Two-Yukawa fluid at a hard wall: Field theory treatment

Abstract

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.

Cluster expansion for the description of condensed state: crystalline cell approach

“…We should note that the descriptions of the considered system in the framework of the Hamiltonians (2.1) and (2.2) are exactly equivalent only in the case when all the terms in the cluster expansion (3.10) are taken into account at the calculation of the single-particle potentials. There are two principal differences between the considered equation (4.7) and the corresponding equations in traditional approaches such as the mean field approximation formulated in the framework of the field theoretical approach [17,18] or the density functional approach [19] well developed for non-lattice fluid systems. The first difference is connected with the presence of the interparticle potential Φ(q n i , q n j ) in equation (4.7) in the exponential form.…”

Maier-Saupe nematogenic fluid with isotropic Yukawa repulsion at a hard wall: Mean field approximation

“…It was shown that the temperature trend of deviation between the order parameter S b calculated with fluctuations included and the MF value is the same as that between computer simulations and the MF value presented in figure 1. In the next paper we plan to include the contribution from fluctuations in the description of a MS nematogenic fluid at a hard wall similar to the way it was done for isotropic Yukawa fluids [18,19].…”

“…In this theory, the contributions from the mean field and from fluctuations are separated. The theory was successfully applied to ionic fluids at a hard wall [14][15][16][17] and to simple fluids with Yukawa-type interactions near a hard wall [18,19]. It was shown that the mean field treatment of a Yukawa fluid at a hard wall reduces to the solution of a non-linear differential equation for the density profile, while the treatment of fluctuations reduces to the OZ equation with the Riemann boundary condition [20].…”

Contact theorems for anisotropic fluids near a hard wall

“…We believe that these exact relations at a surface can be used to verify the accuracy of results from numerical simulations or else to improve DP approximations based on state of the art approximations for the bulk pressure -easier to calculate. We have adopted this procedure for isotropic fluids 14 and intend to apply it to nematic fluids.…”