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

WILEY-V C H VERLAG GMBH

Lugar: Weinheim; Año: 2010 vol. 3 p. 342 - 359

1022-1344

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 thiswork, two numerical inversion methods of 2D pgfs are developed and carefully validated. Theaccuracy obtained with both methods was very satisfactory. The inversion formulas of bothmethods are simple and easy to implement. A simple copolymerization example is used to showthe complete procedure from the derivation of the pgf balances to the recovery of the bivariate molecular weight distribution.