Modeling of nonlinear polymerization in a continuous stirred tank reactor

Mathematical modeling of nonlinear free-radical polymerization systems subject to gel formation is a challenging endeavor. At the gel point the second or higher molecular weight moments diverge to infinity making it impossible to obtain the molecular weight distribution (MWD). The Numerical Fractionation technique (NF) developed by Teymour and Campbell [1994] utilizes a refinement of the classical method of moments. This technique segregates the polymer into two distinct phases, a soluble or sol phase, and an insoluble phase, the gel phase. The sol phase is further segregated into polymer generations for which a set of moments is derived. A set of moments for each generation is used to reconstruct a distribution for that species. The overall polymer MWD is obtained by summing the contribution of each generation. Isolating the gel phase and modeling the sol phase allows for the determination of polymer properties in the pre- and post-gel regimes, the gel point, and the reconstruction of the polymer molecular weight distribution (MWD).; Three different chemistries for continuous non-linear free radical polymerization resulting in gel formation are investigated in detailed and modeled using NF. The first case involves chain transfer to polymer along with termination by combination, the second addresses Vinyl Divinyl Copolymerization (VDV) and the third Ethylene Propylene Diene Terpolymerization (EPDM). The findings of this work illustrate that the validity of the gamma distribution used to reconstruct the individual generation MWDs deteriorates under certain conditions resulting in a broad shoulder at the high chain length end of the NF-overall MWD which does not appear in the actual MWD obtained by the direct solution. The performance of various alternative distributions is investigated in detail for the different polymerization chemistries presented and a theory is developed which significantly enhances the NF-reconstructed MWD and is in agreement with that obtained by the direct solution.; The first instance of an analysis which examines the multiplicity and dynamic behavior of the sol-properties and gel fraction for nonlinear free-radical polymerization, and more specifically non-isothermal VDV copolymerization is presented. A bifurcation analysis reveals interesting dynamic behavior for the reactor system studied and under the influence of non-isothermal effects, illustrates the occurrence of multiple critical gel transitions.