The effect of many-body interactions on the electrostatic force in an array of spherical particles

The effect of many-body interactions on the electrostatic force between spheres in an array of charged spherical particles has been quantified by solving the non-linear Poisson-Boltzmann equation (PBE) using a finite element method (FEM) model. The equation is solved for conditions of constant surface potential. The effect of the dimensionless Debye length scaled radius of the spheres on the electrostatic force between them has been determined and a significant reduction of the force is observed as the dimensionless Debye radius is decreased. Calculations based on the dimensionless separation distance between a pair of charged spheres in isolation confirm an exponential decay of the repulsive electrostatic force as the surface to surface separation distance is increased. In contrast, calculations based on an array of interacting spheres in certain critical packing conditions reveal considerable reduction in the magnitude of the repulsive electrostatic force at separation distances less than half the sphere radius. The latter results are explained by considering the directional cancellation effects of the electrical double layer between adjacent spheres placed in certain orientations within the array. This is believed to be a surprising many-body effect which has been overlooked in previous studies and whose validity can be used to explain the stability and strength of charged sphere arrays under certain critical geometric configurations.