Transforming patterned defects into dynamic poly-regional topographies in liquid crystal oligomers.

We create high-aspect-ratio dynamic poly-regional surface topographies in a coating of a main-chain liquid crystal oligomer network (LCON). The topographies form at the topological defects in the director pattern organized in an array which are controlled by photopatterning of the alignment layer. The defect regions are activated by heat and/or light irradiation to form reversible topographic structures. Intrinsically, the LCON is rubbery and sensitive to temperature changes, resulting in shape transformations. We further advanced such system to make it light-responsive by incorporating azobenzene moieties. Actuation reduces the molecular order of the LCON coating that remains firmly adhered to the substrate which gives directional shear stresses around the topological defects. The stresses relax by deforming the surfaces by forming elevations or indents, depending on the type of defects. The formed topographies exhibit various features, including two types of protrusions, ridges and valleys. These poly-regional structures exhibit a large modulation amplitude of close to 60%, which is 6 times larger than the ones formed in liquid crystal networks (LCNs). After cooling or by blue light irradiation, the topographies are erased to the initial flat surface. A finite element method (FEM) model is adopted to simulate structures of surface topographies. These dynamic surface topographies with multilevel textures and large amplitude expand the application range, from haptics, controlled cell growth, to intelligent surfaces with adjustable adhesion and tribology.

Geometry and mechanics of disclination lines in 3D nematic liquid crystals.

In 3D nematic liquid crystals, disclination lines have a range of geometric structures. Locally, they may resemble +1/2 or -1/2 defects in 2D nematic phases, or they may have 3D twist. Here, we analyze the structure in terms of the director deformation modes around the disclination, as well as the nematic order tensor inside the disclination core. Based on this analysis, we construct a vector to represent the orientation of the disclination, as well as tensors to represent higher-order structure. We apply this method to simulations of a 3D disclination arch, and determine how the structure changes along the contour length. We then use this geometric analysis to investigate three types of forces acting on a disclination: Peach-Koehler forces due to external stress, interaction forces between disclination lines, and active forces. These results apply to the motion of disclination lines in both conventional and active liquid crystals.

Thermophoresis of colloids in nematic liquid crystal.

Thermophoresis, or the directional motion of colloidal particles in liquids driven by a temperature gradient, is of both fundamental interest and practical use. In this work we explore the thermophoresis of colloids suspended in nematic liquid crystals (LCs). We observe that the motion of these colloids is fundamentally different from that in isotropic systems as a result of elastic distortions in the director fields caused by the colloidal inclusions. In the case of a sufficiently large local temperature and gradient, the elastic energy drives negative thermophoresis of immersed particles, which has a strongly nonlinear dependence on temperature. We develop a theory that incorporates elastic energy minimization into the traditional thermophoretic formulation and demonstrated a good agreement with experimental observations. We also examine the temperature dependence of the effective viscosity of the colloids and highlight the large magnitude of the Soret coefficient (|ST| > 5000), which results from the inherent enhancement in thermophoresis due to elastophoretic considerations and suppression of Brownian diffusion in LC media.

Electric field-induced crossover from 3D to 2D topological defects in a nematic liquid crystal: experimental verification.

A substrate was patterned with two pairs of half-integer strength topological defects, (+1/2, +1/2) and (+1/2, -1/2). In a sufficiently thick cell, a disclination line runs in an arch above the substrate connecting the two half integer defects within each pair. The director around the disclination line for the like-sign pair must rotate in 3D, whereas for the opposite-sign defect pair the director lies in the xy-plane parallel to the substrate. For a negative dielectric anisotropy nematic, an electric field applied normal to the substrate drives the director into the xy-plane, forcing the arch of the disclination line of the like-sign pair to become extended along the z-axis. For sufficiently large field the arch splits, resulting in two nearly parallel disclination lines traversing the cell from one substrate to the other. The opposite-sign defect pair is largely unaffected by the electric field as the director already lies in the xy-plane. Experimental results are presented, which are consistent with numerical simulations.

