Electric-Field-Driven Assembly of Dipolar Spheres Asymmetrically Confined between Two Electrodes

Externally applied electric fields have previously been utilized to direct the assembly of colloidal particles confined at a surface into a large variety of colloidal oligomers and nonclose-packed honeycomb lattices (J. Am. Chem. Soc. 2013, 135, 7839-7842). The colloids under such confinement and fields are observed to spontaneously organize into bilayers near the electrode. To extend and better understand how particles can come together to form quasi-two-dimensional materials, we have performed Monte Carlo simulations and complementary experiments of colloids that are strongly confined between two electrodes under an applied alternating current electric field, controlling field strength and particle area fraction. Of particular importance, we control the fraction of particles in the upper vs lower plane, which we describe as asymmetric confinement, and which effectively modulates the coordination number of particles in each plane. We model the particle-particle interactions using a Stockmayer potential to capture the dipolar interactions induced by the electric field. Phase diagrams are then delineated as a function of the control parameters, and a theoretical model is developed in which the energies of several idealized lattices are calculated and compared. We find that the resulting theoretical phase diagrams agree well with simulation. We have not only reproduced the structures observed in experiments using parameters that are close to experimental conditions but also found several previously unobserved phases in the simulations, including a network of rectangular bands, zig zags, and a sigma lattice, which we were then able to confirm in experiment. We further propose a simple way to precisely control the number ratio of particles between different planes, that is, superimposing a direct current electric field with the alternating current electric field, which can be implemented conveniently in experiments. Our work demonstrates that a diverse collection of materials can be assembled from relatively simple ingredients, which can be analyzed effectively through comparison of simulation, theory, and experiment. Our model further explains possible pathways between different phases and provides a platform for examining phases that have yet to be observed in experiments.