A simple procedure for estimating ion coupling from conventional transport coefficients

A simple correlation between membrane conductance, transport numbers and salt leak gives the coupling coefficient, R₁₂, between the anion and cation flows. For R₁₂ = 0, the leak-conductance (LC) ratio is ω_sc_s′/(κ/F²) = τ₁τ₂. If ion and water flows are coupled, osmotic and electroosmotic flow at zero pressure complicate this correlation, enhancing conductance and suppressing salt leak and perm-selectivity. An analysis of transport in hydrophobic membranes, in terms of local equilibria, shows that strong ion association leads to substantial coupling between ion flows. This is expressed in R₁₂ < 0, and ω_sc_s′/(κ/F²) > τ₁τ₂. Applications to experimental results on various membranes show a clear classification by LC ratio into two groups: hydrophobic membranes in which the flows of ion 1 and 2 are coupled, and aqueous membranes in which the important interactions are between that of the ions and water.