Nanoparticle-based hollow microstructures formed by two-stage nematic nucleation and phase separation.

Rapid bulk assembly of nanoparticles into microstructures is challenging, but highly desirable for applications in controlled release, catalysis, and sensing. We report a method to form hollow microstructures via a two-stage nematic nucleation process, generating size-tunable closed-cell foams, spherical shells, and tubular networks composed of closely packed nanoparticles. Mesogen-modified nanoparticles are dispersed in liquid crystal above the nematic-isotropic transition temperature (TNI). On cooling through TNI, nanoparticles first segregate into shrinking isotropic domains where they locally depress the transition temperature. On further cooling, nematic domains nucleate inside the nanoparticle-rich isotropic domains, driving formation of hollow nanoparticle assemblies. Structural differentiation is controlled by nanoparticle density and cooling rate. Cahn-Hilliard simulations of phase separation in liquid crystal demonstrate qualitatively that partitioning of nanoparticles into isolated domains is strongly affected by cooling rate, supporting experimental observations that cooling rate controls aggregate size. Microscopy suggests the number and size of internal voids is controlled by second-stage nucleation.

Making waves in a photoactive polymer film.

Oscillating materials that adapt their shapes in response to external stimuli are of interest for emerging applications in medicine and robotics. For example, liquid-crystal networks can be programmed to undergo stimulus-induced deformations in various geometries, including in response to light. Azobenzene molecules are often incorporated into liquid-crystal polymer films to make them photoresponsive; however, in most cases only the bending responses of these films have been studied, and relaxation after photo-isomerization is rather slow. Modifying the core or adding substituents to the azobenzene moiety can lead to marked changes in photophysical and photochemical properties, providing an opportunity to circumvent the use of a complex set-up that involves multiple light sources, lenses or mirrors. Here, by incorporating azobenzene derivatives with fast cis-to-trans thermal relaxation into liquid-crystal networks, we generate photoactive polymer films that exhibit continuous, directional, macroscopic mechanical waves under constant light illumination, with a feedback loop that is driven by self-shadowing. We explain the mechanism of wave generation using a theoretical model and numerical simulations, which show good qualitative agreement with our experiments. We also demonstrate the potential application of our photoactive films in light-driven locomotion and self-cleaning surfaces, and anticipate further applications in fields such as photomechanical energy harvesting and miniaturized transport.

Gradient-driven diffusion and pattern formation in crowded mixtures.

Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion affects microstructure, which in turn affects diffusivity; a key question is how this complex coupling controls both transport and pattern formation. To examine these mechanisms, we study a two-dimensional multicomponent lattice gas model, where "tracer" molecules diffuse between a source and a sink separated by a solution of sticky "crowder" molecules that cluster to form dynamically evolving obstacles. In the high-temperature limit, crowders and tracers are miscible, and transport may be predicted analytically. At intermediate temperatures, crowders phase separate into clusters that drift toward the tracer sink. As a result, steady-state tracer diffusivity depends nonmonotonically on both temperature and crowder density, and we observe a variety of complex microstructures. In the low-temperature limit, crowders rapidly aggregate to form obstacles that are kinetically arrested; if crowder density is near the percolation threshold, resulting tracer diffusivity shows scaling behavior with the same scaling exponent as the random resistor network model. Though highly idealized, this simple model reveals fundamental mechanisms governing coupled gradient-driven diffusion, phase separation, and microstructural evolution in crowded mixtures.

Modeling out-of-plane actuation in thin-film nematic polymer networks: From chiral ribbons to auto-origami boxes via twist and topology.

