Electrochemical method

Electrochemical methods include potentiometry, cyclic voltammetry and chronoamperometry. These methods as well as other voltammetric methods and the impedance of electrochemical systems are discussed in this chapter. 

At an early date, Nernst also introduced the concept of potentiometry with polarised electrodes5 7, that went together with the many other specialised forms of potentiometric measurements for a wide range of chemical systems8. 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R  

For such a half reaction the free energy is given by the relation  

It also is a measure of the equilibrium constant for the half reaction assuming the activity of electrons is unity and under this condition the following equation is valid  

Electrochemical methods have been used for determinations of species of elements in natural waters. Of the many electrochemical techniques, only a few have proved to be useful for studies of speciation in complex samples, and to possess the sensitivity required for environmental applications. The greatest concern is the measurement of the toxic fraction of a metal in an aqueous sample. The definition of a toxic fraction of a metal is that fraction of the total dissolved metal concentration that is recognised as toxic by an aquatic organism. Toxicity is measured by means of bioassays. Elowever, a universally applicable bioassay procedure cannot be adopted because the responses of different aquatic species to metal species vary. Nevertheless, bioassays should be used as means of evaluation and validation of speciation methods. A condition is that the test species (of the bioassay) should be very sensitive to the metals being studied so as to simulate a worst case situation (Florence, 1992). 

Electrochemical methods are applicable in our case due to the inherent conductivity of the polymers under investigation. As we shall show throughout this work, elec- 

FIGURE 1.22 Emerging tools for communication with dynamic polymer structures. 

FIGURE 1.23 Communicating with a conducting polymer PPy/Cl in solution (a) cyclic voltammetry—a plot of current flow versus the electrical (potential) stimulus applied (b) the electrochemical quartz crystal mircobalance readout—mass polymer versus electrical (potential) stimulus applied (c) the resistometry readout—resistance of the polymer versus the electrical (potential) stimulus applied. (Printed with permission from Materials Science Forum, Vol. 189-190, Characterization of conducting polymer-solution interfacial processes using a new electrochemical method, A. Talaie, G. G. Wallace, 1995, p. 188, Trans Tech Publications, Switzerland.) 

The data in Table 1.4, accepted by many scientists for the best part of a decade, belie the complexity of the controllable dynamic behavior of conducting polymers. 

Oxidation and Reduction Potentials (versus SCE) and Maximum Doping Levels for Selected Conducting Polymers 

Electrochemical methods of detection affinity interactions at surfaces are rather effective, due to their relative simplicity and low cost. An amperometric aptasensor based on a sandwich assay was proposed by Ikebukuro et al. 

Electrochemical indicator methods are based on the use of a redox probe that undergoes an oxidation and reduction transition due to electron transfer from an electrode surface to a probe. In 2005, several papers were published that used methylene blue (MB) as an electrochemical indicator. Methylene blue is a positively charged low-molecular-mass compound that can be reduced by two electrons to leucomethylene blue (LB). The reduction process can be monitored effectively by differential pulse voltammetry, cyclic voltammetry, or coulometry. In the presence of a redox probe Fe(CN)g, the LB is oxidized to MB and system is regenerated (Boon et al., 2000 Ostatna et al. 2005). In papers of Hianik et al. (2005, 2007) the MB was used as an indicator for the detection of interaction of human thrombin with DNA aptamer. The method of detection is shown 

We have shown (Hianik et al., 2007) that this sensor has a sensitivity and detection limit (around 5 nM) comparable to that in the mass detection (QCM) and SPR methods (Ostatna et al., 2008) and is sufficiently selective compared with nonspecific binding of HSA or human immunoglobulin G (IgG). The detection limit obtained is sufficient for detection thrombin in real blood samples (the physiological concentration of thrombin is in the range low nanomolar to low micromolar (Lee and Walt, 2000). 

The affinity of thrombin to the aptamer depends on the ionic strength, on the composition of buffer, and on pH. To check this we used an electrochemical indicator to detect the binding of thrombin to aptamer in the electrolyte of a different concentration of NaCl as well as for three different pH values. 

We also compared how the structnral peculiarities of the aptamer affect the binding of thrombin. For this purpose we used biotinylated DNA aptamers 

Electrochemical methods have been very fashionable in many laboratories since the 1950s, including for studying the corrosion of aluminium. However, theoretical and practical reasons considerably limit the usefulness of these methods for aluminium. (The following remarks apply only to aluminium). 

