  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.
