title: Optimal Feedback Controlled Assembly of Perfect Crystals.
abstract: 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).
authors.affiliation: School of Chemical & Biomolecular Engineering, Georgia Institute of Technology , Atlanta, Georgia 30332, United States.
authors.forename: Xun
authors.initials: X
authors.lastname: Tang
authors.affiliation: Department of Chemical & Biomolecular Engineering, Johns Hopkins University , Baltimore, Maryland 21218, United States.
authors.forename: Bradley
authors.initials: B
authors.lastname: Rupp
authors.affiliation: Department of Chemical & Biomolecular Engineering, Johns Hopkins University , Baltimore, Maryland 21218, United States.
authors.forename: Yuguang
authors.initials: Y
authors.lastname: Yang
authors.affiliation: Department of Chemical & Biomolecular Engineering, Johns Hopkins University , Baltimore, Maryland 21218, United States.
authors.forename: Tara D
authors.initials: TD
authors.lastname: Edwards
authors.affiliation: School of Chemical & Biomolecular Engineering, Georgia Institute of Technology , Atlanta, Georgia 30332, United States.
authors.forename: Martha A
authors.initials: MA
authors.lastname: Grover
authors.affiliation: Department of Chemical & Biomolecular Engineering, Johns Hopkins University , Baltimore, Maryland 21218, United States.
authors.forename: Michael A
authors.initials: MA
authors.lastname: Bevan
keywords: Markov decision process; colloidal assembly; energy landscapes; low dimensional models; stochastic ensemble control