Relaxation behavior in atomic and molecular glasses

Abstract

The time dependence of relaxation for many substances near their glass transition region is often found accurately to obey a ‘‘stretched exponential’’ form, exp[-(t/τ${)}^{\alpha }$], with the stretching exponent in the range 0<α<1. It is the objective of this paper to relate α and τ to gross topographical features of the many-particle potential-energy hypersurface. The multidimensional basin representation for the potential energy, supplied by the inherent structure theory of condensed phases, offers a convenient analytical framework. The relaxation time spectrum for stretched exponential behavior thus is related to the manner in which basins can be aggregated in the multidimensional configuration space into ‘‘metabasins,’’ using a transition free-energy criterion. A conclusion of the analysis is that α should decline with decreasing temperature; some limited experimental and simulational support exists for this proposition. In addition, the usually found non-Arrhenius behavior for τ is connected by the study to the increasing extent of branching and tortuosity of basins inhabited as the temperature declines.