Mathematical modeling of molecular weight distributions in vinyl chloride suspension polymerizations performed with a bifunctional initiator through probability generating functions

Abstract

This paper presents a mathematical model to describe the evolution of the molecular weight distribution (MWD) in vinyl chloride (VCM) free-radical suspension polymerizations performed with a bifunctional initiator, 1,3-di(2-neodecanoylperoxyisopropyl) (DIPND). The model yields, as a function of time, the mass balances for the distinct phases, the monomer conversions, the number- and mass-average molecular weights and the complete MWD of both the growing and dead polymer chains. In order to describe the MWD, the model uses probability generating functions (pgf) to transform the infinite mass balance equations that describe the evolution of the distribution into a reduced and finite set of model equations. The set of pgf-transformed model equations is then solved and inverted numerically. Numerical validation of the proposed numerical scheme was successfully performed with help of published experimental data. As shown throughout many examples, as the dynamics of the molecular weight distributions in vinyl chloride suspension polymerizations is controlled by chain transfer to monomer, the molecular weight distributions of the final polymer resin is little sensitive to the presence of the linear symmetrical bifunctional initiator