Pair interactions between heterogeneous spheres

Surface heterogeneities on colloidal particles may cause nonuniform charge distributions, which result in electrostatic potential profiles differing from those seen when charge is distributed uniformly. This, in turn, can give rise to attractive interactions between pairs of such surfaces which may be of greater magnitude and range than van der Waals attractions. We extend previous work on interactions between pairs of heterogeneous plates to pairs of spheres, with nonuniform constant potential or constant charge boundary conditions. As in the planar case, large attractive free energies can be obtained which are not present in the equivalent uniform surfaces. Additionally, large restraining torques can be found, affecting the rotational motion. These torques are not present in uniform charge models and may go some way toward explaining restraining torques found in some experimental systems.