The most common type of corrosion on aluminium in media close to neutral, i.e. natural media, is pitting corrosion. In this case, the measurement of the corrosion current makes no sense, and it will not give any information on the type of corrosion. 

The electrochemical behaviour of aluminium is strongly influenced by the permanent presence of a natural oxide film on its surface. Therefore, a mixed potential corresponding to the pitting potential is measured on aluminium (see Section B.1.7) this potential represents a threshold below which pitting corrosion can be prevented. 

However, this pitting potential does not have the same meaning as in the case of steel, where initiation is followed by rapid propagation. On aluminium, the initiation of a pit may 

The comparison of the dissolution potentials of aluminium alloys may reach absurdity, for example, leading to a preference for alloys of the 2000 series, which have a dissolution potential far less negative, about — 650 mV, over those of the 5000 series, which have a more electronegative potential, on the order of - 800 mV (Table B.1.3). And yet the latter show excellent corrosion resistance, while alloys of the 2000 series are highly susceptible to pitting corrosion in natural environments. 

Advances in the design of electrochemical cells and a greater understanding of electrochemistry have led to a more widespread use of electrochemistry in effluent clean-up applications. Electrochemical clean-up is not restricted to metal removal, it can be used for the destruction and removal of organic species too. In fact, one of the attractions of electrochemical clean-up is that, under the correct conditions, it can clean-up both inorganic and organic waste in one, simple step. Furthermore, effluents containing more than one metal are also amenable for clean-up. 

Treatment of effluents with electrochemical methods usually relies on changing the formal oxidation state of effluent constituents. For metals a change in oxidation state brings about a large change in properties (see section 14.6.1) which can be used to detoxify effluents. Both the oxidation and reduction of metals are viable effluent treatments, although the reduction of metals to their zero oxidation state is the most common type of operation. 

Theoretically, by poising the potential of an electrochemical cell at a value which is sufficient to reduce chromium(III) but not aluminium(III), chromium could be removed preferentially from solution. As chromium is a common contaminant of bauxitic alloys (the main feedstock for aluminium industry) electrochemistry may provide a means of selectively removing chromium from aluminium products. However, this process may be impractically slow. Much depends on the relative concentrations of aluminium and chromium, temperature, pH and cell design. Nevertheless, standard electrode potentials can be used as a preliminary evaluation of the feasibility of electrochemical methods for clean-up. 

The EOI of organic species appears, at first glance, to have little to do with metal removal from effluents. That is until one considers that for every electro-oxidation/reduction of a metal there must be a respective electro-reduction/oxidation of another species to maintain a charge balance. In many cases the other species is an organic molecule which can be easily oxidised/reduced phenols are examples. Phenols are oxidised to benzoquinones and catechols (scheme 14.5) which themselves can be oxidised to water and carbon dioxide. 

As this oxidation is energetically, relatively easy the overall electrochemical process (which includes reduction of metal and oxidation of phenol) requires comparatively little energy. On the other hand, if the only oxidisable species in solution (other than the metal) is difficult to oxidise (for example a halide ion) then the overall electrochemical process requires more energy. The message is that the whole content of the efflu- 

There are several electrochemical methods, such as cyclic voltammetry, polarography, chronoamperometiy and chronopotentiometry, which can be used to measure homogeneous reaction rates. It is beyond the scope of this text to explore all the variations and intricacies of electrochemical methods, but they are described in several sources. The purpose here is to give some basic background and some examples of the technique. 

The field has a well-developed nomenclature and symbolism. The one-electron electrode reaction is designated by E and a chemical reaction by C. There are extensions of this system, such as E+E for a two-electron electrode reaction, and for reduction and oxidation. Cl and C2 for first- and second-order reactions and Cl for a pseudo-first-order reaction. Cyclic voltammetry is the most widely used technique because of the availability of appropriate instrumentation, and the number of 2q pIications is likely to increase with the recent availability of software to simulate cyclic voltammograms. Such simulations generally are essential for the determination of meaningful kinetic parameters. 

