Phase separation in salt-free symmetric mixtures of oppositely chargedrodlike polyelectrolytes is studied using quasi-analytical calculations.Stability analyses for the isotropic-isotropic and the isotropic-nematic phasetransitions in the mixtures are carried out and demonstrate that electrostaticinteractions favor nematic ordering. Coexistence curves for the symmetricmixtures are also constructed and are used to examine the effects of linearcharge density and electrostatic interaction strength on rodlikepolyelectrolyte complexation. It is found that the counterions are uni- formlydistributed in the coexisting phases for low electrostatic interactionstrengths dictated by the linear charge density of the polyelectrolytes andBjerrum's length. However, the counterions also partition along with therodlike polyelectrolytes with an increase in the electrostatic interactionstrength. It is shown that the number density of the counterions is higher inthe concentrated (or "coacervate") phase than in the dilute (or supernatant)phase. In contrast to such rodlike mixtures, flexible polyelectrolyte mixturescan undergo only isotropic-isotropic phase separation. A comparison of thecoexistence curves for weakly-charged rodlike mixtures with those of analogousflexible polyelectrolyte mixtures reveals that the electrostatic driving forcefor the isotropic-isotropic phase separation is stronger in the flexiblemixtures.
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