Photopolymerization of Vinyl Acrylate Studied by PhotoDSC

The study revealed a new phenomenon in fast free-radical polymerization: .... i.e., polymerization after termination of photointiation6 In eq 1, [M]0 ...
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APPLIED CHEMISTRY Photopolymerization of Vinyl Acrylate Studied by PhotoDSC Igor V. Khudyakov,* William S. Fox, and Michael B. Purvis Alcatel Telecommunications Cable, Claremont, North Carolina 28610

Polymerization of neat vinyl acrylate (VA) photoinitiated by phosphine oxide initiator in a nitrogen atmosphere was studied by photo differential scanning calorimetry (photoDSC). The study revealed a new phenomenon in fast free-radical polymerization: spontaneous temporary cessation of heat release (i.e., temporary termination of the polymerization) or temporary reduction of the polymerization rate. Such a phenomenon, named “stumbling polymerization”, includes a fast initial photopolymerization of VA up to a monomer conversion of ξ ≈ 10%, with the first maximum rate of polymerization achieved not later than at 3 s after the beginning of irradiation under our experimental conditions; a temporary cessation of polymerization; and a resumed photopolymerization up to ξ ≈ 100%. Experiments on photopolymerization of neat VA without a photoinitiator allowed us to obtain the ratio of the termination rate coefficient (2kt) to the propagation rate coefficient (kp); 2kt/kp decreased from ∼300 at the beginning of polymerization to a value of ∼2 at the final stage of polymerization. Introduction The polymerization of solutions of monomers or of neat monomers is usually accompanied by the reduction of the volume of the reactive solution. Dilatometry, one of the standard methods of monitoring the kinetics of (photo)polymerization, is based on the shrinkage of the monomer solution during polymerization.1,2 In the case of fast free-radical photopolymerization of neat acrylates, the rate of acrylate volume change is not necessarily directly proportional to the rate of reaction. For example, it was demonstrated that conversion of double bonds during photopolymerization of some neat diacrylates runs ahead of volume relaxation.3 We can assume that, in extreme cases, a difference in the rate of consumption of double bonds and the rate of change of the volume of the polymerizable solution is so large that chemical reaction temporally ceases as a result of spatial separation of the reagents. Relaxation of the volume of the partially polymerized solution brings reagents (radicals of initiator, macroradicals, and monomer molecules) into contact and thus resumes polymerization. To test this hypothesis, we studied the photopolymetrization of the very reactive vinyl acrylate (VA) by photo differential scanning calorimetry (photoDSC). VA is known and labeled as a “light-sensitive” compound, which testifies to its high reactivity under UV irradiation. Experimental Section VA and isobornyl acrylate (IBOA) were both obtained from Aldrich. The photoinitiator bis(2,4,6-trimethylbenzoyl)phenylphosphine oxide was from Ciba Additives. * To whom correspondence should be addressed. Phone: 828-459-8526. Fax: 828-459-9346. E-mail igor.khudyakov@ cable.alcatel.com.

It has the trade name Irgacure 819, and its name is abbreviated here as BAPO. The concentration of BAPO in solutions was 1-5%. 1,1,1-Trichloroethane was from Fisher. All reagents and the solvent were used as received. We also used VA and IBOA with the inhibitor removed with the help of basic alumina.4 The purities of the compounds used in this work were 95% and higher. We used two photoDSC devices to monitor the heat produced during polymerization. Most of the experiments were done with a Perkin-Elmer photoDSC DPA-7 instrument. An Osram 100- or 200-W Hg lamp was used as the light source. Irradiation of the samples was performed with full light of different intensities. The UV-light intensity (1-55 mW/cm2) was measured with a radiometer/photometer (International Light). We present below results obtained with the DPA-7 instrument with a light intensity of 25 mW/cm2 unless stated otherwise. We also used a DuPont 930 differential photocalorimeter (TA Instruments). The radiation source was a 200-W medium-pressure Hg lamp, with a light intensity of 20 mW/cm2. Experiments with both DSC devices were performed in the usual way.4-6 The instruments were calibrated with indium. Samples were placed into a standard aluminum DSC pan, and the reference aluminum pan was empty. Samples on the pan were flushed with nitrogen for 10 min prior to irradiation. DSC traces, or thermograms, were recorded under isothermal conditions. Each sample had a mass of 3-25 mg, as weighed in air. We weighed chilled VA to minimize evaporation of the samples. PhotoDSC experiments were performed at reduced temperatures. A chilling system was used for the two instruments: it consisted of either a flux of nitrogen from a Dewar flask or the circulation of cooled 2-propanol from a chillier with i-PrOH ice. We present data for experiments perfprmed at 10, 3, and -10 °C.

