Renormalized Surface Charge Density for a Strongly Charged Plate in Asymmetric Electrolytes: Asymptotic Exact Results in Poisson Boltzmann Theory

The Poisson-Boltzmann equation for a strongly charged plate inside a generic charge-asymmetric electrolyte is solved using the method of asymptotic matching. Both near field and far field asymptotic behaviors of the potential are systematically analyzed. Using these expansions, the renormalized surface charge density is obtained as an asymptotic series in terms of the bare surface charge density.