Solidity of viscous liquids. V. Long-wavelength dominance of the dynamics

TL;DR

This paper discusses a model for viscous liquids near the glass transition, emphasizing long-wavelength dynamics and ultralocal free energy, aligning with key experimental observations about glassy and liquid states.

Contribution

It introduces a simple, consistent model based on long-wavelength dominance and ultralocal free energy to explain viscous liquid behavior near the glass transition.

Findings

Model explains lack of long-range order in viscous liquids

Lower compressibility of glasses compared to liquids

Multiple relaxation times in alpha process

Abstract

This paper is the fifth in a series exploring the physical consequences of the solidity of glass-forming liquids. Paper IV proposed a model where the density field is described by a time-dependent Ginzburg-Landau equation of the nonconserved type with rates in $k$ space of the form $\Gamma_0+Dk^2$. The model assumes that $D\gg\Gamma_0a^2$ where $a$ is the average intermolecular distance; this inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) to a good approximation may be taken to be ultralocal. In the present paper we argue that this is the simplest model consistent with the following three experimental facts: 1) Viscous liquids approaching the glass transition do not develop long-range order; 2) The glass has lower compressibility than the liquid; 3) The alpha process involves several decades of relaxation times shorter than the mean relaxation time. The paper proceeds to list six further experimental facts characterizing equilibrium viscous liquid dynamics and shows that these are readily understood in terms of the model; some are direct consequences, others are quite natural when viewed in light of the model.