Molecular theory for the rheology of glasses and polymers

A molecular kinetic theory for the rheology of glass is given. According to this theory, the structure of a glass consists of randomly distributed high-energy sites, which correspond to the frozen-in density fluctuations. These sites are termed as defects. The anelastic deformation associated with the β relaxation in a glass is attributed to the availability of a set of configurational states through the faster, uncorrelated rotational-translational motions of molecules within these defects. These involve a broad distribution of potential energy barriers of lower energy. The nonelastic deformation observed after a long period of time (≫${10}^4$ sec) is associated with the α process and is attributed to the much slower hierarchically constrained motions of the surrounding molecules, which leads to the growth of sheared microdomains within the glassy matrix. The effect of hierarchical constraints within the microstructural regions is essentially as described by Palmer, Stein, Abrahams, and Anderson [Phys. Rev. Lett. 53, 958 (1984)]. At a low temperature when the duration for the measurements is long, or at high temperatures when the number of defects is high, sheared microdomains nucleated at one site grow and merge into the others which were nucleated at other sites, thus leading to an irrecoverable macroscopic deformation or viscous flow. The theory is extended to amorphous polymers in which further restrictions on the number of available configurational states is placed by the strength and directionality of covalent bonds and by the entanglements and junction points between the polymer chains. The number of molecules forming the defects was calculated from the thermodynamic data at T>$T_g$, but at T<$T_g$ it was assumed to be the same as at $T_g$. The result of the theory is a relation practically coinciding with the observed time and temperature dependence of the creep and dynamic-mechanical properties of the glassy state of a material.