Spatiotemporal control of liquid crystal structure and dynamics through activity patterning

Direct patterning of liquid materials on flat and curved substrates using flexible molds with through-hole and post arrays

Liquids undergo continuous deformation in the presence of external shear stresses; however, they are pinned between structures owing to their viscosity. Therefore, reshaping the liquids using their intrinsic material properties and structural interfaces is possible. In this study, we used the template-guided forming (TGF) method to reshape and produce oil patterns on flat and curved substrates. To produce oil patterns, we developed two oil patterning methods: direct heating-based oil patterning (DHOP) and solvent evaporation-based oil patterning (SEOP), which were characterized using various oils and solvents. To overcome the limitation of relying solely on liquid patterning that undergoes complete evaporation, we successfully fabricated liquid films using oil and nonpolar organic solvents that exhibit long-term stability. Therefore, achieving durability and control over the film thickness using nonpolar organic solvents has great potential for future applications in microfluidics. Furthermore, we demonstrated that the SEOP method in conjunction with TGF can produce various and unconventional patterns of an organic photoresist (SU-8), which cannot be produced through standard photolithography. Hence, we conclude that the proposed TFG-based oil pattering methods could be highly useful for producing unconventional and unprecedented patterns on flat and curved substrates for various applications, including microelectronics, optics, filtration and separation, biomedical engineering, and nanotechnology.

Spatiotemporal control of structure and dynamics in a polar active fluid

We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the effective self-propulsion speed as the control parameter (i.e. the means of external actuation). We identify control protocols that achieve outcomes such as relocating asters to targeted positions, forcing propagating solitary waves to reorient to a particular direction, and switching between stationary asters and propagating fronts. We analyze the solutions to identify generic principles for controlling polar active fluids. Our findings have implications for achieving spatiotemporal control of active polar systems in experiments, particularly in vitro cytoskeletal systems. Additionally, this research paves the way for leveraging optimal control methods to engineer the structure and dynamics of active fluids more broadly.

Motor-driven microtubule diffusion in a photobleached dynamical coordinate system

Motor-driven cytoskeletal remodeling in cellular systems can often be accompanied by a diffusive-like effect at local scales, but distinguishing the contributions of the ordering process, such as active contraction of a network, from this active diffusion is difficult to achieve. Using light-dimerizable kinesin motors to spatially control the formation and contraction of a microtubule network, we deliberately photobleach a grid pattern onto the filament network serving as a transient and dynamic coordinate system to observe the deformation and translation of the remaining fluorescent squares of microtubules. We find that the network contracts at a rate set by motor speed but is accompanied by a diffusive-like spread throughout the bulk of the contracting network with effective diffusion constant two orders of magnitude lower than that for a freely-diffusing microtubule. We further find that on micron scales, the diffusive timescale is only a factor of ≈ 3 slower than that of advection regardless of conditions, showing that the global contraction and long-time relaxation from this diffusive behavior are both motor-driven but exhibit local competition within the network bulk.

Surface Topography Induces and Orients Nematic Swarms of Active Filaments: Considerations for Lab-On-A-Chip Devices

Surface-bound molecular motors can drive the collective motion of cytoskeletal filaments in the form of nematic bands and polar flocks in reconstituted gliding assays. Although these "swarming transitions" are an emergent property of active filament collisions, they can be controlled and guided by tuning the surface chemistry or topography of the substrate. To date, the impact of surface topography on collective motion in active nematics is only partially understood, with most experimental studies focusing on the escape of a single filament from etched channels. Since the late 1990s, significant progress has been made to utilize the nonequilibrium properties of active filaments and create a range of functional nanodevices relevant to biosensing and parallel computation; however, the complexity of these swarming transitions presents a challenge when attempting to increase filament surface concentrations. In this work, we etch shallow, linear trenches into glass substrates to induce the formation of swarming nematic bands and investigate the mechanisms by which surface topography regulates the two-dimensional (2D) collective motion of driven filamentous actin (F-actin). We demonstrate that nematic swarms only appear at intermediate trench spacings and vanish if the trenches are made too narrow, wide, or tortuous. To rationalize these results, we simulate the F-actin as self-propelled, semiflexible chains subject to a soft, spatially modulated potential that encodes the energetic cost of bending a filament along the edge of a trench. In our model, we hypothesize that an individual filament experiences a penalty when its projected end-to-end distance is smaller than the trench spacing ("bending and turning"). However, chains that span the channel width glide above the trenches in a force- and torque-free manner ("crowd-surfing"). Our simulations demonstrate that collections of filaments form nematic bands only at intermediate trench spacings, consistent with our experimental findings.

Programming tunable active dynamics in a self-propelled robot

We present a scheme for producing tunable active dynamics in a self-propelled robotic device. The robot moves using the differential drive mechanism where two wheels can vary their instantaneous velocities independently. These velocities are calculated by equating robot's equations of motion in two dimensions with well-established active particle models and encoded into the robot's microcontroller. We demonstrate that the robot can depict active Brownian, run and tumble, and Brownian dynamics with a wide range of parameters. The resulting motion analyzed using particle tracking shows excellent agreement with the theoretically predicted trajectories. Later, we show that its motion can be switched between different dynamics using light intensity as an external parameter. Intriguingly, we demonstrate that the robot can efficiently navigate through many obstacles by performing stochastic reorientations driven by the gradient in light intensity towards a desired location, namely the target. This work opens an avenue for designing tunable active systems with the potential of revealing the physics of active matter and its application for bio- and nature-inspired robotics.

