Charged Plate in Asymmetric Electrolytes: One-loop Renormalization of   Surface Charge Density and Debye Length due to Ionic Correlations
  The self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a $m:-n$ electrolyte. A perturbation series is developed in terms of $g = 4 \pi b/\ell_{\rm {\scriptscriptstyle DB}}$, where $b, \ell_{\rm{\scriptscriptstyle DB}}$ are Bjerrum length and {\em bare} Debye length respectively. To the zeroth order, we obtain nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes ($m \neq n$), the first order (one-loop) correction to mean potential contains a {\em secular term}, which indicates the breakdown of regular perturbation method. Using a renormalizaton group transformation (RG), we remove the secular term and obtain a globally well-behaved one-loop approximation with {\em a renormalized Debye length} and {\em a renormalized surface charge density}. Furthermore, we find that if the counter-ions are multivalent, the surface charge density is renormalized substantially {\em downwards}, and may undergo a change of sign, if the bare surface charge density is sufficiently large. 
Mingnan Ding, Bing S. Lu, and Xiangjun Xing (Department of Physics and   Astronomy, and Institute of Natural Sciences, Shang...
cond-mat.soft cond-mat.stat-mech