Double-Layer-Charging Currents

The great advantage of the RDE over other teclmiques, such as cyclic voltannnetry or potential-step, is the possibility of varying the rate of mass transport to the electrode surface over a large range and in a controlled way, without the need for rapid changes in electrode potential, which lead to double-layer charging current contributions. 

The background (residual) current that flows in the absence of the electroactive species of interest is composed of contributions due to double-layer charging process and redox reactions of impurities, as well as of the solvent, electrolyte, or electrode. 

The simplest, and by far the most common, detection scheme is the measurement of the current at a constant potential. Such fixed-potential amperometric measurements have the advantage of being free of double-layer charging and surface-transient effects. As a result, extremely low detection limits—on the order of 1-100 pg (about 10 14 moles of analyte)—can be achieved, hi various situations, however, it may be desirable to change the potential during the detection (scan, pulse, etc.). 

Figure 39. Current-time variation in nickel pitting dissolution in NaCl solution.89,91 1, double-layer charging current 2, fluctuation-diffusion current 3, minimum dissolution current 4, pit-growth current (Reprinted from M. Asanuma andR. Aogaki, Nonequilibrium fluctuation theory on pitting dissolution. II. Determination of surface coverage of nickel passive film, J. Chem. Phys. 106, 9938, 1997, Fig. 2. Copyright 1997, American Institute of Physics.)...

The presence of a Faradaic electrode reaction of any kind competing with the double layer charging presents a problem in determining the purely capacitive current needed to calculate the surface charge. From a plot of 1 vs. (/ = total electrode current) with a fixed concentration of the ions of the electrode metal dissolved in solution, the surface charge can be obtained [65Butl]. (Data obtained with this method are labelled TC). 

In order to distinguish more clearly between effects induced by the varying potential and kinetic contributions, the continuous oxidation of the three Cj molecules was followed at a constant potential after the potential step. The corresponding faradaic and mass spectrometric (m/z = 44) current transients recorded after 3 minutes adsorption at 0.16 V and a subsequent potential step to 0.6 V (see Section 13.2) are reproduced in Figs. 13.5-13.7. In all cases, the faradaic current exhibits a small initial spike, which is associated with double-layer charging when stepping the electrode potential to 0.6 V. 

The tip current depends on the rate of the interfacial IT reaction, which can be extracted from the tip current vs. distance curves. One should notice that the interface between the top and the bottom layers is nonpolarizable, and the potential drop is determined by the ratio of concentrations of the common ion (i.e., M ) in two phases. Probing kinetics of IT at a nonpolarized ITIES under steady-state conditions should minimize resistive potential drop and double-layer charging effects, which greatly complicate vol-tammetric studies of IT kinetics. 

A related technique is the current-step method The current is zero for t < 0, and then a constant current density j is applied for a certain time, and the transient of the overpotential 77(f) is recorded. The correction for the IRq drop is trivial, since I is constant, but the charging of the double layer takes longer than in the potential step method, and is never complete because 77 increases continuously. The superposition of the charge-transfer reaction and double-layer charging creates rather complex boundary conditions for the diffusion equation only for the case of a simple redox reaction and the range of small overpotentials 77 [Pg.177]

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. 

The Cyclic Voltammetry Experiment. Faradaic and Double-Layer Charging Currents. Ohmic Drop... 

The Faradaic current involves the passage of electrons across the electrode-solution interface. This is not the case with the double-layer charging current, ic, which arises as a consequence of the variation of the electrode potential ... 

The double-layer charging current thus tends toward a plateau equal to Cdv with a rise time equal to RuCd (Figure 1.7). On the reverse scan,... 

In the high-scan-rate range, another valuable approach to minimize ohmic drop is to use very small electrodes, down to micrometric sizes. Decreasing the electrode radius, ro, the resistance Ru increases approximately as 1/ro, but the current decreases proportionally to r. Overall the ohmic drop decreases proportionally to r0. The double-layer charging time constant, RuCd, also... 

Convolution may also be applied to ohmic drop correction in the case where a substantial double-layer charging current is present, unlike the preceding case. It suffices first to extract the Faradaic current from the total current according to equation (1.19) [obtained from equations (1.11)]... 

The possible overlap of the double-layer charging and Faradaic currents requires the following extension of equation (1.10), allowing for the presence of the Faradaic current in accord with the electric scheme in Figure 1.5c ... 

The preceding derivation has assumed implicitly that the double-layer charging current is negligible in front of the Faradaic current or that it can be eliminated by a simple subtraction procedure. In cases where these conditions are not fulfilled, the following treatment will take care of the problem under the assumption that the double-layer capacitance is not affected appreciably by the Faradaic reaction but may nevertheless vary in the potential range explored. The first step of the treatment then consists of extracting the Faradaic component from the total current according to (see Section 1.3)... 

This proportionality to the scan rate is reminiscent of double-layer charging, leading to the appellation pseudo-capacitance, reflecting the fact that a Faradaic type of current is exchanged between the electrode and the molecules attached to the surface. 

Double-layer charging current and ohmic drop are likely to interfere at high scan rates. The procedures for extracting the Faradaic component of the current and correcting the potential axis from the effect of ohmic drop described earlier (see Sections 1.3.2 and 1.4.3) should then be applied. The same is true for the double-layer effect on the electron transfer kinetics (Section 1.4.2). 

FIGURE 2.45. Equivalent circuit for the cell and instrument. WE, RE, and CE, working, reference, and counter electrodes, respectively iph, photocurrent ij/, double-layer charging current Q, double-layer differential capacitance Rc, Ru, cell compensated (by the potentiostat) and uncompensated resistances, respectively Rs, sampling resistance RP, potentiostat resistance E, potential difference imposed by the potentiostat between the reference and working electrodes Vpu, photo-potential as measured across the sampling resistor. Adapted from Figure 1 of reference 51, with permission from Elsevier. 

The agreement between simulated and experimental curves is excellent if the double-layer charging current is taken into account (Section 1.3.1). 

This section is devoted to the establishment of equations (1.12) and (1.13). In addition to the dimensionless variables used previously (Section 6.1.2), we normalize the Faradaic and double-layer charging current,... 

Overlapping of Double-Layer Charging and Faradaic Currents in Potential Step and Double Potential Step Chronoamperometry. Oscillating and Nonoscillating Behavior... 

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