Confined Liquid Crystal Research Articles

Curvature-directed anchoring and defect structure of colloidal smectic liquid crystals in confinement

Abstract Rod-like objects at high packing fractions can exhibit liquid crystalline ordering. By controlling how the rods align near a boundary, i.e. the anchoring, the defects of a liquid crystal can be selected and tuned. For smectic phases, the rods break rotational and translational symmetry by forming lamellae. Smectic defects thereby include both discontinuities in the rod orientational order (disclinations), as well as in the positional order (dislocations). In this work, we use experiments and simulations to uncover the geometrical conditions necessary for a boundary to set the anchoring of a confined, particle-resolved, smectic liquid crystal. We confine a colloidal smectic within elliptical wells of varying size and shape for a smooth variation of the boundary curvature. We find that the anchoring depends upon the local boundary curvature, with an anchoring transition observed at a critical radius of curvature approximately twice the rod length. Surprisingly, the critical radius of curvature for an anchoring transition holds across a wide range of rod lengths and packing fractions. The anchoring controls the defect structure. By analyzing topological charges and networks composed of maximum density (rod centers) and minimum density (rod ends), we quantify disclinations and dislocations formed with varying confinement geometry. Circular confinements, characterized by planar anchoring, promote disclinations, whereas elliptical confinements, featuring antipodal regions of homeotropic anchoring, promote long-range smectic order and dislocations. Our findings demonstrate how geometrical constraints can control the anchoring and defect structures of liquid crystals—a principle that is applicable from molecular to colloidal length scales.

Defect-influenced particle advection in highly confined liquid crystal flows.

We study the morphology of the Saturn ring defect and director structure around a colloidal particle with normal anchoring conditions and within the flow of the nematic host phase through a rectangular duct of comparable size to the particle. The changes in the defect structures and director profile influence the advection behaviour of the particle, which we compare to that in a simple Newtonian host phase. These effects lead to a non-monotonous dependence of the differential velocity of particle and fluid, also known as retardation ratio, on the Ericksen number.

Monte Carlo simulations of chiral and achiral nematic droplets: thermal quenches and role of the elastic constants

ABSTRACTWe used Monte Carlo simulations with an elastically anisotropic pairwise potential to simulate the equilibrium structure of chiral and achiral nematic liquid crystals in spherical confinement under perpendicular and tangential strong anchoring. The stable structures are obtained by a quenching process, where the temperature is a parameter of the system. We calculate and map the distribution of elastic energy corresponding to splay, twist, and bend. Furthermore, we study the effect of changing the ratio of the elastic constants for achiral and low chirality droplets and found a diverse scenario of possible structures. The method described here allows the introduction of temperature and elastic anisotropy naturally within its framework. It is simpler to implement and faster to execute than the Landau-de Gennes (LdG) method used for simulating liquid crystal droplets.

Nematic Liquid Crystals in a Rectangular Confinement: Solution Landscape, and Bifurcation

We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau–de Gennes framework in terms of two geometry-dependent variables: half short edge length and aspect ratio . First, we analytically prove that, for any with a small enough or for a large enough with a fixed domain size, there is a unique stable solution that has two line defects on the opposite short edges. Second, we numerically construct solution landscapes by varying and , and report a novel X state, which emerges from saddle-node bifurcation and serves as the parent state in such a solution landscape. Various new classes are then found among these solution landscapes, including the X class, the S class, and the L class. By tracking the Morse indices of individual solutions, we present bifurcation diagrams for nematic equilibria, thus illustrating the emergence mechanism of critical points and several effects of geometrical anisotropy on confined defect patterns.

Defect patterns of two-dimensional nematic liquid crystals in confinement.

A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface-confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form a deformed texture that may display defect points or defect lines, for which winding numbers can be clearly defined. Here, a particular attention is paid to the case when the liquid crystal molecules prefer to form a boundary nematic texture in parallel to the wall surface (i.e., following the homogeneous boundary condition). A general theory, based on geometric argument, is presented for the relationship between the sum of all winding numbers in the system (the total winding number) and the type of confinement angles and curved segments. The conclusion is validated by comparing the theoretical defect rule with existing nematic textures observed experimentally and theoretically in recent years.

Topology of Orientational Defects in Confined Smectic Liquid Crystals.

We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in pointlike units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive MonteCarlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showing how the observed defect networks can be universally reconstructed from simple building blocks. We further find that the curvature of the confining wall determines the anchoring behavior of grain boundaries, such that the number of nodes in the emerging networks and the location of their end points can be tuned by changing the number and smoothness of corners, respectively.

Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement

Our study of cholesteric lyotropic chromonic liquid crystals in cylindrical confinement reveals the topological aspects of cholesteric liquid crystals. The double-twist configurations we observe exhibit discontinuous layering transitions, domain formation, metastability, and chiral point defects as the concentration of chiral dopant is varied. We demonstrate that these distinct layer states can be distinguished by chiral topological invariants. We show that changes in the layer structure give rise to a chiral soliton similar to a toron, comprising a metastable pair of chiral point defects. Through the applicability of the invariants we describe to general systems, our work has broad relevance to the study of chiral materials.

Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement

Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic colloidal layers dictated by the interplay between entropy and an imposed external topology. Considering an annular confinement as a basic example, a plethora of competing states is found with nontrivial defect structures ranging from laminar states to multiple smectic domains and arrays of edge dislocations, which we refer to as Shubnikov states in formal analogy to the characteristic of type-II superconductors. Our particle-resolved results, gained by a combination of real-space microscopy of thermal colloidal rods and fundamental-measure-based density functional theory of hard anisotropic bodies, agree on a quantitative level.

Programming emergent symmetries with saddle-splay elasticity

The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid’s internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddle-splay arrangements, characterised by the elastic constant {K}_{24}. In most realisations, dominant surface anchoring treatments suppress such deformations, rendering {K}_{24} immeasurable. Here we identify regimes where more subtle, patterned surfaces enable saddle-splay effects to be both observed and exploited. Utilising theory and continuum calculations, we determine experimental regimes where generic, achiral liquid crystals exhibit spontaneously broken surface symmetries. These provide a new route to measuring {K}_{24}. We further demonstrate a multistable device in which weak, but directional, fields switch between saddle-splay-motivated, spontaneously-polar surface states. Generalising beyond simple confinement, our highly scalable approach offers exciting opportunities for low-field, fast-switching optoelectronic devices which go beyond current technologies.

Swimming with small and large amplitude waves in a confined liquid crystal

Boundaries can have a significant impact on the physics of microorganism locomotion. Here we examine the effects of confinement by a rigid boundary or symmetric channel on undulatory locomotion in an anisotropic fluid, treated as a nematic liquid crystal. The competition between hydrodynamics, fluid elasticity, and anchoring conditions results in a complex locomotion problem with unique transport properties. We examine this problem analytically using a well-known mathematical model, an infinite swimming sheet with small wave amplitude, and numerically for large amplitude waves using a modification of the immersed boundary method. For a prescribed stroke and strong planar anchoring in the narrow channel, we demonstrate that the swimming speed approaches its Newtonian value, though the power required to maintain the swimmer’s speed depends on the properties of the liquid crystal. We also show that an unusual prograde swimming (in the direction of transverse wave propagation) theorized to exist at small wave amplitude persists at large amplitude, and that the presence of a sufficiently close boundary returns the swimming behavior to the more standard retrograde motion (opposite the direction of the traveling wave).

Non-equilibrium steady structures of confined liquid crystals driven by a dynamic boundary

Steady structures originating from dynamic self-assembly have begun to show their advantages in new generation materials, and pose challenges to equilibrium self-assembly. In view of the important role of confinement in self-assembly, here, we propose a new type of confinement leading to dynamic steady structures, which opens a new window for the conventional confinement. In our model, we consider the self-assembly of ellipsoids in 2D circular confinement via the boundary performing periodically stretching and contracting oscillation. Langevin dynamics simulations reveal the achievement of non-equilibrium steady structures under appropriate boundary motions, which are novel smectic structures with stable topological defects. Different from the confinement with a static boundary, ellipsoids close to the boundary have variable orientations depending on the boundary motion. Order-order structural transitions, accompanied by the symmetry change and varied defect number, occur with the change of oscillating amplitude and/or frequency of the boundary. Slow and fast dynamics are distinguished according to whether structural rearrangements and energetic adjustment happen or not. The collective motion of confined ellipsoids, aroused by the work performed on the system, is the key factor determining both the structure and dynamics of the self-assembly. Our results not only achieve novel textures of circular confined liquid crystals, but also inspire us to reconsider the self-assembly within the living organisms.

Colloids in confined liquid crystals: a plot twist in the lock-and-key mechanism.

By confining soft materials within tailored boundaries it is possible to design energy landscapes to address and control colloidal dynamics. This provides unique opportunities to create reconfigurable, hierarchically organized structures, a leading challenge in materials science. Example soft matter systems include liquid crystals. For instance, when nematic liquid crystals (NLCs) are confined in a vessel with undulated boundaries, bend and splay distortions can be used to position particles. Here we confine this system in a twist cell. We also study cholesteric liquid crystals, which have an "intrinsic" twist distortion which adds to the ones imposed by the solid boundaries. The cholesteric pitch competes with the other length scales in the system (colloid radius, vessel thickness, wavelength of boundary undulations), enriching the possible configurations. Depending on the pitch-to-radius and pitch-to-thickness ratios the interaction can be attractive or repulsive. By tuning the pitch (i.e. changing the concentration of the chiral dopant), it is possible to selectively promote or inhibit particle trapping at the docking sites.

