Chiral nematic liquid crystals in cylindrical cavities. A classification of planar structures and models of non-singular disclination lines

A part of homotopy theory is applied to classify planar structures in chiral nematic liquid crystals confined to cylindrical cavities. The resulting classification is exact in the approximation of undeformed chiral nematic surfaces. Within this approach the relative stability of possible planar structures with surface and bulk disclination lines is discussed. The number and the shape of these disclinations, which in some cases form spiral structures, are predicted. Further approximate analytical expressions for non-singular director fields close to disclination lines with integral strength are introduced. Our predictions, which are also in agreement with some previously suggested pictures of such director fields, are used to improve stability considerations of the confined planar chiral nematic structures in tubes and droplets.     

Modelling of director equilibrium states in a nematic cell with relief surface

We study two-dimensional equilibrium configurations of nematic liquid crystal (NLC) director in a cell bounded by two parallel surfaces. One surface is planar and the other one is spatially modulated. The relief of the modulated surface is described by a smooth periodic sine-like function. The orientation of NLC director easy axis is assumed to be homeotropic at one cell surface and planar at the other one. The NLC director anchoring with cell surfaces is assumed to be strong. We consider the case where disclination lines occur in the bulk of NLC above the extrema of the modulated surface. These disclination lines run along the crests and troughs of the surface relief. If the orientation of director at both bounding surfaces is of the same type, then NLC director field is continuous. For both configurations mentioned above (with defects and without defects), we obtain analytical expressions for director distribution in the bulk of NLC in the approximation of planar director deformations. Equilibrium distances from disclination lines to the spatially modulated surface are calculated when the defects occur. The dependences of these equilibrium distances on the period and depth of surface relief and the cell thickness are investigated in detail.     

Disclinations dynamics in confined nematic liquid crystals: strong anchoring

We have investigated the dynamics of pair annihilation of disclination lines in strong anchoring. This work is based on the Frank free energy. The director angle, φ(x, y, z), is obtained by the continuous theory. We show that the form of the viscous force in a confined nematic liquid crystal and in strong anchoring is a function of the initial distance between the two disclination lines. The asymptotic velocity, v _asy, is also a function of the initial distance. Our theoretical result on the asymptotic velocity is in good agreement with previous experimental results.     

Nematodynamics and structures in junctions of cylindrical micropores

ABSTRACT

We explore equilibrium structures and flow-driven deformations of nematic liquid crystals confined to 3D junctions of cylindrical micropores with homeotropic surface anchoring. The topological state of the nematic ordering field in such basic unit of porous networks is controlled by nematic orientation profiles in individual pores, anchoring frustration along the edges of joining pores and coupling to the material flow field. We numerically investigate formation of the flow-aligned configurations in single cylindrical pores and pore junctions. Depending on the arrangement of inlet and outlet flows in the junction, we demonstrate existence of numerous stationary nematic configurations, characterised by specific bulk defects and surface disclinations along joining edges. Observed bulk defects are nonsingular escaped structures, disclinations in the form of loops or disclination lines pinned to the joining edges of the pores. Furthermore, we show examples of defect dynamics during the flow-induced topological transformations.     

Two-dimensional director configurations in a nematic-filled cylindrical capillary with the hybrid director alignment on its surface

ABSTRACT

We analytically calculate two-dimensional equilibrium configurations of the nematic liquid crystal (NLC) director in a right cylindrical capillary with the hybrid director alignment on its inner surface. A part of this surface is treated to impose the strong homeotropic alignment, while on the remaining part the strong circular alignment, perpendicular to the capillary axis, is imposed. Owing to the system homogeneity along the capillary axis, a disclination line emerges in the bulk of the NLC, which runs parallel to the axis. It is shown that there exist either one or two equilibrium locations of the disclination line depending on the ratio of capillary surface parts with homeotropic and circular alignment. The technique that allows to obtain an analytical expression for the system free energy as a function of a disclination line location is presented. It considerably simplifies calculations and can be used while solving a variety of problems in which a defect location is sought.     

Effect of an electric field on defects in a nematic liquid crystal with variable surface anchoring

We report experimental studies on defects in a nematic liquid crystal with negative dielectric anisotropy mounted in a cell with perfluoropolymer-coated surfaces. The sample exhibits a discontinuous anchoring transition from planar to homeotropic on cooling at zero or a small electric field, and above a cross-over voltage a continuous ‘inverse Freedericksz transition’, at which the director starts tilting in opposite directions at the two surfaces. Defects of strength ±1/2 are either annihilated or expelled when the director tilts. On the other hand, disclination lines of ±1 which end in partial point defects (boojums) at the surfaces in the planar alignment regime acquire point defects of strength ±1 at the midplane of the cell when the director tilts. At a low enough temperature, the homeotropic anchoring becomes strong, and an electric field above the Freedericksz threshold generates the usual umbilic defects, which follow the dynamic scaling laws found in earlier studies.     

Nematic twist-bend phase under external constraints

ABSTRACT

The recently discovered twist-bend nematic phase, N_TB, has short-pitched heliconical structure with doubly degenerate handedness. In contrast to the classic nematic, in the N_TB phase the director is spontaneously distorted, resulting in unusual elastic properties. The response of the N_TB phase to external stimuli, like chiral doping or applied fields might provide further information about its structure and can find utilisation in practical applications. Here, the N_TB behaviour is theoretically investigated under chiral doping and strong electric fields. We show that the chiral doping removes the N_TB degeneration and modifies the conical tilt angle, leaving the pitch unchanged. Thus, the N_TB helical twisting power is very high and strongly non-linear. Under electric field, we consider separately the ferroelectric, flexoelectric and dielectric couplings. We show that the experiments reported so far disagree with the ferroelectric behaviour, indicating that the N_TB phase is not spontaneously polarised. On the contrary, the observed polar effects fit well with the flexoelectric coupling, confirming the degenerated heliconical structure of the phase. Under very strong fields, we predict a second-order twist-bend nematic – nematic phase transition due to the dielectric torque on the director.     

Disclinations dynamics in confined nematic liquid crystals: strong anchoring

We have investigated the dynamics of pair annihilation of disclination lines in strong anchoring. This work is based on the Frank free energy. The director angle, φ(x, y, z), is obtained by the continuous theory. We show that the form of the viscous force in a confined nematic liquid crystal and in strong anchoring is a function of the initial distance between the two disclination lines. The asymptotic velocity, v _asy, is also a function of the initial distance. Our theoretical result on the asymptotic velocity is in good agreement with previous experimental results.     

Molecular ordering in microconfined liquid crystals: An infrared linear dichroism study

Abstract

The molecular arrangement of 5CB confined within the cylindrical pores of Anopore membranes was characterized by means of the IR-order parameter obtained from linear dichroism measurements of selected IR absorption bands. The treatment of the experimental data includes a local field correction extended to the twisted nematic configuration, yielding order parameters increased by about 30% in comparison with the uncorrected data. The nematic director of 5CB aligns along the pore axes, whereas in lecithin coated Anopore channels, the local nematic director is oriented approximately radially due to the perpendicular anchoring of the 5CB molecules at the pore wall. Doping of 5CB with the chiral agent CB15 yields local nematic directors tilted with respect to the pore axes. The average tilt angle increases up to about 40° at a fraction of CB15, x _cb15 = 0.25 (w/w). These results are discussed in terms of the conical helicoidal and alternatively the radially twisted axial arrangement of the LC molecules within submicrometer cylindrical cavities.     

From understanding structures in antiferro-ferri and ferroelelectric liquid crystals to an unusual electro-optic effect in a bent-core nematic; a celebration of innovative materials

ABSTRACT

The field of liquid crystals is truly multidisciplinary with numerous examples of virtuous circles of interaction between chemistry, physics, theory and engineering resulting in breakthroughs in both fundamental understanding and novel applications. This paper, written to mark John Goodby’s 65th birthday, offers a personal perspective of the synergy between chemistry and physics from a collaboration that has spanned three decades. The first part of the paper reviews some of the physics insights that resulted from chiral liquid crystals fundamental to understanding structures in ferroelectric, ferrielectric and antiferroelectric systems. The second part of the paper describes some of the remarkable consequences of the anomalous elasticity and flexoelectricity found in the nematic phases of bent-core materials. In particular, we present unusual bowing of disclination lines in the nematic phase of a bent-core material in the presence of a field. Finally, the paper summarises some future prospects relating for bent-core materials. The paper by no means captures the amazing breadth of contribution that John’s chemistry has made to the subject, but aims to exemplify how his generous collaborative approach coupled with innovative chemistry and physical insight has led to paradigm changes in our subject.     

The elastic distortion and stability of biaxial nematic liquid crystal on the surface grooves

Fukuda et al. reexamined the Berreman's model which attributes the surface anchoring to the elastic distortion of the uniaxial nematic liquid crystal induced by the grooves of a surface. They showed that at the variance with the assumption made in the original approach of Berreman, the azimuthal distortion of the director cannot be considered as negligibly small. Now this method is generalized to the biaxial nematic liquid crystals, with some approximations for the elastic constants. We obtain an additional term in the elastic distortion energy per unit area which depends on the second power of the cosine of the angle made between the main director n at infinity and the direction of the surface grooves. This additional term describes the distortion energy of the minor director m induced by the surface grooves when the n director is anchored exactly along the grooves. We have studied the stability of the n director around the grooves, and in one-constant model for each director the stability condition is that the elastic constant of the n director is the maximum.     

