Frequency-Dependent Dielectric Permittivity in Poisson-Nernst-Planck Model.

The approaches developed for studying the polarization of molecules and the dynamics of ions in dielectric materials are usually considered separately. The two effects are often believed to take place in different frequency ranges. The low frequency response is usually dominated by ionic migration, whereas the high frequency response is played by molecular polarization. The goal here is to clarify the interplay between free and bound charge densities and their influences on permittivity and impedance profiles by proposing a version of the Poisson-Nernst-Planck (PNP) model that allows to include the effect of a frequency-dependent (and thus not instantaneous) polarizability.

Dynamics of coreless defects during winding up transitions in confined chiral nematic liquid crystals.

Twist-coupled elastic deformations are ubiquitous and in the limelight of interest for next-generation self-shaping materials. Here, we describe how twist dynamics under fixed anchoring lead to bend deformation and defect dynamics in a field-unwound chiral liquid crystal material. We use the Q-tensor dynamics under the Landau-de Gennes formalism in a finite-element mesh to explore the texture pathways from the unwound (homeotropic) to the helical planar structure. Our simulations describe well previously reported experiments and confirm that the process occurs by forming pairs of coreless defects that interact with each other and create quadrupolar structures called Lehmann clusters. The dynamics and coarsening of dipoles and quadrupoles of defects are described. This numerical study describes the full dynamics, which has been sought for several years.

Coarse-grained model of the nematic twist-bend phase from a stable state elastic energy.

The twist-bend nematic (N_{TB}) phase is a doubly degenerated heliconical structure with nanometric pitch and spontaneous bend and twist deformations. It is favored by symmetry-breaking molecular structures, such as bent dimers and bent-core molecules, and it is currently one of the burgeoning fields of liquid-crystal research. Although tremendous advances have been reported in the past five years, especially in molecular synthesis, most of its potential applications are held back by the lack of a proper and definitive elastic model to describe its behavior under various situations such as confinement and applied field. In this work we use a recently proposed stable state elastic model and the fact that the mesophase behaves as a lamellar structure to propose a mesoscopic or coarse-grained model for the N_{TB} phase. By means of standard procedures used for smectic and cholesteric liquid crystals, we arrive at a closed-form energy for the phase and apply it to a few situations of interest. The predicted compressibility for several values of the cone angle and the critical field for field-induced deformation agree well with recent experimental data.

Reliability of Poisson-Nernst-Planck Anomalous Models for Impedance Spectroscopy.

We investigate possible connections between two different implementations of the Poisson-Nernst-Planck (PNP) anomalous models used to analyze the electrical response of electrolytic cells. One of them is built in the framework of the fractional calculus and considers integro-differential boundary conditions also formulated by using fractional derivatives; the other one is an extension of the standard PNP model presented by Barsoukov and Macdonald, which can also be related to equivalent circuits containing constant phase elements (CPEs). Both extensions may be related to an anomalous diffusion with subdiffusive characteristics through the electrical conductivity and are able to describe the experimental data presented here. Furthermore, we apply the Bayesian inversion method to extract the parameter of interest in the analytical formulas of impedance. To resolve the corresponding inverse problem, we use the delayed-rejection adaptive-Metropolis algorithm (DRAM) in the context of Markov-chain Monte Carlo (MCMC) algorithms to find the posterior distributions of the parameter and the corresponding confidence intervals.

Estimating physical properties from liquid crystal textures via machine learning and complexity-entropy methods.

Imaging techniques are essential tools for inquiring a number of properties from different materials. Liquid crystals are often investigated via optical and image processing methods. In spite of that, considerably less attention has been paid to the problem of extracting physical properties of liquid crystals directly from textures images of these materials. Here we present an approach that combines two physics-inspired image quantifiers (permutation entropy and statistical complexity) with machine learning techniques for extracting physical properties of nematic and cholesteric liquid crystals directly from their textures images. We demonstrate the usefulness and accuracy of our approach in a series of applications involving simulated and experimental textures, in which physical properties of these materials (namely: average order parameter, sample temperature, and cholesteric pitch length) are predicted with significant precision. Finally, we believe our approach can be useful in more complex liquid crystal experiments as well as for probing physical properties of other materials that are investigated via imaging techniques.

Effect of dynamically changing the substrate's easy axis on the response time of nematic samples.

Recent discoveries of advanced photocontrolled materials have kindled a great deal of interest on their use as command surfaces that switch easy axis under light radiation. One noticeable point when using switchable surfaces on any application is how the dynamical process propagates to the bulk directors. In this paper, we theoretically study the effect of a relaxing easy axis over time on a nematic sample when finite anchoring energy and surface viscosity are included. We first consider the case where just one of the substrates decay over time in an initially distorted director organization. Next, we assume that both substrates can be switched simultaneously. From the calculated director we obtained the optical profile and finally the molecular response time of the material. The response time depends on both the materials and the surfaces properties including its decay time. Our results might be used for understanding and engineering liquid crystal displays and other electro-optical devices with photocontrolled alignment layers.

Surface induced twist in nematic and chiral nematic liquid crystals: stick-slip-like and constrained motion.

