Free energy landscapes for colloidal crystal assembly

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Abstract
We compute free energy landscapes (FELs) for tunable depletion attraction between micron sized colloids for which the potentials, microscopic phase behavior, and microstructure have been directly measured in previous work. Umbrella sampling in conjunction with NVT Monte Carlo (MC) simulations is used to construct FELs that capture important fluid and crystalline states observed in Stokesian Dynamic (SD) and Brownian Dynamic (BD) simulations using the same depletion potential. Order parameters are identified to produce 1D and 2D FELs at different levels of attraction that indicate transition states and local minima along assembly trajectories towards a perfect FCC crystal. Our results demonstrate a modeling approach that could be used in conjunction with microscopic sensing and actuation (e.g. tunable attraction) to obtain low-defect, single domain, colloidal crystals.

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