Model of populations colonizing a new habitat

We consider the electrostatic interaction between two rigid membranes, with different surface charge densities of opposite sign, across an aqueous solution without added salt. Exact solutions lo the nonlinear Poisson-Boltzmann equation are obtained and their physical meaning discussed. We also calculate the electrostatic contribution to the free energy and discuss the renormalization of the area per head group of the charged lipids arising from the Coulomb interaction.