It is widely known that the vertical deposition of monodisperse microspheres results in a formation of a colloidal crystal with the predominant fcc structure, in which the close-packed layers with the hexagonal symmetry are parallel to the substrate. For layers with hexagonal symmetry there are two possible positions for one layer on top of the previous one (ABA or ABC), which gives rise to stacking faults in colloidal crystals. In this work we have found that under certain conditions vertical co-deposition of two types of microspheres results in formation of fcc colloidal crystals with the square symmetry of layers parallel to the substrate. For layers with square symmetry there is only one possible position of a layer on top of previous one (ABA), which leads to formation of stacking-fault-free colloidal crystal domains. We systematically studied binary colloidal systems with particle size ratios from 0.22 to 0.40 and particle number (small to large) ratios from 0.5 to 3.0. For fixed particle number ratio, different total concentrations were tested for the vertical deposition procedure. It was found that at low total concentrations (~ 0.4 wt.%) square symmetry prevails (~ 70% of the film area). The increase of concentration gradually shifted the preference toward the formation of layers with the hexagonal symmetry. These observations are supported by SEM imaging and laser diffraction domain mapping. The internal structure of binary colloidal crystal films was characterized by small-angle X-ray scattering using a synchrotron radiation. Diffraction patterns and diffraction peak intensity profiles revealed that the observed structure with square layer symmetry corresponds to fcc lattice.

Colloidal self-assembly has been demonstrated as a prime method for the fabrication of multidimensional photonic materials. Particle ‘shape programming&’ can be combined with physical confinement of colloid suspensions to access and stabilize a rich diversity of quasi-2D transition structures as material templates for optical band gap and anomalous refraction properties. Here, wedge-cell confinement is employed to study colloidal phase behavior of hollow fluorescent silica dimers (peanut-shaped) as a function of confinement height. Five distinct transitions are discovered in the range from one to two layers of in-plane oriented dimers. Specifically, each configuration found is a degenerate crystal tiling of the corresponding sphere-based structure along the descriptive order sequence-- 1Δ -->1B--> 2Square -->2Δ where, Δ and Square indicate layers with triangular and square symmetry, respectively. In this scheme the ‘buckled&’ phase is indicted by 1B. Two distinct 2Δ phases are determined for the dimer case, depending on the degree of out-of-plane tilted tiling. Mostly out-of-plane colloidal units in 2ΔI re-assemble to form two layers of predominantly in-plane lying dimers for 2ΔII. These arrangements can be predicted simply from closest packing arguments for incommensurate layer heights and are in agreement with findings from Monte Carlo simulations. Order parameters and distribution functions for positional and bond orientational order, voronoi constructions for detecting defects and number of nearest neighbors, and fast Fourier transforms (FFT) quantitatively characterize each phase from confocal image analysis. The experimental real time video microscopy and theoretical phase diagram will be presented.

Isotropic particles rather easily assemble into the simple face-centered cubic crystal structure. More complex phases are harder to achieve, but have recently been reported using a number of approaches. This presentation focuses on isolating the role of building block shape for self-assembly, which provides insight into the ordering of molecules and the crystallization of colloids, nanoparticles, proteins and viruses. We demonstrate how novel and unusual ordered crystal phases can be achieved with colloids of polyhedral shape and discuss progress in understanding structure from the geometric attributes of the building blocks. Using computer simulations, we investigate 145 convex polyhedra whose assembly arises solely from their anisotropic shape, demonstrating 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 either a liquid crystal, plastic crystal, or crystal can be predicted. P.F. Damasceno, M. Engel, S.C. Glotzer [arXiv:1202.2177], in press (2012).

For hard anisotropic particles the formation of a wide variety of fascinating crystal and liquid-crystal phases is accomplished by entropy alone. A better understanding of these entropy-driven phase transitions will shed light on the self-assembly of colloidal (nano)particles. Using Monte Carlo simulations and free-energy calculations, we determine the phase diagram of colloidal hard superballs, of which the shape interpolates between cubes and octahedra via spheres. We discover not only a stable face-centered cubic (fcc) plastic crystal phase for near-spherical particles, but also a stable body-centered cubic (bcc) plastic crystal close to the octahedron shape. Moreover, coexistence of these two plastic crystals is observed with a substantial density gap. The plastic fcc and bcc crystals are, however, both unstable in the cube and octahedron limit, suggesting that the local curvature, i.e. rounded corners and curved faces, of superballs plays an important role in stabilizing the rotator phases. In addition, we observe a two-step melting phenomenon for hard octahedra, in which the Minkowski crystal melts into a metastable bcc plastic crystal before melting into the fluid phase. For cubes, we find a first-order phase transition between a fluid and a simple cubic crystal phase that is stabilized by a surprisingly large number of vacancies, reaching a net vacancy concentration of ~6.4% near bulk coexistence. Additionally, we determine the phase diagram of colloidal hard platelets and show that the cubatic phase is metastable with respect to the isotropic-columnar phase transition.

Crystallization of a matter has long been a major thrust in chemistry, biochemistry and materials science, with comparable importance at all length scales ranging from atoms to large biomolecules. For example, the assembly of two different types of inorganic nanocrystals with nearly spherical shape into a binary long-range ordered superlattice provides a general route to a large variety of materials. Proceeding from similar considerations, a true daydream of a scientist may be derived - assembly of intrinsically different building blocks if their dimensions are comparable in a certain range. The binary mixtures of nanocrystals typically pack into one of the densest structures at a given size ratio of smaller and larger spheres. Since the appropriate size ratio (typically in the range of 0.3-0.8) is a primary consideration for entropy driven colloidal crystallization of hard spheres, we show that 2-10 nm large nanocrystals can form multicomponent crystals with other species of comparable dimension. We grew novel type of crystalline(superlattice) structures by combining nanocrystals with various inorganic clusters such as giant polyoxometalates and fullerenes. To construct binary superlattices, we used several kinds of building blocks: sterically-stabilized NCs, fullerene derivatives (1-1.3nm), and giant polyoxometalate ("POM") clusters such as 2.5nm {Mo72Fe30}. The integration of polyoxometalate and fullerene clusters into hybrid superlattice with inorganic nanocrystals may introduce unique catalytic, magnetic and electronic functionalities of these building blocks.

