(603e) Modeling Convective Assembly during Colloidal Crystal Growth
Photonic crystals represent a fascinating and potentially extremely useful class of materials engineered to manipulate optical signals. These periodically-structured materials represent the photonic analog to conventional semiconductors. If properly tailored, photonic crystals can exhibit a photonic band gap. Since this property can be utilized to manipulate photons, these materials should enable a variety of optical devices to be combined on ultra-compact optical chips (i.e., all-optical integrated circuits). To move toward this goal, several methods have been explored to obtain photonic crystals. Among these, the self assembly of colloidal microspheres has provided a simple and inexpensive approach. Colloids can be induced to spontaneously organize onto a face-centered cubic (fcc) lattice. While the resulting material, often referred to as a synthetic opal, does not satisfy all the requirements for a photonic band gap, it can be used as a template to synthesize such structures. Accordingly, self-assembled photonic crystals have recently been obtained, which have a photonic band gap and are in a technology-friendly format, directly on a silicon wafer.
This success primarily depends on the formation of high quality synthetic opals. The most perfect planar opals are produced not by slow settling followed by drying, but by a procedure whereby an inclined substrate is placed in a suspension of the silica spheres in ethanol. Under the proper conditions, evaporation of the solvent leads to growth of an ordered packing of more or less uniform thickness on the substrate, starting from a position below the initial level of the contact line at the top of the meniscus. Unfortunately, the details of the mechanism by which these planar opals grow are poorly understood. Experimentally, the procedure is extremely sensitive to the growth conditions. Planar opals are difficult to grow in reasonable yields due to the numerous parameters (colloid concentration, temperature, solvent viscosity, solvent evaporation rate, etc.) that must be simultaneously optimized. Since most applications for inverse opals require the use a large sphere planar opal as the initial template, this difficulty limits the development of self-assembled photonic crystals.
Of particular interest is the role of solvent flow in the assembly of opals. Norris et al. have advanced the convective assembly hypothesis, which posits how the effects of solvent flow in the system could guide planar opal formation in beneficial manners. The idea is that solvent flow through the pore space of close-packed spheres could direct advancing spheres into the clear niches, where flow is higher than into obstructed niches. The action of flow into and across the crystal is argued to reinforce the tendency of a new layer to grow with the desired fcc packing.
Here, we present several models to assess the validity of this hypothesis. We first present results from a global model for flows in the growth system. Specifically, we employ finite element models to compute time-dependent, two-dimensional flows that are driven by solvent evaporation in this system. Importantly, we are able to model the free surface between the solvent and the overlying gas phase, including a rigorous accounting for normal (predominantly capillary) and shear (Marangoni) forces at that surface. At this level of simulation, we do not represent the individual colloidal particles, rather we employ an effective medium approximation to account for their presence. We will then present our initial results from very detailed, local models to compute three-dimensional flows around and through the layers of particles deposited by the process. With this knowledge of flows, we compute the net hydrodynamic force acting upon an incoming particle and model the coupled action of flow and particle motion. This model will be used to assess the mechanism of flow and geometry on placing the incoming particle into a preferred position in the established lattice.