Phase behavior of colloidal superballs: shape interpolation from spheres to cubes

Understanding orientational disorder in crystalline assemblies of hard convex polyhedra

Spontaneous self-assembly of hard convex polyhedra is known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of orientational phase with discrete rotational mobility has been reported in hard particle systems. In this paper, we present a new analysis method for characterizing the orientational phase of a crystal, which is based on algorithmic detection of unique orientations. Using this method, we collected complete statistics of discrete orientations along the Monte Carlo simulation trajectories and observed that particles were equally partitioned among them, with specific values of pairwise orientational differences. These features remained constant across the pressure range and did not depend on rotational mobility. The discrete mobility was characteristic of a distinct equilibrium thermodynamic phase, qualitatively different from the freely rotating plastic phase with continuous orientations. The high pressure behavior with frozen particle orientations was part of that same description and not a non-equilibrium arrested state. We introduced a precise notion of orientational order and demonstrated that the system was maximally disordered at the level of a unit cell, even though individual particles could only take a few discrete orientations. We report the existence of this phase in five polyhedral shapes and in systematically curated shape families constructed around two of them. The symmetry mismatch between the particle and the crystallographic point groups was found to be a predictive indicator for the occurrence of this phase.

Geometrical impacts of platonic particles on nematic liquid crystal dynamics

Platonic-solid-like particles in liquid crystals offer intriguing opportunities for engineering complex materials with tailored properties. Inspired by platonic solids' geometric simplicity and symmetry, these particles possess well-defined shapes such as cubes, tetrahedra, octahedra, dodecahedra, and icosahedra. When dispersed within nematic liquid-crystalline media, these particles interact with the surrounding medium in intricate ways, influencing the local orientational order of liquid crystal molecules. In this work, we implement continuum simulations to study how the combination of particle shape and surface anchoring gives rise to line defects that follow the edges of the particles and how they are affected by the presence of a Poiseuille flow. Platonic-solid-like particles in liquid crystals have shown promise in diverse applications ranging from photonics and metamaterials to colloidal self-assembly and responsive soft materials.

Shape-induced crystallization of binary DNA-functionalized nanocubes

Leveraging the anisotropic shape of DNA-functionalized nanoparticles holds potential for shape-directed crystallization of a wide collection of superlattice structures. Using coarse-grained molecular dynamics simulations, we study the self-assembly of a binary mixture of cubic gold nanoparticles, which are functionalized by complementary DNA strands. We observe the spontaneous self-assembly of simple cubic (SC), plastic body-centered tetragonal (pBCT), and compositionally disordered plastic body-centered tetragonal (d-pBCT) phases due to hybridization of the DNA strands. We systematically investigate the effect of length, grafting density, as well as rigidity of the DNA strands on the self-assembly behavior of cubic nanoparticles. We measure the potential of mean force between DNA-functionalized nanocubes for varying rigidity of the DNA strands and DNA lengths. Using free-energy calculations, we find that longer and flexible DNA strands can lead to a phase transformation from SC to the pBCT phase due to a gain in entropy arising from the orientational degrees of freedom of the nanocubes in the pBCT phase. Our results may serve as a guide for self-assembly experiments on DNA-functionalized cubic nanoparticles.

Rheology and microstructure of thermoresponsive composite gels of hematite pseudocubes and Pluronic F127

Stimuli-responsive materials or smart materials are designed materials whose properties can be changed significantly by applying external stimuli, such as stress, electric or magnetic fields, light, temperature, and pH. We report the linear and nonlinear rheological properties of thermoresponsive composite gels based on submicron-sized hematite pseudocube-shaped particles and a triblock copolymer Pluronic F127 (PF127). These novel composites form hard gels at an elevated temperature of 37 °C. For certain concentrations (<20 w/v. %) of hematite pseudocubes in 17.5 w/v. % of PF127, the gel strength is enhanced and the brittleness of the gels decreases. Higher concentrations (>20 w/v. %) of hematite pseudocubes in PF127 result in weaker and fragile gels. We develop an extensive rheological fingerprint using linear and nonlinear rheological studies. Adsorption of PF127 copolymer molecules on the hematite cube surfaces would further assist the formation of particle clusters along with magnetic interactions to be held effectively in the PF127 micellar network at elevated temperatures. The microscopic structure of these composite gels is visualized through a confocal microscope. Our experiments show that addition of hematite cubes up to 20 w/v. % does not change the rapid thermal gelation of PF127 solutions; hence, the hematite-PF127 composite, which transforms into a hard gel near human body temperature of 37 °C, could be suitable for use in smart drug delivery systems.

