Ion Motion in Electrolytic Cells, Anomalous Diffusion Evidences

We argue that ion motion in electrolytic cells containing Milli-Q water, weak electrolytes, or liquid crystals may exhibit unusual diffusive regimes that deviate from the expected behavior, leading the system to present anomalous diffusion. The Poisson-Nernst-Planck (PNP) diffusional model is used with extended boundary conditions to simulated the charge transfer, accumulation and adsorption - desorption at the electrodes surfaces. We analyze the relation between the electrical conductivity and ionic motion from the experimental data obtained via electrical impedance spectroscopy. We establish the contribution of the surface and bulk effects for the diffusive regimes present in these systems by considering the connection between the impedance and the conductivity, thus enabling the use of Einstein's generalized relation between mobility and diffusion coefficient. We then obtain the frequency dependent diffusion coefficient and relate it with the mean square displacement that characterizes the diffusive process. We also use the PNP model to connect the behavior of the conductivity with the surface or bulk contribution, according to the frequency range.