Cascade of transitions of polyelectrolytes in poor solvents

We develop a scaling model for the dilute solution conformation of a uniformly charged polymer in a poor solvent. We find that there is a range of temperatures and charge densities for which the polymer has a necklace-like shape with compact beads joined by narrow strings. The free energy of a polyelectrolyte in this conformation is lower than in a cylindrical globule because the length of the necklace is larger than that of a cylinder and is proportional to the total charge on the chain. With changing charge on the chain or temperature, the polyelectrolyte undergoes a cascade of abrupt transitions between necklaces with different numbers of beads.