Various experimental and theoretical studies demonstrate that complex stimulus-responsive out-of-plane distortions such as twist of different chirality, emergence of cones, simple and anticlastic bending can be engineered and pre-programmed in a liquid crystalline rubbery material given a well-controlled director microstructure. Via 3-d finite element simulation studies, we demonstrate director-encoded chiral shape actuation in thin-film nematic polymer networks under external stimulus. Furthermore, we design two complex director fields with twisted nematic domains and nematic disclinations that encode a pattern of folds for an auto-origami box. This actuator will be flat at a reference nematic state and form four well-controlled bend distortions as orientational order changes. Device fabrication is applicable via current experimental techniques. These results are in qualitative agreement with theoretical predictions, provide insight into experimental observations, and demonstrate the value of finite element methods at the continuum level for designing and engineering liquid crystal polymeric devices.

Correction: Cholesteric liquid crystals in rectangular microchannels: skyrmions and stripes.

Correction for 'Cholesteric liquid crystals in rectangular microchannels: skyrmions and stripes' by Yubing Guo et al., Soft Matter, 2016, DOI: 10.1039/c6sm01190j.

Cholesteric liquid crystals in rectangular microchannels: skyrmions and stripes.

In this paper, we present experimental and numerical studies on the microstructures of a cholesteric liquid crystal (CLC) confined in rectangular micron-channels. By using a sequence of microfabrication techniques we fabricated the micro-sized channels with accurately controlled size, aspect ratio and homeotropic surface anchoring. Through optical microscopic studies we established a phase diagram for the liquid crystal defect textures as a function of the channel depth and width. For the channel width larger than ∼2 times the cholesteric pitch p, the LC molecules are oriented primarily vertical to the channel when the channel depth is below 0.75p, form bubble domain defects when the channel depth is around 0.75p, and form stripe textures when the cell depth is above the cholesteric pitch p. In addition, the bubble domain size and the stripe texture periodicity are found to grow with the increase of the channel width. For the channel width smaller than ∼2p and the channel depth between 0.6p to 1.1p, no textures can be observed in the channels. Numerical simulations based on a director tensor relaxation approach yield detailed molecular director fields, and show that the bubble domain defects are baby-skyrmions and that the stripes are the first type of cholesteric fingerprints. A comparison with previous experiments and numerical simulations indicates that the size of the microchannels also influences what type of soliton-like topological textures form in the CLCs confined in the channels.

Electrically Induced Twist in Smectic Liquid-Crystalline Elastomers.

As an approach for electrically controllable actuators, we prepare elastomers of chiral smectic-A liquid crystals, which have an electroclinic effect, i.e., molecular tilt induced by an applied electric field. Surprisingly, our experiments find that an electric field causes a rapid and reversible twisting of the film out of the plane, with a helical sense that depends on the sign of the field. To explain this twist, we develop a continuum elastic theory based on an asymmetry between the front and back of the film. We further present finite-element simulations, which show the dynamic shape change.

Spontaneous chiral symmetry breaking in collective active motion.

Chiral symmetry breaking is ubiquitous in biological systems, from DNA to bacterial suspensions. A key unresolved problem is how chiral structures may spontaneously emerge from achiral interactions. We study a simple model of active swimmers in three dimensions that effectively incorporates hydrodynamic interactions. We perform large-scale molecular dynamics simulations (up to 10(6) particles) and find long-lived metastable collective states that exhibit chiral organization although the interactions are achiral. We elucidate under which conditions these chiral states will emerge and grow to large scales. To explore the complex phase space available to the system, we perform nonequilibrium quenches on a one-dimensional Lebwohl-Lasher model with periodic boundary conditions to study the likelihood of formation of chiral structures.

Shape and chirality transitions in off-axis twist nematic elastomer ribbons.

