Comparison of various models to describe the charge-pH dependence of poly(acrylic acid)

The charge of poly(acrylic acid) (PAA) in dilute aqueous solutions depends on pH and ionic strength. We report new experimental data and test various models to describe the deprotonation of PAA in three different NaCl concentrations. A simple surface complexation approach is found to be very successful: the constant capacitance model requires one pKa value and one capacitance for excellent fits to the data, with both parameters depending on ionic strength. The use of a self-consistent set of diffuse double layer parameters with one pKa for flat, spherical, and cylindrical geometry does not result in a satisfactory description of the data, and a number of adjustments to that model were tested to improve the fit. The basic Stern model (BSM) was tested with both plate and cylinder geometry. The cylinder geometry along with strong electrolyte binding was found to be superior to a similar approach involving weak electrolyte binding both in terms of goodness of fit and self-consistency of the parameters. The third approach, the non-ideal competitive consistent adsorption-Donnan (NICCA-Donnan) model, involving one functional group, allows an excellent description of the experimental data. Finally, the polyacid chain was modeled using a mechanistically more realistic self-consistent field (SCF) approach, which allows for radially inhomogeneous distributions of the charges and radial variations in the polymer density and electrostatic potential, while the functional groups can be in protonated, deprotonated, or complexed states. One functional group was insufficient for a satisfactory description of the data. With two segments (one monoprotic, the other diprotic) a reasonable description of the data, including the ionic strength dependence, is achieved, and the tendency of the size of the macro-ion with pH and ionic strength is as expected. This model has the fewest adjustable parameters and is considered the most realistic and comprehensive among the models teste