An exact solution to the electrostatic interaction between an ion-penetrable sphere and an ion-penetrable rod

No exact solution for the free energy of electrostatic interaction fora charged sphere and rod geometry in an electrolyte solution has yet been proposed. This geometry is interesting because it can be applied to describe macromolecules interacting with a random fiber-matrix for modeling of hindered transport in diffusional systems. Here we present an analytical approach that yields an exact solution to the problem for ion-penetrable-also called "soft"-sphere and infinitely long rod. This solution is compared to a published finite-element analysis of the same system with nonpenetrable-also called "hard"-sphere and infinitely long rod maintaining a constant surface charge density restriction. For any ionic strength or ratio of rod radius to sphere radius the ion-penetrable method yields an electrostatic free energy of interaction which is lower than that given by the analysis for hard bodies. This free energy is significantly lower for most parameter value combinations and therefore suggests that one should carefully examine the system being modeled to determine if it is approximated better by a hard body or ion-penetrable body approach. (C) 2000 Academic Press.