. Carmichael and G. L. Hug, J. Phys. Chem. Ref. Data 15, 1 (1986). W. Heinzelmann and H. Labhart, Chem. Phys. Lett. 4, 20 (1969). A. Costellan, Ph.D. Dissertation, University of Bordeaux I, Bordeaux, France, 1974. B. Nickel, Hetv. Chim. Acta 61, 198 (1978). F. Wilkinson, in Organic Molecular Photophysics, Vol. 2, J. B. Birks, Ed., Wiley, London, 1975, p. 95. H. E. Zimmerman and D. H. Paskovich, J. Am. Chem. SOC.86, 2149 (1964). G. L. Closs and B. E. Rabinow, J. Am. Chem. SOC.98, 8190 (1976).
90
SPIN-STATISTICALFACTORS IN DIFFUSION-CONTROLLEDREACTIONS
234. A. M. Trozzoloand W. A. Gibbons, J . Am. Chem. SOC.89,239(1967). 235. (a) K. B. Eisenthal, N. J. Turro, M. Aikawa, J. A. Butcher, Jr., C. DuPuy, G. Hefferon, W. Hetherington, and M. J. McAuliffe, J . Am. Chem. SOC. 102, 6563 (1980). (b) E. V. Sitzmann, J. Langan, and K. B. Eisenthal. J . Am. Chem. SOC.106, 1868 (1984). 236. H. Murai, J. R i b , M. Torres, and 0. P. Strausz, J . Am. Chem. SOC. 103, 6422 (198 1) and references cited. 237. M. S. Platz and J. A. Berson, J . Am. Chem. SOC.98, 6743 (1976). J. A. Berson, Acc. Chem. Res. 11, 446 (1978). 238. F. C. Collins and G. E. Kimball, J . Colloid Sci. 4, 425 (1949).
Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS James Guillet Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 1Al
CONTENTS I. Introduction II. Molecular motion in polymeric solids 111. Diffusionin polymericsolids Iv. Theory of diffusionand permeabilityin polymers V. Solubilityand diffusion VI . Temperature coefficientsfor diffusion VII. Cage reactions VIII. The internal viscosity of polymeric solids Ix. Studiesof cage reactions in polymers X. Photochemistryof polymerscontainingketone groups XI. Polymersfor photolithography XII. Sy nchrotron-radiationstudies xIII. Polyacrylophenones XIV . The photo-Fries reaction xv. Cis-trans isomerization XVI. Photocyclization XVII . Conclusions References 91
Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.
92
PHOTOCHEMISTRY AND MOLECULAR MOTION INSOLID AMORPHOUS POLYMERS
I. INTRODUCTION The purpose of this chapter is to review the kinetics and mechanisms of photochemical reactions in amorphous polymer solids. The classical view for describing the kinetics of reactions of small molecules in the gas phase or in solution, which involves thermally activated collisions between molecules of approximately equivalent size, can no longer be applied when one or more of the molecules involved is a polymer, which may be thousands of times more massive. Furthermore, the completely random motion of the spherical molecules illustrated in Fig. la, which is characteristic of chemically reactive species in both gas and liquid phase, must be replaced by more coordinated motion' when a macromolecule is dissolved or swollen in solvent (Fig. lb). Furthermore, a much greater reduction in independent motions must occur when one considers a solid polymer matrix illustrated in Fig. lc. According to the classical theory of thermal reactions the collisional energy available in the encounter must be sufficient to transfer at least one of the reacting species to some excited-state complex from which the reaction products are derived, The random thermal motion thus acts as an energy source to drive chemical reactions. The restrictions on motion described in Fig. 1 will not alter the average thermal energy of the system, but may result in a different distribution of energy between colliding partners. For example, it may require more collisional energy to induce the excited state in a large polymer molecule which has many degrees of freedom than in a small molecule which has fewer alternative modes of dissipating the energy. Another factor which affects the reactivity of polymer molecules is that the reactants must be expected to achieve a particular geometrical relationship with respect to each other in order to form the excited complex from which reaction occurs. If mobility is severely restricted, this geometry may not be achievable within the lifetime of the excitation, and chemists not familiar with macromolecular reactions might assume that the restrictions of motion in the solid state would be so great that reaction would not occur at all. In fact, this is not the case, and there are many examples of photochemical reactions which are just as efficient in solid polymers as they are in dilute solutions of small-
(a1
(b)
(C)
Figure 1. Restrictions on mobility caused by polymer structure: (a) solution; (b)polymer solution; (c) polymer bulk.
MOLECULAR MOTION IN POLYMERIC SOLIDS
93
molecule analogs. On the other hand, as we will see, there are a number of reactions which are completely inhibited in the solid phase. The key to understanding these effects is to determine how much movement of atoms is required in order to form the geometry of the excited or transition state and to allow separation of products. Reactions differ in these respects, and so one can expect to observe different effects when we study chemical reactions in polymeric systems. To answer these questions we must first understand the kinds of motions which occur in polymeric solids.
11. MOLECULAR MOTION IN POLYMERIC SOLIDS Polyatomic molecules in the gas phase undergo three types of motion: translation, vibration, and rotation. The latter two are quantized, giving rise to spectra; those corresponding to vibration are usually observed in the infrared, whereas those for rotation are normally observed in the microwave region. Electronic spectra, when carefully analyzed, also contain information about both the vibration and rotation of small molecules. Extensive studies of the infrared spectra of polymeric materials in both solution and the solid phase have shown that, in general, the vibration of small groups such as the bending and stretching modes of C=O, and stretching of C-H, C-Cl and C f N are almost unaffected by the presence of the polymer environment. For this reason, infrared spectra can be used to analyze polymer structures and composition because the location of the bands is usually much the same as in small-molecule analogs. However, the rotation spectra of polymeric molecules are much more complex, since they will include rotations not only of the very large polymer itself but also of segments of the molecule and side chains. The rate of these processes will depend very much on the molecular architecture and the flexibility of the polymer chain as well as the viscosity of the medium. For flexible chains in solution, rotation is primarily due to sequential movements of segments of the chain (Fig. 2). These segments are not necessarily defined by the monomer unit from which the polymer is derived, but in hydrocarbon polymers often consist of segmentsof 20 to 50 carbon atoms in length. Segment motion occurs both in dilute solution and in the solid amorphous phase, provided the polymer is above its glass transition, Tg.This characteristic temperature of all amorphous polymers will be considered later. It can be defined for our purposes as the temperature below which this type of coordinated segment motion can no longer occur. An important kinetic difference between a polymer molecule in solution and the same molecule in an amorphous solid phase is that in dilute solution there can be a net translational motion of the center of mass of the polymer as in Fig. 2u, whereas in the solid the rate of this process is exceedingly slow.
94
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
(a1 <-
(C
Figure 2. Types of motion in polymer molecules: (a)translational; (b) segmental rotation; (c) group rotation. Reprinted, with permission, from J. E. Guillet, Polymer Physics and Photochemistry, Cambridge University Press, Cambridge, England, 1985, p. 2.
In the amorphous phase of macromolecules having some degree of chain flexibility we can consider that the solid consists of a large number of interpenetrating flexible chains that approximate a random coil configuration. If such a polymer were cooled slowly to absolute zero, it would be expected that it would achieve its most stable geometry in closest packing corresponding to the lowest-free-energy state. However, because of the large macroscopic viscosity of the solid polymer, it seldom achieves this packing density in finite times unless it undergoes crystallization at a relatively high temperature. As a result, even at absolute zero, the polymer matrix will contain some “free volume.” Free volume in this context could be defined as the space unoccupied by atoms because the maximum packing density cannot be achieved. At 0 K, of course, this free volume will be relatively small, and because there is no energy to activate the molecules, they will not occupy the space. However, as the temperature is increased, thermal motion will begin and the solid will expand. This expansion creates additional free volume and allows small-scale rotations or oscillations of atoms or groups of atoms. The change in specific volume of an amorphous polymer as a function of temperature is shown in Fig. 3. As the free volume increases, the motion of particular groups of polymers is observed at various temperatures which are known as “transition temperatures.” Such solid phase transition temperatures
MOLuluLAR MOTION IN POLYMERlC SOLIDS
I
0
I
150
L
,
I
300
T (K)
t
I
1
450
95
I
600
Figure 3. Specific volume and “free volume” of a polymeric solid.
can be detected by a variety of physical measurements on the polymer, including dielectric relaxation and thermal or mechanical deformation (1). The point designated by Ty in Fig. 3 represents the temperature at which sufficient free volume is available in polystyrene, for example, to observe the motion of phenyl rings at a fkquency of about 10 Hz.As the temperature is raised still further, additional free volume becomes available. At a point indicated by Tg a change in the slope of the specific-volume-temperature curve is observed, which is due to the beginning of the motion of the very long segments of the polymer chain referred to previously. Motion observable below Tg in solid polymers will vary with the chemical nature of the polymer. Specific motions which have been identified in polymer systems, including rotations of phenyl, methyl, carboxyl, carboxylicester, nitrile, and keto groups, as well as conformational transformations. At temperatures above Tgthe motion of flexible chains becomes very rapid and the conformational mobility appears to be nearly as great as if they were dissolved at high dilution in good solvent (2). However, not all transitionsin solid polymers can be identified with specific groups in the chain, for example, those relating to coordinated motion of the backbone atoms such as the so-called “crankshaft motion” in polyethylene. A number of flexible polymer chains can crystallize with a high degree of order and if properly annealed can actually form single crystals. The regular packing of the polymer chain in the crystal and the strength of the lattice interactions are such that penetration of the crystalline region by other molecules is drastically reduced and the free volume required for chemical reaction is usually not available. As a result, chemical reactions in semicrystallinepolymers such as polyethylene will occur primarily in the amorphous phase or at crystal boundaries where sufficient free volume is available. Exceptions to this general rule are photochemical reactions such as those studied by Wegner (3), in which the lattice dimensions of the product are almost identical to that of the reagent crystal, and hence only very small amounts of free volume are required for the transformation to occur.
96
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
A number of important chemical reactions occur in polymer gels, which can be part of membranes or swollen crosslinked polymers. In a typical gel the polymer may represent only 10 or 20% of the total weight of the material, the remainder being made up of solvent molecules. However the gel may appear to be completely solid. In gels it is important to remember that much of mobility and molecular motion is imparted by the solvent rather than by the polymer, and reactions in gels containing a major amount of solvent usually occur with nearly the same velocity as in the pure solvent alone.
III. DIFFUSION IN POLYMERIC SOLIDS The kinetics of many photoprocesses in solid polymers will depend on the rate of diffusion of one or more molecular species. The theory of diffusion-controlled processes has been well developed for reactions in gases and conventional liquids. However, the special nature of polymer solutions requires further consideration. Diffusion in solid polymers occurs as a result of molecular motion under a chemical or physical potential. Whereas in simple liquids diffusion occurs primarily as a result of translational displacements of small molecules, the situation is much more complex in a solid polymer matrix. All of the motions in a polymer chain and its side groups referred to in the previous section will be involved in the diffusion of small molecules through the polymer. With small diffusant molecules such as the permanent gases (e.g.. oxygen, nitrogen, hydrogen, carbon dioxide, and argon) diffusion can occur in solid polymers at temperatures well below the glass transition temperature. It is believed that the translational motion of these molecules in the polymer matrix is assisted by the formation of thermally activated packets of free volume that are caused by small-scale motion of polymer segments or the librational movement of groups attached to the side chains. Bueche (4) has proposed a theory which relates the diffusion constant D to a frequency by the jump distance 6 through
It is expected that the jump distance 6 will be relatively constant from one polymer to the next, and that variations in the diffusion constant are caused primarily by differences in the jump frequency This frequency depends on the probability of collecting a sufficient number of packets of free volume to give a hole of volume v* of sufficient size that the diffusing molecule can move into it. The creation of a hole in the polymer requires the expenditure of a certain quantity of energy Eh, and the probability of forming such a hole can be calculated from Boltzmann statistics to be proportional to exp( -Eh/RT). Application of this theory to both polymeric and small-molecule liquids has given jump distances 6 which correspond roughly to the dimensions of small molecules (i.e., 2-20
+.
97
DIFFUSION IN POLYMERIC SOLIDS
A) and typical jump frequencies ranging from lo4 to lo6 per second. These and
other free-volume theories are described in more detail in Crank and Park (5). The important concept that is central to all free-volume theories is that diffusion occurs in polymers through free volume obtained by minor displacements of side groups or segments of the chain but without net translational displacement of the center of mass of the polymer. As discussed previously, the larger-scale segmental motions which occur above the glass transition impart relatively large amounts of free volume to the system, and the activation energy for diffusion in polymers is significantlyhigher than for conventional small-molecule liquids. As a result of these two factors, the rates of diffusion of small molecules in polymeric solids above the glass transition are often only one or two orders of magnitude below those in ordinary liquids. Amorphous polymers are thus not viscous media in the conventional sense, because the diffusing penetrants are not affected by the motions of the center of mass but only by segment mobility. For example, measurements of the diffusion of naphthalene in polyethylene at 80°C by Heskins and Guillet (6) show an effective viscosity (q,& of about 1 poise, which is slightly higher than that of ethylene glycol but lower than that of glycerin (Table 1). This so-called microviscosity of polymer systems is many orders of magnitude lower than that which would be predicted from the macroscopic properties of the polymeric solid. For example, in solid polyethylene the macroscopic viscosity (q) would be of the order of 10" poise. This important principle has gone unrecognized in many studies of polymer photophysics and photochemistry. As a polymer chain is crosslinked, the coordinated segment motion available for the permeation is reduced, with a consequent reduction in the diffusion constant. However, the macroscopic properties of the polymer are affected more than diffusion. Crosslinking has very little effect on diffusion until the crosslink density exceeds about 3% (7).
TABLE 1. Internal Viscosities qht and kaurforReaction in Various Media at 20°C" kdiff
(L mol-' s-')
Medium
q,,t(piSe)
Hexane Benzene Toluene Ethylene glycol Polyethylene Glycerin
3.1 x 6.5 x 10-3 5.9 x 10-3 0.2 lob
2x 1x 1 x 4x 1x
1o'O 1o'O 10'0
11
6
lo6
%om Ref. 6. bExtrapolated from data at 80°C.
X
108
107
98
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
IV. THEORY OF DIFFUSION AND PERMEABILITY IN POLYMERS The simplesttheory of diffusion in isotropic substances is based on the assumption that the rate of transfer between diffusing molecules through unit cross-section area is proportional to the concentration gradient:
where F is the flux (i.e., the rate of transfer per unit area cross section), c is the concentrationof diffusing substance, and x is the space coordinate measured normal to the section. D is known as the diffusion coefficient, and in the simplest case (Fickian diffusion) is independent of c. If F and c are expressed in the same units, D has dimensions of t2/rand is usually expressed in units of cm2/s. In the case of three-dimensional diffusion through a volume element where D is constant, the fundamental differential equation for diffusion is given by ac
a2c
a2c
- at= D ( T + T
+
A) a2
(3)
Where D is not independent of c, the most general form of the fundamental equation becomes
-= at
div(grad c)
(4)
For diffusion across films or membranes the concentration gradient can often be treated as unidirectional (Le., along the x-axis), in which case Eq. 3 becomes -ac= at
This is known as Fick’s second law.
DS
For a plane sheet or membrane of thickness C whose surfaces are exposed to constant concentrations c1 and c2 of penetrant, a steady state will be reached where the rate of transfer F across all sections is constant and given by
SOLUBILITY AND DIFFUSION
99
In some cases in which a gas or vapor diffuses through a membrane, the surface concentrations may not be known, but provided that Henry’s law is obeyed, c will be proportional to the partial pressure of the gas; thus c =
sp
(7)
where p is the partial pressure and S is called the “solubility” or “solubility coefficient.” The flux under these conditions is given by
where Pis called the permeability, or permeabilitycoefficient,and is given by
P = DS
(9)
V. SOLUBILITY AND DIFFUSION It is important to note that the rates of reactions in solid polymers will be controlled not only by the rate of diffusion but also by the solubility of the permeant in the polymer. For example, the diffusion constant for oxygen is quite large in many polymers, but usually the solubility is very low, and as a result, rates of oxidation tend to be quite small. Experimentalvalues of the permeability P and diffusion constant D for various organic permeants and oxygen in lowdensity polyethylene (8) illustrate this point (see Table 2). The concentration of diffusant, c, is given by c =
P g p
Thus at a given partial pressure p of the diffusing species, one can calculate that the concentration of benzene in polyethylene, for example, would be approximately 3 x lo4 times as great as that of oxygen, thus giving rise to a permeability some two orders of magnitude greater for benzene than for oxygen, in spite of its larger molecular volume. It is possible to determine the diffusion constants and solubilities for organic compounds in polymers by a number of physical methods. Classical methods are well reviewed by Crank and Park (5). More recent methods involving luminescence and inverse gas-liquid chromatography have been reviewed by Guillet (9).
100
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
TABLE 2. Diffusion Constants (0)and Permeabilities (P)for Small Molecules in Low-Density Polyethylenea
Permeant Oxygen Decane Benzene Hexane Carbontetrachloride Ethyl alcohol Ethyl acetate
D X lo6 (cm2s-') 460
3.5 8.2
P x 1010 [cm3(STP)cm
cm-2
s- 1 cmHg-'1
2.9
&W
-
5300 2910 3810
-
513
-
56
Source: Ref. 8.
VI. TEMPERATURE COEFFICIENTS FOR DIFFUSION Since diffusion is a thermally activated process involving small scale translational motions in the penetrant or segment motion in the polymeric medium, the diffusion constant can be expressed in Arrhenius form:
where D, and Ed are the preexponential factor and the activation energy of diffusion, respectively. Typical values for the activation energy Ed for the selfdiffusion of small solvent molecules in conventional liquids are 8-12 kJ/mol, while diffusion in polymeric solids usually shows higher values, ranging from about 20 to 80 kJ/mol. This seems to be related to the greater energy required to displace large polymer segments to provide holes for the diffusing penetrant. Typical values for diffusion constants and activation energies for gases in natural rubber, polyethylene, and polystyrene are shown in Table 3. It can be seen that as the size of the penetrant increases, the diffusion constant decreases but the activation energy increases. As a result, at high temperatures, the rate of diffusion of gases in molten polymers will not be very different from that for conventional liquids. At ambient temperature (25"C), however, values for the rates of gaseous diffusion in ordinary liquids are typically about two orders of magnitude greater than in polymers. For example, for oxygen in cyclohexane, D = 5.3 X cm2/s at 30 "C, as compared with 4.6 x lo-' in low-density polyethylene at the same temperature.
101
CAGE REACTIONS
TABLE 3. Diffusion Constants and Activation Energies for Gases in Polymers at 25°C
Polymer
Gas
Natural rubber (cis-polyisoprene) (amorphous) T = -60°C Polyethylene (semicrystalline) T = -40°C
T = 80°C
DA
(tdmol-’)
216 15.8 11.0 8.9
0.031 1.94 3.7 1.97
18 35 37 36
68 4.6 3.7 1.9
(d = 0.914)
Polystyrene (glassy)
D x 10’ (cm2s-‘)
He
0 2
co2
104 1.1 0.58
0.13 4.48 1.85 17.2 0.0019 0.125 0.128
Ed
25
40
38 46
13 35 36
Source: Reprinted, with permission, from J. E. Guillet, Polymer Physics and Phorochemistry, Cambridge University Press, Cambridge, England, 1985, p. 55.
Luminescence procedures present a powerful method for the determination of diffusion constants for a variety of penetrants in polymer systems, and have been reviewed recently (9).
VII. CAGE REACTIONS The concept of the “cage reaction” is often invoked in polymer chemistry to explain observed differences in reactivity between polymers and small molecules. It is proposed that restrictions on mobility in the solid phase prevent the separation of reactive species, thus causing them to recombine to form the original reactant. The result is a reduction in the efficiency or quantum yield of the process in question. The original concept of cage processes, due to Franck and Rabinowitsch (lo), was invoked to explain the reduction in quantum yields which occur on the photolysis of simple molecules like acetone and iodine when carried out in solution as compared to the gas phase. Extensive studies were carried out by Noyes (11) during the 1950s and 1960s to develop a theoretical understanding,
102
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
Rinwry cage
recombhotion
(a)
Secondary cage recombination (b)
Figure 4. Scheme showing (a) primary and (b) secondary cage recombination.
but it was not until the development of picosecond lasers that the early stages of the processes of separation could be probed experimentally. It is now known that in the dissociation of two radical species, for example, recombination will occur in the primary cage in times from 10 to 100 ps (12). The situation is shown schematically in Fig. 4. The primary radical pair separates with a velocity dependent on the amount of excess energy partitioned into translational velocity along the axis defined by their centers of mass. This translational energy is exchanged by momentum transfer with the surrounding solvent molecules. If, as a result of these first collisions, they rebound to a position where they are within a distance of u of each other, where u is the radius for reactive collision of the species, they will recombine to reform the initial reactant. In iodine atom dissociation this process occurs in about 50 ps. If, on the other hand, their energy is great enough to displace one or more solvent molecules to produce a pair of radicals separated by at least one solvent molecule, then a random diffusion will occur. Because the local concentration is high, there is still a good possibility (> 50%) that the two particles will diffuse to adjacent sites and recombine. This is called “secondary cage recombination,” even though it has nothing to do with restriction of motion by a solvent cage, but is primarily an effect due to the nonuniform distribution of radical species. The probability of reaction depends on the rate of diffusion of the radicals in the medium, the concentration of radicals from other dissociating molecules, and alternative reaction paths, such as H-atom abstraction from the solvent. Many authors have assumed that because of restrictions in mobility in solid polymers, dissociating radicals would undergo efficient recombination in the primary cage. Recently, Moore and Guillet (13) studied the quantum yield for photolysis of benzoyl peroxide in two solvents, benzene and toluene, and in solid polyethylene and polystyrene films:
THE INTERNAL VISCOSITY OF POLYMERIC SOLIDS 0 @ ! ! O O - ! ~
0
103
0
k> 2 W o ->
Products
(12)
In both the solids and in liquid solution the quantum yields were uniformly high ( S 0.8). indicating that primary cage recombination represented at most 20% of the total and did not depend on either the bulk or the microviscosity of the medium. Presumably the separating radicals exchange momentum only with small segments of the polymer chain, and the motion which can occur in the short time scale of the primary cage recombination (10-100 ps) cannot be influenced by the polymeric nature of the solvent. There was also no difference between the quantum yield in polyethylene, which is above its glass transition at 25”C, and in polystyrene, which is well below its Tg, so the glassy nature of the medium also showed little effect. For this reason, any specific “polymer effects,” if indeed they do occur, must be attributed to processes occurring outside the primary cage. Secondary cage recombination, on the other hand, will be affected by the slower rate of diffusion in the polymer matrix. This might be expected to reduce the number of radicals which can escape the region associated their primary partners, thus increasing recombination. Estimates of the probability of escape of radical pairs in solution in conventional solvents have been made by product analysis of the decomposition of diacyl peroxides. For example, Braun et al. (14) estimated that 60 to 80% of the methyl radicals produced in the thermolysisof acetyl peroxide escapegeminate cage recombination. However, Guillet and Gilmer (15) showed that for longer chain C9 and C,, radicals the probability was much lower, ranging from 5% at 76°C to 16% at 262°C. The lower escape probabilities in this case can be attributed to the greater mass of the C9 and C,, radicals and the greater internal viscosity of the mineral-oil solvent.
Vm. THE INTERNAL VISCOSITY OF POLYMERIC SOLIDS Any treatment of diffusion processes in polymers must include estimates of the “internal viscosity” qint of the solid polymer matrix. For example, for recombination of active free radicals which occur at every collision, one can write the rate expression in the form Rate = k&R*I2
(13)
104
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
The simplified form of the Einstein-Smoluchowskiequation gives for radicals land2
where p’ is some collision radius for reaction, dv is Avogadro’s number, and
D 1and D2are the diffusion constants for species 1 and 2, respectively.
We can consider three limiting cases, depending on the relative size of the radical species. Case 1. Two small radicals of equal size. Then Eq. 14 reduces to the Debye equation: kdiff
=
mT
ooorlint
= 2.2 x 105-
T rl
where qintis the “internal” viscosity of the medium. Case 2. One small radical and one large polymer radical. In this case D2 = 0 and
The rate is only one-half that for two small radicals. Case 3. Two polymer radicals. Then
It is not possible to estimate the value of kdiE in this case, but it will remain proportional to T/qint.In concentrated polymer solutions and in solid polymers, diffusion will almost certainly involve movement by reptation and will be very slow. Values for kdiffand qintfor various solvents and polyethylene are also included in Table 1. The average distance a particle can diffuse in time t can be shown to be x = J m
The Stokes equation relates the diffusion constant for a spherical particle of radius r to the internal viscosity qintby
THE INTERNAL VISCOSITY OF POLYMERIC SOLIDS
105
TABLE 4. Diffusion Distance x = -for Spherical Particles of Radius 3 A in Media of Differing Internal Viscosities llht Time of Observation
D
'lint
(PI
(cm2s-')
1 .o 10-1 10-2 10-3 10-4 6X
7x 7x 7x 7x 7x 1.2 x
10-8 10-7 10-5
10-4 10-5
1 ns
10 ns
100ns
1 ms
0.12 0.38 1.2 3.9 13 1.6
0.38 1.3 3.9 13
1.2 3.9 13
3.9 13 40 128 412 52
40
5.3
40
128 16
"Average value for toluene and benzene.
This allows the calculation of diffusion distances n for particles in media with varying internal viscosities qht. Table 4 shows values calculated for particles of radius 3 A-somewhat larger than methyl radicals, but smaller than phenyl groups. It should be noted that these are for thermalized particles, which have lost all the excess kinetic energy imparted to them in the initial dissociation process. The calculations are thus only applicable to secondary cage recombination, not the process occurring in the primary cage. Clearly the threeorder-of-magnitude difference in qintbetween polyethylene and solvents such as benzene or toluene should have important effects on the probability of secondary cage recombination, even for relatively small radical fragments. As the size of the separating radical increases, its probability of escape should also decrease. However, for spherical particles, the effect is not a strong function of the molecular weight. If one assumes that the particle is spherical, then
D where M
=
CX(-$-)''~
molecular weight, and thus the distance diffused in time t is
x
a( + ) " 6
Thus a ten-fold increase in the mass of a spherical particle would only reduce x by a factor of 0.68.
Once the particle becomes a linear polymer, it will diffuse by reptation in a polymer matrix. In this case the scaling law proposed by de Gennes indicates that x would vary as
106
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
X K -
1
M
M. STUDIES OF CAGE REACTIONS IN POLYMERS Because of the relatively slow rates of radical diffusion in polymer matrices, it seems likely that the probability of secondary recombination will depend very much on the separation achieved while the particles are moving apart with the original excess kinetic energy imparted in the primary dissociation step. This, in turn, should depend on the energy of the exciting photon. There is some evidence for this, even in small molecules in solution. For example, Slivinskas and Guillet (16) report a one-hundred-fold increase in the relative yields of Nomsh type I radical products from simple aliphatic ketones, when the reaction is initiated by y-rays rather than ultraviolet light (Table 5). Similar increases were observed in polymeric systems such as in ethylene40 copolymers (17). Early studies by Hartley and Guillet (18) on the photochemical quantum yields for type-I reaction in model ketones of structure R-C(=O)-R showed that the quantum yield in solution at 120°C in p d i n oil decreased continuously from 0.02,when R = 4, to a limiting value of 0.012 at R = 12 (Fig. 5 ) . Model compounds where R > 12 gave values nearly identical with that for R = 12, as did copolymers of ethylene with carbon monoxide. Furthermore, the result was independent of solvent viscosity, being nearly identical in heptane (0.28 cP), dodecane (0.73cP), and parain oil (9.2 CP at 60 "C).The viscosity of paraffin oil is 2.1 CP at 120"C,which is comparable to that of typical organic TABLE 5. Comparison of G-Values for Photolysis (313 nm) and Radiolysis of Symmetrical Aliphatic Ketones at 35°C G (Radiolysis)
G (Photolysis)
CO (1)
Ketone ~~
Methyl Ketone
~~
~~
4-Heptanone 5-Nonanone 6-Undecanone 7-Tndecanone 8-Pentadecanone 12-Tncosanone
~
0.44
0.025 0.020 0.017 0.015 0.012
3.8 2.8 2.4 2.0 1.7 1.5
Ratio GdGn
Alkane/;?
0.12 0.0090 0.0083 0.0085 0.0088 0.0080
0.71 0.43 0.28 0.18 0.065
(1)
0.040
Methyl Ketone (11)
Ratio GI&
0.49 0.51 0.45 0.26 0.092 0.081
1.45 0.88 0.62 0.69 0.71 0.69
Source: Reprinted with permission from J. A. Slivinskas and J. E. Guillet, y-Radiolysis of ketone polymers, Journal of Polymer Science, Polym. Chem. Ed. 11, 3053 (1973). Copyright 1973 John Wiley & Sons, Inc.
STUDIES OF CAGE REACTIONS IN POLYMERS
0
10
20
30
107
40
Chain length
Figure 5. Quantum yield for carbon monoxide evolution ($co) as a function of chain length: temperature, 120°C; solvent, paraffin oil. Reprinted with permission from G. H. Hartley and J. E. Guillet, Photochemistry of Ketone Polymers 11. Studies of Model Compounds, Macromolecules, 1, 415 (1968).
solvents such as toluene and benzene at 20°C. The apparent activation energy for the type-I quantum yield is quite large, namely 4.8 kcal mol-’, whereas the usual E, for a diffusion-controlled process is =2-3 kcal. Both of these considerationssuggest that these quantum yields reflect the effect of the molecular weight of the radical on its escapefrom the primary cage, rather than on secondary diffusive recombination. In our concept of primary-cage recombination, escape should depend on the momentum imparted in the primary dissociation step. The distance reached in the escape trajectory will be proportional to the velocities (v) of the particles. Since the exciting wavelength was the same (313 nm), the total kinetic energy should be very similar for each ketone. From simple kinetic theory the velocity (v) should be proportional to (l/M)”*, where M is the molecular weight of the fragment. If +I is a measure of the probability of escape from the cage, then one might expect that
On the other hand, for secondary diffusiverecombination, Eq.21 would predict
As shown in Table 6, the data of Hartley and Guillet are fitted quite well by Eq. 23 for values of M up to M,.One must conclude that for longer chain flexible
108
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
0 II TABLE6. QuantumYieldsforModel AlkanonesR-C-Rat 120°C inParaffhOi1
(4,)rn
41
R
n-C,H,
0.021 0.024 0.022 0.021 0.021 0.028
0.0212 0.0191 0.0181 0.0154 0.0127 0.0123
n-C5H1 1 n-C6H13
n-C7H,4 n-C11H23 n-C2 lH43
segments, escape must involve indepenent motions of chain segments approximately 12 carbon atoms in length. Additional information regarding structural effects in model polymer ketones was reported by Plooard and Guillet (19), who compared the photochemical quantum yields in solution for the methyl esters of ketone diacids with polyesters containing the same structure:
0
0 II
0 II
II
MeO- C -(CH,), -C-(CH,), -C -OMe (a) n = 2; (b) n = 3; (c) n = 4
0 0 II II COCH2CH2CH2CH2O-C -(CH2),-C- (CH2),-
---
(d) n = 2; (e) n = 3; ( f ) n = 4 TABLE 7. Quantum Yields for Keto Esters and Polyesters Methyl Esters
(a) (b) (c)
n
M
Type I
2 3 4
202 230 258
0.20 0 0.01
Type 0 0.29 0.20
II
Polyesters
4s Other
Total
A0.2 0.12 0
G0.4 0.41 0.23
"Based on reduction in type-I or type4 yields.
M
4s
R~uction Factof
15,000
0.014 0.012 0.013
1/14 1/24 1/15
9,900 6,900
109
PHOTOCHEMISTRY OF POLYMERS CONTAINING KETONE GROUPS
Their results are summarized in Table 7. It is clear that by including the carbonyl in the backbone of a polymer chain a substantial reduction in quantum yield can be expected, even when the photolysis is carried out in solution. For the type-I process this probably results from cage effects, while in the type-I1 it is the reduction in conformational mobility which prevents the formation of the cyclic six-membered intermediate known to be involved in this reaction:
OH
0 II R-C-CH3
<-
I
R-C=CH2
+ CH2=CH-R
This conformational factor will Se discussed further in later sections.
X. PHOTOCHEMISTRY OF POLYMERS CONTAININGKETONEGROUPS The largest body of experimental work on the photochemistry of solid polymers relates to the study of the photolysis of homo- and copolymers of vinyl ketones. In early work, Guillet and Norrish (20) and Wissbrun (21) showed that polymeric ketones such as poly(methylviny1 ketone) and poly(methylisopropeny1ketone) underwent the same classical photochemical reactions as their low-molecularweight analogs. The photophysical and photochemical processes which occur are summarized below:
*
R
R
I
I
c=o
->
(S')
->
(T1 1
->
&
(27) (SO) + hv
110
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMOFU'HOUS POLYMERS
& R I
h" &c - oH
R I
RH'
R R I
R
OH R
I
I
c=o* ic
(32)
This work has been reviewed recently (22). For our present purposes, only
a few of these studieswill be included to illustratespecificpoints about solid-phase
photochemistry. As with simple small-molecule ketones, there are strong effects due to the structure of the ketone and the nature of its substituents on both the quantum yields and the nature of the products. These same structural features are usually reflected in the analogous polymeric molecules. The ketone group is a useful model because it can be excited selectively in the presence of other groups commonly contained in polymer chains, such as the phenyl rings in polystyrene, and so the locus of excitation is well defined. Furthermore, there is a great deal known about the photochemistry of aromatic and aliphaticketones, and one can draw on this body of information in interpreting the results. A further advantage of the ketone chromophore is that it exhibits a number of photochemical processes from the same excited state. Thus one has a probe of the effects of the polymer matrix on these processes by determination of the quantum yields. The competing processes include (1) fluorescence (Eq. 26), (2) phosphorescence (Eq. 27), (3) the Nomsh type-I reaction (Eq. 28), (4) the Nomsh type-I1 reaction (Eq. 29), (5) photoreduction (Eq.30), (6) the
PHOTOCHEMISTRY OF POLYMERS CONTAINING KETONE GROUPS
111
formation of cyclobutanol (Eq.311, and (7) intersystem crossing to the ground state (Eq.32). The polymers discussed here will generally be polymers of ethylene or styrene copolymerized with monomers capable of introducing ketone groups with a variety of structural features. Some of these copolymer structures are shown in Table 8. When a thin film of solid polymer containing a ketone group is cooled to 0 K, no motion of the groups or chain constituents of the polymer is possible. If the film is gradually warmed to room temperature in air and irradiated with UV light, phosphorescence emission is observed. Since this is a strictly electronic transition, no molecular motion is required and the intensity of the emission remains relatively high until certain transition points are observed. If one plots the phosphorescence intensity from thin films of polystyrene or polyethylene in the form of an Arrhenius plot, these transitions are identified by intersections of straight-line portions of the response curve shown in Fig. 6u.As the temperature is increased from 0 K the specific volume of the polymer increases in a manner shown schematically in Fig. 3. As the free volume in the polymer increases, various types of molecular motion begin to occur, and these are identified by the transitions associated with the motion of various subgroups in the polymer. The important ones observable by this experiment (Fig. 6u)are the crankshaft motion of polyethylene at about -85°C and the transition associated with movement of the phenyl ring in polystyrene at about -77°C (Fig. 6b).The minor transition in PE-CO at - 150°C may be related to some form of coordinated motion of the carbonyl group itself.