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The mass of the pan with the sample measured before and after irradiation did not change within experimental error. At least five experiments were performed with each solution under the same conditions, and the average values of the heat released, Q (J/g), were obtained. The shortest time of irradiation provided by the DPA-7 instrument is 0.6 s. We use below the term “prolonged” irradiation for irradiation that lasts 1 min or longer and the term “pulse” irradiation for irradiation with a duration of 0.6 s up to a few seconds, followed by dark periods. All IR spectra were recorded as ATR FT IR spectra with a Nicolet Magna-IR 550 spectrometer, whose spectral resolution is 4 cm-1. The rate of the slow cure of VA was monitored with a CM 1000 cure monitor (Spectra Group Ltd.) at ambient temperature. The measurements were performed as described elsewhere.4 Another method of monitoring the slow cure of VA is real-time (RT) IR spectroscopy. This type of experiments was done in nitrogen atmosphere at ambient temperature and was used to measure the disappearance of the acrylate band at ν ) 1406 cm-1 under irradiation. In experiments with the cure monitor, the RT IR light sources had a low intensity of less than 1 mW/cm2. A lightingcure 200 UV spot light source (Hamamtsu) of variable intensity was used for steady-state irradiation of solutions in the reaction vessel or on top of the diamond crystal of IR spectrometer. In the latter case, the thickness of acrylate on the diamond was a few micrometers. The conversion, ξ, i.e., a percentage or fraction of the VA or IBOA mass consumed during photopolymerization, was monitored by IR spectroscopy, cf. the Results section below. IR spectra of IBOA, VA, and their solutions were taken before, after, and during irradiation. We used IgorPro software in the kinetic analysis.

Figure 1. IR (FT ATR) spectra of VA with BAPO (3%) (a) before and (b) after irradiation for several minutes.

Figure 2. PhotoDSC trace obtained during polymerization of VA (10 mg) with BAPO (3%) at 10 °C. Irradiation started at t ) 1.0 min and ended at t ) 3 min.

Results VA polymerizes upon UV irradiation in inert (nitrogen) atmosphere in the presence of BAPO and even in the absence of BAPO. The absorption spectrum of VA is red-shifted toward the absorption spectrum of most acrylates, and IBOA in particular. (The probable reason for the bathochromic shift in the absorption spectrum of VA is hyperconjugation between the two double bonds in VA.) In the presence of BAPO, VA can be photopolymerized in the air. Figure 1 presents the IR spectra of neat VA in a glass vessel before and after prolonged irradiation. One can see that all acrylate groups (ν ) 1625, 1406, and 812 cm-1)7 were consumed, whereas the vinyl group (1645 cm-1)7,8 does not markedly change upon irradiation. (C-H vibrations were used as the internal standard.)5 Practically the same spectra of cured VA (Figure 1b) were observed under prolonged irradiation in the photoDSC pan or on the crystal of the spectrometer. PolyVA prepared by photopolymerization of neat VA is a gummy substance. VA does not form films upon photopolymerization, in contrast to IBOA. We found that polyVA was soluble in THF and aromatic solvents. Figures 2-5 display the photoDSC traces of VA samples obtained under different conditions. An arrow labeled EXO on all of the photoDSC traces presented in this work demonstrates the direction of heat flow in the exothermic photopolymerization.

Figure 3. PhotoDSC trace obtained during polymerization of VA (10 mg) with BAPO (3%) at 10 °C. The sample was subjected to irradiation by five light pulses, each with a duration of 0.6 s; the pulses started at 0.5, 1.0, 1.5, ... min.

