Spontaneous chirality via long-range electrostatic forces

We consider a model for periodic patterns of charges constrained over a cylindrical surface. In particular we focus on patterns of chiral helices, achiral rings, or vertical lamellae, with the constraint of global electroneutrality. We study the dependence of the patterns' size and pitch angle on the radius of the cylinder and salt concentration. We obtain a phase diagram by using numerical and analytic techniques. For pure Coulomb interactions, we find a ring phase for small radii and a chiral helical phase for large radii. At a critical salt concentration, the characteristic domain size diverges, resulting in an achiral macroscopic phase-segregated structure. We discuss possible consequences and generalizations of our model.