The determination of diffusion coefficients of counter-ions in the ion-exchange membrane by means of batchwise Donnan dialytic experiments

A new method, based on the Nernst-Planck equation, has been proposed for determining diffusion coefficients of counter-ions in an ion-exchange membrane for bi-ionic Donnan dialysis. This method involves dialytic experiments in which both the solution concentration and the membrane potential are measured under the condition controlled by diffusion resistance in the membrane. It also involves mathematical optimization treatment of the experimental data. The K⁺-H⁺ system with a cation-exchange membrane was studied, and the optimum diffusion coefficients of these counter-ions were obtained. The diffusion coefficients were found to vary with the ionic composition of the solution. The theoretical time courses of the concentration and membrane potential calculated by using the optimum diffusion coefficients agreed with the experimental results.