Effets des fluctuations et du confinement dans la description théorique de fluides simples et anisotropes
Auteur / Autrice : | Ivan Kravtsiv |
Direction : | Myroslav Holovko, Dung Di Caprio |
Type : | Thèse de doctorat |
Discipline(s) : | Chimie Physique |
Date : | Soutenance en 2013 |
Etablissement(s) : | Paris 6 |
Mots clés
Résumé
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.