Radial distribution of ions in pores with a surface charge

A sorption model applicable to calculate the radial equilibrium concentrations of ions in the pores of ion-selective membranes with a pore structure is developed. The model is called the radial uptake model. Because the model is applied to a Nafion sulfonic layer with very small pores and the radial uptake model is based on the assumption that continuum equations are applicable, the model is used near its limits of fundamental validity. However, the results indicate that the calculated profiles with the radial uptake model are realistic and similar to literature results (e.g. [J.R. Bontha, P.N. Pintauro, J. Phys. Chem. 96 (1992) 7778; J.R. Bontha, P.N. Pintauro, Chem. Eng. Sci. 49 (1994) 3835]). The membrane microstructure parameters (surface charge density and pore diameter) have been determined by fitting the sorption of sodium as predicted by the radial uptake model to the sorption of sodium as predicted by the so-called modified Pitzer model [J.H.G. Van der Stegen, A.J. van der Veen, H. Weerdenburg, J.A. Hogendoorn, G.F. Versteeg, Fluid Phase Equilibria 157 (1999a) 181]. This modified Pitzer model has proven to be able to predict volume averaged sorption of ions in a sulfonic membrane layer. Via the introduction of a component dependent correction factor in the radial uptake model, the sorption of ions other than sodium could also be fitted to the volume averaged sorption data as predicted by the modified Pitzer model. The correction factors were in the order of magnitude of 0.05–10, and dependent on the concentration of sodium. The necessity of the application of correction factors for the ions other than sodium may have been induced by the assumption that: