Hard-sphere Colloidal Crystals Research Articles

Superheating of grain boundaries within bulk colloidal crystals

Whether grain boundaries (GBs) premelt is a longstanding question, because of the difficulty of direct experimental tests. Here, we focused an optical beam to locally heat single GBs within bulk hard-sphere colloidal crystals, observing the melting dynamics at single-particle resolution by video microscopy. The melting point is determined by analysing both the Lindemann parameter and the critical nucleus size for homogeneous nucleation. We found that all the GBs, including the high-energy GBs, can be superheated and melt via a heterogeneous nucleation mechanism. Based on the classical nucleation theory of GBs, we measured the incubation time and contact angle of the critical nucleus to compute all relevant kinetic factors, as well as the energy barrier, nucleation rate and the diffusion coefficient at the solid–liquid interface under weak superheating. The superheat limits of GBs with various misorientations have also been measured to further explore the instability mechanism. Under traditional uniform heating, premelting occurs only at triple junctions, whereas GBs retain their original structures up to the melting point. The premelted regions at triple junctions further interrupt high-energy GBs from superheating, through intrusion by uniform liquid layers. Overall, our experiments confirm the existence of superheating of GBs.

Role of diffusion in crystallization of hard-sphere colloids.

Vital for a variety of industries, colloids also serve as an excellent model to probe phase transitions at the individual particle level. Despite extensive studies, origins of the glass transition in hard-sphere colloids discovered about 30 y ago remain elusive. Results of our numerical simulations and asymptotic analysis suggest that cessation of long-time particle diffusivity does not suppress crystallization of a metastable liquid-phase hard-sphere colloid. Once a crystallite forms, its growth is then controlled by the particle diffusion in the depletion zone surrounding the crystallite. Using simulations, we evaluate the solid-liquid interface mobility from data on colloidal crystallization in terrestrial and microgravity experiments and demonstrate that there is no drastic difference between the respective mobility values. The insight into the effect of vanishing particle mobility and particle sedimentation on crystallization of colloids will help engineer colloidal materials with controllable structure.

Competing factors in grain boundary loop shrinkage: Two-dimensional hard sphere colloidal crystals.

A grain boundary (GB) loop in a two-dimensional solid is the boundary of a domain or grain whose lattice orientation is mismatched with its uniform surroundings. Understanding the factors that influence the rate at which the interior of a GB loop relaxes to the orientation of its surroundings is an important step toward control and predictability of grain coarsening in general. Recent computational and experimental studies looking at the rate of GB loop shrinkage in two-dimensional colloidal hard sphere solids have uncovered contradictory trends: in experiments, GB loops with low misorientation angles shrank the fastest, while in simulations, they persisted the longest. In this study, the computational system's behavior is brought into qualitative agreement with the experimental results through increasing the lateral packing pressure, decreasing the domain size, and mimicking the experimental protocol used to form the GB loop. Small GB loops with the same misorientation, but displaying either a hexagonal or starlike grain shape depending on the orientation of their six dislocations, are shown to differ in their rates of shrinkage by two orders of magnitude. The evidence suggests that both the barrier to generating new dislocations as well as the pattern of dislocations formed by different GB loop preparation methods will determine which trend is observed.

Structure beyond pair correlations: X-ray cross-correlation from colloidal crystals.

The results of an X-ray cross-correlation analysis (XCCA) study on hard-sphere colloidal crystals and glasses are presented. The article shows that cross-correlation functions can be used to extract structural information beyond the static structure factor in such systems. In particular, the powder average can be overcome by accessing the crystals' unit-cell structure. In this case, the results suggest that the crystal is of face-centered cubic type. It is demonstrated that XCCA is a valuable tool for X-ray crystallography, in particular for studies on colloidal systems. These are typically characterized by a rather poor crystalline quality due to size polydispersity and limitations in experimental resolution because of the small q values probed. Furthermore, nontrivial correlations are observed that allow a more detailed insight into crystal structures beyond conventional crystallography, especially to extend knowledge in structure formation processes and phase transitions.

Nucleation and growth of micellar polycrystals under time-dependent volume fraction conditions

We study the freezing kinetics of colloidal polycrystals made of micelles of Pluronic F108, a thermosensitive copolymer, to which a small amount of silica nanoparticles of size comparable to that of the micelles are added. We use rheology and calorimetry to measure Tc, the crystallization temperature, and find that Tc increases with the heating rate \dot{T} used to crystallize the sample. To rationalize our results, we first use viscosity measurements to establish a linear mapping between temperature T and the effective volume fraction, {\phi}, of the micelles, treated as hard spheres. Next, we reproduce the experimental \dot{T} dependence of the crystallization temperature with numerical calculations based on standard models for the nucleation and growth of hard spheres crystals, classical nucleation theory and the Johnson-Mehl-Avrami-Kolmogorov theory. The models have been adapted to account for the peculiarities of our experiments: the presence of nanoparticles that are expelled in the grain boundaries, and the steady increase of T and hence {\phi} during the experiment. We moreover show that the polycrystal grain size obtained from the calculations is in good agreement with light microscopy data. Finally, we find that the {\phi} dependence of the nucleation rate for the micellar polycrystal is in remarkable quantitative agreement with that found in previous experiments on colloidal hard spheres. These results suggests that deep analogies exist between hard-sphere colloidal crystals and Pluronics micellar crystals, in spite of the difference in particle softness. More generally, our results demonstrate that crystallization processes can be quantitatively probed using standard rheometry.

