Solidity of viscous liquids. IV. Density fluctuations

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 ${\Gamma }_0+D{k}^2$ with $D\gg {\Gamma }_0{a}^2$ 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.

References in corpus (1)

• Solidity of viscous liquids. III. Alpha relaxation

Cited by in corpus (8)

• Investigation of the shear-mechanical and dielectric relaxation processes in two mono-alcohols close to the glass transition
• Solid-that-flows picture of glass-forming liquids
• Ten themes of viscous liquid dynamics
• On the Spectral Shape of the Structural Relaxation in Deeply Supercooled Liquids
• Distance-as-time in physical aging
• Solidity of viscous liquids. V. Long-wavelength dominance of the dynamics
• Swap Monte Carlo for diatomic molecules
• Rheological model for the alpha relaxation of glass-forming liquids and its comparison to data for DC704 and DC705