Structural evolution of granular cubes packing during shear-induced ordering

Packings of granular particles may transform into ordered structures under external agitation, which is a special type of out-of-equilibrium self-assembly. Here, evolution of the internal packing structures of granular cubes under cyclic rotating shearing has been analyzed using magnetic resonance imaging techniques. Various order parameters, different types of contacts and clusters composed of face-contacting cubes, as well as the free volume regions in which each cube can move freely have been analyzed systematically to quantify the ordering process and the underlying mechanism of this granular self-assembly. The compaction process is featured by a first rapid formation of orientationally ordered local structures with faceted contacts, followed by further densification driven by free-volume maximization with an almost saturated degree of order. The ordered structures are strongly anisotropic with contacting ordered layers in the vertical direction while remaining liquid-like in the horizontal directions. Therefore, the constraint of mechanical stability for granular packings and the thermodynamic principle of entropy maximization are both effective in this system, which we propose can be reconciled by considering different depths of supercooling associated with various degrees of freedom.

Cubatic structural transformation of the packing of granular cylinders

Packing structures of granular cylinders with the aspect ratio close to one have been reconstructed with the help of magnetic resonance imaging techniques. By controlling the container boundary conditions and preparation protocols, a structural transformation from a disordered liquid-like state to an orientationally ordered state with cubatic symmetry at a high packing fraction is observed. This ordering process is accompanied by the formation of more faceted contacts, which lower the elastic energy between jammed granular particles to drive the transformation. With the help of Edwards' volume ensemble theory, this granular structural transformation is explained using a phenomenological thermodynamic model and a self-consistent mean-field statistical mechanical model. Both models predict a sharp but continuous change of order parameter when the effective granular temperature is lowered. The intrinsic difference and connection between this granular structural transformation and the entropy-driven phase transition of conventional thermal hard-particle systems are discussed.

Controlling morphology in hybrid isotropic/patchy particle assemblies

Brownian dynamics is used to study self-assembly in a hybrid system of isotropic particles (IPs), combined with anisotropic building blocks that represent special "designer particles." Those are modeled as spherical patchy particles (PPs) with binding only allowed between their patches and IPs. In this study, two types of PPs are considered: Octahedral PPs (Oh-PPs) and Square PPs (Sq-PPs), with octahedral and square arrangements of patches, respectively. The self-assembly is additionally facilitated by the simulated annealing procedure. The resultant structures are characterized by a combination of local correlations in cubatic ordering and a symmetry-specific variation of bond orientation order parameters (SymBOPs). By varying the PP/IP size ratio, we detected a sharp crossover between two distinct morphologies in both types of systems. High symmetry phases, NaCl crystal for Oh-PP and square lattice for Sq-PP, are observed for larger size ratios. For the smaller ones, the dominant morphologies are significantly different, e.g., Oh-PPs form a compact amorphous structure with predominantly face-to-face orientation of neighboring PPs. Unusually, for a morphology without a long-range order, it is still possible to identify well organized coherent clusters of this structure, thanks to the adoption of our SymBOP-based characterization.

Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: One or two phase transitions?

We obtain the phase diagram of the hard core lattice gas with third nearest neighbor exclusion on the triangular lattice using Monte Carlo simulations that are based on a rejection-free flat histogram algorithm. In a recent paper [Darjani et al., J. Chem. Phys. 151, 104702 (2019)], it was claimed that the lattice gas with third nearest neighbor exclusion undergoes two phase transitions with increasing density with the phase at intermediate densities exhibiting hexatic order with continuously varying exponents. Although a hexatic phase is expected when the exclusion range is large, it has not been seen earlier in hard core lattice gases with short range exclusion. In this paper, by numerically determining the entropies for all densities, we show that there is only a single phase transition in the system between a low-density fluid phase and a high density ordered sublattice phase and that a hexatic phase is absent. The transition is shown to be first order in nature, and the critical parameters are determined accurately.

Thermodynamic stability of hard sphere crystals in dimensions 3 through 10

Although much is known about the metastable liquid branch of hard spheres-from low dimension d up to [Formula: see text]-its crystal counterpart remains largely unexplored for [Formula: see text]. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to [Formula: see text], and the dimensional trends suggest that crystal stability likely persists well beyond that point.

