A schematic model for multi-particle dynamics in ion transport: From mean field to nonmean field effects

Banhatti RD, Heuer A

Abstract

Models of ion transport either consider the complex multi-particle ion interaction in an effective way such as the MIGRATION concept of Funke et al. or consider a single particle hopping scenario in appropriately chosen energy landscapes. Here we first summarize some important aspects of ionic transport, stressing in particular the relevance of interaction effects. Furthermore we review a recently presented schematic model of hopping particles interacting via harmonic forces. This system can be mapped on an effective two- (mean field case) or three-body problem (non-mean field case) and we quantify relaxation effects within linear response. We obtain analytical expressions for the observables, which can be readily compared with those of the MIGRATION concept. General implications of our results to ion transport is also discussed with reference to applicability of the mean field vs. the non mean field scenario for the case of coupled and glassy electrolytes.