Nematic fluid at a hard wall in the mean field approximation

Holovko Holovko,Di Caprio Di Caprio,Kravtsiv Kravtsiv

doi:10.5488/cmp.16.14002

Abstract

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.

Highlights

Due to orientational ordering, nematic fluids near a surface show richer behavior than in the case of simple fluids
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]

Summary

Nematic fluid at a hard wall in the mean field approximation

In the framework of a field theoretical approach we study Maier-Saupe nematogenic fluid in contact with a hard wall. 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. 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.

Due to the properties of the Yukawa potential

Нематичний плин бiля твердої поверхнi у наближеннi середнього поля