Using both experiments and finite element simulations, we explore the shape evolution of off-axis twist nematic elastomer ribbons as a function of temperature. The elastomers are prepared by cross-linking the mesogens with planar anchoring of the director at top and bottom surfaces with a 90° left-handed twist. Shape evolution depends sensitively on the off-axis director orientation at the sample midplane. Both experiments and theoretical studies show that when the director at midplane is parallel to either the ribbon's long or short axes, ribbons form either helicoids or spirals depending on aspect ratio and temperature. Simulation studies show that if the director at midplane is off-axis, ribbons never form helicoids, instead evolving to distorted spiral shapes. Experimental studies for two samples with off-axis geometry show agreement with this prediction. Samples in all these geometries show a remarkable transition from right- to left-handed chiral shapes on change of temperature. Simulations predict off-axis samples also change their macroscopic chirality at fixed temperature, depending on the angular offset. These results provide insight into the mechanisms driving shape evolution and macroscopic chirality, enabling engineering design of these materials for future applications.

Morphology transition in lipid vesicles due to in-plane order and topological defects.

Complex morphologies in lipid membranes typically arise due to chemical heterogeneity, but in the tilted gel phase, complex shapes can form spontaneously even in a membrane containing only a single lipid component. We explore this phenomenon via experiments and coarse-grained simulations on giant unilamellar vesicles of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine. When cooled from the untilted L(α) liquid-crystalline phase into the tilted gel phase, vesicles deform from smooth spheres to disordered, highly crumpled shapes. We propose that this shape evolution is driven by nucleation of complex membrane microstructure with topological defects in the tilt orientation that induce nonuniform membrane curvature. Coarse-grained simulations demonstrate this mechanism and show that kinetic competition between curvature change and defect motion can trap vesicles in deeply metastable, defect-rich structures.

Shape selection of twist-nematic-elastomer ribbons.

How microscopic chirality is reflected in macroscopic scale to form various chiral shapes, such as straight helicoids and spiral ribbons, and how the degree of macroscopic chirality can be controlled are a focus of studies on the shape formation of many biomaterials and supramolecular systems. This article investigates both experimentally and theoretically how the chiral arrangement of liquid crystal mesogens in twist-nematic-elastomer films induces the formation of helicoids and spiral ribbons because of the coupling between the liquid crystalline order and the elasticity. It is also shown that the pitch of the formed ribbons can be tuned by temperature variation. The results of this study will facilitate the understanding of physics for the shape formation of chiral materials and the designing of new structures on basis of microscopic chirality.

Modeling elastic instabilities in nematic elastomers.

Liquid crystal elastomers are cross-linked polymer networks covalently bonded with liquid crystal mesogens. In the nematic phase, due to strong coupling between mechanical strain and orientational order, these materials display strain-induced instabilities associated with formation and evolution of orientational domains. Using a three-dimensional finite element elastodynamics simulation, we investigate one such instability, the onset of stripe formation in a monodomain film stretched along an axis perpendicular to the nematic director. In our simulation, we observe the formation of striped domains with alternating director rotation. This model allows us to explore the fundamental physics governing dynamic mechanical response of nematic elastomers and also provides a potentially useful computational tool for engineering device applications.

Shape selection in chiral self-assembly.

Many biological and synthetic materials self-assemble into helical or twisted aggregates. The shape is determined by a complex interplay between elastic forces and the orientation and chirality of the constituent molecules. We study this interplay through Monte Carlo simulations, with an accelerated algorithm motivated by the growth of an aggregate out of solution. The simulations show that the curvature changes smoothly from cylindrical to saddlelike as the elastic moduli are varied. Remarkably, aggregates of either handedness form from molecules of a single handedness, depending on the molecular orientation.

Simulations of helix unwinding in ferroelectric liquid crystals.

In bulk ferroelectric liquid crystals, the molecular director twists in a helix. In narrow cells, this helix can be unwound by an applied electric field or by boundary effects. To describe helix unwinding as a function of both electric field and boundary effects, we develop a mesoscale simulation model based on a continuum free energy discretized on a two-dimensional lattice. In these simulations, we determine both the director profile across the cell and the net electrostatic polarization. By varying the cell size, we show how boundary effects shift the critical field for helix unwinding and lower the saturation polarization. Our results are consistent with experimental data.