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A self-consistent mode coupling theory (MCT) with microscopic inputs ofequilibrium pair correlation functions is developed to analyze electrolytedynamics. We apply the theory to calculate concentration dependence of (i) timedependent 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 withexplicit water are used to check the theoretical predictions. The timedependence of ionic self-diffusion coefficient and the corresponding dynamicstructure factor evaluated from our MCT approach show quantitative agreementwith early experimental and present Brownian dynamic simulation results. Withincreasing concentration, the dispersion of electrolyte friction is found tooccur at increasingly higher frequency, due to the faster relaxation of the ionatmosphere. The wave number dependence of total dynamic structure factorF(k,t), exhibits markedly different relaxation dynamics at different lengthscales. 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. Suchbehaviour allows an intriguing analogy with temperature dependent relaxationdynamics of supercooled liquids. We find that solvation dynamics of a taggedion exhibits a power law decay at long times- the decay can also be fitted to astretched exponential form. The emergence of the power law in solvationdynamics has been tested by carrying out long Brownian dynamics simulationswith varying ionic concentrations. This solvation time correlation and ion-iondynamic structure factor indeed exhibits highly interesting, non-trivialdynamical behaviour at intermediate to longer times that require furtherexperimental and theoretical studies.

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