FRACTAL DYNAMIC THEORY OF GLASSES AND PHYSICAL AGING - LINEAR AND CROSS-LINKED POLYMERS

A new statistical dynamic theory of polymeric glasses for temperatures below the glass transition is presented to address important questions in the glassy-state relaxation and physical aging. We have analyzed the hole dynamics and fluctuations on a fractal lattice and have provided a unified treatment of the KAHR (Kovacs-Aklonis-Huchinson-Ramos) equations, the KWW (Kohlrausch-Williams-Watts) function, the density of states, relaxation time, relaxation time spectrum, and the spatial-dependent local diffusivity of holes. The theory predicts that the physical aging rates of both linear and cross-linked polymers increase from zero above T(g) to a constant below T(g) and then decrease to zero 200 K below T(g). In contrast to all the published expressions, our calculation reveals increasingly smaller activation energies with decreasing temperature in the glassy state. As our analysis is unfolded, a theoretical justification of extending Doolittle's equation from the equilibrium liquid to nonequilibrium glassy states is also revealed.