Studies on the matched potential method for determining the selectivity coefficients of ion-selective electrodes...

A theory is presented that describes the matched potential method (MPM) for the determination of the potentiometric selectivity coefficients (KA,Bpot) of ion-selective electrodes for two ions with any charge. This MPM theory is based on electrical diffuse layers on both the membrane and the aqueous side of the interface, and is therefore independent of the Nicolsky-Eisenman equation. Instead, the Poisson equation is used and a Boltzmann distribution is assumed with respect to all charged species, including primary, interfering and background electrolyte ions located at the diffuse double layers. In this model, the MPM-selectivity coefficients of ions with equal charge (ZA = ZB) are expressed as the ratio of the concentrations of the primary and interfering ions in aqueous solutions at which the same amounts of the primary and interfering ions permselectively extracted into the membrane surface. For ions with unequal charge (ZA not equal to ZB), the selectivity coefficients are expressed as a function not only of the amounts of the primary and interfering ions permeated into the membrane surface, but also of the primary ion concentration in the initial reference solution and the delta EMF value. Using the measured complexation stability constants and single ion distribution coefficients for the relevant systems, the corresponding MPM selectivity coefficients can be calculated from the developed MPM theory. It was found that this MPM theory is capable of accurately and precisely predicting the MPM selectivity coefficients for a series of ion-selective electrodes (ISEs) with representative ionophore systems, which are generally in complete agreement with independently determined MPM selectivity values from the potentiometric measurements. These results also conclude that the assumption for the Boltzmann distribution was in fact valid in the theory. The recent critical papers on MPM have pointed out that because the MPM selectivity coefficients are highly concentration dependent, the determined selectivity should be used not as "coefficient", but as "factor". Contrary to such a criticism, it was shown theoretically and experimentally that the values of the MPM selectivity coefficient for ions with equal charge (ZA = ZB) never vary with the primary and interfering ion concentrations in the sample solutions even when non-Nernstian responses are observed. This paper is the first comprehensive demonstration of an electrostatics-based theory for the MPM and should be of great value theoretically and experimentally for the audience of the fundamental and applied ISE researchers.