Quantum Isotope Effect in Permeation

Abstract

A diffusing penetrant of sufficiently light mass (e.g., H2, D2) dispersed in sufficiently small cavities of certain diffusion systems will possess ground‐state quantizations of energy, both in the cavity and in the transition state, which are not negligible. Hence even at or above room temperature one expects to observe small, but sometimes measurable, differences of activation energy for diffusion and apparent enthalpies of sorption for two isotopic species of the penetrant diffusing in the same medium, providing the mass ratio of the lighter to the heavier isotope is sufficiently small. The change in the apparent enthalpy of sorption is proportional, roughly, to the inverse square of a length available to free motion of the center of mass of the penetrant in the cavity and can thus be used as a measure of the free volume involved in the diffusion. The ratio of the change in diffusionactivation energy to the change in the apparent sorption enthalpy yields a length characteristic of the transition state. Gas transmission of H2, D2, and He through ``synthetic'' natural rubber and polyethylene films was studied from 30° to 60°C. Statistically significant differences in temperature coefficients of permeation, sorption, and diffusion were obtained in these membranes on going from H2 to D2. The implications of these observations are developed.