  We investigate the electrostatic interactions of zwitterionic membranes
immersed in mixed electrolytes composed of mono- and multivalent ions. We show
that the presence of monovalent salt is a necessary condition for the existence
of a finite electrostatic force on the membrane. As a result, the mean-field
membrane pressure originating from the surface dipoles exhibits a non-uniform
salt dependence, characterized by an enhancement for dilute salt conditions and
a decrease at intermediate salt concentrations. Upon addition of multivalent
cations to the submolar salt solution, the separate interactions of these
cations with the opposite charges of the surface dipoles makes the
intermembrane pressure more repulsive at low membrane separation distances and
strongly attractive at intermediate distances, resulting in a discontinuous
like-charge binding transition followed by the membrane binding transition. By
extending our formalism to account for correlation corrections associated with
large salt concentrations, we show that membranes of high surface dipole
density immersed in molar salt solutions may undergo a membrane binding
transition even without the multivalent cations. Hence, the tuning of the
surface polarization forces by membrane engineering can be an efficient way to
adjust the equilibrium configuration of dipolar membranes in concentrated salt
solutions.