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.

Mechanochemical dynamics of collective cells and hierarchical topological defects in multicellular lumens

Collective cell dynamics is essential for tissue morphogenesis and various biological functions. However, it remains incompletely understood how mechanical forces and chemical signaling are integrated to direct collective cell behaviors underlying tissue morphogenesis. Here, we propose a three-dimensional (3D) mechanochemical theory accounting for biochemical reaction-diffusion and cellular mechanotransduction to investigate the dynamics of multicellular lumens. We show that the interplay between biochemical signaling and mechanics can trigger either pitchfork or Hopf bifurcation to induce diverse static mechanochemical patterns or generate oscillations with multiple modes both involving marked mechanical deformations in lumens. We uncover the crucial role of mechanochemical feedback in emerging morphodynamics and identify the evolution and morphogenetic functions of hierarchical topological defects including cell-level hexatic defects and tissue-level orientational defects. Our theory captures the common mechanochemical traits of collective dynamics observed in experiments and could provide a mechanistic context for understanding morphological symmetry breaking in 3D lumen-like tissues.

Timed material self-assembly controlled by circadian clock proteins

Active biological molecules present a powerful, yet largely untapped, opportunity to impart autonomous regulation to materials. Because these systems can function robustly to regulate when and where chemical reactions occur, they have the ability to bring complex, life-like behavior to synthetic materials. Here, we achieve this design feat by using functionalized circadian clock proteins, KaiB and KaiC, to engineer time-dependent crosslinking of colloids. The resulting material self-assembles with programmable kinetics, producing macroscopic changes in material properties, via molecular assembly of KaiB-KaiC complexes. We show that colloid crosslinking depends strictly on the phosphorylation state of KaiC, with kinetics that are synced with KaiB-KaiC complexing. Our microscopic image analyses and computational models indicate that the stability of colloidal super-structures depends sensitively on the number of Kai complexes per colloid connection. Consistent with our model predictions, a high concentration stabilizes the material against dissolution after a robust self-assembly phase, while a low concentration allows circadian oscillation of material structure. This work introduces the concept of harnessing biological timers to control synthetic materials; and, more generally, opens the door to using protein-based reaction networks to endow synthetic systems with life-like functional properties.

Motor crosslinking augments elasticity in active nematics

In active materials, uncoordinated internal stresses lead to emergent long-range flows. An understanding of how the behavior of active materials depends on mesoscopic (hydrodynamic) parameters is developing, but there remains a gap in knowledge concerning how hydrodynamic parameters depend on the properties of microscopic elements. In this work, we combine experiments and multiscale modeling to relate the structure and dynamics of active nematics composed of biopolymer filaments and molecular motors to their microscopic properties, in particular motor processivity, speed, and valency. We show that crosslinking of filaments by both motors and passive crosslinkers not only augments the contributions to nematic elasticity from excluded volume effects but dominates them. By altering motor kinetics we show that a competition between motor speed and crosslinking results in a nonmonotonic dependence of nematic flow on motor speed. By modulating passive filament crosslinking we show that energy transfer into nematic flow is in large part dictated by crosslinking. Thus motor proteins both generate activity and contribute to nematic elasticity. Our results provide new insights for rationally engineering active materials.

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.

Moiré effect enables versatile design of topological defects in nematic liquid crystals

Recent advances in surface-patterning techniques of liquid crystals have enabled the precise creation of topological defects, which promise a variety of emergent applications. However, the manipulation and application of these defects remain limited. Here, we harness the moiré effect to engineer topological defects in patterned nematic liquid crystal cells. Specifically, we combine simulation and experiment to examine a nematic cell confined between two substrates of periodic surface anchoring patterns; by rotating one surface against the other, we observe a rich variety of highly tunable, novel topological defects. These defects are shown to guide the three-dimensional self-assembly of colloids, which can conversely impact defects by preventing the self-annihilation of loop-defects through jamming. Finally, we demonstrate that certain nematic moiré cells can engender arbitrary shapes represented by defect regions. As such, the proposed simple twist method enables the design and tuning of mesoscopic structures in liquid crystals, facilitating applications including defect-directed self-assembly, material transport, micro-reactors, photonic devices, and anti-counterfeiting materials.

Controlling active turbulence by activity patterns

By patterning activity in space, one can control active turbulence. To show this, we use Doi's hydrodynamic equations of a semidilute solution of active rods. A linear stability analysis reveals the resting isotropic fluid to be unstable above an absolute pusher activity. The emergent activity-induced paranematic state displays active turbulence, which we characterize by different quantities including the energy spectrum, which shows the typical power-law decay with exponent -4. Then, we control the active turbulence by a square lattice of circular spots where activity is switched off. In the parameter space lattice constant versus surface-to-surface distance of the spots, we identify different flow states. Most interestingly, for lattice constants below the vorticity correlation length and for spot distances smaller than the nematic coherence length, we observe a multi-lane flow state, where flow lanes with alternating flow directions are separated by a street of vortices. The flow pattern displays pronounced multistability and also appears transiently at the transition to the isotropic active-turbulence state. At larger lattice constants a trapped vortex state is identified with a non-Gaussian vorticity distribution due to the low flow vorticity at the spots. It transitions to conventional active turbulence for increasing spot distance.