We report the experimentally measured behavior of thermally driven regular polygonal platelets that have been lithographically fabricated, dispersed in a liquid, concentrated in a plane using roughness controlled depletion attractions, and observed by optical microscopy. Interactions between the uniform polygons are effectively hard. Pentagons, which cannot fully tile a plane, exhibit an interesting form of a rotational glass transition as well as an unusual spatial colloidal order-to-disorder transition at the highest densities. By contrast, squares having slightly rounded corners at high densities exhibit a crystal-crystal transition between a hexagonal rotator crystal and a rhombic crystal. Perhaps more surprisingly, triangles undergo a transition between an isotropic phase and a triatic liquid crystal phase, which, at higher densities, exhibits a form of local chiral symmetry breaking. Maximization of the combination of translational and rotational entropy is a guiding principle, yet this must be tempered by the possibility of jamming that depends upon particle shape.

Self-assembly of single- and multi-component colloidal nanocrystals into large area superlattices is of great scientific importance for better understanding of the assembly process and for bottom-up integration into functional devices. Over the past few years, a rich array of binary nanocrystal superlattices (BNSLs) has been demonstrated using spherical metallic, magnetic, semiconducting nanocrystals. In this presentation we will focus on recent progress on the high yield synthesis of monodisperse rare earth fluoride nanocrystals that exhibit a spectacular variety of morphologies including nanorods, hexagonal prism, tetragonal or hexagonal platelets, tetragonal bipyramids etc. An interfacial assembly strategy is employed to organize these nanocrystals into superlattices over multiple length scales facilitating nanocrystal characterization and enabling systematic studies of shape-directed assembly. The global and local ordering of these superstructures is programmed by the control over individual nanocrystal&’s anisotropy attributes such as faceting, aspect ratio, corner truncation, interaction patchiness etc. These experimental results together with the Monte Carlo simulations have led us to a better understanding of the important role of anisotropic interactions during self-assembly in addition to entropic contribution. I will also share our recent results in assembling rod-sphere BNSLs and discuss the implications in the design of optical metamaterials using nanocrystalline building blocks.

Ligand-stabilized nanoparticles (NPs) assembled into long-range ordered arrays, also known as “nanoparticle supracrystals (NPSCs)”, are expected to provide a powerful general platform for designing new types of solids. In particular, the NPs are themselves self-assembled structures consisting of a core and a self-assembled monolayer of ligand molecules surrounding it. The self-assembled structure of the NPs themselves can determine the structure of the self-assembled supracrystals. Ligands are of special interest because they control a large set of the nanoparticle properties. The role of the ligands in affecting the structural behavior of NPSCs remains largely unexplored. In this work, we have studied the effect of ligands for two-dimensional (2D) self-assembled NPSCs. We have been able to synthesize monodisperse gold NPs of the same core size but different ligand molecules, and developed a method for monolayer film processing to prepare 2D NPSCs based on a Langmuir assembly through multiple compression cycles.1 Here we will show that ligand interactions have direct consequences on the ordering and symmetry of the assembled NPSCs. We report on a set of NPSC arrays in which small changes in either the NP ligand environment or the ligand configuration geometry induce significant variations in the order parameters of the crystal. First, we show that the packing organization of a 2D NPSC array of hydrophobic alkanethiol ligands varies with subtle chemical changes in the system, leading to a transition between long-range to short-range (almost glassy) ordered phases. This transition is driven by small differences in intermolecular interpenetration of the ligand molecules that can be related to ligand conformation. Second, we show the first 2D NPSC structures to have unique global anisotropic symmetry induced from the local bond orientational asymmetry due to unique interaction between amphiphilic NP ligand shells. This anisotropy leads to polarization-dependent plasmonic properties of the film. 1) Kim, J.Y.; Raja, S.; Stellacci, F., Evolution of Langmuir film of nanoparticles through successive compression cycles. Small 2011, 7, 2526-2532.

Due to their customizability, designer colloidal particles can be excellent proxy systems for other materials that are more difficult to study experimentally. In this paper, we present a series of colloidal glasses where the particles are designed to mimic the relative size, shape, and interaction of atoms in metallic glasses. We create proxies for binary and ternary metals (specifically Cu-Zr and Ca-Mg-Zn) at various compositions within the glass forming range. For the binary proxy we create a mixture of spherical particles with two different radii, where the r₁=0.8r₂. One population of particles is synthesized with a positive surface charge while the other has a negative surface charge, creating a weak attractive force between dissimilar particles. For the ternary system, the radius ratios are r₁=0.81r₂=0.68r₃. Here, the largest particles have a positive charge, while the two smaller particles have a negative charge. Using confocal microscopy and image analysis tools, we analyze structural features of the proxy systems such as the radial distribution function, coordination numbers, Voronoi cell indices, and packing densities and compare our results to experiments and simulations of real metallic glasses. These studies indicate the usefulness of using designer colloids as proxies for atomic scale systems by demonstrating and that several measures of structure can be matched to near quantitative accuracy.

Self-organization under periodic driving is a common feature in many disparate far-from-equilibrium systems. One of the simplest examples is a suspension under cyclic shear, which exhibits a phase transition from a fluctuating state to a reversible state after particles arrange themselves to avoid collisions. While there has been substantial interest in granular packs and their response to shear, the range of accessible states and factors governing self-organization are not well established. Using numerical simulations we show that cyclic shear of a granular material leads to dynamic self-organization into several different phases. We present a phase diagram in strain - friction space which shows chaotic dispersion, crystal formation, vortex patterns and most unusually a disordered limit cyclic in which each particle precisely retraces a different path from other particles making and breaking many contact in each cycle. With John Royer

I describe results that involve two distinct research projects. First, we report that disordered strictly jammed binary sphere packings can be produced with a surprisingly large packing fraction range for sphere radius ratios greater than 0.2. We find that for certain radius ratios, the average densities of maximally random jammed (MRJ) binary sphere packings approach those of the corresponding densest known ordered packings. We also identify an interesting feature of the packing fraction of the jammed backbones with all rattlers excluded. The backbone packing fraction is about 0.624 over the majority of the radius ratio-composition plane, even when large numbers of small spheres are present in the backbone. Second, we describe a remarkable duality between the equilibrium hard-hyperparticle fluid system and the corresponding continuum percolation model of overlapping hyperparticles in d-dimensional Euclidean space. This duality realtionship is applied to obtain estimates of equilibrium freezing points for certain hard hyperparticles and of percolation thresholds for corresponding overlapping hyperparticles.

