Frequency Dependence of Ionic Conductivity in Large-Scale Simulations of Concentrated Electrolytes

The transport of ions in a confined environment underlies a number of important technologies that utilize separations, electrochemistry, and energy storage and delivery. The collective net motion of ions due to an electric field is quantified by the conductivity. At low concentrations and/or low ionic strengths, the conductivity is well explained by the classical transport theories of Debye, Hükel and Onsager. However, at high concentrations and/or high ionic strengths, the screening length acquires values on the order of the ion's diameter, and the inter-ionic correlations become significant, thereby noticeably increasing the complexity of the physical problem. To address this limitation, we investigate the frequency response of concentrated electrolytes using large scale Brownian dynamics simulations coupled with Poisson's equation. We compute the complex conductivity over four orders of magnitude of frequency by applying a sinusoidal electric field whose frequency exponentially increases with time. The analysis is performed with and without inter-particle hydrodynamic interactions over a large range of ionic concentrations, allowing us to find scaling relationships for important descriptors of the frequency-dependent conductivity as a function of the Debye screening length.