Hnw Lekkerkerker

Predicting the gas-liquid critical point from the second virial coefficient

We show that whereas the critical point is very sensitive to the range of interaction, the second virial coefficient has a fairly constant value at the critical temperature. This enables us to predict the critical temperature with fair accuracy. We discuss the connection between the second virial coefficient as a predictor for the critical temperature and the second virial coefficient as predictor in crystal growth as was proposed by George and Wilson [A. George and W. W. Wilson, Acta Crystallogr., Sec. D: Biol. Crystallogr. 50, 361 (1994)].

Computer simulation of rheological phenomena in dense colloidal suspensions with dissipative particle dynamics

The rheological properties of colloidal suspensions of spheres and rods have been studied using dissipative particle dynamics (DPD). We have measured the viscosity as a function of shear rate and volume fraction of the suspended particles. The viscosity of a 30 vol% suspension of spheres displays characteristic shear-thinning behaviour as a function of shear rate. The values for the low- and high-shear viscosity are in good agreement with experimental data. For higher particulate densities, good results are obtained for the high-shear viscosity, although the viscosity at low shear rates shows a dependence on the size of the suspended spheres. Dilute suspensions of rods show an intrinsic viscosity which is in excellent agreement with theoretical results. For concentrated rod suspensions, the viscosity increases with the third power of the volume fraction. We find the same scaling behaviour as Doi and Edwards for the semidilute regime, although the explanation is unclear. The DPD simulation technique therefore emerges as a useful tool for studying the rheology of particulate suspensions.

Phase behaviour of mixtures of colloidal spheres and excluded-volume polymer chains

We study the phase behaviour of mixtures of colloidal spheres and polymers that have an excluded-volume interaction dispersed in a (background) solvent using the concept of free volume theory. The depletion layer thickness is calculated from the negative adsorption of polymer segments around a sphere. The correlation length and thermodynamic properties of the excluded-volume interacting polymer chains in solution are taken into account by using results from the renormalization group theory. For small polymer–colloid size ratios the difference from an ideal description of the polymers is small, while for larger size ratios the gas–liquid coexistence region shifts in the direction of higher polymer concentrations and at the same time the liquid–crystal coexistence region becomes more extended. Both the gas–liquid region and the gas– liquid–crystal region become less extended. These features are compared to experiment.

Theory of the depletion force due to rodlike polymers

The entropic depletion force, in colloids, arises when large particles are placed in a solution of smaller ones, and sterically constrained to avoid them. In this paper, we consider a system of two parallel plates suspended in a semidilute solution of long thin rods of length L and diameter D. By numerically solving an integral equation, which is exact in the “Onsager limit” (D≪L), we obtain the depletion force between the plates. The second integral of this determines (via the Derjaguin approximation) the depletion potential between two large hard spheres of radius R, immersed in a solution of hard rods (satisfying D≪L≪R). The results for this potential are compared with our previous second order perturbation treatment [Y. Mao, M. E. Cates, and H. N. W. Lekkerkerker, Phys. Rev. Lett. 75, 4548 (1995)], as well as with newly computed third order perturbation results. There is good agreement at low and intermediate densities (which validates our numerical procedures for the integral equation) but the gradua...

Liquid crystal phase transitions in dispersions of rod-like colloidal particles

Dispersions are called colloidal when the dispersed particles are larger than common small molecules, say larger than 1 nm, but small enough not to show appreciable sedimentation in normal gravity, say smaller than 1 μm. Colloidal particles are equivalent to molecules and atoms in that they undergo thermal motion. When the particles are monodisperse i.e. all particles have the same or nearly the same size, the colloidal system will exhibit a far-reaching resemblance in its statistical behaviour to atomic and molecular systems. In fact the equilibrium statistical thermodynamic properties of colloidal dispersions may be treated in exactly the same way as in the case of simple liquids by considering the colloidal particles as “supramolecules” in a continuous (but fluctuating) back-ground. The potential which for the case of fluctuating forces replaces the interaction potential between molecules (in vacuo) is the potential of the average forces which act between the dispersed particles, also denoted as potential of mean force. This effective interaction is the input for statistical mechanical theories. Therefore statistical mechanical theories developed for atomic fluids and solids can be applied to colloidal dispersions. The theoretical basis for such a treatment was given by Onsager [1,2,3] and McMillan and Mayer [4].

