Beyond power-law density scaling: Theory, Simulation, and Experiment

TL;DR

This paper demonstrates the limitations of power-law density scaling in supercooled liquids and introduces a more general, single-variable density scaling framework supported by simulations and experiments.

Contribution

It derives a generalized density scaling form applicable to various systems, extending beyond traditional power-law models.

Findings

Power-law density scaling breaks down for large density variations.

A new generalized scaling form fits all studied systems.

Analytical expression for Lennard-Jones systems matches simulations.

Abstract

Supercooled liquids are characterized by relaxation times that increase dramatically by cooling or compression. Many liquids have been shown to obey power-law density scaling, according to which the relaxation time is a function of density to some power over temperature. We show that power-law density scaling breaks down for larger density variations than usually studied. This is demonstrated by simulations of the Kob-Andersen binary Lennard-Jones mixture and two molecular models, as well as by experimental results for two van der Waals liquids. A more general form of density scaling is derived, which is consistent with results for all the systems studied. An analytical expression for the scaling function for liquids of particles interacting via generalized Lennard-Jones potentials is derived and shown to agree very well with simulations. This effectively reduces the problem of understanding the viscous slowing down from being a quest for a function of two variables to a search for a single-variable function.