Selectivity of Polymer Membrane-Based Ion-Selective Electrodes: Self-Consistent Model Describing the Potentiometric Response in Mixed Ion Solutions of Different Charge

Abstract

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.

Studies on the Matched Potential Method for Determining the Selectivity Coefficients of Ion-Selective Electrodes Based on Neutral Ionophores: Experimental and Theoretical Verification

“…[8][9][10][11][12][13][14][15]32 Selectivity coefficients obtained with the MPM reflect the extent of the interference of the practically observed response to the primary ion from various interfering ions. However, it has been pointed out that the MPM is not bound by any model assumption, and therefore the values of the MPM-selectivity coefficient in general lack a predictive ability about the membrane potentials measured with solutions other than those for which it was determined.…”

“…Therefore, the determined MPM selectivity should be used not as "coefficient", but as "factor". 14,15 For mixed ion samples containing the primary and interfering ions, the phase boundary potential can be calculated by a mathematical replacement of the activity of the interfering ion by that of the primary ion. Interestingly, the selectivity factor (k IJ Psel ) derived from the mixed potential model for ions with unequal charge numbers (zA ≠ zB) has no power term.…”

“…Unfortunately, the definition of the selectivity factor (k IJ Psel ) in the mixed potential model is different from that of the MPM-selectivity coefficient: the value of k IJ Psel is given by the ratio of primary and interfering ion activities in the sample solution, which give, when separately measured, the same membrane potential. 14,15 In this paper, a theory based on diffuse double layers 16,17,[25][26][27] is presented that describes directly the MPM-selectivity coefficient for two ions of any charge with the assumption that distribution equilibrium is reached both for the primary and interfering ions at the membrane surface. The validity of the proposed MPM theory were confirmed by comparing the absolute values of the MPM-selectivity coefficients determined from the EMF measurement and those calculated by the proposed theory with the measured complexation stability constants and single ion distribution coefficients for the same systems.…”

“…(1) is now known to be incorrect when two ions of different charges (zA ≠ zB) significantly contribute to the membrane potential. 14,15 This fact implies that the FIM selectivity coefficient based on Eq. (1) is not valid for ions with zA ≠ zB.…”

“…(1) is not valid for ions with zA ≠ zB. However, only recently, a so-called "mixed potential model" was proposed to correctly describe the potentiometric response to mixed ions with different charges, 14,15 which leads to a modification of the FIM selectivity coefficient, K A,B pot , in the Nicolsky-Eisenman equation. Another problem is that K A,B pot in…”