POTENTIOMETRY MEASUREMENTS

Use of the potential of a galvanic cell to measure the concentration of an electroactive species developed later than a number of other electrochemical methods. In part this was because a rational relation between the electrode potential and the concentration of an electroactive species required the development of thermodynamics, and in particular its application to electrochemical phenomena. The work of J. Willard Gibbs1 in the 1870s provided the foundation for the Nemst equation.2 The latter provides a quantitative relationship between potential and the ratio of concentrations for a redox couple [ox l[red ), and is the basis for potentiometry and potentiometric titrations.3 The utility of potentiometric measurements for the characterization of ionic solutions was established with the invention of the glass electrode in 1909 for a selective potentiometric response to hydronium ion concentrations.4 Another milestone in the development of potentiometric measurements was the introduction of the hydrogen electrode for the measurement of hydronium ion concentrations 5 one of many important contributions by Professor Joel Hildebrand. Subsequent development of special glass formulations has made possible electrodes that are selective to different monovalent cations.6 8 The idea is so attractive that intense effort has led to the development of electrodes that are selective for many cations and anions, as well as several gas- and bioselective electrodes.9 The use of these electrodes and the potentiometric measurement of pH continue to be among the most important applications of electrochemistry. 

At an early date Nemst also introduced the concept of potentiometry with polarized electrodes,10 which, together with the many other specialized forms 

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Electrical methods of analysis (apart from electrogravimetry referred to above) involve the measurement of current, voltage or resistance in relation to the concentration of a certain species in solution. Techniques which can be included under this general heading are (i) voltammetry (measurement of current at a micro-electrode at a specified voltage) (ii) coulometry (measurement of current and time needed to complete an electrochemical reaction or to generate sufficient material to react completely with a specified reagent) (iii) potentiometry (measurement of the potential of an electrode in equilibrium with an ion to be determined) (iv) conductimetry (measurement of the electrical conductivity of a solution). 

Close to the drain contact, the simulated potential profile for Uq = -30 V is in good agreement with the observed potentiometry trace shown in Figure 20.2. Based on previous potentiometry measurements on polymer OFETs revealing a substantial potential drop at the drain contact [13], two-dimensional device simulations have suggested that the mobility close to the contacts... 

Comparing the potentiometry measurements in Figure 20.8 obtained on top-contacted pentacene OFETs with the data for the bottom-contacted sample in Figure 20.2, the most striking difference is the absence of a substantial potential drop close to the source contact. The reduction of the contact resistance... 

By differentiating the eleetrie potential U obtained from potentiometry measurements, one obtains the eleetrie field E (x) = -dU/dx in the ehaimel region, eompare Figure 20.9a. In eontrast to the asymmetrie eleetrie field distribution in the untreated pentaeene OFET, in the OTS treated sample the field is rather symmetrie between souree and drain eontaets. 

Table I. Standard Potentials of Transfer between Water and Nitrobenzene for Ions Used in the Potentiometry Measurements...

Potentiometry Measurement of the potential produced by electrochemical cells under equilibrium conditions with no current flow. 

Potentiometry measures the difference in potential between two electrodes immersed in a solution. One of the electrodes probes the solution, while the other serves as a reference. The reference electrode has a constant and reproducible potential which is independent of its environmenL The potential of the probe electrode is the potential at the interface between the solid and liquid phases, where the oxidation and reduction reactions occur. For example, at the interface between a conducting wire and a redox system, there is an exchange of electrons between the wire and the compounds being oxidized and reduced. Equilibrium is achieved when the rates of oxidation and reduction are equal, and the composition of the solution surrounding the electrode is constant. The equilibrium potential is then given by the Nemst Law ... 

The measurement of pK for bases as weak as thiazoles can be undertaken in two ways by potentiometric titration and by absorption spectrophotometry. In the cases of thiazoles, the second method has been used (140, 148-150). A certain number of anomalies in the results obtained by potentiometry in aqueous medium using Henderson s classical equation directly have led to the development of an indirect method of treatment of the experimental results, while keeping the Henderson equation (144). 

Techniques, such as spectroscopy (Chapter 10), potentiometry (Chapter 11), and voltammetry (Chapter 11), in which the signal is proportional to the relative amount of analyte in a sample are called concentration techniques. Since most concentration techniques rely on measuring an optical or electrical signal, they also are known as instrumental techniques. For a concentration technique, the relationship between the signal and the analyte is a theoretical function that depends on experimental conditions and the instrumentation used to measure the signal. For this reason the value of k in equation 3.2 must be determined experimentally. 

The diversity of interfacial electrochemical methods is evident from the partial family tree shown in Figure 11.1. At the first level, interfacial electrochemical methods are divided into static methods and dynamic methods. In static methods no current passes between the electrodes, and the concentrations of species in the electrochemical cell remain unchanged, or static. Potentiometry, in which the potential of an electrochemical cell is measured under static conditions, is one of the most important quantitative electrochemical methods, and is discussed in detail in Section IIB. 

In potentiometry the potential of an electrochemical cell is measured under static conditions. Because no current, or only a negligible current, flows while measuring a solution s potential, its composition remains unchanged. For this reason, potentiometry is a useful quantitative method. The first quantitative potentiometric applications appeared soon after the formulation, in 1889, of the Nernst equation relating an electrochemical cell s potential to the concentration of electroactive species in the cell. ... 

Potentiometric measurements are made using a potentiometer to determine the difference in potential between a working or, indicator, electrode and a counter electrode (see Figure 11.2). Since no significant current flows in potentiometry, the role of the counter electrode is reduced to that of supplying a reference potential thus, the counter electrode is usually called the reference electrode. In this section we introduce the conventions used in describing potentiometric electrochemical cells and the relationship between the measured potential and concentration. 

