Theory of Ortho-Para Hydrogen Separation by Adsorption at Low Temperatures, Isotope Separation

Abstract

A theory of separation of ortho and para hydrogen, by adsorption at low temperatures, is developed by considering the energy levels of a three-dimensional hindered rotator. The Schroedinger equation and boundary conditions are identical with those for prolate spheroidal wave functions and tables of the latter have been employed in calculating the energies as functions of the barrier height. Separation factors, at low surface coverage, have also been computed as a function of barrier height and these pass continuously from unity at zero barrier height over into the limiting separation factor for a two-dimensional rotator (in the adsorbed state) which was used by Sandler in the approximate calculation of separation factors. The theory predicts that ortho hydrogen is more strongly adsorbed than para hydrogen at all barrier heights and that para deuterium is more strongly adsorbed than ortho deuterium. Moreover, the ortho-para hydrogen separation factor is larger at all barrier heights than the para-ortho separation factor for deuterium. These results agree with the experiments of Cunningham, Chapin, and Johnston. Calculated and observed separation factors for hydrogen and deuterium (at low surface coverages) are not in accurate quantitative agreement, however this may be due to the fact that experimental separation factors for both isotopes were not determined under comparable conditions. Calculations have been made first by assuming that rotation and (center of mass) vibration are separable. This model is then refined to take into account the interaction of rotation and vibration. The separation of the hydrogen-deuterium isotopes is also considered. Although the inclusion of interaction between vibration and rotation does not greatly change the ortho-para separation factors, this effect has a marked influence on the calculated isotope separation factors. It is of considerable interest that isotope separation factors are strongly dependent on the ortho-para composition of the isotope mixture, at least at low surface coverages, in the theory developed here.