The jamming transition of frictionless soft spheres coincides with the threshold of mechanical stability. This lends the marginally-jammed solid special properties, including a vanishing ratio of the shear to bulk modulus and a diverging length scale characterizing the minimum size of a cluster that is mechanically rigid. This diverging length gives rise to qualitatively new physics by interfering with the usual plane-wave behavior of low-frequency sound modes. Even the lowest frequency sound modes have wavelengths shorter than the divergent length scale at the jamming transition. As a result, the disorder can never be averaged away and a new class of modes appears, swamping out plane wave behavior all the way down to zero frequency. In this sense, the marginally-jammed solid can be considered the epitome of disorder--the opposite limit from the perfect crystal.

The compaction of soft, frictionless grains simulated via energy minimization under athermal conditions in a periodic cell of fixed-shape has yielded jammed systems of various shapes, e.g., spheres [O&’Hern et al., Phys. Rev. E, 68, 011306 (2003)], ellipses [Mailman et al., Phys. Rev. Lett., 102, 255501 (2009)], Platonic solids [Smith et al., Phys Rev. E, 82,051304 (2011)], and application-inspired shapes [Smith et al., Phys. Chem. Chem. Phys., 14, 7040 (2012); Smith and Fisher, ArXiv: 1205.1073 (2012)]. While soft and hard systems of spheres have exhibited consistency among their jammed densities, the structures predicted for soft [Smith et al., Phys Rev. E,84, 030301 (2011)] and hard [Jiao and Torquato, Phys Rev. E,84, 041309 (2011)] systems of tetrahedra differ. The models employed in these simulations contrast in several other respects, including cell shape variability and granular temperature. In spite of limitations in previous fixed-cell approaches, experimental, frictional tetrahedra were found to exhibit structures very similar to those of soft, frictionless tetrahedra generated by such methods [Smith and Fisher, ArXiv: 1206.2990 (2012)]. In general, a fixed periodic cell shape does not reflect the global degrees of freedom present in isotropic granular media, and the extent of the influence of such a constraint on structure is unclear. In this work a method is introduced for simulating the jamming of athermal, arbitrarily-shaped grains in which global degrees of freedom are relaxed. The independent variable that drives jamming in this approach is the external stress state. In this context strict jamming, coined originally for hard grains [Torquato et al., J. Phys. Chem. B, 105, 11849 (2001)], is achieved via the application of a hydrostatic state of stress. The strict jamming of soft spheres, tetrahedra, and cubes is simulated with this approach, and the relaxation of cell shape is found to influence the predicted jammed structures to varying extents depending on the degree of translational and rotational order in a given system. For systems of spheres and tetrahedra, which exhibit only short-range translational order and are essentially amorphous, strictly jammed structures are very similar to those obtained with a fixed-shape cell. Additionally, soft tetrahedra strictly jammed with the present approach are found to exhibit lesser translational order than hard tetrahedra previously deemed as maximally random jammed. In contrast, nematic order in strictly jammed structures of cubes is suppressed relative to that obtained for fixed cell shape. The present methodology provides a generalized strict jamming framework that is extensible to a variety of athermal, soft materials.

The packing and assembly of anisotropic shapes found in both colloidal and granular matter has recently received much attention. Advances in computer simulations have greatly improved lower bounds for densest packings and led to the discovery of many novel ordered phases of anisotropic particles. Yet, the relationship between structures self-assembled from the disordered state due solely to entropy and the densest packing configurations stable in the limit of high pressure, is not well understood. To understand how and when knowledge of the densest packings suffice to predict the thermodynamically stable phase at lower densities, we investigate a wide range of highly symmetric polyhedral particle families comprising shapes synthesized in recent nanoparticle experiments. We present and discuss situations in which self-assembled phases are both significantly different from, or closely resemble, their densest packings. Our findings provide insight into situations where knowledge of the densest packing is useful for understanding assembly behavior from those where additional information is necessary. [1] Damasceno, PF; Engel, M; Glotzer, SC. ACS Nano 6, 609-614 (2012) [2] Damasceno, PF; Engel, M; Glotzer, SC. [arXiv:1202.2177] In Press (2012) [3] Haji-Akbari, A; Engel, M; Glotzer, SC; J. Chem. Phys. 135, 194101 (2011) [4] Damasceno, PF; Chen, E; Klotsa, D; Engel, M; Glotzer, SC. Preprint.

Linear and semidefinite programming bounds are the most powerful general techniques known for proving bounds on packing densities and related quantities. Bounds based on pair correlations are surprisingly powerful, and they have led to the best asymptotic bounds known as well as numerous exact optimality results in particular cases. However, higher-order correlations have not proven nearly as fruitful. In this talk, I'll survey ongoing theoretical and numerical work aimed at understanding this discrepancy.

Nature has provided us with many beautiful examples of perfect assemblies, as seen in sunflowers, pinecones, and seashells. The natural close-packing of sunflower seeds leads to so called phyllotactic growth, forming spirals both to the left and right while encoding the Fibonacci sequence and the Golden Ratio. In physical confinement, interfacial forces, structural frustration, symmetry breaking, and entropy change can play dominant roles in determining molecular organization. Here, we investigated packing of silica nanoparticles (100 nm-500 nm in diameter) confined in cylindrical polymer micropost arrays (diameter of 1 -2 microns and height of 4-8 microns), and observed spiral formation of the NPs along the sidewall of the posts to maximize the packing density. We hypothesized that the assembly of nanoparticles was driven by the capillary force in the channels during the imprint lithography, and the resulting packing behavior was highly dependent on particle size and uniformity, and post dimension (diameter and height).

The structure and dynamics of colloidal particles bound to the surface of emulsion droplets are governed by both the droplet geometry and interparticle interactions. Particle-laden emulsion droplets may therefore yield additional insight into both self-assembly and the poorly-understood interactions between colloidal particles at liquid-liquid interfaces. We study 4-10 mu;m diameter alkane droplets laden with ~5 micron-sized polymer spheres. Under these conditions, the colloidal particles exhibit nontrivial, rapid, three-dimensional (3D) dynamics. We measure the structure and dynamics of these particles with digital holographic microscopy, which gives millisecond temporal resolution and ~30 nm spatial resolution. Our findings have implications for self-assembly on curved surfaces.

