On the Origin of the Membrane Potential Arising Across Densely Charged Ion Exchange Membranes: How Well Does the Teorell-Meyer-Sievers Theory Work?

A difference in salt concentration in two solutions separated by a membrane leads to an electrical potential difference across the membrane, also without applied current. A literature study is presented on proposed theories for the origin of this membrane potential (ϕm). The most well-known theoretical description is Teorell-Meyer-Sievers (TMS) theory, which we analyze and extend. Experimental data for ϕm were obtained using a cation exchange membrane (CMX, Neosepta) and NaCl solutions (salt concentration from 1 mM to 5 M). Deviations between theory and experiments are observed, especially at larger salt concentration differences across the membrane. At a certain salt concentration ratio, a maximum in ϕm is found, not predicted by the TMS theory. Before the maximum, TMS theory can be used as a good estimate of ϕm though it overestimates the actual value. To improve the theory, various corrections to TMS theory were considered: A) Using ion activities instead of ionic concentration in the external solutions leads to an improved prediction; B) Inhomogeneous distribution of the membrane fixed charge has no effect on ϕm; C) Consideration of stagnant diffusion layers on each side of the membrane can have a large effect on ϕm; D) Reducing the average value of the fixed membrane charge density can also largely affect ϕm; E) Allowing for water transport in the theory has a small effect; F) Considering differences in ionic mobility between co-ions and counterions in the membrane affects ϕm significantly. Modifications C) and F) may help to explain the observed maximum in ϕm.