Defect Interactions in Anisotropic Two-Dimensional Fluids

Statics and dynamics of point boojums, line and modified Saturn ring topological defects in nematic confined geometry

In this paper we study the static structure and the dynamics of topological defects associated with isotropic droplets in nematic environment. Investigations were made in confined geometry of optical cells when the droplet size was of the order of or larger than the gap of the cell. We observed the coexistence of point boojums and Saturn ring or modified Saturn ring defects. We found transformation of the Saturn ring defect to two localized broad defects at increasing the droplet size. At droplet coalescence antipodes of point and localized broad defects were born and the dynamics of their annihilation with existing defects was investigated. We found strong difference in the process of annihilation of point and localized broad defects. Microscope images of isotropic droplets in nematic environment in a planar cell. The director orientation far from the droplets is in horizontal direction. The photographs were taken with crossed vertical and horizontal polarizers (a) and with a single horizontal polarizer (b). The cell thickness is 100 μm. Droplet diameter is less than the cell thickness. 1 and 2 are point boojums, L is the Saturn ring defect.

The structure of disintegrating defect clusters in smectic C freely suspended films

Disclinations or disclination clusters in smectic C freely suspended films with topological charges larger than one are unstable. They disintegrate, preferably in a spatially symmetric fashion, into single defects with individual charges of +1, which is the smallest positive topological charge allowed in polar vector fields. While the opposite process of defect annihilation is well-defined by the initial defect positions, disintegration starts from a singular state and the following scenario including the emerging regular defect patterns must be selected by specific mechanisms. We analyze experimental data and compare them with a simple model where the defect clusters adiabatically pass quasi-equilibrium solutions in one-constant approximation. It is found that the defects arrange in geometrical patterns that correspond very closely to superimposed singular defect solutions, without additional director distortions. The patterns expand by affine transformations where all distances between individual defects scale with the same time-dependent scaling factor proportional to the square-root of time.

Observation of Backflow during the Anihilation of Topologocal Defects in Freely Suspended Smectic Films

Freely suspended films in the smectic C phase are excellent templates for the study of topological defect dynamics. It is well known that, during the annihilation of a pair of disclinations with strengths +/−1, the +1 defect moves faster because it is carried towards its opponent by backflow, whereas the flow in the vicinity of the −1 defect is negligibly small. This backflow pattern is created by the defect motion itself. An experimental confirmation of this theoretical prediction and its quantitative characterization is achieved here by fluorescence labeling. Film regions near the defect positions are labeled and their displacements are tracked optically.

Annihilation trajectory of defects in smectic-C films

In a two-dimensional liquid crystal, each topological defect has a topological charge and a characteristic orientation and hence can be regarded as an oriented particle. Theories predict that the trajectories of annihilating defects depend on their relative orientation. Recently, these predictions have been tested in experiments on smectic-C films. Those experiments find curved trajectories that are similar to the predictions, but the detailed relationship between the defect orientations and the far-field director is different. To understand this difference, we extend the previous theories by adding the effects of elastic anisotropy and find that it significantly changes the curved trajectories.

End-to-end machine learning for experimental physics: using simulated data to train a neural network for object detection in video microscopy

We demonstrate a method for training a convolutional neural network with simulated images for usage on real-world experimental data. Modern machine learning methods require large, robust training data sets to generate accurate predictions. Generating these large training sets requires a significant up-front time investment that is often impractical for small-scale applications. Here we demonstrate a 'full-stack' computational solution, where the training data set is generated on-the-fly using a noise injection process to produce simulated data characteristic of the experimental system. We demonstrate the power of this full-stack approach by applying it to the study of topological defect annihilation in systems of liquid crystal freely-suspended films. This specific experimental system requires accurate observations of both the spatial distribution of the defects and the total number of defects, making it an ideal system for testing the robustness of the trained network. The fully trained network was found to be comparable in accuracy to human hand-annotation, with four-orders of magnitude improvement in time efficiency.

Electric field-driven reconfigurable multistable topological defect patterns

Topological defects appear in symmetry breaking phase transitions and are ubiquitous throughout Nature. As an ideal testbed for their study, defect configurations in nematic liquid crystals (NLCs) could be exploited in a rich variety of technological applications. Here we report on robust theoretical and experimental investigations in which an external electric field is used to switch between pre-determined stable chargeless disclination patterns in a nematic cell, where the cell is sufficiently thick that the disclinations start and terminate at the same surface. The different defect configurations are stabilised by a master substrate that enforces a lattice of surface defects exhibiting zero total topological charge value. Theoretically, we model disclination configurations using a Landau-de Gennes phenomenological model. Experimentally, we enable diverse defect patterns by implementing an in-house-developed Atomic Force Measurement scribing method, where NLC configurations are monitored via polarised optical microscopy. We show numerically and experimentally that an "alphabet" of up to 18 unique line defect configurations can be stabilised in a 4x4 lattice of alternating s=±1 surface defects, which can be "rewired" multistably using appropriate field manipulation. Our proof-of-concept mechanism may lead to a variety of applications, such as multistable optical displays and rewirable nanowires. Our studies also are of interest from a fundamental perspective. We demonstrate that a chargeless line could simultaneously exhibit defect-antidefect properties. Consequently, a pair of such antiparallel disclinations exhibits an attractive interaction. For a sufficiently closely-spaced pair of substrate-pinned defects, this interaction could trigger rewiring, or annihilation if defects are depinned.

