Simple nonlinear equation for structural relaxation in glasses

A wide range of glassy and disordered materials exhibit complex, nonexponential, structural relaxation (aging). We propose a simple nonlinear rate equation δ=a[1-exp(bδ)], where δ is the normalized deviation of a macroscopic variable from its equilibrium value, to describe glassy relaxation. Analysis of extensive experimental data shows that this equation quantitatively captures structural relaxation, where a and b are both temperature- and, more importantly, history-dependent parameters. This analysis explicitly demonstrates that structural relaxation cannot be accurately described by a single nonequilibrium variable. Relaxation rates extracted from the data imply the existence of cooperative rearrangements on a supermolecular scale.