Conformation and dynamics of partially active linear polymers

We perform numerical simulations of isolated, partially active polymers, driven out-of-equilibrium by a fraction of their monomers. We show that, if the active beads are all gathered in a contiguous block, the position of the section along the chain determines the conformational and dynamical properties of the system. Notably, one can modulate the diffusion coefficient of the polymer from active-like to passive-like just by changing the position of the active block. Further, we show that a slight modification of the self-propulsion rule may give rise to an enhancement of diffusion under certain conditions, despite a decrease of the overall polymer activity. Our findings may help in the modelisation of active biophysical systems, such as filamentous bacteria or worms.

A machine learning approach to robustly determine director fields and analyze defects in active nematics

Active nematics are dense systems of rodlike particles that consume energy to drive motion at the level of the individual particles. They exist in natural systems like biological tissues and artificial materials such as suspensions of self-propelled colloidal particles or synthetic microswimmers. Active nematics have attracted significant attention in recent years due to their spectacular nonequilibrium collective spatiotemporal dynamics, which may enable applications in fields such as robotics, drug delivery, and materials science. The director field, which measures the direction and degree of alignment of the local nematic orientation, is a crucial characteristic of active nematics and is essential for studying topological defects. However, determining the director field is a significant challenge in many experimental systems. Although director fields can be derived from images of active nematics using traditional imaging processing methods, the accuracy of such methods is highly sensitive to the settings of the algorithms. These settings must be tuned from image to image due to experimental noise, intrinsic noise of the imaging technology, and perturbations caused by changes in experimental conditions. This sensitivity currently limits automatic analysis of active nematics. To address this, we developed a machine learning model for extracting reliable director fields from raw experimental images, which enables accurate analysis of topological defects. Application of the algorithm to experimental data demonstrates that the approach is robust and highly generalizable to experimental settings that are different from those in the training data. It could be a promising tool for investigating active nematics and may be generalized to other active matter systems.

Pumping Small Molecules Selectively through an Energy-Assisted Assembling Process at Nonequilibrium States

In living organisms, precise control over the spatial and temporal distribution of molecules, including pheromones, is crucial. This level of control is equally important for the development of artificial active materials. In this study, we successfully controlled the distribution of small molecules in the system at nonequilibrium states by actively transporting them, even against the apparent concentration gradient, with high selectivity. As a demonstration, in the aqueous solution of acid orange (AO7) and TMC10COOH, we found that AO7 molecules can coassemble with transient anhydride (TMC10CO)2O to form larger assemblies in the presence of chemical fuel 1-ethyl-3-(3-(dimethylamino)propyl) carbodiimide hydrochloride (EDC). This led to a decrease in local free AO7 concentration and caused AO7 molecules from other locations in the solution to move toward the assemblies. Consequently, AO7 accumulates at the location where EDC was injected. By continuously injecting EDC, we could maintain a stable high value of the apparent AO7 concentration at the injection point. We also observed that this process which operated at nonequilibrium states exhibited high selectivity.

Non-Gaussian anomalous diffusion of optical vortices

Anomalous diffusion of different particlelike entities, the deviation from typical Brownian motion, is ubiquitous in complex physical and biological systems. While optical vortices move randomly in evolving speckle fields, optical vortices have only been observed to exhibit pure Brownian motion in random speckle fields. Here we present direct experimental evidence of the anomalous diffusion of optical vortices in temporally varying speckle patterns from multiple-scattering viscoelastic media. Moreover, we observe two characteristic features, i.e., the self-similarity and the antipersistent correlation of the optical vortex motion, indicating that the mechanism of the observed subdiffusion of optical vortices can only be attributed to fractional Brownian motion (FBM). We further demonstrate that the vortex displacements exhibit a non-Gaussian heavy-tailed distribution. Additionally, we modulate the extent of subdiffusion, such as diffusive scaling exponents, and the non-Gaussianity of optical vortices by altering the viscoelasticity of samples. The discovery of the complex FBM but non-Gaussian subdiffusion of optical vortices may not only offer insight into certain fundamental physics, including the anomalous diffusion of vortices in fluids and the decoupling between Brownianity and Gaussianity, but also suggest a strong potential for utilizing optical vortices as tracers in microrheology instead of the introduced exogenous probe particles in particle tracking microrheology.

Microscopic interactions control a structural transition in active mixtures of microtubules and molecular motors

Microtubules and molecular motors are essential components of the cellular cytoskeleton, driving fundamental processes in vivo, including chromosome segregation and cargo transport. When reconstituted in vitro, these cytoskeletal proteins serve as energy-consuming building blocks to study the self-organization of active matter. Cytoskeletal active gels display rich emergent dynamics, including extensile flows, locally contractile asters, and bulk contraction. However, it is unclear how the protein-protein interaction kinetics set their contractile or extensile nature. Here, we explore the origin of the transition from extensile bundles to contractile asters in a minimal reconstituted system composed of stabilized microtubules, depletant, adenosine 5'-triphosphate (ATP), and clusters of kinesin-1 motors. We show that the microtubule-binding and unbinding kinetics of highly processive motor clusters set their ability to end-accumulate, which can drive polarity sorting of the microtubules and aster formation. We further demonstrate that the microscopic time scale of end-accumulation sets the emergent time scale of aster formation. Finally, we show that biochemical regulation is insufficient to fully explain the transition as generic aligning interactions through depletion, cross-linking, or excluded volume interactions can drive bundle formation despite end-accumulating motors. The extensile-to-contractile transition is well captured by a simple self-assembly model where nematic and polar aligning interactions compete to form either bundles or asters. Starting from a five-dimensional organization phase space, we identify a single control parameter given by the ratio of the different component concentrations that dictates the material-scale organization. Overall, this work shows that the interplay of biochemical and mechanical tuning at the microscopic level controls the robust self-organization of active cytoskeletal materials.