Surface driven pattern formation is an intriguing phenomenon in the liquid crystal field. Owing to its ability to transmit torque, one can generate different patterns by propagating distortions on the optical wavelength scale in the sample from the surface. Here, we theoretically investigate (from the elasticity point of view) twist deformations induced by a rotating easy axis at one surface, by considering the anchoring energy and surface viscosity of nematic and chiral nematic samples. The model is solved analytically in the limit of strong anchoring and numerically for a low anchoring strength situation. Such rotation could be induced, in principle, by light-controlling the orientation of an azobenzene monolayer coated at one of the glass substrates or by an in-plane rotating field. We discuss the role of the surface parameters and the different distortions, and calculate light transmission using the Jones method. Three different regimes are identified: free twist, stick-slip twist, and constrained twist. The results obtained here may be relevant for liquid crystal active waveplates and for determining surface viscosity and the azimuthal anchoring energy.

Ion Motion in Electrolytic Cells: Anomalous Diffusion Evidences.

In this study, we argue that ion motion in electrolytic cells containing Milli-Q water, weak electrolytes, or liquid crystals may exhibit unusual diffusive regimes that deviate from the expected behavior, leading the system to present an anomalous diffusion. Our arguments lie on the investigation of the electrical conductivity and its relationship with the mean square displacement, which may be used to characterize the ionic motion. In our analysis, the Poisson-Nernst-Planck diffusional model is used with extended boundary conditions to simulate the charge transfer, accumulation, and/or adsorption-desorption at the electrode surfaces.

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.

Elastic continuum theory: towards understanding of the twist-bend nematic phases.

The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which K_{22}>K_{33}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

Surface induced phase separation and pattern formation at the isotropic interface in chiral nematic liquid crystals.

We study the pattern formation of a chiral nematic liquid crystal under a wetting transition. In the isotropic-liquid crystal transition, a surface-enhanced effect happens and a thin liquid crystal layer forms at the substrates of the cell. In this confined system, chirality, elastic anisotropy, surface anchoring, and wetting strength interplay. A striped pattern is formed due to the chiral nature of the material and the tilted anchoring at the isotropic boundary. As the wetting layer grows from cooling the sample, first the stripes rotate through a process where dislocation defects are formed. As the wetting layer grows further, the periodicity of the stripe structure changes, and finally a splitting of the stripes occurs. Because of the unique properties of this system, new insights about pitch-thickness ratio, interface anchoring, and elastic anisotropy effect are found. Since the anchoring at the isotropic boundary is weak, the critical ratio between the thickness of the wetting layer and the helical pitch is different from that reported in the literature. We also discover that the elastic anisotropy and elastic constant ratios play a critical role in stripe formation. Because of the similarity with biological fibrous composites (twisted plywood), our system may be used as a synthetic version to mimic the naturally occurring one. We carry out a simulation study to explain the experimental results.

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

We demonstrate theoretically that the presence of ions in insulating materials such as nematic liquid crystals may be responsible for the dielectric spectroscopy behavior observed experimentally. It is shown that, at low frequencies, an essentially non-Debye relaxation process takes place due to surface effects. This is accomplished by investigating the effects of the adsorption-desorption process on the electrical response of an electrolytic cell when the generation and recombination of ions is present. The adsorption-desorption is governed by a non-usual kinetic equation in order to incorporate memory effects related to a non-Debye relaxation and the roughness of the surface. The analysis is carried out by searching for solutions to the drift-diffusion equation that satisfy the Poisson equation relating the effective electric field to the net charge density. We also discuss the effect of the mobility of the ions, i.e., situations with equal and different diffusion coefficients for positive and negative ions, on the impedance and obtain an exact expression for the admittance. The model is compared with experimental results measured for the impedance of a nematic liquid crystal sample and a very good agreement is obtained.

Memory effect in the adsorption phenomena of neutral particles.

The adsorption-desorption phenomenon of neutral particles dissolved in an isotropic fluid is investigated by using a nonsingular kernel in the kinetic equation at the limiting surfaces. To account for the relevance of a memory effect, three types of kernels in the kinetic equation are considered. Similar kernels have been used to investigate nonexponential relaxation including several contexts such as dielectric relaxation, diffusion-controlled relaxation in liquids, liquid crystals, and amorphous polymers. A suitable choice for a temporal kernel can account for the relative importance of physisorption or chemisorption, according to the time scale governing the adsorption phenomena, and can be the key mechanism to understand the specific roles of both processes. By using a general procedure, the time evolution of the density of particles is determined in closed analytical form. The analysis is relevant in the description of the adsorption phenomena in general.

Dependence of the anchoring energy on the applied voltage in a nematic cell.

A nematic liquid crystal cell in the shape of a slab of thickness d and containing ionic impurities is considered in the presence of a dc voltage. A complete theoretical model to determine the electric field distribution across the sample is used to explain the experimental dependence of the effective anchoring energy of the cell on the applied voltage, in the limit of high voltage.

Effective screening length of isotropic liquid samples submitted to an applied voltage.

A cell of isotropic liquid in the shape of a slab of thickness d and containing ionic impurities is considered. It is shown that the screening effect produced by the ionic charges on the external field is characterized by an effective surface length, lambda(S)(U), depending on the applied voltage U. The analysis indicates that lambda(S)(U)) << lambda(D) when the applied voltage is very large, and lambda(S)(U) --> lambda(D) for very small values of the applied voltage, where lambda(D) is the Debye screening length. The presence of the ions is responsible also for a counterpotential, v, that for small U is such to cancel the effective electric field in the sample, whereas in the opposite limit it is inversely proportional to the applied difference of potential.