Electric and magnetic fields directed assembly of colloids in a confined environment

Abstract

Complex materials in nature are bottom-up assembled from simple constituents such as atoms and molecules. Our inability to directly observe their assembly process hinders the rational design of functional materials with advanced properties. However, using colloids to model the assembly of unique structures has been the subject of intense research for several decades, as colloids are a convenient system for studying self and directed assembly. The resulting structures are expected to further the development of new functional materials, such as sensors, electronics, and metamaterials. One way of controlling the particle interactions that direct colloidal assembly is by using an externally applied electric or magnetic field. Recently, this method has been used to assemble a wide assortment of elaborate materials confined near a solid substrate. However, while electric field directed assembly efficiently orders colloids into complex structures, the mechanisms governing the interparticle interactions are not well understood. As such, simulation and theory are used to gain insight into the assembly process. The goal of this thesis is to better understand the interactions and assembly mechanisms of colloids confined near a solid surface. First, Monte Carlo simulations were conducted to model the assembly of colloids in response to an applied electric field. Experiments have shown that under an applied normal electric field, the colloids are confined to a short distance from the surface and spontaneously form two layers. This confinement is asymmetric, in the sense that the number of particles in each layer can be different. The simulations were thus performed upon colloids likewise asymmetrically confined to two layers. Particle pair interactions were modeled using a Stockmayer potential to capture the dipole-dipole interactions induced by the electric field, as well as the steric repulsion between the spherical colloids. By carefully tuning particle areal density, field strength, temperature, and the fraction of particles in direct contact with the electrode surface, a wide array of unique structures was assembled. Isothermal phase diagrams were constructed as a function of dipolar strength and areal density for different degrees of asymmetric confinement. Phase boundaries obtained from simulations are in excellent agreement with an analytical theory based on the energies of several idealized lattices. Many of the simulated results had previously been observed experimentally, including a honeycomb-like network, and a square and triangular bilayer. A comparison between the simulation and experimental phase behavior as a function of the dipole strength and areal density is in good qualitative agreement. Furthermore, several new phases identified in the simulation were later found experimentally, such as networks of zig-zag stripes and rectangular bands. Further control of the interactions governing colloidal assembly can be obtained using orthogonally applied electric and magnetic fields. We use experiments and simulations to show that a monolayer of colloids can be assembled into an array of highly dense but well-separated stripes in response to orthogonal electric and magnetic fields. Furthermore, while an electric field alone can be used to assemble colloids into small clusters confined to a bilayer near the surface of an electrode, the superposition of an orthogonal in-plane magnetic field can direct the assembly of the small clusters into a variety of hierarchical stripes. We find that the stripe architecture can be further tuned by controlling the number ratio of particles in the upper layer to those in the lower layer, leading to the assembly of new stripes, not yet observed in experiments. Of particular interest, the simulations discovered a parameter regime in which the Frank-Kasper sigma phase, the simplest periodic approximant to, as well as the predominant local environment in a dodecagonal quasicrystal, was found. Inspired by this, we further find that by equilibrating at high temperatures, followed by gradual annealing, two-dimensional dodecagonal quasicrystals can be assembled from dipolar colloids over a wide range of parameters. We characterize the assembled quasicrystals in several different ways, including the scattering patterns, global orientational order, local coordination, and phason strain. We find excellent agreement between the parameters obtained from our simulations and those of an ideal Schlottmann quasicrystal. The theoretical energy landscapes of ideal quasicrystals, sigma, and hexagonal phases are determined, and the resulting phase diagrams compare favorably with our simulation results. In summary, the theoretical and simulation results presented in this thesis provide insight into experimentally observed phase behavior of colloids assembled at a surface under applied fields, and provide a framework for new and generally applicable strategies for manufacturing a diversity of structurally rich phases of microscopic particles using only relatively simple fields at a surface.