Nucleation of colloidal cubes using Monte Carlo simulations

Abstract

In this thesis we use Monte Carlo simulations to investigate the nucleation of hard cubes and hard slanted cubes with slant angles between 66 degrees and 84 degrees. First, we examine the phase behaviour by looking at the equations of state, and find our equations of state consistent with literature. Interestingly, for smaller slant angles, the hysteresis between the two phases increases. Next, we explore the structure of both the liquid and crystal phases using the radial distribution function and the Steinhardt order parameter. In particular, we determine local order parameters suitable for distinguishing fluid and crystal phases, based on either translational or orientational order. Finally, we examine nucleation of the simple cubic phase in a system of hard cubes. We first discuss classical nucleation theory and how nucleation rates can be determined from the free-energy barrier. To build the free-energy barrier we make use of umbrella sampling in Monte Carlo simulations. We present some barriers, and discuss the challenges of hard cube nucleation. Interestingly, we found that unlike in systems of e.g. hard spheres, clusters of hard cubes do not form roughly spherical clusters.