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Kinetics of Radical Chain Polymerization: 2. Linear Waves of Macroradical Growth

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Abstract

The chain growth in radical chain polymerization is associated with the wave of transformation of primary radicals into macroradicals. The change in chain length n and molecular mass distribution R(t, n) with time t corresponds to the movement of a wave packet with velocity dn/dt and width ∆(n), both dependent on monomer concentration M(t). The formation of macroradicals in the absence of chain transfer when the rate constant of chain growth K(n) depends on n has been considered, and it has been shown that the packet is described by the Poisson distribution law with the event probability depending on K(n) and t. As K(n) decreases, R(t,n) narrows and its maximum shifts to the region of the minimum of K(n). Relations of K(n), M(t), and R(t, n) to dn/dt and ∆(n) have been found.

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REFERENCES

  1. Ziff, R.M., J. Stat. Phys., 1980, vol. 23, p. 241.

    Article  Google Scholar 

  2. Hendriks, E.M., Ziff, R.M., and Ernst, M.H., J. Stat. Phys., 1983, vol. 31, p. 519.

    Article  Google Scholar 

  3. Kuchanov, S.I., Adv. Polym. Sci., 1992, vol. 103, p. 3.

    Google Scholar 

  4. Spicer, P.T. and Pratsinis, S.E., AIChE J., 1996, vol. 42, p. 1612.

    Article  CAS  Google Scholar 

  5. Davies, S.C., King, J.R., and Wattis, J.A.D., J. Phys. A, 1999, vol. 32, p. 7745.

    Article  Google Scholar 

  6. Leyvraz, F., Phys. Rep., 2003, vol. 383, p. 95.

    Article  CAS  Google Scholar 

  7. Kuchanov, S.I., Slot, H., and Stroeks, A., Prog. Polym. Sci., 2004, vol. 29, p. 513.

    Article  CAS  Google Scholar 

  8. Wattis, J.A.D., Bolton, C.D., and Coveney, P.V., J. Phys. A, 2004, vol. 37, p. 2895.

    Article  CAS  Google Scholar 

  9. Wattis, J.A.D., J. Phys. A, 2006, vol. 39, p. 7283.

    Article  Google Scholar 

  10. Wattis, J.A.D., Physica D (Amsterdam), 2006, vol. 222, p. 1.

    Article  Google Scholar 

  11. Kim, I.P., Kats, E.I., and Benderskii, V.A., High Energy Chem., 2019, vol. 53, no. 4, p. 265.

    Article  CAS  Google Scholar 

  12. Gentekos, D.T., Dupuis, L.N., and Fors, B.P., J. Am. Chem. Soc., 2016, vol. 138, p. 1848.

    Article  CAS  PubMed  Google Scholar 

  13. Lynd, N.A. and Hillmyer, M.A., Macromolecules, 2005, vol. 38, p. 8803.

    Article  CAS  Google Scholar 

  14. Lynd, N.A. and Hillmyer, M.A., Macromolecules, 2007, vol. 40, p. 8050.

    Article  CAS  Google Scholar 

  15. Matyjaszewski, K., Science, 2011, vol. 333, p. 1104.

    Article  CAS  PubMed  Google Scholar 

  16. Plichta, A., Zhong, M., Li, W., Elsen, A.M., and Matyjaszewski, K., Macromol. Chem. Phys., 2012, vol. 134, p. 3834.

    Google Scholar 

  17. Kim, I.P. and Benderskii, V.A., High Energy Chem., 2010, vol. 44, no. 5, p. 357.

    Article  CAS  Google Scholar 

  18. Kim, I.P. and Benderskii, V.A., High Energy Chem., 2011, vol. 45, no. 5, p. 372.

    Article  CAS  Google Scholar 

  19. Kim, I.P. and Benderskii, V.A., High Energy Chem., 2015, vol. 49, no. 1, p. 1.

    Article  CAS  Google Scholar 

  20. Kim, I.P., Martynenko, V.M., Chernyak, A.V., and Benderskii, V.A., High Energy Chem., 2017, vol. 51, no. 4, p. 285.

    Article  CAS  Google Scholar 

  21. Gao, C. and Yan, D., Prog. Polym. Sci., 2004, vol. 29, p. 183.

    Article  CAS  Google Scholar 

  22. Thickett, S.C. and Gilbert, R.G., Polymer, 2007, vol. 48, p. 6965.

    Article  CAS  Google Scholar 

  23. Zhao, T., Zheng, Y., Poly, J., and Wang, W., Nat. Commun., 2013.

  24. Tobita, H., Processes, 2018, vol. 6, p. 1.

    Article  CAS  Google Scholar 

  25. Liu, S., Srinivasan, S., Grady, M.C., Soroush, M., and Rappe, A.M., Int. J. Quantum Chem., 2014, vol. 114, p. 345.

    Article  CAS  Google Scholar 

  26. Yu, Q., Zhou, M., Ding, Y., Jiang, B., and Zhu, S., Polymer, 2007, vol. 48, p. 7058.

    Article  CAS  Google Scholar 

  27. Kim, I.P. and Benderskii, V.A., High Energy Chem., 2019, vol. 53, no. 3, p. 183.

    Article  CAS  Google Scholar 

  28. Loskutov, A.Yu. and Mikhailov, A.S., Vvedenie v sinergetiku (Introduction to Synergetics), Moscow: Nauka, 1990.

  29. Mikhailov, A.S. and Ertl, G., Chem. Phys. Chem, 2009, vol. 10, p. 86.

    Article  CAS  PubMed  Google Scholar 

  30. World Scientific Lecture Notes in Complex Systems, book 11: Engineering of Chemical Complexity, Mikhailov, S.A. and Ertl, G., Eds., Singapore: World Scientific, 2013.

    Google Scholar 

  31. Dodd, R.K., Eilbeck, J.C., Gibbon, J.D., and Morris, H.C., Solitons and Nonlinear Wave Equations, London: Academic, 1982.

    Google Scholar 

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Correspondence to V. A. Benderskii.

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Translated by S. Zatonsky

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Kim, I.P., Benderskii, V.A. Kinetics of Radical Chain Polymerization: 2. Linear Waves of Macroradical Growth. High Energy Chem 53, 341–350 (2019). https://doi.org/10.1134/S0018143919050072

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  • DOI: https://doi.org/10.1134/S0018143919050072

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