Optimal wrapping of liquid droplets with ultrathin sheets

Flower-shaped 2D crystals grown in curved fluid vesicle membranes

The morphologies of two-dimensional (2D) crystals, nucleated, grown, and integrated within 2D elastic fluids, for instance in giant vesicle membranes, are dictated by an interplay of mechanics, permeability, and thermal contraction. Mitigation of solid strain drives the formation of crystals with vanishing Gaussian curvature (i.e., developable domain shapes) and, correspondingly, enhanced Gaussian curvature in the surrounding 2D fluid. However, upon cooling to grow the crystals, large vesicles sustain greater inflation and tension because their small area-to-volume ratio slows water permeation. As a result, more elaborate shapes, for instance, flowers with bendable but inextensible petals, form on large vesicles despite their more gradual curvature, while small vesicles harbor compact planar crystals. This size dependence runs counter to the known cumulative growth of strain energy of 2D colloidal crystals on rigid spherical templates. This interplay of intra-membrane mechanics and processing points to the scalable production of flexible molecular crystals of controllable complex shape.

Shaping a Soft Future: Patterning Liquid Metals

This review highlights the unique techniques for patterning liquid metals containing gallium (e.g., eutectic gallium indium, EGaIn). These techniques are enabled by two unique attributes of these liquids relative to solid metals: 1) The fluidity of the metal allows it to be injected, sprayed, and generally dispensed. 2) The solid native oxide shell allows the metal to adhere to surfaces and be shaped in ways that would normally be prohibited due to surface tension. The ability to shape liquid metals into non-spherical structures such as wires, antennas, and electrodes can enable fluidic metallic conductors for stretchable electronics, soft robotics, e-skins, and wearables. The key properties of these metals with a focus on methods to pattern liquid metals into soft or stretchable devices are summari.

Tensional twist-folding of sheets into multilayered scrolled yarns

Twisting sheets as a strategy to form functional yarns relies on millennia of human practice in making catguts and fabric wearables, but it still lacks overarching principles to guide their intricate architectures. We show that twisted hyperelastic sheets form multilayered self-scrolled yarns, through recursive folding and twist localization, that can be reconfigured and redeployed. We combine weakly nonlinear elasticity and origami to explain the observed ordered progression beyond the realm of perturbative models. Incorporating dominant stretching modes with folding kinematics, we explain the measured torque and energetics originating from geometric nonlinearities due to large displacements. Complementarily, we show that the resulting structures can be algorithmically generated using Schläfli symbols for star-shaped polygons. A geometric model is then introduced to explain the formation and structure of self-scrolled yarns. Our tensional twist-folding framework shows that origami can be harnessed to understand the transformation of stretchable sheets into self-assembled architectures with a simple twist.

Crystal capillary origami capsule with self-assembled nanostructures

The self-assembling mechanism of elasto-capillaries opens new applications in micro and nanotechnology by providing 3D assembly structures with 2D planar unit cells, so-called capillary origami. To date, the final structure has been designed based on the predetermined shape and size of the unit cell. Here, we show that plate-like salt crystallites grow and cover the emulsion interface, which is driven by Laplace pressure. Eventually, it creates a spherical capsule with self-assembled nanostructures. The capsule and the crystallite are investigated by scanning electron microscopy and X-ray diffraction analysis. To explain the mechanism, we develop a theoretical model to estimate the capsule size, the shell thickness, and the conditions necessary to form the shell based on a thin-walled pressure vessel. The proposed crystal capillary origami can fabricate a three-dimensional self-assembled salt capsule without any complicated procedures. We believe that it can offer a new physicochemical avenue for the spontaneous and facile fabrication of water-soluble carrier particles.

Sculpting Liquids with Ultrathin Shells

Thin elastic films can spontaneously attach to liquid interfaces, offering a platform for tailoring their physical, chemical, and optical properties. Current understanding of the elastocapillarity of thin films is based primarily on studies of planar sheets. We show that curved shells can be used to manipulate interfaces in qualitatively different ways. We elucidate a regime where an ultrathin shell with vanishing bending rigidity imposes its own rest shape on a liquid surface, using experiment and theory. Conceptually, the pressure across the interface "inflates" the shell into its original shape. The setup is amenable to optical applications as the shell is transparent, free of wrinkles, and may be manufactured over a range of curvatures.

