Single-parameter aging in the weakly nonlinear limit

TL;DR

This paper analytically derives a universal solution for single-parameter aging in the weakly nonlinear limit, confirming its accuracy through numerical data on a Lennard-Jones glass former.

Contribution

The paper provides an analytical first-order solution for single-parameter aging, linking it to the zeroth-order equilibrium autocorrelation function, and validates it with numerical simulations.

Findings

The first-order solution is universal and expressed in terms of the zeroth-order solution.

Numerical data confirms the theory's accuracy in the weakly nonlinear regime.

Aging behavior can be predicted from equilibrium autocorrelation functions.

Abstract

Physical aging deals with slow property changes over time caused by molecular rearrangements. This is relevant for non-crystalline materials like polymers and inorganic glasses, both in production and during subsequent use. The Narayanaswamy theory from 1971 describes physical aging - an inherently nonlinear phenomenon - in terms of a linear convolution integral over the so-called material time $\xi$. The resulting "Tool-Narayanaswamy (TN) formalism" is generally recognized to provide an excellent description of physical aging for small, but still highly nonlinear temperature variations. The simplest version of the TN formalism is single-parameter aging according to which the clock rate $d\xi/dt$ is an exponential function of the property monitored [T. Hecksher et al., J. Chem. Phys. 142, 241103 (2015)]. For temperature jumps starting from thermal equilibrium, this leads to a first-order differential equation for property monitored, involving a system-specific function. The present paper shows analytically that the solution to this equation to first order in the temperature variation has a universal expression in terms of the zeroth-order solution, $R_0(t)$. Numerical data for a binary Lennard-Jones glass former probing the potential energy confirm that, in the weakly nonlinear limit, the theory predicts aging correctly from $R_0(t)$ (which by the fluctuation-dissipation theorem is the normalized equilibrium potential-energy time-autocorrelation function).