A photoDSC study of solutions of neat VA revealed an interesting phenomenon: the fast initial release of heat during photopolymerization is followed by a temporary cessation of the reaction, cf. Figure 2. The data of Figure 2 and of other experiments on prolonged irradiation of VA demonstrate that the heat released in the first pulse is ca. 10% of the total heat. One can see a temporary cessation of heat release on the plots presented in Figures 3 and 4. We named this phenomenon stumbling polymerization. Under our experimental conditions, we did not observe stumbling polymerization, i.e., splitting of the DSC trace into two, after a single pulse of 0.6 s but did observe it after a single pulse with a duration of 1.8 s and longer.

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Figure 4. PhotoDSC traces obtained during polymerization of VA with BAPO (3%) at -10 °C. Samples with masses of (a) 15 and (b) 20 mg were subjected to irradiation by 10 light pulses, each with a duration of 0.6 s; the pulses started at 0.5, 1.0, 1.5, ... min.

Figure 5. PhotoDSC trace obtained during polymerization of VA with BAPO (3%) at 10 °C with the TA Instruments device. The sample was irradiated during 0.5-1.5 and 2.0-2.5 min.

Figure 6. Standard photoDSC trace obtained during polymerization of IBOA with BAPO (3%) at 10 °C.

We performed experiments with another photoDSC device and with another well-studied acrylate, IBOA,5 with the purpose of investigating criteria for the manifestation of stumbling polymerization. Figure 5 presents a trace obtained for VA on a TA Instruments DSC instrument, which has an acquisition rate that is ca. 10 times lower than that of DPA-7 instrument. One can see only a shallow minimum on the DSC trace, cf. Figure 5. A standard DSC trace for IBOA with no stumbling was obtained with the DPA-7 instrument under similar conditions, cf. Figure 6. The prolonged irradiation of VA or IBOA resulted in the maximum possible heat release from a sample at a given temperature. We obtained 330 ( 30 J/s for IBOA

Figure 7. Kinetics of photopolymerization of IBOA with BAPO (3%) at ambient temperature obtained with (top) cure monitor; (bottom) RT IR, curve a. Curve b presents the fit of the data to first-order kintics. C represents the concentration (IR absorption) of IBOA.

and 450 ( 30 J/g for VA at 10 °C. (The mass of each sample was 5-12 mg.) We irradiated samples of VA with single light pulses with durations of 0.6n s, where n is 1, 2, ..., etc. The temporary cessation of polymerization was observed with relatively large samples (5 mg and more), under a high light intensity, and after a certain irradiation time. Under our experimental conditions, stumbling polymerization was observed when the first peak was reached no later than 3.0 s after the beginning of the prolonged irradiation and after pulsed irradiation with a pulse duration of no less that 1.8 s. In these and our previous experiments,4 within the experimental error of the DSC measurements, we did not observe a difference between VA (IBOA) liberated from an inhibitor and VA (IBOA) used as received. The dilution of VA with 1,1,1-tricholoroethane by not more than ca. two times did not affect the emporary cessation of polymerization. Further dilution led to typical smooth DSC traces. We studied the photopolymerization of VA initiated by BAPO with a cure monitor and RT IR spectroscopy, cf. Experimental Section (Figure 7). Relatively slow photopolymerization of VA initiated by a weak light source in thin layers demonstrated smooth cure curves with both techniques. A cure profile obtained with a cure monitor manifested an “induction period”4 of ca. 80 s. During this 80-s period, the viscosity and polarity of the VA solution did not change enough to be detected by the cure monitor.4 We fit the kinetics of the polymerization of VA obtained by IR spectroscopy (Figure 7) to a first-order law and obtained k ) 0.75 ( 0.05 s-1. The polymerization of neat IBOA was accompanied by the reduction of the volume of the solution with the formation of a transparent polymer. The polymerization of neat VA and a concentrated solution of VA in 1,1,1trichloroethylene resulted in the formation of a gummy (see above) or snow-like polymer. There was no evident decrease in the level of the flask contents after the polymerization of neat VA or a concentrated VA solution in 1,1,1-trichloroethylene.

