Size dependent thermodynamics and kinetics in electric field mediated colloidal crystal assembly

We compare measurements and models of the system size dependent assembly of quasi-two dimensional (2D) colloidal crystals within interfacial quadrupole electrodes. Perturbation theory (PT) and Monte Carlo (MC) simulations are used to make thermodynamic predictions of the voltages required to obtain all particles within a crystalline phase for different system sizes. These results show good agreement with video microscopy (VM) measurements of colloidal crystals containing 75-300 particles. Colloidal assembly kinetic trajectories for the same system sizes are quantified from VM experiments using order parameters (reaction coordinates) to capture real-space local and global hexagonal ordering. These trajectories are fit with a Smoluchowski model to extract configuration dependent free energy and diffusivity landscapes (FEL, DL) that capture the microscopic details of assembly dynamics. Landscape features, such as the number and heights of barriers and local gradients, capture the formation, diffusion, and migration of grain boundaries in polycrystalline states, which are increasingly prevalent for n > 200 but vanish for n < 150. These results demonstrate the importance of system size effects in the formation and annealing of polycrystalline states in colloidal crystallization processes.