Photochemistry and Photobiology, 20**, **: *–*
Decay Kinetics of Benzophenone Triplets and Corresponding Free Radicals in Soft and Rigid Polymers Studied by Laser Flash Photolysis† Peter P. Levin1,2, Alexei F. Efremkin2, Natalie B. Sultimova1, Valery V. Kasparov1 and Igor V. Khudyakov*,§,3 1
Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Moscow, Russia Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia 3 Department of Chemistry, Columbia University, New York, NY 2
Received 8 February 2013, accepted 9 March 2013, DOI: 10.1111/php.12170
ABSTRACT
the best-studied molecules in photochemistry (1). Photoexcitation of B with ns UV–light pulses leads to the formation of triplet state 3B*and subsequently to ketyl radicals BH●, which are formed by H-atom abstraction or electron transfer with subsequent H+ transfer from a donor (1). In a number of polymers one can observe three processes: decay kinetics of 3B*, cage (geminate) recombination of radicals pairs (RP) consisting of BH● and a polymer radical and decay of BH● in the polymer bulk (4,5). The polymer can thus be characterized by the rates and relative contributions of these processes in the overall decay of photoexcited B. Moreover, the magnetic properties of BH● are well known, and MFE on RPs with BH● in microheterogeneous media and viscous liquids have also been studied (6–8). Therefore, MFE during B photoreduction in polymers can give complementary information on the polymer cage. Weiss and co-authors used another informative probe of cage effect in polymers namely derivatives of dibenzyl ketone (DBK) (9,10). B undergoes photoreduction in polymers, whereas DBK experiences Norrish splitting I in polymers. Refs. (4,5,9) and a review article (10) give both good introduction and the current status of research on cage effect dynamics in polymers. This study is an examination of the primary photoreactions of B in polymers of different nature namely hard polystyrene (PS), soft rubbers poly(ethylene-co-butylene) EB and triblock copolymer polystyrene-block-poly(ethylene-ran-butylene)-block-polystyrene SEBS.
The kinetics of transients formed under photoexcitation of benzophenone (B) dissolved in three different polymers was studied by ns laser flash photolysis. These polymers were the soft rubbers poly (ethylene-co-butylene) (EB), polystyrene block-poly(ethylene-ran-butylene)-block-polystyrene (SEBS) and hard polystyrene (PS). We monitored the decay kinetics of triplet state 3B*and of ketyl radicals BH●. We observed exponential decay of 3B* and two-stage decay kinetics of BH●in EB. The first stage is a fast cage recombination of a radical pair (BH●, radical of polymer R●). The second slow stage of BH● decay follows the second-order law with a relatively high rate constant, which corresponds to recombination of BH● in a homogeneous liquid with a viscosity of only ~0.1 P (about five times of 2-propanol viscosity). Application of a magnetic field (MF) of 0.2 T leads to deceleration of both stages of BH● decay in EB by approximately 20%. Decay kinetics of both transients were observed in SEBS. There was no MF effect on BH● decay in SEBS. We only observed 3B* in PS. Decay kinetics of 3B* in this case were described as polychromatic dispersive first-order kinetics. We discuss the effects of polymer structure on transient kinetics and the MF effect.
