Journal of Membrane Science, Vol.240, No.1-2, 25-35, 2004
Statistical mechanics of diffusion in polymers - Conductivity and electroosmosis in ion exchange membranes
The dependency of swelling of an ion exchange membrane and its ion-exchange capacity on the conductivity and electroosmosis are investigated. The analysis is based on a rigorous statistical mechanics theory employing the formalism of the generalized Nernst-Planck equation in the dusty gas membrane model. The simulation uses binary diffusivities computed from experimental data. Some unexpected conclusions can be drawn from the computed transport characteristics: at constant swelling of the polymeric membrane the equivalent conductivity decreases with the exchange capacity; the enhancement of conductivity by electroosmosis is rather poor, in all cases smaller than 15%; conductivity of the material is more dependent on its exchange capacity than on swelling. The calculations confirm that an optimized membrane with low electroosmosis is a highly charged membrane with low swelling. We show that the simple binary theories lead to wrong predictions of the conductivity even qualitatively. Finally, we propose a simple empirical theory, compatible with the generalized Nernst-Planck equation, where the diffusivities increase exponentially with swelling. (C) 2004 Elsevier B.V. All rights reserved.