Phase behavior of a de-ionized binary mixture of charged spheres in the presence of gravity

Microstructural diversity, nucleation paths, and phase behavior in binary mixtures of charged colloidal spheres

We study low-salt, binary aqueous suspensions of charged colloidal spheres of size ratio Γ = 0.57, number densities below the eutectic number density n_E, and number fractions of p = 1.00-0.40. The typical phase obtained by solidification from a homogeneous shear-melt is a substitutional alloy with a body centered cubic structure. In strictly gas-tight vials, the polycrystalline solid is stable against melting and further phase transformation for extended times. For comparison, we also prepare the same samples by slow, mechanically undisturbed deionization in commercial slit cells. These cells feature a complex but well reproducible sequence of global and local gradients in salt concentration, number density, and composition as induced by successive deionization, phoretic transport, and differential settling of the components, respectively. Moreover, they provide an extended bottom surface suitable for heterogeneous nucleation of the β-phase. We give a detailed qualitative characterization of the crystallization processes using imaging and optical microscopy. By contrast to the bulk samples, the initial alloy formation is not volume-filling, and we now observe also α- and β-phases with low solubility of the odd component. In addition to the initial homogeneous nucleation route, the interplay of gradients opens various further crystallization and transformation pathways leading to a great diversity of microstructures. Upon a subsequent increase in salt concentration, the crystals melt again. Wall-based, pebble-shaped β-phase crystals and facetted α-crystals melt last. Our observations suggest that the substitutional alloys formed in bulk experiments by homogeneous nucleation and subsequent growth are mechanically stable in the absence of solid-fluid interfaces but thermodynamically metastable.

Salt-concentration-dependent nucleation rates in low-metastability colloidal charged sphere melts containing small amounts of doublets

We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concentration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while postsolidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The full data set, however, shows an unexpected scaling of the nucleation rate densities with metastability times the number density of particles. Parameterization of our results in terms of classical nucleation theory reveals unusually low interfacial free energies of the nucleus surfaces and nucleation barriers well below the thermal energy. We tentatively attribute our observations to the presence of doublets introduced by the employed conditioning technique. We discuss the conditions under which such small seeds may induce nucleation.

Colloidal Brazil nut effect in microswimmer mixtures induced by motility contrast

We numerically and experimentally study the segregation dynamics in a binary mixture of microswimmers which move on a two-dimensional substrate in a static periodic triangular-like light intensity field. The motility of the active particles is proportional to the imposed light intensity, and they possess a motility contrast, i.e., the prefactor depends on the species. In addition, the active particles also experience a torque aligning their motion towards the direction of the negative intensity gradient. We find a segregation of active particles near the intensity minima where typically one species is localized close to the minimum and the other one is centered around in an outer shell. For a very strong aligning torque, there is an exact mapping onto an equilibrium system in an effective external potential that is minimal at the intensity minima. This external potential is similar to (height-dependent) gravity such that one can define effective "heaviness" of the self-propelled particles. In analogy to shaken granular matter in gravity, we define a "colloidal Brazil nut effect" if the heavier particles are floating on top of the lighter ones. Using extensive Brownian dynamics simulations, we identify system parameters for the active colloidal Brazil nut effect to occur and explain it based on a generalized Archimedes' principle within the effective equilibrium model: heavy particles are levitated in a dense fluid of lighter particles if their effective mass density is lower than that of the surrounding fluid. We also perform real-space experiments on light-activated self-propelled colloidal mixtures which confirm the theoretical predictions.

Crystallization kinetics of colloidal binary mixtures with depletion attraction

In this work the crystallization kinetics of colloidal binary mixtures with attractive interaction potential (Asakura-Oosawa) has been addressed. Parameters such as fraction of crystals, linear crystal dimension and crystal packing have been quantified in order to understand how the crystal formation is driven in terms of the depth of the attractive potential and the composition of the binary mixture (described by the number ratio). It was found that inside the eutectic triangle, crystallization is mainly governed by nucleation and the crystal packing is close to the close-packing of hard spheres. Moving out from the eutectic triangle towards small component results in the crystallization of small spheres. Enrichment of the eutectic mixture with large component results in the crystallization of both large and small spheres, however, the kinetics are completely different from those of the eutectic composition. Crosslinked polystyrene microgels with nearly hard sphere interactions were used as model systems. Attraction was introduced by addition of linear polystyrene. The time evolution of crystallization has been followed by static light scattering.

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.

Exclusion of impurity particles in charged colloidal crystals

Uniformly shaped, charged colloidal particles dispersed in water form ordered "crystal" structures when the interaction between the particles is sufficiently strong. Herein, we report the behavior of "impurity" particles, whose sizes and/or charge numbers are different from those of the bulk, on addition to the charged colloidal crystals. These impurities were excluded from the crystals during the homogeneous crystallization, crystal grain growth, and unidirectional crystallization processes. Such systems will be useful as models for studying the refinement of materials and crystal defects.

Doubled heterogeneous crystal nucleation in sediments of hard sphere binary-mass mixtures

Crystallization during the sedimentation process of a binary colloidal hard spheres mixture is explored by Brownian dynamics computer simulations. The two species are different in buoyant mass but have the same interaction diameter. Starting from a completely mixed system in a finite container, gravity is suddenly turned on, and the crystallization process in the sample is monitored. If the Peclet numbers of the two species are both not too large, crystalline layers are formed at the bottom of the cell. The composition of lighter particles in the sedimented crystal is non-monotonic in the altitude: it is first increasing, then decreasing, and then increasing again. If one Peclet number is large and the other is small, we observe the occurrence of a doubled heterogeneous crystal nucleation process. First, crystalline layers are formed at the bottom container wall which are separated from an amorphous sediment. At the amorphous-fluid interface, a secondary crystal nucleation of layers is identified. This doubled heterogeneous nucleation can be verified in real-space experiments on colloidal mixtures.

Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the phase diagram for 3D, and determine the line free energy in 2D and the height of the nucleation barrier in 2D and 3D for homogeneous and heterogeneous nucleation by solving the respective Euler-Lagrange (EL) equations. We demonstrate that, in the PFC model, the body-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close-packed structures (hcp) compete, while the simple cubic structure is unstable, and that phase preference can be tuned by changing the model parameters: close to the critical point the bcc structure is stable, while far from the critical point the fcc prevails, with an hcp stability domain in between. We note that with increasing distance from the critical point the equilibrium shapes vary from the sphere to specific faceted shapes: rhombic dodecahedron (bcc), truncated octahedron (fcc), and hexagonal prism (hcp). Solving the equation of motion of the PFC model supplied with conserved noise, solidification starts with the nucleation of an amorphous precursor phase, into which the stable crystalline phase nucleates. The growth rate is found to be time dependent and anisotropic; this anisotropy depends on the driving force. We show that due to the diffusion-controlled growth mechanism, which is especially relevant for crystal aggregation in colloidal systems, dendritic growth structures evolve in large-scale isothermal single-component PFC simulations. An oscillatory effective pair potential resembling those for model glass formers has been evaluated from structural data of the amorphous phase obtained by instantaneous quenching. Finally, we present results for eutectic solidification in a binary PFC model.