Rapid growth of large, defect-free colloidal crystals

We demonstrate controlled growth of face-centered cubic (FCC), monodisperse hard-sphere colloidal crystals by centrifugation at up to 3000g onto FCC (100) templates. Such rapid deposition rates often result in an amorphous sediment. Surprisingly, however, growth onto (100) templates results only in single crystals with few or no extended defects. By contrast, deposition onto flat, (111), or (110) templates causes rapid disordering to an amorphous sediment if the dimensionless flux (particle volume fraction × Peclet number) exceeds a critical value. This crystalline-to-amorphous crossover results from the degeneracy of possible stacking positions for these orientations. No such degeneracy exists for growth onto (100). After growth, extended defects can nucleate and grow only if the crystal exceeds a critical thickness that depends on the lattice misfit with the template spacing. The experimental observations of the density of misfit dislocations are accounted for by the Frank–van der Merwe theory, adapted for the depth-dependent variation of lattice spacing and elastic constants that results from the gravitational pressure.

Heterogeneous crystallization of hard-sphere colloids near a wall

We investigate the most basic situation of heterogeneous crystallization: crystallization of hard-sphere colloids in the presence of a flat hard wall. Using a combination of confocal microscopy and nonequilibrium Brownian dynamics simulations, microscopic time-resolved information is obtained on an individual-particle level. Initially, particles near the wall rearrange before an extended regime of crystal growth is found. During growth, we can directly observe a depletion zone in the fluid next to the progressing crystal–fluid interface due to the single-particle information provided by microscopy and simulations. This also allows us to follow the relaxation of the crystal layers and the progression of the crystal–fluid interface. In good agreement between our experiments and simulations, as well as previous studies, the growth rate shows a maximum in its dependence on the bulk volume fraction.

A Brownian dynamic simulation to verify the effective hard-sphere model criterion for the formation of charged colloidal crystals

The mechanism for the formation of colloidal crystals in charge-stabilized colloids is more complicated than that of hard-sphere colloidal crystals. And there is still lack of available criterion for the formation of charged colloidal crystals. The effective hard-sphere model suggests a criterion in which the effective diameter is used as a crucial parameter. In order to test the validity of this criterion, the characteristics of charged colloidal crystals with different effective diameters are investigated using Brownian dynamics simulations in this study. The crystallization behaviors with different geometric particle diameters and repulsive forces are also studied with some fixed effective diameters. In the simulation, the time evolution of crystallization process and the crystal structure during the simulation are characterized by means of the radial distribution functions and bond-order parameters. The results show that the effective hard-sphere model criterion has its reasonableness to some extent. However, the effective diameter cannot be used as the only parameter that influences the formation of charged colloidal crystals. The influence of other parameters should also be taken into account, which indicates that the criterion is one-sided.

Random hcp and fcc structures in thermoresponsive microgel crystals

Monodisperse thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) microgel particles having a diameter of 520 nm were synthesized by free-radical precipitation polymerization and centrifuged to obtain a concentrated suspension. The centrifuged mother suspension was made to self-order into a crystalline state by repeated annealing beyond the volume phase transition (VPT) of the particles. We report here the three-dimensional (3D) real space structure, determined using a confocal laser scanning microscope, of PNIPAM microgel crystal samples prepared by two different recrystallized routes: (1) solidifying a shear melted colloidal liquid (referred as as-prepared sample) and (2) slow cooling of a colloidal liquid (referred as recrystallized sample). We have recorded images of several regions of the crystal with each region containing 15 horizontal crystal planes for determining the in-plane [two-dimensional (2D)] and 3D pair-correlation functions. The 2D pair-correlation function g(r) revealed hexagonal long-range order of particles in the layers with a lattice constant of 620 nm. The analysis of stacking sequence of layers recorded on as-prepared sample has revealed the existence of stacking disorder with an average stacking probability alpha approximately 0.42. This value of alpha together with the analysis of 3D pair-correlation function determined from particle positions revealed the structure of microgel crystals in the as-prepared sample to be random hexagonal close packing. We report the first observation of a split second peak in the 3D g(r) of the microgel crystals obtained from a shear melted liquid. Upon melting the sample above VPT and recrystallizing it the split second peak disappeared and the crystals are found to have a face centered cubic (fcc) structure with alpha approximately 0.95. From simulations, the split second peak is shown to arise from the displacement of some of the B-planes from the ideal hcp positions. The present results are discussed in light of those reported for charged and hard sphere colloidal crystals and plausible reasons for observing two different structures are also explained.

