  Starting with a model Hamiltonian, we study using the uniform expansion
method conformational behavior of polyelectrolytes in the presence and absence
of salt. The uniform expansion method yields all the important local length
scales in the polyelectrolyte: the electrostatic blob size at large fraction of
charges, the thermal blob size at low fraction of charges and the sizes of
pearls (beads) and necklaces (strings) at intermediate fraction of charges. In
the presence of salt, the electrostatic blob size depends on the ionic strength
and increases with the increase in the salt concentration. We determine the
salt concentration at which the pearl necklace intermediates dissolve and the
nature of the transition changes from discontinuous to continuous. This
critical salt concentration corresponds to the length scale where the Debye
screening length is of the order of the necklace length.