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Figure 9. Dependence of 2kt/kp vs ξ for the polymerization of VA at 3 °C in the absence of a photoinitiator, see the text.

Figure 8. (a) PhotoDSC trace obtained during polymerization of VA at 3 °C in the absence of a photoinitiator; (b) calculated ratio of [VA]/R vs time, see the text.

As stated above, VA polymerizes under UV irradiation even in the absence of a photoinitiator. We subjected neat VA to tens of light pulses. No stumbling polymerization was observed in the absence of photoinitiator, cf. Figure 8a. Heat flow is identified with the rate of polymerization R.5,6 We used a known method, described in particular in ref 6, to obtain time- or conversiondependent ratios of the termination and propagation rate coefficients, 2kt/kp, for the polymerization of neat VA. Our analysis involves the use of photoDSC in the determination of the dimensionless 2kt/kp ratio during polymerization, an approach that we shall show provides useful information on photopolymerization. From formal kinetics, eq 1 can be derived for dark or post polymerization, i.e., polymerization after termination of photointiation6

[M]t/Rt - [M]0/R0 ) (2kt/kp)t

(1)

In eq 1, [M]0 (R0) is the monomer concentration (rate of polymerization) at the beginning (t ) 0) of dark polymerization monitoring; [M]t and Rt are the concentration and rate, respectively, at time t. Equation 1 can be used to determine 2kt/kp (which is assumed to be constant over a limited range of conversion ξ). We determined 2kt/kp at different values of ξ as follows. IR spectra show that the photoirradiation of VA on the photoDSC pan for several minutes results in the complete consumption of VA and in the formation of the polymer polyVA. The total heat released, Qtot, during complete polymerization (ξ ) 100%) is presented above in this section. A release of heat during polymerization up to Qtot can be identified with the decrease of the concentration of VA from the initial value of [M]tot to 0. Figure 8a presents the photoDSC traces obtained during the irradiation of neat VA with 30 light pulses. The duration of each pulse is 0.6 s, with 30 s between pulses. The photoDSC trace presents the rate of polymerization dQ/dt (W) ) R.5,6 Most of the observed trace is dark polymerization, lasting 10-20 s after a light pulse, cf. Figure 8a.

Integration of the DSC traces over t allows for an estimation of the heat released during polymerization, Q ) Q(t) (J). Figure 8b presents the time dependent ratio (Qtot - Q)/[dQ/dt] (s). The latter ratio should be equal to [M]/R. We analyzed 30 ascending parts of the curve in Figure 8b, corresponding to five descending parts of the photoDSC trace of Figure 8a. We fit each of the ascending parts of the curve in Figure 8b to a linear law. The piece of each ascending curve corresponding to 5-95% of the ordinate of the curve was analyzed.5 A tangent to each linear fit was identified with 2kt/kp, cf. eq 1. In such a way, we obtained 2kt/kp. Figure 9 presents the dependence of 2kt/kp vs ξ that was obtained from the data of Figure 8b. Discussion An intriguing observation of this work is the phenomenon that we named “stumbling polymerization”. The phenomenon was observed during fast polymerization and is attributed to an essential difference between the rates of polymer formation and volume relaxation (or any other structural rearrangement of a forming polymer). The difference in rates between these two phenomena leads to a situation in which free radicals are spatially separated from monomer molecules of VA. Adjustment of the matrix brings them into contact. We also found that polyVA is practically insoluble in VA. That fact, in our opinion, testifies to the suggestion that reactive radicals are temporarily buried in polyVA. Thermal rearrangement of polyVA in VA brings reactive radicals into contact with nonreacted VA. Thus, Scheme 1 aims to explain the stumbling polymerization observed at moderate conversions: Scheme 1

Here, VA is nonreacted monomer, (VA)n is the polymer polyVA, Q represents the heat released during polymerization, Rn• represents a macroradical, τ is the characteristic time of volume relaxation at a certain conversion, and the brackets designate spatially separated reagents. According to Scheme 1, fast polymerization of neat VA causes negative feedback, which

