(579i) Colloidal Organization at Interfaces for Advanced Materials Applications

Colloidal assembly can be used to form complex materials that depend on the organization and interaction of the constituent particles. Colloids are known to accumulate and organize at fluid interfaces via capillary interactions, the product of the surface tension and change in interfacial area that occurs when particles attach onto interfaces. Capillary interactions move colloids to particular locations to minimize the free energy of the system. These interactions are determined by the particle contact line and interface shape, and are typically orders of magnitude larger (~ 10⁶ K_BT for a 1 micron diameter colloid) than colloidal interactions in suspension. These energy fields can be used to direct, rotate, and assemble anisotropic particles on planar interfaces. Furthermore, even spherical objects have highly directional interactions owing to contact line pinning and associated leading order, long-range quadrupolar distortions. Particles with pinned contact lines make quadrupolar distortions, assemble with quadrupolar symmetries, and migrate to sites of high deviatoric curvature on curved interfaces.

In this work we formulate the curvature capillary energy for two interacting particles on a curved interface. For pinned contact lines, we find curvature capillary energies using the method of reflections. The closed-form analytical expression for the interaction energy has contribution from the individual particle curvature interactions, as well as pair interaction from the two particles. The exact solution in bipolar coordinates agrees when the particles are far from each other, but near contact, the exact solution deviates, indicating that higher order distortions become important near field. In experiments, we study pair interactions of colloids on curved interfaces. Pairs interact with the curvature and migrate along deterministic trajectories when far apart but interact with each other when close enough to dimerize. Observed particle pair trajectories are compared to simulated trajectories obtained from a force balance on each particle equating the drag to the capillary attraction force. In addition to studying pairs, we study aggregates and structures formed at different regions of the interface. These are compared to Monte Carlo and Brownian dynamics simulations base on pair interactions. By studying the underlying physics behind these interactions and assemblies, we develop new rules for organization by using the versatility in the energy landscapes that highly deformable fluid interfaces and colloids provide.