Maier-Saupe nematogenic fluid: field theoretical approach

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.Key words: Maier-Saupe nematogenic fluid, field theoretical approach, interface, contact theorem PACS: 61.30. Gd, 61.30.Hn Due to orientational ordering, nematic fluids near a surface show richer behavior than in the case of simple fluids. Among them are the anchoring phenomena, whereby the surface induces a specific orientation of the nematic director with respect to the surface [1]. In order to understand this phenomenon, during the past decade the Henderson-Abraham-Barker (HAB) approach [2,3], previously developed in the theory of isotropic fluids in contact with solid surfaces [4], has been employed. In this approach, 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]. However, 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.Recently, 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. In this theory, the contributions from the mean field and from the fluctuations are separated. In [11], it was shown that the mean field treatment of a Yukawa fluid near a wall reduces to solving a non-linear differential equation for the density profile while the treatment of fluctuations reduces to the OZ equation with the Riemann boundary condition.In this paper, the density field theory, developed in [11] for simple fluids at a hard wall, will be generalized to nematic fluids at a hard wall. To this end, we consider Maier-Saupe nematogenic fluid model [12,13] as one of the simplest models that account for...

Section: −1mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Nematic fluid at a hard wall in the mean field approximation

Caprio¹,

Holovko²,

Kravtsiv³

2013

“…However, even for RSs of noninteracting particles there are several models where the method developed above can be very useful. One of such examples is connected with the statistical field theory of anisotropic fluids where the RS may be considered as the system of noninteracting rigid rotators (see, for instance, [29]).…”

Section: -4mentioning

confidence: 99%

The method of collective variables: a link with the density functional theory

Patsahan¹,

Mryglod²

2012

Recently, based on the method of collective variables the statistical field theory for multicomponent inhomogeneous systems was formulated [O. Patsahan, I. Mryglod, J.-M. Caillol, Journal of Physical Studies, 2007, 11, 133]. In this letter we establish a link between this approach and the classical density functional theory for inhomogeneous fluids. The powerful tools for the study of equilibrium and non-equilibrium properties of many-particle interacting systems are those based on the functional methods. In many cases the partition function of such systems can be re-expressed as a functional integral after performing the Hubbard-Stratonovich (HS) transformation [1, 2], a simple device proposed in the 50ies. Nearly at the same time another method, the method of collective variables (CVs), that allows one in an explicit way to derive a functional representation for many-particle interacting systems, was developed [3,4]. The method, proposed initially in the 1950s [3][4][5] for the description of the classical charged many particle systems and developed later for the needs of the phase transition theory [6][7][8][9][10], was in fact one of the first successful attempts to attack the problems of statistical physics using the functional integral representation. The CV method is based on: (i) the concept of collective coordinates being appropriate for the physics of the system considered (see, for instance, [11]) and (ii) the functional integral identity(1) valid for classical systems and permitting to derive an exact functional representation for the configurational Boltzmann factor. Being applied to the fluids, the CV method uses the idea of the reference system (RS), one of the basic ideas in the liquid state theory [12].Recently, the rigorous scalar field KSSHE (Kac-Siegert-Stratonovich-Hubbard-Edwards) theory [13,14], which uses the HS transformation, was developed to describe the phase equilibria in simple and ionic fluids. As was shown [15,16], both theories (KSSHE and CVs) are in close relation.Another valuable theoretical approach, which has been extensively employed to study the structural and thermodynamic properties of inhomogeneous systems is the classical density-functional theory (DFT) (for an overview we refer to [17,18]). The central quantity of DFT is the Helmholtz excess free energy expressed as a functional of the single-particle density. There are few systems for which this functional is known exactly. Thus, successful application of DFT critically depends on judicious choice of an appropriate Helmholtz energy functional suitable for the system under investigation [12]. The main goal of this letter is to constitute a link between the CVs based theory and the classical DFT.Let us consider the general case of a classical m-component system consisting of N particles among which there exist N 1 particles of species 1, N 2 particles of species 2, . . . and N m particles of species m.The

“…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]. The density field theory was applied to the description of bulk properties of a nematic fluid in [21,22]. The application of the density field theory to the description of a nematic fluid at a hard wall was initiated in [23].…”

Section: Introductionmentioning

confidence: 99%

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

Holovko¹,

Patsahan²,

Kravtsiv³

et al. 2016

The mean field approximation is formulated within the framework of the density field theory to study the properties of a Maier-Saupe nematogenic fluid near a hard wall. The density and the order parameter profiles are obtained using the analytical expressions derived in the linearized mean field approximation. The temperature dependencies of the contact values of the density and order parameter profiles are analyzed in detail. To estimate a validity of the applied approximations, the obtained theoretical results are compared with the original computer simulation data.