Principles of Potentiometric Measurements

FIGURE 5-1 Schematic diagram of an electrochemical cell for poteiitiometric measurements. 

FIGURE 5-2 Membrane potential reflects the gradient of activity of the analyte ion in the inner and outer (sample) solutions. 

It should be noted again that ISEs sense the activity, rather than the concentration of ions in solution. The tenn activity is used to denote the effective (active) concentration of the ion. The difference between concentration and activity arises because of ionic mteractions (with oppositely charged ions) that reduce the effective eoncentration of the ion. The activity of an ion i in solution is related to its eoneentration, c by 

Equation (5-3) has been wiitten on tlie assumption tliat the electrode responds only to the ion of interest, i. hi practice, no electrode responds exclusively to the ion specified. The actual response of tlie electi ode in a buiaiy mixture of the piimary and mterferuig ions (i and j, respectively) is given by tlie Nikolskii-Eisenman equation (9)  

Aeeordingly, an ISE displays a seleetive response when tire aetivity of die primary ion is mueh lai ger tlian tire suimnation teiin of the mterferents that is, when a, S . Under tliis eondition, tire effect of mterfeiing ions is negligible, and 

The logarithmic response of ISEs can cause major accuracy problems. Very small uncertainties in the measured cell potential can cause large errors. (Recall that an 

Analytical Electrochemistry, Third Edition, by Joseph Wang Copyright 2006 John Wiley Sons, Inc. 

The equipment required for direct potentiometric measurements includes an ion-selective electrode, a reference electrode, and a potential-measuring device (a pH/millivolt meter that can read 0.2mV or better) (Fig. 5.1). Conventional voltmeters cannot be used because only very small currents can be drawn. The reference electrode should provide a highly stable potential for an extended period of time. The ion-selective electrode is an indicator electrode capable of selectively measuring the activity of a particular ionic species (known as the primary or analyte ion). Such electrodes exhibit a fast response and a wide linear range, are not affected by color or turbidity, are not destructive, and are very inexpensive. Ion-selective electrodes can be assembled conveniently in a variety of shapes and sizes. Specially designed cells allow flow or microliter analyses (see, e.g., Section 5-3). 

Another phase boundary potential is developed at the inner surface of the membrane (at the membrane/filling solution interface). The membrane potential corresponds to the potential difference across the membrane  

The potential of the ion-selective electrode is generally monitored relative to the potential of a reference electrode. Since the potential of the reference electrode is fixed, and the activity of the ion in the inner solution is constant, the measured cell potential reflects the potential of the ISE, and can thus be related to the activity of the target ion in the sample solution. Ideally, the response of the ISE should obey the following equation 

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The subject of potentiometric titrations has been exhaustively treated by the classic monograph by Kolthoff and Furman.1 Although the second edition was published in 1931, it is still the definitive work. Unfortunately, it is no longer in print, but it is available in many chemical libraries. A complete and thorough discussion of the principles and theory of potentiometric titrations is provided, together with an extremely extensive summary of the many applications of potentiometric measurements. 

The ion sensitive field-effect transistor (ISFET) is a special member of the family of potentiometric chemical sensors [6,7. Like the other members of this family, it transduces information from the chemical into the electrical domain. Unlike the common potentiometric sensors, however, the principle of operation of the ISFET cannot be listed on the usual table of operation principles of potentiometric sensors. These principles, e.g., the determination of the redox potential at an inert electrode, or of the electrode potential of an electrode immersed in a solution of its own ions (electrode of the first kind), all have in common that a galvanic contact exists between the electrode and the solution, allowing a faradaic current to flow, even when this is only a very small measuring current. 

Since the electromotive force of a cell depends on the activity of the ions of the electrolyte it is possible to determine activities potentiometrically, in particular that of the hydrogen ion which is a measure of acid strength. Strictly, however, the activity of a single ionic species is not measurable, for positive ions always exist in the presence of negative ions. Nevertheless, the mean activity of HCl which is measurable in a cell does conveniently indicate the mean activity of the ions which carry the current, and —logjQ of this activity is the pH of the solution. The basic principle of potentiometric pH determination may be seen by considering a cell divided into two halves by a silver wall coated on both sides with silver chloride ... 

The equipment for potentiometric methods is simple and inexpensive and includes a reference electrode, an indicator electrode, and a potential-measuring device. The principles of operation and design of each of these components are described in the initial. sections of this chapter. Following these discussions, we investigate analytical applications of potentiometric measurements. 

The basic principle behind potentiometric measurements is the development of charge related to the analyte activity in the sample through the Nernst relation ... 

Flame atomic emission spectrometry Basic information on FAES is presented elsewhere in this encyclopedia. Sodium measurements are performed at 590 nm with the use of a propane flame (1925°C). Physiological samples for sodium determination are highly diluted before measurement. The diluent and the calibrator solution contain the same concentration of lithium ions so as to balance flame instability by a concomitant measurement of lithium in the reference beam (the so-called lithium guideHne). At the same time, lithium ions inhibit the ionization of sodium atoms. This procedure cannot be used in the case of therapy with lithium salts. That is why some authors prefer the concomitant measurement of caesium to that of lithium. Dilution adjusts the viscosity of the sample to that of the calibrator solution to produce identical aspiration rate and drop size on nebulization. As other electrolytes interfere with sodium measurement, their concentration in the caH-brator solution must be similar to their concentration in the sample. For the measurement of sodium in urine, calibrator solutions different from those for serum measurement are needed as the electrolyte concentrations in urine samples are quite different from those in serum and their relations are very variable. As the concentration of the electrolytes in serum is rather constant, calibrator solutions for serum measurements can fulfill their function better than those for urine in other words, urine determinations are usually less accurate. FAES proved to be sufficiently reliable to be used as the basic principle of the sodium reference measurement procedure. In routine use, however, FAES is less accurate. Its application is given up by most clinical laboratories in favor of potentiometric measurements... 

