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. Here we propose a new scenario, metric jamming, where rigidification occurs on a surface that has been deformed from its ground state. Unlike classical jamming processes that exhibit discrete mechanical transitions, surprisingly we find that metric jammed states possess mechanical properties continuously tunable between those of classically jammed and conventional elastic media. The compact and curved geometry significantly alters the vibrational spectra of the structures relative to jamming in flat Euclidean space, and metric jammed systems also possess new types of vibrational mode that couple particle and shape degrees of freedom. Our work provides a theoretical framework that unifies our understanding of solidification processes that take place on deformable media and lays the groundwork to exploit jamming for the control and stabilization of shape in self-assembly processes.
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. We also explore the contact mechanics of the gel, finding a transition from Hertzian behavior to non-Hertzian behavior as a function of swelling. Our model, implemented in the Morpho shape optimization environment and validated against an experimentally demonstrated prototypical scenario, can be applied in any dimension, readily adapted to diverse swelling scenarios and extended to use other energies in conjunction.
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.
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.
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. This work demonstrates the importance of, in particular, anisotropic surface interactions in the creation of a free-surface topography.
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. Tuning the ejection and crystallization rates to be comparable, by adjusting the surfactant concentration and quench depth, promotes anisotropic particle growth by continuously ejecting solidified oil from the precursor droplet as the crystallization proceeds. We predict the accessible morphologies using an analytical geometric model that indicates a nonconstant contact angle during the crystallization process. We see that the crystal aspect ratio is dependent on the surfactant concentration, which can be explained as a variation of the maximum growth angle achieved during crystallization.
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. Here we study two-dimensional aggregation and arrested coalescence of emulsions containing â¼1000 droplets and find that the restructuring mechanisms observed for smaller systems have a large effect on local packing in multidroplet aggregates, but surprisingly do not significantly alter overall mass scaling in the aggregates. Specifically, increased regions of hexagonal packing are observed as the droplet solids level, and thus elasticity, is decreased because greater degrees of capillary force-driven restructuring are possible. Diffusion-limited droplet aggregation simulations that account for the restructuring mechanisms agree with the experimental results and suggest a basis for prediction of larger-scale network properties and bulk emulsion behavior.
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. Here we identify regimes where more subtle, patterned surfaces enable saddle-splay effects to be both observed and exploited. Utilising theory and continuum calculations, we determine experimental regimes where generic, achiral liquid crystals exhibit spontaneously broken surface symmetries. These provide a new route to measuring [Formula: see text]. We further demonstrate a multistable device in which weak, but directional, fields switch between saddle-splay-motivated, spontaneously-polar surface states. Generalising beyond simple confinement, our highly scalable approach offers exciting opportunities for low-field, fast-switching optoelectronic devices which go beyond current technologies.
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. In the quasistatic case, defects are induced and distributed to screen the Gaussian curvature. Conversely, if the rate of area change per particle exceeds the diffusion constant of the particles, the evolving surface induces local solidification reminiscent of jamming fronts observed in other colloidal systems. In this regime, the final structure is shown to be strongly affected by the compressive history just prior to arrest, which can be predicted from the extrinsic geometry of the sequence of surfaces in contrast to the intrinsic geometry that governs the static regime.
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. Rheology of the soft particles can be varied independently of shape, enabling control of transport, deformation, and biological response by controlling composition and molecular structure of the additives. The direct observations of formation, and the resultant hexosome shapes, link the particle-scale and mesoscale properties of these novel self-assembled particles and broaden their applications. The micron-scale hexosomes provide a route to understanding the effects of particle size, crystallization rate, and rheology on the production of soft particles with liquid crystalline structure and unique shape and symmetry.