In potentiometry, the concentration of analyte in the cathodic half-cell is generally unknown, and the measured cell potential is used to determine its concentration. Thus, if the potential for the cell in Figure 11.5 is measured at -1-1.50 V, and the concentration of Zn + remains at 0.0167 M, then the concentration of Ag+ is determined by making appropriate substitutions to equation 11.3... 

Buck, R. P. Potentiometry pH Measurements and Ion Selective Electrodes. In Weissberger, A., ed.. Physical Methods of Organic Chemistry, Vol. 1, Part IIA. Wiley New York, 1971, pp. 61-162. Cammann, K. Working with Ion-Selective Electrodes. Springer-Verlag Berlin, 1977. 

Potentiometry is another useful method for determining enzyme activity in cases where the reaction Hberates or consumes protons. This is the so-called pH-stat method. pH is kept constant by countertitration, and the amount of acid or base requited is measured. An example of the use of this method is the determination of Hpase activity. The enzyme hydroly2es triglycerides and the fatty acids formed are neutralized with NaOH. The rate of consumption of NaOH is a measure of the catalytic activity. 

In addition we studied the complexation of ClC+ by the polyamines using microcalorimetry and potentiometry. The enthalpy changes measured are presented as function of the degree of protonation and the amount of CiT bound. 

It may happen that AH is not available for the buffer substance used in the kinetic studies moreover the thermodynamic quantity A//° is not precisely the correct quantity to use in Eq. (6-37) because it does not apply to the experimental solvent composition. Then the experimentalist can determine AH. The most direct method is to measure AH calorimetrically however, few laboratories Eire equipped for this measurement. An alternative approach is to measure K, under the kinetic conditions of temperature and solvent this can be done potentiometrically or by potentiometry combined with spectrophotometry. Then, from the slope of the plot of log K a against l/T, AH is calculated. Although this value is not thermodynamically defined (since it is based on the assumption that AH is temperature independent), it will be valid for the present purpose over the temperature range studied. 

Resistivity measurements are done on meander shaped samples by the standard potentiometrie method in a stirred bath of liquid nitrogen relative to a dummy speeimen For this proeedure of residual re istometry the ultra-high measuring aeeuraey of 3.10 results below 300°C and of 3.10 for annealing treatments at higher temperatures. 

Buck, R. P. Potentiometry, pH measurements and ion-selective electrodes, in Physical Methods of Chemistry, part Ha (eds.) Weissberger, A., Rossiter, B. W., New York, Interscience 1971... 

The main techniques employed in quantitative analysis are based upon (a) the quantitative performance of suitable chemical reactions and either measuring the amount of reagent needed to complete the reaction, or ascertaining the amount of reaction product obtained (b) appropriate electrical measurements (e.g. potentiometry) (c) the measurement of certain optical properties (e.g. absorption spectra). In some cases, a combination of optical or electrical measurements and quantitative chemical reaction (e.g. amperometric titration) may be used. 

This procedure of using a single measurement of electrode potential to determine the concentration of an ionic species in solution is referred to as direct potentiometry. The electrode whose potential is dependent upon the concentration of the ion to be determined is termed the indicator electrode, and when, as in the case above, the ion to be determined is directly involved in the electrode reaction, we are said to be dealing with an electrode of the first kind . 

It is also possible in appropriate cases to measure by direct potentiometry the concentration of an ion which is not directly concerned in the electrode reaction. This involves the use of an electrode of the second kind , an example of which is the silver-silver chloride electrode which is formed by coating a silver wire with silver chloride this electrode can be used to measure the concentration of chloride ions in solution. 

In the Nernst equation the term RT/nF involves known constants, and introducing the factor for converting natural logarithms to logarithms to base 10, the term has a value at a temperature of 25 °C of 0.0591 V when n is equal to 1. Hence, for an ion M+, a ten-fold change in ionic activity will alter the electrode potential by about 60 millivolts, whilst for an ion M2 +, a similar change in activity will alter the electrode potential by approximately 30 millivolts, and it follows that to achieve an accuracy of 1 per cent in the value determined for the ionic concentration by direct potentiometry, the electrode potential must be capable of measurement to within 0.26 mV for the ion M+, and to within 0.13 mV for the ion M2 +. ... 

In view of the problems referred to above in connection with direct potentiometry, much attention has been directed to the procedure of potentio-metric titration as an analytical method. As the name implies, it is a titrimetric procedure in which potentiometric measurements are carried out in order to fix the end point. In this procedure we are concerned with changes in electrode potential rather than in an accurate value for the electrode potential with a given solution, and under these circumstances the effect of the liquid junction potential may be ignored. In such a titration, the change in cell e.m.f. occurs most rapidly in the neighbourhood of the end point, and as will be explained later (Section 15.18), various methods can be used to ascertain the point at which the rate of potential change is at a maximum this is at the end point of the titration. 

In the present chapter consideration is given to various types of indicator and reference electrodes, to the procedures and instrumentation for measuring cell e.m.f., to some selected examples of determinations carried out by direct potentiometry, and to some typical examples of potentiometric titrations. 

The use of a pH meter or an ion activity meter to measure the concentration of hydrogen ions or of some other ionic species in a solution is clearly an example of direct potentiometry. In view of the discussion in the preceding sections the procedure involved will be evident, and two examples will suffice to illustrate the experimental method. 

Potentiometry (discussed in Chapter 5), which is of great practical importance, is a static (zero current) technique in which the information about the sample composition is obtained from measurement of the potential established across a membrane. Different types of membrane materials, possessing different ion-recognition processes, have been developed to impart high selectivity. The resulting potentiometric probes have thus been widely used for several decades for direct monitoring of ionic species such as protons or calcium, fluoride, and potassium ions in complex samples. 

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