Uncompensated resistance

Another practical factor mentioned in Chapter 7 is the solution resistance between working and reference electrodes. This resistance leads to a shift in the potential of the working electrode of IpR where R is the resistance (uncompensated) of the solution. A broadening of the peaks is observed, greater separation between Epa and Epc than predicted theoretically, and the peak currents are lower. Since the peak current increases with sweep rate, this factor becomes more important for large values of v. 

Tapping mode atomic force microscopy Water molecules per acid site, H2O/SO3H Fickian diffusion coefficient of water Self-diffusion coefficient of water Proton mobility Electroosmotic drag coefficient Bulk membrane proton resistance Uncompensated resistance Glass transition temperatme Water volume fraction... 

F. 1.1.1 A simple electronic scheme equiveilent to the electrochemical cell Ru, resistance uncompensated in the regular three-electrode system Q, differential capacity of the double layer Rf, resisttmce to faradaic current at the electrode surface Rq, solution resistemce compensated in the three-electrode system... 

Figure Bl.28.8. Equivalent circuit for a tliree-electrode electrochemical cell. WE, CE and RE represent the working, counter and reference electrodes is the solution resistance, the uncompensated resistance, R the charge-transfer resistance, R the resistance of the reference electrode, the double-layer capacitance and the parasitic loss to tire ground.

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... 

A qualitative measure of the corrosion rate can be obtained from the slope of the curves in Fig. 2. Z INT is given in units of s ohm" . Owing to the presence of the uncompensated ohmic resistance and lack of values for Tafel slopes [Eq. (2)], data in Fig. 2 should be viewed as indicative of significant changes in corrosion rates. Corrosion loss remained low during the first 2 months, followed by a large increase for both flushed samples and controls. The corrosion rate increased when the surface pH reached values of 1 or less. Total corrosion loss as determined from integrated Rp data was less for the control than for the flushed sample. 

Nonfaradaic components associated with the uncompensated resistance between reference electrodes (7 ) and the double layer capacitance (Qi) can be accurately determined by AC impedance measurements. In this technique, a small AC potential perturbation is superimposed to the DC bias, and the resulting AC current is measured as a function of the frequency of modulation. The simplest circuit considered for a polarizable... 

FIG. 7 Simplified equivalent circuit for charge-transfer processes at externally biased ITIES. The parallel arrangement of double layer capacitance (Cdi), impedance of base electrolyte transfer (Zj,) and electron-transfer impedance (Zf) is coupled in series with the uncompensated resistance (R ) between the reference electrodes. (Reprinted from Ref. 74 with permission from Elsevier Science.)... 

FIG. 18 Simplified equivalent circuit for externally biased ITIES under illumination. The perturbations introduced by the photoreactions in Fig. 11 are contained within the generator term g. Cji and are associated with the interfacial capacitance and the uncompensated resistance. (From Ref. 83. Reproduced by permission of the Royal Society of Chemistry.)... 

The thin layer is a source of uncompensated resistance. This can lead to a voltage drop, between the reflective working electrode and the reference electrode. V,R is given by ... 

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. 

Any deviation from the above criteria is indicative of kinetic complications and should be treated individually. However, one case is worthy of note. In non-aqueous solutions, it is commonly observed that AEP, for example, has typical values between 70 and 100 mV owing to the so-called IR drop resulting from the uncompensated and relatively large solution resistance. While IR compensation techniques are available, they are not always reliable, and it is more convenient to compare the measured AEP with that of a known reversible reaction measured under similar conditions. 

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 condition is that there is no significant uncompensated resistance in the electrochemical cell [13,14], The influence of IR-drop increases with SW frequency, the ratio A/p//V2 decreases with frequency and the net peak current is not a linear function of the square-root of frequency. A theoretical example is shown in Fig. 2.4. 

Fig. 2.4 Theoretical dependence of the net peak current of reversible reaction (1.1) on the square-root of SW frequency under the influence of uncompensated resistance in the cell. The dotted line is the expected linear relationship in the absence of resistance. A = 0.0147 cm, n=l,D = 5 X 10- cmVs, cj, = 1 X10-3 = U4 k 2, = 20 mV and AS = -5 mV...

The transfer of anions (CIO4, NO3, SCN , Br , and Cl ) and cations ((CH3)4N+, (C4H9)4N+, Na+, and K+) has been studied according to mechanism (4.12) and (4.13), respectively. In all cases, the voltammetric curves were particularly well developed, with a virtnally constant peak potential and half-peak width, indicating no effect of uncompensated resistance. In all experiments, the transferring ion was... 

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