1. Potentiometry and ISEs
Lecture 3

2. Inconsistency of the values of selectivity coefficients
There are several reasons for the inconsistency of the values of selectivity coefficients presented by various authors, including:
Non-validity of theoretical assumptions that were used in calculations of selectivity coefficients (assumption that both ions have Nernstian response characteristics!!!)
Differences in the membrane composition of different electrodes for the same ion, especially variations of functional groups of plasticizers and nature of additives
Differences in the charges carried by analyte and interferent ions
(4) Differences in analyte activities used in calculating kAB

3. In view of the above considerations, systematic studies were conducted as follows: Theoretical (calculated) values, literature values and additional measured values of selectivity coefficients were critically evaluated with respect to the
method employed
dependence on aA, aB and aA/aB
cases where zA is not equal to ZB
where aA and aB are the activities of the primary ion A and the interfering ion B, respectively, and ZA and zB are the corresponding charges. Thus, present problems were critically evaluated and the most rational recommendations for the method of determining selectivity coefficients for ISEs were made.

4. LIMITATION OF THE NICOLSKY-EISENMAN (N-E) EQUATION
1. KAB with ions of Unequal Charges: A precise description of the glass electrode potential in mixtures of any two monovalent cations was given as an empirical equation by Eisenman et al. as follows: where n is an empirical constant for a given glass composition.

5. When n equals to 1, the Eisenman equation is identical with the equation theoretically predicted by Nicolsky for a monovalent cation selective glass electrode. Indeed, n was found experimentally, in many cases, to be nearly 1. Eisenman et al. regarded KAB as a measure of the sensitivity to the interfering ion B, as compared to that of the primary ion A, for the glass electrode under study.

6. Response of Glass and Membrane electrodes to Monovalent Cations
Eisenman and co-workers extensively studied the electrode response behavior of glass electrodes to binary or ternary mixtures of monovalent cations and established experimentally and theoretically that their equation can describe potential behavior of the glass electrode. Later, they showed theoretically that the potential of a monovalent ion-selective ion-exchange liquid membrane as well as a neutral carrier liquid membrane in a binary mixture of monovalent cations can also be fitted to Eisenman equation, where n =1.

7. Response of Glass and Membrane electrodes to Divalent Cations
Garrels et al. obtained also similar empirical equations for the potentials not only of monovalent but also divalent cation selective glass electrodes with different compositions in mixtures of two divalent cations and of a divalent and a monovalent cations. where zA and zB are the charges of the primary and interfering ions and are 1 or 2. Ross reported that the electrode potential of a calcium ion-selective liquid ion-exchange membrane electrode immersed in mixed solutions containing Ca2+ and Mr+ (r = 1 or 2) can be fitted by the above equation, where n = 1.

8. The Accepted Version of N-E Equation
On the basis of these studies, the following N-E equation was eventually established:
This equation assumes the Nernstian electrode response not only to the primary but also to interfering ions.
In the late 1960s, several different workers started using the N-E equation to determine the selectivity coefficients for multivalent cation selective electrodes, such as Ca2+ and La3+ selective liquid membrane electrodes.

9. 2. Variation of activities /charges
When the ratio of charges of primary ion to the interfering ion was varied, the selectivity coefficients calculated are either unrealistically large or small depending on whether the ion of higher charge was considered as the primary or the interfering ion. These distorted values can be explained as being due to the power term: in the N-E equation, meaning that the N-E equation , in general, is not valid for cases when zA#zB, Meanwhile, it was reported by Bagg et al. that the potential of a calcium ion-selective liquid membrane electrode in mixed solutions of CaCl2 -M+X-, i.e., zA#zB, did not obey the N-E equation, but followed the equation:

10. Modification of the N-E Equation
To reduce the effect of the power term, Buck proposed the following modified N-E equation: based on the theoretical consideration and digital simulation. This equation becomes identical to the N-E equation for IzA|= IzBI = 1, but is different in other cases, including for IzBI = 2, 3, and 4. Bucks modified N-E equation (above) also assumes Nernstian response to interfering ions as well. Selectivity coefficients obtained based on this equation exhibit a weaker power-term dependence as compared to those based on the conventional N-E equation.

