Theory of physical aging in polymer glasses

Abstract

A statistical segment scale theory for the physical aging of polymer glasses is proposed and applied. The approach is based on a nonlinear stochastic Langevin equation of motion and the concept of an effective free energy which quantifies temporary localization, collective barriers, and the activated segment hopping process. The key collective structural variable that plays the role of the dynamic order parameter for aging is the experimentally measurable nanometer and longer wavelength amplitude of density fluctuations, S0 . The degree of local cooperativity, and the bare activation energy of the high-temperature Arrhenius process, are determined in the molten state by utilizing experimental measurements of the glass temperature and dynamic crossover time, respectively. A first-order kinetic equation with a time varying rate is proposed for the temporal evolution of S0 which is self-consistently and nonlinearly coupled with the mean segmental relaxation time. The theory has been applied to study physical aging of the alpha relaxation time, shear relaxation modulus, amplitude of density fluctuations, cohesive energy, absolute yield stress, and fictive temperature of polymethylmethacrylate and other glasses over a range of temperatures. Temperature-dependent logarithmic and effective power-law aging is predicted at intermediate times. Time-aging time superposition is found for the mechanical relaxation function. A strongly asymmetric aging response is predicted for up and down temperature jump experiments. Comparison of the approach with the classic phenomenological model is presented.