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.

Probing active nematics with in situ microfabricated elastic inclusions.

In this work, we report a direct measurement of the forces exerted by a tubulin/kinesin active nematic gel as well as its complete rheological characterization, including the quantification of its shear viscosity, η, and its activity parameter, α. For this, we develop a method that allows us to rapidly photo-polymerize compliant elastic inclusions in the continuously remodeling active system. Moreover, we quantitatively settle long-standing theoretical predictions, such as a postulated relationship encoding the intrinsic time scale of the active nematic in terms of η and α. In parallel, we infer a value for the nematic elasticity constant, K, by combining our measurements with the theorized scaling of the active length scale. On top of the microrheology capabilities, we demonstrate strategies for defect encapsulation, quantification of defect mechanics, and defect interactions, enabled by the versatility of the microfabrication strategy that allows to combine elastic motifs of different shapes and stiffnesses that are fabricated in situ.

Design rules for controlling active topological defects.

Topological defects play a central role in the physics of many materials, including magnets, superconductors, and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses and drive chaotic flows stirring the fluid. The intimate connection between defect textures and active flow suggests that properties of active materials can be engineered by controlling defects, but design principles for their spatiotemporal control remain elusive. Here, we propose a symmetry-based additive strategy for using elementary activity patterns, as active topological tweezers, to create, move, and braid such defects. By combining theory and simulations, we demonstrate how, at the collective level, spatial activity gradients act like electric fields which, when strong enough, induce an inverted topological polarization of defects, akin to a negative susceptibility dielectric. We harness this feature in a dynamic setting to collectively pattern and transport interacting active defects. Our work establishes an additive framework to sculpt flows and manipulate active defects in both space and time, paving the way to design programmable active and living materials for transport, memory, and logic.

Intercellular friction and motility drive orientational order in cell monolayers.

Spatiotemporal patterns in multicellular systems are important to understanding tissue dynamics, for instance, during embryonic development and disease. Here, we use a multiphase field model to study numerically the behavior of a near-confluent monolayer of deformable cells with intercellular friction. Varying friction and cell motility drives a solid-liquid transition, and near the transition boundary, we find the emergence of local nematic order of cell deformation driven by shear-aligning cellular flows. Intercellular friction contributes to the monolayer's viscosity, which significantly increases the spatial correlation in the flow and, concomitantly, the extent of nematic order. We also show that local hexatic and nematic order are tightly coupled and propose a mechanical-geometric model for the colocalization of [Formula: see text] nematic defects and 5-7 disclination pairs, which are the structural defects in the hexatic phase. Such topological defects coincide with regions of high cell-cell overlap, suggesting that they may mediate cellular extrusion from the monolayer, as found experimentally. Our results delineate a mechanical basis for the recent observation of nematic and hexatic order in multicellular collectives in experiments and simulations and pinpoint a generic pathway to couple topological and physical effects in these systems.

Tunable three-dimensional architecture of nematic disclination lines.

Disclination lines play a key role in many physical processes, from the fracture of materials to the formation of the early universe. Achieving versatile control over disclinations is key to developing novel electro-optical devices, programmable origami, directed colloidal assembly, and controlling active matter. Here, we introduce a theoretical framework to tailor three-dimensional disclination architecture in nematic liquid crystals experimentally. We produce quantitative predictions for the connectivity and shape of disclination lines found in nematics confined between two thinly spaced glass substrates with strong patterned planar anchoring. By drawing an analogy between nematic liquid crystals and magnetostatics, we find that i) disclination lines connect defects with the same topological charge on opposite surfaces and ii) disclination lines are attracted to regions of the highest twist. Using polarized light to pattern the in-plane alignment of liquid crystal molecules, we test these predictions experimentally and identify critical parameters that tune the disclination lines' curvature. We verify our predictions with computer simulations and find nondimensional parameters enabling us to match experiments and simulations at different length scales. Our work provides a powerful method to understand and practically control defect lines in nematic liquid crystals.

Migration and division in cell monolayers on substrates with topological defects.

Collective movement and organization of cell monolayers are important for wound healing and tissue development. Recent experiments highlighted the importance of liquid crystal order within these layers, suggesting that +1 topological defects have a role in organizing tissue morphogenesis. We study fibroblast organization, motion, and proliferation on a substrate with micron-sized ridges that induce +1 and -1 topological defects using simulation and experiment. We model cells as self-propelled deformable ellipses that interact via a Gay-Berne potential. Unlike earlier work on other cell types, we see that density variation near defects is not explained by collective migration. We propose instead that fibroblasts have different division rates depending on their area and aspect ratio. This model captures key features of our previous experiments: the alignment quality worsens at high cell density and, at the center of the +1 defects, cells can adopt either highly anisotropic or primarily isotropic morphologies. Experiments performed with different ridge heights confirm a prediction of this model: Suppressing migration across ridges promotes higher cell density at the +1 defect. Our work enables a mechanism for tissue patterning using topological defects without relying on cell migration.

