Singleparameter aging in the weakly nonlinear limit
Abstract
Physical aging deals with slow property changes over time caused by molecular rearrangements. This is relevant for noncrystalline 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 socalled material time $\xi$. The resulting "ToolNarayanaswamy (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 singleparameter 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 firstorder differential equation for property monitored, involving a systemspecific 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 zerothorder solution, $R_0(t)$. Numerical data for a binary LennardJones 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 fluctuationdissipation theorem is the normalized equilibrium potentialenergy timeautocorrelation function).
 Publication:

arXiv eprints
 Pub Date:
 June 2022
 arXiv:
 arXiv:2206.05131
 Bibcode:
 2022arXiv220605131M
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Materials Science
 EPrint:
 Thermo 2, 160 (2022)