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).

We report a simple depletion potential that captures measured potentials and phase behavior for micrometer-sized colloids in the presence of unadsorbing charged micelles, charged nanoparticles, nonionic macromolecules, and nonionic hydrogel particles. Total internal reflection microscopy (TIRM) is used to measure net potentials between colloids and surfaces, and video microscopy (VM) is used to measure quasi-2D phase behavior in the same material systems. A modified Asakura-Oosawa (AO) depletion potential is developed to accurately quantify particle-wall potentials and interfacial crystallization via particle-particle potentials in Monte Carlo (MC) simulations. The modified AO potential includes effective depletant sizes, accurate osmotic equations of state, and partition coefficients. Partition coefficients are used as the sole adjustable fitting parameter, although an approach to their theoretical prediction from depletant density profiles is also presented. Our results demonstrate a model that accurately captures depletion interactions and phase behavior in a variety of material systems.

The ability to assemble nano- and micro- sized colloidal components into highly ordered configurations is often cited as the basis for developing advanced materials. However, the dynamics of stochastic grain boundary formation and motion have not been quantified, which limits the ability to control and anneal polycrystallinity in colloidal based materials. Here we use optical microscopy, Brownian Dynamic simulations, and a new dynamic analysis to study grain boundary motion in quasi-2D colloidal bicrystals formed within inhomogeneous AC electric fields. We introduce “low-dimensional” models using reaction coordinates for condensation and global order that capture first passage times between critical configurations at each applied voltage. The resulting models reveal that equal sized domains at a maximum misorientation angle show relaxation dominated by friction limited grain boundary diffusion; and in contrast, asymmetrically sized domains with less misorientation display much faster grain boundary migration due to significant thermodynamic driving forces. By quantifying such dynamics vs. compression (voltage), kinetic bottlenecks associated with slow grain boundary relaxation are understood, which can be used to guide the temporal assembly of defect-free single domain colloidal crystals.

We report direct measurements of poly-(ethylene oxide) (PEO) mediated depletion attraction between colloids and surfaces using total internal reflection microscopy (TIRM) and in quasi-2D colloidal phase behavior using video microscopy (VM). PEO concentration dependent particle-wall depletion attraction is accurately quantified by a modified Asakura−Oosawa (AO) potential. The modified AO potential employs an equation of state, depletion length, and partition coefficient computed using results from renormalization group (RG) theory. Quasi-2D phase behavior measurements are in excellent agreement with Monte Carlo (MC) simulations using the same modified AO potential. The analytically simple modified AO depletion potential accurately captures depletion attraction for a realistic excluded volume polymer system, which suggests it can be generalized to other material systems.

In this instructional review, we discuss how to control individual colloids and ensembles of colloids using electric fields. We provide background on the electrokinetic transport mechanisms and kT-scale equilibrium colloidal interactions that enable such control. We also describe the experimental configurations, microscopy methods, image analyses, and material systems for which these mechanisms have been successfully employed. Methods are presented for creating various structures including colloidal chains, quasi-2D colloidal crystals, and 3D colloidal crystals. We also describe electric-field-mediated feedback control of the colloidal crystal size as well as colloidal crystal assembly and disassembly. Finally, we discuss future extensions of these methods that aim to incorporate accurate colloidal crystallization dynamic models into electric-field-mediated feedback control to allow rapid assembly, disassembly, and repair of defect-free colloidal structures.