Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance

TL;DR

This paper advances the theoretical understanding of strongly correlating liquids, exploring their scale invariance, simulation results, ensemble effects, and thermodynamic connections, particularly focusing on van der Waals liquids and their properties.

Contribution

It provides a detailed analysis of the scaling behavior, simulation insights, and thermodynamic interpretations of liquids with hidden scale invariance, extending previous work on strongly correlating liquids.

Findings

Strong virial-potential energy correlations in certain liquids.

Scale invariance properties of inverse power-law potentials.

Connection between correlations and thermodynamic parameters like Gruneisen.

Abstract

In this third paper of the series, which started with [N. P. Bailey et al., J. Chem. Phys. 129, 184507 and 184508 (2008)], we continue the development of the theoretical understanding of strongly correlating liquids - those whose instantaneous potential energy and virial are strongly correlated in their thermal equilibrium fluctuations at constant volume. The existence of such liquids was detailed in previous work which identified them, based on computer simulations, as a large class of liquids, including van der Waals liquids but not, e.g., hydrogen-bonded liquids. We here discuss the following: (1) The scaling properties of inverse power-law and extended inverse power-law potentials (the latter include a linear term which "hides" the approximate scale invariance); (2) results from computer simulations of molecular models concerning out-of-equilibrium conditions; (3) ensemble dependence of the virial / potential energy correlation coefficient; (4) connection to the Gruneisen parameter; (5) interpretation of strong correlations in terms of the energy-bond formalism.