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leads to either the temporary retardation or the complete termination of polymerization. The following formula was suggested to account for the volume contraction with conversion (ξ) during polymerization at constant temperature9-11

V(ξ) ) V0(1 + ξ)

(2)

where  is the volume expansion factor determined by  ) (Fm - Fp)/Fp and Fm and Fp are the densities of monomer and polymer, respectively. It is assumed that the volume of a polymerizable mixture is determined only by the conversion ξ, eq 2 and that the volume contraction follows an increase in ξ without a delay. We have a more complicated case in which V is a function of ξ and time, and the essence of this process is reflected by eq 3

V(ξ,t) ) V0(1 + ξ) + ∆V(ξi) exp(-ti/τi)

(3)

where τi has the same meaning as τ defined above, ξi represents several intermediate conversions at which polymerization terminates for a short time, and ∆V is the excess volume. ∆V quickly decreases with time ti; in a simple possible approach, that decrease is exponential. At ti . τi, eq 2 reduces to eq 1. In a broader sense, the second term in eq 3 reflects relaxation of a volume of a solution VA/polyVA, which proceeds more slowly than polymerization. Variation of V(ξ,t) probably occurs smoothly during polymerization, whereas polymerization itself, as we have mentioned already, temporary terminates or essentially reduces in rate. Experiments on slow polymerization performed with photoDSC, cure monitor, and RT IR spectroscopy (Figure 7) did not reveal any unexpected kinetics. A faster photopolymerization measured with RT IR at reduced temperatures might reveal unusual kinetics. It is likely that the volume relaxation has a stronger temperature dependence than the polymerization rate and that stumbling reaction is vividly observed at reduced temperatures. Our results testify to the suggestion that, at room temperature, or especially at reduced temperatures, the volume relaxation is probably slow compared to the rate of the fast photopolymerization. A number of reports in the literature describe oscillation phenomena in rather complex systems with freeradical polymerization12-15 with an adequate quantitative analysis.12,13 However, we do not see a direct relevance between these reports and our stumbling photopolymerization in the very simple system of acrylate and a photoinitiator. To the best of our knowledge, there are no reports in the literature on the propagation and termination rate constants of VA in any media or on kp/x2kt. One can assume that VA has very high rate of polymerization. We note that the rate constant of addition of phosphoruscentered radicals of a phosphine oxide initiator to VA is one the highest values reported thus far in the literature, namely, kadd ≈ 3.3 × 107 M-1 s-1 (ethyl acetate, room temperature).16 The loose gummy form of polyVA allows us to monitor the dark polymerization of VA after pulse irradiation up to the very high conversion of ξ ≈ 0.9, cf. Figure 8. The solubility of polyVA suggests a linear, noncrosslinked structure for this polymer. The same conclusion was made about polyVA prepared by free-radical, anionic, and other polymerizations of solutions of VA.7,8,17,18 It

