Hans Joachim Schöpe

Precursor-mediated crystallization process in suspensions of hard spheres.

We report on a large scale computer simulation study of crystal nucleation in hard spheres. Through a combined analysis of real- and reciprocal-space data, a picture of a two-step crystallization process is supported: First, dense, amorphous clusters form which then act as precursors for the nucleation of well-ordered crystallites. This kind of crystallization process has been previously observed in systems that interact via potentials that have an attractive as well as a repulsive part, most prominently in protein solutions. In this context the effect has been attributed to the presence of metastable fluid-fluid demixing. Our simulations, however, show that a purely repulsive system (that has no metastable fluid-fluid coexistence) crystallizes via the same mechanism.

Comparison of colloidal effective charges from different experiments

We present measurements of effective charges in de-ionized aqueous suspensions of highly charged spherical latex colloids. For crystalline ordered samples the shear modulus G was measured using torsional resonance spectroscopy. It increases with increasing particle number density n. From fits of theoretical expressions based on a Debye–Huckel-type pair interaction potential, an effective charge ZG* was derived. On the other hand the effectively transported charge Zσ* was determined from the n dependence of the suspension conductivity. Both effective charges are independent of n within experimental error. For most species they scale with the ratio of radius to Bjerrum length. For all species, however, Zσ* is found to be systematically larger than ZG* by some 40%.

Effect of polydispersity on the crystallization kinetics of suspensions of colloidal hard spheres when approaching the glass transition

We present a comprehensive study of the solidification scenario in suspensions of colloidal hard spheres for three polydispersities between 4.8% and 5.8%, over a range of volume fractions from near freezing to near the glass transition. From these results, we identify four stages in the crystallization process: (i) an induction stage where large numbers of precursor structures are observed, (ii) a conversion stage as precursors are converted to close packed structures, (iii) a nucleation stage, and (iv) a ripening stage. It is found that the behavior is qualitatively different for volume fractions below or above the melting volume fraction. The main effect of increasing polydispersity is to increase the duration of the induction stage, due to the requirement for local fractionation of particles of larger or smaller than average size. Near the glass transition, the nucleation process is entirely frustrated, and the sample is locked into a compressed crystal precursor structure. Interestingly, neither polydispersity nor volume fraction significantly influences the precursor stage, suggesting that the crystal precursors are present in all solidifying samples. We speculate that these precursors are related to the dynamical heterogeneities observed in a number of dynamical studies.

Crystallization kinetics of polydisperse hard-sphere-like microgel colloids: Ripening dominated crystal growth above melting

Highly cross-linked polystyrene microgel colloids dispersed in an index and density matching solvent provide a system with hard-sphere-like interactions, where gravity effects are effectively minimized. They are a suitable target for time-resolved observations of solidification in purely repulsive systems. We have investigated the crystallization kinetics at increasing undercooling using time resolved light scattering. Crystallization starts always with the formation of compressed, structurally heterogeneous precursor domains. In the coexistence region the precursors, after being converted into true crystallites, start growing fast by assimilating particles from the melt. The resulting polycrystalline material consists of high quality crystals and seems not to undergo long time-scale rearrangements. As the particle concentration grows, the higher undercooling and reduced particle mobility increasingly compromise the conversion-growth process. The growth of crystallites relies then on much slower ripeninglike processes, while refining of the crystal structure is detected up to the longest observed times.

Microscopic investigations of homogeneous nucleation in charged sphere suspensions

We studied the homogeneous nucleation kinetics of an aqueous suspension of charged colloidal spheres under de-ionized conditions. Samples of equilibrium crystalline structure were shear molten and the metastable melt left to solidify after cessation of shear. At low particle number densities n, corresponding to low metastability of the melt, nucleation was monitored directly via video microscopy. We determined the nucleation rates gamma(t) by counting the number of newly appearing crystals in the observation volume per unit time. Using a suitable discrete adaptation of Avramis [J. Chem. Phys. 7, 1003 (1939); ibid.8, 212 (1940); ibid.9, 177 (1941)] model for solidification via homogeneous nucleation and subsequent growth, we calculate the remaining free volume VF(t) to obtain the rate densities J(t) = gamma(t)/VF(t). We observe J(t) to rise steeply, display a plateau at a maximum rate density Jmax, and to decrease again. With increased n the plateau duration shrinks while Jmax increases. At low to moderate number densities fully solidified samples were analyzed by microscopy to obtain the grain-size distribution and the average crystallite size angle brackets(L). Under the assumption of stationarity, we obtained the nucleation rate density J(Avr), which increased strongly with increasing n. Interestingly, J(Avr) agrees quantitatively to Jmax and to J(Avr) as obtained previously from scattering data taken on the same sample at large n. Thus, by combination of different methods, reliable nucleation rate densities are now available over roughly one order of magnitude in n and eight orders of magnitude in J.

