General Framework for the Application of PGF Transforms to Polymerization Systems

ASTEASUAIN, MARIANO; BRANDOLIN, ADRIANA; SARMORIA, CLAUDIA

Mar del Plata

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

Universidad de Mar del Plata

Molecular weight and molecular weight distribution (MWD) of polyolefins greatly affect their final properties. These and other molecular properties are determined by complex relationships between several variables that take part of the reaction process. Here, mathematical models that describe molecular weight and MWD are powerful prediction tools. Free radical reactions are involved both in the synthesis and the post-reactor modification of polyolefins. Models of these processes usually begin by setting up kinetic equations and drawing from them mass balances of the polymerizing species. This results in an infinitely large system of equations, which may be made tractable by several techniques. To calculate average quantities, the moment method is appropriate. To calculate MWD some authors assume its shape and calculate its parameters from the first few moments. Others solve the MWD at a few points of the degree of polymerization. Laplace transforms and the statistical approach have also been employed. We have used probability generating functions (pgf) in the prediction of MWD in several free radical reaction systems. These transforms are defined for discrete distributions, and require no knowledge of the final distribution.  Two steps are involved in the use of the method: first, transforming the mass balances and solving the resulting finite system of equations; second, inverting the result to recover the MWD.  The transformation step may be cumbersome and time-consuming if one applies it from scratch for every single system.  However, if one recognizes that there are many common blocks to different free-radical systems, since some reactions appear in more than one system, it is possible to generalize the method.  In this work we aim to give the reader the necessary tools to apply pgf transforms to mass balances in a generalized way.