Evaluating alternative electrostatic potential models for polyacrylamide-co-acrylate in aqueous solution

The capabilities of three simplified analytical equations to accurately model electrostatic interactions during proton binding and release by linear anionic polyelectrolytes in aqueous solution were evaluated. The impermeable sphere (IS), Donnan (DN), and cylindrical (CY) electrostatic models were fit to experimental acid-base titration curves of linear polyacrylamide-co-acrylate having ionizable site densities ranging from ca. 10-35%. The titrations were conducted in 0.003-0.12. M NaCl solutions and the sum of squared errors from modeled and experimental data was used as a comparative index of each model's capability. In addition, the relative size of each polyelectrolyte was estimated from its measured specific viscosity and then compared against the values obtained from the fitting procedure for the size parameter that each model contained. Although the IS and DN electrostatic models could be used to obtain reasonably good fits to each titration curve, the size parameter values obtained by each model were not reflective of the actual polyelectrolyte sizes, indicating that the models had limited physical meaning and that the size parameter was essentially just an additional fitting parameter in each model. In contrast, the CY model was not only more effective in its ability to fit the titration data but also provided a better physical representation of the polyelectrolyte size. Therefore, for polyelectrolytes that remain essentially linear or are only loosely coiled such that counter ions are free to travel throughout the polymer structure, we conclude that the CY model and its morphological representation of a cylindrical polyelectrolyte are more valid and realistic than the IS and DN models and their representation of polyelectrolytes as spheres.