New insights into the mechanism of triplet radical-pair combinations. The persistent radical effect masks the distinction between in-cage and out-of-cage processes

Article abstract of DOI:10.1021/ja067461q

Steady-state and laser-pulsed irradiations of dibenzyl ketone (ACOB ₀) and derivatives with a p-methyl or a p-hexadecyl chain (ACOB ₁ and ACOB₁₆, respectively) have been conducted in polyethylene films with 0, 46, and 68% crystallinities. Calculation of the fractions of in-cage combinations of the triplet benzylic radical-pair intermediates based on photoproduct yields, F_c, from ACOB ₁₆ are shown to be incorrect as a result of the kinetic consequences of drastically different diffusion coefficients for the benzyl and p-hexadecylbenzyl radicals. Careful analyses of the transient absorption traces, based upon a new model developed here, allow the correct cage effects to be determined even from ACOB₀. The model also permits the rate constants for radical-pair combinations and escape from their cage of origin to be calculated using either an iterative fitting procedure or a very simple one which requires only k_-CO and the intensities of the transient absorption immediately after the flash and after the in-cage portion of reaction by the benzylic radicals is completed. Values of the rate constant for decarbonylation of the initially formed arylacetyl radicals, k_-CO, have been measured from the rise portions of the laser-flash transient absorption traces. They confirm the assertion from results in liquid alkane media that decarbonylation rates are independent of microviscosity. The data separate components of a reaction from an (in-cage) "cage effect" and an (out-of-cage) "persistent radical effect" that are responsible for formation of AB-type (i.e., decarbonylated) products. The effects here are a consequence of vastly different rates of diffusion for coreacting A· and B· benzylic radicals rather than segregation of the radicals in different parts of a hetereogeneous environment (which leads to an excess of AA and BB products). Heretofore, observation of exclusive formation of AB products has been attributed to in-cage combinations of geminate radical pairs. We show that not to be the case here and provide methodologies which may be used for testing the importance of the "persistent radical effect" component of reaction.

Full text of DOI:10.1021/ja067461q

Published on Web 03/29/2007
New Insights into the Mechanism of Triplet Radical-Pair
Combinations. The Persistent Radical Effect Masks the
Distinction between In-Cage and Out-of-Cage Processes
Carlos A. Chesta,*,†,‡ Jyotirmayee Mohanty,§,| Werner M. Nau,*,§
Urbashi Bhattacharjee,† and Richard G. Weiss*,†
Contribution from the Department of Chemistry, Georgetown UniVersity,
Washington, DC 20057-1227, Departamento de Qu´ımica, UniVersidad Nacional de R´ıo Cuarto,
5800-R´ıo Cuarto, Argentina, School of Engineering and Science, Jacobs UniVersity Bremen,
Campus Ring 1, D-28759 Bremen, Germany, and Bhabha Atomic Research Centre,
Mumbai-400 085, India
Received October 23, 2006; E-mail: weissr@georgetown.edu
Abstract: Steady-state and laser-pulsed irradiations of dibenzyl ketone (ACOB0) and derivatives with a
p-methyl or a p-hexadecyl chain (ACOB1 and ACOB16, respectively) have been conducted in polyethylene
films with 0, 46, and 68% crystallinities. Calculation of the fractions of in-cage combinations of the triplet
benzylic radical-pair intermediates based on photoproduct yields, Fc, from ACOB16 are shown to be incorrect
as a result of the kinetic consequences of drastically different diffusion coefficients for the benzyl and
p-hexadecylbenzyl radicals. Careful analyses of the transient absorption traces, based upon a new model
developed here, allow the correct cage effects to be determined even from ACOB0. The model also permits
the rate constants for radical-pair combinations and escape from their cage of origin to be calculated using
either an iterative fitting procedure or a very simple one which requires only k-CO and the intensities of the
transient absorption immediately after the flash and after the in-cage portion of reaction by the benzylic
radicals is completed. Values of the rate constant for decarbonylation of the initially formed arylacetyl radicals,
k-CO, have been measured from the rise portions of the laser-flash transient absorption traces. They confirm
the assertion from results in liquid alkane media that decarbonylation rates are independent of microviscosity.
The data separate components of a reaction from an (in-cage) “cage effect” and an (out-of-cage) “persistent
radical effect” that are responsible for formation of AB-type (i.e., decarbonylated) products. The effects
here are a consequence of vastly different rates of diffusion for coreacting A‚ and B‚ benzylic radicals
rather than segregation of the radicals in different parts of a hetereogeneous environment (which leads to
an excess of AA and BB products). Heretofore, observation of exclusive formation of AB products has
been attributed to in-cage combinations of geminate radical pairs. We show that not to be the case here
and provide methodologies which may be used for testing the importance of the “persistent radical effect”
component of reaction.
Introduction
impeded by spin and enthalpic considerationssevery encounter
conceptually can lead to products and in-cage combinations can
Analyses of the chemical fates and dynamic courses of
geminate singlet radical pairs, generated during photo-Fries
reactions of aromatic esters1 and photo-Claisen reactions of
aromatic ethers,2 have allowed intimate details of in-cage (i.e.,
cages of origin) and out-of-cage motions to be probed in a
variety of media.3-5 In part, those insights have been possible
because in-cage combinations of singlet radical pairs are not
be exceedingly fast.6 The same is not true of triplet radical pairs
whose combination requires concomitant intersystem crossing
(3) (a) Xu, J.; Weiss, R. G. Photochem. Photobiol. Sci. 2005, 4, 348-358. (b)
Gu, W.; Weiss, R. G. Tetrahedron 2000, 56, 6913-6925. (c) Xu, J.; Weiss,
R. G. Org. Lett. 2003, 5, 3077-3080. (d) Gu, W.; Warrier, M.; Schoon,
B.; Ramamurthy, V.; Weiss, R. G. Langmuir 2000, 16, 6977-6981.
(4) (a) Warrier, M.; Kaanumalle, L. S.; Ramamurthy, V. Can. J. Chem. 2003,
81, 620-631. (b) Arumugam, S.; Vutukuri, D. R.; Thayumanavan, S.;
Ramamurthy, V. J. Am. Chem. Soc. 2005, 127, 13200-13206. (c)
Kaanumalle, L. S.; Nithyanandhan, J.; Pattabiraman, M.; Jayaraman, N.;
Ramamurthy, V. J. Am. Chem. Soc. 2004, 126, 8999-9006.
† Georgetown University.
‡ Universidad Nacional de R´ıo Cuarto.
(5) (a) Giancaterina, S.; Rossi, A.; Rivaton, A.; Gardette, J. L. Polym. Degrad.
Stab. 2000, 68, 133-144. (b) Sanchez, A. M.; Veglia, A. V.; de Rossi,
R. H. Can. J. Chem. 1997, 75, 1151-1155. (c) Lu, F. F.; Wu, L. Z.; Zhang,
L. P.; Tung, C. H.; Zheng, L. Q. Chin. J. Org. Chem. 2006, 26, 599-609.
(d) Gu, W.; Bi, S.; Weiss, R. G. Photochem. Photobiol. Sci. 2002, 1, 52-
59. (e) Tung, C.-H.; Wu, L.-Z.; Zhang, L.-P.; Li, H.-R.; Yi, X.-Y.; Song,
K.; Xu, M.; Yuan, Z.-Y.; Guan, J.-Q.; Wang, H.-W.; Ying, Y.-M.; Xu,
X.-H. Pure Appl. Chem. 2000, 72, 2289-2298. (f) Tung, C.-H.; Xu, X.-H.
Tetrahedron Lett. 1999, 40, 127-130.
§ Jacobs University Bremen.
| Bhabha Atomic Research Centre.
(1) (a) Miranda, M. A.; Galindo, F. In Molecular and Supramolecular
Photochemistry; Ramamurthy, V., Schanze, K. S., Eds.; Marcel Dekker:
New York, 2003; Vol. 9, Chapter 2. (b) Miranda, M. A.; Galindo, F. In
CRC Handbook of Organic Photochemistry and Photobiology, 2nd ed.;
Horspool, W. M., Lenci, F., Eds.; CRC Press: Boca Raton, FL, 2003;
Chapter 42.
(2) Galindo, F. J. Photochem. Photobiol., C: Photochem. ReVs. 2005, 6, 123-
(6) Nakagaki, R.; Hiramatsu, M.; Watanabe, T.; Tanimoto, Y.; Nagakura, S.
J. Phys. Chem. 1985, 89 3222-3226.
138.
9
5012
J. AM. CHEM. SOC. 2007, 129, 5012-5022
10.1021/ja067461q CCC: $37.00 © 2007 American Chemical Society

Mechanism of Triplet Radical-Pair Combinations
A R T I C L E S
Scheme 1
Scheme 2. Limiting Cases for Combinations of A‚/B‚ Radical
Pairs Showing Expected Product Distributions in the Absence of
Scavengers
(ISC). Thus, obtaining detailed kinetic information about the
in-cage combination of triplet radical pairs involves additional
mechanistic considerations and, usually, processes that occur
on longer time scales. The generally slower rate of combinations
of triplet radical pairs offers additional opportunities and several
new experimental challenges.
