Work hardening in colloidal crystals.

Colloidal crystals exhibit interesting properties1-4 that are in many ways analogous to their atomic counterparts. They have the same crystal structures2,5-7, undergo the same phase transitions8-10, and possess the same crystallographic defects11-14. In contrast to these structural properties, the mechanical properties of colloidal crystals are quite different from those of atomic systems. For example, unlike in atomic systems, the elasticity of hard-sphere colloidal crystals is purely entropic15; as a result, they are so soft that they can be melted just by stirring16,17. Moreover, crystalline materials deform plastically when subjected to increasing shear and become stronger because of the ubiquitous process of work hardening18; but this has so far never been observed in colloidal crystals, to our knowledge. Here we show that hard-sphere colloidal crystals exhibit work hardening. Moreover, despite their softness, the shear strength of colloidal crystals can increase and approach the theoretical limit for crystals, a value reached in very few other materials so far. We use confocal microscopy to show that the strength of colloidal crystals increases with dislocation density, and ultimately reaches the classic Taylor scaling behaviour for atomic materials19-21, although hard-sphere interactions lack the complexity of atomic interactions. We demonstrate that Taylor hardening arises through the formation of dislocation junctions22. The Taylor hardening regime, however, is established only after a transient phase, and it ceases when the colloidal crystals become so hard that the strain is localized within a thin boundary layer in which slip results from an unconventional motion of dislocations. The striking resemblance between colloidal and atomic crystals, despite the many orders of magnitude difference in particle size and shear modulus, demonstrates the universality of work hardening.

Ultrasoft silicone gels with tunable refractive index for traction force microscopy.

We formulate and characterize silicone gels near the gelation threshold with tunable refractive index, 1.4 < n < 1.49, and small viscoelastic moduli, G'∼1 Pa, for use in traction force microscopy. The near-critical gels have low-frequency storage plateau moduli between 50 Pa and 1 Pa, with loss moduli that are more than fifty times lower at low frequencies. The gels are linearly elastic up to strains of at least 50%. The refractive index of the gel is tuned to eliminate spherical aberrations during confocal imaging thereby minimizing signal loss when imaging through thick gel substrates. We also develop an index-matched colloidal particle, stabilized by a silicone brush, that can be dispersed throughout the gel. These particles can be used to determine the deformation of the gel. The combination of mechanical and optical properties of these near-critical gels extends the lower limit of stresses that can be measured with traction force microscopy to single mPa values, while minimizing optical aberrations.

Microscopic origins of the crystallographically preferred growth in evaporation-induced colloidal crystals.

Unlike crystalline atomic and ionic solids, texture development due to crystallographically preferred growth in colloidal crystals is less studied. Here we investigate the underlying mechanisms of the texture evolution in an evaporation-induced colloidal assembly process through experiments, modeling, and theoretical analysis. In this widely used approach to obtain large-area colloidal crystals, the colloidal particles are driven to the meniscus via the evaporation of a solvent or matrix precursor solution where they close-pack to form a face-centered cubic colloidal assembly. Via two-dimensional large-area crystallographic mapping, we show that the initial crystal orientation is dominated by the interaction of particles with the meniscus, resulting in the expected coalignment of the close-packed direction with the local meniscus geometry. By combining with crystal structure analysis at a single-particle level, we further reveal that, at the later stage of self-assembly, however, the colloidal crystal undergoes a gradual rotation facilitated by geometrically necessary dislocations (GNDs) and achieves a large-area uniform crystallographic orientation with the close-packed direction perpendicular to the meniscus and parallel to the growth direction. Classical slip analysis, finite element-based mechanical simulation, computational colloidal assembly modeling, and continuum theory unequivocally show that these GNDs result from the tensile stress field along the meniscus direction due to the constrained shrinkage of the colloidal crystal during drying. The generation of GNDs with specific slip systems within individual grains leads to crystallographic rotation to accommodate the mechanical stress. The mechanistic understanding reported here can be utilized to control crystallographic features of colloidal assemblies, and may provide further insights into crystallographically preferred growth in synthetic, biological, and geological crystals.

Stiffness of the interface between a colloidal body-centered cubic crystal and its liquid.

