Ohmic resistances

Because some substances may preferentially adsorb onto the surface of the electrode, the composition near the iaterface differs from that ia the bulk solution. If the cell current is 2ero, there is no potential drop from ohmic resistance ia the electrolyte or the electrodes. Yet from the thermodynamic analysis it is seen that there is a measurable cell potential. The question from where this potential arises can be answered by considering the iaterface. 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

With eveiy change in ion concentration, there is an electrical effect generated by an electrochemical cell. The anion membrane shown in the middle has three cells associated with it, two caused by the concentration differences in the boundaiy layers, and one resulting from the concentration difference across the membrane. In addition, there are ohmic resistances for each step, resulting from the E/I resistance through the solution, boundary layers, and the membrane. In solution, current is carried by ions, and their movement produces a fric tion effect manifested as a resistance. In practical applications, I R losses are more important than the power required to move ions to a compartment wim a higher concentration. 

Internal ohmic resistance of fresh cells, Q ] (approx.) Expected Capacity, [mAh 0.3 0.2 0.15 0.1... 

The latter equals IRwc where RWc is the ohmic resistance between the working and counter electrode. Experimentally it is rather easy to measure the riohmic.wc term using the current interruption technique as shown in Figure 4.9. Upon current interruption the ohmic overpotential r 0i,mjCtwc vanishes within less than 1 ps and the remaining part of the overpotential which vanishes much slower is t w+T c (Eq. 4.9). 

Due to the small amplitude of the superimposed voltage or current, the current-voltage relationship is linear and thus even charge-transfer reactions, which normally give rise to an exponential current-potential dependence (Chapter 4), appear as resistances, usually coupled with a capacitance. Thus any real ohmic resistance associated with the electrode will appear as a single point, while a charge transfer reaction (e.g. taking place at the tpb) will appear ideally as a semicircle, i.e. a combination of a resistor and capacitor connected in parallel (Fig. 5.29). 

Figure 5.30 exemplifies such a behaviour of a Pd catalyst electrode deposited on YSZ and exposed to CH4/02 mixtures.54 The resistance R is associated with the ohmic resistance of the electrode while the semicircles labeled Q and Ci- are associated with the charge transfer reaction... 

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. 

We can see here that at very low frequencies, R, tends toward the sum R + Rp and Cj tends toward infinity. At very high frequencies, R, becomes equal to R and Cj becomes equal to Q. Therefore, by extrapolating the experimental data to zero and to infinite frequency, we basically can find the kinetic reaction parameter Ry (or p) and the EDL capacitance as well as the electrolyte s ohmic resistance. 

These electrode reactions snstain a continuous flow of electrons in the external circuit. The OH ions produced by reaction (19.4) in the vicinity of the positive electrode are transported through the electrolyte toward the negative electrode to replace OH ions consumed in reaction (19.3). The electric circuit as a whole is thus closed. Apart from the OCV, the current depends on the cell s internal resistance and on the ohmic resistance present in the external circuit. Current flow will stop as soon as at least one of the reactants is consumed. 

However, under working conditions, with a current density j, the cell voltage E(j) decreases greatly as the result of three limiting factors the charge transfer overpotentials r]a,act and Pc,act at the two electrodes due to slow kinetics of the electrochemical processes (p, is defined as the difference between the working electrode potential ( j), and the equilibrium potential eq,i). the ohmic drop Rf. j, with the ohmic resistance of the electrolyte and interface, and the mass transfer limitations for reactants and products. The cell voltage can thus be expressed as... 

Another parameter essential for quantitative applications of micropipettes is the internal ohmic resistance, R. It is largely determined by the solution resistance inside the narrow shaft of the pipette, and can be minimized by producing short (patch-type) pipettes. The micropipette resistance has been evaluated from AC impedance measurements. Beattie et al. measured the resistance of micropipettes filled with aqueous KCl solutions (0.01, 0.1, and 1 M) [18b]. The value obtained for a 3.5/am-radius pipette was within the range from 10 to 10 As expected, the tip resistance was inversely proportional to the concentration of KCl in the filling solution. In ref. 18b, the effect of pipette radius on the tip resistance was evaluated using a constant concentration of KCl. The pipette resistance varied inversely with the tip radius. The iR drop was found to be 4.5-8 mV for the pipette radii of 0.6 to 19/rm when 10 mM KCl was used. 

Further, if within the electrical circuit the ohmic resistance R can be neglected, the ic wave leads to the potential by 90°, as is known, which means that shows a positive 7t/2 phase angle shift ( between tt/2 and zero. Our main objective in AC polarography, however, is the faradaic current, so a separating condenser is placed between the amplifier and normal resistor in order to filter out the d.c. current and to evaluate the ac current component. As we want to understand the relationship between idc(i ) and iac(i ) as a function of Edc and Eac applied, we may consider Fig. 3.41(a) and (b). 

Apart from the above requirement of a low ohmic resistance, it is nevertheless recommended to use a three-electrode system in view of the more precise establishment of the dme potential. 

In the ac circuit of the polarographic cell there is such an external ohmic resistance that via the alternating voltage (300 V) together with a superimposed dc the voltage over the cell alternates from 0 to -2V vs. an SCE within these limits oxidation of Hg and reduction of Na+ (electrolyte) to Na(Hg) remains sufficiently restricted. 

In addition, the emf to be applied must overcome the ohmic resistance of the solution and the cathode counter potential, which are respectively,... 

Since model compounds reveal well-defined cyclic voltammograms for the Cr(CNR)g and Ni(CNR)g complexes (21) the origin of the electroinactivity of the polymers is not obvious. A possible explanation (12) is that the ohmic resistance across the interface between the electrode and polymer, due to the absence of ions within the polymer, renders the potentially electroactive groups electrochemically inert, assuming the absence of an electronic conduction path. It is also important to consider that the nature of the electrode surface may influence the type of polymer film obtained. A recent observation which bears on these points is that when one starts with the chromium polymer in the [Cr(CN-[P])6] + state, an electroactive polymer film may be obtained on a glassy carbon electrode. This will constitute the subject of a future paper. 

In an analysis of an electrode process, it is useful to obtain the impedance spectrum —the dependence of the impedance on the frequency in the complex plane, or the dependence of Z" on Z, and to analyse it by using suitable equivalent circuits for the given electrode system and electrode process. Figure 5.21 depicts four basic types of impedance spectra and the corresponding equivalent circuits for the capacity of the electrical double layer alone (A), for the capacity of the electrical double layer when the electrolytic cell has an ohmic resistance RB (B), for an electrode with a double-layer capacity CD and simultaneous electrode reaction with polarization resistance Rp(C) and for the same case as C where the ohmic resistance of the cell RB is also included (D). It is obvious from the diagram that the impedance for case A is... 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

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