Analytical solution voltammetry

The largest division of interfacial electrochemical methods is the group of dynamic methods, in which current flows and concentrations change as the result of a redox reaction. Dynamic methods are further subdivided by whether we choose to control the current or the potential. In controlled-current coulometry, which is covered in Section IIC, we completely oxidize or reduce the analyte by passing a fixed current through the analytical solution. Controlled-potential methods are subdivided further into controlled-potential coulometry and amperometry, in which a constant potential is applied during the analysis, and voltammetry, in which the potential is systematically varied. Controlled-potential coulometry is discussed in Section IIC, and amperometry and voltammetry are discussed in Section IID. 

Table 8.76 shows the main characteristics of voltammetry. Trace-element analysis by electrochemical methods is attractive due to the low limits of detection that can be achieved at relatively low cost. The advantage of using standard addition as a means of calibration and quantification is that matrix effects in the sample are taken into consideration. Analytical responses in voltammetry sometimes lack the predictability of techniques such as optical spectrometry, mostly because interactions at electrode/solution interfaces can be extremely complex. The role of the electrolyte and additional solutions in voltammetry are crucial. Many determinations are pH dependent, and the electrolyte can increase both the conductivity and selectivity of the solution. Voltammetry offers some advantages over atomic absorption. It allows the determination of an element under different oxidation states (e.g. Fe2+/Fe3+). 

The so-called indicator electrodes must be considered as microelectrodes, which means that the active surface area is very small compared with the volume of the analyte solution as a consequence, the electrode processes cannot perceptibly alter the analyte concentration during analysis in either non-faradaic potentiometry or faradaic voltammetry. 

Fig. 7.25 Analytical solution in Cyclic Square Wave Voltammetry (SWV) for different situations with respect to the bulk concentrations of the ion (Eq. (7.50)). (a) net currents (b) forward (solid lines), and reverse (dashed lines) components. 7iim,ingress, ss = AzFD ac out, cj ln = 0,

Verbrugge M, Liu P. Analytic solutions and experimental data for cyclic voltammetry and constant-power operation of capacitors consistent with HEV applications. Journal of the Electrochemical Society 2006 153(6) A1237-A1245. 

Polarography (discovered by Jaroslav Heyrovsky in 1922) is a technique in which the potential between a dropping mercury electrode and a reference electrode is slowly increased at a rate of about 50 200 mV min while the resultant current (carried through an auxihary electrode) is monitored the reduction of metal ions at the mercury cathode gives a diffusion current proportional to the concentration of the metal ions. The method is especially valuable for the determination of transition metals such as Cr, Mn, Fe, Co, Ni, Cu, Zn, Ti, Mo, W, V, and Pt, and less than 1 cm of analyte solution may be used. The detection hmit is usually about 5 X 10 M, but with certain modifications in the basic technique, such as pulse polarography, differential pulse polarography, and square-wave voltammetry, lower limits down to 10 M can be achieved. 

In cyclic voltammetry, both the oxidation and reduction of the metal complex (called the analyte from now on) will take place in one electrochemical cell. This cell houses the analyte solution as well as three electrodes, the working electrode, the auxiliary electrode and the reference electrode. Electron transfer to and from the metal complex takes place at the working electrode surface (Fig. A.2.2) and does so in response to an applied potential, /iapp, at the electrode surface. During the experiment, current develops at the surface as a result of the movement of analyte to and from the electrode as the system strives to maintain the appropriate concentration ratio (0, through electron transfer, as specified by the Nemst equation. 

Hydrodynamic voltammetry Voltammetry performed with the analyte solution in constant motion relative to the electrode surface produced by pumping the solution past a stationary electrode or by moving the electrode through the solution. 

Another recent study highlighting a redox-active label employs metal colloids to signal target-probe hybridization. Magnetic beads derivatized with single-stranded DNA probe sequences were used to capture target and reporter sequences that had been labeled with nanoparticles composed of ZnS, PbS, or CdS. The beads were then physically removed from the analyte solution, and the particles were dissolved in acid. After adsorption of these ions onto solid electrodes, stripping voltammetry was used to quantify the... 

Reproducible Hmiiing currents can be achieved rapidly when either the analyte solution or the working electrode is in continuous and reproducible motion. I, inear-scan voltammetry in which the solution or the electrode is in constant motion is called hydrodynamic voltammetry. In this chapter, we will focus much of our attention on hydrodynamic voltammetry. 

