We perform numerical simulations to study self-assembly of nanoparticles mediated by an elastic planar surface. We show how the nontrivial elastic response to deformations of these surfaces leads to anisotropic interactions between the particles resulting in aggregates having different geometrical features. The morphology of the patterns can be controlled by the mechanical properties of the surface and the strength of the particle adhesion. We use simple scaling arguments to understand the formation of the different structures, and we show how the adhering particles can cause the underlying elastic substrate to wrinkle if two of its opposite edges are clamped. Finally, we discuss the implications of our results and suggest how elastic surfaces could be used in nanofabrication.
Emulsions comprising isotropic fluid drops within a nematic host are of interest for applications ranging from biodetection to smart windows, which rely on changes of molecular alignment structures around the drops in response to chemical, thermal, electric and other stimuli. We show that absorption or desorption of trace amounts of common surfactants can drive continuous transformations of elastic multipoles induced by the droplets within the uniformly aligned nematic host. Out-of-equilibrium dynamics of director structures emerge from a controlled self-assembly or desorption of different sur…
Monopole-like electrostatic interactions are ubiquitous in biology and condensed matter, but they are often screened by counter-ions and cannot be switched from attractive to repulsive. In colloidal science, where the prime goal is to develop colloidal particles that mimic and exceed the diversity and length-scales of atomic and molecular assembly, electrostatically charged particles cannot change the sign of their surface charge or transform from monopoles to higher-order multipoles. In liquid-crystal colloids, elastic interactions between particles arise to minimize the free energy associate…
Active assembly and non-reciprocal dynamics of elastic membranes
The Martin Fisher School of Physics, Brandeis University（布兰迪斯大学马丁·费舍尔物理学院）；Department of Physics, University of California at Santa Barbara（加州大学圣塔芭芭拉分校物理系）；School of Physics, Georgia Institute of Technology（佐治亚理工学院物理学院）；Kavli Institute of Theoretical Physics（卡弗里理论物理研究所）；Leinweber Institute for Theoretical Physics, University of Chicago（芝加哥大学莱因韦伯理论物理研究所）；James Frank Institute, University of Chicago（芝加哥大学詹姆斯·弗兰克研究所）
Elastic sheets with macroscopic dimensions are easy to deform by bending and stretching. Yet shaping nanometric sheets by mechanical manipulation is hard. Here we show that nanoparticle self-assembly could be used to this end. We demonstrate by Monte Carlo simulation that spherical nanoparticles adhering to the outer surface of an elastic nanotube can self-assemble into linear structures as a result of curvature-mediated interactions. We find that nanoparticles arrange into rings or helices on stretchable nanotubes, and as axial strings on nanotubes with high rigidity to stretching. These self…
Self-assembly of colloidal particles is poised to become a powerful composite material fabrication technique, but remains challenged by a limited control over the ensuing structures. We develop a new breed of nematic colloids that are physical analogs of a mathematical surface with boundary, interacting with the molecular alignment field without inducing defects when flat. However, made from a thin nanofoil, they can be shaped to prompt formation of self-compensating defects that drive pre-programmed elastic interactions mediated by the nematic host. To show this, we wrap the nanofoil on all t…
A rigid cylinder placed on a soft gel deforms its surface. When multiple cylinders are placed on the surface, they interact with each other via the topography of the deformed gel which serves as an energy landscape; as they move, the landscape changes which in turn changes their interaction. We use a combination of experiments, simple scaling estimates and numerical simulations to study the self-assembly of cylinders in this elastic analog of the Cheerios effect for capillary interactions on a fluid interface. Our results show that the effective two body interaction can be well described by an…
Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterize their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positio…
We use numerical simulations to show how noninteracting hard particles binding to a deformable elastic shell may self-assemble into a variety of linear patterns. This is a result of the nontrivial elastic response to deformations of shells. The morphology of the patterns can be controlled by the mechanical properties of the surface, and can be fine-tuned by varying the binding energy of the particles. We also repeat our calculations for a fully flexible chain and find that the chain conformations follow patterns similar to those formed by the nanoparticles under analogous conditions. We propos…