Designer Nanomaterials through Programmable Assembly

Nanoparticles have long been recognized for their unique properties, leading to exciting potential applications across optics, electronics, magnetism, and catalysis. These specific functions often require a designed organization of particles, which includes the type of order as well as placement and relative orientation of particles of the same or different kinds. DNA nanotechnology offers the ability to introduce highly addressable bonds, tailor particle interactions, and control the geometry of bindings motifs. Here, we discuss how developments in structural DNA nanotechnology have enabled greater control over 1D, 2D, and 3D particle organizations through programmable assembly. This Review focuses on how the use of DNA binding between nanocomponents and DNA structural motifs has progressively allowed the rational formation of prescribed particle organizations. We offer insight into how DNA-based motifs and elements can be further developed to control particle organizations and how particles and DNA can be integrated into nanoscale building blocks, so-called "material voxels", to realize designer nanomaterials with desired functions.

Magnetic Coupling in Colloidal Clusters for Hierarchical Self-Assembly

Manipulating the way in which colloidal particles self-organize is a central challenge in the design of functional soft materials. Meeting this challenge requires the use of building blocks that interact with one another in a highly specific manner. Their fabrication, however, is limited by the complexity of the available synthesis procedures. Here, we demonstrate that, starting from experimentally available magnetic colloids, we can create a variety of complex building blocks suitable for hierarchical self-organization through a simple scalable process. Using computer simulations, we compress spherical and cubic magnetic colloids in spherical confinement, and investigate their suitability to form small clusters with reproducible structural and magnetic properties. We find that, while the structure of these clusters is highly reproducible, their magnetic character depends on the particle shape. Only spherical particles have the rotational degrees of freedom to produce consistent magnetic configurations, whereas cubic particles frustrate the minimization of the cluster energy, resulting in various magnetic configurations. To highlight their potential for self-assembly, we demonstrate that already clusters of three magnetic particles form highly nontrivial Archimedean lattices, namely, staggered kagome, bounce, and honeycomb, when focusing on different aspects of the same monolayer structure. The work presented here offers a conceptually different way to design materials by utilizing preassembled magnetic building blocks that can readily self-organize into complex structures.

Classifying Crystals of Rounded Tetrahedra and Determining Their Order Parameters Using Dimensionality Reduction

Using simulations we study the phase behavior of a family of hard spherotetrahedra, a shape that interpolates between tetrahedra and spheres. We identify 13 close-packed structures, some with packings that are significantly denser than previously reported. Twelve of these are crystals with unit cells of N = 2 or N = 4 particles, but in the shape regime of slightly rounded tetrahedra we find that the densest structure is a quasicrystal approximant with a unit cell of N = 82 particles. All 13 structures are also stable below close packing, together with an additional 14th plastic crystal phase at the sphere side of the phase diagram, and upon sufficient dilution to packing fractions below 50-60% all structures melt. Interestingly, however, upon compressing the fluid phase, self-assembly takes place spontaneously only at the tetrahedron and the sphere side of the family but not in an intermediate regime of tetrahedra with rounded edges. We describe the local environment of each particle by a set of l-fold bond orientational order parameters q̅l, which we use in an extensive principal component analysis. We find that the total packing fraction as well as several particular linear combinations of q̅l rather than individual q̅l's are optimally distinctive, specifically the differences q̅4 - q̅6 for separating tetragonal from hexagonal structures and q̅4-q̅8 for distinguishing tetragonal structures. We argue that these characteristic combinations are also useful as reliable order parameters in nucleation studies, enhanced sampling techniques, or inverse-design methods involving odd-shaped particles in general.

Self-assembly and entropic effects in pear-shaped colloid systems. I. Shape sensitivity of bilayer phases in colloidal pear-shaped particle systems

The role of particle shape in self-assembly processes is a double-edged sword. On the one hand, particle shape and particle elongation are often considered the most fundamental determinants of soft matter structure formation. On the other hand, structure formation is often highly sensitive to details of shape. Here, we address the question of particle shape sensitivity for the self-assembly of hard pear-shaped particles by studying two models for this system: (a) the pear hard Gaussian overlap (PHGO) and (b) the hard pears of revolution (HPR) model. Hard pear-shaped particles, given by the PHGO model, are known to form a bicontinuous gyroid phase spontaneously. However, this model does not replicate an additive object perfectly and, hence, varies slightly in shape from a "true" pear-shape. Therefore, we investigate in the first part of this series the stability of the gyroid phase in pear-shaped particle systems. We show, based on the HPR phase diagram, that the gyroid phase does not form in pears with such a "true" hard pear-shaped potential. Moreover, we acquire first indications from the HPR and PHGO pair-correlation functions that the formation of the gyroid is probably attributed to the small non-additive properties of the PHGO potential.

