Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers

Nonreciprocal chirality conversion in spatiotemporal evolutions of nematic colloidal entanglement

In soft matter systems, there is a wealth of topological phenomena, such as singular disclination lines and nonsingular defects of skyrmions and hopfions. In a liquid crystal (LC), the topological nature of disclination lines and colloids induces chiral colloidal entanglements. How the chirality of the entanglements is deterministically created and how the chirality conversion is actuated in the disclinations with Möbius strip topology have never been explored. Here, we create colloidal entanglements with designed chirality in the nematic disclination loops with Möbius topology. An irreversible process of chirality change is revealed if we move the colloidal entanglement along the loops. A nonreciprocal chirality conversion in the dynamical colloidal entanglements is demonstrated, which is induced by the interplay between topological profiles and the geometrical curvature of the disclination loop. Colloidal entanglements in opposite chirality are templated in arbitrary shapes of disclination lines. This work opens opportunities to design smart colloidal materials.

Light-driven dancing of nematic colloids in fractional skyrmions and bimerons

Materials with full and fractional skyrmions are important for fundamental studies and can be applied as information carriers for applications in spintronics or skyrmionics. However, creation, direct optical observation and manipulation of different skyrmion textures remain challenging. Besides, how the transformation of skyrmion textures directs the dynamics of colloids is not well understood. Here, we use experiments, simulations and theory to demonstrate that fractional skyrmion and bimeron strings can be created in a nematic liquid crystal (LC) through incompatible interfaced topological patterns. Moreover, distinct topological profiles are realized in the same skyrmion string loop. The light-actuated transformations of fractional skyrmion textures in both straight and loop geometry drive colloidal assemblies to exhibit exotic dynamic behaviors. Finally, fractional skyrmions with arbitrary shapes can be used as templates for a variety of exquisite colloidal assemblies. This work provides opportunities for designing new smart material to control self-assembly and transport of colloids.

Topology-driven collective dynamics of nematic colloidal entanglement

Entanglement in a soft condensed matter system is enabled in the form of entangled disclination lines by using colloidal particles in nematic liquid crystals. These topological excitations are manifested as colloidal entanglement at equilibrium. How to further utilize nonequilibrium disclination lines to manipulate colloidal entanglement remains a nontrivial and challenging task. In this work, we use experiments and simulations to demonstrate the reconfigurations of nematic colloidal entanglement in light-driven spatiotemporal evolutions of disclination lines. Colloidal entanglement can sense subtle changes in the topological structures of disclination lines and realize chirality conversion. This conversion is manifested as the "domino effect" of the collective rotation of colloids in the disclination lines. By programming the topological patterns and the geometry of the disclination lines, colloidal entanglement can be assembled and split. More remarkably, a double-helix entangled structure can be formed by controlling the changes in the morphology of the disclination lines. Thus, this work will provide opportunities to program colloidal composites for smart materials and micromachines.

Collective transport and reconfigurable assembly of nematic colloids by light-driven cooperative molecular reorientations

Nanomotors in nature have inspired scientists to design synthetic molecular motors to drive the motion of microscale objects by cooperative action. Light-driven molecular motors have been synthesized, but using their cooperative reorganization to control the collective transport of colloids and to realize the reconfiguration of colloidal assembly remains a challenge. In this work, topological vortices are imprinted in the monolayers of azobenzene molecules which further interface with nematic liquid crystals (LCs). The light-driven cooperative reorientations of the azobenzene molecules induce the collective motion of LC molecules and thus the spatiotemporal evolutions of the nematic disclination networks which are defined by the controlled patterns of vortices. Continuum simulations provide physical insight into the morphology change of the disclination networks. When microcolloids are dispersed in the LC medium, the colloidal assembly is not only transported and reconfigured by the collective change of the disclination lines but also controlled by the elastic energy landscape defined by the predesigned orientational patterns. The collective transport and reconfiguration of colloidal assemblies can also be programmed by manipulating the irradiated polarization. This work opens opportunities to design programmable colloidal machines and smart composite materials.

Biotropic liquid crystal phase transformations in cellulose-producing bacterial communities

Biological functionality is often enabled by a fascinating variety of physical phenomena that emerge from orientational order of building blocks, a defining property of nematic liquid crystals that is also pervasive in nature. Out-of-equilibrium, "living" analogs of these technological materials are found in biological embodiments ranging from myelin sheath of neurons to extracellular matrices of bacterial biofilms and cuticles of beetles. However, physical underpinnings behind manifestations of orientational order in biological systems often remain unexplored. For example, while nematiclike birefringent domains of biofilms are found in many bacterial systems, the physics behind their formation is rarely known. Here, using cellulose-synthesizing Acetobacter xylinum bacteria, we reveal how biological activity leads to orientational ordering in fluid and gel analogs of these soft matter systems, both in water and on solid agar, with a topological defect found between the domains. Furthermore, the nutrient feeding direction plays a role like that of rubbing of confining surfaces in conventional liquid crystals, turning polydomain organization within the biofilms into a birefringent monocrystal-like order of both the extracellular matrix and the rod-like bacteria within it. We probe evolution of scalar orientational order parameters of cellulose nanofibers and bacteria associated with fluid-gel and isotropic-nematic transformations, showing how highly ordered active nematic fluids and gels evolve with time during biological-activity-driven, disorder-order transformation. With fluid and soft-gel nematics observed in a certain range of biological activity, this mesophase-exhibiting system is dubbed "biotropic," analogously to thermotropic nematics that exhibit solely orientational order within a temperature range, promising technological and fundamental-science applications.

