Linear double-layer-charging currents

Fig. 5. The effect of double layer charging current on linear sweep voltammograms at different sweep rates. Reprinted with permission from ref. 21.

We cannot discuss the linear sweep method properly without appreciating the importance of the double-layer-charging current in this type of experiment. We use the simple equation ... 

Therefore the electrochemical response with porous electrodes prepared from powdered active carbons is much increased over that obtained when solid electrodes are used. Cyclic voltammetry used with PACE is a sensitive tool for investigating surface chemistry and solid-electrolyte solution interface phenomena. The large electrochemically active surface area enhances double layer charging currents, which tend to obscure faradic current features. For small sweep rates the CV results confirmed the presence of electroactive oxygen functional groups on the active carbon surface. With peak potentials linearly dependent on the pH of aqueous electrolyte solutions and the Nernst slope close to the theoretical value, it seems that equal numbers of electrons and protons are transferred. 

These equations cannot be used at higher overpotentials 77 > kT/e0. If the reaction is not too fast, a simple extrapolation by eye can be used. The potential transient then shows a steeply rising portion dominated by double-layer charging followed by a linear region where practically all the current is due to the reaction (see Fig. 13.2). Extrapolation of the linear part to t = 0 gives a good estimate for the corresponding overpotential. 

Figure 6.15 Plot of peak current (/p) in a voltammogram (either linear-sweep or cyclic) against analyte concentration. The linear portion obeys the Randles-SevCik equation, while the horizontal plateau at low Ca aiyie values is usually caused by non-faradaic components of Ip, such as double-layer charging.

Fig. 7.43. Idealized galvanostatic result shown as a plot of potential against time at constant current density. A-B is largely double layer charging through the current and becomes used increasingly by electrons crossing the irrterfacial region. About one-fourth to one-half of this section in practice is linear and can be used to obtain the capacity of the interface from iL= C dVIdt B-C shows the current changeover to be entirely taken up (at C) with electrons crossing the interfacial region.

For the pseudo-capacity of adsorbed intermediates and for double-layer charging, cyclic voltammetric currents increase linearly with the sweep rate. For diffusion-controlled currents, the variation of the current increases with the square root of the sweep rate. 

Both the double-layer charging and the faradaic charge transfer are non-linear processes, i.e. the charging current density, jc, and the faradaic... 

The elimination of double layer charging components, as stated by Bruckenstein et al., results firstly from an almost constant charging current in a linear potential... 

Figure 6.2.3 Effect of double-layer charging at different sweep rates on a linear potential sweep voltammogram. Curves are plotted with the assumption that Cd is independent of E. The magnitudes of the charging current, ic, and the faradaic peak current, /p, are shown. Note that the current scale in (c) is lOX and in (d) is lOOX that in (a) and (b).

As mentioned already (Sect. 2.1.4.1), at short times scales, i.e. fast scan rates, LSV or CV curves at ultramicroelectrodes still attain the conventional peak shape related to linear diffusion. Under these conditions, another advantage of such electrodes becomes apparent the small electrode area, resulting in a small double layer capacity (hence a small time constant RCi), and a small current i (hence a small iR drop). Artifacts due to double layer charging and uncompensated iR drop become less prominent, and consequently high scan rates up to 10 V s can be used [39] as compared to the limit of a few 10Vs at conventional electrodes. Furthermore, specific techniques allow the recording of i /f-drop free voltammograms even at i > 10 V s [50]. 

As the sweep is linear, the x-axis is both a voltage and time axis. The charge transferred from the sweep generator to the cell is therefore proportional to the area between the curve and the x-axis (=0 mA). If the enclosed areas over and under the x-axis are equal, no net charge is supplied to the system. The currents may be due either to double-layer charging, sorption at the metal surface, or electrode reactions. 

Semi-infinite linear diffusion is considered in the Randles model, and the capacitive current is separated from the faradaic current, which is justified only when different ions take part in the double-layer charging and the charge transfer processes (i.e., a supporting electrolyte is present at high concentrations). Finite diffusion conditions should be considered for well-stirred solutions when the diffusion takes place only within the diSusion layer, and also in the case of siuface films that have a finite thickness. However, the two cases are different, since in the previous... 

This last point, which has been ignored until now, in fact imposes limitations on all transient techniques. Essentially, in addition to the faradaic current flowing in response to a potential perturbation, there is also a current due to the charging of the electrochemical double-layer capacitance (for more details see Chapter 5). In chronoamperometry this manifests itself as a sharp spike in the current at short times, which totally masks the faradaic current. The duration of the double layer charging spike depends upon the cell configuration, but might typically by a few hundred microseconds. Since It=o cannot be measured directly it is necessary to resort to an extrapolation procedure to obtain its value, and whilst direct extrapolation of an /Vs t transient is occasionally possible, a linear extrapolation is always preferable. In order to see how this should be done we must first solve Pick s 2nd Law for a potential step experiment under the conditions of mixed control. The differential equations to be solved are... 

RALEIGH I wish to make the point that if you want to use a solid-electrolyte cell to measure diffusion coefficients in this way, you don t necessarily have to measure the double layer capacitance and electron redistribution characteristics in the electrolyte. When you apply a d.c. bias that fixes a significant activity of the diffusant at the substrate surface, double-layer charging should be completed fairly soon. If you plot the cell current versus and get a significant linear... 

In most cases, a linear fit of the linear, positive part of the LSV curve to 0 V reflects well the hydrogen crossover current. However, the oxidation current under the voltage sweeping contains also contributions of the double layer charging... 

In specific, voltammetric curves are collected in a narrow potential window (several tens of mV) at different sweep rates [31]. If double layer charging is the only process, a strait linear relationship between the current in the middle of potential window and the sweep rate is obtained. Differential capacitance of the interface (Cd) is obtained as ... 

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