Spatial-Decomposition Analysis of Electrical Conductivity in Mixtures of Ionic Liquid and Sodium Salt for Sodium-Ion...

Ionic liquid (IL)-based electrolytes are a promising material for the development of sodium-ion batteries, and their performance can be quantified by electrical conductivity. In this highly concentrated ionic system, the correlated motions of ion pairs are influential on the ionic transport properties. Herein, all-atom analyses are conducted through molecular dynamics simulations to bridge the macroscopically observable electrical conductivity with the molecular pictures of correlated motion of ion pairs. The analysis is applied to three mixtures of IL with sodium salt that are relevant to the electrolyte for a sodium-ion battery: [1-ethyl-3-methylimidazolium, Na][bis(fluorosulfonyl)amide] ([C₂C₁im, Na][FSA]), [N-methyl-N-propylpyrrolidinium, Na][FSA] ([C₃C₁pyrr, Na][FSA]), and [K, Na][FSA]. The computational results on electrical conductivities are in agreement with the experimental reports, and their dependency on temperature and sodium-ion composition is reproduced well. The overall contributions from cross-correlated motions are found to be negative in all the IL mixtures; thus, the total conductivities are less than their Nernst-Einstein estimates. The spatial view of cross-correlated motions is further obtained by decomposing the time correlation functions of velocities according to the distances between ion pairs. It is observed that ion pairs are moving in the same direction for ∼0.3 ps when they were initially within the first coordination shell, followed by motions toward opposite directions. The cross-correlation terms are also dissected into local and nonlocal components, and it is commonly seen for all the ion pairs that the local component is negative for cation-anion pairs and is positive for cation-cation and anion-anion pairs. The motions of ion pairs are accompanied by a "backflow" that manifests in the form of the nonlocal component whose sign is opposite to the corresponding local component. In fact, the contributions of the correlated motions of ions to the electrical conductivity are not localized to contact pairs and extend spatially beyond the first coordination shell of the cation-anion pairs.