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

Jeppe C Dyre

doi:10.1103/physreve.76.041508

Abstract

This paper is the fifth in a series exploring the physical consequences of the solidity of highly viscous 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 Gamma0+Dk2. If a is the average intermolecular distance, the model assumes that DGamma0a2. 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, i.e., with the property that equal-time field fluctuations are uncorrelated in space. Paper IV also briefly discussed how to generalize the model by including the molecular orientational fields, the stress tensor fields, and the potential energy density field. In the present paper it is argued 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 of viscous liquid dynamics and shows that these follow naturally from the model.

Highlights

The idea that viscous liquids approaching the calorimetric glass transition are solidlike goes back in time at least to Kauzmann’s and Goldstein’s famous papers from 1948 and 1969 ͓1,2͔
A paper utilizing arguments from solid-state elasticity in viscous liquid dynamics preceding this series was a joint publication with Olsen and Christensen in 1996, where the “shoving model” for the temperature dependence of the viscosityor relaxation timewas proposed13͔
Mode-coupling theory48,49͔ is an interesting case where cooperativity enters via the coupling of single-particle motion to the surroundings, resulting in a modification of the single-particle motion with drastic consequences at low temperaturesinfinite relaxation time at a finite temperature in the simplest and most studied version of the theory

Summary

INTRODUCTION

The idea that viscous liquids approaching the calorimetric glass transition are solidlike goes back in time at least to Kauzmann’s and Goldstein’s famous papers from 1948 and 1969 ͓1,2͔. A paper utilizing arguments from solid-state elasticity in viscous liquid dynamics preceding this series was a joint publication with Olsen and Christensen in 1996, where the “shoving model” for the temperature dependence of the viscosityor relaxation timewas proposed13͔ According to this and related elastic models14,15͔ the activation energy is proportional to the instantaneous shear modulus Gρthe shear modulus measured on a very short time scale. Starting from the BEL model, it was argued that the ␻−1/2 high-frequency behavior arises from a long-time tail mechanism operating over a range of times shorter than the ␣ relaxation time This was justified by a solidity-based argument with the irrelevance of momentum conservation as an important ingredient, allowing for the center of mass to move following a flow event.

THREE FACTS OF VISCOUS LIQUID DYNAMICS

THE SIMPLEST MODEL FOR EQUILIBRIUM

DISCUSSION