6. TERMINATION
6.4 Conclusions
SP-PLP-ESR is a novel pulsed laser polymerization method for detailed measurements into termination rate coefficients, kt. In this method single pulse initiation is combined with time-resolved ESR detection of the decay in pulse-laser-induced radical concentration.
As was already mentioned, it is rather difficult to report tabulated values of kt because of the chain-length dependence of the termination rate coefficient and because of its strong dependence on monomer conversion in some cases [37]. On the other hand, it is possible to give chain length-averaged kt values for a specific monomer conversion, <kt>, as well as chain length-averaged kt values for a certain chain length region. In the present work all averaged kt values are reported for the chain length region 1 < i < 1000 and monomer conversion below 30 per cent.
The data for the systems studied in this work is summarized in Tab. 6.2.
Tab. 6.2 Rate coefficients of bulk polymerization of some methacrylates at low conversion (0 to 30 %).
The conversion dependence of the average termination rate coefficients, <kt>1<i<1000, in bulk homopolymerizations of DMA, CHMA and BzMA determined at 0 °C and ambient pressure are presented in Fig. 6.17.
Inspection of Fig. 6.17 shows that DMA, CHMA and BzMA exhibit a constant average kt up to 30 per cent of conversion.
Monomer kp / All coefficients refer to 0 °C and ambient pressure
* obtained using equation for ideal kinetics (Eq. 3.6),
I obtained using Eq. 6.4
II obtained using Eq. 6.5 for intervals i < 100
5.0 5.5 6.0 6.5 7.0 7.5
lo g [< > /( L ·m ol ·s )] k
t1<<1000i–1–10.00 0.10 0.20 0.30
X
DMA CHMA BzMA
Fig. 6.17 The conversion dependence of the average termination rate coefficients,
<kt>1<i<1000, in bulk homopolymerizations of DMA (circles), CHMA (triangles) and BzMA (squares) determined at 0 °C and ambient pressure.
The results for DMA bulk polymerization show close agreement with the literature kt data obtained using the established SP-PLP-NIR technique.
The termination rate coefficients between two monomeric free radicals, kt0, are not measured directly in SP-PLP-ESR but result from the experimental data. Direct and reliable measurements of termination rate coefficients, kt, for a variety of small molecule radicals in a variety of solvents and over wide ranges of temperature have shown that in general one should have kt0 = 1⋅109 L⋅mol–1⋅s–1 in free-radical polymerization [39,40,41]. In fact, it is easy to show that the Smoluchowski equation predicts kt0 ≈ 109 L⋅mol–1⋅s–1 for free-radical polymerization in dilute solution [42]. The values of kt0 obtained in this work using Eq. 6.4 seem to be an underestimate. It could be explained as follows: the power-law dependence in Eq. 6.4 was derived for large coiled radicals [28]. Thus, kt0 characterizes the termination behavior of a fictitious species which is large and coiled but of chain length unity. In other words, the obtained values of kt0 are those that would be true if monomeric radicals behaved as macroradical coils. It comes as no surprise that kt0, which is extrapolated from the data obtained for macroradicals, does not coincide with the experimentally determined radical-radical combination rate coefficients for small radical-radicals.
6.TERMINATION 113 The results obtained so far provide strong support for the recently proposed composite model, in which termination rate coefficients, starting from small radicals, first considerably decrease, e.g., with a power-law exponent of α1 = 0.5, and subsequently, e.g., at chain lengths above i = 100, decrease to a weaker extent, e.g., with the theoretically predicted power-law exponent α2 = 0.16.
SP-PLP-ESR is particularly well suited for studies into the termination kinetics of low kp and low kt monomers, such as methacrylates with bulky ester groups or itaconates. With ESR spectrometers of enhanced time resolution being available, SP-PLP-ESR should become widely applicable toward the detailed analysis of free-radical termination kinetics.
The given examples illustrate that the novel method allows the chain-length dependence of kt
to be investigated within the entire range of chain lengths. This is the main advantage of the SP-PLP-ESR technique in comparison with other SP-PLP methods, in which one is usually restricted to one particular chain length region.
6.5 R
EFERENCES[1] Buback, M.; Egorov, M.; Gilbert, R. G.; Kaminsky, O. F.; Olaj, G. T.; Russell, G. T.;
Vana, P.; Zifferer, G. Macromol. Chem. Phys. 2002, 203, 2570.
[2] Olaj, O.F.; Schnöll-Bitai, I. Eur. Polym. J. 1989, 25, 635.
[3] Olaj, O.F.; Bitai, I.; Hinkelmann, F. Macromol. Chem. 1987, 188, 1689.
[4] Gao, J.; Penlidis, A. J. M. S. Rev. Macromol. Chem. Phys. 1996, C36, 199.
