Mathematical Modeling of Bivariate Distributions of Polymer Properties Using 2-D Probability Generating Functions. Part I: Numerical Inversion Methods

ASTEASUAIN, MARIANO; BRANDOLIN, ADRIANA

MACROMOLECULAR THEORY AND SIMULATIONS

John Wiley & Sons

Lugar: Weinheim, Alemania; Año: 2010 vol. 19 p. 342 - 359

1022-1344

This is the first of two works 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 bidimensional distribution using 2-D probability generating functions (pgf). A key step of this method is the inversion of the transforms. In this work, two numerical inversion methods of 2-D 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.