Fluid hydrogen at high density: Pressure dissociation

Abstract

We develop a model for the Helmholtz free energy of fluid hydrogen at high density and high temperature. This model aims at describing both pressure and temperature dissociation and ionization and bears directly on equations of state of partially ionized plasmas, as encountered in astrophysical situations and high-pressure experiments. This paper focuses on a mixture of hydrogen atoms and molecules and is devoted to the study of the phenomenon of pressure dissociation at finite temperatures. In the present model, the strong interactions are described with realistic potentials and are computed with a modified Weeks-Chandler-Andersen fluid perturbation theory that reproduces Monte Carlo simulations to better than 3%%u~. Perturbations of the internal partition functions of H and H2 arising in the nonideal fluid are treated self-consistently with a recently developed occupation probability formalism. Theoretical Hugoniot curves derived from our model are in excellent agreement with experimental data. Pressure dissociation occurs over a narrow density range above 0.5 g/cm' and is remarkably temperature insensitive. Molecules remain the dominant species even at high densities. PACS number(s): 52.25.Jm, 64.30.+t, 05.70.Ce, 65.50.+ m j.INTRODUCTION The past decade has seen tremendous progress in our understanding of dense matter physics, on both the experimental and theoretical fronts. Dynamic compression experiments have revealed exciting new phenomena, such as pressure dissociation in (N2) [1,2], an increase of conductivity upon compression in an initially insulating material (Oz) [3], and they have probed intermolecular potentials down to separations as small as 1.5 A. In particular, experiments on hydrogen and deuterium have determined the H2-Hz interaction potential at high densities [4]Cryogenic samples of solid molecular hydrogen have been compressed to pressures of about 2.5X10 atm, revealing a phase transition in the molecular solid and evidence for reduction of the band gap at the highest pressure reached [5 -7]. This last phenomenon holds the promise of observing the much sought after metallic state of hydrogen in the near future.On the other hand, the recent discovery of global oscillations in Jupiter [8] as well as the achievements of helioand astero-seismology [9,10] give us new information on the interior structure of stars and giant planets, and consequently on the properties of matter under extreme thermodynamic conditions. They offer a unique chance to probe the accuracy of the theoretical models and stress the need for improved equations of state (EOS), particularly in the regime of partial ionization. Indeed, pressure ionization, as well as molecular dissociation, represents a thorny problem in modeling the properties of dense matter. Important advances in statistical physics over the last decade offer the opportunity for significant improvements in our comprehension of this poorly understood phenomenon.Most of the extensive theoretical work on hydrogen has focused on the zero-temperature isotherm whe...

The helium content and age of the Hyades:

“…4). Sophisticated EOSs, including collective effects, have been designed to study the Sun (MHD EOS, Mihalas et al 1988; OPAL EOS, Rogers et al 1996) and very-low mass stars and planets (as the SC EOS, Saumon & Chabrier 1991). The effects of the EOS on the models are illustrated in Fig.…”

The Equation of State of Fluid Hydrogen at High Density

“…This potential is slighly softer than the potential used in our calculations (Ross et al 1983;Saumon and Chabrier 1991). Given the lack of information for the H-H and H2-H potentials at high density, we mimicked many-body effects by softening arbitrarily the repulsive part of the potentials respectively by 20% and 35%.…”

“…In section II, we give a short presentation of our free energy model, which has been presented extensively elsewhere (Saumon and Chabrier 1991, 1992). In section III, we discuss in detail the P P T predicted by our model whereas a comparison with other models is discussed in Section IV.…”

Sound velocities in shocked liquid deuterium

“…The equation of state (EOS) along the principal Hugoniot was determined by Nellis, et al (1), and theoretical models were developed subsequently. (2,3) Recently, new shock temperature measurements led to the development of a new model, in which the effective molecular dissociation energy decreases with decreasing volume. (4) Extrapolation of those results to pressures above 100 GPa indicated that deuterium would be substantially more compressible in this pressure region than previously thought.…”

“…This suggests the measurement of derivative quantities such as sound velocity or the Grüneisen parameter, both of which should be sensitive to the to the rate of change of compressibility. The sound velocity c of a rarefaction wave is given by (1) where P is pressure, ρ density, and the derivative is at constant entropy S. The sound velocity is also related to the Grüneisen parameter through the expression (7) (2) where the Grüneisen parameter given by (3) can be obtained from shock Hugoniot experiments. Measurements of the sound velocity using the overtake method (8) can provide high accuracy, and an unambiguous test of our understanding of dense, hot, fluid deuterium.…”