Phase behaviour of deionized binary mixtures of charged colloidal spheres

We review recent work on the phase behaviour of binary charged sphere mixtures as a function of particle concentration and composition. Both size ratios Γ and charge ratios Λ are varied over a wide range. Unlike the case for hard spheres, the long-ranged Coulomb interaction stabilizes the crystal phase at low particle concentrations and shifts the occurrence of amorphous solids to particle concentrations considerably larger than the freezing concentration. Depending on Γ and Λ, we observe upper azeotrope, spindle, lower azeotrope and eutectic types of phase diagrams, all known well from metal systems. Most solids are of body centred cubic structure. Occasionally stoichiometric compounds are formed at large particle concentrations. For very low Γ, entropic effects dominate and induce a fluid-fluid phase separation. Since for charged spheres the charge ratio Λ is also decisive for the type of phase diagram, future experiments with charge variable silica spheres are suggested.

Competition between heterogeneous and homogeneous nucleation near a flat wall

We studied the competition between heterogeneous and homogeneous nucleation of an aqueous suspension of charged colloidal spheres close to the container walls. Samples of equilibrium crystalline structure were shear-melted and the metastable melt left to solidify after the cessation of shear. The crystallization kinetics was monitored using time-resolved scattering techniques: at low particle number densities n we applied an improved static light scattering method while at large particle concentrations ultra-small-angle x-ray scattering was applied for the first time. Our results show some unexpected behavior: the heterogeneous nucleation at the container walls is delayed in comparison to the homogeneous bulk nucleation and its rate density appears surprisingly slightly smaller, demonstrating the complexity of the observed crystallization process.

Experimental determination of effective charges in aqueous suspensions of colloidal spheres

Abstract We determined the low frequency conductivity σ , the phase behaviour and the shear modulus G of colloidal fluids, respectively solids prepared from deionised aqueous suspensions of highly charged spherical particles. Conductivity measures the number of freely moving small ions Z * σ and thus relates to the ion condensation process in the electric double layer under conditions of finite macro-ion concentrations. Phase behaviour and elasticity data are consistently described by a Debye–Huckel pair potential assuming pair-wise additive macro-ion interactions. Like Z * σ , also the effective charges Z * G derived from the elasticity data scales with the ratio of macro-ion radius to Bjerrum length. Z * G is, however, smaller than Z * σ . These findings are discussed in terms of recent experimental and theoretical results which suggest a reduction of the charge by both counter-ion condensation and many body terms in the effective particle interaction at finite concentration.

Heterogeneous nucleation of colloidal melts under the influence of shearing fields

Large, oriented single crystals may be obtained from shear melts of colloidal particles after nucleation at the container walls. We are here interested in the processes occurring during the initial phase of their formation. Using different microscopic and scattering techniques we here studied highly charged suspensions of spherical particles, dispersed in low salt or deionized water, in single and double wall confinement, during and after cessation of shear. While the equilibrium phase of our colloidal solids is body centred cubic, the shear induced precursors of heterogeneous nuclei consist of wall based, oriented, registered or freely sliding layers with in plane hexagonal symmetry. Cessation of shear initiates a complex heterogeneous nucleation process. If the layer structures are space filling, they register to form a meta-stable randomly stacked close packed hexagonal crystal. In double wall confinement the transformation to the equilibrium body centred cubic structure occurs on long timescales via nucleation and subsequent lateral growth. For non-space filling, wall based layer structures we find indications of competition between the decay of the layers in favour of the shear melt and their stabilization through registering and subsequent coverage by an epitaxially growing wall crystal. From quantitative growth curve measurements we obtain the initial wall crystal thickness d0, which may serve as a lower bound to the extension of the layer structures under shear. We observe a pronounced dependence of d0 on both former shear conditions and meta-stability of the melt.

Crystallization in charged two-component suspensions

We report on the crystallization of colloidal crystals comprising of charged particles with different size ratio dispersed in thoroughly deionized water. Single components were characterized carefully and their nucleation behavior was investigated before the preparation of mixtures. Mixtures investigated at constant particle number densities showed body centred cubic structure, conductivity, and shear moduli comply with the assumption of a randomly substituted crystal. Most importantly, for the first time we obtain the dependence of the nucleation rate densities in dependence on the composition and (for one fixed composition) the particle number density. The process of nucleation in random substitutional crystals is found to be similar to the one-component case.