INTRODUCTION Experimental studies of cage (geminate) recombination of radicals and magnetic field effects (MFE) in microheterogeneous media like micelles and zeolites were pioneered by Turro et al. (1,2). The kinetics of cage recombination in viscous liquids have also been previously described (3). We have expanded this research direction to solid polymers (4,5). Polymers restrict mobility of free radicals compared to nonviscous liquids, which allows examination of cage recombination kinetics and MFE. We demonstrated that ns laser photolysis of benzophenone (B) provides valuable information on elementary reactions in polymers, and on polymer properties as well (4,5). B is one of
MATERIALS AND METHODS Materials. B and solvents were obtained from Sigma-Aldrich and used as received. The polymers used in this study were as follows: PS with Mw = 100 kg mol1, poly(ethylene-co-butylene) (EB) grade Engage 7467 (Mw = 74 kg mol1, crystallinity 12% (11), both from Dow and polystyrene-block-poly(ethylene-ran-butylene)-block-polystyrene (SEBS) with Mw = 118 kg mol1 from Sigma-Aldrich (analog of Kraton G1650 of Kraton). SEBS has 29% of PS (12). The purchased polymers were purified as follows: they were dissolved in chloroform, twice precipitated from chloroform solution by iso-propanol, air dried and finally dried in a vacuum at ambient temperature. Devices. The absorption spectra and kinetics of formation and decay of intermediates were measured with a nanosecond laser photolysis apparatus (4,5,13,14). A PRA LN 1000 N2 laser (with pulse duration of 1 ns and emission wavelength of k 337 nm), operating at ≤10 Hz frequency was used as an excitation source. Acquisition and averaging of kinetic curves (128 laser pulses) were performed by a UF258 high-speed
*Corresponding author email:
[email protected] (Igor V. Khudyakov) §Current address: Igor V. Khudyakov, Solutia, a subsidiary of Eastman, VA, USA †This manuscript is part of the Special Issue in honour of Dr Nicholas Turro © 2013 The American Society of Photobiology
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digitizer (Sweden) connected to a PC, based on Intel Core i7 processor. Each initial kinetic curve contained 1216 bits of points or a number of data 409665536, with the time interval between the points being 4– 400 ns. The vertical resolution was 8 bit. The data presented in this study are average values obtained by processing at least ten kinetic curves under the aforementioned conditions. All kinetic measurements were made at 20°C in a fused silica cell 1 cm 9 1 cm 9 3 cm. A polymer films with B (cf. below) was placed in the cell. The air was removed from the samples by prolonged evacuation. In experiments with magnetic field (MF) application, the cell was placed between the poles of a permanent magnet (magnetic flux density B = 0.2 T). Laser flash irradiated area of only 1 mm 9 2 mm. After each experiment (128 laser pulses) the cell of cm size was slightly moved up or down to enable irradiation of a fresh portion of the film. Preparation of polymer films. Films were cast from solutions of B and a polymer in chloroform on a cellophane support. The solvent was evaporated slowly and films were air dried prior to drying in a vacuum at ambient temperature. Cellophane support was delaminated using water, and the films were subsequently air dried. The thickness of the prepared films was 100 lm, and the density of polymers was measured. Film thickness was used as the optical path l alongside with extinction coefficients e during calculations of second-order rate constants. The prepared films had a concentration of 0.1 M B in the solid polymers.
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Peter P. Levin et al.
O.D. x 10
2
6 c 4 b 2 a 0 0
2
4
6
8
time, μs
10
Figure 2. Kinetics of 3B* measured at k 630 nm obtained under laser flash photolysis of EB film (a) Decay kinetics of 3B* and BH● measured at k 545 nm without (b) and with (c) magnetic field in the same film. Solid black lines in this and subsequent Figures are the computer fit of experimental curves to theoretical formulas described in the text.
RESULTS AND DISCUSSION B in EB film
O.D. x 10
3
Triplet state of B. Laser excitation of B in EB films leads to the formation of triplet state 3B* (1). 3B* has a characteristic absorption spectrum (Fig. 1a) (1,4,5). The observed spectrum in tested films is similar to the known absorption spectrum of 3B* in other media: it has kmax = 525 nm and a shoulder at 600–700 nm (Fig. 1a). The decay kinetics of 3B* were measured in the spectral area k > 600 nm, where absorption by other transients is negligible. In particular, we selected k = 630 nm for kinetic measurements (Fig. 2a). The decay kinetics of 3B* in EB film was nicely simulated by a single exponent (Fig. 2a) with the first-order rate constant kT, presented in Table 1. 3B* completely decayed during 0.5 μs (Fig. 2a). We have observed dispersive kinetics of 3B* decay in a number of other polymers in which the reactivity of C–H bonds toward 3B* and rates of radiationless decay of 3B* apparently depend upon the microenvironment (4,5,15,16). We conclude that 3B* behaves in EB as it would within a homogeneous matrix similar to a liquid. Relatively high kT in EB testified to the high reactivity of C–H bonds in EB, which contains tertiary C–H bonds with low BDE.
