Shape-induced frustration of hexagonal order in polyhedral colloids

Multistep Crystallization of Dynamic Nanoparticle Superlattices in Nonaqueous Solutions

Crystallization is a universal phenomenon underpinning many industrial and natural processes and is fundamental to chemistry and materials science. However, microscopic crystallization pathways of nanoparticle superlattices have been seldom studied mainly owing to the difficulty of real-time observation of individual self-assembling nanoparticles in solution. Here, using in situ electron microscopy, we directly image the full self-assembly pathway from dispersed nanoparticles into ordered superlattices in nonaqueous solution. We show that electron-beam irradiation controls nanoparticle mobility, and the solvent composition largely dictates interparticle interactions and assembly behaviors. We uncover a multistep crystallization pathway consisting of four distinct stages through multi-order-parameter analysis and visualize the formation, migration, and annihilation of multiple types of defects in nanoparticle superlattices. These findings open the door for achieving independent control over imaging conditions and nanoparticle assembly conditions and will enable further study of the microscopic kinetics of assembly and phase transition in nanocolloidal systems.

Particle movements provoke avalanche-like compaction in soft colloid filter cakes

During soft matter filtration, colloids accumulate in a compressible porous cake layer on top of the membrane surface. The void size between the colloids predominantly defines the cake-specific permeation resistance and the corresponding filtration efficiency. While higher fluxes are beneficial for the process efficiency, they compress the cake and increase permeation resistance. However, it is not fully understood how soft particles behave during cake formation and how their compression influences the overall cake properties. This study visualizes the formation and compression process of soft filter cakes in microfluidic model systems. During cake formation, we analyze single-particle movements inside the filter cake voids and how they interact with the whole filter cake morphology. During cake compression, we visualize reversible and irreversible compression and distinguish the two phenomena. Finally, we confirm the compression phenomena by modeling the soft particle filter cake using a CFD-DEM approach. The results underline the importance of considering the compression history when describing the filter cake morphology and its related properties. Thus, this study links single colloid movements and filter cake compression to the overall cake behavior and narrows the gap between single colloid events and the filtration process.

Orientational Disorder in Epitaxially Connected Quantum Dot Solids

Periodic arrays of strongly coupled colloidal quantum dots (QDs) may enable unprecedented control of electronic band structure through manipulation of QD size, shape, composition, spacing, and assembly geometry. This includes the possibilities of precisely engineered bandgaps and charge carrier mobilities, as well as remarkable behaviors such as metal-insulator transitions, massless carriers, and topological states. However, experimental realization of these theoretically predicted electronic structures is presently limited by structural disorder. Here, we use aberration-corrected scanning transmission electron microscopy to precisely quantify the orientational disorder of epitaxially connected QD films. In spite of coherent atomic connectivity between nearest neighbor QDs, we find misalignment persists with a standard deviation of 1.9°, resulting in significant bending strain localized to the adjoining necks. We observe and quantify a range of out-of-plane particle orientations over thousands of QDs and correlate the in-plane and out-of-plane misalignments, finding QDs misoriented out-of-plane display a statistically greater misalignment with respect to their in-plane neighbors as well. Using the bond orientational order metric ψ₄, we characterize the 4-fold symmetry and introduce a quantification of the local superlattice (SL) orientation. This enables direct comparison between local orientational order in the SL and atomic lattice (AL). We find significantly larger variations in the SL orientation and a statistically robust but locally highly variable correlation between the orientations of the two differently scaled lattices. Distinct AL and SL behaviors are observed about a grain boundary, with a sharp boundary in the AL orientations, but a more smooth transition in the SL, facilitated by lattice deformation between the neighboring grains. Coupling between the AL and SL is a fundamental driver of film growth, and these results suggest nontrivial underlying mechanics, implying that simplified models of epitaxial attachment may be insufficient to understand QD growth and disorder when oriented attachment and superlattice growth occur in concert.

Metastable orientational order of colloidal discoids

The interplay between phase separation and kinetic arrest is important in supramolecular self-assembly, but their effects on emergent orientational order are not well understood when anisotropic building blocks are used. Contrary to the typical progression from disorder to order in isotropic systems, here we report that colloidal oblate discoids initially self-assemble into short, metastable strands with orientational order—regardless of the final structure. The model discoids are suspended in a refractive index and density-matched solvent. Then, we use confocal microscopy experiments and Monte Carlo simulations spanning a broad range of volume fractions and attraction strengths to show that disordered clusters form near coexistence boundaries, whereas oriented strands persist with strong attractions. We rationalize this unusual observation in light of the interaction anisotropy imparted by the discoids. These findings may guide self-assembly for anisotropic systems in which orientational order is desired, such as when tailored mechanical properties are sought.

The pathways available for self-assembly are affected by the shape anisotropy of the building blocks, but the details are still unclear. Here, Hsiao et al. show that colloidal discoids self-assemble into metastable states with orientational order when kinetic trapping is incorporated as a design principle.

