Particle shape and entropy play critical roles in order-disorder transitions; examples include liquid crystals and crystals formed from hard polyhedra. With few exceptions, colloidal crystals reported in the literature form from convex particles, for which the roles of particle shape and entropy are well explored. However, recent experimental work has shown that a cubic diamond lattice, elusive but long sought after for its wide and robust photonic band gap, can be assembled from non-convex particles. Here, we use simulations to explore the crystallization of colloidal diamond from non-convex tetrahedral-lobed patchy particles (TLPPs). Our results show how the entropic cost of binding, measured using umbrella sampling, can be tuned through subtle changes to the particle geometry. Geometric constraints, uniquely provided by the particle's non-convex features, select the staggered bond conformation required for cubic diamond. These constraints and the entropy associated with them can be geometrically tuned to vary the flexibility of the bonds. Depending on the particle geometry, TLPPs form liquid, diamond, or amorphous structures. Importantly, all geometrical parameters can be controlled in experiments, which should lead to larger crystals with less disorder, improving the resulting photonic band gap.

Understanding the motion of particles with multivalent ligand-receptors is important for biomedical applications and material design. Yet, even among a single design, the prototypical DNA-coated colloids, seemingly similar micrometric particles hop or roll, depending on the study. We shed light on this problem by observing DNA-coated colloids diffusing near surfaces coated with complementary strands for a wide array of coating designs. We find colloids rapidly switch between 2 modes: They hop—with long and fast steps—and crawl—with short and slow steps. Both modes occur at all temperatures around the melting point and over various designs. The particles become increasingly subdiffusive as temperature decreases, in line with subsequent velocity steps becoming increasingly anticorrelated, corresponding to switchbacks in the trajectories. Overall, crawling (or hopping) phases are more predominant at low (or high) temperatures; crawling is also more efficient at low temperatures than hopping to cover large distances. We rationalize this behavior within a simple model: At lower temperatures, the number of bound strands increases, and detachment of all bonds is unlikely, hence, hopping is prevented and crawling favored. We thus reveal the mechanism behind a common design rule relying on increased strand density for long-range self-assembly: Dense strands on surfaces are required to enable crawling, possibly facilitating particle rearrangements.

Through the strategic design of base sequences in DNA brushes, it is possible to adjust the interaction parameters between DNA-coated colloidal microspheres in tandem with their DNA grafting density and buffer conditions, resulting in a shift in their melting temperature. Multiple DNA-coated colloids can be assembled into hierarchical colloidal superstructures in a stepwise manner by tuning their respective melting temperatures. Here, the controlled introduction of mismatched base pairs into complementary DNA brushes provides an additional means of tuning the interparticle interactions. We find that precise control over the melting temperature can be achieved by strategically designing the type, position, or number of mismatched base pairs introduced in otherwise self-complementary DNA brushes. The use of two sets of particles coated with self-complementary DNA with dissimilar mismatched bases enables the realization of temperature-dependent binding with distinct melting temperatures. Using self-complementary DNA brushes with mismatched base pairs, two sets of colloidal particles are programmed with temperature-dependent orthogonal interactions to promote the stepwise assembly of the FCC-crystalline core-shell superstructures. Furthermore, to demonstrate the versatility of manipulating DNA sequences to engineer precise control over colloidal assembly, we demonstrate that CsCl-crystalline core-shell superstructures can be assembled from a ternary colloidal mixture by using complementary DNA brushes without or with mismatched bases.

Concentrated colloidal suspensions and emulsions are amorphous soft solids, widespread in technological and industrial applications and studied as model systems in physics and material sciences. They are easily fluidized by applying a mechanical stress, undergoing a yielding transition that still lacks a unified description. Here, we investigate yielding in three classes of repulsive soft solids, using analytical and numerical modelling and experiments probing the microscopic dynamics and mechanical response under oscillatory shear. We find that at the microscopic level yielding consists in a transition between two distinct dynamical states, which we rationalize by proposing a lattice model with dynamical coupling between neighboring sites, leading to a unified state diagram for yielding. Leveraging the analogy with Wan der Waals's phase diagram for real gases, we show that distance from a critical point plays a major role in the emergence of first-order-like vs second-order-like features in yielding, thereby reconciling previously contrasting observations on the nature of the transition.

