Generalized Einstein relations from a three-temperature theory of gaseous ion transport

Generalized Einstein relations between mobility and diffusion coefficients are derived within the framework of a recently developed three-temperature kinetic theory of gaseous ion transport. A previously assumed connection between diffusion and differential mobility is firmly established within low-order approximations of the kinetic theory. Equations are obtained for the approximate calculation of the unobservable parallel and perpendicular ion temperatures, and for two higher moments of the ion velocity distribution function that appear as correction terms in the generalized Einstein relations. The present theory is tested on inverse-power potentials and on several alkali ion-noble gas systems, and is compared to two previous semi-empirical generalized Einstein relations. Simple procedures are recommended for the estimation of the parameters and correction terms that occur, to permit approximate calculation of gaseous ion diffusion coefficients from mobility data without the need of a computer or specific knowledge of the ion-neutral interaction potential.