Single-parameter aging in the weakly nonlinear limit

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).

References in corpus (16)

• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
• Atomic-scale relaxation dynamics and aging in a metallic glass probed by X-ray photon correlation spectroscopy
• Glassy Aging Dynamics
• Time-temperature superposition in viscous liquids
• Relaxation and physical aging in network glasses: a review
• Physical aging studied by a device allowing for rapid thermal equilibration
• Physical ageing studied by a device allowing for rapid thermal equilibration
• RUMD: A general purpose molecular dynamics package optimized to utilize GPU hardware down to a few thousand particles
• Separation of time-scales and reparametrization invariance for aging systems
• Predicting nonlinear physical aging of glasses from equilibrium relaxation via the material time
• Evidence of growing spatial correlations during the aging of glassy glycerol
• Generalized single-parameter aging tests and their application to glycerol
• A molecular perspective on the yield and flow of polymer glasses: The role of enhanced segmental dynamics during active deformation
• Aging of CKN: Modulus versus conductivity analysis
• Single-parameter aging in a binary Lennard-Jones system
• A spectroscopic cell for fast pressure jumps across the glass transition line