Capillary-Force-Driven Self-Assembly of 4D-Printed Microstructures

Capillary-force-driven self-assembly is emerging as a significant approach for the massive manufacture of advanced materials with novel wetting, adhesion, optical, mechanical, or electrical properties. However, academic value and practical applications of the self-assembly are greatly restricted because traditional micropillar self-assembly is always unidirectional. In this work, two-photon-lithography-based 4D microprinting is introduced to realize the reversible and bidirectional self-assembly of microstructures. With asymmetric crosslinking densities, the printed vertical microstructures can switch to a curved state with controlled thickness, curvature, and smooth morphology that are impossible to replicate by traditional 3D-printing technology. In different evaporating solvents, the 4D-printed microstructures can experience three states: (I) coalesce into clusters from original vertical states via traditional self-assembly, (II) remain curved, or (III) arbitrarily self-assemble (4D self-assembly) toward the curving directions. Compared to conventional approaches, this 4D self-assembly is distance-independent, which can generate varieties of assemblies with a yield as high as 100%. More importantly, the three states can be reversibly switched, allowing the development of many promising applications such as reversible micropatterns, switchable wetting, and dynamic actuation of microrobots, origami, and encapsulation.

Computational and Experimental Approaches to Controlling Bacterial Microcompartment Assembly

Bacterial microcompartments compartmentalize the enzymes that aid chemical and energy production in many bacterial species. They are postulated to help bacteria survive in hostile environments. Metabolic engineers are interested in repurposing these organelles for non-native functions. Here, we use computational, theoretical, and experimental approaches to determine mechanisms that effectively control microcompartment self-assembly. We find, via multiscale modeling and mutagenesis studies, the interactions responsible for the binding of hexamer-forming proteins in a model system, the propanediol utilization bacterial microcompartments from Salmonella enterica serovar Typhimurium LT2. We determine how the changes in the microcompartment hexamer protein preferred angles and interaction strengths can modify the assembled morphologies. We demonstrate that such altered strengths and angles are achieved via amino acid mutations. A thermodynamic model provides guidelines to design microcompartments of various morphologies. These findings yield insight in controlled protein assembly and provide principles for assembling microcompartments for biochemical or energy applications as nanoreactors.

Wetting and wrapping of a floating droplet by a thin elastic filament

We study the wetting of a thin elastic filament floating on a fluid surface by a droplet of another, immiscible fluid. This quasi-2D experimental system is the lower-dimensional counterpart of the wetting and wrapping of a droplet by an elastic sheet. The simplicity of this system allows us to study the phenomenology of partial wetting and wrapping of the droplet by measuring angles of contact as a function of the elasticity of the filament, the applied tension and the curvature of the droplet. We find that a purely geometric theory gives a good description of the mechanical equilibria in the system. The estimates of applied tension and tension in the filament obey an elastic version of the Young-Laplace-Dupré relation. However, curvatures close to the contact line are not captured by the geometric theory, possibly because of 3D effects at the contact line. We also find that when a highly-bendable filament completely wraps the droplet, there is continuity of curvature at the droplet-filament interface, leading to seamless wrapping as observed in a 3D droplet.

Clay nanolayer encapsulation, evolving from origins of life to future technologies

Clays are the siblings of graphite and graphene/graphene-oxide. There are two basic ways of using clays for encapsulation of sub-micron entities such as molecules, droplets, or nanoparticles, which is either by encapsulation in the interlayer space of clay nanolayered stacked particles ("the graphite way"), or by using exfoliated clay nanolayers to wrap entities in packages ("the graphene way"). Clays maybe the prerequisites for life on earth and can also be linked to the natural formation of other two-dimensional materials such as naturally occurring graphite and its allotropes. Here we discuss state-of-the-art in the area of clay-based encapsulation and point to some future scientific directions and technological possibilities that could emerge from research in this area.