Patterning of morphogenetic anisotropy fields.

Orientational order, encoded in anisotropic fields, plays an important role during the development of an organism. A striking example of this is the freshwater polyp Hydra, where topological defects in the muscle fiber orientation have been shown to localize to key features of the body plan. This body plan is organized by morphogen concentration gradients, raising the question how muscle fiber orientation, morphogen gradients and body shape interact. Here, we introduce a minimal model that couples nematic orientational order to the gradient of a morphogen field. We show that on a planar surface, alignment to a radial concentration gradient can induce unbinding of topological defects, as observed during budding and tentacle formation in Hydra, and stabilize aster/vortex-like defects, as observed at a Hydra's mouth. On curved surfaces mimicking the morphologies of Hydra in various stages of development-from spheroid to adult-our model reproduces the experimentally observed reorganization of orientational order. Our results suggest how gradient alignment and curvature effects may work together to control orientational order during development and lay the foundations for future modeling efforts that will include the tissue mechanics that drive shape deformations.

Shape multistability in flexible tubular crystals through interactions of mobile dislocations.

We study avenues to shape multistability and shape morphing in flexible crystalline membranes of cylindrical topology, enabled by glide mobility of dislocations. Using computational modeling, we obtain states of mechanical equilibrium presenting a wide variety of tubular crystal deformation geometries, due to an interplay of effective defect interactions with out-of-tangent-plane deformations that reorient the tube axis. Importantly, this interplay often stabilizes defect configurations quite distinct from those predicted for a two-dimensional crystal confined to the surface of a rigid cylinder. We find that relative and absolute stability of competing states depend strongly on control parameters such as bending rigidity, applied stress, and spontaneous curvature. Using stable dislocation pair arrangements as building blocks, we demonstrate that targeted macroscopic three-dimensional conformations of thin crystalline tubes can be programmed by imposing certain sparse patterns of defects. Our findings reveal a broad design space for controllable and reconfigurable colloidal tube geometries, with potential relevance also to architected carbon nanotubes and microtubules.

Periodic Defect Engineering of Iron-Nitrogen-Carbon Catalysts for Nitrate Electroreduction to Ammonia.

Iron-nitrogen-carbon single atom catalyst (SAC) is regarded as one of the promising electrocatalysts for NO3 - reduction reaction (NO3 RR) to NH3 due to its high activity and selectivity. However, synergistic effects of topological defects and FeN4 active moiety in Fe-N-C SAC have rarely been investigated. By performing density functional theory (DFT) calculations, 13 defective graphene FeN4 with 585, 484, and 5775 topological line defects are constructed, yielding 585-68-FeN4 with optimal NO3 RR catalytic activity, high selectivity, as well as robust anti-dissolution stability. The high NO3 RR activity on 585-68-FeN4 is well explained by the high valence state of Fe center as well as asymmetric charge distribution on FeN4 moiety influenced by 5- and 8-member rings. This DFT work provides theoretical guidance for engineering NO3 RR performance of iron-nitrogen-carbon catalysts by modulating periodic topological defects.

Highly Curved Defect Sites: How Curvature Effect Influences Metal-Free Defective Carbon Electrocatalysts.

Topological defects are widely recognized as effective active sites toward a variety of electrochemical reactions. However, the role of defect curvature is still not fully understood. Herein, carbon nanomaterials with rich topological defect sites of tunable curvature is reported. The curved defective surface is realized by controlling the high-temperature pyrolytic shrinkage process of precursors. Theoretical calculations demonstrate bending the defect sites can change the local electronic structure, promote the charge transfer to key intermediates, and lower the energy barrier for oxygen reduction reaction (ORR). Experimental results convince structural superiority of highly-curved defective sites, with a high kinetic current density of 22.5 mA cm-2 at 0.8 V versus RHE for high-curvature defective carbon (HCDC), ≈18 times that of low-curvature defective carbon (LCDC). Further raising the defect densities in HCDC leads to the dual-regulated products (HCHDC), which exhibit exceptionally outstanding ORR activity in both alkaline and acidic media (half-wave potentials: 0.88 and 0.74 V), outperforming most of the reported metal-free carbon catalysts. This work uncovers the curvature-activity relationship in carbon defect for ORR and provides new guidance to design advanced catalysts via curvature-engineering.

