The Rosenfeld-Tarazona expression for liquids' specific heat: A numerical investigation of eighteen systems

TL;DR

This study evaluates the Rosenfeld-Tarazona expression for liquids' specific heat across eighteen diverse systems, confirming its accuracy mainly for Roskilde simple liquids with strong virial-potential energy correlations, even under confinement.

Contribution

It demonstrates that the RT expression accurately predicts specific heat for Roskilde simple liquids and extends its applicability to confined molecular liquids, supported by isomorph theory.

Findings

RT expression is accurate for Roskilde simple liquids.

Strong virial-potential energy correlation predicts RT accuracy.

Density dependence of specific heat aligns with isomorph theory.

Abstract

We investigate the accuracy of the expression of Rosenfeld and Tarazona (RT) for the excess isochoric heat capacity, C_V^{ex} \propto T^{-2/5}, for eighteen model liquids. Previous investigations have reported no unifying features of breakdown for the RT expression. Here liquids with different stoichiometric composition, molecular topology, chemical interactions, degree of undercooling, and environment are investigated. We find that the RT expression is a better approximation for liquids with strong correlations between equilibrium fluctuations of virial and potential energy, i.e., Roskilde simple liquids [Ingebrigtsen et al., Phys. Rev. X 2, 011011 (2012)]. This observation holds even for molecular liquids under severe nanoscale confinement, the physics of which is completely different from the original RT bulk hard-sphere fluid arguments. The density dependence of the specific heat is predicted from the isomorph theory for Roskilde simple liquids, which in combination with the RT expression provides a complete description of the specific heat's density and temperature dependence.