Work

The work focuses on the study of structural, thermodynamic, and elastic properties of spatially and orientationally inhomnogeneous fluids. To this end we investigate a number of systems confined by a hard wall with pair potentials describing soft repulsion, long-range attraction, and anisotropic interaction between particles. The research was conducted in the framework of a field theory formalism in the mean field approximation (MFA) and the Gaussian approximation. An exact contact theorem for spatially confined systems was used to ensure the consistency of each approximation. Furthermore, for the case of a mean field anisotropic fluid, the author provides the first known formulation and proof of the contact theorem. Explicit analytical expressions for the pair correlation function, the density profile, the order parameter profile, the adsorption coefficient, the elasticity constant, the free energy, and the pressure are derived. These quantities are analyzed as functions of the density, the temperature, and the parameters of the pair potential. For spatially confined isotropic systems the results obtained are compared to computer simulations data and are found to be in a very good agreement. Moreover, we show that the Gaussian approximation can provide a clearly better description of the system as compared to the MFA. We find that under certain conditions a spatially confined fluid can exhibit a non-trivial behavior due to fluctuation effects. One consequence is a non-monotonous behavior of the adsorption coefficient as a function of the temperature or the density. Furthermore, the adsorption can change sign if the temperature or the density is changed. We demonstrate that for an orientationally-inhomogeneous fluid the results obtained provide a correct description of the Goldstone modes appearing in the nematic liquid crystal phase. The possibility of the loss of nematic ordering at a confining interface is conjectured.