Experimental Confirmation of the Universal Law for the Vibrational Density of States of Liquids

TL;DR

This study experimentally confirms the universal vibrational density of states law for liquids, showing a linear relationship at low energies across various real liquids, and evaluates its implications for thermodynamic properties.

Contribution

It provides experimental validation of the universal vibrational density of states law for liquids, extending previous simulations to real systems and analyzing their thermodynamic behavior.

Findings

Universal law g(ω) ~ ω confirmed for water, metals, and polymers.

Effective relaxation rates extracted from experimental data.

Model predictions align with measured specific heat values.

Abstract

An analytical model describing the vibrational phonon density of states (VDOS) of liquids has long been elusive, mainly due to the difficulty in dealing with the imaginary modes dominant in the low-energy region, as described by the instantaneous normal mode (INM) approach. Nevertheless, Zaccone and Baggioli have recently developed such a model based on overdamped Langevin liquid dynamics. The model was proposed to be the universal law for the vibrational density of states of liquids. Distinct from the Debye law, g({\omega}) ~ {\omega}2, for solids, the universal law for liquids reveals a linear relationship, g({\omega}) ~ {\omega}, in the low-energy region. The universal law has been successfully verified with computer simulated VDOS for Lennard-Jones liquids. We further confirm this universal law with experimental VDOS measured by inelastic neutron scattering on real liquid systems including water, liquid metal, and polymer liquids. We have applied this model and extracted the effective relaxation rate for the short time dynamics for each liquid. The model has been further evaluated in the predication of the specific heat. The results have been compared with the existing experimental data as well as with values obtained by different approaches.