Determination of polymer chain length distributions by numerical inversion of z-transforms

Abstract

A numerical technique is presented for evaluation of the polymer chain length distribution in polymerization reaction engineering models whose governing equations can be represented in the z-transform domain. The method is based upon an appropriate z-transform inversion relationship that has the form of an inverse discrete Fourier transform which can be efficiently evaluated by the fast Fourier transform algorithm using various existing computer software. The approach is illustrated through several example problems involving polymerization systems and comparisons are made to other alternate solution methods. One of the example problems includes a complex reaction network for polycarbonate polymerization as a novel application. It is shown that the proposed technique requires an order-of-magnitude less computer time to evaluate the polymer MWD when compared to direct numerical integration.