A simple harmonic model as a caricature for mismatch and relaxation effects for ion hopping dynamics in solid electrolytes

TL;DR

This paper introduces a simple harmonic mean-field model to analyze ion hopping dynamics in solid electrolytes, providing analytical insights into relaxation processes and connecting them to the phenomenological CMR approach.

Contribution

The paper develops an analytically solvable mean-field model that captures key features of ion hopping and relaxation, linking it to existing phenomenological models.

Findings

Model reproduces relaxation behaviors observed in experiments.

Analytical solutions clarify the roles of single-particle and multi-particle processes.

Comparison with CMR shows the model's relevance to real ion dynamics.

Abstract

We formulate a simple harmonic mean-field model with N+1 particles and analyse the relaxation processes following a jump of one of these particles. Either the particle can jump back (single-particle route) or the other N particles adjust themselves (multi-particle route). The dynamics of this model is solved analytically in the linear response regime. Furthermore we relate these results to a phenomenological approach by Funke and coworkers (concept of mismatch and relaxation: CMR) which has been successfully used to model conductivity spectra in the field of ion dynamics in solid electrolytes. Since the mean-field model contains the relevant ingredients of the CMR-approach, a comparison of the resulting rate equations with the CMR-equations becomes possible. Generalizations beyond the mean-field case are discussed.