The self-assembly of DNA-coated colloids into highly-ordered structures offers great promise for advanced optical materials. However, control of disorder, defects, melting, and crystal growth is hindered by the lack of a microscopic understanding of DNA-mediated colloidal interactions. Here we use total internal reflection microscopy to measure in situ the interaction potential between DNA-coated colloids with nanometer resolution and the macroscopic melting behavior. The range and strength of the interaction are measured and linked to key material design parameters, including DNA sequence, polymer length, grafting density, and complementary fraction. We present a first-principles model that screens and combines existing theories into one coherent framework and quantitatively reproduces our experimental data without fitting parameters over a wide range of DNA ligand designs. Our theory identifies a subtle competition between DNA binding and steric repulsion and accurately predicts adhesion and melting at a molecular level. Combining experimental and theoretical results, our work provides a quantitative and predictive approach for guiding material design with DNA-nanotechnology and can be further extended to a diversity of colloidal and biological systems.

Self-assembling colloidal particles into clathrate hydrates requires the particles to have tetrahedral bonds in the eclipsed conformation. It has been suggested that colloidal particles with eclipsed triangular-shaped patches can form clusters in the eclipsed conformation that leads to colloidal clathrate hydrates. However, in experiments, patches have been limited to circular shapes due to surface energy minimization. Here, we extend the particle synthesis strategy and show that colloidal particles with triangular patches can be readily fabricated by controlling the viscosity of the liquid oil droplets during a colloidal fusion process. The position, orientation, curvature, shape, and size of the patches are all exclusively determined by the intrinsic symmetry of the colloidal clusters, resulting in dipatch particles with eclipsed patches and tetrahedral patchy particles with patch vertices pointing toward each other. Patch curvature can be controlled by tuning the viscosity of the oil droplets and using different surfactants. Using strain-promoted azide-alkyne cycloaddition, single-stranded DNA can be selectively functionalized on the patches. However, after annealing these particles, dipatch particles form chains because the patches are too small to form clathrate hydrates. Under certain conditions, tetrahedral triangular patchy particles should prefer the eclipsed conformation, as it maximizes DNA hybridization. However, we observe random aggregates, which result from having triangular patches that are too big. We estimate that tetrahedral patchy particles that can crystallize need to be less than 1 μm in diameter.

Total internal reflection microscopy (TIRM) measures changes in the distance between a colloidal particle and a transparent substrate by measuring the intensity of light scattered by the particle when it is illuminated by the evanescent field that is created from light totally internally reflected at the substrate interface. From these measurements, the height-dependent effective potential $\varphi(z)$ between the colloidal particle and the substrate can be measured. The spatial resolution with which TIRM can resolve the height $z$ and effective potential $\varphi(z)$ is limited by the intrinsic shot noise of the photon counting process used to measure the scattered light intensity. We develop a model to determine the spatial resolution with which TIRM can measure $\varphi(z)$ and verify its validity with simulations and experiments. We establish the critical role of shot noise and intensity integration time $\tau$ in TIRM measurements of colloidal interaction potentials, which is a trade-off between minimizing shot noise and preserving the spatial resolution of the potential.

Colloidal clusters are prepared by assembling positively charged cross-linked polystyrene (PS) particles onto negatively charged liquid cores of swollen polymer particles. PS particles at the interface of the liquid core are closely packed around the core due to interfacial wetting. Then, by evaporating solvent in the liquid cores, polymers in the cores are solidified and the clusters are cemented. As the swelling ratio of PS cores increases, cores at the center of colloidal clusters are exposed, forming patchy colloidal clusters. Finally, by density gradient centrifugation, high-purity symmetric colloidal clusters are obtained. When silica-PS core-shell particles are swollen and serve as the liquid cores, hybrid colloidal clusters are obtained in which each silica nanoparticle is relocated to the liquid core interface during the swelling-deswelling process breaking symmetry in colloidal clusters as the silica nanoparticle in the core is comparable in size with the PS particle in the shell. The configuration of colloidal clusters is determined once the number of particles around the liquid core is given, which depends on the size ratio of the liquid core and shell particle. Since hybrid clusters are heavier than PS particles, they can be purified using centrifugation.

