Uncompensated ohmic drops

Figure 4.10. Use of the current interruption technique to measure the uncompensated ohmic drop, T 0hmic,wr> between the working (W) and reference (R) electrode.

In voltammetric experiments, electroactive species in solution are transported to the surface of the electrodes where they undergo charge transfer processes. In the most simple of cases, electron-transfer processes behave reversibly, and diffusion in solution acts as a rate-determining step. However, in most cases, the voltammetric pattern becomes more complicated. The main reasons for causing deviations from reversible behavior include (i) a slow kinetics of interfacial electron transfer, (ii) the presence of parallel chemical reactions in the solution phase, (iii) and the occurrence of surface effects such as gas evolution and/or adsorption/desorption and/or formation/dissolution of solid deposits. Further, voltammetric curves can be distorted by uncompensated ohmic drops and capacitive effects in the cell [81-83]. 

Laviron55 has recently noted that linear potential sweep or cyclic voltammetry does not appear to be the best method to determine the diffusion coefficient D of species migrating through a layer of finite thickness since measurements are based on the shape of the curves, which in turn depend on the rate of electron exchange with the electrode and on the uncompensated ohmic drop in the film. It has been established that chronopotentiometric transition times or current-time curves obtained when the potential is stepped well beyond the reduction or oxidation potential are not influenced by these factors.55 An expression for the chronopotentiometric transition has been derived for thin layer cells.66 Laviron55 has shown that for a space distributed redox electrode of thickness L, the transition time (r) is given implicitly by an expression of the form... 

Thus, the first step of any remedial action will usually be to minimize the value of the uncompensated ohmic drop. The design of the cell and the electrodes are the principal means of achieving this objective. 

Peter et al. [18] emphasized the role of the effect of uncompensated ohmic drop, and analyzed the current transients within the framework of the two-dimensional electrocrystallization model, taking into account instantaneous and progressive nu-cleations. Three-dimensional expansion of growth centers was also considered. It was found that the reduction is only rapid as long as the film remains in its conducting state. (A more detailed analysis of this problem is provided in Sect. 6.6.) It was also suggested that the electroneutrality is maintained by fast proton transport at short times. 

Finally, it is worth mentioning that LaCroix et al [28] reported in 1989 ultrafast electrical response data on a timescale of 100 ps for pANI film (ca. 0.2 pm thickness) in 2 m sulphuric acid using an ultramicroelectrode (ca. 0.2 mm area) with appropriate correction for uncompensated ohmic drop. However, the optical response data are reported in arbitrary units and thus they are difficult to evaluate with a view to practical uses. In general, it would seem that 100 ps are not a viable reference timescale for electrochromic response, at least for conventional electrochromic devices. 

Returning to the three-electrode setup, it could seem that no ohmic drop would affect the measurement of the potential difference between the working and reference electrodes, since there is practically no current flow between both electrodes. However, this is not totally true. The reference electrode is located at a given distance from the working electrode surface, and, as a result of this separation, the potential difference measured contains a part of the ohmic drop in the solution which is called residual ohmic drop, IRU (with I being the current and Ru the uncompensated resistance). For more details concerning the minimization of the ohmic distortion of the current-potential response, see Sects. 1.8 and 5.4. 

One of the main disadvantages of voltammetric techniques like CV is the distortion caused by the combination of the double-layer charging process with the ohmic drop, related to the uncompensated resistance of the solution, Ru (see Sect. 1.9). This distortion can be very significant for macroelectrodes. 

In order to confirm this behavior, the cyclic voltammograms obtained at a planar electrode in CV and SCV (for A = 5 mV) for a Nemstian charge transfer process at different values of the scan rate are shown in Fig. 5.11. The effect of the ohmic drop and charging current has been considered by including an uncompensated resistance Ru = 0.1 K 2 and a double-layer capacitance Cdi = 20pFcm 2. 

In order to avoid the distortion caused by these two effects, the usual approach is to compensate the resistance Ru by a positive feedback loop (this is imperative in systems like plasticized membranes for which the uncompensated resistance can be of the order of megaohms [32-34]). Another possibility is to use microelectrodes, for which a decrease in the measured current is obtained which minimizes the ohmic drop and charging current distortion (see Sects. 2.7 and 5.4.1). 

As stated in Sect. 5.2.3.4, there is always a potential difference generated by the flow of faradaic current I through an electrochemical cell, which is related to the uncompensated resistance of the whole cell (Ru). This potential drop (equal to IRU) can greatly distort the voltammetric response. At microelectrodes, the ohmic drop of potential decreases strongly compared to macroelectrodes. The resistances for a disc or spherical microelectrode of radius rd or rs are given by (see Sect. 1.9 and references [43, 48-50]). 

Fig. 8. General equivalent circuit of an electrochemical cell. C double layer capacitance qSDL potential drop across the double layer Zp faradaic impedance Rij series resistance (comprising the uncompensated ohmic cell resistance and all external resistances). V is a potentiostatically fixed voltage drop. (It differs from the potentiostatically applied voltage by the constant potential drop across the RE see footnote 3).

Ohmic drop distortion — Distortion of an electrochemical response caused by uncompensated ohmic resistance (see - IRU (ohmicpotential) drop). 

The peak-potential difference A p depends mainly on the kinetic parameter i/t, as illustrated in Table 2. By measurement of A p as a function of v for a given system, k° can be estimated. However, great care should be exerted to ensure that uncompensated resistance does not contribute to the value of A p, since this would hamper the procedure. Clearly, the use of ultramicroelectrodes can be recommended for this kind of measurements, as the ohmic drop is much smaller here compared to microelectrodes of normal size. This is particularly true when high sweep rates are required for determining large values of k° (see Section 2.4)... 

Ideally no current flows through the reference electrode therefore, j r = 0 and jjohmic.WR = 0 should be the case. In practice, the first assumption is usually good for reasonably nonpolarizable reference electrodes, since the parasitic uncompensated current flowing through the reference electrode is usually very small. The ohmic drop, however, between the working and reference electrodes, that is, J ohmic,WR may in general, and particularly in solid-state electrochemistry, not be... 

The importance of knowing the exact value of the ohmic drop or uncompensated resistance in an electrochemical system has been pointed out by many workers. In studies of the kinetics of electrode processes by potentiostatic techniques, the ohmic potential drop produces a distortion of the steady state polarization curve which, if uncorrected, will yield erroneous values of the characteristic parameters (Tafel slope, reaction orders) of the electrode reactions (Fig. 6.2). 

The effect of uncompensated IR drop on corrosion rate determination using polarization resistance measurements was discussed in depth by Mansfeld [1-3]. He showed that in electrochemical measurements of the polarization resistance the experimental value Rp is the sum of the true value Rp and the uncompensated ohmic resistance R which is essentially the electrolyte resistance but can also contain the resistance of surface films. 

When performing polarization measurements an error due to the ohmic drop over the uncompensated resistance will be included in the potential between the working and the reference electrode. The significance of this error is decided by the ratio between the value of the uncompensated resistance and the polarization resistance of the system. The uncompensated resistance can be minimized by careful design of the cell and the positioning of the electrodes. Several methods of instrumental compensation of the ohmic drop are available, of which the interrupt methods are the most versatile. Such methods are applied during the polarization measurements. 

Figure 3. Cyclic voltammetry of hexamethylbenzene, 10 mM, in acetonitrile, 0.6 M NBU4BF4, at a 5 m radius gold disk ultramicroelectrode, at the scan rates given in kV.s on each set of on-line ohmic drop compensated or uncompensated voltanunograms. 22 C. ...

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