Explaining the specific heat of liquids based on instantaneous normal modes

TL;DR

This paper develops a theory explaining the specific heat of liquids by incorporating instantaneous normal modes, linking vibrational dynamics to thermodynamic properties and fitting experimental data across various liquids.

Contribution

It introduces a novel analytical model based on INMs that accounts for saddle points and predicts the temperature dependence of liquid specific heat.

Findings

The theory explains the decrease of specific heat with temperature.

It fits experimental data for atomic and molecular liquids.

It correlates energy barriers with specific heat slope.

Abstract

The successful prediction of the specific heat of solids is a milestone in the kinetic theory of matter, due to Debye (1912). No such success, however, has ever been obtained for the specific heat of liquids, which has remained a mystery for over a century. A theory of specific heat of liquids is derived here using a recently proposed analytical form of the vibrational density of states (DOS) of liquids, which takes into account saddle points in the liquid energy landscape via the so-called instantaneous normal modes (INMs), corresponding to negative eigenvalues (imaginary frequencies) of the Hessian matrix. The theory is able to explain the typical monotonic decrease of specific heat with temperature observed in liquids, in terms of the average INM excitation lifetime decreasing with T (in accordance with Arrehnius law), and provides an excellent single-parameter fitting to several sets of experimental data for atomic and molecular liquids. It also correlates the height of the liquid energy barrier with the slope of the specific heat in function of temperature in accordance with the available data. These findings demonstrate that the specific heat of liquids is controlled by the instantaneous normal modes, i.e. by localized, unstable (exponentially decaying) vibrational excitations, and provide the missing connection between anharmonicity, saddle points in the energy landscape, and the thermodynamics of liquids.