  We study the phase diagram and the pion modes in the electrically neutral two
flavor PNJL model. One of the main result of this paper is that when electrical
neutrality is required, pions do not condense in the ground state of the model:
the isospin chemical potential $\mu_I = -\mu_e/2$ is always smaller than the
value required for pion condensation to occur. Moreover we investigate on the
pions and $\sigma$ mass spectra. We find that the qualitative behavior of the
masses resembles that obtained in the NJL model. We close this paper by
studying the intriguing possibility that a bound state with the quantum numbers
of the pions can be formed above the chiral phase transition.
