Integrating chemistry, fluid flow, and mechanics to drive spontaneous formation of three-dimensional (3D) patterns in anchored microstructures.

Enzymatic reactions in solution drive the convection of confined fluids throughout the enclosing chambers and thereby couple the processes of reaction and convection. In these systems, the energy released from the chemical reactions generates a force, which propels the fluids' spontaneous motion. Here, we use theoretical and computational modeling to determine how reaction-convection can be harnessed to tailor and control the dynamic behavior of soft matter immersed in solution. Our model system encompasses an array of surface-anchored, flexible posts in a millimeter-sized, fluid-filled chamber. Selected posts are coated with enzymes, which react with dissolved chemicals to produce buoyancy-driven fluid flows. We show that these chemically generated flows exert a force on both the coated (active) and passive posts and thus produce regular, self-organized patterns. Due to the specificity of enzymatic reactions, the posts display controllable kaleidoscopic behavior where one regular pattern is smoothly morphed into another with the addition of certain reactants. These spatiotemporal patterns also form "fingerprints" that distinctly characterize the system, reflecting the type of enzymes used, placement of the enzyme-coated posts, height of the chamber, and bending modulus of the elastic posts. The results reveal how reaction-convection provides concepts for designing soft matter that readily switches among multiple morphologies. This behavior enables microfluidic devices to be spontaneously reconfigured for specific applications without construction of new chambers and the fabrication of standalone sensors that operate without extraneous power sources.

Achieving controllable and reversible snap-through in pre-strained strips of liquid crystalline elastomers.

Deformable, elastic materials that buckle in response to external stimuli can display "snap-through", which involves a transition between different, stable buckled states. Snap-through produces a quick release of stored potential energy, and thus can provide fast actuation for soft robots and other flexible devices. Liquid crystalline elastomers (LCEs) exposed to light undergo a phase transition and a concomitant mechanical deformation, allowing control of snap-through for rapid, large amplitude actuation. Using both a semi-analytical model and finite element simulations, we focus on a thin LCE strip that is clamped at both ends and buckles due to an initially imposed strain. We show that when this clamped, strained sample is exposed to light, it produces controllable snap-through behavior, which can be regulated by varying the light intensity and the area of the sample targeted by light. In particular, this snap-through can be triggered in different directions, allowing the system to be reset and triggered multiple times. Removing the light source will cause the system to settle into one of two stable states, enabling the encoding and storage of information in the system. We also highlight a specific case where removing the light source removes the induced buckling and returns the material to an initially flat state. In this case, the system can be reset and form a new shape, allowing it to function as a rewriteable haptic interface.

Self-Propelling Macroscale Sheets Powered by Enzyme Pumps.

Nanoscale enzymes anchored to surfaces act as chemical pumps by converting chemical energy released from enzymatic reactions into spontaneous fluid flow that propels entrained nano- and microparticles. Enzymatic pumps are biocompatible, highly selective, and display unique substrate specificity. Utilizing these pumps to trigger self-propelled motion on the macroscale has, however, constituted a significant challenge and thus prevented their adaptation in macroscopic fluidic devices and soft robotics. Using experiments and simulations, we herein show that enzymatic pumps can drive centimeter-scale polymer sheets along directed linear paths and rotational trajectories. In these studies, the sheets are confined to the air/water interface. With the addition of appropriate substrate, the asymmetric enzymatic coating on the sheets induces chemically driven, buoyancy flows that controllably propel the sheet's motion on the air/water interface. The directionality and speed of the motion can be tailored by changing the pattern of the enzymatic coating, type of enzyme, and nature and concentration of the substrate. This work highlights the utility of biocompatible enzymes for generating motion in macroscale fluidic devices and robotics and indicates their potential utility for in vivo applications.

Interlinking spatial dimensions and kinetic processes in dissipative materials to create synthetic systems with lifelike functionality.

Biological systems spontaneously convert energy input into the actions necessary to survive. Motivated by the efficacy of these processes, researchers aim to forge materials systems that exhibit the self-sustained and autonomous functionality found in nature. Success in this effort will require synthetic analogues of the following: a metabolism to generate energy, a vasculature to transport energy and materials, a nervous system to transmit 'commands', a musculoskeletal system to translate commands into physical action, regulatory networks to monitor the entire enterprise, and a mechanism to convert 'nutrients' into growing materials. Design rules must interconnect the material's structural and kinetic properties over ranges of length (that can vary from the nano- to mesoscale) and timescales to enable local energy dissipations to power global functionality. Moreover, by harnessing dynamic interactions intrinsic to the material, the system itself can perform the work needed for its own functionality. Here, we assess the advances and challenges in dissipative materials design and at the same time aim to spur developments in next-generation functional, 'living' materials.

