DNA-mediated two-dimensional colloidal crystallization above different attractive surfaces

We explore the formation of "floating" two-dimensional colloidal crystals above weakly attractive surfaces that are either positively or negatively charged. In particular, we studied crystal formation above positively charged poly-L-lysine-poly(ethylene glycol) surfaces with and without short single-stranded DNA and above negatively charged bovine albumin serum-streptavidin multilayers. Confocal microscopy revealed the evolution of crystals several micrometers above all three surfaces. Interestingly, the "flying height" of crystals was found to depend on the surface coating. All crystalline structures remained remarkably stable over weeks, even under high salt conditions. Neither lifting the crystals nor lowering them by means of buoyancy forces destroyed them.     

Aggregation-fragmentation in a model of DNA-mediated colloidal assembly

We present results from an off-lattice Monte Carlo simulation of DNA-mediated colloidal assembly. In this simulation, the aggregation-fragmentation of a binary mixture of DNA-coated colloidal particles is studied through a simplified model of base-pair hybridization. Bonding between monomers is modeled as a simple temperature-sensitive A/B-type interaction, where type A and B monomers can bond to only the opposite type (no A/A or B/B attachments are allowed). The actual chemistry of base-pair hybridization is not included in the model. The morphological structures of the clusters formed as well as the kinetics of growth are analyzed in our 2D simulations. The fractal dimension and kinetic growth exponents for clusters formed near the DNA "melting" temperature agree with those seen previously for 2D diffusion-limited cluster aggregation (DLCA) models. The clusters appear more compact, exhibiting signs of local order at intermediate temperature values. At higher temperatures, the formation of large clusters is not favorable under the action of temperature-dependent fragmentation, and the system eventually reaches a steady state as a collection of small aggregates. The temperature profile for this dissolution of the colloidal assembly is sharp, indicating that the selective hybridization process provides a highly sensitive measurement tool. At high temperatures, we analyze the steady-state behavior of the average cluster size in terms of an aggregation-fragmentation model.     

A general theory of DNA-mediated and other valence-limited colloidal interactions

We present a general theory for predicting the interaction potentials between DNA-coated colloids, and more broadly, any particles that interact via valence-limited ligand-receptor binding. Our theory correctly incorporates the configurational and combinatorial entropic factors that play a key role in valence-limited interactions. By rigorously enforcing self-consistency, it achieves near-quantitative accuracy with respect to detailed Monte Carlo calculations. With suitable approximations and in particular geometries, our theory reduces to previous successful treatments, which are now united in a common and extensible framework. We expect our tools to be useful to other researchers investigating ligand-mediated interactions. A complete and well-documented Python implementation is freely available at http://github.com/patvarilly/DNACC.     

Kinetic stages of single-component colloidal crystallization

To harness the full potential of colloidal self-assembly, the dynamics of the transition between colloids in suspension to a colloidal crystalline film should be better understood. In this report, the structural changes during the self-assembly process in a vertical configuration for colloids in the size range 200-400 nm are monitored in situ, using the transmission spectrum of the colloidal assembly treated as an emergent photonic crystal. It is found that there are several sequential stages of colloidal ordering: in suspension, with a larger lattice parameter than the solid state, in a close-packed wet state with solvent in the interstices, and, finally, in a close-packed dry state with air in the interstices. Assuming that these stages lead continuously from one to another, we can interpret colloidal crystallization as being initiated by interparticle forces in suspension first, followed by capillary forces. This result has implications for identifying the optimum conditions to obtain high-quality nanostructures of submicrometer-sized colloidal particles.     