Topological defects produce kinks in biopolymer filament bundles.

Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate, analytically, numerically, and experimentally, that such bundles can be kinked, that is, have localized regions of high curvature that are long-lived metastable states. We propose three possible mechanisms of kink stabilization: a difference in trapped length of the filament segments between two cross-links, a dislocation where the endpoint of a filament occurs within the bundle, and the braiding of the filaments in the bundle. At a high concentration of cross-links, the last two effects lead to the topologically protected kinked states. Finally, we explore, numerically and analytically, the transition of the metastable kinked state to the stable straight bundle.

Machine learning active-nematic hydrodynamics.

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.

Emergence of dynamic vortex glasses in disordered polar active fluids.

In equilibrium, disorder conspires with topological defects to redefine the ordered states of matter in systems as diverse as crystals, superconductors, and liquid crystals. Far from equilibrium, however, the consequences of quenched disorder on active condensed matter remain virtually uncharted. Here, we reveal a state of strongly disordered active matter with no counterparts in equilibrium: a dynamical vortex glass. Combining microfluidic experiments and theory, we show how colloidal flocks collectively cruise through disordered environments without relaxing the topological singularities of their flows. The resulting state is highly dynamical but the flow patterns, shaped by a finite density of frozen vortices, are stationary and exponentially degenerated. Quenched isotropic disorder acts as a random gauge field turning active liquids into dynamical vortex glasses. We argue that this robust mechanism should shape the collective dynamics of a broad class of disordered active matter, from synthetic active nematics to collections of living cells exploring heterogeneous media.

Submersed micropatterned structures control active nematic flow, topology, and concentration.

Coupling between flows and material properties imbues rheological matter with its wide-ranging applicability, hence the excitement for harnessing the rheology of active fluids for which internal structure and continuous energy injection lead to spontaneous flows and complex, out-of-equilibrium dynamics. We propose and demonstrate a convenient, highly tunable method for controlling flow, topology, and composition within active films. Our approach establishes rheological coupling via the indirect presence of fully submersed micropatterned structures within a thin, underlying oil layer. Simulations reveal that micropatterned structures produce effective virtual boundaries within the superjacent active nematic film due to differences in viscous dissipation as a function of depth. This accessible method of applying position-dependent, effective dissipation to the active films presents a nonintrusive pathway for engineering active microfluidic systems.

Topological braiding and virtual particles on the cell membrane.

Braiding of topological structures in complex matter fields provides a robust framework for encoding and processing information, and it has been extensively studied in the context of topological quantum computation. In living systems, topological defects are crucial for the localization and organization of biochemical signaling waves, but their braiding dynamics remain unexplored. Here, we show that the spiral wave cores, which organize the Rho-GTP protein signaling dynamics and force generation on the membrane of starfish egg cells, undergo spontaneous braiding dynamics. Experimentally measured world line braiding exponents and topological entropy correlate with cellular activity and agree with predictions from a generic field theory. Our analysis further reveals the creation and annihilation of virtual quasi-particle excitations during defect scattering events, suggesting phenomenological parallels between quantum and living matter.

Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals.

Lyotropic chromonic liquid crystals are water-based materials composed of self-assembled cylindrical aggregates. Their behavior under flow is poorly understood, and quantitatively resolving the optical retardance of the flowing liquid crystal has so far been limited by the imaging speed of current polarization-resolved imaging techniques. Here, we employ a single-shot quantitative polarization imaging method, termed polarized shearing interference microscopy, to quantify the spatial distribution and the dynamics of the structures emerging in nematic disodium cromoglycate solutions in a microfluidic channel. We show that pure-twist disclination loops nucleate in the bulk flow over a range of shear rates. These loops are elongated in the flow direction and exhibit a constant aspect ratio that is governed by the nonnegligible splay-bend anisotropy at the loop boundary. The size of the loops is set by the balance between nucleation forces and annihilation forces acting on the disclination. The fluctuations of the pure-twist disclination loops reflect the tumbling character of nematic disodium cromoglycate. Our study, including experiment, simulation, and scaling analysis, provides a comprehensive understanding of the structure and dynamics of pressure-driven lyotropic chromonic liquid crystals and might open new routes for using these materials to control assembly and flow of biological systems or particles in microfluidic devices.

Evolution of Emergent Monopoles into Magnetic Skyrmion Strings.

