A linkage moment approach to modeling condensation polymerization with multiple monomers. II. Extension to nonlinear polymers

In a previous article, a general model for the condensation copolymerization of mono and bifunctional monomers was developed in which the sequence length distribution was calculated statistically from the concentrations of linkages (e.g., CONH) labeled by the identities of the participating monomer units. A set of balance equations for the effect of each major reaction upon these concentrations, those of the end groups, and the moments of the chain‐length distribution completed the general model framework for linear polymers. In this article, this technique is extended to the case of nonlinear polymerizations with multifunctional monomers capable of branch or gel formation. This modification is required because in nonlinear polymerization, the moments of the chain‐length distribution diverge at the gel point, and the traditional description of the sequence length distribution is only well defined for macromolecules consisting of a single backbone chain. Although the balance equations for the end group and linkage concentrations presented in the previous article are completely transferable, the statistical techniques must be modified to accommodate branch and network chain architectures. By coupling the general kinetic model with the recursive approach of Macosko and Miller for the calculation of sol/gel properties, one can describe the microstructures of a wide variety of systems such as those in which the copolymer has a blocky microstructure caused by interchange reactions between multiple components. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 266–274, 2001