Interfacial colloidal crystallization via tunable hydrogel depletants

We demonstrate an approach using temperature-dependent hydrogel depletants to thermoreversibly tune colloidal attraction and interfacial colloidal crystallization. Total internal reflection and video microscopy are used to measure temperature-dependent depletion potentials between approximately 2 microm silica colloids and surfaces as mediated by approximately 0.2 microm poly-N-isopropylacrylamide (PNIPAM) hydrogel particles. Measured depletion potentials are modeled using the Asakura-Oosawa theory while treating PNIPAM depletants as swellable hard spheres. Monte Carlo simulations using the measured potentials predict reversible, quasi-2D crystallization and melting at approximately 27 degrees C in quantitative agreement with video microscopy images of measured microstructures (i.e., radial distribution functions) over the temperature range of interest (20-29 degrees C). Additional measurements of short-time self-diffusivities display excellent agreement with predicted diffusivities by considering multibody hydrodynamic interactions and using a swellable hard sphere model for the PNIPAM solution viscosity. Our findings demonstrate the ability to quantitatively measure, model, and manipulate kT-scale depletion attraction and phase behavior as a means of formally engineering interfacial colloidal crystallization.     

Stacking fault structure in shear-induced colloidal crystallization

We report measurements of the spatial distribution of stacking faults in colloidal crystals formed by means of an oscillatory shear field at a particle volume fraction of 52% in a system where the pair potential interactions are mildly repulsive. Stacking faults are directly visualized via confocal laser scanning microscopy. Consistent with previous scattering studies, shear orders the initially amorphous colloids into close-packed planes parallel to the shearing surface. Upon increasing the strain amplitude, the close-packed direction of the (111) crystal plane shifts from an orientation parallel to the vorticity direction to parallel the flow direction. The quality of the layer ordering, as characterized by the mean stacking parameter, decreases with strain amplitude. In addition, we directly observe the three-dimensional structure of stacking faults in sheared crystals. We observe and quantify spatial heterogeneity in the stacking fault arrangement in both the flow-vorticity plane and the gradient direction, particularly at high strain amplitudes (gamma> or =3). At these conditions, layer ordering persists in the flow-vorticity plane only over scales of approximately 5-10 particle diameters. This heterogeneity is one component of the random layer ordering deduced from previous scattering studies. In addition, in the gradient direction, the stacking registry shows that crystals with intermediate global mean stacking probability are comprised of short sequences of face-centered cubic and hexagonal close-packed layers with a stacking that includes a component that is nonrandom and alternating in character.     

Kinetic analyses of colloidal crystallization in shear flow

Colloidal crystallization kinetics is studied in the shear flow of a suspension of colloidal silica spheres (110 nm in diameter), using a continuously-circulating type of stopped flow cell system. The crystallization rate from a suspension containing a small amount of nuclei and/or single crystals is high compared with that from a suspension containing no nuclei and/or single crystals. Crystal growth takes place at shear rates smaller than 3.4 s^–1 and at sphere concentrations higher than a volume fraction of 0.004.     

Directing the self-assembly of nanocrystals beyond colloidal crystallization

This article gives an overview of recent progress in the self-assembly of nanocrystals. Classic self-assembly of nanocrystals, so-called colloidal crystallization driven by van der Waals interactions, is highlighted first with an emphasis on the recent realization of binary colloidal crystals. Next, new developments in the integration of nanocrystals into clusters based on electrostatic interactions, hydrogen bonding and dipole-dipole interactions are summarized, shedding light on the defined control of the interactions between the nanocrystals. Finally, the fabrication of heterogenous nanocrystals, obtained via either phase selective modification at the water/oil interface or facet-selective crystal growth on non-spherical nanocrystals is discussed. These last materials may provide significant building blocks for mimicking molecular self-assembly.     

Modified spin-coating technique to achieve directional colloidal crystallization

Fabricating large single crystals with colloidal spheres as building blocks is challenging and of competitive interest. Spin-coating of colloids offers a robust technique, which is highly reproducible in obtaining colloidal crystals even at fast dynamical regimes; however, these crystals are intrinsically polycrystalline due to the axial symmetry of spin-coating. We report a new method that applies a nonuniform electric field during the spin-coating process. By arranging the field direction to be stationary in the rotating frame, we are able to break the axial symmetry and to orient the colloids along one predefined direction. By regulating the applied field strength, we demonstrate local control over the orientation of the crystallites, and thus, the orientation is determined by the applied field strength.     

