Crosslinking kinetics: Partitioning according to number of crosslinks

To mathematically describe crosslinking kinetics for polymers, we have proposed a novel method that accounts for the number of crosslinks, that is, partitioning according to number of crosslinks (PANC). By contrast, the well-known method of numerical fractionation tracks generations of crosslinked molecules, defined to include a range of crosslinks. The proposed crosslinking kinetics yield a population balance model that provides moments and hence measurable average properties such as number average molecular weight and weight average molecular weight, polydispersity and average crosslink number. The gel points for batch and continuous-flow stirred-tank reactors are derived. Because the usual closure methods do not yield satisfactory convergence, new representations for post-gelation moments are proposed. The results realistically show how the moments change with time in the post-gel region.