The Nikolsky-Eisenman equation and phase boundary potential model

1 The Nikolsky-Eisenman equation and phase boundary potential model 

Most ionophores form complexes not only with the analyte ion but also with the aqueous co-ions. Interference by co-ions is a major origin of experimental errors in the analysis. The Nemst equation (7.1.1), however, does not describe the contribution of the interfering ions to the measured potential. Traditionally, the influence of the interfering ions on the potentiometric responses has been described using the Nikolsky-Eisenman equation (38) 

Importantly, the potentials must be measured in activity ranges in which the electrode responses are Nemstian to the ions (39). While this requirement for equilibrium conditions 

To address the theoretical limitation of the Nikolsky-Eisemnan equation, a more general description of the equihbrium responses of hquid membrane ISEs in mixed ion solutions was proposed (41). The model is based on phase boundary potentials under an equilibrium exchange of an analyte and an interfering co-ion at the membrane/sample solution interface. With ionophore-based membranes, the ion-exchange process is followed by complexation of the ions with an ionophore, where free ionophore was assumed to be always present in excess to simplify the model. The charge of the ions was not fixed so that their effect on the potentiometric responses can be addressed by the model. Under equilibrium conditions, the model demonstrated that the Nikolsky-Eisemnan equation is valid only for ions with the same charge (zj = Zj). The selectivity coefficient, however, can still be used in the new model to quantify the potentiometric responses in the mixed ion solution. For example, the potentiometric responses to a monovalent cation in the presence of a divalent cation are given as 

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