Jan K. G. Dhont

Long‐time self‐diffusion of spherical colloidal particles measured with fluorescence recovery after photobleaching

Long‐time self‐diffusion coefficients in concentrated colloidal dispersions of silica spheres, with various interaction potentials, were measured with the fluorescence recovery after photobleaching technique. Charge stabilized spheres were measured in solutions of LiCl in dimethylformamide with varying ionic strength. Sterically stabilized hard‐sphere‐like stearyl silica dispersions were studied in cyclohexane. The fluorophore used, fluorescein‐isothiocyanate, was covalently attached to the surface of the spheres (for the charged particles) or buried inside the silica core (for the hard spheres). The particles were characterized by electrophoresis, static and dynamic light scattering, and transmission electron microscopy. The experimental results are discussed and compared with existing theories on long‐time self‐diffusion.

A Time Resolved Static Light Scattering Study on Nucleation and Crystallization in a Colloidal System

Abstract The crystallization process in a colloidal system of slightly charged spherical particles is studied with time-resolved static light scattering. The induction time, the crystallization rate, the scattered intensity after completion of the crystallization process, and the width of the Bragg peaks are found to be strongly dependent on the concentration of the initially metastable colloidal fluid. Assuming a simple crystal geometry, quantities such as the size of the crystallites, the number concentration of the crystallites, and nucleation and crystallite growth rates, as functions of the concentration, are calculated from those experimental quantities.

On the calculation of the self-diffusion coefficient of interacting Brownian particles

We consider two ways to calculate the self‐diffusion coefficient of interacting Brownian particles. The first approach is based on the calculation of the mean square displacement of a Brownian particle starting from the Smoluchowski equation. In the second approach the self‐diffusion coefficient is obtained as the product of the thermodynamic driving force and the mobility. The advantages and limitations of the two methods are discussed.

Rheology and structural arrest of casein suspensions

The rheology of milk powder suspensions is investigated up to very high concentrations, where structural arrest occurs. The main component of the milk powder investigated is casein, so that the suspensions can be regarded as casein suspensions. Four concentration regimes are identified. For effective casein volume fractions less than 0.54 the concentration dependence of the zero-shear viscosity is similar to that of hard-sphere suspensions. However, due to the elastic deformation of the caseins, the viscosity does not diverge at the hard sphere glass transition. In the volume-fraction range of 0.55-0.61 the viscosity exhibits a surprisingly weak dependence on concentration. The shape of the curve of the shear viscosity versus concentration deviates from hard sphere behavior in an unusual way, due to the observation of a region of almost constant viscosity. This concentration regime is followed by a regime where the viscosity steeply increases, eventually diverging at an effective volume fraction of 0.69. Frequency dependent rheology and diffusing wave spectroscopy measurements indicate that the suspensions are jammed for volume fractions above 0.69. Finally we found the concentration dependence of the relative zero-shear viscosity of casein suspensions to be very similar with the one of the micro-gels at volume fractions below 0.50 and above 0.55, which are know to shrink above a certain volume fraction, due to osmotic stress.

Fluid-fluid phase separation in colloid-polymer mixtures studied with small angle light scattering and light microscopy

Mixtures of colloidal silica spheres and polydimethylsiloxane in cyclohexane with a colloid-polymer size ratio of about one were found to phase separate into two fluid phases, one which is colloid-rich and one which is colloid-poor. In this work the phase separation kinetics of this fluid-fluid phase separation is studied for different compositions of the colloid-polymer mixtures, and at several degrees of supersaturation, with small angle light scattering and with light microscopy. The small angle light scattering curve exhibits a peak that grows in intensity and that shifts to smaller wave vector with time. The characteristic length scale that is obtained from the scattering peak is of the order of a few μm, in agreement with observations by light microscopy. The domain size increases with time as t13, which might be an indication of coarsening by diffusion and coalescence, like in the case of binary liquid mixtures and polymer blends. For sufficiently low degrees of supersaturation the angular scattering intensity curves satisfy dynamical scaling behavior.

A comparison between the long-time self-diffusion and low shear viscosity of concentrated dispersions of charged colloidal silica spheres

Measurements are presented of the long‐time self‐diffusion coefficient and of the low shear limiting viscosity of dispersions of charge stabilized colloidal silica spheres. Long‐time self‐diffusion coefficients were measured using fluorescence recovery after photobleaching (FRAP), the theory of which is presented and generalized to Gaussian laser beams. The particles, suspended in solutions of LiCl in dimethylformamide, interacted via a screened Coulomb potential, the range of which was varied through the ionic strength. Measurements were made up to volume fractions beyond freezing where a coexistence occurred between a colloidal crystal and a colloidal fluid. It is often speculated that the long‐time self‐diffusion coefficient and the low shear viscosity of a dispersion are related through a simple Stokes–Einstein‐like relation, but this expectation is not confirmed by the experiments. A slightly modified relation, however, does seem to provide a reasonable empirical description of the data.