Topological defects are fundamental concepts in physics, but little is known about the transition between distinct types across different dimensionalities. In topological magnetism, as in field theory, the transition between 1D strings and 0D monopoles is a key process whose observation has remained elusive. Here, we introduce a novel mechanism that allows for the controlled stabilization of emergent monopoles and show that magnetic skyrmion strings can be folded into monopoles. Conversely, they act as seeds out of which the entire string structure can unfold, containing its complete information. In chiral magnets, this process can be observed by resonant elastic X-ray scattering when the objects are in proximity to a polarized ferromagnet, whereby a pure monopole lattice is emerging on the surface. Our experimental proof of the reversible evolution from monopole to string sheds new light on topological defects and establishes the emergent monopole lattice as a new 3D topological phase.

Melting of Unidirectional Charge Density Waves across Twin Domain Boundaries in GdTe3.

Solids undergoing a transition from order to disorder experience a proliferation of topological defects. The melting process generates transient quantum states. However, their dynamic nature with a femtosecond lifetime hinders exploration with atomic precision. Here, we suggest an alternative approach to the dynamic melting process by focusing on the interface created by competing degenerate quantum states. We use a scanning tunneling microscope (STM) to visualize the unidirectional charge density wave (CDW) and its spatial progression ("static melting") across a twin domain boundary (TDB) in the layered material GdTe3. Combining the STM with a spatial lock-in technique, we reveal that the order parameter amplitude attenuates with the formation of dislocations and thus two different unidirectional CDWs coexist near the TDB, reducing the CDW anisotropy. Notably, we discovered a correlation between this anisotropy and the CDW gap. Our study provides valuable insight into the behavior of topological defects and transient quantum states.

Hydrogen Evolution Reactivity of Pentagonal Carbon Rings and p-d Orbital Hybridization Effect with Ru.

Topological defects are inevitable existence in carbon-based frameworks, but their intrinsic electrocatalytic activity and mechanism remain under-explored. Herein, the hydrogen evolution reaction (HER) of pentagonal carbon-rings is probed by constructing pentagonal ring-rich carbon (PRC), with optimized electronic structures and higher HER activity relative to common hexagonal carbon (HC). Furthermore, to improve the reactivity, we couple Ru clusters with PRC (Ru@PRC) through p-d orbital hybridization between C and Ru atoms, which drives a shortcut transfer of electrons from Ru clusters to pentagonal rings. The electron-deficient Ru species leads to a notable negative shift in d-band centers of Ru and weakens their binding strength with hydrogen intermediates, thus enhancing the HER activity in different pH media. Especially, at a current density of 10 mA cm-2, PRC greatly reduces alkaline HER overpotentials from 540 to 380 mV. And Ru@PRC even exhibits low overpotentials of 28 and 275 mV to reach current densities of 10 and 1000 mA cm-2, respectively. Impressively, the mass activity and price activity of Ru@PRC are 7.83 and 15.7 times higher than that of Pt/C at the overpotential of 50 mV. Our data unveil the positive HER reactivity of pentagonal defects and good application prospects.

Pseudocapacitive Potassium-Ion Intercalation Enabled by Topologically Defective Soft Carbon toward High-Rate, Large-Areal-Capacity, and Low-Temperature Potassium-Ion Batteries.

Carbonaceous materials are widely investigated as anodes for potassium-ion batteries (PIBs). However, the inferior rate capability, low areal capacity, and limited working temperature caused by sluggish K-ions diffusion kinetics are still primary challenges for carbon-based anodes. Herein, a simple temperature-programmed co-pyrolysis strategy is proposed for the efficient synthesis of topologically defective soft carbon (TDSC) based on inexpensive pitch and melamine. The skeletons of TDSC are optimized with shortened graphite-like microcrystals, enlarged interlayer spacing, and abundant topological defects (e.g., pentagons, heptagons, and octagons), which endow TDSC with fast pseudocapacitive K-ion intercalation behavior. Meanwhile, micrometer-sized structure can reduce the electrolyte degradation over particle surface and avoid unnecessary voids, ensuring a high initial Coulombic efficiency as well as high energy density. These synergistic structural advantages contribute to excellent rate capability (116 mA h g-1 at 20 C), impressive areal capacity (1.83 mA h cm-2 with a mass loading of 8.32 mg cm-2 ), long-term cycling stability (capacity retention of 91.8% after 1200 h cycling), and low working temperature (-10 °C) of TDSC anodes, demonstrating great potential for the practical application of PIBs.