Hydrogen-helium demixing from first principles: From diamond anvil cells to planetary interiors

An accurate determination of the immiscibility of helium in hydrogen has a direct impact on the understanding of the interior structure and of the evolution of Jovian planets. We extend our previous work on hydrogen-helium mixtures [Morales, Schwegler, Ceperley, Pierleoni, Hamel, and Caspersen, Proc. Natl. Acad. Sci. (USA) 106, 1324 (2009)] to lower pressures and lower temperatures, across the molecular dissociation regime in hydrogen to the low-pressure molecular liquid. Using density-functional-theory-based molecular dynamics together with thermodynamic integration techniques, we calculate the Gibbs free energy of the dense liquid as a function of pressure, temperature, and composition. We address the importance of the nonideal entropy of mixing in the solubility of helium in hydrogen and find that it is critically important in the molecular regime. The resulting demixing temperatures smoothly connect measurements done in diamond anvil cells to the high-temperature and -pressure conditions found in giant planet interiors.