Charge induced pattern formation on surfaces: Segregation in cylindrical micelles of cationic-anionic peptide-amphiphiles

Micelles, vesicles, and films composed of two species of incompatible heterogenous molecules exhibit full internal segregation of the component species. This macroscopic segregation can be inhibited by oppositely charging the two different molecular species. The degree of compatibility achieved by the charges leads to either fully homogenous mixtures or to local segregation and the possible formation of regular patterns. We investigate the induction of periodic surface patterns by the presence of opposite charges in flat films and cylindrical micelles. In the strong segregation limit the incompatibility between species can be described by a line tension parameter γ. The size of the patterns formed is of the order of a characteristic size L∼(γ/σ²)^1/2, where σ is the surface charge density. The pattern symmetry on flat surfaces is function only of the fraction of area covered by the components, f: lamellar for 0.34<f<0.66 and hexagonal otherwise. In cationic and anionic mixtures aggregated into cylindrical micelles the symmetry and size of the surface charged domains depends also on the radius R of the cylinder. For large radii the patterns are similar to those in the plane, but for small radii only lamellar patterns are formed. At high salt concentration the surface domain size jumps discontinuously to an infinite value, resulting in macroscopic phase segregation.