Dynamics of colloidal crystals in shear flow

We investigate particle dynamics in nearly hard sphere colloidal crystals submitted to a steady shear flow. Both the fluctuations of single colloids and the collective motion of crystalline layers as a whole are studied by using a home-built counter rotating shear cell in combination with confocal microscopy. Firstly, our real space observations confirm the global structure and orientation as well as the collective zigzag motion as found by early scattering experiments. Secondly, dynamic processes accompanying the shear melting transition are followed on the particle level. Local rearrangements in the crystal are seen to occur more frequently with increasing shear rate. This shear-enhanced particle mobility is quantified by measuring the random particle displacements from time-tracked particle coordinates. We find that shear induced melting takes place when these random displacements reach 12% of the particle separation, reminiscent of the Lindemann criterion for melting in equilibrium systems. In addition, a dynamic criterion for melting, based on the relative importance of the long time self diffusion compared to the short time self diffusion, is discussed.

Monte Carlo simulations of in-plane stacking disorder in hard-sphere crystals

On-lattice Monte Carlo simulations of colloidal random-stacking hard-sphere colloidal crystals are presented. The model yields close-packed crystals with random-stacking hexagonal structure. We find a significant amount of in-plane stacking disorder, which slowly anneals in the course of the simulation. The in-plane stacking disorder leads to lateral broadening of the stacking-disorder-induced Bragg rods. It is found that not only the scattering intensity, but also the width is modulated along the Bragg rods.

In-Plane Stacking Disorder in Polydisperse Hard Sphere Crystals

We demonstrate that in random-stacking hard-sphere colloidal crystals the stacking disorder not only exists in the direction perpendicular to the close-packed layers, but also extends in the lateral direction. The existence of such in-plane stacking disorder is suggested by a recent observation of lateral broadening of the Bragg scattering rods in microradian X-ray diffraction and is further confirmed here by real-space confocal microscopy in two hard-sphere colloidal systems with different relative gravity effects. Due to the in-plane stacking disorder, the hexagonal planes consist of islands with different lateral A, B, and C positions with characteristic line defects in between them. The real-space layer-by-layer stacks of images also reveal the 3-D structure of the defects. The chance zeta to find another line-defect above a line-defect in the layer below turns out to be close to 1/2--independent of relative gravity--which can be explained by the two different stacking options above a defect. The stacking of a few sets of several line defects situated on top of each other turns out to be predominantly FCC-like.

Non-Affine Structural Evolution of Soft Colloidal Crystalline Latex Films under Stretching as Observed via Synchrotron X-ray Scattering

A polymer dispersion consisting of soft latex spheres with a diameter of 135 nm was used to produce a crystalline film with face-centered cubic (fcc) packing of the spheres. Different from conventional small-molecule and hard-sphere colloidal crystals, the crystalline latex film in the present case is soft (i.e., easily deformable). The structural evolution of this soft colloidal latex film under stretching was investigated by in-situ synchrotron ultra-small-angle X-ray scattering. The film exhibits polycrystalline scattering behavior corresponding to fcc structure. Stretching results not only in a large deformation of the crystallographic structure but also in considerable nonaffine deformation at high draw ratios. The unexpected nonaffine deformation was attributed to slippage between rows of particles and crystalline grain boundaries. The crystalline structure remains intact even at high deformation, suggesting that directional anisotropic colloidal crystallites can be easily produced.

Hard sphere crystal nucleation and growth near large spherical impurities

We report how large spherical impurities affect the nucleation and growth of hard spherecolloidal crystals. Both the impurities and the colloids are fluorescently labelledpolymethylmetacrylate particles and are dispersed in an optically and densitymatching solvent mixture. Crystal growth, initiated either at the impurity surface,or at the sample bottom, was studied by imaging sequences of two-dimensionalxy-slices in the plane of the impurity’s centre of mass with a laser scanning confocalmicroscope. At least two factors determine whether a large impurity can functionas a seed for heterogeneous nucleation: timescales and impurity curvature. Thecurvature needs to be sufficiently low for crystal nuclei to form on the impuritysurface. If bulk crystal growth has already approached the impurity, bulk growthis dominant over growth of crystallites on the impurity surface. Such surfacecrystallites eventually reorient to adapt to the overall bulk crystal symmetry.

Line tension controls wall-induced crystal nucleation in hard-sphere colloids.

