Nikolski equation

As a consequence, the Nikolski equation will be more complicated, especially if the interfering ion has a different valence. For instance, when, in addition to the ion A with valence zA, the interfering ion B has a valence zB, the ion-exchange equilibrium (cf., eqn. 2.76) is... 

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... 

Fig. 3.1. Dependence of ise on activity of the determinand J Curve 1 data according to Nikolsky equation (3.1.7). Curve 2 limit of detection.

It can be seen that different charge numbers on the participating ions considerably complicate the resultant expression, which no longer has the form of the Nikolsky equation (3.1.7) (similar complications occur in the Planck liquid-junction theory). TheE igE versus logajt(l) dependence (see fig. 3.3, plotted for /Tejjch7j 7K + A = 1.25 x 10" and const = 0) is characterized by asymptotes... 

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. 

With an ideal electrode (5.26) and (5.27) could be used directly to compute the titration curve. However, with an ISE it is necessary to consider interferences and to calculate the potential from the Nikolsky equation. If it is assumed that interferents are present both in the sample and in the titrant, then the electrode potential is given by [133, 134],... 

Equation (9.8.26) is known as the Nikolsky equation [10]. More complex versions of this equation have been derived for the case that the interfering ion has a different charge than the ion being determined, or there is more than one interfering ion. 

This has the same form as the Nikolsky equation (9.8.26) derived for solid-state membranes. 

The ion exchange process in solutions of indifferent electrolytes can be described in the most general way by the Nikolsky equation, which for rather concentrated (non-ideal) solutions can be written as... 

A glass pH electrode exhibits the so-called alkaline error, which means that in the alkaline pH range the potential response is influenced by the presence of sodium ions. The study of this behavior gave rise to the Nikolsky equation,... 

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. 

The theory of (ion-selective) potentiometry has already been introduced in Section 28.2.2.5. Here it is necessary only to remind the reader of the Nernst equation and the Nemst-Nikolsky equation, both of which are used in the evaluation of potentiometric measurements. 

The Nemst-Nikolsky equation on the other hand takes into consideration the influence of interfering ions on the potential of an ISE ... 

Pm, the solution-membrane or solution - in-sula-tor interfacial potential, depends on the activity of the ions in the analyte solution according to the Nemst-Nikolsky equation [Eq. (6), Section 28.2.3.1.1] for ISFETs with an additional membrane, or according to a similar equation (see below) for ISFETs with a solution - insulator interface. 

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