Ohmic cell impedance

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).

The above argument, along with the evidences presented in Sections 5.3.2.1-5.3.2.2, indicates that other transport mechanisms than diffusion-controlled lithium transport may dominate during the CT experiments. Furthermore, the Ohmic relationship between Jiiu and A indicates that internal cell resistance plays a critical role in lithium intercalation/deintercalation. If this is the case, it is reasonable to suggest that the interfacial flux of lithium ion is determined by the difference between the applied potential E pp and the actual instantaneous electrode potential (t), divided by the internal cell resistance Keen- Consequently, lithium ions barely undergo any real potentiostatic constraint at the electrode/electrolyte interface. This condition is designated as cell-impedance-controlled lithium transport. 

Active query methods measure cell impedance, which is then correlated to SoC. The technique often superimposes an active signal (a low amplitude, characteristic high-frequency square or sinusoidal current pulse) onto the battery and then uses a transfer function on the response waveform to determine the ohmic polarization or a direct correlation to SoC. One permutation of this technique uses the voltage response to indigenous current spikes to map impedance in a similar way. This method provides reasonable results, but if hardware is involved it is often complex and expensive even sensors will require a relatively high-speed data acquisition bus to minimize the slew between voltage and current. 

Widely known is the approximation of the measured impedance spectra by a CN LS fit procedure, which results in a model function represented by an equivalent circuit [22]. However, this approach necessitates an a priori definition of the ECM. Consequently, the ECM is appHed without knowing the number and nature of ohmic and polarization processes contributing to the total cell impedance. This leads to a severe ambiguity of the adopted model [1]. 

Experimentally, there are several ways to determine the ohmic cell resistance. If the V-I curve has a substantial linear portion (in the center), the slope of this curve usually closely approximates the ASR of the cell. Only in such a linear portion of the V-I curve the ohmic resistance is dominant, and hence the determination of the ASR valid. Sometimes, a more accurate way to determine the ohmic resistance is from impedance spectroscopy. In an impedance spectrum of a fuel cell, the ohmic resistance is the real value of the impedance of the point for which the imaginary impedance is zero (Figure 2-5). As can be seen in the example, the ohmic resistance is invariant with gas concentration. The part of the impedance that is related to mass transport and kinetics, however, changes markedly with anode feed composition. 

Where, OCV = open circuit voltage, V VL = cell voltage, V R = total cell impedance, milliohms Ro = cell internal ohmic resistance, milliohms Rpl = first internal polarization resistance, milliohms Rp2 = second internal polarization resistance, milliohms IL = cell load current, A... 

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 two main techniques for measuring electrode losses are current interrupt and impedance spectroscopy. When applied between cathode and anode, these techniques allow one to separate the electrode losses from the electrolyte losses due to the fact that most of the electrode losses are time dependent, while the electrolyte loss is purely ohmic. The instantaneous change in cell potential when the load is removed, measured using current interrupt, can therefore be associated with the electrolyte. Alternatively, the electrolyte resistance is essentially equal to the impedance at high frequency, measured in impedance spectroscopy. Because current-interrupt is simply the pulse analogue to impedance spectroscopy, the two techniques, in theory, provide exactly the same information. However, because it is difficult to make a perfect step change in the load, we have found impedance spectroscopy much easier to use and interpret. 

In a H2/02 (air) fuel cell, in general, the spectra, i.e., the Nyquist plots obtained by EIS measurements, very often have three features, which are denoted as high-frequency, medium-frequency, and low-frequency. The high-frequency region of an impedance spectrum is associated with the internal ohmic resistance and the contact capacitance in the granular electrode structure of the membrane electrode assemblies, whereas the medium- and low-frequency regions represent the charge-... 

Figure 5.32. Impedance plots for single cells at ambient temperature, a Nation 117. Cell voltage and ohmic drop corrected potential (in parenthesis) ( ) 0.9 V (0.9 V) ( ) 0.8 V (0.81 V) (A) 0.70 V (0.76 V) ( ) 0.6 V (0.74 V) ( ) 0.5 V (0.74 V). b Nafion 112. Cell voltage and ohmic drop corrected potential (in parenthesis) ( ) 0.9 V (0.9 V) ( ) 0.8 V (0.81 V) (A ) 0.70 V (0.73 V) ( ) 0.6 V (0.67 V) ( ) 0.5 V (0.61 V). Plots were corrected for the high-frequency resistances. Left detail of the high-frequency regions [29]. (Reprinted from Journal of Electroanalytical Chemistry, 503, Freire TJP, Gonzalez ER. Effect of membrane characteristics and humidification conditions on the impedance response of polymer electrolyte fuel cells, 57-68, 2001, with permission from Elsevier.)...

Figure 5.34. Electric equivalent circuit for the impedance spectra in Figure 5.37. Ref. ohmic resistance Rct charge-transfer resistance CPE constant phase element IV Warburg element. The subscripts a and c denote anode and cathode, respectively [36]. (Modified from Boillot M, Bonnet C, Jatroudakis N, Carre P, Didierjean S, Lapicque F. Effect of gas dilution on PEM fuel cell performance and impedance response. Fuel Cells 2006 6 31-7. 2006 John Wiley Sons Limited. Reproduced with permission, and with the permission of the authors.)...

Ahn et al. have developed fibre-based composite electrode structures suitable for oxygen reduction in fuel cell cathodes (containing high electrochemically active surface areas and high void volumes) [22], The impedance data obtained at -450 mV (vs. SCE), in the linear region of the polarization curves, are shown in Figure 6.22. Ohmic, kinetic, and mass transfer resistances were determined by fitting the impedance spectra with an appropriate equivalent circuit model. 

To increase fundamental knowledge about ionic resistance, it is important to develop a methodology to experimentally isolate the contributions of the various cell components. Electrochemical impedance spectroscopy has been widely used by Pickup s research group to study the capacitance and ion conductivity of fuel cell catalyst layers [24-27] they performed impedance experiments under a nitrogen atmosphere, which simplified the impedance response of the electrode. Saab et al. [28] also presented a method to extract ohmic resistance, CL electrolyte resistance, and double-layer capacitance from impedance spectra using both the H2/02 and H2/N2 feed gases. In this section, we will focus on the work by Pickup et al. on using EIS to obtain ionic conductivity information from operational catalyst layers. 

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