The quantitative analysis requires knowledge of the rate(s) of the heterogeneous electrode reaction(s), reagent diffusion coefficients and the transfer coefficient. If the electrode reaction is reversible, most of these parameters can be determined from the CV experiments. The formal reduction potential, differs from the standard potential, °, because the latter is obtained by extrapolation to infinite dilution, while the former refers to the actual experimental conditions of ionic strength and temperature. For a fast, reversible process, E° = j,2 10 mV if the diffusion coefficients of the oxidized and reduced forms are within a factor of two. Potentials are reported relative to some standard electrode, such as ferrocene/ferrocinium ion, saturated calomel, SCE, or Ag/AgCl, and this must be taken into account in comparing results from different sources. 

One restriction on these methods is that the medium must contain an inert electrolyte to maintain electrical conductivity. Typically, 0.1 M tetraalkylammonium salts of PF,. , CFjSO, or CIO are used. Problems can arise due to adsorption of reagents on the electrodes and uncertainties in the chemical characterization of the product of the electrode reaction. The experiment can give the number of electrons, n, involved and the reduction potential. Then, the nature of the electrochemically generated reagent often is inferred by chemical reasoning and analogy. It is possible to couple the system to some spectroscopic technique, such as EPR or IR spectroscopy with transparent electrodes, to give further characterization. 

The electrochemical behavior of aqueous Cu(II) and Cu(I) complexed by 2,9-dimethyl 1,10-phenanthroline, DMP, has been studied by Lei and Anson. The measurements involved cyclic and rotating-disk voltammetry with glassy carbon electrodes at pH S.2 in a buffer containing 0.04 M aqueous acetic, phosphoric and boric acids, at ambient temperature. Glassy carbon electrodes were used to minimize adsorption of electroactive species on the electrode. If the initial ratio of DMP to Cu(II) is then a normal CV is observed and assigned to the following reactimi  

Several electrochemical techniques have been devised for the study of fast reactions. These methods require that one of the species involved in the reaction of interest be electroactive, so that the reaction under study is coupled to an electrode 

This is sometimes described as a competitive method, the coupling species O being involved in two separate reactions. 

The electrode current depends on the rates of the coupled reactions, but by suitable adjustment of the electrode potential (into the diffusion current region for the electrode reaction) the rate of the reduction reaction can be made so fast that the current depends only on the rate of the prior chemical reaction. The dependence of the observed current on the presence of the chemical reaction is a measure of the rate. 

Now at some pH comparable to pK, two waves are observed, corresponding to the reduction of both HA and A. The currents are proportional to the concentrations of the electroreducible species. Because the pH and pK are known, the concentrations of HA and A in the bulk solution can be calculated. It is then found that the observed polarographic currents cannot be accounted for on tbe basis of the known bulk concentrations. It is concluded that the ratio of the concentrations at the electrode surface is different from the ratio of bulk concentrations, and this is a consequence of the coupling between the chemical and electrode processes. In the pyruvic acid system, HA can be converted to the hydroxy acid by the electrode 

The theory of rate measurements by electrochemistry is mathematically quite difficult, although the experimental measurements are straightforward. The techniques are widely applicable, because conditions can be found for which most compounds are electroactive. However, many questionable kinetic results have been reported, and some of these may be a consequence of unsuitable approximations in applying theory. Another consideration is that these methods are mainly applicable to aqueous solutions at high ionic strengths and that the reactions being observed are not bulk phase reactions but are taking place in a layer of molecular dimensions near the electrode surface. Despite such limitations, useful kinetic results have been obtained. 

Wagner pioneered the use of solid electrolytes for thermochemical studies of solids [62], Electrochemical methods for the determination of the Gibbs energy of solids utilize the measurement of the electromotive force set up across an electrolyte in a chemical potential gradient. The electrochemical potential of an electrochemical cell is given by  

Solid electrolytes are frequently used in studies of solid compounds and solid solutions. The establishment of cell equilibrium ideally requires that the electrolyte is a pure ionic conductor of only one particular type of cation or anion. If such an ideal electrolyte is available, the activity of that species can be determined and the Gibbs energy of formation of a compound may, if an appropriate cell is constructed, be derived. A simple example is a cell for the determination of the Gibbs energy of formation of NiO  

