Solving the Poisson−Boltzmann Equation for Two Parallel Cylinders

The electrostatic interaction between two parallel charged cylinders of arbitrary diameters a 1 and a 2 is studied by solving numerically the nonlinear Poisson−Boltzmann equation. A limit of particular interest is that of a charged cylinder interacting with a charged plane ( a 1 → ∞). The interaction free energy is calculated, as a function of the separation distance between the cylinders, for either fixed charge density or mixed (fixed charge, fixed potential) boundary conditions.