Crystallography may be the gold standard of protein structure determination, but obtaining the necessary high-quality crystals is akin to prospecting for the precious mineral. The fields of structural biology and soft matter have independently sought out fundamental principles to rationalize the process, but the conceptual differences and the limited crosstalk between the two disciplines have prevented a comprehensive understanding of the phenomenon to emerge. We present a computational study of proteins from the rubredoxin family that bridges the two fields. Using atomistic simulations, we first characterize the crystal contacts, and then parameterize patchy-particle colloidal models. Comparing the phase diagrams of these models with experimental results enables us to critically examine the assumptions behind the two approaches and to reveal key features of protein-protein interactions that facilitate crystallization.

Icosahedral shapes have been identified in molecular crystalline shells such as large viral shells or fullerenes. We demonstrate that other geometries, including Platonic and Archimedean polyhedra, arise spontaneously in shells formed by more than one component (1). We describe the buckling of a crystalline shell with two coexisting elastic components, at different relative concentrations. Our work explains the principles to design various hallow polyhedra and the existence of regular and irregular polyhedral shells observed in viruses, organelles archaea and halophilic organisms. We provide computational and experimental evidence of the spontaneous buckling phenomena in shells made of mixtures of cationic and anionic amphiphiles, where electrostatics drives their co-assembly (2), and orders the assembly into faceted ionic structures with various crystalline domains. 1. G. Vernizzi, R. Sknepnek, and M. Olvera de la Cruz, Proc. Natl. Acad. Sci. USA, 118, 4292-4296 (2011). 2. M. A. Greenfield, L. C. Palmer, G. Vernizzi, M. Olvera de la Cruz, and S. I. Stupp, J. Am. Chem. Soc., 131, 12030-12031 (2009).

The epitaxial assembly of toric focal conic domain (TFCD) arrays of smectic-A liquid crystals onto pillar arrays is studied. The 3D nature of the pillar array is crucial to confine and direct the formation of TFCDs on the top of each pillar and between neighboring pillars, leading to highly ordered square and hexagonal array TFCDs persisting deeply into the bulk.

Curved surfaces of non-zero Gaussian curvature impose frustrating geometric constraints on crystallization. The crystallization process can be changed dramatically by the special geometry. Here, we present experimental studies of crystallization of colloidal particles on the spherical water-oil interface of emulsion droplets. We observed the formation of large single crystal domains with highly anisotropic, ribbon-like shapes. We found that curvature constrains the crystals to grow anisotropically, which minimizes the elastic energy. The finding may provide general guidelines for material scientists and engineers to build ordered crystalline structures on curved surfaces. We will discuss both experimental observations and theoretical analysis during the presentation.

In this work we consider a minimal model for an active colloidal fluid in the form of self-propelled Brownian hard spheres that interact purely through excluded volume interactions. Despite the absence of an aligning interaction, this system shows the signatures of an active fluid, including anomalous number fluctuations and phase separation behavior. Using simulations and analytic modeling, we quantify the phase diagram and separation kinetics. The dense phase is a unique material that we call an active hexatic, which exhibits the structural signatures of a crystalline solid near the crystal-hexatic transition point, but dynamical and transport properties associated with a viscoelastic fluid.

Electric field manipulation of droplets has many applications, for example in emulsion technology and microfluidics. In “leaky-dielectrics”, such as oils, electric surface stress can induce hydrodynamic flow in and around the droplet (G.I. Taylor 1964). Here we present observations on isolated oil-in-oil emulsion drops in DC electric fields. The drops contain mono-disperse colloidal particles or poly-disperse colloidal clay. We show that electrohydrodynamic flow instabilities can induce a variety of static or dynamic colloidal structures on the drop surface, including jammed colloidal shells, colloidal rings and colloidal vortices.

In the last decade, interest for colloidal particles with anisotropic composition has considerably increased due to the potential benefits of these entities in multiple areas of materials science. Indeed, controlling the morphology and/or the composition of colloidal particles is an absolute necessity if one intends to master their physico chemical properties. Anisotropic particles can be classified in multi-compartment particles and patchy particles that present different patches at their surface. We have reported the synthesis of large quantities of binary colloidal molecules that consist of a central silica core surrounded by a precise number of polystyrene (PS) nodules [A. Perro et al., Angew. Chem. Int. Ed., 2009, 48, 361]. In this presentation, we will show that we have considerably improved the synthesis of these so-called “colloidal molecules” during the last year, so that the tetrahedral, hexagonal, octagonal,hellip;, colloidal structures can now be produced in large quantities with a yield higher than 90% versus the number of silica seeds. These binary entities can be considered as patchy silica particles bearing a controlled number of well-located hydrophobic PS patches. We will also show that we succeeded in promoting the growth of the silica core of these colloidal molecules. While growing, the silica surface conforms to the shape of the PS nodules. After removal of the latter, large quantities of silica particles with a precise number of concave patches are produced. Since it is possible to specifically functionalize the silica surface before removing the organic nodules, the patchy particles are capable of directional interactions with other ones. Their assembly into precise and predictable structures can be now envisaged.

One of the new frontiers of quasicrystal (QC) research in the 21st century are the various soft quasicrystals seen, e.g., in polymer, micellar, and dendrimer systems [1-3]. Here we report the formation of 10-fold, 12-fold, and 18-fold quasicrystals in Monte Carlo simulations of two-dimensional hard-core/square-shoulder particles [4]. Despite the purely repulsive and isotropic pair interaction, this system displays a variety of aperiodic phases which are characterized by bond-orientational order arising from the competition between the hard-core and soft-shoulder length scales. We scanned the phase diagram for quasicrystals by varying temperature, the packing fraction ρ, and the shoulder-to-core ratio lambda; = 1 + σ/R; here σ is the thickness of the shoulder and R is the core radius. Table 1 shows the ranges of lambda; and ρ where quasicrystals are formed at certain temperature. We observed that the 18-fold quasicrystal is closely related to the 12-fold random quasicrystal, since it is composed of equilateral triangles and 80°-100° rhombi so that all angles involved are multiples of 20°. [1] K. Hayashida, T. Dotera, A. Takano, and Y. Matsushita, Phys. Rev. Lett. 98, 195502 (2007). [2] T. Dotera, Israel J. Chem. 51, 1197 (2011). [3] T. Dotera, J. Polym. Sci. Pol. Phys. 50, 155 (2012). [4] M. A. Glaser, G. M. Grason, R. D. Kamien, A. Koscaron;mrlj, C. D. Santangelo, and P. Ziherl, EPL 78, 46004 (2007).

