Electrostatic Interactions of a String-Like Particle with a Charged Plate

Abstract

The electrostatic interactions for a string-like particle with a charged plate are investigated on the basis of the Poisson–Boltzmann equation under the Debye–Hückel approximation. During the interaction, the plate is assumed to be with constant surface potential or constant surface charge density. The interaction energy is found to consist of two terms. The first term is simply the result of Gouy–Chapman theory, and it is the work required to insert a ghost particle into the undisturbed electric field established by the electrolyte solution and the charged wall. The second term represents the interaction between the particle and its image with respect to the plate. The interaction energy, which is nondimensionalized byQΨp0, depends on the distance between the particle and the plate, the contour length, and the orientation of the particle.Qis the total charge carried by the particle, and Ψp0is the undisturbed surface potential. At short distance, the relative importance of the image to the plate contribution grows with increasing κQ/Ψp0. ForQΨp0> 0, the interaction can become attractive if κQ/Ψp0is large enough. Here κ−1is the Debye screening length. The results have been applied to fiber- and ring-like particles. Analytical expressions are obtained in some limiting cases. The free energy contributions due to the plate and the image are maxima when the plane containing the fiber or the ring is perpendicular to the wall. The effect of nonuniform charge distribution of the fiber has also been discussed.