Comparison of Poisson‐Boltzmann and condensation model expression for the colligative properties of cylindrical polyions

Abstract

Abstract Closed‐form expression have been derived for the polyelectrolyte contribution to the colligative properties of solutions containing rodlike polyions in the presence of excess added salt. The derivations are based on: the conventional Poisson‐Boltzmann equation for cylindrical symmetry; the thermodynamics of the cell model developed by Marcus [ J. Chem. Phys. 23 , 1057–1068 (1955)]; and an equation derived from the cylindrical Poisson‐Boltzmann cell model by Anderson and Record [ Biophys. Chem. 11 , 353–360 (1980)]. Subject to the inherent limitations of the Poisson‐Boltzmann approximation [Fixman (1979) J. Chem. Phys. 70 , 4995–5005], the resulting expressions are nevertheless applicable outside the “limit of infinite dilution.” They conform over a range of salt concentrations to the limiting laws deduced by Manning from the hypothesis of counterion condensation [ J. Chem. Phys. 51 , 924–933 (1969)]. This hypothesis is found to be compatible with the Poisson‐Boltzmann cell model but is not required in the derivation of the thermodynamic coefficients presented here. It is demonstrated that the magnitude of the polyion axial charge density plays a critical role in determining the low‐salt limiting forms of the colligative properties obtained from the Poisson‐Boltzmann equation, in close analogy with Manning's model.