Unifying the Temperature Dependent Dynamics of Glasses

Abstract

Strong changes in bulk properties, such as modulus and viscosity, are observed near the glass transition temperature, T_{g}, of amorphous materials. For more than a century, intense efforts have been made to define a microscopic origin for these macroscopic changes in properties. Using transition state theory, we delve into the atomic/molecular level picture of how microscopic localized relaxations, or "cage rattles," translate to macroscopic structural relaxations above T_{g}. Unit motion is broken down into two populations: (1) simultaneous rearrangement occurs among a critical number of units, n_{\alpha}, which ranges from 1 to 4, allowing a systematic classification of glasses that is compared to fragility; (2) near T_{g}, adjacent units provide additional free volume for rearrangement, not simultaneously, but within the "primitive" lifetime, {\tau}_{1}, of one unit rattling in its cage. Relaxation maps illustrate how Johari-Goldstein \{beta} relaxations stem from the rattle of n_{\alpha} units. We analyzed a wide variety of glassy materials, and materials with glassy response, using literature data. Our four-parameter equation fits "strong" and "weak" glasses over the entire range of temperatures and also extends to other glassy systems, such as ion-transporting polymers and ferroelectric relaxors. The role of activation entropy in boosting preexponential factors to high "unphysical" apparent frequencies is discussed.