Models for ionic contribution to the complex dielectric constant of nematic liquid crystals

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.

Analysis of Optical Performance Degradation in an Ion-Doped Liquid-Crystal Cell with Electrical Circuit Modeling

We reported electrical circuit modeling to analyze the optical performance degradation in an ion-doped liquid-crystal (LC) cell, which exhibited advantages, such as excellent optical performance and simple switching process, but suffered from long-term reliability issues. When an electric field was applied to the cell for an extended period of time, the optical performance became nonuniform, and the haze in the opaque state decreased. By measuring the impedance and fitting the measured data by using an equivalent circuit model, we confirmed the changes of the parameters in the electrochemical impedance spectroscopy and electrophysical properties of the ion-doped LC cell with time. According to the measurement of the optical and physical characteristics, the optical performance degradation was caused mainly by the ionic materials.

Introduction of effective dielectric constant to the Poisson-Nernst-Planck model

The Poisson-Nernst-Planck (PNP) model has been widely used for analyzing impedance or dielectric spectra observed for dilute electrolytic cells. In the analysis, the behavior of mobile ions in the cell under an external electric field has been explained by a conductive nature regardless of ionic concentrations. However, if the cell has parallel-plate blocking electrodes, the mobile ions may also play a role as a dielectric medium in the cell by the effect of space-charge polarization when the ionic concentration is sufficiently low. Thus the mobile ions confined between the blocking electrodes can have conductive and dielectric natures simultaneously, and their intensities are affected by the ionic concentration and the adsorption of solvent molecules on the electrodes. The balance of the conductive and dielectric natures is quantitatively determined by introducing an effective dielectric constant to the PNP model in the data analysis. The generalized PNP model with the effective dielectric constant successfully explains the anomalous frequency-dependent dielectric behaviors brought about by the mobile ions in dilute electrolytic cells, for which the conventional PNP model fails in interpretation.

Magnetic control of flexoelectric domains in a nematic fluid

The formation of flexoelectric stripe patterns (flexodomains) was studied under the influence of external electric and magnetic fields in a nematic liquid crystal. The critical voltage and wavevector of flexodomains were investigated in different geometries by both experiments and simulations. It is demonstrated that upon altering the orientation of the magnetic field with respect to the director, the critical voltage and wavenumber behave substantially differently. In the geometry of the twist Freedericksz transition, a non-monotonic behavior as a function of the magnetic field was found.

Comment on "Modeling of electrode polarization for electrolytic cells with a limited ionic adsorption"

Recently, Sawada [Phys. Rev. E 88, 032406 (2013)] proposed a model to take into account the dielectric dispersion of ionic origin in a weak electrolyte cell. We first show that the model is based on questionable assumptions. Next, we point out an error in the author's calculation of the current in the external circuit. Finally, we demonstrate why some criticism on recent papers is irrelevant.

Modeling of electrode polarization for electrolytic cells with a limited ionic adsorption

Dilute electrolytic cells filled with chlorobenzene containing small amounts of tetrabutylammonium tetraphenylborate show anomalous dielectric dispersions in low-frequency regions. We propose a new model for electrode polarization in order to analyze the dielectric behavior of the dilute electrolytic cells. The model comprises two capacitive components: One is the space-charge polarization accompanied with a specific ionic adsorption on electrodes, and the other is the electrode capacitance which is brought about by an electronic spillover from the electrode surface. This model can primarily explain the anomalous frequency-dependent dielectric behavior of the electrolytic cells not only with low electrolyte concentrations, but also with high concentrations and can correctly describe the characteristics of the electrode polarization reflected in the dielectric spectra.

Examination of methods to determine free-ion diffusivity and number density from analysis of electrode polarization

Electrode polarization analysis is frequently used to determine free-ion diffusivity and number density in ionic conductors. In the present study, this approach is critically examined in a wide variety of electrolytes, including aqueous and nonaqueous solutions, polymer electrolytes, and ionic liquids. It is shown that the electrode polarization analysis based on the Macdonald-Trukhan model [J. Chem. Phys. 124, 144903 (2006); J. Non-Cryst. Solids 357, 3064 (2011)] progressively fails to give reasonable values of free-ion diffusivity and number density with increasing salt concentration. This should be expected because the original model of electrode polarization is designed for dilute electrolytes. An empirical correction method which yields ion diffusivities in reasonable agreement with pulsed-field gradient nuclear magnetic resonance measurements is proposed. However, the analysis of free-ion diffusivity and number density from electrode polarization should still be exercised with great caution because there is no solid theoretical justification for the proposed corrections.

Three to six ambiguities in immittance spectroscopy data fitting

Several important ambiguities in immittance spectroscopy (IS) model data-fitting results are identified and illustrated by means of complex-nonlinear-least-squares (CNLS) fits of experimental and synthetic frequency response data. A well-known intrinsic ambiguity, following from Maxwell's electromagnetic equations, arises from the indistinguishability in external measurements of conduction and displacement currents. Usual fit models for either dielectric or conductive-system situations, such as the Davidson-Cole one, only involve a strength parameter, a dielectric constant, a characteristic relaxation time, and a fractional exponent and lead to no additional ambiguities. But the situation is different for more powerful and useful general models, such as ordinary or anomalous diffusion Poisson-Nernst-Planck ones: PNP and PNPA, used here, whose historical background, current status, and applicability are described and discussed herein. They apply to two different kinds of experimental IS situations and involve several additional, potentially free fit parameters, such as the mobilities of positive and negative charge carriers, and generation-recombination parameters that determine the partial or complete dissociation of a neutral entity of concentration N(0) into positive and negative charge carriers of equal concentration, c(0). Then, several additional ambiguities appear that may require information about the material system involved for their adequate resolution.

Utility of continuum diffusion models for analyzing mobile-ion immittance data: electrode polarization, bulk, and generation-recombination effects

Consequences of the well-known Poisson-Nernst-Planck (PNP) continuum equations of charge motion in liquids or solids for ordinary or anomalous diffusion are investigated for an electrochemical cell with completely blocking electrodes. Previous work is summarized and much of it is shown to be independent of earlier published results and incomplete, with little comparison made between ordinary and anomalous diffusion. Such comparison is provided here and also includes variation of the mobility ratio of the mobilities of positive and negative charges from equality to charge of only one sign mobile. New generation-recombination effects are demonstrated for a range of mobility ratios, with particular attention given to those present for the case of charge of only one sign mobile. No previous analyses of experimental data with PNP models using complex-least-squares fitting have been published. Here such a model is found to fit frequency response data well for a hydrogel and to lead to estimates of physically meaningful parameters such as the diffusion constant and ionic concentration. PNP analysis of a synthetic data set derived from experimental results for liquid electrolytes refutes claims made in the original publication dealing with it, but verifies and extends an interesting analysis equation proposed there. PNP fitting of data for solids, including ones showing colossal low-frequency-limiting dielectric constants, suggests that they may often be well described as arising from simple diffuse-charge double-layer effects, and that continuum microscopic models such as the PNP, in series with a conducting Debye response model, may be sufficient for fitting well an appreciable amount of data involving ion hopping and trapping behavior.