Biomimetic growth in polymer gels.

By modeling gels growing in confined environments, we uncover a biomimetic feedback mechanism between the evolving gel and confining walls that enables significant control over the properties of the grown gel. Our new model describes the monomer adsorption, polymerization and cross-linking involved in forming new networks and the resultant morphology and mechanical behavior of the grown gel. Confined between two hard walls, a thin, flat "parent" gel undergoes buckling; removal of the walls returns the gel to the flat structure. Polymerization and cross-linking in the confined parent generates the next stage of growth, forming a random copolymer network (RCN). When the walls are removed, the RCN remains in the buckled state, simultaneously "locking in" these patterns and increasing the Young's modulus by two orders of magnitude. Confinement of thicker gels between harder or softer 3D walls leads to controllable mechanical heterogeneities, where the Young's modulus between specific domains can differ by three orders of magnitude. These systems effectively replicate the feedback between mechanics and morphology in biological growth, where mechanical forces guide the structure formation throughout stages of growth. The findings provide new guidelines for shaping "growing materials" and introducing new approaches to matching form and function in synthetic systems.

Engineering confined fluids to autonomously assemble hierarchical 3D structures.

The inherent coupling of chemical and mechanical behavior in fluid-filled microchambers enables the fluid to autonomously perform work, which in turn can direct the self-organization of objects immersed in the solution. Using theory and simulations, we show that the combination of diffusioosmotic and buoyancy mechanisms produce independently controlled, respective fluid flows: one generated by confining surfaces and the other in the bulk of the solution. With both flows present, the fluid can autonomously join 2D, disconnected pieces to a chemically active, "sticky" base and then fold the resulting layer into regular 3D shapes (e.g. pyramids, tetrahedrons, and cubes). Here, the fluid itself performs the work of construction and thus, this process does not require extensive external machinery. If several sticky bases are localized on the bottom surface, the process can be parallelized, with the fluid simultaneously forming multiple structures of the same or different geometries. Hence, this approach can facilitate the relatively low-cost, mass production of 3D micron to millimeter-sized structures. Formed in an aqueous solution, the assembled structures could be compatible with biological environments, and thus, potentially useful in medical and biochemical applications.

Strain-Stiffening Hydrogels with Dynamic, Secondary Cross-Linking.

Hydrogels are water-swollen, typically soft networks useful as biomaterials and in other fields of biotechnology. Hydrogel networks capable of sensing and responding to external perturbations, such as light, temperature, pH, or force, are useful across a wide range of applications requiring on-demand cross-linking or dynamic changes. Thus far, although mechanophores have been described as strain-sensitive reactive groups, embedding this type of force-responsiveness into hydrogels is unproven. Here, we synthesized multifunctional polymers that combine a hydrophilic zwitterion with permanently cross-linking alkenes, and dynamically cross-linking disulfides. From these polymers, we created hydrogels that contain irreversible and strong thiol-ene cross-links and reversible disulfide cross-links, and they stiffened in response to strain, increasing hundreds of kPa in modulus under compression. We examined variations in polymer composition and used a constitutive model to determine how to balance the number of thiol-ene vs disulfide cross-links to create maximally force-responsive networks. These strain-stiffening hydrogels represent potential biomaterials that benefit from the mechanoresponsive behavior needed for emerging applications in areas such as tissue engineering.

Chemically Driven Multimodal Locomotion of Active, Flexible Sheets.

The inhibitor-promoter feedback loop is a vital component in regulatory pathways that controls functionality in living systems. In this loop, the production of chemical A at one site promotes the production of chemical B at another site, but B inhibits the production of A. In solution, differences in the volumes of the reactants and products of this reaction can generate buoyancy-driven fluid flows, which will deform neighboring soft material. To probe the intrinsic interrelationship among chemistry, hydrodynamics, and fluid-structure interactions, we model a bio-inspired system where a flexible sheet immersed in solution encompasses two spatially separated catalytic patches, which drive the A-B inhibitor-promotor reaction. The convective rolls of fluid generated above the patches can circulate inward or outward depending on the chemical environment. Within the regime displaying chemical oscillations, the dynamic fluid-structure interactions morph the shape of the sheet to periodically "fly", "crawl", or "swim" along the bottom of the confining chamber, revealing an intimate coupling between form and function in this system. The oscillations in the sheet's motion in turn affect the chemical oscillations in the solution. In the regime with non-oscillatory chemistry, the induced flow still morphs the shape of the sheet, but now, the fluid simply translates the sheet along the length of the chamber. The findings reveal the potential for enzymatic reactions in the body to generate hydrodynamic behavior that modifies the shape of neighboring soft tissue, which in turn modifies both the fluid dynamics and the enzymatic reaction. The findings indicate that this non-linear dynamic behavior can be playing a critical role in the functioning of regulatory pathways in living systems.

