  We use coarse-grained Monte Carlo simulations to study the elastic properties
of charged membranes in solutions of monovalent and pentavalent counterions.
The simulation results of the two cases reveal trends opposite to each other.
The bending rigidity and projected area increase with the membrane charge
density for monovalent counterions, while they decrease for the pentavalent
ions. These observations can be related to the counterion screening of the
lipid charges. While the monovalent counterions only weakly screen the Coulomb
interactions, which implies a repulsive Coulomb system, the multivalent
counterions condense on the membrane and, through spatial charge correlations,
make the effective interactions due the charged lipids attractive. The
differences in the elastic properties of the charged membranes in monovalent
and multivalent counterion solutions are reflected in the mechanisms leading to
their mechanical instability at high charge densities. In the former case, the
membranes develop pores to relieve the electrostatic tensile stresses, while in
the latter case, the membrane exhibit large wavelength bending instability.
