Theory of Ion-Selective Electrodes

Earlier studies on theoretical thin membranes were continued by Teorell [S] and Meyer and Sievers [6], who in their theory attempted to interpret the behavior of practical, thick membranes, in contact on both sides with solutions containing the sort of ion which can produce a membrane potential. This initiated further research and many workers studied the perm-selective properties of ion-selective electrode membranes. As a result, ion transport across thick ion-selective membranes was considered as the basic concept of the theory of ion-selective electrodes. This theory was further elaborated by Eisenmann, Simon, and Buck. 

In the 1950s I studied the adsorption properties of silver iodide in the laboratory of Professor Schulek. This work later gave me the idea that the chemisorption of iodide ions on silver iodide precipitate could serve as the basis for the operation of an iodide-sensing electrode. Indeed, silver iodide embedded in paraffin became an ideal ion-selective electrode [7]. This electrode was later used to study the origin of the selectivity of precipitate-based ion-selective electrodes, and in the 1960s to show that the defect structure of the crystal only affects the standard potential (E ) of the electrode. 

As mentioned in Sec. 1, Donnan [2] was the first to present a theoretical approach to describe the potential established on the surface of gels. Since a gel layer is formed on a glass surface soaked in an aqueous solution, this approach seemed to be applicable to describe the behaviour of glass electrodes. 

In his ingenious concept Nikolsky [3] explained the effect of interfering ions on the response of ion-selective electrodes in terms of an ion exchange equilibrium. From this consideration came the following  

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. 

---

Pungor E (1998) The theory of Ion Selective Electrodes. Anal Sci 14 249-256 Bakker E, Buhlmann P, Pretsch E (2004) The phase-boundary potential model. Talanta 63 3-20... 

The theory of ion-selective electrode response is well developed, due to the works of Eisenman, Buck and others [23], Three models used for the description of the ISE response through the years, namely kinetic, membrane surface (or space charge) and phase boundary potential (PBP) models, although being seemingly contradictory, give similar results in most cases [7], The first two sophisticated models are out of the scope of the present chapter, as the PBP model, despite its simplicity, satisfactorily explains most of the experimental results and thus has become widely applicable. The... 

In conclusion, it should be mentioned that extraction parameters (the equilibrium constants of exchange reactions and ion-pair stabilities) were introduced into the theory of ion-selective electrodes in [2, 31,33, 34, 35,69]. The theory of ISEs with a liquid membrane and a diffusion potential in the membrane was extended by Buck etal. [11, 13, 14, 73, 74] and Morf [54]. 

J. Koryta, Theory of ion-selective electrodes, in Ion-Selective Microelectrodes... 

Pungor has presented evidence that the establishment of an electrode potential is caused by charge separation, due to chemisorption of the primary ion (H ) from the solution phase onto the electrode surface, that is, a surface chemical reaction. Counter ions of the opposite charge accumulate in the solution phase, and this charge separation represents a potential. A similar mechanism applies to other ion-selective electrodes (below). [See E. Pungor, The New Theory of Ion-Selective Electrodes, Sensors, 1 (2001) 1-12 (this is an electronic journal www. mdpi.net/sensors). ... 

In electro-gravimetric analysis the element to be determined is deposited electroly tically upon a suitable electrode. Filtration is not required, and provided the experimental conditions are carefully controlled, the co-deposition of two metals can often be avoided. Although this procedure has to a large extent been superseded by potentiometric methods based upon the use of ion-selective electrodes (see Chapter 15), the method, when applicable has many advantages. The theory of the process is briefly discussed below in order to understand how and when it may be applied for a more detailed treatment see Refs 1-9. 

The search for models of biological membranes led to the formation of a separate branch of electrochemistry, i.e. membrane electrochemistry. The most important results obtained in this field include the theory and application of ion-exchanger membranes and the discovery of ion-selective electrodes (including glass electrodes) and bilayer lipid membranes. 

This type of membrane consists of a water-insoluble solid or glassy electrolyte. One ionic sort in this electrolyte is bound in the membrane structure, while the other, usually but not always the determinand ion, is mobile in the membrane (see Section 2.6). The theory of these ion-selective electrodes will be explained using the glass electrode as an example this is the oldest and best known sensor in the whole field of ion-selective electrodes. 

The second edition of Ion-Selective Electrodes contains a survey of the theory and applications of ion-selective electrodes based on the literature published up to mid-1981. Because of the rapid progress in the whole field and the very large amount of diverse data, a compact and unified treatment of the theory has been attempted. The technology and the applications have also been updated. In view of these facts we have had to write practically a new book. In contrast to the first edition, only a selective list of references could be included in the book, because otherwise we would have to deal with more than four thousand references. 

A different direction in ion-selective electrode research is based on experiments with antibiotics that uncouple oxidative phosphorylation in mitochondria [59]. These substances act as ion carriers (ionophores) and produce ion-specific potentials at bilayer lipid membranes [72]. This function led Stefanac and Simon to obtain a new type of ion-selective electrode for alkali metal ions [92] and is also important in supporting the chemi-osmotic theory of oxidative phosphorylation [69]. The range of ionophores, in view of their selectivity for other ions, was broadened by new synthetic substances [1,61]. 

Eisenman, Theory of membrane electrode potentials an examination of the parameters determining the selectivity of solid and liquid ion exchangers and of neutral sequestering molecules. Chapter 1 of Ion-Selective Electrodes (ed. R A Durst), National Bureau of Standards, Washington (1969). 

In the past the prominent investigators (1-6) of electrolyte solutions were able to measure only the mean activity coefficient of the salt. The development of ion-selective electrodes has made the measurement of the activity of many ions possible. The development, reliability, and general theory of many different ion-selective electrodes is discussed extensively in a National Bureau of Standards (NBS) publication edited by Durst (7). 

