General Potential for Anisotropic Colloid-Surface Interactions.

Abstract

A general closed-form, analytical potential is developed for the interaction of planar surfaces with superellipsoidal particles (which includes shapes such as spheres, ellipsoids, cylinders, polygons, superspheres, etc.). The Derjaguin approximation is used with DLVO half-space interactions (e.g., electrostatics and van der Waals) to yield potentials for arbitrary particle-wall separation and orientation. The resulting potential is a function of the minimum distance between surfaces and the particle's local Gaussian curvature at the minimum distance position. The validity of the solution is reported in terms of the local Gaussian curvature (Γ) and characteristic interaction range (e.g., Debye length, κ-1, for electrostatics) based on the limits of the Derjaguin approximation. This solution is limited for superellipsoids with convex shapes and orientations where the condition κ/Γ1/2 > 2 is satisfied. The potentials reported in this work should be useful for modeling a wide range of natural and synthetic nonspherical and anisotropic colloidal particles in environmental, biological, and advanced material applications.