We explore micropatterned director structures of aqueous lyotropic chromonic liquid crystal (LCLC) films created on square lattice cylindrical-micropost substrates. The structures are manipulated by modulating the LCLC mesophases and their elastic properties via concentration through drying. Nematic LCLC films exhibit preferred bistable alignment along the diagonals of the micropost lattice. Columnar LCLC films, dried from nematics, form two distinct director and defect configurations: a diagonally aligned director pattern with local squares of defects, and an off-diagonal configuration with z…
We demonstrate a novel route of spatially organizing the colloid arrangements on the polymer-grafted substrate by use of self-consistent field and density functional theories. We find that grafting of polymers onto a substrate can effectively control spatial dispersions of deposited colloids as a result of the balance between colloidal settling force and entropically elastic force of brushes, and colloids can form unexpected ordered structures on a grafting substrate. The depositing process of colloidal particles onto the elastic "soft" substrate includes two steps: brush-mediated one-dimensio…
Hydrogels are widespread soft materials, which can serve a wide range of applications. The control over the viscoelastic properties of the gel is of paramount importance. Ongoing environmental issues have raised the consumer's concern towards the use of more sustainable materials, including hydrogels. However, are greener materials compatible with high functionality? In a safe-by-design approach, this work demonstrates that functional hydrogels with in situ responsivity of their elastic properties by external stimuli can be developed from entirely ``sustainable'' components, a biobased amphiph…
Spherical microparticles dispersed in nematic liquid crystals have been extensively investigated in the past years. Here, we report experimental studies on the elastic deformation, colloidal interaction and self-assembly of hematite microcubes with homeotropic surface anchoring in a nematic liquid crystal. We demonstrate that the colloidal interaction and self-assembly of cubic colloids are orientation dependent. In a notable departure from the conventional microspheres, the microcubes stabilise diverse structures, such as bent chains, branches, kinks and closed-loops. The microcubes reorient …
We study mutual alignment and interactions between colloidal particles of dissimilar shapes and dimensions when dispersed in a nematic host fluid. Convex pentagonal and concave starfruit-shaped nanoprisms and microspheres induce dipolar or quadrupolar director structures. The ensuing elastic pair interactions between microspheres and nanoprisms are highly dependent on the nanoparticle shape being omnidirectionally attractive for convex prisms but strongly anisotropic for concave prisms. Elastic deformations due to spherical particles cause well-defined alignment of complex-shaped nanoparticles…
Spherical neodymium-iron-boron magnets are perman-ent magnets that can be assembled into a variety of structures due to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings, and chiral cylinders of magnets. Based on energy estimates and simple experiments, we introduce an effective magnetic bending stiffness for a chain of magnets and show that, used in conjunction with classic resul…
The surprising recent discoveries of quasicrystals and their approximants in soft matter systems poses the intriguing possibility that these structures can be realized in a broad range of nano- and micro-scale assemblies. It has been theorized that soft matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remains elusive. Here, we use computer simulation and free energy calculations to demonstrate a simple design heuristic for assembling quasicrystals and approximants in soft matter systems. Our study builds on pr…
Triply-periodic networks are among the most complex and functionally valuable self-assembled morphologies, yet they form in nearly every class of biological and synthetic soft matter building blocks. In contrast to simpler assembly motifs -- spheres, cylinders, layers -- TPN assemblies require molecules to occupy variable local domain shapes, confounding attempts to understand their formation. Here, we examine the double-gyroid (DG) network phase of block copolymer (BCP) melts, a prototypical soft self-assembly system, by using a geometric formulation of the strong stretching theory (SST) of B…
A mesoscopic coarse-grain model for computationally-efficient simulations of biomembranes is presented. It combines molecular dynamics simulations for the lipids, modeled as elastic chains of beads, with multiparticle collision dynamics for the solvent. Self-assembly of a membrane from a uniform mixture of lipids is observed. Simulations at different temperatures demonstrate that it reproduces the gel and liquid phases of lipid bilayers. Investigations of lipid diffusion in different phases reveals a crossover from subdiffusion to normal diffusion at long times. Macroscopic membrane properties…
