Cecam Workshop On Effective Interactions And Phase Transitions In Colloidal Suspensions PDF Download

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.