Light scattering of colloidal dispersions in non-polar solvents at finite concentrations. Silic spheres as model particles for hard-sphere interactions

Static and dynamic light-scattering studies are reported for spherical model particles in non-polar solvents. The model particles have a core of silica and a dense surface layer of octadecylalcohol chains which makes them ‘oil soluble’. The refractive-index difference between particles and solvent is very small and so dispersions can be studied by means of light scattering up to high concentrations. Multiple-scattering effects are considered briefly. In cyclohexane the particles show repulsive forces which can be described by a hard-sphere interaction. The small refractive-index differences can also be used to detect differences in optical density in the silica core. The periphery of the core is found to be more dense than the centre. Furthermore, the small natural spread in refractive index of the particles can be used to differentiate between collective-diffusion and self-diffusion processes. Differences in refractive indexes can also be obtained by variations in the particle synthesis. In this way it is possible to study self-diffusion by following the motion of tracer particles.

Viscoelasticity of suspensions of long, rigid rods

A microscopic theory for the viscoelastic behaviour of suspensions of rigid rods with excluded volume interactions is presented, which is valid in the asymptotic limit of very long and thin rods. Stresses arising from translational and rotational Brownian motion and direct interactions are calculated for concentrations up to (L/D) (with L the length; D, the thickness of the rods; and their volume fraction). It is argued that for very long and thin rods, contributions to the stress arising from hydrodynamic interactions vanish asymptotically with increasing aspect ratio relative to the single particle contribution. As will be discussed, this is supported by calculations of Shaqfeh and Fredrickson (Phys. Fluids A2 (1990) 7), although convergence to negligible hydrodynamics interactions with increasing aspect ratio is very slow (for aspect ratios larger than ≈50, the contribution of hydrodynamic interactions to the stress is at most ≈20%). It is argued that the pair-correlation function is in good approximation given by the Boltzmann exponential of the pair-interaction potential. The neglect of hydrodynamic interactions and the use of the Boltzmann exponential approximation for the pair-correlation function allows the microscopic evaluation of stresses in terms of concentration and the orientation order parameter tensor to within a Ginzburg–Landau expansion up to third order, without having to resort to thermodynamic arguments. The orientational order parameter tensor in turn is obtained from an equation of motion that is derived from the N-particle Smoluchowski equation. The resulting expression for the stress tensor and the equation of motion are similar to, but also in some respects significantly differing from, the well known theory due to Doi, Edward and Kuzuu. Analytic expressions are derived for linear and leading order non-linear, viscoelastic response functions. It is found that the zero shear viscosity varies linearly in concentration. The Huggins coefficient vanishes like the square of the shear-rate. Such a linear concentration dependence of the zero shear viscosity for very long and thin rods is also found in simulations by Claeys and Brady (J. Fluid Mech. 251 (1993) 443) and Yamane et al. (J. Non-Newtonian Fluid Mech. 54 (1994) 405) for the long rods, but is in contradiction with the Berry–Russel theory (J. Fluid Mech. 180 (1987) 475), where interactions are treated in an approximate, orientationally pre-averaged fashion. In addition, we find a Maxwellian frequency dependence of response functions at zero shear-rate. Highly non-linear viscoelastic response functions at higher shear-rates are computed numerically. Among other things, we find normal stress differences that do not change sign as a function of shear-rate and higher order harmonic response functions that are qualitatively different for the paranematic and nematic states.

‘‘Aging’’ of the structure of crystals of hard colloidal spheres

We study the development of the structure of crystals of colloidal hard spheres in time when gravity effects are minimal and polydispersity is small (<3%). The initial stacking of the close-packed hexagonal layers that make up the crystals is varied by applying various types of shear stress during nucleation of the crystals. The experimental powder diffraction patterns are consistent with a fraction of a faulted-twinned face-centered cubic (fcc) structure that grows at the expense of randomly stacked crystallites. If a faulted-twinned fcc structure is generated initially, no change is found over a considerable time. The present observations rule out the possibility that a randomly stacked structure is the equilibrium structure of colloidal crystals of (nearly) hard spheres, and point to the thermodynamic or kinetic stability of faulted-twinned fcc crystals in these systems.

Electric-field induced transitions in suspensions of charged colloidal rods

We explore transitions in suspensions of fd virus at a low ionic strength, induced by external electric fields at frequencies where double layers are polarized. On the basis of the different optical morphologies, phase/state diagrams are constructed in the field-amplitude versus frequency plane and the field-amplitude versus concentration plane. Due to interactions between polarized double layers, for low frequencies, various phases and dynamical states are found: a nematic phase, a striped phase and a dynamical state where nematic domains melt and reform. At relatively high frequencies of a few kHz, a uniform homeotropic phase is induced. The various phases and states are characterized by means of polarization microscopy, birefringence, dynamic light scattering and video-correlation spectroscopy. An expression is derived for the attenuation of the electric field due to electrode polarization, which is tested experimentally. This theory is used to correct phase/state diagrams for electrode polarization.