Development of a general mathematical framework for modeling diffusion-controlled free-radical polymerization reactions

Abstract

A new theoretical framework is proposed for modeling diffusion-controlled free-radical po- lymerization reactions. Termination and propagation rate constants as well as initiator efficiency are expressed in terms of a reaction-limited term and a diffusion-limited one. The latter is shown to depend on the diffusion coefficient of the corresponding species (i.e., polymer, monomer, primary radicals) and an effective reaction radius. All parameters appearing in the diffusion-limited part of the kinetic rate constants have a clear physical meaning and can be evaluated in terms of the physical and transport properties of the reacting species. It is shown that the proposed approach for modeling diffusion-controlled reactions does not require the introduction of critical break points to mark the onset of various diffusional effects (Le., gel effect, glass effect). The ability of the present model to elucidate the mechanism of diffusion-controlled reactions is demonstrated by analyzing the free-radical polymerizations of styrene and methyl methacrylate initiated by the thermal decomposition of AIBN, AIBME, AVN, and LPO chemical initiators. It is shown that, at high conversions, initiator efficiency strongly depends on the size of initiator molecules. The present model predictions are in excellent agreement with experimental data on monomer conversion, total radical concentration, and average molecular weights measured in different laboratories by ODriscoll and Huang42 and Zhu et al.l0