Potential pulse

Sensitivity In many voltammetric experiments, sensitivity can be improved by adjusting the experimental conditions. For example, in stripping voltammetry, sensitivity is improved by increasing the deposition time, by increasing the rate of the linear potential scan, or by using a differential-pulse technique. One reason for the popularity of potential pulse techniques is an increase in current relative to that obtained with a linear potential scan. 

Time, Cost, and Equipment Commercial instrumentation for voltammetry ranges from less than 1000 for simple instruments to as much as 20,000 for more sophisticated instruments. In general, less expensive instrumentation is limited to linear potential scans, and the more expensive instruments allow for more complex potential-excitation signals using potential pulses. Except for stripping voltammetry, which uses long deposition times, voltammetric analyses are relatively rapid. 

In hydrodynamic voltammetry the solution is stirred either by using a magnetic stir bar or by rotating the electrode. Because the solution is stirred, a dropping mercury electrode cannot be used and is replaced with a solid electrode. Both linear potential scans or potential pulses can be applied. 

In stripping voltammetry the analyte is first deposited on the electrode, usually as the result of an oxidation or reduction reaction. The potential is then scanned, either linearly or by using potential pulses, in a direction that removes the analyte by a reduction or oxidation reaction. 

The difference between the various pulse voltammetric techniques is the excitation waveform and the current sampling regime. With both normal-pulse and differential-pulse voltammetry, one potential pulse is applied for each drop of mercury when the DME is used. (Both techniques can also be used at solid electrodes.) By controlling the drop time (with a mechanical knocker), the pulse is synchronized with the maximum growth of the mercury drop. At this point, near the end of the drop lifetime, the faradaic current reaches its maximum value, while the contribution of the charging current is minimal (based on the time dependence of the components). 

As pointed out above, an STM tip can be used to nucleate and grow single clusters. In this type of experiment, cluster deposition on a STM tip is achieved when it is retracted about 10 to 20 run from the substrate surface. Under these conditions, where the feedback loop is disabled, absence of mechanical contact between the tip and the substrate in ensured. Then a positive potential pulse is applied to the tip, the metal deposited on it is dissolved, and it diffuses toward the substrate surface, where a nucleus develops and grows to yield a cluster, typically 20 nm wide. 

To overcome these problems, most voltammetric detectors have used pulsed waveforms such as staircase , squarewaveand differential pulseThe current is sampled at the end of the pulse after the charging current has decayed. In addition, because the charging current is typically the major current source, iR problems are not as severe. Last has described a coulostatic detector based on charge pulses instead of potential pulses which eliminates iR and charging current... 

The most commonly used waveform for in vivo voltammetric measurements is square-wave. This involves the application of a potential pulse to the working electrode for a fixed time at fixed intervals. The current is measurai at the end of the potential pulse to minimize capacitive charging current contributions. This waveform is shown in Fig. 15 A. 

Regularly repeat i potential pulses will establish a steady state condition at the electrode surface where diffusion just replenishes the concentration of the compound... 

To improve the selectivity of chronoamperometric in vivo analysis, a differential measurement ta hnique has been employed Instead of a single potential pulse, the potential is alternately pulsed to two different potentials giving rise to the name double chronoamperometry. This waveform is shown in Fig. 15 B. Because the current contributions of individual electroactive components add linearly to produce the observed current output, the difference in current response at the two potentials is the current due to only those compounds which are oxidized at the higher potential and not oxidized at the lower potential. This system provides two responses, the current due to easily oxidized compounds and the current due to harder to oxidize compounds. This gives greater selectivity than the direct chronoamperometric method. 

Various types of controlled-potential pulsing are shown in Fig. 5.18. The simplest case is the single-pulse potentiostatic method (Fig. 5.18A). The current-time (I-t) curves obtained by this method have already been described in Section 5.4.1, Eq. (5.4.10) and (5.4.14). 

A baseline potential pulse followed each current pulse in order to strip extracted ions from the membrane phase and, therefore, regenerated the membrane, making it ready for the next measurement pulse. This made sure that the potentials are sampled at discrete times within a pulse that correspond to a 6m that is reproducible from pulse to pulse. This made it possible to yield a reproducible sensor on the basis of a chemically irreversible reaction. It was shown that the duration of the stripping period has to be at least ten times longer than the current pulse [53], Moreover the value of the baseline (stripping) potential must be equal to the equilibrium open-circuit potential of the membrane electrode, as demonstrated in [52], This open-circuit potential can be measured prior to the experiment with respect to the reference electrode. 

Fig. 13. Sampled-current voltammograms recorded at a stationary Pt electrode in solutions of Cu(I) in the 60.0 m/o AlCl3-EtMeImCl melt at 40 °C. The Cu(I) concentrations were ( ) 10.0, ( ) 25.0, and (A) 50.0 mmol L-1. The current was sampled at 10 s following the application of each potential pulse. Adapted from Tierney et al. [45] by permission of The Electrochemical Society.

The understanding of the nature of transient current after the imposition of a potential pulse is fundamental to the development of voltammetry and its analytical applications. Consider the same reaction, O+ne- = R, taking place in a quiet solution at a potential such that the reaction is diffusion controlled. Figure 18b.6a shows the pulse and Fig. 18b.6b shows the concentration gradient O as a function of time and distance from the electrode surface. 

Differential Pulse Voltammetry. As illustrated in Figure 38, in the Differential Pulse Voltammetry (DPV) the perturbation of the potential with time consists in superimposing small constant-amplitude potential pulses (10 < AEpUise <100 mV) upon a staircase waveform of steps of constant height but smaller than the previous pulses (1 < AEbase < 5 mV). 

