The effect of size ratio on the sphere structure factor in colloidal sphere-plate mixtures.

Binary mixtures of colloidal particles of sufficiently different sizes or shapes tend to demix at high concentration. Already at low concentration, excluded volume interactions between the two species give rise to structuring effects. Here, a new theoretical description is proposed of the structure of colloidal sphere-plate mixtures, based on a density expansion of the work needed to insert a pair of spheres and a single sphere in a sea of them, in the presence or not of plates. The theory is first validated using computer simulations. The predictions are then compared to experimental observations using silica spheres and gibbsite platelets. Small-angle neutron scattering was used to determine the change of the structure factor of spheres on addition of platelets, under solvent contrast conditions where the platelets were invisible. Theory and experiment agreed very well for a platelet/sphere diameter ratio D∕d = 2.2 and reasonably well for D∕d = 5. The sphere structure factor increases at low scattering vector Q in the presence of platelets; a weak reduction of the sphere structure factor was predicted at larger Q, and for the system with D∕d = 2.2 was indeed observed experimentally. At fixed particle volume fraction, an increase in diameter ratio leads to a large change in structure factor. Systems with a larger diameter ratio also phase separate at lower concentrations.

Structure of colloidal sphere-plate mixtures.

In addition to containing spherical pigment particles, coatings usually contain plate-like clay particles. It is thought that these improve the opacity of the paint film by providing an efficient spacing of the pigment particles. This observation is counterintuitive, as suspensions of particles of different shapes and sizes tend to phase separate on increase of concentration. In order to clarify this matter a model colloidal system is studied here, with a sphere-plate diameter ratio similar to that found in paints. For dilute suspensions, small angle neutron scattering revealed that the addition of plates leads to enhanced density fluctuations of the spheres, in agreement with new theoretical predictions. On increasing the total colloid concentration the plates and spheres phase separate due to the disparity in their shape. This is in agreement with previous theoretical and experimental work on colloidal sphere-plate mixtures, where one particle acts as a depleting agent. The fact that no large scale phase separation is observed in coatings is ascribed to dynamic arrest in intimately mixed, or possibly micro-phase separated structures, at elevated concentration.

Depletion effects in smectic phases of hard-rod-hard-sphere mixtures.

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the tau parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for tau, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the tau parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts tau approximately d (3). Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for spherocylinders and spheres, the tau parameter should be of order unity as d tends to infinity.

Modeling benzene with single-site potentials from ab initio calculations: a step toward hybrid models of complex molecules.

Extensive ab initio calculations at the MP2/6-31G* level have been carried out to sample the energy surface for the interactions of the benzene dimers. This database has been used to parameterize two anisotropic single-site models, meant to be used as building blocks in hybrid models of complex, liquid crystal forming molecules. A quadrupolar Gay-Berne (GBQIII) and an S-function (SF) Corner potentials have been obtained in this way. Their ability to reproduce, qualitatively at least, the phase diagram as well as energetic and structural properties of benzene has been tested with Monte Carlo simulations and compared with previous literature potentials, GBQI [S. Gupta et al., Mol. Phys. 65, 961 (1988)] and GBQII [T. R. Walsh, Mol. Phys. 100, 2867 (2002)]. It turned out that GBQI showed no melting transition in the temperature range explored (100-400 K), while GBQII underwent a phase transition from solid to gas, with no liquid phase. Conversely, both models parameterized on our database of ab initio interaction energies (GBQIII and SF) gave rise to a stable liquid phase. Melting has been observed between 100 and 150 K (GBQIII) and in the range 300-350 K (SF), i.e., substantially below and slightly above the experimental value at ambient pressure, 278 K. The description of the crystal structure of benzene at atmospheric pressure is also in better agreement with experimental data if the SF model is used, while positional correlations in the liquid are better described by the GBQIII potential. The S-function potential is also computationally more convenient. These results could be useful in the semirealistic modeling of more complex molecules.