Theory of relaxation and elasticity in polymer glasses

The recently developed activated barrier hopping theory of deeply supercooled polymer melts [K. S. Schweizer and E. J. Saltzman, J. Chem. Phys. 121, 1984 (2004)] is extended to the nonequilibrium glass state. Below the kinetic glass temperature Tg, the exact statistical mechanical relation between the dimensionless amplitude of long wavelength density fluctuations, S0, and the thermodynamic compressibility breaks down. Proper extension of the theory requires knowledge of the nonequilibrium S0 which x-ray scattering experiments find to consist of a material specific and temperature-independent quenched disorder contribution plus a vibrational contribution which varies roughly linearly with temperature. Motivated by these experiments and general landscape concepts, a simple model is proposed for S0 (T). Deep in the glass state the form of the temperature dependence of the segmental relaxation time is found to depend sensitively on the magnitude of frozen in density fluctuations. At the (modest) sub- Tg temperatures typically probed in experiment, an effective Arrhenius behavior is generically predicted which is of nonequilibrium origin. The change in apparent activation energy across the glass transition is determined by the amplitude of frozen density fluctuations. For values of the latter consistent with experiment, the theory predicts a ratio of effective activation energies in the range of 3-6, in agreement with multiple measurements. Calculations of the shear modulus for atactic polymethylmethacrylate above and below the glass transition temperature have also been performed. The present work provides a foundation for the formulation of predictive theories of physical aging, the influence of deformation on the alpha relaxation process, and rate-dependent nonlinear mechanical properties of thermoplastics.