Maximally mixing active nematics

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) "topological entropy"-the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.

Measuring response functions of active materials from data

From flocks of birds to biomolecular assemblies, systems in which many individual components independently consume energy to perform mechanical work exhibit a wide array of striking behaviors. Methods to quantify the dynamics of these so-called active systems generally aim to extract important length or time scales from experimental fields. Because such methods focus on extracting scalar values, they do not wring maximal information from experimental data. We introduce a method to overcome these limitations. We extend the framework of correlation functions by taking into account the internal headings of displacement fields. The functions we construct represent the material response to specific types of active perturbation within the system. Utilizing these response functions we query the material response of disparate active systems composed of actin filaments and myosin motors, from model fluids to living cells. We show we can extract critical length scales from the turbulent flows of an active nematic, anticipate contractility in an active gel, distinguish viscous from viscoelastic dissipation, and even differentiate modes of contractility in living cells. These examples underscore the vast utility of this method which measures response functions from experimental observations of complex active systems.

Light-activated microtubule-based two-dimensional active nematic

We assess the ability of two light responsive kinesin motor clusters to drive dynamics of microtubule-based active nematics: opto-K401, a processive motor, and opto-K365, a non-processive motor. Measurements reveal an order of magnitude improvement in the contrast of nematic flow speeds between maximally- and minimally-illuminated states for opto-K365 motors when compared to opto-K401 construct. For opto-K365 nematics, we characterize both the steady-state flow and defect density as a function of applied light. We also examine the transient behavior as the system switches between steady-states upon changes in light intensities. Although nematic flows reach a steady state within tens of seconds, the defect density exhibits transient behavior for up to 10 minutes, showing a separation between small-scale active flows and system-scale structural states. Our work establishes an experimental platform that can exploit spatiotemporally-heterogeneous patterns of activity to generate targeted dynamical states.

Friction-mediated phase transition in confined active nematics

Using a minimal continuum model, we investigate the interplay between circular confinement and substrate friction in active nematics. Upon increasing the friction from low to high, we observe a dynamical phase transition from a circulating flow phase to an anisotropic flow phase in which the flow tends to align perpendicular to the nematic director at the boundary. We demonstrate that both the flow structure and dynamic correlations in the latter phase differ from those of an unconfined, active turbulent system and may be controlled by the prescribed nematic boundary conditions. Our results show that substrate friction and geometric confinement act as valuable control parameters in active nematics.

Programmable spatial deformation by controllable off-center freestanding 4D printing of continuous fiber reinforced liquid crystal elastomer composites

Owing to their high deformation ability, 4D printed structures have various applications in origami structures, soft robotics and deployable mechanisms. As a material with programmable molecular chain orientation, liquid crystal elastomer is expected to produce the freestanding, bearable and deformable three-dimensional structure. However, majority of the existing 4D printing methods for liquid crystal elastomers can only fabricate planar structures, which limits their deformation designability and bearing capacity. Here we propose a direct ink writing based 4D printing method for freestanding continuous fiber reinforced composites. Continuous fibers can support freestanding structures during the printing process and improve the mechanical property and deformation ability of 4D printed structures. In this paper, the integration of 4D printed structures with fully impregnated composite interfaces, programmable deformation ability and high bearing capacity are realized by adjusting the off-center distribution of the fibers, and the printed liquid crystal composite can carry a load of up to 2805 times its own weight and achieve a bending deformation curvature of 0.33 mm^-1 at 150 °C. This research is expected to open new avenues for creating soft robotics, mechanical metamaterials and artificial muscles.

Spatio-temporal patterning of extensile active stresses in microtubule-based active fluids

Microtubule-based active fluids exhibit turbulent-like autonomous flows, which are driven by the molecular motor powered motion of filamentous constituents. Controlling active stresses in space and time is an essential prerequisite for controlling the intrinsically chaotic dynamics of extensile active fluids. We design single-headed kinesin molecular motors that exhibit optically enhanced clustering and thus enable precise and repeatable spatial and temporal control of extensile active stresses. Such motors enable rapid, reversible switching between flowing and quiescent states. In turn, spatio-temporal patterning of the active stress controls the evolution of the ubiquitous bend instability of extensile active fluids and determines its critical length dependence. Combining optically controlled clusters with conventional kinesin motors enables one-time switching from contractile to extensile active stresses. These results open a path towards real-time control of the autonomous flows generated by active fluids.

Dissipation and energy propagation across scales in an active cytoskeletal material

Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system's total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system's total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.

