Estimating ionic conductivity of ionic liquids: Nernst–Einstein and Einstein formalisms

Ionic conductivity plays an important role in the application of ionic liquids as electrolytes in next-generation batteries and electrochemical applications and is often estimated using the Nernst-Einstein formalism in molecular simulation-based studies. The Nernst-Einstein formalism is useful for dilute systems where ions do not interact with each other, restricting its applicability to dilute solutions. However, this approximation fails in concentrated solutions where ion interactions become significant, which is usually encountered for pure ionic liquids. These ion-ion correlations can dramatically affect ionic conductivity predictions in comparison to that computed under the Nernst-Einstein formalism. This study highlights the challenges associated with calculating ionic conductivity using Einstein formalism and subsequently provides a workflow for such calculations. It has been found that a minimum trajectory length of 60 ns is required to achieve converged results for Einstein ionic conductivity. Guidance is also given to reduce the computational resource requirements for Einstein conductivity determination. This simplification will enable researchers to estimate Einstein conductivity in ionic liquids more efficiently.