12 10
10 8
8
a
-
I-!
-
6 2 C
c 6 4
4
2
2
'
4
6
8
10
4
6
8
1
0
0
IOOO/OK
Figure 6. Arrhenius plots for phosphorescence intensity for (a) poly(ethy1ene-1% CO) and (b)poly(styrene-5% PVK),showing transition temperatures and activation energies.
TABLE 8. Structures of Ketone Copolymers Studied Copolymer
Structure
Structure Number
Poly(ethylene-co-carbon monoxide) (PE-CO)
Poly(ethy1ene-co-methyl vinyl ketone) (PE-MVK)
Poly(ethylene-co-methyl isopropenyl ketone) (PE-MIPK)
* c=o I
CH 3
Poly(styrene-co-methyl vinyl ketone) (PS-MVK)
isopropenyl ketone) (PS-MIPK)
Poly(styrene-co-rerrbutyl vinyl ketone) (PS-tBVK)
rn
112
v
CH 3
n 3 C - cI CH3
3
vinyl ketone) (PS-PVK)
IV
VI
PHOTOCHEMISTRY OF POLYMERS CONTAINING KETONE GROUPS
113
TABLE 8 (Continued) Copolymer
Structure
Structure Number
Poly(styrene-co-phenyl isopropenyl ketone) (PS-PIPK)
The straight-line portion of the Arrhenius curve above about 100 K observed in both cases is attributed to quenching of the phosphorescence emission by oxygen, and the slope of this curve accurately reflects the activation energy associated with the permeability of the oxygen quencher. This effect can be used (23,24) as a means of measuring the rates of oxygen diffusion in a variety of polymers. As a general rule, the activation energy for a given process in a solid matrix can be related to the amount of free volume required for that process (9), so that small-scale motions requiring small amounts of free volume adjacent to the moving group will have low activation energies, whereas those requiring larger packets of free volume will have large activation energies. Typically, the activation energies for diffusion of oxygen in polymers range from 7 to 10 kcal mol-' , whereas those for small-scale rotations or methyl and methoxy groups are of the order of 1 to 3 kcal mol-'. In early work, Hartley and Guillet (25) associated the reduction in c$= in PE-CO at about -40°C with restrictions in conformational mobility associated with the glass transition, Tg. However, measurable values of c$ll were observed down to about -100°C due to the Occurrence of a crankshaft motion of the polyethylene backbone chains which permitted the formation of the cyclic intermediate (Eq.25) required for reaction within the lifetime of the n-T* excited state of the carbonyl (I 20 ns). The activation energy for $n below -40°C was 2 2 kcal mol-', which is similar to that of the crankshaft motion. Below - 100°C this motion is frozen out and no further photochemistry is observed. On the other hand, in the absence of quencher the photophysical processes of fluorescence and phosphorescence may be quite efficient. In early photochemical studies it was shown (26) that the quantum efficiency for the type-I processes in polymers containing ketone groups is highly sensitize
114
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
to the location of the ketone group with respect to polymer chain, as shown in structures A and B below:
When the ketone is in the backbone of the polymer, the excitation of the ketone produces two polymeric radicals which must separate from each other within a short period of time in order to produce chemical products. If, however, the ketone group is in a side chain, as in structure B, then a polymeric radical is formed simultaneously with a small radical fragment. This second fragment can diffuse relatively rapidly through the polymer solid, and the quantum yields are increased by at least one order of magnitude (26-28). In a previous section it was demonstrated that a substantial reduction in quantum yields was observed when the ketone group was included in the backbone of a polyester chain. A similar variation in the quantum yield of the Norrish type-I process is illustrated in Fig. 7 for solid copolymers of ethylene containing
lrrodiotion time (hours)
Figure 7. Relative rates for carbonyl loss (type I) in films of ethylene-ketone copolymers under nitrogen at constant light intensity (26). Reprinted with permission from F. Sitek, J. E. Guillet, and M. Heskins, Some aspects of the photolysis and photochemistry of PE containing ketone groups, Journal of Polymer Science-Polymer Symposia, 57,35 1 (1976). Copyright 1976, John Wiiey & Sons, Inc.
PHOTOCHEMISTRY OF POLYMERS CONTAINING KETONE GROUPS
115
three different ketone structures. The ketone groups in the backbone of the polymer chain in PE-CO copolymer show much lower quantum yields than those from the secondary or tertiary structures induced by copolymerization of methyl vinyl ketone (MVK) and methyl isopropenyl ketone (MIPK) with ethylene. In the latter two cases, the Nomsh type-I cleavage produces a small radical and a polymer radical, and the small radical has a much greater probability of escaping the cage. The quantum yields for type-I and type-I1 processes at various temperatures are summarized in Table 9. The significant increase in type-I quantum yields in structures I1 (PE-MVK, PE-MIPK) and 111appears to occur with a concomitant reduction in type 11,indicatingthat the two reactions are indeed in competition. Further confirmation of the important effect of solid-phase transitions in polymer photochemistry was reported by Dan and Guillet (29). They studied the quantum yields of chain scission, as a function of temperature in thin solid films of vinyl ketone homo- and copolymers. For polymers where the Nonish type-I1 mechanism was possible, large increases in were observed at and above the glass transition Tg. Figure 8 shows this effect in a styrene copolymer containing about 5% phenyl vinyl ketone (PVK). Below Tg,& is about 0.07, but at Tg it rises to about 0.3, a value similar to that observed for photolysis in solution at 25°C. A similar effect was observed with poly(methy1 methacrylateco-methylvinyl ketone) (PMMA-MVK) and PVK homopolymer. The generality of this effect suggests that even in the solid phase above Tg, the conformational freedom of large segments of the polymer chain is comparable to that in solution, and consequently one should expect equivalent chemical reactivity. When this effect was first discovered, it was important to determine whether or not it was a general phenomenon applicable to all photochemical reactions in solid polymer systems. Fortunately this is not the case, and only those reactions requiring relatively large amounts of free volume, such as the Nomsh type 11, will show this strong effect at the glass transition temperature. For example, Table 10 shows data on the type-I quantum yield (loss of
+,,
+=
TABLE 9. Quantum Yields for Ketone Ethylene Copolymers Polymers
1%CO
2% MVK
2% MIPK
T("C)
+I
+n
+I
+U
+I
23 35 54.5 69.5
0.073 0.065 0.074 0.054
0.074 0.099 0.065 0.057
0.22 0.23 0.15 0.12
0.044 0.034 0.016 0.014
0.25 0.23 0.15 0.11
~~~~~
Source: Ref. 28.
+ll
0.048 0.039 0.019 0.004
0.32
-
1
I
I
-
0.24
-
-
0.16
-
-
In
a"
-
TABLE 10. Temperature Effects for Type4 Reaction in PS-MIPK Copolymer Films at 313 nm in N, +-co 23 64 89 104
0.26 0.26 0.30 0.32
Source: Ref. 30.
TABLE 11. Quantum Yields for the Irradiationof Poly(styrene-co-vinyl Aromatic Ket0nes)s at 313 nm in N, Co-monomer
PVK PVK PVK PVK PIPK
(")
T
@-CO
Film
Film
Film
Solution
1.1 3.6 7.6 7.6 6.1
23 23 23 55 23
0.20 0.21 0.22 0.23 0.32
0.19 0.18 0.20
0.043 0.054 0.072
0.08
-
0.13 0.15 0.42 0.53 0.36
@OH
-
@S
-
Source: Ref. 30. "Determined by W spectropbotometry with the homopolymers as standards.
116
+;
M01-8~
POLYMERS FOR PHOTOLITHOGRAPHY
117
carbonyl) in films of poly(styrene-co-methyl isopropenyl ketone) irradiated at 313 nm in nitrogen (30). There is a small but continuous increase in the quantum yield from 23 to 104"C, but no discontinuous change is observed in the region of Tg, which is around 98°C for these polymers. The total loss of carbonyl is considered to be the sum of the type-I and photoreduction (Eq.30) processes, both of which apparently require very small volumes of activation in order to occur. It is interesting to note that in many cases the efficiency of radical reactions in solid glassy polymers appears to be unaffected by the polymer matrix. In the case of type-I reactions in solid polystyrene we have observed that the efficiency of radical escape when at least one of the radicals is a small molecule is similar in polymeric glasses to that observed in solution. One can deduce from this that polymeric glasses are not particularly good at trapping radical species unless they are cooled to very low temperatures. As shown in Table 11, the photoreduction process is quite efficient in phenyl vinyl ketone copolymers with styrene. Because of the rapid intersystem crossing in the phenyl ketone chromophore, it seems likely that both the reduction and chain scission processes proceed via the intermediacy of the triplet state. An interesting feature shown in Table 11 is that, with PVK copolymers (structure VII), +-co corresponds almost exactly to +OH, suggesting that photoreduction (or cyclization) is the major route for loss of carbonyl in these polymers. However, with PIPK copolymers, +-co is four times as great as We suggest that in this case, because of the greater stability of the tertiary radical formed, the major loss of carbonyl in these polymers (structure VIH) is by the Nomsh type-I reaction. Because of mobility restrictions for the type-I1 process in the solid phase, the quantum yield +I appears to be significantlyhigher than in solution.
XI. POLYMERS FOR PHOTOLITHOGRAPHY The development of microlithography for the production of microcircuits has created new interest in obtaining polymers which undergo efficient chain scission when exposed to UV or other patterning radiation, including electron beams and soft x-rays. Ketone-containing polymers have been used commercially for such purposes, but are also of interest in establishing the mechanism of photochemical reactions in solid polymers. Whereas in ethylene40 copolymers and their structural analogs (type A), both type4 and type-I1 processes can lead to chain scission in the primary photochemical act, it was assumed in early studies that in structures containing pendant carbonyl, only the type-I1 process would lead to chain scission and have a reduction in molecular weight via
11% PHOTocHEMlSTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
Norrisb type Il
More recently it has been shown (30) that efficient chain scission can occur also from the type-I process followed by p-scission: hv
(34) + 3-scission
>
Norrish type I, followed by fhcission
Extensive studies have been reported on copolymers of styrene with a variery of ketone functional groups introduced by copolymerization with substituted vinyl ketone monomers. The copolymer structures are shown schematically in Table 8. The quantum yields in the styrene ketone copolymers are highly dependent on the structure of the ketone group included in the polymer. For example, the quantum yield for the type-I process is 0.09 in MVK copolymers where the substituent on the ketone group is a methyl group, but increases to 0.45 where the substituent is tertiary butyl (30):
-I -
HJC
C
CH3
CH3
-'
(36) +
'k-CH3 I CH3
+
C=O
Depending on the fate of the secondary polymer radical produced, this could lead to either chain scission or crosslinking in the solid phase. Similartrends were observed when the same films were exposed to synchrotron and electron-beamradiation (31). The higher efficiency of the type-I reaction in these structures is attributed to the formation of more stable radicals from the tertiary butyl than from the methyl ketone. Adding an additional substituent to
POLYMERS FOR PHOTOLITHOGRAPHY
119
the carbon a to the carbonyl group creates still further stability in the radical formed by type I and still higher sensitivity to both light and y-rays. For example, poly(t-butyl isopropenyl ketone) (structure IX) is one of the most sensitive polymers yet developed, both as a near-UV and as an electron-beamresist (32):
M
Studies were also made of the photochemistry of styrene copolymers containing minor amounts (2-7%) of the ketone monomers to minimize the effects of energy transfer and migration. The polymers were photolyzed in thin (-0.1 mm) solution-cast films and in solution. In the latter case the rates could be followed by automatic viscometry using the procedure described by Kilp et al. (33,34) and by Nemzek and Guillet (35). Chemical changes in the solid state were followed by FTIR spectroscopy. The major chemical changes which occur are the loss of ketone carbonyl function (+-co), the formation of hydroxyl (+OH), and changes in molecular weight (&). In solution the major change in molecular weight is due to chain scission by the Norrish type-I1 process (Eq.29). There is some contribution due to p-scission of the akyl radical formed by the type-I process, particularly in the MIPK and t-BVK polymers. Loss of carbonyl occurs from photoreduction or the formation of cyclobutanolrings, and also from vaporization of the aldehyde formed by hydrogen abstraction by acyl radicals formed in the Norrish type-I process. As in the case of the corresponding ethylene copolymers, the quantum yields of carbonyl loss are substantiallydifferent for the copolymers, being fastest for t-BVK, slower for MIPK, and least efficient for MVK copolymers. These polymers are of potential interest as photoresists, and their photochemistry was also studied in very thin (1-4 pm) films which were spun cast on polished salt plates. After irradiation in a standard xenon arc photoilluminator, the loss of carbonyl could be determined from FTIR measurements. Experiments were carried out both at 254 nm (deep UV) and 313 nm (near UV). Typical rate curves are shown in Fig. 9. The results at 254 and 313 nm are qualitatively similar, in that the same order of relative sensitivity is observed. Microelectronic devises are now manufactured using a variety of photosensitive polymers (photoresists) to define the geometry of the circuits and to construct
120
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
I 0.5
-
I
I
I
I
Irradiation time (min)
Figure 9. Irradiation of ketone copolymers at 254 nm: 1, = 0.024 mW cm-2.
circuit elements such as transistors, resistors, capacitors, etc. Current manufacturing practice has now reached a level of precision at which the number of such devices which can be placed on a silicon chip is limited by the wavelength of the light used in the patterning step. For this reason it is now important to develop polymers which are sensitive to raadiation having shorter effective wavelengths, such as electron beams and soft x-rays. With both of these high-energy radiations, the primary events induced are the formation of high-energy ions and electrons, whose recombination yields showers of secondary electrons with lower energy. After both elastic and inelastic scattering by the medium, ultimately these electrons reach energies where they can interact with valence electrons to produce secondary ions. In polar media, ions may have appreciable lifetimes and can generate chemical products via well-known ionic reaction mechanisms. However, in relatively nonpolar polymeric solids such as polyethylene and polystyrene, most of the chemical products seem to arise from recombinations of the ions with each other or with low-energy electrons to provide molecules or groups in highly excited electronic states. These will lose energy by collisional processes, and in the absence of alternative energy-dissipatingpathways may eventually populate the lowest-energy singlet and triplet states of the molecule or chromphore. Experimental evidence for this is derived, for example, from product studies on the y-irradiation of ketones which show that the predominant reactions are the Nomsh types I and 11, which are known to result from direct excitation of these states via the absorption of UV photons. Furthermore, polystyrene emits fluorescence from excimer states whose spectra are nearly identical to those observed when excited by W radiation. Recently it has been shown (36) that electron-beam irradiation of styrene-vinyl ketone copolymers show higher yields of type-I radicals than expected from UV photolysis measurements. It seems clear that some part of the excess energy of high-energy photons and electrons is imparted to the translation kinetic energy
SYNCHROTRON-RADIATIONSTUDIES
121
of the separating radical fragments, thus carrying them farther apart before they start their “thermalized” random diffusion. For example, Noyes (11) has calculated that for methyl radicals separation of the primary pair by a critical distance = 5 A reduces the probability of reencounter to 50%. This probability drops off rapidly as the distance exceeds 5 A. These considerations should apply generally to cases where at least one of the separating fragments is small enough to diffuse like a spherical particle. However, when the two fragments are both polymeric, diffusion becomes much more restricted.
XII. SYNCHROTRON-RADIATION STUDIES The use of soft x-radiation from a synchrotron source has certain advantages for the production of microcircuitry. In particular, the short wavelength of the x-ray photons (1-50 A) should provide higher pattern resolution in production devices, thereby increasing the density of circuit elements on the chips, with a concomitant improvement in speed. It was therefore of interest to see if the same chemical selectivity observed in the photoresponse of these styrene-ketone polymers in the near and deep W extended to processes induced by the absorption of soft x-ray photons with energies two to three orders of magnitude greater than those in the UV region. Earlier experiments by Slivinskas and Guillet (37) on poly(styrene-co-methyl vinyl ketone) using y-radiation suggested that this might indeed be the case. The relationships between processes induced by high-energy radiation in polymers and photochemistry has been reviewed recently by Guillet (22). The Stanford Synchrotron source was used for exposure of film samples to synchrotron radiation. The window size on this instrument was 2 mm X 12 mm. The small size of the window severely restricted the amount of material which could be exposed, but there was enough to measure changes in the ZR spectrum by FTIR. After this measurement the molecular-weight changes were estimated by highpressure liquid-exclusionchromatography (GPC) using polystyrene standards for calibration. Measurements of the sensitivity were made in two ways: 1. Loss of ketone carbonyl was determined by FI’IR on the exposed samples
by measuring the relative absorbance A at 1700 cm-’. The ratio (MA)17oo was adjusted for film thickness using the styrene bands at 1600, 1495, and 1455 cm-’. This value is proportional to the rates of the Nomsh type-I and photoreduction processes in the copolymer. 2. Changes in molecular weight result from scission in the backbone of the polymer chain.
122
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
A measure Z of the sensitivityto main-chain scission can be derived as follows. The number of photons absorbed is
n = ZAb
(37)
where Z is incident intensity per unit area. A is the absorption coefficient, C is the film thickness, and a is the area exposed. a is the same for all films irradiated, and kz = w , the weight of film exposed. Therefore
n = iAw
(38)
The quantum yield 4 is the number of bond scissions S which occur per photon absorbed. From stoichiometric considerations (35)
where @ and Mnare the original and final number-average molecular weight of the polymer. Therefore
We can define a response function
which is related to the quantum yield 4 by
4
=- z
ZA
Since the x-ray absorbance A is likely to be identical for the styrene copolymer films used in this experiment, Z will be proportional to the quantum yield when the films are exposed to equal intensities Z of radiation. Representative values (31) for the carbonyl loss and molecular-weight change for three styrene-vinyl ketone copolymers are summarized in Table 12. It is clear from the carbonyl-loss data that the relative sensitivity of these films to synchrotron radiation is the same as for UV exposure. This has important implications for the design of photoresists for soft x-ray patterning.
123
FOLYACRYLOPHENOhFS
TABLE 12. Relative Sensitivity of Styrene-Vinyl Ketone Copolymers to Synchrotron Radiation
CarbonylLoss
Copolymers PS-3% MVK P S d % MIPK PS-7% tBVK
Chain Scission
Z (TYFI + Type 11)
(8) (Type 1)
5
2.1
13 25
4.8 4.9
Xm. POLYACRYLOPHENOIWS The polyacrylophenones represent another important category of photosensitive polymers. Substitution on the phenyl ring can alter both the efficiency and mechanistic pathway to reaction products (38). Early work (39) showed that the photochemistry could be related to that of small-molecule analogs. Work at the Slovak Academy of Sciences (40) has extended to a very large number of substituted derivatives. In common with other ketone systems, the quantum yields for chain scision are reduced significantly in the solid phase. Some of this is due to the restrictions on molecular mobility, which reduce the quantum yields of type-II photoprocesses. Another important factor is the extensive triplet migration, which, in the solid phase, leads to quenching by reaction products (41). such as the olefin produced by the type-11 photoprocess. Recently, studies have been reported (42) on the solid-phase photochemistry of para-substituted poly(acry1ophenone)s which degrade primarily by t y p e 4 processes:
R
R
i
The results are summarized in Table 13. Substitution with fluorine gives values comparable to the unsubstituted polymer, but C1 and ethyl substituents reduce the sensitivity and the para-methoxy compound has a very low quantum yield, probably because of a long-lived triplet state (7 G 4.6 ms) (43) which is easily quenched by oxygen or other impurities in the film.
124
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
TABLE 13.
Quantum Yields for Chain Scission (+& for Substituted Poly(acry1ophenone)s in the Solid Phase at 313 nm
TgCC)
R
H
F -c1 -c2H5
4%
73.5
0.14 0.15
89 51.5
0.05
--OCH,
0.06 0.001
Source: Ref. 42.
XIV.
THE PHOTO-FRIES REACTION
The photo-Fries reaction occurs readily in solid polymers and is observable in phenyl esters, particularly in poly(pheny1acrylate)and poly(pheny1methacrylate) and their derivatives. The course of the reaction can be followed very easily by ultraviolet spectroscopy, since the product hydroxy ketones have strong absorbance at 260 and 320 nm (Fig. 10). Reaction occurs with equal efficiency in small model compounds in solution and in the polymers in the solid phase (44). An Arrhenius plot of the quantum yield for the para product (Fig. 11) shows a linear increase up to 294 K, above which no further change in quantum efficiency is observed, either above or below the glass transition temperature.
200
300 350 400 Wavelength (nm)
250
figure 10. Absorption spectra of a PPA film after different periods of irradiation at room temperature, using light of wavelengths between 220 and 340 nm from an AEI mediumpressure mercury lamp. Reprinted with permission from s. K. L. Li and J. E. Guillet, Studies of the photo-Fries reaction in solid poly(phenylacrylate), Macromolecules, 10, 840 (1977). Copyright 1977, American Chemical Society.
CISTRANS ISOMERIZATION
125
I 03/TOK
Feure 11. Arrhenius plot of the formation ofp-hydroxyphenonegroups as measured by absorbance changes at 265 nm. The transition temperatures of the polymer are also included. Reprinted with permission from S. K. L. Li and J. E. Guillet, Studies of the photo-Fries reaction in solid poly(phenylacry1ate). Macromolecules, 10, 840 (I 977). Copyright 1977, American Chemical Society.
The linear portion of the curve has an activation energy of 1.8 kcal mol-' and is believed to be associated with the activated process involving small motions of the phenyl ring on the ester group. The positions of the transitions were determined by the phosphorescence method (23) and are shown in the figure. The activation energy for the ortho product is 1.2 kcal mol-', which presumably reflects the smaller amount of motion required to move to the ortho than to the para position. The small value of the activation energy is presumably associated with the very small volume required for the rotation of the phenoxy radical before it recombines to form the hydroxy ketone.
XV. CIS-TRANS ISOMERIZATION One of the simplest photochemical processes which can be observed in solid polymers is the photoisomerization of a double bond in olefins such as stilbene. The reaction can be followed easily by spectrophotometric methods, and the irradiation can take place in thin polymer films. The amount of free volume required is relatively small, but will obviously depend on the substituentsattached to the double bond. In early studies, Gegiou et al. (45) showed that the quantum
126 PHOTOCHEMISTRY AND
MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
yield of cis-trans isomerization of stilbene itself decreased with increasing viscosity of the medium. It was also shown that a polymer matrix such as poly(isobuty1ene)did not inhibit the photoisomerizationas long as the temperature was above the glass transition temperature Tg.Above Tgthe photoisomerization followed first-order kinetics, but below that temperature the kinetics were very complex and suggest the occurrence of a multiplicity of different first-order processes. It was postulated that an increase in free volume was necessary for the transforma5on of trans to cis stilbene:
H\
,
c=c
/
/c6H5~~pitive
'
H
H
\
c=c
/
c6H5
H
\ c6H5
and that restrictions on the rotation of the phenyl groups in the polymer matrices reduced the quantum yield of the process. It was suggested that stilbenemolecules were located in a range of different guest sites associated with differing amounts of free volume. The situation is equivalent to having a spectrum of microscopic viscosities, each determining the rate constant for the observed process. This phenomenon now has been observed in a wide variety of similarphotocyclizations and reaarrangements in polymer matrices, and it now seems to be a general phenomenon. Modem theories of glassy polymers propose that submicroscopic voids exist in the polymer matrix with a range of surface free energies associated with their distribution and size. Location of the probe molecule at or near one of these voids would provide a variety of environments which would give rise to the spectrum of rate constants.
XM. PHOTOCYCLIZATION Photocyclization is a particularly valuable route to the formation of cyclic compounds. There is a wide variety of photocyclization reactions reported in the literature of organic photochemistry, but relatively few of these have been carried out in solid polymers. The earliest reports concern the photodimerization of cinnamic acid derivatives, leading to crosslinking in solid polymers. These polymers have important applications as commercial photoresists. The chemistry has been reviewed by Delzenne (46)and Williams (47). Other similar photoreactive groups such as chalcones (48), coumarins (49). and dibenzazepines (50) have been proposed for similar applications. Photocyclodimerization is now considered to be a major factor in mutagenesis in DNA and polynucleotides. The reaction involves the photoinduced dimerization of pyrimidine bases such as thymine. The crosslinkingwhich results causes a defect in the coding sequence and can cause other cell damage.
127
PHOTOCYCLEATION
Meador and Wagner (5 1) have reported that a-(0-toly1)acetophenone undergoes a photocyclization reaction via the intramolecular abstraction of the yhydrogen, with a quantum yield close to unity: H hv
3 1 3 nm’ benzene
(45)
The ketone absorbs available solar energy in the 280-360-nm region, but the product 2-phenyl-2-indanol is transparent above 280 nm. This is of particular value because the reaction can be run to a high degree of conversion with no interference by light absorption by the product. Guillet et al. (52)have shown that solar photochemicalreactions can be carried out using crosslinked poly(ethyleneviny1acetate) (EVA) beads as a solvent. The beads can be exposed in solar ponds and the products recovered by extraction. Figure 12 shows data on the rate of photolytic conversion of the a-(0-toly1)acetophenone when exposed in the solid bead and in benzene solution. Identical rates and quantum yields were observed in both media, showing that the rate of cyclizationsof this type are independentof the internal viscosity of the medium. Bimolecular cyclizations, as might be expected, are more sensitive to the nature of the polymeric medium. Several studies have been reported of examples of the cycloaddition reaction
60
I
0
45
-
I
I
1
1
-
Solution
Beads
0 C
Joules/cm*
Figure 12. Photoconversion of a-(o-toly1)acetophenone as a function of absorbed dose in benzene solution and in solid EVA beads. Reprinted with permission from J. E. Guillet, W. K. MacInnis, and A. E. Redpath, Prospects for solar synthesis. 11. Study of the photocyclization of a-(0-toly1)acetophenone in solution and in crosslinked ethylene-vinyl acetate beads. Canadian Journal of Chemistry, 63, 1333 (1985).
128
PHOTCKHEhUSTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
R' fwvCRXR.nrr
R' + 'C-X R.f
I
hv>
R'--C-X
I
-CR---CR-
(46)
I
An early example is the photo reaction of benzophenone with cis-polyisoprene
(53). This reaction occurs readily in both the solid phase and solution to give polymers of unusual structure:
The inclusion of the large ring system into the polymer backbone increases the chain stiffness, and hence the glass transition temperature Tg also increases. Table 14 shows the rapid rise in Tg with irradiaation time. In the solid state, complete conversion is inhibited above about 70%, presumably because of restrictions on the diffusion of benzophenone to the remaining double bonds in the polymer. Holden and Guillet (54) have reported the photoaddition of a variety of olefins to thin films of poly(viny1benzophenone):
>
6
-CCH2-CH-CH2-CHO'C
b
g
R
z
R3
R4
(47)
Conversions of up to about 80% oxetane were observed (Table 15), and quantum yields in the solid phase were independent of temperature between 23 and 65°C and relativey low (0.012). No change was observed at the glass transition temperature (Tg = 40°C). Such a result agrees with a number of studies of diffusion coefficientsand equilibrium solubilitiesof gases in amorphous polymer, which show that there is often no abrupt change in diffusivity or solubility at Tg for gases that are small in relation to the polymer repeating unit. A summary of the processes involved in the solid-phase cycloaddition is proposed ir. the following:
129
PHOTOCYCLIZATION
TABLE 14. Glass Transition Temperature of Polyisoprene and Its PhotochemicalAdduct with RenzophenoneDetermined by DSC Irradiation Time (min)
Conversion
0
15 30 45
60
120
Tg
(%)
("C)
0 29.6 38.2 42.0 48.5 57.4
-64.9 31 37.8 37.6 41.2 45.8
TABLE 15. Properties of Cycloadducts between Poly(styrene-coVinylbenzophenone)a and Various Olefins Olefins
h1
Conversion to Oxetane (%)
unreacted Ketone (%)
(dLg-9
79 72 82 61
2 7 1 11
0.44 1.49 1.09 0.50
Isobutene ZMethyl-2-butene 2-Methyl-2-hexene 2,3-Dimethyl-2-butene
"[q] = 1.43 dL g-', in benzene at 3O.O"C. q n benzene at 30.0"C.
42C=0 2(b2C=O* (TI) Excitation hu
T,
-
A 42C=0 TI
t
+ hv'
4,C=O
I
4
(48)
Phosphorescence
(49)
Nonradiative decay
(50)
1%
PHoTocHEMlsTRY AND MOLECULAR MOTION IN SOLID AMORPHOUS POLYMERS
T1 + (CH&C=CH,
+26-OH
+
CH3 * I CH2-C=CH,
(52)
The quantum yield of oxetane formation is then equal to the rate of photocycloaddition divided by the sum of rates of all processes which deactivate the ketone triplet (Eq. 54):
where a = k2/(k2 + k3), and [I] and [RH] are the effective concentrations of isobutene and of polymer hydrogen, respectively. It is clear from Eq. 54 that , , , , ,$ is a function not only of the rate of photocycloaddition but of the rates of all other triplet deactivating processes. It is possible that changes in kl may be offset by changes in one or more terms in the denominator of Eq. 54, which would lead to a quantum yield of oxetane formation apparently independent of temperature.
XVII.
CONCLUSIONS
What can be seen from the foregoing examples is that one can use the photochemistry of small model compounds to predict the photochemistry of a polymeric material provided that certain structural features are included and that one has some idea of the free volume required for the conformational changes or molecular motions necessary for the formation of the excited state and rearrangement or disproportionation into products. It can be concluded that reactions which require very little change in the geometry of the excited state from that of the reactants should proceed as well in solid glassy polymer matrices as in solution. Dissociation of free radical pairs will be relatively efficient in the solid state if one of the components is a small free radical, but will be significantly inhibited if both components are polymer radicals. Reactions which can be considered to be associated with caged radicals, such as the photo-Fries and certain internal cyclizations, will require very little free volume and can be expected to be quite efficient in solid polymers, even below the glass transition, whereas photochemical processes like the Norrish type-11process will be expected to be substantially reduced in glassy polymers below Tgunless the geometry of the cyclic six-membered ring is particularly favored by steric factors in the chain, so that the most stable conformation corresponds to that required for reaction. And finally, bimolecular reactions which require the diffusion of a small-molecule
REFERENCES
131
reagent to a species in a polymer matrix will depend on both the diffusion constant and the solubility of the material in the matrix. However, it should be noted that diffusion in solid glassy matrices, particularly of small molecules, is much higher than would be predicted from the bulk viscosity of the medium. Solid polymers generally have internal viscosities only two to three orders of magnitude less than those for simple liquids such as b e m n e or hexane, so that under suitable conditions quite efficient bimolecular reaction can be induced to occur by diffusional processes in polymeric materials.
REFERENCES 1. R. Haward, in Molecular Behavior and the Development of Polymer Materials, A. Ledwith and A. M. North, Eds., Chapman and Hall, London, 1975. 2. E. Dan and J. E. Guillet, Macromolecules 6 , 230 (1973). 3. G. Wegner, Pure Appl. Chem. 49, 443 (1977). 4. F. Bueche, Physical Properties of Polymers, Interscience, New York, 1%2. 5. J. Crank and G. S . Park, Dimsion in Polymers, Academic Press, London, 1968. 6. M. Heskins and J. E. Guillet, Macromolecules 3, 224 (1970). 7, R. M. Barrer and G. Skirrow, J. Polym. Sci. 3 , 549 (1948). 8. J. Brandrup and E. H. Immergut, Eds., Polymer Handbook, 2nd ed., Wiley, New York, 1975. 9. J. E. Guillet, in Photophysical and Photochemical Tools in Polymer Science, M. A. Winnik, Ed., Reidel, Dordrecht, 1986. 10. J. Franck and E. Rabinowitsch, Trans. Faraday SOC.30, 120 (1934). 11. R. M. Noyes, Progr. React. Kinet. 1, 128 (1961). 12. T. J. Chuang, G. W. Hoffman, and K. B. Eisenthal, Chem. Phys. Lett. 25, 201 (1974). 13. J. W. Moore and J. E. Guillet, manuscript in preparation. 14. W. Braun, L. Rajbenback, andF. R. Eirich, J . Phys. Chem. 66,1951 (1962). 15. J. E. Guillet and J. C. Gilmer, Can. J. Chem. 47, 4405 (1969). 16. J. A. Slivinskas and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 11, 3043 (1973). 17. J. A. Slivinskas and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 12, 1469 (1974). 18. G. H. Hartley and J. E. Guillet, Macromolecules 1, 413 (1968). 19. P. I. Plooard and J. E. Guillet, Macromolecules 5 , 405 (1972).
