Restricted dislocation motion in crystals of colloidal dimer particles

Dumbbell Impurities in 2D Crystals of Repulsive Colloidal Spheres Trap Dislocations

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 differences in the dumbbell length determine whether it induces a local distortion of the lattice or traps a dislocation, and determine how the dumbbell moves inside the repulsive hexagonal lattice. Our results provide new routes toward controlling material properties and understanding fundamental questions in phase transitions through particle-bound dislocations.

Hexagonal vortices enable faster colloidal crystal grain coarsening

We find that localized rotations of hexagonal clusters of particles occur during rapid dissolution of grain boundary loops in two-dimensional colloidal crystals. These particle vortices, or rotating "granules," are distinct from established models for grain boundary diffusion, which predict that a crystal grain enclosed within another crystal will dissolve at a constant rate. Our measurements of colloidal crystal experiments and Brownian dynamics simulations reveal grain boundary motion that is described by two distinct processes: slow dissolution due to the diffusion of individual particles, and rapid dissolution due to collective granule rotation. In the latter process, hexagonal clusters of particles rotate together in granules whose shape and position are determined by the underlying moiré pattern. Furthermore, these vortices guide cooperative strings of particles that move along the edges of the hexagonal granules. Including this vortex mechanism may improve models for grain coarsening in polycrystalline materials, ultimately offering improved predictions for the time evolution of material properties.

Grain splitting is a mechanism for grain coarsening in colloidal polycrystals

In established theories of grain coarsening, grains disappear either by shrinking or by rotating as a rigid object to coalesce with an adjacent grain. Here we report a third mechanism for grain coarsening, in which a grain splits apart into two regions that rotate in opposite directions to match two adjacent grains' orientations. We experimentally observe both conventional grain rotation and grain splitting in two-dimensional colloidal polycrystals. We find that grain splitting occurs via independently rotating "granules" whose shapes are determined by the underlying triangular lattices of the two merging crystal grains. These granules are so small that existing continuum theories of grain boundary energy are inapplicable, so we introduce a hard sphere model for the free energy of a colloidal polycrystal. We find that, during splitting, the system overcomes a free energy barrier before ultimately reaching a lower free energy when splitting is complete. Using simulated splitting events and a simple scaling prediction, we find that the barrier to grain splitting decreases as grain size decreases. Consequently, grain splitting is likely to play an important role in polycrystals with small grains. This discovery suggests that mesoscale models of grain coarsening may offer better predictions in the nanocrystalline regime by including grain splitting.

Preparation, properties, and applications of magnetic hematite microparticles

Hematite microparticles are becoming increasingly important components in the soft matter field. The remarkable combination of magnetic and photocatalytic properties that characterize them, coupled with the variety of uniform and monodisperse shapes that they can be synthesized in, makes them a one of a kind colloidal model system. Thanks to these properties, hematite microparticles have been recently applied in several important soft matter applications, spanning from novel colloidal building blocks for self-assembly to necessary tools to investigate and understand fundamental problems. In this review article we provide a detailed overview of the traditional methods available for the preparation of hematite microparticles of different shapes, devoting special attention on some of the most common hiccups that could hider a successful synthesis. We furthermore review the particles' most important physico-chemical properties and their most relevant applications in the soft matter field.

Sculpting crystals one Burgers vector at a time: Toward colloidal lattice robot swarms

Plastic deformation of crystalline materials with isotropic particle attractions proceeds by the creation and migration of dislocations under the influence of external forces. If dislocations are produced and migrated under the action of local forces, then material shape change can occur without the application of surface forces. We investigate how particles with variable diameters can be embedded in colloidal monolayers to produce dislocations on demand. We find in simulation that when embedded clusters of variable diameter particles are taken through multiple cycles of swelling and shrinking, large cumulative plastic slip is produced by the creation and biased motion of dislocation pairs in the solid for embedded clusters of particular geometries. In this way, dislocations emitted by these clusters (biased "dislocation emitters") can be used to reshape colloidal matter. Our results are also applicable to larger-scale swarms of robotic particles that organize into dense ordered two-dimensional (2D) arrangements. We conclude with a discussion of how dislocations fulfill for colloids the role sought by "metamodules" in lattice robotics research and show how successive applications of shear as a unit operation can produce shape change through slicing and swirling.

"Colloid-Atom Duality" in the Assembly Dynamics of Concave Gold Nanoarrows

We use liquid-phase transmission electron microscopy (TEM) to study self-assembly dynamics of charged gold nanoarrows (GNAs), which reveal an unexpected "colloid-atom duality". On one hand, they assemble following the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory for colloids when van der Waals attraction overruns slightly screened electrostatic repulsion. Due to concaveness in shape, GNAs adopt zipper motifs with lateral offset in their assembly matching with our modeling of inter-GNA interaction, which form into unconventional structures resembling degenerate crystals. On the other hand, further screening of electrostatic repulsion leads to merging of clusters assembled from GNAs, reminiscent of the coalescence growth mode in atomic crystals driven by minimization of surface energy, as we measure from the surface fluctuation of clusters. Liquid-phase TEM captures the initial formation of highly curved necks bridging the two clusters. Analysis of the real-time evolution of neck width illustrates the first-time observation of coalescence in colloidal assemblies facilitated by rapid surface diffusion of GNAs. We attribute the duality to the confluence of factors (e.g., nanoscale colloidal interaction, diffusional dynamics) that we access by liquid-phase TEM, taking turns to dominate at different conditions, which is potentially generic to the nanoscale. The atom aspect, in particular, can inspire utilization of atomic crystal synthesis strategies to encode structure and dynamics in nanoscale assembly.

