Charge inversion on membranes induced by multivalent-counterion fluctuations

Abstract

Based on the two state model, we study the condensation of counterions on oppositely chargedmembranes in the presence of monovalent salts. Using the Gaussian approximation, weevaluate the contribution of two-dimensional charge fluctuation to the free energy,from which the number of condensed counterions is determined self-consistently.It is shown that charge inversion can occur upon the addition of divalent ionsof millimolar range, or of trivalent ions of micromolar range. The driving forcefor the overcharging mechanism is the charge correlation induced by thermalfluctuation, in which the multivalency of the counterions plays a crucial role.