Exact solution to linearized Poisson-Boltzmann equation: Ion-penetrable membranes bearing nonuniformly distributed fixed charges

Abstract

The Poisson-Boltzmann equation governing the electrostatic potential distribution of an ion-penetrable particle immersed in an arbitrary a:b electrolyte solution is discussed. The particle, which mimics biological cells and some artificial membranes, carries nonuniformly distributed fixed charges. Three types of particle, including planar, cylindrical, and spherical, and two classes of nonuniform fixed charge distributions are investigated. These distributions all yield the same amount of fixed charges in the membrane phase, which is independent of the geometry of a particle. Under the condition that the potential is low, the exact distribution of the electrostatic potential and the free energy of the system under consideration are derived. ? 1995 American Institute of Physics.