Electrical Impedance Response of Liquid Crystals and Anomalous Diffusion: A Fractional Approach

We analyze the electrical impedance response established in terms of the time-fractional approach formulation of the Poisson-Nernst-Planck model by considering a general boundary condition. The total current across the sample is solenoidal, as the Maxwell equations require, and the boundary conditions can be related to different scenarios. We also study the behavior of the electrical conductivity and its connection with the ionic spreading in the sample to establish the diffusion regime present in the system in the low-frequency limit. Furthermore, we investigate impedance spectroscopy measurements of a nematic liquid crystal cell and observe a good agreement between the experimental data and the model.