  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 macroscopic phase segregation of the components and
restoring chiral symmetry. We discuss possible consequences and generalizations
of our model.