Confined active matter in external fields

We analyze a dilute suspension of active particles confined between walls and subjected to fields that can modulate particle speed as well as orientation. Generally, the particle distribution is different in the bulk compared to near the walls. In the bulk, particles tend to accumulate in the regions of low speed, but in the presence of an orienting field normal to the walls, particles rotate to align with the field and accumulate in the field direction. At the walls, particles tend to accumulate pointing into the walls and thereby exert pressure on walls. But the presence of strong orienting fields can cause the particles to reorient away from the walls, and hence shows a possible mechanism for preventing contamination of surfaces. The pressure at the walls depends on the wall separation and the field strengths. This work demonstrates how multiple fields with different functionalities can be used to control active matter under confinement.

Defect self-propulsion in active nematic films with spatially varying activity

We study the dynamics of topological defects in active nematic films with spatially varying activity and consider two set-ups: (i) a constant activity gradient and (ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like +1/2 defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the +1/2 defect and has no effect on the -1/2 that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The +1/2 defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The -1/2 defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries.

Polarity and chirality control of an active fluid by passive nematic defects

Much like passive materials, active systems can be affected by the presence of imperfections in their microscopic order, called defects, that influence macroscopic properties. This suggests the possibility to steer collective patterns by introducing and controlling defects in an active system. Here we show that a self-assembled, passive nematic is ideally suited to control the pattern formation process of an active fluid. To this end, we force microtubules to glide inside a passive nematic material made from actin filaments. The actin nematic features self-assembled half-integer defects that steer the active microtubules and lead to the formation of macroscopic polar patterns. Moreover, by confining the nematic in circular geometries, chiral loops form. We find that the exact positioning of nematic defects in the passive material deterministically controls the formation and the polarity of the active flow, opening the possibility of efficiently shaping an active material using passive defects.

Structures, thermodynamics and dynamics of topological defects in Gay-Berne nematic liquid crystals

Topological defects are a ubiquitous phenomenon across different physical systems. A better understanding of defects can be helpful in elucidating the physical behaviors of many real materials systems. In nematic liquid crystals, defects exhibit unique optical signatures and can segregate impurities, showing their promise as molecular carriers and nano-reactors. Continuum theory and simulations have been successfully applied to link static and dynamical behaviors of topological defects to the material constants of the underlying nematic. However, further evidence and molecular details are still lacking. Here we perform molecular dynamics simulations of Gay-Berne particles, a model nematic, to examine the molecular structures and dynamics of +1/2 defects in a thin-film nematic. Specifically, we measure the bend-to-splay ratio K₃/K₁ using two independent, indirect measurements, showing good agreement. Next, we study the annihilation event of a pair of ±1/2 defects, of which the trajectories are consistent with experiments and hydrodynamic simulations. We further examine the thermodynamics of defect annihilation in an NVE ensemble, leading us to correctly estimate the elastic modulus by using the energy conservation law. Finally, we explore effects of defect annihilation in regions of nonuniform temperature within these coarse-grained molecular models which cannot be analysed by existing continuum level simulations. We find that +1/2 defects tend to move toward hotter areas and their change of speed in a temperature gradient can be quantitatively understood through a term derived from the temperature dependence of the elastic modulus. As such, our work has provided molecular insights into structures and dynamics of topological defects, presented unique and accessible methods to measure elastic constants by inspecting defects, and proposed an alternative control parameter of defects using temperature gradient.

Topological defect-mediated morphodynamics of active-active interfaces

Physical interfaces widely exist in nature and engineering. Although the formation of passive interfaces is well elucidated, the physical principles governing active interfaces remain largely unknown. Here, we combine simulation, theory, and cell-based experiment to investigate the evolution of an active-active interface. We adopt a biphasic framework of active nematic liquid crystals. We find that long-lived topological defects mechanically energized by activity display unanticipated dynamics nearby the interface, where defects perform "U-turns" to keep away from the interface, push the interface to develop local fingers, or penetrate the interface to enter the opposite phase, driving interfacial morphogenesis and cross-interface defect transport. We identify that the emergent interfacial morphodynamics stems from the instability of the interface and is further driven by the activity-dependent defect-interface interactions. Experiments of interacting multicellular monolayers with extensile and contractile differences in cell activity have confirmed our predictions. These findings reveal a crucial role of topological defects in active-active interfaces during, for example, boundary formation and tissue competition that underlie organogenesis and clinically relevant disorders.

Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity

Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices.

Competing instabilities reveal how to rationally design and control active crosslinked gels

How active stresses generated by molecular motors set the large-scale mechanics of the cell cytoskeleton remains poorly understood. Here, we combine experiments and theory to demonstrate how the emergent properties of a biomimetic active crosslinked gel depend on the properties of its microscopic constituents. We show that an extensile nematic elastomer exhibits two distinct activity-driven instabilities, spontaneously bending in-plane or buckling out-of-plane depending on its composition. Molecular motors play a dual antagonistic role, fluidizing or stiffening the gel depending on the ATP concentration. We demonstrate how active and elastic stresses are set by each component, providing estimates for the active gel theory parameters. Finally, activity and elasticity were manipulated in situ with light-activable motor proteins, controlling the direction of the instability optically. These results highlight how cytoskeletal stresses regulate the self-organization of living matter and set the foundations for the rational design and optogenetic control of active materials.

