Solidity of viscous liquids. IV. Density fluctuations

TL;DR

This paper develops a theoretical framework describing density fluctuations in highly viscous liquids, proposing a Ginzburg-Landau model with long-wavelength dominance and predicting specific frequency-dependent bulk modulus behavior.

Contribution

It introduces a novel density fluctuation model based on a long-wavelength dominated Ginzburg-Landau equation and extends the theory to include stress, energy, and orientation fields.

Findings

Predicts asymmetric frequency dependence of bulk modulus

Shows Debye behavior at low frequencies

Derives high-frequency loss decay as ω^{-1/2}

Abstract

This paper is the fourth in a series exploring the physical consequences of the solidity of highly viscous liquids. It is argued that the two basic characteristics of a flow event (a jump between two energy minima in configuration space) are the local density change and the sum of all particle displacements. Based on this it is proposed that density fluctuations are described by a time-dependent Ginzburg-Landau equation with rates in k-space of the form $\Gamma_0+Dk^2$ with $D\gg\Gamma_0a^2$ where $a$ is the average intermolecular distance. The inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) may be taken to be ultra local. As an illustration of the theory the case with the simplest non-trivial Hamiltonian is solved to second order in the Gaussian approximation, where it predicts an asymmetric frequency dependence of the isothermal bulk modulus with Debye behavior at low frequencies and an $\omega^{-1/2}$ decay of the loss at high frequencies. Finally, a general formalism for the description of viscous liquid dynamics, which supplements the density dynamics by including stress fields, a potential energy field, and molecular orientational fields, is proposed.