Light-Powered, Fuel-Free Oscillation, Migration, and Reversible Manipulation of Multiple Cargo Types by Micromotor Swarms.

Through experiments and simulations, we show that fuel-free photoactive TiO2 microparticles can form mobile, coherent swarms in the presence of UV light, which track the subsequent movement of an irradiated spot in a fluid-filled microchamber. Multiple concurrent propulsion mechanisms (electrolyte diffusioosmotic swarming, photocatalytic expansion, and photothermal migration) control the rich collective behavior of the swarms, which provide a strategy to reversely manipulate cargo. The active swarms can autonomously pick up groups of inert particles, sort them by size, and sequentially release the sorted particles at particular locations in the microchamber. Hence, these swarms overcome three obstacles, limiting the utility of self-propelled particles. Namely, they can (1) undergo directed, long-range migration without the addition of a chemical fuel, (2) perform diverse collective behavior not possible with a single active particle, and (3) repeatedly and controllably isolate and deliver specific components of a multiparticle "cargo". Since light sources are easily fabricated, transported, and controlled, the results can facilitate the development of portable devices, providing broader access to the diagnostic and manufacturing advances enabled by microfluidics.

Control over emergence and alignment of transient blisters in thermo-responsive gels using hierarchically patterned substrates.

Surfaces with tunable microscale textures are vital in a large variety of technological applications, including heat transfer, antifouling and adhesion. To facilitate such broad-scale use, there is a need to create surfaces that undergo reconfigurable changes in topology and thus, enable switchable functionality. To date, there is a relative dearth of methods for engineering surfaces that can be actuated to change topography over a range of length scales, and hence, form tunable hierarchically structured layers. Combining modeling and experiments, we design a geometrically patterned, thermo-responsive poly (N-isopropylacrylamide) gel film that undergoes controllable hierarchical changes in topology with changes in temperature. At the bottom, the film is covalently bound to a solid, curved substrate; at the top, the film encompasses longitudinal rectangular ridges that are oriented perpendicular to the underlying cylindrical curves. At temperatures below lower critical solution temperature (LCST), the swollen gel exhibits 3D variations in polymer density and thickness defined by the gel's top and bottom topography. As the temperature rises above LCST, the interplay between the upper ridges and lower curves in the gel drives non-uniform, directional solvent transport, the nucleation and propagation of a phase-separated higher-density skin layer, and the resulting pressure buildup within the film. These different, interacting kinetic processes lead to an instability, which produces transient microscopic blisters in the film. Through simulations, we show how tuning the width of the ridges modifies the propagation of a skin layer and creates localized pressure build-up points, which enables control over the emergence, distribution, and alignment of the microscopic blisters. Additionally, we provide a simple argument to predict the size of such microscopic features. Experiments confirm our predictions and further highlight how our computational model enables the rational design of topographical transitions in these tunable films. The development of actuatable, hierarchically structured films provides new routes for achieving switchable functionality in actuators, drug release systems and adhesives.

Self-regulated non-reciprocal motions in single-material microstructures.

Living cilia stir, sweep and steer via swirling strokes of complex bending and twisting, paired with distinct reverse arcs1,2. Efforts to mimic such dynamics synthetically rely on multimaterial designs but face limits to programming arbitrary motions or diverse behaviours in one structure3-8. Here we show how diverse, complex, non-reciprocal, stroke-like trajectories emerge in a single-material system through self-regulation. When a micropost composed of photoresponsive liquid crystal elastomer with mesogens aligned oblique to the structure axis is exposed to a static light source, dynamic dances evolve as light initiates a travelling order-to-disorder transition front, transiently turning the structure into a complex evolving bimorph that twists and bends via multilevel opto-chemo-mechanical feedback. As captured by our theoretical model, the travelling front continuously reorients the molecular, geometric and illumination axes relative to each other, yielding pathways composed from series of twisting, bending, photophobic and phototropic motions. Guided by the model, here we choreograph a wide range of trajectories by tailoring parameters, including illumination angle, light intensity, molecular anisotropy, microstructure geometry, temperature and irradiation intervals and duration. We further show how this opto-chemo-mechanical self-regulation serves as a foundation for creating self-organizing deformation patterns in closely spaced microstructure arrays via light-mediated interpost communication, as well as complex motions of jointed microstructures, with broad implications for autonomous multimodal actuators in areas such as soft robotics7,9,10, biomedical devices11,12 and energy transduction materials13, and for fundamental understanding of self-regulated systems14,15.

