Session Z34: Topological Defects in Soft/Active/Biological Matter II

Topological Structures in Polar Liquid Crystals

Ferroelectric nematic liquid crystal is a novel state of soft matter discovered in very recent years, that exhibits simultaneously high fluidity and ferroelectricity. The polar nature of its order parameter has significant impact on possible topological structures. Here, we investigated how topological defects in the N_F liquid crystals can be affected and controlled by the orientation fields at confining flat surfaces. By imprinting predesigned director patterns at confining surfaces, we observe that various topological structures can be created and manipulated in a programmable way.    

Influence of confining surface Gaussian curvature on the winding character of nematic disclination lines

In liquid crystals on curved surfaces, topological point-defects are attracted to Gaussian curvature of like sign. We have recently shown that this coupling extends to the surface endpoints of curvilinear disclinations of 3D nematic liquid crystals, in the context of a hybrid-aligned system with one double-undulated, homeotropic boundary and one flat boundary with degenerate planar anchoring. This system exhibits a large space of multistable configurations of disclination lines, whose properties we explore here. In this work, we use Landau-de Gennes numerical modeling to investigate how Gaussian curvature at the boundary surface influences the winding characters of disclination lines in the bulk. These winding characters are observed to vary rapidly along the defect contours. We calculate the rotation vector describing the defect's local winding geometry, and we use these calculations alongside energetic arguments to understand the heterogeneity of the multistable disclination landscape.   

Numerical study of chiral structures from achiral liquid crystals using Ball-Majumdar singular potential model

Recent experiments have shown that certain species of lyotropic chromonic nematic liquid crystal (LCLC) systems have spontaneously exhibited chirality when confined to particular domains, despite the molecules themselves being achiral. For a cylindrical domain with homeotropic anchoring, so-called twisted escaped radial (TER) configurations in which a single +1 disclination escapes to the third dimension via twisting, and twisted polar planar (TPP) configurations in which two +1/2 disclinations form a double-helix structure are formed as systems relax. These configurations are made possible by the small twist elastic constants of LCLCs relative to their bend and splay elastic constants, though energetic arguments on this point are still under debate. We present a study of these systems using a Ball-Majumdar singular potential computational field theory. With this model we are able to sweep through parameters controlling the elastic twist constant and the domain dimensions in order to characterize stability and decay paths of twisted configurations. This analysis is supplemented by using the disclination kinematic law to understand defect motion in the case of the TPP configuration.   

Complementary tensorial measures of disclination line winding character

Whereas disclinations in two-dimensional nematics are point defects with quantized, half-integer winding numbers, the disclination lines of three-dimensional nematics are much more complicated: The nematic director winds about a rotation vector that can vary continuously in time and along the defect’s contour, resulting in continuously variable winding character (wedge, twist, and their intermediates). This poses challenges for characterizing disclination lines in nematic orientation fields from experiment or simulation. Recently, a second-rank tensorial calculation was proposed that allows the rotation vector to be determined from the orientation field in the vicinity of a disclination (Schimming and Viñals, Soft Matter 18: 2234 (2022); Schimming and Viñals, arXiv:2308.04496 (2023)). Here, we demonstrate that the rotation vector can also be calculated from an alternative measure, based on a second-rank pseudotensor defined on either the director field or the Q-tensor field. Furthermore, the two tensorial descriptions are complementary, in that each fails for a different type of disclination winding. We also explore the importance of saddle-splay distortions as a scalar measure of disclination winding character.   

Elasticity and topological defects: a common thread between soft and hard materials

A unified kinematical basis for the description of topological defects in soft or hard materials, based on a characterization of integrability of specified distortion fields will be discussed. This kinematics will be embedded into a continuum mechanical framework consistent with non-negative dissipation. The resulting model will be illustrated through select examples of disclination statics and dynamics in nematic liquid crystals and, separately, experimentally observed grain and subrain boundaries in a hard metal.   

Analytical predictions of topological defect interactions in active nematics.

In active nematics, topological defects may be motile and are sources for flow generation. Predicting and controlling the behavior of defects has practical applications for collective motion, colloidal assembly, and material transport. Here, we build off of a recently developed analytical method for predicting defect motion in passive nematics and extend it to defects in active nematics. By using appropriate approximations for the nematic order parameter and velocity fields, we find analytical expressions for the velocity of +1/2 and -1/2 winding number topological defects as a function of their distance and orientation. We test our predictions with numerical simulations of the full nonlinear equations governing the nematic order parameter.   

