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

摘要

Based on the model of the Wigner-Seitz cell, the surface potential of the spherical macroparticle (radius a) expands in terms of the monopole (q). A dipole (p) model is assumed for ananisotropic boundary condition of the nonlinear Poisson-Boltzmann equation. Using the finite element method implemented by the FlexPDE software, the potential distribution around the macroparticle is obtained for different ratios p/qa. The calculated results for the potential show that there is attractive region in the vicinity of the macroparticle when vertical bar p/qa vertical bar>1.1, and noticeably there is a potential well behind the macroparticle when vertical bar p/qa vertical bar=1.1, i.e., there exists both an attractive region and a repulsive region simultaneously. This means that the attractive interaction between macroparticles may arise from the anisotropic distribution of the surrounding plasmas, which well explains some experimental observations.