Analytical solution to Poisson-Boltzmann equation for two interacting parallel identical plates with constant surface potential

摘要

In this paper, we suggest an analytical solution to Poisson-Boltzmann equation for the calculation of potential distributions between two identical plates with high constant surface potential. Our expression fits well to the exact values of the potential between two parallel plates. Numerical results indicate that this analytical solution provides accurate description for the dimensionless distance ≤ 2. The suggested solution can be successfully applied in calculating the potential for identical plates with high or moderate surface potentials. A simple analytical expression for the energy of interactions between two identical plates with constantly high surface potential is also given. The solutions in analytical, exact and numerical forms become indistinguishable when y _0 ≥ 3, κx ≤ 4 and y _0 = 2.0, κx ≤ 3, respectively. When y _0 = 2.0, κx ≤ 1.2, the approximate solution is in close agreement with the exact solution.