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.