Patrick Wette

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%.

Colloids as model systems for metals and alloys: a case study of crystallization

Metallic systems are widely used as materials in daily human life. Their properties depend very much on the production route. In order to improve the production process and even develop novel materials a detailed knowledge of all physical processes involved in crystallization is mandatory. Atomic systems like metals are characterized by very high relaxation rates, which make direct investigations of crystallization very difficult and in some cases impossible. In contrast, phase transitions in colloidal systems are very sluggish and colloidal suspensions are optically transparent. Therefore, colloidal systems are often discussed as model systems for metals. In the present work, we study the process of crystallization of charged colloidal systems from the very beginning. Charged colloids offer the advantage that the interaction potential can be systematically tuned by a variation of the particle number density and the salt concentration. We use light scattering and ultra-small angle x-ray scattering to investigate the formation of short-range order in the liquid state even far from equilibrium, crystal nucleation and crystal growth. The results are compared with those of equivalent studies on metallic systems. They are critically assessed as regards similarities and differences.

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.

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.

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.

Communications: Complete description of re-entrant phase behavior in a charge variable colloidal model system

In titration experiments with NaOH, we have determined the full phase diagram of charged colloidal spheres in dependence on the particle density n, the particle effective charge Z(eff) and the concentration of screening electrolyte c using microscopy, light and ultrasmall angle x-ray scattering (USAXS). For sufficiently large n, the system crystallizes upon increasing Z(eff) at constant c and melts upon increasing c at only slightly altered Z(eff). In contrast to earlier work, equilibrium phase boundaries are consistent with a universal melting line prediction from computer simulation, if the elasticity effective charge is used. This charge accounts for both counterion condensation and many-body effects.

Drude-type conductivity of charged sphere colloidal crystals : Density and temperature dependence

We report on extensive measurements in the low-frequency limit of the ac conductivity of colloidal fluids and crystals formed from charged colloidal spheres suspended in de-ionized water. Temperature was varied in a range of 5 degrees C < Theta < 35 degrees C and the particle number density n between 0.2 and 25 microm(-3) for the larger, respectively, 2.75 and 210 microm(-3) for the smaller of two investigated species. At fixed Theta the conductivity increased linearly with increasing n without any significant change at the fluid-solid phase boundary. At fixed n it increased with increasing Theta and the increase was more pronounced for larger n. Lacking a rigorous electrohydrodynamic treatment for counterion-dominated systems we describe our data with a simple model relating to Drudes theory of metal conductivity. The key parameter is an effectively transported particle charge or valence Z(*). All temperature dependencies other than that of Z(*) were taken from literature. Within experimental resolution Z(*) was found to be independent of n irrespective of the suspension structure. Interestingly, Z(*) decreases with temperature in near quantitative agreement with numerical calculations.