8 6 4
a
2
b
0 500
550
600
650
700 λ, nm
Figure 1. Absorption spectra of transients obtained under laser flash photolysis of B in EB film with a delay after laser flash of: (a) 20 ns; (b) 0.5 ls. O.D. refers to optical density in this and subsequent Figures.
Table 1. Rate constants of 3B* decay, recombination and dissociation of radical pairs, cage effect values ϕ† and recombination of BH● in the polymer bulk‡ in EB in Earth’s magnetic field and in external magnetic field. Parameter
B0
B = 0.2 T
kT 9 106, s1§ kobs 9 106, s1§ kesc 9 106, s1§ krec 9 106, s1§ ϕ§ k4 9 107, M1 s1¶
6.9 1.2 0.89 0.31 0.26 11
6.9 1.0 0.89 0.11 0.10 8.9
†Cf. Scheme 1 and Eq. (2). ‡Cf. this Section below. §Determination error 10%. ¶Determination error 5%.
Cage reaction of ketyl radical BH●. A new transient is observed at ~0.5 μs after the laser flash (cf. Fig. 1b). This new transient is the well-documented ketyl radical of B formed in the reaction: (1,4,7) 3
B þ RH ! 3 ½BH R ;
ð1Þ
where RH is a polymer matrix with labile tertiary C–H groups. BH● has a characteristic absorption maximum at kmax = 545 nm (cf. Fig. 1b) (1,4,5,13), so we studied the decay of BH● at kmax. Obviously, the optical absorption of C-centered aliphatic radical R● locates at much shorter wavelength and its absorption coefficient is small and we did not observe R●. Therefore, 3B* and BH● can be differentiated in EB by their absorption spectra and by the fact that the radicals decay much slower than triplet state (Fig 2a–c). Comparison of initial absorption 3B* at k 525 nm with the absorption of BH● at k 545 nm 0.5 μs after laser pulse (cf. Fig. 1a,b) demonstrates that practically all 3B* yielded BH●. This comparison included the literature data on extinction coefficients in benzene: e530 = 7220 and e545 = 4600 M1 cm1 of 3 * B and BH●, respectively (16,17). Thus, practically all 3B* decays according to reaction (1). Initially formed triplet radical pair (G-pair) either dissociates into free radicals or recombines within a polymer cage, as shown in Scheme 1: (3,8).
Photochemistry and Photobiology
-2
(O.D.) x 10
4
cag e
esc
ape
BH. + R.
-1
3
BH.....R.