132
PHOTOCHEMISTRY AND MOLECULAR MOTION IN SOLID AMORF'HOUS WLYMERS
20. J. E. Guillet and R. G. W. Nomsh, Proc. R. SOC.London, Ser. A 233, 153 (1955). 21. K. F. Wissbrun, J. Am. Chem. Soc. 81, 58 (1959). 22. J. E. Guillet, Polymer Photophysics and Photochemistry, CambridgeUniversity Press, Cambridge, 1985, Ch. 10. 23. A. C. Somersall, E. Dan, and J. E . Guillet, Macromolecules 7,233 (1974). 24. J. E. Guillet and M. Andrews, manuscript in preparation. 25, G. H. Hartley and J. E. Guillet, Macromolecules 1 , 165 (1968). 26. F. Sitek, J. E. Guillet, andM. Heskins, J. Polym. Sci. SymposiumNo. 57, 343 (1976). 27. J. E . Guillet, Naturwissenschafien 59, 503 (1972). 28. S. K. L. Li and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 18, 2221 (1980). 29. E. Dan and J. E. Guillet, Macromolecules, 6 , 230 (1973). 30. J. E. Guillet, S. K.L. Li, and H. C. Ng, in Materials for Microlithography, L. F. Thompson, C. G. Willson, and J. M. J. Frechet, Eds., ACS Symp. Ser. No. 266, 1984, p. 165. 31. J. E. Guillet, S. K.L. Li, S. A. MacDonald, and C. G. Willson, in Materials for Microlithography, L. F. Thompson, C. G. Willson and J. M. J. Frechet, Eds., ACS Symp. Ser. No. 266, 1984, p. 389. 32. S. A. MacDonald, H. Ito, C. G. Willson, J. W. Moore, H. M. Gharapetian, and J. E. Guillet, in Materialsfor Microlithography, L. F. Thompson, C. G. Willson, and J. M. J. Frechet, Eds., ACS Symp. Ser. No. 266, 1984, p. 179. 33. T. Kilp, B. Houvenaghel-Defoort, W. Panning, and J. E. Guillet, Rev. Sci. Instrum. 47, 1496 (1976). 34. T. Kilp and J. E. Guillet, Macromolecules 10,90 (1977). 35. T. L. Nemzek and J. E. Guillet, Macromolecules 10, 94 (1977). 36. S. A. M. Hesp, M.Sc. Thesis, University of Toronto, 1987; S. A. M. Hesp and J. E. Guillet, manuscript in preparation. 37. J. A. Slivinskas and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 11, 3057 (1973). 38. P. Hrdlovic and I. Lukac, in Developments in Polymer Degradation 4 , N. Grassie, Ed., Applied Science, London, 1982. 39. F. J. Golemba and J. E. Guillet, Macromolecules 5 , 212 (1972). 40. I. Lukac and P. Hrdlovic, Polym. Photochem. 2, 277 (1982). 41. T. Kilp and J. E. Guillet, Macromolecules 14, 1680 (1981). 42. P. Hrdlovic and J. E. Guillet, Polym. Photochem. 7, 423 (1986). 43. P. Hrdlovic, J. C. Scaiano, I. Lukac, and J. E. Guillet, Macromolecules 19, 1637 (1986).
REFERENCES
133
44. S. K. L. Li and J. E. Guillet, Mucromlecules 10, 840 (1977). 45. D. Gegiou, K. A. Muszkat, and E. Fischer, J. Am. Chem. SOC.W,12 (1968). 46. G. A. Delzenne, Znd. Chim. Belg. 34, 249 (1974). 47. J. L. R. Williams, Fortschr. Chem. Forsch. 13, 227 (1969). 48. K. S. Lyalikov, G. L. Gaeva, and N. A. Evlasheva, Tr. Leningrad Znsr. Kinoinzh. 16, 42 (1970). 49. R. Anet, Can. J. Chem. 40, 1249 (1962). 50. P. Hyde, L. J. Kricka and A. Ledwith, J. Polym. Sci., Polym. Lett. Ed. 11, 415 (1973). 51. M. A. Meador and P. J. Wagner, J. Am. Chem. SOC. 105, 4484 (1983). 52. J. E. Guillet, W. K. MacInnis, and A. E. Redpath, Can. J. Chem. 63, 1333 (1985). 53. H. C. Ng and J. E. Guillet, Mucromlecules 10, 866 (1977). 54. D. A. Holden and J. E. Guillet, J. Polym. Sci., Polym. Chem. Ed. 18, 565 (1980).
Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.
PHOTOCHEMISTRY OF SIMPLE OLEFINS: CHEMISTRY OF ELECTRONIC EXCITED STATES OR HOT GROUND STATE? Guy J. Collin apartement des Sciences Fondamentales, Universit6 du Qukbec B Chicoutimi, Chicoutimi, Qudbec, Canada G7H 2B1
CONTENTS
I. Introduction II. The ethylene case III. The methyl substitutedethylenes A. Propene B . Other methylated ethylenes IV. The other acyclic olefins A. The p(C-C) bond rupture B . The excess energy distribution C. Photosensitization D. The isomerizationof acyclic alkenes E. Conclusion V. The cyclic monoolefins A. The fragmentationprocesses in direct photolysis B . Fragmentation in photosensitizedexperiments C. Isomerizationprocesses D. Conclusion VI . Conclusion Acknowledgments References 135
136
PHOTOCHEMISTRY OF SIMPLE OLEFINS
I. INTRODUCTION The very far UV and vacuum UV photochemistry of gaseous alkenes has been studied for more than 25 years. Several laboratories have looked at the stability of the photoexcited molecules at various wavelengths. The absorption threshold for alkenes is located between 200 and 230 nm, depending on the number of alkyl substituents attached to the double bond (1,2). Of course, the use of the true resonance line or mercury (A = 184.9 nm) was very easy. However, wavelengths as short as 104.2 nm have been used, i.e. at energies much higher than the ionization onset of these molecules: 10.51 3 I.P.(alkenes) B 8.4 eV (3). Much of this work has been performed at 147.0 nm (8.4 eV). At this point it must be mentioned that the 1980s have seen the availability of rare gas-halide excimer lasers that produce light in this spectrum region. Thus, the variety of experimental conditions is large. In all cases, fragmentation processes have been observed. In some of these studies, the geometric cis-trans isomerization process as well as different structural ones have been reported. Conversely, photoexcited ethylenic compounds are not known to fluoresce very efficiently (4). On the other hand, spectroscopy has undergone many developments. Through the use of supercomputers, ab inifio calculations are more and more powerful. Although many details are still lacking or are even controversial, the nature and energetics of various electronic excited states for this group of molecules are better understood (2,5). Since the absorption of a photon will create an electronically excited molecule, it is tempting to look at the properties of each of thesse states in order to get a better insight into the different reaction pathways leading to products (6). It is the aim of this review to update the links between the photochemical behavior of ethylenic molecules and their electronic properties. In the past 20 years, several studies have been published (7). In order to keep the length of this review as short as possible. we shall avoid making a systematic review of all the earlier references.
II. THE ETHYLENE CASE Of course, ethylene is the first and the simplest molecule of this group. Its direct photochemistry has been studied for many years; several laboratorieshave looked at various aspects of its behavior under various photon beams. One of the first studies, if not the first, appeared in 1961 (8): it identified two main fragmentation channels involving the 147.0 nm photoexcited molecule:
THE E"XYLENE CASE
137
with +2 z +3. One year later, by photolyzing CH2CD2, Okabe and McNesby showed that the terminal elimination of hydrogen dominates the 1,2-elimination (9), giving rise to the formation of a vinylydene intermediate:
Moreover, both works agree that it is not necessary to call upon the formation of vinyl radical intermediates. If transient vinyl radicals are formed in the process in Eq. 3, they must have sufficient internal energy to decompose in a very short time before collision. In fact, at a longer wavelength, it was later observed that part of the acetyleneformation involves energized vinyl radicals (1Oa). Moreover, the observed decomposition rate constant is in good agreement with what can be calculated by using Rice-Ramsperger-Kassel-Marcus (RRKM) assumptions (lob):
C2H2
+
H
(8)
The 184.9 nm photolysis of C2H4 was studied by Borrell et al. (1 1) and Glasgow et al. (12). The latter group undertook a systematic study between 147.0 and 193.1 (a carbon lamp) nm and made the following remarks: (1) the process in Eq. 2-the molecular elimination of hydrogen-is independent of various parameters tested (pressure, temperature, wavelength), and 42 0.42 between 147.0 and 184.9 nm and between 0.1 and 100 Tom; (2) the process in Eq. 3 decreases with increasing pressure and increases with increasing photon energy; (3) the processs in Eq.6 decreases with an increase in photon energy. Hara and Tanaka, one year later, arrived at somewhat different conclusions and values, although the latter are in the same range (1Oa). The photochemistry of liquid and solid ethylene at 184.9 nm shows that the ratio of the free radical to the molecular decomposition is about 0.03 in the liquid at - 160°C (14). The same work indicatesthat there was isotopic scrambling in the various unreacted dideuterioethylenes. This scrambling was assumed to involve the relaxation of excited ethylene to ethylidene and may be followed by the molecular elimination of H2:
PHOTOCHEMISTRY OF SIMPLE OLEFINS
138
in agreement with the isotopic scrambling reported in the acetylene product formed in the 147.0 nm solid phase photolysis of CH2CD2 (15). It was also proposed that the formation of methylcyclopropane involves the reaction of excited ethylidene with ethylene in the solid phase (16). Finally, the study of ethylene photosensitization (A = 253.7 nm) involving a triplet excited state shows similar processes leading to fragmentation (H2 + C2H2)in competition with pressure quenching, cis-trans isomerization, and isotopic scrambling (17). Decomposition of ethylene into acetylene and hydrogen was scarcely observed for the Cd(3P1)-photosensitizedreaction over the 275-350°C range: A = 326.1 nm (17a). The mechanism involved in the direct photochemistry of ethylene has been recently questioned by Laufer (18). He observed by absorption spectroscopy (A = 137.4 nm( the formation of a triplet (3B2)vinylidene with a quite high quantum yield, probably in a secondary process (18b). Thus, no one can preclude the involvement of triplet intermediates, although they are generally ignored. More disturbing is the fact that at the shortest delay times attainable with his system, i.e. 4 ps after the flash, he was unable to observe acetylene (Fig. 1). Since it is admitted that the singlet vinylidene radical has a very short lifetime (T < lo-" s with respect to rearrangement to acetylene), he concluded that there is no evidence of the formation of ground state 'A, vinylidene.
I
I
10
8 In
c c 3
6
.,
/-x
,'
'
I
I
x; I
/.
I
'
/=/',
'\
\
x
\ \ \
.
\
1 . 7
.l_i
.... .
.
0
Time ( p s )
X,
Figure 1. Time profdes for acetylene (0)and vinylidene (3B2)( x ) in the flash photolysis of ethylene (arbitrary units and different y-scales). Reprinted with permission from Ref. 18a and 18b. Copyright Elsevier Sequoia SA.
THE ETHYLENE CASE 205
c
>
139
X/nm
185
180
170
160
1.2
ln
2
W
n
0.0
48.10
54.58 Frequency
55.56
/
cm-'
59.61 Y
lo3
63.66
Figure 2. The absorption spectrum of ethylene. Broken line: nitrogen pressurized (104 am) spectrum. From Ref. 13 with kind permission of the authors.
The absorption threshold for ethylene is located at 200 nm (Fig. 2). Its spectrum consists of diffuse bands which become a continuum at shorter wavelengths. The diffuse bands as well as the continuum are ascribed to the IT* + IT transition (1,2,5). The first singlet Rydberg band is superimposed on the V +N transition: h = 174 nm. Upon addition of a high pressure of nitrogen, there is an important broadening of the Rydberg bands on the high energy side of the spectrum, while the V +- N transition is not affected (2). This relative simplicity in the absorption spectrum does not reveal all the available excited states, and it is a very difficult or even impossible task to link the photochemical processes and the different known excited states (5,19) (see Fig. 3) - or the calculated one (20) (see Table 1). It must be emphasized that there is a tremendous need for more experimental and theoretical information to get a better insight into the spectroscopy of ethylene (5). In fact, several recent studies from various laboratories have shown how complex and fascinating is the field of excited states of ethylene (5). Different techniques or approaches are used: absorption spectroscopy (2 1-23), magnetic circular dichroism (24), photoelectron spectroscopy (25,26), electron (27) and ion impact (28), multiphoton ionization (29), ab inifio calculations (30,31), etc. At this point, it is relevant to note that theoretical work using ab initio MO-CZ methods indicates that the reactions of twisted singlet excited ethylene, to give directly either the lowest singlet state of vinylidene+H2 or ethylidene, are easy pathways that have relatively low computed activation energies, in partial contradiction with Laufer's observation reported above. The fragmentation of
140
PHOTOCHEMISTRY OF SIMPLE OLEFINS
I*.
‘E
Figure 3. Schematic potential energy diagram for ethylene.
+
the singlet ethylidene, giving rise to acetylene H2formation, is also calculated not to be difficult (32). Finally, the authors add that they are far from a complete knowledge of the photochemical processes, although “it would be best not to describethe product-forming processes as arising from a conceptually hot groundstate molecule” (32). In short, the photochemistry of ethylene seems better explained in terms of undefined electronic excited state(s) where vinylidene as well as ethylidene transient species may be involved and molecular as well as atomic hydrogen species are formed.
III. THE METHYL SUBSTITUTED ETHYLENES A.
Propene
The simplest alkene of this subgroup is propylene. Its first vacuum UV photochemistry study was published in 1965 (33) and was followed by several others (34-36). For example, at 147.0 nm, many products were identified. From partially deuterated material, as well as from the effect of added nitric oxide, the molecular formation of hydrogen and methane was observed as well as those of hydrogen
141
THE METHYL SUBSTITUTED ETHYLENES
TABLE 1. Excited States of Ethylene-h, Upper State Configuration 3
Symmetry
Frequency, (cm- I)
eV
*B,,
1B3"
35,200 53,720 57,338 61,300 62,790 62,905 65,735 66,875 69,080 69,531 71,813
B3u B1u
75,250
vert., 4.36 advert., 6.66 advert., 7.1 1 vert., 7.60 advert., 7.78 advert.,7.80 advert., 8.15 advert., 8.29 advert., 8.56 advert., 8.62 advert., 8.90 advert.,8.98 advert.,9.33
(.rr,.rr*)
3(.rr,3s)
*BSU
'(.rr,3S)
lB3u
'(a,.rr*)
lBlU
3(a
.3PY) (.rr,3PY) 3(.rr93px) '(a93px) 3(.rr,3do) '(?r,3do) '(.rr,3dS) '(.rrr,4s) (.rr,3dxz) '(.rr94P)
3B1,
1
lB1,
3Ag 3B3u lB3u 1
'
B2,
Source: Refs. 5 , 19, 31.
atoms and methyl radicals. Although there was no indicationof measured quantum yields, a rough estimate indicates that many more methyl radicals appear than methane molecules:
W(iso-C4HIo)
+
Q'(CH4) 2 @'(C2H6)
+ CPr(l-C4Hs)
= 0.114
(1)
In this equation isobutane, ethane, and 1-butene are supposed to be formed in the appropriate combination reactions of methyl radicals plus a suitable radical. Since methane is partly formed in disproportionationreactions of methyl radical with other radical species, the abovementioned ratio is an upper value of the relative importance of the molecular elimination of methane. The relative importance of the moleculm elimination of hydrogen is not so obvious, although, at most, it counts for less than 20% of the acetylene yield. The 163.3 nm (37) and 184.9 nm photolysis (38,39) were documented much more, and a very good knowledge of the photoexcited molecule was attained. At 184.9 nm, the molecular elimination of either methane (@ = 0.04) or hydrogen (a = 0.02) is of less importance than the primary p (C-H) and (Y (C-C) bond ruptures: CP = 0.63 and 0.36, respectively (39). It appears from Table 2 that the elimination of molecular products increases with increasing photon energy at the expense of the simple rupture of the C-C or C-H bonds (36):
142
PHOTWHEh%lSTRYOF SIMPLE OLEFINS
+ CH4 , C3H$* C3H4 + H2 , C3Hg* C3H3 + H , C3HZ* +C2Hg + CH3.
-
C3H$* 4 C*H, __*
Ab initio SCF-MO calculations have been reported on the fundamental electronic state of propylene (42). They reveal that an internal 1,3-sigmatropic hydrogen shift may be in competition with the fragmentation of the excited molecule. In other words, this rearrangement may occur before the fragmentation takes place. From symmetry considerations, one can say that the ground state forbidden suprafacial reaction is allowed in the singlet excited state. Conversely, the antarafacial process, which is allowed in the ground state, is forbidden in the excited state. It must be added that from geometric consideration this antarafacial transfer is of very low probability (43). In the condensed phase photochemistry of propylene, the major primary processes occumng in the 149.5-174.5 nm range are the molecular detachment of methane acetylene and to a smaller extent hydrogen C3H4 (44).These observations are rather in contradictionwith the above reported gas phase results. However, these results can be explained on the basis of a fast stabilizing process in the matrix, involving either the electronic excited molecule or the hot electronic ground state or both. Recombination of radical fragments in the cage may also be part of the explanation. No quantum yields are available, so that further discussion is risky. Let us say only that the molecular products are similar to those observed in the gas phase at 184.9 nm. The triplet photochemistry of propylene has also been studied by several laboratories and in different conditions (40). Cis-trans isomerization is the main process and is observed in the presence of various sensitizers. As far as fragmentation is concerned, the C-C and C-H bond ruptures are observed in a 0.125h.O ratio (40a). In the case of the Hg(3P,) photosensitization of transpropylene-l,3,3,3-d4, no isomerization to propylene-2,3,3,3-d4 was observed. This is in marked contrast to the observation of the internal 1,2-hydrogen atom transfer observed in ethylene (4Oc). There is also formation of tiny amounts of cyclopropane and molecular methane and hydrogen (40). Coming back to the a(C-C)/P(C-H) primary split ratio (Table 3), it would be valuable to compare these values with that obtained either in the thermal pyrolysis of propene or in chemical activated systems. For example, in shock tube experiments (1650-2300 K), the dominant bimolecular initiation reaction leads to the C-C bond rupture, although a possible contribution of the p(C-H) bond rupture cannot be excluded (50). This is also observed in the decomposition of hot propene formed from ethylcarbene [(E)(C3H$) Z 414 kJ/mol]: a(C-C)/ P(C-H) 22 (51). Conversely, hot propene formed by the addition of singlet methylene to ethylene [(E)(C3Ha) % 464492 kJ/mol) gives rise to C-H bond
+
+
40a
~~~~~~~~~~~~~
-
0.2
-
11
89
40b
-
-
-
1-1.4 1-1.4 80-86 10-17
253.7+184.9a
"Photosensitization,relative yields only. 9onization potential: I.P.(propene) = 9.73 eV (41).
Total Ref.
+
C2H2 + CH4 C3H4 + H2 C3H5 H CzH3 + CH3 CzH4 + CH2 CYCIO-C~H~ [C3W1+ + e-
253.7a
0.90 38
-
-
0.03
0.40
0.04 0.02(?) 0.41
184.9
39
1.05
-
0.00
-
0.04 0.02 0.63 0.36
Quantum Yields for Sensitized and Direct Photochemistry of Propene
ProcessC,H$*
TABLE 2.
0.97 37
-
0.565 0.335 0.02
0.05(?)
163.3
20.68 36
-
-
0.21 0.06
0.27 0.04
20.68 36
0.30'
-
20.05
20.34
123.6
a0.03 20.34
147.O
144
PHOTOCHEMISTRY OF SIMPLE OLEFINS
TABLE 3. Relative Importance of the or(C-C) and p(C-H) Primary Splits in the Photolysis of Some Olefins Olefin
Ref.
Propene
163.3 184.9 253.7 174 184.9 174 184.9 202.6-206.2 253.7 184.9 >200
Isobutene cis-2-Butene
trans-2-Butene 2-Methyl-1-butene
0.59 0.571 (0=0.054) 0.11,0.12 0.90 0.95 (0=0.10) 1.02 0.96 2 0.13 1.45 0.4 1.35 2 0.20 0.73
37 39 40 39 39 45 46 47 48 46 49
rupture with a rate twice that of the C-C (52). One must add that the propene system is not an easy one, since in many cases it involves a chain mechanism and, as is known, vinyl radicals react with propene. If the C-C bond rupture is the main primary process occurring in the thermal system, this would suggest that the fragmentation of the photoexcited molecule does not involve the fundamental state. Another alternative proposal resides in the dependence of the a(C-C)/P(C-H) ratio on the energy content of the propene molecule. Unfortunately, there is some controversy about RRKM results (53).
B.
Other Methylated Ethylene
Other methylated ethylenes have been studied by different laboratories. One of the fust studies involved the irradiation of cis-2-butene at 202.6-206.2 nm at pressures between 20 adn 500 Ton (47). The collisional stabilization of the trans isomer competes with the first order decomposition reactions: cis-2-C4Hg*
-
C3H5 + CH3,
c~s-~-C~HZ* +C4H7
+
H,
k
k
2
5.0 lo8 s-'
(15)
3.5 lo8 s-1
(16)
It is concluded that the cleavage reactions occur after rapid internal conversion to the ground electronic state. Moreover, the cis-trans isomerization and isomerization to 1-butene(5% of the total reaction) occur in a short time compared to the time between deactivating collisions even at 500 Torr (47). This model can be reasonably extended to the other methylated ethylenes from their absorption
THE m
n SUBSTITUTED ETHYLENES
145
threshold to, and including, 147.0 nm. For example, the photolysis of isobutene is known to produce mainly allene and propyne plus methyl radicals and hydrogen atoms at all wavelengths (3934). The problem arises from the identification of the products coming from either the primary p(C-H) or the a(C-C) bond ruptures. This problem has recently been solved: the a(C-C)/p(C-H) ratio is in the 0 . W 0.95 range at 184.9 and 174.0 nm (39). This value must be compared with those observed in different systems (Table 3). A very interesting and intriguing effect appears to be attached to the number and location of the methyl substituents: this effect may be due to the electrophilic property of the methyl groups. Of course, the experimental a(C-C)/p(C-H) primary split ratio is very dependent on how correct and accurate the active mechanism is. Taking the recently calculated values from our own experiments (39,46), we were unable to link the increase in this ratio (going from 0.57 in propene to 1.35 in trans-2-butene) to any simple property of these molecules (39). In fact, it is likely that the a(C-C)/ p(C-H) ratio is not dependent on only one parameter. The variation of this ratio may be discussed in terms of spectroscopy. Both Rydberg and valence states are populated at 184.9 nm. Do the two fragmentation pathways result from the same excited state or different ones? If each exit channel is linked to one electronic state, the a(C-C)/p(C-H) ratio can be explained in terms of differences in the absorption process. Another possibility resides in the above mechanism itself. It is consistent with the view that the internal conversion of electronic excitation energy to vibrational energy preceeded the bond cleavage process. However, it cannot be precluded that bond cleavage is part of the conversion process itself.
150
170
Wavelength
/
nm
190
Figure 4. The UV absorption spectrum of I-butene. Reprinted with permission from Ref. 41. Copyright (1962) American Institute of Physics.
146
PHOTOCHEMISTRY OF SIMPLE OLEFINS
In that case, the geometry of the molecule may play a role in the redistribution of energy. In all cases, the quantum yield of the molecular elimination of either methane or hydrogen is considered to be smaller than 0.05. Thus, the main primary processes involve either the a(C-C) or the B(C-H) bond ruptures. This observation differs from that made for ethylene, where at least 40% of the fragmentation involves the molecular elimination of hydrogen. May this behavior be linked to the differences observed in the absorption spectra? At least, it may be said that well-defined absorption bands, one of which is probably Rydberg in nature, are observed in the ethylene spectrum. Conversely, the spectra of methyl substituted ethylenes are rather unstructured (1). The W absorption spectrum of l-butene is shown in Figure 4. We shall come back later to this pint. One interestingreport must be mentioned here. On direct excitation in solution at 228.8-214.4 or 213.9 nm, cis-trans isomerization is the major reaction path observed both in cis- and tram-2-butene. Moreover, dimers-tetramethylcyclobutanes-are formed, and this formation is stereospecific (55):
Thus, it seems possible that these products arise from an excited 2-butene molecule originally having either the cis or the trans structure. From the known structures of the electronic excited states of ethylene, this excited molecule may be the Rydberg excited state, whose structure is not far from the original planar structure (Fig. 3). The involvement of either the ‘V and 3R states-which have a skew structure-will lead to nonstereospecific cyclobutane derivatives. A theoretical study of the addition process has shown from the localized state correlation diagram that the ?r,R(3s)Rydberg singlet state of ethylene can interact with the ground state of another ethylene molecule (56). Moreover, a very rapid reduction in the extent of photochemical cyclodimerization of liquid 2-butene as a result of dilution was observed. It was tentatively suggested that bimolecular diffusional kinetics are not adequate for description of B* B +-dimer reactions and that something like a solvent cage effect is operative. It seems possible that the excitationprocess itself involves pairs of adjacent molecules which are directly excited to excimers. Similar explanation was also proposed for the formation of dimeric compounds in the irradiation of 1,3-~yclohexadieneat long wavelength (57).
+
THE OTHER ACYCLIC OLEFINS
147
The direct or sensitized cis-trans photoisomerization has been described by many authors (58). The Hg$Pr) photoisomerizationwas explained on the basis of vibrationally excited triplet molecules. In the case of the Cd(3Pl), the photosensitization of unsaturated hydrocarbons mainly results in the cis-trans process. The main difference between mercury and cadmium sensitization resides in the lower energy content delivered in cadmium experiments: 366.4 in comparison with 469.4 kllmol (59). A very recent study of the zinc photosensitization of 2butene concludes with the cis-trans isomerization process as the main process (60).
IV. THE OTHER ACYCLIC OLEFINS A.
The p(C-C) Bond Rupture
In this category appear all the alkenes having at least one p(C-C) bond. The Occurrenceof the primary P(C-C) bond rupture in acyclic olefins was first shown to be the main process by Callear and Lee. Using a flash photolytic system (A > 160 nm), they generated various allylic radicals and were thus able to measure the electronic spectrum of these radicals in the 210-250 nm region (61). The quantum yields of the rupture of this bond is @ 2 0.8 (47,49,62). For example, the 147.0 and 163.3 nm photolysis of n-1-hexene leads to the primary p(C-C) bond rupture with a high quantum value (63):
This simple mechanism leads to the well-known Stern-Volmer equation: the ethylene quantum yield is linked to the total pressure through the following expression (66):
where the @-values are the quantum yields measured at any pressure and the @,-value is the quantum yield obtained by extrapolation to zero pressure. Figure
PHOTOCHEMISTRY OF SIMPLE OLEFINS
148
x lo3 Nm-*
a
12
12
0
20
LO
Pressure / Torr
80
60
100
Figure 5. The reciprocals of the ethylene quantum yields in th3 photolysis of n-l-hexene at various wavelengths versus the pressure. From Ref. 63b.
5 shows the good linearity obtained from the Stern-Volmer plot. From the @,-value, @&,H4) 2 0.9, the relative importance of the processes in Eqs. 20-21 may be seen. Thus, more than 80% of the absorption of photon leads to the ethylene formation through the primary p(C-C) bond rupture, followed by the secondary fragmentation of the energized n-propyl intermediate (Table 4). The 184.9 nm photolysis of 2,3- and 3,3-dimethyl-l-butene has also been recently studied. As in the previous case, the p(C-C) bond rupture is the main primary process observed. In fact, the @o(CH3)-valuesmeasured at zero pressure are close to unity (67a). This situation was also observed in cis-3-hexene and 4methyl-cis-2-pentene (67b). From the slope/interceptratios, the kJkd-values may be obtained. These Stern-Volmer plots are shown in Fig. 6:
[@(CH,)]-' =
4-l
+ $-I 5 [MI kd
x103 4
Alkene
Nm-2
a
12
16
pressure / Torr
Figure 6. The reciprocals of the primary methyl radical quantum yields in the 184.9 nm photolysis of 2,3(0) and 3,3-dimethyl-l-butene (a),cis-3-hexene (a),and 4-methyl-cis2-pentene (0) versus the pressure. From Ref. 67.
TABLE 4. Quantum Yields for Direct and SensitizedPhotochemistry of 1-Hexene ~
Direct
~~~~~~~
Sensitized"
Process n-1-C6€€@-+
147.0
163.3
184.9
253.7
C3H-T + C3H5 CZH3 + C4H9 2C3H6 C2H5 + C4H7 (CH,)2-CyClO-C,H6 CH~-CYC~O-C~H~ cyclo-C& * 2
0.80 0.05 0.06 0.15
0.65 0.10 0.04 0.10
0.75
Not observed
0.03, 0.13
Total Ref.
1.06 63b
0.89 63a
0.995 63b
0.08
Z0.14
Z0.07 0.01 0.005 0.225" 75
"1-hexene is also among the products: recyclization of 1,&hexanediyl radicals.
149
150
PHOTOCHEMISTRY OF SIMPLE OLEFINS
TABLE 5. Quantum Yield Valuesof the Major Processes in the Photofragmentation of n-Butene and n-1-Penteneat Various Wavelengths
Quantum Yield
n-Butene Wavelength (nm) 184.9 174.0 147.0 123.6
Energy (eV) 6.4 7.1
8.4
10.0
Ref. 62 68a 69a 69b
n-Pentene
PW-C) (C-W Cleavage Cleavage 0.71 0.66 0.51 0.29
0.12 0.22 0.26 20.23
Ref. 62 68b 70a 70b
C-C
C-H
-
-
0.64
0.08
0.47
0.26
0.16 0.24
The importance of the p(C-C) bond cleavage seems to be sensitive to the incident wavelength. For example, Table 5 shows the quantum yields of the p(C-C) and the C-H bond ruptures. Obviously, the importance of the p(C-C) bond rupture decreases with a decrease in the wavelength or, better said, an increase in the incident energy. Conversely, the C-H cleavage becomes more and more important at greater energy. These results are in agreement with a fragmentation taking place from the hot ground state, where it is well known that the p(C-C) bond is the weakest one (64).Moreover, from the Stern-Volmer plot of the methyl radical quantum yield, the ks/kd ratio may be obtained (Eq.111). By assuming that k, is the rate constant for the stabilizing collision process (obtained from the gas kinetic theory), or using the process in Eq. 22b as an internal clock, kd may be estimated. From these values, the lifetimes of the photoexcited molecules may be obtained: they are shown in Table 6. Taking advantage of the general P(C-C) bond cleavage shown above, recent studies involving an excimer ArF laser have been published. The 193.2 nm ArF laser line pumps an electronic excited state of various substituted alkenes, and the absorption spectra of transient substituted ally1 radicals were observed with time. From these results, the formation rates of allylic radicals have been observed. The lifetimes of the photoexcited molecules so calculated are reported in Table 6 (71), as well as those measured from the Stern-Volmer plots of the methyl radical quantum yields described above. First, it must be said that the results agree fairly well, if one takes into account the two diffeient families of experiments: see, for example, the n-I-hexene values. Moreover, in the C6 family, the lessening of the lifetime of the vibrationally excited molecule is probably a direct consequence of the number of available reaction channels (1 in 1-hexene, 2 in 2,3-dimethyl-l-butene, and 3 in 3,3-dimethyl-l-butene) and also a slight decrease of activation energy with an increase of the ramification of the parent molecule (67).
THE OTHER ACYCLiC OLEFINS
151
TABLE 6. Lifetimes of the Far UV Photoexcited Unsaturated Akenes Alkene 2,fDimethyl2-butene n-1-Hexene n-1-Hexene cis-3-Hexene 4-Methyl-2-pentene 2.3-Dimethyl1-butene 3,3-DimethylI-butene 1-Heptene 2,3-Dirnethyl2-pentene 2,3,3-Trimethyl1-butene
A (nm)
~(ns)
Origin"
Ref.
193.2
70
Abs. sp.
71b
184.9 193.2 184.9 184.9 184.9
2 5 r 2 2 3
s.-v.
s.-v. s.-v. s.-v.
67 71b 67b 67b 67a
S.-V.
67a
184.9
1
0.35
Abs. sp.
193.2 193.2
33 37
Abs. sp. Abs. sp.
71b 71a
193.2
17.9
Abs. sp.
71a
"S.-V.: Results from Stern-Volmer plots of one of the primary fragmentation processes; Abs. sp.: results from the absorption spectra of the primary ally1 fragments.
More recently, N. Nakashima et al. made a systematic study of the 2-methyl-lalkene family
H,C=C(CH3)CH2),CH$*
CH,C(CH,)CH,
+ (CHz),CH3
(23)
m = 0 , . . . ,5 They confirmed the trend reported above: the bigger the molecule is, the longer is its lifetime and the smaller is its dissociationrate constant (Table 7). Moreover, the dissociation rate constants so measured are in good agreement with RRKM calculations (Fig. 7) (72). All these results may be rationalized on the grounds of the following mechanism:
TABLE 7. Dissociation Rate"kdof Various 2-Methyl-1-alkenesat 193.2 nm (Eq. 23) m
Olefm 2-Methyl-1-butene 2-Methyl-1-pentene 2-Methyl-1-hexene 2-Methyl-1-heptene 2-Methyl-1-0ctene 2-Methyl-1 -nonene
kd(106s-') >300 150 19 4.5 1.25 < 0.5
"Obtained from absorption spectroscopy: Ref. 72.
m : see
process 23
Figure 7. The relation between observed (0)and RRKM (0) calculated rate constants for the decomposition of various photoexcited 2-methyl-1-alkene molecules at 193.2 nm. From Ref. 72 with kind permission of the authors.
152
THE OTHER ACYCLIC OLEFINS
153
B. The Excess Energy Distribution Coming back to the n-1-hexene system (Eqs. 20-21), the k& ratio for the excited n-C3Hq intermediates can be extracted from either the Stern-Volmer intercept with the pressure axis or the slopehtercept ratio. For example, in n-1-hexene and in terms of pressure, the k& value is 160 Torr at 147.0 nm. Using the RRKM calculations made by Rabinovitch and Setser (73), this value leads to an excess internal energy of 87.8 kJ/mol for the n-propyl precursor. By taking into account the energy needed for the reaction in Eq. 21a one can attribute an internal energy of 217 kJ/mol to the n-propyl radicals (62) formed in the process in Eq. 20. The photon energy is 811 kJ/einstein at 147.0 nm. Since an energy of 297 kJ/mol is required for the primary p(C-C) bond rupture (Eq.20), 8 11 - 297 = 5 14 kJ/mol must be distributed among the fragments. If the n-propyl fragment has 217 kJ/mol, the ally1 species will have the difference, i.e. = 514 - 217 = 297 kJ/mol. Since the splitting of the photoexcited molecule results from the transformation of vibrational energy, a large amount of translational energy is not expected in the fragments, although some energy may be released in relative motions (66). If this is true, then on neglecting this translational energy, the smaller fragment C3H5carries more energy (58%) than the larger fragment C3H7,which has 42%. The fragmentation of the photoexcited molecule probably occurs for long enough after its formation to allow an internal redistribution of the energy in the vibrational framework of the molecule, but not long enough for a complete randomization of this internal energy. This deduction agrees very well with Chesick’s earlier statement in that the cleavage occurs after rapid internal conversion to the ground electronic state (47). It must be recalled at this point that various RRKM calculations may be used (step ladder model, exponential model, etc.). Each of them involves various assumptions and several adjusted parameters. If vibration frequencies of the starting alkenes are relatively well known, those of the excited complex must be approximated and some of them are chosen to fit experimental values. Thus, the observed agreement may be fortuitous and cannot preclude the possibility that bond cleavage is actually part of the internal conversion process itself. Other vibrations might be “coreceiver” modes. Although the primary C-H bond rupture has a low quantum yield in the photolysis of 1-akene, Niedzielski et al. have confrmed the possibility that hydrogen atoms formed in the 8.4 and 10.0 eV photolysis of 1-butene may be hot (74). In their experiments, the addition of a hydrogen atom to the double bond gives rise to a vibrationally hot butyl radical. This hot butyl radical may eventually decompose, leading to the formation of propene. From kinetic treatment and using a plot of the rate constant for dissociation versus excess
PHOTOCHEMISTRY OF SIMPLE OLEFINS
154
energy reported by Rabonivotch and Setser (73), the energy of these hot atoms can be estimated to be 0.26 eV (25 kJ/mol) and 0.6 eV (58 kJ/mol) at 147.0 and 123.6 nm, respectively. Unfortunately, in this system, hydrogen atoms are formed in the primary as well as secondary fragmentation processes. Thus, the process leading to these hot atoms is not obvious, although on thermodynamic grounds, it can be reasonably assumed that they are formed in the primary fragmentation processes.