Scattering from colloidal cubic silica shells: Part II, static structure factors and osmotic equation of state

HYPOTHESIS

The shape of colloidal particles affects the structure of colloidal dispersions. The effect of the cube shape on the thermodynamics of colloidal cube dispersions has not yet been studied experimentally. Static light scattering measurements on colloidal cubic silica shells at finite concentrations allows us to measure the structure factor of colloidal cube fluids and to test theoretical predictions for the equation of state of hard convex superballs.

EXPERIMENTS

Hollow silica nanocubes of varying concentrations in N,N,-dimethylformamide were studied with static light scattering. The structure factor was extracted from the scattering curves using experimental form factors. From this experimental structure factor, the specific density of the particles, and the osmotic compressibility were obtained. This osmotic compressibility was then compared to a theoretical equation of state of hard superballs.

FINDINGS

The first experimental structure factors of a stable cube fluid are presented. The osmotic compressibility of the cube fluid can be described by the equation of state of a hard superball fluid, showing that silica cubes in N,N,-dimethylformamide with LiCl effectively interact as hard particles.

Scattering from colloidal cubic silica shells: Part I, particle form factors and optical contrast variation

HYPOTHESIS

Colloidal cubic silica shells, prepared from cuprous oxide cubes, with a typical size of 100 nm are promising model particles for scattering studies on dilute, as well as concentrated fluids, of non-spherical colloids.

EXPERIMENTS

Small angle X-ray scattering, and static light scattering are employed to determine form factors of cubic silica shells and silica covered cuprous oxide cubes. Contrast variation experiments are performed to assess the refractive index and optical homogeneity of the cubic silica shells, which is important for the extension of the scattering study to concentrated dispersions of cubic shells in Part II (Dekker, submitted for publication).

RESULTS

The experimental form factors, which compare well to theoretical form factors, manifest cubic silica shells that are dispersed as single stable colloids with a shape intermediate between a sphere and a perfect cube. Contrast variation demonstrates that the silica shells are optically homogeneous, with a refractive index that is independent of the shell thickness. The results presented here open up the possibility to extract structure factors from light scattering measurements on concentrated cube dispersions in Part II.

Self-assembly of charged colloidal cubes

In this work, we show how and why the interactions between charged cubic colloids range from radially isotropic to strongly directionally anisotropic, depending on tuneable factors. Using molecular dynamics simulations, we illustrate the effects of typical solvents to complement experimental investigations of cube assembly. We find that in low-salinity water solutions, where cube self-assembly is observed, the colloidal shape anisotropy leads to the strongest attraction along the corner-to-corner line, followed by edge-to-edge, with a face-to-face configuration of the cubes only becoming energetically favorable after the colloids have collapsed into the van der Waals attraction minimum. Analysing the potential of mean force between colloids with varied cubicity, we identify the origin of the asymmetric microstructures seen in experiment.

Hard convex lens-shaped particles: Characterization of dense disordered packings

Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is "optimal" in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction ϕ_{MRJ}≃0.73 [G. Cinacchi and S. Torquato, Soft Matter 14, 8205 (2018)1744-683X10.1039/C8SM01519H]. This value is only a few percent lower than ϕ_{DKP}=0.76210⋯, the packing fraction of the corresponding densest-known crystalline (degenerate) packings [G. Cinacchi and S. Torquato, J. Chem. Phys. 143, 224506 (2015)JCPSA60021-960610.1063/1.4936938]. By exploiting the appreciably reduced propensity that a system of such optimal lenses has to positionally and orientationally order, disordered packings of them are progressively generated by a Monte Carlo method-based procedure from the dilute equilibrium isotropic fluid phase to the dense nonequilibrium MRJ state. This allows us to closely monitor how the (micro)structure of these packings changes in the process of formation of the MRJ state. The gradual changes undergone by the many structural descriptors calculated here can coherently and consistently be traced back to the gradual increase in contacts between the hard particles until the isostatic mean value of ten contact neighbors per lens is reached at the effectively hyperuniform MRJ state. Compared to the MRJ state of hard spheres, the MRJ state of such optimal lenses is denser (less porous), more disordered, and rattler-free. This set of characteristics makes them good glass formers. It is possible that this conclusion may also hold for other hard convex uniaxial particles with a correspondingly similar aspect ratio, be they oblate or prolate, and that, by using suitable biaxial variants of them, that set of characteristics might further improve.

