Integral equation theory for nematic fluids

Abstract

The traditional formalism in liquid state theory based on the calculation of the pair distribution function is generalized and reviewed for nematic fluids. The considered approach is based on the solution of orientationally inhomogeneous Ornstein-Zernike equation in combination with the Triezenberg-Zwanzig-Lovett-Mou-BuffWertheim equation. It is shown that such an approach correctly describes the behavior of correlation functions of anisotropic fluids connected with the presence of Goldstone modes in the ordered phase in the zero-field limit. We focus on the discussions of analytical results obtained in collaboration with T.G. Sokolovska in the framework of the mean spherical approximation for Maier-Saupe nematogenic model. The phase behavior of this model is presented. It is found that in the nematic state the harmonics of the pair distribution function connected with the correlations of the director transverse fluctuations become long-range in the zero-field limit. It is shown that such a behavior of distribution function of nematic fluid leads to dipole-like and quadrupole-like long-range asymptotes for effective interaction between colloids solved in nematic fluids, predicted before by phenomenological theories.

Maier-Saupe nematogenic fluid: field theoretical approach

“…This problem is connected with approximation (4.9) which leads to (4.34). We should mention that in previous works [2,3,7] carried out in the mean spherical approximation equation (4.34) is not true and the problem being discussed does not appear. We think that for point particles we can also solve this problem by introducing an additional isotropic interaction.…”

“…A specific feature of the considered molecular fluid is a broken symmetry which appears in the absence of an orienting external field. In [2,3,7] using the Lovett-Mou-Buff-Wertheim equation [21, 22] an exact relation for orientationally non-uniform fluids was obtained: ∇ ∇ ∇ Ω1 ln ρ(Ω 1 ) = dr 12 dΩ 2 C(r 12 , Ω 1 Ω 2 )∇ ∇ ∇ Ω2 ρ(Ω 2 ), (4.29) where C(r 12 , Ω 1 Ω 2 ) is the direct correlation function which in the RPA is given by equation (4.9). Equation (4.29) is also known as the integro-differential form of the Ward identity [2,7,23].…”

“…A specific feature of the considered molecular fluid is a broken symmetry which appears in the absence of an orienting external field. In [2,3,7] using the Lovett-Mou-Buff-Wertheim equation [21, 22] an exact relation for orientationally non-uniform fluids was obtained:…”

“…Maier-Saupe nematogenic fluid [1] is one of the simplest models that account for the isotropicnematic phase transition in the liquid crystal phase. The properties of this model have been intensively studied by the liquid theory methods such as integral equations for correlation functions [2][3][4][5][6][7]. In the integral equation theory there is a problem of the correctness of taking the fluctuation effects into account, the treatment of which depends on closure relations used in integral equations.…”

“…For the purpose of simplification, in this paper we consider a fluid of point particles. However, in the future we hope to modify the obtained results for non-point particles using the mean spherical results [2,3,7] as it was done for a non-point ionic system [16].…”