Advanced Modeling of Polymer Non-Linear Stress Relaxation – Poly(methylmethacrylate) and Polycarbonate - André, José Reinas (2013)
Sound models of temperature- and strain-dependent (non-linear) stress relaxation are still lacking. Recent work has shown that focusing on polymers’ local backbone strains and stresses provides an adequate basis for developing such models and accurately predicting experimental stress relaxation moduli (to within 1-2% relative errors), the values of meaningful physical parameters and long time behavior, from experiments spanning only a few hours. The modeling strategy is summarized and physically discussed, and applied to two amorphous polymers – PMMA and PC. The numerical values obtained for the model parameters are also physically discussed in detail, supporting a view of the stress relaxation process where a temperature-dependent, truncated log-normal, distribution of local cooperative (or clustering) transitions become involved, at and above a minimum (or primitive) relaxor size. Within this view, cooperativity (average and maximum cluster size) increases with decreasing temperatures. Beyond the reasonably accurate description of the experiments, the model succeeds in predicting (1) the effect of increases in the fully relaxed modulus, E∞, as in semi-crystalline or strongly cross-linked polymers, (2) the strict inapplicability of time-temperature and strain-time super-positions, (3) an extended, Kohlrausch-Williams-Watts, type of relaxation response spanning 12 or more time decades, and (4) specific, meaningful, physical parameters - a minimum activation energy (similar to those of corresponding β-type transitions), the (occupied + free) volume of the primitive relaxor, and the approximate crossover temperature, Tc, and frequency, νc, both of critical importance in condensed matter dynamics. The model also has the potential of incorporating the effect of changes in free volume.