Potential—time waveforms

FIGURE 3-1 Chronoamperometric experiment (a) potential-time waveform (b) change of concentration profiles with time (c) the resulting current—time response. 

FIGURE 3-11 Potential-time waveform used in alternating current (AC) voltammetry. 

FIGURE 3-12 Anodic shipping voltammetry the potential-time waveform (a), along with the resulting voltammogram (b). 

Hoekstra, J. C. and Johnson, D. C., Comparison of potential-time waveforms for the detection of biogenic amines in complex mixtures following their separation by liquid chromatography, Anal. Chem., 70, 83, 1998. 

This method was developed further by superimposing the square-wave signal onto a staircase signal [20,21]. Some of the possible potential-time waveforms are shown in Fig. 1.7. Usually, each square-wave cycle occurs during one stair-... 

As an alternative to a stepwise variation with time, a continuously changing potential may be imposed. Though other possibilities have been used [42, 43], a linearly changing potential—time waveform, known as a potential ramp [Fig. 17(a)], is the most common. The technique has many names, including linear sweep voltammetry [44]. If the direction of the ramp is reversed [Fig. 17(b)], the technique is often termed cyclic voltammetry (see Chap. 3), though this name is more appropriately applied after sufficient ramp reversals [Fig. 17(c)] have caused the experiment to become periodic. 

Note that in this case (Q,JQ ) is only dependent of Ep, i.e., it has an stationary character being independent of the potential-time waveform applied [48], and has an analogous dependence on the potential to that shown by the normalized voltammetric current (///d,c) obtained for a reversible charge transfer reaction under diffusion control (see Eq. (2.36)). Equation (6.132) can be written as... 

The Qf E curve for a reversible two-electron transfer taking place in a monolayer is independent of time (i.e., it has a stationary character) and, therefore, is independent of the potential-time waveform applied to the electrode, as in the case of a reversible one-electron transfer reaction. It is also important to highlight that the normalized charge, has a identical expression to that for the normalized transient current 7 v N obtained for solution soluble species when the NPV technique is applied to an electrode with any geometry (see curves in Fig. 3.16, and Eq. (3.141)), and also to the normalized stationary current obtained for solution soluble species when any potential-time waveform is applied for ultramicroelectrodes with any geometry. 

By inserting the solutions proposed in Eq. (6.189) and condition (6.175) in Eq. (6.185), recurrent expressions for coefficients 8lp) and are deduced [68] and by inserting these expressions into (6.191) the current is calculated. These expressions allow us to obtain limiting cases like the reversible and irreversible ones which have a discrete character which makes them applicable to any multipulse technique by simply changing the potential time waveform, including the continuous limit of Cyclic Voltammetry. Moreover, they are independent of the kinetic formalist considered for the process. 

Scheme 7.2 Differential multipulse voltammetry (DMPV). (a) Potential-time waveform, (b) current-potential response. The black dots in (a) indicate the time at which the current is measured...

In order to show the distribution of the applied potential between the outer and the inner interface in the case of systems with two polarized interfaces, the potential time waveform used in SWV is depicted in Scheme 7.5. The applied potential, E (red line), and the outer ( out, blue line) and inner potentials ( "", green line) have been plotted. 

Scheme 7.5 Potential-time waveform of SWV obtained from Eq. (7.5) ( , red line), and its distribution between the outer interface ( °ul, dark blue line) and the inner interface ( "", green line). The three index potentials (the outer index potential, out,mdex, the inner index potential, """ index, and the membrane index potential, mdex) are also included (blue line, dark green line, and black line, respectively). Inset figure Distribution of the applied potential red line), between the outer and the inner interfaces (dark blue line and green line, respectively). jnitiai = —450mV,...

J. C. Hoekstra and D. C. Johnson, Comparison of Potential-Time Waveforms for the Detection of Biogenic Amines in Complex Mixtures Following Their Separation by Liquid Chromatography, Anal. Chem. 70, 83-88, (1998). 

The potential-time waveform is represented in Fig. 10.10. Pulses superimposed on a potential ramp have also been employed for microprocessor control the staircase waveform is clearly simpler to put into operation. 

Differential staircase voltammetry — In this variation of staircase - voltammetry the current is sampled twice on each tread of the staircase potential-time waveform. The difference between the two currents sampled on the same step is amplified and recorded as a function of the... 

