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Mode coupling theory of electrolyte dynamics: Time dependent diffusion, dynamic structure factor and solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) dynamic structure factor of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics (BD) with implicit water molecules and molecular dynamics (MD) method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding dynamic structure factor evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of total dynamic structure factor F(k,t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behaviour allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times- the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. This solvation time correlation and ion-ion dynamic structure factor indeed exhibits highly interesting, non-trivial dynamical behaviour at intermediate to longer times that require further experimental and theoretical studies.