Biferroelectricity of a homochiral organic molecule in both solid crystal and liquid crystal phases

Ferroelectricity, existing in either solid crystals or liquid crystals, gained widespread attention from science and industry for over a century. However, ferroelectricity has never been observed in both solid and liquid crystal phases of a material simultaneously. Inorganic ferroelectrics that dominate the market do not have liquid crystal phases because of their completely rigid structure caused by intrinsic chemical bonds. We report a ferroelectric homochiral cholesterol derivative, β-sitosteryl 4-iodocinnamate, where both solid and liquid crystal phases can exhibit the behavior of polarization switching as determined by polarization–voltage hysteresis loops and piezoresponse force microscopy measurements. The unique long molecular chain, sterol structure, and homochirality of β-sitosteryl 4-iodocinnamate molecules enable the formation of polar crystal structures with point group 2 in solid crystal phases, and promote the layered and helical structure in the liquid crystal phase with vertical polarization. Our findings demonstrate a compound that can show the biferroelectricity in both solid and liquid crystal phases, which would inspire further exploration of the interplay between solid and liquid crystal ferroelectric phases.

Ferroelectricity normally exists in either solid crystals or liquid crystals. Here, the authors report a homochiral organic compound which shows ferroelectricity in both solid crystal and liquid crystal phases.

Dispersion of activity at an active-passive nematic interface

Efficient nutrient mixing is crucial for the survival of bacterial colonies and other living systems known as active nematics. However, the dynamics of this mixing is non-trivial as there is a coupling between nutrients concentration and velocity field. To address this question, we solve the hydrodynamic equation for active nematics to model the bacterial swarms coupled to an advection-diffusion equation for the activity field, which is proportional to the concentration of nutrients. At the interface between active and passive nematics the activity field is transported by the interfacial flows and in turn it modifies them through the generation of active stresses. We find that the dispersion of this conserved activity field is subdiffusive due to the emergence of a barrier of negative defects at the active-passive interface, which hinders the propagation of the motile positive defects.

Spontaneous organization and phase separation of skyrmions in chiral active matter

Skyrmions are topologically protected vortex-like excitations that hold promise for applications such as information processing and electron manipulation. Here we combine theoretical analysis and numerical simulations to show that skyrmions can spontaneously emerge in chiral active matter without external confinements or regulation. Strikingly, these activity-driven skyrmions can either self-organize into a periodic, stable square lattice consisting of half Néel skyrmions and antiskyrmions, where the in-plane flows display an antiferromagnetic vortex array, or undergo phase separation between skyrmions with different topological numbers. We identify that the emerging skyrmion dynamics stems from the competition between the chiral and polar coherence length scales dictated by the interplay of intrinsic chirality, polarity, and elasticity in the system. Our results reveal unanticipated topological excitations, self-organization, and phase separation in non-equilibrium systems and also suggest a potential way towards engineering complicated bespoke skyrmionic structures through manipulating active matter.

Active nematic gel with quenched disorder

With quenched disorder, we introduce two-dimensional active nematics suspended in an incompressible fluid. We write the coarse-grained hydrodynamic equations of motion for slow variables, viz. density, orientation, and flow fields. The quenched disorder is introduced such that it interacts with the local orientation at every point with some strength. Disorder strength is tuned from zero to large values. We numerically study the defect dynamics and system kinetics and find that the finite disorder slows the ordering. The presence of fluid induces large fluctuation in the orientation field, further disturbing the ordering. The large fluctuation in the orientation field due to the fluid is so dominant that it reduces the effect of the quenched disorder. We have also found that the disorder effect is almost the same for both the contractile and extensile nature of active stresses in the system. This study can help to understand the impact of quenched disorder on the ordering kinetics of active gels with nematic interaction among the constituent objects.

Thermodynamic Control of Activity Patterns in Cytoskeletal Networks

Biological materials, such as the actin cytoskeleton, exhibit remarkable structural adaptability to various external stimuli by consuming different amounts of energy. In this Letter, we use methods from large deviation theory to identify a thermodynamic control principle for structural transitions in a model cytoskeletal network. Specifically, we demonstrate that biasing the dynamics with respect to the work done by nonequilibrium components effectively renormalizes the interaction strength between such components, which can eventually result in a morphological transition. Our work demonstrates how a thermodynamic quantity can be used to renormalize effective interactions, which in turn can tune structure in a predictable manner, suggesting a thermodynamic principle for the control of cytoskeletal structure and dynamics.

Optimal transport and control of active drops

Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here, we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural "gather-move-spread" strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension and active controls generates richer behavior with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework and begins to pave the way for the spatiotemporal manipulation of active matter.

The fate of liquid crystal topological defects on chemically patterned surfaces during phase transitions

Controlling topological defects in liquid crystals (LCs) is an essential element in the development of areas such as directed self-assembly and micropatterning materials. However, during the phase transition on confined patterned surfaces, how the morphologies in one liquid crystalline phase change from deformations or defects into another phase is much less known. Here, we examine the fate of defects in a LC confined on a patterned surface during smectic-A-nematic and nematic-isotropic phase transitions, using experiments and simulation analyses. Upon heating from smectic-A to nematic, a Toric focal conical domain (TFCD) melts into a +1 converging boojum defect, which then transitioned into a concentric configuration as temperature increases, attributed to a steeper decrease of the bend and twist modulus compared to splay modulus. During cooling, TFCDs are developed from two distinct pathways depending on the cooling rates. Our continuum simulation recapitulates these transformations and provides elastic constant-based explanations for the two pathways. Although the phase transition pathways of defects are independent of the geometry of the confined patterns, the arrangement of FCDs is highly dependent on the size and shape of the patterns. Taken together, this simple approach offers promising opportunities for tuning the micro- or nano-patterning of topological defects in liquid crystals.

