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In the framework of a field theoretical approach we study Maier-Saupe nematogenic fluid in contact with a hard wall. The pair interaction potential of the considered model consists of an isotropic and an anisotropic Yukawa terms. In the mean field approximation the contact theorem is proved. For the case of the nematic director being oriented perpendicular to the wall, analytical expressions for the density and order parameter profiles are obtained. It is shown that in a certain thermodynamic region the nematic fluid near the interface can be more diluted and less orientationally ordered than in the bulk region.Key words: Maier-Saupe nematogenic fluid, field theoretical approach, interface, contact theorem PACS: 61.30. Gd, 61.30.Hn Due to orientational ordering, nematic fluids near a surface show richer behavior than in the case of simple fluids. Among them are the anchoring phenomena, whereby the surface induces a specific orientation of the nematic director with respect to the surface [1]. In order to understand this phenomenon, during the past decade the Henderson-Abraham-Barker (HAB) approach [2,3], previously developed in the theory of isotropic fluids in contact with solid surfaces [4], has been employed. In this approach, the description of the fluid density profile reduces to the solution of the Ornstein-Zernike (OZ) integral equation for the fluid particle-wall distribution function calculated from the known fluid particle distribution function in the bulk. In the framework of the HAB approach, the application to the bulk of the nematic model, analytically solvable at the level of the mean spherical approximation (MSA) [5], makes it possible to investigate the role of orientational-dependent molecular interactions with the surface in anchoring phenomena [2,3]. However, in the MSA, this approach does not take into account the contribution from long-range molecular interactions and, as a result, does not satisfy the exact relation known as the contact theorem [6,7]. According to this theorem, the contact value of the particle density near a hard wall for a neutral fluid is determined by the pressure of the fluid in the bulk volume.Recently, the density field theory, previously developed for ionic fluids near a hard wall [8][9][10], has been applied to the description of simple fluids with Yukawa-type interactions near a hard wall [11]. In both cases, the developed approach yielded correct results. In this theory, the contributions from the mean field and from the fluctuations are separated. In [11], it was shown that the mean field treatment of a Yukawa fluid near a wall reduces to solving a non-linear differential equation for the density profile while the treatment of fluctuations reduces to the OZ equation with the Riemann boundary condition.In this paper, the density field theory, developed in [11] for simple fluids at a hard wall, will be generalized to nematic fluids at a hard wall. To this end, we consider Maier-Saupe nematogenic fluid model [12,13] as one of the simplest models that account for...

We apply a field-theoretical approach to study the structure and thermodynamics of a two-Yukawa fluid confined by a hard wall. We derive mean field equations allowing for numerical evaluation of the density profile which is compared to analytical estimations. Beyond the mean field approximation, analytical expressions for the free energy, the pressure, and the correlation function are derived. Subsequently, contributions to the density profile and the adsorption coefficient due to Gaussian fluctuations are found. Both the mean field and the fluctuation terms of the density profile are shown to satisfy the contact theorem. We further use the contact theorem to improve the Gaussian approximation for the density profile based on a better approximation for the bulk pressure. The results obtained are compared to computer simulation data.

We adopt a field theoretical approach to the study of the structure and thermodynamics of a homogeneous Maier-Saupe nematogenic fluid interacting with anisotropic Yukawa potential. In the mean field approximation we retrieve a standard Maier-Saupe theory for liquid crystals. In this theory, the single-particle distribution function is expressed via the second order Legendre polynomial of molecule orientations. In the Gaussian approximation we obtain analytical expressions for correlation functions, free energy, pressure, chemical potential, and elasticity constant. Subsequently we find corrections due to fluctuations and show that the singleparticle distribution function now contains Legendre polynomials of higher orders. We also use Ward symmetry identities to set a simple condition for correlation functions.

Condensed 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.

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A solid ionic conductor with cation conductivity in the interelectrode region is studied. Due to their large size, the anions are considered fixed and form a homogeneous neutralizing electric background. The model can be used to describe properties of ceramic conductors. For a statistical mechanical description of such systems, which are characterized by short-range Van der Waals interactions and long-range Coulomb interactions, an approach combining the collective variables method and the method of mean cell potentials is used. This formalism was applied in our previous work [Bokun G., Kravtsiv I., Holovko M., Vikhrenko V., di Caprio D., Condens. Matter Phys., 2019, 29, 3351] to a homogeneous state and in the present work is extended to an inhomogeneous case induced by an external electric field. As a result, mean cell potentials become functionals of the density field and can be described by a closed system of integral equations. We investigate the solution of this problem in the lattice approximation and study charge and electric field distributions in the interelectrode region as functions of plate electrode charges. The differential electric capacitance is subsequently calculated and discussed.