L. R. Evangelista

An elementary course on the continuum theory for nematic liquid crystals

Variational calculus theory of elasticity 1 - fundamentals theory of elasticity II - applications molecular models subsurface deformations in nematics.

Adsorption phenomena and anchoring energy in nematic liquid crystals

NEMATIC LIQUID CRYSTALS: FUNDAMENTALS AND BULK PROPERTIES Nematic Order Parameters Maier-Saupe Approach for the Nematic-Isotropic Phase Transition Continuum Description of the Nematic Phase External Field Contribution to the Elastic Energy Density Equilbrium Configuration in Strong and Weak Anchoring Situations NEMATIC LIQUID CRYSTALS: SURFACE PROPERTIES Anchoring The Anchoring Energy Function Periodic Deformations in Nematic Liquid Crystals Spontaneous Periodic Distortions in Nematic Liquid Crystals: Dependence on the Tilt Angle Theoretical Models for the Surface Free Energy Stochastic Contribution to the Anchoring Energy: Deviation from the Rapini-Papolar Expression Validity of the Elastic Model for Nematic Surface Anchoring Energy Contribution of the Smectic-Nematic to the Surface Energy TEMPERATURE DEPENDENCE OF THE SURFACE FREE ENERGY Thermal Relaxation Model of Surface Director Gliding in Lyotropic Liquid Crystals Thermal Renormalization of the Anchoring Energy Temperature Induced Surface Transition in Nematic Liquid Crystals Oriented by Evaporated SiOx A Local Self-Consistent Approach to the Phase Transition at the Nematic Liquid Crystal - Wall Interface SURFACE ADSORPTION OF PARTICLES: GENERAL CHARACTERISTICS Introduction Statement of the Problem: Langmuirs Isotherm Surface Adsorption and Anchoring Transition Photo-Manipulation of the Anchoring Strength of Photochromic Nematic Liquid Crystal Adsorption of Magnetic Grains in Magnetic Fluids Selective Ionic Adsorption in Liquid Crystals SURFACE ELECTRIC FIELD-INDUCED INSTABILITIES IN NEMATIC LIQUID CRYSTALS SAMPLE The General Electrostatic Model Analysis I: Variation Solution of the Eigenvalue Problem Analysis II: Series Solution of the Eigenvalue Problem Role of the Elastic Term Linear in the Spatial Derivatives of the Nematic Director in a 1D Geometry Conclusions IONS AND NEMATIC SURFACE ENERGY: BEYOND THE EXPONENTIAL APPROXIMATION FOR THE ELECTRIC FIELD OF IONIC ORIGIN Introduction Theoretical Model: Non-Linear Poisson-Boltzman Equation External Electric Field Effect in the Nematic Anchoring Energy Contribution to the Surface Energy of Dielectric Origin Conclusions ADSORPTION PHENOMENON AND EXTERNAL FIELD EFFECT ON AN ISOTROPIC LIQUID CONTAINING IMPURITIES Introduction The Model The Charge and Field Distributions Ionic Adsorption in the Absence of External Equilibrium Distribution of Charges Extensions of the Model Influence of the Adsorption Energy in the Dieletric Contribution to the Anchoring Energy FERMILIKE DESCRIPTION OF THE ADSORPTION PHENOMENON Introduction The Fermi-Like Model Application: Ion Adsorption in Isotropic Fluids Limits Numerical Results Conclusions

Fractional Diffusion Equation and Impedance Spectroscopy of Electrolytic Cells

The influence of the ions on the electrochemical impedance of a cell is calculated in the framework of a complete model in which the fractional drift-diffusion problem is analytically solved. The resulting distribution of the electric field inside the sample is determined by solving Poissons equation. The theoretical model to determine the electrical impedance we are proposing here is based on the fractional derivative of distributed order on the diffusion equation. We argue that this is the more convenient and physically significant approach to account for the enormous variety of the diffusive regimes in a real cell. The frequency dependence of the real and imaginary parts of the impedance are shown to be very similar to the ones experimentally obtained in a large variety of electrolytic samples.

A Connection Between Anomalous Poisson–Nernst–Planck Model and Equivalent Circuits with Constant Phase Elements

A connection between the impedance spectroscopy response of anomalous Poisson-Nernst-Planck (PNPA) diffusional models and of equivalent circuits containing constant phase elements (CPE) is established for a typical electrolytic cell. The analysis is carried out in the limit of low frequency in order to highlight the surface effects and to explore how they can be connected to the presence of CPE in the circuit. It is shown that, depending on the choice of the equivalent circuit, the action of these elements can be the same as the one obtained by using integro-differential boundary conditions to describe anomalous diffusive processes in the framework of PNPA models. The predictions are also compared with an experimental data obtained from an electrolytic solution.

Anomalous diffusion and memory effects on the impedance spectroscopy for finite-length situations

The contribution of ions to the electrical impedance of an electrolytic cell limited by perfect blocking electrodes is determined by considering the role of the anomalous diffusion process and memory effects. Analytical solutions for fractional diffusion equations together with Poissons equation relating the effective electric field to the net charge density are found. This procedure allows the construction of general expressions for the electrochemical impedance satisfying the Kramers-Kronig relations when the diffusion of ions in the cell is characterized by the usual, as well as by anomalous, behavior.

Nonlocal Diffusion in Porous Media: A Spatial Fractional Approach

AbstractOne-dimensional diffusion problems in bounded porous media characterized by the presence of nonlocal interactions are investigated by assuming a Darcy’s constitutive equation of convolution integral type. A power law attenuation function is implemented: Analogies and differences of the flow-rate-pressure law with respect to other nonlocal and fractal models are outlined. By means of the continuity relationship, the fractional diffusion equation is then derived. It involves spatial Riemann-Liouville derivatives with a noninteger order consisting of between 1 and 2. The solution is obtained numerically using fractional finite differences, and results are presented in both the transient and the steady-state regimes. Eventually, the physical meaning of fractional operators is discussed and potential applications of the analysis are suggested.

A Model for Selective Ion Adsorption Including van der Waals Interaction

A model for the selective adsorption phenomenon in an isotropic liquid accounting for a van der Waals interaction between the ions and the surface is presented, in the framework of the Poisson-Boltzmann theory. The fundamental equations governing the electric field distribution are exactly solved for low and high potential regimes.

Anomalous Diffusion Effects on the Electrical Impedance Response of Liquid-Crystalline Systems

The electrical impedance response of six nematic liquid crystals samples is analyzed by means of an extension of the Poisson-Nernst-Planck diffusional model. This formulation includes fractional derivatives of distributed order governing the behavior of the bulk density of mobile charges, whose solutions are subjected to integro-differential equations accounting for the boundary conditions. The role of the intrinsic surface lengths involved in the adsorption-desorption phenomena at the electrodes is emphasized, in order to analyze the frequency dependence of the real and imaginary parts of the electrical impedance experimentally obtained.

Spectrum of the Fermi-Linearized Extended Hubbard Model on a Dimer

The extension of the Hubbard model proposed in refs. [1], [2] includes a diagonal term designed to account for Coulomb interaction between nearest neighbour sites. In the present note we discuss the spectrum of the fermi-linearized[3] version of such model on a dimer, assuming spin-independent hopping amplitudes.

FREEDERICKSZ-LIKE TRANSITIONS IN COMPENSATED NEMATIC LIQUID CRYSTALS

The occurrence of the Freedericksz transitions at the inversion point of the main dielectric anisotropy in nematic liquid crystals is discussed. It is shown that, if this kind of order-disorder phase transition can take place, they are always of the first order. The critical fields are evaluated, and the relative phase diagram is discussed.