We report on a numerical study of the effect of a smooth, hard wall on the crystallization of hard-sphere colloids. We find that the presence of the wall drastically lowers the barrier for crystal nucleation, but it does not eliminate it. Crystal nucleation becomes noticeable at pressures that are some 5% above the coexistence value. The first particles to crystallize on the wall form a (111) plane. Initially, this crystallite grows laterally, rather than in the third dimension. The free energy of the critical crystal nucleus on the wall is about 2 orders of magnitudes lower than in the bulk. Analysis of the numerical data indicates that, at coexistence, the (111) plane is at the threshold of wetting the wall. The nucleation barrier is dominated by line tension.

High-resolution small-angle x-ray diffraction study of long-range order in hard-sphere colloidal crystals.

The long-range order parameters in single crystals of hard colloidal spheres grown in sediments of colloid-polymer mixtures are determined using synchrotron small-angle x-ray diffraction with a resolution of 10(-6) of the wave vector. The interplanar positional order derived from the width of lattice reflections extends over at least 500 lattice planes. The lattice planes are orientationally correlated within approximately 0.1 degrees throughout the crystals, whereas the stacking of hexagonal planes remains random.

Diffusive growth of polydisperse hard-sphere crystals

Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e., mixtures of infinitely many components with sizes drawn from a continuous distribution. We model the crystallization of hard-sphere colloids (with/without attractions) from an initially amorphous phase. Although the polydisperse hard-sphere phase diagram has been widely studied, it is not straightforwardly applicable to real colloidal crystals, since they are inevitably out of equilibrium. The process by which colloidal crystals form determines the size distribution of the particles that comprise them. Once frozen into the crystal lattice, the particles are caged so that the composition cannot subsequently relax to the equilibrium optimum. We predict that the mean size of colloidal particles incorporated into a crystal is smaller than anticipated by equilibrium calculations. This is because small particles diffuse fastest and therefore arrive at the crystal in disproportionate abundance.

Fabrication of large-area face-centered-cubic hard-sphere colloidal crystals by shear alignment

We make hard-sphere colloidal crystals from polymethyl methacrylate spheres suspended in organic solvents at high volume fractions. The samples are crystallized between two glass plates separated by 10-\ensuremath{\mu}m spacer beads. We study the optical scattering from these systems and describe methods for discriminating between the various crystal packings. Crystals formed simply by increasing the volume fraction beyond the liquid-solid phase transition tend to be small and predominantly random close packed. However, we find that by forming these crystals while applying controlled shear to the glass plates, large-area single crystals can be made. These crystals are much more regular and appear to be predominantly twinned face-centred cubic. The creation of single-orientation face-centred cubic crystals appears possible when shear is applied in one direction.

Controlled growth of hard-sphere colloidal crystals

Three-dimensional ordered colloidal systems with lattice constants comparable to the wavelength of visible light might find important application as photonic crystals1, optic filters and switches2, and chemical sensors3. Colloidal crystallization has been actively studied4,5,6,7,8, leading to the development of several methods to control the self-assembly of the colloidal particles; examples include colloidal epitaxy9 and space-based reduced-gravity techniques10,11. Here we report a method to control the nucleation and growth of hard-sphere colloidal crystals that relies on the use of temperature gradients to define a density gradient. This is somewhat counterintuitive as temperature does not play a role in determining the hard-sphere phase diagram. We obtain hard-sphere single crystals (size ∼3 mm) from a sample in a concentration regime that would remain in the liquid state in the absence of a temperature gradient. We expect the method to have applications in controlling the ordering and growth of various ‘soft’ systems including colloids, copolymers, emulsions and proteins.

Linear viscoelasticity of hard sphere colloidal crystals from resonance detected with dynamic light scattering.

We present measurements of the high-frequency shear modulus and dynamic viscosity for nonaqueous hard sphere colloidal crystals both in normal and microgravity environments. All experiments were performed on a multipurpose PHaSE instrument. For the rheological measurements, we detect the resonant response to oscillatory forcing with a dynamic light scattering scheme. The resonant response for colloidal crystals formed in normal and microgravity environments was similar, indicating that the bulk rheological properties are unaffected by differing crystal structure and crystallite size within the experimental error. Our high-frequency shear modulus seems reasonable, lying close to Frenkel and Ladd's predictions [Phys. Rev. Lett. 59, 1169 (1987)] for the static modulus of hard sphere crystals. Our high-frequency dynamic viscosity, on the other hand, seems high, exceeding Shikata and Pearson [J. Rheol. 38, 601 (1994)] and van der Werff et al.'s measurements [Phys. Rev. A 39, 795 (1989)] on the high-frequency dynamic viscosity for metastable fluids. The measurements are in the linear regime for the shear modulus but may not be for the dynamic viscosity as Frith et al. [Powder Technol. 51, 27 (1987)] report that the dynamic viscosity passes through a maximum with strain amplitude.