The Numerical Solution of the Nonlinear Poisson-Boltzmann Equation Under the Anisotropic Boundary Condition for Colloidal Plasmas

Based on the model of the Wigner-Seitz cell, the surface potential of the sphericalmacroparticle (radius a) expands in terms of the monopole (q). A dipole (p) model is assumedfor an anisotropic boundary condition of the nonlinear Poisson-Boltzmann equation. Using thefinite element method implemented by the FlexPDE software, the potential distribution aroundthe macroparticle is obtained for different ratios p/qa.The calculated results for the potentialshow that there is an attractive region in the vicinity of the macroparticle when |p/qa|>1.1, andnoticeably there is a potential well behind the macroparticle when |p/qa|=1.1, i.e., there existsboth an attractive region and a repulsive region simultaneously. This means that the attractiveinteraction between macroparticles may arise from the anisotropic distribution of the surroundingplasmas, which well explains some experimental observations.