Electrostatic potential around charged finite rodlike macromolecules: nonlinear Poisson-Boltzmann theory

In this paper, we show that the far field electrostatic potential created by a highly charged finite size cylinder within the nonlinear Poisson-Boltzmann (PB) theory, is remarkably close to the potential created within the linearized PB approximation by the same object at a well-chosen fixed potential. Comparing the nonlinear electrostatic potential with its linear counterpart associated to a fixed potential boundary condition (called the effective surface potential), we deduce the effective charge of the highly charged cylinder. Values of the effective surface potential are provided as a function of the bare surface charge and Debye length of the ionic solution. This allows to compute the anisotropic electrostatic interaction energy of two distant finite rods.