Dynamic modeling of crosslinking and gelation in continuous ethylene–propylene–diene polymerization reactors using the pseudo–kinetic constant approach

Abstract

A dynamic model for continuous ethylene–propylene–diene terpolymerization reactors in which crosslinking and gel formation are attributable to reactions between the pendant double bonds of diene units has been developed. The model is applicable to other types of crosslinking reactions such as those due to aging, polymer blending, and vulcanization. The polymer properties at the gel point and in the post-gel region are computed using the numerical fractionation method. Direct application of this method to the prediction of terpolymer properties in the gel or post-gel region can lead to severe numerical problems, due to large differences in order of magnitude of various moments across the generations. These problems are overcome by applying a pseudo-kinetic rate constant method, i.e., by constructing a moment model for a pseudo-homopolymer that approximates the behavior of the actual terpolymer under the long chain and quasi-steady state assumptions. The pseudo-homopolymer model is then used as the basis for application of the numerical fractionation method. We show that the proposed dynamic model is capable of predicting realistic polydispersities and molecular weight distributions even near the gel point with as few as 11 generations, and in the post-gel region with as few as five generations. The largest steady-state polydispersities of the soluble polymer are obtained when the crosslinking rate just exceeds the critical value for gelation. The steady-state polydispersity decreases exponentially in the post-gel region at higher values of the rate constant, while the sol fraction decreases in a more linear fashion. The overall molecular weight distribution (MWD) of the sol is constructed assuming a Schulz two parameter distribution for each generation. For the industrial case of a small number of crosslinks, the first two generations contribute the most to the MWD, which is unimodal. The tail of the MWD is longest near the initial gelation time; the tail is shortened in the post-gel region as higher generations are consumed.