Quasicrystals are an exotic class of matter with long-range order but without periodicity. For decades their formation was thought to be possible in simulation only in the presence of inter-particle potentials with competing length scales e.g. potentials with multiple maxima and minima. Using molecular simulation of hard facetted polyhedra, we demonstrate that entropy alone can promote the formation of quasicrystals, and energetic interactions are therefore not a prerequisite. In particular, we observe that hard tetrahedra [1] and hard triangular bipyramids [2] form dodecagonal quasicrystals, which are the first quasicrystals reported in hard particle systems. We show that they are entropically favored over the densest packings of the corresponding systems. They also possess interesting dynamical properties in the form of a novel type of phason flip [2, 3]. The existence of hard particle quasicrystals demonstrates the potential of geometric anisotropy in promoting complex crystallographic structures. 1. Haji-Akbari A., Engel M., et al. Nature 463: 773-777 (2009). 2. Haji-Akbari A., Engel M., Glotzer S. C., Phys. Rev. Lett. 107: 215702 (2011). 3. Haji-Akbari A., Engel M., Glotzer S. C., J. Chem. Phys. 135: 194101 (2011).

Micelles can form ordered lyotropic liquid crystalline phases, which usually are periodic, exhibiting cubic symmetry. We have found that block copolymer micelles with large shell/core ratios form lyotropic quasicrystalline phases of 12- or 18-fold rotational symmetry. [1] The structures have been characterized by small-angle synchrotron x-ray (SAXS) and scanning small-angle neutron scattering (SANS). Ongoing experiments indicate that the stability of these phases extends to larger block copolymer micelles and even core/shell-microgels, which opens the possibility to use quasicrystalline structures for photonic applications. [1] S. Fischer et al., Proc. Natl. Acad. Sci (2011), 108, 1810.

Sphere forming diblock copolymers generally self-assemble on a body centered cubic lattice, as anticipated by mean-field theory. However, recent small-angle X-ray scattering and transmission electron microscopy experiments have demonstrated a rich assortment of packing symmetries in low molecular weight poly(isoprene-b-lactide) (IL) diblocks and poly(styrene-b-isoprene-b-styrene-ethylene oxide) (SISO) triblock terpolymers, including the Frank-Kasper sigma phase, a simple hexagonal arrangement, and a dodecagonal quasicrystal morphology. We have interpreted these non-traditional structures in terms of modifications to the effective particle-particle interaction potential, reflecting departures from classical stretching of Gaussian chain configurations and the inhomogeneous distribution of block segments around the spherical core domains. This presentation will demonstrate how a tetrablock molecular architecture offers unparalleled flexibility in controlling domain packing through the strategic sequencing of specific block types based on the combination of binary segment-segment interaction parameters.

There is growing interest in recent years in the ability to grow quasicrystals and other complex structures, whose building blocks are on a mesoscopic scale of tens to thousands of nanometers. These range from artificially constructed metamaterials, such as photonic quasicrystals, to self-assembled soft-matter quasicrystals^1-3. In addition to having promising applications, especially in the optical domain, these materials give us the opportunity to study quasicrystals in ways that were impossible before. As time permits, I will discuss a few aspects of our ongoing work on these systems, ranging from our recent explanation of the stability of certain quasicrystals composed of soft isotropic particles^4,5, to the design of nonlinear photonic quasicrystals for optical frequency conversion⁶. [1] Zeng, Ungar, Liu, Percec, Dulcey, & Hobbs, Nature428 (2004) 157. [2] Hayashida, Dotera, Takano, & Matsushita, Phys. Rev. Lett.98 (2007) 195502. [3] Talapin, Shevchenko, Bodnarchuk, Ye, & Murray, Nature461 (2009) 964. [4] Lifshitz & Diamant, Phil. Mag.87 (2007) 3021. [5] Barkan, Diamant, & Lifshitz, Phys. Rev. B83 (2011) 172201. [6] Lifshitz, Arie, & Bahabad, Phys. Rev. Lett.95 (2005) 133901.

The surprising discoveries of quasicrystals and their approximants in soft-matter systems poses the intriguing possibility that these structures can be realized in a broad range of nanoscale and microscale assemblies. It has been theorized that soft-matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remains elusive. Here, we use computer simulation and free-energy calculations to demonstrate a simple design heuristic for assembling quasicrystals and approximants in soft-matter systems. Our study builds on previous simulation studies of the self-assembly of dodecagonal quasicrystals and approximants in minimal systems of spherical particles with complex, highly specific interaction potentials. We demonstrate an alternative entropy-based approach for assembling dodecagonal quasicrystals and approximants based solely on particle functionalization and shape, thereby recasting the interaction-potential-based assembly strategy in terms of simpler-to-achieve bonded and excluded-volume interactions. Here, spherical building blocks are functionalized with mobile surface entities to encourage the formation of structures with low surface contact area, including non-close-packed and polytetrahedral structures. The building blocks also possess shape polydispersity, where a subset of the building blocks deviate from the ideal spherical shape, discouraging the formation of close-packed crystals. We show that three different model systems with both of these features—mobile surface entities and shape polydispersity—consistently assemble quasicrystals and/or approximants. We argue that this design strategy can be widely exploited to assemble quasicrystals and approximants on the nanoscale and microscale. In addition, our results further elucidate the formation of soft-matter quasicrystals in experiment. C.R. Iacovella, A.S. Keys and S.C. Glotzer, PNAS 108, 20935-20940 (2011).