Dibenzyl ketone (ACOB0) and its derivatives, including those
which are asymmetrically substituted with groups on one of
the phenyl rings (ACOBn), have been frequently employed as
precursors of triplet radical pairs. They have been studied
extensively since the discovery by Engel7 and Robbins and
Eastman8 in 1970 that irradiation of ACOB0 and its derivatives
results in a classic Norrish type I process in which the first
homolytic step from the triplet state leads to an arylacetyl/
benzylic radical pair. Especially in high viscosity organic
solvents at room temperature, loss of carbon monoxide from
the arylacetyl part is sufficiently rapid to compete with cage-
escape by one of the radicals. Thus, a large fraction of the
ensuing pairs of benzylic radicals, A‚/B‚,9 can be formed in
the reaction cavity of their origin while retaining the triplet spin
multiplicity of the ketone excited state. The A‚/B‚ pairs either
combine within their cage of origin, yielding AB exclusively,
or escape and react after reencounters (if no trapping species is
present in the medium), yielding principally AA, AB, and BB
(Scheme 1).
On the basis of many studies in diverse media and under
different stimuli, the nature and kinetics of the motions of A‚
and B‚ are thought to be well understood.10 In fact, the product
distributions from combinations of A‚ and B‚ have been used
by many others11 and us12 to assess the abilities of various media
to influence translational and rotational motions as well as
electron spin interconversions in the presence of external
magnetic fields or as a result of isotopic enrichment.13
Here, we examine the photochemical reactions of the parent
molecule, ACOB0, and two ACOBn in which a methyl or
hexadecyl chain has been appended to the para position of one
of the aromatic rings, ACOB1 or ACOB16, respectively, within
media consisting of n-hexane and three types of polyethylenes
of different crystallinities. The results from these experiments
have allowed us to introduce and to test a model which assesses
quantitatiVely the importance of the “persistent radical effect”14
for small radicals (case 3 of Scheme 2). Analyses of our data
according to the model indicate that the commonly used cage-
recombination factor, Fc (eq 1), that relates product yields to
the fraction of in-cage and out-of-cage combinations by the A‚/
B‚ radical pairs, becomes inValid when the rates of diffusion
of the radicals are Very different. Thus, the persistent radical
effect becomes a dominant process during the photolyses of
ACOB16.
[AB] - [AA] - [BB]
[AB] + [AA] + [BB]
Fc )
(1)
The possible scenarios for combinations of A‚/B‚ radical pairs
initially in a cage are summarized in Scheme 2. Each has been
observed experimentally to some degree. Implicit in the form
of eq 1 are the assumptions that 1:2:1 ratios of AA, AB, and
(13) See for instance: (a) Turro, N. J.; Buchachenko, A. L.; Tarasov, V. F.
Acc. Chem. Res. 1995, 28, 69-80. (b) Step, E. N.; Tarasov, V. F.;
Buchachenko, A. L.; Turro, N. J. J. Phys. Chem. 1993, 97, 363-373. (c)
Tarasov, V. F.; Ghatlia, N. D.; Buchachenko, A. L.; Turro, N. J. J. Am.
Chem. Soc. 1992, 114, 9517-9526. (d) Turro, N. J.; Zhang, Z. Tetrahedron
Lett. 1989, 30, 3761-3764. (e) Turro, N. J.; Cheng, C. C.; Wan, P.; Chung,
C. J.; Mahler, W. J. Phys. Chem. 1985, 89, 1567-1568. (f) Gould, I. R.;
Turro, N. J.; Zimmt, M. B. In Advances in Physical Organic Chemistry;
Bethell, D., Ed.; Academic Press: London, 1984; Vol. 20, pp 1-53. (g)
Baretz, B. H.; Turro, N. J. J. Am. Chem. Soc. 1983, 105, 1309-1316. (h)
Turro, N. J.; Chung, C.-J.; Lawler, R. G.; Smith, W. J., III. Tetrahedron
Lett. 1982, 23, 3223-3226. (i) Turro, N. J.; Chow, M.-F.; Chung, C.-J.;
Kraeutler, B. J. Am. Chem. Soc. 1981, 103, 3886-3891. (j) Turro, N. J.;
Mattay, J. Tetrahedron Lett. 1980, 21, 1799-1802. (k) Kraeutler, B.; Turro,
N. J. Chem. Phys. Lett. 1980, 70, 270-275. (l) Hwang, K. C.; Roth,
H. D.; Turro, N. J.; Welsh, K. M. J. Phys. Org. Chem. 1992, 5, 209-217.
(14) (a) Bachmann, W. E.; Wiselogle, F. Y. J. Org. Chem. 1936, 1, 354-382.
(b) Perkins, M. J. J. Chem. Soc. 1964, 5932-5935. (c) Fischer, H. Chem.
ReV. 2001, 101, 3581-3610. (d) Studer, A. Chem.sEur. J. 2001, 7, 1159-
1164.
(7) Engel, P. S. J. Am. Chem. Soc. 1970, 92, 6074-6076.
(8) (a) Robbins, W. K.; Eastman, R. H. J. Am. Chem. Soc. 1970, 92, 6076-
6077. (b) Robbins, W. K.; Eastman, R. H. J. Am. Chem. Soc. 1970, 92,
6077-6079.
(9) Except as necessary for clarity, the subscript designating the specific nature
of the B radicals is omitted.
(10) See for instance: (a) Buchachenko, A. L. Chem. ReV. 1995, 95, 2507-
2528. (b) Tarasov, V.; Ghatlia, N. D.; Buchachenko, A.; Turro, N. J.
J. Phys. Chem. 1991, 95, 10220-10229.
(11) (a) Ruzicka, R.; Barakova, L.; Klan, P. J. Phys. Chem. B 2005, 109, 9346-
9353. (b) Veerman, M.; Resendiz, M. J. E.; Garcia-Garibay, M. A. Org.
Lett. 2006, 8, 2615-2617. (c) Petrova, S. S.; Kruppa, A. I.; Leshina, T. V.
Chem. Phys. Lett. 2004, 385, 40-44. (d) Aspe´e, A.; Maretti, L.; Scaiano,
J. C. Photochem. Photobiol. Sci. 2003, 2, 1125-1129. (e) Lipson, M.; Noh,
T. H.; Doubleday, C. E.; Zaleski, J. M.; Turro, N. J. J. Phys. Chem. 1994,
98, 8844-8850. (f) Roberts, C. B.; Zhang, J.; Brennecke, J. F.; Chateauneuf,
J. E. J. Phys. Chem. 1993, 97, 5618-5623.
(12) Hrovat, D. A.; Liu, J. H.; Turro, N. J.; Weiss, R. G. J. Am. Chem. Soc.
1984, 106, 5291-5295.
9
J. AM. CHEM. SOC. VOL. 129, NO. 16, 2007 5013

A R T I C L E S
Chesta et al.
Figure 1. HPLC chromatograms (λdet ) 270 nm) of the photoproduct distribution of ACOB16 in (a) n-hexane and (b) PE46. The UV absorption spectra of
the products as obtained in situ from the diode array detector of the HPLC are shown as well. The retention time of ACOB16 under the conditions of this
chromatogram is ca. 50 min. The AA and BB peaks in spectrum a are not equal in size because their molar extinction coefficients differ at 270 nm.
Results and Discussion
BB are always obtained from out-of-cage combinations (case
4 of Scheme 2) and exclusive formation of AB signifies
complete in-cage reaction (case 2 of Scheme 2). There is an
intrinsic ambiguity, therefore, because an excess of AB may
result from case 2 or case 3.
Most experimental details, including the syntheses of 1-(4-
hexadecylphenyl)-3-phenyl-2-propanone (ACOB16) and its ex-
pected photoproducts, are reported in the Supporting Informa-
tion. Polyethylene films are designated according to their degree
of crystallinity: PE0, PE46, and PE68 have 0, 46, and 68%
crystallinities, respectively. Their properties have been reported
elsewhere.19,21
Steady-State Irradiations. Irradiations were conducted at
>300 nm, in the long wavelength absorption bands of the
ACOBn (Supporting Figure S1), to produce 1(n,π*) states. Since
AA, AB, and BB photoproducts do not absorb at >300 nm,
their primary ratios were quantified easily by HPLC (Figure
1a) after correction of the peak areas for detector responses.