Equilibrium interfaces were established between body-centered cubic (BCC) crystals and their liquid using charged colloidal particles in an electric bottle. By measuring a time series of interfacial positions and computing the average power spectrum, their interfacial stiffness was determined according to the capillary fluctuation method. For the (100) and the (114) interfaces, the stiffnesses were 0.15 and 0.18 [Formula: see text] (σ: particle diameter), respectively, and were isotropic in the plane of the interface. For comparison, similar charged colloids were used to create an interface between a face-centered cubic (FCC) crystal and its liquid. Its stiffness was significantly larger: 0.26 [Formula: see text] This result gives experimental support to the explanations offered for the preferential nucleation of BCC over FCC in metallic alloys.

Direct observation of crystallization and melting with colloids.

We study the kinetics of crystal growth and melting of two types of colloidal crystals: body-centered cubic (BCC) crystals and face-centered cubic (FCC) crystals. A dielectrophoretic "electric bottle" confines colloids, enabling precise control of the motion of the interface. We track the particle motion, and by introducing a structural order parameter, we measure the jump frequencies of particles to and from the crystal and determine from these the free-energy difference between the phases and the interface mobility. We find that the interface is rough in both BCC and FCC cases. Moreover, the jump frequencies correspond to those expected from the random walk of the particles, which translates to collision-limited growth in metallic systems. The mobility of the BCC interface is greater than that of the FCC interface. In addition, contrary to the prediction of some early computer simulations, we show that there is no significant asymmetry between the mobilities for crystallization and melting.

Direct Observation of Entropic Stabilization of bcc Crystals Near Melting.

Crystals with low latent heat are predicted to melt from an entropically stabilized body-centered cubic symmetry. At this weakly first-order transition, strongly correlated fluctuations are expected to emerge, which could change the nature of the transition. Here we show how large fluctuations stabilize bcc crystals formed from charged colloids, giving rise to strongly power-law correlated heterogeneous dynamics. Moreover, we find that significant nonaffine particle displacements lead to a vanishing of the nonaffine shear modulus at the transition. We interpret these observations by reformulating the Born-Huang theory to account for nonaffinity, illustrating a scenario of ordered solids reaching a state where classical lattice dynamics fail.

Crystallization of undercooled liquid fenofibrate.

Formulation of hydrophobic drugs as amorphous materials is highly advantageous as this increases their solubility in water and therefore their bioavailability. However, many drugs have a high propensity to crystallize during production and storage, limiting the usefulness of amorphous drugs. We study the crystallization of undercooled liquid fenofibrate, a model hydrophobic drug. Nucleation is the rate-limiting step; once seeded with a fenofibrate crystal, the crystal rapidly grows by consuming the undercooled liquid fenofibrate. Crystal growth is limited by the incorporation of molecules into its surface. As nucleation and growth both entail incorporation of molecules into the surface, this process likely also limits the formation of nuclei and thus the crystallization of undercooled liquid fenofibrate, contributing to the good stability of undercooled liquid fenofibrate against crystallization.

Mechanical testing of colloidal solids with millipascal stress and single-particle strain resolution.

We introduce a technique, traction rheoscopy, to carry out mechanical testing of colloidal solids. A confocal microscope is used to directly measure stress and strain during externally applied deformation. The stress is measured, with single-mPa resolution, by determining the strain in a compliant polymer gel in mechanical contact with the colloidal solid. Simultaneously, the confocal microscope is used to measure structural change in the colloidal solid with single particle resolution during the deformation. To demonstrate the utility and sensitivity of this technique, we deform a hard-sphere colloidal glass in simple shear, and from the macroscopic shear strain and measured stress determine the stress-strain curve. Using the stress-strain curve and measured shear modulus, we decompose the macroscopic shear strain into an elastic and a plastic component. We also determine a local strain tensor for each particle using the changes in its nearest-neighbor distances. These local strains are spatially heterogeneous throughout the sample, but, when averaged, match the macroscopic strain. A microscopic yield criterion is used to split the local strains into subyield and yielded partitions; averages over these partitions complement the macroscopic elastic-plastic decomposition obtained from the stress-strain curve. By combining mechanical testing with single-particle structural measurements, traction rheoscopy is a unique tool for the study of deformation mechanisms in a diverse range of soft materials.

Dislocation interactions during plastic relaxation of epitaxial colloidal crystals.

