The system of mobile ions in lattice models: Screening effects, thermodynamic and electrophysical properties

The lattice fluid model of the system with short range and long range Coulomb interactions is suggested. In the framework of the collective variables method, the screening of the Coulomb interactions in the bulk is considered. It is shown that the Debye length includes additional concentration dependence inversely proportional to the square root of the mean concentration of vacant sites like what is known at the plane boundary. The Coulomb interaction contribution to the free energy of the system is calculated in the approach close to the mean spherical approximation and is given in an analytical form. The influence of the variation of the crystal field near the system boundary on the structure and characteristics of the electric double layer is investigated. As compared to the system with equal crystal potentials at the lattice sites throughout the system the pronounced difference for the electric capacitance appears at low absolute values of the surface potential and it is more pronounced for negative electric potentials. The capacitance diverges as the potential values at which the electric field tends to zero and attains negative values in regions of the surface potentials depending on their polarity and values of the surface crystal potential. Negative values of the capacitance may indicate the thermodynamic instability of the system that can result from neglecting the short range interaction contribution.Comment: 20 pages, 5 figure

Phase Behavior of the Patchy Colloids Confined in the Patchy Porous Media

A simple model for functionalized disordered porous media is proposed and the effects of confinement on self-association, percolation and phase behavior of a fluid of patchy particles are studied. The media is formed by a randomly distributed hard-sphere obstacles fixed in space and decorated by a certain number of off-center square-well sites. The properties of the fluid of patchy particles, represented by the fluid of hard spheres each bearing a set of the off-center square-well sites, are studied using an appropriate combination of the scaled particle theory for the porous media, Wertheim's thermodynamic perturbation theory, and the Flory-Stockmayer theory. To assess the accuracy of the theory a set of computer simulations have been performed. In general, predictions of the theory appear to be in a good agreement with computer simulation results. Confinement and competition between the formation of bonds connecting the fluid particles, and connecting fluid particles and obstacles of the matrix, give rise to a re-entrant phase behavior with three critical points and two separate regions of the liquid-gas phase coexistence

Short- and long-range contributions to equilibrium and transport properties of solid electrolytes

International audienceCondensed ionic systems are described in the framework of a combined approach that takes into account both long-range and short-range interactions. Short-range interaction is expressed in terms of mean potentials and long-range interaction is considered in terms of screening potentials. A system of integral equations for these potentials is constructed based on the condition of the best agreement of the system of study with the reference system. In contrast to the description of media with short-range interactions, in this text the reference distribution includes not only the field of mean potentials but also Coulomb interaction between particles. A one-component system made of ions in a neutralizing background of fixed counterions is considered. The model can be used to describe solid ionic conductors. In order to study the movement of cations on the sites of their sub-lattice, the lattice approximation of the theory is employed based on the calculation of the pair distribution function. Using the collective variables approach, a technique improving the starting expression for this function is proposed. Notably, the neglected terms in the expansion of this function are approximated by single-particle terms ensuring that the normalization condition is satisfied. As a result, the applicability of the theory is extended to a wide region of thermodynamic parameters. The chemical potential and the diffusion coefficient are calculated showing the possibility of phase transitions characteristic of the system

Effets des fluctuations et du confinement dans la description théorique de fluides simples et anisotropes