The left-hand side of the cell, the working electrode, has its Pq2 fixed by the Ni + NiO equilibrium pressure, while on the right-hand side the reference electrode has Po2 given by the air atmosphere. Alternatively, a buffer may be used on the reference electrode side. The left- and right-hand side half-cell reactions are respectively 

When a perfect ionic conductor electrolyte is used, 

Among the oxygen ion conductors, CaO or Y2C 3 stabilized Zr02 (CSZ and YSZ) [67, 68], and Y2C 3 or La203 stabilized Th02 [69] are frequently used. CSZ and YSZ are limited to oxygen partial pressures in the range from 10-13 to 1010 Pa at 1273 K [68], Lower partial pressures are allowed with the thoria-based 

Nanocrystalline cerium (IV) oxide powders with an average particle size of 10 -14 nm have been prepared by the cathodic base electrogeneration method.The nanocrystalline Ce02 powders are prepared in the cathode compartment of a divided electrochemical cell. The cathode is a platinum wire and the anode is a platinum mesh electrode. The cathode compartment in the divided cell contained 0.5 moM cerium (III) nitrate and 0.5 moM ammonium nitrate, and the anode compartment contained 0.5 moM ammonium nitrate. The two compartments are separated with a medium porosity glass fiit. The electrochemical synthesis is run in the galvanostatic mode at a current density of 1 A-cm and the particle size is controlled by adjusting the solution temperature. 

Transient electrochemical techniques are most commonly used in studies of electrochemical transformations of electroactive polymers, since surface layers contain rather small amounts of material (usually less than 10 molcm ). Galvanostatic or potentiostatic methods are often applied during electropolymerization, and poten-tiostatic techniques are also used in combination with other techniques, e.g., spec-troelectrochemistry or EQCM, when the goal is to obtain results at equilibrium. EIS measurements are usually carried out at a series of constant potentials. 

Electrochemistry is a scientific discipline with a well developed system of theories and quantitative relationships. It has many applications and uses in both fundamental and applied areas of chemistry—in the study of corrosion phenomena, for example, for the study of the mechanisms and kinetics of electrochemical reactions, as a tool for the electrosynthesis of organic and inorganic compounds, and in the solution of quantitative analytical problems. This last area will be emphasized in the next four chapters. 

Like all the other acidity functions, W0(H) equals pH in dilute aqueous solution. In strong acids, this function should be a logarithmic measure of the proton activity as long as the normal potential of the redox system, ferrocene-ferricinium, is constant. This was, however, not the case in very strong acid solutions because ferrocene underwent protonation. Other electrochemical pH indicators have been proposed, such as quinine-hydroquinone or semiquinone-hydroquinone, the basicity of which can be modified by substitution on the aromatic ring. These electrochemical indicators have been used with success by Tremillon and co-workers48 for acidity measurements in anhydrous HF and HF containing superacids. 

Corrosion occurs at a rate determined by equilibrium between opposing electrochemical reactions. The rate of any given electrochemical process depends on the rates of two conjugate reactions proceeding at the surface of the metal. Transfer of metal atoms from the lattice to the solution (anodic reaction) with the liberation of electrons and consumption of these electrons by some depolarisers (cathodic reaction). When these two reactions are in equilibrium, the flow of electrons from each reaction of balanced and no net electron flow (current) occurs. Various methods are available for the determination of dissolution rate of metals in corrosive environments but electrochemical methods employing polarisation techniques are by far most widely used. The corrosion rate (CR) is evaluated by mass loss method considering uniform corrosion. The Corrosion rate is determined by the following formula as per standard [102]. 

W is weight loss (mg), A is area of the specimen (cm ), D is density of the specimen (gm/cm ), T is exposure time (hours) and unit pm/year is micro-metre/year. Indirect methods of corrosion rate measurement involve anodic/ cathodic reaction, consideration of current potential relationship or polarisation resistance values. Tafel extrapolation method is the most popular laboratory methods for measuring corrosion rate of a metal from electrochemical data in a corrosive medium. 

Since kinetics and mechanism of corrosion is controlled by electrochemical principles, the technique based on electrochemical methods is used to determine the corrosion rate and understand the mechanism of corrosion process. The testing methods are based on principle of accelerating the corrosion process without changing the environment and the corrosion rates can be measured without removing the test specimens. 