Friction between solids is responsible for many phenomena like earthquakes, wear or crack propagation. Unlike macroscopic objects which only touch locally due to their surface roughness, spatially extended contacts form between atomically flat surfaces. They are described by the Frenkel-Kontorova model which considers a monolayer of interacting particles on a periodic substrate potential. In addition to the well-known slip-stick motion such models also predict the formation of kinks and antikinks which largely reduce the friction between the monolayer and the substrate. Here, we report the direct observation of kinks and antikinks in a two-dimensional colloidal crystal which is driven across different types of ordered substrates. We show that the frictional properties only depend on the number and density of such excitations which propagate through the monolayer along the direction of the applied force. In addition, we also observe kinks on quasicrystalline surfaces which demonstrates that they are not limited to periodic substrates but also occur under more general conditions.

Large face-centered cubic single crystals of micron-size hard-sphere silica colloidal particles were prepared by centrifugation or sedimentation onto (100) templates. They were studied by tracking the particles in space and time by confocal microscopy. The point defects observed in these crystals include single vacancies, divacancies, vacancy-impurity clusters and interstitials. The large size of our samples allows us to obtain new experimental data on the mobility of these defects, and on the related free energies of their transition states. Measurements of the volume relaxation around the defects are compared to earlier computer simulations. The interaction of vacancies with partial dislocations, including their annihilation, has been observed in detail on the particle level.

Lightweight materials for construction and protection purposes are of great need. A common way to reduce a materials&’ density is given by the introduction of porous networks as for example in metallic foams. Here we employ a bottom up method to fabricate well-defined meso- and macroporous materials consisting of hollow silica nanoparticles (HSNP). HSNPs are synthesized via a sacrificial templating method, which allow access to a wide range of hollow spheres with adjustable diameter and shell thickness. Using colloidal self-assembly techniques, well-ordered particle monolayers, double layers and trilayers are obtained. Their mechanical resistance and capability to absorb energy are characterized by indentation using a 10 µm sphere nanoindenter. We give insight into the elastic regime[1, 2] and assess the irreversible plastic deformation at large penetration depths. Due to the well-defined materials, we can establish a structure-property relationship. We find specific energy absorption capabilities of up to 100 kJ/kg for neat particle films. Finally, we fabricated thick particle and composite films using two distinct polymers, a polyacrylate and a polyurethane. The energy dissipation of such bulk films depends on the particle geometry and the polymer matrix, and also ranges in the tens of kJ/kg. [1] Yin, J.; Retsch, M.; Lee, J.-H.; Thomas, E. L.; Boyce, M. C., Mechanics of Nanoindentation on a Monolayer of Colloidal Hollow Nanoparticles. Langmuir 2011, 27 (17), 10492-10500. [2] Yin, J.; Retsch, M.; Thomas, E. L.; Boyce, M. C., Collective Mechanical Behavior of Multilayer Colloidal Arrays of Hollow Nanoparticles. Langmuir 2012, 28 (13), 5580-5588.

Colloidal nanoparticle (NP) superlattice (SL) metamaterials hold the promise of novel and tunable collective properties due to the periodic NP arrangement. One challenge in attaining this goal has been the need to supplant empirical methods of SL development by rational design and fabrication. We show here that we can understand, and presumably, control, NP assembly better through resolving the kinetics and intricate interactions governing the growth of 3D single NP SLs (SNSLs) and binary NP SLs (BNSLs) in solution by combining controlled solvent evaporation and in situ, real-time small angle X-ray scattering (SAXS). Specifically, we learn how NP size affects the rate of assembly of SNSLs and the mechanism of how co-existing SNSLs and BNSLs form.The ordered nature of the structures formed was probed by high-resolution SEM and small angle x-ray scattering.

The inclusion of guest molecules into a host lattice through van der Waals interactions, π-π interactions, and hydrogen bonding is an ordinary phenomenon that occurs in the formation of molecular crystals. Host-guest inclusion chemistry has been commonly used to design and construct molecular crystals with desired physical and chemical properties for the needs of various applications, for example, host-guest crystals with noncentral symmetry for the use in second-harmonic generation and cocrystals containing active pharmaceutical ingredients for drug delivery system and formulation. As analogues of molecular crystals, three-dimensional nanocrystal superlattices are ordered assemblies comprising one or more types of nanocrystal building blocks. To date, a variety of small molecules and polymers have been used to mediate the assembly of colloidal nanocrystals, resulting in the preparation of a variety of organic/inorganic nanocomposites that exhibit unique optical, magnetic, electric, catalytic, or mechanical properties. However, because most of these organic/inorganic nanocomposites do not adopt a three-dimensional-ordered structure [e.g., face-centered cubic], little progress has been made to date in the structural control of three-dimensional nanocrystal superlattices using host-guest inclusion chemistry. Here, we report a host-guest chemistry approach to controlling structures of nanocrystal superlattices through a molecular inclusion process. Upon addition of an appropriate amount of guest molecules such as squalane, polyisoprene, and 4-cyano-4&’-pentylbiphenyl into a nanocrystal suspension, the resulting nanocrystal superlattices adopted non-close-packed structures [e.g., from face-centered cubic to body-centered cubic] and changed their morphologies to form superparticles. Our mechanistic studies revealed that these guest molecules can strongly tailor the kinetic process in superlattice formation, resulting in the formation of non-close-packed nanocrystal superlattices. The insights gained in this study are not only important for making nanocrystal superlattices with desirable architectures but also open a new way of synthesizing novel organic/inorganic composite materials.

Materials with properties that depend on applied voltage are essential components of industrially relevant devices: electronic materials (e.g., transistors and sensors), electrochromic materials (e.g., windows), electrocatalysts (e.g., fuel cells), and electromagnets (e.g., sensors and transducers). Here we describe an entirely new class of materials that we have named “nanoparticle electrides”. These are positively charged nanoparticles that are charge compensated by free, un-bound electrons. When a small potential is applied, the electride is formed and the material increases electrical conductivity by several orders of magnitude. We describe the physical properties of these materials and show how they can be used to build several electronic and magnetic devices, including transistors, diodes, sensors, and the most sensitive thermistor yet: for every degree C change in temperature, the electride changes electrical conductivity by 26%. We further demonstrate how these electronic elements can be combined to build electronic circuits entirely from these nanoparticles, including a half-adder logic circuit and random access memory.

