Generalized selectivity description for polymeric ion-selective electrodes based on the phase boundary potential model

A generalized description of the response behavior of potentiometric polymer membrane ion-selective electrodes is presented on the basis of ion-exchange equilibrium considerations at the sample–membrane interface. This paper includes and extends on previously reported theoretical advances in a more compact yet more comprehensive form. Specifically, the phase boundary potential model is used to derive the origin of the Nernstian response behavior in a single expression, which is valid for a membrane containing any charge type and complex stoichiometry of ionophore and ion-exchanger. This forms the basis for a generalized expression of the selectivity coefficient, which may be used for the selectivity optimization of ion-selective membranes containing electrically charged and neutral ionophores of any desired stoichiometry. It is shown to reduce to expressions published previously for specialized cases, and may be effectively applied to problems relevant in modern potentiometry. The treatment is extended to mixed ion solutions, offering a comprehensive yet formally compact derivation of the response behavior of ion-selective electrodes to a mixture of ions of any desired charge. It is compared to predictions by the less accurate Nicolsky–Eisenman equation. The influence of ion fluxes or any form of electrochemical excitation is not considered here, but may be readily incorporated if an ion-exchange equilibrium at the interface may be assumed in these cases.