The Osmotic Pressure of Electrostatically Stabilized Colloidal Dispersions

A mathematical model for predicting the osmotic pressure of electrostatically stabilized colloids has been developed. The model is based on detailed descriptions of the colloidal interactions within an electrostatically stabilized dispersion. Electrostatic interactions are accounted for by a Wigner-Seitz cell approach including a numerical solution of the nonlinear Poisson-Boltzmann equation. London-van der Waals forces are calculated using a computationally efficient means of approximating screened, retarded Lifshitz-Hamaker constants. Configurational entropy effects are calculated using an equation of state giving excellent agreement with molecular dynamic data. These descriptions of colloidal interactions are used to develop an a priori model, with no adjustable parameters, that allows quantitative prediction of the osmotic pressure of colloidal dispersions as a function of zeta potential (and hence pH), colloid size, ionic strength, and colloid concentration. The model shows good agreement with literature experimental data for the osmotic pressure of the protein bovine serum albumin (BSA). A charge regulation model for the BSA surface has also been developed from knowledge of the amino acid groups giving rise to the protein charge. A comparison of zeta potentials calculated from this model with experimentally determined values for dilute BSA dispersions shows good agreement for a wide range of conditions. The charge regulation model has also been incorporated into the osmotic pressure prediction, resulting in excellent agreement between theory and experiment.