Although constant potential and constant charge density
The electrical potential distribution of a system containing mulmodels are idealized descriptions, they are widely adopted tiple charged surfaces with a general boundary condition is investifor the purpose of a simpler mathematical treatment. In pracgated theoretically. Here, a surface can assume a constant potentice, various surface conditions can be assumed. These intial/charge density, or an arbitrary combination of the two, i.e., a clude, for example, charge-regulated surfaces (1-7) and surmixed boundary condition; the latter is of particular significance faces of dynamic nature (8). In these cases, a mixed boundin practice. Typical example includes surfaces containing various ary-valued problem, i.e., a certain combination of the ionizable functional groups, charge-regulated surfaces, dynamic potential and charge density is specified at surface, needs to surface conditions, and patchwise charged surfaces. A systematic be solved. An important special case of this type of problem iterative method is proposed for the resolution of the linearized Poisson-Boltzmann equation governing the electrical potential is that which involves a nonuniform boundary condition (9distribution of the system under consideration. The sufficient and 12), such as patchwise distribution of surface charges (13). necessary condition under which the method proposed is applica-In general, since the orthogonal property of the eigenfuncble is discussed. Since the coefficients in the expression for the tions associated with the general solution of a PBE cannot boundary condition at surface can be an arbitrary function, the be employed directly, solving a mixed boundary-valued present problem is a generalized Robin problem. The conventional problem is nontrivial. constant potential (Dirichlet) problem and constant surface Previous efforts were mainly based on the interactions charge (Neumann) problem can be recovered as special cases of of two charged surfaces. Glendinning and Russel (14), for the present model. A criterion is proposed to decide whether the example, examined the electrostatic interaction between two separation distances between particles is appropriate for various identical spheres under Debye-Huckle condition for the case approximate procedures, e.g., pairwise addition and linear superof fixed surface potential/charge density. A multipole expanposition. We show that a system containing a large number of surfaces can be simulated by one which has relatively few surfaces. sion technique was used. Ohshima considered the potential