Phase diagram of a system of hard cubes on the cubic lattice

We study the phase diagram of a system of 2×2×2 hard cubes on a three-dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased: disordered, layered, sublattice ordered, and columnar ordered. In the layered phase, the system spontaneously breaks up into parallel slabs of size 2×L×L where only a very small fraction cubes do not lie wholly within a slab. Within each slab, the cubes are disordered; translation symmetry is thus broken along exactly one principal axis. In the solidlike sublattice-ordered phase, the hard cubes preferentially occupy one of eight sublattices of the cubic lattice, breaking translational symmetry along all three principal directions. In the columnar phase, the system spontaneously breaks up into weakly interacting parallel columns of size 2×2×L, where only a very small fraction cubes do not lie wholly within a column. Within each column, the system is disordered, and thus translational symmetry is broken only along two principal directions. Using finite-size scaling, we show that the disordered-layered phase transition is continuous, while the layered-sublattice and sublattice-columnar transitions are discontinuous. We construct a Landau theory written in terms of the layering and columnar order parameters which is able to describe the different phases that are observed in the simulations and the order of the transitions. Additionally, our results near the disordered-layered transition are consistent with the O(3) universality class perturbed by cubic anisotropy as predicted by the Landau theory.

Unusual packing of soft-shelled nanocubes

Space-filling generally governs hard particle packing and the resulting phases and interparticle orientations. Contrastingly, hard-shaped nanoparticles with grafted soft-ligands pack differently since the energetically interacting soft-shell is amenable to nanoscale sculpturing. While the interplay between the shape and soft-shell can lead to unforeseen packing effects, little is known about the underlying physics. Here, using electron microscopy and small-angle x-ray scattering, we demonstrate that nanoscale cubes with soft, grafted DNA shells exhibit remarkable packing, distinguished by orientational symmetry breaking of cubes relative to the unit cell vectors. This zigzag arrangement occurs in flat body-centered tetragonal and body-centered cubic phases. We ascribe this unique arrangement to the interplay between shape and a spatially anisotropic shell resulting from preferential grafting of ligands to regions of high curvature. These observations reveal the decisive role played by shell-modulated anisotropy in nanoscale packing and suggest a plethora of new spatial organizations for molecularly decorated shaped nanoparticles.

DEM simulation of the local ordering of tetrahedral granular matter

The formation and growth of local order clusters in a tetrahedral granular assembly driven by 3D mechanical vibration were captured in DEM (discrete element method) dynamic simulation using a multi-sphere model. Two important kinds of clusters, dimer and wagon wheel structures, were observed based on which the growth behavior and mechanism of each local cluster with different orientations/structures were investigated. The results show that during vibration, dimer clusters are formed first and then most of them grow into linear trimers and tetramers. Wagon wheel clusters are also frequently observed that grow into hexamers and, further, octamer and nonamer local clusters. Coordination number (CN) evolution indicates that the decrease of local mean CN can be regarded as the signal for the formation of local clusters in the tetrahedral particle packing system. Nematic order metric analysis shows that although the two basic structures (dimer and wagon wheel structures) grow into complex local clusters during packing densification, these local clusters are randomly distributed in the tetrahedral particle packing system. Stress analysis indicates that the dimer-based local clusters are mostly formed in the compaction state of the tetrahedral particle packing system during the vibrated packing densification process. In comparison, the wagon wheel-based local clusters need much stronger interaction forces from tetrahedral particles during vibrated packing densification.

