Thermodynamics of dense molecular hydrogen-helium mixtures at high pressure

Current equations of state of dense molecular hydrogen-helium mixtures are not experimentally verified beyond densities of ∼0.3 g cm^-3. We have used effective intermolecular pair potentials derived from recent shock wave experiments on liquid hydrogen (W.J. Nellis, A.C. Mitchell, M. van Thiel, G.J. Devine, R.J. Trainor, and N. Brown 1983, J. Chem. Phys. 79, 1480-1486) and helium (W.J. Nellis, N.C. Holmes, A.C. Mitchell, R.J. Trainor, G.K. Governo, M. Ross, and D.A. Young 1984, Phys. Rev. Lett. 53, 1248-1251) in Monte Carlo simulations of mixtures of hydrogen and helium at densities up to 1.2 g cm^-3. A model interaction Helmholtz free energy has been derived which accurately reproduces the results of the Monte Carlo calculations. This free energy also reproduces the experimental data to densities of ∼0.6 g cm^-3. The equation of state derived from the free energy expression will be useful in preparing improved interior models of the Jovian planets, especially Saturn. The pressure of the molecular hydrogen to metallic hydrogen presumed first-order phase transition is also calculated. Uncertainties in the rotational and vibrational frequencies of the compressed hydrogen molecule translate into an uncertain transition pressure of 3-5 Mbar.