Geometry underlies the mechanical stiffening and softening of an indented floating film

A basic paradigm underlying the Hookean mechanics of amorphous, isotropic solids is that small deformations are proportional to the magnitude of external forces. However, slender bodies may undergo large deformations even under minute forces, leading to nonlinear responses rooted in purely geometric effects. Here we study the indentation of a polymer film on a liquid bath. Our experiments and simulations support a recently-predicted stiffening response [D. Vella and B. Davidovitch, Phys. Rev. E, 2018, 98, 013003], and we show that the system softens at large slopes, in agreement with our theory that addresses small and large deflections. We show how stiffening and softening emanate from nontrivial yet generic features of the stress and displacement fields.

3D Self-Assembled Microelectronic Devices: Concepts, Materials, Applications

Modern microelectronic systems and their components are essentially 3D devices that have become smaller and lighter in order to improve performance and reduce costs. To maintain this trend, novel materials and technologies are required that provide more structural freedom in 3D over conventional microelectronics, as well as easier parallel fabrication routes while maintaining compatability with existing manufacturing methods. Self-assembly of initially planar membranes into complex 3D architectures offers a wealth of opportunities to accommodate thin-film microelectronic functionalities in devices and systems possessing improved performance and higher integration density. Existing work in this field, with a focus on components constructed from 3D self-assembly, is reviewed, and an outlook on their application potential in tomorrow's microelectronics world is provided.

Elastocapillary adhesion of a soft cap on a rigid sphere

We study the capillary adhesion of a spherical elastic cap on a rigid sphere of a different radius. Caps of small area accommodate the combination of flexural and in-plane strains induced by the mismatch in curvature, and fully adhere to the sphere. Conversely, wider caps delaminate and exhibit only partial contact. We determine the maximum size of the cap enabling full adhesion and describe its dependence on experimental parameters through a balance of stretching and adhesion energies. Beyond the maximum size, complex adhesion patterns such as blisters, bubbles or star shapes are observed. We rationalize these different states in configuration diagrams where stretching, bending and adhesion energies are compared through two dimensionless parameters.

Capillary Origami with Atomically Thin Membranes

Small-scale optical and mechanical components and machines require control over three-dimensional structure at the microscale. Inspired by the analogy between paper and two-dimensional materials, origami-style folding of atomically thin materials offers a promising approach for making microscale structures from the thinnest possible sheets. In this Letter, we show that a monolayer of molybdenum disulfide (MoS₂) can be folded into three-dimensional shapes by a technique called capillary origami, in which the surface tension of a droplet drives the folding of a thin sheet. We define shape nets by patterning rigid metal panels connected by MoS₂ hinges, allowing us to fold micron-scale polyhedrons. Finally, we demonstrate that these shapes can be folded in parallel without the use of micropipettes or microfluidics by means of a microemulsion of droplets that dissolves into the bulk solution to drive folding. These results demonstrate controllable folding of the thinnest possible materials using capillary origami and indicate a route forward for design and parallel fabrication of more complex three-dimensional micron-scale structures and machines.

Programming curvilinear paths of flat inflatables

Inflatable structures offer a path for light deployable structures in medicine, architecture, and aerospace. In this study, we address the challenge of programming the shape of thin sheets of high-stretching modulus cut and sealed along their edges. Internal pressure induces the inflation of the structure into a deployed shape that maximizes its volume. We focus on the shape and nonlinear mechanics of inflated rings and more generally, of any sealed curvilinear path. We rationalize the stress state of the sheet and infer the counterintuitive increase of curvature observed on inflation. In addition to the change of curvature, wrinkles patterns are observed in the region under compression in agreement with our minimal model. We finally develop a simple numerical tool to solve the inverse problem of programming any 2-dimensional (2D) curve on inflation and illustrate the application potential by moving an object along an intricate target path with a simple pressure input.