11. This weaker power-term dependence is due to the power term being 1/|ZBl instead of ZA/ZB. In the N-E equation, the term varies from (aB)4 to (aB)1/4, assuming that the value of +4 is a maximum charge of zA and zB, while in Buck's modified equation, (aB) 1/l ZBl varies from aB to (aB)1/4. The numerical range of variation for the magnitude of the activity term for interfering ions in the modified equation is obviously smaller than that in the N-E equation. However, the modified equation still does not appear to yield values which can be used readily for the interpretation of selectivity values.

12. From the above experimental and numerical considerations, it is concluded that selectivity coefficients based on the conventional N-E equation, including its modified versions, for cases with ions of unequal charge are inaccurate and unacceptable. The reason for this is that the validity of Eisenman described earlier was tested only for the glass electrode that senses alkali metal cations, and its extension to the ions of different charge and to other types of membranes can not be justified. Recommendations are, therefore, needed to use a method independent of the N-E equation, for calculating selectivity coefficients for systems with ions of different charges.

13. 3. Non-Nernstian Behavior of Interfering Ions
When a new electrode is constructed, log a vs. E relations are measured first. The response of the ion selective electrode to the primary ion should show a Nernstian response, to be accepted. Nernstian responses for interfereing ions are not even tested. However, in presence of interfering ions, as far as the validity for the use of the N-E equation is concerned, this involves a fatal paradox, because the N-E equation assumes a Nernstian behavior for interfering ions as well.

14. calibration curves of some of the most typical representative electrodes were experimentally reexamined, including a F- ISE, a Br- ISE, a NO3- ISE, two Ca2+ ISEs and a K+ ISE at oC. The results clearly show that the calibration curves for most of the interfering ions exhibit non-Nernstian slopes, although each primary ion leads to a Nernstian slope: A F- ISE based on LaF3 showed a typical Nernstian slope of -59 mv/decade for F-; however, only -32 mv/decade for OH-. A Br- ISE based on AgBr/Ag2S also shows a slope of -59 mV/decade for Br-, but -53 mV/decade for Cl-. Also, a Ca2+ ISE exhibits a slope of 29 mV/decade for Ca2+, but 24 mV/decade and 8 mV/decade for Sr2+ and Ba2+, respectively.

15. A Ca2+ ISE based on an ion-exchanger, calcium salt of bis(4- octylphenyl)phosphate, gave a slope of 28 mV/decade for Ca2+, but 10 mV/decade for Mg2+, 19 mV/decade for Cd2+, and 24 mV/decade for Sr2+. A NO3- ISE based on an ion-exchanger gave a slope of -55 mV/decade for NO3-, but -40 mV/decade for Cl-, -50 mV/decade for Br-, -59 mV/decade for I- and -162 mV/decade for Cl04-. A K+ ISE based on valinomycin shows a Nernstian slope of 59 mV/decade for K+, Rb+ and Cs+. Among these popular ISEs, only the valinomycin based K+ ISE was thus found to show a Nernstian behavior for both primary and some of interfering ions. If one tries to be faithful to the original assumption of the N-E equation and KAB values, problems arise.

16. Like the case of the power-term problem with ions of unequal charge, this is another inherent problem of the N-E equation. Again the N-E equation was established essentially for the glass electrode and interfering alkali metal ions, therefore it was initially not expected to be used universally for all kinds of modern ISEs for which interfering ions are often expected to exhibit non-Nernstian slopes.

