Cholesteric liquid crystals (CLCs) have a characteristic length scale given by the pitch of the twisted stacking of their constituent rod-like molecules. Under homeotropic anchoring conditions where the molecules prefer to orient perpendicular to an interface, cholesteric interfaces exhibit striped phases with stripe widths commensurate with the pitch. Conversely, planar anchoring conditions have the molecules remain in the plane of the interface so that the CLC twists perpendicular to it. Recent work [L. Tran et al. Phys. Rev. X 7, 041029 (2017)] shows that varying the anchoring conditions dramatically rearranges the CLC stripe pattern, exchanging defects in the stripe pattern with defects in the molecular orientation of the liquid crystal molecules. We show with experiments and numerical simulations that the CLC stripes also undergo an undulation instability when we transition from homeotropic to planar anchoring conditions and vice versa. The undulation can be interpreted as a transient relaxation of the CLC resulting from a strain in the cholesteric layers due to a tilting pitch axis, with properties analogous to the classic Helfrich-Hurault instability. We focus on CLC shells in particular and show that the spherical topology of the shell also plays an important role in shaping the undulations.
We study elastic interactions between colloidal particles and deformation landscapes of undulations in a cholesteric liquid crystal under an electric field applied normal to cholesteric layers. The onset of undulation instability is influenced by the presence of colloidal inclusions and, in turn, layers' undulations mediate the spatial patterning of particle locations. We find that the bending of cholesteric layers around a colloidal particle surface prompts the local nucleation of an undulations lattice at electric fields below the well-defined threshold known for liquid crystals without incl…
The base for this manuscript was laid down by the studies carried out in the article by Senyuk B, et. al. Proceedings of SPIE. 2005; 5936: 59360W-1-9. In the present manuscript, a planar layer of the photosensitive cholesteric, based on the chiral dopant 2-(4'-phenylbenzylidene)-p-menthane-3-one dissolved in the nematic E7, under the alternating electric field was explored. In particular, the influence of UV exposure and the value of the azimuthal anchoring energy on electro- and photoswitching of undulation instabilities was considered. Due to the decrease in a ratio between the LC cell thick…
In this paper, we propose a suitable surface energy expression for cholesteric liquid crystals. We show that there exists a symmetry allowed term for chiral nematics that doesn't appear in the traditional Rapini-Papoular surface energy form. We discuss some consequences of this new surface anchoring term.
We examine the influence of bidirectional anchoring on the unwinding of a planar cholesteric liquid crystal induced by the application of a magnetic field. We consider a liquid crystal layer confined between two plates with the helical axis perpendicular to the substrates. We fixed the director twist on one boundary and allow for bidirectional anchoring on the other by introducing a high-order surface potential. By minimizing the total free energy for the system, we investigate the untwisting of the cholesteric helix as the liquid crystal attempts to align with the magnetic field. The transiti…
We consider helical configurations of a cholesteric liquid crystal (CLC) sandwiched between two substrates with homogeneous director orientation favored at both confining plates. We study the CLC twist wavenumber $q$ characterizing the helical structures in relation to the free twisting number $q_0$ which determines the equilibrium value of CLC pitch, $P_0=2π/q_0$. We investigate the instability mechanism underlying transitions between helical structures with different spiral half-turn numbers. Stability analysis shows that for equal finite anchoring strengths this mechanism can be dominated b…
In this work we numerically study the switching dynamics of a 2D cholesteric emulsion droplet immersed in an isotropic fluid under an electric field, which is either uniform or rotating with constant speed. The overall dynamics depend strongly on the magnitude and on the direction (with respect to the cholesteric axis) of the applied field, on the anchoring of the director at the droplet surface and on the elasticity. If the surface anchoring is homeotropic and a uniform field is parallel to the cholesteric axis, the director undergoes deep elastic deformations and the droplet typically gets s…
We experimentally study how the cholesteric pitch, $P$, depends on the equilibrium one, $P_0$, in planar liquid crystal (LC) cells with both strong and semistrong anchoring conditions. The cholesteric phase was induced by dissolution in the nematic LC the right-handed chiral dopant 7-DHC (7-dehydrocholesterol, provitamin $D_3$) which transforms to left-handed tachysterol under the action of UV irradiation at the wavelength of 254 nm. By using the model of photoreaction kinetics we obtain dependencies of isomers concentrations and thus the equilibrium pitch on UV irradiation dose. The cholester…
Selective reflection of light by oblique helicoidal cholesteric (ChOH) can be tuned in a very broad spectral range by an applied electric field. In this work, we demonstrate that the peak wavelength of the selective reflection can be controlled by surface alignment of the director in sandwich cells. The peak wavelength is blue-shifted when the surface alignment is perpendicular to the bounding plates and red-shifted when it is planar. The effect is explained by the electric field redistribution within the cell caused by spatially varying heliconical ChOH structure. The observed phenomenon can …
