Kinetic modeling of hyperbranched polymerization involving an AB2 monomer reacting with substitution effect

A model is developed in the form of one or two partial differential equations (master Smoluchowski-like equations) that describe evolution of the size distribution of polymer species formed in a step-growth polymerization of an AB(2) monomer. Groups B react with a substitution effect; i.e., they are initially equally reactive, but the reactivity of the second B group changes as the first has reacted. One master equation is sufficient to model formation of branched molecules only. Two are needed to take into account intramolecular cyclization. Monte Carlo simulations of the same process are used to verify the results of applying the kinetic model. The model can be applied to calculate various molecular parameters in polymerizing systems, including various average degrees of polymerization, size distribution of acyclic and cycle-containing polymer molecules, degree of branching, etc. Explicit formulas describing the dependence of some of these quantities on time or conversion degree are derived for the random system, i.e., the system reacting without substitution effect.