The severe difficulty to resolve simultaneously both the macroscopic deformation process and the dislocation dynamics on the atomic scale limits our understanding of crystal plasticity. Here we use colloidal crystals, imaged on the single particle level by high-speed three-dimensional (3D) confocal microscopy, and resolve in real-time both the relaxation of the epitaxial misfit strain and the accompanying evolution of dislocations. We show how dislocation interactions give rise to the formation of complex dislocation networks in 3D and to unexpectedly sharp plastic relaxation. The sharp relaxation is facilitated by attractive interactions that promote the formation of new dislocations that are more efficient in mediating strain. Dislocation networks form fragmented structures, as dislocation growth is blocked by either attractive interactions, which result in the formation of sessile dislocation junctions, or by repulsion from perpendicular segments. The strength of these blocking mechanisms decreases with the thickness of the crystal film. These results reveal the critical role of dislocation interactions in plastic deformation of thin films and can be readily generalized from the colloidal to the atomic scale.

Visualizing dislocation nucleation by indenting colloidal crystals.

The formation of dislocations is central to our understanding of yield, work hardening, fracture, and fatigue of crystalline materials. While dislocations have been studied extensively in conventional materials, recent results have shown that colloidal crystals offer a potential model system for visualizing their structure and dynamics directly in real space. Although thermal fluctuations are thought to play a critical role in the nucleation of these defects, it is difficult to observe them directly. Nano-indentation, during which a small tip deforms a crystalline film, is a common tool for introducing dislocations into a small volume that is initially defect-free. Here, we show that an analogue of nano-indentation performed on a colloidal crystal provides direct images of defect formation in real time and on the single particle level, allowing us to probe the effects of thermal fluctuations. We implement a new method to determine the strain tensor of a distorted crystal lattice and we measure the critical dislocation loop size and the rate of dislocation nucleation directly. Using continuum models, we elucidate the relation between thermal fluctuations and the applied strain that governs defect nucleation. Moreover, we estimate that although bond energies between particles are about fifty times larger in atomic systems, the difference in attempt frequencies makes the effects of thermal fluctuations remarkably similar, so that our results are also relevant for atomic crystals.

Correlation Tracking: Using simulations to interpolate highly correlated particle tracks.

Despite significant advances in particle imaging technologies over the past two decades, few advances have been made in particle tracking, i.e., linking individual particle positions across time series data. The state-of-the-art tracking algorithm is highly effective for systems in which the particles behave mostly independently. However, these algorithms become inaccurate when particle motion is highly correlated, such as in dense or strongly interacting systems. Accurate particle tracking is essential in the study of the physics of dense colloids, such as the study of dislocation formation, nucleation, and shear transformations. Here, we present a method for particle tracking that incorporates information about the correlated motion of the particles. We demonstrate significant improvement over the state-of-the-art tracking algorithm in simulated data on highly correlated systems.

The microfluidic nebulator: production of sub-micrometer sized airborne drops.

Many powders employed in the food and pharmaceutical industries are produced through spray drying because it is a cost efficient process that offers control over the particle size. However, most commercially available spray-driers cannot produce drops with diameters below 1 µm, limiting the size of spray-dried particles to values above 300 nm. We recently developed a microfluidic spray-drier that can form much smaller drops than commercially available spray-driers. This is achieved through a two-step process: first, the microfluidic spray-drier operates in the dripping regime to form 100 µm diameter primary drops in air and, second, subjects them to high shear stresses due to supersonic flow of air to break them into many much smaller secondary drops. In this paper, we describe the two essential steps required to form sub-µm diameter airborne drops inside microfluidic channels. We investigate the influence of the device geometry on the ability to operate the microfluidic spray-drier in the dripping regime. Moreover, we describe how these primary drops are nebulized into many secondary drops that are much smaller than the smallest dimension of the spray-drier channels.

Stabilization of the Amorphous Structure of Spray-Dried Drug Nanoparticles.

The bioavailability of hydrophobic drugs strongly increases if they are formulated as amorphous materials because the solubility of the amorphous phase is much higher than that of the crystal. Moreover, the stability of these particles against crystallization during storage increases with decreasing particle size. Hence, it is advantageous to formulate poorly water soluble drugs as amorphous nanoparticles. The formulation of an amorphous structure is often difficult because many of these drugs have a high propensity to crystallize. This difficulty can be overcome if drugs are spray-dried using a microfluidic nebulator we recently developed. However, these nanoparticles agglomerate when they come in contact with each other, and this compromises the stability of their amorphous structure through crystallization. To improve their stability, we coat the nanoparticles with a sterically stabilizing polymer layer; this can be accomplished by co-spraying them with an excipient. However, this excipient must meet strict solubility limits, which severely limit the choice of polymers. Alternatively, the nanoparticles can be sterically stabilized by spraying them directly into a polymeric matrix; this enables a much wider choice of stabilizing polymers.