We investigate theoretically the wetting properties of cholesteric liquid crystals at a planar substrate. If the properties of substrate and of the interface are such that the cholesteric layers are not distorted the wetting properties are similar to those of a nematic liquid crystal. If, on the other hand, the anchoring conditions force the distortion of the liquid crystal layers the wetting properties are altered, the free cholesteric-isotropic interface is non-planar and there is a layer of topological defects close to the substrate. These deformations can either promote or hinder the wetti…
Cholesteric liquid crystals experience geometric frustration when they are confined between surfaces with anchoring conditions that are incompatible with the cholesteric twist. Because of this frustration, they develop complex topological defect structures, which may be helicoids or skyrmions. We develop a theory for these structures, which extends previous theoretical research by deriving exact solutions for helicoids with the assumption of constant azimuth, calculating numerical solutions for helicoids and skyrmions with varying azimuth, and interpreting the results in terms of competition b…
The dynamics of a quasi two-dimensional isotropic droplet in a cholesteric liquid crystal medium under symmetric shear flow is studied by lattice Boltzmann simulations. We consider a geometry in which the flow direction is along the axis of the cholesteric, as this setup exhibits a significant viscoelastic response to external stress. We find that the dynamics depends upon the magnitude of the shear rate, the anchoring strength of the liquid crystal at the droplet interface and the chirality. While for low shear rate and weak interface anchoring the system shows a non-Newtonian behavior, a New…
We develop a theory of point defects in cholesterics and textures in spherical droplets with normal anchoring. The local structure of chiral defects is described by singularity theory and a smectic-like gradient field establishing a nexus between cholesterics and smectics mediated by their defects. We identify the defects of degree $-2$ and $-3$ observed experimentally with the singularities $D_4^{-}$ and $T_{4,4,4}$, respectively. Radial point defects typical of nematics cannot be perturbed into chiral structures with a single handedness by general topological considerations. For the same rea…
We explore the rheology and flow-induced morphological changes of cholesteric liquid crystal patterns subject to Poiseuille flow within a slab geometry, and under different anchoring conditions at the wall. Our focus is particularly on the behaviour of Cholesteric Fingers of the first kind and of Blue Phase II. Depending on the applied pressure gradient, we observe a number of dynamic regimes with different rheological properties. Our results provide the first insight into the flow response of cholesteric phases with fully two- or three-dimensional director field patterns and normal and planar…
We simulate colloids (radius $R \sim 1μ$m) trapped at the interface between a cholesteric liquid crystal and an immiscible oil, at which the helical order (pitch p) in the bulk conflicts with the orientation induced at the interface, stabilizing an ordered array of disclinations. For weak anchoring strength W of the director field at the colloidal surface, this creates a template, favoring particle positions eitheron top of or midway between defect lines, depending on $α= R/p$. For small $α$, optical microscopy experiments confirm this picture, but for larger $α$ no templating is seen. This ma…
We study the phase behaviour of cholesteric liquid crystal shells with different geometries. We compare the cases of tangential and no anchoring at the surface, focussing on the former case, which leads to a competition between the intrinsic tendency of the cholesteric to twist and the anchoring free energy which suppresses it. We then characterise the topological phases arising close to the isotropic-cholesteric transition. These typically consist of quasi-crystalline or amorphous tessellations of the surface by half-skyrmions, which are stable at lower and larger shell size respectively. For…
We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature and pore width is studied. Two phenomena are observed: (i) an isotropic-cholesteric transition which exhibits an oscillatory structure with respect to pore width, and (ii) an infinite set of winding transitions caused by commensuration effects between cholesteric pitch and pore width. The latter transitions have been predicted and analysed by other authors for choleste…
We propose a hybrid lattice Boltzmann algorithm to simulate the hydrodynamics of colloidal particles inside a liquid crystalline host. To validate our algorithm, we study the static and the microrheology of a colloid in a nematic, with tangential anchoring of the director field at the particle surface, and we confirm theories and experiments showing that the drag force in a nematic is markedly anisotropic. We then apply our method to consider the case of a colloid inside a cholesteric, and with normal anchoring at the surface. We show that by tuning the ratio between particle size and choleste…
