  Polyelectrolytes in poor solvents show a necklace structure where collapsed
polymer pearls are linked to stretched strings. In the present paper the
elasticity of such chains is studied in detail. Different deformation regimes
are addressed. The first is the continuous regime, where many pearls are
present. A continuous force extension relation ship is calculated. The main
contribution comes from the tension balance and the electrostatic repulsion of
consecutive pearls. The main correction term stems from the finite size of the
pearls, which monitors their surface energy. For a finite amount of pearls
discontinuous stretching is predicted. Finally counterion effects are discussed
qualitatively.