C. Photosensitization The H S ( ~ Pphotosensitization ~) of alkenes gives rise to the cis-trans isomerization, [1,3J-sigmatropic hydrogen shift, and cyclization of a triplet biradical, after internal hydrogen atom shifts. The vibrationally excited triplet states of 1-hexene and 2-octene were proposed to be involved in an olefinic type I1 reactions consisting of an intramolecular 1,Shydrogen abstraction through a six membered transition states and subsequent reaction of the resulting radicals. This was shown to be in sharp contrast to the well-established allylic C-C and C-H bond cleavage of alkenes without y-hydrogen (75). The results are also very different from those observed in direct photolysis (Table 4). For example, in the case of 1pentene, at pressure around 100 Tom, k26&6&2&k2a = 100:35:7: 1 (76):
-
1.s-shin
3(
1-C5H10) * CH2CH2CH2tHCH3__* methylcyclobutane I ,CshiH
3( 1-C5H10) 3(
l-C5HI0)
3( l-C5Hlo)
I .3-sbift
1.4-shift
CH3tHCH26HCH34 cis-dimethylcyclopropane 0
.
-
CH,CH2CHCHCH3 4 cis-
CH2CH2CH2CH2tH2
+
+ trans-2-pentene
cyclopentane
(264 (26b) (26~) (264
More recently, a detailed study of the Hg(3Pl) photosensitization of 3-methyl1-butene was published (77): ethane is a major product (@ S 0.07) as well as olefinic and methyl substituted cyclopropane isomers (CP S 0.08). The addition of molecular oxygen removes the 2-pentene formation (@ = 0.06). Thus, it may be assumed that the Hg (3P1) photosensitization of 3-methyl-1-butenemainly results in the primary p(C-C) bond rupture. Conversely, the dimethylcyclopropane yield decreases slightly in the presence of oxygen. A mechanism mainly involving both vibrationally excited and thermalized triplet 2-methylbuta-1,3-diyl radicals was proposed. These radicals are formed from the excited triplet 3methyl-1-butene through an internal hydrogen atom shift. A similar mechanism was also proposed in the case of the Hg(3PI)photosensitization of 3,3-dimethyl-1butene (78):
THE OTHER ACYCLIC OLEFINS
3A* ,A*
Hg('Pi)
-
3M1B
__*
,(3MlB)*
CH,
(M)
__f
,(A)
3A* 4 '(A*)
+
-+
3[cH2CH(CH3)6HCH3]*
155
(27)
(3A*> CH3CHCHCH2
(28)
-
__*
dimethyl-1,2-cyclopropane
dimethyl-l,2-cyclopropane
(29) (30)
D. The Isomerization of Acyclic Alkenes The photoisomerization of acyclic alkenes is well documented in both the direct and the photosensitized experiments (79). Of course, the cis-trans process does not need to be discussed here: see above and (58). Let us only recall that in direct photochemistry it has been linked to the skew structure of the '(n,n*) excited state (80). The internal methyl shift was attributed to the Rydberg '[n,R(3s)] electronic state. This process is particularly efficient in the gaseous and liquid phase photoirradiation of tetramethylethylene (81-83):
(CH,),C=C(CH3)2 [(CH3)3C-C-CH3] [(CH3)&-C-CH31
(C6H12)Ry
-
[(CH3)3C-C-CH3]
(CH3)3CCH=CH2 (DMB) (CH,),C
CH2 / - kHCH, (TMC)
(31)
(32) (33)
The ratio (b(DMB)/(b(TMC) is independent of wavelength between 184.9 and 228.8 nm (82,83) and temperature between 10 and 70°C (82), and is equal to 1.5 +- 0.15. These reactions are believed to involve the formation of a carbene transient intermediate(80). This carbene intermediateundergoes either an internal hydrogen atom transfer with the formation of 3,3-dimethyl-l-butene (Eq.32) or an insertion of the carbene center in a C-H bond of the remote methyl groups with the formation of trimethylcyclopropane (Eq. 33). The importance of this methyl shift (Eq.31) increases with the number of alkyl substituents around the double bond (83). It is known that this number has a stronger effect on the energy of the singlet Rydberg '(n,3s) excited state than on the 'V(n,n*) state (20,80).Both transitions are lowered in energy, but the Rydberg states are much more affected. Figure 3 gives the vertical excitation for the pertinent processes. As far as the absorption spectrum of tetramethylethylene is concerned, it shows a strong V + N absorption band with its maximum centered at 185 nm. Another band, well separated from the previous one, is located between 210 and 240 nm (48000 - 42000 cm-'). In a thin polycrystalline film (T = 23 K), this band is
I
I
I
L _ _ -
Cd
4.0
4.4
Wovenumber
I
Zn
4.8
I' I' 1 Hg
ArF
/
52
I
-
5.6
cm-'
Figure 8. The absorption spectrum of tetramethylethylene in the gas phase. From Ref. 83 with kind. permission of the authors.
000
BOO
-
I
E
7
x
600
500
Figure 9. Effects of the number of methyl substituents on energy levels in ethylenic compounds.
156
THE OTHER ACYCLIC OLEFINS
157
severely perturbed (2) and it corresponds to a IT --5, R(3s) transition: this is shown in Fig. 8. Unfortunately, the values for the 0,O transition are not so well known. This is important, since the minimum energy for the V(IT,IT*)excited state may be lowered by as much as 2.2 eV in ethylene (25). The energy minima of the 'R(IT,~s)and the 'V(~,P*)of ethylene are 6.8 and 5.42 eV, respectively (2,5). In tetramethylethylene,the same minima may be located in the 5 .O-5.2 eV range (2). Then, the photoexcited molecules, by internal conversion, may pass from one excited hypersurface to the other, and the relative energy of the two states has a strong effect on both populations. In other words, Fig. 9 gives strong support to the involvement of the Rydberg excited states in the methyl shift processes. The internal 1,Zdouble bond shift, or in other words the sigmatropic [1,3]hydrogen atom shift, was also observed in many cases. For example, 1-pentene is formed upon direct photoirradiation of gaseous cis-2-pentene: 4 = 0.02, (84); and cis- and trans-2-octene are formed in the pentane solutions of I-octene (85). This transfer was also observed in more substituted acyclic alkenes (82): see Table 8. Again, the quantum yield for the 1,3-H transfer increases with the number of alkyl substituents around the double bond. On the other hand, the 2,3-dimethyl-l-butene/3,3-dimethyl-1-butene ratio decreases with an increase in the wavelength from 184.9 to 228.8 nm (82b). It is possible that at the lower wavelength, a relatively high energy carbene is produced which leads to the formation of the terminal alkene. Kropp has retained the T,U* excited state as one of the candidates for this process (81). Conversely, Inoue et al. have rather proposed the u,,(CH2) +a*(C=C), or the IT(C=C) ---* o$(CH,) charge transfer excitation as an alternative (82a,b). Unfortunately, ub initio calculations on electronic statess of monoolefins are rather uncommon. One very interesting paper by Bouman and Hansen appeared recently (20). They used a random phase approximation including an extended basis set and well-chosen geometries. They got good agreement with experimental values of vertical excitation energies for ethylene, propene, and the two 2-butenes. They showed that successive methylation results in roughly additive red shift for the Rydberg excitations. Conversely, the two valence excitations, m + m* and or --* IT*, are notably less sensitive to methylation. Finally, the cry +IT*transition lies at much higher energies, 9.2-9.5 eV, than the energy available at 184.9 nm, in disagreement with the above mechanism. Recently, we have studied the infrared multiphoton irradiation of cis-2-pentene. In this kind of experiment, it is hoped that the photoexcited molecule will not accumulate too much energy, so that it will stay on the electronic ground state. Provided that the fluence of the photon beam is higher than 4 J/cm2, there is a large amount of fragmentation among the heated molecules as well as some 1-pentene formation (86). Thus, although it is not very efficient, the 1,3-hydrogen shift is an open channel from the hot ground
=
0.045 0.017 0.02 0.028 0.18
Not observed 1-Pentene 4-Methyl-1-pentene
2-Methyl-I-butene 3-Methyl-1-butene 3-Methyl-1-pentene 2-Ethyl-1-butene 2.3-Dimethyl- 1-butene
1 -Alkene cis-2-Pentene 4-Methy l-cis2-pentene 2-Methyl2-butene 3-Meth yl-cis2-pentene 2,3-Dimethyl2-butene
‘Quantum values measured in the presence of 3-5 a m of added propane (82b).
0.025 0.04
Product
Alkenes
1,3-HTransfer
TABLE 8. PbotoisOmeriZation of Gaseous Alkenes at 184.9 nm
0.017
0.03 0.05 3,3-Dimethyl-l-butene Trimethyl- 1,1,2-~yclopropane
0.009
0.01
0.015 0.01
+a
Dimethyl-1.1-cyclopropane 2,3-Dimethyl-1 -butene
cis- 1,2-Dimethylcyclopropane
Not observed 2-Methyl-1-butene Iwpropylcyclopropane
Product
CH3Transfer
THE OTHER ACYCLIC OLERNS
159
state. Of course, this result does not preclude the involvement of an electronic excited state in the UV photoinitiated 1,3-hydrogen shift. At this point it is relevant to recall the very low fluorescence quantum yields measured in olefinic systems (the more substitued the double bone is, the higher the quantum yield is): +(fluorescence) = in tetramethylethylene when it is excited in the 184.9-228.8 nm region in either the gas or the solution phase. The lifetime of the emitter was measured in the picosecond range, and it was proposed that this emitter is a Rydberg singlet excited state (4). It was reported very recently that the lifetime of a fluorescent excited state in tetramethylethylene vapor when excited at 235 nm is 20.8 & 0.9 ns (87),a rather long lifetime for a singlet state. This suggests a very drastic wavelength effect. We have also noticed that the 184.9 nm photosiomerization of gaseous tetramethylethylene gives rise to the formation of trimethyl-l,1,2-cyclopropane,and the electronic precursor- probably a Rydberg singlet state-of this cyclopropane derivative might be responsible for the observed fluorescence (83). The structural isomerization of olefins through triplet electronic excited states has already been recalled: see Eqs. 23-26.
E. Conclusion The conclusion to this review on the photochemical behavior of acyclic alkenes is that it is not easy to establish clearly the fate of various electronic excited states. First, it seems that ethylene is a very specific case. The formation of its photoproducts is better explained in terms of electronic excited states. Proofs are however needed to confirm this assumption. The fragmentation products of the other acyclic alkenes can be reasonably explained on the basis of the fragmentation of the hot ground states formed after internal conversion from singlet electronic excited states. Isomerization processes involving an internal methyl shift are reasonably linked to the Rydberg electronic singlet state. This process is particularly efficient in tetramethylethylene. Finally, the origin of the internal 1,3-hydrogen shift is still a matter of debate. This process may involve either a very hot ground state or an electronic singlet excited state. Figure 10 shows a schematic potential energy diagram of a photoexcited substituted ethylene molecule. It is assumed that the absorption of a photon is made through the V -+ N transition, and that triplet states are ignored as well as the decomposition of the electronic excited state into electronic excited fragments. The left hand side of the graph is highly speculative as far as the 1,3-hydrogen atom shift is concerned. The right hand side includes the cis-trans isomerization process, bond rupture, internal 1,2-alkyl shift, and reference to infrared multiphoton photochemistry.
PHOTOCHEMISTRY OF SIMPLE O E F h %
160
Figure 10. Schematic behavior of various electronic states of substituted ethylenic compounds.
V. THE CYCLIC MONOOLEFINS A.
The Fragmentation Processes in Direct Photolysis
Reports of the photofragmentation of various cyclic monoolefins were published at the beginning of the seventies. Particularly, Doepker et al. made a systematic study of different C4H6 isomers illuminated in the 104.2-147.0 nm range. In this range of energy (E > 8.4 eV, 811 kJ/mol), all the studied photoexcited molecules undergo fragmentation. This is obviously true for cyclobutene (89a) and methylenecyclopropane(89b). In both cases, the main fragmentation process gives rise to the formation of ethylene and acetylene. Vinylacetylene is also a major product. Two hydrogen atoms rather than one molecule of hydrogen are formed in the same process: C4H$* --*CZH, C4HZ* +C4H4
+
CZH,
+ 2H
At 184.9 nm, the fragmentation as well as the isomerization of substituted cyclobutenes, namely bicyclo[3.2 .O]hept-6-ene and bicyclo[4.2 .O]oct-7-ene, were studied in pentane solutions. Acetylene and cycloalkenes are the major photoproducts, whereas the Woodward-Hoffmann allowed ring opening gives rise to 1,3-cyclodienes with lower quantum yields (90).
THE CYCLIC MONOOLEFINS
161
The 147.0 nm photofragmentation of methylenecyclobutane was also important (91). An important molecular fragmentation process has been identified it leads to the formation of allene and ethylene, probably in one step. However, due to the high energy content, the primary products are relatively unstable and suffer further fragmentation. Thus, excited allene molecules further decompose and, among secondary products, C3H3radicals appear. These radicals were observed through the formation of 1-butyne-4,4,4-d3 and 1,Zbutadiene4,4,4-d3 when a mixture of methylenecyclobutaneand CD31 is photolyzed. It is known thtt the C 3 5 species may exist in two different electronic structures: CH=C-CH, and CH=C=CH2 (92). However, it was very difficult to measure the quantum value for this species because of its high reactivity towards monomer. Thus, the fragmentation pattern of the photoexcited molecule was hardly established. A little bit later, the photolysis of vinylcyclopropane was studied in the same energy range. In this case, the fragmentation is dependent on the cyclopropane ring and gives rise to an important methylene elimination process: CP = 0.20 ? 0.04 at 147.0 nm. This process was shown to be of general occurrence in various alkylated cyclopropanes (93). R-cyclo-C,HT*
__*
'CH,
+ RCH=CH2
(36)
The 8.4 eV photodecomposition of cyclopentene was also studied in the same laboratory. Ethylene, acetylene, and cyclopentadiene are the major products, although a high yield of hydrogen atoms was also observed (94). On the other hand, methylenecyclobutane (a= 0.04) and bicyclo[2.1 .O]pentane (a= 0.03) were the only primary products observed in the 184.9 nm photochemistry of n-heptane solution of cyclopentene (95). The formation of 1,4-pentadiene (CP = 0.01) was ascribed to secondary processes. Very recently we have undertaken a systematic study of the 184.9 nm gas phase photochemistry of cyclopentene at pressures from 1 Torr to 6 atm of added propane. Again at low pressure, ethylene (0 = 0.12), acetylene (CP = 0.03), allene (CP = 0.06), and cyclopentadiene (0= 0.22) are the main products (96). About 80% of the formation of cyclopentadiene involves the elimination of a hydrogen molecule in agreement with the Woodward-Hoffmann allowed 1,4 concerted molecular elimination process (97). Moreover, several isomers are also formed provided
162
PHOTOCHEMISTRY OF SIMF'LE OLEFINS
+
the total pressure is raised to appropriate values. For example, the (cis trans) 1,3-pentadienequantum yield increases from 0.00 at a pressure of 1 Torr to 2 0.33 at a pressure of 100 Torr of added propane, and it eventually decreases with a further increase in the propane pressure. Similar behavior is also observed for the quantum yields of 1,Cpentadiene and vinylcyclopropane, although the pressure scales must be shifted at higher pressure: Qmm(1,Cpentadiene) = 0.22 at 300 Ton and @-(vinylcyclopropane) = 0.21 at 3 atm. Similar results were observed at 213.8 nm, although the maxima for the quantum yields are observed at somewhat lower pressures. This effect may reasonably be attached to the lower energy content of the photoexcited molecules formed at 213.8 nm. These results are included in Figures 11 and 12. The formation of these isomers was assumed to involve the primary fragmentationof s(C-C) bond in the photoexcited molecule. The so-formed allyl-alkyl radical is allowed to recyclize (cyclopentene and vinylcyclopropane are the products) and to rearrange through internal hydrogen atom shifts (1,Cpentadiene and 1,3-pentadiene are among the products). Although these products are isomers of the starting material, their formation is explained in terms of fragmentation rather than isomerization processes (96). This mechanism is in agreement with the fragmentation of hot vinylcyclopropane molecules formed through the addition of a singlet methylene radical on 1.3-butadiene (98). The photolysis of cyclohexene is particularly well documented in the 105184.9 nm wavelength (99-101). The main products are ethylene and 1,3-
1o3
1 oo
N m-2
1 0' 1 o2 Propane pressure
/
1D6
1o3 Torr
1 o4
Figure 11. The 213.8 nm photoirradiationof cyclopentene. The quantum yields of various products at different pressures of added propane.
THE CYCLIC MONOOLEFINS
163
2 Nm-2
Propane
pressure
/ Torr
Figure 12. The 213.8 nm photoirradiation of cyclopentene.The quantum yields of various products at different pressures of added propane. butadiene: they are formed from a molecular elimination process-a retro-DielsAlder reaction-in agreement with Woodward-Hoffmann rules: = 0.8 at 184.9 nm (102):
This process has also been observed in cis- and nuns-3,4-dimethylcyclohexene. The 2-butene formed retains the originid cis or trans structure:
Conversely, the direct 184.9 nm photolysis of the cyclic C,, C8, and C9 monomers leads to the formation of a,w-dienes and vinylcycloalkanes (100,103) through
164
PHOTOCHEMISTRY OF SIMPLE OLEFINS
B. Fragmentation in the Photosensitized Experiments The fragmentation of H S ( ~ Pphotosensitized ~) cis-4,5-dimethylcyclohexenedoes not conserve the original cis structure in 2-butene (104). In this case the mechanism is thought to involve a triplet allyl-alkyl radical. This intermediate may decompose at low pressure or may recombine, giving rise to the original alkene or vinylcyclobutane (105):
+d=‘
[i] *
=
+=\=/
b+d
A review of various processes occumng in the Hg 6(3P1)photosensitization of cyloolefins was published by De M a d et al. (106); see Table 9. Vinylcycloalkanes were the major product observed in cyclopentene and l-methylcyclopentene. From extrapolation of the quantum yields of cyclopropanes to zero pressure and by combining these values with the estimated quantum efficiencies of other proceses, they calculated that “two-thirds of the triplet cyclopentene molecules always return to the ground state without requiring collisional stabilization” (106). They concluded that the occurrence of such an intersystem crossing to the ground state is a general phenomenon in mercury photosensitization of cyclic olefins. However, cyclooctene (107) and cyclononene (103) do not seem to follow this pattern completely. The formation of various bicycloalkanes is now important, as well as that of a,o-dienes. The former products are the result of an internal hydrogen atom transfer from an appropriate methylene group to the olefinic double bond with a subsequent or simultaneous C-C bond formation (Table 10). It is not clear if these bicyclocompounds are the result of the hot ground state or the triplet excited state. On the other hand, the am-diene
TABLE 9. Comparison of the Quantum Yields of Various Processes in the Hg 6@,) Photosensitization of Gaseous Cycloolefins Cycloolefin Cyclopentene 1-Methylcyclopentene Cyclohexene 3-Methylcyclohexene Cycloheptene Cyclooctene Cyclononeneb Methylenecyclopropane Methylenecyclobutane Methylenecyclopentane
RetroDiels-Alders
Intersystem Crossing
Ring Contraction to Vinylcycloalkanes
-
0.6 0.6
0.35 0.3
0.2 0.04
0.7
0.06 0.05
-
c0.83 0.9
-
-
?
-
-
0.85
?
>0.9
<0.05, ZO
0.0
-
Source: Ref. 106. “From Ref. 103.
TABLE 10. Formation of Bicycloalkanes and a,o-Dienes in the Hg 6(’P1) Photosensitizationof Cycloalkenes
Yield (wmol)
Cycloolefin Bicyclo [4.1.O]heptane [4.2.O]octane [3.3 .O]octane [4.3.0]nonane [5.2.0lnonane [6.1 .O]nonane a,o-Dienes
Cycloheptene (Ref. 108) 0.088”
0.025“
Cyclooctene (Ref. 107)
0.98 0.17
0.97
cis-
Cyclononene (Ref. 103)
60.23 20.54 1.18 0.07
“Quantum values.
165
166
PHOTOCHEMISTRY OF SIMPLE OLEFINS
formation seems to involve a similar p(C-C) bond rupture, as is reported above, in the direct photolysis of cyclopentene, cycloheptene, cyclooctene, etc. :
C. Isomerhation Processes Very recently, a good review of the 184.9 nm photoisomerization of olefins and strained cycloolefins was published by Adam andd Oppenllinder (109). For the smallest members of this group, one of the more important studies comes from Fields and Kropp (110): they observed tht the liquid or solution photochemistry of C5-C, monocyclic monoolefins gives rise to a variety of mono- and bicyclic isomers, whose formationmay be explained in terms of a carbeneintermediate:
These reactions were also reported by Inoue et al. (100). Later Srinivasan and Brown reinterpretedthe mechanism in terms of two different intermediates(1 11): the first one is that just reported above; the second is included in the following reaction:
The total quantum yields of the isomeric products are generally in the 0.02-0.10 range at 184.9 nm (112). The [1,3]-sigmatropic shift was also observed (113):
THE CYCLIC MONOOLEFINS
83 '/*
167
10%
In the same work, the shift was observed in molecules where the cycle was attached in the 1,l position of an ethylenic molecule: the process in Eq. 49. The formation of the cyclopentene molecule is much favored over the other isomer: the shift seemed to be favored by the a-strain of the cyclopentene ring. Thus, it was concluded that the migration may be due in part to the emergence of the P,U* state as the lowest-lying excited state (1 12). Very recently we have restudied the 184.9 nm photochemistry of cyclohexene. At high pressure, there is formation of methylenecyclopentane and bicyclo[3.1 .O]hexane. The Stern-Volmer plots for the quantum yields of these isomers appear in Figs. 13 and 14. It is clear from these results that these isomers do not involve the same precursor. In the same manner, in the 184.9 nm photochemistry of cyclopentene, the methylenecyclobutanequantum yield increases with an increase in the pressure of added propane. Conversely, we have not seen any formation of bicyclo[2.l.O]pentane. At 213.8 nm (that is at a lower energy), the formation of methylenecyclobutaneand bicyclo[2.1.O]pentane was observed at high pressure of added propane (Fig. 11). Clearly, both products are formed in somewhat different pressure scales (1 14). Thus, it is also fakly safe to assume that two different precursors are involved in such formations. More particularly, from the Stern-Volmer plots of methylenecyclobutane and ethylene, the lifetime of an excited methylenecyclobutanemolecule can be estimated:
c
L, 100
8 Y
50
0
0.01
[Pmssurel-'
/
(Torr1-l
0.02
Figure 13. The reciprocals of the bicyclo[3.1 .O]hexane quantum yields versus the recip rocal of the pressure of added propane in the 184.9nm photoirradiationof cyclohexene.
PHOTOCHEMISTRY OF SIMPLE OLEFINS
168
Y
B
Y
0 [Propane
0.25 pressure]-'
/
0.5 (Torrl-'
1
Figure 14. The reciprocals of the methylenecyclopentane quantum yields versus the reciprocals of the pressure of addedairin the 184.9 nm photoirradiationof cyclohexene.
The following Stern-Volmer equations apply to this mechanism:
=
From Figs. 15 and 16, the following kgk: values were estimated to be 11.5 atm from both Stem-Volmer plots at 184.9 nm. By assuming kl as being the rate constant of the physical collision process, the lifetime of the very excited precursor is around 10 picoseconds. One interesting approach to synthesize trans-cycloalkene must be recalled here. It was developed by using the singlet photosensitization of cis-cycloalkene. This isomerization takes place via a singlet mechanism, which involves a nonvertical energy transfer from an excited aromatic ester to the cycloalkenes (1 15). For example, it has been shown that the direct and sensitized photolysis gave quite different photostationary wanskis ratios after prolonged irradiation of cyclooctene. The ratios are 1.0 and 0.05 in the direct 184.9 nm and the sensitized liquid singlet, respectively (116).
=
THE CYCLIC MONOOLEFB'S
0.5
80
x lo-'
N-' m
169
1
Figure 15. The Stern-Volmer plot for the methylenecyclobutane quantum yields measured in the 184.9 nm photoirradiation of cyclopentene.
D. Conclusion First, it seems reasonable to link the fragmentationprocesses, mainly the p(C-C) bond rupture as well as the rectro-Diels-Alder process, to the hot ground state formed through either the internal conversion of the excited singlet state or the intersystem crossing from the triplet excited state. On the other hand, part of the isomers are formed from electronic excited states. Methylene cycloalkane and bicyclo[n.l.O]alkane are probably the results of the isomerization of the Rydberg electronic singlet state, at least in cyclopentene and cyclohexene. The a,o-dienes formed in the triplet photochemistry of the higher members of the cycloalkene series probably involve an internal hydrogen atom transfer in the
6
0
2 Propane
4
pressure
/
Atm
6
Figure 16. The Stern-Volmer plot for the ethylene quantum yields measured in the 184.9 nm photoirradiation of cyclopentene.
170
PHOTOCHEMISTRY OF SIMPLE OLEFINS
hot ground state of the allyl-alkyl radicals. Conversely, it is likely that the formation of bicyclocompoundsis the result of internal hydrogen atom migration in the triplet excited states (117).
M. CONCLUSION The above material seems a little bit confusing, and a simple trend in the fate of photoexcited molecules is not obvious. Ethylene seems to be a special case, although it is tempting to l i t h e molecular elimination from photoexcited acyclic olefins to the electronic excited state. Similarly, some of the isomerization products observed in either the high pressure or the liquid phase experimentson both acyclic and cyclic olefins are very likely linked to electronic excited state(s). The singlet Rydberg excited state is very often suggested to be involved in these processes. Conversely, it seems more appropriate to retain the fundamental and very hot ground state as an intermediate leading to the primary fragmentation processes, involving a bond rupture. In short, there is an obvious need for more research both at the theoretical and experimental levels.
ACKNOWLEDGMENTS The author would like very much to thank Professors C. Sandorfy (Universite de Montdal), G. R. De Mar6 (Universitk Libre de Bruxelles), and E. Evleth (Universitk de Paris VI) for many helpful discussions. We would like also very much to thank Professor N. Nakashima (Institutefor Molecular Science, Okazaki) for providing us with very recent results, and particularly Fig. 9. Financial help from the Natural Sciences and Engineering Research Council of Canada was much appreciated. Note added on proof: Recently, a review of the photochemistry of allyl-, vinyl-, and alkylidenecyclopropaneswas published (118). It adds very interesting mechanistic details as well as relative importance of cleavage, fragmentation, and isomerization pathways for these compounds in pentane solutions.
REFERENCES 1. A. J. Merer and R. S. Mulliken, Chem. Reviews 69, 639 (1968), and references cited therein. 2. M. B. Robin, in Higher Excited States of Polyatomic Molecules, Vol. 11, Academic Press, New York, 1975, and references cited therein.
REFERENCES
171
3. H. M. Rosenstock, K. Draxl, B. W. Steiner, and J. T. Herron, J. Phys. Chem. Ref. Data 6 , Suppl. 1 (1977), and references cited therein. 4. F. Hirayama and S. Lipsky, J. Chem. Phys. 62, 576 (1975).
5. M. B. Robin, in Higher Excited States of Polyatomic Molecules, Vol. 111, Academic Press, New York, 1985, pp. 213/236, and references cited therein. 6. (a) L. Salem, Zsr. J. Chem., 14, 89 (1975); (b) L. Salem, Science, 191, 822 (1976). 7. See for example: (a) K. J. Crowley and P. H. Mazzocchi, in The Chemistry ofAlkenes, Vol. 2, J. Zabicky, Ed., Wiley-Interscience,New York, 1970, pp. 267-325; (b) J. D. Coyle, Chem. SOC. Rev. 3, 329 (1974); (c) G. Kaupp, Angew. Chem. Int. Ed. Engl. 17, 150 (1978); (d) Yu. I. Dorofeev and V. E. Skurat, Russ. Chem. Rev. 51, 527 (1982). 8. M. C. Sauer, Jr. and L. M. Dorfman, J. Chem. Phys. 35, 497 (1961). 9. H. Okabe and J. R. McNesby, J . Chem. Phys. 36, 601 (1962). 10. (a) H. Hara and I. Tanaka, Bull. Chem. SOC. Japan 46, 3012 (1973); (b) H. Hara and I. Tanaka, Bull Chem. SOC.Japan 47, 1543 (1974). 11. P. Borrell, P. Cashmore, and A. E. Plan, J . Chem. SOC.A , 3063 (1968). 12. (a) L. C. Glasgow and P. Potzinger, J . Phys. Chem. 76, 138 (1972); (b) P. Potzinger, L. C. Glasgow, and G. von Biinau, 2. Nuturf. 27a, 628 (1972). 13. M. B. Robin and N. A. Kuebler, J. Mol. Spectr. 33, 274 (1970). 14. S.-I. Hirokami and R. J. Cvetanovii, J. Phys. Chem. 78, 1254 (1974). 15. R. Gorden, Jr. andP. Ausloos, J. Res. Natl. Bur. Stand. 75A,141(1971). 16. E. Tschuikow-Roux, J. R. McNesby, W. M. Jackson, and J. L. Faris, J. Phys. Chem. 71, 1531 (1967). 17. (a) S. Tsunashima, S.-I. Hirokami, and S. Sato, Can. J. Chem. 46, 995 (1968), and references cited therein; (b) S. Sato, Znt. Un. Pure Appl. Chem., Org. Phatochem. 2, 87 (1967) (Int. Symp. Enschede). 18. (a) A. H. Laufer, J. Photochem. 27, 267 (1984); (b) A. Fahr and A. H. Laufer, J. Photochem. 34, 261 (1986). 19. Y.-P. Lee and G. C. Pimentel, J. Chem. Phys. 75, 4241 (1981). 20. T. D. Bouman and A. E. Hansen, Chem. Phys. Lett. 117, 461 (1985), and references cited therein. 21. R. S. Mulliken, 1. Chem. Phys. 71, 556 (1979). 22. R. McDiarmid, J. Phys. Chem. 84, 64 (1980). 23. E. T. Nelson and C. K. N. Patel, Proc. Natl. Acud. Sci. U.S.A. 78, 702 (1981). 24. P. 'A. Snyder, P. N. Schatz, and E. M. Rowe, Chem. Phys. Lett. 110, 508 (1984).
172
PH~OCHEMISTRYOF SIMPLE OLEFINS
25. D. M. Mintz and A. Kuppermann, J . Chem. Phys. 71, 3499 (1979). 26. J. CarlierandR. Botter, J . ElectronSpectr. Rel. Phenom. 17,91(1979). 27. D. G. Wilden and J. Comer, J . Phys. B: Atom. Mofec. Phys. 12, L371 (1979). 28. Y. Sato, K. Satake, and H. Inouye, Bull. Chem. SOC.Japan 55, 1290 (1982). 29. A. Gedanken, N. A. Kuebler, and M. B. Robin, J . Chem. Phys. 76,46 (1982). 30. C. Petrogonlo, R. J. Buenker, and S. D. Peyerimhoff, J . Chem. Phys. 76, 3655 (1982). 31. M. H. Palmer, A. J. Beveridge, I. C. Walker, and T. Abuain, Chem. Phys. 102, 63 (1986). 32. (a) E. M. Evleth and A. Sevin, J . Am. Chem. SOC. 103, 7414 (1981); (b) J. D. Goddard, Chem. Phys. LRtt. 83, 312 (1981). 33. D. A. Becker, H. Okabe, and J. R. McNesby, J . Phys. Chem. 69, 538 (1965). 34. S. Arai, S . Shida, and T. Nishikawa, Bull. Chem. Soc. Japan 39, 2548 (1966). 35. E. Tschuikow-Roux, J . Phys. Chem. 71, 2355 (1967). 36. J. Niedzielski, W. Makulski, and J. Gawlowski, J . Photochem. 19, 123 (1982). 37. G. J. Collin, H. Deslauriers, and J. DeschCnes, Can. J . Chem. 57, 870 (1979). 38. P. Borrell, A. Cervenka, andJ. W. Turner,J. Chem. SOC.B , 2293 (1971). 39. H. Deslauriers and G. J. Collin, J . Chim. Phys. 82, 1033 (1985). 40. (a) M. Avrahami and P. Kebarle, J. Phys. Chem. 67, 354 (1963); (b) C. A. Heller and A. S. Gordon, J . Chem. Phys. 42, 1262 (1965); (c) S . 4 . Hirokami and S. Sato, Bull. Chem. SOC. Japan 43, 2389 (1970). 42. W. R. Rodwell, W. J. Bouma, and L. Radom, Znt. J . Quunt. Chem. 18, 107 (1980). 42. W. R. Rodwell, W. J. Bouma, andL. Radom, Int. J. Quant. Chem. 18, 107 (1980). 43. (a) J. A. Hush, in Concepts in Theoretical Organic Chemisrry, Allyn & Bacon, Boston, 1974, pp. 67 ff.; (b) R. G. Pearson, in Symmetry Rules for Chemical Reactions, Wiley-Interscience, New York, 1976, pp. 95-96, 469-470. 44. W. A. Guillory and S. G. Thomas, Jr., J . Phys. Chem. 79,692 (1975). 45. A. Wieckowski and G. J. Collin, J. Phys. Chem. 81, 2592 (1977). 46. H. Deslauriers, W. Makulski, and G. J. Collin, Can. J. Chem. 65, 1631 (1987).