The sensitivity of any analytical technique can be greatly increased by introducing a preliminary pre-concentration step, eg solvent extraction. In stripping voltammetry an electrochemical preconcentration technique is used. The analyte is concentrated, from very dilute solutions, by electrolysis to an insoluble product which collects at the electrode and can be subsequently determined with a very high sensitivity. The method is applicable only to a limited number of important analytes. Stripping voltammetry requires the use of solid or stationary electrodes, (2.7). 

A. Molina, C. Serna, Q. Li, E. Laborda, C. Batchelor-McAuley, and R. G. Compton. Analytical solutions for the study of multi-electron transfer processes by staircase, cyclic and differential voltammetries at disc microelectrodes, J. Phys. Chem. C 116, 11470-11479 (2012). 

L. Camacho, J. J. Ruiz, C. Serna, A. Molina, and F. Martinez-Ortiz. Reverse pulse voltammetry and polarography A general analytical solution. Can. J. Chem. 72, 2369 (1994). 

A. Molina, C. Serna, and J. Gonzalez. General analytical solution for a catalytic mechanism in potential step techniques at hemispherical microelectrodes Apphcations to chronoamperometry, cyclic staircase voltammetry and cyclic linear sweep voltammetry, J. Electroanal. Chem. 454, 15-31 (1998). 

Polarography is voltammetry conducted with a dropping-mercury electrode. The cell in Figure 17-11 has a dropping-mercury working electrode, a Pt auxiliary electrode, and a calomel reference electrode. An electronically controlled dispenser suspends one drop of mercury from the tip of a glass capillary tube immersed in analyte solution. A measurement is made in 1 s, the drop is released, and a fresh drop is suspended for the next measurement. There is always fresh, reproducible metal surface for each measurement. 

To predict the electrochemical response when the problem has no known or simple analytical solution, e.g. cyclic voltammetry, microelectrodes, coupled chemical reactions, etc. 

Simulations of ac voltammetry are rare. There is the work of Hayes et al (1974A, 1974B) and Bond et al (1976). These authors examined specific electrochemical situations Hayes et al (1974A) dealt with disproportionation and (1974B) irreversible dimerisation Bond et al (1976) with the interplay of ac and LSV. No analytical solutions for these exist as yet. These workers assumed that the dc and ac components of all quantities are independent. The assumption is reasonable for sufficiently small ac amplitudes and sufficiently high frequencies of the ac modulation. Then, the ac solution can be obtained analytically from the dc solution, and one needs only to simulate the latter. 

As with microelectrodes, diffusive transport to nanoelectrodes on conventional voltammetric timescales is dominated by convergent, as opposed to planar, diffusion. Therefore, for a simple electron transfer process, the voltammetric response at steady state is characterised by a sigmoidal shape. Simulation of such voltammetry requires solution of the diffusion equation typically with a Nemstian or Butler-Vofiner boundary condition for the rate of electron transfer at the electrode surface, depending on its reversibility. For simple, uniformly accessible, electrode geometries analytical solutions of these equations are available, and so for a disk electrode we obtain the familiar equation for the current (iiim) in the limit of diffusion control ... 

The variation of the diffusion layer thicknesses at planar, cylindrical, and spherical electrodes of any size was quantified from explicit equations for the cases of normal pulse voltammetry, staircase voltammetry, and linear sweep voltammetry by Molina and coworkers (Molina et al., 2010a). Important limiting behaviours for the linear sweep voltammetry current-potential curves were reported in all the geometries considered. These results are of special physical relevance in the case of disk and band electrodes which possess non-uniform current densities since general analytical solutions were derived for the above-mentioned geometries for the first time. Explicit analytical expressions for diffusion layer thickness of disk and band electrodes of any size under transient conditions... 

Stripping voltammetry involves the pre-concentration of the analyte species at the electrode surface prior to the voltannnetric scan. The pre-concentration step is carried out under fixed potential control for a predetennined time, where the species of interest is accumulated at the surface of the working electrode at a rate dependent on the applied potential. The detemiination step leads to a current peak, the height and area of which is proportional to the concentration of the accumulated species and hence to the concentration in the bulk solution. The stripping step can involve a variety of potential wavefomis, from linear-potential scan to differential pulse or square-wave scan. Different types of stripping voltaimnetries exist, all of which coimnonly use mercury electrodes (dropping mercury electrodes (DMEs) or mercury film electrodes) [7, 17]. 

In voltammetry the working electrode s surface area is significantly smaller than that used in coulometry. Consequently, very little analyte undergoes electrolysis, and the analyte s concentration in bulk solution remains essentially unchanged. 

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