Effects of Ion Size and Valence on Ion Distribution in Mixed Counterion Systems of a Rodlike Polyelectrolyte Solution. 2. Mixed-Valence Counterion Systems†

The characteristics of the ion distributions are investigated in the systems of salt-free polyelectrolyte solution with mixed-valence counterions using a cylindrical cell model. The mixtures of two species of the counterion having different valences are simulated systematically by means of the Monte Carlo method in a primitive model of the rodlike polyelectrolyte solution. The comparisons of the free fractions and the selectivity coefficients by this method are performed with the numerical solutions of the Poisson−Boltzmann equation. A significant accumulation of the multivalent counterions found in the Monte Carlo simulations is examined under various conditions. The differences between both methods and additional effects of ion size are discussed in terms of the relation to the simple counterion condensation theory and the effect of ion−ion correlations.