Theory of nematic–smectic phase separation in thin twisted liquid crystal cells

Recently it has been shown experimentally by the authors that a highly twisted thin nematic cell at low temperatures can separate into a smectic A region in the middle of the cell surrounded by twisted nematic layers at the boundaries. In this case the twist is expelled into the nematic layers and the nematic–smectic A transition temperature is strongly depressed. We present a thermodynamic theory of such a phase transition in a twisted nematic cell, taking into account that the smectic A slab inside the nematic cell can be stable only if the decrease of free energy in the smectic region overcomes the increase in distortion energy of the twist deformation in the nematic layers plus the energy of the nematic–smectic A interface. In such a system the equilibrium thickness of the smectic A slab corresponds to the minimum of the total free energy of the whole cell, which includes all the bulk and surface contributions. Existing experimental data are at least qualitatively explained by the results of the present theory. This opens a unique possibility to study the properties of the nematic–smectic interface which is perpendicular to the smectic layers.     

Theory of nematic-smectic phase separation in thin twisted liquid crystal cells

Recently it has been shown experimentally by the authors that a highly twisted thin nematic cell at low temperatures can separate into a smectic A region in the middle of the cell surrounded by twisted nematic layers at the boundaries. In this case the twist is expelled into the nematic layers and the nematic-smectic A transition temperature is strongly depressed. We present a thermodynamic theory of such a phase transition in a twisted nematic cell, taking into account that the smectic A slab inside the nematic cell can be stable only if the decrease of free energy in the smectic region overcomes the increase in distortion energy of the twist deformation in the nematic layers plus the energy of the nematic-smectic A interface. In such a system the equilibrium thickness of the smectic A slab corresponds to the minimum of the total free energy of the whole cell, which includes all the bulk and surface contributions. Existing experimental data are at least qualitatively explained by the results of the present theory. This opens a unique possibility to study the properties of the nematic-smectic interface which is perpendicular to the smectic layers.     

Orientational order and finite strain in nematic elastomers

Nematic elastomers exhibit large, spontaneous shape changes at the transition from the high-temperature isotropic phase to the low-temperature nematic phase. These finite deformations are studied here in the context of a nonlinear, properly invariant, variational theory that couples the orientational order and elastic deformation. The theory is based on the minimization of a free-energy functional that consists of two contributions: a nematic one due to the interaction of the mesogenic units and an elastic one arising from the stretching of the cross-linked polymer chains. Suitable choices for these two contributions allow for large, reversible, spontaneous shape changes in which the elastic deformation can affect the isotropic-nematic transition temperature. The change in transition temperature as well as the magnitude of the resulting spontaneous deformation is illustrated for various parameter values. The theory includes soft elasticity as a special case but is not restricted to it.     

Determination of elastic constants of a binary system (7CPB+9.CN) showing nematic,induced smectic Ad and re-entrant nematic phases

The temperature variation of the splay and bend elastic constants of a binary system exhibiting nematic-induced smectic A_d and re-entrant nematic phases measured by electric field-induced Freedericksz transition method has been reported. As bend deformation is not permitted in the smectic A phase, bend elastic constant (K₃₃) could only be determined in the nematic and re-entrant nematic phases. In both the nematic phases, the splay elastic constant has the same order of magnitude and does not show any pretransitional effect. However, in the induced smectic A_d phase, the value of K₁₁ is about one to two orders higher than that in the nematic phases. The bend elastic constant shows a strong pretransitional effect near the nematic–smectic and smectic–re-entrant nematic phase transitions. The influence of the presence of the induced smectic phase is observed even in those mixtures which have no induced smectic phases. As the smectic phase is approached, the ratio K₃₃/K₁₁ increases rapidly and diverges to infinity.     

Analysis of shear flow alignment of nematic liquid crystals at low shear stress based on catastrophe theory

The low stress shear flow alignment of a nematic liquid crystal in the presence of strong anchoring at the boundaries is analysed. Layers with pretilted director orientation are taken into account. Two kinds of symmetric deformations are assumed. They differ in the director distribution in the vicinity of the boundaries. The analysis is carried out using an expansion of the free energy of the layer in powers of the maximum deformation angle. The results have qualitative character. The condition for the threshold behaviour and the stability of the solutions are discussed. The deformation may develop continuously or discontinuously. The transition between two kinds of deformation is predicted. The facts already known are confirmed and supplemented.     

