Thomas Palberg

Crystallization kinetics of repulsive colloidal spheres

Colloidal spheres interacting via a purely repulsive potential provide an excellent model system to study the kinetics of solidification from the melt. Such systems are readily accessible by comparably simple yet powerful optical methods like time resolved static light scattering and microscopy, reviewed in the first part of this paper. We then present results from our own recent studies within a framework of data available from literature. In particular we investigated nucleation and growth of hard sphere crystals using combined Bragg and small angle light scattering and of charged sphere crystals using Bragg microscopy. Special attention is given to the range of validity of classical nucleation theory and of Wilson Frenkel growth and a discussion of kinetic prefactors for both processes.

Electrophoresis of colloidal dispersions in the low-salt regime

We study the electrophoretic mobility of spherical charged colloids in a low-salt suspension as a function of the colloidal concentration. Using an effective particle charge and a reduced screening parameter, we map the data for systems with different particle charges and sizes, including numerical simulation data with full electrostatics and hydrodynamics and experimental data for latex dispersions, on a single master curve. We observe two different volume fraction-dependent regimes for the electrophoretic mobility that can be explained in terms of the static properties of the ionic double layer.

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.

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%.

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.

Grain size control in polycrystalline colloidal solids

Recent experiments on the static and dynamic properties of polycrystalline colloidal solids show a pronounced influence of morphological details. Here we investigate several possibilities to vary systematically one key morphological parameter, namely the average crystallite radius rc of polycrystalline solids. We report measurements of rc as observed by microscopy in well‐characterized Yukawa model suspensions. The pair energy of interaction is systematically varied through precise experimental adjustment of the suspension parameters packing fraction Φ, number of ionic surface groups N, and concentration of screening ions c. The average size is found to systematically decrease with increasing interaction. At fixed suspension parameters we performed solidification under shear, i.e., in the presence of alternating electric fields. We report preliminary results in dependence on both the electric field strength and frequency. The grain size increases with increasing shear rates. It shows a complex behavior as...

On the electrophoretic mobility of isolated colloidal spheres

We studied the electrophoretic mobility μ of highly charged colloidal spheres in very dilute low salt aqueous suspension. We combined experiments on individual particles and ensemble averaged measurements. In both cases μ was observed to be independent of particle size and surface chemistry. Corresponding effective charges Zμ*, however, scaled with the ratio of particle size to Bjerrum length λB: Zμ* = Aa/λB with a coefficient . Our results are discussed in comparison to other charge determination experiments and charge renormalization theory and with respect to the issue of charge polydispersity.

Independent ion migration in suspensions of strongly interacting charged colloidal spheres

We report on systematic measurements of the low-frequency conductivity sigma in aqueous suspensions of highly charged colloidal spheres. Sample preparation in a closed tubing system results in precisely controlled number densities of 10(16) m-3 < or = n < or = 10(19) m-3 (packing fractions of 10(-7) < or = phi < or = 10(-2)) and electrolyte concentrations of 10 < or = c < or = 10(-3) mol l-1. Due to long-range Coulomb repulsion, some of the systems show a pronounced fluid or crystalline order. Under deionized conditions we find sigma to depend linearly on the packing fraction with no detectable influence of the phase transitions. Further, at constant packing fraction sigma increases sublinearly with the increasing number of dissociable surface groups N. As a function of c the conductivity shows pronounced differences depending on the kind of electrolyte used. We propose a simple yet powerful model based on the independent migration of all species present and the additivity of the respective conductivity contributions. It takes account of small ion macro-ion interactions in terms of an effectively transported charge. The model successfully describes our qualitatively complex experimental observations. It further facilitates quantitative estimates of sigma over a wide range of particle and experimental parameters.

Conductivity of deionized two-component colloidal suspensions

The low frequency ac-conductivity of deionized aqueous suspensions comprising of charged latex spheres is investigated. For the one-component cases σ increases linearly with particle number density n, irrespective of the suspension structure. Two-component mixtures are found to form substitutional crystals and no phase separation is observed for small size differences. Then σ is proportional to the sum of the individual conductivity contributions. Further at fixed composition the linear increase with n is retained. The effects can be well described with an extension of Hessinger’s conductivity model to two-component systems.

RESPONSE OF THE ELASTIC PROPERTIES OF COLLOIDAL CRYSTALS TO PHASE TRANSITIONS AND MORPHOLOGICAL CHANGES

We report on the shear modulus G of colloidal crystals formed from thoroughly deionized suspensions of charged latex spheres. G is measured as a function of particle number density n. Body- and face-centered-cubic (bcc and fcc) crystal structures are observed by simultaneously performed static light scattering, and a broad coexistence region is found between (2.7±0.1)×1018 m−3⩽n⩽(4.8±0.2)×1018 m−3. Below n=1019 m−3, G closely follows theoretical predictions for both bcc and fcc, while it stays constant throughout the transition region. Above n=1019 m−3, G still observes the predicted n-dependence but with values larger than expected. While in that region, an upper bound of particles per crystallite is estimated from scattering data to be on the order of 104; the abrupt change in G cannot be solely attributed to the gradual morphological transition from polycrystalline to nanocrystalline materials.