Exploration du comportement de phase et de la nucléation de sphères dures colloïdales à l'aide de simulations numériques

To date, hard spheres remain the most ubiquitous model system for colloidal suspensions: they play a central role in our understanding of the fundamentals of phase behavior and their simple interactions allow for easy theoretical handling and efficient simulating. Despite this, our understanding of classical phase transitions in systems that deviate slightly from the monodisperse hard-sphere case is still lacking, and nucleation rates predictions obtained from experimental and simulation results still show a considerable discrepancy. In this thesis, we design and exploit several simulation tools for probing the behavior of both slightly soft spherical particles, and for polydisperse hard spheres. First, together with experimental collaborators, we examine the free-energy barrier associated with the early stages of crystal nucleation in colloidal suspensions of hard spheres, and perform a careful comparison of the characteristics of small crystal nuclei in simulations and experiments. Going beyond the simple hard-sphere case, we explore a novel algorithm for simulating continuous models using an event-driven approach. This method allows us to efficiently probe phase behavior and nucleation in systems of soft spheres, even in the limit of extremely steep interaction potentials. Using this, we demonstrate that the softness of the interaction does not play a strong role in the spontaneous formation of Laves phases crystals in binary mixtures of almost-hard spheres. Finally, we investigate the phase behavior of size polydisperse systems, mapping out the freezing line of polydisperse hard-sphere fluids as a function of polydispersity. We also provide evidence that nucleation in these systems preferentially occurs in regions that are rich in large particles, which act as nucleation precursors. In short, this thesis provides several new insights into the behavior of colloidal hard spheres, as well as new simulation tools to explore their behavior.