# Correlations from ion-pairing and the Nernst-Einstein equation

## TL;DR

This paper introduces a new approximation method for ionic conductivity based on the Nernst-Einstein equation, emphasizing ion clustering and correlations, which improves estimates and physical understanding in concentrated electrolytes.

## Contribution

The authors develop a computationally efficient approximation that models ionic aggregates as non-interacting charge carriers, capturing ion-ion correlations and clustering effects.

## Key findings

- Reproduces experimental negative cation transference numbers at high salt concentrations.
- Confirms negatively charged clusters involving cations cause transference number reversal.
- Provides better conductivity estimates with lower computational cost.

## Abstract

We present a new approximation to ionic conductivity well suited to dynamical atomic-scale simulations, based on the Nernst-Einstein equation. In our approximation, ionic aggregates constitute the elementary charge carriers, and are considered as non-interacting species. This approach conveniently captures the dominant effect of ion-ion correlations on conductivity, short range interactions in the form of clustering. In addition to providing better estimates to the conductivity at a lower computational cost than exact approaches, this new method allows to understand the physical mechanisms driving ion conduction in concentrated electrolytes. As an example, we consider Li$^+$ conduction in poly(ethylene oxide), a standard solid-state polymer electrolyte. Using our newly developed approach, we are able to reproduce recent experimental results reporting negative cation transference numbers at high salt concentrations, and to confirm that this effect can be caused by a large population of negatively charged clusters involving cations.