Self-assembly and crystallisation of indented colloids at a planar wall

We report experimental and simulation studies of the structure of a monolayer of indented ("lock and key") colloids, on a planar surface. On adding a non-absorbing polymer with prescribed radius and volume fraction, depletion interactions are induced between the colloids, with controlled range and strength. For spherical particles, this leads to crystallisation, but the indented colloids crystallise less easily than spheres, in both simulation and experiment. Nevertheless, simulations show that indented colloids do form plastic (rotator) crystals. We discuss the conditions under which this occurs, and the possibilities of lower-symmetry crystal states. We also comment on the kinetic accessibility of these states.

Shape-induced chiral ordering in two-dimensional packing of snowmanlike dimeric particles

Understanding the distinctive phase behaviors in random packing due to particle shapes is an important issue in condensed matter physics. In this paper, we investigate the random packing structure of two-dimensional (2D) snowmen via wax-snowman packing experiments and Brownian dynamics simulations. Both experiments and simulations reveal that neighboring snowmen have a strong short-range orientational correlation and consequently locally form particular conformations. A chiral conformation is dominant for high area fractions near the jamming condition (φ>0.8), and the proportion of the chiral conformation increases with γ. We also found that the attractive interaction does not have a significant impact on the results. The geometry of chirally ordered snowmen causes a mismatch with 2D crystalline symmetries and thus inhibits the development of long-range spatial order, despite the strong orientational correlation between neighbors.

Density functional theory for hard polyhedra

Using the framework of geometry-based fundamental-measure theory, we develop a classical density functional for hard polyhedra and their mixtures and apply it to inhomogeneous fluids of Platonic solids near a hard wall. As revealed by Monte Carlo simulations, the faceted shape of the polyhedra leads to complex layering and orientational ordering near the wall, which is excellently reproduced by our theory. These effects can be verified in real-space experiments on polyhedral colloids.

Continuous phase transformation in nanocube assemblies

The phase behavior of 3D assemblies of nanocubes in a ligand-rich solution upon solvent evaporation was experimentally investigated using small-angle x-ray scattering and electron microscopy. We observed a continuous transformation of assemblies between simple cubic and rhombohedral phases, where a variable angle of rhombohedral structure is determined by ligand thickness. We established a quantitative relationship between the particle shape evolution from cubes to quasispheres and the lattice distortion during the transformation, with a pathway exhibiting the highest known packing.

Structural signature of slow dynamics and dynamic heterogeneity in two-dimensional colloidal liquids: glassy structural order

Glassy states are formed if crystallization is avoided upon cooling or increasing density. However, the physical factors controlling the ease of vitrification and the nature of glass transition remain elusive. Among various glass-forming systems, colloidal liquids are one of the most ideal glass-forming systems because of the simplicity and controllability of the interactions. We use numerical simulations of two-dimensional polydisperse and binary hard discs to tackle both of these longstanding questions. For polydisperse systems, we systematically control the polydispersity, which can be regarded as the strength of frustration effects on crystallization. We reveal that crystal-like hexatic order grows in size and lifetime with an increase in the colloid volume fraction or with a decrease in polydispersity (or frustration). We stress that hexatic ordering in hard disc systems is a direct consequence of dense packing and a manifestation of low configurational entropy. Our study suggests an intriguing scenario that the strength of frustration controls both the ease of vitrification and the nature of the glass transition. Vitrification may be a process of hidden crystal-like ordering under frustration for this system. This may provide not only a physical basis for glass formation, but also an answer to another longstanding question on the structure of amorphous materials: 'order in disorder' may be an intrinsic feature of a glassy state of many materials. For binary mixtures, on the other hand, the relevant structural feature linked to slow dynamics is not hexatic order, but an amorphous structure of low structural entropy. These results suggest that slow dynamics is associated with bond orientational order linked to the crystal for a weakly frustrated system, whereas to amorphous structures of low configurational entropy for a strongly frustrated system. This suggests an intrinsic link between structure and dynamics in glass-forming materials: slow dynamics is linked to structuring ('glassy ordering') towards low configurational entropy. We discuss the nature of 'glassy order' responsible for slow dynamics.

Formation and grain analysis of spin-cast magnetic nanoparticle monolayers

Ligand-stabilized magnetic nanoparticles (NPs) with diameters of 4-7 nm were spin-cast into monolayers on electron-transparent silicon nitride (SiN) substrates. SiN membranes facilitate detailed high-resolution characterization of the spin-cast monolayers by transmission electron microscopy (TEM) and approximate spin-casting onto wafers. Suspending the NPs in hexanes and pretreating the substrate with ultraviolet light and ozone (UVO) gives the best results. Computer-aided analysis of the arrays elucidates their grain structures, including identification of the grain boundaries and defects and measurements of the grain orientations and translational correlation lengths. Narrow NP size distributions result in close-packed arrays with minimal defects and large grains containing thousands of NPs. Edge dislocations, interstitials, vacancies, and overlapping NPs were observed. Deviations from close packing occur as the normalized standard deviation of the sample's size distribution increases above approximately 11%. Polydisperse size distributions and deviations from spherical NP shapes frustrate assembly and prevent ordered packing.