Activity gradients in two- and three-dimensional active nematics

We numerically investigate how spatial variations of extensile or contractile active stress affect bulk active nematic systems in two and three dimensions. In the absence of defects, activity gradients drive flows which re-orient the nematic director field and thus act as an effective anchoring force. At high activity, defects are created and the system transitions into active turbulence, a chaotic flow state characterized by strong vorticity. We find that in two-dimensional (2D) systems active torques robustly align +1/2 defects parallel to activity gradients, with defect heads pointing towards contractile regions. In three-dimensional (3D) active nematics disclination lines preferentially lie in the plane perpendicular to activity gradients due to active torques acting on line segments. The average orientation of the defect structures in the plane perpendicular to the line tangent depends on the defect type, where wedge-like +1/2 defects align parallel to activity gradients, while twist defects are aligned anti-parallel. Understanding the response of active nematic fluids to activity gradients is an important step towards applying physical theories to biology, where spatial variations of active stress impact morphogenetic processes in developing embryos and affect flows and deformations in growing cell aggregates, such as tumours.

Catapulting of topological defects through elasticity bands in active nematics

Active materials are those in which individual, uncoordinated local stresses drive the material out of equilibrium on a global scale. Examples of such assemblies can be seen across scales from schools of fish to the cellular cytoskeleton and underpin many important biological processes. Synthetic experiments that recapitulate the essential features of such active systems have been the object of study for decades as their simple rules allow us to elucidate the physical underpinnings of collective motion. One system of particular interest has been active nematic liquid crystals (LCs). Because of their well understood passive physics, LCs provide a rich platform to interrogate the effects of active stress. The flows and steady state structures that emerge in an active LCs have been understood to result from a competition between nematic elasticity and the local activity. However most investigations of such phenomena consider only the magnitude of the elastic resistance and not its peculiarities. Here we investigate a nematic liquid crystal and selectively change the ratio of the material's splay and bend elasticities. We show that increases in the nematic's bend elasticity specifically drives the material into an exotic steady state where elongated regions of acute bend distortion or "elasticity bands" dominate the structure and dynamics. We show that these bands strongly influence defect dynamics, including the rapid motion or "catapulting" along the disintegration of one of these bands thus converting bend distortion into defect transport. Thus, we report a novel dynamical state resultant from the competition between nematic elasticity and active stress.

Fabrication of Arrays of Topological Solitons in Patterned Chiral Liquid Crystals for Real-Time Observation of Morphogenesis

Topological solitons have knotted continuous field configurations embedded in a uniform background, and occur in cosmology, biology, and electromagnetism. However, real-time observation of their morphogenesis and dynamics is still challenging because their size and timescale are enormously large or tiny. Liquid crystal (LC) structures are promising candidates for a model-system to study the morphogenesis of topological solitons, enabling direct visualization due to the proper size and timescale. Here, a new way is found to rationalize the real-time observation of the generation and transformation of topological solitons using cholesteric LCs confined in patterned substrates. The experimental demonstration shows the topologically protected structures arise via the transformation of topological defects. Numerical modeling based on minimization of free energy closely reconstructs the experimental findings. The fundamental insights obtained from the direct observations pose new theoretical challenges in understanding the morphogenesis of different types of topological solitons within a broad range of scales.

Active depletion torque between two passive rods

The active depletion torque experienced by two anisotropic objects in an active bath is a conceptional generalization of the equilibrium entropic torque. Using Brownian dynamics simulations, we compute the active depletion torque suffered by two passive rods immersed in an ensemble of active Brownian particles. Our results demonstrate that the active depletion torque is qualitatively different from its passive counterpart. Interestingly, we find that the active depletion torque can be greatly affected by the external constraint applied on the rotational degree of freedom of the rods, and even the direction may be changed with the orientational constraint, which is in contrast to the equilibrium depletion torque. The main reason for the remarkable features of the active depletion torque is that the active particles can significantly accumulate in the vicinity of the rods due to persistent self-propulsion, which is sensitively dependent on the constraint strength and the rod configurations. Our findings could be relevant for understanding the self-assembly and dynamics of anisotropic macromolecules in living environments.

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.

Self-rotation regulates interface evolution in biphasic active matter through taming defect dynamics

Chirality can endow nonequilibrium active matter with unique features and functions. Here, we explore the chiral dynamics in biphasic active nematics composed of self-rotating units that continuously inject energy and angular momentum at the microscale. We show that the self-rotation of units can regularize the boundaries between two phases, rendering sinusoidal-like interfaces, which allow lateral wave propagation and are characterized by chains of ordered antiferromagnetic cross-interface flow vortices. Through the spontaneous coordination of counter-rotating units across the interfaces, topological defects excited by activity are sorted spatiotemporally, where positive defects are locally trapped at the interfaces but, unexpectedly, are transported laterally in a unidirectional rather than wavy mode, whereas inertial negative defects remain spinning in the bulks. Our findings reveal that individual chirality could be harnessed to modulate interfacial morphodynamics in active systems and suggest a potential approach toward controlling topological defects for programmable microfluidics and logic operations.