Active transformations of topological structures in light-driven nematic disclination networks

SignificanceTopological defects are marvels of nature. Understanding their structures is important for their applications in, for example, directed self-assembly, sensing, and photonic devices. There is recent interest in active motion and transformation of topological defects in active nematics. In these nonequilibrium systems, however, the motion and transformation of disclinations are difficult to control, thereby hindering their applications. Here, we propose a surface-patterned system engendering periodic three-dimensional disclinations, which can be excited by light irradiation and undergo a programmable transformation between different topological states. Continuum simulations recapitulating these topological structures characterize the bending, breaking, and relinking events of the disclinations during the nonequilibrium process. Our work provides an alternative dynamic system in which active transformation of topological defects can be engineered.

Review: knots and other new topological effects in liquid crystals and colloids

Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.

Light-driven dynamic Archimedes spirals and periodic oscillatory patterns of topological solitons in anisotropic soft matter

Oscillatory and excitable systems commonly exhibit formation of dynamic non-equilibrium patterns. For example, rotating spiral patterns are observed in biological, chemical, and physical systems ranging from organization of slime mold cells to Belousov-Zhabotinsky reactions, and to crystal growth from nuclei with screw dislocations. Here we describe spontaneous formation of spiral waves and a large variety of other dynamic patterns in anisotropic soft matter driven by low-intensity light. The unstructured ambient or microscope light illumination of thin liquid crystal films in contact with a self-assembled azobenzene monolayer causes spontaneous formation, rich spatial organization, and dynamics of twisted domains and topological solitons accompanied by the dynamic patterning of azobenzene group orientations within the monolayer. Linearly polarized incident light interacts with the twisted liquid crystalline domains, mimicking their dynamics and yielding patterns in the polarization state of transmitted light, which can be transformed to similar dynamic patterns in its intensity and interference color. This shows that the delicate light-soft-matter interaction can yield complex self-patterning of both. We uncover underpinning physical mechanisms and discuss potential uses.

Topological defects in cholesteric liquid crystals induced by monolayer domains with orientational chirality

Unless stabilized by colloids or confinement with well-defined boundary conditions, defects in liquid crystals remain elusive short-lived objects that tend to disappear with time to minimize the medium's free energy. In this work we use multimodal three-dimensional imaging to visualize cholesteric director structures to show that self-assembled chiral molecular monolayer domains can stabilize topologically constrained defect configurations when in contact with a cholesteric liquid crystal. The cholesteric liquid crystal, having features of both coarse-grained lamellar and nematic liquid crystal with chiral symmetry breaking, allows us to explore the interplay of chirality and implications of layering on the formed defects and director configurations.

Electric-field modulation of liquid crystal structures in contact with structured surfactant monolayers

We present experiments in which we use an electric field to switch between different configurations in the cellular patterns induced in a confined nematic liquid crystal by the contact with a surfactant monolayer that features lateral order and surface defects. By using different combinations of far-field alignment and mesogen dielectric anisotropy, we unravel the nature and stability of point defects and disclinations resulting from the hybrid boundary conditions.

Annihilation dynamics of stringlike topological defects in a nematic lyotropic liquid crystal

Topological defects can appear whenever there is some type of ordering. Its ubiquity in nature has been the subject of several studies, from early Universe to condensed matter. In this work, we investigated the annihilation dynamics of defects and antidefects in a lyotropic nematic liquid crystal (ternary mixture of potassium laurate, decanol and deionized-destillated water) using the polarized optical light microscopy technique. We analyzed Schlieren textures with topological defects produced due to a symmetry breaking in the transition of the isotropic to nematic calamitic phase after a temperature quench. As result, we obtained for the distance D between two annihilating defects (defect-antidefect pair), as a function of time t remaining for the annihilation, the scaling law D ∝ t(α), with α = 0.390 and standard deviation σ = 0.085. Our findings go in the direction to extend experimental results related to dynamics of defects in liquid crystals since only thermotropic and polymerics ones had been investigated. In addition, our results are in good quantitative agreement with previous investigations on the subject.

Supramolecular organization and heterochiral recognition in Langmuir monolayers of chiral azobenzene surfactants

We study the self-assembly of novel azobenzene-based chiral surfactants at the air/water interface, and find that while the pure enantiomers lack the ability to organize in ordered mesophases, the racemic mixture spontaneously forms a hexatic phase at low lateral pressures, which we detect by means of Brewster angle microscopy. This work provides a unique example of heterochiral recognition in which the racemic monolayer is not only condensed with respect to the pure enantiomers, but causes an ordered mesophase to form. Although hexatic order vanishes at high surface pressures, long-range orientational order is regained for all compositions upon monolayer collapse, which proceeds through the formation of birefringent trilayers with a well-defined lateral microstructure, as revealed by atomic force microscopy.

Antipersistent behavior of defects in a lyotropic liquid crystal during annihilation

We report on the dynamical behavior of defects of strength s=±1/2 in a lyotropic liquid crystal during the annihilation process. By following their positions using time-resolved polarizing microscopy technique, we present statistically significant evidence that the relative velocity between defect pairs is Gaussian distributed, antipersistent, and long-range correlated. We further show that simulations of the Lebwohl-Lasher model reproduce quite well our experimental findings.