Theory of defect motion in 2D passive and active nematic liquid crystals

The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the dynamics of orientational order is coupled with backflow of the fluid, and because a liquid crystal has several distinct viscosity coefficients. Here, we suggest a coarse-grained, variational approach, which describes the motion of defects as effective "particles". For passive liquid crystals, the theory shows how the drag depends on defect orientation, and shows the coupling between translational and rotational motion. For active liquid crystals, the theory provides an alternative way to describe motion induced by the activity coefficient.

Length segregation in mixtures of spherocylinders induced by imposed topological defects

We explore length segregation in binary mixtures of spherocylinders of lengths L1 and L2 which are tangentially confined on a spherical surface of radius R. The orientation of the spherocylinders is constrained along an externally imposed direction field on the sphere which is either along the longitude or the latitude lines of the sphere. In both situations, integer orientational defects at the poles are imposed. Using computer simulations we show that these topological defects induce a complex segregation picture also depending on the length ratio factor γ = L2/L1 and the total packing fraction η of the spherocylinders. When the binary mixture is aligned along the longitude lines of the sphere, shorter rods tend to accumulate at the topological defects of the polar caps whereas longer rods occupy the central equatorial area of the spherical surface. In the reverse case of latitude ordering, a new state can emerge where longer rods are predominantly both in the cap and in the equatorial areas and shorter rods are localized in between. As a reference situation, we consider a defect-free situation in the flat plane and do not find any length segregation there at similar γ and η; hence, the segregation is purely induced by the imposed topological defects. We also develop an Onsager-like density functional theory which is capable of predicting length segregation in ordered mixtures. At low density, the results of this theory are in good agreement with the simulation data.

Interplay of structure, elasticity, and dynamics in actin-based nematic materials

Achieving control and tunability of lyotropic materials has been a long-standing goal of liquid crystal research. Here we show that the elasticity of a liquid crystal system consisting of a dense suspension of semiflexible biopolymers can be manipulated over a relatively wide range of elastic moduli. Specifically, thin films of actin filaments are assembled at an oil-water interface. At sufficiently high concentrations, one observes the formation of a nematic phase riddled with [Formula: see text] topological defects, characteristic of a two-dimensional nematic system. As the average filament length increases, the defect morphology transitions from a U shape into a V shape, indicating the relative increase of the material's bend over splay modulus. Furthermore, through the sparse addition of rigid microtubule filaments, one can gain additional control over the liquid crystal's elasticity. We show how the material's bend constant can be raised linearly as a function of microtubule filament density, and present a simple means to extract absolute values of the elastic moduli from purely optical observations. Finally, we demonstrate that it is possible to predict not only the static structure of the material, including its topological defects, but also the evolution of the system into dynamically arrested states. Despite the nonequilibrium nature of the system, our continuum model, which couples structure and hydrodynamics, is able to capture the annihilation and movement of defects over long time scales. Thus, we have experimentally realized a lyotropic liquid crystal system that can be truly engineered, with tunable mechanical properties, and a theoretical framework to capture its structure, mechanics, and dynamics.

Smectic monolayer confined on a sphere: topology at the particle scale

The impact of topology on the structure of a smectic monolayer confined to a sphere is explored by particle-resolved computer simulations of hard rods. The orientations of the particles are tangential to the sphere and either free or restricted to a prescribed director field with a latitude or longitude orderings. Depending on the imprinted topology, a wealth of different states are found including equatorial smectic with isotropic poles, equatorial smectic with empty poles, a broken egg-shell like modulated smectic, a capped nematic with equatorial bald patches, equatorial nematic with empty poles, and a situation with 4 or 8 half-strength topological defects. Potentially these states could be verified in experiments with Pickering emulsions of droplets with colloidal rods. The unique nature of dipolar structures consisting of positive and negative half-strength disclinations is revealed. These structures, classified by their density and interaction with other defects in the system, relieve the strain of the poles by separating closely positioned half-strength defects. The proximity of these structures to the half-strength defects might enhance the structural diffusion of the defects across the system.

Kibble-Zurek Scaling during Defect Formation in a Nematic Liquid Crystal

Symmetry-breaking phase transitions are often accompanied by the formation of topological defects, as in cosmological theories of the early universe, superfluids, liquid crystals or solid-state systems. This scenario is described by the Kibble-Zurek mechanism, which predicts corresponding scaling laws for the defect density ρ. One such scaling law suggests a relation ρ≈τ_Q^-1/2 with τ_Q the change of rate of a control parameter. In contrast to the scaling of the defect density during annihilation with ρ≈t^-1 , which is governed by the attraction of defects of the same strength but opposite sign, the defect formation process, which depends on the rate of change of a physical quantity initiating the transition, has only rarely been investigated. Herein, we use nematic liquid crystals as a different system to demonstrate the validity of the predicted scaling relation for defect formation. It is found that the scaling exponent is independent of temperature and material employed, thus universal, as predicted.