Abstract
We adopt a field theoretical approach to study the structure and thermodynamics of a homogeneous Maier-Saupe nematogenic fluid interacting with anisotropic Yukawa potential. In the mean field approximation we retrieve the standard Maier-Saupe theory for liquid crystals. In this theory the density is expressed via the second order Legendre polynomial of molecule orientations. In the Gaussian approximation we obtain analytical expressions for the correlation functions, the elasticity constant, the free energy, the pressure, and the chemical potential. We also use Ward symmetry identities to set a simple condition for the correlation functions. Subsequently we find corrections due to fluctuations and show that density now contains Legendre polynomials of higher orders.
Highlights
Maier-Saupe nematogenic fluid [1] is one of the simplest models that account for the isotropicnematic phase transition in the liquid crystal phase
For the first time the field theoretical approach is applied to the description of correlation functions and thermodynamic properties of molecular anisotropic fluids
By expanding the Hamiltonian in powers of density fluctuations we examine the system in the mean field and Gaussian approximations
Summary
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 order to treat the fluctuations more properly and to control the level of this treatment, in this paper we will apply the field theoretical approach This is the first time the field theoretical approach is applied to the description of anisotropic molecular fluids. We calculate the correction to the mean field single-particle distribution function due to fluctuations which is expressed in terms of the fourth order Legendre polynomials of molecule orientations. 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]
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