Perfectly ordered states are targets in diverse molecular to microscale systems involving, for example, atomic clusters, protein folding, protein crystallization, nanoparticle superlattices, and colloidal crystals. However, there is no obvious approach to control the assembly of perfectly ordered global free energy minimum structures; near-equilibrium assembly is impractically slow, and faster out-of-equilibrium processes generally terminate in defective states. Here, we demonstrate the rapid and robust assembly of perfect crystals by navigating kinetic bottlenecks using closed-loop control of electric field mediated crystallization of colloidal particles. An optimal policy is computed with dynamic programming using a reaction coordinate based dynamic model. By tracking real-time stochastic particle configurations and adjusting applied fields via feedback, the evolution of unassembled particles is guided through polycrystalline states into single domain crystals. This approach to controlling the assembly of a target structure is based on general principles that make it applicable to a broad range of processes from nano- to microscales (where tuning a global thermodynamic variable yields temporal control over thermal sampling of different states via their relative free energies).

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Optical microscopy measurements are reported for single anisotropic polymer particles interacting with nonuniform ac electric fields. The present study is limited to conditions where gravity confines particles with their long axis parallel to the substrate such that particles can be treated using quasi-2D analysis. Field parameters are investigated that result in particles residing at either electric field maxima or minima and with long axes oriented either parallel or perpendicular to the electric field direction. By nonintrusively observing thermally sampled positions and orientations at different field frequencies and amplitudes, a Boltzmann inversion of the time-averaged probability of states yields kT-scale energy landscapes (including dipole-field, particle-substrate, and gravitational potentials). The measured energy landscapes show agreement with theoretical potentials using particle conductivity as the sole adjustable material property. Understanding anisotropic particle-field energy landscapes vs field parameters enables quantitative control of local forces and torques on single anisotropic particles to manipulate their position and orientation within nonuniform fields.

We report a closed-form analytical model for energy landscapes of ellipsoidal particles in non-uniform high-frequency AC electric fields to identify all possible particle positions and orientations. Three-dimensional equilibrium positions and orientations of prolate (r = r < r), oblate (r = r > r), and scalene (r≠r≠r) ellipsoids are reported vs. field frequency and amplitude, which are determined from energy landscape minima. For ellipsoids within non-uniform electric fields between co-planar parallel electrodes, the number of configurations of position and orientation is 6 for prolate, 5 for oblate, and 9 for scalene ellipsoids. In addition, for coplanar electrodes, conditions are identified when particles can be treated using a quasi-2D analysis in the plane of their most probable elevation near an underlying surface. The reported expressions are valid for time-averaged interactions of ellipsoid particles in arbitrary AC electric field configurations, such that our results are applicable to electromagnetic tweezers interacting with particles having an appropriate material property contrast with the medium in the frequency range of interest.