Computer simulation studies of anisotropic systems. XI. Second- and fourth-rank molecular interactions

The Maier-Saupe theory for nematic liquid crystals provides a reasonable account of their orientational order and its temperature dependence. The theory is based on second-rank anisotropic interactions and its predictions can be improved by the introduction of higher-rank terms as in the Humphries-James-Luckhurst theory. However comparison with the properties of real nematogens does not allow an unambiguous test of the theory because the form of the pair potential is unknown. This is not the case for computer simulations where the intermolecular potential is defined. We have therefore undertaken a Monte Carlo study of the influence fourth-rank interactions on nematic behaviour and report the results of our simulations here. The model nematogen used as a reference is that developed by Lebwohl and Lasher in which the particles are confined to the sites of a simple cubic lattice and interact via a second-rank anisotropic potential. The simulation gives the internal energy, the heat capacity at constant volume and the second-rank order parameter as a function of temperature, as well as the nematic-isotropic transition temperature. These results are used to provide the first unambiguous test of the Humphries-James-Luckhurst theory. We also discuss the changes in the transition temperature which are caused by the introduction of the fourth-rank term in the pair potential using thermodynamic perturbation theory for the Helmoltz free energy.     

The phase transition temperatures of a liquid crystal determined from FT-IR spectra explored by principal component analysis

The FT-IR spectra of a thin layer of pure 4-chloro-2'-hydroxy-4'-pentyloxyazobenzene (CHPAB) were studied as a function of temperature. A detailed analysis of the intensity variations was performed by a method based on principal component analysis (PCA). It was shown that the phase transition temperatures obtained by means of PCA and those determined by differential scanning calorimetry (DSC), the most widely used technique in the field, were nearly identical. The PCA results revealed that the transition from solid to a liquid crystalline (LC) phase (smectic A) is more drastic phase transition in terms of infrared absorption changes. The nematic to isotropic phase transition is much less infrared sensitive. Very much smaller absorption changes are associated with the transition between the smectic and nematic mesophases. The pattern of the intensity changes strictly is correlated with the orientation of the CHPAB molecules towards the surface windows due to the surface-induced homeotropic alignment of LC molecules. The important role of hydrogen bonding interaction on the observed transition is disclosed.     

A new configurational transition in inhomogeneous nematics

At the wall in a hybrid cell with strong anchoring, the nematic director is parallel to one wall and perpendicular to the other. Usually, the free energy is minimized by a configuration where the director orientation changes continuously with position across the cell. The boundary conditions can also be satisfied, however, by a biaxial configuration without such rotation. Under certain conditions, such as under increased curvature strains, a transition can take place between these configurations. The transition typically occurs when the wavelength of the deformation becomes comparable to the coherence length of the material. The hybrid cell considered is a simple illustrative example; in real systems, such a transition may be expected in highly strained thermotropics, or in strained lyotropics which are easily made biaxial.     

Thermodynamics of activated phase transitions of 8CB: DSC and MC calorimetry

The present paper reports the heating rate effect on the phase transitions of a pure liquid crystal octylcyanobiphenyl (8CB) with use of Differential Scanning Calorimetry (DSC) and Modulation Calorimetry (MC) techniques. The DSC runs were taken at various temperature ramp rates from 20 to 0.5 K/min for heating and cooling scans. Well-defined endothermic/exothermic peaks were found at the melting/crystallization, smectic-A to nematic (SmA-N), and nematic to isotropic (N-I) transitions on heating/cooling scans, respectively. All transitions shift in temperature significantly with different ramp rates. The temperature shift of C(p) peaks between heating and cooling scans indicates the order of the transitions. In addition, all transitions follow an Arrhenius behavior. The activation energy of a transition increases as the total energy involved in the transition decreases. The respective enthalpy and entropy change of each transition provides information on the Gibbs free energy. The significance of the results is discussed in terms of the order of transitions. A comparative analysis of MC and DSC techniques highlights the significance of the two techniques. MC is a practicable tool for observing the phase dynamics whereas DSC is a good tool for studying the rate kinematics of the transitions.     

Elasticity of a Nematic Polymer in the Infinite Molecular Chain Limit

Some of the consequences of constructing a nematic phase out of infinitely long non-rigid molecules are discussed. The basic idea consists in the fact that splay deformation is difficult in a nematic composed of long molecules and becomes strictly impossible in the infinite molecular chain limit. Some of the implications of this effect for low energy elastic deformations in a polymer nematic liquid crystal are explored. A practically important example of the interaction of a long molecular chain nematic with an undulating surface is worked out.     

