Fraction of Condensed Counterions around a Charged Rod: Comparison of PoissonBoltzmann Theory and Computer Simulations
Abstract
We investigate the phenomenon of counterion condensation in a solution of highly charged rigid polyelectrolytes within the cell model. A method is proposed which  based on the charge distribution function  identifies both the fraction of condensed ions and the radial extension of the condensed layer. Within saltfree PoissonBoltzmann (PB) theory it reproduces the well known fraction 11/xi of condensed ions for a Manning parameter xi>1. Furthermore, it predicts a weak salt dependence of this fraction and a breakdown of the concept of counterion condensation in the high salt limit. We complement our theoretical investigations with molecular dynamics simulations of a celllike model, which constantly yield a stronger condensation than predicted by PB theory. While the agreement between theory and simulation is excellent in the monovalent, weakly charged case, it deteriorates with increasing electrostatic interaction strength and, in particular, increasing valence. For instance, at a high concentration of divalent salt and large xi our computer simulations predict charge oscillations, which meanfield theory is unable to reproduce.
 Publication:

Macromolecules
 Pub Date:
 January 2000
 DOI:
 10.1021/ma990897o
 arXiv:
 arXiv:condmat/9906277
 Bibcode:
 2000MaMol..33..199D
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics
 EPrint:
 8 pages, 6 figures, using RevTeX style, revised version, 1 figure and more pertinent remarks concerning the failure of the energy criterion