Publisher's Note: Imaging grain boundary grooves in hard-sphere colloidal bicrystals [Phys. Rev. E 94, 042604 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.94.042604.

Imaging grain boundary grooves in hard-sphere colloidal bicrystals.

Colloidal particles were sedimented onto patterned glass slides to grow three-dimensional bicrystals with a controlled structure. Three types of symmetric tilt grain boundaries between close-packed face-centered-cubic crystals were produced: Σ5(100),Σ17(100), and Σ3(110). The structure of the crystals and their defects were visualized by confocal microscopy, and characterized by simple geometric measurements, including image difference, thresholding, and reprojection. This provided a quick and straightforward way to detect the regions in which the atoms are mobile. This atomic mobility was higher at the grain boundaries and close to the solid-liquid interface. This method was compared to the more conventional analysis based on the calculation of the local order parameter of the individual particles to identify the interface. This was used in turn to identify the presence of grooves at the grain-boundary-liquid triple junction for every type of grain boundary, except for the twin [Σ3(110)], for which no groove could be detected. Images of these grooves were processed, and the angle linking the grain boundary energy to the solid-liquid interfacial energy was measured. The resulting values of the grain boundary energy were compared to estimates based on the density deficit in the boundary.

Anisotropic elasticity of experimental colloidal Wigner crystals.

Colloidal particles interacting via a long-range repulsion can, in contrast to hard-sphere systems, exhibit crystalline ordering at low volume fraction. Here we experimentally investigate the structure and properties of such "colloidal Wigner crystals." We find a body-centered-cubic crystalline phase at volume fractions of ϕ≳15%, which exhibits large fluctuations of individual particles from their average positions. We determine the three independent crystalline elastic constants and find that these crystals are very compliant and highly anisotropic.

NANOPARTICLES. Production of amorphous nanoparticles by supersonic spray-drying with a microfluidic nebulator.

Amorphous nanoparticles (a-NPs) have physicochemical properties distinctly different from those of the corresponding bulk crystals; for example, their solubility is much higher. However, many materials have a high propensity to crystallize and are difficult to formulate in an amorphous structure without stabilizers. We fabricated a microfluidic nebulator that can produce amorphous NPs from a wide range of materials, even including pure table salt (NaCl). By using supersonic air flow, the nebulator produces drops that are so small that they dry before crystal nuclei can form. The small size of the resulting spray-dried a-NPs limits the probability of crystal nucleation in any given particle during storage. The kinetic stability of the a-NPs­on the order of months­is advantageous for hydrophobic drug molecules.

Structural rearrangements that govern flow in colloidal glasses.

Structural rearrangements are an essential property of atomic and molecular glasses; they are critical in controlling resistance to flow and are central to the evolution of many properties of glasses, such as their heat capacity and dielectric constant. Despite their importance, these rearrangements cannot directly be visualized in atomic glasses. We used a colloidal glass to obtain direct three-dimensional images of thermally induced structural rearrangements in the presence of an applied shear. We identified localized irreversible shear transformation zones and determined their formation energy and topology. A transformation favored successive ones in its vicinity. Using continuum models, we elucidated the interplay between applied strain and thermal fluctuations that governs the formation of these zones in both colloidal and molecular glasses.

Visualization of dislocation dynamics in colloidal crystals.

The dominant mechanism for creating large irreversible strain in atomic crystals is the motion of dislocations, a class of line defects in the crystalline lattice. Here we show that the motion of dislocations can also be observed in strained colloidal crystals, allowing detailed investigation of their topology and propagation. We describe a laser diffraction microscopy setup used to study the growth and structure of misfit dislocations in colloidal crystalline films. Complementary microscopic information at the single-particle level is obtained with a laser scanning confocal microscope. The combination of these two techniques enables us to study dislocations over a range of length scales, allowing us to determine important parameters of misfit dislocations such as critical film thickness, dislocation density, Burgers vector, and lattice resistance to dislocation motion. We identify the observed dislocations as Shockley partials that bound stacking faults of vanishing energy. Remarkably, we find that even on the scale of a few lattice vectors, the dislocation behavior is well described by the continuum approach commonly used to describe dislocations in atomic crystals.