Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties

TLDR

Counterion condensation on polyions reduces their charge density below a critical value, a key observation underpinning the theory. The authors derive limiting‑law expressions for the osmotic coefficient, Donnan salt‑exclusion factor, and mobile‑ion activity coefficients, treating uncondensed ions within the Debye–Hückel approximation. Comparison with literature data demonstrates quantitative agreement between the theory and experiment.

Abstract

Formulas are derived for the osmotic coefficient, the Donnan salt-exclusion factor, and the mobile-ion activity coefficients in a polyelectrolyte solution with or without added sample salt. The formulas, which contain no adjustable parameters, are based on the (theoretical) observation by several workers that counterions will “condense” on the polyion until the charge density on the polyion is reduced below a certain critical value. The uncondensed mobile ions are treated in the Debye–Hückel approximation. In a restricted sense, the formulas are “limiting laws,” and this aspect is discussed at length. Detailed comparison with experimental data in the literature is given; agreement of the theory with experiment is usually found to be quantitative.