A Novel Approach to Population Balance Modeling of Reactive Polymer Modification Leading to Branching

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.