Sublattice melting is the loss of order of one lattice component in binary or ternary ionic crystals upon increase in temperature. A related transition has been predicted in colloidal crystals. To understand the nature of this transition, we study delocalization in self-assembled, size asymmetric binary colloidal crystals using a generalized molecular dynamics model. Focusing on BCC lattices, we observe a smooth change from localized-to-delocalized interstitial particles for a variety of interaction strengths. Thermodynamic arguments, mainly the absence of a discontinuity in the heat capacity, suggest that the passage from localization-to-delocalization is continuous and not a phase transition. This change is enhanced by lattice vibrations, and the temperature of the onset of delocalization can be tuned by the strength of the interaction between the colloid species. Therefore, the localized and delocalized regimes of the sublattice are dominated by enthalpic and entropic driving forces, respectively. This work sets the stage for future studies of sublattice melting in colloidal systems with different stoichiometries and lattice types, and it provides insights into superionic materials, which have potential for application in energy storage technologies.
Gel-immobilized colloidal crystals were prepared to obtain hybrid plasmonic-photonic crystals, in which electric field enhancement to a greater extent than that due to localized surface plasmons (LSP) alone was expected due to coupling between LSP and the photonic band. Polystyrene colloidal crystals immobilized by the N-(hydroxymethyl)acrylamide gel were immersed in an aqueous dispersion of gold nanoparticles (AuNPs). Then, the gel-immobilized colloidal crystals were picked out and immersed in an ionic liquid mixture. The surfaces of the gel-immobilized colloidal crystals immersed in the AuNP…
According to classical nucleation theory, a crystal grows from a small nucleus that already bears the symmetry of its end phase - but experiments with colloids now reveal that, from an amorphous precursor, crystallites with different structures can develop.
A fundamental challenge in materials design is linking building block attributes to crystal structure. Addressing this challenge is particularly difficult for systems that exhibit emergent order, such as entropy-stabilized colloidal crystals. We combine recently developed techniques in inverse design with machine learning to construct a model that correctly classifies the crystals of more than ten thousand polyhedral shapes into 13 different structures with a predictive accuracy of 96% using only two geometric shape measures. With three measures, 98% accuracy is achieved. We test our model on …
Throughout the physical sciences, entropy stands out as a pivotal but enigmatic concept that, in materials design, often takes a backseat to energy. Here, we demonstrate how to precisely engineer entropy to achieve desired colloidal crystals. We demonstrate the inverse design of hard particles that assemble six different target colloidal crystals due solely to entropy maximization. Our approach efficiently samples $10^8$ particle shapes from 88- and 192-dimensional design spaces to discover thermodynamically optimal shapes. We design particle shapes that self assemble known crystals with optim…
Colloidal assembly represents a powerful method for the fabrication of functional materials. In this article, we describe how acoustic radiation forces can guide the assembly of colloidal particles into structures that serve as microscopic elements in novel acoustic metadevices or act as phononic crystals. Using a simple three-dimensional orthogonal system, we show that a diversity of colloidal structures with orthorhombic symmetry can be assembled with megahertz-frequency (MHz) standing pressure waves. These structures allow rapid tuning of acoustic properties and provide a new platform for d…
We have performed Monte Carlo simulations of hard spheres on a pattern under gravity. We have found that a crystal formed at a moderate gravity strength contains essentially no defects while one formed at a higher strength gravity contains a significant amount of defects. This result suggests the possibility of using gravitational-tempering in a colloidal epitaxy to reduce the number of defects in colloidal crystals. Moreover, we wish to emphasize the possibility to obtain a perfect crystal.
A silica colloidal crystal obtained by centrifugation at 9 G for 2 days in water was annealed by additional stronger centrifugation at 50 G for 5 days. The number of the striations observed in the colloidal crystal under crossed polarized light decreased at some parts in a growth container after additional centrifugation, while the number alse increase at the other parts. The decrease probably shows the shrinkage of the stacking disorders under high gravity, while the increase probably shows the production of new stacking disorder.