On the parallel-perpendicular transition for a nematic phase at a wall

We use an Onsager-level density functional theory to investigate the behaviour of the nematic phase in contact with a solid wall. The nematic consists of hard rigid rods having perfect uniform alignment and uniform spatial density. In the absence of any particle-wall interactions besides excluded-volume forces, we predict a director orientation parallel to the wall. We show that this preference for parallel alignment is due to the entropy associated with the larger volume available to the particles in their parallel orientation. An adsorption energy favouring normal alignment gives rise to a transition from a high temperature parallel orientation to a low temperature normal orientation. We derive expressions for the temperature of this transition, relating it explicitly to the wall adsorption energy, particle axial ratio, and nematic density. Effects such as layering near the wall and imperfect nematic order are argued not to be necessary for the existence of this transition.     

A new configurational transition in inhomogeneous nematics

Abstract

At the wall in a hybrid cell with strong anchoring, the nematic director is parallel to one wall and perpendicular to the other. Usually, the free energy is minimized by a configuration where the director orientation changes continuously with position across the cell. The boundary conditions can also be satisfied, however, by a biaxial configuration without such rotation. Under certain conditions, such as under increased curvature strains, a transition can take place between these configurations. The transition typically occurs when the wavelength of the deformation becomes comparable to the coherence length of the material. The hybrid cell considered is a simple illustrative example; in real systems, such a transition may be expected in highly strained thermotropics, or in strained lyotropics which are easily made biaxial.     

Heterogeneous equilibria and the kinetics of isotropic liquid-nematic phase transition in a multicomponent mixture 4-alkyl-4′-cyanobiphenyls

The isotropic liquid-nematic phase transition and the kinetics of growth of nematic phase drops during this phase transition were studied by polarization optical microscopy and IR spectroscopy for a four-component system during cooling. The statistical drop size distribution was described in terms of the equilibrium thermodynamics of irreversible processes. An analysis of the time dependences of the mean diameter of drops showed the presence of two kinetic stages of nematic phase growth and allowed them to be described by the universal law of cluster growth. In conformity with the Gibbs phase rule, nematic phases with different compositions can coexist at equilibrium.     

Theory of nematic networks with finite extensibility

A statistical molecular model of polymer networks, which takes into account inter-molecular orientational interaction and constancy of the chain contour length, is proposed. A simple formula for the network free energy valid for any deformations is obtained. A system of equations which describes orientational-elastic interactions in polymer networks is derived. The influence of deformation and degree of cross linking on the conditions of network phase transition into the orientationally ordered state of the nematic type is studied. The deformation curves considerably deviate from those predicted by the classical elasticity theory. A comparison of the proposed theory with experimental data for natural rubbers is carried out.     

Numerical analysis of the radial-axial structure transition with an applied field in a nematic droplet

In this paper the director configurations and the free energies of a nematic droplet with a surface normal anchoring condition are calculated numerically. For this surface anchoring, a transition occurs between the radial and axial structures with respect to an applied field. In the calculation of the director configurations, the position of a disclination has been fixed. Comparing the free energies for different disclinations, the stable position which gives the minimum free energy is found. In calculating the free energy of a droplet, it is assumed that the free energy density of the nematic phase does not exceed the isotropic free energy density, so that the large distortion in the vicinity of the disclination causes a nematic-isotropic transition and the free energy density of the disclination core becomes equal to the isotropic free energy density. The director configuration in a droplet is calculated as a function of an applied field for different isotropic free energy densities, elastic constant ratios and droplet shapes. The relation between the radial-axial structure transition and these factors are clarified.     

The effect of surface polarity of glass on liquid crystal alignment

The effects of the surface polarity of a glass substrate on the orientation of nematic liquid crystals (LCs) were studied using the polarised optical microscope and Fourier-transform infrared spectroscopy. On the surface of oxygen plasma treated glass, a homeotropic alignment of LCs was induced for LCs with negative dielectric anisotropy. This suggests that vertical orientation of LCs could be induced on a polar glass substrate without using an LC alignment layer. Upon cooling towards the isotropic–nematic transition, E7 with positive dielectric anisotropy changes its LC arrangement to isotropic, homeotropic, planar orientations in order. The nematic LC anchoring transition of E7 was interpreted by considering the competition between van der Waals forces and dipole interactions that control the alignment of LC molecules on a polar glass surface.