Cascade Theory of Substitution Effects in Nonequilibrium Polycondensation Systems

Abstract

The substitution effect of neighboring groups on the statistical quantities in nonequilibrium condensation polymerization is analyzed by the vectorial cascade theory. In equilibrium condensation polymerization, the substitution is affected by the conversional distribution of building (monomer) units. In nonequilibrium condensation polymerization, however, it needs to be expressed by the distribution function of the local connection of links. The average degree of polymerization and the critical point of gelation are obtained by generalizing the conventional cascade theory. The molecular mass distribution is evaluated by direct recurring calculations with a cutoff in the original probability generation function or in the Groebner base. Compared with conventional treatment by Lagrange's expansion, the evaluation method developed here requires less computer memory. This allows us to complete the calculations within a reasonable time. As a typical example, formulation of the probability generating function for the first-shell substitution effect in trifunctional unit systems and the calculation of their molecular mass distribution are given.