Non-constancy of the bulk resistance of ionophore-based ion-selective membranes within the Nernstian response range: A semi-quantitative explanation

The non-constancy of the bulk resistance of solvent-polymeric ion-selective membranes containing ionophores is semi-quantitatively explained in view of micro-heterogeneity of membranes due to water uptake. Membranes are considered containing a dispersed aqueous sub-phase (water droplets) within the organic sub-phase (plasticized polymer). It is assumed that charged species in the membrane (ion-ionophore complexes and ion-exchanger ions) are confined in the organic sub-phase owing to their lipophilicity. This entails two inferences: (1) part of the membrane volume is excluded from the transportation of charged species, and (2) the average path length of the charged species transfer across membranes increases because these species have to circumvent water droplets. Because of this, the membrane bulk resistance increases along with the increase of water uptake. The presented results of the theoretical account based on this conjecture are consistent with experimental data. The increase of water uptake alongside the dilution of the external aqueous solution is considered thermodynamically. It is shown that the increase of water uptake from diluted solutions with almost constant chemical potential of water is caused by an interplay between the osmotic pressure, surface tension at the water - polymer matrix curved interface and the elasticity of the membrane matrix.