Modelling structural relaxation in polymeric glasses using the aggregation–fragmentation concept

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 (CRR). Any CRR is thought of as a string of elementary clusters (EC). Fragmentation of the string may occur at random time at any border between ECs. Two string can aggregate at random time to produce a new string. The processes of aggregation and fragmentation are treated as thermally activated, and the rate of fragmentation is assumed to grow with temperature more rapidly than that for coalescence. This implies that only elementary clusters are stable at the glass transition temperature Tg, whereas below Tg, CRRs containing several ECs remain stable as well. A nonlinear differential equation is developed for the distribution of CRRs with various numbers of ECs. Adjustable parameters of the model are found by fitting experimental data for polycarbonate, poly(methyl methacrylate), polystyrene and poly(vinyl acetate). For all materials, 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.