Interfacial dynamics and the static profile near a single wall in a model colloid–polymer mixture

We report measurements on gas–liquid phase-separating colloid–polymer mixtures. A horizontally placed optical microscope with long-working-distance objectives enables us to see effects of gravity on phase separation kinetics and hence see the complete phase separation from beginning to end. Furthermore, the static profile near a single wall is analysed giving surface tensions in good agreement with scaling predictions as well as results from another experimental technique. The contact angle remains, however, intangible.

Tactoids of Plate-Like Particles: Size, Shape, and Director Field

We studied, by means of polarized light microscopy, the shape and director field of nematic tactoids as a function of their size in dispersions of colloidal gibbsite platelets in polar and apolar solvents. Because of the homeotropic anchoring of the platelets to the interface, we found large tactoids to be spherical with a radial director field, whereas small tactoids turn out to have an oblate shape and a homogeneous director field, in accordance with theoretical predictions. The transition from a radial to a homogeneous director field seems to proceed via two different routes depending in our case on the solvent. In one route, the what presumably is a hedgehog point defect in the center of the tactoid transforms into a ring defect with a radius that presumably goes to infinity with decreasing drop size. In the other route, the hedgehog defect is displaced from the center to the edge of the tactoid, where it becomes virtual again going to infinity with decreasing drop size. Furthermore, quantitative analysis of the tactoid properties provides us with useful information on the ratio of the splay elastic constant and the anchoring strength and the ratio of the anchoring strength and the surface tension.

Phase diagram of hard colloidal platelets: a theoretical account

We construct the complete liquid crystal phase diagram of hard plate-like cylinders for variable aspect ratio using Onsagers second virial theory and employing the Parsons–Lee decoupling approximation to account for higher-body interactions in the isotropic and nematic fluid phases. The stability of the solid (columnar) state at high packing fraction is included by invoking a simple equation of state based on a Lennard–Jones–Devonshire cell model which has proven to be quantitatively reliable over a large range of packing fractions. By employing an asymptotic analysis based on the Gaussian approximation we are able to show that the nematic–columnar transition is universal and independent of particle shape. The predicted phase diagram is in qualitative agreement with simulation results.

Anomalous stability of aqueous boehmite dispersions induced by hydrolyzed aluminium poly-cations

Abstract Aqueous dispersions of colloidal boehmite rods turn into strong gels when the concentration of (1–1) electrolyte concentrations becomes exceeds 50 mM. However, after addition of aluminium chlorohydrate (ACH) the rods remain stable up to salt concentrations as high as 2 M. Moreover the boehmite-ACH dispersions with an aspect ratio of 19 quickly separate into an isotropic and a liquid crystal nematic phase above a typical threshold concentration of 2 v/v%. It is known that ACH forms polynuclear cations at mild acidic conditions. The anomalous stability as encountered in these dispersions is explained by assuming that these hydrolyzed poly-cations cause a shift of the charge carrying surface.

Density profiles and thermodynamics of rod-like particles between parallel walls

A study has been made of the density profile of mutually avoiding rod-like particles in the space between two parallel plates, held in equilibrium with a bulk phase of isotropic, semidilute rods, using a self-consistent integral equation which becomes exact as the rod aspect radio L/D → ∞. Computer simulation investigations of finite aspect ratio systems also have been undertaken, and the extended Gibbs adsorption isotherm used to express the free energy (as a function of plate separation) in terms of an integral of the surface excess with respect to chemical potential. This allows thermodynamic properties, such as surface tension and the depletion force between plates, to be found. For L/D → ∞, the results confirm both the thermodynamic consistency of the integral equation, and the accuracy of previous work on the depletion force (based on calculating only the contact density of rods at the walls). To extract thermodynamic data from the simulations, the same Gibbs isotherm method is very efficient, as it...