Pressure fluctuations in isotropic solids and fluids

TL;DR

This paper investigates pressure fluctuations in isotropic solids and fluids, emphasizing the stress fluctuation approach to determine elastic moduli, and provides theoretical and numerical validation of the relation between the compression modulus and pressure fluctuations.

Contribution

It demonstrates that elastic moduli can be obtained directly from stress fluctuations without microscopic displacement fields, and derives a specific relation for the compression modulus in NPT ensembles.

Findings

Derived the relation K_row|P = P_id (2 - P_id/K) for the compression modulus.

Showed that stress fluctuation methods can be used to determine elastic properties.

Validated theoretical predictions with numerical simulations.

Abstract

Comparing isotropic solids and fluids at either imposed volume or pressure we investigate various correlations of the instantaneous pressure and its ideal and excess contributions. Focusing on the compression modulus K it is emphasized that the stress fluctuation representation of the elastic moduli may be obtained directly (without a microscopic displacement field) by comparing the stress fluctuations in conjugated ensembles. This is made manifest by computing the Rowlinson stress fluctuation expression K_row of the compression modulus for NPT-ensembles. It is shown theoretically and numerically that K_row|P = P_id (2 - P_id/K) with P_id being the ideal pressure contribution.