Current-potential curves, quantitative

In voltammetry (abbreviation of voltamperometry), a current-potential curve of a suitably chosen electrochemical cell is determined, from which qualitative and/or quantitative analytical data can be obtained. 

The Effect of Illumination. In an alkaline solution, an n-GaP electrode, (111) surface, under illumination shows an anodic photocurrent, accompanied by quantitative dissolution of the electrode. The current-potential curve shows considerable hysterisis as seen in Fig. 2 the anodic current, scanned backward, (toward less positive potential) begins to decrease at a potential much more positive than the onset potential of the anodic current for the forward scanning, the latter being slightly more positive than the Ug value in the dark, Us(dark). 

The measurement of peak potentials during LSV neglects much of the information present in the wave. For purely kinetic waves, the wave shape is dependent upon the mechanism of the process and can be used to distinguish between mechanisms. Although conclusions can be drawn by the direct comparison of the shape of the current-potential curve with theoretical data, such a comparison is subjective. Several procedures have been developed to analyse LSV wave shapes quantitatively for mechanism analysis. 

Little can be gleaned about the nature of the alloy interface from only the cyclic current-potential curves. An important question that needs to be addressed is whether or not the cychc vol-tammograms are accompanied by changes in the surface composition of the alloy while a qualitative solution to this problem can easily be obtained from multiple voltammetric scans, a quantitative answer is fundamentally necessary. In fact, a more critical matter involves the stability the PtsCo alloy under fuel-cell operating conditions that is, after prolonged use at the OCP in an 02-saturated solution. All of these issues can be simultaneously tackled if the surface composition of the PtsCo alloy is monitored as a function of time at a given applied potential. For such measurements, the alloy electrode is withdrawn from the 02-saturated electrolyte at the test potential and, prior to transfer into the surface analysis chamber, rinsed in deaerated ultrapure (Millipore) water to remove emersed sulfuric acid. The results are shown in Fig. 11. 

In the case of a diffusion-controlled reaction a current-potential curve can be evaluated quantitatively. The diffusion equation has to be solved again by using time-dependent boundary conditions. The mathematics, however, are very complicated and cannot be shown here. They end up with an integral equation which has to be solved numerically [11]. The peak current, /p, for a diffusion-controlled process (reversible reaction) is found to be... 

In the case of semiconductor electrodes, it is impossible to obtain the same information because the energy bands are fixed at the surface and any potential variation occurs only across the space charge layer. Here the maximum rate constant is expected if the peak of the distribution curve occurs at the lower edge of the conduction band of an n-type semiconductor. Therefore, the experimental results obtained with the modified metal electrodes, are of great importance for the quantitative analysis of rate constants from current-potential curves measured with semiconductor electrodes (see e.g. Section 7.3.4). 

More recently time-resolved techniques have been applied for studying photocarrier dynamics at the semiconductor-liquid interface. One of the main motivations is that such studies can lead to an estimation of the rate at which photo-induced charge carriers can be transferred from the semiconductor to a redox acceptor in the solution. This method is of great interest because rate constants for the transfer of photocarriers cannot be obtained from current-potential curves as in the case of majority carrier transfer (Section 7.3.5). The main aim is a detailed understanding of the carrier dynamics in the presence of surface states. The different recombination and transfer processes can be quantitatively analyzed by time-resolved photoluminescence emitted from the semiconductor following excitation by picosecond laser pulse. Two examples are shown in Fig. 7.60 [82, 83]. 

The current-potential curve for n- and p-type electrodes look similar to those given in Fig. 7.10, i.e. the anodic current increases exponentially with potential for a p-type electrode and it saturates at a low value for an n-type electrode in the dark. A quantitative evaluation showed that the slope of the current-potential at a p-type electrode exhibits an ideal slope of 60 mV/decade as illustrated by a semilogarithmic plot of the current potential curve (Fig. 8.5) [8]. This is an ideal situation insofar as the current is proportional to the hole density at the surface, as already discussed in detail in Chapter 7. Using the thin slice method, it was shown that the oxidation of the Si electrode occurred entirely via the valence band and that there was no injection of electrons into the conduction band. In addition it was found by coulometric analysis that two and not four charges were required for the dissolution of one Si atom [8, 9]. Whereas about... 