Revealing a Vacancy Analog of the Crowdion Interstitial in Simple Cubic Crystals

Vacancies in simple cubic crystals of hard cubes are known to delocalize over one-dimensional chains of several lattice sites. Here, we use computer simulations to examine the structure and dynamics of vacancies in simple cubic crystals formed by hard cubes, right rhombic prisms (slanted cubes), truncated cubes, and particles interacting via a soft isotropic pair potential. We show that these vacancies form a vacancy analog of the crowdion interstitial, generating a strain field which follows a soliton solution of the sine-Gordon equation, and diffusing via a persistent random walk. Surprisingly, we find that the structure of these "voidions" is not significantly affected by changes in density, vacancy concentration, and even particle interaction. We explain this structure quantitatively using a one-dimensional model that includes the free-energy barrier particles have to overcome to slide between lattice sites and the effective pair interaction along this line. We argue that voidions are a robust phenomenon in systems of repulsive particles forming simple cubic crystals.

Continuum percolation-based tortuosity and thermal conductivity of soft superball systems: shape dependence from octahedra via spheres to cubes

Understanding the effect of particle shape on the percolation threshold, tortuosity and thermal conductivity of soft (geometrical overlapping) particle systems is very crucial for the design and optimization of such materials, including colloids, polymers, and porous and fracture media. In this work, we first combine the excluded-volume theory with the Monte Carlo simulations to determine the percolation threshold for a family of soft superballs, the shape of which interpolates between octahedra and cubes via spheres. Then, we propose two continuum percolation-based models to respectively obtain the tortuosity and effective thermal conductivity of soft superball systems considering their percolation behavior, where monodisperse overlapping superballs are uniformly distributed in a homogeneous solid matrix. Specifically, both models cover the whole feasible range of superball volume fractions, including near the percolation threshold. Comparison with extensive experimental, numerical and theoretical results confirms that the present models are capable of precisely predicting the percolation threshold, tortuosity and thermal conductivity of such systems. Furthermore, we apply the proposed models to probe the influence of particle shape on these important parameters. Our results show that the decreasing percolation threshold and tortuosity as soft particles become more anisotropic is consistent with increasing conductivity. It suggests that the anisotropic-shaped inclusion phase is more conducting than the spherical inclusion phase. The present theoretical strategies and conclusions may provide sound guidance for the synthesis of colloidal and polymer superballs.

Synthesis of Hollow Silica Nanocubes with Tuneable Size and Shape, Suitable for Light Scattering Studies

We present a preparation method for hollow silica nanocubes with tuneable size and shape in the range required for light scattering studies. Cuprous oxide nanocubes are prepared by a water-assisted polyol method. By adjusting the water content, the size of the nanocubes can be tuned in the range of 40–120 nm. These cubes function as a shape template in the subsequent coating with Stöber silica, resulting in core-shell nanocubes. Dissolving the core with nitric acid results in hollow silica nanocubes with sizes ranging from 80–120 nm and cubicity shape parameters between 3 and 6.5.

Phase behaviour of colloidal superballs mixed with non-adsorbing polymers

Inspired by experimental work on colloidal cuboid-polymer dispersions (Rossi et al., Soft Matter, 7, 4139 (2011)) we have theoretically studied the phase behaviour of such mixtures. To that end, free volume theory (FVT) was applied to predict the phase behaviour of mixtures of superballs and non-adsorbing polymer chains in a common solvent. Closed expressions for the thermodynamic properties of a suspension of hard colloidal superballs have been derived, accounting for fluid (F), face-centred cubic (FCC) and simple cubic (SC) phase states. Even though the considered solid phases are approximate, the hard superballs phase diagram semi-quantitatively matches with more evolved methods. The theory developed for the cuboid-polymer mixture reveals a rich phase behaviour, which includes not only isostructural F₁-F₂ coexistence, but also SC₁-SC₂ coexistence, several triple coexistences, and even a quadruple-phase coexistence region (F₁-F₂-SC-FCC). The model proposed offers a tool to asses the stability of cuboid-polymer mixtures in terms of the colloid-to-polymer size ratio.

Experimental Study of Ordering of Hard Cubes by Shearing

We experimentally analyze the compaction dynamics of an ensemble of cubic particles submitted to a novel type of excitation. Instead of the standard tapping procedure used in granular materials we apply alternative twists to the cylindrical container. Under this agitation, the development of shear forces among the different layers of cubes leads to particle alignment. As a result, the packing fraction grows monotonically with the number of twists. If the intensity of the excitations is sufficiently large, an ordered final state is reached where the volume fraction is the densest possible compatible with the boundary condition. This ordered final state resembles the tetratic or cubatic phases observed in colloids.