Surface Chemistry Enhancements for the Tunable Super-Liquid Repellency of Low-Surface-Tension Liquids

Super-hydrophobic, super-oleo(amphi)phobic, and super-omniphobic materials are universally important in the fields of science and engineering. Despite rapid advancements, gaps of understanding still exist between each distinctive wetting state. The transition of super-hydrophobicity to super-(oleo-, amphi-, and omni-)phobicity typically requires the use of re-entrant features. Today, re-entrant geometry induced super-(amphi- and omni-)phobicity is well-supported by both experiments and theory. However, owing to geometrical complexities, the concept of re-entrant geometry forms a dogma that limits the industrial progress of these unique states of wettability. Moreover, a key fundamental question remains unanswered: are extreme surface chemistry enhancements able to influence super-liquid repellency? Here, this was rigorously tested via an alternative pathway that does not require explicit designer re-entrant features. Highly controllable and tunable vertical network polymerization and functionalization were used to achieve fluoroalkyl densification on nanoparticles. For the first time, relative fluoro-functionalization densities are quantitatively tuned and correlated to super-liquid repellency performance. Step-wise tunable super-amphiphobic nanoparticle films with a Cassie-Baxter state (contact angle of >150° and sliding angle of <10°) against various liquids is demonstrated. This was tested down to very low surface tension liquids to a minimum of ca. 23.8 mN/m. Such findings could eventually lead to the future development of super-(amphi)omniphobic materials that transcend the sole use of re-entrant geometry.

Buckling of geometrically confined shells

We study the periodic buckling patterns that emerge when elastic shells are subjected to geometric confinement. Residual swelling provides access to range of shapes (saddles, rolled sheets, cylinders, and spherical sections) which vary in their extrinsic and intrinsic curvatures. Our experimental and numerical data show that when these moderately thick structures are radially confined, a single geometric parameter - the ratio of the total shell radius to the amount of unconstrained material - predicts the number of lobes formed. We present a model that interprets this scaling as the competition between radial and circumferential bending. Next, we show that reducing the transverse confinement of saddles causes the lobe number to decrease with a similar scaling analysis. Hence, one geometric parameter captures the wave number through a wide range of radial and transverse confinement, connecting the shell shape to the shape of the boundary that confines it. We expect these results to be relevant for an expanse of shell shapes, and thus applicable to the design of shape-shifting materials and the swelling and growth of soft structures.

Conforming nanoparticle sheets to surfaces with Gaussian curvature

Nanoparticle monolayer sheets are ultrathin inorganic-organic hybrid materials that combine highly controllable optical and electrical properties with mechanical flexibility and remarkable strength. Like other thin sheets, their low bending rigidity allows them to easily roll into or conform to cylindrical geometries. Nanoparticle monolayers not only can bend, but also cope with strain through local particle rearrangement and plastic deformation. This means that, unlike thin sheets such as paper or graphene, nanoparticle sheets can much more easily conform to surfaces with complex topography characterized by non-zero Gaussian curvature, like spherical caps or saddles. Here, we investigate the limits of nanoparticle monolayers' ability to conform to substrates with Gaussian curvature by stamping nanoparticle sheets onto lattices of larger polystyrene spheres. Tuning the local Gaussian curvature by increasing the size of the substrate spheres, we find that the stamped sheet morphology evolves through three characteristic stages: from full substrate coverage, where the sheet extends over the interstices in the lattice, to coverage in the form of caps that conform tightly to the top portion of each sphere and fracture at larger polar angles, to caps that exhibit radial folds. Through analysis of the nanoparticle positions, obtained from scanning electron micrographs, we extract the local strain tensor and track the onset of strain-induced dislocations in the particle arrangement. By considering the interplay of energies for elastic and plastic deformations and adhesion, we construct arguments that capture the observed changes in sheet morphology as Gaussian curvature is tuned over two orders of magnitude.

Microscopic details of a fluid/thin film triple line

In recent years, there has been a considerable interest in the mechanics of soft objects meeting fluid interfaces (elasto-capillary interactions). In this work we experimentally examine the case of a fluid resting on a thin film of rigid material which, in turn, is resting on a fluid substrate. To simplify complexity, we adapt the experiment to a one-dimensional contact geometry and examine the behaviour of polystyrene and polycarbonate films directly with confocal microscopy. We find that the fluid meets the film in a manner consistent with the Young-Dupré equation when the film is thick, but transitions to what appears similar to a Neumann-like balance when the thickness is decreased. However, on closer investigation we find that the true contact angle is always given by the Young construction. The apparent paradox is a result of macroscopically measured angles not being directly related to true microscopic contact angles when curvature is present. We model the effect with an Euler-Bernoulli beam on a Winkler foundation as well as with an equivalent energy-based capillary model. Notably, the models highlight several important lengthscales and the complex interplay of tension, gravity, and bending in the problem.