Analytical applications of electrochemistry, where the objectives are well defined, have fared better. There is a long list of papers going back twenty years on the applications of computers and then microprocessors. Reviews of this subject appear in the Fundamental Reviews sction of Analytical Chemistry (see refs. 8 and 9). In general, the aim in electroanalytical methods is to avoid interfering effects, such as the ohmic loss and the double layer capacity charging, and to use the Faradaic response peak current-potential curve as an analytical tool. Identification of the electroactive species is achieved by the position of the response peak on the potential axis and "pattern recognition , and quantitative analysis by peak shape and height. A recent development is squarewave voltammetry [10]. 

Let us now consider the particular cell in Figure 1.1.3 and discuss in a qualitative way the current-potential curve that might be obtained with it. In Section 1.4 and in later chapters, we will be more quantitative. We first might consider simply the potential we would measure when a high impedance voltmeter (i.e., a voltmeter whose internal resistance is so high that no appreciable current flows through it during a measurement) is placed across the cell. This is called the open-circuit potential of the cell. ... 

With only a qualitative understanding of the experiments described in Section 5.1.1, we saw that we could predict the general shapes of the responses. However, we are ultimately interested in obtaining quantitative information about electrode processes from these current-time or current-potential curves, and doing so requires the creation of a theory that can predict, quantitatively, the response functions in terms of the experimental parameters of time, potential, concentration, mass-transfer coefficients, kinetic parameters, and so on. In general, a controlled-potential experiment carried out for the electrode reaction... 

Selection of scan parameters. As mentioned earher, the scan rate significantly influences the shape and quantitative features of voltammograms. Usually, a variation of v gives important information. There are, however, other scan-related parameters that may affect the current/potential curves. In computer controlled instruments, the ideal linear variation of E is often simulated using a staircase function (Fig. 7). The response from such an excitation function... 

Even though the aim of this presentation is not to outline quantitative relationships, it is nonetheless interesting to know a property which characteristically emerges when these curves are described in quantitative terms. It is indeed possible to show that for simple redox systems with very close transport parameters (in the example below, the diffusion coefficients of the two ions of the Fe VFe " couples are taken as equal) the value of the current for the standard potential is equal to half the sum of the limiting currents (see figure 4.26 in section 4.3.3.2). in other words, the half-wave potential, and the standard potential are identical. When systems contain both elements of a redox couple at the outset, then this particular detail has little impact on how the current-potential curves are plotted in qualitative terms, since the Nernst law allows one... 

When establishing a method for determining redox kinetics, one can consider using the value of the slope of the current-potential curve for the open-circuit potential. However, it is impossible to assign a specific slope value to a fast couple because this slope is highly dependent on the limiting anodic and cathodic currents. To approach this issue from a quantitative point of view, one can start from the expression of the polarisation resistance around the equilibrium potential (see section 4.3.3.4). 

One can use current-potential curves, whether qualitative or quantitative, as a particularly powerful tool in understanding and/or predicting the reactions occurring in various situations, as well as for accounting for the corresponding working points (t/, I). 

The polarisation of an electrode is a function of the current flowing through it, and the product nils usually positive . Here we will give some quantitative equations but keep to simple cases. These examples highlight the key phenomena involved, and their impact on the shape of the steady-state current-potential curves. 

Corresponding current-potential curves measured with differently doped Sn02 electrodes could be quantitatively evaluated by using the above equation.The whole set of curves could be interpreted by assuming one single A value. Values obtained for various redox systems are given in Table 4. 

This section will explore the quantitative behavior of current-potential curves (voltammetry) and steady-state current measurements in flowing solution prior to considering liquid chromatographic assays. A similar examination of quiet solutions is reserved for the section on in vivo measurements. (In this and all subsequent voltammetry discussions, only oxidation reactions are treated, not because reductions are unimportant, but because there are to date few, if any, neurochemical applications.)... 

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