Spatially varying colloidal phase behavior on multi-dimensional energy landscapes.

A method is reported to determine equilibrium concentration profiles and local phase behavior of colloids on multi-dimensional energy landscapes. A general expression is derived based on local particle concentration and osmotic pressure differences that are balanced by forces on colloids due to energy landscape gradients. This analysis is applied to colloidal particles in high frequency AC electric fields within octupolar electrodes, where the energy landscape can be shaped in two dimensions. These results are also directly applicable to any particles having induced dipoles in spatially non-uniform electromagnetic fields. Predictions based on modeling colloids with an effective hard disk equation of state indicate inhomogeneous solid and fluid states coexisting on different shaped energy landscapes including multiple minima. Model predictions show excellent agreement with time-averaged Brownian dynamic simulations at equilibrium. Findings demonstrate a general approach to understand colloidal phase behavior on energy landscapes due to external fields, which could enable control of colloidal microstructures on morphing energy landscapes and the inverse design of fields to assemble hierarchically structured colloidal materials.