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.