Dynamic properties of simple liquids: Dependence on the softness of the potential core

Brownian motion with time-dependent friction and single-particle dynamics in liquids

A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic diffusion in a mean-time-dependent harmonic force field. A modified, non-Markovian Langevin equation is utilized to derive an equation of motion for the velocity autocorrelation function with time-dependent friction coefficient. Numerical solution of the equation gives an excellent account of the velocity autocorrelation function in Lennard-Jones liquids, liquid alkali, and transition metals over a broad range of density and temperature. Derivation of the equation of motion leads to a self-consistent expression for the time dependence of friction coefficient. Our results demonstrate that the nature of time dependence of the friction coefficient changes dramatically with the liquid density. At low and moderate densities, the dynamic friction decays exponentially whereas it increases exponentially at high liquid densities. Our findings provide an opportunity for a different outlook of the Brownian description of atomic dynamics in liquids.

State dependent particle dynamics in liquid alkali metals

This paper gives a survey of the particle dynamics in the liquid alkali metals observed with inelastic x-ray and neutron scattering experiments. Liquid rubidium and sodium are chosen as model fluids to represent the behaviour of this group of fluids. In the dense metallic monatomic melt the microscopic dynamics is characterized by collective excitations similar to those in the corresponding solids. The collective particle behaviour is appropriately described using a memory function formalism with two relaxation channels for the density correlation. A similar behaviour is found for the single particle motion where again two relaxation mechanisms are needed to accurately reproduce the experimental findings. Special emphasis is given to the density dependence of the particle dynamics. An interesting issue in liquid metals is the metal to non-metal transition, which is observed if the fluid is sufficiently expanded with increasing temperature and pressure. This causes distinct variations in the interparticle interactions, which feed back onto the motional behaviour. The associated variations in structure and dynamics are reflected in the shape of the scattering laws. The experimentally observed features are discussed and compared with simple models and with the results from computer simulations.

Velocity autocorrelation function for simple liquids and its application to liquid metals and alloys

The single-particle Brownian motion in simple monatomic liquids has been described with the help of the equation of motion in terms of velocity autocorrelation function psi(t) , where the particle is assumed to diffuse in a mean-time-dependent field. The equation of motion which is a second order differential equation in psi(t) has been solved in terms of nth order Bessel functions of the first and second kind. The solution is, in fact, the generalization of the solution given by Glass and Rice (GR) [Phys. Rev. 176, 239 (1968)] for low density fluids. The generalized solution is an improvisation over the one by GR and the results demonstrate that, for high density liquids such as liquid metals where the GR solution fails to give a reasonable account of psi(t) , the generalized solution could be very useful to calculate psi(t) . The present approach has been applied to the liquid alkali metals and binary alloys. The results are found to be in close agreement with the molecular dynamics results.

Molecular dynamics study of the longitudinal modes in disparate-mass binary liquid mixtures

A series of molecular dynamics simulations of simple liquid binary mixtures of soft spheres with disparate-mass particles were carried out to investigate the origin of the marked differences between the dynamic structure factors of some liquid binary mixtures such as the Li0.7Mg0.3 and Li0.8Pb0.2 alloys. It is shown that the facility for observing peaks associated with fast-propagating modes in the partial Li-Li dynamic structure factor of Li0.8Pb0.2 should be mainly attributed to the structure of this alloy, which is characterized by an incipient ABAB ordering as found in molten salts. The longitudinal dispersion relations at intermediate wave vectors obtained from the longitudinal current spectra are very similar for the two alloys and reflect the existence of both fast-and slow-propagating modes of kinetic character associated with light and heavy particles, respectively. The influence of the hardness of the repulsive potential cores as well as the composition of the mixture on the longitudinal collective modes is also discussed.

Velocity cross-correlations and atomic momentum transfer in simple liquids with different potential cores

Time correlation functions between the velocity of a tagged particle and velocities of particles within specified ranges of initial separations have been obtained by molecular dynamics simulation. These correlation functions have allowed us to analyze the momentum transfer between particles in different coordination shells. Two simple liquids at very different densities and two purely repulsive potentials with very different softnesses have been considered. The longitudinal correlations, which are the velocity cross-correlations along the initial direction defined by the centers of two given particles, have been calculated separately. It has been proven that these correlations should be attributed to particles both in front of and behind the central one. As with propagating longitudinal modes, they are strongly dependent on the softness of the potential core. Some characteristic features of the velocity correlation functions after the initial rise should be related to nonlongitudinal correlations. It has been shown that velocity cross-correlations between distinct particles cannot only be attributed to the direct interactions among particles, but also to the motions induced by the movement of a tagged particle on their neighbors.