DNA-mediated assembly of Au bipyramids into anisotropic light emitting kagome superlattices.

Colloidal crystal engineering with DNA allows one to design diverse superlattices with tunable lattice symmetry, composition, and spacing. Most of these structures follow the complementary contact model, maximizing DNA hybridization on building blocks and producing relatively close-packed lattices. Here, low-symmetry kagome superlattices are assembled from DNA-modified gold bipyramids that can engage only in partial DNA surface matching.

Classification of complex local environments in systems of particle shapes through shape symmetry-encoded data augmentation.

Detecting and analyzing the local environment is crucial for investigating the dynamical processes of crystal nucleation and shape colloidal particle self-assembly. Recent developments in machine learning provide a promising avenue for better order parameters in complex systems that are challenging to study using traditional approaches. However, the application of machine learning to self-assembly on systems of particle shapes is still underexplored.

Space-tiled colloidal crystals from DNA-forced shape-complementary polyhedra pairing.

Generating space-filling arrangements of most discrete polyhedra nanostructures of the same shape is not possible. However, if the appropriate individual building blocks are selected (e.g.

Rationalizing Euclidean Assemblies of Hard Polyhedra from Tessellations in Curved Space.

Entropic self-assembly is governed by the shape of the constituent particles, yet a priori prediction of crystal structures from particle shape alone is nontrivial for anything but the simplest of space-filling shapes. At the same time, most polyhedra are not space filling due to geometric constraints, but these constraints can be relaxed or even eliminated by sufficiently curving space. We show using Monte Carlo simulations that the majority of hard Platonic solids self-assemble entropically into space-filling crystals when constrained to the surface volume of a 3-sphere.

Complex motion of steerable vesicular robots filled with active colloidal rods.

While the collective motion of active particles has been studied extensively, effective strategies to navigate particle swarms without external guidance remain elusive. We introduce a method to control the trajectories of two-dimensional swarms of active rod-like particles by confining the particles to rigid bounding membranes (vesicles) with non-uniform curvature. We show that the propelling agents spontaneously form clusters at the membrane wall and collectively propel the vesicle, turning it into an active superstructure.

Colloidal quasicrystals engineered with DNA.

In principle, designing and synthesizing almost any class of colloidal crystal is possible. Nonetheless, the deliberate and rational formation of colloidal quasicrystals has been difficult to achieve. Here we describe the assembly of colloidal quasicrystals by exploiting the geometry of nanoscale decahedra and the programmable bonding characteristics of DNA immobilized on their facets.

Tunable assembly of host-guest colloidal crystals.

Entropy compartmentalization provides new self-assembly routes to colloidal host-guest (HG) structures. Leveraging host particle shape to drive the assembly of HG structures has only recently been proposed and demonstrated. However, the extent to which the guest particles can dictate the structure of the porous network of host particles has not been explored.

Entropy compartmentalization stabilizes open host-guest colloidal clathrates.

Clathrates are open crystals in which molecules are arranged in a hierarchy of polyhedral cages that encapsulate guest molecules and ions. As well as holding fundamental interest, molecular clathrates serve practical purposes, such as for gas storage, and their colloidal counterparts also appear promising for host-guest applications. Here using Monte Carlo simulations, we report the entropy-driven self-assembly of hard truncated triangular bipyramids into seven different host-guest colloidal clathrate crystals with unit cells ranging from 84 to 364 particles.

Inverse design of triblock Janus spheres for self-assembly of complex structures in the crystallization slot digital alchemy.

The digital alchemy framework is an extended ensemble simulation technique that incorporates particle attributes as thermodynamic variables, enabling the inverse design of colloidal particles for desired behavior. Here, we extend the digital alchemy framework for the inverse design of patchy spheres that self-assemble into target crystal structures. To constrain the potentials to non-trivial solutions, we conduct digital alchemy simulations with constant second virial coefficient.

Photonically active bowtie nanoassemblies with chirality continuum.

Chirality is a geometrical property described by continuous mathematical functions. However, in chemical disciplines, chirality is often treated as a binary left or right characteristic of molecules rather than a continuity of chiral shapes. Although they are theoretically possible, a family of stable chemical structures with similar shapes and progressively tuneable chirality is yet unknown.

Self-Assembly of Atomically Aligned Nanoparticle Superlattices from Pt-FeO Heterodimer Nanoparticles.

Multicomponent nanoparticle superlattices (SLs) promise the integration of nanoparticles (NPs) with remarkable electronic, magnetic, and optical properties into a single structure. Here, we demonstrate that heterodimers consisting of two conjoined NPs can self-assemble into novel multicomponent SLs with a high degree of alignment between the atomic lattices of individual NPs, which has been theorized to lead to a wide variety of remarkable properties. Specifically, by using simulations and experiments, we show that heterodimers composed of larger FeO domains decorated with a Pt domain at one vertex can self-assemble into an SL with long-range atomic alignment between the FeO domains of different NPs across the SL.

Engineering the Thermodynamic Stability and Metastability of Mesophases of Colloidal Bipyramids through Shape Entropy.

