Analytical solution of the linearized Poisson–Boltzmann equation in cylindrical coordinates

Abstract

By separating the electrical potential into an applied part and an internally induced part, we can write the linearized Poisson–Boltzmann equation as two equations, each of which can be transformed into a modified Bessel equation. The reciprocal of the Debye length is written as the product of a constant and an axial-dependent function that describes the ionic strength distribution. It is possible to solve for the applied part of the potential only when the function is know explicitly, but the solution of the internally induced part remains completely general. The complete solution provides a means for testing assumptions of various ionic strength distributions within the accuracy of the linearized Poisson–Boltzmann equation. (AIP)