T Gaskell

Longitudinal modes, transverse modes and velocity correlations in liquids: II

By constructing a microscopic form for the velocity field the authors have derived an expression for the velocity autocorrelation function in a simple liquid. It represents an analysis of the correlation function in terms of the longitudinal and transverse momentum current densities and correctly describes both the long and short time behaviour. The authors have applied the result to a model of liquid rubidium in order to see how the collective modes in the system influence the individual particle motion. It is found that the longitudinal current component is responsible for the oscillatory behaviour of the velocity autocorrelation function; the principle peak in the associated frequency spectrum is generated by the coupling of the particle velocity to the transverse current; the coupling to the longitudinal current produces the peak or shoulder at higher frequencies which is observed in computer experiments; and the diffusion coefficient is determined almost entirely by the transverse current component.

Self-diffusion in liquid metals: A generalized stokes-einstein equation

Abstract The concept of a microscopic velocity field is invoked to describe atomic dynamics in liquids. In particular, it leads to an excellent description of the velocity autocorrelation function in simple liquid metals. This provides some justification for using the framework to investigate the diffusion mechanism. We demonstrate a Stokes-Einstein type of relationship between the self-diffusion and shear viscosity coefficients, which is confirmed experimentally in simple liquid metals near the melting point.

Velocity correlations, cooperative effects and relative diffusion in simple liquids

A study of momentum transfer in liquids has been carried out by computer simulation of the process in a Lennard-Jones fluid. The data have also been compared with theoretical predictions. The conclusions emphasise the importance of understanding cooperative dynamical effects amongst nearest and next-nearest neighbours when discussing single-particle motion. The authors also investigate the relative diffusion of a pair of atoms that are initially nearest neighbours, and show how cooperative effects slow the relative motion.

A self-consistent theory of single-particle motion in ordinary and supercooled liquids

The mean square displacement of a tagged particle in a liquid is known to exhibit a diffusive linear time dependence beyond a microscopic timescale. By making use of simple mode-coupling concepts the authors derive a set of analytic self-consistent equations for the relevant dynamical quantities in this regime, namely the diffusion coefficient and the intercept. The results of the theory are successfully compared with the data obtained by simulation experiments in different systems.

Self-diffusion and relative diffusion processes in liquids: microdynamic and hydrodynamic points of view

A microdynamic theory for the self-diffusion coefficient, which involves a wave-number-dependent viscosity, eta (q), is successfully tested on a hard-sphere system. The models the authors introduce for eta (q) are adapted to the Lennard-Jones fluid. New molecular dynamics data for the relative diffusion coefficient, in which the initial separation of two particles appears as an additional degree of freedom, are reported for this fluid. A systematic investigation of near-neighbour pairs shows (i) clear evidence of effects that slow their relative motion and (ii) that the relative diffusion coefficient varies remarkably smoothly with separation. The theory is extended to interpret the results and it is shown that the expressions for both types of diffusion coefficient take a form that is strongly reminiscent of a hydrodynamic treatment. This, the authors suggest, is why hydrodynamic theories (e.g. the Stokes-Einstein equation for the self-diffusion coefficient, and the Oseen approach to relative diffusion) appear to be applicable even at an atomic level. They emphasise, instead, the essentially microscopic nature of the diffusion process in monatomic liquids.

Wavevector-Dependent Shear Viscosity in Lennard-Jones Liquids

Computer simulation data for the generalized wavevector-dependent shear viscosity η(q) are reported for the first time in a Lennard-Jones fluid. The transverse current autocorrelation functions are also presented. The results are carefully compared with simple viscoelectric theory. Although the latter is found to give a respectable description of the data, discrepancies are pointed out.

An improved description of three-particle correlations in liquids and a modified Born-Green equation

The application of the superposition approximation for the three-particle distribution function in a liquid, within the context of the Born-Green equation, is re-examined. It is shown how to correct this approximation for configurations in which one particle is well separated from the other two, and then demonstrated explicitly for the dipole-induced dipole pair potential that this correction is consistent with the known asymptotic expression for the radial distribution function. A modified form of the Born-Green equation is proposed which contains this improved description of triplet correlations.

Atomic dynamics and momentum transfer in dense liquids

A simple representation for the velocity field is used to investigate momentum transfer in a dense liquid. An appropriate method of discussing the process is by means of the time-dependent correlation of the initial velocity of an atom with the velocities of a group of atoms, within a sphere, whose centre is the location of the same atom at some later time. As the auto-correlation contribution decays, the correlation with the velocities of the surrounding atoms builds up as the momentum transfer progresses. The technique is applied to a liquid metal and a rigid-sphere fluid. It is shown how the information obtained in this way may be used to gain some physical insight into atomic dynamics in liquids.

Ionic dynamics in the strongly coupled one-component plasma

The highly organised collective modes which the plasma can support greatly influence the single-particle motion. The effects are quantitatively assessed through a theory of the velocity autocorrelation function, and the discussion is extended to include momentum transfer in this system. The dominant role of the plasma oscillations is clear, but the coupling to the transverse collective modes is also emphasised, producing a more comprehensive physical picture of ionic dynamics.

Transverse current correlations in simple liquids

An approximate expression for the memory function associated with transverse current correlations have been evaluated for models both of liquid rubidium and liquid argon. Results for the frequency spectrum of the current correlation function are also presented for a range of wavenumbers and compared, where possible, with those obtained from computer simulation studies. From the memory function an expression for the shear viscosity coefficient may be derived, but the values obtained for the latter near the melting points of the liquids are of the order of 40% smaller than the experimentally determined values.