REFERENCES
173
47. J. P. Chesick, J. Chem. Phys. 45, 3934 (1966). 48. P. Kebarle and M. Avrahami, J. Chem. Phys. 38, 700 (1963). 49. F. Bayrakceken, J. H. Brophy, R. D. Fink, and J. E. Nicholas, J . Chem. SOC.,Faraahy Trans. 169, 228 (1973). 50. J. H. Kiefer, M. Z. Al-Alami, and K. A. Budach, J. Phys. Chem. 86, 808 (1982). 51. J. M. Figuera, E. Fernandez, and M. J. Avila, J. Phys. Chem. 78, 1348 ( 1974). 52. J. W. Simons, B. S. Rabinovitch, and F. H. Dorer, J. Phys. Chem. 70, 1076 (1966). 53. (a) A. U. Acuiia, J. M. Figuera, and V. Menendez, Anal. Real SOC.ESP. Fis, Quim. 67, 181 (1973); (b) W. Makulski, J. Gawlowski, and J. Niedzielski, J. Phys. Chem. 85, 2950 (1981). 54. (a) P. Borrell and P. Cashmore, Trans. Faraday Sac. 65, 558 (1969); (b) J. Herman, K. Herman, and P. Ausloos, J. Chem. Phys. 52, 28 (1970). 55. H. Yamazaki, R. J. CvetanoviC, and R. S. Irwin, J. Am. Chem. SOC.98, 2198 (1976). 56. E. M. Evleth and E. Kassab, Can. J. Chem. 61, 306 (1983). 57. (a) G. 0. Schenck, S.-P. Mannsfeld, G. Schomburg, and C. H. Krauch, 2. Narurforsch., B 19, 18 (1964); (b) Y. L. Bahurel, D. J. MacGregor, T. L. Penner, and G. S. Hammond, J. Am. Chem. SOC.94,637 (1972). 58. J. Saltiel, J. D’Agostino, E. D. Megatity, L. Metts, K. R. Neuberger, M. Wrighton, and 0. C. Zafirious, Org. Phorochem. 3, 1 (1973), and references cited therein. 59. (a) R. S. Konar and B. DeB. Darwent, J. Indian Chem. SOC. 53, 891 (1976); (b) S. Tsunashima and S. Sato, Rev. Chem. Int. 4, 201 (1979). 60. S. Yamamoto, N. Nobusada, Y. Sueishi, and N. Nishimura, Chem. Lett., 723 (1985). 61. (a) A. B. Callear and H. K. Lee, Nature 213, 693 (1967); (b) A. B. Callear and H. K. Lee, Trans. Faraduy SOC.64, 308 (1968); (c) A. B. Callear and H. K. Lee, Trans. Faraday SOC.64, 2017 (1968). 62. P. Borrell, P. Cashmore, A. Cervenka, and F. C. James, J. Chim. Phys., 229 (1970). 63. (a) H. Deslauriers and G. J. Collin, J. Photochem. 12, 249 (1980); (b) H. Deslauriers, G. J. Collin, andB. Simard, J. Phorochem. 21, 19(1983). 64. (a) W. Tsang, Int. J. Chem. Kiner. 1, 245 (1969); (b) W. Tsang, Znr. J. Chem. Kinet. 10, 1199 (1978). 65. W. E. Falconer, B. S. Rabinovitch, and R.J. CvetanoviC, J. Chem. Phys. 39, 40 (1963).
174
PHOTOCHEMISTRY OF SIMPLE OLEFlNS
66. W. Forst, in Theory of Unimolecular Reactions, Academic Press, New York, 1973, pp. 235 ff. 67. (a) H.Deslauriers and G. J. Collin, Can. J. Chem. 63,62 (1985); (b) G. J. Collin and H. Deslauriers, Can. J. Chem. 63,944 (1985). 68. (a) G. J. Collin and A. Wiqckowski, J. Photochem. 8, 103 (1978); (b) A. Wiqckowski and G. J. Collin, Can. J. Chem. 56, 1435 (1978). 69. (a) J. Niedzielski, W. Makulski, and J. Gawlowski, J. Photochem. 9, 519 (1978); (b) J. Niedzielski, P. Geblewicz, and J. Gawlowski, J. Photochem. 10, 287 (1979). 70. (a) J. Gawlowski, J. Niedzielski, and A. Wiqckowski, J. Photochem. 12, 321 (1980); (b) J. Niedzielski and J. Gawlowski, J. Photochem. 14, 323 (1980). 71. (a) N. Nakashima, N. Shimo, N. Ikeda, and K. Yoshihara, J . Chem. Phys. 81, 3738 (1984); (b) N. Shimo, N. Nakashima, N. Ikeda, and K. Yoshihara, J. Photochem. 32, 279 (1986). 72. N. Nakashima, N. Ikeda, N. Shimo, and K. Yoshihara, presented at XIIth Int. Conf. Photochem., Tokyo, 1985; and private communication. 73. B. S. Rabinovitch and D. W. Setser, Adv. Photochem. 3, 1 (1964). 74. J. Gawlowski and G. J. Collin, J. Photochem. 23, 241 (1983). 75. Y. Inoue, S. Takamuku, andH. Sakurai, Can. J. Chem. 54,3117 (1976). 76. D. W. Placzek and B. S. Rabinovitch, Can. J . Chem. 43, 820 (1964), 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87.
and references cited therein. (a) D. C. Montague, J. Chem. SOC., Faraday Trans. 1 7 7 , 262 (1977); (b) D. C. Montague, J. Chem. SOC., Faraday Trans. Z 77, 277 (1977). D. C. Montague, J. Chem. SOC., Faraday Trans. Z 75, 398 (1975). See, for example, N. J. Turro, in Modern Molecular Photochemistry, BenjamidCummings, Menlo Park, Calif. 1978. P. J. Kropp, Molecular Photochem. 9, 39 (1978-79). P. J. Kropp, E. J. Reardon, Jr., Z. 1. F. Gaibel, K. F. Williard, and J. H. Hattaway, Jr., J. Am. Chem. SOC. 95, 7058 (1973). (a) Y. Inoue, T. Mukai, and T. Hakushi, Chem. Lett., 1665 (1983); (b) G. J. Collin and H. Deslauriers, Can. J. Chem. 63, 1424 (1985). F. H. Watson, Jr. and S. P. McGlynn, Theoret. Chim. Acta 21,309 (197 1). G. R. De Mark, G. J. Collin, H. Deslauriers, and J. Gawlowski, J. Photochem. 30,407 (1985). Y. Inoue, T. Mukai, and T. Hakushi, Chem. Lett., 1725 (1984). (a) R. H. Back and G. J. Collin, J. Phys. Chem. 90, 5684 (1986); (b) F. D. Lewis, P. Teng, and E. Weitz, J. Am. Chem. SOC.108,2818 (1986). M. A. Wickramaaratchi, J. M. Preses, and R. E. Weston, Jr., Chem. Phys. Lett. 120, 491 (1985).
REFERENCES
175
88. P. J. Kropp, Org. Photochem. 4, 1 (1979). 89. (a) A. DeLeon and R. D. Doepker, J. Phys. Chem. 75, 3656 (1971); (b) K. L. Hill and R. D. Doepker, J. Phys. Chem. 76, 3153 (1972).
90. Y. Inoue, M. Sakae, and T. Hakushi, Chem. Lett., 1495 (1983). 91. C.-K. Tu and R. D. Doepker, J. Photochem. 1, 271 (1972-73). 92. P. Kebarle, J. Chem. Phys. 39, 2218 (1963). 93. (a) G. J. Collin, J. Chim. Phys. 74, 302 (1977), Table 2; (b) E. Lopez and R. D. Doepker, J. Phys. Chem. 83, 573 (1979). 94. C.-K. Tu and R. D. Doepker, J . Photochem. 3, 13 (1974). 95. W. Adam and T. Oppenltinder, J. Am. Chem. SOC. 107, 3924 (1985). 96. (a) W. Makulski and G. J. Collin, J. Phys. Chem. 91,708 (1987); (b) G. J. Collin, H. Deslauriers, and W. Makulski, J. Photochem. 39, 1(1987). 97. K. G. Kosnik and S. W. Benson, J. Phys. Chem. 87, 2790 (1983). 98. P. M. Crane and L. T. Rose, J. Phys. Chem. 79, 403 (1975). 99. (a) M. D. Sevilla and R. A. Holroyd, J. Phys. Chem. 74, 2459 (1970); (b) R. Lesclaux, S. Searles, L. W. Sieck, and P. Ausloos, J. Chem. Phys. 100. 101.
102. 103. 104. 105.
106. 107. 108. 109.
53, 3336 (1970). Y. Inoue, S. Takamuku, and H. Sakurai, J. Chem. Soc., Perkin Trans. ZZ, 1635 (1977). G. J. Collin and H. Deslauriers, Can. J. Chem. 61, 1970 (1983). R. B. Woodward and R. Hoffman, in The Conservation of Orbital Symmetry, Verlag Chemie, Weinhein, 1970. Y. Inoue, S . Takamuku, and H. Sakurai, Bull. Chem. SOC. Japan 49, 1147 (1976). Y. Inoue, S. Takamuku, and H. Sakurai, Bull. Chem. SOC. Japan 48, 3101 (1975). (a) G. R. De Mar& 0. P. Strausz, and H. E. Gunning, Can. J. Chem. 43, 1329 (1965); (b) G . R. De Mark, Bull. Chem. Soc. Belges 81, 459 (1972). G. R. De Mark, N. Antheunis, J. Olbregts, and M. Termonia, J. Phorochem. 4, 299 (1975), and references cited therein. S. Takamuku, K. Moritsugu, and H. Sakurai, Bull. Chem. SOC.Japan 44, 2562 (1971). Y. Inoue, M. Kadohira, S. Takamuku, and H. Sakurai, Tetrah. Lett. 5 , 459 (1974). W. Adam and T. Oppenlhder, Angew. Chem. 25, 661 (1986).
110. T. R. Fields and P. J. Kropp, J. Am. Chem. SOC. 96, 7559 (1974). 111. R. Srinivasan and K. H. Brown, J. Am. Chem. SOC. 100, 4602 (1978).
176
PHoTocHEMlSTRY OF SIMPLE OLEFINS
112. H.-P. Schuchmann, C. Von Sonntag, and R. Srinivasan, J . Phorochem. 15, 159 (1981). 113. P. J. Kropp, H. G . Fravel, Jr., and T. R. Fields, J . Am. Chem. Soc. 98, 840 (1976). 114. G. J. Collin, H. Deslauriers, and W. Makulski, J . Photochem., 39, 1 (1987). 115. Y . Inoue, S. Takamuku, Y. Kunitomi, and H. Sakurai, J . Chem. SOC. Perkin Trans. ZZ, 1672 (1980). 116. Y. Inoue, S. Takamuku, and H. Sakurai, J . Chem. SOC.Chem. Comm., 423 (1976). 1 17. G . J. Collin and G . R. De Mar& J . Phorochem. 38, 205 (1987). 118. W. J. Leigh and R. Srinivaszn, Acc. Chem. Res., 20, 107 (1987).
Advances in Photochemistry, Volume14 Edited by ,David H. Volman, George S. Hammond, Klaus Gollnick Copyright © 1988 John Wiley & Sons, Inc.
THE DECOMPOSITION OF ALKYL NITRITES AND THE REACTIONS OF ALKOXYL RADICALS Julian Heicklen Department of Chemistry and Center for Air Environment Studies, The Pennsylvania State University, University Park, Pennsylvania 16802
Dedicated to Yuri Tarnopolsky, chemist and soviet Jew, who served in a labor camp in Chita, Siberia because of his desire to emigrate.
CONTENTS 1. Introduction 11. Photolysis of alkyl nitrites A. Ultraviolet absorption B . Photodecomposition C . Primary process quantum yield D. Formation of excited products E. Summary 111. Thermal decomposition of alkyl nitrites A. Earlywork B. Mechanism C. Modem studies IV. Reactions of alkoxyl radicals with NO, ratio A. RO NO disproportionation-to-combination B . RO + NO2disproportionation-to-combinationratio C. Relative rate of RO with NO and NO, D . Rate coefficient for RO + NO
+
177
THE DECOMPOSI'IION OF ALKm NITRITES
178
+
E. Rate coefficient for RO NO2 V. Decomposition and isomerization of alkoxyl radicals A. Decomposition 1. CH30 2. C2H.30 3. i-C3H70 4. n-C3H70 and i-C4&0 5. S-C4H90 6. t-C4HgO 7. 2-C5Hl,O 8. t-Amoxyl 9. (CF3)2C(O)CH3 and CF3C(O)(CH& 10. Phenoxyl 11. summary B Isomerization VI. Reactions of alkoxyl radicals with O2 A. Early work B CH30and CD30 C. C*H,O, i-C,H,O, n-C3H70, and i-C4H90 D . n-C&O and s-C4H90 E. Comparison of results for simple alkoxy radicals F. Other radicals VII. Other reactions of alkoxyl radicals A. Reactions with radicals B . Abstraction of H atoms from molecules 1. CH30 2. CZHSO 3. i-C3H70 4. t-C4H90
. .
5.
s-C4&0
C. Addition reactions D. Reaction with O3 Acknowledgements References
I. INTRODUCTION The reactions of akoxyl radicals are important in combustion and in polluted atmospheres. Therefore there has been considerable interest in studying their reactions. Overall reviews of the field were made from 1959 to 1972 (Gray and
PHOTOLYSIS OF ALKYL NlTRlTEs
179
Williams, 1959; Gray et al., 1967; Heicklen, 1968; Howard, 1972), but no general update seems to have appeared. However, Ban (1979) has reviewed the thermochemistry and thermal-decomposition kinetics for alkoxyl radicals and alkyl nitrites. It is the purpose of the present review to report all work through June, 1986 (and some later) on the reactions of alkoxy radicals. In addition, since alkoxyl radicals often are produced in laboratory experiments from alkyl nitrites, the photochemical and thermal decomposition of these species will also be reviewed. The units used for rate coefficients will be molar and seconds. Activation energies will be given in kcavmole. The symbol 8 represents RT In 10 where R is 1.987 x kcdmole-K. For reactants which give more than one set of products, the reaction channels are split into a, b, c, etc. Thus the overall reaction 2 has two channels, reactions 2a and 2b, with k2 = k2= k2b. Prefix abbreviations are: n, normal; i, iso; c, cyclo; s, secondary; t, tertiary.
+
11. PHOTOLYSIS OF ALKYL NITRITES
A. Ultraviolet Absorption The absorption spectrum of gaseous methyl nitrite at 25°C is shown in Fig. 1. The first band has structure in the region 290-380 nm. At higher wavelengths the absorption is very weak and drops rapidly with increasing wavelength, though some absorption exists to 435 nm. Below 290 nm, the absorption rises sharply and reaches a maximum at 214 nm. An enlarged absorption spectrum of the region >280 nm is given in Fig. 2. The absorption of HONO results from a singlet n+vr* electronic transition (King and Moule, 1962). Presumably the same is true of alkyl nitrites. The absorption is complicated because it is a composite of cis and trans isomers (Elkins and Kuhn, 1935;Tarte, 1952). This causes a change in relative intensities with wavelength as the temperature, and thus the relative abundance, of the isomers changes. The absorption of alkyl nitrites in the region from 25000-30000 cm-' was studied by Elkins and Kuhn (1935), who found evidence for two different electronic transitions, based on the variation of the circular dichroism and anisotropic factor of alkyl nitrites. According to Sidman (1958), the major part of the absorption should be due to the n--yTT*transition involving oxygen nonbonding electrons. However, Calvert and Pins (1966) believe the n%* transition involves a lone-pair electron on the nitrogen atom. The photoabsorption cross section at 366 nm is (1.79 2 0.03) X cm2, independent of temperature from 25 to 150°C (Wiebe and Heicklen, 1973). Other results at cm2 cm2 (Pate et al., 1974) and (1.74 ? 0.16) X 25°C are 1.84 X (Taylor et al., 1980).
180
THE DECOMPOSITTON OF ALKYL
WAVELENGTH. nm
Figure 1. Photoabsorption spectrum of gaseous CH,ONO 91980) with permission of John Wiley and Sons, Inc.
at
298 K. From Taylor et al.
The photoabsorption cross sections in Figs. 1 and 2 are in good agreement. The cross section at the wavelengths of maximum absorption in the two bands (339 and 214 nm) are: at 339 nm, 3.1 x cm2 (Calvert and Pitts, 1966), 3.4 X cm2 (Napier and Nomsh, 1967), and (3.24 2 0.16) X cm2 (Taylor et al., 1980); and at 214 nm, 4.97 x lo-'* cm2 (Napier and Nomsh, 1967), 4.2 x cm2 (Calvert and Pitts, 1966), (4.59 & 0.58) X lo-'* cm2 (Taylor et al., 1980), and (4.2 +- 0.4) X cm2 (Lahmani et al., 1980a). Lahmani et al. (1980a) have shown that below 190 nm, the absorption of CH30N0 continues to decrease to a minimum at 2168 nm. It then increases to a maximum at 139 nm, which has an extinction cross section of (3.33 & 0.08)
PHOTOLYSIS OF ALKYL NITRlTES
181
Wavelength, A
Figure 2. Absorption spectra at 25°C of: (1) CH,ONO(g), (2) (CH,)CONO(g). From Calvert and Pitts (1966) with permission of Drs. Jack Calvert and James Pitts, Jr.
X cm2,considerablylarger than the maximum of (4.6 f 0.4) x cm2 at 215 nm. The ultraviolet absorption spectra of t-C4H90N0, C2H,0N0, i-C3H70N0, n-C3H70N0, i-C4H90N0, and n-C4H90N0 are shown in Figs. 2-7, respectively. These spectra are similar to that for CH30N0. They have a banded structure from 310 to 400 nm and a very strong continuum below 300 nm. However, the peak absorption in the banded region is at 339 nm for CH30N0 and -380 nm for t-C,H,ONO. For the other compounds the spectra are almost identical and the peak absorptions occur at 3: 358 nm. The absorption cross sections are listed in Table 1 . At 366 nm, they are all about 1.3 X cm2 independent of temperature, except for CH30N0, where it is 1.8 x cm2 independent of temperature. The band spacings in the absorption spectrum were first given by Thompson and Purkis (1936) and Purkis and Thompson (1936) for CH30N0, C2H50N0, s-C4H90N0, and isoamyl nitrite. Their results are shown in Fig. 8.
B. Photodecomposition The photodecomposition pathways of alkyl nitrites have been reviewed by Calvert and Pitts (1966). Earlier a review of the photolysis of complex organic nitrites in solution was given by Akhtar (1964). Since the review of Calvert and Pitts
0.00
,
260
I
280
I
300
I
320
340
I
3€Q
WAVELENGTH
I
380
I
400
I
420
I
440
( nm )
Figure 3. The utraviolet absorption spectrum of C2H50NO(g) (0.012%C2H50N0 in N,) at 25°C. From Morabito (1985) with permission.
Figure 4. The ultraviolet absorption spectrum of CC,H,ONO vapor at 25°C. From McMillan et al. (1971) with permission of American Elsevier Publishing C o . , Inc. 182
4.00-
'
I
I
I
I
I
I
I
Yz
3
K
v) 0
m
a
I
_
-
3.503.00-
I
n-C,H,ONO
. I
-
2.50-/ 2.00-
-
1.50-
-
1.00-
-
0.50-
-
0.00-
I
I
I
I
I
I
I
1
I
I
I
000-
I
I
I
I
I
I
280
300
320
340
360
380
I
I
- C&ONO
I
400
I
I
420
440
WAVELENGTH (nm)
Figure 6. The ultraviolet absorption spectrum of i-C4H90N0 in n-hexane solution at 25°C. From Morabito (1985) with permission.
183
THE DECOMPOSITION OF ALKYL NITRlTEs
184
260
200
300
320
340
360
WAVELENGTH
380
400
420
440
(nml
Figure 7. The ultraviolet absorption spectrum of n-C4&ON0 in n-hexane solution 25°C. From Morabito (1985) with permission.
at
(1966), Heicklen (1973) has briefly reviewed the photochemistry of CH,ONO. However there appears to have been no comprehensive review in 20 years. Apparently the first study of the photodecomposition of alkyl nitrites was performed by Purkis and Thompson (1936), who used irradiation from a full mercury arc. They photolyzed CH30N0 and C2H,0N0. In the case of CH,ONO, gaseous products consisted mainly of N2 and N20. Also found was a white solid believed to be parafomaldehyde. With C2H50N0, they found N2, N20, CH,, and CO as gaseous products and a liquid which gave a positive identification for aldehydes. They concluded that the primary process was direct molecular decomposition to HNO plus the aldehyde, with the HNO subsequentlydisproportionating to H 2 0 N20. Thompson and Dainton (1937) extended these studies to n-C3H70N0, i-C3H70N0, s-C4&ON0, and t-C4H90N0 and reached the same conclusion. However a number of years later Gray and Style (1952) investigated the photodecomposition of CH30N0 at 366 nm from 30 to 156°C. They explained their results in terms of primary rupture of the CH,O-NO bond,
+
RON0
+ hu
-
RO
+ NO
(14
since they found NO as a product. The formation of NO and CH20 as products was confmed by Tarte (1953), who photolyzed CH30N0 with a full arc. He
PHOTOLYSIS OF ALKYL "WTES
185
TABLE 1. Photoabsorption Cross Section IJ of RON0 A
iemp.
m
nm
"C
U
cm*/molecule
Reference
CH30N0
366
25 to 150
339
25
214
25
1.79 x 10-19 1.84 x 1 0 - l ~ 1.74 x 10-19 3.1 x 10-19 3.4 x 10-19 3.24 x 10-19 4.2 X lo-'* 4.97 x 10-'8 4.59 x 10-'8 4.2 X lo-''
Wiebe and Heicklen (1973) Pate et al. (1974) Tayloret al. (1980) Calvert and Pitts (1966) Napier and Nomsh (1967) Tayloretal. (1980) Calvert and Pitts (1966) Napier and Norrish (1967) Taylor et al. (1980) Lahmani et al. (1980a)
C,H,ONO
366
-148t0120
1.20 x 10-19
Zabarnick and Heicklen (1985a)
n-C3H,0N0 Zabamick and Heicklen (1985b) 1.25 x
366
-26 to 120
366
-8to 120
1.30 x
366
-8 to 120
1.37 x
i-C4H90N0
Zabamick and Heicklen (1985~)
n-C4H90N0
Morabito andHeicklen(1987)
also found NO in the photolysis of n-C,H,ONO and n-C4H90N0, but not in a number of other C3-C5 alkyl nitrites. A major advance was made by Brown and Pimentel(1958), who found CH20 and HNO as the initial photoprcducts in a solid Ar matrix at 20 K with photolysis of CH30N0 between 240 and 360 nm from a mercury arc. They identified these products by low-temperature infrared spectroscopy. Confirmation that HNO was produced was given by Dalby (1958), who observed its absorption spectrum in the wavelength region 650-770 nm in the flash photolysis of isa-amyl nitrite. McGraw and Johnston (1969) also observed HNO by its infrared absorption at 3300 cm-'. Hanst and Calvert (1959) showed from product analysis that the primary process in CH30N0 photolysis at wavelengths >310 nm from a mercury lamp could be explained by 0-N bond cleavage, Eq. la. By doing experiments in the absence and presence of large amounts of Oz, they were able to show that there was no formation of CH, NO,, CH, NO 0, or CH30N 0. This was deduced from the fact that the products expected from these free radicals
+
+
+
+
THE DECOMPOSITION OF mcnm
186 Y.
cm-'
34OOo.
-
-
33000.
-
-
32000 . 320727 '4 939
t
31000 -
311331
3oooo -
30139-7 959 V 291mIT 1011
290002800027000 2600025000 -
V
2816931039 V 27130-pj 1068 26062=p
894 33784=, 882 3 3 1 % ~ 8 b 32082 32788"; 32734N3 795 9 32257-1.b 31939" A 890 8$5 3 1 3 6 7 - d 31104=C A - 9k6 30441-A 33680- b
-
31776-P 87 !
V
34518-1
-
'v6
8 b 30148--b 30120=r4 923 994 t 29197;29154-d~ 1020
q5
2 8 1 7 7 - r n 2816971040 1069 27137*)
c
27100-)
t
1163
1
-1
,3200
b
- 3400
-
1116
4 I
- 3600
c
- 3800
990 28498--1 27382-
1708
2567q
(b) Ethyl
(c) sec-Butyl
,3000
-
294481
1518
25582(d) Amy1
- 913
x, A
(a)Methyl
4Ooo
Figure 8. Band spacing in the absorption spectra of (a) CH,ONO, (b) C2H50N0, (c)sC,H,ONO, and (d) iso-my1 nitrite. From Purkis and Thompson (1936) with permission of The Royal Chemical Society.
were absent. The products observed by Brown and Pimentel (1958) could then be explainedby the reaction of CH30 NO, which could proceed by two paths,
+
+ NOM.,CH,ONO
CH~O
-CH2O
-I-HNO
At room temperature the HNO disappears by disproportionation 2HNO -N2O
+ H20
(3)
which accounts for the N,O observedby the early workers (Purkis and Thompson, 1936; Thompson and Dainton, 1937; Gray and Style, 1952). Kabaskalian and Townley (1962a) also showed that the primary process gave RO + NO in a series of alkyl nitrites photolyzed in benzene solution. They deduced this from the products formed which were aldehydes and alcohols, the products expected from the disproportionation of RO radicals. For RO radicals
187
PHOTOLYSIS OF ALKYL IWlUTES
larger than C2H50, they also saw the decomposition products (aldehydes or ketones) expected from these radicals. This conclusion was supported by the work of McGarvey and McGrath (1964), who found that NO absorption reached a maximum within 50 psec after the flash photolysis of a whole series of alkyl nitrites. In the case of CH30N0 the W absorption spectrum of CH30 was also seen (McGrath and McGarvey, 1964; McGarvey and McGrath, 1964). Free radicals also were detected by electron paramagnetic resonance in CH30N0 photolysis at 77 K from a mercury arc by Bielski and Timmons (1964). Further confirmation came from Ohbayashi et al. (1977), who observed emission spectra of CH30, C2H50.i-C3H70,and NO in the photolysis of the corresponding alkyl nitrites by iodine, mercury, xenon, and krypton lamps; and by Sanders et al. (1980), who measured the laser-induced fluorescence from CH30 produced in the 266-nm photolysis of CH,ONO. During the 1960sthe photochemistry of t-C4H90N0was studiedby McMillan and his coworkers. Earlier Coe and Doumani (1948) had shown the products to be CH3N0 + acetone in the vapor-phase photolysis at 25°C with aquartz mercury lamp. Coe and Doumani had concluded that these products probably were formed by a molecular elimination. However in his fust study, McMillan (1962) photolyzed t-C4&ON0 at 253.7 nm and found that the quantum yield of acetone was pressure dependent. He interpreted his results via the mechanism t-C$&ONO
+ hv
-
t-C4H90t
t-C4H90t -CH3 t-C4&Ot CH, t-C4&0
+
+ NO
acetone
+ M t-C4H90 + M + NO -CH,NO + NO t-C4H90N0 4
(la) (4) (5)
(6)
(24
where the superscript refers to excess energy. From his results, McMillan concluded that the quantum efficiency +la 20.84 at 26°C and 20.97 2 0.04 at 99°C. In a similar analysis of the photolysis of C2H5(CH3)2CON0(amyl nitrite), McMillan et al. (1971) concluded that = 1.O at 253.7 nm and 25”C, and Durant and McMillan (1966)concluded that +la = 1.O at 366 nm and 114°C. McMillan (1963) photolyzed t-C&ONO at 366 nm and 25°C in the presence of 15N0 to measure the exchange via the back reaction of t-C,H90 with I5NO. Under these conditions he found that “hot” radical production was small, since wacetone} = 0.04. He found wr-C4&0 ”NO} tobe0.99 0.03 andconcluded that +la was 1.0. However, in his experiments the 15N0 pressure was at least 14.5 TOK,so that exchange could have occurred with electronically excited t-C4&ON0. Thus the primary quantum yield in t-C4&ON0 photolysis at 366 nm is still unknown. However, if +la is <1.0, then the ”NO exchange with the excited CH30N0 would have to be 100% efficient.
THE DECOMPOSITION OF ALKYL MTRITEs
188
McMillan et al. (1964) confirmed the formation of CH3N0 in the gas-phase photolysis of t-C,qONO with a full arc (-75% of the radiation absorbed was below 255 nm) by using in sinc infrared absorption spectroscopy. In the presence of small amounts of O2 (which scavenge CH3 radicals) the CH3N0 production occurred with an induction period, thus indicating that it was coming from a precursor that reacts competitivelywith NO and 0,(presumably CH3radicals).
C. Primary Process Quantum Yield The first indication that the quantum yield for photodecomposition of CH30N0 was <1.O was given by Napier and Norrish (1967). When they flashed photolyzed CH30N0 in a large excess of N2, the long-wavelength bands of the spectrum almost disappeared, then returned to near the initial intensity at long delays. Coincident with the disappearance of bands, a short-wavelength continuum appeared at 290-300 nm and then decayed over the same period during which the nitrite bands returned. The minimum in the CH30N0 absorption and maximum in the new continuum occurred at 34 psec after the flash. The presence of excess NO had no effect on the time delay. The investigators interpreted their results in terms of formationof a thermal isomer in equilibriumwith CH30N0. Schuck and Stephens (1967) photolyzed C2H50N0in a 60-Lreaction vessel at concentrations of 0.58-62 mTorr at room temperature with peak energy at 350 nm and a distribution such that 85% of the energy was between 330 and 375 nm. They found that the initial quantum yield of C2H,0N0 disappearance dropped from 0.99 at their lowest pressure to <0.089 as the pressure was raised to 1 atm of N,. Increasing the pressure of C2H50N0 or NO also decreased the quantum yield. They interpreted these results in terms of both a direct cleavage reaction (la) and the formation of an excited molecule RONO* which could decompose directly to acetaldehyde + HNO at low pressure, but which could be collisionally stabilized at pressures > 15 mTorr C,H,ONO. This was deduced from the fact that C2H50N0 disappearance shifted from second-order decay below 15 mTorr to first-order decay above 15 mTorr. Ludwig and McMillan (1969) photolyzed i-C3H70N0at several wavelengths and temperatures. They found CH3CH0 and CH3COCH3 as products, which they interpreted as coming from CC3H70N0
+ hv
__*
gi-C3H,0t
-
i-C3H70t -CH3CH0 i-C3H70 + NO
+M
+ (1 - c)i-C3H70 + NO + CH3
i-C3H70N0
----*CH3COCH3
+ HNO
(la) (4)
189
PHOTOLYSIS OF ALKYL NITRITES
This mechanism predicts that +la
= @{CH3CHO}
+
k2b
cP{CH3COCH3}
Ludwig and McMillan adopted the value of kZdkz = 0.18 given by Hughes and Phillips (1967), and obtained the values of +la listed in Table 2. The value of +la is considerably less than unity. It increases slightly with temperature and is independent of wavelength. for C2H,0N0 was first The question of the value of the magnitude of addressed by McMillan et al. (1971). The rate law predicts
TABLE 2. Primary Quantum Yield for RO Production in RON0 Photolysis
R
CH3 C2H@
i-C3H70
X,(nm)
366 366 366 366 366 366 366
T,"C
= 25 25 25
'ha
c1.0 c0.75 0.33
50 c0.58 -48 to 120 0.29O 23 0.28 26 0.32-0.36 85
t-CaH90
327 39 1 253.7
n -C H 0
366
i-C4H90 n-C4H90 t-C,H 11 0
366 366 253.7 366
125 26
0.33 0.31 26 20.84 99 a0.97 23 0.37 +- O.Olb 50 0.36 & O.Olb -26 to 120 0.38 2 0.04b -8to 120 0.19 +- 0.02' -8t0 120 0.19 5 0.04 25 1.o 114 1.o
Reference
Napier and Nomsh (1967) Wiebeetal. (1973) This work McMillanetal. (1971) Zabarnick and Heicklen (1985a) Morabito and Heicklen (1985a) Ludwig and McMillan (1969)
McMillan (1962) McMillanetal. (1971) Zabarnick and Heicklen (1985b) Zabarnick and Heicklen (1985~) Morabito and Heicklen (1987) McMillanetal. (1971) Durant and McMillan ( 1966)
"Quantumyield is <0.003 for CH3CH0 + HNO productionand <0.002 for C,H, See text. %ese quantum yields are based on different values of kZ&. 'As corrected by Morabito and Heicklen (1985b).
+ NOz production.