Photolysis of ACOB1 or ACOB16 in n-hexane yielded AA, AB,
and BB as the only detected photoproducts in a ca. 1:2:1
distribution (i.e., all reaction occurs out-of-cage22 or with zero
cage effect; case 4 of Scheme 2 applies). The values of Fc
calculated from the steady-state experiments are collected in
The limitations of eq 1 have been recognized qualitatively
by Bohne and co-workers who examined the partitioning of
radicals from asymmetrically substituted dibenzyl ketones
between aqueous and micellar environments,15 and quantitatively
by Turro and co-workers who altered the probabilities of
combination of benzylic radicals by placing one inside and
another outside zeolite cages during polymerization reactions
(case 1 of Scheme 2).16 Both of these are examples of
microphase separation. Although the dependence of the com-
bination of radicals on their relative rates of diffusion in media
without microphase separations is well documented in polym-
erization reactions,14c,17 it is not in photochemical reactions of
“small” molecules, such as dibenzyl ketones. Perhaps as a
corollary, an easily tractable method for identifying the true
cage effects in such systems has not been developed.18
The model presented here allows the true cage effects to be
assessed and the rate constants associated with the various
combination steps to be calculated. It removes the mechanistic
ambiguity from the limiting cases 2 and 3. Furthermore, it is
easily adaptable to a wide variety of reactions and media where
the diffusion rates of two radical species are very different (i.e.,
the “persistent radical effect”) or the cage effects cannot be
calculated from photoproduct distributions (N.B., ACOB0).
(15) (a) Kleinman, M. H.; Shevchenko, T.; Bohne, C. Photochem. Photobiol.
1998, 68, 710-718. (b) Kleinman, M. H.; Shevchenko, T.; Bohne, C.
Photochem. Photobiol. 1998, 67, 198-205.
(16) Lei, X.-G.; Jockusch, S.; Ottaviani, M. F.; Turro, N. J. Photochem.
Photobiol. Sci. 2003, 2, 1095-1100.
(17) See for instance: (a) Studer, A. Chem. Soc. ReV. 2004, 33, 267-273. (b)
Fischer, H. In AdVances in Controlled/LiVing Radical Polymerization;
Matyjaszewski, K., Ed.; ACS Symposium Series 854; American Chemical
Society: Washington, DC, 2003, pp 10-23.
(18) Methods that are not generally applicable to monomeric systems or easily
amenable to closed solutions are available. See for instance: (a) Fischer,
H. J. Polym. Sci., Part A: Polym. Chem. 1999, 37, 1885-1901. (b) Tang,
W.; Fukuda, T.; Matyjaszewski, K. Macromolecules 2006, 39, 4332-4337.
(c) Karatekin, E.; O’Shaughnessy, B.; Turro, N. J. J. Chem. Phys. 1998,
108, 9577-9585.
The method relies on analyses of transient absorption kinetics
from flash photolyses. We apply it here to calculate the correct
fractions of in-cage and out-of-cage combinations by the triplet
benzylic radical pairs from ACOB0, ACOB1,19 and ACOB16
which are created in polyethylene (PE) films and to demonstrate
the limitations of relying on eq 1.
(19) Bhattacharjee, U.; Chesta, C. A.; Weiss, R. G. Photochem. Photobiol. Sci.
2004, 3, 287-295 and references therein.
(20) (a) Tsentalovich, Y. P.; Kurnysheva, O. A.; Gritsan, N. P. Russ. Chem.
Bull. Int. Ed. 2001, 50, 237-240. (b) Tsentalovich, Y. P.; Fischer, H. J.
Chem. Soc., Perkin. Trans. 1994, 2, 729-733. (c) Zhang, X.; Nau, W. M.
J. Phys. Org. Chem. 2000, 13, 634-639. (d) Claridge, R. F. C.; Fischer,
H. J. Phys. Chem. 1983, 87, 1960-1967. (e) Tokumura, K.; Ozaki, T.;
Nosaka, H.; Saigusa, Y.; Itoh, M. J. Am. Chem. Soc. 1991, 113, 4974-
4980. (f) Maouf, A.; Lemmetyinen, H.; Koskikallio, J. Acta Chem. Scand.
1990, 44, 336-338. (g) Turro, N. J.; Gould, I. R.; Baretz, B. H. J. Phys.
Chem. 1983, 87, 531-532. (h) Lunazzi, L.; Ingold, K. U.; Scaiano, J. C.
J. Phys. Chem. 1983, 87, 529-530. (i) Kurnysheva, O. A.; Gritsan, N. P.;
Tsentalovich, Y. P. Phys. Chem. Chem. Phys. 2001, 3, 3677-3682.
(21) Brown, G. O.; Guardala, N. A.; Price, J. L.; Weiss, R. G. J. Phys. Chem.
B 2002, 106, 3375-3382.
In addition, a conclusive demonstration of the independence
of the rate of decarbonylation of arylacetyl radicals, k-CO, on
viscosity in paraffinic media,20 and an assessment of the
dependence of the true Fc on the degree of crystallinity of the
polyethylene host and the length of the alkyl chain (R) in the
ACOBn are presented. Although the independence of k-CO on
medium viscosity has been inferred from data obtained in liquid
n-alkanes, it has not been extrapolated to extremely viscous
microenvironments, such as those afforded by the polyethylenes.
(22) (a) Turro, N. J. Proc. Natl. Acad. Sci. U.S.A. 1983, 80, 609-621. (b) Gould,
I. R.; Turro, N. J.; Zimmt, M. B. In Advances in Physical Organic
Chemistry; Bethell, D., Ed.; Academic Press: London, 1984; Vol. 20, pp
1-53. (c) Turro, N. J. Chem. Commun. 2002, 2279-2292. (d) Turro, N. J.
Acc. Chem. Res. 2000, 33, 637-646.
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Mechanism of Triplet Radical-Pair Combinations
A R T I C L E S
Table 1. Rate Constants and FcAB Values at 290 K Calculated from Laser-Flash (LF) Photolysis Experiments According to the Model and Fc
Values from Steady-State (SS) Photolyses Conducted at 295 Ka
polyethylene
ACOB0
ACOB1
ACOB16
PE0b
k-CO/106 s-1
4.6 ( 0.5
6.0 ( 0.3
6.2 ( 0.3
4.7 ( 0.2
4.7 ( 0.3c
7.4 ( 0.9
k
dAB/104 s-1
7.5 ( 0.9
11.0 ( 0.5
5.4 ( 0.2
kr/104 s-1
FcAB
4.7 ( 0.2
5.0 ( 0.2
0.38 ( 0.04
4.7 ( 0.7
8.6 ( 0.9
11.0 ( 0.2
0.55 ( 0.04 (0.55)
0.40 ( 0.04
5.5 ( 0.2
9.4 ( 0.3
11.0 ( 0.1
0.55 ( 0.05 (0.55)
0.51 ( 0.03
5.6 ( 0.5
7.4 ( 0.4
12 ( 1
0.61 ( 0.07 (0.61)
0.67 ( 0.04
0.33 ( 0.01
PE46d,e
k-CO/106 s-1
kdAB/104 s-1
kr/104 s-1
FcAB
>5f
16.0 ( 0.2
14.0 ( 0.1
0.46 ( 0.02
1.00 ( 0.04
>5f
Fc
PE68d,e
k-CO/106 s-1
kdAB/104 s-1
kr/104 s-1
FcAB
4.8 ( 0.6
7.8 ( 0.8
13.0 ( 0.4
11.0 ( 0.1
0.44 ( 0.06 (0.50)
1.00 ( 0.04
9 ( 1
0.53 ( 0.01 (0.54)
Fc
n-hexanee
k-CO/106 s-1
Fc
6.420c
0.01 ( 0.0319
-0.01 ( 0.04
a Except as indicated, all laser-flash data are averages from 10 laser shots on one spot of an aerated film. In the fitting routines using the model, k-CO was
fixed to the values from fits of the rise portions of transient absorption traces. Where reliable values of ∆ODomax and ∆ODeo were available from transient
absorption traces, values of FcAB from optical density measurements and eq 9 are included in parentheses. b For ACOB0 from one shot-averaged decay trace
in each of two different films. c Stored for 1 month under an argon atmosphere. d For ACOB1 average from four separate shot-averaged decay traces from
four different spots on one film. e Errors limits are the t-test confidence intervals calculated at 95% confidence. f No accurate measurement possible because
of strong scattering and fast kinetics.
Table 1. In other isotropic liquid media, as well, Fc from ACOB1
is nearly zero.19
There, microscopic spatial separation of the different species
by size or solubility make the probability of collisions between
A‚ and B‚ very small and favor self-reactions (case 1). Related
interpretations based on a separation of reaction space cannot
be invoked here because polyethylene films are not microphase-
compartmentalized systems (i.e., the entire reaction space outside
the crystalline regions is accessible to all solute species). Thus,
the walls of the reaction cavities (or cages)26 afforded by the
completely amorphous polymer, PE0, consist of somewhat
disorganized polymer chains that are able to relax relatively
rapidly3b in response to shape changes by the ACOBn. The
partially crystalline polymers, PE46 and PE68, place the ACOBn
in a mixture of amorphous and interfacial cages. The latter
consist of the lateral edges of lamellar crystallites on one side
and amorphous chains on the other; they are thought to be more
organized and have higher microviscosities than the completely
amorphous cages. However, both types attenuate the rates of
diffusion of species such as the ACOBn and their fragments,27
and both influence the ability of fragments to move within a
cage.3,26
From a practical standpoint, the presence of some micrometer-
range crystalline objects19,21 in the PE films causes significant
scattering of the incident radiation (and some apparent broaden-
ing of the absorption bands). For this reason, concentrations of
the dibenzyl ketones were approximated by using the molar
extinction coefficients in n-hexane and setting the baselines with
reference to an undoped PE film; for example, see Supporting
Figure S2. Irradiations of ACOB16 in the PE films at room
19
temperature produced AB exclusively (Figure 1b). ACOB1
yielded ratios of AB/(AA + BB) which are much larger than
the 1/1 expected statistically: 3.0 in PE46 and 5.1 in PE68.
