UCLA

In this thesis, we describe the observation of self-organized two-dimensional phases composed of simple components having non-trivial shapes which interact only by hard repulsions and are entropically excited. Through experiments and computational modeling, we investigate and explain how certain particle shapes self-organize into interesting two-dimensional phases. In order to obtain large quantities of precisely replicated particles having custom shapes for the experiments, we make a colloidal system composed of lithographically fabricated particles. As a preface to our work for dense systems, we design a novel Fourier tracking method to measure the rotational diffusion of Brownian colloidal polygons confined to two dimensions (2D) in a dilute dispersion.

Systems of convex platelet Brownian particles, capable of interdigitation, are osmotically compressed to high densities in a tilted barometric column. An equilibrated alternating stripe crystal (ASX) phase is observed at high particle density. Digital-wide-field-of-view microscopic imaging of the complete column enables us to obtain the 2D osmotic equation of state for the system and to determine the structural characteristics of the ASX phase which dominates, over a hexagonal crystal (HX) at high densities.

We introduce and apply a translational-rotational cage model (TRCM) in order to explain the experimentally observed preference for ASX over HX. The TRCM, based on a collision detection routine, determines the total number of states accessible to a mobile tri-star particle within an ASX and a HX cage. We find that the additional translational states permitted by the ASX phase exceeds the number of additional rotational states permitted by the HX phase, thus setting ASX as the entropically preferred phase. The TRCM is also used to explain the chiral symmetry breaking observed in a system of rhombs which form a rhombic lattice under high osmotic compression. In both cases, the TRCM is able to explain the phase behavior observed where models based on rotations or translations alone could not. We anticipate that future, more sophisticated programs could be designed with the TRCM which, through optimization and feed-back, would be able to make more predictive assessments on similar systems.