Molecular Weight Distribution Calculation through Numerical Inversion of Probability Generating Functions

ASTEASUAIN, MARIANO; BRANDOLIN, ADRIANA; SARMORIA, CLAUDIA

Mar del Plata

Simposio; I Simposio Binacional Argentino-Chileno de Polímeros; 2001

Universidad Nacional de Mar del Plata

Mathematical models of polymerization reactions are usually based on the resolution of the mass balance equations that involve the kinetic steps of the polymerization process. If one is interested in calculating the molecular weight distribution of polymerizing species, the necessary balance equations form an infinite set. Several techniques are available to treat these infinite systems, as mentioned in another work of this symposium.We have successfully applied probability generating functions (pgf) to transform the infinite mass balances. The result is a finite set of differential equations. From the integration of this system it is possible to obtain the pgf transform of the molecular weight distribution.The distribution must then be obtained by means of an appropriate inversion of its transform. In our previous works, we have applied adaptations of inversion methods designed for Laplace transforms to perform the pgf inversion. In this work, we analyze the feasibility of using a method designed specifically for the inversion of probability generating functions.