An excess of AB has been associated traditionally with a
mixture of case 2 and case 4 in Scheme 2 and analyzed using
eq 1.22 Accordingly, the exclusive formation of AB from
ACOB16 in both PE46 and PE68 films would indicate a cage
effect of unity, while the photoproduct ratios from ACOB1
would correspond to 67% and 51% cage effects in PE68 in
PE46, respectively (Table 1). On the basis of the joint analysis
of photoproduct ratios and laser-flash photolysis data, the
observed excess of AB in the polymer films is not (or not
exclusively) a result of the cage effect but rather of the persistent
radical effect (case 3 in Scheme 2).14 Accordingly, the more
slowly diffusing B‚ radicals are trapped preferentially by the
more mobile benzyl radicals (A‚). Our kinetic model separates,
for the first time, the components of the reaction from the in-
cage reaction (case 2) and of the persistent radical effect (case
3) that contribute to the excess yields of AB.
Laser-Flash (Pulsed) Irradiations. Laser-flash photolyses
of the ACOB0, ACOB1, and ACOB16 in the PE films produced
transient absorptions (with maxima near 320 nm) which are
(25) In media such as zeolites, rearrangement isomers of dibenzyl ketones have
been observed in addition to the products in Scheme 1. We found no
evidence for formation of isomers of ACOB1 or ACOB16 that would result
from recombination of the initial acyl/benzylic radical pairs after irradiations
in n-hexane or the polyethylene films. (a) Kaanumalle, L. S.; Gibb, C. L.
D.; Gibb, B. C.; Ramamurthy, V. J. Am. Chem. Soc. 2004, 126, 14366-
13467. (b) Kaanumalle, L. S.; Nithyanandhan, J.; Pattabiraman, M.;
Jayaraman, N.; Ramamurthy, V. J. Am. Chem. Soc. 2004, 126, 8999-
9006. (c) Frederick, B.; Johnston, L. J.; de Mayo, P.; Wong, S. K. Can. J.
Chem. 1984, 62, 403-410. (d) Turro, N. J.; Zhang, Z. Tetrahedron Lett.
1987, 28, 5637-5640.
(26) (a) Weiss, R. G.; Ramamurthy, V.; Hammond, G. S. Acc. Chem. Res. 1993,
26, 530-536. (b) Ramamurthy, V.; Weiss, R. G.; Hammond, G. S. In
AdVances in Photochemistry; Volman, D. H., Hammond, G. S., Neckers,
D. C., Eds.; Wiley-Interscience: New York, 1993; Vol. 18, pp 67-234.
(27) (a) He, Z.; Hammond, G. S.; Weiss, R. G. Macromolecules 1992, 25, 1568-
1575. (b) Jenkins, R. M.; Hammond, G. S.; Weiss, R. G. J. Phys. Chem.
1992, 96, 496-502. (c) Lu, L.; Weiss, R. G. Macromolecules 1994, 27,
219-225. (d) Taraszka, J. A.; Weiss, R. G. Macromolecules 1997, 30,
2467-2473.
These results are in contrast to observations of reduced cage
effects (i.e., excess yields of AA and BB photoproducts) or even
negative values of Fc according to eq 1 from photolyses of
substituted dibenzyl ketones in micelles15 and zeolites.23-25
(23) Turro, N. J.; Lei, X.-G.; Jockusch, S.; Li, W.; Liu, Z.; Abrams, L.; Ottaviani,
M. F. J. Org. Chem. 2002, 67, 2606-2618.
(24) Turro, N. J.; Lei, X.-G.; Niu, S.; Liu, Z.; Jockush, S.; Ottaviani, M. F.
Org. Lett. 2000, 2, 3991-3994.
9
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A R T I C L E S
Chesta et al.
of the initial rise to the time-resolved rise has been reported in
some cases to approach 2:1.20c,g,h This deviation has been
attributed to some photo-induced decarbonylation of arylacetyl
radicals during the laser flash.20c,g,h In our PE films, the ratio
was significantly larger than that in solution (ca. 4:1 in Figure
3a). However, this ratio (as well as the transient kinetics)
appeared to be independent of the laser-pulse energies in the
range of 40 to 120 mJ; two-photon processes (i.e., secondary
photolysis of the initially formed arylacetyl radicals within the
laser pulse) do not seem to be the major contributor to the
pronounced immediate rise. Alternatively, it has been suggested,
although not yet substantiated fully, that the weak tail of the
absorption spectrum of arylacetyl radicals may contribute to the
immediate rise.20c,g,h
Very similar transient traces and decay kinetics were observed
when different spots on one polymer film were photolyzed or
when the experiments were repeated on the same spot with a
second series of laser pulses. The latter comportment was
expected because only a very small fraction of the ketone is
converted by each laser pulse. Although it was not possible to
follow the conversion of starting ketone by UV absorbance
changes after one or two pulses, significant decomposition was
achieved at high laser energies (>120 mJ) and after >100 laser
shots: the samples became more opaque at the irradiated spots
and visual inspection of the PE0 samples showed bubble
formation, presumably from CO.
Assignment of Rise and Decay Components. Within the
time windows covered in Figure 3, fits of the decay portions of
the traces according to first-order kinetic models (assuming
pseudo-unimolecular, in-cage processes) produced more con-
sistent and better fits than when second-order fits (expected for
diffusion-dependent, bimolecular, out-of-cage combinations as
previously observed in nonviscous solvents20d) were employed.
The magnitudes of the calculated second-order rate constants
(2kr) were unreasonably large (1-5 × 109 M-1 s-1) given the
known rates of self-diffusion of molecules of similar size and
shape in polyethylene films.27,28 Furthermore, the decays from
one film that had been equilibrated in air and in argon
atmospheres for 1 month prior to pulsed photolyses were
indistinguishable over the time scale <20 µs (Figure 5). This
observation requires that the kinetics in the viscous polymer
matrices is not dictated by bimolecular diffusive processes (such
as the radical scavenging by molecular oxygen) on this “short”
time scale, but presumably by pseudo-unimolecular in-cage
combinations of benzylic radicals. Accordingly, we interpret
the protracted rise at <1 µs to decarbonylation of an arylacetyl
radical (k-CO) and the decay at <20 µs to in-cage radical-pair
combinations (kr). The values of k-CO will be discussed after
an assessment of the decay portions of the traces.
Figure 2. Interpolated normalized transient absorption spectra for benzylic
radicals from ACOB0 (‚‚‚) and ACOB16 (s) in 1.4 mm thickness PE0 films.
Spectra were obtained in a step-scan mode with 1 nm intervals and after
240 ns (ACOB0) or 400 ns (ACOB16) time delays.
characteristic of benzyl and p-alkylbenzyl radicals (Figure 2).20
The spectra resemble closely the previously reported solution
spectra (N.B., λmax ) 316 nm for the benzyl radical and λmax
)
320 nm for the p-methylbenzyl radical).20d A slight bathochro-
mic shift of ca. 1-2 nm and band broadening, which may be
due to instrumental settings and/or the polymer matrix, were
noted. Spectra from photolyses of both ACOB1 and ACOB16
contained a shoulder at 322 nm which is attributed to p-
alkylbenzyl radicals.
The kinetics of radical decay in the different polymers was
monitored at a ca. 5 nm spectral bandwidth which was
sufficiently large to allow a satisfactory monitoring light
intensity, but sufficiently small to remove most of the scatter
from the 308 nm excitation. Scattered light could be almost
eliminated for the transparent amorphous PE0 film (Figure 3),
but it remained significant for the partially crystalline PE46 and
PE68, and was most severe for the latter containing ACOB16
(Figure 4a). The interference from scattered light reduced the
accuracy of our determinations of k-CO, especially (see later).
