Bulk Nematic Liquid Crystals Research Articles

Density-functional theory of surfacelike elasticity of nematic liquid crystals

Based on the density-functional theory, we show that the splay-bend surfacelike bulk elastic constant ${\mathrm{K}}_{13}$ is an artifact of the phenomenological as well as the gradient expansion construction of the curvature elastic free energy of nematic liquid crystals, while the saddle-splay constant ${\mathrm{K}}_{24}$ is real and approximately obeys an extended Nehring-Saupe relation ${\mathrm{K}}_{24}$ \ensuremath{\geqslant}(${\mathrm{K}}_{11}$ -${\mathrm{K}}_{22}$ )/2, with ${\mathrm{K}}_{11}$ and ${\mathrm{K}}_{22}$ being the splay and twist Frank constants, respectively. The result ${\mathrm{K}}_{13}$ =0 automatically resolves the Oldano-Barbero pathology, which inevitably accompanies a nonzero ${\mathrm{K}}_{13}$ , and gives a concrete rationale for the conventional approaches in the continuum theory disregarding the surfacelike elasticity. The source of an apparently nonzero ${\mathrm{K}}_{13}$ in previous microscopic theories is discussed in detail and is demonstrated to be a result of an inconsistent use of a nonlocal-to-local mapping of the elastic free-energy functional at the boundary. The absence of ${\mathrm{K}}_{13}$ can be regarded as a type of Cauchy relation in the nematic continuum theory in the sense that it is not directly rooted in any of the macroscopic symmetries existing in the nematic phase, but is a general consequence of the particular algebraic form of the nonlocal free-energy term from which ${\mathrm{K}}_{13}$ derives; its linearity in the distortion amplitude and the symmetry of the relevant direct correlation function with respect to the permutation of a molecular pair leads always to the vanishing ${\mathrm{K}}_{13}$ . In this respect, ${\mathrm{K}}_{13}$ =0 applies not only to nematic liquid crystals but also to a more general class of phases such as cholesteric liquid crystals, whose structure can be viewed as a weak modulation of a translationally invariant phase. We finally consider the elastic description of nematic liquid crystals in the presence of real interfaces. The present formulation allows a straightforward decomposition of the elastic excess free energy into the bulk contribution and the interfacial excess in the Gibbs sense. The bulk part yields the bulk Oseen-Frank elastic free-energy density along with the ${\mathrm{K}}_{24}$ term evaluated at the Gibbs dividing surface as an unambiguous local quantity. The interfacial excess, when gradient expanded, reduces to the surface free-energy density comprised of the anchoring energy, surface-excess Oseen-Frank elastic energy, ${\mathrm{K}}_{24}$ -like term, and elastic free-energy contributions reflecting the broken symmetry at the interface. The ${\mathrm{K}}_{24}$ -like term is formally similar to the bulk ${\mathrm{K}}_{24}$ term, but is no longer an intrinsic property of bulk nematic liquid crystal, as it depends also on the nature of the medium with which the nematic liquid crystal is in contact.

Interfacial structural transitions in nematic liquid crystals

The orientation taken by a bulk nematic liquid crystal in contact with a substrate can vary with certain parameters, leading to anchoring transitions. Such bulk reorientations are the result of structural transitions taking place in the region of the liquid crystal close to the substrate-the interfacial region-which are driven by the molecules located at the substrate surface. Starting from the experimentally measured orientational distribution of these molecules, it is possible to predict correctly the orientational behaviour of the rest of the liquid crystal and in particular the anchoring transitions.

Bulk-induced alignment of nematic liquid crystals by photopolymerization

A novel technique to produce uniform alignment of nematic liquid crystals is presented. The technique is based on producing an anisotropic polymer network in the bulk nematic liquid crystal by polymerizing a photoresist material. Both uniform planar alignment and homeotropic alignment can be obtained depending on the curing conditions. In the case of planar alignment, the nematic director orientation is governed by the direction of the polarization vector of the linearly polarized ultraviolet light, thus making it possible to produce a defined azimuthal orientation of the nematic director. This technique obviates the need to give any previous treatment to the bounding substrates and as such should be independent of the nature of the substrate.

Evidence of pronounced positional order at the graphite–liquid crystal interface of a bulk nematic material

We present scanning tunneling microscopy images of a bulk nematic liquid crystal, viz., 4′-n-hexyl-4-cyanobiphenyl, on the surface of graphite. These images clearly show the existence of pronounced positional order at the solid–liquid crystal interface for a material with no positional order in the bulk. A feature of the molecular arrangement is the pronounced interdigitation of the aromatic cores. The unit cell consists of two opposing molecules, the aromatic core of one of them lying flat on the graphite surface, while the core of the adjacent molecule lies on its side. The packing arrangement also features large open spaces of uncovered substrate between the alkyl tails. The molecular arrangement is compared with that of the smectic alkylcyanobiphenyls.

Transition of an oriented nematic liquid crystal to a glass with a nematic order - determination of the order parameter

A bulk nematic liquid crystal sample was oriented by a magnetic field, and solidified by quenching in liquid nitrogen. The resultant glass retained the nematic order. So, it was possible to determine the order parameter by diamagnetic susceptibility measurements. Ours results, on paraazoxyanisole, were in good agreement with those deduced by Saupe and Maier from Foex' experiments on a solid monocrystal, and with N.M.R. data.