Abstract
Generalized Einstein relations (GER) connecting ion diffusion coefficients with the mobility are extended to include internal degrees of freedom and inelastic collisions. The Boltzmann equation is solved by means of a four-temperature theory that includes as parameters the gas temperature, two translational ion temperatures, and one internal ion temperature. The results reduce in the limit of elastic collisions to those obtained by Waldman and Mason from a three-temperature theory. In addition, an analytic procedure is developed for the calculation of the unobservable ion temperatures and correction terms that appear in the GER. The analytic procedure is checked by comparison with numerical results and experimental data for the elastic-collision limit. The general results are tested numerically with an inelastic two-state model and with a semiempirical analysis of experimental results on K + in H 2 and N 2. More details on ion-molecule inelastic collisions are needed for further progress.
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