190
THE DECOMPOSITION OF A L K n NITRlTEs
where CzH50
+ NO
C2H50N0 -CH3CHO
+ HNO
(2a) (2b)
With the value of k2dk2 = 0.23 reported by Arden et al. (1964), and the values of @{CH3CHO}measured by McMillan et al. (1971), they computed +la to be 0.59 2 0.01 at 23°C and 0.58 2 0.01 at 50°C. However, these measurements were made in the Torr pressure range of reactants, so that reaction 2a was not in the high-pressure regime. Thus their estimates are too high. A more accurate estimate was made by the same method by Zabarnick and Heicklen (1985a), who found that at higher total pressures (>lo0 Torr), WCH3CHO} = 0.070 -t 0.006, independent of temperature from -48 to 120°C. They used this value along with the average value of k2dk2 = 0.24 found by Phillips and coworkers in three separate studies (Arden et al., 1964; Livermore and Phillips, 1966; East et al., 1968) to deduce from Eq. b that +la = 0.29 & 0.03 independent of temperature from -48 to 120°C with 366-nm radiation. for n-C3H,0N0 McMillan et al. (1971) used the same analysis to estimate at 366 nm. They assumed 5 = 0.00 and k2dk2 = 0.23, the same value as for C2H50 radicals. With these values they deduced +,a = 0.37 2 0.01 at 23°C and 0.36 2 0.01 at 50°C. Zabarnick and Heicklen (1985b) used the same analysis and computed +la = 0.38 -+ 0.04 independent of temperature from -26 to 120"C, using a value of k d k 2 = 0.30 measured by East and Phillips (1970). Thus McMillan et al. and Zabarnick and Heicklen obtained the same value for +,a, but this is fortuitous (and inexplicable), since they used different values for k2dk2. Unfortunately, McMillan et al. (1971) did not list their values of WC2H5CHO}, so it is not clear whether there is a real discrepancy in the data or a computational error. For the sake of consistency, we will assume a computational error. In an analogous manner, Zabarnick and Heicklen (1985a) deduced that +la = 0.24 -+ 0.02 independent of temperature from -8 to 120°C in the photolysis of i-C4H90N0 at 366 nm using k2dk2 = 0.27, which is the average of the values found for C2H50and n-C3H70radicals. Since then Morabito and Heicklen (1985b) have measured k&k2 = 0.33 k 0.03, so that +,a becomes 0.19 ? 0.02. Likewise Morabito and Heicklen (1987) deduced +la = 0.19 -+ 0.04 independent of temperature from -8 to 120°C in the photolysis of n-C4H90N0 at 366 nm, using k2dk2 = 0.29 -C 0.05 (Morabito and Heicklen, 1985b). The question of the value of the primary quantum yield to produce CH30 + NO was addressed by Wiebe et al. (1973). They photolyzed CH30N0 at 366 nm and 25°C in the presence of "NO so that they could measure the CH301'N0 formed in reaction 2a as well as the N20 produced from the HNO formed in should be given by 2 ~ 3 o N Z 0 } that of reaction 2b. The primary quantum yield, ala. + @{CH3015NO}.This sum was found to be 0.75 2 0.01 at high pressure; thus
PHOTOLYSIS OF ALKYL, NllWTES
191
Wiebe et al. (1973) concluded that it represented +la. However, subsequent work with higher alkyl nitrites (Morabito and Heicklen, 1985a) has shown that 15N0 can exchange with the photoexcited alkyl nitrite, which does not undergo decomposition. Thus +la might be less than 0.75. Cox et al. (1980) photolyzed CH30N0 with homogeneous radiation from 310 to 410 nm with peak intensity at 350 nm and measured the quantum yield for CH30N0 removal to be 1.0 at a total pressure of 1 a m of N2 or N2 + 02.This is difficult to believe in the absence of 02,since some CH30N0 must be re-formed from the reaction of CH30 with NO. Another way to obtain the primary quantum yield +la is from a knowledge of k 4 k 2 = 0.33 at 174°C obtained from thermal sources of CH30 radicals by Arden et al. (1964), since at low NO pressures but high total pressure
and k2Jk2 is temperature independent (see Section IV-A). Both McGraw and Johnston (1969) and Wiebe and Heicklen (1973) obtained a value of 0.055 for wN20} at low NO pressures and high total pressure. Likewise Zellner (1986) flash-photolyzed CH30N0 at 351 nm and found Q>{CH20}= 0.12. Thus $la = 0.33 at 366 nm, and most of the absorbed light does not lead to products: CH3ONO
+ h~
CH30NO*
(1b)
where the asterisk (*) indicates electronic excitation. There is an incompatibility between the direct measurements for +la and that obtained from k2,,/k2.This is a problem that still needs to be resolved. However, in view of the results of Napier and Norrish (1967), we tentatively favor the value for +la = 0.33. Tuck (1977) photolyzed C2H50N0 with the polarized output of a lser at 347 nm and observed the angular dependence of the photofragments. His conclusion was that the photodissociation process occurs in less than the time for one rotation, thus implying the absence of a long-lived excited state at 347 nm, which is in a valley between two absorption bands. However, 366 nm is at a band peak where both a long-lived excited state and a continuum could overlap. Morabito and Heicklen (1985a) have shown that for the alkyl nitrites RONO* exchanges with "NO via the competition RONO*
+
-
15~0
RO
-
15~0
-RONO RONO*
RON0
+
+ NO
(7a)
15~0
(7b) (8)
THE DECOMPOSmON OF ALKYL NKRITES
192
This mechanism leads to the rate law
where it is assumed that [l4N0] is sufficiently low not to quench RONO* or react with RO to any significant extent. Since for CH30N0 photolysis at 366 nm, one has qCH3015NO}+ 2 q N 2 0 } = 0.75 2 0.01, +la = 0.33, and +la = 0.67, the left-hand side of Eq. a can be evaluated. The experiments of Wiebe et al. (1973) were done with [l5N0] = 5.6 +- 2.9 Torr.The value of k7a/k7 is not known for CH30NO*, but it is close to 1.0 for C2H50NO*and decreases towards 0.50 as the complexity of the alkyl nitrite increases (Morabito and Heicklen, 1985a). Thus we can assume that k7a/k7 * 1.0. With this assumption, k8/k7 = 1.8 X M. Jacox and Rook (1982) photolyzed CH30N0 at 14 K in a solid Ar matrix and observed the products by infrared spectroscopy. They found that the threshold for photodecomposition lies near 370 nm (77.3 kcdmole), with no evidence for photoisomerization at longer wavelengths. Thus the photodissociation threshold is at a very much greater energy than the dissociation energy of 684 nm (41.8 kcdmole) reported by Batt et al. (1974). The possibility of other primary photodecomposition processes was investigated by Zabarnick and Heicklen (1985a). They photolyzed C,H50N0 at 366 nm in the presence of either C3H6or i-C4H10 to scavenge the C2H50 radicals. They found that (P{N,O} dropped to zero, and concluded that the quantum yield HNO was for the direct photodecomposition of C2H50N0 to CH30N0 C0.003. Additional experiments with added NO2 showed that @{C2H5N0J <0.002, thus ruling out the possibility of a direct photodecompositionto C2H5 + NO2. The value of the magnitude of +la was thrown into doubt by the work of Rose (1979), working in McMillan’s laboratory. He photolyzed C2H50N0 at 366 nm and 296 K in the presence of excess NO2 and measured @{C2H50N02} and @{CH,CHO}. He assumed that these products resulted from
+
C2H50
+ NO2 %C2H50N02 + HN02 -CH3CHO
Corrections for the CH3CH0 produced resulting from photodecomposition of NO, followed by 0-atom attack on C2H50N0 were made. He found (P{C2H50NOJ = 0.93 -t 0.05, and from his results concluded that bJba= 0.09 +- 0.01. Thus +la should be 1.0. found by Rose can be explained if NO, exchanges The high value for with C,H,ONO* formed by absorption of the radiation:
193
PHOTOLYSIS OF ALKYL,
Since the sum @{C2H50NOJ + @{CH3CHO} found by Rose was 1.02 f 0.05, then reactions 10b and 8 could be of no importance under their conditions. This is consistent with the fact that there was no dependence of the quantum yields with NO2 pressure from 0.10 to 0.85 Torr. Thus klo&lo <0.03 and kslklo <2 X loM6 M.With the value of +la = 0.28 reported by Morabito and Heicklen (1985a), bdk, becomes 0.29 2 0.03. In a similar fashion, Rose (1979) photolyzed n-C3H70N0 and s-C4H90N0 in the presence of NO2 at 366 nm and 2 3 T , and came to the same conclusion for s-CH4H90N0 is not known, but that +la = 1.0. The actual value for that for n-C3H70N0 is 0.38 ? 0.04. Since Q>(n-C3H70N02} was measured to be 0.89 ? 0.04, we can estimate kgdk, = 0.26 2 0.03. Morabito and Heicklen (1985a) showed that the fraction of light absorbed that did not lead to photodissociation gave an electronically excited state that could exchange with "NO. They studied the photolysis of C2H50N0, nC3H70N0, n-C,H,ONO, and i-C4H,0N0 at 366 nm and 23°C in the presence of I5NO. The indicated mechanism from their result was
-
RONO -t hv -+ RO
+ NO
(la)
RONO*
RONO*
+
1 5 ~ 0-+
RO
1 5 ~ 0
+ NO-RON0
-
+ NO
(74
+ 15~0 + NO
--RONO RONO*
(1b)
(7b) (7)
RONO* -RON0 RO
+
1 5 ~ 0
RO
(8)
__*aldehyde RO
+ NO
(2a 15N)
1 5 ~ 0
+
Hi5N0
RONO
-aldehyde
(2b "N) (2a 14N)
+
HNO
(2b I4N)
RO +decomposition or isomerization
( I 1)
194
THE DECOMPOSlTION OF ALKn
where the rate coeffiients h ( l 5 N ) = k,(14N) = k, k2b(15N) = k~b('~N) = k2b, and k7 = k7a + km if the small kinetic isotope effect is ignored. They envisioned the isotope exchange reaction to proceed as follows:
RONO*
+
15~0
RO15N0
+ NO
RONO
+1
5 ~ 0
In the case where 14N0 is used, the two paths given by reactions 7a and 7b are indistinguishable. The steady-state rate law based on the above mechanism is
+
[l4N0]. Values of = 1.0 - + l a y +l,,k2,4 where [NO]= = [l5N0] k2, and kll/k2 were available from other studies, where k2 = k2a + k2,,. Thus the left-hand side of the equation could be computed and plotted versus [I5NO]-'. For C2H50NOya better straight-line plot was obtained with + l b = 0.28 rather than the 0.29 adopted by Zabarnick and Heicklen (1985a), and this value was used in the computations. The plot for n-C,H70N0 is shown in Fig. 9, and it is linear. From the least-squares values for the slopes k8/(k7a+la) and intercepts k,[NO],/ (+lak7a['5NO])yvalues of k8/k, and k7$k7 could be computed, and they are also listed in Table 3. From an inspection of the results in Table 3, we can conclude that kg/k7 = (2.7 & 0.5) x (3.4 +- 1.1) x (1.30 & 0.16) x and (2.3 & 0.3) X M, and that k7a/k7 = 1.0, 1.0,0.56 & 0.03, and0.64 k 0.04, respectively, for C2H50N0, n-C,H70N0, CC4HgON0,and n-C4H90N0. The uncertainties represent estimated absolute errors. There is no apparent trend in the values for kg/k7. However, k7Jk7 decreases as the molecular complexity increases. Perhaps this reflects the possibility that the intermediate RO(N0h can have more transient stability for more complex molecules and let k7a/k7approach the statistically expected value of 0.50. Finally we comment on the fact that Schuck and Stephens (1967) found quantum yields of 1.O for C2H50N0 photodecomposition at =350 nm and very
0 0
I
125
I
250
I
375
1 5.m
I
625 I"NOI-',
I
750
I
875
I
I
la00 1125
I
I
12.50 13.75
Tor,-'
I
ISM)
Figure 9. Plot of
versus [15NO]-1 for n-CSH70NO with +lb = 0.38, &,k4,,/k4 = 0.115, and k,,/k, = 0.0032 Tom. [15NO]/[NO]T = 0.887. From Morabito and Heicklen (1985a) with permission of John W.iley & Sons.
TABLE 3. Values of Rate Coefficient Ratios Involving RONO* at 23°C ~
R CH3 C2H5
n-C3H,ONO i-C4H90NO n-CdHgONO
k7$k7a
1 .ob 1 .oo 1 .oO 0.56 2 0.03 0.64 2 0.04
"For "NO. bAssumed.
105k8/k7,M 18.0 2.7 2 0.5 3 . 4 2 1.1 1.30 k 0.16 2.3 0.3
*
~~~~
Reference
I
From data of Wiebe et al. (1973) Morabito and Heicklen ( 1985)
195
1%
THE DECOMPOSITION OF ALKYL. IWRITES
low pressures. This suggests that RONO* may be formed with sufficient vibrational energy to photodissociate unless stabilized by collision. The photodecomposition of the higher nitrites lead to the formation of hydroxynitroso compounds. The overall reaction is
,7i-
\F -7-
,"",p 4
0
This reaction was first shown to proceed by Barton et al. (1960,1961). However, this reaction does not proceed as written, but through the usual C-O cleavage reaction. The alkoxyl radicals formed can transfer an H atom,
to yield a radical which adds to NO to give 1 1 1 1 HOC-C-C-CNO
1
1
1
1
Kabasakalian et al. (1962a. 1962b) and Kabasakalian and Townley (1962a, 1962b) showed that for this reaction to proceed the nitrite needed a chain of at least four carbon atoms. Lower nitrites did not show this reaction. A review of these reactions was given by Nussbaum and Robinson (1962) and by Akhtar (1964).
D. Formation of Excited Products McMillan (1962) photolyzed r-butyl nitrite at 253.7 and 313.0 nm and found that acetone was the major product, with CH30N02 and N2 as minor products. He noticed that the acetone quantum yield decreased with increasing pressure. Therefore he interpreted the acetone as coming from decompositionof an excited r-butoxyl radical, which could be stabilized by collision. Thus the primary process is
PHOTOLYSIS OF ALKYL NllWlES
RON0
+
&Rot + (1 - &)RO
h~
197
+ NO
-
(14
where 5 is the fraction of radicals with sufficient energy to decompose f-C4H90t
CH3COCH3
(4)
if not collisionally stabilized f-C4€&,0t
+M
__*
t-C4H90
+M
(5)
The collisionally stabilized alkoxyl radicals are removed by NO. From a study of the competition between reactions 4 and 5 , the following rate law is found:
@{acetone)-' =
(1 + k4 k5[M1 )
Values of the parameters 5+la and k5/k4 are listed in Table 4. The work was extended to 366 nm (McMillan, 1963), using the same techniques. These results are also in Table 4. It can be seen that the fraction of excited radicals, increases with temperature and incident wavelength from 0.04 at 366 nm and 25°C to 0.97 at 253.7 nm and 99°C. From these latter results, +la must be close to unity at 253.7 tun. It also can be seen from Table 4 that k5/k4 for C2H6 as a quenching gas increases from 253.7 to 313.0 n-n. This indicates that not only is the excited radical yield changed, but the degree of excitation increases with incident energy. The photodecomposition of t-C5H,,ON0 (C,H,C(CH,),ONO) was studied by Durant and McMillan (1966). The t-C5Hl10 radical produced in the primary process can decompose in two ways:
The sum of the quantum yields of formation of the two ketones was found to be unity at both 366 and 253.7 nm;thus +la = 1.O at both wavelengths. However the ratio of the quantum yields for the two ketones changed with pressure. The high-pressure ratio is that expected for thermal t-C5H,,O radical decomposition. Thus from the shift in ratio as a function of temperature the fractions of excited radicals produced could be deduced (McMillan et al., 1971), and they are listed in Table 4. Likewise Ludwig and McMillan (1969)deduced the fraction of excited radicals produced in the photolysis of i-C3H,0N0 from @{CH3CHO},since the CH3CH0 comes from
~
CZHSONO
r-C4H,0N0
RON0
~~
-
-
C2H6
-
t-C4&ON0
N2
C2H6
r-C,H,ONO NO
M
26 26 26
253.7 327.0 366.0 366.0 366.0 39 1.O 253.7
253.7
26 26
253.7 366
25
125 26 25
85
26 26 26 26 79 99 26 25 25
Temp., "C
253.7 253.7 253.7 253.7 253.7 253.7 313.0 366.0 253.7
A, nm
-
1.o 0.05
0.45
0.86 0.122 0.029 0.080 0.095 0.013 0.67
-
Christie and Hetherington (1977)
-
Ludwig and McMillan ( 1969)
McMillanetal. (1971)
McMillanetal. (1971)
McMillan (1963) Christie and Hetherington ( 1977)
Reference
Christie and Hetherington (1977)
}
}
'
-
-
-
-
36.1
7.2
0.87 0.87 0.87 0.87 0.94 20.97 0.2 0.04 0.87
ksfk4, hf-
TABLE 4. Parameters for Excited Alkoxyl Radical Production in Alkyl Nitrite Photolysis
PHOTOLYSIS OF A L K n
199
The values for qCH3CHO} = are listed in Table 4 for a variety of wavelengths and temperatures. Wiebe and Heicklen (1973) argued that the pressure dependence that they saw on (P{N20}in the photolysis of CH30N0 at 366 nm probably was due to decay of energetic CH30 produced in the primary process. However, a more likely explanation is that the pressure effect seen in their studies was due to the chaperone effect in the recombination of CH30 and NO. There is no evidence that hot CH30 radicals are formed with 366-nm photolysis. Christie and Hetherington (1977) photodecomposed t-butyl, isopropyl, and ethyl nitrites at 253.7 nm. They found respective values for t+laof 0.87,0.67, and 0.45. Their result agrees exactly with that of McMillan (1962) for tC,H,ONO, but is somewhat lower than the value 0.86 reported for i-C3H70N0 (McMillan et al., 1971). A few studies have investigated the energy in the NO fragment. Lahmani et al. (1980a, 1980b) photodissociated CH30N0 at wavelengths from 110 to 160 nm, where CH30N0 shows a diffuse absorption spectrum. The formation of NO in the A 'X+ (v'=0,1,2), C 211(v'=O), and D '2 (v'=O) states has been observed. The quantum yields for formation of the three states are, respectively, 0.18 & 0.03 at 144 nm, 0.07 2 0.02 at 138 nm, and 0.05 r 0.02 at 120 nm. The experimental energy threshold to produce each NO excited state is in agreement with the bond dissociation energy D(CH30-NO} = 1.8 eV. The total quantum yield of detected excited fragments was 0.4 at 120-125 nm. The vibrational energy in the NO (A 2s+)state was very nearly statistical. From this it was deduced that an important part of the excess energy went into the CH30 radical. Lahmani et al. (1986) examined alignment effects in highly rotating NO in the fnst excitedvibrationallevel produced from the photodissociationof CH30N0 at 355 nm. From polarization experiments, the rotational angular momentum of the NO was shown to be aligned preferentially along the transition moment of the parent molecule. The results were consistent with an impulsive dissociation with fragments recoiling close to the initial molecular plane. Radhakrishnan and Estler (1983) photolyzed CH30N0, C2H50N0, and nC,H,ONO at 382-383 nm under collision-free conditions. They found very large and nonthermal NO rotational excitation (Emt > 2100 cm-') from CH30N0. However, for C2H50N0 and n-C,H,ONO, the rotational temperature could be characterized by temperatures of 350 and 250 K, respectively. Keller et al. (1986) measured the photofragment time-of-flight mass spectra of the photodecomposition of CH30N0 at 248 and 350 nm. They found the respective translational energies in the NO to be 6940 & 180 and 4070 & 180 cm-'. and in the CH30 to be 6710 -C 170 and 3930 & 170 cm-I.
200
THE DE€OMPOSlTION OF ALKYL NKRITES
E. Summary The photodecomposition of alkyl nitrites proceeds exclusively by 0-N bond NO at all wavelengths. However, the quantum yield scission to give RO appears to be considerably less than one at 366 nm and possibly at other wavelengths where absorption is into a band of the absorption spectrum. At 366 nm, most of the alkoxyl radicals are produced without enough excess energy to enhance the unimolecular radical decomposition rates. However, the energetic radical yield increases with incident photon energy. The NO produced is highly rotationaly excited at 355 and 382 nm. Electronically excited NO has been observed for photolysis at 110-160 nm.
+
III. THERMAL DECOMPOSITION OF ALKYL NITRITES A. Early Work The thermal decomposition of alkyl nitrites was first studied by Steacie and Shaw (1934a). They showed that the decomposition of CH30N0 was homogeneous and unimolecular from 33.3 to 5 13.5 Torr and 190 to 24 1"C with a rate coefficient of 1.84 X 1013exp(-36.4/Rn sec-'. The overall stoichiometry of the decomposition was CH30NO __* NO
+
'/2CH20
+
'/2CH30H
(13)
which suggests that the initial reaction is cleavage of the CH30-N0 bond. At lower pressures (0.05 to 50 Torr) at 210-240°C, the rate coefficient fell with decreasing pressure as shown in Fig. 10 (Steacie and Calder, 1936). The solid lines are fitted with RRK theory assuming 13degrees of freedom and a molecular diameter of 5.0 X lo-' cm. Steacie and Rosenberg (1936) extended the data at 217.5"C from 650 Torr to 39 atm and found no further increase in rate coefficient. Carter and Travers (1937) examined at 200°C in a complex experiment referred to as the "method of detailed analyses." They concluded (erroneously) that there was no justification for first-order kinetics. However, they were the first to report N20 as a product, which we now know comes from HNO formed in the reaction of CH,O with NO. Steacie and his coworkers examined the thermal decomposition of several other simple alkyl nitrites. Steacie and Shaw (1934b) studied C2HSON0 at 190-24O"C. They found the reaction to be homogeneous and first-order with a rate coefficient of 1.39 X 1014 exp(-37.7/RT) sec-'. There was no falloff in the rate constant for pressures down to 55 Torr. Steacie and Shaw also examined the thermal decomposition of n-C3H70N0 (Steacie and Shaw, 1935a) and GC3H,0N0 (Steacie and Shaw, 1935b) from
THERMAL DECOMPOSITION OF ALKYL NITRITES
201
0
d c
i
d.
0
V."
-2.4
-1.8
-1.2
-0.6 0.0 0.6 Log P
1.2
1.8
Figure 10. Effect of pressure on time to 40% decomposition of CH30N0. C w e : (1) 514.4 K; (2) 504.4 K; (3) 494.3 K, (4) 484.3 K. Full circles from Steacie and Calder
(1936); open circles from Steacie and Shaw (1934a). From Steacie and Calder (1936)
with permission of the American Institute of Physics.
170 to 210°C. In both cases, the reactions were homogeneous and first-order, the respective rate coefficients being 2.75 x 1014 exp(-37.65/RT) sec-' and 1.26 X 1014exd-37.OIRn sec-'. There was no falloff in rate coefficients at any pressures used, which went down to 60.8 Ton for n-C3H70N0 and 33.3 Torr for i-C3H70N0. n-C4H90N0 pyrolysis was studied by Steacie and Smith (1936) from 50 to 400 TOK pressure and 170 to 212°C. The reaction was also homogeneous and first-order, but they were not able to obtain an accurate Anhenius expression for the rate coefficient. However, at 189.9"C the rate coefficient was 8.88 X sec-'. This confiied the trend in increasing rate coefficient with complexity of the molecule as shown in Table 5. Steacie and Katz (1937) examined the thermal decomposition of C,H,ONO and n-C3H70N0at low pressures to study the falloff in rate coefficient at reduced pressure! (down to 0.02 Tom for C2H50NO). They found their results to be in complete accord with Kassel's theory. The pressures for a factor-of-2 decrease in rate coefficient, P ~ , are ~ , about 0.4 TOK for C2H50N0 at 484-505 K and
TABLE 5. Rate Coefficients for Alkyl Nitrite Decomposition at 189.9"C RON0
CH30NO CzHsONO i-C3H,ONO wC~H~ONO n-CdHQONO
1o4k_,,, sec-' 0.97 1.89 3.70 3.95 8.88
Reference
Steacie and Shaw (1934a) Steacieand Shaw (1934b) Steacie and Shaw (1935b) Steacieand Shaw (1935a) Steacie and Smith (1936)
THE DECOMPOSITION OF unNITWITS
202
about 0.2 TOITfor n-C,H,ONO at 484 K. These can be compared with values of about 4 TOITfor CH30N0 at 484-514 K (Steacie and Calder, 1936). Rice and Rodowskas (1935) examined the decomposition of C2H50N0. At low pressures of C,H,ONO diluted in an inert gas at 425°C. they showed with the use of tellurium mirrors that CH, radicals were produced, and that they were the only radicals to react with tellurium in their system. These results were explained in terms of the mechanism C2HsONO *CZHSO
-
C2H50-CH3
CH3
+ NO
+ CHZO + CH3CHO + NO
+ C,H5ONO---*CH4 2CH3 + Te (CH3)*Te
(-24 (4) (14) (15)
The activation energy of the reaction was found to be 34.3 703 to 803 K.
&
3 kcallmole from
B. Mechanism There appear to have been no further studies on the thermal decomposition of alkyl nitrites until 1949. Then two more complex nitrites were studied. Kornblum and Oliveto (1949) examined the thermal decompositionof optically active 2-octyl nitrite in the liquid phase at 100°C. Optically pure d-2-octanol was obtained in excellent yield, thus showing that 2-octoxyl radicals were produced, and that these did not racetnize. Kuhn and DeAngelis (1954) looked at the thermal decomposition of vicinal dinitrites. The vapor-phase decompositions of propane-l,2-dinitrite, butane-2,3dinitrite, and cis- and trans-cyclohexane-1,2-dinitrite all proceed via the overall reaction RCH(ON0)-CH(ON0)R
2NO
+ 2RCHO
(16)
Thus the reaction appears to proceed via elimination of the two NO groups accompanied by C-C bond scission. However, in the liquid phase the products of decomposition of butane-2,3-dinitrite were mainly RC(0) -C(O)R and (RCHOH), as well as NO. This suggests that the initially formed free radical is stable long enough to abstract an H atom from the parent compound. This sequence would be repeated by both reactants, so that the initially formed radical would become the dialcohol, and the secondary radical, which had lost an H atom, would become the diketone.
THERMAL DECOMPOSITION OF ALKYL. NITWTES
203
Adler et al. (1955) examined the pyrolysis of n-C3H70N0, i-C3H70N0, n-C4&ON0, i-C4H90N0, and s-C4H90N0 at 230-240°C. They found that the akoxyl radical formed in pyrolysis decomposed as follows:
where the split occurs more easily the larger the R group. Gowenlock and Trotman (1956) have shown that the alkyl radicals can then react with NO to produce nitrosoalkanes, RNO . Yoffe (1954) studied the thermal decomposition of t-C4H90N0 both in the vapor phase at 340°C in a flow system and in isopropylbenzene solution under a N2 atmosphere at 80°C. In both cases the products were consistent with bond cleavage to give t-C4H90 + NO as the initial step. Gray (1954) observed chemiluminescence from the decomposition of CH30N0 and C2H50N0 from 290 to 400°C. The chemiluminescence, which was attributed to RO radicals, is facilitated by increasing the temperature, by adding inert gases, and by decreasing the surface/volume ratio. In the presence of O2 or NO,, luminescence occurs readily and explosive ignition could also occur. For C2H50N0, the reciprocal initial concentration for luminescence has an activation energy of 30 kcal/mole. For CH30N0, the activation energy varies with temperature. Nagiev et al. (1956a, 1956b) studied the thermal decomposition of nC3H70N0 and n-C4H90N0. They found the respective rate coefficients to be 1.6 X 1013 exp(-34.7/RT) and 4.53 X 1013 exd-36.2IRT) sec-'. Levy (1956a) reported on the thermal decomposition of C2H50N0 at 10-50 Ton and temperatures of 161, 181, and 201°C. The addition of large amounts of NO did not materially affect the reaction rate, but increased both the CH,CHO and N20 yields. In the presence of CH3CH0, the rate increased sharply but N20 was not produced. These results were explained by the mechanism
-
C2HSONO C ; C 2 H 5 0 C2HSO
+ NO
2HNO
C2H5O
+
__*
HNO
N20
HNO-C2HSOH
+ NO
+ CH3CH0
+ H2O
+ NO
(-2a,2a) (2b) (3) (17)
The fact that NO additions did not reduce the rate of reaction indicated that C~HSO was not reacting to any significant extent with CzHSONOor with itself. Furthermore, since increasing NO increased CH3CH0 and N20, reaction 17 was becoming less important. Finally, the results in the presence of CH3CH0 could be explained by
THE DJXOMPOSmON OF ALKYL NTnUTES
204
C2H50
+ CH3CH0 -C2H50H
+ CH3C0
(18)
Thus the rate went up and N20 went down because reactions 2a and 2b were reduced in importance, since the C2H50radicalswere being scavengedby reaction 18. This mechanism leads to the limiting rate laws at low [NO] and [CH3CHO], where reaction 17 is dominant in removing HNO, of
-d[C,H,ONO]
dt
-
2k2&2,[RONO] k2
= 2R{CH3CHO} = 2R{C2H50H} (g)
and
For high values of [NO] or [CH,CHO], where reaction 17 is negligible, the rate law is
As we shall see later, k2,4k2, = 0.30, so that the effective rate coefficient is 0.46k-,, at low [NO] and [CH3CHO], 0.23k-,, at high [NO] and low [CH3CHO], and k2,at high [CH,CHO]/[NO]. Since NO is produced in reaction -2a, there are no experiments at truly low [NO], so the rate coefficient -0.3kF2, at all NO pressures, but increases to k - , at high [CH3CHO]/[NO]. Furthermore, in the absence of added CH,CHO, R{N,O} is near zero at low [NO], rises toward 0.12k-2,[RONO] as [NO] is increased, and then drops back toward zero as [CH3CHO]/[NO] is increased. Meanwhile R{CH,CHO} is near 0.23k-,,[CH30NO] at low [NO] and [CH3CHO], rises toward 0.23k-2,[CH30NO] as [NO] increases, and drops back toward zero as [CH,CHO]/[NO] increases. R{N20}/R{CH3CHO} goes from near zero at low [NO] toward 0.5 as the [NO] is raised, independent of the added CH3CH0 pressure. These conclusions are all in accord with Levy’s results, and f i n n y establishedthe mechanism of reaction as given above. From Levy’s data kVza = 6.1 x 1013 exp(-(37.5 2 0.5)/ RT) sec-’. Levy (1956b) extended his studies to i-C3H70N0, n-C3H70N0, and tC4H90N0. He found that the rates of thermal decomposition of these nitrites were sharply decelerated by the addition of NO. The NO reduced the importance of alkoxyl radical decomposition reactions but increased the N 2 0 produced. Thus
THERMALDEColMpoSITION OF ALKYl. NlTRITEs
205
these results supported the mechanism developed by Levy (1956a) for C2HSON0 decomposition. Gray and Williams (1960) reexamined the pyrolysis of CH30N0 at 178-3 15°C in static and flow systems. They found an activation energy of 36.4 kcal/mole. The N 2 0 yield was always about 0.13 mole N 2 0 per mole CH30N0 decomposed, which supported Levy's mechanism (reactions 2, 3, 17, and 18 above). The pyrolysis of CH30N0 also was reexamined by Phillips (1961) between 150 and 240°C. He found that the reaction was frrst-order and proceeded by
-
CH30N0 A CH30 CH30
+ NO
2CH30
NO
CH30N0
-CH20
2HNO
+
H20
f
HNO
+ NZO
CHzO
+ CH30H
However his rate coefficients,like those of Shaw and Trotman-Dickenson (1960), were about half those given by Steacie and Shaw (1934a). The free-radical nature of the reaction was shown by adding cyclohexene, a free-radical scavenger. This increased the yields of CH30H and NO, and almost eliminated N20. The rate coefficient found by Phillips for CH30N0disappearance was 10'2.2exp{-34.3/ R n sec-'. Napier and Nomsh (1967) spectroscopically observed HNO in the pyrolysis of CH,ONO, and showed that its concentration increased with added NO. This confirmed that HNO was an intermediate, and that it was formed by reaction of NO with CH30. Ferguson and Phillips (1965) examined the pyrolysis of i-C3H70N0at 175200°C and 35 Torr pressure. Their results confirmed the presence of HNO as an intermediate. Likewise Marta and Seres (1966) studied the thermal decomposition of CzHSONO at 200-230°C and 20-200 Torr. Their results substantiated the mechanism of Levy (1956a). Marta and Sees found k-2a = 4.58 x 1013expi-36.69IRT) sec-'. The thermal decomposition of CH30N0 in shock waves was studied at 7801OOO"K and 0.35-1.6 atm (Zaslonko et al., 1970). The rate coefficient was found to be 10'2.9 exp(-34.O/RT} sec-' by measuring the absolute intensity of the light emission from electronically excited CH20 and HNO produced in the reaction. Their rate-coefficient expression gives rate coefficients a factor of 1.5-2.0 higher than obtained by extrapolation of the results of Steacie and Shaw (1934a) and a factor of 5.8-6.1 higher than obtained by extrapolation of the results of Phillips (1961). This is because the back reaction is not important at the higher temperatures, since the CH30 radical decomposesbefore recombining with the NO produced. The thermal decompositionof aromatic nitrites was investigated by Gray and
THE DECOMPOSlTION OF ALKYL NlTRlTH
206
coworkers. Gray et al. (1960) studied the thermal decompositionof benzyl nitrite at 100-215°C in liquid, gas, and solution. Decomposition occurs by 0-N bond cleavage in a unimolecdar reaction to give C&CH20 and NO. The decomposition of 1-phenylethyl nitrite was studied by Gray et al. (1961) in solution and as the pure liquid from 80 to 140OC. Again decomposition occurs by 0-N bond cleavage in a unimolecular reaction. Gray et al. (1961) showed that alicyclic alkoxyl radicals were produced in the thermal decomposition of cyclohexyl- and 1-methylcyclohexylnitrite.
C. ModernStudies In the 1970s. a substantial effort was made by Batt and his coworkers to obtain accurate Arrhenius parameters for the thermal decomposition of simple alkyl nitrites in the gas phase. Batt et al. (1974) used bomb calorimetry to obtain the heats of combustion of several alkyl nitrites. From these they obtained the enthalpies of formation, and these are listed in Table 6. Also listed in Table 6 are the enthalpies of formation of the corresponding alkoxyl radicals obtained from the pyrolysis of dialkyl peroxides. When these data were combined with AH'&8 {NO} = 21.6 k 0.3 kcal/mole, values for D(Ro-NO} could be obtained. These are listed in Table 6 and are all about 4 1.5 k c d m l e .They are considerably higher than the activation energies for decompositionreported by earlier workers. Thus Batt's laboratory started on a program to redetennine the Arrhenius parameters for RONO decomposition. Batt and Milne remeasured the decay rates of CH30N0 (Batt et al., 1977), C2H50N0(Batt and Milne, 1977b), i-C3H,0N0 (Batt and Milne, 1977a). and
TABLE 6. Thennochemical Data for RONO" kcallmole, A@{RONO>, kcaVmole
R
- 16.0 f 0.2'
Me Et n-Pr i-Pr n-Bu i-Bu S-BU t-Bu
-24.5' -28.4 -31.9 -34.8 -36.1 -36.5 -41.0 ~~
f1 5 1 2 1
f1 f1 2 1
(298" K)
Af$CRO>, kcaVmole 4.2 -4.1 -9.9 -12.5 -13.9 -15.7 -17.0 -21.7
2 0.7 f 0.7 2 1.5 f 0.7 f1 2 1 2 1 +- 0.7
~
"From Ban et al. (1974) with permission of John Wiley and Sons, Inc. %om Silverwood and Thomas (1%7). 'From Benson et al. (1%9).
