Isotope effects in phase equilibria; a new tool for the study of intermolecular forces

Abstract

The renascence of interest in isotope effects in phase equilibria during the past decade has provided a new body of experimental data pertaining to intermolecular forces. Concurrent advances in the quantum theory of the liquid and solid states have led to the formulation of the mass dependence of the quantum partition function and its temperature dependence. The theory shows that in the first approximation the isotope effects in phase equilibria are determined by the mean value of the second derivative of the intermolecular potential. For monatomic systems a new set of molecular parameters have been derived for neon, krypton, and xenon based on the WHALLEY-SCHNEIDER parameters for argon. For the condensed rare gases, it has been shown that independent particle models, e.g. anharmonic Einstein model of the crystal and quantum cell models in the liquid, cannot account for the observed isotope effects. The isotope effect on melting is discussed in terms of the structure of the solid and the nearest neighbor numbers of the liquid.For polyatomic molecules, a wealth of new information and a number of new phenomena associated with intermolecular forces have been discovered. It is found that in the first approximation the intermolecular potential appears as the sum of atomic interactions. A development of this method leads to a direct and quantitative explanation of a number of hitherto incomprehensible phenomena. Isotopic substitution provides a direct demonstration of hindered rotation in the liquid. Two new types of quantum effects associated with molecular rotation have been found. The first type is a coupling of the molecular rotation with the molecular translation in the field of the intermolecular force. The effect persists even for free rotation and is most pronounced for molecules with small moments of inertia. The effect has been quantitatively investigated through the phase equilibrium behaviour of the isotopic and rotational forms of hydrogen. The second effect is a coupling of the molecular rotation with the molecular vibration in the field associated with the hindered rotation. A quantitative investigation of this rotation-vibration interaction has been made by the study of the vapor pressures of the deuteroethylenes. Studies of isotopic phase equilibria together with molecular spectroscopy of the condensed state provide information concerning the perturbation of the intramolecular vibrations by the intermolecular forces.