5
Products
O.D. x 10
3
on ati nin m o c e re cag
3
We imply by “recombination” here bimolecular reaction between these two radicals which could be disproportionation as well. As an approximation, the recombination and cage escape are considered as first-order reactions with corresponding krec and kesc, s1 (3,8). This is so-called exponential model of the cage or of RP. It should be assumed that R●, a radical centered on the polymer chain and has very low translational mobility, and BH● escapes the cage. The usually modest signal-to-noise ratio observed during the study of cage kinetics justifies in a sense such approximation, and some overlay of a cage recombination and recombination in the polymer bulk prohibits high accuracy. The rate constant of caged radicals decay is kobs = krec + kesc, s1, and the cage effect values: (3) ð2Þ
are presented in the Table 1. In accordance with our expectations, application of MF leads to a decrease of krec and ϕ (Fig 2b,c, Table 1) (6–8). The MFE value bG is defined as: bG ¼ ðuo uB Þ=uo ¼ 0:58
ð3Þ
Superscripts B and o distinguish reactions in MF and in Earth’s MF, respectively. ϕ decreased twofold in MF, as shown in Table 1. The observed MFE is most probably due to the action of hyperfine coupling (HFC) mechanism (1,6–8). Application of moderate MF leads to removal from the intersystem crossing T+ and T levels of an RP, and bG should be 2/3 if HFC mechanism operates alone (1,6–8). (The value 2/3 can be obtained using Eqs. (2) and (3) of the simplified exponential model and a suggestion that kesc ≫ krec and krecB = 1/3 9 kreco [1,6–8].) That is apparently our case, and bG [Eq. (3)] is equal to 2/3 with bG’s determination error (20%). krecB is approximately three times less than kreco in accordance with HFC mechanism and kesc > krec (Table 1). The action of spin-orbit coupling in the pair and the relaxation mechanism may result in the exact bG value being somewhat less than 2/3, Eq. (3) (6). As expected, kesc does not depend upon MF within the determination error of this value (Table 1) (8). Decay of BH● in the polymer bulk. BH●, which escaped the cage, slowly decays in the polymer bulk (Fig. 3) and participates in two concurrent reactions: BH þ R ! B þ RHðpredominantlyÞ
ð4Þ
BH þ BH ! BH BHðpinacolÞ
ð5Þ
Observed BH● decay fits well to the second-order kinetic law like it would be only reaction (4) or (5), cf. Fig. 3c. However, the system is relatively stable photochemically (amount of [BH●]o did not decrease noticeably even after 100+ laser pulses) demonstrating that the reaction (4) is the dominating one. The
8 6 4 2
Scheme 1. Two reactions of a radical pair.
u ¼ krec =kobs
3
2
0.0
b
0.5
1.0
1.5 time, ms
2.0
a
1
.
c
0 0.0
0.5
1.0
1.5
time, ms
2.0
Figure 3. Decay kinetics of BH● measured at k 545 nm at times ≥1 ls obtained under laser flash photolysis of B in EB films with (a) and without (b) external MF and in SEBS at times ≥0.1 ms (c). Insert: A fit of curve (c) into the second-order kinetic law.
“mixed-radical back-reaction” (17), i.e. disproportionation is known for BH●. The rate constant k4 is presented in the Table 1. According to Debye formula, diffusion-controlled bimolecular reactions proceed with kdiff ~ 108 M1 s1 in a liquid with a viscosity of ~0.1 P (1,8). The obtained k4 is close to kdff. The observed diffusion of low-MW molecules through rubbery polymers is usually smooth and easy (18–20). Diffusion of molecules through rubber is strongly facilitated by high segmental mobility, large amount of free volume, low cross-linking density or even lack of cross-linking. Our three polymers are known to not be cross-linked at all (11,12), and they are soluble in solvent, as mentioned above. Thus, it is not surprising that the decay of BH● is fast and most likely diffusion controlled in EB with its low Tg = 58°C (11). Application of MF leads to the expected deceleration of reaction (4), cf. Fig. 3a,b, Table 1 (6). Interestingly, the EB matrix allows fast movement of low-MW radicals like a liquid of moderate viscosity, and demonstrates essential cage effect and MFE like a liquid of high viscosity. Polymer chains in the block copolymer EB are structured: they have individual relatively large blocks of polyethylene (long methylene chains) and of polybutylene. This causes a significant percent of crystallinity in EB namely 12%, cf. above (11). Apparently, this structure of EB results in the formation of “microreactors” (1) either in the vicinity of polyethylene crystalline fragments or between ethyl brushes of polybutylene. Magnetic field effects. We observed MFE on cage radical pairs (G-pairs) and radical pairs formed in the polymer bulk (F-pairs), cf. Fig 3a,b (6). We concluded that G- and F-pairs consist of the same two radicals [BH● … R●]. We use a simple approach for comparison of MFEs on the same pair in the same solvent (21). The probability of recombination of F-pairs in the Earth’s MF is: po ¼ 0:25 þ 0:75 uo ¼ 0:44
ð6Þ
The similar probability in the field is: pB ¼ 0:25 þ 0:75 uB ¼ 0:33
ð7Þ
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Peter P. Levin et al.
