Fractional Diffusion Equation and the Electrical Impedance: Experimental Evidence in Liquid-Crystalline Cells

The electrical impedance data of different nematic liquid-crystal cells are analyzed inthe framework of a model in which the diffusion of mobile ions in the bulk is governed by afractional diffusion equation of distributed order. The boundary conditions at the electrodes limitingthe sample are described by an integro-differential equation governing the kinetic at the interfacethat embodies, in particular, the usual kinetic equation for describing the adsorption−desorptionprocess at the electrodes but is expressed in terms of a temporal kernel that can be chosen to coverscenarios that are not suitably described within the usual framework of blocking electrodes. Theanalysis is carried out by supposing that the positive and negative ions have the same mobility andthat the electric potential profile across the sample satisfies the Poisson’s equation. The results covera rich variety of scenarios, including the ones connected to anomalous diffusion.