Open Circuit Potential. Metal immersed in an aqueous solution develops an electric potential at its surface called open circuit potential (OCP) which is a characteristic of the metal solution system. The magnitude of OCP is measured with respect to reference electrode with the help of high impedance voltmeter and potentiostat is used to polarise or displace equilibrium potential of specimen in the negative (cathodic) or positive (anodic) direction with reference to OCP. This is manipulating the rates (ionic currents) of respective cathodic and anodic half-cell electrochemical reactions. The electrochemical potential of a metal in a certain solution is dependant on the type of the metal, the composition of the solution and its pH, oxygen content and temperature [104, 105]. 

Polarisation Test Method. This method is used to determine the corrosion rate. Polarisation resistance (Rp) is the resistance of specimen to oxidation during the application of an external potential in DC corrosion measurement methods. The CR and /corr are related to Rp and can be calculated from equation given below and polarisation resistance is related to Ton according to Stem Geary relation [106]. 

A graphite rotating disk electrode maintained at 0.5 V is used to monitor the reaction of Ru(NHj)5 as it is being oxidized by Oj to RulNKj) . The limiting current is proportional to [RufNHj) ] and there is no interference by O2 or the product. The electrode is rotated at 3600 rpm to ensure rapid mixing of reactants within seconds, since reaction times are 20-30 s. See Ref. 333. Square-wave amperometry has been linked to stopped-flow to measure reaction half-lives as short as 5 ms. 

Polarographic probes that respond specifically to concentrations of Oj, CO2 or SOj are very useful. They have decided advantages over the more clumsy manometric monitoring. Their use is limited to slow reactions or the continuous-flow approach, because of the relatively long response time of the probe. An 02-eleetrode system for incorporation in a spectrophotometer cuvette, for simultaneous monitoring of [Oj] and spectral changes, has been deseribed. 

Early cyclic voltammetric (CV) studies158,159 established that tetraalkyl hydrazines give chemically reversible one-electron oxidations with no evi- 

2-dimethyltetrahydropyridazine (111), the NMR methods (see Section III,C,2) only detect the ae conformation, whereas CV enables AG° (ee ae) to be estimated as almost certainly above 3 kcal mol 1.161 

low-temperature CV provides a complementary technique to the NMR method for the conformational analysis of cyclic hydrazines. 

The fast chemical reaction method of studying conformational equilibria has been analyzed in detail.163 

suppose that the species which is discharged (the depolarizer) is involved in an equilibrium of the type 

Yet a third situation may be considered where the depolarizer is regenerated by a chemical reaction—e.g.. 

In such a situation a catalytic current is measured. The crux of the electrochemical methods is to relate the ratio of kinetic, or catalytic, and diffusion currents to the rate coefficients of the respective rate-limiting chemical processes. In fact, the currents are comparatively easy to measure, and simple and cheap apparatus is available for doing this. The main disadvantage is that the theory is somewhat difficult to apply quantitatively. 

Four main methods which use electrode processes have been developed, although a few others are being investigated of these, by far the most work has been done on the first. 

Group 1, in yhich a steady voltage is applied between the electrodes  

Various cells are available for the detection of phosgene. In one example [2093a], the test gas is fed into a solution of potassium iodide, and the liberated iodine reduced at the cathode (c/. Section 3.2.1.2). Ion-selective electrodes have also been adapted for the 

indirect, methods for the electrochemical determination of phosgene are based upon the measurement of chlorine as a result of pyrolysis [1174,2093a]. 

Other aspects of high pressure electrochemistry kinetics can be obtained from a review by two of the leading experts.118 

The existence of various oxidation states of technetium indicates the possibility of using polarographic, coulomclric, and potentiometric techniques for its determination. 

The composition of alloys can be very conveniently and rapidly established by VIM, using the technique of differential pulse voltammetry [17]. Also, 

In the case of battery materials, the interparticle diffusion effects within a normally starved electrolyte cell design force standard voltammetric or coulometric experiments to be extremely time consuming. However, when working with small 

VIM also allows the observation of reaction products that are unstable in solution when working under conditions that allow for electrochemical reaction of the compound while at the same time preventing macroscopic dissolution processes. For example, the rapid isomerization of c/5-[Cr(CO)2(dpe)2] (dpe Ph2PCH2CH2PPh2) to the trans form in solution was elegantly avoided in the solid state, and so the proposed square scheme involving the cis/cis and the transltrans couples was nicely proved [22], 

VIM is suitable when the kinetics of electrochemical dissolution of particles is of interest because information on size and shape of the particles is desired [23-26], Theoretical aspects of VIM have been addressed in several papers. These studies concern the geometry of the progressing electrochemical reaction [27-29], the influence of the conductivity of solutions [30], and also the question whether electrical insulators may yield measurable currents [31]. The interested reader is referred to these publications. 

