  A binary mixture of oppositely charged components confined to a plane such as
cationic and anionic lipid bilayers may exhibit local segregation. The relative
strength of the net short range interactions, which favors macroscopic
segregation, and the long range electrostatic interactions, which favors
mixing, determines the length scale of the finite size or microphase
segregation. The free energy of the system can be examined analytically in two
separate regimes, when considering small density fluctuations at high
temperatures, and when considering the periodic ordering of the system at low
temperatures (F. J. Solis and M. Olvera de la Cruz, J. Chem. Phys. 122, 054905
(2000)). A simple Molecular Dynamics simulation of oppositely charged monomers,
interacting with a short range Lennard Jones potential and confined to a two
dimensional plane, is examined at different strengths of short and long range
interactions. The system exhibits well-defined domains that can be
characterized by their periodic length-scale as well as the orientational
ordering of their interfaces. By adding salt, the ordering of the domains
disappears and the mixture macroscopically phase segregates in agreement with
analytical predictions.
