Orientation-dependent electrical double-layer interactions. I. Rodlike macroions of finite length

Abstract

The orientation-dependent electrical double-layer interaction between two thin rodlike macroions of finite length is considered. Starting from an expression for the interaction free energy as a double integral of the Green's function for the linearized Poisson-Boltzmann equation, we obtain several useful analytical approximations. For certain rod configurations, we obtain simple analytical approximations to the double-layer interaction that are quantitatively accurate at physically relevant rod separations and electrolyte concentrations. For a general rod configuration, specified by the separation and three angles, we develop a generalized multipole expansion of the double-layer interaction energy, which converges rapidly if the rod length is not much larger than the center-of-mass rod separation or the Debye length. The orientation dependence of the double-layer repulsion can then be quantitatively accounted for in terms of the screened charge-quadrupole and quadrupole-quadrupole interactions. Furthermore, we show that the double-layer repulsion between finite rods depends on the rod orientations even at arbitrarily large separation. © 1995 American Institute of Physics.