A unified analytical treatment of the acid-dissociation equilibria of weakly acidic linear polyelectrolytes and the conjugate acids of weakly basic linear polyelectrolytes

The influence of added sodium chloride concentration levels on the acid-dissociation equilibria of a weakly acidic linear polyelectrolyte and a conjugate acid of weakly basic linear polyelectrolyte has been investigated potentiometrically by use of polyacrylic acid (PAA) and poly(N-vinylimidazole) (PVIm) as examples of polyelectrolytes. Both equilibria are strongly influenced by the degree of dissociation of the polyacids as well as the concentration levels of sodium chloride due to an electrostatic effect originating from the negatively or positively charged polymer surfaces. These have been analyzed in a unified manner by taking accounts of two-phase properties of the charged linear polyions. Distribution of counterions and coions between a polyelectrolyte phase formed around the polymer skeleton and a bulk solution phase has been rationalized by a Donnan’s relation. Introduction of a volume term for the polyelectrolyte phase permits definition of averaged concentrations of mobile ions in the vicinity of the polyion molecules, which enables us to define hypothetical intrinsic acid-dissociation constants in the polyion domain. The intrinsic constants estimated by extrapolation of apparent acid-dissociation constants at zero-charge state are in good agreement with the acid-dissociation constants of the monomer analogs of the polymers, i.e., acetic acid for PAA and imidazole for PVIm, respectively. The difference between the apparent and intrinsic acid-dissociation constants for PVIm was much higher than that for PAA at defined degree of dissociation of the polyacids, even though the separations of the functionalities fixed on the linear polymers are approximately equal to each other.