Koryta, J. Theory and application of ion-selective electrodes. Anal. Chim. Acta 61, 329-411 (1972). 

Koryta, J. Theory and applications of ion-selective electrodes. Part II. Anal. Chim. Acta 91, 1-85 (1977). Whitfield, M. Sea water as an electrolyte solution p. 43-171, Riley, J.P. and Skirrow, G., ed., "Chemical... 

The potential built at the interface in the presence of the transfer of more than one ionic species is a kind of mixed potential, as pointed out by Koryta in the context of ion-selective electrodes [45]. The theory of the mixed potential at the ITIES was presented for the case in the presence of supporting electrolyte [46] and then extended to the case in the absence of supporting electrolyte [47]. Consider the cell... 

Durst, R. A. Ion-Selective Electrodes in Science, Medicine, and Technology, Amer. Sci., 59, 353 (1971). A short, easily readable article on the theory, functioning, and applications of ion-selective electrodes. 

To decipher this complexity, electrochemistry at the polarized liquid-liquid interface developed over the past two decades has been proven to be a powerful tool, as shown in elucidation of the mechanism of ion-pair extraction [1 ] and the response of ion-selective electrodes of liquid-membrane type to different types of ions [5 7]. Along this line, several attempts have been made to use polarized liquid liquid interfaces for studying two-phase Sn2 reactions [8-10], two-phase azo-coupling [11], and interfacial polymerizations [12]. Recently, kinetic aspects of complexation reactions in facilitated ion transfer with iono-phores and the rate of protonation of amines have been treated quantitatively [13-16]. Their theoretical framework, which was adapted from the theories of kinetic currents in polaro-graphy, can be directly applicable to analyze quantitatively the chemical reactions in the two-phase systems. In what follows is the introduction to recent advances in electrochemical studies of the chemical reactions at polarized liquid liquid interfaces, mainly focusing on... 

Koryta J (1990) Theory and applications of ion-selective electrodes, part 8. Analytica Chimica Acta 233 1-30. 

The research program included also both the theory and practical aspects of ion-selective electrodes. Important part of these studies was the research oti the selectivity of such sensors and interferents and the change of selectivity imder influence of various factors. Potentiometric enzymatic sensors and sensors based oti pH-electrodes were developed and used in clinical chemistry. Kinetic model of the biosensors response with consideration of all proteolytic reactions of substrates and products of enzymatic reactions and transport processes in the membranes was elaborated. Conducting polymers and bilayer Upid membranes were used to design sensors and biosensors. 

Morf, W.E., E. Pretsch, and N.F. de Rooij. 2009. Memory effects of ion-selective electrodes Theory and computer simulation of the time-dependent potential response to multiple sample changes. J. Electroanal. Chem. 633 137-145. 

The subscripts i and j in Eq. (6.2) refer to the primary and interfering ions, respectively, and is the potentiometric selectivity coefficient. varies for each interfering irai, and depends upon the precise membrane composition. The lower the value of log the more highly the interfering ion is discriminated. (For a detailed review of ion-selective electrodes, including selectivity theory and a detailed account of ISE response, see Chap. 9.)... 

Ion-selective electrodes (ISEs) with ionophore-based membranes allow for quantification of a large number of analytes in various matrixes. Tailoring of the composition of the membranes to comply with the analytical task, requires advanced theory of membrane response. Most of theoretical descriptions include nonrealistic extra-thermodynamic assumptions, in the first place it is assumed that some kind of species strongly predominate in membranes. Ideally, a rigorous theory of ISE response should be based on strict thermodynamics. However, real ISE membranes are too complex. Therefore, known attempts aimed at rigorous thermodynamic description of ISEs proved to be fraritless. 

Various types of research are carried out on ITIESs nowadays. These studies are modeled on electrochemical techniques, theories, and systems. Studies of ion transfer across ITIESs are especially interesting and important because these are the only studies on ITIESs. Many complex ion transfers assisted by some chemical reactions have been studied, to say nothing of single ion transfers. In the world of nature, many types of ion transfer play important roles such as selective ion transfer through biological membranes. Therefore, there are quite a few studies that get ideas from those systems, while many interests from analytical applications motivate those too. Since the ion transfer at an ITIES is closely related with the fields of solvent extraction and ion-selective electrodes, these studies mainly deal with facilitated ion transfer by various kinds of ionophores. Since crown ethers as ionophores show interesting selectivity, a lot of derivatives are synthesized and their selectivities are evaluated in solvent extraction, ion-selective systems, etc. Of course electrochemical studies on ITIESs are also suitable for the systems of ion transfer facilitated by crown ethers and have thrown new light on the mechanisms of selectivity exhibited by crown ethers. 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

Ion-selective electrodes are now well understood in terms of the underlying theory, and this has made it possible for new sensing principles to emerge that make use of the thousands of chemical receptors originally developed for ion-selective electrodes. One is the field of optical sensors, which has not been discussed here because it is outside the focus of this chapter. Such so-called bulk optodes do not require electrical connectivity between the sensing and detection unit and are therefore more easily brought into various shapes and sizes, including particle formats, which suit the need of modem chemical analysis. 

This field is therefore at an exciting stage. Ion-selective electrodes have a proven track record in terms of clinical and biomedical analysis, with a well-developed theory and a solid history of fundamental research and practical applications. With novel directions in achieving extremely low detection limits and instrumental control of the ion extraction process this field has the opportunity to give rise to many new bioana-lytical measurement tools that may be truly useful in practical chemical analysis. 

---