Revisiting the phonon theory of liquid heat capacity: low-frequency shear modes and intramolecular vibrations

TL;DR

This paper revisits the phonon theory of liquid heat capacity, proposing new models for low-frequency shear modes and incorporating intramolecular vibrations, leading to improved agreement with experimental data across temperature ranges.

Contribution

It introduces alternative models for low-frequency shear modes in liquids and incorporates intramolecular vibrations into the phonon theory, enhancing its accuracy.

Findings

Overdamped liquid-like mode model best fits experimental data

Purely gas-like mode treatment causes inaccuracies at high temperatures

Original phonon model performs well only at low temperatures

Abstract

Modeling the heat capacity of liquids present fundamental difficulties due to the strong intermolecular particle interactions and large diffusive-like displacements. Based on the experimental evidence that the microscopic dynamics of liquids closely resemble those of solids, a phonon theory of liquid thermodynamics has been developed. Despite its success, the phonon theory of liquids relies on the questionable assumption that low-frequency shear excitations are propagating in nature and follow a Debye density of states. Furthermore, the same framework does not capture the contribution of intramolecular vibrations, which play a significant role in molecular liquids. In this work, we revisit the phonon theory of liquid heat capacity, introducing alternative approaches to model low-frequency shear modes. In particular, we consider the recently proposed idea of treating such modes as pure kinetic and we propose a novel approach based on identifying those low-frequency excitations as overdamped liquid-like modes with linear in frequency density of states. Moreover, we complete the theory by incorporating the effects of intramolecular vibrations. By comparing the theoretical predictions from these different approaches with the available data for the heat capacity of several liquids, we present a comprehensive evaluation of the original model and the newly proposed extensions. Despite all approaches perform well at low-temperatures, our results indicate that modeling low-frequency modes as overdamped liquid-like excitations yields the most accurate agreement with the data in the whole temperature range. Conversely, we demonstrate that treating these excitations as purely gas-like leads to significant inaccuracies, particularly at high temperatures.