  We compute the phase diagram of salt-free polyelectrolyte solutions using a
modified Debye-Huckel Approach. We introduce the chain connectivity via the
Random Phase Approximation with two important modifications. We modify the
electrostatic potential at short distances to include a bound on the
electrostatic attractions at the distance of closest approach between charges.
This modification is shown to act as a hard core in the phase diagram of
electrolyte solutions. We also introduce a cut-off on the integration of the
modes of wave length smaller than the size over which the chains are strongly
perturbed by the electrostatic interactions. This cut-off is shown to be
essential to predict physical phase diagram in long chain solutions.
