  The osmotic coefficient of solutions of rod-like polyelectrolytes is
considered by comparing current theoretical treatments and simulations to
recent experimental data. The discussion is restricted to the case of
monovalent counterions and dilute, salt-free solutions. The classical
Poisson-Boltzmann solution of the cell model correctly predicts a strong
decrease in the osmotic coefficient, but upon closer look systematically
overestimates its value. The contribution of ion-ion-correlations are
quantitatively studied by MD simulations and the recently proposed DHHC theory.
However, our comparison with experimental data obtained on synthetic,
stiff-chain polyelectrolytes shows that correlation effects can only partly
explain the discrepancy. A quantitative understanding thus requires theoretical
efforts beyond the restricted primitive model of electrolytes.
