Ion diffusion and momentum correlation functions in dilute electrolytes

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Abstract
The convergent cluster expansion of the ion-ion momentum time correlation functions in a dilute electrolyte, recently derived by Friedman, is applied here for the calculation of the limiting law for ion self-diffusion. Considering only the non-chain cluster terms leads to a result analogous to the Debye-Hückel limiting law for ionic conductivity. Taking into account the additional chain terms leads to exactly the Onsager result. We also use the cluster expansion to determine the long-time behaviour of the ion momentum time auto-correlation function, which we find goes as t -3/2, with a coefficient proportional to the square root of the solute concentration. Similar results are given for the associated memory function and the ion-ion momentum time correlation function.

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