Shape-dependent effective diffusivity in packings of hard cubes and cuboids compared with spheres and ellipsoids

We performed computational screening of effective diffusivity in different configurations of cubes and cuboids compared with spheres and ellipsoids. In total, more than 1500 structures are generated and screened for effective diffusivity. We studied simple cubic and face-centered cubic lattices of spheres and cubes, random configurations of cubes and spheres as a function of volume fraction and polydispersity, and finally random configurations of ellipsoids and cuboids as a function of shape. We found some interesting shape-dependent differences in behavior, elucidating the impact of shape on the targeted design of granular materials.

Nanoparticle Shape Influences the Magnetic Response of Ferro-Colloids

The interesting magnetic response of conventional ferro-colloid has proved extremely useful in a wide range of technical applications. Furthermore, the use of nano/micro- sized magnetic particles has proliferated cutting-edge medical research, such as drug targeting and hyperthermia. In order to diversify and improve the application of such systems, new avenues of functionality must be explored. Current efforts focus on incorporating directional interactions that are surplus to the intrinsic magnetic one. This additional directionality can be conveniently introduced by considering systems composed of magnetic particles of different shapes. Here we present a combined analytical and simulation study of permanently magnetized dipolar superball particles; a geometry that closely resembles magnetic cubes synthesized in experiments. We have focused on determining the initial magnetic susceptibility of these particles in dilute suspensions, seeking to quantify the effect of the superball shape parameter on the system response. In turn, we linked the computed susceptibilities to the system microstructure by analyzing cluster composition using a connectivity network analysis. Our study has shown that by increasing the shape parameter of these superball particles, one can alter the outcome of self-assembly processes, leading to the observation of an unanticipated decrease in the initial static magnetic susceptibility.

How cube-like must magnetic nanoparticles be to modify their self-assembly?

Systems whose magnetic response can be finely tuned using control parameters, such as temperature and external magnetic field strength, are extremely desirable, functional materials. Magnetic nanoparticles, in particular suspensions thereof, offer opportunities for this controllability to be realised. Cube-like particles are particularly mono-disperse examples that, together with their favourable packing behaviour, make them of significant interest for study. Using a combination of analytical calculations and molecular dynamics we have studied the self-assembly of permanently magnetised dipolar superballs. The superball shape parameter was varied in order to interpolate the region between the already well-studied sphere system and that of the recently investigated cube. Our findings show that as a superball particle becomes more cubic the chain to ring transition, observed in the ground state of spherical particles, occurs at an increasingly larger cluster size. This effect is mitigated, however, by the appearance of a competing configuration; asymmetric rings, a conformation that we show superballs can readily adopt.

Observation of solid-solid transitions in 3D crystals of colloidal superballs

Self-organization in anisotropic colloidal suspensions leads to a fascinating range of crystal and liquid crystal phases induced by shape alone. Simulations predict the phase behaviour of a plethora of shapes while experimental realization often lags behind. Here, we present the experimental phase behaviour of superball particles with a shape in between that of a sphere and a cube. In particular, we observe the formation of a plastic crystal phase with translational order and orientational disorder, and the subsequent transformation into rhombohedral crystals. Moreover, we uncover that the phase behaviour is richer than predicted, as we find two distinct rhombohedral crystals with different stacking variants, namely hollow-site and bridge-site stacking. In addition, for slightly softer interactions we observe a solid-solid transition between the two. Our investigation brings us one step closer to ultimately controlling the experimental self-assembly of superballs into functional materials, such as photonic crystals.

Depletion-driven crystallization of cubic colloids sedimented on a surface

Cubic colloids, sedimented on a surface and immersed in a solution of depletant molecules, were modeled with a family of shapes which smoothly varies from squares to circles. Using Wang-Landau simulations with expanded ensembles, we observe the formation of rhombic lattices, square lattices, hexagonal lattices, and a fluid phase. This systematic investigation includes locating transitions between all combinations of the three lattice structures upon changing the shape and transitions between the fluid and crystal upon changing the depletant concentration. The rhombic lattice deforms smoothly between square-like and hexagonal-like angles, depending on both the shape and the depletant concentration. Our results on the effect of the depletant concentration, depletant size, and colloid shape to influence the stability of the fluid and the lattice structures may help guide experimental studies with recently synthesized cubic colloids.