Designing active particles for colloidal microstructure manipulation via strain field alchemy

Defects in a crystal can exert forces on each other via strain field interactions. Here we explore the strain-field-mediated interaction between an anisotropic interstitial probe particle and dislocation microstructures in a colloidal crystal composed of particles interacting via steep repulsive isotropic potentials. We optimize the interaction between probe particle and dislocation with the anisotropic shape of the probe as a free parameter. Such alchemical optimization is typically carried out upon the explicitly defined interaction potential parameters; instead, we optimize the strain field of the probe and then map back to particle shape. We distinguish this tactic from other alchemical methods as 'strain alchemy'. We report several findings: (1) a robust mapping exists between strain field calculation methods (the method of eigenstrains) and strains produced by an anisotropic interstitial, (2) optimization of strain field interactions in the strain domain permits rapid evaluation of candidate shapes for interstitials, (3) interstitial mobility barriers can be estimated from the strain field, and (4) strongly interacting and highly mobile interstitial particles can be found that are capable of driving dislocation glide with applied force. Active particle-induced dislocation glide is examined for the cases of edge dislocation arrays and extrinsic dislocation loops. For edge dislocations, particle geometries of alternating large and small diameter segments were found to interact most strongly. For dislocation loops, interstitials with a single small radius segment surrounded by large radius segments are best.

Local Melting Attracts Grain Boundaries in Colloidal Polycrystals

We find that laser-induced local melting attracts and deforms grain boundaries in 2D colloidal crystals. When a melted region in contact with the edge of a crystal grain recrystallizes, it deforms the grain boundary-this attraction is driven by the multiplicity of deformed grain boundary configurations. Furthermore, the attraction provides a method to fabricate artificial colloidal crystal grains of arbitrary shape, enabling new experimental studies of grain boundary dynamics and ultimately hinting at a novel approach for fabricating materials with designer microstructures.

Tuning Patchy Bonds Induced by Critical Casimir Forces

Experimental control of patchy interactions promises new routes for the assembly of complex colloidal structures, but remains challenging. Here, we investigate the role of patch width in the assembly of patchy colloidal particles assembled by critical Casimir forces. The particles are composed of a hydrophobic dumbbell with an equatorial hydrophilic polymer shell, and are synthesized to have well-defined patch-to-shell area ratios. Patch-to-patch binding is achieved in near-critical binary solvents, in which the particle interaction strength and range are controlled by the temperature-dependent solvent correlation length. Upon decreasing the patch-to-shell area ratio, we observe a pronounced change of the bonding morphology towards directed single-bonded configurations, as clearly reflected in the formation of chain-like structures. Computer simulations using an effective critical Casimir pair potential for the patches show that the morphology change results from the geometric exclusion of the increasingly thick hydrophilic particle shells. These results highlight the experimental control of patchy interactions through the engineering of the building blocks on the way towards rationally designed colloidal superstructures.

Orientational dynamics of fluctuating dipolar particles assembled in a mesoscopic colloidal ribbon

We combine experiments and theory to investigate the dynamics and orientational fluctuations of ferromagnetic microellipsoids that form a ribbonlike structure due to attractive dipolar forces. When assembled in the ribbon, the ellipsoids display orientational thermal fluctuations with an amplitude that can be controlled via application of an in-plane magnetic field. We use video microscopy to investigate the orientational dynamics in real time and space. Theoretical arguments are used to derive an analytical expression that describes how the distribution of the different angular configurations depends on the strength of the applied field. The experimental data are in good agreement with the developed model for all the range of field parameters explored. Understanding the role of fluctuations in chains composed of dipolar particles is important not only from a fundamental point of view, but it may also help understanding the stability of such structures against thermal noise, which is relevant in microfluidics and laboratory-on-a-chip applications.

Density functional theory for polymeric systems in 2D

We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.

Dimer covering and percolation frustration

Covering a graph or a lattice with nonoverlapping dimers is a problem that has received considerable interest in areas, such as discrete mathematics, statistical physics, chemistry, and materials science. Yet, the problem of percolation on dimer-covered lattices has received little attention. In particular, percolation on lattices that are fully covered by nonoverlapping dimers has not evidently been considered. Here, we propose a procedure for generating random dimer coverings of a given lattice. We then compute the bond percolation threshold on random and ordered coverings of the square and the triangular lattices on the remaining bonds connecting the dimers. We obtain p_{c}=0.367713(2) and p_{c}=0.235340(1) for random coverings of the square and the triangular lattices, respectively. We observe that the percolation frustration induced as a result of dimer covering is larger in the low-coordination-number square lattice. There is also no relationship between the existence of long-range order in a covering of the square lattice and its percolation threshold. In particular, an ordered covering of the square lattice, denoted by shifted covering in this paper, has an unusually low percolation threshold and is topologically identical to the triangular lattice. This is in contrast to the other ordered dimer coverings considered in this paper, which have higher percolation thresholds than the random covering. In the case of the triangular lattice, the percolation thresholds of the ordered and random coverings are very close, suggesting the lack of sensitivity of the percolation threshold to microscopic details of the covering in highly coordinated networks.