Self-Generated Convective Flows Enhance the Rates of Chemical Reactions.

In chemical solutions, the products of catalytic reactions can occupy different volumes compared to the reactants and thus give rise to local density variations in the fluid. These density variations generate solutal buoyancy forces, which are exerted on the fluid and thus "pump" the fluid to flow. Herein, we examine if the reaction-induced pumping accelerates the chemical reaction by transporting the reactants to the catalyst at a rate faster than passive diffusion. Using both simulations and experiments, we show a significant increase in reaction rate when reaction-generated convective flow is present. In effect, through a feedback loop, catalysts speed up reactions not only by lowering the energy barrier but also by increasing the collision frequency between the reactants and the catalyst.

Solutal-buoyancy-driven intertwining and rotation of patterned elastic sheets.

The intertwining of strands into 3D spirals is ubiquitous in biology, enabling functions from information storage to maintenance of cell structure and directed locomotion. In synthetic systems, entwined fibers can provide superior mechanical properties and act as artificial muscle or structural reinforcements. Unlike structures in nature, the entwinement of synthetic materials typically requires application of an external stimulus, such as mechanical actuation, light, or a magnetic field. Herein, we use computational modeling to design microscale sheets that mimic biology by transducing chemical energy into mechanical action, and thereby self-organize and interlink into 3D spirals, which spontaneously rotate. These flexible sheets are immersed in a fluid-filled microchamber that encompasses an immobilized patch of catalysts on the bottom wall. The sheets themselves can be passive or active (coated with catalyst). Catalytic reactions in the solution generate products that occupy different volumes than the reactants. The resulting density variations exert a force on the fluid (solutal buoyancy force) that causes motion, which in turn drives the interlinking and collective swirling of the sheets. The individual sheets do not rotate; rotation only occurs when the sheets are interlinked. This level of autonomous, coordinated 3D structural organization, intertwining, and rotation is unexpected in synthetic materials systems operating without external controls. Using physical arguments, we identify dimensionless ratios that are useful in scaling these ideas to other systems. These findings are valuable for creating materials that act as "machines", and directing soft matter to undergo self-sustained, multistep assembly that is governed by intrinsic chemical reactions.

Dynamic behavior of chemically tunable mechano-responsive hydrogels.

Using theory and simulation, we model the mechanical behavior of gels that encompass loops and dangling chain ends. If the loops remain folded and dangling ends are chemically inert, then these topological features just serve as defects. If, however, the loops unfold to expose the hidden ("cryptic") binding sites and the ends of the dangling chains are reactive, these moieties can form bonds that improve the gel's mechanical properties. For gels with a lower critical solubility temperature (LCST), we systematically switch on the possible unfolding and binding events. To quantify the resulting effects, we derive equations for the gel's equilibrium and dynamic elastic moduli. We also use a finite element approach to simulate the gel's response to deformation and validate the analytic calculations. Herein, we show that the equilibrium moduli are highly sensitive to the presence of unfolding and binding transitions. The dynamical moduli are sensitive not only to these structural changes, but also to the frequency of deformation. For example, when reactive ends bind to exposed cryptic sites at T = 29 °C and relatively high frequency, the storage shear modulus is 119% greater than the corresponding equilibrium value, while the storage Young's modulus is 109% greater than at equilibrium. These findings provide guidelines for tuning the chemical reactivity of loops and dangling ends and the frequency of deformation to tailor the mechano-responsive behavior of polymer networks.

Resonant amplification of enzymatic chemical oscillations by oscillating flow.

Using theory and simulation, we analyzed the resonant amplification of chemical oscillations that occur due to externally imposed oscillatory fluid flows. The chemical reactions are promoted by two enzyme-coated patches located sequentially on the inner surface of a pipe that transports the enclosed chemical solution. In the case of diffusion-limited systems, the period of oscillations in chemical reaction networks is determined by the rate of the chemical transport, which is diffusive in nature and, therefore, can be effectively accelerated by the imposed fluid flows. We first identify the natural frequencies of the chemical oscillations in the unperturbed reaction-diffusion system and, then, use the frequencies as a forcing input to drive the system to resonance. We demonstrate that flow-induced resonance can be used to amplify the amplitude of the chemical oscillations and to synchronize their frequency to the external forcing. In particular, we show that even 10% perturbations in the flow velocities can double the amplitude of the resulting chemical oscillations. Particularly, effective control can be achieved for the two-step chemical reactions where during the first half-period, the fluid flow accelerates the chemical flux toward the second catalytic patch, while during the second half-period, the flow amplifies the flux to the first patch. The results can provide design rules for regulating the dynamics of coupled reaction-diffusion processes and can facilitate the development of chemical reaction networks that act as chemical clocks.

Using Dissipative Particle Dynamics to Model Effects of Chemical Reactions Occurring within Hydrogels.

Computational models that reveal the structural response of polymer gels to changing, dissolved reactive chemical species would provide useful information about dynamically evolving environments. However, it remains challenging to devise one computational approach that can capture all the interconnected chemical events and responsive structural changes involved in this multi-stage, multi-component process. Here, we augment the dissipative particle dynamics (DPD) method to simulate the reaction of a gel with diffusing, dissolved chemicals to form kinetically stable complexes, which in turn cause concentration-dependent deformation of the gel. Using this model, we also examine how the addition of new chemical stimuli and subsequent reactions cause the gel to exhibit additional concentration-dependent structural changes. Through these DPD simulations, we show that the gel forms multiple latent states (not just the "on/off") that indicate changes in the chemical composition of the fluidic environment. Hence, the gel can actuate a range of motion within the system, not just movements corresponding to the equilibrated swollen or collapsed states. Moreover, the system can be used as a sensor, since the structure of the layer effectively indicates the presence of chemical stimuli.

Controllable growth of interpenetrating or random copolymer networks.

Interpenetrating and random copolymer networks are vital in a number of industrial applications, including the fabrication of automotive parts, damping materials, and tissue engineering scaffolds. We develop a theoretical model for a process that enables the controlled growth of interpenetrating network (IPNs), or a random copolymer network (RCN) of specified size and mechanical properties. In this process, a primary gel "seed" is immersed into a solution containing the secondary monomer and crosslinkers. After the latter species are absorbed into the primary network, the absorbed monomers are polymerized to form the secondary polymer chains, which then can undergo further crosslinking to form an IPN, or undergo inter-chain exchange with the existing network to form a RCN. The swelling and elastic properties of the IPN and RCN networks can be tailored by modifying the monomer and crosslinker concentrations in the surrounding solution, or by tuning the enthalpic interactions between the primary polymer, secondary monomer and solvent through a proper choice of chemistry. This process can be used repeatedly to fabricate gels with a range of mechanical properties from stiff, rigid materials to soft, flexible networks, allowing the method to meet the materials requirements of a variety of applications.

Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution.

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to "pump" the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid-structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets' initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.

Achieving Independent Control over Surface and Bulk Fluid Flows in Microchambers.

To fully realize the potential of microfluidic platforms as useful diagnostic tools, the devices must be sufficiently portable that they function at the point-of-care, as well as remote and resource-poor locations. Using both modeling and experiments, here we develop a standalone fluidic device that is driven by light and operates without the need for external electrical or mechanical pumps. The light initiates a photochemical reaction in the solution; the release of chemical energy from the reaction is transduced into the spontaneous motion of the surrounding fluid. The generated flow is driven by two simultaneously occurring mechanisms: solutal buoyancy that controls the motion of the bulk fluid and diffusioosmosis that regulates motion near the bottom of the chamber. Consequently, the bulk and surface fluid flows can be directed independently of one another. We demonstrate that this exceptional degree of spatiotemporal control provides a new method for autonomously transporting different-sized particles in opposite directions within the chamber. Thus, one device can be used to both separate the particles and drive them to different locations for further processing or analysis. This property is particularly useful for analyzing fluids that contain multiple contaminants or disease agents. Because this system relies on intrinsic hydrodynamic interactions initiated by a portable, small-scale source of light, the device provides the desired level of mobility vital for the next generation of functional fluidic platforms.