Simple nonlinear equation for structural relaxation in glasses

Nonlinear susceptibilities and higher-order responses related to physical aging: Wiener-Volterra approach and extended Tool-Narayanaswamy-Moynihan models

Large-amplitude thermal excursions imposed on deeply supercooled liquids modulate the nonlinear time evolution of their structural rearrangements. The consequent aftereffects are treated within a Wiener-Volterra expansion in laboratory time that allows one to calculate the associated physical-aging and thermal response functions. These responses and the corresponding higher-harmonic susceptibilities are illustrated using calculations based on the Tool-Narayanaswamy-Moynihan (TNM) model. The conversion from laboratory to material time is thoroughly discussed. Similarities and differences to field-induced higher-harmonic susceptibilities are illustrated using Lissajous and Cole-Cole plots and discussed in terms of aging nonlinearity parameters. For the Lissajous plots, banana-type shapes emerge, while the Cole-Cole plots display cardioidic and other visually appealing patterns. For application beyond the regime in which conventional single-parameter aging concepts work, the Wiener-Volterra material-time-series is introduced as the central tool. Calculations and analyses within this general framework in conjunction with suitable choices of higher-order memory kernels and employing correspondingly extended TNM models yield at least qualitative agreement with recent large-perturbation physical aging experiments. Implications for differential scanning calorimetry and related methods are discussed. The introduced concepts and analyses provide a solid foundation for a generalized description of nonlinear thermal out-of-equilibrium dynamics of glass forming materials, differing from the nonlinear responses known from rheology and dielectric spectroscopy.

Distance-as-time in physical aging

Although it has been known for half a century that the physical aging of glasses in experiments is described well by a linear thermal-history convolution integral over the so-called material time, the microscopic definition and interpretation of the material time remains a mystery. We propose that the material-time increase over a given time interval reflects the distance traveled by the system's particles. Different possible distance measures are discussed, starting from the standard mean-square displacement and its inherent-state version that excludes the vibrational contribution. The viewpoint adopted, which is inspired by and closely related to pioneering works of Cugliandolo and Kurchan from the 1990s, implies a "geometric reversibility" and a "unique-triangle property" characterizing the system's path in configuration space during aging. Both of these properties are inherited from equilibrium, and they are here confirmed by computer simulations of an aging binary Lennard-Jones system. Our simulations moreover show that the slow particles control the material time. This motivates a "dynamic-rigidity-percolation" picture of physical aging. The numerical data show that the material time is dominated by the slowest particles' inherent mean-square displacement, which is conveniently quantified by the inherent harmonic mean-square displacement. This distance measure collapses data for potential-energy aging well in the sense that the normalized relaxation functions following different temperature jumps are almost the same function of the material time. Finally, the standard Tool-Narayanaswamy linear material-time convolution-integral description of physical aging is derived from the assumption that when time is replaced by distance in the above sense, an aging system is described by the same expression as that of linear-response theory.

Single-parameter aging in a binary Lennard-Jones system

This paper studies physical aging by computer simulations of a 2:1 Kob-Andersen binary Lennard-Jones mixture, a system that is less prone to crystallization than the standard 4:1 composition. Starting from thermal-equilibrium states, the time evolution of the following four quantities is monitored by following up and down jumps in temperature: potential energy, virial, average squared force, and the Laplacian of the potential energy. Despite the fact that significantly larger temperature jumps are studied here than in typical similar experiments, to a good approximation, all four quantities conform to the single-parameter-aging scenario derived and validated for small jumps in experiments [T. Hecksher, N. B. Olsen, and J. C. Dyre, J. Chem. Phys. 142, 241103 (2015)]. As a further confirmation of single-parameter aging with a common material time for the four different quantities monitored, their relaxing parts are found to be almost identical for all temperature jumps.

Plasticity and aging of folded elastic sheets

We investigate the dissipative mechanisms exhibited by creased material sheets when subjected to mechanical loading, which comes in the form of plasticity and relaxation phenomena within the creases. After demonstrating that plasticity mostly affects the rest angle of the creases, we devise a mapping between this quantity and the macroscopic state of the system that allows us to track its reference configuration along an arbitrary loading path, resulting in a powerful monitoring and design tool for crease-based metamaterials. Furthermore, we show that complex relaxation phenomena, in particular memory effects, can give rise to a nonmonotonic response at the crease level, possibly relating to the similar behavior reported for crumpled sheets. We describe our observations through a classical double-logarithmic time evolution and obtain a constitutive behavior compatible with that of the underlying material. Thus the lever effect provided by the crease allows magnified access to the material's rheology.

Fast contribution to the activation energy of a glass-forming liquid

This paper presents physical-aging data for the silicone oil tetramethyl-tetraphenyl trisiloxane. The density and the high-frequency plateau shear modulus [Formula: see text] were monitored following temperature jumps starting from fully equilibrated conditions. Both quantities exhibit a fast change immediately after a temperature jump. Adopting the material-time formalism of Narayanaswamy, we determine from the dielectric loss at 0.178 Hz the time evolution of the aging-rate activation energy. The relative magnitude of the fast change of the activation energy differs from that of the density, but is identical to that of [Formula: see text] In fact, the activation energy is proportional to [Formula: see text] throughout the aging process, with minor deviations at the shortest times. This shows that for the silicone oil in question the dynamics are determined by [Formula: see text] in-as well as out of-equilibrium.

Isomorph theory of physical aging

This paper derives and discusses the configuration-space Langevin equation describing a physically aging R-simple system and the corresponding Smoluchowski equation. Externally controlled thermodynamic variables like temperature, density, and pressure enter the description via the single parameter T_s/T, in which T is the bath temperature and T_s is the "systemic" temperature defined at any time t as the thermodynamic equilibrium temperature of the state point with density ρ(t) and potential energy U(t). In equilibrium, T_s ≅ T with fluctuations that vanish in the thermodynamic limit. In contrast to Tool's fictive temperature and other effective temperatures in glass science, the systemic temperature is defined for any configuration with a well-defined density, even if it is not close to equilibrium. Density and systemic temperature define an aging phase diagram, in which the aging system traces out a curve. Predictions are discussed for aging following various density-temperature and pressure-temperature jumps from one equilibrium state to another, as well as for a few other scenarios. The proposed theory implies that R-simple glass-forming liquids are characterized by the dynamic Prigogine-Defay ratio being equal to unity.

Nonmonotonic Aging and Memory Retention in Disordered Mechanical Systems

We observe nonmonotonic aging and memory effects, two hallmarks of glassy dynamics, in two disordered mechanical systems: crumpled thin sheets and elastic foams. Under fixed compression, both systems exhibit monotonic nonexponential relaxation. However, when after a certain waiting time the compression is partially reduced, both systems exhibit a nonmonotonic response: the normal force first increases over many minutes or even hours until reaching a peak value, and only then is relaxation resumed. The peak time scales linearly with the waiting time, indicating that these systems retain long-lasting memory of previous conditions. Our results and the measured scaling relations are in good agreement with a theoretical model recently used to describe observations of monotonic aging in several glassy systems, suggesting that the nonmonotonic behavior may be generic and that athermal systems can show genuine glassy behavior.