Thin films of BaTi03 [11] and lead zirconate titanate [12] have been prepared by cathodic reduction. Konno and co-workers [13] have obtained thin films of La, M Cr03 (M = Ca, Sr) by heat treatment (700 °C, 10 min) of the hydroxy-chromate precursor obtained by cathodic reduction of a mixed metal nitrate solution containing (NH )2Cr20.j. Films of LaFeOj are prepared by heat treatment of an electrosynthesized hydroxide precursor at 7(X) °C (which is much lower than the temperature ( 1000 C) used in the conventional ceramic preparation) 

Essentials of Inorganic Materials Synthesis, First Edition. C.N.R. Rao and Kanishka Biswas. 2015 John Wiley Sons, Inc. Published 2015 by John Wiley Sons, Inc. 

FIGURE 10.6.1 Schematic diagrams of (a) the electrochemical cell and (h) the rotating disc electrode. 

Monosnlfides of U, Gd, Th and other metals are obtained from a solution of the normal valent metal sulfide and chloride in an NaCl/KCl eutectic. LaB is prepared by taking La Og and B Og in an LiBO /LiF melt and by using gold electrodes. Crystalline transition metal phosphides are prepared from solutions of oxides with alkali metal phosphates and halides. 

As mentioned earlier, intercalation of alkali metals in host solids is readily accomplished electrochemically. It is easy to see how both intercalation (reduction of the host) and deintercalation (oxidation of the host) are processes suited for this method. Thus, lithium intercalation is carried out by using lithium anode and a lithium salt in a non-aqueous solvent. 

Boillat et al. (2010) developed improvements in the spatial resolution of neutron imaging specifically for application in fuel cell imaging, where the resolution requirement in different directions may vary by one order of magnitude, thus making anisotropic setups attractive. A maximal spatial resolution of 8.7 pm could be reached. For the transient studies, the combination of a high resolution of 20 pm with exposure times of 10 s proved to resolve the water evolution, both temporally and spatially. 

Roy and Orazem (2008) conducted impedance measurements to gain insight into flooding of a single PEMFC. The flooding of gas-diffusion layer pores in the fuel cell has been associated with increases in the internal cell resistance and in the impedance response of the fuel cell. The formation and removal of water droplets is an inherently stochastic process which increases the stochastic errors observed in impedance measurements. A measurement technique oriented toward 

EXPERIMENTAL METHODS FOR INVESTIGATING FUEL CELL STACKS 

Yang et al. (2010) developed an EIS technique to characterize a DMFC under various operating conditions. A silver/silver chloride electrode was used as an external reference electrode to probe the anode and cathode during fuel cell operation. The external reference was sensitive to the anode and cathode as current was passed in the working DMFC. The impedance spectra and DMFC polarization curves were investigated systematically as a function of air and methanol flow rates, methanol concentration, temperature, and current density. Water flooding in the cathode was also examined. 

In a paper by Wasterlain et al. (2011) a new instrument developed in-lab is proposed to satisfy the requirements of electrochemical impedance studies to be led on large fuel cell plants made of numerous individual cells. Moreover, new voltammetry protocols dedicated to PEMFC stack analysis are described. They enable, for example, the study of membrane permeability and loss of platinum activity inside complete PEMFC assemblies. In the first part, a new electrochemical impedance spectrometer that makes testing large FC stacks possible has been presented. To validate this acquisition system and to demonstrate some of its capabilities, some experiments were conducted on a 20-cell PEMFC stack. In the second part, voltanunetry experiments were conducted on short FC stacks with a commercial potentiostat. The fuel crossover phenomenon in a three-cell PEMFC stack was analyzed using the linear sweep voltametric (LSV) method. The crossover rates were determined for each individual cell inside the complete assembly and for the entire stack as well. 

