Simple Models of Directly Measured Energy Landscapes for Different Shaped Particles in Nonuniform AC Electric Fields

We report direct measurements of potential energy landscapes for different shaped colloidal particles interacting with nonuniform AC electric fields. Epoxy particle shapes investigated include disks, ellipses, squares, rectangles, and rhombuses, which are all part of the superelliptical prism shape class and are chosen to systematically vary particle anisotropy and corner features. The measurement configuration consists of noninteracting single particles sedimented onto microscope slides within electric fields between parallel coplanar electrodes. Thermally sampled positions and orientations of single particles in nonuniform fields are tracked in an optical microscope, and measured potential energy landscapes are obtained via Boltzmann inversions. We develop a new analytically simple model that captures all measured energy landscapes for superelliptical prism shaped colloidal particles with electrostatic double layers. The model recovers known validated potentials for spherical and ellipsoidal particles, and therefore captures energy landscapes for a variety of different colloidal particle sizes, shapes, and materials reported in prior studies.