The 5 nm spectral bandwidth was too large to permit the
decay kinetics of the benzyl and p-alkylbenzyl radicals (maxima
separated by ∼4 nm; Figure 2) to be monitored individually
when both were present. Therefore, the monitoring wavelength
was set at 320 nm, where the concomitant decay of both species
can be followed. This is near the wavelength where their molar
extinction coefficients are the same (compare ꢀ316 ) 8800 (
600 M-1 cm-1 for the benzyl radical and ꢀ320 ) 7400 ( 200
M-1 cm-1 for the p-methylbenzyl radical).20d
The transient absorption traces (e.g., Figures 3 and 4) show
features in three different time domains: an initial (“instanta-
neous”) rise, a time-resolved rise, and a decay. The initial rise
is attributed to the fast homolysis of dibenzyl ketone triplets
(i.e., Norrish type I cleavage), yielding a benzylic and arylacetyl
radical pair. The time-resolved rise is from formation of
additional benzylic radicals as decarbonylation of the arylacetyl
radical occurs. The decay is due to the combination of benzylic
radicals (as well as trapping of benzylic radicals by molecular
oxygen or trap sites within the polymer matrices at much longer
times; vide infra).
Analyses of Decays of Benzyl Radical Absorbances. The
values associated with the decay portions of the transient traces
were not directly assigned to the rate constants for in-cage
radical pair combinations because it is necessary to include the
concurrent cage escape processes. Also, the cage effects as
defined by eq 1 and the resulting mechanistic implications
provide an inadequate description of the time-resolved experi-
mental data. The contrast is most apparent when the fate of the
benzylic radicals is followed on long time scales after a laser
On the basis of a mechanism in which irradiation of dibenzyl
ketones results in cleavage of one benzylic-carbonyl bond and
the loss of CO proceeds subsequently in a dark reaction
(Scheme 3),20 the ratio of the change of optical densities (∆ODs)
for the initial “instantaneous” rise and the protracted rise in the
early time portions should be 1:1. In solution phases, the ratio
(28) Zimerman, O. E.; Cui, C.; Wang, X.-C.; Atvars, T. D. Z.; Weiss, R. G.
Polymer 1998, 39, 1177-1185.
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Mechanism of Triplet Radical-Pair Combinations
A R T I C L E S
Figure 3. Transient rise and decay profiles at 320 nm upon pulsed irradiation of ACOB0 or ACOB1 in PE0 films over (a) 2 and (b) 8 µs time scales. The
fittings of the traces in panel a using a biexponential growth and decay function are shown in red. They were performed to extract the decarbonylation rate
constants.
Figure 4. Transient rise and decay profiles at 320 nm upon pulsed irradiation of ACOB16 in PE68 at ca. 2 (a) and 8 µs (b) time scales. The ∆OD values
after 2 µs do not match in the two traces because they were recorded on different samples.
flash. Thus, if the unity Fc values for ACOB16 in the PE films
means that all radicals combine in-cage, the transient absorbance
should reach a plateau value near zero after no more than a
few µs; it does not. Instead, significant transient absorbance
extended into the ms time range for all ACOBn (Figure 5),
providing evidence that a significant fraction of radicals had
escaped from their original cages. Similar inconsistencies
between cage effects calculated by eq 1 and from pulsed
transient data were found for ACOB1. On the ms time scale,
the observed dynamic quenching by oxygen (Figure 5), which
diffuses much more rapidly than the benzylic radicals (vide
infra), does not require significant translational diffusion by the
benzylic radicals. However, the presence of some AA and BB
from ACOB1 does.
The important conclusion at this point is that the large cage
effects calculated from the photoproducts according to eq 1 are
sometimes inconsistent with much smaller cage effects revealed
by transient decay data. An additional factor must be invoked
to explain the preferential formation of AB photoproducts from
ACOB1 and ACOB16 in the PE films. As mentioned above, that
factor appears to be the persistent radical effect, which is based
on very different diffusion rates for A‚ and B‚ (case 3 of
Scheme 2).14
The values of k-CO for ACOB0 are known to depend
somewhat on solvent polarity.20a,b The value for k-CO in PE0,
(4.6 ( 0.5) × 106 s-1, is between those reported in n-hexane
(6.4 × 106 s-1) and in acetonitrile (2.0 × 106 s-1).20c More
importantly, the similarity of the values in all of the PE films
and low viscosity alkane and isoalkane solvents confirms the
lack of dependence of k-CO on viscosity that was inferred from
studies in n-alkanes;20b,g,h decarbonylation rates of acyl radicals
depend primarily on temperature and the polarity of their
immediate environments.20b,c
Nevertheless, as expected from results with di-p-substituted
dibenzyl ketones,20c-e the average k-CO values for ACOB1 and
ACOB16 (i.e., where decarbonylation of a mixture of phenyl-
acetyl and p-alkylphenylacetyl radicals is being measured) were
ca. 30% higher than that for ACOB0 in PE0. In accordance with
the Hammond postulate,29 alkylation enhances decarbonylation
rates because the products, p-alkylbenzyl radicals, are more
stable than the benzyl radical.30 Additionally, the degree of
crystallinity of the PE matrices had no effect on the k-CO values
from ACOB0 and ACOB1; the errors introduced by scattering
did not permit the same correlation to be established for
ACOB16.
Differential Diffusion of Benzylic Radicals. Different rates
of radical diffusion should influence the distributions of
photoproducts by changing the fraction of in-cage combinations
and the distribution of products from out-of-cage combinations.
In principle, the transient decays on the millisecond time scale
(Figure 4) could have yielded direct information on the mutual
diffusion rates and the bimolecular combination rate constants
Decarbonylation Rate Constants. To obtain the values of
k-CO in Table 1, the rise and early decay were fitted together
using two exponential terms (Figure 3a). The reported values,
from at least three independent measurements on three different
polymer films, have been corrected for the effects of scattered
light where required. As mentioned above, the k-CO values for
ACOB1 and ACOB16 are weighted averages for phenylacetyl
and p-alkylphenylacetyl radicals.
(29) Hammond, G. S. J. Am. Chem. Soc. 1955, 77, 334-338.
(30) Vollenweider, J.-K.; Paul, H. Int. J. Chem. Kinet. 1986, 18, 791-800.
9
J. AM. CHEM. SOC. VOL. 129, NO. 16, 2007 5017

A R T I C L E S
Chesta et al.
Scheme 3. General Kinetic Scheme Showing all Steps Included in the Fitting Model and Separated in Different Time Regimesa
a For the steps involving out-of-cage events, I and J represent either fragments A or B. As demonstrated in Supporting Information, no assumptions about
the absolute values of the dissociation equilibrium constants, KIJ, are necessary for the interpretation of the experimental data in the <30 µs time regime.
kinetic analysis was attempted. Instead, the diffusive properties
of these radicals were estimated.
The benzyl (mass 91) and p-methylbenzyl (mass 105) radicals
from ACOB1 have nearly identical sizes and shapes, and their
mass ratio, 1:1.2, is also very similar. In contrast, the benzyl
and hexadecylbenzyl (mass 315) radicals from ACOB16, with
mass ratio 1:3.5 and very different sizes and shapes, should
diffuse at very different rates. For instance, at 25 °C in
cyclohexane, the propyl radical (mass 43) has a rate constant
for self-termination of 17.0 × 108 M-1 s-1 and a diffusion
coefficient of 8.0 × 10-6 cm2 s-1, whereas the 1-octadecyl
radical (mass 253) values are 4.1 × 108 M-1 s-1 and 2.7 ×
10-6 cm2 s-1 31
. These values for the diffusion coefficients are
ca. one-third those calculated using the Smoluchowski-Einstein
model for translational diffusion and suggest that the radicals
are associated with the solvent environments more strongly than
are the corresponding alkanes.
Figure 5. Normalized relative ∆OD transient traces for ACOB0 in a PE0
film that was equilibrated with air (s) and (partially) deoxygenated by
leaving it under an Ar atmosphere for 1 month (‚‚‚). The early time portion
of the trace is expanded in the inset.
In general, solvent plays a very important role in governing
reactions and reaction pathways. Solute-solvent attractive
interactions (i.e., “solvent friction”) slow solute diffusion,32 and
benzyl and other radicals move slower than their parent
of the different benzylic radicals. However, since the kinetics
of reactive carbon-centered radicals on the millisecond time scale
is inevitably affected (and presumably limited) by radical
scavengers (molecular oxygen in even the Ar-saturated film and
an unknown concentration of polymer trap sites), no further
(31) Burkhart, R. D.; Boynton, R. F.; Merrill, J. C. J. Am. Chem. Soc. 1971,
93, 5013-5017.
(32) Yamaguchi, T.; Kimura, Y. Mol. Phys. 2000, 98, 1553-1563.
