Potentiometric Acid−Base Titration of a Colloidal Solution

Abstract

An improved method for evaluating acid−base titration data obtained from the potentiometric titration of solutions containing highly charged colloidal particles, such as proteins or ionic micelles, is presented. The use of the method is demonstrated in the determination of the charge number, as a function of pH, of a colloid, in this case the protein lysozyme titrated in differing sodium chloride concentrations. The method involves an improved calculation of the electrostatic potential and the concentration profiles of ions, e.g., the hydrogen ion, surrounding the charged colloidal particles. It uses a numerical program that solves the Poisson−Boltzmann (PB) equation in a cell model. Knowledge of the concentration profile of hydrogen ions enables a correct calculation of the amounts of hydrogen ions that have protonated the protein, thus the charge number at differing pH. The PB calculation provides an estimation of the solution concentration of hydrogen ions at the surface of the protein. It is shown that this surface concentration correlates well with the charge number on the protein over the wide pH range of 1.5−12, thus also at highly acidic pH, where the colloid is highly charged. This has been difficult to achieve before.