Chain-length-dependent termination rate processes in free-radical polymerizations. 2. Modeling methodology and application to methyl methacrylate emulsion polymerizations

Abstract

Results are presented from modeling of extensive methyl methacrylate seeded emulsion polymerization data. Both chemically initiated and γ radiolysis initiated experiments were modeled; in the latter type of experiments the system is removed from the γ-source, thereby providing kinetic data which are particularly sensitive to termination processes. While the data cannot be fitted consistently and meaningfully with conventional termination models, all are fitted in a unified way using the description of Russell et al. (Macromolecules 1992, 25, 2459). Fitting completely without adjustable parameters gives quite acceptable agreement with these sensitive experimental data, and exact accord is obtained with minor, and physically reasonable, parameter changes. The model description is applicable to free-radical polymerizations at intermediate and high conversion (i.e., above c**). Its main feature is that it takes full account of the dependence of termination rate coefficients on radical chain length, while still requiring only modest computational resources. The most important model parameters are therefore experimental diffusion coefficients for monomer as a function of weight fraction polymer, and exponents for the scaling of oligomeric and polymeric diffusion coefficients with degree of polymerization. For emulsion systems, desorption (exit) kinetics are included, and the theory of Maxwell et al. (Macromolecules 1991, 24, 1629) for the rate of chemical initiation is found to be accurate. The modeling indicates that the predominant mode of termination above c** and prior to the glass transition involves a short free radical, usually one formed by transfer, and a long entangled macroradical; above the glass transition, this dominant model involves two long entangled macroradicals encountering as a result of propagation (reaction diffusion). The origin of the Trommsdorff effect is the slowing with conversion of the termination rates of shorter chains, this being brought about by the increase with conversion of viscosity and of tendency to become entangled.