Equation of state and stability of the helium-hydrogen mixture at cryogenic temperature

Abstract

The equation of state and the stability of the helium-molecular hydrogen mixture at cryogenic temperature up to moderate pressure are studied by means of current molecular physics methods and statistical mechanics perturbation theory. The phase separation, segregation and hetero-coordination are investigated by calculating the Gibbs energy depending on the mixture composition, pressure and temperature. Low temperature quantum effects are incorporated via cumulant approximations of the Wigner-Kirkwood expansion. The interaction between He and H2 is determined by Double Yukawa potentials. The equation of state is derived from the hard sphere system by using the scaled particle theory. The behavior of the mixture over a wide range of pressure is explored with the excess Gibbs energy of mixing and the concentration fluctuations in the long wavelength limit. The theory is compared to cryogenic data and Monte-Carlo calculation predictions. Contrary to previous similar works, the present theory retrieves the main features of the mixture below 50 K, such as the critical point and the condensation-freezing curve, and is found to be usable well below 50 K. However, the method does not distinguish the liquid from the solid phase. The binary mixture is found to be unstable against species separation at low temperature and low pressure corresponding to very cold interstellar medium conditions, essentially because H2 alone condenses at very low pressure and temperature, contrary to helium. PACS. 64.10.+h General theory of equations of state and phase equilibria -64.75.Gh Phase separation and segregation in model systems (hard spheres, Lennard-Jones, etc.) -64.75.Ef Mixing

Simulations of galactic disks including a dark baryonic component

“…But since H 2 is usually mixed with about 10% of helium in mass, it was for many years not clear how to describe the equation of state of this mixture in such conditions. Recently, Safa & Pfenniger (2008) succeeded in describing this mixture for astrophysically interesting conditions with chemo-physical methods, reproducing its main characteristics like the critical point and the condensation curve, as well as predicting the conditions of He-H 2 separation. Work is in progress to apply these results to the cold interstellar gas.…”

“…We are aware of the degree of simplification of our model compared to the complexity of the ISM. A more complex model should include the dark component, the CO-undetected metalpoor warmer H 2 gas that may exist in the outskirts of galactic disks (Papadopoulos et al 2002), and possible effects related to phase transition and separation in the He-H 2 mixture at very cold temperature (Safa & Pfenniger 2008).…”

Ab Initio Equation of State for Hydrogen-Helium Mixtures With Recalibration of the Giant-Planet Mass-Radius Relation

“…For the helium EOS, we recommend our first-principles computation (Militzer 2009) because it provides simulation data points for the pressure, P , internal energy, E, Helmholtz free energy, F , and entropy, S, over a wide parameter range and a thermodynamically consistent free energy fit for interpolation. For available hydrogen EOS work, we refer to the recent review by McMahon et al (2012) but there has also been a considerable theoretical effort compute the hydrogen EOS with semianalytical techniques (Dharma-wardana & Perrot 2002;Kraeft et al 2002;Rogers & Nayfonov 2002;Safa & Pfenniger 2008;Ebeling et al 2012;Alastuey & Ballenegger 2012). If the perturbation in the helium fraction is sufficiently small, one may use the SC EOS for simplicity.…”

Formation of H2-He substellar bodies in cold conditions

“…Streett 1973;Koci et al 2007;Becker et al 2014) and especially in conditions similar to gas giant planets (Vorberger et al 2007;Saumon et al 1995). Taking quantum effects into account, Safa & Pfenniger (2008) calculate the thermodynamic properties of H 2 -He mixtures below critical temperature from the known intermolecular potentials and obtain the critical point and stability of the mixture itself.…”