Non-Debye relaxation in the dielectric response of nematic liquid crystals: surface and memory effects in the adsorption-desorption process of ionic impurities

Diffusion in Heterogenous Media and Sorption—Desorption Processes

We investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusion coefficient, i.e., K(x) = D|x|−η, with −1 < η and D = const, respectively. This system is analyzed in a semi-infinity region, i.e., the system is defined in the interval [0,∞) for an arbitrary initial condition. The solutions are obtained and display anomalous spreading, that is, the dynamics may be viewed as anomalous diffusion, which in turn is related, and hence, the model can be directly applied to several complex systems ranging from biological fluids to electrolytic cells.

Frequency dispersion in the fractional Langmuir approximation for the adsorption–desorption phenomena

We propose that a kinetic equation of fractional order may be used to account for the frequency dispersion of the effective parameters in the framework of the Langmuir approximation for the adsorption–desorption phenomena. A frequency dependence of these parameters naturally arises in this formalism, indicating that it may play a similar role of a generalization of the Langmuir isotherm obtained from a homogeneous distribution of relaxation times. The fractional approach formalism opens the possibility to consider different relaxation regimes characterizing the interfacial behaviour of electrolytic cells, and may be a powerful tool to interpret complex impedance spectroscopy data.

Influence of dielectric layers on estimates of diffusion coefficients and concentrations of ions from impedance spectroscopy

We present the analysis of the impedance spectra for a binary electrolyte confined between blocking electrodes with dielectric layers. An expression for the impedance is derived from Poisson-Nernst-Planck equations in the linear approximation taking into account the voltage drop on the dielectric layer. The analysis shows that characteristic features of the frequency dependence of the impedance are determined by the ratio of the Debye length and the effective thickness of the dielectric layer. The impact of the dielectric layer is especially strong in the case of high concentrated electrolytes, where the Debye length is small and thus comparable to the effective thickness of the dielectric layer. To verify the model, measurements of the impedance spectra and transient currents in a liquid crystal 4-n-pentyl-4^{'}-cyanobiphenyl (5CB) confined between polymer-coated electrodes in cells of different thicknesses are performed. The estimates for the diffusion coefficient and ion concentration in 5CB obtained from the analysis of the impedance spectra and the transient currents are consistent and agree with previously reported data. We demonstrate that calculations of the ion parameters from the impedance spectra without taking into account the dielectric layer contribution lead in most cases to incorrect results. Application of the model to analyze violations of the low-frequency impedance scaling and contradictions in the estimates of the ion parameters recently found in some ionic electrolytes are discussed.

Anomalous diffusion and transport in heterogeneous systems separated by a membrane

Diffusion of particles in a heterogeneous system separated by a semipermeable membrane is investigated. The particle dynamics is governed by fractional diffusion equations in the bulk and by kinetic equations on the membrane, which characterizes an interface between two different media. The kinetic equations are solved by incorporating memory effects to account for anomalous diffusion and, consequently, non-Debye relaxations. A rich variety of behaviours for the particle distribution at the interface and in the bulk may be found, depending on the choice of characteristic times in the boundary conditions and on the fractional index of the modelling equations.

Warburg's impedance revisited

The derivation of Warburg's impedance presented in several books and scientific papers is reconsidered. In the past it was obtained by assuming that the total electric current across the sample is just due to the diffusion, and that the external potential applied to the electrode is responsible for an increase of the bulk density of charge described by Nernst's model. We show that these assumptions are not correct, and hence the proposed derivations are questionable. When the electrochemical impedance of a cell of an insulating material where external charges are injected of a given sign is correctly determined, in the high frequency region the real and imaginary parts do not follow the trends predicted by Warburg's impedance. The analysis presented in this paper is relevant to a symmetric cell, in the Nernstian approximation. It can be easily generalized to the case of an asymmetric cell, assuming boundary conditions where the conduction current across the electrodes is proportional to the surface electric field.

Realization of Multi-Stable Ground States in a Nematic Liquid Crystal by Surface and Electric Field Modification

Owing to the significant price drop of liquid crystal displays (LCDs) and the efforts to save natural resources, LCDs are even replacing paper to display static images such as price tags and advertising boards. Because of a growing market demand on such devices, the LCD that can be of numerous surface alignments of directors as its ground state, the so-called multi-stable LCD, comes into the limelight due to the great potential for low power consumption. However, the multi-stable LCD with industrial feasibility has not yet been successfully performed. In this paper, we propose a simple and novel configuration for the multi-stable LCD. We demonstrate experimentally and theoretically that a battery of stable surface alignments can be achieved by the field-induced surface dragging effect on an aligning layer with a weak surface anchoring. The simplicity and stability of the proposed system suggest that it is suitable for the multi-stable LCDs to display static images with low power consumption and thus opens applications in various fields.

Unusual diffusing regimes caused by different adsorbing surfaces

A confined liquid with dispersed neutral particles is theoretically studied when the limiting surfaces present different dynamics for the adsorption-desorption phenomena. The investigation considers different non-singular kernels in the kinetic equations at the walls, where the suitable choice of the kernel can account for the relative importance of physisorption or chemisorption. We find that even a small difference in the adsorption-desorption rate of one surface (relative to the other) can drastically affect the behavior of the whole system. The surface and bulk densities and the dispersion are calculated when several scenarios are considered and anomalous-like behaviors are found. The approach described here is closely related to experimental situations, and can be applied in several contexts such as dielectric relaxation, diffusion-controlled relaxation in liquids, liquid crystals, and amorphous polymers.