Liquid, liquid crystal, and crystal states of different shaped colloids in nonuniform fields via osmotic force balance.

This article presents a model based on an osmotic force balance (OFB) to predict equilibrium density profiles and microstructural states—liquid, nematic, and crystal—of variously shaped colloidal particles in quasi-two-dimensional (2D) systems subjected to nonuniform alternating current (AC) electric fields. The model integrates newly developed equations of state for superelliptical prism particles, including disks, ellipses, squares, and rectangles, and balances local osmotic pressure against dipole-field interactions to determine particle density distributions. Validation against Monte Carlo simulations and optical microscopy experiments demonstrates that the model accurately predicts particle densities and phase states across a range of particle shapes, sizes, system dimensions, and field strengths. These findings provide a quantitative framework for designing and controlling colloidal assemblies in interfacial materials and devices using electric fields.