We study theoretically the formation of long-wavelength instability patterns observed at spreading of nematic droplets on liquid substrates. The role of surface-like elastic terms such as saddle-splay and anchoring in nematic films of submicron thickness is (re)examined by extending our previous work [Manyuhina et al EPL, 92, 16005 (2010)] to hybrid aligned nematics. We identify the upper threshold for the formation of stripes and compare our results with experimental observations. We find that the wavelength and the amplitude of the in-plane director undulations can be related to the small bu…
We study cholesteric order in liquid crystal shells with planar degenerate anchoring. We observe that the bipolar and radial configurations intensively reported for bulk droplets have a higher degree of complexity when the liquid crystal is confined to a spherical shell. The bipolar configuration is replaced by a structure where the boojums are linked to a stack of disclination rings that spans the shell, while the radial configuration exhibits a double helix structure where two disclinations wind around each other. Our results confirm recent numerical simulations and highlight the complexity …
The description of point defects in chiral liquid crystals via topological methods requires the introduction of singular contact structures, a generalisation of regular contact structures where the plane field may have singularities at isolated points. We characterise the class of singularities that may arise in such structures, as well as the subclass of singularities that can occur in a Beltrami field. We discuss questions of global existence, and prove that all singular contact structures with nonremovable singularities are overtwisted. To connect the theory to experiment we also discuss no…
We numerically study the dynamics of quasi-two dimensional cholesteric liquid crystal droplets in the presence of a time-dependent electric field, rotating at constant angular velocity. A surfactant sitting at droplet interface is also introduced to prevent droplet coalescence. The dynamics is modeled following a hybrid numerical approach, where a standard lattice Boltzmann technique solves the Navier-Stokes equation and a finite difference scheme integrates the evolution equations of liquid crystal and surfactant. Our results show that, once the field is turned on, the liquid crystal rotates …
A systematic computational and scaling analysis of defect textures in polygonal arrangement of cylindrical particles embedded in a cholesteric (Ch) liquid crystal matrix is performed using the Landau de Gennes model for chiral self assembly, with strong anchoring at the particles' surface. The defect textures and LC phases observed are investigated as a function of chirality, elastic anisotropy, particle polygonal arrangement and particle size. The presence of a polygonal network made of N circular inclusions results in defect textures of a net charge of -(N-2)/2 per unit polygonal cell. As th…
Chirality is a recurrent theme in the study of biological systems, in which active processes are driven by the internal conversion of chemical energy into work. Bacterial flagella, acto-myosin filaments and microtubule bundles are active systems which are also intrinsically chiral. Despite some exploratory attempt to capture the relations between chirality and motility, no intrinsically chiral system has ever been analyzed so far. To address this gap in knowledge, here we study the effects of internal active forces and torques on a three-dimensional droplet of cholesteric liquid crystal (CLC) …
Within the framework of Oseen-Frank theory, we analyse the static configurations for chiral liquid crystals. In particular, we find numerical solutions for localised axisymmetric states in confined chiral liquid crystals with weak homeotropic anchoring at the boundaries. These solutions describe the distortions of two-dimensional skyrmions, known as either \textit{spherulites} or \textit{cholesteric bubbles}, which have been observed experimentally in these systems. Relations with nonlinear integrable equations have been outlined and are used to study asymptotic behaviors of the solutions. By …
Cholesteric Liquid Crystals (CLCs), subject to externally applied magnetic fields and confined between two parallel planar surfaces with strong homeotropic anchoring conditions, are found to undergo transitions to different types of helicoidal configurations with disclinations. Analytical and numerical studies are performed in order to characterise their properties. In particular, we produce a phase diagram for the transitions from the nematic state to the helicoidal phases in terms of the molecular chirality and the strength of the applied magnetic field.
Within the framework of continuum theory, we draw a parallel between ferromagnetic materials and nematic liquid crystals confined on curved surfaces, which are both characterized by local interaction and anchoring potentials. We show that the extrinsic curvature of the shell combined with the out-of-plane component of the director field gives rise to chirality effects. This interplay produces an effective energy term reminiscent of the chiral term in cholesteric liquid crystals, with the curvature tensor acting as a sort of anisotropic helicity. We discuss also how the different nature of the …
We give the global homotopy classification of nematic textures for a general domain with weak anchoring boundary conditions and arbitrary defect set in terms of twisted cohomology, and give an explicit computation for the case of knotted and linked defects in $\mathbb{R}^3$, showing that the distinct homotopy classes have a 1-1 correspondence with the first homology group of the branched double cover, branched over the disclination loops. We show further that the subset of those classes corresponding to elements of order 2 in this group have representatives that are planar and characterise the…
