Selectivity of polymer membrane-based ion-selective electrodes: self-consistent model describing the potentiometric response in mixed ion solutions of different charge.

Despite its well-documented limitations, the semiempirical Nicolsky-Eisenman equation is used throughout the existing analytical literature to describe the selectivity of modern polymer membrane-based ion-selective electrodes (ISEs). In this paper, a new quantitative description for the response/selectivity function based on ion-extraction equilibria at the sample/membrane interface is presented. The proposed selectivity formalism clearly illustrates the range of validity for the conventional Nicolsky-Eisenman formalism. Extended equations are derived describing the electrode response in an exact manner, particularly with respect to analyte and interfering ions of different charge. The expression obtained corresponds to the matched potential method proposed previously by Christian and co-workers on the basis of solely empirical observations. Selectivity coefficients required for a given analytical problem with a predefined maximum error can now be predicted more accurately. Such predictions with respect to analyte and interfering ions of varying charges differ by 1-2 orders of magnitude in comparison to the selectivity values required on the basis of the extended Nicolsky-Eisenman formalism.