The values of ϕo,B were taken from Table 1.The experimental MFE value bF is defined as: B o o kbulk Þ=kbulk ¼ 0:19 bF ¼ ðkbulk
ð8Þ
Calculated MFE is defined as: bF ¼ ðpB po Þ=po ¼ 0:25
ð9Þ
For the values of po,B cf. Eqs. (6) and (7). Thus, properly compared experimental and calculated bF values are similar. Calculation of bF accounts for MFE on G-pairs namely the values of ϕo,B .This similarity of MFEs [Eqs. (8) and (9)] is in accordance with our hypothesis that the polymer environment in F- and G- cages of EB is practically the same and that HFC is the predominant mechanism of MFE. B in PS film Laser photoexcitation of B in PS leads to the appearance of only 3 * B , characterized by its known absorption spectrum at all times of examination (from several ns to 100 μs). The decay kinetics of 3B* in PS did not follow exponential law (Fig. 4a). The kinetics of chemical reactions in most solid polymers are governed by different laws than kinetics in liquids. They are usually dispersive kinetics due to the distribution of species reactivity with different environments. A possible promising approach for quantitative description of kinetics in polymers was suggested in a study referenced in (22). It is assumed that first-order elementary reactions in polymers have a Gaussian distribution of the logarithm of first-order rate constants (22). Such a suggestion leads to the following analytical expression for the kinetic curve: CðtÞ pffiffiffi ¼ p Cð0Þ
Z1 expðx2 Þ exp½kav t expðcxÞdx;
ð10Þ
1
where C(t) and C(0) are current and initial concentrations of reagents, respectively, kav is the average value of the first-order rate constant and c is the width of distribution. Our previous experiments on kinetics in polymers demonstrated the usefulness of
O.D. x 10
3
5 4 3 a
2 1 b 0 0
10
20
30
time, μs
40
Figure 4. Decay kinetics of 3B* measured at k 630 nm obtained under laser flash photolysis of B in PS (a) and SEBS (b) films. Data in (a) were fitted to dispersive first order (10), and data shown in (b) were fitted to a combination of the first order and dispersive first order (10), as described in the text.
Eq. (10) (4,5). Here, we used Eq. (10) to simulate kinetics of 3B* decay (Fig. 4a). The values of kav and c obtained as a result of the fit of experimental data (Fig. 4a) into Eq.(10) are presented in Table 2. c-Values obtained in PS (Table 2) are similar to the values obtained previously for decay of 3B*in other polymers (4,5). The obtained kav is much higher than that of poorly reactive 3 * B in siloxane (5), but significantly less than kav obtained for relatively soft urethane acrylates (as compared to PS) (4). We assume that 3B* still decays predominantly by fast reaction (1) despite the lack of BH● in this experiment. It is probable that the primary product—a contact triplet radical pair or a loose molecule—is formed in a conformation favorable for fast recombination in the triplet state due to spin-orbit coupling in the contact RP, which may be considered as a quasi molecule. The hard matrix of PS holds radicals together long enough to allow such recombination. The characteristic time of recombination of similar triplet contact RPs in liquids or in microheterogeneous media is assumed to be less than 1 μs (23–25). B in SEBS film It is known that SEBS is a continuous polyolefin matrix of EB with embedded PS fragments (18). In this case, the PS contributes 29% of SEBS mass. Obviously B is distributed between EB and PS phases of SEBS. We assume that decay kinetics of 3B* in EB and decay kinetics of 3B* in PS contribute to the observed 3 * B decay kinetics. Kinetics of decay in EB is first order, whereas kinetics of decay in PS is dispersive, cf. Sections B in EB film and B in PS film above. In accordance with these suggestions, the observed decay of 3B* at k 630 nm was satisfactorily described by the sum of the first-order kinetics (kT) and dispersive kinetics (kav, c), cf. Fig. 4b. These values, which were obtained by computer simulation with relative contributions of