Cylinder morphology of a stretched and twisted ribbon

A rich zoology of morphologies emerges from a simple stretched and twisted elastic ribbon. Despite a lot of interest, all the observed shapes are not quantitatively described. This is the case of the cylindrical shape that prevails at large tension and twist, which emerges from a transverse buckling instability of the helicoid. Here, we propose a simple description of this cylindrical shape. By comparing its energy to the energy of other configurations, helicoidal and facetted, we are able to determine its location on the tension-twist phase diagram. The theoretical predictions are in good quantitative agreement with the experimental results and complement previous results from linear stability analysis.

Partial wetting of thin solid sheets under tension

We consider the equilibrium of liquid droplets sitting on thin elastic sheets that are subject to a boundary tension and/or are clamped at their edge. We use scaling arguments, together with a detailed analysis based on the Föppl-von-Kármán equations, to show that the presence of the droplet may significantly alter the stress locally if the tension in the dry sheet is weak compared to an intrinsic elasto-capillary tension scale γ2/3(Et)1/3 (with γ the droplet surface tension, t the sheet thickness and E its Young modulus). Our detailed analysis suggests that some recent experiments may lie in just such a "non-perturbative" regime. As a result, measurements of the tension in the sheet at the contact line (inferred from the contact angles of the sheet with the liquid-vapour interface) do not necessarily reflect the true tension within the sheet prior to wetting. We discuss various characteristics of this non-perturbative regime.

Liquid Letters

Using the interfacial jamming of cellulose nanocrystal (CNC) surfactants, a new concept, termed all-liquid molding, is introduced to produce all-liquid objects that retain the shape and details of the mold with high fidelity, yet remain all liquid and are responsive to external stimuli. This simple process, where the viscosity of the CNC dispersion can range from that of water to a crosslinked gel, opens tremendous opportunities for encapsulation, delivery systems, and unique microfluidic devices. The process described is generally applicable to any functionalized nanoparticles dispersed in one liquid and polymer ligands having complementary functionality dissolved in a second immiscible liquid. Such sculpted liquids retain all the characteristics of the liquids but retain shape indefinitely, very much like a solid, and provide a new platform for next-generation soft materials.

Nanocomposite capsules with directional, pulsed nanoparticle release

The precise spatiotemporal delivery of nanoparticles from polymeric capsules is required for applications ranging from medicine to materials science. These capsules derive key performance aspects from their overall shape and dimensions, porosity, and internal microstructure. To this effect, microfluidics provide an exceptional platform for emulsification and subsequent capsule formation. However, facile and robust approaches for nanocomposite capsule fabrication, exhibiting triggered nanoparticle release, remain elusive because of the complex coupling of polymer-nanoparticle phase behavior, diffusion, phase inversion, and directional solidification. We investigate a model system of polyelectrolyte sodium poly(styrene sulfonate) and 22-nm colloidal silica and demonstrate a robust capsule morphology diagram, achieving a range of internal morphologies, including nucleated and bicontinuous microstructures, as well as isotropic and non-isotropic external shapes. Upon dissolution in water, we find that capsules formed with either neat polymers or neat nanoparticles dissolve rapidly and isotropically, whereas bicontinuous, hierarchical, composite capsules dissolve via directional pulses of nanoparticle clusters without disrupting the scaffold, with time scales tunable from seconds to hours. The versatility, facile assembly, and response of these nanocomposite capsules thus show great promise in precision delivery.

