Primary and secondary effective charges for electrical double layer systems with asymmetric electrolytes

Abstract

We show that the screening of the electrostatic potential in electrolytes can in exact theory be expressed in terms of a generalized screened Colomb potential, analogous to the Yukawa potential from the Debye–Hückel approximation, provided the source charge of the potential is renormalized. The renormalized charge distribution is identical to that of a “dressed particle” in dressed ion theory, DIT, of Kjellander and Mitchell. Using DIT we analyze the leading terms of the decay of density profiles and electrostatic potential outside a charged planar wall in contact with 1:2 electrolytes. The formalism leads in a natural manner to the definition of a primary and a secondary effective charge of an object immersed in an electrolyte. These charges are associated with the leading and second leading decay modes of the potential, which have different decay lengths. It is found that both leading terms in the decay are important; together, they give in many cases a very good representation of the density profiles and the potential for distances larger than about a couple of ionic diameters from the wall. When varying the actual (bare) surface charge density σ of the wall, two points of zero effective surface charge density are found: one at low (but nonzero) and one at high value of σ. The former occurs when the counterions are monovalent and the latter when the counterions are divalent and the electrolyte concentration is sufficiently high. Both are associated with effective charge reversals where the surface appears to attain a charge of opposite sign compared to its bare charge. The double layer interaction between two equally charged particles is attractive at large separations at a point of zero effective surface charge.