Colloidal nanocrystals (NCs) constitute a powerful set of building blocks with widely tunable electronic, magnetic, catalytic and optical properties. We will explore how NCs of controlled crystal size, shape, structure and surface passivation can be assembled to form metamaterials with collective properties that are a function of the composition of the NCs and the coupling between these building blocks. These metamaterials will be formed into new thin films and integrated into nanoscale devices and systems. Briefly, the current best practices in the synthesis and purification of NC's will be presented with a focus on shape controlled Nano photonic building blocks including semiconductor NCs (Quantum Dots), rare earth doped nanophosphors and plasmonic nanorods. I will then focus on emerging methods to assemble these NCs together with other electrically and magnetically and optically active NCs to form multicomponent periodic (superlattices) and aperiodic (Quasicrystalline) structures. Specific examples will be provided in which differently sized CdSe, CdTe, PbS, PbSe, PbTe, CuInSe2, FePt, CoPt3, Fe3O4, CoFe2O4, Au, Ag, Pd, Cu, and NaYF4:Re, LiGdF4:Re (Re=rare earths) NCs into a rich array of multi-functional nanocomposites. A novel method to direct superlattice formation by interfacial assembly and transfer will be highlighted as well as effort to template the assembly with lithographic techniques. The design rules for directed assembly of NC systems based on single componet, binary and ternary NC superlattices and glassy assmeblies will described along with exciting new oportunities to opotunities to design quasicrystalline NC films will be shared. The potenial of these periodic, glassy and aperiodic metamaterials to impact areas of energy conversion, and optoelectronics will be explored.

The crystallographic parameters of atomic and ionic solids are fixed by the size and coordination number of their elemental building blocks, thus restricting the types of structures that can be formed. We have demonstrated that these limitations can be overcome using spherical nucleic acids (SNAs) as “artificial atoms” in nanoparticle superlattice assemblies. These three-dimensional conjugates consist of densely functionalized, highly oriented nucleic acids covalently attached to the surface of inorganic nanoparticles. The strength and length of the programmable DNA “bonds” between these structures can be adjusted by varying DNA sequence and length, and the properties of the “atoms” can be adjusted by varying nanoparticle size, shape, and composition. We have developed design rules for this assembly process, analogous to Pauling&’s Rules for ionic solids but ultimately more powerful. These rules can be used as a guide for the rational construction of functional nanoparticle-based materials for plasmonic, photonic, and catalytic applications.

The structural flexibility and interaction programmability provided by DNA offer ample possibilities to direct the organization of nanoscale objects into well defined systems, as well as to control their structural transformations on demand. We have studied the assembly of clusters and extended 2D and 3D lattice architectures from nanoscale components of multiple types driven by DNA recognition and chain effects. Our work explores how DNA-encoded interactions between inorganic nano-components can guide the formation of well-defined superlattices, how the morphology of self-organized structures can be regulated in-situ, and what molecular and geometrical factors govern a phase behavior. The role particle anisotropy, chain effects and external stimuli on a structure formation and its transformation will be discussed in details. The novel strategies on assemblies of 3D lattices with the pre-designed symmetries will be presented. Research is supported by the U.S. DOE Office of Science and Office of Basic Energy Sciences under contract No. DE-AC-02-98CH10886.

We present a direct-write technique for assembly of microscale 3D colloidal crystals on flat substrates, using polystyrene microspheres as a model system. To assemble crystals, we use a custom-built high-resolution liquid manipulation system to dispense colloidal suspensions through a capillary tip. The process begins by forming a liquid bridge between the capillary tip and a temperature-controlled substrate positioned by a 3D motorized stage. Nucleation occurs at the liquid-substrate contact line and crystal growth proceeds tangent and normal to the meniscus contour. In situ regulation of dispensing rate, retraction speed of the tip, and substrate temperature, enable precise control of the liquid bridge profile. This control facilitates vertical precipitation of 3D colloid crystals having predetermined shapes including cones and cylindrical towers. We find that, when the particle concentration in the liquid bridge is low, the precipitated structures have hexagonal crystal packing; at high concentration the packing is amorphous. This results from interplay between lateral capillary forces and normal capillary forces (i.e., wet granular cohesion) between the particles. Transition between these phases is elucidated using video microscopy during assembly and confocal microscopy of the assembled structure. Finally, we demonstrate direct-write assembly of discrete particle clusters by pinning the liquid bridge to arrays of microfabricated posts on substrates. Refinement of this technique would enable scalable fabrication of 3D particle assemblies for applications such as photonics and tissue engineering; and also enable new studies of granular mechanics at the micro-scale.

Crystalline nanoparticle arrays and superlattices with well-defined geometries can be synthesized by using appropriate electrostatic, hydrogen bonding, or biological recognition interactions. DNA is well-suited for superlattice synthesis as a structure-directing ligand because its programmability allows for a priori control over the lattice symmetries and lattice constants of the nanoparticle superstructures. While superlattices with many distinct geometries can be produced with these approaches, one can envision significantly increasing the library of synthetically achievable lattices by developing a strategy that allows some of the nanoparticles within a binary lattice to be replaced with “spacer” entities that contain no inorganic core but are appropriately constructed to mimic the behavior of their inorganic counterparts during assembly and crystallization. The inclusion of these spacer entities within a known binary superlattice would effectively “delete” one set of nanoparticles without affecting the positions of the other set. For example, by deleting the center particle from a body-centered cubic (bcc) or cesium chloride (CsCl) lattice, a simple cubic lattice can be synthesized. In this work, we show how hollow DNA nanostructures can be used as “three dimensional spacers” within nanoparticle superlattices assembled through programmable DNA interactions. We show that this strategy can be used to form superlattices with five distinct symmetries, including one that has never before been observed in any synthetic or naturally-occuring crystalline material.

