Charge distribution on annealed polyelectrolytes

We investigate the equilibrium charge distribution along a single annealed polyelectrolyte chain under different conditions. The coupling between the conformation of the chain and the local charge distribution is described for various solvent qualities and salt concentration. In salt free solution, we find a slight charge depletion in the central part of the chain: the charges accumulate at the ends. The effect is less important if salt is added to the solution since the charge inhomogeneity is localized close to the chain ends over a distance of order of the Debye length. In the case of poor solvent conditions we find a different charge per monomer in the beads and in the strings in the framework of the necklace model. This inhomogeneity leads to a charge instability and a first order transition between spherical globules and elongated chains.