Thermodynamic and Structural Phase Behavior of Colloidal and Nanoparticle Systems.

Abstract

We design and implement a scalable hard particle Monte Carlo simulation toolkit (HPMC), and release it open source. Common thermodynamic ensembles can be run in two dimensional or three dimensional triclinic boxes. We developed an efficient scheme for hard particle pressure measurement based on volume perturbation.

We demonstrate the effectiveness of low order virial coefficients in describing the compressibility factor of fluids of hard polyhedra. The second virial coefficient is obtained analytically from particle asphericity and can be used to define an effective sphere with similar low-density behavior. Higher-order virial coefficients --- efficiently calculated with Mayer Sampling Monte Carlo --- are used to define an exponential approximant that exhibits the best known semi-analytic characterization of hard polyhedron fluid state functions.

We present a general method for the exact calculation of convex polyhedron diffraction form factors that is more easily applied to common shape data structures than the techniques typically presented in literature. A proof of concept user interface illustrates how a researcher might investigate the role of particle form factor in the diffraction patterns of different particles in known structures.

We present a square-triangle dodecagonal quasicrystal (DQC) in a binary mixture of nanocrystals (NCs). We demonstrate how the decoration of the square and triangle tiles naturally gives rise to partial matching rules via symmetry breaking in layers perpendicular to the dodecagonal axis. We analyze the geometry of the experimental tiling and, following the ``cut and project'' theory, lift the square and triangle tiling pattern to four dimensional space to perform phason analysis historically applied only in simulation and atomic systems. Hard particle models are unsuccessful at explaining the stability of the binary nanoparticle super lattice. However, with a simple isotropic soft particle model, we are able to demonstrate seeded growth of the experimental structure in simulation. These simulations indicate that the most important stabilizing properties of the short range structure are the size ratio of the particles and an A--B particle attraction.