Voltammetry sampled current

A large number of potential-relaxation and current-relaxation techniques have been developed in 1950s-1980s for fast kinetic measurements (8). The later advances in UMEs resulted in a less frequent use of relaxation techniques in kinetic experiments. Because of the space limitations, only one large-perturbation method (sampled-current voltammetry) and one small-perturbation technique (alternating current voltammetry) will be considered. 

Equation (15.6) describes the shape of a sampled-current voltammogram for a general case of a quasi-reversible ET reaction  

The kinetic zones in sampled-current voltammetry are determined by the value of the kinetic parameter A° = k°t il+0/Do, and the quasi-reversibility region can be expressed as 10 A° 2 (for details, see reference (1, p. 196)). 

The most general way to determine kinetic parameters from sampled-current voltammetry is to fit an experimental i/i vs. E dependence to the theory [equation (15.6)] using IF, a, and E° as adjustable parameters. This can be done using a number of commercially available programs, e.g., TableCurve 2D. 

Alternatively, one can determine point-by-point by calculating Fj(A) from the experimental i/i values using equation (15.6), and then finding X either numerically or from the table of Fj function. Once X is determined, one can use equation (15.7) to calculate kf for a given F, provided that both Dq and E° values are known, a and k° cm be found from the slope and the intercept of the linear lnA f vs. E plot, respectively. 

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Sampled current voltammetry uses a staircase voltage profile for measurements with successive, static drops of Hg. One second after each voltage step, charging current is nearly 0. but there is still substantial faradaic current from the redox reaction. 

Sampled current voltammetry — Voltammetry using current data acquired using current sampling (see -> current sampling). Recording of current responses for most voltammetric techniques is based on some form of current sampling. An older name for sampled current voltammetry is tast voltammetry . 

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... 

Figure 4. Sampled current voltammetry a) Potential step experiments for E equal to fg + 100 mV (lowest curve), Eq + 50 mV, Eq, Eq — 50 mV, and q — 100 mV. b) The current recorded at 50 ms is plotted versus the step potential E as the sigmoid curve. The points shown in (a) are included in (b).

Now suppose we sample the current at some fixed time r into each of these step experiments then we can plot the sampled current, /(r), V5. the potential to which the step takes place. As shown in Figures 5A.3b and 5.1.3c, the current-potential curve has a wave shape much like that encountered in earlier considerations of steady-state voltammetry under convective conditions (Section 1.4.2). This kind of experiment is called sampled-current voltammetry, several forms of which are in common practice. The simplest, usually operating exactly as described above, is called normal pulse voltammetry. In this chapter, we will consider sampled-current voltammetry in a general way, with the aim of establishing concepts that apply across a broad range of par-... 

Figure 5.1.3 Sampled-current voltammetry, (a) Step waveforms applied in a series of experiments, (b) Current-time curves observed in response to the steps, (c) Sampled-current voltammogram.

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... 

Actually one need not even apply steps. It is satisfactory to change the potential linearly with time and to record the current continuously, as long as the rate of change is small compared to the rate of adjustment in the steady state. Section 6.2.3 contains a discussion of the required conditions in more quantitative terms. Virtually all sampled current voltammetry at UMEs is carried out experimentally in this linear-sweep form, but the results are the same as if a normal sampled-current voltammetric protocol were employed, except with respect to the charging-current background [see Sections 6.2.4 and 7.3.2(c)]. 

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). 

Sampled-Current Voltammetry for Quasireversible and Irreversible Electrode Reactions 191... 

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. 

Figure 5.5.2 General kinetic function for chronoamperometry and sampled-current voltammetry.

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... 

TABLE 5.5.1 Wave Shape Characteristics at 25°C in Sampled-Current Voltammetry... 

In making measurements by sampled-current voltammetry, one would obtain traces like those in Figure 5.6.1. The diffusion current for the first wave can be subtracted from the total current of the composite wave to obtain the current attributable to O alone. That is. 

At UMEs, the picture is quite different, because the currents are extremely small consequently, the error in potential control in a voltammetric experiment is often much smaller than in the same experiment with an electrode of conventional size. Consider, for example, a disk UME with radius tq at which we desire to carry out sampled-current voltammetry. What are the conditions that will allow the recording of a voltammogram in which the half-wave potential is shifted less than 5 mV by the effect of uncompensated resistance ... 

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