Energy and diffusivity landscapes, colloidal forces and assembly

Understanding dynamics of concentrated colloidal systems in the presence of different interactions and external fields provides a basis to predict the temporal evolution of colloidal microstructures in diverse phenomena including suspension rheology and colloidal crystallization. However, a microscopic theory of concentrated colloidal dynamics does not yet exist that rigorously includes both statistical mechanical and fluid mechanical contributions. In this dissertation a comprehensive analysis of colloidal dynamics is implemented to accomplish two goals: 1) the analysis of microscopy experiments to determine conservative and dissipative colloidal forces and 2) the dynamic modeling of colloidal assembly. Both goals are accomplished by means of analyzing the Smoluchowski equation (SE) to describe the dynamic evolution of colloidal systems.;Conservative and dissipative forces are extracted from a SE analysis of measured particle excursions normal to an underlying substrate from Total Internal Reflection Microscopy (TIRM) data. An initial test of the analysis via simulated experiments is done, followed by the measurement of depletion induced interactions and hydrodynamic contributions due to adsorbing and non-adsorbing polymer brushes. This is the first time theories regarding both conservative and dissipative forces are validated by means of a non-intrusive experimental methodology.;The development of models for colloidal assembly starts with the construction of free energy landscapes (FEL), from Monte Carlo equilibrium simulations, and analyzing their features in terms of order parameters. Dynamics are characterized by order-parameter based SE models that accurately capture the dynamic evolution of initially disordered colloidal fluid configurations into colloidal crystals. After identifying appropriate order parameters to monitor colloidal crystallization, we first show that umbrella sampling methods in conjunction with Monte Carlo simulations produce the same FEL as our SE analysis of dynamic simulation data. With this foundation, we then use the SE analysis to extract "diffusivity landscapes" from the simulations to pose dynamic models of colloidal crystallization. Finally, we demonstrate the use of these SE models for describing first passage times between different states, compared to results from direct simulation. Knowledge of these dynamic models enable the understanding of underlying phenomena in crystallizing systems, as well as enabling the design, optimization and control of colloidal crystal assembly processes.