A programmable environment for shape optimization and shapeshifting problems.

Soft materials underpin many domains of science and engineering, including soft robotics, structured fluids, and biological and particulate media. In response to applied mechanical, electromagnetic or chemical stimuli, such materials typically change shape, often dramatically. Predicting their structure is of great interest to facilitate design and mechanistic understanding, and can be cast as an optimization problem where a given energy function describing the physics of the material is minimized with respect to the shape of the domain and additional fields.

Jamming on convex deformable surfaces.

Jamming is a fundamental transition that governs the behavior of particulate media, including sand, foams and dense suspensions. Upon compression, such media change from freely flowing to a disordered, marginally stable solid that exhibits non-Hookean elasticity. While the jamming process is well established for fixed geometries, the nature and dynamics of jamming for a diverse class of soft materials and deformable substrates, including emulsions and biological matter, remains unknown.

An energy-optimization method to study gel-swelling in confinement.

We recast the problem of hydrogel swelling under physical constraints as an energy optimization problem. We apply this approach to compute equilibrium shapes of hydrogel spheres confined within a jammed matrix of rigid beads and interpret the results to determine how confinement modifies the mechanics of swollen hydrogels. In contrast to the unconfined case, we find a spatial separation of strains within the bulk of the hydrogel as the strain becomes localized to an outer region.

A phase diagram of morphologies for anisotropic particles sculpted from emulsions.

Hypothesis: A micron-scale oil-in-water emulsion droplet frozen in the presence of surfactants can be induced to eject the crystallizing solid from its liquid precursor. This dynamic process produces highly elongated solids whose shape depends critically on the rate of crystallization and the interfacial properties of the tri-phase system.

Experiment: By systematically varying the surfactant concentration and cooling protocol, including quenching from different temperatures as well as directly controlling the cooling rate, we map out the space of possible particle morphologies as a function of experimental control parameters.

Structural Landscapes in Geometrically Frustrated Smectics.

A phenomenological free energy model is proposed to describe the behavior of smectic liquid crystals, an intermediate phase that exhibits orientational order and layering at the molecular scale. Advantageous properties render the functional amenable to numerical simulation. The model is applied to a number of scenarios involving geometric frustration, leading to emergent structures such as focal conic domains and oily streaks and enabling detailed elucidation of the very rich energy landscapes that arise in these problems.

Elongation and percolation of defect motifs in anisotropic packing problems.

We examine the regime between crystalline and amorphous packings of anisotropic objects on surfaces of different genus by continuously varying their size distribution or shape from monodispersed spheres to bidispersed mixtures or monodispersed ellipsoidal particles; we also consider an anisotropic variant of the Thomson problem with a mixture of charges. With increasing anisotropy, we first observe the disruption of translational order with an intermediate orientationally ordered hexatic phase as proposed by Nelson, Rubinstein and Spaepen, and then a transition to amorphous state. By analyzing the structure of the disclination motifs induced, we show that the hexatic-amorphous transition is caused by the growth and connection of disclination grain boundaries, suggesting this transition lies in the percolation universality class in the scenarios considered.

Spontaneous Anchoring-Mediated Topography of an Orientable Fluid.

A topography in a Newtonian fluid occurs if there is a disturbance near the surface. But what if there is no such disturbance? We show by optical profilometry that a thin nematic film resting on a topological-defect-patterned substrate can exhibit a hill or divot at the opposing free (air) interface in the absence of a topological disturbance at that interface. We propose a model that incorporates several material properties and that predicts the major experimental features.

Crystal Comets: A Geometric Model for Sculpting Anisotropic Particles from Emulsions.

Microscopic high aspect ratio particles have many applications including enhanced delivery of active ingredients and food stability. Here, we develop a simple, scalable process that produces particles with a continuously controllable aspect ratio. Oil-in-water emulsion droplets are quenched and crystallize in the presence of surfactants that facilitate the ejection of the solid oil phase from its liquid precursor.

Aggregation in viscoelastic emulsion droplet gels with capillarity-driven rearrangements.

Arrested, or partial, coalescence of viscoelastic emulsion droplets can occur when elastic resistance to deformation offsets droplet surface area minimization. Arrest is a critical element of food and consumer product microstructure and performance, but direct studies of structural arrest and rearrangement have been carried out using only two or three droplets at a time. The question remains whether the behavior of small numbers of droplets also occurs in larger, more realistic many-droplet systems.

Geometry and kinetics determine the microstructure in arrested coalescence of Pickering emulsion droplets.

Arrested coalescence occurs in Pickering emulsions where colloidal particles adsorbed on the surface of the droplets become crowded and inhibit both relaxation of the droplet shape and further coalescence. The resulting droplets have a nonuniform distribution of curvature and, depending on the initial coverage, may incorporate a region with negative Gaussian curvature around the neck that bridges the two droplets. Here, we resolve the relative influence of the curvature and the kinetic process of arrest on the microstructure of the final state.

Programming emergent symmetries with saddle-splay elasticity.

The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid's internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddle-splay arrangements, characterised by the elastic constant [Formula: see text]. In most realisations, dominant surface anchoring treatments suppress such deformations, rendering [Formula: see text] immeasurable.

Large Hexosomes from Emulsion Droplets: Particle Shape and Mesostructure Control.

