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تسجيل مستخدم جديدCharged Plate in Asymmetric Electrolytes: One-loop Renormalization of Surface Charge Density and Debye Length due to Ionic Correlations
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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 ($m eq n$), 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.
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