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As the feature size of new devices continues to decrease so too does the feasibility of top-down methods of patterning them. In many cases bottom-up methods are replacing the existing methods of assembly, as having building blocks self-organize into the desired structure appears, in many cases, to be a much more advantageous route. Self-assembled nanoparticulate films have a wide range of potential applications; high-density magnetic media, sensing arrays, meta-materials and as seeds for 3D photonic crystals to name a few. Thus, it is critical that we understand the fundamental dynamics of pattern formation on the nanoparticulate and colloidal scale so that we may have better control over the formation and final quality of these structures. We study computationally the self-organization of colloidal particles in 2D using both Monte Carlo and dynamic simulation We present 3 studies employing Monte Carlo simulation. In the first study, Monte Carlo simulations were used to understand the experimental observation of highlyordered 2D arrays of bidisperse, stabilized gold nanoparticles. It was shown that the LS lattice forms with the addition of interparticle forces and a simple compressive force, revealing that bidisperse lattice formation is, in fact, a dynamic process. It was evident that the LS lattice forms in large part because the particles within the lattice reside in their respective interparticle potential wells. In the second Monte Carlo study, this information was used to predict size-ratios and surface coverages for novel lattice structures. These predictions are intended to guide experimentalists in their search for these exciting new structures. In the third study it was shown that polydisperse amounts of amorphous-silicon nanoparticles could form 2D clusters exhibiting long-range orientational order even in the absence of translational order. Monte Carlo simulations were performed, which included lateral capillary forces and a simple stabilizing repulsion, resulting in structures that were strikingly similar to the experimentally observed In the fourth study we used dynamic simulation to study the hydrodynamicallyassisted self-organization of DNA-functionalized colloids in 2D. It was shown that hydrodynamic forces allow a more thorough sampling of phase space than through thermal or Brownian forces alone.

This dissertation explores the changes in structure of colloidal systems on the introduction of repulsive interactions. Colloidal gels are well understood when all particle interactions are attractive, but their structure is fundamentally changed when repulsive interactions compete with those attractive interactions, as in the case of a binary gel of oppositely charged particles. Similarly, colloidal crystals are well understood when interactions are approximately hard-sphere, but again, the structure and material properties change when a long-range repulsion is introduced, giving a colloidal `Wigner' crystal. My research quantitatively investigates these effects in experimental model systems. I use confocal microscopy to directly image in three dimensions suspensions of micron-scale colloidal particles which are monodisperse, index- and density-matched, fluorescent, and electrostatically charged. I use standard image-processing techniques to obtain the precise location of each particle in the imaging volume in order to analyze both global and local structure. In the case of the binary gel, I observe gelation of oppositely charged particles, controlled by varying the total particle volume fraction, the interaction strength, and the mixing ratio of the two particle species. I find that contrary to commonly studied purely attractive gels, in which weakly quenched gels are more compact and less tenuous, particles in these binary gels form fewer contacts and the gels become more tenuous as we approach the gel line, and the average attractive bond number emerges as a critical parameter for gelation. This suggests that a different mechanism governs gel formation and structure in binary gels, in which attractive and repulsive interactions compete. In the case of the long-range-repulsive colloidal `Wigner' crystals, I find a body-centered-cubic crystalline phase at particle volume fractions near 15%, in contrast to the face-centered-cubic crystalline phase found at volume fractions above 50% for hard spheres. The soft interactions in these repulsive crystals permit large fluctuations, with typical particle displacements up to 20% of the nearest-neighbor spacing. I determine the three independent crystalline elastic constants, and find that the crystals are very compliant (c ~ 5-40mPa), and strongly anisotropic at all volume fractions studied. I also observe a sharp interface between the fluid and crystalline phases. / Physics

Relationships between structure and dynamics have been well studied in molecular fluids, both in computer simulations and in experiments. However, the development of simple structure-dynamics relationships would also be useful in understanding colloidal fluids. Colloidal fluids display differentiated component dynamics, are made of polydisperse particles, have soft interactions and have a separation of length and time scales. In this dissertation work, we have used computer simulations to generalize some structure-dynamics scaling laws, originally formulated for molecular fluids, in a way that successfully accounts for these important aspects of colloidal suspensions. To begin, we examine a two-component mixture of ultrasoft Gaussian-core particles through molecular dynamics simulations. This fluid shows an anomalous dynamic crossover where the larger particles become more diffusive than the smaller particles. However, this dynamic crossover is accompanied by a corresponding structural crossover for a component-specific structural order metric. In the light of this structural order metric, the fluid is non-anomalous with respect to the relationship between static structuring and diffusivity. Next, we show that accounting for the many-component nature of even modestly polydisperse fluids is important for accurately characterizing their structure-dynamics relationships. We demonstrate this for colloids with short-range attractions through new Monte Carlo simulation techniques and through theoretical calculations carried out in the dilute limit. From here, we present a new generalized framework to non-dimensionalize diffusivity so that it will have an approximately one-to-one relationship with excess entropy. This method involves rescaling diffusivity with dilute-limit analyses that can be analytically and systematically executed. We tested this framework through a combination of molecular dynamics simulations, Brownian dynamics simulations and Monte Carlo simulations. The results of the simulations demonstrate that this framework can account for particle size asymmetry, particle additivity, interaction strength and some solvent effects. Finally, we present a new, simple equation that relates non-dimensionalized forms of diffusivity from molecular dynamics and Brownian dynamics simulations. This simple relationship is tested for inverse power law fluids, as well as a suite of ultrasoft fluids that show structural and dynamic anomalies. / text

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