Advertisement

Simulation of Radical Polymerization Using Fixed Coefficients

  • M. N. PatrushevaEmail author
  • E. R. Muhamedzyanova
  • R. M. Khuzakhanov
Article
  • 9 Downloads

Abstract

The calculation of the number-average degree of polymerization is considered exemplified by the radical polymerization of styrene, which is carried out at 343, 348, and 353 K. The system of differential equations on the graph using corrections specified as formulas has been applied for the calculation. When using the minimum set of initial data, the error of the calculated and experimental values is 40, 33.3, and 37.5% at 343, 348, and 353 K, respectively. The inverse kinetic problem has been solved.

Keywords:

differential equation on the graph mathematical model radical polymerization degree of polymerization styrene 

Notes

REFERENCES

  1. 1.
    Benson, S.W, The Foundations of Chemical Kinetics, New York: McGraw-Hill, 1960.Google Scholar
  2. 2.
    Vol’pert, A.I. and Khudyaev, S.I., Analiz v klassakh razryvnykh funktsii i uravneniya matematicheskoi fiziki (Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics), Moscow: Nauka, 1975.Google Scholar
  3. 3.
    Galeev, E.R., Lezhneva, N.V., Elizarov, V.V., and Elizarov, V.I., Mathematical modeling of the polymerization of butyl rubber, Vestn. Tekhnol. Univ., 2016, vol. 19, no. 23, p. 92.Google Scholar
  4. 4.
    Ulitin, N.V., Tereshenko, K.A., Deberdeev, T.R., Nasyrov, I.I., Samarin, E.V., and Kalinina, D.Sh., Pseudolive radical polymerization of butyl acrylate in the presence of trithiocarbonates: Modeling the kinetics and regulation of the molecular mass characteristics of the polymer, Theor. Found. Chem. Eng., 2015, vol. 49, no. 1, pp. 75–83.  https://doi.org/10.1134/S0040579515010145 CrossRefGoogle Scholar
  5. 5.
    Aminova, G.A., Antonova, I.O., Bronskaya, V.V., Manuiko, G.V., Ignashina, T.V., and Ismagilova, A.I., Mathematical modeling of the synthesis of butyl rubber, Vestn. Kazan. Tekhnol. Univ., 2012, vol. 15, no. 4, p. 103.Google Scholar
  6. 6.
    Tefera, N., Weickert, G., Bloodworth, R., and Schweer, J., Free radical suspension polymerization kinetics of styrene up to high conversion, Macromol. Chem. Phys., 1994, vol. 195, pp. 3067–3085.  https://doi.org/10.1002/macp.1994.021950906 CrossRefGoogle Scholar
  7. 7.
    Khanukaeva, I.A. and Kolesnikov, G.S., Study of the kinetics of styrene polymerization in viscous media, Vysokomol. Soedin., Ser. A, 1968, vol. 10, no. 5, p. 1127.Google Scholar
  8. 8.
    Bagdasar’yan, Kh.S., Teoriya radikal’noi polimerizatsii (The Theory of Radical Polymerization), Moscow: Nauka, 1966.Google Scholar
  9. 9.
    Sawada, H., Thermodynamics of Polymerization, New York: Marcel Dekker, 1976.Google Scholar
  10. 10.
    Ismagilova, A.S. and Spivak, S.I., Matematicheskoe modelirovanie khimicheskikh protsessov (Mathematical Modeling of Chemical Processes), Ufa: Bashk. Gos. Univ., 2014.Google Scholar
  11. 11.
    Krasnov, K.S., Vorob’ev, N.K., Godnev, I.N., Vasil’eva, V.N., Vasil’ev, V.P., Kiseleva, V.L., Belonogoe, K.N., and Gostikin, V.P., Fizicheskaya khimiya. V 2 kn. Kn. 2. Elektrokhimiya. Khimicheskaya kinetika i kataliz (Physical Chemistry, vol. 2: Electrochemistry: Chemical Kinetics and Catalysis), Moscow: Vysshaya Shkola, 1995.Google Scholar
  12. 12.
    Vol’pert, A.I., Differential equations on graphs, Mat. Sb., 1972, vol. 88 (130), no. 4 (8), p. 578.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • M. N. Patrusheva
    • 1
    Email author
  • E. R. Muhamedzyanova
    • 1
  • R. M. Khuzakhanov
    • 1
  1. 1.Institute of Polymers, Kazan National Research Technological UniversityKazanRussia

Personalised recommendations