the potential distribution around a cylinder and the effective An accurate analytic expression of the surface charge density/ surface potential of a cylinder. Finally we derive expressions surface potential relationship for an infinitely long cylindrical for the double-layer interaction energy and force between colloidal particle in a solution of general electrolytes is derived two cylinders at large separations on the basis of the method from an approximate solution to the nonlinear cylindrical Poissonof Brenner and Parsegian (4). Boltzmann equation. The mathematical procedure is based on a method developed previously by Ohshima, Healy, and White for 2. NONLINEAR CYLINDRICAL POISSON-BOLTZMANN the case of a sphere (J. Colloid Interface Sci. 90, 17 (1982)). EQUATION AND ITS APPROXIMATE SOLUTION Comparison is made with exact numerical results. Accurate expressions for the potential distribution around a cylinder and the
Consider an infinitely long cylindrical colloidal particle
effective surface potential of a cylinder are also derived. Finally, of radius a immersed in an electrolyte solution. Let the elecexpressions for the double-layer interaction energy and force between two cylinders at large separations are derived on the basis trolyte be composed of N ionic mobile species of valence z i of the method of Brenner and Parsegian (Biophys. J. 14, 327 and bulk concentration (number density) n i (i Γ
1, 2, . . . , (1974)). α§ 1998 Academic Press N), where Ν N iΓ
1 z i n i Γ
0, since electroneutrality holds in the Key Words: surface charge density; surface potential; cylindrical bulk solution phase. We assume that the electric potential particle; electrolyte solution. c(r) at a radial distance r from the axis of the cylinder (measured relative to the bulk solution phase, where c(r) Γ
0) obeys the cylindrical Poisson-Boltzmann equation,