Electrical Double-Layer Interactions of Regular Arrays of Spheres

Abstract

Electrostatic interactions are computed for three-dimensional regular arrays of spheres. Tetrahedral array of four spheres, octahedral array of six spheres, cubic array of eight spheres, and periodic arrays of spheres in body-centered cubic (BCC) and face-centered cubic (FCC) structures are considered. Based on the linearized Poisson-Boltzmann equation the electrostatic free energy is computed for both constant surface potential and constant surface charge conditions. Facilitating the complex geometry of the problem, the boundary element method is used. Test results for two-sphere interactions are in excellent agreement with existing exact solutions even at very small Debye length. The results for multisphere interactions are compared with those obtained by the pairwise additivity approximation. For BCC and FCC arrays comparison is made to the results from the pairwise additivity approximation and from the spherical cell model. At small Debye length the pairwise additivity approximation predicts the interactions reasonably well. At large Debye length, however, the cell model furnishes much better estimates. In addition, the electrostatic free energy difference between BCC and FCC structures at given particle concentration is found to be too small to assess any physical significance.