Multiscale computer simulation of the immature HIV-1 virion

Multiscale computer simulations, employing a combination of experimental data and coarse-graining methods, are used to explore the structure of the immature HIV-1 virion. A coarse-grained (CG) representation is developed for the virion membrane shell and Gag polypeptides using molecular level information. Building on the results from electron cryotomography experiments, the simulations under certain conditions reveal the existence of an incomplete p6 hexameric lattice formed from hexameric bundles of the Gag CA domains. In particular, the formation and stability of the immature Gag lattice at the CG level requires enhanced interfacial interactions of the CA protein C-terminal domains (CTDs). An exact mapping of the CG representation back to the molecular level then allows for detailed atomistic molecular dynamics studies to confirm the existence of these enhanced CA(CTD) interactions and to probe their possible origin. The multiscale simulations further provide insight into potential CA(CTD) mutations that may disrupt or modify the Gag immature lattice assembly process in the immature HIV-1 virion.

Confinement-controlled self assembly of colloids with simultaneous isotropic and anisotropic cross-section

The phase behavior of building blocks with mushroom cap-shaped particle morphology is explored under 2D and quasi-2D confinement conditions. Fast confocal microscopy imaging of the particles sedimented in a wedge cell reveals a range of mono- and bilayer structures partially directed by the isotropic and anisotropic profiles of the particle geometry. The sequence of phases tracked with increasing confinement height includes those reported in spheres, in addition to the more complex rotator and orientation-dependent phases observed for a class of short rod-like colloids. In the later case, the major particle axis reorients with respect to the substrate. Closest packing considerations provide rationale for the observed 1Delta (hexagonal)-1Buckled-1Sides (rotator)-2square (square)-2Delta (hexagonal)-2Sides (rotator) structural transitions with height.

Frustrated rotator crystals and glasses of Brownian pentagons

Two-dimensional Brownian dispersions of microscale pentagonal platelets exhibit rich structural and dynamical behavior as the particle area fraction, phi(A), is increased. As phi(A) is raised above 0.66, a rotator crystal forms, and while in an equilateral hexagonal lattice, pentagons still explore all angles as they rotationally diffuse. At larger phi(A), the interference of the tips of neighboring pentagons causes rotational dynamical heterogeneity; particle rotations become nonergodic, the hallmark of a frustrated rotator crystal. Upon further compression, the quenched-in rotational disorder and inability of pentagons to fully tile a flat plane creates spatial defects, precluding access to a dense striped crystalline packing.

Effect of particle shape on the density and microstructure of random packings

We study the random packing of non-spherical particles by computer simulation to investigate the effect of particle shape and aspect ratio on packing density and microstructure. Packings of cut spheres (a spherical segment which is symmetric about the centre of the sphere) are simulated to assess the influence of a planar face on packing properties. It turns out that cut spheres, in common with spherocylinders and spheroids, pack more efficiently as the particle's aspect ratio is perturbed slightly from unity (the aspect ratio of a sphere) to reach a maximum density at an aspect ratio of approximately 1.25. Upon increasing the aspect ratio further the cut spheres pack less efficiently, until approximately an aspect ratio of 2, where the particles are found to form a columnar phase. The amount of ordering is sensitive to simulation parameters and for very thin disks the formation of long columns becomes frustrated, resulting in a nematic phase, in marked contrast to the behavior of long thin rods which always randomly pack into entangled isotropic networks. With respect to coordination numbers it appears that cut spheres always pack with significantly fewer contacts than required for isostatic packing.

Colloidal hard spheres: cooking and looking

In this article we highlight our recent work on the development of crosslinked core-shell polymethyl-methacrylate colloids and their application as colloidal model hard spheres for quantitative confocal microscopy. Moreover, we demonstrate that synthesizing colloids () does not only lead to the final core-shell particles, but also to "intermediate-product-particles", which are interesting in their own right and offer additional possibilities for various physical experiments (). In particular, we focus on the application of crosslinked latex particles as microgel particles, non-spherically shaped particles as model particles for shape-induced geometrical frustration and the final core-shell particles for the direct measurement of thermodynamic properties using quantitative real-space confocal microscopy.

Variable orbital coupling in a two-dimensional quantum-dot solid probed on a local scale

The optoelectronic properties of semiconductor quantum-dot (QD) solids depend on the electronic structure of the building blocks and their interactions. Disorder may affect the coupling on a local scale. We have measured the density of states of 2D arrays of PbSe QDs site by site using scanning tunneling spectroscopy. It markedly differs from that of isolated QDs due to electronic coupling in the array. We observe strong local variations in the coupling strength with two prototypical cases: delocalization of the conduction electrons only, and full coupling with both hole and electron delocalization over the QD sites in the array.