Figure 1.13. Chronoamperometric experiment (a) potential-time waveform (b) change in concentration profiles as time progresses (c) the resulting current-time response [19]. (From Wang J. Analytical electrochemistry. 2006 Wiley-VCH. Reproduced with permission.)...

Voltammetry in unstirred solution where the predominant mode of mass transport is limited to diffusion is one of the most useful techniques for the study of electrochemical reactions [l-5,8-l 1]. Most often, a triangular potential-time waveform with equal positive and negative slopes is used, and usually also the initial potential (Einitiai) and final potential (Efinai) are the same as illustrated in Fig. 1(a). This has given rise to the term cyclic voltammetry (CV). However, sometimes the voltage sweep is continued to include one or more additional E-t half-cycles or includes more complicated sawtooth-like waveforms to meet special needs. 

Figure 1. (a) Potential-time waveform for a triangular voltage sweep between — 1 and —2 V at a sweep rate (v) of 0.1 Vs and (b) a simulated (DigiSim) voltammogram for a substrate that is reduced at Ep = —1.57 V to a product or intermediate, the oxidation of which is observed at... 

The three-electrode system is connected to a potentiostat, which controls the potential of the working electrode while monitoring the resulting current. Besides the widely used fixed-potential measurements, such instruments can apply other potential-time waveforms such as potential step, linear scan, pulse excitations that may be useful in certain sensing applications. Such instruments are commercially available from various sources, listed in table 5.1. A three-... 

Figure Bl.28.5. Applied potential-time waveforms for (a) normal pulse voltammetry (NPV), (b) differential pulse voltammetry (DPV), and (c) square-wave voltammetry (SWV), along with typical voltammograms obtained for each method.

Fig. 3. Potential-time waveforms used for (A) differential pulse polarography (B) square-wave polarography.

Figure 5.22. Three-step potential-time waveform for pulsed amperometric detection at a noble-metal electrode. E et is the appropriate potential for the desired surface-catalyzed reaction applied for a time tjet composed of a delay time, tjei, and a short period at the end of the detection period, tint, during which the current is sampled. Following the detection process, the electrode is cleaned by oxidative desorption concurrent with surface oxide formation using a step change in the applied potential to Eoxd for time t xd-The oxide-coated electrode is reactivated by a negative step potential Ered for time t d sufficient to remove the oxide layer prior to the next cycle of the waveform.

Figure 8.5. Potential-time waveform used in ASV. [a] Deposition of metai ions, [b] Rest period to allow solution to become quiscent. (c] Potential is driven positive of the oxidation potential of the metal fiim.

Figure 8.6. Potential-time waveform for [a] linear sweep voltammetry and [b] differential pulse voltammetry.

Fig. 5 Normal pulse voltammetry (a) potential-time waveform and (b) schematic voltammogram.

Linear sweep voltammetry and cyclic voltammetry [23-25] Potential-time waveforms employed for potential sweep measurements are shown in Figs. 4 and 5a. Linear sweep voltammetry involves sweeping potential between two limited values Ej and E2 at a controlled sweep rate v. A more useful method is cyclic voltammetry in which the potential sweep is reversed usually at the same sweep rate on reaching... 

Fig. 8. The potential-time waveform in differential pulse voltmametry (a) and a differential pulse voltammogram (b).

Fig. 9. A potential-time waveform for differential normal pulse voltammetry (a) and resulting current-potential curves (b).

Square-wave voltammetry The potential-time waveform and current measuring scheme for this technique is shown in Fig. 10. The waveform consists of a symmetrical square-wave (peak to peak amplitude 2Es ) superimposed on a staircase wave of step height AE and a period t. The response current is sampled at the end of both the forward (If) and reverse (If) half cycle. A difference current dl is determined as... 

The simplest potential-time waveform that is applied to an electrode is that of a constant potential, which is known as dc amperometry. The high sensitivity and selectivity of ED is ideally suited for complex samples, as evinced by its application to the determination of neurotransmitters in complex biological samples (e.g., brain extracts). Neurotransmitters are typically aromatic compounds (e.g., phenols, aminophenols, catecholamines, and other metabolic amines), which are detected easily by anodic reactions at a constant (dc) applied potential at inert electrodes [53, 54]. 

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