A novel approach to population balance modeling of reactive polymer modification leading to branching

Abstract

The mathematical treatment of polymer modification systems, described by population balances containing convolution is discussed. The two-dimensional case (molecular weight vs. number of branch points) was considered by utilizing approximations of distributions, expanding them in terms of Gaussian basis functions. Three branching reactions were addressed: chain backbone to chain end point coupling; three-functional coupling of chain ends; and crosslinking. The results were compared to those of Monte Carlo (MC) simulations. Good agreement was observed, although the quality of a distribution as generated by the numerical approach is much better in view of the strong scatter in the MC data.