Solution resistance, uncompensated

The polarization equation, including the effect of the uncompensated solution resistance between the metal specimen and the reference electrode, can be written as 

From this equation, the expression for the idealized polarization-resistance technique can be obtained by differentiation as  

The error due to the neglect of the solution resistance can then be expressed by comparing /corr.caic calculated from Eq. (5) with /corr.true Calculated from Eq. (28)  

The magnitude of both the polarization resistance and the uncompensated solution resistance varies inversely with the area of the specimen, assuming that the geometrical arrangement of 

For other corrosion-rate determination techniques, the error can be obtained from numerical simulations using Eq. 

Inclusion of the IRU term in consideration of the apparent electrode potential (f app) during LSV results in 

The effect of Ru on LSV peak potentials has long been recognised and has been the subject of a number of investigations [36—42]. In practice, what is observed in resistive solutions during LSV measurements is that the wave is flattened and the reduction peak is shifted to more negative potentials. Since the current increases with vxn, the problem is accentuated as the sweep rate is increased. 

The Ru problem was treated in detail by Nicholson [36] using theoretical methods. He found that the IRU term has approximately the same effect on LSV and CV waves as quasi-reversible charge transfer [36]. Thus, an effective means of handling this problem is of especial importance to heterogeneous kinetic studies. 

The second method relies on the fact that, for small potential intervals, (A2 p )meas — (AjFp)real is nearly linearly related to Ru [38, 39]. This 

Voltammetric data for the reduction of benzonitrile (BN) in iV,iV-dimethylformamide as a function of i fa 

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It should be pointed out that not all of the iR drop is removed by the potentiostatic control. Some fraction, called iRu (where Ru is the uncompensated solution resistance between the reference and working electrodes) will still be included in the measured potential. This component may be significantly large when resistive nonaqueous media are used, and thus may lead to severe distortion of the... 

Figure 15 shows a set of complex plane impedance plots for polypyr-rolein NaC104(aq).170 These data sets are all relatively simple because the electronic resistance of the film and the charge-transfer resistance are both negligible relative to the uncompensated solution resistance (Rs) and the film s ionic resistance (Rj). They can be approximated quite well by the transmission line circuit shown in Fig. 16, which can represent a variety of physical/chemical/morphological cases from redox polymers171 to porous electrodes.172... 

Figure 16. General transmission-line model for a conducting polymer-coated electrode. CF is the faradaic pseudo-capacitance of the polymer film, while Rt and Rt are its electronic and ionic resistance, respectively. R, is the uncompensated solution resistance.

The exact calculation of icorr for a given time requires simultaneous measurements of Rp and anodic and cathodic Tafel slopes (/> and be). Computer programs have been developed for the determination of precise values of /corr according to Eqs. (2) and (3). Experimental values of Rp (2p contain a contribution from the uncompensated solution resistance... 

Figure 9 The ideal assembly of a three-electrode cell. Rs= (compensated) solution resistance Rnc = uncompensated solution resistance...

AEpij 59 mV) at the lowest scan rates shown, but the voltammograms become quasireversible at scan rates above 0.01 V s . Therefore, as expected, the transition to quasireversible behavior is observed at dramatically lower scan rates at the 30NEE than would be observed at a macroelectrode. It is again important to emphasize that the increase in AEp observed is not due to uncompensated solution resistance [25]. 

Figure 6J3 Schematic representation of a Luggin capillary used for minimizing IR drop. Calculations of uncompensated solution resistance require a knowledge of the distance d between the reference tip of the capillary and the working electrode (depicted here as a dropping-mercury electrode (DME)).

The second factor is associated with the fact that all electrolyte solutions exhibit finite resistance to the flow of current. Thus, the potential that is measured (Em eas) between the working and reference electrodes consists of two contributors, the real thermodynamic potential Cereal) and that arising from uncompensated solution resistance (IRU)... 

Experimental measurements1,2 of the uncompensated solution resistance indicate that it changes rapidly with distance in the immediate vicinity of the mercury drop, and attains an approximately constant limiting value at a distance greater than about 0.5 cm. The latter corresponds to a distance roughly 10 times the maximum radius of the mercury drop. This is illustrated in Figure 6.2, where the potential of a reference electrode in a movable Luggin capillary probe at different distances from the mercury drop has been measured with respect to an identical reference electrode located several centimeters away from the drop on the side opposite the counter electrode. An important feature... 

Thus, the current decreases exponentially with time. Here, E is the magnitude of the potential step, while Rs is the (uncompensated) solution resistance. 

Electro chemists are aware of the annoying residual uncompensated solution resistance Ru between the Luggin probe and the working electrode, see for example [74]. Although it is possible in principle to compensate fully for the iR error thus introduced [131,132], this is rarely done, as it introduces, in practice, undesirable instrumental oscillations or, in the case of damped feedback [132], sluggish potentiostat response. 

Data obtained using these reference couples may be compared with analytical solutions for the peak current, limiting current or voltammetric waveshape (see Sections 3 and 4). Non-compliance of experiment and theory is indicative of malfunctioning instrumentation, poor experimental design (i.e. an unacceptably large uncompensated solution resistance) or a faulty electrode. 

Care should always be taken when interpreting the results of cyclic voltammetric experiments to ensure that the effects of the double-layer capacitance and uncompensated solution resistance are considered (see Section 2). Peak currents should be corrected for the baseline capacitative charging current (for example by running a background voltammogram in the absence of the electroactive species), and as the charging current is... 

Fig. 3C Uncompensated solution resistance, in units of Q. cni, and the corresponding potential drop, for a current density of 0.4 mAlcm, as a function of the distance from the electrode surface. Calculated for a solution having a specific conductivity of K = 0.01 S/cm, and an electrode of radius 0.05 cm.

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... 

V/s. The lower limit is determined by the need to maintain the total time of the experiment below 10-50 seconds (i.e., before mass transport by convection becomes important). The upper limit is determined by the double-layer charging current and by the uncompensated solution resistance, as discussed in Section 25.2. 

In Fig. 8D, we compared the potential applied to the interface during linear potential sweep with and without an uncompensated solution resistance. Clearly, the error is a maximum at the peak, where the current has its highest value. Just before and during the peak, the effective sweep rate imposed on the interphase is much less than that applied by the instrument. The assumption that v = constant, which has been used as one of the boundary conditions for solving the diffusion equation, does not apply. In this sense the experiment is no longer conducted "correctly". 

The iR potential drop due the uncompensated solution resistance associated with different geometries was discussed in Section 8.3. For a spherical electrode, which is of interest here, we can write (cf. Eq. 8C)... 

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