  We present theoretical and numerical studies on stiff, linear
polyelectrolytes within the framework of the cell model. We first review
analytical results obtained on a mean-field Poisson-Boltzmann level, and then
use molecular dynamics simulations to show, under which circumstances these
fail quantitatively and qualitatively. For the hexagonally packed nematic phase
of the polyelectrolytes we compute the osmotic coefficient as a function of
density. In the presence of multivalent counterions it can become negative,
leading to effective attractions. We show that this results from a reduced
contribution of the virial part to the pressure. We compute the osmotic
coefficient and ionic distribution functions from Poisson-Boltzmann theory with
and without a recently proposed correlation correction, and also simulation
results for the case of poly(para-phenylene) and compare it to recently
obtained experimental data on this stiff polyelectrolyte. We also investigate
ion-ion correlations in the strong coupling regime, and compare them to
predictions of the recently advocated Wigner crystal theories.
