Simple nonlinear equation for structural relaxation in glasses

Abstract

A wide range of glassy and disordered materials exhibit complex, non-exponential, structural relaxation (aging). We propose a simple nonlinear rate equation δ = a [1−exp (b δ)], 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 non-equilibrium variable. Relaxation rates extracted from the data imply the existence of cooperative rearrangements on a super-molecular scale.

Nonmonotonic Aging and Memory Retention in Disordered Mechanical Systems

“…Examples range from time-dependent resistivity in disordered conductors [1][2][3][4][5], flux creep in superconductors [6,7], dynamics of spin glasses [8][9][10][11], structural relaxation of colloidal glasses [12,13], time-dependence of the static coefficient of friction [14][15][16], thermal expansion of polymers [17,18], compaction in agitated granular systems [19], and crumpling of thin sheets under load [20,21]. The ubiquity of slow relaxation phenomena suggests the existence of common underlying physical principles [22][23][24][25][26][27][28]. However, as slow relaxation is usually a smooth featureless process, it is hard to discern between the different descriptions using experiments.…”

Communication: Direct tests of single-parameter aging

“…This is necessary because a differential equation for only R(t) cannot account for the nonlinearity, whereas a differential equation involving only ∆X(t) cannot lead to nonexponentiality in the linear limit. There are other approaches to describing physical aging than the standard TN theory [36,56]. The common "singleparameter" assumption of all simple theories is that the quantity monitored correlates to the clock rate γ.…”

Two-subsystem thermodynamics for the mechanics of aging amorphous solids

“…which is identical to the evolution equation (1) discussed in [34]. Particularly, for constant a and b, the solution is given by [34] …”