Colloidal crystals are commonly formed by sedimentation of an initially-dilute colloidal suspension onto a patterned template. Here, we demonstrate controlled growth of face-centered cubic (FCC), monodisperse hard-sphere colloidal crystals by centrifugation at up to 3000g onto FCC (100) templates. Slow sedimentation rates were previously believed necessary to grow large, perfect crystals while avoiding forming an amorphous sediment. Surprisingly, however, growth onto (100) templates results only in single crystals with few or no extended defects. Rapid deposition onto flat, (111), or (110) templates can result in crystalline-to-amorphous crossover if the dimensionless flux (particle volume fraction x Peclet number) exceeds a critical value. This crossover at high flux is a result of the degeneracy of possible stacking positions for these growth orientations. No such degeneracy exists for (100), on which defect-free crystals can be grown at high dimensionless flux to arbitrary thickness. After growth, extended defects (dislocations, stacking faults) can nucleate and grow only if the crystal exceeds a critical thickness that depends on the lattice misfit with the template spacing. We report measurements of the density of these misfit dislocations as a function of final crystal thickness, and compare these results with calculations from the Frank-van der Merwe theory, adapted to account for the variation of elastic constants and lattice spacing with crystal thickness that result from the gravitational pressure. Final defect concentrations are independent of centrifugation rate and deposition time.

We report the use of an applied electric field to produce anisotropic orientational order in micron-sized Brownian colloidal rods. The suspensions, because of their slow Brownian dynamics, undergo equilibrium self-assembly only on long time scales. Application of an electric field significantly accelerates the kinetics of assembly. The spatial and orientational structure of the assemblies is imaged in three dimensions using confocal microscopy and quantified by means of image processing. We analyze our results in terms of the underlying electrokinetics of the system, as well as connecting the observed field-induced orientational order to the equilibrium isotropic-nematic transition predicted for repulsive rods. The results show a change from isotropic to nematic orientation followed by a transition from mobile to glassy dynamics as the Direct-Current (DC) electric field strength across the homogeneous rods is increased. We also report the formation of a Body-Centered Tetragonal crystal structure for these assembled rods. Finally, we synthesize patchy rods and show that this anisotropy in the pair-potential gives rise to new possibility for the characterization of self-assembly structures

We describe two new kinds of colloids with directional bonding and specific programmable interactions. The first kind of colloids work by a lock-and-key mechanism in which spherical colloids of a specific radius bind with “pacman” particles that have a hemispherical inclusion of similar radius. Spherical colloids of the whose radius do not closely match that of the spherical inclusion of the pacman particles do not bind. The second type of colloids are patchy colloids — colloids with “valence” — whose patches have well defined symmetries, including triangular, tetrahedral, and other common and uncommon symmetries. Patches on different particles interact via specific programmable complementary ssDNA hybridization. This allows the assembly of a wide variety of new colloidal structures than have never before been realized.

We study small clusters of spherical colloidal particles bound to one another through short-range attractive interactions. Previous experimental and theoretical studies have explored the ground states of such systems as well as the self-assembly kinetics of Janus colloids, but few studies have examined the transition states and the dynamics of transitions in clusters of isotropic spherical particles. We use optical tweezers to build clusters of up to 12 particles held together by depletion forces or DNA interactions, and we study their dynamics using optical microscopy and digital holographic microscopy. These techniques allow us to track all the particles in the cluster, on timescales small compared to diffusion. We find that the transition state probabilities agree well with a theoretical model that accounts for the free energy along the entire pathway. The dynamics of the transitions shed some light on how particles roll and slip over one another to form new bonds.

Despite research dating back more than 200 years, it is still unknown how to connect the mechanical response of an amorphous granular material unambiguously to the shape of its constituents. From a practical point of view, this is problematic since granular materials like sand, grain, and pharmaceuticals are essential in engineering and industry. At a fundamental level, granular systems represent prototypes for far-from-equilibrium behavior. Thus, understanding the relationship between microscopic shape and macroscopic response can shed light on other amorphous systems like foams, dense colloids and molecular glasses. A key difficulty arises from the vast range of possible shapes, making it seem infeasible to isolate which candidates generate a particular response. In this talk I will demonstrate that particle shape can, however, be explored efficiently when viewed in a fresh context: artificial evolution. Representing arbitrary particle shapes by "granular molecules” consisting of bonded spheres, we have used simulations to evolve these shapes and 3D printing to verify the results experimentally. Using this approach, we find predictive motifs linking particle shape to packing stiffness and have discovered a particle shape that self-confines to produce granular packings that stiffen, rather than weaken, under compression. I will discuss opportunities to explore particle shape for effective jamming and to design granular matter with optimized properties for applications ranging from soft robotics to architecture.

We introduce a new spatial partitioning problem called filling[1], which combines aspects of traditional packing and covering problems from mathematical physics. Filling involves the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. We investigate the mathematical space of filling solutions and provide a heuristic for finding the optimal filling solutions for polygons filled with disks of varying radii. We consider the properties of ideal distributions of N disks as N→infin;. By using filling solutions, traditional and widely available molecular dynamics software packages can be used to study ensembles of colloidal and nanoscale particles with complicated convex and concave shapes. Three dimension filling solutions may also provide guidance for constructing shaped particles from droplets and bubbles. [1] Phillips, Anderson, Huber, Glotzer, The Optimal Filling of Shapes, PRL, 2012

Self-assembled superstructures represent a novel class of materials, which presents interesting properties not only from the point of view of optical, magnetic and charge transport properties, but also in their mechanical behavior, which is strictly dependent on their structural morphology. Mechanical solidity is not straightforward to appraise, because the way the weak forces that drive the assembly process translate into mechanical solidity is not trivial. On the other hand, mechanical properties are important for design purposes and gaining insight on the topic is a necessary step towards devices development. We measured the low-strain stiffness of geometrically interlocked superstructures produced by self-assembly of multibranched CdSe/CdS nanocrystals by deterministic nanocompression, through a multi-step, Atomic Force Microscopy-aided procedure. We show that these superstructures were found to exhibit higher stiffness than what should be expected from a disordered porous material of the same chemical composition, and can be modeled, instead, like truss structures, with a direct dependence of stiffness on the relative density. The possibility of coupling the well known functional properties to the classical macroscopic advantages of truss structures over bulk materials opens the route for mechanical-based applications, as could be nanocomposites backbones or nanoscale shock absorbers.

We demonstrate that it is possible to create essentially arbitrary structures from DNA labelled colloidal spheres, with yield approaching one hundred percent over a reasonable temperature range. Doing this requires assembling structures out of a particles each of which is labelled differently. The maximum yield is determined by a kinetic effect, and hence bond strengths need to be a carefully chosen combination of reversible and irreversible bonds.