Voltammetry staircase

FIGURE 3-10 Potential-time wavefonn used in staircase voltammetry. 

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Osteryoung J 1991 Square-wave and staircase voltammetry at small electrodes Microelectrodes Theory and Applications (Nate ASI Series) ed M I Montenegro, M A Queiros and J L Daschbach (Dordrecht Kluwer)... 

Sodium-silicate glass, 151 Sol-gel films, 120, 173 Solid electrodes, 110 Solid state devices, 160 Solvents, 102 Speciation, 84 Spectroelectrochenristry, 40 Spherical electrode, 6, 8, 9, 61 Square-wave voltammetry, 72, 92 Staircase voltammetry, 74 Standard potential, 3 Standard rate constant, 12, 18 Stripping analysis, 75, 79, 110 Supporting electrolyte, 102 Surface-active agents, 79... 

The method of potentiostatic pulses is sometimes combined with the DME (called pulse polarography). hi this case the pulse frequency should match the drop frequency, where each pulse is used at a definite time in the drop life, hi Barker s method, large pulse amphrndes are used. Other versions of the potentiostatic pulse technique are square-wave and staircase voltammetry here smaU-amphtude pulses are used. 

The Model 384B (see Fig. 5.10) offers nine voltammetric techniques square-wave voltammetry, differential-pulse polarography (DPP), normal-pulse polar-ography (NPP), sampled DC polarography, square-wave stripping voltammetry, differential pulse stripping, DC stripping, linear sweep voltammetry (LSV) and cyclic staircase voltammetry. 

The adsorption behavior of the psychotropic drug flunitrazepam (256) at the hanging mercury drop electrode was studied by staircase voltammetry and by adsorptive stripping differential pulse voltammetry. 256 can be determined down to nanomolar levels by using adsorptive preconcentration prior to the differential pulse voltammetry scan. The method was applied to determination of 256 in human urine530. 

The validity of the theoretical predictions is yet not experimentally rigorously confirmed by a model experimental system, although the theory has a safe background in the theory and experiments of similar potential ptrlse techniques as well as cyclic staircase voltammetry. 

Concerning more general application of mercury electrode in the studies on com-plexation equilibria, one should mention the paper by Jaworski et al. [59], who have investigated oxidation of mercury microelectrode in solutions with thiocyanates without any background electrolyte added. In the experiments, normal pulse voltammetry and staircase voltammetry were used. The authors have developed a general procedure for the determination of the stability constants, based on the data taken from the voltammograms. They have applied it to the analysis of Hg(II)-SCN complexes. 

The simplest controlled potential experiment is the potential step [34] illustrated in Fig. 15. Such experiments are sometimes termed chrono-amperometry , signifying that the current (-ampero-) is measured (-metry) as a function of time (chrono-). Sometimes, two steps, as in a double-step experiment [34] [Fig. 16(a)], or a sequence of small steps, as in staircase voltammetry [35—37] [Fig. 16(b)], are applied. When the potential of the working electrode is changed by a step for only a brief period of time before being returned to its original (or near to its original) value, we speak of a pulse . There are many varieties of pulse voltammetry [38—41], some of which are discussed in Chap. 4. 

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. 

In this section, we will show that the stationary responses obtained at microelectrodes are independent of whether the electrochemical technique employed was under controlled potential conditions or under controlled current conditions, and therefore, they show a universal behavior. In other words, the time independence of the I/E curves yields unique responses independently of whether they were obtained from a voltammetric experiment (by applying any variable on time potential), or from chronopotentiometry (by applying any variable on time current). Hence, the equations presented in this section are applicable to any multipotential step or sweep technique such as Staircase Voltammetry or Cyclic Voltammetry. 

