Orientational ordering of charged colloids

This thesis studies orientational ordering of charged colloidal particles, which appears if the particles are not spherically symmetric. Generally, this is the case. The nonspherical aspects of colloidal particles can be either due to shape or to chemical surface properties. The question we address is: when do such nonspherical properties become important in the collective behavior of colloidal particles? To answer this question, we theoretically investigate the equilibrium properties of charged colloidal particles. We have chosen charge particles for three reasons. First, electrostatic effects are generally present in colloidal suspensions. Second, there were, and still are, many opportunities in this field to answer existing questions or raise new ones. Third, the effective interactions between charged colloidal particles are relatively easy to describe. In the end, we hope to describe collective properties that can be obtained through the equilibration of a system. The way we treat particle orientations is through orientational distributions. Analogous to particle-position distributions, we find configurations that minimize the free energy, thereby predicting the equilibrium state. We distinguish four types of phases that describe equilibrium configurations: isotropic fluid, liquid crystal, plastic crystal, and aligned crystal. The isotropic-fluid phase is characterized by a lack of both positional and orientational ordering. Fluids that display orientational ordering but no (complete) positional ordering are denoted liquid crystals. Conversely, in the case of a plastic crystal there is complete positional ordering but no orientational ordering. The aligned-crystal phase exhibits both orientational and positional ordering. We view particles of different orientation as particles belonging to different species. Such a description is easily implemented in a grand-canonical ensemble to find the most favorable distribution of particle orientations in a system. In this thesis, we apply the description to systems of colloidal particles that are either rodlike in shape and homogeneously charged, or heterogeneously charged and spherical. In chapter 2, we treat the phase behavior of short charged rods. We construct a mapping onto systems of hard rods with effective dimensions. The liquid-crystal phases that are predicted in these systems are no longer present for rods of sufficiently high charge, because their interactions are essentially isotropic. Chapter 3 is based on a charge renormalization scheme, which defines a relation between the nonlinear and linearized descriptions of electrostatic interactions between charged colloidal particles. This scheme is traditionally applied to spherical particles with homogeneous surface charge, but we apply it to colloidal spheres of heterogeneous surface charge. Finally, we present two models in which we apply bifurcation theory to a linearized description for heterogeneously charged spheres. In chapter 4 we introduce a cell model, which we employ in chapter 5 to describe fluid phases, as it lacks any positional ordering of the colloidal particles. The second model is treated in chapter 6 and puts the particles on a fixed lattice, which characterizes the positional ordering in solids. In both cases we investigate the possibility of an isotropic-to-aligned transition of the orientational distribution. In the fluid phase we find none, whereas the solid phase exhibits two possible transitions.