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5018 J. AM. CHEM. SOC. VOL. 129, NO. 16, 2007

Mechanism of Triplet Radical-Pair Combinations
A R T I C L E S
molecules in both alkane and hydroxylic solvents.33 Also, the
rates of diffusion of small guest molecules in the very viscous
polyethylene films are much slower (ca. 10-4) than in a liquid
such as n-hexane,27 and the difference between the rates of
diffusion of the benzyl and p-hexadecylbenzyl radical may be
increased further in polyethylene films; diffusion rates of
p-methylbenzyl and benzyl radicals, produced in the photolysis
of ACOB1 are probably very similar even in PE films.
kdBB DB.37(vi) Diffusion of a radical A‚ (or C˙ OA) and a radical
B‚ (or C˙ OB) can be expressed by an average rate constant:
kdAB ) /2(kdAA + kdBB). (vii) The rate constants for all spin-
1
forbidden, triplet radical-pair combinations, kr, are the same
(steps 6, 9, 13, 17, and 21 in Supporting Information).20c We
note that some of the in-cage processes may, in principle, be
influenced by collisions between A‚/B‚ triplet radical pairs and
molecular oxygen.38 However, the fact that the value of kr is
unchanged in the presence and absence of molecular oxygen
when ACOB0 is flash irradiated in PE0 (as indicated by the
early decay portion in Figure 5) requires that such collisions
have a very small influence on the rate of intersystem crossing
by A‚/B‚ triplets. (viii) The rate constants for “in-cage” and
“out-of-cage” decarbonylation of C˙ OR (R ) A or B) radicals,
k-CO, are the same (steps 7, 9, 11, and 12 in Supporting
Information) because the loss of CO is controlled by the
environment, temperature, and nature of R of an acyl radical.
The environments are very similar, the temperature is constant,
and the differences between the decarbonylation rates of
phenylacetyl and (p-methylphenyl)acetyl (and, presumably, (p-
hexadecylphenyl)acetyl) are known to differ by ca. 30%,20c an
amount that is large relatively but small in absolute terms. (ix)
Pairs of free radicals combine at rates proportional to their rates
of diffusion. (x) Rates of AB, AA, and BB formation from out-
of-cage reactions (triplet steps 15, 19, and 23 and singlet steps
16, 20, and 24 in Supporting Information) are determined by
spin statistics of radical-pair encounters. Formation of products
from the singlet pairs within a cage (kfIJ, where I and J represent
either of the benzylic radicals) is not shown explicitly in the
mechanism because it is assumed that the rate constant for
photoproduct formation from singlet pairs (k1r ) is much larger
A Kinetic Model Including the Persistent Radical Effect.
The mechanism in Scheme 3, which has been used in the
quantitative analyses and fittings of the transient traces in the
shorter (µs) time domains, is more elaborate than the steps
usually invoked.20 Even so, Scheme 3 is incomplete. It ignores
possible consequences from secondary cage effects (i.e., escape
by one radical and its subsequent return to the same cage),34
although such processes are expected in viscous media such as
polyethylene. Also, it is applicable only to systems in which
diffusion is Fickian.35 When application of the Smoluchowski
equation is not appropriate (e.g., when the radical centers are
attached to polymer chains whose repetition controls the
motions), more complicated models must be employed.36 Note
that the rate constant, kr, represents actually the rate of hyperfine
coupling-induced intersystem crossing, followed by fast, spin-
allowed bond formation.19 On the basis of the comparable
hyperfine coupling constants in the closely related benzylic
radicals, we assume that kr(A+A) and kr(B+B) are comparable;
kr(A+COA) may be slightly different, but this rate does not
affect Fc. The more important simplifications and assumptions
bearing directly on the kinetic expressions are listed as fol-
lows: (i) The triplet states of the ACOBn are the immediate
precursors of all lysis steps. (ii) Reactions involving formation
of the potential photoproducts, ACOA, BCOB, ACOCOA,
ACOCOB, and BCOCOB, are neglected because they were not
observed in our experiments. (iii) Probabilities for cleavage of
the A-C or B-C bonds (kR) in ACOBn3 are the same. (iv) The
diffusion coefficients D for radicals of each pair, A‚ and C˙ OA
and B‚ and C˙ OB, are the same because of their similar sizes
and shapes. (v) The rate constant for diffusion involving two
of radical A‚ (steps 18, 19, and 20 in Supporting Information)
or two of radical B‚ (steps 22, 23, and 24 in Supporting
Information), kdAA and kdBB, respectively, are proportional to
than that for cage radical escape (i.e., k1 . kdIJKIJ), so that kfIJ
r
=
1/4kdIJKIJ even in fluid media.20d,39 (xi) The laser pulses
produce a homogeneous distribution of radicals across the
irradiated polymer spot. This condition is important for analyses
of bimolecular processes. They are not examined per se here.
From Scheme 3 and these assumptions, a set of eight
simultaneous differential equations (eqs 25-33 in Supporting
Information) can be written to describe the rate processes. If
the intensity of radiation absorbed by ACOBn is invariant with
time and conversion (i.e., steady-state photolysis), the concen-
trations of all of the transient species, including the radical
intermediates, are constant (i.e., the steady-state assumption
holds), and d[AB]/dt, d[AA]/dt, and d[BB]/dt are equal to
constants. Hence, as long as the time required for the intermedi-
ates to achieve the steady-state condition is negligibly short
compared to that for the total photolysis, Fc can be written as
the corresponding diffusion coefficients: kdAA
DA and
(33) (a) Okamoto, K.; Hirota, N.; Terazima, M. J. Phys. Chem. A 1997, 101,
5269-5277. (b) Terazima, M.; Okamoto, K.; Hirota, N. J. Chem. Phys.
1995, 102, 2506-2515.
(34) (a) Rice, S. A. In Diffusion-Limited Reactions. ComprehensiVe Chemical
Kinetics; Bamford, C. H., Tipper, C. F. H., Compton, R. G., Eds.;
Elsevier: Amsterdam, The Netherlands, 1985; Vol. 25, pp 1-400. (b)
Burshtein, A. I. In Unified Theory of Photochemical Charge Separation.
AdVances in Chemical Physics; Prigogine, I., Rice, S. A., Eds.; Wiley: New
York, 2000; Vol. 114, pp 419-587.
(35) Crank, J. The Mathematics of Diffusion, 2nd ed.; Oxford Press: Oxford,
1975.
(36) (a) Neogi, P., Ed. Diffusion in Polymers; Marcel Dekker: New York, 1996.
(b) Vieth, W. R. Diffusion in and Through Polymers; Hanser: Munich,
Germany, 1991.
(d[AB]/dt) - (d[AA]/dt) - (d[BB]/dt)
(d[AB]/dt) + (d[AA]/dt) + (d[BB]/dt)
Fc )
(2)
From eq 2 and the differential equations mentioned above, it
(37) Smoluchowski, M. v. Z. Phys. Chem. 1917, 92, 129-168.
(38) The concentration of oxygen (from air) in a PE film is ∼4 × 10-4 M.38a
In a low-density PE at room temperature, the diffusion coefficients for
toluene (a model which overestimates somewhat the diffusion coefficients
of benzyl and p-methylbenzyl32,33) and molecular oxygen are ∼2 × 10-8
cm2/s38b and ∼4.6 × 10-7 cm2/s,38c respectively. Assuming a collision radius
(F′) of 5 Å and kdif ) 4πF′N(D1 + D2)/1000, a value of ∼108 L/mol-s is
calculated. Then, the rate of collision of molecular oxygen with a benzylic
radical is ∼4 × 104 s-1, somewhat slower than (but comparable to) the
rate of the in-cage reactions (kr) (see Table 1). (a) Michaels, A. S.; Bixler,
H. J. J. Polym. Sci. 1961, L, 393-412. (b) Saleem, M.; Asfour, A.-F. A.;
De Kee, D. J. Appl. Polym. Sci. 1989, 37, 617-625. (c) Michaels, A. S.;
Bixler, H. J. J. Polym. Sci. 1961, L, 413-439.
(39) The actual processes for combination of free radicals from the singlet
channel are more complex than what is shown here. The simplified
1
expression of the rate constants as
/ kdIJKIJ in eq 16, 20, and 24 of the
4
model in Supporting Information is warranted because singlet f triplet
radical-pair intersystem crossing should be much slower than an in-cage
combination, and in-cage combinations of alkyl singlet radical-pairs is a
barrierless process that can compete favorably with diffusion even in fluid
solutions39a,b (and, therefore, certainly in our PE films). (a) Strauss, O. P.;
Lown, J. W.; Gunning, H. E. in ComprehensiVe Chemical Kinetics;
Bamford, C. H., Tippen, C., Eds.; Elsevier: Amsterdam, The Netherlands,
1973; Vol. 5, p 566 and references therein. (b) Ward, H. R. Acc. Chem.
Res. 1972, 5, 18-24.
9
J. AM. CHEM. SOC. VOL. 129, NO. 16, 2007 5019

A R T I C L E S
Chesta et al.
can be shown that
equations as is done in Supporting Information. In essence, FcAB
is a function of the rate constants, kdAB, kr, and k-CO (eq 4), and
it calculates the efficiency of escape of the geminate radical
pairs from their initial cages. If kdAB . kr or kdAB . k-CO (or
both), FcAB ) 0; if some “in-cage” radical-pair combination
occurs, FcAB > 0 (i.e., AB is more than 50% of the total
photoproduct population), and 100% of the in-cage combination
corresponds to FcAB ) 1. In contrast, the generalized expression
of Fc measures all possible routes to form AB, including those
resulting from differences between the diffusion coefficients of
FcAB + R- (1 - FcAB
)
Fc )
(3)
FcAB + R+ (1 - FcAB
)
where FcAB (eq 4) is a cage effect factor and R- and R+ (eqs 60
and 61 of Supporting Information) are complex expressions
defined in Supporting Information.
kr
k-CO
FcAB
)
(4)
(
)(
)
kr + kdAB k-CO + kdAB
A‚ and B‚. As noted previously, Fc ) FcAB only if kdAA ) kdBB
.
