A model for structural relaxation in amorphous glassy polymers based on the aggregation-fragmentation theory

Governing equations are derived for the kinetics of physical aging in polymeric glasses. An amorphous polymer is treated as an ensemble of cooperatively rearranged regions (CRRs). Any CRR is thought of as a string of elementary clusters (ECs). Fragmentation of the string occurs at random times at any border between ECs. Two strings aggregate at random instants to produce a new string. Aggregation and fragmentation are treated as thermally activated processes, and the rate of fragmentation is assumed to grow with temperature more rapidly than the rate of coalescence. A nonlinear differential equation is developed for the distribution of CRRs with various numbers of ECs. Adjustable parameters of the model are found by the fitting of experimental data for polycarbonate, poly(methyl methacrylate), polystyrene, and poly(vinyl acetate) (PVA). Fair agreement is established between observations and results of numerical simulation. For PVAc, the relaxation spectrum found by matching data in a calorimetric test is successfully employed to predict experimental data in a shear relaxation test.