Nikolski selectivity coefficient

The Nikolsky equation (3.1.7) frequently corresponds to the ise versus logflj dependence only in those regions where (3.1.8) or (3.1.10) is valid and is thus of ten only an operational formula with the same asymptotes as the actual ise versus log aj dependence. Nonetheless, the selectivity coefficient obtained from (3.1.7) is important in estimating the ISE selectivity, although this equation cannot be used where the igE versus log aj dependence is clearly curved. In the intercept of the asymptotes to (3.1.7), log aj has value log further discussion the operational value of the... 

Thus the Nikolsky equation (3.1.7) with selectivity coefficient... 

If the diffusion potential in the membrane is neglected, this equation yields relationships for the membrane potential, for the ISE potential and for the selectivity coefficient. It is apparent that formation of complexes with various numbers of ions in the membrane does not affect the dependence of the ISE potential on the activities of the determinand and interferent according to the Nikolsky equation. 

The fixed interference method (FIM). The potential of an ion-selective electrode is measured in solutions of constant activity of interfering ion (a,-) and varying activity of the primary ion (a,). The selectivity coefficient, K ", is calculated from the relevant calibration graph plotted for the ion of interest, i. The intersection of the extrapolated linear portions of the response curve indicates the value of a, which is used to calculate Kp° from the Nikolsky-Eisenman equation ... 

The separate solution method (SSM). The potential of a cell comprising an ISE and a reference electrode is measured in two separate solutions one containing only the primary ion i ( )), the other containing the interfering ion j (Ej), at the same activity (a, = aj). The value of the selectivity coefficient can be calculated on the basis of the Nikolsky-Eisenman equation ... 

This fundamental equation was introduced by Boris P. Nikolsky (1900-1990) in 1939 after returning from the Gulag at White Sea-Baltic Canal. It is valid both for finely-dispersed bodies and for high-molecular ionites. However, exchange coefficients, like selectivity coefficients, are no constants as their value depends on the type of ground, adsorbate and on water composition. Nevertheless, they are most widely used. For the fresh water where activities coefficients of dissolved ions are close to 1, is valid equation... 

Despite the wide use of the Nikolsky-Eisenman equation and the selectivity coefficients, it is not so obvious whether this equation is valid when both analyte and interfering ions significantly contribute to the phase boundary potentials (for example, near the detection limit in Figure 7.2B). The equation was originally derived under equilibrium conditions for ions with the same charge number (specifically, Zi = Zj = 1) and then extended empirically (40). The experimental potentiometric responses in mixed ion solutions may deviate from the Nikolsky-Eisenman equation when the (1) experimental... 

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... 

When using the selectivity constant or coefficient (k) mentioned by ISE suppliers, one must be sure that if the ion under test and the interfering ion have different valence the exponent in the activity term according to Nikolski has been taken into account it has become common practice to mention the interferent concentration that results in a 10% error in the apparent ion concentration these data facilitate the proper choice of an ISE for a specific analytical problem. Often maximum levels for no interference are indicated. 

In view of the diffusion theories it was assumed that K is affected by the mobilities of the ions in the membrane, thus the potentiometric selectivity, + K, but - m K, where m is the ratio of the mobilities of the two competing ions in the membrane or a more complicated function (see Eisenmann [9]). is the coefficient to be inserted into the Nikolsky equation. 

---