Modeling insight into the diffusion-limited cause of the gel effect in free radical polymerization

The molecular-level cause of the gel effect in free radical polymerization, associated with a decrease in the termination rate parameter with increasing conversion, is studied by experimental and modeling approaches. The predictive Vrentas-Duda free volume theory serves as a basis for modeling as it handles quantitatively the temperature and polymer concentration dependencies of monomer diffusion. The polymer concentration (c) dependencies of various diffusional processes fit an expression of the form [D_m(c)/D_m(0)]^ξx,m, where D_m is the monomer diffusion coefficient and D_m expresses the power-law dependence of the diffusional process of interest (x) relative to that of monomer (m). Relevant values of ξ_x,m vary from ∼ 0.8 for segmental mobility, to ∼1-2 or 3 for oligomeric diffusion, to ∼ 3.0-3.5 for unentangled polymer diffusion, and to ∼ 9.5-10 for entangled polymer diffusion. If the very high conversion regime, where issues unrelated to the origin of the gel effect add unnecessary complications, is avoided, the modeling of conversion-time data requires only that the polymer concentration dependence of the termination reaction, caused by a diffusional process cited above, must be taken into account. Comparison of ξ_x,m values needed to fit various methyl methacrylate conversion-time data (values of 1.1-5.0 were required, increasing with increasing molecular weight of the polymer produced) with those needed for different diffusion types indicates that termination is governed by diffusion of the shortest radical chains present in significant number. In contrast to some "short-long" termination theories that commonly distinguish "short" and "long" as unentangled and entangled, this study finds that entanglements are irrelevant in distinguishing "short" from "long". Styrene polymerizations yield ξ_x,m values substantially below 1. This is ascribed to chain transfer, supported by the fact that methyl methacrylate systems with chain transfer agent show similar suppressed gel effect behavior. The very low ξ_x,m values result in part from the reduced polymer concentration dependence of k_t associated with the highly mobile short radical chains obtained in chain transfer reactions. While systems with significant chain transfer must be studied further, this modeling approach should serve as a robust basis for a more complete description of termination under various conditions.