Nicolsky-Eisenman equation

The Nicolsky-Eisenman equation (15-8) is predicated on equal charges for the primary (A) and interfering (X) ions [E. Bakker, R. Meruva, E. Pretsch, and M. Meyerhoff, Selectivity of Polymer Membrane-Based Ion-Selective Electrodes, Anal. Chem. 1994, 66, 3021]. Recipes for measuring selectivity... 

A convenient approach to the case is the use of ANNs, as first demonstrated by the seminal work by Bos and Van der Linden [46]. ANNs generate black-box models, which have shown special abilities to describe nonlinear responses obtained with sensors of different families. Unfortunately, these tools create models only from a large amount of departure information, the training set, which must be carefully obtained [47]. The extra information is in account of the absence of a thermodynamical or physical model, for example the Nicolsky-Eisenman equation. 

Figure 45.3 shows the response surface obtained for ammonium ISE in presence of potassium ion as interference. This surface has been generated from the experimental data of the seven previous calibration sequences, fitting them to the Nicolsky-Eisenman equation with SigmaPlot 2000 software and plotted with 3D visualization options. The experimental data also appear in the figure as black symbols. In the same way, the fitted response surfaces for potassium and generic ISEs can be easily generated. 

An alternative to the Nicolsky-Eisenman equation to model this space is using an electronic tongue that consists of an array of nonspecific, poorly selective, chemical sensors with cross-sensitivity to different compounds in the solution, and an appropriate chemometric tool for the data processing. In our case, three ISEs and an ANN model is used. 

Potentiometric detectiOTi is based on the induced potential on a membrane which is semi-permeable and ion selective. When certain ions pass through the semipermeable membrane while others do not, different ion activities at both sides of the membrane result in the buildup of a potential difference which is measured and monitored against a fixed potential of a reference electrode. A unique feature of potentiometric detection is that the detection signal does not scale down when the size of the electrode decreases. The potential response of the membrane electrode is given by the Nicolsky-Eisenman equation ... 

Historically, potentiometric selectivity coefficients were used to assess the extent of interference in a mixed sample by use of the so-called Nicolsky-Eisenman equation [9] ... 

When the electrode is selective for but not specific to the ion of interest (the principal ion), the Nicolsky-Eisenman equation applies (Eq. 3) ... 

Figure 7.3 Sodium calibration curves in a background of 0.001 or 0.0001 M CaCl2, for an Na+-selective electrode based on a membrane of Na+-2 in DOS/PVC (2 1, w/w). Solid line according to equation (7.3.6) dotted lines according to Nicolsky-Eisenman equation (7.3.1) when Na+ (upper curve) or Ca (lower curve) is assumed to be the primary ion. From reference (41). Copyright 1994 American Chemical Society.

The potential response of the membrane electrode is given by the Nicolsky-Eisenman equation ... 

This equation was first derived by Nicolsky in 1937, who thus introduced the potentiometric selectivity coefficient. Later some authors empirically extended it for ions of different charges using as the second term in Equation 22.8. The resulting empirical Nicolsky-Eisenman equation is, however, inconsistent since different results are obtained if the two ions are interchanged. This led to plenty of confusions, and different other selectivity measures were proposed since the simple fundamental meaning of Kff was not recognized. 

The fixed interference method (FIM) The potential of the ISE is measured in solutions of constant activity of interfering ion, Uj and varying activities of the primary ion. The selectivity coefficient, Kf/ , 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 from the Nicolsky-Eisenman equation ... 

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

The previously accepted the so-called Nicolsky-Eisenman equation, written as... 

Another type of indicator electrodes are the ion-selective electrodes (ISEs). The potential of an ISE follows the Eisenman-Nicolsky equation ... 

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