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Abstract Linear defect‐disclinations are of fundamental interest in understanding complex structures explored by soft matter physics, elementary particles physics, cosmology, and various branches of mathematics. These defects are also of practical importance in materials applications, such as programmable origami, directed colloidal assembly, and command of active matter. Here an effective engineering approach is demonstrated to pattern molecular orientations at two flat confining surfaces that produce complex yet designable networks of singular disclinations of strength 1/2. Depending on the predesigned director patterns at the bounding plates, the produced disclinations are either surface‐anchored, connecting desired sites at the boundaries, or freely suspended in bulk, forming ordered arrays of polygons and wavy lines. The capability is shown to control the radius of curvature, size, and shape of disclinations by varying uniform alignment orientation on one of these confining plates. The capabilities to precisely design and create highly complex 3D disclination networks promise intriguing applications in stimuli‐responsive reconfigurable materials, directed self‐assembly of molecules, micro‐ and nanoparticles, and transport and sorting in microfluidic applications. 

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. 

In a crystalline solid under mechanical stress, a Frank-Read source is a pinned dislocation segment that repeatedly bows and detaches, generating concentric dislocation loops. We demonstrate that, in nematic liquid crystals, an analogous Frank-Read mechanism can generate concentric disclination loops. Using experiment, simulation, and theory, we study a disclination segment pinned between surface defects on one substrate in a nematic cell. Under applied twist of the nematic director, the pinned segment bows and emits a new disclination loop which expands, leaving the original segment intact; loop emission repeats for each additional 180° of applied twist. We present experimental micrographs showing loop expansion and snap-off, numerical simulations of loop emission under both quasistatic and dynamic loading, and theoretical analysis considering both free energy minimization and the balance of competing forces. We find that the critical stress for disclination loop emission scales as the inverse of segment length and changes as a function of strain rate and temperature, in close analogy to the Frank-Read source mechanism in crystals. Lastly, we discuss how Frank-Read sources could be used to modify microstructural evolution in both passive and active nematics. 

Exotic structures with interesting physical and chemical properties can be achieved by self-organizing engineered building blocks. The central aim for self-assembly is to precisely control the position and orientation of individual building blocks. In this work, we use topological defects (disclinations) in nematic liquid crystals as templates to direct the self-assembly of colloidal particles into designable 3D structures. By photopatterning preprogrammed molecular orientations at two confining surfaces, we created pre-designable disclination networks and characterized their interactions with spherical colloidal particles. We find that colloidal particles are attracted to different disclinations depending on the orientation of the point defect (elastic dipole) around the colloids. We demonstrate that the positions, network structures, and orientation of the elastic dipoles of the colloidal chains can be pre-designed and reconfigured with remote illumination of polarized light. 

Disclinations in nematic liquid crystals are of great interest both theoretically and practically. The ability to create and reconfigure disclinations connecting predetermined points on substrates could enable novel applications such as directed self-assembly of micro/nanoparticles and molecules. In this study, we present a novel approach to design and create disclination interconnects that connect predetermined positions on substrates. We demonstrate that these interconnects can be switched between different states by re-writing photoalignment materials with linearly polarized light, and can be switched between degenerate states using electric fields. The demonstrated strategy allows for creation of multi-scale designer disclination networks and promises potential applications in directed assembly of colloidal micro-/nano-particles, command of active matter, and liquid crystal microfluidics 

Abstract Cellulose-based systems are useful for many applications. However, the issue of self-organization under non-equilibrium conditions, which is ubiquitous in living matter, has scarcely been addressed in cellulose-based materials. Here, we show that quasi-2D preparations of a lyotropic cellulose-based cholesteric mesophase display travelling colourful patterns, which are generated by a chemical reaction-diffusion mechanism being simultaneous with the evaporation of solvents at the boundaries. These patterns involve spatial and temporal variation in the amplitude and sign of the helix´s pitch. We propose a simple model, based on a reaction-diffusion mechanism, which simulates the observed spatiotemporal colour behaviour. 

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. 

Liquid crystal elastomers (LCEs) hold a major promise as a versatile material platform for smart soft coatings since their orientational order can be predesigned to program a desired dynamic profile. In this work, we introduce temperature-responsive dynamic coatings based on LCEs with arrays of singular defects-disclinations that run parallel to the surface. The disclinations form in response to antagonistic patterns of the molecular orientation at the top and bottom surfaces, imposed by the plasmonic mask photoalignment. Upon heating, an initially flat LCE coating develops linear microchannels located above each disclination. The stimulus that causes a non-flat profile of LCE coatings upon heating is the activation force induced by the gradients of molecular orientation around disclinations. To describe the formation of microchannels and their thermal response, we adopt a Frank–Oseen model of disclinations in a patterned director field and propose a linear elasticity theory to connect the complex spatially varying molecular orientation to the displacements of the LCE. The thermo-responsive surface profiles predicted by the theory and by the finite element modeling are in good agreement with the experimental data; in particular, higher gradients of molecular orientation produce a stronger modulation of the coating profile. The elastic theory and the finite element simulations allow us to estimate the material parameter that characterizes the elastomer coating's response to the thermal activation. The disclination-containing LCEs show potential as soft dynamic coatings with a predesigned responsive surface profile. 

A substrate was patterned with two pairs of half-integer strength topological defects, (+½, +½) and (+½, −½). 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 already lies in the xy-plane. Experimental results are presented, which are consistent with numerical simulations.