[5] Buback, M., Hippler, H., Schweer, J., Vögele, H.-P., Makromol. Chem., Rapid Commun. 1986, 7, 261.
[6] Beuermann, S.; Buback, M. Prog. Polym. Sci. 2002, 27, 191.
[7] Kowollik, C. Ph. D. Thesis, Göttingen, 1999. [8] Feldermann, A. Ph. D. Thesis, Göttingen, 2003.
[9] Buback, M.; Egorov, M.; Junkers, T.; Panchenko, E. Macromol. Rapid Commun.
2004, 25, 1004.
[10] Smith, G. B.; Russell, G. T.; Heuts, J. P. A. Macromol. Theory Simul. 2003, 12, 299.
[11] Allen, P. E. M.; Patrick, C. R. Macromol. Chem. 1961, 47, 154.
[12] Olaj, O. F.; Kornherr, A.; Zifferer, G. Macromol. Rapid Commun. 1997, 18, 997.
[13] Olaj, O. F.; Kornherr, A.; Zifferer, G. Macromol. Rapid Commun. 1998, 19, 89.
[14] Olaj, O. F.; Vana, P.; Kornherr, A.; Zifferer, G. Macromo. Chem. Phys. 1999, 200, 2031.
[15] Schweer, J. Ph. D. Thesis, Göttingen, 1988.
[16] Le Guillou, J. C.; Zinn-Justin, J. Phys. Rev. B : Condens. Matter 1980, 21, 3976.
[17] Clay, P. A.; Gilbert, R. G.; Russell, G. T. Macromolecules 1987, 20, 850.
[18] Olaj, O. F.; Zifferer, G. Macromol. Chem., Rapid Commun. 1982, 3, 549.
[19] Khokhlov, A. R. Macromol. Chem., Rapid Commun. 1981, 2, 633.
[20] Piton, M. C.; Gilbert, R. G.; Chapmann, B. E.; Kuchel, P. W. Macromolecules 1993, 26, 4472.
[21] Kamachi, M. J. Polym. Sci. Part A: Polym. Chem. 2002, 40, 269.
[22] Kamachi, M.; Kajiwara, A. Macromol. Symp. 2002, 179, 53.
[23] Zhu, S.; Tian, Y.; Hamielec, A. E. Macromolecules 1990, 23, 1144.
[24] Junkers, T. Private communication.
[25] Buback, M.; Egorov, M.; Junkers, T.; Panchenko, E. Macromol. Chem. Phys. 2005, 206, 333.
[26] Vana, P.; Yee, L. H.; Davis, T.P. Macromolecules 2002, 35, 3008.
6.TERMINATION 115
[27] Buback, M.; Egorov, M.; Feldermann, A. Macromolecules 2004, 37, 1768.
[28] Fridman, B.; O’Shaughnessy,B. Macromolecules 1993, 26, 5726.
[29] Wisnudel, M.B.; Torkelson, J. M. J. Polym. Sci., Part B: Polym. Phys. 1996, 34, 2999.
[30] de Kock, J. B. L.; van Herk, A. M.; German, A. L. J. Macromol. Sci. Part C: Polym.
Rev. 2001, 41, 199.
[31] Vana, P.; Davis, T. P.; Barner-Kowollik, C. Macromol. Rapid Commun. 2002, 23, 952.
[32] Buback, M.; Kuchta, F.-D. Macromol. Chem. Phys. 1997, 198, 1455.
[33] Ogo, Y.; Yokawa, M.; Imoto, T. Macromol. Chem. 1973, 171, 123.
[34] Moore, P. W.; Clouston, J. G.; Chaplin, R. P. J. Polymer Sci., Polym. Chem. Ed. 1981, 19, 1659 and 1671.
[35] Buback, M.; Kuelpmann, A.; Kurz, C. Macromol. Chem. Phys. 2002, 203, 1065.
[36] Kurz, C. Ph. D. Thesis, Göttingen, 1994.
[37] Handbook of Radical Polymerization, Matyjaszewski, K.; Davis, T. P., Eds.; Wiley-Interscience: New York, 2002.
[38] Beuermann, S.; Buback, M.; Davis, T. P.; Garcia, N.; Gilbert, R. G.; Hutchinson, R.
A.; Kajiwara, A.; Kamachi, M.; Lacik, I.; Russell, G. T. Macromol. Chem. Phys. 2003, 204, 1338.
[39] Fischer, H.; Paul, H. Acc. Chem. Res. 1987, 20, 200.
[40] Mahabadi, H. K. Macromolecules 1985, 18, 1319.
[41] Buback, M.; Busch, M.; Kowollik, C. Macromol. Theory Simul. 2000, 9, 442.
[42] Russell, G. T. Macromol. Theory Simul. 1995, 4, 497.