Order from Disorder

Colloidal particles, i.e. particles at the nanometer scale, experience random motion (Disorder), generated by collisions with molecules of the surrounding medium, known as \emph{Brownian motion}. This motion allows colloidal particles to explore the configuration space. As a consequence, they are able to reach the most (thermodynamically) favorable structure (Order). This process is known as self-assembly. The title of this thesis, Order from Disorder, is referring to the self-assembly process, which is studied here. More specifically, we use computers to simulate models of several colloidal systems. The thesis is divided in two main themes; in the first part we study colloidal systems where the particles interact with each other, while in the second part, we study hard particle systems i.e. non-interacting particles that do not overlap. Colloids dispersed in a binary solvent mixture experience long-ranged solvent-mediated interactions (critical Casimir forces) upon approaching the critical demixing point of the solvent mixture. It is poorly understood how colloids will self-assemble under these conditions. In chapter 2, we use a two-dimensional lattice model, and perform extensive Monte Carlo simulations investigating the phase behavior of the system. The large difference in length scales between colloid and solvent, and the critical slowing down as the critical point is approached, make the study of the three-dimensional system computationally difficult. We overcome these problems in chapter 3 by developing a geometric cluster algorithm that enables us to study the scaling of the effective potentials in the two-dimensional system, and more importantly, the full ternary mixture of colloidal hard spheres. Motivated by recent experiments where a lamellar mesophase was observed when adding an organic salt to a binary solvent mixture, we develop an efficient lattice model to study this system in chapter 4. We treat the solvent mixture and electrostatics explicitly, by combining the simplicity of our lattice model and the efficiency of the Maggs' auxiliary field method for treating the electrostatics. We find rich mesophase behavior, resembling the phase behavior of diblock copolymers. We further analyze the ion distribution, and behavior of the lamellar phase as a function of the salt concentration and temperature and build a simple mean-field theory capable of describing our observations. In chapter 5, we investigate the phase behavior of thin rhombic platelets using Monte Carlo simulations, and in chapter 6 we develop a highly efficient event-driven Molecular Dynamics algorithm that enables us to perform simulations on general convex particles. Using this algorithm we study the full phase behavior of hard rhombic particles, by simulating 68 different particle shapes. Upon expansion from the space-filling crystal structure, we find 10 different ordered phases, including a biaxial nematic phase. A biaxial \emph{smectic} phase is shown for the first time in a simulation study. In chapter 7, motivated by experiments, on cubic Fe3O4 nanoparticles and EuF3 nanoplatelets confined in emulsion droplets, we investigate the behavior of of hard cubes and round platelets under spherical confinement using Monte Carlo simulations. For the cubes, we study the crystallization process upon compression. The hard round platelets, exhibit a twisted columnar phase, which we thoroughly investigate