Dynamics of Dense Supercritical Neon at the Transition from Hydrodynamical to Single-Particle Regimes

Abstract

The dynamic structure factor, S͑Q, E͒, of neon has been studied by inelastic x-ray scattering and by molecular dynamic simulation in the momentum transfer region Q 1 25 nm 21 at T 295 K and P 3 kbar. At this density, comparable to that of the liquid at ambient pressure, the shape of S͑Q, E͒ evolves from a Brillouin triplet towards a complex single line shape, which precurs the shape expected for single-particle behavior. The data, analyzed using the three mode model of the molecular hydrodynamics, show the absence of positive dispersion in the sound velocity and a minimum in the dispersion curve. [S0031-9007(98)05931-6] PACS numbers: 51.10. + y, 61.10.Eq, 61.20.Ja, 78.70.Ck During the past decades, much effort has been devoted to studying the dynamic structure factor, S͑Q, E͒, of dense fluids in both liquid and gaseous phases. One of the aims is the understanding of the transition from the hydrodynamics regime towards the so-called kinetic one [1], as a function of the density r and of the exchanged momentum Q. These two different regimes can be distinguished by a length scale characteristic of the system. This is often chosen as the Enskog mean free path l E defined as l E l B ͞g͑r 0 ͒, where l B is the Boltzmann mean free path, l 21 B prr 2 0 ͞2, and g͑r 0 ͒ is the pair distribution function evaluated at the particles' radius r 0 . For excitations with wavelength 2p͞Q much larger than l E , the fluid appears as a continuum, and the Navier-Stokes equation can be used to derive the S͑Q, E͒. At intermediate Q values Ql E ഠ 1, the breakdown of the hydrodynamics theory is expected to occur. For Ql E ¿ 1, the dynamics becomes that of a single free particle between two collisions with its neighbors. In the two limit cases the dynamic structure factor has a well-known shape and a simple physical interpretation: (i) In the small Ql E limit there are three modes. These are, respectively, the two Stokes and anti-Stokes compression (sound) modes, which disperse linearly with a slope corresponding to the adiabatic velocity of sound, and the heat diffusion mode, which is centered at zero energy transfer and has a width proportional to D T Q 2 , D T being the thermal diffusion coefficient. (ii) In the high Ql E limit, within the impulse approximation, the line shape reflects the initial state momentum distribution, i.e., the Boltzmann distribution. Here, the S͑Q, E͒ reduces to a Gaussian centered at the recoil energyh 2 Q 2 ͞2M, where M is the particle mass.The extension of a three mode description of S͑Q, E͒ beyond the hydrodynamic limit, where Ql E approaches unity, has been suggested by kinetic theory [2] and several molecular dynamics studies performed with both hard spheres [3] and Lennard-Jones potentials [4]. Firm experimental data covering in detail the whole transition region up to Q m , the Q value of the first maximum in the static structure factor, are not yet available in high density fluids above the critical point, in spite of the speculative interest to have a complete overview of all dynamic processes at b...

Collective dynamics in noble-gas and other very simple classical fluids

“…Experimental data in the room-temperature gas, at a pressure of 0.3 GPa and a density close to that of the liquid phase, were found in agreement with LJ-simulated spectra, whose collective modes were then analyzed in terms of the GRB model [51] in the range 1 < Q/nm −1 < 25, showing the absence of positive dispersion. This marks a difference with respect to the liquid [48], though the densities are similar.…”

The Spectrum of Density Fluctuations of Noble Gases Probed by THz Neutron and X-ray Spectroscopy

“…Furthermore, in liquid phase samples an "anomalous" Q-dependence was also reported for the sound absorption coefficient, as derived from the width of inelastic peaks, z s . Conversely, all these dispersive effects seem to disappear at extreme supercritical conditions [40,62,65,66].…”

“…The first IXS measurement on a dense noble gas was performed on deeply supercritical neon (T = 295 K, n = 29.1 atoms/nm 3 ) and discussed in combination of a MD simulation on a Lennard-Jones model representative of the same sample [65]. In Figure 7, two representative IXS spectra (upper panels) and corresponding MD simulations (lower panels) are compared (middle panels) after the former have been multiplied with the detailed balance factor and convoluted with the instrumental energy resolution function.…”

“…Based on the fit of MD spectra reported in Figure 8 and discussed in Refs. [65][66][67], one could conclude that, at least for dense supercritical neon, Qh is as high as 7.5 nm −1 . According to the plot, the transport parameters derived from best-fit results through Equations (3a-c) are essentially consistent with the macroscopic, or hydrodynamic, limit at least for Q lower than the values included in the shadowed area.…”

“…In Figure 9 it can be Figure 8. The relevant transport parameters deduced from the fits of of IXS spectra of deeply supercritical neon [67] and those of MD spectra from a Lennard Jones model representative of the same sample [65]. The shadowed area roughly locates the transition from the extended hydrodynamics and the mesoscopic regime.…”