Soft, rotationally symmetric particles of dispersed hexagonal liquid crystalline phase are produced using a method previously developed for cubosome microparticle production. The technique forms hexosome particles via removal of ethanol from emulsion droplets containing monoolein, water, and one of the various hydrophobic molecules: vitamin E, hexadecane, oleic acid, cyclohexane, or divinylbenzene. The unique rotational symmetry of the particles is characterized by optical microscopy and small-angle X-ray scattering to link particle phase, shape, and structure to composition.

Arrested Coalescence of Viscoelastic Droplets: Ellipsoid Shape Effects and Reorientation.

The stable configurations formed by two poroelastic, ellipsoid-shaped droplets during their arrested coalescence have been investigated using micromanipulation experiments. Ellipsoidal droplets are produced by millifluidic emulsification of petrolatum into a yield stress fluid that preserves their elongated shape. The liquid meniscus between droplets can transmit stress and instigate movement of the droplets, from their initial relative position, in order to minimize doublet surface energy.

Modeling deformation and chaining of flexible shells in a nematic solvent with finite elements on an adaptive moving mesh.

A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations.

Defect structure and percolation in the packing of bidispersed particles on a sphere.

We study packings of bidispersed spherical particles on a spherical surface. The presence of curvature necessitates defects even for monodispersed particles; bidispersity either leads to a more disordered packing for nearly equal radii, or a higher fill fraction when the smaller particles are accommodated in the interstices of the larger spheres. Variation in the packing fraction is explained by a percolation transition, as chains of defects or scars previously discovered in the monodispersed case grow and eventually disconnect the neighbor graph.

Arrested coalescence of viscoelastic droplets: triplet shape and restructuring.

The stability of shapes formed by three viscoelastic droplets during their arrested coalescence has been investigated using micromanipulation experiments. Addition of a third droplet to arrested droplet doublets is shown to be controlled by the balance between interfacial pressures driving coalescence and internal elasticity that resists total consolidation. The free fluid available within the droplets controls the transmission of stress during droplet combination and allows connections to occur via formation of a neck between the droplets.

Competition of lattice and basis for alignment of nematic liquid crystals.

Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here we consider how such alignment can be achieved using a periodic square lattice of circular or elliptical motifs. In particular, we examine ways in which the lattice and motif can combine to favor differing orientations.

The role of curvature anisotropy in the ordering of spheres on an ellipsoid.

Non-spherical emulsion droplets can be stabilized by densely packed colloidal particles adsorbed at their surface. In order to understand the microstructure of these surface packings, the ordering of hard spheres on ellipsoidal surfaces is determined through large scale computer simulations. Defects in the packing are shown generically to occur most often in regions of strong curvature; however, the relationship between defects and curvature is nontrivial, and the distribution of defects shows secondary maxima for ellipsoids of sufficiently high aspect ratio.

Simulating defect textures on relaxing nematic shells.

Two nematic shells brought in contact coalesce in order to reduce their combined interfacial tension, and, following this topological transition, relax to an equilibrium state. In this work, we study the defect textures as the combined shell shape evolves. By varying the sizes of the shells, we perform a quasistatic investigation of the director field and the defect valence on the doublet.

Semi-automatic quantification of neurite fasciculation in high-density neurite images by the neurite directional distribution analysis (NDDA).

Background: Bundling of neurite extensions occur during nerve development and regeneration. Understanding the factors that drive neurite bundling is important for designing biomaterials for nerve regeneration toward the innervation target and preventing nociceptive collateral sprouting. High-density neuron cultures including dorsal root ganglia explants are employed for in vitro screening of biomaterials designed to control directional outgrowth.

Neuronal growth as diffusion in an effective potential.

Current understanding of neuronal growth is mostly qualitative, as the staggering number of physical and chemical guidance cues involved prohibit a fully quantitative description of axonal dynamics. We report on a general approach that describes axonal growth in vitro, on poly-D-lysine-coated glass substrates, as diffusion in an effective external potential, representing the collective contribution of all causal influences on the growth cone. We use this approach to obtain effective growth rules that reveal an emergent regulatory mechanism for axonal pathfinding on these substrates.

Direct measurement of surface-induced orientational order parameter profile above the nematic-isotropic phase transition temperature.

The spatial and temperature dependence of the surface-induced orientational order parameter S(z,T) was determined in the isotropic phase. An optical fiber was immersed in a thin liquid crystal layer and the retardation was measured as a function of the fiber's height above the surface, from which the model-independent S(z,T) was deduced with resolution View Article and Find Full Text PDF

Polar-horizontal versus polar-vertical reverse-tilt-domain walls: influence of a pretilt angle below the nematic-isotropic phase transition.

On cooling through the isotropic-to-nematic phase transition in a cell whose substrates induce a large pretilt angle theta0 from the vertical direction, but with no preferential azimuthal orientation, tilt domains appear. The boundary walls between reverse tilt domains are found to be bendlike and twistlike when theta0(T=TNI) is sufficiently large just below the isotropic-nematic phase transition temperature TNI--i.e.

Diverging elasticity and director uniformation in a nanopatterned cell near the nematic-smectic-A phase transition.

The stylus of an atomic force microscope is used to scribe herringbone patterns of various wavelengths into a polyimide-coated substrate. The patterns serve as a template for alignment of the liquid crystal octyloxycyanobiphenyl and impose a bend distortion in the liquid crystal in the vicinity of the herringbone apexes. The pretransitional behavior of the liquid crystal is observed by polarized microscopy as it is cooled through the nematic-smectic- A phase transition, facilitating direct visualization of the extrapolation length, which is related to the trade-off between elastic and anchoring forces.