The Donnan potential-surface potential relationship for a cylindrical soft particle in an electrolyte solution

Transcendental equations, which avoid integration of the nonlinear Poisson-Boltzmann equations, are presented for obtaining the relationship between the Donnan potential and surface potential of a cylindrical soft particle (i.e., a polyelectrolyte-coated cylindrical particle) in a symmetrical electrolyte solution. Numerical results obtained by the present method are in excellent agreement with exact results obtained by solving the nonlinear cylindrical Poisson-Boltzmann equations both inside and outside the polyelectrolyte layer.