  Phase separation in salt-free symmetric mixtures of oppositely charged
rodlike polyelectrolytes is studied using quasi-analytical calculations.
Stability analyses for the isotropic-isotropic and the isotropic-nematic phase
transitions in the mixtures are carried out and demonstrate that electrostatic
interactions favor nematic ordering. Coexistence curves for the symmetric
mixtures are also constructed and are used to examine the effects of linear
charge density and electrostatic interaction strength on rodlike
polyelectrolyte complexation. It is found that the counterions are uni- formly
distributed in the coexisting phases for low electrostatic interaction
strengths dictated by the linear charge density of the polyelectrolytes and
Bjerrum's length. However, the counterions also partition along with the
rodlike polyelectrolytes with an increase in the electrostatic interaction
strength. It is shown that the number density of the counterions is higher in
the concentrated (or "coacervate") phase than in the dilute (or supernatant)
phase. In contrast to such rodlike mixtures, flexible polyelectrolyte mixtures
can undergo only isotropic-isotropic phase separation. A comparison of the
coexistence curves for weakly-charged rodlike mixtures with those of analogous
flexible polyelectrolyte mixtures reveals that the electrostatic driving force
for the isotropic-isotropic phase separation is stronger in the flexible
mixtures.