the two suggested types of decay, are presented in Table 2. We assume that the relative contribution of decay of 3B* in EB and PS phases is proportional to the concentration of the starting B in one or another fraction. It follows from Table 2 that the contribution of 3B*/PS to kinetics is much higher than the contribution of PS into SEBS. Apparently, B is congested in the PS fraction of SEBS because PS has benzene rings that favor B solubility (19). We observed an absorption of BH● upon complete 3B* decay at t > 100 μs. Semiquantitative estimations based on initial concentrations of 3B*and BH● lead to the conclusion that only 20% of initial 3B* decays into BH●, which is in accordance with a fraction of 3B* decaying in EB (Table 2). 3B* decay in PS (fraction) does not lead to BH●, cf. above. Decay kinetics of BH● in the polymer bulk are described by the second-order law and most likely occur according to reaction (4), cf. Fig. 3c. The k4 value is presented in Table 2, which shows that k4 obtained in SEBS is slightly less than k4 in EB (Table 1). Unfortunately, cage recombination is not observed in SEBS due to being masked by the relatively slow decay of 3B* in PS fraction. There is no MFE on the decay of BH● in SEBS or, more precisely, |bF| ≤ 2%, cf. Table 2. EB and SEBS have similar physical/mechanical properties (11,12). The Tg of both polymers is 58; 60°C, elongation to break 560%; 600%, Shore A hardness 52; 72. Both polymers have polyethylene and polybutylene blocks. While we observed MFE in EB, we did not observe it in SEBS. Diffusion or penetration of low-MW molecules and radicals through polymers has studied in great detail, cf. e.g. (19,20).
Photochemistry and Photobiology
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Table 2. Rate constants of 3B* and BH• decay in PS and SEBS. SEBS PS
EB fraction 5
kav 9 10 , s c
1
4.2 2.5
6
1
PS fraction
kT 9 10 , s
7.2
Mass fraction‡ Contribution into kinetics† k4 9 107, M1 s1§
71% 20%
5
1
kav 9 10 , s c Mass fraction‡ Contribution into kinetics†
7.2 3.1 29% 80%
6.8
†See text for definition and explanation of parameters. ‡According to the manufacturer, cf. Materials Section. §Determination error of 5%, using the same e545 and the same optical path l; k4 refers to decay in SEBS.
However, diffusion on a microscopic scale and during short time interval is less well understood. Occurrence of MFE requires repetitive or successive contacts of radicals, which in our case involve BH● and the macroradical R● (6). In the case of EB, F- or G-pairs have a high probability of being produced or meeting partners inside a microreactor where segmental diffusion is relatively low. We suggested earlier that microreactors can be defined as either volumes in the proximity of polyethylene crystalline fragments or volumes between ethyl brushes of polybutylene. SEBS is a random block copolymer without any crystallinity (12), and therefore F-pairs in SEBS have a low probability of meeting inside ethyl brushes of polybutylene that are in a low concentration within triblock SEBS. The latter suggestion explains, in our opinion, the lack of MFE in SEBS. The principles of random walking and repetitive contacts in polymeric media and the reactivity of polymer radicals are currently not well developed. Repetitive contacts between a lowMW radical with a specific polymer atom, e.g. an atom bearing a free valence, may not occur at all due to high segmental mobility. A polymer chain at T ≫ Tg quickly changes its configuration during random wandering of the low-MW radical in the vicinity of the radical center of polymeric R●. The polymer radical center can become temporary hidden, and the polymer chain during segmental movements can simply push away low-MW radical. Acknowledgements—This work was partially supported by the Russian Academy of Sciences under Presidium Programs no. 7 and 8 and by the RFBR (Project no. 13-03-00396a). IVK is grateful to the late Professor N. J. Turro for valuable discussions on the cage effect problems over the years.
