Screening of a macroion by multivalent ions: a new boundary condition for the Poisson-Boltzmann equation and charge inversion

Screening of a macroion by multivalent counterions is considered. It is sho wn that ions form strongly correlated liquid at the macroion surface. Cohes ive energy of this liquid leads to strong additional am-action of counterio ns to the surface. Away from the surface this attraction is taken into acco unt by a new boundary condition for the Poisson-Boltzmann equation. This eq uation is solved with the new boundary condition for a charged Bat surface and a long cylinder. For a cylinder Onsager-Manning theory looses its unive rsality so that apparent charge of the cylinder is smaller than their theor y predicts and depends on its bare charge. It can also vanish or change sig n. (C) 1999 Elsevier Science B.V. All rights reserved.