The dynamic properties of monatomic liquids

Abstract

The computer simulation and inelastic neutron scattering studies of simple, monatomic liquids are reviewed, together with the theory appropriate for their interpretation. All three aspects of the dynamic properties of monatomic liquids began a new era of development around 1965, and the review is concerned chiefly with the experiments and theory reported in the intervening decade.Computer simulation (molecular dynamics) studies have featured strongly in the development of non-equilibrium statistical mechanics techniques for the calculation of correlation functions that enter the various measured susceptibilities. In fact molecular dynamics studies of systems interacting via continuous potentials have developed to the level of sophistication where they set a standard for neutron scattering experiments. The neutron experiments are difficult to perform with high accuracy, yet they offer a unique means of investigating the dynamics of simple liquids in the domain of wavevectors and frequencies larger than about 0.05 A-1 and 5 x 1011 s-1 respectively. The problems faced in analysing neutron data to the level required today are reviewed in detail, with particular attention to multiple scattering corrections. A review of neutron experiments on monatomic liquids shows that surprisingly few bear close scrutiny today. Theory has developed through the rigorous generalization of the Markovian theory of fluctuations set out by Landau and Lifshitz (1959). The development has taken the form of a generalized Langevin equation, proposed by Zwanzig (1961) and Mori (1965a), which provides a framework within which neutron and molecular dynamics data may be interpreted. The technique is reviewed, related to linear response theory, and used to summarize the recent theories.

Time-Oscillating Lyapunov Modes and the Momentum Autocorrelation Function

“…A possible explanation for this relation is proposed. The auto-correlation function can be observed directly by the neutron and light scattering experiments [15,17] and is connected to transport coefficients using linear response theory [18], so this result gives quantitative evidence of a connection between the Lyapunov modes and an experimentally accessible quantity.…”

Collective dynamics of simple liquids: A mode-coupling description

“…To find a theoretical description of the dynamics of simple monatomic liquids in the microscopic frequency and wavenumber regime (involving inverse Angstroms and inverse picoseconds), which is accessible to inelastic neutron and X-ray scattering, is already a long-standing issue [1][2][3][4][5]. One of the important quantities of interest is the dynamical structure factor S(q, ω), which is the spaceand-time Fourier transform of the density-density correlation function.…”

“…This is so, because within such a description the moment sum rules, which follow from the conservation laws, are obeyed automatically. It is widely believed [1][2][3][4]11] that the frequency moments c (n) q = ∞ −∞ dωω n S(q, ω)) of S(q, ω), essentially determine the dispersion of the collective vibrational excitations of the liquid. The formalism is called generalized hydrodynamics because for small energies and momenta it goes over into linearized hydrodynamics [2][3][4].…”

“…In fact S(q, ω) is just the Fourier transform of the density-density correlation function F q (t). A simple approach was to use a phenomenological ansatz M q (t) ∝ e −t/τq [1] and to fit the function τ q to the experimental or simulational data. However, such a single-exponential ansatz was already shown to be insufficient to fit early simulation data of Lennard-Jones Argon [12] in the early days of this subject.…”

Ultrahigh-Energy-Resolution Inelastic X-Ray Scattering Spectroscopy

“…The line drawn in Fig. 7 was calculated using a viscoelastic model, derived in [12,13] for a monoatomic fluid, which includes fluctuations in the particle density and the energy density beyond the hydrodynamic limit. There is good agreement between the calculated curve and the X-ray data within the error bars.…”