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.     

Kinetic studies of colloidal crystallization of thermo-sensitive gel spheres of poly(N-isopropylacrylamide)

Crystal growth rate coefficients, k of the colloidal crystallization of thermo-sensitive gel spheres of poly(N-isopropylacrylamide) were measured from the time-resolved reflection spectroscopy mainly by the inverted mixing method in the deionized state. Crystallization of colloidal silica spheres were also measured for comparison. The k values of gel and silica systems increased sharply as the sphere concentration and suspension temperature increased. The k values of gel system were insensitive to the degree of cross-linking in the range from 10 to 2?mol% of cross-linker against amount of the monomer in mole and decreased sharply when the degree of cross-linking decreased further to 0.5?%. The k values increased as gel size increased. The k values of gel systems at 20?°C were small and observed only at the very high sphere concentration in volume fraction, whereas those at 45?°C were high but smaller than those of silica systems. Induction time (t _i) after which crystallization starts, increased as the degree of cross-linking increased and/or the gel size decreased at any temperatures, when comparison was made at the same gel concentration. The t _i values at 45?°C were high and decreased sharply with increasing sphere concentration, whereas those at 20?°C were high only at the very high sphere concentrations. Significant difference in the k and t _i values between the soft gels and hard silica spheres was clarified. These kinetic results support that the electrical double layers play an important role for the gel crystallization in addition to the excluded volume of gel spheres. It is deduced further that the electrical double layers of the gel system form from the vague interfaces (between soft gel and water phases) compared with those of typical colloidal hard sphere system.     

Engineering DNA-mediated colloidal crystallization

DNA is a powerful and versatile tool for nanoscale self-assembly. Several researchers have assembled nanoparticles and colloids into a variety of structures using the sequence-specific binding properties of DNA. Until recently, however, all of the reported structures were disordered, even in systems where ordered colloidal crystals might be expected. We detail the experimental approach and surface preparation that we used to form the first DNA-mediated colloidal crystals, using 1 mum diameter polystyrene particles. Control experiments based on the depletion interaction clearly indicate that two standard methods for grafting biomolecules to colloidal particles (biotin/avidin and water-soluble carbodiimide) do not lead to ordered structures, even when blockers are employed that yield nominally stable, reversibly aggregating dispersions. In contrast, a swelling/deswelling-based method with poly(ethylene glycol) spacers resulted in particles that readily formed ordered crystals. The sequence specificity of the interaction is demonstrated by the crystal excluding particles bearing a noninteracting sequence. The temperature dependence of gelation and crystallization agree well with a simple thermodynamic model and a more detailed model of the effective colloidal pair interaction potential. We hypothesize that the surfaces yielded by the first two chemistries somehow hinder the particle-particle rolling required for annealing ordered structures, while at the same time not inducing a significant mean-force interaction that would alter the self-assembly phase diagram. Finally, we observe that particle crystallization kinetics become faster as the grafted-DNA density is increased, consistent with the particle-particle binding process being reaction, rather than diffusion limited.     

Kinetic inhibitor of hydrate crystallization

We present the results of a combined theoretical/experimental study into a new class of kinetic inhibitor of gas hydrate formation. The inhibitors are based on quaternary ammonium zwitterions, and were identified from a computational screen. Molecular dynamics simulations were used to characterize the effect of the inhibitor on the interface between a type II hydrate and natural gas. These simulations show that the inhibitor is bifunctional, with the hydrophobic end being compatible with the water structure present at the hydrate interface, while the negatively charged functional group promotes a long ranged water structure that is inconsistent with the hydrate phase; the sulfonate-induced structure was found to propagate strongly over several solvation shells. The compound was subsequently synthesized and used in an experimental study of both THF and ethane hydrate formation, and was shown to have an activity that was comparable with an existing commercial kinetic inhibitor: PVP.     

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.     

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.     

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.     

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.     

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.     

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.     

Techniques for analyzing the early stages of crystallization reactions

This paper will — in a semi-review-like form — describe the problems in analyzing nucleation reactions, and approaches towards a solution of these problems. Attempts to pinpoint the nucleation event can start from the solution state, and the development of precursors for the solid state can be traced with mass spectrometry. Alternatively, one can try to obtain information on ever earlier stages of the solids formation itself, thus approaching the nucleation event from the side of the solid already formed. A highly suitable tool for this purpose is a tubular reactor, where crystallization reactions can be carried out continuously.     

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.     

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.     

The initial stages of crystallization of polyethylene from the melt

Synchrotron x-radiation has been used to follow the development of low-angle diffraction in sharp fractions of polyethylene. The polymer is shown to crystallize in very thin lamellae which rapidly thicken in a single step to twice, three times, or four times the original thickness. This dramatic refolding is more pronounced at higher crystallization temperatures. After the sudden integral jumps in fold length, the thick lamellae continue to grow thicker logarithmically with time. The significance of these findings for the most basic issues of polymer crystallization and for the experimental methodology of its study is highlighted.     

Kinetic aspects in the drying dissipative crack patterns of colloidal crystals

Kinetics of the dissipative structure formation in the course of drying the colloidal crystals of silica spheres (103 nm in diameter) in aqueous deionized suspension on a rinsed cover glass has been studied by the close-up video observation. The patterns of the broad ring of the hill accumulated with the spheres coexisted with the many spoke-like cracks. The characteristic convection flow of the spheres and the interactions between the spheres and substrate were important for the pattern formation. Cracks formed suddenly in the course of drying along the outside edge first, then toward the center, and stopped around the middle point between the outside edges and the frontier of suspension area. The further growth of the cracks took place at the adjacent place of the previous crack side by side and cooperatively. After the fast formation of these cooperative spoke-like cracks was completed, then all the crack lines further developed very slowly and simultaneously toward the center with the similar rate as that of the movement of the drying frontier of the suspension area toward center. Rates of the fast and slow modes of crack formation were 6.2 mm/s and 0.0098 mm/s, respectively, at the sphere concentration of 0.033 in volume fraction.