Short-time diffusivity of dicolloids

The short-time diffusivity of dicolloid particles as a function of particle volume fraction ϕ from 0.01 ≤ ϕ ≤ 0.6 is measured using diffusing wave spectroscopy. The diffusivities of symmetric and asymmetric dicolloids are compared with similarly sized spheres. The short-time diffusivity is independent of salt concentration and decreases with increasing volume fraction for both spheres and asymmetric dicolloids. Symmetric dicolloids have a higher diffusivity than spheres at similar volume fractions. This difference is accounted for by rescaling the dicolloid volume fraction based on the ratio of the random close-packing volume fractions of spheres and dicolloids. Finally, a useful method is provided for calculating the diffusivity of symmetric dicolloid particles of arbitrary aspect ratio based on the calculated hydrodynamic resistance of Zabarankin [Proc. R. Soc. A 463, 2329 (2007)].

Predictive self-assembly of polyhedra into complex structures

Predicting structure from the attributes of a material's building blocks remains a challenge and central goal for materials science. Isolating the role of building block shape for self-assembly provides insight into the ordering of molecules and the crystallization of colloids, nanoparticles, proteins, and viruses. We investigated 145 convex polyhedra whose assembly arises solely from their anisotropic shape. Our results demonstrate a remarkably high propensity for thermodynamic self-assembly and structural diversity. We show that from simple measures of particle shape and local order in the fluid, the assembly of a given shape into a liquid crystal, plastic crystal, or crystal can be predicted.

The physics of the colloidal glass transition

As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.

Degenerate quasicrystal of hard triangular bipyramids

We report a degenerate quasicrystal in Monte Carlo simulations of hard triangular bipyramids each composed of two regular tetrahedra sharing a single face. The dodecagonal quasicrystal is similar to that recently reported for hard tetrahedra [Haji-Akbari et al., Nature (London) 462, 773 (2009)] but degenerate in the pairing of tetrahedra, and self-assembles at packing fractions above 54%. This notion of degeneracy differs from the degeneracy of a quasiperiodic random tiling arising through phason flips. Free energy calculations show that a triclinic crystal is preferred at high packing fractions.

Dislocations and vacancies in two-dimensional mixed crystals of spheres and dimers

In colloidal crystals of spheres, dislocation motion is unrestricted. On the other hand, recent studies of relaxation in crystals of colloidal dimer particles have demonstrated that the dislocation dynamics in such crystals are reminiscent of glassy systems. The observed glassy dynamics arise as a result of dislocation cages formed by certain dimer orientations. In the current study, we use experiments and simulations to investigate the transition that arises when a pure sphere crystal is doped with an increasing concentration of dimers. Specifically, we focus on both dislocation caging and vacancy motion. Interestingly, we find that any nonzero fraction of dimers introduces finite dislocation cages, suggesting that glassy dynamics are present for any mixed crystal. However, we have also identified a vacancy-mediated uncaging mechanism for releasing dislocations from their cages. This mechanism is dependent on vacancy diffusion, which slows by orders of magnitude as the dimer concentration is increased. We propose that in mixed crystals with low dimer concentrations vacancy diffusion is fast enough to uncage dislocations and delay the onset of glassy dislocation dynamics.

Glassy dislocation dynamics in 2D colloidal dimer crystals

Although glassy relaxation is typically associated with disorder, here we report on a new type of glassy dynamics relating to dislocations within 2D crystals of colloidal dimers. Previous studies have demonstrated that dislocation motion in dimer crystals is restricted by certain particle orientations. Here, we drag an optically trapped particle through such dimer crystals, creating dislocations. We find a two-stage relaxation response where initially dislocations glide until encountering particles that cage their motion. Subsequent relaxation occurs logarithmically slowly through a second process where dislocations hop between caged configurations. Finally, in simulations of sheared dimer crystals, the dislocation mean squared displacement displays a caging plateau typical of glassy dynamics. Together, these results reveal a novel glassy system within a colloidal crystal.

Nonequilibrium phases for driven particle systems with effective orientational degrees of freedom

We show that a rich variety of nonequilibrium phases can be realized for interacting particles moving over a periodic substrate when the particles have effective internal orientational degrees of freedom. We specifically study driven colloidal molecular crystals where it has been established that n-merization produces effective orientational degrees of freedom. This system exhibits a polarization effect within the pinned phase, a remarkable variety of sliding phases, and has no single particle pinning regime. Similar dynamics should occur for other driven systems with effective orientational degrees of freedom such as sliding diatomic or higher-order states.