Sound Velocities of Generalized Lennard-Jones (n - 6) Fluids Near Freezing.

Sergey Khrapak

doi:10.3390/molecules26061660

Abstract

In a recent paper [S. Khrapak, Molecules 25, 3498 (2020)], the longitudinal and transverse sound velocities of a conventional Lennard–Jones system at the liquid–solid coexistence were calculated. It was shown that the sound velocities remain almost invariant along the liquid–solid coexistence boundary lines and that their magnitudes are comparable with those of repulsive soft-sphere and hard-sphere models at the fluid–solid phase transition. This implies that attraction does not considerably affect the magnitude of the sound velocities at the fluid–solid phase transition. This paper provides further evidence to this by examining the generalized Lennard–Jones (n − 6) fluids with n ranging from 12 to 7 and demonstrating that the steepness of the repulsive term has only a minor effect on the magnitude of the sound velocities. Nevertheless, these minor trends are identified and discussed.

Highlights

Sound velocities are important characteristics of a substance
Since the shear modulus is smaller than the longitudinal one and there are two shear and one longitudinal mode in 3D systems, the contribution from shear modes dominates, leading to the conclusion that ct/vT should be approximately constant at the fluid–solid phase transition [7]
The relation between the sound velocities and excess energy and pressure derived by Zwanzig and Mountain [13] for the conventional (12-6) LJ potential has been generalized to the case of (n − 6) potential

Summary

Introduction

Sound velocities are important characteristics of a substance. They are directly related to long-wavelength excitations—phonons, which play a crucial role in condensed matter, materials science, and soft matter. It is important to understand mechanisms that can affect and regulate sound velocities in various situations. In simple atomic systems with smooth pairwise interaction potentials, the sound velocities can be expressed as sums over atoms involving the first and second derivatives of the interaction potential (see below). In isotropic situations (in gases and liquids), these sums can be expressed as integrals involving the radial distribution function g(r). The sound velocities are completely determined by the shape of the interaction potential and the atomic structure of the system (which are, interrelated)

Methods

Results

Conclusion