The electrostatic interactions for a string-like particle with a tion efficiency . charged plate are investigated on the basis of the Poisson-Boltz-The extensive investigations on the electrical double-layer mann equation under the Debye-Hu Β¨ckel approximation. During interactions were focused on the interactions between two the interaction, the plate is assumed to be with constant surface spherical colloid particles (11-18) which play an essential potential or constant surface charge density. The interaction enrole in determining the behavior of colloidal systems. The ergy is found to consist of two terms. The first term is simply the interaction between a charged sphere and a charged planar result of Gouy-Chapman theory, and it is the work required to wall has previously been investigated by Kaplan et al. for insert a ghost particle into the undisturbed electric field established by the electrolyte solution and the charged wall. The second term the constant surface potential condition (19,. Recently, represents the interaction between the particle and its image with Stahlberg et al. calculated the electrostatic interaction energy respect to the plate. The interaction energy, which is nondimenfor a sphere-wall system under the condition of constant sionalized by QC p0 , depends on the distance between the particle surface charge density on both surfaces by solving the linearand the plate, the contour length, and the orientation of the partiized Poisson-Boltzmann equation ( ). An exact expression cle. Q is the total charge carried by the particle, and C p0 is the of the electrostatic energy of an ion-penetrable sphere interundisturbed surface potential. At short distance, the relative imacting with a hard plate has been given by Ohshima and portance of the image to the plate contribution grows with increas-Kondo (1) for both the constant surface charge density and ing kQ/C p0 . For QC p0 ΓΊ 0, the interaction can become attractive the constant surface potential cases.
if kQ/C p0 is large enough. Here k 01 is the Debye screening length.
Nonspherical colloidal particles are also abundant in na-
The results have been applied to fiber-and ring-like particles.
Analytical expressions are obtained in some limiting cases. The ture and industrial applications. Charged particulates of rod free energy contributions due to the plate and the image are maxtype include, for example, tobacco mosaic virus (21), and ima when the plane containing the fiber or the ring is perpendicuacid-hydrolyzed cellulose crystallites ( ) and clay particles lar to the wall. The effect of nonuniform charge distribution of are known to have the shape of disk (23). In contrast to the fiber has also been discussed. α§ 1998 Academic Press spherical particles, little attention has been focused on in-Key Words: electrostatic interactions; Poisson-Boltzmann equavestigating electrical double-layer interactions between nontion; image method; fiber; ring particle. spherical objects such as ion-penetrable spheroids (24), rodlike particles (25-27), and disk-like particulates (28, 29), and also little is known about the electrostatic interactions 527