It is also clear that if kdAA * kdBB and the radicals are not
separated in different microspaces within the medium, Fc >
There are two practical limiting conditions for Fc:
(1) Radical A‚ is the same as radical B‚ (as in the case of
irradiations of ACOB0), so that kdAA ) kdBB, R- ) 0, R+ ) 1,
and Fc ) FcAB. It is not possible to measure Fc experimentally
from the product yields of ACOB0 since AA, AB, and BB have
the same molecular structures. However, because of the similar
structures and diffusivities of A‚ and B‚ from ACOB1, the
approximation that kdAA = kdBB should be valid and FcAB values
from laser-flash experiments (vide infra) should be almost the
same as those for Fc from steady-state irradiations (i.e., the
relative yields of AA, AB, and BB).
(2) When A‚ and B‚ have very different rates of diffusion,
so that the value of Fc can be evaluated in the limit, kdBB/kdAA
f 0 (taking arbitrarily kdAA . kdBB, in keeping with the nature
of B‚ from ACOBn when n is a large number). To do so requires
an estimation of the partial limits of the three terms in each
expression for R- and R+.
FcAB
.
Analyses of Laser-Flash (Pulsed) Irradiations of Dibenzyl
Ketones. It is apparent that the concentrations of the reaction
intermediates, as well as the concentrations of the photoproducts,
are time dependent in pulsed experiments, and the value of Fc
is time dependent also (i.e., Fc(t)). Obtaining an analytical
expression for Fc(t) is a formidable task, requiring the solution
to the eight simultaneous differential equations (eqs 25-33) in
Supporting Information. It is possible to discern more easily
the qualitative changes in Fc that occur over time from
preliminary analyses of the transient absorption traces.
Immediately after a laser pulse, a defined number of radical
pairs is created. In the short (ca. 0-20 µs) time interval, Fc )
1 because the only radical combination processes that occur
are in-cage. Only at later times, when cage-escaped radicals
encounter each other, do AA and BB photoproducts begin to
appear. Hence, in the first 20 µs after a laser pulse, Fc g FcAB
even when kdAA ) kdBB! In the longer time regime, radicals
combine to give AA, AB, and BB in a 1:2:1 statistical ratio if
kdAA ) kdBB. Under these conditions, AA and BB accumulate
as the reaction proceeds, but since out-of-cage product formation
leads to [AB] ) [AA] + [BB], the value of Fc will approach
that of FcAB as time progresses and the two will be equal at
time ) ∞ (practically, less than 100 ms after the laser pulse).
This case applies exactly to ACOB0 and approximately to
ACOB1.
FcAB + Rlim (1 - FcAB
)
Lim
(Fc) )
) 1 (5)
kdBB/kdAAf0
FcAB + Rlim (1 - FcAB
)
Equation 5 (eq 72 of Supporting Information), the product of
that exercise, leads to the prediction that if kdAA . kdBB, Fc
approaches unity independent of the absolute Values of kdAA
and FcAB. Consequently, the value of Fc (calculated from steady-
state photoproduct yields and eq 1) is not the true cage effect
factor as a direct consequence of the unequal diffusivities of
radicals A‚ and B‚ and the resultant enhancement of “out-of-
cage” formation of AB.
However, if kdAA . kdBB, as in the case of ACOB16, a vastly
different scenario unfolds with time. Again, in the very early
time regime, (∆t1), Fc(∆t1) ) 1. As time progresses (for a short
transient period, ∆t2), some of those radicals A‚ which have
not combined with a radical B‚ will escape more easily from
their cages of origin and encounter other A‚ or B‚ radicals to
yield AA or AB via out-of-cage combinations. Because A‚ reacts
with itself and B‚ in this time regime, while the self-reaction
pathway for B‚ is severely attenuated because of its limited
mobility, the concentration of B‚ will increase rapidly. As a
consequence, the concentration of the slower moving (and,
therefore, more slowly combining) B‚ will increase rapidly.
During the next transient period (∆t3), radicals A‚ are confronted
with a large excess of radicals B‚, so that the formation of AB
is much more probable than formation of AA and BB (i.e.,
Fc(∆t3) ) 1). Only during the final stages (∆t4), when nearly
all radicals of A‚ have reacted (mainly with B‚), are the
remaining unreacted radicals B‚ expected to form BB. Thus,
during two transient periods, apparent Fc(∆t) values are
predicted to be very small or even negative as a result of
temporal concentration excesses of A‚ or B‚. Ideally, in the
This situation is tantamount to “the persistent radical effect”
(case 3 in Scheme 2).14 Conceptually, the low diffusivity of B‚
makes the probability of it finding another radical B‚ very small.
As a result, the concentration of B‚ in the photostationary state
will exceed that of radical A‚. Also, the diffusion rate constant
associated with the formation of AB (kdAB) is not dramatically
affected when kdAA . kdBB: although a radical Bn‚ (where n is
large and (kdBB/kdAA) f 0) can be considered as “static” during
its lifetime in a very high viscosity medium (such as a PE
matrix), the high mobility of radicals A‚ allows them to diffuse
to sites occupied by radicals B‚ to produce AB because kdAB
)
k
dAA/2. Hence, although the large accumulation of B‚ in the
photostationary state of a constant intensity irradiation experi-
ment favors the formation of BB, it is offset by the relatively
small value of kdBB; although kdAA is large, the formation of
AA is offset by the small [A˙ ]2. As a result, the efficiency of
out-of-cage formation of AB is greatly enhanced, independent
of the value of the true cage effect factor FcAB
.
The reason why FcAB always represents a true cage effect
factor while Fc does not, becomes apparent after analyzing the
9
5020 J. AM. CHEM. SOC. VOL. 129, NO. 16, 2007

Mechanism of Triplet Radical-Pair Combinations
A R T I C L E S
Figure 6. Transient absorption profile monitored at 320 nm for laser-pulsed
photolysis of ACOB1 in PE68 at 293 K (black) and the best fit according
to our model (red), as well as the estimated values of ∆OD0, ∆OD0max, and
Figure 7. Transient absorption profiles (black) monitored at 320 nm for
laser-pulsed photolysis of ACOB0 and best fits according to the fitting
model; PE0 (red), PE46 (blue), and PE68 (green) at 293 K.
∆OD0 .
e
ima in the traces (∆OD0max) according to eq 6 (eq 84 of
Supporting Information), where θr )kr/(k-CO + kr + kdAB).
absence of radical scavengers, the concentration of AA (formed
mainly during ∆t2) should equal the concentration of [BB]
(formed mainly during ∆t4) when the concentrations are summed
over all times after a laser flash.
∆ODomax ) 2(1 - θr)∆ODo
(6)
Although these mechanistic peculiarities cannot be established
in experimental detail with our current techniques, FcAB, which
always gives the true cage effect factor, is obtainable by applying
our model to the transient absorption traces in the 0-20 µs time
regime, either by fitting the traces or from the graphically
calculated absorptions (see below).
In fluid media, it is reasonable to assume that kdAB . kr + k-CO
,
and therefore the 1:1 ideal relationship should be nearly
achieved. In the polyethylene films, we have shown previously3b
(and our data fits indicate) that k-CO . kr + kdAB and, therefore,
the absorption profiles also show a similar behavior. In practice,
we estimate ∆OD0max graphically from the transient absorption
traces, and this value is used to calculate an initial estimate of
∆OD0. The value of ∆OD0 is adjusted during the process to
optimize the fit to a transient absorption profile. Table 1 contains
the optimized values of kr, kdAB and FcAB from these fits.
Approximate values of FcAB can be calculated also from the
(graphically) estimated values of ∆OD0max and ∆ODe0
(Figure 6). In the long-time regime (at least 20 µs after a laser
pulse), the absorbance is due mainly to free radicals A‚ and B‚
(eq 7). Thus, eq 8 can be written, and, after appropriate
treatment, it becomes eq 9 (eqs 88 and 94 of Supporting
Information).
Application of the Model. As noted above, preliminary
analyses of our laser-flash data clearly indicate (as expected)
that the decays in the transient traces derive from in-cage, first-
order combinations of the benzylic radicals at earlier times and
from second-order, out-of-cage combinations (as well as pseudo-
first-order scavenging processes) at later times. Fortunately, for
fitting purposes, the in-cage combinations in the PE films are
well separated in time from the other decay processes. R-Cleav-
age and acyl decarbonylation are virtually complete in <2 µs,
and triplet radical-pair combinations and radical escape from
geminate reaction cages proceed in the 0-20 µs time period.