On a clean surface of an Fci7Cr alloy in a 0.5M NaCl electrolyte, corrosion is accelerated as pitting corrosion when a potential pulse of 1 s duration extending from the passive region and above the pitting potential is applied. Gugler et al. ° showed by in situ AFM that in this case the pitting corrosion was initiated close to an inclusion on the surface (Fig. 8). Such a surface defect may act as a center for pit nucleation, as was... 

Figure 8. An Fe-17Cr stainless steel surface near a handle-shaped inclusion observed by AFM in 0.5M NaCl. (a) Surface at the corrosion potential of -240 mV (SCE). (b) Surface after application of a potential pulse of I s to 650 mV to initiate pitting, then anodically polarized at ISO mV (SCE). The pitting potential is approximately 350 mV. (Reprinted from Ref. 30 by permission of The Institute of Materials. London.)...

The overall effect of the preceding chemical reaction on the voltammetric response of a reversible electrode reaction is determined by the thermodynamic parameter K and the dimensionless kinetic parameter . The equilibrium constant K controls mainly the amonnt of the electroactive reactant R produced prior to the voltammetric experiment. K also controls the prodnction of R during the experiment when the preceding chemical reaction is sufficiently fast to permit the chemical equilibrium to be achieved on a time scale of the potential pulses. The dimensionless kinetic parameter is a measure for the production of R in the course of the voltammetric experiment. The dimensionless chemical kinetic parameter can be also understood as a quantitative measure for the rate of reestablishing the chemical equilibrium (2.29) that is misbalanced by proceeding of the electrode reaction. From the definition of follows that the kinetic affect of the preceding chemical reaction depends on the rate of the chemical reaction and duration of the potential pulses. 

The variation of the peak current with the electrode kinetic parameter k and chemical kinetic parameter e is shown in Fig. 2.31. When the quasireversible electrode reaction is fast (curves 1 and 2 in Fig. 2.31) the dependence is similar as for the reversible case and characterized by a pronounced minimum If the electrode reaction is rather slow (curves 3-5), the dependence A fJ, vs. log( ) transforms into a sigmoidal curve. Although the backward chemical reaction is sufficiently fast to re-supply the electroactive material on the time scale of the reverse (reduction) potential pulses, the reuse of the electroactive form is prevented due to the very low kinetics of the electrode reaction. This situation corresponds to the lower plateau of curves 3-5 in Fig. 2.31. 

Pr = It couples the role of adsorption strength together with the diffusion mass transport on the time scale of potential pulses. If the adsorption is very weak, Pr > 1.23, the response of reaction (2.144) is equivalent to the simple reaction of a dissolved redox couple (2.157). 

The response of a reversible reaction (2.146) depends on two dimensionless adsorption parameters, Pr and po. When pR = po the adsorbed species accomplish instantaneously a redox equilibrium after application of each potential pulse, thus no current remains to be sampled at the end of the potential pulses. The only current measured is due to the flux of the dissolved forms of both reactant and product of the reaction. For these reasons, the response of a reversible reaction of an adsorbed redox couple is identical to the response of the simple reaction of a dissolved redox couple (2.157), provided Pr = po- As a consequence, the real net peak current depends linearly on /J, and the peak potential is independent of the frequency. If the adsorption strength of the product decreases, i.e., the ratio increases, the net peak current starts to increase (Fig. 2.73). Under these conditions, the establishment of equilibrium between the adsorbed redox forms is prevented by the mass transfer of the product from the electrode surface. Thus, the redox reaction of adsorbed species contributes to the overall response, causing an increase of the current. In the hmiting case, when ]8o —0, the reaction (2.146) simplifies to reaction (2.144). 

The effect of the volume and the surface catalytic reaction is sketched in Figs. 2.80 and 2.81, respectively. Obviously, the voltammetric behavior of the mechanism (2.188) is substantially different compared to the simple catalytic reaction described in Sect. 2.4.4. In the current mechanism, the effect of the volume catalytic reaction is remarkably different to the surface catalytic reaction, revealing that SWV can discriminate between the volume and the surface follow-up chemical reactions. The extremely high maxima shown in Fig. 2.81 correspond to the exhaustive reuse of the electroactive material adsorbed on the electrode surface, as a consequence of the synchronization of the surface catalytic reaction rate, adsorption equilibria, mass transfer rate of the electroactive species, and duration of the SW potential pulses. These results clearly reveal how powerful square-wave voltammetry is for analytical purposes when a moderate adsorption is combined with a catalytic regeneration of the electroactive material. This is also illustrated by a comparative analysis of the mechanism (2.188) with the simple surface catalytic reaction (Sect. 2.5.3) and the simple catalytic reaction of a dissolved redox couple (Sect. 2.4.4), given in Fig. 2.82. 

Duration of potential pulse, s Sampling time, s Resting time, s... 

The decay of a radical-anion can be followed directly by generating the intermediate within the cavity of an esr spectrometer through application of a controlled potential pulse to the cathode of a thin electrochemical cell [46]. Loss of the radical-anion is then followed by decay of the esr signal. Decay is second order in radical-ion concentration for dimethyl fumarate (k = 160 M s ) and for cin-namonitrile (k = 2.1 x 10 M s ) in dimethylformamide with tetrabutylammonium counter ion. Similar values for these rate constants have been obtained using purely electrochemical techniques [47]. 

---