Recovery of molecular weight distributions from transformed domains. Part II. Application of numerical inversion methods

This work is a part of a study aiming at developing tools for the prediction of complete molecular weight distributions (MWDs) of polymers at the exit of a reactor. This reactor may be a synthesis reactor or one used to modify a preexisting resin. In this work, we analyse the suitability of three methods for the numerical inversion of probability generating functions (pgfs), those due to Papoulis, de Hoog and Garbow. The three methods have been proposed in the literature for the inversion of Laplace transforms. We show how to adapt them to the problem at hand, and apply them to two situations. The first one is the recovery of experimentally measured MWDs, through a process that consists of finding the pgf of the distribution, numerically inverting it and comparing the result with the known MWD. The second one is to solve the pgf balances of polymerisation systems with known MWDs, and comparing those MWD with the ones that result from the inversion with the three methods. We discuss the relative advantages of each. inversion method and propose guidelines for their proper use with unknown MWD functions. (C) 2002 Elsevier Science Ltd. All rights reserved.