The Theory of Liquid Ion-exchange Membrane Ion-selective Electrodes Based on the Concept of the Mixed Ion-transfer Potential

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Abstract
The theory of liquid ion-exchange membrane ion-selective electrodes has been developed on the basis of the concept of the zero-current potential, or the mixed potential in the presence of interfering ions, of ion transfer at the interface between a liquid membrane and a sample solution. Under the assumptions of the reversible ion transfer at the interface, the presence of supporting electrolytes in both phases, and the monovalency of all relevant ions, theoretical equations for the mixed potential are derived for two cases; the primary and interfering ions have 1) the same charge sign and 2) the opposite sign. The selectivity coefficients of the ion-selective electrodes can be expressed as a function of the difference between the standard ion-transfer potentials of the primary and interfering ions, the ratios of the mass-transfer coefficients of the ions, and the ratios of the concentrations of the ions. The theoretical prediction has been shown to be applicable to an interpretation of the response of liquid-membrane ion-selective electrodes.