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 increasi ng conversion, is studied by experimental and modeling approaches. The pred ictive Vrentas-Duda free volume theory serves as a basis for modeling as it handles quantitatively the temperature and polymer concentration dependenc ies of monomer diffusion. The polymer concentration (c) dependencies of var ious diffusional processes fit an expression of the form [D-m(c)/D-m(0)](xi x,m), where D-m is the monomer diffusion coefficient and xi(x,m) expresses the power-law dependence of the diffusional process of interest (x) relati ve to that of monomer (m). Relevant values of xi(x,m), vary from similar to 0.8 for Segmental mobility, to similar to 1-2 or 3 for oligomeric diffusio n, to similar to 3.0-3.5 for unentangled polymer diffusion, and to similar to 9.5-10 for entangled polymer diffusion. If the very high conversion regi me, where issues unrelated to the origin of the gel effect add unnecessary complications, is avoided, the modeling of conversion-time data requires on ly that the polymer concentration dependence of the termination reaction, c aused by a diffusional process cited above, must be taken into account. Com parison of xi(x,m) values needed to fit various methyl methacrylate convers ion-time data (values of 1.1-5.0 were required, increasing with increasing molecular weight of the polymer produced) with those needed for different d iffusion types indicates that termination is governed by diffusion of the s hortest radical chains present in significant number. In contrast to some " short-long" termination theories that commonly distinguish "short" and "lon g" as unentangled and entangled, this study finds that entanglements are ir relevant in distinguishing "short" from "long". Styrene polymerizations yie ld xi(x,m) values substantially below 1. This is ascribed to chain transfer , supported by the fact that methyl methacrylate systems with chain transfe r agent show similar suppressed gel effect behavior. The very low xi(x,m) v alues result in part from the reduced polymer concentration dependence of k (t) associated with the highly mobile short radical chains obtained in chai n 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.