17. Selectivity Coefficients Relation to Method Used
The evaluation of the selectivity coefficients should give the same result independently of the detailed measurement procedure, including the method employed, and of the activities of the ions A and B at which selectivity coefficients are determined. But the dependence of KAB on the method, or aA and/or aB values, at which KAB values are determined, occurs when the response of the electrode to the primary and/or the interfering ions is non-Nernstian. On the other hand, even for Nernstian slopes of interferents and for the same activities of primary and interfering ions, the N-E equation will, most of the time, fail when the charges are different.

18. A METHOD INDEPENDENT OF THE N-E EQUATION
The necessity to develop methods, if any, independent of the Nicolsky-Eisenman equation, appears to be first discussed by Gadzekpo and Christian only in They proposed the "matched potential method", which is totally independent of the N-E equation, to overcome the above-stated difficulties in obtaining accurate selectivity coefficients when ions of unequal charge are involved.

19. This method does not depend on the Nicolsky–Eisenman equation at all
This method does not depend on the Nicolsky–Eisenman equation at all. In this method, the potentiometric selectivity coefficient is defined as the activity ratio of primary and interfering ions that give the same potential change under identical conditions. At first, a known activity (aA') of the primary ion solution is added into a reference solution that contains a fixed activity (aA) of primary ions, and the corresponding potential change (∆E) is recorded. Next, a solution of an interfering ion is added to the reference solution until the same potential change (∆E) is recorded. The selectivity coefficient is calculated from the relation:

21. The characteristics of the matched potential method are:
The charges of the primary and interfering ions do not need to be taken into consideration
Nernstian responses are assumed neither to the primary nor interfering ions.
These characteristics lead to the following advantages:
1. The power-term problem for ions of unequal charge disappears
This method is widely applicable, even to non-Nernstian interfering ions. However, this method is independent of the N-E equation or its modified forms, and it is therefore difficult to correlate the values of KAB with other methods. In other words, the values obtained by this method should be regarded as of practical significance.
Results obtained by the matched potential methods are supposed to be the same as results obtained by other methods when ZA = ZB and the response is Nernstian.

22. CONCLUSIONS
1. Although the N-E equation requires both the primary and interfering ions to lead to Nernstian responses, few electrodes seem to exhibit a Nernstian behavior for both the primary and interfering ions. As a result of this, most reports have violated the prerequisite for the use of the N-E equation (a Nernstian response for both ions). This is the major reason for the activity dependence of KAB and non-equality of KAB values based on different methods.

23. In addition, the N-E equation and modifications of it were not found to be well suited when ions of different charge were involved. Selectivity coefficients obtained were either unrealistically large or small, depending on whether the ion of higher charge was considered as the primary or interfering ion. This problem resulted from the use of the N-E equation for ions of unequal charge.
As expected from its measurement procedure, the matched potential method was found to give KAB values quantitatively identical to those obtained with the N-E equation based method when both the primary and interfering ions lead to Nernstian responses and have equal charges.

24. RECOMMENDATIONS 1. Under the condition that both the primary and interfering ions lead to Nernstian responses, the N-E equation or its modification is recommended for calculation of selectivity coefficients when ions of equal charge are involved. 2. When ions of unequal charges are involved, the matched potential method is recommended, as it gives practical KAB values. 3. When interfering ions and/or the primary ion do not satisfy the Nernstian condition, the matched potential method is recommended also, even if the charges of the primary and interfering ions are equal.

26. Uncertainties with ISEs
The logarithmic response of ISEs can cause major accuracy problems. Very small uncertainties in the measured cell potential can thus cause large errors. (an uncertainty of ±1mV corresponds to a relative error of ~4% in the concentration of a monovalent ion). Since potential measurements are seldom better than 0.1mV uncertainty, best measurements of monovalent ions are limited to about 0.4% relative concentration error. In many practical situations, the error is significantly larger. The main source of error in potentiometric measurements is actually not the ISE, but rather changes in the reference electrode junction potential, namely, the potential difference generated between the reference electrolyte and sample solution.

