Mathematical modeling of bivariate polymer property distributions using 2D probability generating functions, 1 - Numerical inversion methods

Abstract

This is the first of two papers presenting a new mathematical method for modeling bivariate distributions of polymer properties. It is based on the transformation of the infinite mass balances describing the evolution of a two-dimensional distribution using 2D probability generating functions (pgf). A key step of this method is the inversion of the transforms. In this work, two numerical inversion methods of 2D pgfs are developed and carefully validated. The accuracy obtained with both methods was very satisfactory. The inversion formulas of both methods are simple and easy to implement. A simple copolymerization example is used to show the complete procedure from the derivation of the pgf balances to the recovery of the bivariate molecular weight distribution.