A Landau theory is presented for the structural transition of electrically stabilized colloidal crystals under shear. The model suggests that a structural transition from an ordered layered colloidal crystal into a disordered structure occurs at a critical shear stress. The shear induced structural transition is related to a change of the rheological properties caused by the variation of the microstructure which can be verified by scattering experiments. The theory is used to establish the shape of the flow curves. A good qualitative agreement with experimental results can be achieved, while a…
Less-defective colloidal crystals can be used as photonic crystals. To this end, colloidal epitaxy was proposed in 1997 as a method to reduce the stacking defects in the colloidal crystals. In this method, face-centered cubic (fcc) (001) stacking is forced by a template. In fcc (001) stacking, in contract to fcc {111} stacking, the stacking sequence is unique and thus the stacking fault can be avoided. Additionally, in 1997, an effect of gravity that reduces the stacking disorder in hard-sphere (HS) colloidal crystals was found. Recently, we have proposed a gravitational tempering method based…
We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and used to analyse colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We fur…
We report an experimental study of the elastic properties of a two-dimensional (2D) colloidal crystal subjected to light-induced substrate potentials. In agreement with recent theoretical predictions [H.H. von Gruenberg and J. Baumgartl, Phys. Rev. E 75, 051406 (2007)] the phonon band structure of such systems can be tuned depending on the symmetry and depth of the substrate potential. Calculations with binary crystals suggest that phononic band engineering can be also performed by variations of the pair potential and thus opens novel perspectives for the fabrication of phononic crystals with …
There is growing interest in functional, adaptive devices built from colloidal subunits of micron size or smaller. A colloidal material with dynamic mechanical properties could facilitate such microrobotic machines. Here we study via computer simulation how active interstitial particles in small quantities can be used to modify the bulk mechanical properties of a colloidal crystal. Passive interstitial particles are known to pin dislocations in metals, thereby increasing resistance to plastic deformation. We extend this tactic by employing anisotropic active interstitials that travel super-dif…
We study the vibrational spectrum and the low energy modes of a three dimensional colloidal crystal using confocal microscopy. This is done in a two-dimensional cut through a three-dimensional crystal. We find that the observed density of states is incompatible with the standard Debye form in either two or three dimensions. These results are confirmed by numerical simulations. We show that an effective theory for the projections of the modes onto the two-dimensional cut describes the experimental and simulation data in a satisfactory way.
Aiming at fabrication of hybrid plasmonic-photonic crystals, gel-immobilized colloidal crystals made of a polystyrene colloidal suspension and an N-(Hydroxy methyl)acrylamid-based gel were immersed into an aqueous dispersion of gold nanoparticles. Atomic force microscope (AFM) observations have been performed for the gel-immobilized colloidal crystals with gold nanoparticles deposited on their surfaces. In the present study, the diameter of a colloidal sphere was c.a. 190 nm. The diameter of a gold nanoparticle was the same as in a preliminary study, c.a. 40 nm. Various immersion times up to t…
We consider the theory of fluctuations of a colloidal solid observed in a confocal slice. For a cubic crystal we study the evolution of the projected elastic properties as a function of the anisotropy of the crystal using numerical methods based on the fast Fourier transform. In certain situations of high symmetry we find exact analytic results for the projected fluctuations.
Using computer simulations we explore how grain boundaries can be removed from three-dimensional colloidal crystals by doping with a small fraction of active colloids. We show that for sufficient self-propulsion, the system is driven into a crystal-fluid coexistence. In this phase separated regime, the active dopants become mobile and spontaneously gather at the grain boundaries. The resulting surface melting and recrystallization of domains result in the motion of the grain boundaries over time and lead to the formation of a large single crystal. However, when the self-propulsion is too low t…
Using simulations we explore the behaviour of two-dimensional colloidal (poly)crystals doped with active particles. We show that these active dopants can provide an elegant new route to removing grain boundaries in polycrystals. Specifically, we show that active dopants both generate and are attracted to defects, such as vacancies and interstitials, which leads to clustering of dopants at grain boundaries. The active particles both broaden and enhance the mobility of the grain boundaries, causing rapid coarsening of the crystal domains. The remaining defects recrystallize upon turning off the …
The formation and dynamics of a wide variety of binary two-dimensional ordered structures and superlattices are investigated through a phase field crystal model with sublattice ordering. Various types of binary ordered phases, the phase diagrams, and the grain growth dynamics and structural transformation processes, including the emergence of topological defects, are examined. The results are compared to the ordering and assembly of two-component colloidal systems. Two factors governing the binary phase ordering are identified, the coupling and competition between the length scales of two subl…
We study the conditions under which and how an imposed cluster of fixed colloidal particles at prescribed positions triggers crystal nucleation from a metastable colloidal fluid. Dynamical density functional theory of freezing and Brownian dynamics simulations are applied to a two-dimensional colloidal system with dipolar interactions. The externally imposed nucleation clusters involve colloidal particles either on a rhombic lattice or along two linear arrays separated by a gap. Crystal growth occurs after the peaks of the nucleation cluster have first relaxed to a cutout of the stable bulk cr…
The collective diffusion effects in system of a colloidal particles in a liquid crystal has been proposed. In this article described peculiarity of collective diffusion colloidal particles in a liquid crystal, which can be observe experimentally. The diffusion coefficient should be crucial dependence from temperature and concentration of particles. In system colloidal particles arise from the elastic distortion of the elastic director field the inter-particle interaction. These interaction can cause nontrivial collective behavior, as the results the non-monotonic dependence collective diffusio…
We successfully fabricated large grains of silica colloidal crystals in an inverted-triangle internal-shaped container (inverted-triangle container) by centrifugation. The largest grain in the container was much larger than that in a container which has a flat bottom and constant width (flat-bottomed container). The edged bottom of the inverted-triangle container eliminated the number of the grains, and then the broadened shape of the container effectively widened the grains.