27. The junction potential is caused by an unequal distribution of anions and cations across the boundary between two dissimilar electrolyte solutions (which results in ion movement at different rates). When the two solutions differ only in the electrolyte concentration, such liquid junction potential is proportional to the difference in transference numbers of the positive and negative ions and to the log of the ratio of the ions activities on both sides of the junction.

28. Changes in the reference electrode junction potential result from differences in the composition of the sample and standard solutions (e.g., on switching from whole blood samples to aqueous calibrants). One approach to alleviate this problem is to use standard solutions with an electrolyte composition similar to the sample. This, however, will not eliminate the problem completely.

29. ISEs as Chemical Sensors
A chemical sensor can be defined as a small device that allows the transformation of chemical information into an optical or electrical signal that can be processed by an instrument. ISEs are Potentiometric ion sensors based on ion-selective membranes. They respond to the activity of the analyte ion, whose logarithmic value is proportional to the membrane electrical potential measured relative to a reference electrode. Several kinds of ion-selective membrane are known including glass, plasticized polymers, or various crystalline materials. The best known example is probably the pH glass electrode.

30. At present, the most versatile ion-selective membrane consists of an organic polymeric matrix containing a lipophilic ligand and a lipophilic ionic species. The key components of the membrane are the lipophilic ion and the ionophore. The former guarantees the operation of the ISE by keeping the total amount of measuring ions inside the membrane constant, while the latter assures a selective response of the ISE to the target ion. Ion-selective electrodes are cheap and simple devices that can be miniaturized, allow on-line and in-situ measurements. Ideally they consume no analyte during the measurement and usually do not need sample preparation. They are widely applied, especially in clinical analysis.

31. Examples of ISE

32. The pH Electrodes
The most common potentiometric device is the pH electrode. This electrode has been widely used for pH measurements for several decades. Besides direct pH measurements, the pH glass electrode is commonly employed as the transducer in various gas and biocatalytic sensors, involving proton-generating/consuming reactions. Its remarkable success is attributed to its outstanding analytical performance, in particular its extremely high selectivity for hydrogen ions, its remarkably broad response range, and its fast and stable response. The phenomenon of glass selectivity was reported by Cremer in Glass pH electrodes of different configurations and dimensions have been in routine use since the early 1940s following their commercial introduction by Beckman.

33. The Glass Electrode
The first commercial glass electrodes were manufactured using Corning 015, a glass with a composition of approximately 22% Na2O, 6% CaO, and 72% SiO2. When immersed in an aqueous solution, the outer approximately 10 nm of the membrane becomes hydrated over the course of several hours. Hydration of the glass membrane results in the formation of negatively charged sites, G–, that are part of the glass membrane’s silica framework. Sodium ions, which are able to move through the hydrated layer, serve as the counter ions.

34. Hydrogen ions from solution diffuse into the membrane and, since they bind more strongly to the glass than does Na+, displace the sodium ions: giving rise to the membrane’s selectivity for H+. The transport of charge across the membrane is carried by the Na+ ions. The potential of glass electrodes obeys the equation over a pH range of approximately 0.5–9 :

35. The principle of operation of the pH electrode is based upon the fact that if there is a gradient of hydrogen ion activity across the membrane this will generate a potential the size of which is determined by the hydrogen ion gradient across the membrane. Moreover, since the hydrogen ion concentration on the inside is constant (due to the use of 0.1 M hydrochloric acid) the observed potential is directly dependent upon the hydrogen ion concentration of the test solution. In practice a small junction or asymmetry potential is also created in part as a result of linking the glass electrode to a reference electrode.

40. Asymmetry Potential
When a membrane of a glass ion selective electrode is immersed in a solution having the same concentration as that of the internal fill solution , then there should be no measureable potential difference. If such a potential exists, this potential is referred to as asymmetry potential. It is usually few mV (can be up to 40 mV).