3D Printing by Multiphase Silicone/Water Capillary Inks

3D printing of polymers is accomplished easily with thermoplastics as the extruded hot melt solidifies rapidly during the printing process. Printing with liquid polymer precursors is more challenging due to their longer curing times. One curable liquid polymer of specific interest is polydimethylsiloxane (PDMS). This study demonstrates a new efficient technique for 3D printing with PDMS by using a capillary suspension ink containing PDMS in the form of both precured microbeads and uncured liquid precursor, dispersed in water as continuous medium. The PDMS microbeads are held together in thixotropic granular paste by capillary attraction induced by the liquid precursor. These capillary suspensions possess high storage moduli and yield stresses that are needed for direct ink writing. They could be 3D printed and cured both in air and under water. The resulting PDMS structures are remarkably elastic, flexible, and extensible. As the ink is made of porous, biocompatible silicone that can be printed directly inside aqueous medium, it can be used in 3D printed biomedical products, or in applications such as direct printing of bioscaffolds on live tissue. This study demonstrates a number of examples using the high softness, elasticity, and resilience of these 3D printed structures.

Liquid droplets on a free-standing glassy membrane: Deformation through the glass transition

In this study, micro-droplets are placed on thin, glassy, free-standing films where the Laplace pressure of the droplet deforms the free-standing film, creating a bulge. The film's tension is modulated by changing temperature continuously from well below the glass transition into the melt state of the film. The contact angle of the liquid droplet with the planar film as well as the angle of the bulge with the film are measured and found to be consistent with the contact angles predicted by a force balance at the contact line.

Reversible Shape Transformation of Ultrathin Polydopamine-Stabilized Droplet

Here we report on the flattening of water droplets using an ultrathin membrane of autopolymerized polydopamine at the air/water interface. This has only been previously reported with the use of synthetic or extracted peptides, two-dimensional designed synthetic peptide thin films with thicknesses of several tens of nanometers. However, in the previous study, the shape of the water droplet was changed irreversibly and the phenomenon was observed only at the air/water interface. In the present study, an ultrathin polydopamine membrane-stabilized droplet induced the flattening of a water droplet at the air/liquid and liquid/liquid interfaces because a polydopamine membrane was spontaneously formed at these interfaces. Furthermore, a reversible transformation of the droplet to flat and dome shape droplets were discovered at the liquid/liquid interface. These are a completely new system because the polydopamine membrane is dynamically synthesized at the interface and the formation speed of the polydopamine membrane overcomes the flattening time scale. These results will provide new insight into physical control of the interfacial shapes of droplets.

Mechanics of a granular skin

Magic sand, a hydrophobic toy granular material, is widely used in popular science instructions because of its nonintuitive mechanical properties. A detailed study of the failure of an underwater column of magic sand shows that these properties can be traced to a single phenomenon: the system self-generates a cohesive skin that encapsulates the material inside. The skin, consisting of pinned air-water-grain interfaces, shows multiscale mechanical properties: they range from contact-line dynamics in the intragrain roughness scale, to plastic flow at the grain scale, all the way to sample-scale mechanical responses. With decreasing rigidity of the skin, the failure mode transforms from brittle to ductile (both of which are collective in nature) to a complete disintegration at the single-grain scale.

Geometry-Driven Folding of a Floating Annular Sheet

Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where an annular polymer sheet floating on an air-water interface is subjected to different tensions on the inner and outer rims. The sheet folds and wrinkles into many distinct morphologies that break axisymmetry. These states can be understood within a recent geometric approach for determining the gross shape of extremely bendable yet inextensible sheets by extremizing an appropriate area functional. Our analysis explains the remarkable feature that the observed buckling transitions between wrinkled and folded shapes are insensitive to the bending rigidity of the sheet.

From Cylindrical to Stretching Ridges and Wrinkles in Twisted Ribbons

Twisted ribbons under tension exhibit a remarkably rich morphology, from smooth and wrinkled helicoids, to cylindrical or faceted patterns. This complexity emanates from the instability of the natural, helicoidal symmetry of the system, which generates both longitudinal and transverse stresses, thereby leading to buckling of the ribbon. Here, we focus on the tessellation patterns made of triangular facets. Our experimental observations are described within an "asymptotic isometry" approach that brings together geometry and elasticity. The geometry consists of parametrized families of surfaces, isometric to the undeformed ribbon in the singular limit of vanishing thickness and tensile load. The energy, whose minimization selects the favored structure among those families, is governed by the tensile work and bending cost of the pattern. This framework describes the coexistence lines in a morphological phase diagram, and determines the domain of existence of faceted structures.