Colloidal particles trapped at an interface between two fluids can form a wide range of different structures. Replacing one of the fluid with a liquid crystal increases the complexity of interactions and results in a greater range of possible structures. New behaviour emerges when colloidal particles interact with defects in the liquid crystal phases. Here we discuss the templating of colloids at a cholesteric isotropic interface.
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…
We propose a simple theoretical model which explains a formation of dipolar 2D and 3D colloidal structures in nematic liquid crystal. Colloidal particles are treated as effective hard spheres interacting via their elastic dipole, quadrupole and octopole moments. It is shown that octopole moment plays an important role in the formation of 2D and 3D nematic colloidal crystals. We generalize this assumption on the case of the external electric field and theoretically explain a giant electrostriction effect in 3D crystals observed recently [A. Nych et al., Nature Communications \textbf{4}, 1489 (2…
We demonstrate a variety of ordered patterns, including hexagonal structures and chains, formed by colloidal particles (droplets) at the free surface of a nematic liquid crystal (LC). The surface placement introduces a new type of particle interaction as compared to particles entirely in the LC bulk. Namely, director deformations caused by the particle lead to distortions of the interface and thus to capillary attraction. The elastic-capillary coupling is strong enough to remain relevant even at the micron scale when its buoyancy-capillary counterpart becomes irrelevant.
In this article is proposed the general approach to determination the character of the interaction between colloidal particles in a different liquid crystals. The main idea of this approach are in the presentation of the colloidal particle as sours of the possible deformation of the ground state of the director field. The ground state of liquid crystal imposes restrictions on the possible deformations and as result determine the character of the interaction between the colloidal particles. Based on this approach the Coulomb like interaction between dipole particles in a cholesteric liquid crys…
The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field crystal model is proposed which involves less approximations than the standard phase-field crystal model. We finally test the validity of these phase-field crystal model…
Stress relaxation in crystalline solids is mediated by the formation and diffusion of defects. While it is well established how externally-generated stresses relax, through the proliferation and motion of dislocations in the lattice, it remains relatively unknown how crystals cope with internal stresses. We investigate, both experimentally and in simulations, how highly localized stresses relax in two-dimensional soft colloidal crystals. When a single particle is actively excited, by means of optical tweezing, a rich variety of highly collective stress relaxation mechanisms results. These mani…
Control of physical behaviors of nematic colloids and colloidal crystals has been demonstrated by tuning particle shape, topology, chirality and surface charging. However, the capability of altering physical behaviors of such soft matter systems by changing particle shape and the ensuing responses to external stimuli has remained elusive. We fabricated genus-one nematic elastomeric colloidal ring-shaped particles and various microstructures using two-photon photopolymerization. Nematic ordering within both the nano-printed particle and the surrounding medium leads to anisotropic responses and …
We investigate the elastic and yielding properties of two dimensional defect-free mono-crystals made of highly monodisperse droplets. Crystals are compressed between two parallel boundaries of which one acts as a force sensor. As the available space between boundaries is reduced, the crystal goes through successive row-reduction transitions. For small compression forces, the crystal responds elastically until a critical force is reached and the assembly fractures in a single catastrophic global event. Correspondingly there is a peak in the force measurement associated with each row-reduction. …
Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures comprised of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure i…
Micrometre sized colloidal particles can be viewed as large atoms with tailorable size, shape and interactions. These building blocks can assemble into extremely rich structures and phases, in which the thermal motions of particles can be directly imaged and tracked using optical microscopy. Hence, colloidal particles are excellent model systems for studying phase transitions, especially for poorly understood kinetic and nonequilibrium microscale processes. Advances in colloid fabrication, assembly and computer simulations have opened up numerous possibilities for such research. In this Review…
Using numerical simulations we show that a variety of novel colloidal crystalline states and multi-step melting phenomena occur on square and triangular two-dimensional periodic substrates. At half-integer fillings different kinds of frustration effects can be realized. A two-step melting transition can occur in which individual colloidal molecules initially rotate, destroying the overall orientational order, followed by the onset of interwell colloidal hopping, in good agreement with recent experiments.
