Nicolsky equation

A general equation, called the Nicolsky equation, can be written for mixtures of two ions of different charges ... 

The above discussions illustrate the ideal application of the Nicolsky equation. As mentioned, selectivity coefficients may not be really constant, and the values determined will depend on the method of evaluation. One of two approaches is generally... 

We mentioned that selectivity coefficients determined using the Nicolsky equation often vary, depending on relative concentrations and measurement conditions, and the equation does not dpply if the response is non-Nemstian (often the case with secondary ions). The matched potential method is an attempt to deal with this. Bakker and co-workers introduced a new formulism that provides a.clear interpretation of the matched potential method, elegantly deriving an equation based on ion exchange in which the last term in Equation 13.49 becomes where... 

In practice, the selectivity of polymer membrane electrodes can be evaluated using the well known Nicolsky equation ... 

Ions with the same charge sign as the analyte may be sensed by the electrode. In this case, the Nicolsky equation is often approximately valid ... 

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

The Nicolsky equation With common pH instruments, the Nemst equation can accurately predict the pH of an unknown solution, over the pH range 2 to 12. At more extreme values of pH, some response to other ionic species in solution begins to become apparent. This is the so-called salt error. For example, a vahnomydn-doped BLM for K" " suffers from some interference because of Na+. A better equation proposed by Nicolsky should be used. Accordingly,... 

Chloride activity measurements are done in the same manner as the potassium measurements, except that the Nernst equation was used instead of the Nicolski equation to describe the potential difference due to the difference of chloride activities between the inside and outside of the cell. We know that there are no interfering ions in the solution on the outside. We assume that there are no interfering anions inside the cell. This assumption is necessary because we simply do not have any information about what ions are present and what their activities are. 

Necturus maculosus. Renal Tubules, 109 Nephron, Ionic Activities, 77, 89, 109 Nernst Equation, 14, 166 Nicolsky Equation, 14-15, 146, 160... 

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 ... 

The Nicolsky-Eisenmann equation or its different varieties [6,7] give a theoretical background for the determinations. The equation was proposed originally for explaining the alkaline ion interferences (the alkaline error) observed in the case of pH-selective glass electrodes ... 

The Nicolsky-Eisenmann equation supposes that the response of the primary and the interfering ions is similar. It is generally not true. More complex equations, for example [8], can give better fitting to the experimental observations. 

In the equal activity (concentration) method, a vertical line is drawn in the dynamic range of the electrode response of the calibration graph. We read the j and 2 1" ues and get the A = j - 2 difference. From the simplified Nicolsky-Eisenmann equation, we obtain... 

Indexes just indicate that the AE is measured in mV and S in mV/decade units. In reality, however, the two calibration curves are not parallel. The Nicolsky-Eisenmann equation is not rigorously followed. Therefore, depending on where the horizontal or vertical lines are drawn, different selectivity coefficient values can be obtained with the separate solution methods. Therefore, it is recommended that the selectivity coefficient be measured in the range of the ionic concentration of the samples using mixed solution methods. 

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