Vertical Alignment of Liquid Crystal on Sustainable 2,4-Di-tert-butylphenoxymethyl-Substituted Polystyrene Films

We synthesized sustainable 2,4-di-tert-butylphenoxymethyl-substituted polystyrenes (PDtBP#, # = 88, 68, 35, and 19, where # is molar percent contents of 2,4-di-tert-butylphenoxymethyl moiety), using post-polymerization modification reactions in order to study their liquid crystal (LC) alignment behaviors. In general, LC cells fabricated using polymer film with higher molar content of 2,4-di-tert-butylphenoxymethyl side groups showed vertical LC alignment behavior. LC alignment behavior in LC cell was related to the surface energy of the polymer alignment layer. For example, when the total surface energy value of the polymer layer was smaller than about 29.4 mJ/m2, vertical alignment behaviors were observed, generated by the nonpolar 2,4-di-tert-butylphenoxymethyl moiety with long and bulky carbon groups. Orientation stability was observed at 200 °C in the LC cells fabricated using PDtBP88 as the LC alignment layer. Therefore, as a natural compound modified polymer, PDtBP# can be used as a candidate LC alignment layer for environmentally friendly applications.

Logic operations with active topological defects

Logic operations performed by semiconductor-based transistors are the basis of modern computing. There is considerable interest in creating autonomous materials systems endowed with the capability to make decisions. In this work, we introduce the concept of using topological defects in active matter to perform logic operations. When an extensile active stress in a nematic liquid crystal is turned on, +1/2 defects can self-propel, in analogy to electron transport under a voltage gradient. By relying on hydrodynamic simulations of active nematics, we demonstrate that patterns of activity, when combined with surfaces imparting certain orientations, can be used to control the formation and transport of +1/2 defects. We further show that asymmetric high- and low-activity patterns can be used to create effective defect gates, tunnels, and amplifiers. The proposed active systems offer the potential to perform computations and transmit information in active soft materials, including actin-, tubulin-, and cell-based systems.

Capillary Flow Characterizations of Chiral Nematic Cellulose Nanocrystal Suspensions

Studying the flow-induced alignment of anisotropic liquid crystalline materials is of major importance in the 3D printing of advanced architectures. However, in situ characterization and quantitative measurements of local orientations during the 3D printing process are challenging. Here, we report a microfluidic strategy integrated with polarized optical microscopy (POM) to perform the in situ characterization of the alignment of cellulose nanocrystals (CNCs) under the shear-flow condition of the 3D printer's nozzle in the direct ink writing process. To quantify the alignment, we exploited birefringence measurements under white and monochromatic light. We show that the flow-induced birefringence patterns are significantly influenced by the initial structure of the aqueous CNC suspensions. Depending on the CNC concentration and sonication treatment, various structures can form in the CNC suspensions, such as isotropic, chiral nematic (cholesteric), and nematic (gel-like) structures. In the chiral nematic phase, in particular, the shear flow in the microfluidic capillary has a distinct effect on the alignment of the CNC particles. Our experimental results, complemented by hydrodynamic simulations, reveal that at high flow rates (Er ≈ 1000), individual CNC particles align with the flow exhibiting a weak chiral structure. In contrast, at lower flow rates (Er ≈ 241), they display the double-twisted cylinder structure. Understanding the flow effect on the alignment of the chiral liquid crystal can pave the way to designing 3D printed architectures with internal chirality for advanced mechanical and smart photonic applications.

Nano/Micromotors in Active Matter

Nano/micromotors (NMMs) are tiny objects capable of converting energy into mechanical motion. Recently, a wealth of active matter including synthetic colloids, cytoskeletons, bacteria, and cells have been used to construct NMMs. The self-sustained motion of active matter drives NMMs out of equilibrium, giving rise to rich dynamics and patterns. Alongside the spontaneous dynamics, external stimuli such as geometric confinements, light, magnetic field, and chemical potential are also harnessed to control the movements of NMMs, yielding new application paradigms of active matter. Here, we review the recent advances, both experimental and theoretical, in exploring biological NMMs. The unique dynamical features of collective NMMs are focused on, along with some possible applications of these intriguing systems.

Sorting Gold and Sand (Silica) Using Atomic Force Microscope-Based Dielectrophoresis

Additive manufacturing-also known as 3D printing-has attracted much attention in recent years as a powerful method for the simple and versatile fabrication of complicated three-dimensional structures. However, the current technology still exhibits a limitation in realizing the selective deposition and sorting of various materials contained in the same reservoir, which can contribute significantly to additive printing or manufacturing by enabling simultaneous sorting and deposition of different substances through a single nozzle. Here, we propose a dielectrophoresis (DEP)-based material-selective deposition and sorting technique using a pipette-based quartz tuning fork (QTF)-atomic force microscope (AFM) platform DEPQA and demonstrate multi-material sorting through a single nozzle in ambient conditions. We used Au and silica nanoparticles for sorting and obtained 95% accuracy for spatial separation, which confirmed the surface-enhanced Raman spectroscopy (SERS). To validate the scheme, we also performed a simulation for the system and found qualitative agreement with the experimental results. The method that combines DEP, pipette-based AFM, and SERS may widely expand the unique capabilities of 3D printing and nano-micro patterning for multi-material patterning, materials sorting, and diverse advanced applications.