Self-assembly of nanoparticles can enable composites with pre-designed properties but remains challenged by reproducing structural diversity of atomic and molecular crystals. We combine anisotropic elastic and weakly screened electrostatic interactions to guide both orientational and triclinic positional self-ordering of inorganic nanocrystals in a nematic fluid host. The lattice periodicity of these low-symmetry colloidal crystals is more than an order of magnitude larger than the nanoparticle size. Orientations of nanocrystals, as well as crystallographic axes of ensuing triclinic colloidal …
Structural rearrangement of polystyrene colloidal crystals under dry sintering conditions has been revealed by in situ grazing incidence X-ray scattering. Measured diffraction patterns were analysed using distorted wave Born approximation (DWBA) theory and the structural parameters of as-grown colloidal crystals of three different particle sizes were determined for in-plane and out-of-plane directions in a film. By analysing the temperature evolution of diffraction peak positions, integrated intensities, and widths the detailed scenario of structural rearrangement of crystalline domains at a n…
Colloidal particles suspended in liquid crystals can exhibit various effective anisotropic interactions that can be tuned and utilized in self-assembly processes. We simulate a two-dimensional system of hard disks suspended in a solution of dense hard needles as a model system for colloids suspended in a nematic lyotropic liquid crystal. The novel event-chain Monte Carlo technique enables us to directly measure colloidal interactions in a microscopic simulation with explicit liquid crystal particles in the dense nematic phase. We find a directional short-range attraction for disks along the di…
The mechanical properties of crystalline materials can be substantially modified under confinement. Such modified macroscopic properties are usually governed by the altered microstructures and internal stress fields. Here, we use a parallel plate geometry to apply a quasi-static squeeze flow crushing a colloidal polycrystal while simultaneously imaging it with confocal microscopy. The confocal images are used to quantify the local structure order and, in conjunction with Stress Assessment from Local Structural Anisotropy (SALSA), determine the stress at the single-particle scale. We find that …
We propose a simple seedless approach to assemble millimeter sized monolayer single colloidal crystals with desired orientations at predetermined locations on an unstructured charged substrate. This approach utilizes the millimeter-ranged fluid flow on the bottom glass substrate induced by an ion exchange resin (IEX) fixed on top of the closed sample cell. This fluid flow increases with decreasing height of the sample cell and increasing radius R of the IEX. For a single inverted pump, millimeter sized monolayer single crystals of hexagonal close packing can be obtained. For two closely spaced…
We present a systematic study of the frequency band structure of acoustic waves in crystals consisting of nonoverlapping solid spheres in a fluid. We consider colloidal crystals consisting of polystyrene spheres in water, and an opal consisting of close-packed silica spheres in air. The opal exhibits an omnidirectional frequency gap of considerable width; the colloidal crystals do not. The physical origin of the bands are discussed for each case in some detail. We present also results on the transmittance of finite slabs of the above crystals.
The lack of detailed balance in active colloidal suspensions allows dissipation to determine stationary states. Here we show that slow viscous flow produced by polar or apolar active colloids near plane walls mediates attractive hydrodynamic forces that drive crystallization. Hydrodynamically mediated torques tend to destabilize the crystal but stability can be regained through critical amounts of bottom-heaviness or chiral activity. Numerical simulations show that crystallization is not nucleational, as in equilibrium, but is preceded by a spinodal-like instability. Harmonic excitations of th…
We investigate the influence of geometric confinement on the free energy of an idealized model for charge-stabilized colloidal suspensions. The mean-field Poisson-Boltzmann formulation for this system predicts pure repulsion among macroionic colloidal spheres. Fluctuations in the simple ions' distribution provide a mechanism for the macroions to attract each other at large separations. Although this Casimir interaction is long-ranged, it is too weak to influence colloidal crystals' dynamics.
