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.

Graphical abstractPotential distribution across a polyelectrolyte layer.Figure optionsDownload full-size imageDownload as PowerPoint slide