Potential sweeps principles

Again, application of the principle to the simple potential-step method appears trivial or superfluous. However, it is of quite great important for other types of potential control, namely double potential step, cyclic potential step [73], and especially the linear potential sweep method [21, 22, 73]. In all these techniques, sets of data Jf ( ) /f (f) E can be obtained, thus enabling kt(E) to be determined from eqn. (100). For more details, the reader is referred to the quoted textbooks. 

By proper treatment of the linear potential sweep data, the voltammetric i-E (or i-t) curves can be transformed into forms, closely resembling the steady-state voltammetric curves, which are frequently more convenient for further data processing. This transformation makes use of the convolution principle, (A.1.21), and has been facilitated by the availability of digital computers for the processing and acquisition of data. The solution of the diffusion equation for semi-infinite linear diffusion conditions and for species O initially present at a concentration Cq yields, for any electrochemical technique, the following expression (see equations 6.2.4 to 6.2.6) ... 

Laboratory studies of foam flow in porous media suggest that the relative foam mobility is approximately inversely proportional to the permeability. This means that foam has potential as a flow-diverting agent, in principle sweeping low-permeability regions as effectively as high-permeability regions [716]. 

When the reaction has adsorbed chemical intermediates, the surface concentration of which is potential dependent, the situation is difficult and was first put into a quantitative theory by Conway and Gileadi in 1962 and in more detail by Srinivasan and Gileadi in 1967. However, these pioneer authors dealt with submonolayers of simple entities such as H. How to deal with the potential-dependent intermediates in such a (still fairly simple) reaction such as methanol oxidation is not yet in sight (It can be done in principle, but there is still no knowledge of the kinetics of the reactions of the radical intermediates and how they are connected to the sweep rate.)... 

A complete comprehension of Single Pulse electrochemical techniques is fundamental for the study of more complex techniques that will be analyzed in the following chapters. Hence, the concept of half-wave potential, for example, will be defined here and then characterized in all electrochemical techniques [1, 3, 8]. Moreover, when very small electrodes are used, a stationary current-potential response is reached. This is independent of the conditions of the system prior to each potential step and even of the way the current-potential was obtained (i.e., by means of a controlled potential technique or a controlled current one) [9, 10]. So, the stationary solutions deduced in this chapter for the current-potential curves for single potential step techniques are applicable to any multipotential step or sweep technique such as Staircase Voltammetry or Cyclic Voltammetry. Moreover, many of the functional dependences shown in this chapter for different diffusion fields are maintained in the following chapters when multipulse techniques are described if the superposition principle can be applied. 

A linear approximation of the potential is certainly too sweeping a simplification. In reality, Vr varies with the internuclear separation and usually rises considerably at short distances. This disturbs the perfect (mirror) reflection in such a way that the blue side of the spectrum (E > Ve) is amplified at the expense of the red side (E < 14).t For a general, nonlinear potential one should use Equations (6.3) and (6.4) instead of (6.6) for an accurate calculation of the spectrum. The reflection principle is well known in spectroscopy (Herzberg 1950 ch.VII Tellinghuisen 1987) the review article of Tellinghuisen (1985) provides a comprehensive list of references. For a semiclassical analysis of bound-free transition matrix elements see Child (1980, 1991 ch.5), for example. 

In linear sweep voltammetry the potential scan is done in only one direction, stopping at a chosen value, Eu for example at t = tx in Fig. 9.1. The scan direction can be positive or negative and, in principle, the sweep rate can have any value. 

A sensitivity increase and lower detection limit can be achieved in various ways with the use of voltammetric detectors rather than amperometry at fixed potential or with slow sweep. The principle of some of these methods was already mentioned application of a pulse waveform (Chapter 10) and a.c. voltammetry (Chapter 11). There is, nevertheless, another possibility—the utilization of a pre-concentration step that accumulates the electroactive species on the electrode surface before its quantitative determination, a determination that can be carried out by control of applied current, of applied potential or at open circuit. These pre-concentration (or stripping) techniques24"26 have been used for cations and some anions and complexing neutral species, the detection limit being of the order of 10-10m. They are thus excellent techniques for the determination of chemical species at trace levels, and also for speciation studies. At these levels the purity of the water and of the... 

Gas solid interactions are difficult to study systematically in conventional reactors but can readily be studied in a specialized type of temperature scanning reactor intended for this type of process, the stream swept reactor (SSR). In principle this is a batch reactor containing the solid through which the fluid phase flows sweeping out any desorbed material or reaction products to a detector at the outlet. Reactors of this type are also potentially applicable in adsorption studies and will be discussed in Chapter 5 under the heading TS-SSR. 

Figure 16. Principle of linear sweep voltammetry (A) and cyclic voltammetry (B) Top Variation of voltage with time Bottom Resulting current-potential curves...

The principle of the technique is illustrated in Fig. 1.65. From Fig. 1.65 we note that a series of pulses of amplitude A (usually from 5 50 mV) are superimposed on a slow sweep rate (ca. lmVs ) linear potential ramp that acts as a slowly changing baseline. The pulse is repeated after a time T >, and the pulse has a duration To t. The current is measured over a fixed time interval 8t just before and again toward the end of the pulse, as indicated in Fig. 1.65. The differential pulse voltammogram then simply consists of a plot of the difference in these two current measurements A/ = i To) — i r) as a function of the base potential E. 

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