42. The following potentials are the most significant: E1 = potential difference between the pH sensitive glass membrane and the liquid to be measured. E2 = potential difference between the electrolyte in the glass electrode and the inner face of the glass membrane. E3 = potential difference between the electrode pin and the electrolyte in the glass electrode. E4 = potential difference between the electrolyte and the electrode pin in the reference electrode. E5 = potential difference that occurs at the interface of two liquids with different concentrations, namely the electrolyte and the process liquid.

43. The total sum (Et) of these potential differences is measured by the pH- Analyzer: Et = E1 + E2 + E3 + E4 + E5 However, E2 , E3 , E4 , and E5 are all constants, and the potential measured by the pH meter will practically be E1. or: Et = E1 E = constant + (RT/F) In [H+]outer E = Constant * pHouter

44. The ideal conditions described above cannot always be completely realized in practice. A small potential difference may exist when the glass and the reference electrode are both immersed in a liquid of similar properties and pH value to the electrolyte. Et = Constant – ( pHouter) + Easy This potential difference is called the asymmetric potential of the measuring system.

45. Alkaline Error
At high pH value the hydrogen ion activity is low and the sodium ions replace the hydrogen ions in the outer gel layer of the glass membrane. As a result, a pH value that is lower than the actual value of the sample solution will be measured. Under extreme conditions the glass membrane responds only to sodium ions. This occurs at a pH greater than 9–10, where the glass membrane may become more responsive to other cations, such as Na+ , Li+ and K+ , this is called the alkaline error. Replacing Na2O and CaO with Li2O and BaO extends the useful pH range of glass membrane electrodes to pH levels greater than 12.

46. A,Corning 015/H2SO4;
B, Corning 015/ HCl;
C,Corning 015 /1M Na+;
D,Beckman-GP/1M Na+ ;
E, L&N BlackDot/1M Na+ ;
F,Beckman E/1M Na+ ;

47. In order to minimize the contribution of alkaline errors, pH electrode manufacturers use special glass membranes for electrodes that are used to measure high alkaline values (high pH). The composition of the glass membrane will, to a large extent, determine the electrode's response time and its sensitivity to ions other than H+. However, there is no types of glass membrane currently available that has zero alkaline error. Some error will always exist.

48. Temperature effect on pH

49. Glass Electrodes for Other Ions
The response of some glass membranes to monovalent cations other than H+ at high pH led to the development of glass membranes possessing a greater selectivity for other cations. For example, a glass membrane with a composition of 11% Na2O, 18% Al2O3, and 71% SiO2 is used as a Na+ ion-selective electrode. Other glass electrodes have been developed for the analysis of Li+, K+, Rb+, Cs+, NH4+, Ag+, and Tl+.

50. Acid Error
At very low pH values acid molecules are absorbed by the gel layer leading to a decrease in the hydrogen ion (H+) activity in the gel layer. The pH measurement, therefore, shows a higher pH value than the actual value of the measured solution. The acid error changes very little with temperature and is only relevant for very low pH values. Usually below 1.00 pH. However, for these situations, you can get measuring electrodes with membrane glasses having specifically low acid errors.

51. Two-point Calibration

52. The electromotive force (EMF) of a pH sensor under ideal conditions is expressed by line “3” in the figure. In practice, the electrode shows the characteristic that is expressed by line “1” because of different properties or aging of the pH sensor. To correct this, a zero adjustment (asymmetry potential adjustment) and a span adjustment (potential slope adjustment) by the pH analyzer are required. First, perform a zero point adjustment using a standard solution with a pH value close to pH 7. The line is shifted from “1” to “2” laterally so it passes through the zero point. Next, perform a span adjustment using a standard solution with a span pH (typically pH 4 or pH 9). The slope is adjusted so the line is rotated from “2” to “3”. Like this, the zero point is adjusted to pH 7 based on the EMF of a pH sensor and the span is adjusted with reference to the difference from pH 7.