Exploring the Formation of Initial Disclination Loops of Active Nematics through Particle-Based Simulations

The dynamics of active nematics are dominated by the spontaneous creation and annihilation of defects, a phenomenon which does not occur in passive equilibrium systems. While the loops and networks formed by 3D disclinations in active nematics has recently become a research focus, the underlying mechanics governing the emergence of initial disclinations from an ordered background remains unclear. In this work, we propose a simple model for the formation of an initial disclination loop within the framework inspired by biaxial nematics. We analyze this model with large-scale particle-based simulations of 3D dry active nematic filaments, performed over a range of activity and filament bending modulus values. Surprisingly, we find that the topological properties of initial loops (the prevalence of wedge-twist or pure-twist type configurations) are highly sensitive to microscopic simulation parameters. By analyzing simulation trajectories, we attribute this correlation to the interplay of two competing time scales: the undulation of directors and the nucleation of defects.   

Cooperative motion and granule rotation during rapid grain shrinking in colloidal crystals

In 2D polycrystals, fully enclosed grain boundary loops tend to dissolve over time. Our colloid experiments show that grain boundary loops shrink via two processes: steps of rapid dissolution and plateaus of slow dissolution. This contradicts continuum theory, which predicts a constant rate of dissolution. We find that the periods of rapid dissolution involve the cooperative motion of particles together in rotating, hexagonal ‘granules.’ During such granule rotation, particle displacements follow a string-like pattern as previously observed in glassy dynamics at grain boundaries, but here we find that motion is directed along the outlines of the underlying Moiré pattern. Furthermore, we employ Brownian Dynamics simulations of grain boundary loops to study the effect of crystal area fraction, finding that tighter crystals shrink more quickly, via cooperative hexagonal granule rotation. Collectively these results point to the importance of cooperative granule rotation in enabling rapid grain dissolution.   

Inducing point defects in 3D colloidal crystals

Crystal defects are imperfections that can crucially influence the properties of crystalline materials. Colloidal crystals serve as useful model systems to study defect phenomena due to their similarities with atomic crystal systems. Although several types of defects have been studied in colloidal crystals, the lack of experimental control over point defect formation provides a challenge for studying the diffusion and interaction phenomena of these defects. We developed a model system in which point defect formation in 3D colloidal crystals can be controlled in-situ. This system consists of poly(N-isopropyl acrylamide) microgels embedded in a crystal of non-responsive poly(2,2,2-trifluoroethyl methacrylate) colloids. Heating this mixed particle system results in shrinking of the embedded microgels, and subsequently induces the formation of vacancy-interstitial pairs. Using temperature-controlled confocal microscopy experiments we study the formation of the point defects in 3D colloidal crystals, and are able to visualize the local lattice strain after interstitial defect formation. The experimental model system presented here provides the unique opportunity to shed new light on the interplay between point defects, the mechanisms of their diffusion, and collective dynamics.   

Controlling Topological Defects in Colloidal Crystal Shells of Hard Superballs

Just as a soccer ball cannot be made solely with hexagonal patches, spherical particles confined to the surface of a sphere cannot arrange densely into a hexagonal lattice without disclinations. In physical systems such as Pickering emulsions, in which droplets are stabilized by colloidal particles added to the droplet interface, these disclinations and defect scars decorate the surface with icosahedral symmetry. Here we use hard particle Monte Carlo simulations to determine the effect of particle shape and lattice preference in flat space on the structure and distribution of defects in spherical shells filled densely with colloidal particles whose shape varies continuously from a sphere to a cube. We describe defect scar analogues for these systems and show how the scar pattern relates to particle shape.   

Model Predictive Control of Active Brownian Particles

Control of active matter systems offers significant potential for various applications, such as directed self-assembly and microactuation. In this study, we propose a feedback control framework for controlling noninteracting Active Brownian Particles (ABPs) at the population level. To achieve control, we adopt Model Predictive Control (MPC), an optimization-based approach that tunes model inputs to achieve desired objectives. The model governing our MPC scheme is based on the Smoluchowski equation, with additional terms accounting for self-propulsion and an actuated external field that influences particle orientations. Leveraging this setup, we apply our feedback control framework to a Brownian dynamics simulation of ideal ABPs. The outcomes of our control simulations demonstrate the versatility and effectiveness of the proposed framework. Notably, our controller successfully achieves multiple objectives, including particle tracking of a specified target, splitting of the particle population into distinct groups, and control over the average particle velocity. These results highlight the potential of MPC in steering active matter systems and pave the way for exciting new opportunities in the field.   

Using potentials to model the crystallography of bee honeycomb under geometric frustration

Honeybees are known to collectively construct highly regular hexagonal structures of the honeycomb in a distributive manner, that optimizes the use of wax. When faced with various geometric constraints, such as boundaries or connecting combs with different orientations, the resulting comb is irregular, with several topological defects. In this work, we study this process using 3D-print experimental frames with imprinted foundations, which impose a precise geometric frustration. We find that the structure of the honeycomb under various frustrations show clear evidence of recurring patterns. We show that these patterns can be explained as the results of an energy minimization process through simulated annealing. We explore different potentials, ranging from interactions inspired from atomistic crystallography (e.g., Lennard-Jones) to potentials that aim to rationalize the minimization process that rules the honeybee behavior.