The first five articles in this issue emphasize equilibrium phases and structures. The hard sphere properties of sterically stabilized particle suspensions are examined in the article by van Megan, Pusey and Bartlett, a colloidal compound is discussed by Hachisu and attractive interactions are shown to produce a full complement of phase transitions including a liquid/gas transition by Emmett and Vincent. Recent theoretical interest in the nature of melting in two dimensions has led to the investigation of the melting transition in colloidal systems where the particles are constrained to a single layer. Murray, Van Winkle and Wenk present experimental results supporting the view that two dimensional melting is mediated by two second order transitions, while Tang, Armstrong, Mockler and O'Sullivan present results suggesting a first order process in a similar colloidal monolayer.

Colloidal suspensions describe particles with size from typically a few nanometers to a few microns which are dispersed in a medium. In physics, in chemistry, and in biology colloids play an important role and the study of colloidal systems underwent a recent renaissance. This is based on the development of experimental techniques, the availability of extensive computer simulations and well-developed theoretical approaches. From a technological point of view, the relevance of micro- and nanostructured materials and the presence of colloids in nature and everyday life motivates study of this rich field. In this thesis the phase behavior and the effective interactions of colloidal suspensions in bulk, in contact with surfaces, and in confined geometry are studied. For mixtures of particles with hard-core interactions the model introduced by Asakura, Oosawa and Vrij provides an appropriate starting-point. Based on that model the free-volume theory and the density functional theory are employed. In experimental systems one faces particles with properties such as the size or the shape which are described by a distribution. To capture that issue a generalized approach based on free-volume theory for treating mixtures of colloids and a polydisperse depletion agent is presented. Within that approach it is possible to treat size and morphology polydispersity. A depletion agent with a bimodal distribution possessing two length scales can be studied. Though the Asakura-Oosawa-Vrij model describes a simple fluid - a mixture of hard spheres and ideal polymer - the phenomenology is rather rich: in contact with a wall one finds layering and wetting effects and in confined geometry of a narrow pore one finds capillary condensation. The competition between both effects manifests itself in thermodynamic properties like the excess colloid adsorption and the solvation force between the two confining walls. Solvent phase separation complicates the evaluation of interparticle interactions between the solute particles. We address this question for the wall-colloid and the colloid-colloid geometry. For a non-spherical particle the effect of curvature on thermodynamic quantities is studied.

The focus of my Ph.D work is to develop and apply computer simulation methods for understanding the properties of colloidal suspensions. Since colloidal suspensions typically contain different species and display a complicated spectrum of effective interactions, a wealth of interesting features has been observed and a wide range of applications has been established. However, the presence of various species with very different length and time scales causes a severe slow-down in simulations of such multi-component systems. Although available computational power continues to increase steadily, modeling such systems can make the simulations prohibitively expensive, so that further progress will critically depend on algorithmic advances. One of the main results in my Ph.D study is the development of a novel Monte Carlo method that alleviates this slow-down problem. The so-called generalized geometric cluster algorithm applies geometric transformations to identify clusters of particles. Owing to the non-local and rejection-free features of cluster moves, typical efficiency improvements achieved by this algorithm amount to several orders of magnitude as compared to conventional simulation methods. In this thesis, a detailed description of the geometric cluster algorithm, including its properties, efficiency, applications and future extensions are presented. Using the generalized geometric cluster algorithm, we have carried out a comprehensive study of effective interactions between micron-sized silica spheres, induced by highly charged zirconia nanoparticles. Explicit modeling of the colloidal particles and nanoparticles demonstrates that the effective interactions induced by nanoparticles are responsible for a colloidal stabilization mechanism recently discovered in experiments. To study the phase behavior of colloidal fluids, the geometric cluster algorithm has been incorporated into the Restricted Gibbs ensemble where the density and concentration fluctuations that drive phase transitions can be probed directly. We have developed a finite-size scaling theory that relates these density fluctuations to those of the grand-canonical ensemble, thereby enabling accurate location of critical points and coexistence curves of multi-component fluids. Several illustrative examples are presented. The development of the geometric cluster algorithm makes it possible to simulate colloidal solutions containing highly size-asymmetric species that are inaccessible to conventional simulation algorithms. Further applications and developments of variants of the geometric cluster algorithm will arise in future studies.