A COMPARATIVE-STUDY OF THE MASTER EQUATION APPROACH AND THE DISCRETE GALERKIN METHOD FOR THE SIMULATION OF FREE-RADICAL POLYMERIZATION

The present article deals with the mathematical treatment of free radical polymerization reactions. As a typical example the synthesis of poly(methyl methacrylate) under realistic experimental conditions is investigated. Since the mathematical treatment of the kinetic rate equations raises severe numerical problems, alternative approaches are required. In this paper two of these methods, i.e. the discrete Galerkin method and the master equation approach, are compared. The discrete Galerkin method circumvents difficulties encountered by the direct integration of the kinetic rate equations but requires much a priori knowledge of the chemical reaction system. Within the framework of the master equation approach the polymerization reaction is regarded as a stochastic process. For the simulation of this stochastic process a modified algorithm is presented. The example of the polymerization of methyl methacrylate shows that the master equation approach is an efficient tool in the simulation of free radical polymerization reactions.