Abstract
Protonation equilibria of monomeric acid mixtures and of polyelectrolytes such as polyacrylic acid and fulvic acid have been studied by potentiometry. The observed degree of dissociation (α) as a function of pH obeys a simple integral equation assuming an unknown distribution of various ′intrinsic′ pK sites (f) and a global electrostatic effect for polymers (ΔpK). The latter can be estimated from the cylindrical Poisson-Boltzmann theory. The equation has the familiar form of convolution of signal (f) and response (αsite) functions, and can be solved by standard techniques of spectrum analysis. The resulting pK histogram f(pK) is useful for characterization of acid mixtures and environmental polyelectrolytes. Linear-programming (simplex) algorithm is shown to give a fairly discrete, delta-function-like histogram that successfully reproduces the composition of the acid mixture. Gauss-Seidel least-squares algorithm tends to result in a continuous distribution composed of broader peaks.
