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.