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.     

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.     

Spontaneously modulated chiral nematic structures of flexible bent-core liquid crystal dimers

ABSTRACT

We report the induction of spontaneously undulated chiral nematic structures of liquid crystal (LC) dimers with rigid aromatic molecular arms linked by flexible chains with an odd number of carbons. When a small amount of chiral dopants (CD) are added to the dimers, we find the formation of different stripe textures on cooling 4–10 μm films in the nematic phase. The temperature where the stripes form depends on the film thickness and the direction of the stripes depends on the CD concentrations. We show that the experimentally observed stripes are due to undulation instabilities that spontaneously form as a result of the anomalously small bend elastic constant that prefers director bend instead of twist deformation, the opposite of the situation in usual cholesteric LCs.     

Optical microscopy study for director patterns around disclinations in side-chain liquid crystalline polymer films

Polarizing optical microscopy is employed to study director fields around disclinations in side-chain liquid crystalline polymer films. Optical black brushes together with stripes around disclinations are observed. The stripes run parallel to the local director and thus decorate overall patterns of nematic director around disclinations. Three director patterns involving radial, spiral, and circular microstructures of a positive integer disclination with s = +1 and one hyperbolic pattern of a negative integer disclination with s = -1 are observed in the thin film. It is found that the specific configurations of a pair of (+1, -1) disclinations form during the late stage of annihilation. Increasing the film thickness leads to disclination instability. We observe that black four-brushes of disclinations with s = +/-1 split into black two-brushes, where two types of director patterns of disclinations with half-integer strengths of s = +/- 1/2 produce. Theoretical analysis is presented to explain this instability.     

高分子液晶向列相的向错结构

高分子液晶态向错结构在正交偏振片下呈现出具有不同数目黑刷子的纹影织构，是由于分子指向矢取向排列上的不连续性所引起的一种光学效应。近年来，高分子液晶态向错结构的研究已取得了较大进展，发展和应用片晶装饰、条带织构装饰和表面裂纹装饰等技术可以在电镜和偏光显微镜下直接观察各种向错结构。本文简要介绍高分子液晶态向列相的向错和反转壁结构的几何学、高强度向错以及近年在实验上观察各类型向错形态的研究进展。     

A tensor model of liquid crystalline polymers: application to basic disclination processes

One of the features of liquid crystalline polymers (LCPs) is their strong elastic anisotropy, which means they have unequal elastic constants. Elastic anisotropy plays a crucial role in the microstructure and macroscopic properties of LCPs. In this paper, the effect of unequal elastic constants on microstructure is investigated without an external field by using a deterministic tensorial approach. In this model, the evolution of the director field can be viewed as a process driven towards the state of zero elastic torque. A tensor expression of the elastic torque is used so that the nematic symmetry is automatically conserved. In simulations of bulk samples, disclination lines of strength half and escaped integer disclinations are observed. The distortion fields around the disclinations are found to depend on elastic anisotropy. If the twist constant is the lowest, as is the case for main chain liquid crystalline polymers, the disclination lines are predominantly of the twist type.     

Nematic director configurations in high pretilt, parallel aligned layers

We describe the director configurations associated with a negative dielectric anisotropy, high pretilt (typically ~ 85°) nematic cell. A number of distinct director configurations are observed, with both a transition to a spontaneously twisted state and a nucleated transition mediated by disclination line movement. We discuss the role of surface pretilt and elastic constant anisotropy on behaviour and give results on the relative energetic stability of the director states.     

A tensor model of liquid crystalline polymers: application to basic disclination processes

One of the features of liquid crystalline polymers (LCPs) is their strong elastic anisotropy, which means they have unequal elastic constants. Elastic anisotropy plays a crucial role in the microstructure and macroscopic properties of LCPs. In this paper, the effect of unequal elastic constants on microstructure is investigated without an external field by using a deterministic tensorial approach. In this model, the evolution of the director field can be viewed as a process driven towards the state of zero elastic torque. A tensor expression of the elastic torque is used so that the nematic symmetry is automatically conserved. In simulations of bulk samples, disclination lines of strength half and escaped integer disclinations are observed. The distortion fields around the disclinations are found to depend on elastic anisotropy. If the twist constant is the lowest, as is the case for main chain liquid crystalline polymers, the disclination lines are predominantly of the twist type.