Sampled-current voltammetry reversible

In a sampled current voltammetry experiment, small potential steps are made progressively as shown in Figure 4(a) within the typical limits of -I- 200 mV and Eq — 200 mV for a reversible process. The i versus E curve can be constructed (Figure (4b)) with the following characteristics for the reversible process the limiting current, i, obtained at — < —118 mV, is proportional to Cq, Ey — E... 

SAMPLED-CURRENT VOLTAMMETRY FOR REVERSIBLE ELECTRODE REACTIONS... 

Sampled-Current Voltammetry for Reversible Electrode Reactions 177... 

In sampled-current voltammetry, our goal is to obtain an /(t)-E curve by (a) performing several step experiments with different final potentials E, (b) sampling the current response at a fixed time r after the step, and (c) plotting i r) V5. E. Here we consider the shape of this curve for a reversible couple and the kinds of information one can obtain from it. 

Figure 5.4.1 Characteristics of a reversible wave in sampled-current voltammetry.

These equations describe the voltammogram for a reversible system in sampled-current voltammetry as long as semi-infinite linear diffusion holds. It is interesting to compare... 

The plateau current of a simple reversible wave is controlled by mass transfer and can be used to determine any single system parameter that affects the limiting flux of electroreactant at the electrode surface. For waves based on either the sampling of early transients or steady-state currents, the accessible parameters are the fi-value of the electrode reaction, the area of the electrode, and the diffusion coefficient and bulk concentration of the electroactive species. Certainly the most common application is to employ wave heights to determine concentrations, typically either by calibration or standard addition. The analytical application of sampled-current voltammetry is discussed more fully in Sections 7.1.3 and 7.3.6. 

Because the half-wave potential for a reversible wave is very close to, sampled-current voltammetry is readily employed to estimate the formal potentials for chemical systems that have not been previously characterized. It is essential to verify reversibility, because En2 can otherwise be quite some distance from E (see Sections 1.5.2 and 5.5 and Chapter 12). 

In this section, we will treat the one-step, one-electron reaction O + R using the general (quasireversible) i-E characteristic. In contrast with the reversible cases just examined, the interfacial electron-transfer kinetics in the systems considered here are not so fast as to be transparent. Thus kinetic parameters such as kf, and a influence the responses to potential steps and, as a consequence, can often be evaluated from those responses. The focus in this section is on ways to determine such kinetic information from step experiments, including sampled-current voltammetry. As in the treatment of reversible cases, the discussion will be developed first for early transients, then it will be redeveloped for the steady-state. 

So far, it has been most convenient to think of (5.2.24) as describing the current-time response following a potential step however it also describes the current-potential curve in sampled-current voltammetry, just as we understood (5.4.17) to do for reversible systems. At a fixed sampling time r, A becomes f 0), which is a function... 

Pulse voltammetry — A technique in which a sequence of potential pulses is superimposed to a linear or staircase voltage ramp. The current is usually measured at the end of the pulses to depress the - capacitive (charging) current. Depending on the way the pulses are applied and the current is sampled we talk about - normal pulse voltammetry, reverse pulse voltammetry and - differential pulse voltammetry. Several other, less popular pulse techniques are offered in commercial voltammetric instrumentation. Some people consider - square-wave voltammetry as a pulse technique. 

Square-wave voltammetry is a large-amplitude differential technique in which a waveform composed of a symmetric square wave, superimposed on a base staircase potential, is applied to the working electrode (8) (Fig. 3.9). The current is sampled twice during each square-wave cycle, once at the end of the forward pulse (at h) and once at the end of the reverse pulse (at t2). Since the square-wave modulation amplitude is very large, the reverse pulses cause the reverse reaction of the product (of the forward pulse). The difference between the two measurements is plotted versus the base staircase potential. 

The elimination of the capacitive current in the case of - differential pulse voltammetry (DPV) is achieved by sampling the current twice before pulse application and at the end of the pulse. The basis for that elimination is the very different time dependence of both current components Ic exponentially dropping with time, and If decreasing with r1/2, at least in reversible cases (- Cottrell equation). 

Differential Pulse Voltammetry (DPV). There are two main differences between differential pulse and NPV. The waveform for DPV, Figure 10(b), involves a pulse of amplitude AEpuise like that of the normal pulse sequence but the step back down is not to the initial potential, instead it is to a specific differential that is used during the measurement. Also, there are two sampling periods for each pulse, once at the end of the potential step up, like in NPV, and an additional sampling period at the end of the step down in potential, after which the difference in the two signals is recorded hence the name DPV. This pulse sequence results in a current signal response different from that of NPV, shown in Figure 10(b). If the electrochemical process is reversible, the peak half width, A p/2, is determined by equation (9), ... 

The special case of square-wave voltammetry (SWV) is worth noting separately from other alternating current techniques because it is both more rapid and more sensitive than DPP/DPV. In SWV, the applied potential waveform is a staircase with constant step height on which is superimposed an asymmetrical forward and reverse voltage pulse of constant amplitude and very short duration, typically less than 10 ms. Thus, the entire polarogram may be run in about approximately 1 s, with the enhanced sensitivity of the method owing to sampling of the current at the end of both the forward and reverse directions of the pulse. 

Convective renewal. When normal pulse voltammetry is carried out in a convective system, as at a rotating disk, one can rely on stirring to renew the diffusion layer while the potential is held at E. This can be true even if the chemistry cannot be reversed electrolytically, as in the case where the species created in the pulse decays to an inactive product. The convection can also affect the current sampled in each pulse, so that the theoretical expectation based on diffusion theory is exceeded. However the error is often either irrelevant (as in analytical applications where calibration is possible) or fairly small (because a pulse of short... 

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