A phase boundary potential model for apparently "twice-Nernstian" responses of liquid membrane ion-selective electrodes

A model that describes divalent cation responses of liquid membrane ion-selective electrodes based on acidic ionophores and ionic sites is presented. Response slopes for membranes with ionophore and anionic sites are predicted to change from Nernstian to apparently "twice-Nernstian" and then back to Nernstian again as the pH of the sample solution decreases, A maximum measuring range for apparently "twice-Nernstian" responses is expected for membranes with 50 mol % anionic sites relative to the ionophore, On the other hand, membranes with ionophore and cationic sites are expected to give only Nernstian responses, either to divalent cations at high pH or to H+ at low pH. The validity of the present model has been confirmed experimentally with the two Ba2+-selective carboxylate ionophores monensin and lasalocid and the Ca2+-selective organophosphate ionophore bis(2-heptylundecyl) phosphate. Addition of anionic sites gave apparently "twice-Nernstian" slopes for monensin at pH 7.0 (56.6 mV/decade), for lasalocid at pH 4.0 (53.3 mV/decade), and for bis(2-heptylundecyl) phosphate at pH 3.5 (53.6 mV/decade). Membranes with cationic sites showed only pH responses at the respective pH, The apparently "twice-Nernstian" responses as discussed here are the first examples of super-Nernstian responses that can be explained with a quantitative model based on thermodynamic equilibria.