Soft materials can self-assemble into highly structured phases which replicate at the mesoscopic scale the symmetry of atomic crystals. As such, they offer an unparalleled platform to design mesostructured materials for light and sound. Here, we present a bottom-up approach based on self-assembly to engineer three-dimensional photonic and phononic crystals with topologically protected Weyl points. In addition to angular and frequency selectivity of their bulk optical response, Weyl materials are endowed with topological surface states, which allows for the existence of one-way channels even in…
We study the interaction of small hydrophobic particles on the surface of an ultra-soft elastic gel, in which a small amount of elasticity of the medium balances the weights of the particles. The excess energy of the surface of the deformed gel causes them to attract as is the case with the generic capillary interactions of particles on a liquid surface. The variation of the gravitational potential energies of the particles resulting from their descents in the gel coupled with the superposition principle of Nicolson allow a fair estimation of the distance dependent attractive energy of the par…
We model the spontaneous assembly of a capsid (a virus's closed outer shell) from many copies of identical units, using entirely irreversible steps and only information local to the growing edge. Our model is formulated in terms of (i) an elastic Hamiltonian with stretching and bending stiffness and a spontaneous curvature, and (ii) a set of rate constants for addition of new units or bonds. An ensemble of highly irregular capsids is generated, unlike the well-known icosahedrally symmetric viruses, but (we argue) plausible as a way to model the irregular capsids of retroviruses such as HIV. We…
Self-assembly of colloidal particles due to elastic interactions in nematic liquid crystals promises tunable composite materials and can be guided by exploiting surface functionalization, geometric shape and topology, though these means of controlling self-assembly remain limited. Here, we realize low-symmetry achiral and chiral elastic colloids in the nematic liquid crystals using colloidal polygonal concave and convex prisms. We show that the controlled pinning of disclinations at the prisms edges alters the symmetry of director distortions around the prisms and their orientation with respec…
Microbullet particles, cylinders with one blunt and one spherical end, offer a novel platform to study the effects of anisotropy and curvature on colloidal assembly in complex fluids. Here, we disperse microbullets in 4-cyano-4'-pentylbiphenyl (5CB) nematic liquid crystal (NLC) cells and form oriented elastic dipoles with a nematic point defect located near the curved end. This feature allows us to study particle interactions as a function of dipole alignment. By careful control of the surface anchoring at the particle surface and the confining boundaries, we study the interactions and assembl…
Colloidal particles at complex fluid interfaces and within films assemble to form ordered structures with high degrees of symmetry via interactions that include capillarity, elasticity, and other fields like electrostatic charge. Here we study microparticle interactions within free-standing smectic-A films, in which the elasticity arising from the director field distortion and capillary interactions arising from interface deformation compete to direct the assembly of motile particles. New colloidal assemblies and patterns, ranging from 1D chains to 2D aggregates, sensitive to the initial wetti…
Many biological and synthetic materials self-assemble into helical or twisted aggregates. The shape is determined by a complex interplay between elastic forces and the orientation and chirality of the constituent molecules. We study this interplay through Monte Carlo simulations, with an accelerated algorithm motivated by the growth of an aggregate out of solution. The simulations show that the curvature changes smoothly from cylindrical to saddle-like as the elastic moduli are varied. Remarkably, aggregates of either handedness form from molecules of a single handedness, depending on the mole…
Crystallography may be the gold standard of protein structure determination, but obtaining the necessary high-quality crystals is also in some ways akin to prospecting for the precious metal. The tools and models developed in soft matter physics to understand colloidal assembly offer some insights into the problem of crystallizing proteins. This topical review describes the various analogies that have been made between proteins and colloids in that context. We highlight the explanatory power of patchy particle models, but also the challenges of providing guidance for crystallizing specific pro…
A lattice model with soft repulsion followed by attraction is developed for a monolayer of hybrid core-shell particles self-assembling at an interface. The model is solved exactly in one dimension. One, two or three periodic structures and variety of shapes of the pressure-density isotherms may occur in different versions of the model. For strong interactions the isotherm consists of vertical segments separated by plateaus. The range of order depends strongly on the strength of attraction and on the density. Our results agree with experimental observations.
