Rodlike polyelectrolyte solutions: Effect of the many-body Coulomb attraction of similarly charged molecules favoring weak nematic ordering at very small polymer concentration

The correlation free energy of the many-body Coulomb interactions in the solution of rodlike polyelectrolytes with counterions is calculated. For this purpose a theory of the Debye-Huckel type, based on the density functional approach, is developed. We have shown that for all the analyzed regimes electrostatic interactions of similarly charged rods are attractive independent of their mutual orientation. Coexistence of weakly and highly ordered nematic phases at intermediate degrees of ionization of the molecules is predicted. It is shown that the electrostatic attractive forces favor liquid-crystalline ordering and stabilize a weakly ordered nematic phase at very small polymer concentrations. In other words, isotropic solutions of charged rods are in many cases intrinsically unstable with respect to orientational ordering.