Stimuli-responsive surface crystallization of phospholipids from bimodal colloidal particles

These studies focus on the effect of phospholipids in the presence of ionic surfactants on the behavior of poly(methylmethactrylate/n-butyl acrylate) (p-MMA/nBA) colloidal particles during film formation. With the presence of two surfactants, it is possible to obtain particles that exhibit two distinct particle sizes. The presence of hydrogenated soybean phosphatidylcholine (HSPC) and sodium dioctyl sulfosuccinate (SDOSS), which stabilize these bimodal colloidal dispersions, has a significant effect on the mobility of individual components during coalescence. Specifically, the presence of HSPC inhibits migration of SDOSS to the film-air (F-A) interface. Furthermore, the presence of electrolyte species such as aqueous CaCl2 has a very pronounced effect on film formation. When the Ca2+/HSPC ratio is 0.1/1.0, SDOSS is released to the F-A interface during coalescence. At 2.0/1.0 Ca2+/HSPC, HSPC diffuses to the F-A interface and crystalline domains consisting of HSPC are formed. This stimuli-responsive behavior is confirmed using IRIR imaging that ultimately exhibits different surface morphologies. These studies illustrate for the first time that it is possible to control the release of two different surface-active species during coalescence that form crystalline domains.     

Effect of crystallization rate and colloidal stability on structural rearrangements during growth of colloidal monolayers

The structural rearrangements during growth of colloidal crystals were investigated using a combination of light microscopy and image analysis based on a Delaunay triangulation procedure. We followed the creation and disappearance of square lattice domains during the convection-promoted formation of colloidal monolayers by drying. We found that the concentration of square lattice domains increased with the crystal growth rate and that there is a direct relation between the concentration of square lattice domains formed at the crystal-suspension interface and the lower concentration of these domains in the colloidal monolayer; hence, the degree of rearrangement from square lattice domains to a close-packed triangular structure is not significantly affected by the crystal growth rate for colloidally stable suspensions. The colloidal stability, manipulated by the addition of salt, has a profound influence on the structural features of the growing monolayers. Particles that adhere strongly to each other, and to the substrate, tend to resist rearrangement; hence, the defect density is high in the colloidal monolayers and the structural reorganization of the square lattice domains to the more stable close-packed triangular structure occurred gradually over large distances from the crystal-suspension interface.     

Nucleation rate measurement of colloidal crystallization using microfluidic emulsion droplets

An emulsion crystallization method has been demonstrated to measure the nucleation rate of a thermoresponsive colloidal poly-N-isopropylacrylamide (PNIPAM) system. The colloidal PNIPAM suspension was injected into a microfluidic flow-focusing device to generate monodispersed droplets in oil. The temperature was controlled to fine tune the volume fraction of the PNIPAM particles, and the microfluidic flow rate was varied to change the droplet sizes, thus altering the nucleation volume. Using independent droplets, we can isolate the nucleation events to eliminate the interactions among crystallites that existed in bulk or large droplet systems. Therefore, we were able to carry out accurate nucleation rate measurements of colloidal crystals. This emulsion crystallization method is promising for bridging the gap among theories, simulations, and experiments for nucleation kinetics studies.     

Critical concentration for colloidal crystallization determined with microliter centrifuged suspensions

We report an elegant method using centrifugal sedimentation for determining the critical particle concentration for colloidal crystallization. A small amount of a dilute suspension of monodispersed particles stored in a flat capillary cell was centrifuged to temporarily generate a nonequilibrium gradient of the particle concentration including a crystalline-noncrystalline phase boundary in the cell. In the recovering process after the centrifugation, the particle concentration of the crystalline phase at the boundary was found to always have the equilibrium value, although the global concentration distribution evolved with time. The critical concentration was determined based on spatially resolved spectrometry. The present method requires only one batch of a suspension of the order of microliters and is applicable up to high concentration regions near the closest packing without the effect of the particle aggregation.     

