Surface charge density surface potential relationship for a cylindrical particle in an electrolyte solution

An accurate analytic expression of the surface charge density/surface potential relationship for an infinitely long cylindrical colloidal particle in a solution of general electrolytes is derived from an approximate solution to the nonlinear cylindrical Poisson-Boltzmann equation. The mathematical procedure is based on a method developed previously by Ohshima, Healy, and White for the case of a sphere (J. Colloid Interface Sci. 90, 17 (1982)). Comparison is made with exact numerical results. Accurate expressions for the potential distribution around a cylinder and the effective surface potential of a cylinder are also derived. Finally, expressions for the double-layer interaction energy and force between two cylinders at large separations are derived on the basis of the method of Brenner and Parsegian (Biophys. J. 14, 327 (1974)). (C) 1998 Academic Press.