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We investigate the phenomenon of counterion condensation in a solution ofhighly charged rigid polyelectrolytes within the cell model. A method isproposed which -- based on the charge distribution function -- identifies boththe fraction of condensed ions and the radial extension of the condensed layer.Within salt-free Poisson-Boltzmann (PB) theory it reproduces the well knownfraction 1-1/xi of condensed ions for a Manning parameter xi>1. Furthermore, itpredicts a weak salt dependence of this fraction and a breakdown of the conceptof counterion condensation in the high salt limit. We complement ourtheoretical investigations with molecular dynamics simulations of a cell-likemodel, which constantly yield a stronger condensation than predicted by PBtheory. While the agreement between theory and simulation is excellent in themonovalent, weakly charged case, it deteriorates with increasing electrostaticinteraction strength and, in particular, increasing valence. For instance, at ahigh concentration of divalent salt and large xi our computer simulationspredict charge oscillations, which mean-field theory is unable to reproduce.Comment: 8 pages, 6 figures, using RevTeX style, revised version, 1 figure and  more pertinent remarks concerning the failure of the energy criterio

Fraction of Condensed Counterions around a Charged Rod: Comparison of Poisson−Boltzmann Theory and Computer Simulations