Generalized Einstein relation: Application to ions in molecular gases

Viehland and Mason have developed a method of calculating diffusion coefficients of gaseous ions from measured ionic mobilities by means of a generalized Einstein relation. Their method has been tested with our data on longitudinal diffusion coefficients for alkalimetal ions in atomic gases and found to give excellent results over a very wide range of the energy parameter $\frac{E}{N}$. (Here $E$ is the intensity of the electric field in our drift tube mass spectrometer, and $N$ is the number density of the gas molecules in the drift tube.) In this paper we extend the test of the generalized Einstein relation to ${\mathrm{K}}^{+}$ ions in ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{H}}_2$, NO, CO, and C${\mathrm{O}}_2$, to ${\mathrm{Na}}^{+}$ ions in C${\mathrm{O}}_2$, and to ${\mathrm{O}}^{-}$ ions in ${\mathrm{O}}_2$. The main objective is to assess the validity of the relation for molecular gases, in which inelastic collisions occur at the higher values of $\frac{E}{N}$. Such collisions are not allowed for in the theory on which the Viehland-Mason method is based. We demonstrate that the generalized Einstein relation gives extremely good results for ${\mathrm{K}}^{+}$ in ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and CO. In the other cases, the agreement between theory and experiment is not close at very high values of $\frac{E}{N}$, but is much better than has been obtained by the alternative approaches previously available.