This contribution describes the synthesis of colloidal di-patch particles functionalized with DNA on the patches and their assembly into colloidal superstructures via cooperative depletion and DNA-mediated interactions. The assembly into flower-like Kagome, brick-wall like monolayer, orthogonal packed single or double layers, wrinkled monolayer, and colloidal honeycomb superstructures can be controlled by tuning the particles' patch sizes and assembly conditions. Based on these experimental results, we generate an empirical phase diagram. The principles revealed by the phase diagram provide guidance in the design of two-dimensional (2D) materials with desired superstructures. Our strategy might be translatable to the assembly of three-dimensional (3D) colloidal structures.

We describe a general procedure for the large-scale fabrication of bowl-shaped colloidal particles using an emulsion templating technique. Following this method, single polymeric seed particles become located on individual oil droplet surfaces. The polymer phase is subsequently plasticized using an appropriate solvent. In this critical step, the compliant seed is deformed by surface tension, with the droplet serving as a templating surface. Solvent evaporation freezes the desired particle shape and the oil is subsequently removed by alcohol dissolution. The resulting uniformly-shaped colloidal particles were studied using scanning electron and optical microscopy. By adjusting the droplet size and the seed particle diameter, we demonstrate that the final particle shape can be controlled precisely, from shallow lenses to deep bowls. We also show that the colloid's uniformity and abundant quantity allowed the depletion-mediated assembly of flexible colloidal chains and clusters.

Total internal reflection microscopy (TIRM) measures changes in the distance between a colloidal particle and a transparent substrate by measuring the scattering intensity of the particle illuminated by an evanescent wave. From the distribution of the recorded separation distances, the height-dependent effective potential φ(z) between the colloidal particle and the substrate can be measured. In this work, we show that spatial resolution with which TIRM can measure φ(z) is limited by the photon counting statistics of the scattered laser light. We develop a model to evaluate the effect of photon counting statistics on different potential profiles using Brownian dynamics simulations and experiments. Our results show that the effect of photon counting statistics depends on spatial gradients ∂φ/∂z of the potential, with the result that sharp features tend to be significantly blurred. We further establish the critical role of photon counting statistics and the intensity integration time τ in TIRM measurements, which is a trade-off between narrowing the width of the photon counting distribution and capturing the instantaneous position of the probe particle.

Patchy particles with shape complementarity can serve as building blocks for assembling colloidal superstructures. Alternatively, encoding information on patches using DNA can direct assembly into a variety of crystalline or other preprogrammed structures. Here, we present a tool where DNA is used both to engineer shape and to encode information on colloidal particles. Two reactive oil emulsions with different but complementary DNA (cDNA) brushes are assembled into CsCl-like crystalline lattices. The DNA brushes are recruited to and ultimately localized at the junctions between neighboring droplets, which gives rise to DNA-encoded faceted patches. The emulsions are then solidified by ultraviolet (UV) polymerization, producing faceted patchy particles. The facet size and DNA distribution are determined by the balance between the DNA binding energy and the elastic deformation energy of droplets. This method leads to a variety of new patchy particles with directional interactions in scalable quantities.