Maximally dense random packings of cubes and cuboids via a novel inverse packing method

The packings of cubes and cuboids (i.e., "elongated" or "compressed" cubes) are ubiquitous in nature. The high symmetry and space-tiling nature of such particles make them easily packable in dense configurations with a high degree of orientational and translational order. In this paper, we devise a novel inverse packing method that enables one to generate dense hard-particle packings with a controllable degree of disorder/order quantified by predefined order metrics via stochastic Monte Carlo optimizations. We employ the inverse packing method to generate and investigate the maximally dense random packings (MDRPs) of hard cubes and cuboids with aspect ratio α, in which a series of newly introduced normalized local cubatic order parameters sensitive to the onset of any spatial order in packings of cubes and cuboids is minimized. The density of the MDRP of cubes is φ ≈ 0.637, which increases as the shape deviates from the cube limit (α = 1) and reaches the maximal values for cuboids with aspect ratios α = 0.7 or 1.5. These special α values associated with local density extrema are almost identical for those associated with the random packings of spherocylinders, spheroids and superellipsoids, suggesting a universal influence of shape elongation on random packing density. Our inverse packing method can be readily utilized to study the MDRPs of other hard particles and the normalized local cubatic order parameter introduced here is applicable to other shaped particles characterized by three principal axes.

Exploring the zone of anisotropy and broken symmetries in DNA-mediated nanoparticle crystallization

In this work, we present a joint experimental and molecular dynamics simulations effort to understand and map the crystallization behavior of polyhedral nanoparticles assembled via the interaction of DNA surface ligands. In these systems, we systematically investigated the interplay between the effects of particle core (via the particle symmetry and particle size) and ligands (via the ligand length) on crystallization behavior. This investigation revealed rich phase diagrams, previously unobserved phase transitions in polyhedral crystallization behavior, and an unexpected symmetry breaking in the ligand distribution on a particle surface. To understand these results, we introduce the concept of a zone of anisotropy, or the portion of the phase space where the anisotropy of the particle is preserved in the crystallization behavior. Through comparison of the zone of anisotropy for each particle we develop a foundational roadmap to guide future investigations.

Rheology of cubic particles suspended in a Newtonian fluid

Many real-world industrial processes involve non-spherical particles suspended in a fluid medium. Knowledge of the flow behavior of these suspensions is essential for optimizing their transport properties and designing processing equipment. In the present work, we explore and report on the rheology of concentrated suspensions of cubic-shaped colloidal particles under steady and dynamic shear flow. These suspensions exhibit a rich non-Newtonian rheology that includes shear thickening and normal stress differences at high shear stresses. Scalings are proposed to connect the material properties of these suspensions of cubic particle to those measured for suspensions of spherical particles. Negative first normal stress differences indicate that lubrication hydrodynamic forces dominate the stress in the shear-thickened state. Accounting for the increased lubrication hydrodynamic interactions between the flat surfaces of the cubic particles allows for a quantitative comparison of the deviatoric stress in the shear-thickened state to that of spherical particles. New semi-empirical models for the viscosity and normal stress difference coefficients are presented for the shear-thickened state. The results of this study indicate that cubic particles offer new and unique opportunities to formulate colloidal dispersions for field-responsive materials.

Rheology and dynamics of colloidal superballs

Recent advances in colloidal synthesis make it possible to generate a wide array of precisely controlled, non-spherical particles. This provides a unique opportunity to probe the role that particle shape plays in the dynamics of colloidal suspensions, particularly at higher volume fractions, where particle interactions are important. We examine the role of particle shape by characterizing both the bulk rheology and micro-scale diffusion in a suspension of pseudo-cubic silica superballs. Working with these well-characterized shaped colloids, we can disentangle shape effects in the hydrodynamics of isolated particles from shape-mediated particle interactions. We find that the hydrodynamic properties of isolated superballs are marginally different from comparably sized hard spheres. However, shape-mediated interactions modify the suspension microstructure, leading to significant differences in the self-diffusion of the superballs. While this excluded volume interaction can be captured with a rescaling of the superball volume fraction, we observe qualitative differences in the shear thickening behavior of moderately concentrated superball suspensions that defy simple rescaling onto hard sphere results. This study helps to define the unknowns associated with the effects of shape on the rheology and dynamics of colloidal solutions.