seems that we reached, or almost reached, the expected limit when both propagation and termination are controlled by diffusion5 and that we obtained the lowest value of 2kt/kp ≈ 2, cf. Figure 9. In similar experiments with IBOA, we were able to reach only 2kt/kp ≈ 20 at 50 °C.5 It was concluded that the polymerization of VA in solutions at elevated temperatures is accompanied by cyclopolymerization with the formation of polymers with δ-lactone or larger cyclic units.7,17 However, cyclization does not much affect our estimations of the 2kt/kp ratio. Cyclization includes isomerization of a macroradical; evidently cyclization does not change the total concentration of Rn•. The contribution of intramolecular cyclization is lower in neat VA Than in the solutions of VA studied in refs 7 and 17 because of the larger contribution of intermolecular propagation at high concentrations of VA. Thus, the kp and kt values discussed above are two effective rate coefficients that do not account for any difference in the reactivities of linear and cyclized Rn•. (It is known that, even in the case of free-radical polymerization without cyclization or other complications, both kp and 2kt are chain-lengthdependent.19,20 Strictly speaking, they are not kinetic rate constants, and they are usually effective coefficients in a standard formal kinetic treatment.) The IR spectra of polyVA obtained in this work are similar to those reported elsewhere.7,8 An important conclusion is that the vinyl group remains essentially intact during polymerization. The rates of addition of phosphorus-centered radicals to acrylic groups are ∼15 times higher than the rates of addition of the same radicals to vinyl groups in VA.16 One should expect that, at high conversions of VA, the vinyl group should also react with radicals. There was a natural concern that the observed phenomenon might be related to any device effect and not to photopolymerization per se. We have evidence, however, that this is not the case. Stumbling polymerization was observed for two ranges of heat flow detection (up to 320 mW and up to 720 mW). We were not able to reach even the 320-mW heat flow limit in our experiments. If a limit is reached, the device demonstrates a horizontal line at 320 or 720 mW but does not demonstrate any oscillations in the heat release. If the heat flow occurs faster in reality than the data acquisition, the DSC trace will be presented with a certain lag, but such a lag cannot lead to any oscillations. We ran experiments with the photoDSC apparatus from TA Instruments that collects ca. 10 times fewer points during a given time period than the photoDSC instrument from Perkin-Elmer, cf. the Results section above. The phenomenon of stumbling polymerization was less evident with the TA device, cf. Figure 5. A slow device essentially “overlooks” stumbling polymerization as a result of its low acquisition rate. The evaporation of VA should result in heat flow of the opposite sign and could lead to the observation of two peaks on a DSC trace instead of the usual DSC trace with one maximum. However, we consider such a reason for stumbling polymerization improbable because the mass of our samples did not change during photopolymerization. The splitting of the central peaks (cf. Figures 3 and 4), rather than the first peak, in a DSC trace testifies to the fact that the new phenomenon lies in the physics and chemistry of the system and not in the detection method.

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In fact, it is known that the highest rate of polymerization is achieved after a certain level of conversion of monomer into polymer because of the gel effect. We believe that it is logical that, in a series of pulses, stumbling polymerization is observed not during the first light pulse or the last light pulse, where conversion is very small (ξ ≈ 0.05) or rather high (ξ ≈ 0.8), but during the second and third (and fourth) pulses (Figures 3 and 4), where the viscosity has been increased and dead polymer chains have been forming. Conclusions The aim of this paper was to demonstrate the experimental observation of a new phenomenon called stumbling polymerization. We found the following requirements for the occurrence of stumbling polymerization: isothermal conditions of reaction and fast polymerization of a certain mass of monomer. A probable additional requirement is the formation of a loose structure of an acrylate polymer. “Fast” polymerization means a relatively high concentration of effective photoinitiator and/ or a relatively high light intensity. In our experiments with VA, we noticed that stumbling polymerization takes place under prolonged irradiation when the first maximum in heat evolution is achieved no longer than at 3 s after the initiation of irradiation and for a “certain mass” of no less than 5 mg of VA. The rate of polymerization and the mass are two critical parameters in the splitting of DSC curves. We envision a multitude of necessary experiments for the further exploration of this phenomenon, such as determining the temperature dependence of stumbling polymerization and identifying its occurrence by other techniques and with other monomers. Literature Cited (1) Fouassier, J.-P. Photoinitiation, Photopolymerization, and Photocuring: Fundamentals and Applications; Hanser: Munich, Germany, 1995. (2) Vedeneev, A. A.; Khudyakov, I. V.; Golubkova, N. A.; Kuzmin, V. A.; Irinyi, G. External Magnetic Field Effect on the Dye-Photoinitiated Polymerization of Acrylamide. J. Chem. Soc., Faraday Trans. 1990, 86, 3545. (3) Klosterboer, J. G.; van de Hei, G. M. M.; Gossink, R. G.; Dortant, G. C. M. The Effect of Volume Relaxation and Thermal Mobilization of Trapped Radicals on the Final Conversion of Photopolymerized Diacrylates. Polym. Commun. 1984, 25, 322. (4) Khudyakov, I. V.; Legg, J. C.; Purvis, M. B.; Overton, B. J. Kinetics of Photopolymerization of Acrylates with Functionality of 1-6. Ind. Eng. Chem. Res. 1999, 38, 3353.

