Counterion condensation theory revisited: Limits on its applicability



Metropolis Monte Carlo and Poisson–Boltzmann calculations were done to quantitatively assess the conditions under which counterion condensation (CC) theory could be considered valid. The fundamental prediction of condensation theory, that the number of counterions bound to a polyelectrolyte molecule can be predicted by a single parameter describing the linear charge density of the charged system, was shown to be quantitatively correct for a range of conditions. To define the number of counterions bound, it was necessary to use an energy-based criterion by which ions that interact with the polyion with an energy less than –kT were considered bound. Using this criterion, Monte Carlo calculations on systems consisting of charged cylinders and a neutralizing number of counterions in a dielectric continuum showed that the number of bound counterions was quantitatively predictable by the CC relation (1–1/ξ) for systems with a linear charge density and dimensions approaching those of duplex or triplex DNA. Poisson–Boltzmann (PB) calculations on cylinders with different linear charge densities and radii have been done to assess the limits of the CC prediction that the number of counterions bound is a constant even as the bulk concentration of electrolyte in the surrounding is increased. As in the case of the MC calculations, the validity of the CC prediction is seen to increase with increasing linear charge density of the charged cylinder. The agreement between PB and CC is seen to be very good for highly charged cylinders. The results described here provide justification for the use of CC theory for interpreting experimental data on polyelectrolytes of the approximate dimensions and linear charge density of duplex or triplex DNA. © 1993 John Wiley & Sons, Inc.