Generalized Ornstein-Zernike approach to many-particle equilibrium correlation functions

J. BŁawzdziewicz, B. Cichocki and R. Hołyst

Physica A: Statistical Mechanics and its Applications 1989, 157, 857-890

A new generalization of the Ornstein-Zernike equation for the functions describing equilibrium correlations between two groups of particles is proposed. The generalized direct correlation functions for two groups of particles are introduced, and the integral equations relating these functions to “full” correlations are derived. The derivation is based on diagrammatic analysis of the correlation functions. As an analogue of a cutting (nodal) vertex in the standard analysis leading to the Ornstein-Zernike equation we consider now a cutting set of vertices. Possible applications of the proposed formalism to the actual calculation of three- and four-particle equilibrium correlation functions are indicated.

Exact sum rules and geometrical packing effects in the system of hard rods near a hard wall in three dimensions

R. Hołyst

Molecular Physics 1989, 68, 391-400

Exact statistical mechanical sum rules for the pressure p and surface grand potential Θ s of system of hard-rods near a hard wall are derived. The system is studied in the nonlocal version of Onsager low-density approximation. Θ s , the equilibrium density and the nematic order parameter profiles at the bulk nematic-isotropic coexistence are calculated. The nonlocal approximation is shown to satisfy the pressure sum rule. From the behaviour of the profiles we conclude that the geometrical packing effects manifest themselves most strongly in the density profile and rather weakly in the order parameter profiles.

Comparative study of the nematic phase-isotropic phase transition in systems of uniaxial hard cores

R. Hołyst

Molecular Physics 1989, 68, 381-390

We apply the smoothed density approximation to study the nematic phase-isotropic phase transition (N-I) for the following systems: hard ellipsoids of revolution (HE), hard spherocylinders (HSC), and cylinders (HC). We find that the transition is very sensitive to the shape of the hard core modelling a liquid crystal molecule. In the case of HC, the nematic phase can exist in the whole range of elongations x, while for HE and HSC the nematic density at the transition exceeds the close packing density in some range of x, around x = 1. Also the dependence on x of the nematic order parameter, Q, the density, Δη, and entropy, ΔS, jumps at N–I transition is completely different for HC in comparison to HE and HSC.

Quasi-wetting on a sphere

R. Hołyst and A. Poniewierski

Physica A: Statistical Mechanics and its Applications 1988, 149, 3, 622-630

Wetting phenomena on a sphere of radius R are studied in the context of the Sullivan model. Neither a first nor a continuous transition is found for finite R. Only in the strict limit of R→∞ a second-order transition appears. For temperatures T higher than the wetting temperature in a flat geometry, Tw, the thickness l of the enhanced density layer, which forms on the surface of the sphere, is for large R proportional to In R.

Director orientation at the nematic-phase–isotropic-phase interface for the model of hard spherocylinders

R. Holyst and A. Poniewierski

Phys. Rev. A 1988, 38, 1527

A fluid of hard spherocylinders is studied in the Onsager model adapted to a nonuniform system. The interfacial properties at nematic-phaseisotropic-phase coexistence are considered. It is found that the angle between the director and the normal to the interface is approximately 60° and does not depend on the length-to-width ratio L/D of the spherocylinder. The nematic-phaseisotropic-phase surface tension, however, tends linearly to zero as D/L→0. It is also argued that the anisotropic hard-core repulsion favors the perpendicular alignment at the nematic free surface. The results concerning the tilt angle are in good agreement with experimental studies for nCB (n=5,6,7,8) [(4-n-alkyl-4-cyano)biphenyl].

Nematic alignment at a solid substrate: The model of hard spherocylinders near a hard wall

A. Poniewierski and R. Hołyst

Phys. Rev. A 1988, 38, 3721

A system of hard spherocylinders near an impenetrable wall is studied in the low-density Onsager approximation. Using a simple local approximation for the one-particle distribution function, we show that the preferred orientation of the nematic director is parallel to the wall. The density and order-parameter profiles are calculated. The nematic main order parameter Q is enhanced near the wall even though the density is reduced. The wall-induced biaxiality P is small in the interfacial region. We find that wetting by the nematic phase should occur at the nematic-isotropic coexistence.

Density-Functional Theory for Nematic and Smectic – A Ordering of Hard Spherocylinders

A. Poniewierski and R. Hołyst

Phys. Rev. Lett. 1988, 61, 2461

A density-functional theory, based on the smoothed density approximation, is presented in order to study phase transitions in systems of hard spherocylinders with full translational and orientational degrees of freedom. We find both the nematic-isotropic and the nematicSmecticA phase transition in a wide range of length-to-width ratios LD. The predictions of our theory are in good agreement with results of computer simulations and we recover Onsager’s limit of LD. We also make some comments about application of the theory to systems of hard ellipsoids.

Nematic-wall surface tension for perfectly aligned hard linear molecules

R. HOŁYST AND A. PONIEWIERSKI

Molecular Physics 1988, 65, 1081-1087

We study a system of hard elongated molecules near a hard wall, placed in a strong bulk ordering field. The field fixes the tilt angle ϑ t and increases the order parameter Q. We show that in the case of perfect alignment (Q = 1) the nematic-wall surface tension (γ) does not have the usual form of a polynomial in cos2 ϑ t . Using a simple local approximation for the one-particle distribution function we find an analytical expression for γ(ϑ t ) for the system of hard cylinders and also calculate γ(ϑ t ) numerically for the system of hard spherocylinders.

Wetting on a spherical surface

R. HOŁYST AND A. PONIEWIERSKI

Phys. Rev. B 1987, 36, 5628

It is shown in the framework of the Cahn model [J. Chem. Phys. 66, 3667 (1977)] that the wetting layer, which forms on a spherical surface, always has a finite thickness llnR where R is the radius of a sphere. The temperature Tw of a first-order wetting transition is higher in a spherical geometry than in a flat one. The shift of the transition temperature Tw is proportional to lnR/R for large R.

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