Quantum Effects in Liquid Hydrogen

Abstract

The thermodynamic description of a nonideal two‐component solution is developed for the case where the excess free energy of mixing in the liquid has its origin in the volume change on mixing. The equilibrium condition is calculated for the real gas. The equilibrium vapor—liquid distribution is related to the partition functions of the components in the liquid phase and the ideal gas. This relationship affords a basis for the calculation of the partition function ratios HT/H₂ and DT/D₂ in the liquid phase from experimental data. Partition function ratios of HD/H₂, D₂/H₂, and T₂/H₂ in the liquid state are derived from vapor‐pressure data. It is shown that the method of ordered quantum corrections is an inconvenient one for the description of the quantum effects in liquid hydrogen in its various isotopic forms. ``Lattice'' zero‐point energy differences for the isotopic liquid hydrogens are derived from the partition functions under the assumption of free rotation in the liquid. A large asymmetry effect is found for the heteronuclear species HD, HT, and DT. The ``lattice'' zero‐point energy of HT is 5.54°K greater than that of D₂, which has the same molecular weight. The structural effect of the molecule is shown to be a consequence of quantum mechanical coupling of rotation with the libration of the molecule in the condensed phase. Comparisons are made with two simple models of the coupling, both of which give qualitative agreement with experiment but overemphasize the coupling. A coupling parameter is derived from the experimental data to describe the translation—rotation interaction in an anharmonic potential field. It is shown that the anharmonic correction to the thermodynamic properties of condensed hydrogen is large.