Charge renormalization and asymptotic decay in classical Coulomb systems

Abstract
Dressed Ion Theory (DIT), an exact statistical mechanical formalism for classical Coulomb fluids in the primitive model, is expressed in terms of the mean electrostatic potential and the dielectric function of the electrolyte. This leads to a natural definition of a renormalized charge distribution that take the same role as the bare source charge has in linear response theory. Furthemore, pnmary and secondary effective charges and permittivitties of the electrolyte are introduced. They play an important role in the asymptotic behaviour of distribution functions at large separations ; the effective charges describe how strongly the ionic distribution close to a central particle affects the distant behaviour of the electrostatic potential. The theory is utilized to analyse the asymptotic behaviour of the potential outside a charged surface in contact with an aqueous solution of an asymmetric electrolyte. It is found that the behaviour of the electric double layer is described quantitatively by the two leading asymptotic terms at distances larger than a couple of ionic diameters from the surface. Two different points of zero effective surface charge density are found - both occurring at non-zero values of actual (bare) surface charge.