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

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.

v2: matching the published version to appear in PRB

References in corpus (12)

• Heat capacity of liquids: an approach from the solid phase
• Emergence and evolution of $k$-gap in spectra of liquid and supercritical states
• Universal law for the vibrational density of states of liquids
• Explaining the specific heat of liquids based on instantaneous normal modes
• Experimental Confirmation of the Universal Law for the Vibrational Density of States of Liquids
• Modelling of liquid internal energy and heat capacity over a wide pressure-temperature range from first principles
• Atomic dynamics in fluids: Normal mode analysis revisited
• Viscosity and diffusion in life processes and tuning of fundamental constants
• Experimental observation of gapped shear waves and liquid-like to gas-like dynamical crossover in active granular matter
• On the temperature dependence of the density of states of liquids at low energies
• Emergence of Debye scaling in the density of states of liquids under nanoconfinement
• Generalized Rosenfeld-Tarazona scaling and high-density specific heat of simple liquids

Cited by in corpus (2)

• Heat capacity of dense liquids: A link between two-phase model and melting temperature scaling
• Vibrational model of entropy in dense two-dimensional fluids