A. Poniewierski

Theory of the Nematic-Isotropic Transition in a Restricted Geometry

Abstract We discuss, using a Landaude Gennes formalism, the nematic-isotropic transition temperature for a system placed between two parallel plates, subject to identical homeotropic or homogeneous boundary conditions at each plate. The temperature at the phase transition may increase or decrease as the inverse sample thickness, D-1, increases, depending on the nature of the boundary conditions. In all cases the transition terminates at a critical point for sufficiently large D-1, beyond which the nematic and isotropic phases are no longer distinct. The phase transition temperature is well described by a liquid crystal analogy of the Kelvin equation which can be generalized to give an exact Clausius-Clapeyron relation. Under many circumstances the system behaves from a thermodynamic point of view as though it were in a bulk ordering field. The finite geometry restricts the growth of nematic or isotropic wetting films. We discuss the disjoining pressure experiment of Horn, Israelachvili and Perez [15]. Fin...

Hard sphere cavity in a liquid‐density functional approach

The system of particles, interacting via a reasonably realistic intermolecular potential, in contact with a hard spherical wall is studied. The weighted density approximation is used to determine the density distribution and the liquid–wall surface tension. The effect of the wall curvature on the density at contact and the surface tension is investigated. The predictions of the model calculations are compared with the results of the computer simulations and a qualitative agreement is found. It is suggested that the asymptotic expansion of the surface tension and the density at contact in powers of the curvature may not be valid for cavities of microscopic size.

Phase behavior of a nematic liquid crystal in contact with a chemically and geometrically structured substrate

A nematic liquid crystal in contact with a grating surface possessing an alternating stripe pattern of locally homeotropic and planar anchoring is studied within the Frank-Oseen model. The combination of both chemical and geometrical surface pattern leads to rich phase diagrams, involving a homeotropic, a planar, and a tilted nematic texture. The effect of the groove depth and the anchoring strengths on the location and the order of phase transitions between different nematic textures is studied. A zenithally bistable nematic device is investigated by confining a nematic liquid crystal between the patterned grating surface and a flat substrate with strong homeotropic anchoring.

Shape of the nematic-isotropic interface in conditions of partial wetting

A nematic liquid crystal in contact with a solid substrate is studied in the partial wetting regime. Both a mesoscopic Landau-de Gennes theory and a macroscopic effective interface Hamiltonian approach are considered. A generalized Young equation for the balance of forces at the three-phase contact line is derived, which takes into account corrections due to distortions of the nematic director field. It is also shown that the asymptotic form of the separation of the nematic-isotropic interface from the substrate has a logarithmic correction to the usual linear behaviour. The characteristic length scale of this correction is given by the ratio K/(2σNI), where K and σNI are the average elastic constant and the nematic-isotropic surface tension, respectively, and is of the order of a few hundred angstroms. Then, a simple form of an effective interface Hamiltonian is proposed, and results consistent with the predictions of the Landau-de Gennes theory are obtained. It is shown, in the framework of this macroscopic approach, that the line tension associated with the contact line remains finite, when the thermodynamic limit is taken, if the anchoring at both the nematic-substrate and the nematic-isotropic interfaces is homeotropic. However, in the case of different anchoring directions, the line tension diverges logarithmically with the system size.

Local structure of microemulsion

Correlation function between surfactant particles aligned along common direction is calculated in the Ciach–Ho/ye–Stell lattice model. We find that in the longitudinal direction antiferromagnetic ordering occurs in the whole region of stability of the homogeneous phase. A typical distance between neighboring oppositely oriented amphiphiles is different from the characteristic size of water domains. In the transversal direction, the form of the correlation function is related to the structure of the ordered low‐temperature phase in coexistence with the microemulsion. In the proximity of the lamellar phase the correlation function decays monotonically indicating local ‘‘lamellar’’ ordering, while near the cubic bicontinuous phase it exhibits damped oscillations around zero.

Effective free-energy method for nematic liquid crystals in contact with structured substrates

We study the phase behavior of a nematic liquid crystal confined between a flat substrate with strong anchoring and a patterned substrate whose structure and local anchoring strength we vary. By first evaluating an effective surface free-energy function characterizing the patterned substrate, we derive an expression for the effective free energy of the confined nematic liquid crystal. Then we determine phase diagrams involving a homogeneous state in which the nematic director is almost uniform and a hybrid aligned nematic state in which the orientation of the director varies through the cell. Direct minimizations of the free-energy functional were performed in order to test the predictions of the effective free-energy method. We find remarkably good agreement between the phase boundaries calculated from the two approaches. In addition, the effective free-energy method allows one to determine the energy barriers between two states in a bistable nematic device.

Nematic liquid crystal in contact with periodically patterned surfaces

Nematic liquid crystals confined between two different substrates, possessing alternating stripe patterns of planar and homeotropic anchoring, are studied within the Frank–Oseen theory, in which the anchoring energy function is given by the Rapini–Papoular expression. By numerical minimization of the free energy we determine phase transitions between uniform and distorted nematic textures. The calculations reveal that these phase transitions can be triggered by changing the shift of the stripe patterns with respect to each other. A hybrid nematic cell model together with an effective anchoring strength can be used to describe the phase behaviour for sample thicknesses larger than the periodicity of the stripe pattern. Rich phase behaviour is predicted for the case of a generalized expression for the surface free energy.

Anchoring transitions in the nematic‐substrate system: Study of the Landau–de Gennes model

We study the phenomenon of anchoring and anchoring transitions in the nematic‐substrate system using the Landau–de Gennes formalism. The free‐energy functional is expanded around the bulk tensor nematic order parameter up to the second‐order terms. This quadratic approximation is used to find an explicit condition for the anchoring direction in a semi‐infinite system, and then the phase boundaries between the homeotropic, planar, and conical anchorings are determined. In the cases that we have studied the quadratic approximation predicts a first order homeotropic–conical transition and a first order or continuous planar–conical transition. It also predicts a simple asymptotic expression for the free energy of a finite system, when the sample thickness is large and the deviation of the director from the anchoring direction is small. This asymptotic formula leads in a natural way to the definition of the geometrical measure of the anchoring strength b. However, the quadratic approximation is insufficient t...

Anchoring of a nematic liquid crystal on an anisotropic substrate

A nematic liquid crystal in contact with a flat solid substrate is studied by means of a mesoscopic Landau-de Gennes theory. It is assumed that the substrate is anisotropic, i.e. the directions x and y in the surface of the substrate are not equivalent, and the only symmetry is the mirror symmetry y ↦ - y. Assuming the simplest form of the bare surface free energy, where only the linear terms in the nematic order parameter are taken into account, we study anchoring directions induced by the interaction of the liquid crystal with the substrate. A phase diagram in terms of the surface fields and the temperature is obtained. Depending on the values of the surface fields we find four types of anchoring: the symmetric planar anchoring, with the director along x, the symmetric tilted anchoring, with the director in the xz plane, the antisymmetric planar anchoring, with the director along y, and the asymmetric tilted anchoring, with the director tilted with respect to all three axes.

The writhing on the wall: first tentative steps toward a comprehensive theory of liquid crystal surfaces

A Commentary on the paper ”Theory of the nematic‐isotropic transition in a restricted geometry„, by A. Poniewierski and T.J. Sluckin. First published in Liquid Crystals, 2, 281‐311 (1987).