WRO-NOI, kcahole 41.8 2 0.9 42.0 2 1.3 40.1 2 1.8 41.0 t 1.3 42.5 f 1.5 42.0 f 1.5 41.1 4 1.5 41.1 2 1.3
THERMAL DECOMPOSlTfON OF ALKYL NITRITES
207
t-C45ONO (Baa and Milne, 1976). They obtained larger Arrhenius parameters than previous workers by studying the decompositions in the presence of additives which either scavenged the alkoxyl radical (i-C4Hlo) or aided their thermal decomposition (CF, at = 0.9 atm). Their values are more in agreement with the thermochemical data and RRKM theory. These values, as well as those found in earlier studies, are listed in Table 7. For the t-C,H,ONO decay, they also found a direct molecular path to give i-C4H8 + HONO which could not be quenched by free-radical scavengers: t-C,H,ONO
-
i-C4Hs
+ HONO
(20)
with log{A, sec-’} = 12.9 +- 0.4 and an activation energy of 33.6 2 0.8 kcal/mole (Batt and Milne, 1974). Likewise traces of olefin were found in the decomposition of C,H,ONO and i-C3H70N0, and these were attributed to reaction paths analogous to Eq. 20. For the CH30N0, C2HsON0, and i-C3H70N0 decays Batt and his coworkers suggested that some aldehyde 4- HNO was produced by direct 4-center elimination to explain the “excess” aldehyde expected based on ratios k2dk2. In light of more recent work (Batt et al., 1978b), there appears to be no reason to include the 4-center elimnination mechanism in a homogeneous process. However, there was evidence that a heterogeneous process may be operative for i-C3H70N0 (Batt and Milne, 1977a). Mendenhall et al. (1975) studied the thermal decomposition of f-C4H90N0 using the very-low-pressure pyrolysis technique from 525 to 765 K. The highpressure first-order Arrhenius parameters were log{A, sec-’} = 15.8 with an activation energy of 39.3 kcal/mole. Mendenhall et al. (1975) also obtained evidence for the molecular elimination process in t-C,H90N0 from the excess decomposition at low temperatures over that predicted from RRKM theory as shown in Fig. 11. They attributed this process to heterogeneous decay to give i-C4H, a d HONO. However, an analogous process for i-C3H70N0, i-C3H70N0
-
C3H6 + HONO
(20)
was seen by Batt et al. (1978b) with log{A, sec-’} = 12.7 and an activation energy of 37.9 kcal/mole. These Arrhenius parameters, as well as those obtained by Batt and Milne (1976), are reasonable values for a homogeneous 6-center elimination reaction. Batt et al. (1978b) also ascertained that no HNO was produced by molecular elimination from C,HSONO or i-C3H70N0, but that it came entirely from disproportionation of NO with alkoxyl radicals. Other studies from Batt’s laboratory concerned the decomposition of sC4H90N0(Batt and McCulloch, 1976b) and t-CSH,lONO (Batt et al., 1978a). In the case of s-C4H,0N0, a molecular elimination to produce CH3COC2HS+
THE DECOMPOSITION OF ALKYL NITRlTEs
208 10'
I
I
700
800
102
1
10-1
500
600 TPK
Figure 11. First-order reaction rate coefficients for the very-low-pressure pyrolysis of t-C,H,ONO for collision numbers of 11200, 2,470 (0); 387 From Mendenhall et al. (1975) with permission of John Wiley and Sons, Inc.
a);
(a).
HNO was reported. However, in lieu of the later conclusion of Batt et al. (1978b) that no HNO is formed by a homogeneous molecular elimination in the lower alkyl nitrites, it is not likely to occur in s-C4H90N0 either. The Arrhenius parameters for alkyl nitrite decomposition are listed in Table 7. All of these results have been summarized by Batt (1979). The homogeneous decompositionsproceed by 0-N bond cleavage to give RO + NO with activation energies of -41 kcal/mole and Arrhenius preexponential factors of about 1 x 1OI6sec-'. There does not appear to be any direct elimination to give aldehydes plus HNO. However both r-C4H,0N0 and i-C3N70N0 do give alkenes plus HONO in a molecularelimination,though thismay be in a heterogeneousprocess.
RW\CI?ONS OF ALKOXYL RADICALS WlTH NO,
TABLE 7.
209
Rate Coefficients for the Thermal Decomposition of RONO E-b, kCaYmole
References
36.4 36.4 34.3" 34.0 41.2 f 1.2
Steacie and Shaw (1934a) Gray and Williams (1960) Phillips (1961) Zaslonko et al . (1970) Battetal. (1974)
13.79 13.66 16.0 f 0.4
37.7 34.3 2 0.3 37.5 2 0.5 36.7 41.8 2 0.9
Steacie and Shaw (1934b) Rice and Rodowskas (1935) Levy ( I956a) Marta and Seres ( 1966) Batt and Milne (1977b)
170-210 = 227
14.44 13.20
37.7 34.7
Steacie and Shaw (1935a) Nagievetal. (1956a, 1956b)
i-Pr
170-210 130-160
14.10 16.2 f 0.4
37.0 41.0 2 0.8
Steacie and Shaw (1935b) Batt and Milne (1977a)
n-Bu
170-212
13.66
36 36.2
Steacie and Smith (1936) Nagiev et al. (1956a)
Temp. Range, "C
log{A-z,, sec-'}
190-241 178-315 150-240 507-727 170-200
13.26
190-240 430-530 161-20 1 200-230 162-2 18
14.14
n-Pr
R Me
Et
-
-
12.2 12.9 15.8 % 0.6
-
-
S-BU
130-200
16.2 f 0.4
40.9 2 0.8
Batt and McCulloch (1976b)
t-Bu
377492 120-160
15.8 16.3 f 0.4
39.3 40.3 f 0.8
Mendenhall et al. (1975) Batt and Milne (1976)
?-Am
120-190
16.3 f 0.1
40.3 f 0.1
Batt el al. (1978a)
"Corrected by Batt el al. (1974) to 38.9 kcal/mole.
IV. REACTIONS OF ALKOXYL RADICALS WITH NO, A.
RO
+ NO Disproportionation-to-CombinationRatio
It has been known since the 1950s that alkoxyl radicals add to NO and NO2. This early work has been reviewed by Gray et al. (1967) and by Heicklen and Cohen (1968), and all of it will not be discussed here. It was shown by Levy (1953) that C2H50 radicals could add to NO, and later inferred by him (Levy, 1956a, 1956b) that alkoxyl radicals could aansfer an H atom to NO to give HNO, which could then form H20 N20 by self-annihilation:
+
RO.
+ NO,
RONO,
(24
210
THE DECOMPOSITION OF ALKYL
RlRzCHO
+ NO,
RlR2CO
+ HNOx
(2b)
The first study of the disproportionation-to-combination ratio of alkoxyl radicals with NO was made by McMillan (1961), who photolyzed diisopropyl peroxide at 230-290 nm in the presence of NO. From the ratio of (CH,),CO to i-C3H70N0produced he could deduce kidk,.His values are given in Table 8. In the 1960sa series of studies was undertaken by Phillips and his collaborators to measure the relative rate coefficientsfor addition and disproportionation.They thermally decomposed dialkyl peroxides in the presence of NO and measured the amounts of RONO and aldehyde produced. From these data they could from which k2&3 can be deduced, and these values are listed deduce k&, in Table 8. Estimates of k2, could be made from the equilibrium constant and rate coefficients for the thermal decomposition of RONO. These also are listed in Table 8. Livermore and Phillips (1966) also studied the thermal decomposition of C2H50 in the presence of NO at 200°C at very low pressures in a flow system. They found reaction 2a to be pressure dependent and follow a Lindemann mechanism with a half-reaction pressure of 0.08-1.6 Torr of (C2H5O), as a chaperone. This agrees exactly with the results of Steacie and Calder (1936), who found a similar half-reaction pressure for the reverse reaction. Rebbert (1963) photolyzed C2H50N0 at 366 nm and 25°C to produce C2H50 radicals. In the presence of NO, he measured C2H50N0and CH3CH0 to obtain kalk2b -3.3. Baker and Shaw (1965) pyrolyzed (CH30)2,(C2H5O)2, and (r-C&0)2 at 130°C in the presence of NO and NO2. They measured CH20 as CO and CH3CH0 as C02 produced in further oxidation. From these compounds and the amounts of RONO, formed, relative rate coefficients could be obtained, and they are given in Table 8. Ludwig and McMillan (1967) pyrolyzed (CC,H,O), in the presence of 200 Torr N2 from 120 to 180°C. The ratio [(CH,),CO]/[(CH,),CHONO] produced in the reaction was temperature dependent below 160°C, but temperature independent at 0.17 above 160°C. The temperature-dependentportion was shown to be due to a surface reaction which gave excess (CH3)2C0.This heterogeneous process was overwhelmed at the higher temperatures, and k2dkz, was taken to be 0.17 at 160-18OoC, exactly the same as found by McMillan (1961) at lower temperatures. Yee Quee and Thynne (1968) studied the thermal decomposition of (i-C&0)2 in the presence of NO. They obtained k2dk, = 0.15 & 0.02 independent of temperature at 121.5-158.7"C from the ratio of CH3COCH3and i-C3H70N0 produced. Four studies employed the photolysis of CH30N0 in order to obtain k2,/k2 (McGraw and Johnston, 1969; Wiebe and Heicklen, 1973; Wiebe et al., 1973; Glasson, 1975). However, in all cases high values for the primary photodecompo-
REACTTONS OF ALKOXYL RADICALS WITH NO,
211
sition quantum yield were used. Thus these studies were really suited to determine this yield rather than W k , . Additional values of k2dk2 were obtained by Morabito and Heicklen (1985b). They examined the thermal decomposition of several alkyl nitrites in the presence of 15N0. By measuring the RO'%JO and aldehyde produced they had a direct determination of k d k Z b .Their results also are given in Table 8. Single determinations exist for k2dk2 for CH30, n-C4H90, i-C&o, and S-C&O of 0.33, 0.29 & 0.05, 0.33 2 0.03, and 0.21 0.02, respectively. Three determinations for CzH50radicals give 0.23,0.23, and 0.25; and another gives >0.16. For i-C3H70, five values range from 0.13 to 0.18. Two values for n-C3H70 are 0.30 f 0.01 and 0.26 & 0.03. Thus for those systems with more than one determination good agreement is achieved. For t-C4H90, which has no abstractable a-H atoms, the ratio is zero. Table 9 summarizes the values of k2Jk2 as a function of the number of H atoms on the a carbon atom. For those radicals with no a H atoms, no abstraction occurs and k24k2 = 0. The methoxyl radical, which has three a H atoms, has the largest value of k2Jk2 = 0.33. The value for k,dk2 is less for radicals with two a H atoms, and even less for radicals with one a H atom. However within each group, the ratio k2dk2 increases with the complexity of the radical. Thus k, = 0.16 for i-C&o, but 0.21 for s-C4H90. It increases from 0.23 to 0.33 as RO goes from C2H50 to n-C3H70to n-C4H90to i-C4H90. If only the number of a H atoms were responsible for the value of k2dkz, we would expect the values to be in the ratios of 0, 1, 2, and 3 for k2dkb. Taking k2dk2a = 0.50 for CH30 would give 0.17 and 0.33 for radicals with one and two OL H atoms. These values are approximately what is observed, but, except for C2H50,the observed values are slightly larger than expected from this simple prediction. Since neither reaction 2a nor 2b has an activation energy, we must look for other reasons for the radical complexity effect. Presumably the stronger van der Waals attractive forces in the bulkier radical tend to pull the incoming NO group more toward the hydrocarbon end and away from the oxygen-atom end of the radical. Thus the relative collision frequency of the NO with an H atom is enhanced compared to that with the oxygen atom.
*
B. RO
+ NOz Disproportionation-to-CombinationRatio
Measurement of the ratio kgdk, has been made for CH30, C2H50, and n-C3H70, and attempted for S-C4H90 radicals. In the case of CH30 radicals, there is considerable uncertainty in the results, though all studies agree that k9dk9 zs 0.1. For C,H50, Baker and Shaw (1965) pyrolyzed (C2H5O)Z at 130°C in the presence of NO2 and reported k&, = 0.31 2 0.02. Rose (1979), who photolyzed alkyl nitrites at 366 nm in the presence of NO2 at 25"C, reported k9dk9, = 0.09 & 0.01 from the acetaldehyde produced, assuming a primary quantum
N -+
-53 to + 200 25
27
167198 119148 22
25
110
"0.013f
e
-
9.92
-0.036 20.007f
eo.1
e
9.9=.b
-
9.92 ~k0.03~
-
20.6'
10.1
-
-
772
61-
740 k0.03" ~9.85"
90
-
25
-
-
kO.01
0.09
k9dk9
167-
log{ba. M-l-sec-'}
+ HONO (9b)
55-
R'O
9.57 +0.03" 9.73
k2dk2
+ NOz
-
bdkz,, W'-sec-'}
RONOz (9a); RO
Press, Tom
4
>80
+ NO,
130
174
Temp. Range, "C
(2b); RO
+
CHJ + hv + NO CH30N0 + hw(366 nm) CH30N0 pyrolysis (CH30)2 pyrolysis CH30NO hv(266 nm) F + CH30H
+
(CH30)2 pyrolysis (CH3Oh pyrolysis CH3 NO2
Source of RO
+ HNO
Zellner (1986)
(1985)
McCaully et al.
Batt and Rattray (1979) Sanders et al. (1980) Fortuno (1982)
Battet al. (1977)
Shaw (1 965) Phillips and Shaw (1965) Johnston and Heicklen ( 1966) Wiebe et al. (1973)
Baker and
Ardenetal. (1964)
Reference
TABLE 8. Rate Coeilicientsfor Reactions of Alkoxyl Radicalswith NO and NO2: RO + NO +RON0 ( 2 ~ ) RO ; + NO +R'O
2
200682
13-32
80 = 680 (CF4) 2-760
150 (N2)
30-63
35-57
>200
95135 130
200
25 162197 25
175
26
77
160180 105149 121159 128158
(CF4)
= 680
-
30155
(Nz)
>80
25-37
28
-
0.18 r0.02 0.13 r0.02
0.16 20.02 0.15
-
-
-
-
-
-
0.13 kO.01
-
-
-
k 0 .03B
9.80
-
0.22 20.02
-
0.25 k0.03 >O. 16
-
2 0.03
0.23
-
0.29 %0.03h
-
0.31 50.02
-
(i'C3H7°)2 pyrolysis (i'C3H70)z pyrolysis (i-C3H70)2 pyrolysis (i-C3H70NO) pyrolysis
+
Morabito and Heicklen (1985b)
Arden et al. ( 1964) Baker and Shaw ( 1965) Livemore and Phillips (1966) East et al. (1968) Batt and Milne (1977b) Rose ( 1979)
Rebbert (1963)
Ludwig and McMillan (1967) Hughes and Phillips (1967) Yee Quee and Thynne (1968) Batt and Milne (1977a)
(i-C3Wh McMiIIan ( 1 961) hv(230-290 nm)
C,HSONO, + hv(366 nm) (CzH5O)z pyrolysis (C2H50)2 pyrolysis (CZHSO), pyrolysis C2H5 + NO, CZHSONO pyrolysis CZHSONO + hv(366 nm) C,H,ONO pyrolysis
N
G
2281
100150 300540 25
150 (NZ)
25139
175
100140
(N2)
= 10.1 0.21 20.02
0.33 20.03
0.29 20.05
175
0.30 20.01
0.26 20.03
150
10.8
-
31
10.16 2 0.40'
175
2-760
-
1-50
22111
TABLE 8. (Continued)
-
-
-
-
9 3
10.28
2 0.08i
-
RO = s-C.,H90
-
RO = i-C4H90
-
RO = n-C4H90
0.26 +0.03h
-
RO = n-C3H,0
-
i-C4H90N0 pyrolysis
n-C4H90N0 pyrolysis
+ hv(366 nm) n-C3H70N0 pyrolysis
(n-C&0)2 pyrolysis nC3H70NO2 pyrolysis n-C3H70N0
i-C3H70NO + hv(366 nm)
Walker and Phillips (1968)
Morabito and Heicklen (198513)
Morabito and Heicklen (1985b)
Morabito and Heicklen (1985b)
East and Phillips (1970) Mendenhall et al. (1975) Rose ( 1979)
Ballaet al. (1985)
-
-
10.4,
1
2-
22"
10.5 -C 0.2'
-
-
0
= t-CdHpO
I
RO = t-amoxyl
RO
-
t-amylONO pyrolysis
(t-C&@h pyrolysis t-C,&ONO py ro1y si s t-C,H&NO pyrolysis
S-C,H,ONO pyrolysis
"Based on log{k2,, M-'-sec-'} = 10.00. bBased on k2dk2 = 0.33, k&, = 0.1, and k2/k9 = 1.3 'Equilibrium calculation from reverse rate coefficient. = 0.33. dBased on k,&, 'At low pressure k2s = (8.0k 1.1) x 10" M-2-sec-' (Fortuno, 1982) or 9.4 X 10" M-*-sec-' (25°C)(McCaully et al., 1985). based on log{ba, M-'-sec-'} = 9.82 8Based on log{k,,, M-'-sec-'} = 10.2and kZa/k9,,= 2.5 'Corrected for +h = 0.28 and 0.38,respectively, for CzHSONOand n-C,H,ONO. 'Assumes kzdkz = 0.16. Value for log#+} = Iog{b, + hb}. 'Assuming log{kJ = 10.3. 'Pressure not given. Experiments done in excess CF,. '"i-C,H,,or CF,.
155
120-
0.4'
I
-
-
9.8'
-
-
10.07 rtrO.O$
-
-
>77
130150 377492 119158
-
0.4'
10.4-C -
I
131160
Batt et al. (1978a)
Baker and Shaw, (1965) Mendenhall et al. (1975) Batt andMilne ( 1976)
Batt and McCulloch (1 976b)
3
2
1
0
No. of ci HAtoms
n-C3H70 n-C4H90 i-C4H90 CH30
C2H50
t-C4H90 t-amyl i-C3H70 s-C~H~O
RO
0 0 0.16 2 0.02 0.21 k 0.02 0.23 f 0.02 0.28 f 0.03 0.29 f 0.05 0.33 f 0.03 0.33
k2dk2 0 0 0.19 0.26 0.30 0.39 0.41 0.50 0.50
k2dk2a
1.5 2 0.5 1.5 k 0.5 1.5 2 0.5 1.5 f 0.5 1.5 k0.5 1.5 20.5 1.5 2 0.5 1.5 2 0.5 1.5 -t 0.5
k2dk9a
0.05 k 0.05
-
r0.33 ~0.26
-
0 0
k9dkg
log{k,,*
10.3 k 0.2 10.3 k 0.2 10.3 2 0.2 10.3 k0.2 10.2 k0.2 10.3 f 0.2 10.3 f 0.2 10.3 f 0.2 10.0 5 0.1
M - '-sec-'}
TABLE 9. Recommended Values for Reactions of Alkoxyl Radicals with NO and NOz
REACTIONS OF ALKOXYL RADICALS WITH NO,
217
yield for alkyl nitrite photodecomposition of 1.O. In an analogous manner, Rose found k9dk9, = 0.11 -C 0.01 and 0.08 & 0.08 for n-C3H70 and s-C4H90 radicals, respectively. However, as discussed in Section 11-C, the primary quantum yields for photodecomposition of C2H50N0 and n-C3H70N0 are, respectively, 0.28 and 0.38. Thus kdka = 0.41 +- 0.04 for C2H50 and 0.35 ? 0.03 for n-C&O. The primary quantum yield for s-C4H90N0 photolysis is not known, so bdkafor S-C4H9O cannot be computed. It is difficult to see why the ratio k9dk9 is so much smaller for CH30 radicals than for larger alkoxyl radicals. More verification is needed before any of these values can be accepted.
C. Relative Rate of RO with NO and NOz Phillips and Shaw (1965) heated mixtures of CH3CH0, NO, NO2, and neopentane to 55 or 90°C.The CH3CH0 decomposed to give CH, radicals, which reacted with NO2 to give CH30 radicals: CH3
CH30NOt CH30NOt
CH30 CH30
-
+ N02+CH30NOt +
M -+
+ NO CH30N0 + M CH30
+ NO-CH30N0
+
NO2 -CH,0N02
This mechanism leads to the rate law
Phillips and Shaw found that the ratio [CH30NO]/[CH30N02] did not depend on the total pressure, but only on [NO]/[NO,]. Thus they concluded that the reaction in Eq. 23 was negligible under their conditions. From their data kZa/k9, = 1.86 t 0.14 at 90°C. The conclusion that Eiq. 23 is negligible is in agreement with the theoretical prediction of Gray (1955). However, Patsevich et al. (1958) reported that C2H5radicals could react with NO2 at - 15 to 96°C to give C2H50N0 directly. Now C2H50N0is more complex than CH30N0, so that lower pressures would be required to stabilize it, and there may be no conflict between the conclusions of Phillips and Shaw and of Patsevich et al. However, if some CH30N0 is formed in reaction 23, then k2a/k9a will be (1.86.
THE DECOMPOSlTlON OF ALKYL IWRlTES
218
Johnston and Heicklen (1966) photolyzed CH31 in an excess of NO at room temperature to produce CH30 and NO2. From the CH,ONO and CH30N02 produced they obtained an approximate value for = 1.4. Wiebe et al. (1973) photolyzed CH30N0 at 366 nm and 25°C in the presence of NO and NOz. They measured the quantum yield of CH30N02. The rate law for CH30N02 formation is
wba
where +,a is the quantum yield of CH30 production. Their analysis was based on their measured value of 0.76 for +la, which may be only 0.33. Their data are replotted in Fig. 12. The best fit of the data gives an intercept less than 3.0, which is not possible if
28
I
I
I
I
I
I
I
0
REAcIlONS OF ALKOXYL RADICALS WITH NO,
219
CH30N02 produced, they deduced kdb,. Both rate coefficients are pressure dependent, but they reach their high-pressure limiting value in the presence of >500 Torr CF4. Under these conditions k&ba = 2.03 & 0.47 independent of temperature from 119 to 148°C if the surface-to-volume ratio was sufficiently low. (Reaction 2a appeared to have some heterogeneous component.)
D. Rate Coeficient for RO
+ NO
Mendenhall et al. (1975) studied the very-low-pressurepyrolysis of t-C4H,0N0 and measured the rate coefficient for decomposition from 377 to 492°C. From this value and the estimated equilibrium constant they computed log{k2,, W 1 sec-'} = 9.8. In a series of papers from Baa's laboratory, the kinetics of the thermal decomposition of RONO were studied (see Section III-C). From these data and thermochemical data for RONO, RO, and NO, the reverse reaction rate coefficients could be determined: RO
+ NO
-
RONO
(2a)
These values are listed in Table 8. For all the compounds studied, k2a = 1010.1-'0.5 W'-sec-' independent of temperature. Sanders et al. (1980) produced CH,O from the flash photolysis of CH30N0 at 266 nm and measured its rate coefficient of reaction with NO to be (1.25 f 0.07) x 10" M-'-sec-', using laser-induced fluorescence to monitor CH30 removal and HNO appearance. This result is in exact agreement with that of Baa et al. (1977). Choo and Benson (1981) have argued that the values for the RO NO rate coefficients for all alkoxyl radicals reported by Baa's group are too large by a factor of 5 . However, Ban and Robinson (1982) have responded to Choo and Benson and reported that their most recent measurements on the gas-phase decomposition of t-C,H,O radicals support their earlier reported values for the RO NO rate coefficients. Further information on the rate coefficients for the reactions in Eqs. 2a and 2b is given in some recent papers. Gutman and Nelson (1983) used laser-induced fluorescence to study the addition reactions of the C2H30 radical with O2 and NO. The bimolecular rate coefficients for the reaction with NO were observed over the major portion of the transition region from the low- to high-pressure limits and give at room temperature ko = (2.36 f 0.31) X lOI3 W2-sec-' with N2 as a chaperone and k" = (1.51 f 0.18) X 10" M-'-sec-'. However the C2H30 radical has two resonance forms,
+
+
220
THE DECOMPOSITION OF ALKYL NITRITES
Ab in& theoretical considerations indicate that the ground electronic state is essentially the carbon-centered radical, and the first excited electronic state is the oxygen-centered radical (Dupuis et al., 1982). Thus the measured rate coefficient is probably for the carbon-centered radical, and need not correlate with information on alkoxyl radical reactions. Balla et al. (1985) have used the flash photolysis of i-C3H70N0at 355 nm to measure the rate coefficients for the reactions of i-C3H70with NO, NO,, and O,, by monitoring i-C3H70decay using laser-induced fluorescence. They found k2 = (7.3 f 1.7) X lo9 exp((+ 0.62 2 0.14)/0} M-'-sec-' at 22-105°C and 1-50 Torr pressure. This expression gives an average value over their temperature range of 1.8 X 10" M-'-sec-', which is somewhat smaller than that of = 3 X 10" M-l-sec-' reported by Batt and Milne (1977a), though the two values are well within the reported uncertainties. Zellner (1986) reported on the pressure dependence of the CH30 NO reaction in the presence of 5-300 Torr He. From the data obtained in his laboratory at 298 K, he deduced that k,, = 8.4 X lo9 M-l-sec-' in the high-pressure limit and 1.1 X 1014Md2-sec-' in the low-pressure limit for He as a chaperone. The low-pressure value is based on a long extrapolation of the data and is about 12 times as large as reported by Fortuno (1982) or McCaully et al. (1985). The values of k2, increase slightly with the complexity of the molecule. The computed values from Batt's group increase from 10g{k2,, M-'-sec-'} = 10.1 for CH30 to 10.5 for more complex alkoxyl radicals. The direct measurements in McDonald's laboratory give 10g{k2,, M-'-sec-'} = 9.92 for CH30 and 10.16 for i-C3H70. Zellner (1986) also finds kza = 9.92 for CH30. Based on these data we recommend log{k,,, M-l-sec-'} = 10.0 for CH30, 10.2 for C2H50, and 10.3 for C3-C5 alkoxyl radicals.
+
E. Rate Coefficient for RO
+ NOz
Mendenhall et al. (1975) studied the very-low-pressurepyrolysis of n-C3H70N02 and measured the rate coefficient for decomposition from 300 to 540°C. From this value and the estimated equilibrium constant they computed 10g{k9,, Msec-'} = 9.5. McCaulley et al. (1985) studied the reactions of CH30 with NOz by using laser-induced fluorescence to monitor CH,O produced by direct IR laser dissociation of C&OCH3 in a flow tube. Downstream NO, was added in large excess to convert the CH3radicals produced to CH30 radicals in a rapid reaction. The reaction of CH30 with NO, was of mixed order under their conditions. By assuming that reaction 9a was third-order and reaction 9b was second-order, they deduced rate coefficients of k9, = (9.4-2-5) +3.3 x 10'2(T/300)-4.5't:3 K 2 sec-' and kSb = (5.t?T;t5) x lo9 exp((-ll50;:~)fT} M-'-sec-'. These give room-temperature values of ba= 9.4 x 10" M-'-sec-' and k9,, = (1.2 2
'-
DECOMPOSITION AND ISOMERlZAnON OF ALKOXYL RADICALS
221
10') M-'-sec-'. Another direct measurement of haand kSbwas done by Fortuno (1982), who used laser magnetic resonance to monitor CH30 decay in the presence of NO, and obtained k9b = (2.5 2 0.5) X 10' M-l-sec-' at room temperature by extrapolating the pressure dependence of k9 to zero pressure. He also obtained = (8.0 2 1.1) X lo', K2-sec-' at 300 K. In their study of the reaction of i-C3H70 with NO,, Balla et al. (1985) found the results to be slightly dependent on laser power. However, their results extrapolated to zero laser power give an average value of h = (1.9 4 0.3) X 10" M-l-sec-' from 295 to 384 K, the same value that they found for k2. All other studies have determined the ratio h,/k2,. From the data of Wiebe et al. (1973), we get a ratio of 1.3 for CH30 radicals. However, the other competitive studies give ratios of k2a/k9a = 2.7 (Baker and Shaw, 1965) and 2.03 ? 0.47 (Batt and Rattray, 1979) for CH,O, 2.5 (Baker and Shaw, 1965) for C2H50, and 1.7 (Baker and Shaw, 1965) for r-C4H90. Thus there is some uncertainty regarding the values of ha.Until further information becomes available we recommend using k2a/k9a = 1.5 2 0.5.
V. DECOMPOSITION AND ISOMERIZATION OF ALKOXYL RADICALS A. Decomposition Early reviews of the thermochemistry and reactivity of alkoxyl radicals were given by Gray and Williams (1959), Hershenson and Benson (1962), Gray et al. (1967), Heicklen (1968), and Kerr and Lloyd (1968). The work discussed in those reviews was mostly qualitative and will not be discussed here. The Arrhenius expressions that were reported are included in Table 10. 1. CH30. From their data on @{CH30} = 3.8 & 0.2 kcawmole, Batt and McCulloch (1976a) estimated that = 21.3 kcallmole for the reaction
ale
Furthermore if AGIe is taken to be 25.4 cam-mole, and if the rate of the reverse reaction is the same as that for H + C,H,, then log{klle, sec-'} was estimated by them to be 14.2 - 25/9. 2. C2H50.Leggett and Thynne (1970) studied the thermal decomposition of the C2H50 radical from 149 to 176°C by using the pyrolysis of (C,HSO), a; a radical source. They foundtheratecoefficient tobe 10'2.'5exp{-22. URT) sec- .
h2
w
+
CH304 CH20 H CzH50 + M -+ CH3 + CH2O + M C2H50--* CH, + CH2O C2HSO --* CH, + CH20 C2H50 + CH3 + CH,O C2H5O + CH3CHO + H i-C,H,O + CH3 + CH3CHO i-C3H,0 -+ CH, + CH3CHO i-C,H,O + M -+ CH3 + CH3CHO + M i-C3H,O --* CHg + CH3CHO
Reaction
20-230 20-230
160-200
160-200
-
14.36
35
175-200
-
13.21
-
-
16.5
12.65
14.4
15.0
-
-
12.15
=10
12.6
=14.2
log@)
23-63 (C-CrjH,,)
-
5.3-30
-
Torr
Ress.,
149-176
-
15-195
-
Temp. "C E, kcaYmole
11.8
8.3
17.2
16.0
23.4
21.6
22.1
17
25 13
-
TABLE 10. Rate Coeffkients for Decomposition of Akoxyl RadieaEP
+hv
-
iX3H70NO pyrolysis i-C3H70N0 pyrolysis i-C3H,ONO pyrolysis
Estimate
(CzHsOh pyrolysis Estimate
-
C2H5C(0)OC2HS
-
Source of RO
~~~~
Gray e t d . (1967)'
Coxetal. (1966)
Leggett and Thyme (1970) Batt and Milne (1977b) Batt and Milne (1977b) Ferguson and Phillips (1965) Coxetal. (1966)
Gray et al. (1967)'
McCulloch (1976a) Wijnen (1960)*
Batt and
Reference
+
+
CC3H,0 -+ CH3 + CH3CHO S-CdHgo --* CH3CHO + C2H5 S-C&go M + CH3CHO f C2H5 + M s - C ~ H ~+ O CH$HO f C2H5 t+C4Hg-+ CH3 + (CH3)zCO t-C4H90 -+ CH3 + (CH3,ZCO t-C4H90 --f CH3 + (CH3)zCO t-C4H,0 M +, CH3 + (CH3)zCO + M r-C4Hg0+ CH3 + (CH,),CO t-C&gO CH3 + (CH,),CO t-C,H,O -+ CH3 + (CH,)-/ZO
130-170
25-1500
14.5 & 0.6
15.9
17.0
15.4
119-158
13.4 12
15.5 11.2
10-60
-
125-163
22.8
17.5
125-163 10-60
16.5
15.5
-
17.1
15.6
-
15,3
10.6
14.8
14.26
167-197
12-200
17.5
16.11
12-200
150-190
150-190
17.3
14.6
20-760
333-373
* 1.2
t-CdHgONO pyrolysis t-C,GONO pyrolysis
-
2,2’-Azopmpane + hu S-C~H~ONO pyrolysis s-C~H~ONO pyrolysis S-C~H~ONO pyrolysis
Banand Milne (1976) Batt and Robinson ( I 982)
Yee Quee and Thynne (1967) Yee Quee and Thynne (1967) Heicklen (1968)‘
A1 k e e l and Waddington (1984) East and Phillips (1967) East and Phillips ( 1967) Batt and McCulloch (1976b) Hershenson and Benson (1962p Gray et al. (1967)‘
C*HS+ co (Ar)
1307
(Ar]
304-684
0.2
0.20
11.4Ok
k
43.9 & 0.9
47.7 & 1.4
12.0
7371157 727-
380-684
18.7
13.8 r 0.8
14.8
0.4
E, kcal/mole
160
_t
'Units of A are sec-' for first-order reaction; K ' - s e c - ' for second-order reactions. bAs analyzed by Heicklen (1968). 'Xeview of earlier data. dAs recalculated by Batt and Milne (1976).
Phenoxyl-+ C& + co
+ CH3
14.1
logI4
14.3 ? 1
160-190
t-Am0 (C&&CO + t-Am0 += CH,COC,HS PhenoxyI +
>I500
Tom
press.,
14.5 5 0.2
90-140
"C
Temp.
2-pentoxyl --f CH3CH0 + n-C3H7
Reaction
TABLE 10. ( C o n h u e 4
pyrolysis
C6H5@33
pyrolysis
C6H5mH3
2-Pentyl peroxide pyrolysis r-AmONO pyrolysis t- AmONO pyrolysis
Source ofRO
( 1978a)
Lin and Lin (1985) Lin and Lin (1986)
Batt et al. (1978a) Battetal.
D6N et al. ( 1986)
Reference
DECOMPOSITION AND ISOMERIZATIONOF ALKOXYL RADICALS
225
Estimates of the thermal-decomposition rate coefficients of C2HS0 radicals have been made by Batt and Milne (1977b) based on thermochemical data and comparisons with similar reactions. Their results are listed in Table 10.