Self-assembling colloidal particles in the cubic diamond crystal structure could potentially be used to make materials with a photonic bandgap1–3. Such materials are beneficial because they suppress spontaneous emission of light1 and are valued for their applications as optical waveguides, filters and laser resonators4, for improving light-harvesting technologies5–7 and for other applications4,8. Cubic diamond is preferred for these applications over more easily self-assembled structures, such as face-centred-cubic structures9,10, because diamond has a much wider bandgap and is less sensitive to imperfections11,12. In addition, the bandgap in diamond crystals appears at a refractive index contrast of about 2, which means that a photonic bandgap could be achieved using known materials at optical frequencies; this does not seem to be possible for face-centred-cubic crystals3,13. However, self-assembly of colloidal diamond is challenging. Because particles in a diamond lattice are tetrahedrally coordinated, one approach has been to self-assemble spherical particles with tetrahedral sticky patches14–16. But this approach lacks a mechanism to ensure that the patchy spheres select the staggered orientation of tetrahedral bonds on nearest-neighbour particles, which is required for cubic diamond15,17. Here we show that by using partially compressed tetrahedral clusters with retracted sticky patches, colloidal cubic diamond can be self-assembled using patch–patch adhesion in combination with a steric interlock mechanism that selects the required staggered bond orientation. Photonic bandstructure calculations reveal that the resulting lattices (direct and inverse) have promising optical properties, including a wide and complete photonic bandgap. The colloidal particles in the self-assembled cubic diamond structure are highly constrained and mechanically stable, which makes it possible to dry the suspension and retain the diamond structure. This makes these structures suitable templates for forming high-dielectric-contrast photonic crystals with cubic diamond symmetry. Self-assembly of cubic diamond crystals is demonstrated, by using precursor clusters of particles with carefully placed ‘sticky’ patches that attract and bind adjacent clusters in specific geometries.

Assembling colloidal particles using site-selective directional interactions into predetermined colloidal superlattices with desired properties is broadly sought after, but challenging to achieve. Herein, we exploit regioselective depletion interactions to engineer the directional bonding and assembly of non-spherical colloidal hybrid microparticles. We report that the crystallization of a binary colloidal mixture can be regulated by tuning the depletion conditions. Subsequently, we fabricate triblock biphasic colloids with controlled aspect ratios to achieve regioselective bonding. Without any surface treatment, these biphasic colloids assemble into various colloidal superstructures and superlattices featuring optimized pole-to-pole or centre-to-centre interactions. Additionally, we observe polymorphic crystallization, quantify the abundancy of each form using algorithms we developed and investigate the crystallization process in real time. We demonstrate selective control of attractive interactions between specific regions on an anisotropic colloid with no need of site-specific surface functionalization, leading to a general method for achieving colloidal structures with yet unforeseen arrangements and properties.

In periodically sheared suspensions there is a dynamical phase transition, characterized by a critical strain amplitude γ_{c}, between an absorbing state where particle trajectories are reversible and an active state where trajectories are chaotic and diffusive. Repulsive nonhydrodynamic interactions between "colliding" particles' surfaces have been proposed as a source of this broken time reversal symmetry. A simple toy model called random organization qualitatively reproduces the dynamical features of this transition. Random organization and other absorbing state models exhibit hyperuniformity, a strong suppression of density fluctuations on long length scales quantified by a structure factor S(q→0)∼q^{α} with α>0, at criticality. Here we show experimentally that the particles in periodically sheared suspensions organize into structures with anisotropic short-range order but isotropic, long-range hyperuniform order when oscillatory shear amplitudes approach γ_{c}.

Janus colloids with one attractive patch on an otherwise repulsive particle surface serve as model systems to explore structure formation of particles with chemically heterogeneous surfaces such as proteins. While there are numerous computer studies, there are few experimental realizations due to a lack of means to produce such colloids with a well-controlled variable Janus balance. Here, we report a simple scalable method to precisely vary the Janus balance over a wide range and selectively functionalize one patch with DNA. We observe, via experiment and simulation, the dynamic formation of diverse superstructures: colloidal micelles, chains, or bilayers, depending on the Janus balance. Flexible dimer chains form through cooperative polymerization while trimer chains form by a two-stage process, first by cooperative polymerization into disordered aggregates followed by condensation into more ordered stiff trimer chains. Introducing substrate binding through depletion catalyzes dimer chains to form nonequilibrium rings that otherwise do not form.