Electron Spin Resonance Spectrometery (E.S.R) iseyond the scope of this volume. (J.Chem.Educ., 53(1976)394). 

However, briefly the technique applies to species with unpaired electrons. When these are placed in a magnetic field, the interaction between this field and that produced by the unpaired electrons lifts the spin degeneracy. As a result, a frequency of maximum absorption is observed in the microwave spectral region. Oxidation states of some metal complexes can be established by their esr spectra. 

Electric conductivity provides highly useful information on the association of surfactants in solution. The conductivity is measured in a thermostated cell calibrated with a standard KCl solution. Polarization is avoided by using alternating current or applying short pulses of opposing polarity. The conductance data are related to the surfactant concentration by one of the following graphic presentations  

The specific conductivity is plotted against the surfactant concentration [273-276] (Fig. 9.14), or against the square root of the surfactant concentration [277]. 

The equivalent conductivity is plotted against the square root of surfactant concentration [272,278]. 

If an ionic surfactant is completely dissociated, the specific conductivity increases below the cmc linearly with increasing surfactant concentration. The slope of the linear function is the sum of the individual ionic conductivities. Above the cmc, in an ideal case the concentration of surfactant monomers and, consequently, the conductivity are constant. In a real system, the micelles are ionic and contribute to conductivity. Hence, the conductivity increases with increasing surfactant concentration but with a lower slope than below the cmc. The break in the conductivity curve indicates the cmc [279]. 

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Electrochemical methods may be classified into two broad classes, namely potentiometric metiiods and voltannnetric methods. The fonner involves the measurement of the potential of a working electrode iimnersed in a solution containing a redox species of interest with respect to a reference electrode. These are equilibrium experiments involving no current flow and provide themiodynamic infomiation only. The potential of the working electrode responds in a Nemstian maimer to the activity of the redox species, whilst that of the reference electrode remains constant. In contrast, m voltannnetric methods the system is perturbed... 

Bard A J and Falkner L R 1980 Electrochemical Methods—Fundamentals and Applications (New York Wiley)... 

For in-depth coverage of electrochemical methods including mathematical derivations. 

Marecek and colleagues developed a new electrochemical method for the rapid quantitative analysis of the antibiotic monensin in the fermentation vats used during its production. The standard method for the analysis, which is based on a test for microbiological activity, is both difficult and time-consuming. As part of the study, samples taken at different times from a fermentation production vat were analyzed for the concentration of monensin using both the electrochemical and microbiological procedures. The results, in parts per thousand (ppt), are reported in the following table. 

Although there are only three principal sources for the analytical signal—potential, current, and charge—a wide variety of experimental designs are possible too many, in fact, to cover adequately in an introductory textbook. The simplest division is between bulk methods, which measure properties of the whole solution, and interfacial methods, in which the signal is a function of phenomena occurring at the interface between an electrode and the solution in contact with the electrode. The measurement of a solution s conductivity, which is proportional to the total concentration of dissolved ions, is one example of a bulk electrochemical method. A determination of pH using a pH electrode is one example of an interfacial electrochemical method. Only interfacial electrochemical methods receive further consideration in this text. 

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. 

The largest division of interfacial electrochemical methods is the group of dynamic methods, in which current flows and concentrations change as the result of a redox reaction. Dynamic methods are further subdivided by whether we choose to control the current or the potential. In controlled-current coulometry, which is covered in Section IIC, we completely oxidize or reduce the analyte by passing a fixed current through the analytical solution. Controlled-potential methods are subdivided further into controlled-potential coulometry and amperometry, in which a constant potential is applied during the analysis, and voltammetry, in which the potential is systematically varied. Controlled-potential coulometry is discussed in Section IIC, and amperometry and voltammetry are discussed in Section IID. 

An electrochemical method in which the current required to exhaustively oxidize or reduce the analyte is measured. 

In potentiometry, the potential of an electrochemical cell under static conditions is used to determine an analyte s concentration. As seen in the preceding section, potentiometry is an important and frequently used quantitative method of analysis. Dynamic electrochemical methods, such as coulometry, voltammetry, and amper-ometry, in which current passes through the electrochemical cell, also are important analytical techniques. In this section we consider coulometric methods of analysis. Voltammetry and amperometry are covered in Section 1 ID. 

An electrochemical method in which we measure current as a function of the applied potential. 

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