We investigate the impact of confinement and density field fluctuations on equilibrium properties of simple and anisotropic fluids. A field theory formalism is applied to systems with Yukawa-like potentials and Maier-Saupe nematogenic fluids in the bulk and in the vicinity of a hard wall. For Yukawa and two-Yukawa fluids at a surface, the mean field approximation (MFA) reduces to a system of non-linear differential equations. The exact contact theorem is used to research the consistency of the approximations. Indeed, in the MFA, based on a pressure invariant, the contact theorem (CT) is verified. Beyond, in the Gaussian approximation, analytical expressions for density profiles, adsorption coefficient, and free energy are derived. Once more, the CT condition is satisfied. Fluctuations lead to density depletion at the wall regardless of the sign of interaction. As a result, for some systems an oscillatory density profile and a non-monotonous adsorption coefficient as a function of temperature or bulk density are observed. In the case of systems with the Maier-Saupe potential of interaction, the MFA retrieves the standard Maier Saupe theory of liquid crystals. Analytical expressions for the correlation functions, the free energy, and the elasticity constant are derived. At a hard wall in the MFA a system of equations containing generalized biaxial order parameters is obtained. The CT is verified regardless of the angle between the surface and the director. For homeotropic alignment, expressions for the density and the order parameter profiles are derived. Analytical expressions for the pair correlation function are calculated. The possibility of the loss of nematic ordering at a confining interface is conjectured.Nous étudions les effets du confinement et des fluctuations de densité sur les propriétés d'équilibre de liquide simples et anisotropes. Une théorie des champs est utilisée pour étudier des potentiels de type Yukawa et des fluides nématiques de type Maier-Saupe en volume et au voisinage d'un mur dur. Pour des fluides avec un ou deux potentiels de Yukawa, l'approximation de champ moyen (AdCM) se réduit à un système d'équations différentielles non linéaires. Le théorème de contact (TdC) est utilisé pour vérifier la cohérence des différentes approximations. De fait, en ACM, l'existence d'un invariant pour la pression permet de vérifier la validité du TdC. Au-delà, dans l'approximation gaussienne, nous dérivons des expressions analytiques pour les profils, le coefficient d'adsorption et l'énergie libre. Ici aussi le TdC est satisfait. Les fluctuations conduisent à une dépletion des profils de densité au mur quelque soit le signe de l'interaction. En conséquence, pour certains systèmes, nous observons des oscillations dans le profil de densité et un comportement non-monotone du coefficient d'adsorption en fonction de la température et de la densité. Pour les systèmes de type Maier-Saupe, l'AdCM redonne la théorie de Maier-Saupe pour les cristaux liquides. Nous obtenons des expressions analytiques pour les fonctions de corrélation, l'énergie libre et la constante d'elasticité. A un mur dur en AdCM un systèmes d'équations comprenant des paramètres d'ordres biaxiaux généralisés est obtenu. Le TdC est vérifié quelque soit l'angle entre la surface et la directrice du nématique. Pour un alignement homéotropique, des expressions du profil de densité du paramètre d'ordre sont obtenus. Des expressions analytiques des fonctions de corrélation de paires sont dérivées. On conjecture alors la possibilité d'une perte de l'ordre nématique au voisinage de l'interface.PARIS-BIUSJ-Biologie recherche (751052107) / SudocSudocFranceF

Ionic Soft Matter: Modern Trends in Theory and Applications

This book is for researchers interested in the statistical mechanical modeling of charged substance as well as for those working in chemical physics, physical chemistry, biophysics and environmental science. The book consists of state of the art reviews of the recent experimental, theoretical and simulation studies on ionic criticality, polyelectrolytes, proton transport in fuel cell membranes, and the design of DNA arrays. A significant portion of the book deals with discussions of the fundamental and applied problems of important phenomena such as ion association, ion adsorption, ion solvation, electrical double layer, thin colloidal film stability, ion collective dynamics, ion screening, etc. using a level of argumentation that is common and understandable for mathematicians, physicists, chemists, biologists and engineers. The book concludes with chapter on physical properties of fuel-containing materials from the inside of the troubled Chornobyl sarcophagus

On the contact conditions for the density and charge profiles in the theory of electrical double layer: From planar to spherical and cylindrical geometry

In this paper, starting from the Bogoliubov-Born-Green-Yvon equations of the liquid-state theory, we formulate two equivalent approaches for the calculation of the total density profile and of the charge density profile of ionic fluids near nonplanar charged surfaces. In the framework of these approaches, we establish exact conditions, that a particular point of these profiles should satisfy, in the form of contact theorems. These contact theorems for the total density profile and the charge density profile are obtained by direct integration of a system of equations derived from the Bogoliubov-Born-Green-Yvon equations. The contact theorems for both profiles have nonlocal character. It is shown that the contact value of the total density profile for uncharged surfaces is characterized by the bulk pressure and the surface tension. The contact theorems are applied to the cases of spherical and cylindrical surfaces. It is shown that the contact theorem for the total density profile coincides with the recent results obtained by W. Silvester-Alcantara, D. Henderson and L.B. Bhuiyan Mol. Phys., 113, 3403, 201