We report several types of entropy-driven phase transition behaviors in hard bipyramid systems using Monte Carlo simulations. Bipyramidal nanoparticle shapes are synthesizable from gold and silver, with sizes ranging from tens to hundreds of nanometers. We report numerous colloidal crystalline phases with varying symmetries and complexities as the bipyramid aspect ratio and base polygon are varied.

Arrays of Colloidal Single Crystals Engineered with DNA in Lithographically Defined Microwells.

Lithographically defined microwell templates are used to study DNA-guided colloidal crystal assembly parameters, including superlattice position, habit orientation, and size, in an effort to increase our understanding of the crystallization process. In addition to enabling the synthesis of arrays of individual superlattices in arbitrary predefined patterns, the technique allows one to study the growth pathways of the crystals via scanning electron microscopy. Importantly, a Volmer-Weber (VM) (island formation)-like growth mode is identified, which has been reproduced via simulations.

Entropically engineered formation of fivefold and icosahedral twinned clusters of colloidal shapes.

Fivefold and icosahedral symmetries induced by multiply twinned crystal structures have been studied extensively for their role in influencing the shape of synthetic nanoparticles, and solution chemistry or geometric confinement are widely considered to be essential. Here we report the purely entropy-driven formation of fivefold and icosahedral twinned clusters of particles in molecular simulation without geometric confinement or chemistry. Hard truncated tetrahedra self-assemble into cubic or hexagonal diamond colloidal crystals depending on the amount of edge and vertex truncation.

Symmetry-breaking in patch formation on triangular gold nanoparticles by asymmetric polymer grafting.

Synthesizing patchy particles with predictive control over patch size, shape, placement and number has been highly sought-after for nanoparticle assembly research, but is fraught with challenges. Here we show that polymers can be designed to selectively adsorb onto nanoparticle surfaces already partially coated by other chains to drive the formation of patchy nanoparticles with broken symmetry. In our model system of triangular gold nanoparticles and polystyrene-b-polyacrylic acid patch, single- and double-patch nanoparticles are produced at high yield.

Shape memory in self-adapting colloidal crystals.

Reconfigurable, mechanically responsive crystalline materials are central components in many sensing, soft robotic, and energy conversion and storage devices. Crystalline materials can readily deform under various stimuli and the extent of recoverable deformation is highly dependent upon bond type. Indeed, for structures held together via simple electrostatic interactions, minimal deformations are tolerated.

Curvature-controlled geometrical lensing behavior in self-propelled colloidal particle systems.

In many biological systems, the curvature of the surfaces cells live on influences their collective properties. Curvature should likewise influence the behavior of active colloidal particles. We show using molecular simulation of self-propelled active particles on surfaces of Gaussian curvature (both positive and negative) how curvature sign and magnitude can alter the system's collective behavior.

Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices.

The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal cocrystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote-and, in some cases, may be necessary for-the self-assembly of a binary cocrystal.

Evaporation-Driven Coassembly of Hierarchical, Multicomponent Networks.

Self-assembly is an increasingly popular approach to systematically control the formation of complex, multicomponent materials with structural features orders of magnitude larger than the constituent colloidal nanocrystals. Common approaches often involve templating prefabricated patterns to control particle organization- or programming-specific interactions between individual building blocks. While effective, such fabrication methods suffer from major bottlenecks due to the complexity required in mask creation for patterning or surface modification techniques needed to program directed interactions between particles.

Structural Color Spectral Response of Dense Structures of Discoidal Particles Generated by Evaporative Assembly.

Structural color─optical response due to light diffraction or scattering from submicrometer-scale structures─is a promising means for sustainable coloration. To expand the functionality of structural color, we introduce discoidal shape anisotropy into colloidal particles and characterize how structural color reflection can be engineered. Uniaxial compression of spheres is used to prepare discoids with varying shape anisotropy and particle size.

A theory of entropic bonding.

Entropy alone can self-assemble hard nanoparticles into colloidal crystals of remarkable complexity whose structures are the same as atomic and molecular crystals, but with larger lattice spacings. Molecular simulation is a powerful tool used extensively to study the self-assembly of ordered phases from disordered fluid phases of atoms, molecules, or nanoparticles. However, it is not yet possible to predict colloidal crystal structures a priori from particle shape as we can for atomic crystals from electronic valency.

The emergence of valency in colloidal crystals through electron equivalents.

Colloidal crystal engineering of complex, low-symmetry architectures is challenging when isotropic building blocks are assembled. Here we describe an approach to generating such structures based upon programmable atom equivalents (nanoparticles functionalized with many DNA strands) and mobile electron equivalents (small particles functionalized with a low number of DNA strands complementary to the programmable atom equivalents). Under appropriate conditions, the spatial distribution of the electron equivalents breaks the symmetry of isotropic programmable atom equivalents, akin to the anisotropic distribution of valence electrons or coordination sites around a metal atom, leading to a set of well-defined coordination geometries and access to three new low-symmetry crystalline phases.