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Steady State and Equilibrium in Reversible Copolymerization at Constant Comonomer Concentrations
Author(s) -
Szymanski R.,
Sosnowski S.,
Cypryk M.
Publication year - 2017
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.201700039
Subject(s) - comonomer , copolymer , monte carlo method , thermodynamics , equilibrium constant , constant (computer programming) , steady state (chemistry) , statistical physics , chemistry , polymer chemistry , materials science , physics , mathematics , polymer , organic chemistry , statistics , computer science , programming language
Selected aspects of copolymerization processes carried on at constant comonomer concentrations are analyzed theoretically and modeled by Monte Carlo method. It is confirmed that some combinations of initial parameters lead to stationary conditions of copolymer formation for both irreversible and reversible systems which can be regarded as the first‐order Markov chain process. However, this study shows that for many copolymerization systems the stationary conditions are attained only at high number‐average degree of polymerization DP n , and for some reversible copolymerizations, attaining equilibrium, stationary conditions are not observed at all. The analysis shows that the chain length distribution (CLD) for copolymerization carried out under steady state conditions at constant comonomer concentrations, equal to equilibrium concentrations for infinitely high DP n , is approximately described by the modified Bessel and exponential functions. This type of CLD is analytically proved and confirmed by the Monte Carlo simulations for the analogous homopolymerization process.