Electrostatic and mechanical properties of a flat lipid bilayer containing ionic lipids: Possibility for formation of domains with different surface charges

The electrostatic and the mechanical properties of a flat lipid bilayer, containing ionic lipid, are studied theoretically. The degree of dissociation of the molecules of the ionic lipid and the free energy of the system due to the electrostatic interactions are obtained as a function of the relative concentration of the ionic lipid in the membrane. The classical approach to the calculation of the free energy of the electric double layer, used by Verwey and Overbeek, is developed in order to take into account that the membrane is not a reservoir of ions. A concentration interval of the ionic lipid, where phase separation into domains with different surface charges appears and the existence of a particular concentration of the ionic lipid, revealing critical properties, are predicted. The contribution of the electrostatic interactions to the stretching elasticity of the bilayer is determined.