Nikolski-Eisenman equation

Use the Nikolski-Eisenman equation to explain why lowering the detection limit requires careful attention to the selectivity of the resulting ISE. 

In practice, however, deviation from the ideal electrode behavior is common, and an additional contribution to the total measured ion activity has to be considered due to the presence of the interfering ion j in the sample solution. Under these conditions the ion-selective electrode potential can be approximated by the Nikolsky-Eisenman 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 ... 

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)... 

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... 

The Nikolsky-Eisenman equation and a more general phase boundary model discussed in Section 7.3.1 are based on a common assumption that a well-defined amount of a free ionophore is always present in the membrane, implying that the membrane always functions on the basis of an ionophore-based mechanism. As discussed in Section 7.3.2, however, the... 

The non-equilibrium ion-exchange processes can cause deviation of the potentiometric responses from those predicted by the Nikolsky-Eisenman equation and the equilibrium phase boundary potential model. 

An ideal analytical sensor should specifically and quantitatively detect a single ion. This would mean that the membrane potential would be affected by only one particular ion in solution. Potentiometric probes are rarely specific to a given ion and are commonly selective to a series of ions. Their response will selectively respond to a certain type of ion but will be affected by the presence of other ions leading to interferences. In the case of a solution with only two types of ions where ion (j) wonld interfere with the potentiometric response of the primary ion (i), the measnred cell potential can be approximated to the Nikolsky-Eisenman equation ... 

Due to the temperature dependence, the potentiometric measurements must be carried out at a constant temperature. If interferences are relevant, an extended expression of the Nemst equation, the Nikolsky-Eisenman equation, should be used (Scholz, 2010) ... 

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