By applying our model to the events occurring within the
first 20 µs after the ns-duration laser pulses, all terms represent-
ing second-order radical combination processes in eqs 25-33
in Supporting Information can be ignored, allowing the simpli-
fied equations to be solved. Thus, the transient traces can be
fitted empirically40 according to Scheme 3 to obtain the rate
‚
‚
∆OD = ꢀl{[A] + [B]}
(7)
(8)
k
dABK
1
1
-
=
AB t
∆ODoe
∆OD
ꢀl
constants needed to calculate FcAB. The values of k-CO
,
determined from the rise portions of the transient traces, are
kept constant while kr and kdAB are varied. Figure 6 is a typical
transient absorption profile and fit. Other examples showing
fits to transient absorptions from irradiations of ACOB0 and
ACOB16 in PE0, PE46, and PE68 are included in Supporting
Information.
As is seen in Figure 6, the sharp initial increase in the
absorbance (as well as interference from scattered light up to
50 ns after the laser pulses, in particular for the crystalline
samples) did not allow the ∆OD at t ) 0 (∆ODo) to be estimated
with reasonable precision. However, a value of ∆OD0 can be
calculated from the extrapolated zero-time absorbance max-
∆ODoe
∆ODomax
FcAB ) 1 -
(9)
The implicit advantage of eq 9 over the fitting routine (vide
infra) is that FcAB can be estimated directly from knowledge of
only the maximum absorbance extrapolated at time zero
(∆ODomax) and the absorbance from the total concentrations of
benzylic radicals which escape from their initial cages
(∆ODoe). In practice, despite the residual absorbance from
benzylic radicals undergoing second-order combinations (i.e.,
benzylic radicals which escape from their geminate cage and
react very slowly), ∆ODoe should not differ substantially from
the absorbance in the plateau and, therefore, can be taken
directly from the transient absorbance traces as shown in
Figure 6.
(40) Fitting of the experimental transient absorption traces was performed using
the generalized reduced gradient (GRG2) nonlinear optimization code.
Lasdon, L. S.; Warren, A. D.; Jain, A.; Ratner, M. ACM Trans. Math.
Software 4; Association for Computing Machinery: New York, 1978; pp.
34-50.
9
J. AM. CHEM. SOC. VOL. 129, NO. 16, 2007 5021

A R T I C L E S
Chesta et al.
However, as shown in Figure 7, this approach is not always
possible. The calculated values of FcAB for ACOB0 in PE46
(blue curve) and PE68 are nearly the same (∼0.55 and 0.54,
respectively) using both methods. However, there is no obvious
way to estimate ∆ODoe from the decay for PE0 (red curve). In
this case, our simulation of the decay portion of the trace using
the parameters obtained from the iterative fitting method
suggests that the plateau region is achieved only after 25-
30 µs. Thus, the actual period over which the transient traces
need be recorded to employ eq 9 must be determined empirically
for each sample. Regardless, when reliable values of ∆ODmo ax
and ∆ODoe are available, the values of FcAB calculated by
fitting the whole trace and using eq 9 are the same within
experimental error. This practical observation is reassuring
because it indicates the internal consistency of the model.
General Considerations and Conclusions. The data in
Table 1 are reasonable and self-consistent. Note that k-CO is
impervious to the degree of crystallinity of the PE matrices and
matches the values found in fluid solutions of similar polarity,
where such comparisons are possible.
The kr from one of the ACOBn did increase between the
completely amorphous PE0 and partially crystalline (PE46 and
PE68) films, but the differences among the kr values in one PE
film for the 3 ACOBn are nearly the same. The tentative
conclusion from these data is that the in-cage radical combina-
tion rates may increase slightly in more confining environments.
Small changes in the rates of in-cage combination of singlet
radical pairs (generated by irradiation of aromatic esters) have
also been observed when the crystallinity of the PE media is
changed.3b In those cases, in-cage combinations must involve
rotational as well as translational motions within a cage. A
combination of A‚/B‚ radical pairs requires only (but is not
limited to) rotational motions.
Crystallinity is only one of several factors that contribute to
the nature of the sites of PE in which radical pairs combine.41
The kr in Table 1 are 2-3 orders of magnitude lower than the
analogous values obtained for the combination of singlet radical
pairs in the same media.3 Since the singlet radical pairs from
the aromatic esters are similar in size to the A‚/B‚ from the
ACOBn, and the steric requirements for combination of the
singlet pairs are more severe than those of the A‚/B‚ triplets,
the rate-limiting process for in-cage combination of the triplets
must be intersystem crossing.19
The lower kr in PE0 than in PE46 and PE68 is consistent
with our prior observations that ‘stiffer’ walls of reaction cages,
such as those in interfacial regions of the partially crystalline
PEs, force pairs of radicals to interact more intimately than when
the walls are softer (as in amorphous regions of a PE).3 An
additional contributor may be ordering effects of the pairs of
benzylic radicals imposed in interfacial regions. If held pref-
erentially on the surface of a crystallite,42 an A‚/B‚ pair would
be able to find an appropriate orientation for combination
through in-plane rotational motions only.
The larger value of kdAB for ACOB16 than for ACOB0 or
ACOB1 in the 3 PE films may be indicative of more than one
type of cage even within the amorphous regions. We conjecture
that the ACOB16, because of strong London dispersive interac-
tions with long, unbranched segments of the polymer chains,
are able to reside preferentially in cages which differ somewhat
from those preferred by ACOB0 and ACOB1. If that is correct,
what appears to be faster random diffusional motion over an
average distance by a p-hexadecylbenzyl radical may, in fact,
be slower directed motion over shorter distances. Some hints
that this may be the case come from related observations in
photo-Fries reactions of 4-dodecylphenyl phenylacetate in PE
films.43 To address this issue and to determine the chain length
at which the limiting conditions for R- and R+ no longer hold,
future studies will include measurements of rates and cage
effects from radical pairs of ACOBn where 16 > n > 1.
Regardless, it is gratifying that the values of Fc and FcAB are
the same in some cases and differ in others as would be
predicted conceptually by the model.
From a practical standpoint, the model allows kinetic data
for reactions by radicals which diffuse at very different rates
within a “single-phase” medium to be analyzed quantitatively.
It fills a large gap in our ability to understand and exploit the
“persistent radical effect” in a wide range of reactions and media.
Although applied here to the photolyses of dibenzyl ketones,
the model is applicable to many other reactions, including some
involving nonradical intermediates and faster singlet-radical pair
combinations.
In conclusion, reliance on product distributions using the
customary equation for calculating Fc based on product yields
does not always provide the true cage effect. The model
developed and applied here does. It is quite tractable whenever
diffusion of the intermediate radicals is Fickian. Unfortunately,
it is not a substitute for models which treat polymerizations
where radicals diffuse in non-Fickian motions.14,18 Finally, we
note that even apparently simple, well-established photochemical
systems may have hidden complexities which can lead to
erroneous conclusions.
Acknowledgment. This article is dedicated to Professor Chen-
Ho Tung of the Technical Institute of Physics and Chemistry
and the Institute of Chemistry of the Chinese Academy of
Sciences on the occasion of the 70th anniversary of his birth.
We thank Dr. Chuping Luo for performing some of the XRD
experiments. R.G.W. thanks the U.S. National Science Founda-
tion (NSF) for its support of the research performed at
Georgetown. Georgetown University, CONICET, NSF, and the
Universidad Nacional of R´ıo Cuarto are thanked by C.A.C. for
enabling his sabbatical year at Georgetown. W.M.N. thanks the
International University Bremen for support within the graduate
program, “Nanomolecular Science.” The authors also express
their gratitude to the reviewers for several important suggestions
and constructive criticisms.
(41) (a) Gu, W.; Hill, A. J.; Wang, X.; Cui, C.; Weiss, R. G. Macromolecules
2000, 33, 7801-7811. (b) Xu, J.; Weiss, R. G. J. Org. Chem. 2005, 70,
1243-1252.
(42) (a) Wang, C.; Xu, J.; Weiss, R. G. J. Phys. Chem. B 2003, 107, 7015-
7025. (b) Konwerska-Hrabowska, J. Appl. Spectrosc. 1985, 39, 434-437.
(c) Jang, Y. T.; Phillips, P. J.; Thulstrup, E. W. Chem. Phys. Lett. 1982,
93, 66-73. (d) Parikh, D.; Phillips, P. J. J. Chem. Phys. 1985, 83, 1948-
1951. (e) Phillips, P. J. Chem. ReV. 1990, 90, 425-436.
(43) Luo, C.; Passin, P.; Weiss, R. G. Photochem. Photobiol. 2006, 82, 163-
170.
Supporting Information Available: A detailed Experimental
section and a complete derivation of the kinetic models for
treatment of steady-state and laser-flash derived data. This
material is available free of charge via the Internet at
http://pubs.acs.org.
JA067461Q
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5022 J. AM. CHEM. SOC. VOL. 129, NO. 16, 2007