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.
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...
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