Double-layer charging time constant

To minimize absorption from the solution, optical thin layer cells have been designed. The working electrode has the shape of a disc, and is mounted closely behind an IR-transparent window. For experiments in aqueous solutions the intervening layer is about 0.2 to 2 ftm thick. Since the solution layer in front of the working electrode is thin, its resistance is high this increases the time required for double-layer charging - time constants of the order of a few milliseconds or longer are common - and may create problems with a nonuniform potential distribution. 

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... 

Figure 17.2.7 Normalized ECL from 0.38 mM DPA in acetonitrile containing 0.1 M TBAPFg at a Pt disk (radius = 1 jm) (solid lines) and corresponding simulated curves (dashed lines) as a function of frequency of potential pulse. Simulations for = 2 X 10 /M/s and double-layer charging time constant, of 0.10 psec. Adapted with permission from reference (14b).

The effect of changing system parameters (e.g., corrosion potential, Tafel slopes, etc.) has been treated qualitatively. The effect of double-layer charging time has also been dis-cussed. " In most cases, the charging time is negligible compared to the usual measurement times, but unreasonably long measurement times, on the order of hours, may be required for systems with very low conductivity solutions and for low corrosion rates (that is, when the rc time constant of the double layer is large). For transient experimental techniques, the time-dependent effects manifest themselves as frequency or scan-rate dependence of the results. - -... 

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]

Galvanostatic Transient Technique. In the galvanostatic method a constant-current pulse is applied to the cell at equilibrium state and the resulting variation of the potential with time is recorded. The total galvanostatic current ig is accounted for (1) by the double-layer charging, /ji, and (2) by the electrode reaction (charge transfer), i. ... 

The total current ig is kept constant, but its two components, /ji and do change in time. At the beginning of the pulse (microseconds range) the total current ig is uti-hzed mainly for the double-layer charging and Eq. (4.13) reduces to... 

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.

At constant potential, in a simple reaction with no surface intermediates, the i—t line will tend to become constant after the double-layer charging is over. If at this time the current density is well below the limiting current density, iL (Section 7.9.10), there should be nothing to interfere with the continuation of the steady-state constant current. If the current density after double-layer charging is above the limiting current, the current will decline with time. This is discussed quantitatively in Chapter 8. 

Figure 8.9 shows a somewhat idealized potentiostatic relation. Here, a poten-tiostat controls the electrode potential and one observes the current as a function of time. At higher times, the current becomes transport controlled. How may one eliminate this influence and get back to apart of the (t)v—f relation influenced by neither double-layer charging nor diffusion control so that the exchange current and rate constant of the electrode reaction can be obtained (Bockris)... 

In all the numerical examples illustrated thus far, the potential changes across the interface were primarily governed by xu rather than by amplifier characteristics. Under these conditions, it is a simple matter to calculate the current due to double-layer charging if Ru and Cdl are known or can be estimated. The peak value of this current is equal to the change in potential divided by Ru and it decays exponentially thereafter. Following a given number of time constants, the contribution of the charging current to the total current measured can be determined and thereby the extent of error in the quantity of interest, the faradaic current, can be estimated. 

Basically, the impedance behavior of a porous electrode cannot be described by using only one RC circuit, corresponding to a single time constant RC. In fact, a porous electrode can be described as a succession of series/parallel RC components, when starting from the outer interface in contact with the bulk electrolyte solution, toward the inner distribution of pore channels and pore surfaces [4], This series of RC components leads to different time constant RC that can be seen as the electrical response of the double layer charging in the depth of the electrode. Armed with this evidence, De Levie [27] proposed in 1963 a (simplified) schematic model of a porous electrode (Figure 1.24a) and its related equivalent circuit deduced from the model (Figure 1.24b). 

We might be tempted to measure the currents at a very short time after switching, since this leads to the highest sensitivity and allows measurement of the highest rate constants. On the other hand, it is in this time period that interference by double-layer charging and by distortion of the pulse shape by an uncompensated solution resistance is most severe. This is why the ratio / // is commonly measured over a... 

The preceding method (Section 6.3.1) relies completely on the limited equilibration of the ion distribution in solution, due to the hindered diffusion. Additionally, the charging time of the double layer can be exploited for the local machining of surfaces. As mentioned in Section 6.2.2, the time constant for the double-layer charging is given by the product of solution resistance and double-layer capacity. In the above experiments employing the tip of an STM, which is a few nms distance to the surface, as local counter electrode this time constant is well below nanoseconds, even for diluted electrolytes. Nonetheless, for electrode separations in the... 

An alternative approach to decrease the time constant of electrochemical systems rests on the use of the miniaturized ITIES. Micron-scale ITIES use a micropipette to support the aqueous phase [98]. Subsequently an alternative approach, using micro-holes formed by laser ablation of thin polymer films, was reported [99]. The advantage of the micron-scale approach is that the radial diffusive flux to such an inlaid interface reaches a steady state, so the problems of transient current methods due to the double-layer charging constant are avoided. The low currents measured at such interfaces, due to their small size,... 

A 0.1 cm electrode with Cd = 20 pFIcm is subjected to a potential step under conditions where R is 1, 10, or 100 n. In each case, what is the time constant, and what is the time required for the double-layer charging to be 95% complete ... 

The classical DME has two principal disadvantages. First, it has a constantly changing area, which complicates the treatment of diffusion and creates a continuous background current from double-layer charging. Second, its time scale is controlled by the lifetime of the drop, which cannot be varied conveniently outside the range of 0.5-10 s. 

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