A Smoluchowski model of crystallization dynamics of small colloidal clusters

We investigate the dynamics of colloidal crystallization in a 32-particle system at a fixed value of interparticle depletion attraction that produces coexisting fluid and solid phases. Free energy landscapes (FELs) and diffusivity landscapes (DLs) are obtained as coefficients of 1D Smoluchowski equations using as order parameters either the radius of gyration or the average crystallinity. FELs and DLs are estimated by fitting the Smoluchowski equations to Brownian dynamics (BD) simulations using either linear fits to locally initiated trajectories or global fits to unbiased trajectories using Bayesian inference. The resulting FELs are compared to Monte Carlo Umbrella Sampling results. The accuracy of the FELs and DLs for modeling colloidal crystallization dynamics is evaluated by comparing mean first-passage times from BD simulations with analytical predictions using the FEL and DL models. While the 1D models accurately capture dynamics near the free energy minimum fluid and crystal configurations, predictions near the transition region are not quantitatively accurate. A preliminary investigation of ensemble averaged 2D order parameter trajectories suggests that 2D models are required to capture crystallization dynamics in the transition region.     

Multistep crystal nucleation: a kinetic study based on colloidal crystallization

Crystallization via an amorphous precursor, the so-called multistep crystallization (MSC), plays a key role in biomineralization and protein crystallization. MSC has attracted much attention in the past decade, but a quantitative understanding of it has so far not been available. The major challenge is that the kinetics governing the nucleation of crystals occurring in the metastable amorphous precursor remains unclear. In this study, the kinetics of MSC is addressed experimentally. Most importantly, a mathematical method is developed to calculate the local nucleation rate of the crystals in the amorphous precursor, which is not accessible to conventional methods. This local nucleation rate is critical to the understanding of MSC, but it has never been dealt with experimentally because of the difficulties of in situ observation. With the local crystal nucleation rates, the supersaturation for crystallization and the crystal-liquid interfacial free energy in the amorphous precursor are evaluated.     

Evolution of size and shape in the colloidal crystallization of gold nanoparticles

The addition of dodecanethiol to a solution of oleylamine-stabilized gold nanoparticles in chloroform leads to aggregation of nanoparticles and formation of colloidal crystals. Based on results from dynamic light scattering and scanning electron microscopy we identify three different growth mechanisms: direct nanoparticle aggregation, cluster aggregation, and heterogeneous aggregation. These mechanisms produce amorphous, single-crystalline, polycrystalline, and core-shell type clusters. In the latter, gold nanoparticles encapsulate an impurity nucleus. All crystalline structures exhibit fcc or icosahedral packing and are terminated by (100) and (111) planes, which leads to truncated tetrahedral, octahedral, and icosahedral shapes. Importantly, most clusters in this system grow by aggregation of 60-80 nm structurally nonrigid clusters that form in the first 60 s of the experiment. The aggregation mechanism is discussed in terms of classical and other nucleation theories.     

Kinetics study of crystallization with the disorder-bcc-fcc phase transition of charged colloidal dispersions

Structure transformation (disorder-bcc-fcc) in charged colloidal dispersions, as a manifestation of the Ostwald's step rule, was confirmed by means of reflection spectrum (RS) measurements in our previous study. By taking advantage of a reflection spectrum containing plenty of information about the crystallization behaviors, time-dependent changes of parameters associated with the crystal structure and composition during the disorder-bcc-fcc transition are reported by treating the data from RS in this article. In addition, Avrami's model is adopted to analyze the transition process and investigate the transition rate. On the basis of the above investigations, associated kinetic features of crystallization with the disorder-bcc-fcc transition are described.     

Unidirectional crystallization of charged colloidal silica due to the diffusion of a base

Dilute aqueous dispersions of charged colloidal silica (particle volume fraction = approximately 0.03-0.04, particle diameter = 110 nm) exhibit unidirectional crystal growth due to the diffusion of a weak base, pyridine (Py). Similar diffusion-crystallization is enabled by a salt of a weak acid and a strong base, sodium hydrogen carbonate (NaHCO3). The resulting crystals consist of columnar (or cubic) crystal grains with a maximum height of a few centimeters and a maximum width of 1 cm. The crystal growth process is attributed to a combination of (i) the diffusion of Py or NaHCO3 accompanied by a charging reaction of the silica particles and (ii) the charge-induced crystallization of the silica colloids. Theoretical growth curves based on the reaction-diffusion model for the case of Py were in good agreement with the observed curves. We also report the immobilization of the resulting large crystals by using a polymer hydrogel matrix.