Voltammetry hydrodynamic

LCEC is a special case of hydrodynamic chronoamperometry (measuring current as a function of time at a fixed electrode potential in a flowing or stirred solution). In order to fully understand the operation of electrochemical detectors, it is necessary to also appreciate hydrodynamic voltammetry. Hydrodynamic voltammetry, from which amperometry is derived, is a steady-state technique in which the electrode potential is scanned while the solution is stirred and the current is plotted as a function of the potential. Idealized hydrodynamic voltammograms (HDVs) for the case of electrolyte solution (mobile phase) alone and with an oxidizable species added are shown in Fig. 9. The HDV of a compound begins at a potential where the compound is not electroactive and therefore no faradaic current occurs, goes through a region 

As discussed in Section 2 material may reach the electrode surface by diffusion or convection. In cyclic voltammetry at a stationary electrode, and assuming that migration can be neglected, diffusion is the sole form of mass transport. However, material may additionally be transported to the electrode by convection. This genre of voltammetry, where convection is a dominant form of mass transport, is described as hydrodynamic voltammetry. The focus in Section 4 will be on the use of rotating disc and channel electrodes in studies 

Hydrodynamic voltammetric techniques have the major advantage of being steady-state techniques (see Section 1). Consequently, it is easy to measure limiting currents and half-wave potentials (see below for their definition) as a function of the convective parameter (i.e. flow rate, electrode angular velocity) in the absence of significant problems arising from capacitative charging currents. 

The potential profile associated with hydrodynamic techniques usually takes the form of a linear sweep between two potentials in which the oxidation or reduction processes of interest occur. As for cyclic voltammetry, the gradient of the ramp represents the scan rate. However, for steady-state techniques, the scan rate used must be sufficiently slow to ensure that the steady state is attained at every potential during the course of the voltammetric scan. The upper value of the scan rate that may be used under the steady-state regime is therefore restricted by the rate of convective mass transport of material to the electrode surface. The faster the rate of convective mass transport the faster the scan rate that may be used consistent with the existence of steady-state conditions. 

In order to probe the kinetics of the C step in an ECE process fully, the voltammetric response must be measured over a sufficiently wide range of mass transport rates so that N tt varies between one and two. For particularly rapid processes, this requirement implies that very fast rates of mass transport are required in order to avoid N tt being equal to two at all transport rates. 

Conversely for slow reactions, low rates of mass transport will be required to achieve significant deviations from A eff equalling one. Consequently, it can be appreciated that it is a study of the competition between the rates of mass transport and chemical kinetics that leads to the quantitative determination of electrode reaction mechanisms in hydrodynamic voltammetry. Importantly, for each hydrodynamic technique, there is one assessable convective transport parameter that directly relates to the kinetic time-scale. 

Electrochemical systems where the mass transport of chemical species is due to diffusion and electromigration were studied in previous chapters. In the present chapter, we are going to consider the occurrence of the third mechanism of mass transfer in solution convection. Although the modelling of natural convection has experienced some progress in recent years [1], this is usually avoided in electrochemical measurements. On the other hand, convection applied by an external source forced convection) is employed in valuable and popular electrochemical methods in order to enhance the mass transport of species towards the electrode surface. Some of these hydrodynamic methods are based on electrodes that move with respect to the electroljAic solution, as with rotating electrodes [2], whereas in other hydrodynamic systems the electrolytic solution flows over a static electrode, as in waU-jet [3] and channel electrodes [4]. 

When both diffusion and convection act in solution, the flux of a species j is given by 

The characteristics of the fluid velocity depend on the design of the hydrodynamic cell and the flow pattern. The latter is said to be laminar when the solution flows smoothly and constantly in parallel layers such that the predominant velocity is that in the direction of the flow. Laminar flow conditions are desirable since accurate descriptions of the solution hydrodynamics are available. On the other hand, under turbulent flow conditions the solution motion is chaotic and the velocities in the directions perpendicular to that of the flow are significant. The transition between the laminar and turbulent regimes is defined in terms of the dimensionless Re5molds number, Re, that is proportional to the relative movement rate between the electrode and solution, and the electrode size, but inversely proportional to the kinematic viscosity of the solution. Thus, for low Re values the flow pattern is laminar and it transits to turbulent as Re increases. For example, in a tubular channel the laminar regime holds for Re 2300. 

Prom Eq. (8.1), the corresponding material balance equation establishes 

In practice, the electrode and electrochemical cell as well as the experimental conditions are selected in order that transport by diffusion and convection dominates in one direction and Eq. (8.4) greatly simplifies. In the following sections we are going to consider two of the most popular hydrodynamic systems the rotating disc electrode and the channel electrode. In both cases the mathematical problem can be reduced to a form analogous to that introduced in previous chapters for diffusion-only problems and then the same numerical strategies can be employed. 

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Determination of limiting current and halfwave potential in linear scan hydrodynamic voltammetry. 

In hydrodynamic voltammetry current is measured as a function of the potential applied to a solid working electrode. The same potential profiles used for polarography, such as a linear scan or a differential pulse, are used in hydrodynamic voltammetry. The resulting voltammograms are identical to those for polarography, except for the lack of current oscillations resulting from the growth of the mercury drops. Because hydrodynamic voltammetry is not limited to Hg electrodes, it is useful for the analysis of analytes that are reduced or oxidized at more positive potentials. 

Faraday s law (p. 496) galvanostat (p. 464) glass electrode (p. 477) hanging mercury drop electrode (p. 509) hydrodynamic voltammetry (p. 513) indicator electrode (p. 462) ionophore (p. 482) ion-selective electrode (p. 475) liquid-based ion-selective electrode (p. 482) liquid junction potential (p. 470) mass transport (p. 511) mediator (p. 500) membrane potential (p. 475) migration (p. 512) nonfaradaic current (p. 512)... 