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. The action of the liquid meniscus causes the ellipsoidal droplets to undergo rolling and reorientation events because of their unique ellipsoid shape and associated variation in the surface curvature. The final configuration of the droplets is controlled by the balance between interfacial Laplace pressure and internal elasticity, as well as a constraint force that resists complete minimization of surface energy. Geometric and surface energy calculations are used to map the possible and most likely configurations of the droplet pairs. Experimental deviations from the calculations indicate the magnitude and potential origin of the constraint force resisting full equilibration. Droplet aspect ratio and elasticity are both shown to influence the degree of reorientation and stability of the droplets at energy extrema. Higher aspect ratios drive greater reorientation and better agreement with final doublet configurations predicted by energy minimization. Lower elasticity droplets undergo secondary deformations at high aspect ratios, further broadening the space of possible morphologies.
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. From this model, we determine the influence of the shell elasticity, nematic elasticity, and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multibody interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments.
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.
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. The anisotropy of three-droplet systems adds complexity to the symmetric case of two-droplet aggregates because of the multiplicity of orientations possible for the third droplet. When elasticity dominates, the initial orientation of the third droplet is preserved in the triplet's final shape. When elasticity is dominated by the interfacial driving force, the final shape can deviate strongly from the initial positioning of droplets. Movement of the third droplet to a more compact packing occurs, driven by liquid meniscus expansion that minimizes the surface energy of the triplet. A range of compositions and orientations are examined and the resulting domains of restructuring and stability are mapped based on the final triplet structure. A geometric and a physical model are used to explain the mechanism driving meniscus-induced restructuring and are related to the impact of these phenomena on multiple droplet emulsions.
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. Using Monte Carlo simulation and continuum elasticity we find, for circular motifs, that the coverage fraction controls both the polar anchoring angle and a transition in the azimuthal orientation. If the circles are generalized to ellipses, arbitrary control of the effective easy axis and effective anchoring potential becomes achievable by appropriate tuning of the ellipse motif relative to the periodic lattice patterning. This has possible applications in both monostable and bistable liquid crystal device contexts.
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. As with packings on spherical surfaces, additional defects beyond those required by topology are observed as chains or "scars". The transition point, however, is found to be softened by the anisotropic curvature which also partially orients the scars. A rich library of symmetric commensurate packings are identified for low particle number. We verify experimentally that ellipsoidal droplets of varying aspect ratio can be arrested by surface-adsorbed colloids.
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. Regimes are found where positive and negative defects exist due to the large negative Gaussian curvature at the neck. Using large-scale computer simulations, we determine how annihilating defect pairs on coalescing shells are selected and the stage of coalescence at which annihilation occurs.
Computer Simulation , Liquid Crystals , Models, Theoretical , Monte Carlo Method
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. Although some semi-automated image processing methods exist for quantification of neurite outgrowth, methods to quantify axonal fasciculation in terms of direction of neurite outgrowth are lacking. NEW METHOD: This work presents a semi-automated program to analyze micrographs of high-density neurites; the program aims to quantify axonal fasciculation by determining the orientational distribution function of the tangent vectors of the neurites and calculating its Fourier series coefficients ('c' values). RESULTS: We found that neurite directional distribution analysis (NDDA) of fasciculated neurites yielded 'c' values of ≥â¼0.25 whereas branched outgrowth led to statistically significant lesser values of <â¼0.2. The 'c' values correlated directly to the width of neurite bundles and indirectly to the number of branching points. COMPARISON WITH EXISTING METHODS: Information about the directional distribution of outgrowth is lost in simple counting methods or achieved laboriously through manual analysis. The NDDA supplements previous quantitative analyses of axonal bundling using a vector-based approach that captures new information about the directionality of outgrowth. CONCLUSION: The NDDA is a valuable addition to open source image processing tools available to biomedical researchers offering a robust, precise approach to quantification of imaged features important in tissue development, disease, and repair.
Image Processing, Computer-Assisted/methods , Neurites/physiology , Neurons/cytology , Analysis of Variance , Animals , Cell Polarity/physiology , Cells, Cultured , Chick Embryo , Ganglia, Spinal/cytology , In Vitro Techniques , Optical Imaging , Tubulin/metabolism
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.
Axons/metabolism , Models, Neurological , Animals , Cerebral Cortex/cytology , Kinetics , Rats
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