The principle of resistance measurement involves either a dc Wheatstone bridge, as shown in the bottom sketch of Fig. 3.4, or a potentiometric arrangement in which the voltage drop over a standard resistor in series with the thermometer is determined. The potentiometer is described in Fig. 3.5 as part of the discussion of thermocouples. The calculation of Eqs. (4) to (7) shows how the lead resistances Rq and Rj can be eliminated in precision thermometry by performing two measurements (a and b) with reversed leads coimected to the bridge circuit. The measured resistances are represented by the unknown resistance by R. ... 

In case of potentiometric measurements with microelectrode arrays, complete micro-reference electrodes have been suggested. The term complete microreference electrode is used here for such reference electrodes that consist of the same parts as conventional macroelectrodes. Their operating principle is essentially identical to that of the latter. Major difference is the size. Needle-type reference electrodes are frequently used for miniaturisation. The Ag/AgCl system (or a similar one) is hosted in a capillary with dimensions in the millimetre range. The capillary is thinned at one end, and the orifice houses the liquid junction. Commercially available complete reference microelectrodes have capillaries with an outer diameter of 1-2 mm at the end. The liquid junction is realised by a ceramic frit or a fibre. A real micro-reference electrode has been described by Kitade and coworkers [26]. They used a commercially available Femtotip capillary tube as the electrode body. Such tips have a capillary with an outer diameter of 1 pm and are usually used for microinjection into adherent and suspension cells. The tip is filled with a KCl agar gel to realise the liquid junction. The bare part of the silver wire has to be covered with a polystyrene membrane to avoid any additional potential between the inner electrolyte solution and the bare silver wire. 

The principles of potentiometric imaging are far simpler than those of amperometric imaging. In the amperometric mode, the tip directly interacts with the concentration profiles of the redox mediator by consuming one redox form and producing the other. Hence, the measurement severely alters... 

Where R is the gas constant, T is the temperature, and F is the Faraday constant. Caused by the logarithmic correlation between the gas concentration and the voltage signal, the potentiometric measurement is best suited for measurements of small amounts of oxygen. A well-known application of this principle has been realized in the so called lambda-probe for automotive applications where they are used to control the lambda value within a small interval around 1 = 1. The lambda-value is defined by the relation between the existing air/fuel ratio and the theoretical air/fuel ratio for a stoichiometric mixture composition ... 

The international standard for measurement of resistivity of rubbers is ISO 185317 which details one procedure only, the potentiometric or four electrode method. The principle of the method is shown in Figure 13.2 the strip test piece has metal current electrodes clamped at each end and is... 

Potentiometric measurements are done under the condition of zero current. Therefore, the domain of this group of sensors lies at the zero-current axis (see Fig. 5.1). From the viewpoint of charge transfer, there are two types of electrochemical interfaces ideally polarized (purely capacitive) and nonpolarized. As the name implies, the ideally polarized interface is only hypothetical. Although possible in principle, there are no chemical sensors based on a polarized interface at present and we consider only the nonpolarized interface at which at least one charged species partitions between the two phases. The Thought Experiments constructed in Chapter 5, around Fig. 5.1, involved a redox couple, for the sake of simplicity. Thus, an electron was the charged species that communicated between the two phases. In this section and in the area of potentiometric sensors, we consider any charged species electrons, ions, or both. 

The principle of their operation is the same, but the method of implementation of the sensor is largely dependent on the conditions of the application. Thus, a zirconia sensor for measurement of 02 in molten steel (1,600°C) has to be designed in such a way that the thermal expansion coefficients of the different layers in this device are matched. On the other hand, a room-temperature potentiometric oxygen sensor can be constructed (Yamazoe et al., 1987) by using another set of materials ... 

Application and Principle This procedure is used to determine the lipase activity in preparations derived from microbial sources and animal pancreatic tissues. The assay is based on the potentiometric measurement of the rate at which the preparations will catalyze the hydrolysis of tributyrin. 

Although the basic principles of type III potentiometric sensors are apphcable for gaseous oxide detection, this should not obscure the fact that these sensors still require further development. This is especially true in view of the kinetics of equilibria and charged species transport across the solid electrolyte/electrode interfaces where auxiliary phases exist. Real life situations have shown that, in practice, gas sensors rarely work under ideal equilibrium conditions. The transient response of a sensor, after a change in the measured gas partial pressure, is in essence a non-equilibrium process at the working electrode. Consequently, although this kind of sensor has been studied for almost 20 years, practical problems still exist and prevent its commercialization. These problems include slow response, lack of sensitivity at low concentrations, and lack of long-term stability. " It has been reported " that the auxiliary phases were the main cause for sensor drift, and that preparation techniques for electrodes with auxiliary phases were very important to sensor performance. ... 

Differential Titration.—The object of potentiometric titration is to determine the point at which AEjAv is a maximum, and this can be achieved directly, without the use of graphical methods, by utilizing the principle of differential titration. If to two identical solutions, e.g., of sodium chloride, are added v and v + 0.1 cc. respectively of titrant, e.g., silver nitrate, the difference of potential between similar electrodes placed in the two solutions gives a direct measure of AEjAVy where Av is 0.1 cc., at the point in the titration corresponding to the addition of t + 0.05 cc. of silver nitrate. The e.m.f. of the cell made up of these two electrodes will thus be a maximum at the end-point. 

The gas-sensing configuration described above forms a very useful basic unit for potentiometric measurements of biologically important species. In principle, the immobilized or insolubilized biocatalyst is placed on a conventional ion-selective electrode used to measure the decrease in the reactants or the increase in products of the biochemical reaction. The biocatalyst include... 

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