Abstract
A mathematical model of two-phase frontal polymerization in a moving conversion layer is proposed. Using fractional differential-integral calculus, an analytical solution for temperatures in the vicinity of the phase boundary (melting-polymerization) and the dependence of temperature at the front on the rate of the motion of the phase transition boundary are obtained. A formula for the front advancement rate that agrees with the experimental results is found, and a method for estimating the effective activation energy of frontal polymerization is proposed.
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J. A. Pojman, D. L. Fortenberry, and V. M. Ilashenko, Int. J. Self-Propagating High-Temp. Synth. 6, 335 (1997).
A. D. Pomogailo, S. P. Davtyan, A. A. Tomchak, et al., in Proceedings of the VIII All-Union Symposium on Combustion and Explosion. Kinetics and Combustion, Chernogolovka, 1986, p. 8.
V. S. Savost’yanov, A. D. Pomogailo, S. P. Davtyan, and D. A. Kritskaya, in Proceedings of the XVI All-Union Chugaev Conference on Chemistry of Complex Compounds, Krasnoyarsk, 1987, Part 1, p. 189.
G. I. Dzhardimalieva, A. D. Pomogailo, and V. A. Volpert, J. Inorg. Organomet. Polym. 12, 1 (2002).
D. Wöhrle and A. D. Pomogailo, Metal Complexes and Metals in Macromolecules. Synthesis, Structures and Properties (Wiley-VCH, Weinheim, 2003), p. 667.
Al. Al. Berlin, G. M. Trofimova, L. K. Pakhomova, et al., J. Polym. Sci., Part C, No. 16, 2323 (1967).
N. N. Semenov, Khim. Tekhnol. Polim., Nos. 7–8, 196 (1960).
A. D. Pomogailo and G. I. Dzhardimalieva, Vysokomol. Soedin., Ser. A 46, 437 (2004) [Polymer Science, Ser. A 46, 250 (2004)].
L. P. Kholpanov and V. Ya. Shkadov, Hydrodynamics with a Dividing Surface (Nauka, Moscow, 1990) [in Russian].
L. P. Kholpanov, S. E. Zakiev, and A. D. Pomogailo, Dokl. Akad. Nauk 395, 211 (2004).
G. V. Shkadinskaya and K. G. Shkadinskii, Dokl. Akad. Nauk 397, 358 (2004).
S. P. Davtyan, A. F. Hambartsumyan, D. S. Davtyan, et al., Eur. Polym. J. 38, 2423 (2002).
A. G. Merzhanov, A. M. Stolin, V. I. Yukhvid, et al., Int. J. Self-Propagating High-Temp. Synth. 11, 45 (2002).
G. V. Zhizhin, Macrokinetics in Frontal Polymerization Reactors (Politekhnika, St. Petersburg, 1992), p. 129 [in Russian].
L. P. Kholpanov, S. E. Zakiev, and V. A. Fedotov, Teor. Osn. Khim. Tekhnol., No. 2, 1 (2003).
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives and Some of Their Applications (Nauka i Tekhnika, Minsk, 1987) [in Russian].
V. A. Ditkin and A. P. Prudnikov, Operational Calculus (Vysshaya Shkola, Moscow, 1966) [in Russian].
Thermophysical and Rheological Characteristics of Polymers: A Handbook, Ed. by Yu. S. Lipatov (Naukova Dumka, Kiev, 1977) [in Russian].
B. V. Lebedev and N. N. Smirnova, in Chemical Thermodynamics of Polyalkanes and Polyalkenes (Nizhegorod. Gos. Univ., Nizhni Novgorod, 1999), p. 274 [in Russian].
T. A. Bykova, B. V. Lebedev, V. N. Larina, et al., Vysokomol. Soedin., Ser. A 45, 921 (2003) [Polymer Science, Ser. A 45, 545 (2003)].
N. M. Emanuel’ and A. G. Knorre, Chemical Kinetics (Vysshaya Shkola, Moscow, 1962; Wiley, New York, 1973).
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This work is dedicated to Vadim Isaakovich Irzhak on his 70th birthday.
Original Russian Text © L P. Kholpancv, S.E. Zakiev, A.D. Pomogailo, 2006, published in Vysokomolekulyarnye Soedineniya, Ser. A, 2006, Vol. 48, No. 1, pp. 16–24.
This work was supported by the Russian Foundation for Basic Research, project nos. 04-03-32634 and 05-03-32254.
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Kholpanov, L.P., Zakiev, S.E. & Pomogailo, A.D. Two-phase frontal polymerization of metal-containing monomers. Polym. Sci. Ser. A 48, 11–17 (2006). https://doi.org/10.1134/S0965545X06010020
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DOI: https://doi.org/10.1134/S0965545X06010020