All general typical variables considered in this chapter for a particular reaction scheme, for example the half-wave potential, are of fundamental interest for its characterization in any electrochemical technique. Moreover, as indicated in the previous chapter, all the current-potential expressions deduced here under stationary conditions (when microelectrodes are used) are applicable to any multipotential step or sweep electrochemical techniques like Staircase Voltammetry or Cyclic Voltammetry. 

Cyclic Staircase Voltammetry and Cyclic Voltammetry at Electrodes... 

It is of interest at this point to compare the study of Multipulse Chronoamperometry and Staircase Voltammetry with those corresponding to Single Pulse Chronoamperometry and Normal Pulse Voltammetry (NPV) developed in Chaps. 2 and 3 in order to understand how the same perturbation (i.e., a staircase potential) leads to a sigmoidal or a peak-shaped current-potential response as the equilibrium between two consecutive potential pulses is restored, or not. This different behavior is due to the fact that in SCV the current corresponding to a given potential pulse depends on the previous potential pulses, i.e., its history. In contrast, in NPV, since the equilibrium is restored, for a reversible process the current-potential curve is similar to a stationary one, because in this last technique the current corresponding to any potential pulse is independent of its history [8]. 

Staircase Voltammetry and Linear Sweep Voltammetry in Single and Cyclic Modes... 

In Staircase Voltammetry (SCV), a sequence of potential pulses of identical time length t defining a staircase of potentials is applied to the system with no recovery of the initial equilibrium at any moment of the experiment (see Scheme 5.2). In this technique, the difference between two consecutive potential pulses, IA I, is constant, and the ratio v = A /t is defined as the scan rate. 

If the potential is inverted at a given value (inversion or final potential) until the initial potential is reached again, the two above techniques are denoted Cyclic Staircase Voltammetry (CSCV) and Cyclic Voltammetry (CV), respectively (see Scheme 5.3). The potential waveform in CV can be written as a continuous function of time... 

In this section, general Eq. (5.23) will be applied to Cyclic Staircase Voltammetry (CSCV) and Cyclic Voltammetry (CV). Note that for CSCV the length of each potential pulse is identical, i.e., i - Ti = = z p z and the current is usually measured at the end of the application of each pulse in such a way that the time elapsed between the measurement of mth and pth currents is given by Eq. (5.30). 

In Sects. 2.3 and 4.2.4.1, the electrochemical response corresponding to ion transfer processes through liquid membranes in single potential pulse and double potential pulse techniques has been discussed. In this section, these processes are analyzed with multipulse techniques, mostly with Staircase Voltammetry and Cyclic Voltammetry. 

This chapter offers a study of the application of the multipulse and sweep techniques Cyclic Staircase Voltammetry (CSCV) and Cyclic Voltammetry (CV) to the study of more complex electrode processes than single charge transfer reactions (electronic or ionic), which were addressed in Chap. 5. 

In this section, the general analytical expression for the current-potential response (Eq. (6.15)) is particularized for the electrochemical techniques Cyclic Staircase Voltammetry (CSCV) and Cyclic Voltammetry (CV). Thus, the expression for the CSCV and CV currents of multi-electron processes at electrodes of any geometry and size is... 

A C++ code to calculate the response of two-electron reversible electrode processes in Staircase Voltammetry at disc, (hemi)spherical, and cylindrical electrodes of any radius can be found in Appendix J... 

The different assumptions needed to make a statement of this problem will be presented in the following section. Then the general solution corresponding to the application of a sequence of potential pulses to attached molecules giving rise to simple charge transfer processes and particular solution corresponding to Multipulse Chronoamperometry and Chronocoulometry and Staircase Voltammetry will be deduced. Cyclic Voltammetry has a special status and will be discussed separately. Finally, some effects that cause deviation from the ideal behavior and more complex reaction schemes like multielectronic processes and chemical reactions in the solution coupled to the surface redox conversion will be discussed. 

Equations (6.130) and (6.131) are applicable for any multipulse technique such as Staircase Voltammetry (SCV) and Square Wave Voltammetry (SWV). 

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