Optimization of a Liquid Crystal‐based Sensory Platform for Monitoring Enzymatic Glucose Oxidation

Managing glucose levels in human blood is extremely important for the treatment of diabetes. Here, an innovative sensory strategy has been developed to monitor the enzymatic activities of glucose and glucose oxidase by using confined liquid crystal (LC) birefringent droplet patterns. Acidic products released during the glucose oxidation process lead to a slight decrease in the pH of aqueous systems that can be monitored by pH‐sensitive LC materials. Of the existing pH‐sensitive LC materials, dodecanoic acid‐doped 4‐cyano‐4′‐pentylbiphenyl is inexpensive and easily adjusted to satisfy the 7.4 ± 0.05 pH requirement of human blood. Moreover, the orientational alignment of capillary‐confined pH‐responsive LCs can be disrupted at the aqueous/LC interface following a slight decrease in the critical pH of aqueous reaction systems, which results in an optical signal that can be observed with the naked eye by using polarizing optical microscopy. Based on the stable LC droplet patterns generated by the cylindrical confinement system, the functionalized LCs can selectively detect glucose at concentrations as low as 0.1 pM. This study further advances the previously reported LC‐based glucose monitoring systems by reducing production costs and instituting a smarter LC sensory design. This improved system shows potential for the use in clinical bioassay applications.

Recent theoretical development in confined liquid-crystal polymers

Liquid-crystal polymers in confined system is a fundamental issue in soft matter. Theoretical method plays animportant role in studying these systems. The intention of this work is to give a thorough reviewof the theoretical methodologies used in tackling confined liquid crystals. At first, some basic concept of liquid crystal, such as a vital order parameter for orientation, phases of liquid crystal, the uniaxial and biaxial of liquid crystal, are presented. After that, a brief review of the development of liquid-crystal theories, which include the Onsager model, the Maier-Saupe model, the McMillanmodel, the Landau-de Gennes expansion, the Frank elastic model and the self-consistent field model for liquid-crystal polymers, are given. All these theories havetheir own advantages and disadvantages. For example, the phenomenological Frank elastic model is the most widely used model due to its simplicity. In contrast, parameters in the self-consistent field model are physically meaningful, however, it is rather complicated. During recent decades, with these theories and suitable boundary treatment, plenty confined liquid crystal systems are investigated. In this review, we focus on three kinds of confined systems: 1) the surface wetting behavior in slits; 2) the two-dimensional liquid crystals confined by a boundary line and 3) defects in the orientational field of rigid rods on spherical surface. Results arrived from different At the end of this review, we give a list of frontier issues and an outlook for thecoming ten years.

Orientation of liquid crystal molecules in polydimethylsiloxane micro-channels

ABSTRACTThe orientation of liquid crystal (LC) molecules confined in polydimethylsiloxane micro-channels, which are produced using mould-replica technique, with a rectangular cross section, is studied. The rod-like molecules of the LC adopt the vertical anchoring at every surface of the channels. The macroscopic alignment of the confined LC can be changed by altering the aspect ratio of the channels. The change in the macroscopic alignment of the LC is attributed directly to the restructuring of the proportion of the number of molecules anchored to the respective surfaces due to the changes in specific area of the bounding surface of the channels. Solutions for the elastic energy function obtained using conformal mapping method were used to predict director profile of the LC in the confinement.

Molecular ordering of the discotic liquid crystal HAT6 confined in mesoporous solids

An optical polarimetry study of the orientational order of a discotic liquid crystal (DLC), 2,3,6,7,10,11-hexakis(hexyloxy)triphenylene (HAT6), confined into parallel-aligned cylindrical nanochannels of mesoporous alumina, silica, and silicon membranes as a function of temperature and channel radius (3.4–21.0nm) is presented. In contrast to the bulk state, the birefringence resulting from the confined discotic liquid crystal, exhibits a continuous temperature evolution and is positive indicating a dominating face-on (homeotropic) type molecular ordering with respect to the channel walls. Pronounced hysteresis effects observed in the experiment are traced to different nucleation sites of the low-temperature phase upon cooling and the high-temperature phase upon heating. Deviations from the Gibbs–Thomson scaling of the phase transition temperature for channel diameters below 10nm are traced to splay distortions of the confined liquid crystal.

Neural-network approach to modeling liquid crystals in complex confinement.

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

Colloidal liquid crystals in rectangular confinement: theory and experiment.

We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.

Phase behaviour of lyotropic liquid crystals in external fields and confinement

This mini-review discusses the influence of external fields on the phase behaviour of lyotropic colloidal liquid crystals. The liquid crystal phases reviewed, formed in suspensions of highly anisotropic particles ranging from rod- to board- to plate-like particles, include nematic, smectic and columnar phases. The external fields considered are the earth gravitational field and electric and magnetic fields. For electric and magnetic fields single particle alignment, collective reorientation behaviour of ordered phases and field-induced liquid crystal phase transitions are discussed. Additionally, liquid crystal phase behaviour in various confining geometries, e.g. slit-pore, circular and spherical confinement will be reviewed.

Modelling of the phase transition of nanoscale confined liquid crystal

By dividing the bulk melting entropy, a simple thermodynamic model without any adjustable parameter for the size-dependent melting transition temperature has been extended to interpret the melting and freezing transitions of liquid crystals (LCs) confined in nanopores. The results show that as the size of the nanopore decreases, the melting, clearing and freezing transition temperatures of LCs drop. The transition temperatures directly depend on the density of hydrogen bond at the interface between inner pore wall and LC molecules. The model predictions agree well with the corresponding experimental results of LCs p-azoxyanisole and 4-pentyl-4′-cyanobiphenyl confined in nanopores.