Isomorph theory of physical aging

Abstract

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, pressure enter the description via the single parameter $T_{\mathrm{s}}/T$ in which $T$ is the bath temperature and $T_{\mathrm{s}}$ is the "systemic" temperature defined at any time $t$ as the thermodynamic equilibrium temperature of the state point with density $\rho (t)$ and potential energy $U(t)$. In equilibrium $T_{\mathrm{s}}\cong T$ 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 in any sense 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 a dynamic Prigogine-Defay ratio of unity.

References in corpus (20)

• Pressure-energy correlations in liquids. I. Results from computer simulations
• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Strong pressure-energy correlations in van der Waals liquids
• Pressure-energy correlations in liquids. II. Analysis and consequences
• Explaining why simple liquids are quasi-universal
• Common mechanism of thermodynamic and mechanical origin for ageing and crystallisation of glasses
• On the long-waves dispersion in Yukawa systems
• Feasibility of single-order parameter description of equilibrium viscous liquid dynamics
• Invariants in the Yukawa system's thermodynamic phase diagram
• Freezing and melting line invariants of the Lennard-Jones system
• Hidden scale invariance of metals
• Direct tests of single-parameter aging
• Single-order-parameter description of glass-forming liquids: A one-frequency test
• Glass-forming liquids: One or more "order" parameters?
• Scaling of the dynamics of flexible Lennard-Jones chains. II. Effects of harmonic bonds
• Studies of the Lennard-Jones fluid in 2, 3, and 4 dimensions highlight the need for a liquid-state 1/d expansion
• Tuning Pairwise Potential Can Control the Fragility of Glass-Forming Liquids: From Tetrahedral Network to Isotropic Soft Sphere Models
• Density scaling and quasiuniversality of flow-event statistics for athermal plastic flows
• Effect of density on the physical aging of pressure-densified polymethylmethacrylate
• A simple nonlinear equation for structural relaxation in glasses

Cited by in corpus (9)

• Experimental evidence of a state-point dependent scaling exponent of liquid dynamics
• Generalized single-parameter aging tests and their application to glycerol
• From sub-aging to hyper-aging in structural glasses
• Isomorph theory beyond thermal equilibrium
• Scaling properties of liquid dynamics predicted from a single configuration: Small rigid molecules
• Isomorph invariance of dynamics of sheared glassy systems
• Comparing zero-parameter theories for the WCA and harmonic-repulsive melting lines
• Isomorphs in sheared binary Lennard-Jones glass: Transient response
• Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Pseudoisomorphs for Harmonic-Bonded Molecules