Quantitative theory of orientational behavior of rodlike polyelectrolytes in dilute solution is developed. We find that in salt-free solutions many-body Coulomb interactions between macro- and counterions favor nematic ordering. It is shown that the orientationally isotropic phase of the solution becomes unstable toward nematic ordering at polymer concentration smaller than the overlap concentration. Our predictions are consistent with experimental observations for synthetic polyelectrolytes -phenylene)sulfonates in aqueous solutions.
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