EXPLORING THE MAXWELL-STEFAN DESCRIPTION OF ION-EXCHANGE

In ion exchange, water and several ions diffuse simultaneously, with d ifferent velocities. They are driven by activity, electrical and press ure gradients. We describe these complicated processes with the Maxwel l-Stefan equation. This equation for multicomponent diffusion requires one diffusivity or friction coefficient for each pair of components i n the mixture. In this article, we explore the behaviour of these coef ficients in the liquid and solid phases of ion exchange. Friction coef ficients between ions and liquid are similar to those between uncharge d species. They increase with the size of the ions, and depend only we akly on composition. Friction coefficients between positive and negati ve ions are much larger, especially between ions with multiple charges . They decrease with increasing concentrations. Ions of like charge us ually have negative friction coefficients; their behaviour mirrors tha t of ions with unlike charges. The many coefficients in the solid can only be obtained by combining data on ion exchange and electrodialysis membranes. In the matrix, we can estimate friction coefficients with water from free solution values and a 'tortuosity' correction. Frictio n between counter-ions and the charged matrix is important. It is much larger than the (free solution with tortuosity) prediction. This is e specially so for ions with multiple charges. This type of friction als o seems to depend on the polymer morphology. At the high concentration s in the matrix, friction coefficients between different counter-ions with a like charge are usually positive. The friction can be appreciab le. Our knowledge of friction coefficients within the solid is still i ncomplete; we end with a few remarks on this.