Capillary Origami Inspired Fabrication of Complex 3D Hydrogel Constructs

Hydrogels have found broad applications in various engineering and biomedical fields, where the shape and size of hydrogels can profoundly influence their functions. Although numerous methods have been developed to tailor 3D hydrogel structures, it is still challenging to fabricate complex 3D hydrogel constructs. Inspired by the capillary origami phenomenon where surface tension of a droplet on an elastic membrane can induce spontaneous folding of the membrane into 3D structures along with droplet evaporation, a facile strategy is established for the fabrication of complex 3D hydrogel constructs with programmable shapes and sizes by crosslinking hydrogels during the folding process. A mathematical model is further proposed to predict the temporal structure evolution of the folded 3D hydrogel constructs. Using this model, precise control is achieved over the 3D shapes (e.g., pyramid, pentahedron, and cube) and sizes (ranging from hundreds of micrometers to millimeters) through tuning membrane shape, dimensionless parameter of the process (elastocapillary number Ce ), and evaporation time. This work would be favorable to multiple areas, such as flexible electronics, tissue regeneration, and drug delivery.

Elastic membranes in confinement

An elastic membrane stretched between two walls takes a shape defined by its length and the volume of fluid it encloses. Many biological structures, such as cells, mitochondria and coiled DNA, have fine internal structure in which a membrane (or elastic member) is geometrically 'confined' by another object. Here, the two-dimensional shape of an elastic membrane in a 'confining' box is studied by introducing a repulsive confinement pressure that prevents the membrane from intersecting the wall. The stage is set by contrasting confined and unconfined solutions. Continuation methods are then used to compute response diagrams, from which we identify the particular membrane mechanics that generate mitochondria-like shapes. Large confinement pressures yield complex response diagrams with secondary bifurcations and multiple turning points where modal identities may change. Regions in parameter space where such behaviour occurs are then mapped.

Mimosa Origami: A nanostructure-enabled directional self-organization regime of materials

One of the innate fundamentals of living systems is their ability to respond toward distinct stimuli by various self-organization behaviors. Despite extensive progress, the engineering of spontaneous motion in man-made inorganic materials still lacks the directionality and scale observed in nature. We report the directional self-organization of soft materials into three-dimensional geometries by the rapid propagation of a folding stimulus along a predetermined path. We engineer a unique Janus bilayer architecture with superior chemical and mechanical properties that enables the efficient transformation of surface energy into directional kinetic and elastic energies. This Janus bilayer can respond to pinpoint water stimuli by a rapid, several-centimeters-long self-assembly that is reminiscent of the Mimosa pudica's leaflet folding. The Janus bilayers also shuttle water at flow rates up to two orders of magnitude higher than traditional wicking-based devices, reaching velocities of 8 cm/s and flow rates of 4.7 μl/s. This self-organization regime enables the ease of fabricating curved, bent, and split flexible channels with lengths greater than 10 cm, demonstrating immense potential for microfluidics, biosensors, and water purification applications.

Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets

Wrinkle patterns in compressed thin sheets are ubiquitous in nature and technology, from the furrows on our foreheads to crinkly plant leaves, from ripples on plastic-wrapped objects to the protein film on milk. The current understanding of an elementary descriptor of wrinkles--their wavelength--is restricted to deformations that are parallel, spatially uniform, and nearly planar. However, most naturally occurring wrinkles do not satisfy these stipulations. Here we present a scheme that quantitatively explains the wrinkle wavelength beyond such idealized situations. We propose a local law that incorporates both mechanical and geometrical effects on the spatial variation of wrinkle wavelength. Our experiments on thin polymer films provide strong evidence for its validity. Understanding how wavelength depends on the properties of the sheet and the underlying liquid or elastic subphase is crucial for applications where wrinkles are used to sculpt surface topography, to measure properties of the sheet, or to infer forces applied to a film.