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. 

This experiment introduces hydrodynamic voltammetry using a rotating working electrode. Its application for the quantitative analysis of K4Fe(CN)6 is demonstrated. 

The purity of a sample of K3Fe(CN)6 was determined using linear-potential scan hydrodynamic voltammetry at a glassy carbon electrode using the method of external standards. The following data were obtained for a set of calibration standards. 

The use of an amperometric detector is emphasized in this experiment. Hydrodynamic voltammetry (see Chapter 11) is first performed to identify a potential for the oxidation of 4-aminophenol without an appreciable background current due to the oxidation of the mobile phase. The separation is then carried out using a Cjg column and a mobile phase of 50% v/v pH 5, 20 mM acetate buffer with 0.02 M MgCl2, and 50% v/v methanol. The analysis is easily extended to a mixture of 4-aminophenol, ascorbic acid, and catechol, and to the use of a UV detector. 

Heterogeneous rate constants, 12, 113 Hofmeister sequence, 153 Hybridization, 183, 185 Hydrodynamic boundary layer, 10 Hydrodynamic modulation, 113 Hydrodynamic voltammetry, 90 Hydrodynamic voltammogram, 88 Hydrogen evolution, 117 Hydrogen overvoltage, 110, 117 Hydrogen peroxide, 123, 176... 

Data on the electrochemistry of the telluride ion in alkaline media are relatively limited. Mishra et al. [53] studied the oxidation of Te to Te° at solid electrodes, focusing on the intermediate step(s) of this process, and in particular, the possibility of detecting ditelluride Te via rotating ring disk electrode (RRDE) methodology. Oxidation beyond the elemental state to TeO and TeO was also studied using cyclic and hydrodynamic voltammetry. 

Gunasingham, H. and Fleet, B., Hydrodynamic voltammetry in continuous-flow analysis, in Electroanalytical Chemistry A Series of Advances, Vol. 16, Bard, A. J., Ed., Marcel Dekker, New York, 1989, 89. 

Wangfuengkanagul and Chailapakul [9] described the electroanalysis of ( -penicillamine at a boron-doped diamond thin film (BDD) electrode using cyclic voltammetry. The BDD electrode exhibited a well-resolved and irreversible oxidation voltammogram, and provided a linear dynamic range from 0.5 to 10 mM with a detection limit of 25 pM in voltammetric measurement. In addition, penicillamine has been studied by hydrodynamic voltammetry and flow injection analysis with amperometric detection using the BDD electrode. 

It is important to recognize that all forms of hydrodynamic voltammetry are steady-state methods in that the current at a given potential is independent of both scan direction and time. In fact, identical voltammograms can be obtained by controlling the current and monitoring the potential response. This is, however, rarely done in practice. 

Figure 5.2 Small-amplitude voltammetric techniques (a) various small-amplitude waveforms are imposed on a dc ramp (normally only one waveform is used in a given experiment) (b) the sigmoidal dc response is typical of dc polarography and hydrodynamic voltammetry. The greatest amplitudes for the small-amplitude current (Aiac) are achieved on the rising part of the dc current, where the small-amplitude voltage signal causes the greatest change in the surface concentrations (c) small-amplitude current response versus applied dc potential.

This is an appropriate point at which to comment on the common practice of evaluating the formal potential from voltammetric measurements. When a reversible response is obtained in voltammetry, what is actually measured is the reversible half-wave potential, E1/2, which (except for hydrodynamic voltammetry) is related to the formal potential by a term involving the diffusion coefficients of the oxidized and reduced forms of the half-reaction, D0 and DR, respectively. 

Nagels, L. J., Mush, G., and Massart, D. L. (1989). Rapid-scan hydrodynamic voltammetry and cyclic voltammetry of pharmaceuticals in flow injection analysis conditions. J. Pharm. Biomed. Anal. 7 1479-1483. 

Convection terms commonly crop up with the dropping mercury electrode, rotating disk electrodes and in what has become known as hydrodynamic voltammetry, where the electrolyte is made to flow past an electrode in some reproducible way (e.g. the impinging jet, channel and tubular flows, vibrating electrodes, etc). This is discussed in Chap. 13. 

Hydrodynamic electrodes — are electrodes where a forced convection ensures a -> steady state -> mass transport to the electrode surface, and a -> finite diffusion (subentry of -> diffusion) regime applies. The most frequently used hydrodynamic electrodes are the -> rotating disk electrode, -> rotating ring disk electrode, -> wall-jet electrode, wall-tube electrode, channel electrode, etc. See also - flow-cells, -> hydrodynamic voltammetry, -> detectors. 

Hydrodynamic voltammetry — is a voltammetry technique featuring an electrolyte solution which is forced to flow at a constant speed to the electrode surface. -> mass transport of a redox species enhanced in this way results in higher current. The forced flow can be accomplished either by agitation of the solution (solution stirring, or channel flow), or the electrode (electrode rotation, see -> rotating disk electrode or vibration,... 

Reynolds number— The Reynolds number, Re, is defined by the ratio of inertial forces to viscous forces, or vLp/t] for flow rate, v, characteristic length, L, density of the medium, p, and - viscosity of the medium, rj. It has been used electrochemically for an estimation of laminar flow against turbulent flow in hydrodynamic voltammetry for controlling flow rates [i]. Flows with Re less than ca. 2300 are laminar flows although the transition to a turbulent flow depends on flow configuration. 

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