The self assembly of core-corona discs interacting via anisotropic potentials is investigated using Monte Carlo computer simulations. A minimal interaction potential that incorporates anisotropy in a simple way is introduced. It consists in a core-corona architecture in which the center of the core is shifted with respect to the center of the corona. Anisotropy can thus be tuned by progressively shifting the position of the core. Despite its simplicity, the system self organize in a rich variety of structures including stripes, triangular and rectangular lattices, and unusual plastic crystals.…
Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellisation, emulsion formation, and polymer mixing principles are well understood. However, the principles behind emergence of structures with competing length scales in soft matter systems remain an open question. Examples include the droplet-inside-droplet assembly in many biomacromolecular systems undergoing liquid-liquid phase separation, analogous multiple emulsion formation in oil-surfactant-water formulations, and polymer core-shell particles with internal struc…
Soft particles are known to overlap and form stable clusters that self-assemble into periodic crystalline phases with density-independent lattice constants. We use molecular dynamics simulations in two dimensions to demonstrate that, through a judicious design of an isotropic pair potential, one can control the ordering of the clusters and generate a variety of phases, including decagonal and dodecagonal quasicrystals. Our results confirm analytical predictions based on a mean-field approximation, providing insight into the stabilization of quasicrystals in soft macromolecular systems, and sug…
We present a simple method for accessing the elastic properties of microscopic deformable particles. This method is based on measuring the pressure-induced deformation of soft particles as they are forced through a tapered glass microcapillary. It allows us to determine both the compressive and the shear modulus of a deformable object in one single experiment. Measurements on a model system of poly-acrylamide microgel particles exhibit excellent agreement with measurements on bulk gels of identical composition. Our approach is applicable over a wide range of mechanical properties and should th…
Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a longstanding question in the field of granular matter. Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation …
The relationship between interactions, flexibility and disorder in proteins has been explored from many angles: folding upon binding, flexibility of the core relative to the periphery, entropy changes, etc. In this work, we provide statistical evidence for the involvement of highly mobile and disordered regions in complex assembly. We ordered the entire set of X-ray crystallographic structures in the PDB into hierarchies of progressive interactions involving identical or very similar protein chains, yielding 40205 hierarchies of complexes with increasing numbers of partners. We then examine th…
We study colloidal particles in a nematic-liquid-crystal-filled microfluidic channel and show how elastic interactions between the particle and the channel wall lead to different particle dynamics compared with conventional microfluidics. For a static particle, in the absence of a flow field, the director orientation on the particle surface undergoes a rapid transition from uniform to homeotropic anchoring as a function of the anchoring strength and the particle size. In the presence of a flow field, in addition to fluid viscous stresses on the particle, nematic-induced elastic stresses are ex…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control such assemblies remain poorly understood, nevertheless. Using classical density functional theory we demonstrate how the intrinsic length scales and their interplay in terms of interspecies molecular interactions can be used to tune soft matter self-assembly. We apply our strategy to two different soft binary mixtures to create guidelines for tuning intermol…
We demonstrate scaffolding of plasmonic nanoparticles by topological defects induced by colloidal microspheres to match their surface boundary conditions with a uniform far-field alignment in a liquid crystal host. Displacing energetically costly liquid crystal regions of reduced order, anisotropic nanoparticles with concave or convex shapes not only stably localize in defects but also self-orient with respect to the microsphere surface. Using laser tweezers, we manipulate the ensuing nanoparticle-microsphere colloidal dimers, probing the strength of elastic binding and demonstrating self-asse…
Self-assembly is one of the crucial mechanisms allowing to design multifunctional materials. Soft hybrid materials contain components of different nature and exhibit competitive interactions which drive self-organisation into structures of a particular function. Here we demonstrate a novel type of a magnetic hybrid material where the molecular tilt can be manipulated through a delicate balance between the topologically-assisted colloidal self-assembly of \rev{magnetic nanoparticles} and the anisotropic molecular interactions in a liquid crystal matrix.
Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacrylamide hydrogel particles introduced in a spinning drop tensiometer. We determine the equilibrium shapes of the beads from the competition between the centrifugal force and the restoring elastic and surface forces. Considering the beads as neo-Hookean up to large deformations, we show that their elastic modulus and surface energy constant can be simultaneously deduced from their equilibrium shape. A…
We propose a model for the elastic properties of RNA gels. The model predicts anomalous elastic properties in the form of a negative Poisson ratio and shape instabilities. The anomalous elasticity is generated by the non-Gaussian force-deformation relation of single-stranded RNA. The effect is greatly magnified by broken rotational symmetry produced by double-stranded sequences and the concomitant soft modes of uniaxial elastomers.
We study an elasticity model for compressed protein monolayers or particle rafts at a liquid interface. Based on the microscopic view of hard-core particles with soft shells, a bead-spring model is formulated and analyzed in terms of continuum elasticity theory. The theory can be applied, for example, to hydrophobin-coated air-water interfaces or, more generally, to liquid interfaces coated with an adsorbed monolayer of interacting hard-core particles. We derive constitutive relations for such particle rafts and describe the buckling of compressed planar liquid interfaces as well as their appa…
We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals to assemble colloidal particles trapped at the liquid crystal interface into reconfigurable structures with complex symmetries and packings. Spherical colloids with homeotropic anchoring trapped at the interface between air and the nematic liquid crystal 5CB create quadrupolar distortions in the director field causing particles to repel and consequently form close-packed assemblies with a triangular habit. Here we report on complex, open structures organized via interactions with defects in the bulk. Specifi…
Solid interfaces have intrinsic elasticity. However, in most experiments, this is obscured by bulk stresses. Through microscopic observations of the contact-line geometry of a partially wetting droplet on an anisotropically stretched substrate, we measure two surface-elastic constants that quantify the linear dependence of the surface stress of a soft polymer gel on its strain. With these two parameters, one can predict surface stresses for general deformations of the material in the linear-elastic limit.
The optically induced oscillatory response of a spherical two-component, shell-core structured, nanoparticle by nodeless elastic vibrations of soft peripheral shell against hard and dynamically immobile inner core is considered. The eigenfrequencies of the even-parity, spheroidal and odd-parity torsional vibrational modes trapped in the finite-depth shell are obtained which are of practical interest for modal specification of individual resonances in spectra of resonant scattering of long wavelength electromagnetic waves by ultrafine particles.
We study the elastic properties of soft solids containing air bubbles. Contrary to standard porous materials, the softness of the matrix allows for a coupling of the matrix elasticity to surface tension forces brought in by the bubbles. Thanks to appropriate experiments on model systems, we show how the elastic response of the dispersions is governed by two dimensionless parameters: the gas volume fraction and a capillary number comparing the elasticity of the matrix to the stiffness of the bubbles. We also show that our experimental results are in good agreement with computations of the shear…
Liquid-crystal networks consist of weakly crosslinked polymers that are coupled to liquid-crystal molecules. The resultant hybrid system has rich elastic properties. We develop a phase field model to describe mechanical properties of a hexagonal liquid-crystal network. The hexagonal liquid-crystal network is found to have soft shear deformations. The elastic properties are predicted analytically and confirmed with numerical simulations. In addition the model incorporates non-linear elasticity and dislocations or disclinations.
The self-assembly of submerged cold-plasma-treated polyethylene beads is reported. The plasma-treated immersed millimetrically-sized polyethylene beads formed well-ordered 2D quasi-crystalline structures. The submerged floating of light polyethylene beads is possible due to the energy gain achieved by the wetting of the high-energy plasma-treated polymer surface prevailing over the energy loss due to the upward climb of the liquid over the beads. The capillary immersion attraction force is responsible for the observed self-assembly. The observed 2D quasi-crystalline structures demonstrate disl…
We study elastic interactions between colloidal particles and deformation landscapes of undulations in a cholesteric liquid crystal under an electric field applied normal to cholesteric layers. The onset of undulation instability is influenced by the presence of colloidal inclusions and, in turn, layers' undulations mediate the spatial patterning of particle locations. We find that the bending of cholesteric layers around a colloidal particle surface prompts the local nucleation of an undulations lattice at electric fields below the well-defined threshold known for liquid crystals without incl…