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8. Khudyakov, I. V. (2013) Transient free radicals in viscous liquids. Res. Chem. Interm. 39, 781–804. 9. Abraham, S., I. Ghosh, W. M. Nau, C. Chesta, S. J. Pas, A. J. Hill and R. G. Weiss (2012) In-cage and out-of-cage combinations of benzylic radical pairs in the glassy and melted states of poly(alkyl methacrylate)s. Photochem. Photobiol. Sci. 11, 914–924. 10. Chesta, C.A. and R. G. Weiss (2010) Dynamics of radical pair processes in bulk polymers. In Carbon-centered free radicals and radical cations, (Edited by M. D. E. Forbes), pp. 281–324. Wiley, Hoboken, NJ. 11. Dow (2012) ENGAGETM Literature. Available at: http://www.dow. com/elastomers/lit/engage_lit.htm. Accessed on 15 September 2013. 12. Roland, C. M. (1999) Kraton G1600 SEBS. In Polymer Data Handbook, (Edited by J. E. Mark), pp. 161–164. Oxford University, London. 13. Kutsenova, A. V., N. B. Sultimova and P. P. Levin (2010) Kinetic characteristics of the photoreduction of benzophenone in solid polymers in the presence of 4-halogen substituted penols. Russ. J. Phys. Chem. 4, 834–838. 14. Kutsenova, A. V., P. P. Levin and V. B. Ivanov (2002) Molecular dynamics and evolution of radical pairs in glassy polymers. Russ. J. Polym. Sci. Ser B. 44, 124–126. 15. Kawai, A., M. Hirakawa, T. Abe, K. Obi and K. Shibuya (2001) Specific solvent effects on the structure and reaction dynamics of benzophenone ketyl radical. J. Phys. Chem. A 105, 9628–9636. 16. Hurley, J. K., N. Sinai and H. Linschitz (1983) Actinometry in monochromatic flash photolysis: The extinction coefficient of triplet benzophenone and quantum yield of triplet zinctetraphenylporphyrin. Photochem. Photobiol. 38, 9–14. 17. Inbar, S., H. Linschitz and S. G. Cohen (1981) Nanosecond flash studies of reduction of benzophenone by aliphatic amines. quantum yields and kinetic isotope effects. J. Amer. Chem. Soc. 103, 1048–1054. 18. Hamley, I.W. (2004) Introduction to block copolymers. In Developments in Block Copolymer Science and Technology (Edited by I.W. Hamley), pp. 5–13. Wiley, New York, NY. 19. Kovarski, A. L. (1997) Molecular Dynamics of Additives in Polymers. VSP BV, Utrecht. 20. George, S. C. and S. Thomas (2001) Transport phenomena through polymeric systems. Prog. Polym. Sci. 26, 985–1017. 21. Margulis, L. A., I. V. Khudyakov and V. A. Kuzmin (1985) Magnetic field effect on radical recombination in a cage and in the bulk of a viscous solvent. Chem. Phys. Lett. 119, 244–250. 22. Albery, W. J., P. N. Bartlett, C. P. Wilde and J. R. Darwent (1985) A general model for dispersed kinetics in heterogeneous systems. J. Am. Chem. Soc. 107, 1854–1858. 23. Levin, P. P., Y. N. Malkin and V. A. Kuzmin (1990) Laser flash photolysis study of ketone-phenol-cyclodextrin inclusion complexes. Geminate recombination kinetics of triplet radical pairs. Chem. Phys. Lett. 175, 74–78. 24. Levin, P. P. and V. A. Kuzmin (1992) Magnetic field, additive and structural effects on the decay kinetics of micellized triplet radical pairs. Role of diffusion, spin-orbit coupling and paramagnetic relaxation. Chem. Phys. 162, 79–93. 25. Levin, P. P., N. B. Sultimova and O. N. Chaikovskaya (2005) Kinetics of fast reactions of triplet states and radicals under photolysis of 4,4’-dimethylbenzophenone in the presence of 4-halogen substituted phenols in micellar solutions of sodium dodecyl sulfate in magnetic field. Russian Chem. Bull. 54, 1433–1438.