(5) Williams, R. M.; Khudyakov, I. V.; Purvis, M. B.; Overton, B. J.; Turro, N. J. Direct and Sensitized Photolysis of Phosphine Oxide Polymerization Photoinitiators in the Presence and absence of a Model Acrylate Monomer: A Time-Resolved EPR, Cure Monitor, and PhotoDSC Study. J. Phys. Chem. B 2000, 104, 10437. (6) Tryson, G. R.; Shultz, A. R. A Calorimetric Study of Acrylate Photopolymerization. J. Polym. Sci., Polym. Phys. 1979, 17, 2059. (7) Fukuda, W.; Nakao, M.;. Okumura, K.; Kakiuchi, H. Polymerizations of Vinyl Methacrylate and Vinyl Acrylate. J. Polym. Sci. A 1972, 10, 237. (8) Pokrovskaya, E. M.; Komarov, N. V.; Klochkova, T. V.; Pushkareva, K. S. Anionic Polymerization of Vinyl Acrylate. Izv. Vyssh. Uchebn. Zaved. 1984, 27, 961. (9) Chiu, W. Y.; Carratt, G. M.; Soong, D. S. A Computer Model for the Gel Effect in Free-Radical Polymerization. Macromolecules 1983, 16, 348. (10) Achilias, D. S.; Kiparissides, C. Development of a General Mathematical Framework for Modeling Diffusion-Controlled FreeRadical Polymerization Reactions. Macromolecules 1992, 25, 3739. (11) Seth, V.; Gupta, S. K. Free Radical Polymerization Associated with the Tromsdorff Effect Under Semibatch Reactor Conditions: An Improved Model. J. Polym. Eng. 1995, 15, 283. (12) Kurbatov, V. A.; Ivanova, A. N.; Furman, G. A.; Denisov, E. T. Kinetic Model of Oscillating Polymerization of Styrene Inhibited by Phenols. Khim. Fizika 1984, 3, 1316. (13) Gorot, K. F.; Kozak, G. Yu.; Marinchenko, A. V.; Bondar, M. V.; Przhonskaya, O. V.; Tikhonov, E. A. Polymethine Dye Photobleaching Kinetics During Radical Polymerization. Zh. Prikl. Spektrosk. 1988, 49, 573. (14) Kiryukhin, D. P.; Barelko, V. V.; Barkalov, I. M. Travelling Waves of Cryochemical Reactions in Radilolyzed Systems. High Energy Chem. 1999, 33, 133. (15) De Freitas, M. F.; Pinto, J. C. Dynamics of Continuous Isobutylene Cationic Polymerizations. J. Appl. Polym. Sci. 1996, 60, 1109. (16) Weber, M.; Khudyakov, I. V., Turro, N. J. J. Phys. Chem. B, manuscript submitted. (17) Fukuda, W.; Yamano, Y.; Tsuriya, M.; Kakiuchi, H. Mechanism of Copolymerizations of Vinyl Acrylate, Methacrylate, and R-Chloroacrylate. Polym. J. 1982, 14, 127. (18) Kanno, S.; Syouji, Y.; Hosoi, M.; Sato, R.; Takeishi, M. Group Selective Linear Polymerization of Vinyl Acrylate Using 9-Borabicyclo[3.3.1]nonane. Polym. Int. 1997, 42, 367. (19) Olaj, O. F.; Vana, P.; Zoder, M.; Kornherr, A.; Zifferer, G. Is the Rate Constant of Chain Propagation kp in Radical Polymerization Really Chain-Length Independent? Macromol. Rapid Commun. 2000, 21, 913. (20) Burshtein, A. I.; Khudyakov, I. V.; Yakobson, B. I. Fast Reactions between Radicals. Pseudodiffusion Control. Prog. React. Kinet. 1984, 13, 221.

Received for review January 25, 2001 Revised manuscript received April 24, 2001 Accepted May 8, 2001 IE010082F