The concept of a local linear elastic strain field is commonly used in the metallurgical research community to approximate the collective effect of atomic displacements around crystalline defects. Here we show that the elastic strain field approximation is a useful tool in colloidal systems. For colloidal crystals with repulsive particle interaction potentials, given similar mechanical properties, sharper potentials lead to: 1) free energies of deformation dominated by entropy, 2) lower variance in strain field fluctuations, 3) increased tension-compression asymmetry near dislocation core regi…
Using a phase field crystal model we study the structure and dynamics of a drop of colloidal suspension during evaporation of the solvent. We model an experimental system where contact line pinning of the drop on the substrate is non-existent. Under such carefully controlled conditions, evaporation of the drop produces an ordered or disordered arrangement of the colloidal residue depending on the initial average density of solute and the drying rate. We obtain a non-equilibrium phase boundary showing amorphous and crystalline phases of single component and binary mixtures of colloidal particle…
Impurity-induced defects play a crucial role for the properties of crystals, but little is known about impurities with anisotropic shape. Here, we study how colloidal dumbbells distort and interact with a hexagonal crystal of charged colloidal spheres at a fluid interface. We find that subtle changes in the dumbbell length induce a transition from a local distortion to a particle-bound dislocation, and determine how the dumbbell moves inside the repulsive hexagonal lattice. Our results provide new routes towards controlling material properties through particle-bound dislocations.
Colloidal particles disturb the alignment of rod-like molecules of liquid crystals, giving rise to long-range interactions that minimize the free energy of distorted regions. Particle shape and topology are known to guide this self-assembly process. However, how chirality of colloidal inclusions affects these long-range interactions is unclear. Here we study the effects of distortions caused by chiral springs and helices on the colloidal self-organization in a nematic liquid crystal using laser tweezers, particle tracking and optical imaging. We show that chirality of colloidal particles inter…
We demonstrate that nature has produced a close-packed helical twisted filamentous material in the biomineralization of the mollusc. In liquid crystals, twist-bend nematics have been predicted and observed. We present and analyse evidence that the helical biomineral microstructure of mollusc shells may be formed from such a liquid-crystal precursor.
Using positional data from video-microscopy and applying the equipartition theorem for harmonic Hamiltonians, we determine the wave-vector-dependent normal mode spring constants of a two-dimensional colloidal model crystal and compare the measured band-structure to predictions of the harmonic lattice theory. We find good agreement for both the transversal and the longitudinal mode. For $q\to 0$, the measured spring constants are consistent with the elastic moduli of the crystal.
We study colloidal ordering and disordering on two-dimensional periodic substrates where the number of colloids per substrate minima is two or three. The colloids form dimer or trimer states with orientational ordering, referred to as colloidal molecular crystals. At a fixed temperature such that, in the absence of a substrate, the colloids are in a triangular floating solid state, upon increasing the substrate strength we find a transition to an ordered colloidal molecular crystal state, followed by a transition to a disordered state where the colloids still form dimers or trimers but the ori…
The progress of realizing colloidal structures mimicking natural forms of organization in condensed matter is inherently limited by the availability of suitable colloidal building blocks. To enable new forms of crystalline and quasicrystalline self-organization of colloids, we develop truncated pyramidal particles that form nematic elastic dipoles with long-range electrostaticlike and geometry-guided low-symmetry short-range interactions. Using a combination of nonlinear optical imaging, laser tweezers, and video microscopy, we characterize colloidal pair interactions and demonstrate unusual f…
DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but applications of this technology are limited by poor understanding and control over the dynamical crystallization pathways. To address this challenge, we use microfluidics to quantify the self-assembly dynamics of DNA-programmed colloidal crystals, from thermally-activated nucleation through reaction-limited and diffusion-limited phases of crystal growth. Our detailed measurements of the temperature and concentration dependence of the kinetics at all stages along the crystallization pathway provide a s…
Assembly of colloidal particles on fluid interfaces is a promising technique for synthesizing two-dimensional micro-crystalline materials useful in fields as diverse as biomedicine1, materials science2, mineral flotation3 and food processing4. Current approaches rely on bulk emulsification methods, require further chemical and thermal treatments, and are restrictive with respect to the materials employed5-9. The development of methods that exploit the great potential of interfacial assembly for producing tailored materials have been hampered by the lack of understanding of the assembly process…
Ferrofluids are familiar as colloidal suspensions of ferromagnetic nanoparticles in aqueous or organic solvents. The dispersed particles are randomly oriented but their moments become aligned if a magnetic field is applied, producing a variety of exotic and useful magneto-mechanical effects. A longstanding interest and challenge has been to make such suspensions macroscopically ferromagnetic, that is having uniform magnetic alignment in absence of a field. Here we report a fluid suspension of magnetic nanoplates which spontaneously aligns into an equilibrium nematic liquid crystal phase that i…
