  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, whereas
below this temperature, 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 in calorimetric tests 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.
