Interacting Brownian particles and correlations in superionic conductors

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Abstract
The role of correlations in superionic conductors is studied in a model of interacting Brownian particles in a periodic potential. A general expression for the ac and dc conductivity is derived and applied to potentials of the Frenkel-Kontorova type with two different periods. The dc conductivity exhibits an oscillatory behavior as a function of the concentration of mobile ions. The absolute maximum of the conductivity of one-dimensional ionic conductors is predicted to occur for concentrations of about 0.75-0.8 ions per well. The model is applied to K-Hollandite for a quantitative analysis of the transport mechanism, showing up short-range correlations rather than collective excitations.