Uma análise de espectros de impedância utilizando o modelo de Poisson-Nernst-Planck com difusão anômala

Abstract

The electrical impedance data of five nematic liquid crystal samples is analyzed by means of a generalization of the standard Poisson-Nernst-Planck (PNP) continuum diffusion model. We develop the PNP-A model proposed here supposing that the positive and negative ions have the same mobility and the electric potential profile inside the sample satisfies the Poisson's equation. In the framework of PNP-A model, the diffusion of the mobile ions in the bulk is governed by a time fractional diffusion equation of distributed order to incorporate the possibility of different diffusive regi- mes in the sample. The boundary conditions at the electrodes limiting the sample are described by an integro-differential equation that dictates the kinetic at the interface and embodies, in particular, the usual kinetic equation for describing the adsorption- desorption process at the electrodes. These boundary conditions are expressed in terms of a temporal kernel that can be chosen to cover scenarios that are not sui- tably described within the usual framework of blocking electrodes. The numerical fitting of the experimental data showed that is not necessary to consider anomalous diffusive regimes in the bulk in order to obtain a better result, but is mandatory to consider a non-usual or "anomalous" response behavior at the interface to explain the trends of the experimental results. In this sense, we have obtained a set of effective "surface lengths" that enabled to perceive the existence of these anomalous diffusion process. We consider that this result can be useful to broaden the knowledge about the phenomena that take place at the interface of systems like the ones studied here.