3. i-C&O. Ferguson and Phillips (1965) examined the pyrolysis of iC3H70N0 at 175-200°C and 35 Torr pressure. By measuring the ratio of CH3CH0 to (CH3),C0 produced they could measure the relative ratio k, IJk2b:
Their results give kl 1c/k2b = I O ~ . ~ ~ ~16.0IRT) X P ( - M. Based on a value of k2b - 109.58M-1-sec-1(see SectionIV-D), kllc = 10'3.21e x d - 16.O/RT}sec-'. The results of Ferguson and Phillips are in the pressure falloff region. Thus Cox et al. (1966) measured the rate coefficient from 160 to 200°C and from 20 to 230 Torr to obtain high- and low-pressure limiting values of kl1,/kzb. They obtained log{A,dA~,,, M-'} = -4.78 and log{A2dAyl,} = -3.07 with E~~ = 17.2 and - E~~ = 8.3 kcaUmole. With kZb = 109.58M-'-sec-', exp(-8.3/RT} one has k;,, = 10'4.36 exp(-17.2/RT) sec-' and kyle = 1012.65 sec-I. The photooxidation of trans-2,2'-azopropane has been studied by A1 k e e l and Waddington (1984) between 333 and 434 K. The whole system was computer modeled. From the CH3CH0 yield, the pressure falloff behavior was determined for
-
(CH3)2CH0%CH3
+ CH3CH0
(1 1c)
The results at four temperatures are shown in Fig. 13. These data are well fitted by RRK theory using log{A;l,, sec-'} = 14.6 and ETlc = 17.3 kcaUmole. Balla et al. (1985) made direct measurements of i-C&O radical decomposition from 2 to 296 Torr N2at 378 and 406 K. They found the reaction to be in the pressure falloff regime at all pressures studied. Their results are shown in Fig. 14, where they have included the high-pressure limiting rate coefficientscomputed from Batt's (1979) Arrheniusexpression of log{k71,, sec-I} = 14.6 0.5 - (17.2 & I)/€). This expression gives k;,, = 2.2 X lo5 and 4.5 X lo4 sec-I, respectively, at 406 and 378 K. The data of Balla et al. suggest larger high-pressure limits. The results of A1 k e e l and Waddington (1984) are in good agreement with those of Cox et al. (1966). The Arrhenius parameters of Ferguson and Phillips (1965) are lower and lead to rate coefficients about 22% of those from the other studies at 180°C.
*
226
1.5
s
1.0
c) l
0
200 lG00 600 Total pressure (Torr)
Figure 13. Effect of total pressure on the rate coefficient for the decomposition of (CH,),CHO radical: 0,333 K; 343 K; 0 , 353 K;0, 373 K. From A1 Akeel and Waddington (1984) with permission of the Royal Society of Chemistry. n-C&,O and i-C4€&0. Zabarnick and Heicklen (1985b, 1985c) photolyzed n-C3H70N0 and i-C,H,ONO at 366 nm to produce the alkoxyl radicals. Decomposition of the alkoxyl radicals was studied relative to their reaction with NO. At 150 Torr total pressure of N,, the relative rate coefficients k11/k2were (3.3 & 0.3) x lo-', (5.1 f 1.0) x lo-', and (2.3 f 0.2) X M at 55, 88, and 120°C, respectively, for n-C3H70, and (4.6 f 1.0) X (2.8 tr 0.3) x and (5.8 tr 2.2) x M at 23, 55, and 88"C, respectively, for i-C41-L,0 radicals. These results are all in the pressure-dependent regime and cannot be compared directly with either kY1/k2or kyI/k2.
4.
5. s-C4&0. East and Phillips (1967) used a similar technique to measure the decomposition of s-C4H90 to C,H, + CH,CHO at 150-190"C and 12-200 Torr '} = -6.39 and lOg{A2dA:lb} = -4.54 pressure. They found lOg{A2dA:1br With q 1 b - E2b = 17.5 and q l b - &, = 10.6 kcallmole. with k2b =
i 8 DECOMPOSITION AND ISOMERlzAnoN OF ALKOXYL RADICALS
A
A
A
227
a+
A
t
A
A
A=406K
0 =378K
I o3
TOTAL 10 PRESSURE ( T O R R I
1
100
Figure 14. Pressure dependence of the rate coefficient for the thermal decomposition of i-C3H,0 radicals. The high-pressure limit values are from Batt (1979). From Balla et al. (1985) with permission of Elsevier Science Publishers.
lo9.', M-'-sec-', one has kylb = 1 0 ' 6 ~ ' 1 e x ~ - 1 7 . 5 / RSeC-' ~ and kylb = 10'4.26exp(-10.6/RT) M-'-sec-'. Ban and McCulloch (1976b) measured the decompositionof s-C4&0 relative to its rate of addition with NO in the pyrolysis of s-C4H90N0 at 167-197°C:
They found a rate coefficient of 10'4.9-15.3'esec-' at about 1 atm pressure (mostly NO) based on k2, = M-l-sec-' and k2& = 0.26. With our adopted value of k,, = 10lO.~M-l-sec-', their rate coefficient k,,, becomes 10'4.8-'5.3'e sec-'. This rate coefficient should be close to the high-pressure limiting value. They also estimated kllc = 10'4.9-i9/esec-', for the decomposition to form CzHSCHO CH3.
+
228
THE DECOMPOSITION OF ALKYL NKRllES
Drew et al. (1985) studied the thermal decomposition of S-C&o radicals generated from the reaction of F atoms with s-C4H90H. They found CH3CH0 and C2H5CH0 as products, which they assumed came from
No CH3COC2H5was found, so that the reactions in Eqs. 1l b and 1lc accounted for all the decomposition. From 398.6 to 493.3 K they found E l , , - E l l c = -2.68 -+ 0.19 kcaVmole andA,,~A,,, = 0.59 & 0.14, independent of pressure from 80 to 600 Ton.
6. t-C,&O. The pyrolysis of (t-C4&O)2 was studied in the presence of NO at 398-436 K and at 10-60 Tom pressure by Yee Quee and Thynne (1967). The decompositionof the t-C4H90radical was studied in competition with its reaction with NO. The relative rate was pressure dependent. Extrapolation through a Lindemann mechanism gave log{k&lc} = -5.17 f 0.81 + (13.4 & 1.7)/8 and log{k&~,,, M - I } = -7.17 k 0.77 + (22.8 1.6)/8. With log{k,,, M-'-sec-'} = 10.3, one haslog{k~,,,M-'-sec-'} = 15.5 - 13.4/8 and log{kyl,, sec-'} = 17.5 - 22.8/8. Batt and Milne (1976) studied the thermal decay of the t-C4H90radical in comparison with its reaction with NO in the pyrolysis of t-C4H90N0. This reaction was pressure dependent at 0.025-0.9 atm and 160°C. Over the temperaturerange of 119-158"C, the high-pressurelimiting rate coefficient for
*
t-C4&0 d C H 3
+
(CH3),C0
(11C)
was 10'5.5exd-17.0/Rn sec-' based on a value of k2, = M-'-sec-'. M-'-sec-', then k l l c = If we use our adopted value of k2a = exd- 17.0/Rn sec-'. Fuke et al. (1981) used a thermal-lensingstudy in the photolysis of (t-C,H,O), to determine the rate coefficient for r-C4&0 in solution at 27 2 1°C. The rate coefficient was found to be (9 f 1) x lo4 M-'-sec-' in acetonitrile and (5.3 -C 0.5) X lo4 M-'-sec-' in benzene. The difference in the two values probably is caused by differences in the cage effect in the two solutions. Batt and Robinson (1982) made a detailed study of the pressure dependence for the decomposition of t-C4H90 radicals at 130-170°C and 25-1500 Tom pressure. Their data at 402.6 K are shown in Fig. 15. With their data and the treatment recommended by Oref and Rabinovitch (1968), they concluded that their results extrapolated to a value for log{k~lc,sec-'} = 14.6 -t 0.6 - (15.9 ? 1.2)/8 based on log{k,, M-'-sec-'} = 10.3.
DECOMPOSITION AND ISOMERJZATION OF ALKOXYL. RADICALS
229
a
I
f ,
1.5
I
I
2.0 2.5 log iPITorr)
0
1
3.0
Figure 15. log{k,,,} vs log(pressure of added gas} for the decomposition of the t-BuO radical at 402.6 K. X , CF,; 0 , SF,. Computed curves: solid, CF,; dot-dash, SF,; dashed, N,. From Batt and Robinson (1982) with permission of John Wiley and Sons.
7. 2-CsHll0. D6bi et al. (1986) studied the decomposition of 2-pentoxyl radicals obtained from the pyrolysis of 2-pentyl peroxide, C3H7CH(6)CH3__* CH,CHO
+ n-C,H,
(1 10
relative to its combination with NO at pressures above 1500 Torr and temperatures of 363-413 K. They found log{kllflkza, M} = 3.8 & 0.4 - (13.8 0.8)/8. With our recommended value of kza = 10.3, one has log{kllf, sec-'} = 14.1 & 0.4 (13.8 0.8ye.
*
-
8. t-Amoxyl. Batt et al. (1978a) examined the gas-phase pyrolysis of r-amyl nitrite in the presence of NO at 160-190"C. In this way they studied the competition between
230
-
THE DECOMPOSITION OF ALKYL IWlUTES
&Am0
+ NO
t-AmONO
and
From the variation in the acetone yield with NO pressure, klldk2, could be measured. Baa et al. (1977) obtained log{k,,,, sec-'} = 14.7 f 0.2 (14.3 -t l)/0 using their measured value for kza = 10'0.520.2M-'-sec-'. With our recommended value of kz, = M-'-sec-', one has log{kll,, sec-'} = 14.5 2 0.2 - (14.3 f 1)/0. Batt et al. (1978a) also found that at 160°C, k l , ~ k l l , = 80 where reaction l l c is
-
?-Am0
-
C2HSCOCH3 + CH,
(11c)
From this result they concluded that log{kll,, sec-'} = 15.0 - 18.718, which we correct to 14.8 - 18.7/0.
9. (CF3)2C(6)CH3and CF3C(b)C(CH3)2.Drew and Kerr (1983) prepared hexafluoro-t-butoxyl radicals from the reaction
F
+ (CF,),C(OH)CH,
__*
HF
+ (CF,hC(6)CH3
(24)
Over the temperature range 40WjOO K, the radical decomposes exclusively by loss of CF, rather than CH,, the ratio of rate coefficients being 2 8 0 . Likcwise Ken and Wright (1984) examined the decomposition of CF,C(O)(CH,), prepared from the reaction of F atoms with CF,C(OH)(CH3)2. They found that at 361-600 K,decomposition occurred exclusively by loss of the CF, groups, the ratio of CF, to CH3 loss being 275. 10. Phenoxyl. The decomposition of phenoxyl radicals was first studied by Colussi et al. (1977), who found the rate coefficient to be 10 -+ 5 sec-' at lo00 K:
This reaction was studied over the temperature range 1010-1430 K by Lin and Lin (1985), who prepared the radicals from the shock-tube decomposition of C&150CH3in Ar at 0.5-0.9 atm total pressure. They monitored the CO produced as a function of reaction time and determinedkll, = * 0-2exp((-24,000 2 690)/nsec-'. The low preexponential factor supported a tight cyclic activation complex as suggested by Colussi et al. (1977):
DECOMPOSITION AND ISOMEREATIONOF ALKOXYL RADICALS
231
In a subsequent study Lin and Lin (1986) studied the decomposition of methyl phenyl ether (anisole) in incident shock waves in Ar at 1000-1580 K and 0.4-0.9 atm. Some runs were also done with ally1 phenyl ether as the source of phenoxyl radicals. They deduced k,,, = 1011.40*o.20exp((-22,100 450)/T) sec-' from kinetic modeling of the CO formed.
*
11. Summary. Batt (1979) reviewed all the data and gave recommended values for the high-pressure limiting rate coefficients. These are given in Table 11. The Arrhenius parameters in some cases are estimated and in other cases are based on extrapolation from data in the pressure falloff regime. Furthermore the Arrhenius preexponential factors are based on knowledge of the rate coefficients of competitive reactions used to obtain the data. TABLE 11. Thermochemical and Kinetic Data for Alkoxyl Radicals log{A, sec-'}
Reaction
E, kcallmole-'
hH" (298) kcdmole-'
-
r-Am0 fMEK + Me b M , K Et 14.8
+
-
r-BuO+M2K sBuO
+ Me
,MEK+Me EtCHO+Me \ACH + Et
seC-1
4.4 13.8
1.4
4.8 x 104
17.0
5.6
1.08 x 103 -
-
-
14.9 14.9
19 15.3
11.7 6.0 2.6
9.3 4.8 x i d 3.4 x 10-2
,MzK
+H
14.3
21.5
12.2
\AcH
+Me
14.6
17.2
7.0
14.4
23.4
16.5
1.7 x 1 0 - ~
CH,O+Me
(15.0)
21.6
12.9
0.14
+H
14.2
27.5
22.3
1.1 x 10-6
i-PI0
,
AcH+H
EtO
15.5
k(298 K},
Me0 --t CH,O
Source: Batt (1979), with permission of John Witey and Sons, Inc.
97
THE DECOMFOSlTION OF ALKYL NITRlTEs
232
TABLE 12. Estimated ArrheniuS Parameters of Akoxyl Radical Decomposition Reactions
Reaction (CH3)3CO +CH3 + (CH3)2CO (CH3)2CHO +CH3 CHSCHO CH3CH2O +CH3 + CH2O (CH~)~(C~HS)CO +C2H, + ( C H W O +CH3 CH3(C,H,)CO C2HS(CH3)CHO +C2H5 CH3CHO
E,
hH0,
log {A, sec-'}
kcdmole
kcdmole
14.1 13.8 13.6 13.6 13.8 13.6
15.3 16.8 20.0 12.4 (10.7) 16.1 13.5 (11.8) 15.6
5.8 8.4 13.2 1.2 4.7 4.7
9.7
0.2 2.1 8.1
~~
+
+ +
+
CH20 C2HSCH20+C2H5 i-C3H7(CH3)2CO +K 3 H 7 (CH3)ZCO i-C3H7(CH3)CH0+i-C3H7 CH3CH0 CC3H7CH20-+ K 3 H 7 + CH20
+ +
13.7 13.6 13.7 13.7
10.3 12.4
9.0
Source: Choo and Benson (1981), with permission of John Wiley and Sons, Inc.
Choo and Benson (1981) estimated the preexponential factors for the rate coefficients of alkoxyl radical decay by comparison with similar reactions. With these values and measured rate coefficients, they computed activation energies. Their results are listed in Table 12. The preexponential factors are all given by log{A, sec-'} = 13.6-14.1, considerably lower than the measured values. Drew and Kerr (1983) pointed out that the values of Choo and Benson are about 10 times lower than predicted from equilibrium constants at 423 K. An examination of all the data shows that the high-pressure limiting decompositions which give H atoms have log{A,,,, sec-'} = 14.3, whereas those that give alkyl radicals have log{A, ,sec- '} = 15.O. Therefore these values are taken as universal A factors for these reactions, and, where necessary, the activation energies have been recomputed to fit the data using these preexponential factors. The recommended recalculated values for the high-pressure limiting activation energies are given in Table 13. For those decomposition reactions which give H atoms, the activation energies lie in the range of 21-25 kcallmole, with the activation energy decreasing as the molecular complexity increases. If the radical decomposes to give CH, radicals, and it contains no higher alkyl groups, then the activation energy decreases from about 21.6 to 16.5 kcallmole as the complexity increases. If the radical is capable of decomposing to give an akyl radical larger than CH,, but still decomposes to give a CH, radical, the activation energies are in the same range (16.5-21.5 kcaVmole), and the activation energy also decreases with increasing complexity. For alkoxyl radicals that decompose to give alkyl radials larger than CH3, the
,
233
DECOMPOSITION AND ISOMERJZATION OF ALKOXK RADICALS
TABLE 13. Recommended Limiting High-Pressure Arrhenius Parameters for Akoxyl Radical Decomposition
Reaction
E, kcal/mole
Reaction Giving H Atoms (log(A, sec-'} = 14.3) CH30+CH,O H C2H50 CH3CH0 H i-C3H70+(CH3)2C0+ H
+
+
= 25
23.3 21.5
Radicals That Can Only Give CH, (or H ) (log(Asec-'} = 15.0) 21.6 C2H5O +CH20 + CH3 i-C3H,0 +CH3CH0 CH, 17.5 16.5 t-C,H,O -+ (CH3)2CO+ CH,
+
Other Radicals That Can Give CH3 (log(A, sec-'} = 15.0) s-C,H,O +C2H5CH0 + CH, t-Am0+C2H5COCH3+ CH,
19.1 18.7
Reactions That Give C2H, or C3H7 (log{A,sec-'} = 15.0) s-C~H,) CH3CHO C2H5 t-Am0-(CH,),CO + C2H5 2-C5H,,O+CH3CH0 + n-C,H7
15.4 15.3 15.4
+
activation energy is lowest of all and is about 15.4 kcal/mole. There is less information on the low-pressure limiting rate coefficient for alkoxyl decomposition. However the limited data that do exist suggest that the preexponential factors drop to 1.8% or less of their high-pressure values. The activation energies are lower by =50% in their low-pressure limits.
B. Isomerization The isomerization of allcoxyl radicals by the shift of a hydrogen atom from a carbon atom to the oxygen atom to give a hydroxyalkyl radical has been suggested in hydrocarbon combustion. These suggestions have been reviewed by Fish (1964). Chow et al. (1970) have shown that such reactions can occur in the room temperature photolysis of 1-pentylnitrite and menthyl nitrite,
ON0
menthyl nitrite
234
THE DECOMRXITION OF ALKYL NlTRrES
Likewise Carter et al. (1976) and Baldwin et al. (1977) have suggested that such reactions could explain the formation of some products in photochemical smog. However, there is no evidence that such reactions occur in akoxyl radicals except for those which contain a hydrogen atom on the &carbon position:
I 1
H I
a-C-7-L-C I a $ ? $
-
1 1 1 .
HO-C-C-C-CI I I I
This isomerization occurs through a six-membered ring intermediate and thus has minimal strain-energy contribution to the activation energy. In particular Batt et al. (1981) have estimated that Iog{klla, sec-'} = 13.05 f 0.5 - (5680 & 5Oo)lT for H-atom migration in CH30 radicals to form CH20H radicals. This estimate gives a value of 485 sec-' for klla at 548 K, which is larger than the upper limit of 70 sec-' at 548 K measured by Fortuno (1982). The first experimental evidence that reaction l l a could occur was given by Baldwin and Golden (1978) in the low-pressure pyrolysis of n-butyl nitrite at 590-750 K. In the presence of DI, both CH3CH2CH2CH,0D and CH2DCH2CH2CH20Hwere observed. Their results suggested a value of klla = 9.2 X lo8 sec-' at 690 K. Both Carter et al. (1976) and Baldwin and Golden (1978) estimated kllafor exp(-7.7/RT) sec-', n-C4&0 radicals to be lo".' expC-8.9/RT) and respectively. In the photolysis of n-C4H90N0 at 366 nm and 25"C, Rose (1979) found that isomerization of n-C4H90 occurred in competition with reaction with NO2. He reported kllJkg, = (2.8 2 0.5) x M at 25°C. Taking ks, = 1.34 X 10" M-'-sec-' gives klla= 3.74 X lo5 sec-'. However, the only measurements over a temperature range were made by Morabito and Heicklen (1987), who studied the reaction from -8 to 120°C in the photolysis of nC4H90N0. From @{n-C3H,CHO}, they were able to deduce 1n{kllJk2, M} = 1.92 k 1.60 - (4014 & 509)/T.With a value of k2 = 2.8 x 10" M-l-sec-', one has log{klla, sec-'} = 11.28 f 0.69 - (8.0 & l.O)/e, in reasonable agreement with the earlier estimates. This expression gives a room-temperature rate coefficient klla= 2.47 x Id sec-', which is about 66% of the value given by Rose and 79% of the value actually found by Morabito and Heicklen at 23°C. The isomerization of 2-pentoxyl radicals was studied by D6M et al. (1986), who prepared the radical, either by pyrolysis or photolysis of 2-pentyl peroxide or by photolysis of 2-pentyl nitrite. The isomerization reaction was studied in competition with the decompositionreaction, which was measured independently in the same study. The isomerized radical was trapped by addition of CH3radicals to give 2-hexanol. From 279 to 385 K, one has log{k,,$kllf} = -(3.1 f 0.2) + (4.0 & 0.4)/0 where reaction l l a is
-
RJZACllONS OF A L K O X n RADICALS WlTH O2
C3H,CH(6)CH3
CH3CHOHC2H4CH2*
235
(1la)
With log{kl1, M-'-sec-'} = 14.1 - 13.818, one has log{klla,M-'-sec-'} = 0.7) - (9.8 2 o.s)/e. (11.0 At 279 and 301 K, the CH3 radicals can also react directly with 2-pentoxyl, CH3CH(6)C3H7 + CH3
as well as with themselves,
CH3CH(OCH,)C3H,
(25)
so that klla/k;k2/k2, could be evaluated. Since k25 and k26 have no activation energy, the activation energy for the ratecoefficient ratio is that for klla. This was found to be 9.0 2 1.6 kcal/mole. Since this value was lower than that found by the other method, the value recommended by D6M et al. (1986) for Ella was 9.5 2 1.1 kcallmole. The rate coefficients for alkoxyl radical isomerization are given in Table 14. The direct measurements for n-C,&O and 2-C5H, both give a preexponential factor of log{A, la, sec-'} 2 11.1. However, the activation energy for 2-pentoxyl isomerization appears to be larger than that for n-C4H90 radicals, though the values all lie within the experimental uncertainties.
M. REACTIONS OF ALKOXYL RADICALS WITH 0 2
A. Early Work The early work on this reaction was reviewed by McMillan and Calvert (1965) and by Heicklen (1968). Most of this work was qualitative, and led to the inference that alkoxyl radicaals could react with O2by H-atom transfer. However, as pointed out by Heicklen (1968), two studies led to estimates for the rate coefficients. Cerfontain and Kutschke (1962), in the photolysis of (C2H5),N2, estimated the relative importance between C2H50 + and
0 2 +CH3CHO f
HO2
(27)
400
3113
6-112
-
Press., Tom
-8-120
-
"C -
Temp.,
11.020.7
11.8 11.4 11.2820.69
13.0520.5
sec - '1
log{A,,,,
b(2-C5H1,O), pyrolysis or 2-CSHl10NOphotolysis.
"As reported by Carter et al. (1979).
2-Pentoxyl
n-C4H90
CH30
Radical
9.521.1
8.9 7.7 8.0k1.0
11.3+- 1.0
Eilal
kcallmole
Severalb
Estimate Estimate n-C4H,0N0
Estimate
+ hu
Sourceof RO
References
D6bC et al. (1986)
Carter et al. (1976)" Baldwin andGolden (1978) Mortabito and Heicklen (1987)
Battetal. (1981)
TABLE 14. Rate Coefkients for Isomerization of Alkoxyl Radicals by H-Atom Migration
REACTIONS OF ALKOXYL RADICALS WITH O2
237
Their computations showed that k27 was roughly equal to k28 at both 118 and 152°C. However, their system was complex, and they made a number of assumptions. For example, they neglected the reactions of H02 radicals, which almost surely must be incorrect. Nevertheless, k28 can be assumed equal to the rate coefficient for H abstraction by C2H50 from C2H5C02C2H5by analogy. Thus, if Cerfontain and Kutschke's conclusion is correct, then k28 C= k27 N- lo8.' exd- 5.5JRn M- '-set- . The competition
'
+ O2 -H02
+ aldehyde 2RO +ROH + aldehyde
RO
(27) (19a)
was studied by Heicklen and Johnston (1962a, 1962b) in the photooxidation of alkyl iodides at 25°C. They found k27/ki/t = 1.97 X and 4 X M-'12 - sec-'12, respectively, for R = CH, and C2H5.Since kI9, is C= M-'-sec-', respectively, at 25°C. M-'-sec-', k27 becomes 103.4and Both of these early studies established the importanceof the reaction of alkoxyl radicals with 02.HovGever, as we shall see, the estimates of the rate coefficients were much too low. A further study which indicated that &C&O reacted with O2 was done by Milne and Steel (1968), who photooxidized azoisopropane at 25 and -27°C. Recent work (Zellner, 1986) in which both CH30 and CH20 were measured by laser-induced fluorescence gave a yield of 0.85 f 0.15 for CH20 from the O2 + CH30 reaction.
B. CH30 a d CD30 In the 1970s, after it became clear that the alk0xyl-0~reaction was important in photochemical smog chemistry, an effort was made to determine the rate coefficient for the CH,O + O2 reaction. Wiebe et al. (1973) examined the reaction at 25°C in the photooxidation of CH30N0 at 366 nm in the presence of NO2. They monitored the CH30N02 produced in the competitive reaction CH30
+ NO,
-
CH30N02
(94
From this reaction and the competition between NO and 0, for CH,O, they determined k271k2 = 4.7 x CH30 CH30
-
+ O2 -CH20
+ NO
+
CH,ONO
-CH20
H02
+ HNO
238
THE DECOMPOSITION OF ALKYL NITRlTEs
where the NO2 was produced from the reaction of H02 with NO. They used their measured primary quantum yield +la = 0.76 in their analysis. However, since their values for @{CH30NOJ in the absence of 0,were compatible with this value, their reported value for k27/k2 should be correct. With our recommended value of k2 = 1.5 X 10" M-'-sec-', k27 becomes 7.0 X 10' M-'-sec-'. In a similar experiment Glasson (1975) obtained k27/k2 = (4.5 ? 0.6) X With k2 = 1.5 X 10" M-'-sec-', k27 becomes 6.8 X lo5 M-l-sec-'. Alcock and Mile (1975) studied the photolysis of azomethane in the presence of O2 and 2,3-dimethylbutane. In order to interpret their data, they found it necessary to incorporate reaction 27. From model calculations of their data they deduced that k27 = 1.2 X lo6 M-l-sec-' at 100°C. They also reinterpreted the data of Home and Whytock (1967) and obtained k27 = (0.46-1.8) X lo6 M-l-sec-' at 1 0 0 " ~ . The reaction was studied at higher temperaturesby Barker et al. (1977). They examined the thermal decomposition of (CH30)2 at 396-442 K in the presence of NO, and 0,.From the competition between reactions 9a and 27 they obtained log{k2,, M-'-sec-'} = (8.5 ? 1.5) - (4.0 -+ 2.8)/0 for ha= 109.8*0.5 M-'-sec-'. In a similar experiment at 110-16OoC, Batt zkd Robinson (1979) obtained log{kz7, M-I-sec-'} = 9.0 ? 0.6 - (4.8 & l.l)/fJ. This expression gives a value of 105.6M-'-sec-' at 298 K. Cox et al. (1980) also used the same competitive reactions, but used the photolysis of CH30N0 at 299-423 K as the source of CH30. Their photolysis radiation was homogeneous from 310 to 410 nm with a peak intensity at 350 nm. Their results were based on their measured primary quantum yield for CH30-radicalproduction of 1.O. They combined their data with all previous data to get an Arrhenius expression for log(k27, M-'-sec-'} = 7.9 & 0.2 - (2.7 2 0.7)/0. Direct measurements were made for the reactions of CH30 with 0,by monitoring the radical concentrations (Gutman et al., 1982). The CH30 radicals were produced by the 266-nm photolysis of CH30N0. The rate coefficient for the CH30 + 0, reaction from their study along with the results of several other studies was fitted by the expression k27 = 6.3 X lo7 exp(-2.6/RT} M-l-sec-' from 140 to 355"C, in excellent agreement with the composite value reported by Cox et al. (1980). Fortuno (1982) measured the decay of CH,O by laser magnetic resonance in the presence of 0,in a flow-tube experiment. The CH30 radicals were generated by the reaction of F atoms with CH30H. This system also produces CH20H, which reacts rapidly with 0,to produce HO,, which in turn reacts with CH30. Fortuno's analysis attempted to sort out the various paths for CH30 removal, andhedete~minedk,~ = (3.65 & 0.41) X 1O8K'-sec-'from 100to275"C. Lorenz et al. (1985) measured the rate coefficients for the reaction of CH30 with 0,at 300-500 K using laser flash photolysis of CH30N0 at 248 nm. The CH30 radicals were monitored by laser-inducedfluorescence. The rate coefficient
REACI'IONS OF ALKOXYL RADICALS WITH 0, lo7,
u,
I
0
I
239
I
I
I
2.60
285
3.10
I
0
-
-
106
-
0
-
1.60
I 1.85
2.10
2.35
lo3I T ,
OK-'
3.35
0
Figure 16. Anhenius plot for the CH30/02 reaction rate coefficient: , Wiebe et al. (1973); 0,Glasson (1975); 4,Alcock and Mile (1975); V, Mendenhall et al. (1975); 0 ,Barker et al. (1977); 0,Batt and Robinson (1979); 0,Cox et al. (1981); H, Gutman et al. (1982); A, Lorenz et al. (1985); 0, Fortuno (1982).
for the CH30 + O2reaction was reported to be (3.3 -t 1.2) X 107exp{- lOOO/T} M-l-sec-'. A composite Arrhenius plot of all the data is shown in Fig. 16. The data obtained from relative rate measurements have been corrected to be consistent with our recommended values for k2a = 1.O X 10" M-'-sec-' and ha= 6.67 x lo9M-'-sec-'. With these corrections, the data fit a least-squares expression of log{kZ7,M-l-sec-'} = 7.71 f 0.13 - (2.57 f 0.22)/8. Fortuno's data are much higher than those of the other investigators and were omitted from the regression analysis. The reaction of CD30 with 0, was studied by Weaver et al. (1975), who prepared CD,O from the photolysis of CD3N2CD3at 25°C. They found kZ7/k&; = 9.7 X lo-, (M-sec)-'" for the reactions
240
-
THE DECOMPOSlTION OF ALKm NERITFS
CD30
+ O2
CD,O
2CD30 -CD30D
+ DO2 + CD20
(27) (19a)
The rate coefficient for reaction 19ais probably similar to that for its hydrogenated analog, i.e. kI9, 2 2 x 10" M-I-sec-'. Thus kZ7 1: 1.4 >no4 M-'-sec-', about 0.020 times as large at 298 K as the rate coefficient for the reaction of its hydrogen analog. With the assumption that the C-H stretching frequency is 3200 cm-' , the expected shift in zero-point energies between CH30 and CD30 would be 465 cm-', which would predict an 89% reduction, compared to the observed 5.5 times as large as the reduction of 98%. Thus the predicted value is measured value. Further work needs to be done on this system to resolve the discrepancy.
-
C. C2H50, CC3H70, n-C3H70, and i-C4H90 The first quantitative study of the reaction of C2H50 with 0,was made by Gutman et al. (1982). They measured the rate coefficient directly by monitoring the concentration of C2H5O radicals, which were produced in the 266-nm photolysis of C2H,0N0. They found the rate coefficient to be 4.8 x lo6 M-'sec-' at 23°C and 5.9 x lo6 M-'-sec-' at 80°C. In a series of papers, Zabarnick and Heicklen (1985a, 1985b, 198%) measured the rate coefficients for the reactions of CZHSO, n-C3H70, and i-C4H90radicals with 0,.They prepared the radicals from the photolysis of the corresponding alkyl nitrite at 366 nm and studied the competition between NO and 0, for the radical. They found the relative rate coefficients to fit the expressions l ~ g { k ~ ~ / k ~ } = -2.17 f 0.14- (1.84 & 0.19)/8forC2H50from--48to+120"C,log{k2,/k2} = -2.17 -+ 0.20 - (1.75 -+ 0.23)/8 for n-C&70 from -26 to +88"C, and log{k2,/k2} = -2.15 & 0.22 - (1.66 & 0.32)/8 for i-C4H90 from -8 to 120°C. With the adopted values for k2 for the corresponding reactions, namely log k2 = 10.31, 10.46, and 10.46, one obtains log k27 = 8.14 - 1.84/8, 8.29 1.75/6, and 8.31 - 1.66/8, respectively. Balla et al. (1985) measured the rate coefficient for the i-C3H70 0,reaction by directly monitoring the i-C3H70 radicals produced in the flash photolysis of i-C3H70N0 at 355 nm. They found the rate coefficient to be (9.1 f 4.22) X lo6 exd-0.39 -t 0.28/RT) M-l-sec-' at 25-110°C and 1-50 Torr pressure. This expression gives a room-temperature rate coefficient similar to those of other C,-C4 alkoxyl radical (except for s-C4H90)reactions with 0,.However, the Arrhenius parameters are very much smaller for the i-CsH70 + O2 reaction. It is difficult to understand why this should be.
+
REACTIONS OF ALKOXYL RADICALS WITH 0,
241
Morabito and Heicklen (1987) used the same technique as Zabarnick and Heicklen to measure the rate coefficient for the n-C&O + O2 reaction. They found ln{k,,/k,} = -4.09 2 0.54 -(1178 2 176)IT from 23 to 88°C. With log{k,, M-I-sec-'} = 10.46 this gives l ~ g { k M-'-sec-'} ~~, = 8.68 - (1178 5 176)/ 2.3031: This expression gives a similar room-temperaturerate coefficient to that obtained from the C2H50 0, and n-C3H70 0, reactions. However, the Arrhenius parameters are considerably higher for the n-C4H90 reaction. This may reflect experimental uncertainty, both because the experimental temperature range was small and because the analysis was complicated by the presence of the reaction of Eq. 1la, which occurs only in the n-C4H90 system. The photooxidation of n-C4H90N0 in air at 298 5 2 K was studied by Niki et al. (1981b). They studied the competition between
+
n-C&@
+
+ 02-H02
and n-C4H90
-
+ nC3H7CH0
HOCH2CH2CH2CH2
(27)
(1 la)
by measuring the quantum yield of n-C3H7CH0 production. They assumed that reaction 1l a leads to no further formation of n-C3H7CH0, which conflicts with the later findings of Morabito and Heicklen (1987). Nevertheless, based on their analysis, they reported k27[02]/klla= 0.23 2 0.03 at 700 Torr of air. If we take log{klla, sec-I} to be 11.28 5 0.69 - (4014 2 509)/2.3033, then kZ7 = 7.9 x lo6 M-l-sec-' at 298 K, in good agreement with the finding of Morabito and Heicklen (1987). Another study of the reaction of n-C4H90 and S-C&@ radicals with 0, was made by Cox et al. (1981). They produced their radicals from the reaction of HO with n-C4HIoin N2-02 mixtures. For the n-C4H90 system they monitored the n-C3H7CH0 yield to obtain klla/kZ7= (2.5 2 0.8) x lo-' M at 1 atm pressure and 293 K. Based on log{k,,,, sec-'] = 11.28 & 0.69 - (8.0 2 l.O)/e, one has k27 = 1.04 x lo7 M-'-sec-', again in good agreement with the findings of the other studies. For the s-C4H90 radical, Cox et al. (1981) found k