3.4 Correlation of EIS with Other Electrochemical Techniques
3.4.1 EIS and the Polarization Curve
ct c
d R
C ω
α
= cos (3.128)
Knowing ωc and α, parameters b and Cd can be obtained.
124 X-Z. Yuan, C. Song, H. Wang and J. Zhang
(CLs), resulting in a drastic drop in cell performance [17]. Figure 3.13 also shows the difference between the theoretical cell potential (1.23 V) and the thermoneutral voltage (1.4 V), which represents the energy loss under reversible conditions (the reversible loss) [18]. Very often, polarization curves are converted to power density versus current density plots by multiplying the cell voltage by the current density at each point of the curve.
Figure 3.13. Typical polarization curve for a PEMFC [14]. (Modified from Barbir F. PEM fuel cells: theory and practice. New York: Elsevier Academic Press, ©2005, with permission from Elsevier.)
As shown in Figure 3.13, the voltage losses can be analyzed from the polarization curve. Generally, the voltage losses consist of four parts: (1) loss due to gas crossover; this is represented by the open circuit voltage (OCV), which is lower than the thermodynamic voltage; (2) loss due to activation resistance; (3) loss due to ohmic resistance; and (4) loss due to mass transport limitation.
Consequently, the cell voltage of a PEMFC, Ecell, can be expressed using the following equation [12]
ηint η η η η
= − − − − −
cell rev mix act ohm conc
E E (3.129)
Let us discuss the terms in Equation 3.129 one by one:
1. Erev (reversible cell potential). Erev can be expressed as
3 5
1.229 0.85 10 ( 298.15) 4.3085 10 [ln( 2) 1/ 2 ln( 2)]
rev
H O
E T
T p p
−
−
= − × −
+ × + (3.130)
where T,
H2
P , and PAir are absolute fuel cell temperature (K), partial pressure of hydrogen (Pa), and partial pressure of air (Pa), respectively.
Under standard conditions, Erev equals 1.229 V.
2. ηint (internal loss). ηint is associated with gas crossover through the membrane. This loss equates to an internal current and remains constant even under open circuit conditions. It does not contribute to the output current or power, and decreases the electron conduction in the membrane.
3. ηmix (mixed potential). As discussed in Chapter 1, the mixed potential is composed of both the cathodic O2/H2O reaction potential and the Pt/PtO anodic reaction potential. The reported mixed cathode potential is around 1.06 V (versus SHE) at standard conditions (25°C, 1.0 atm) with an O2
partial pressure dependence of 15 mV/atm[19, 20]. Therefore, the value of
rev int mix
E −η −η is what we called open circuit voltage, denoted as EOCV. 4. ηact (activation or kinetic loss). ηact is associated with the driving force of the
electrode reaction. In practice, hydrogen and oxygen must move and attach to the surfaces of the anode and cathode in order to achieve a self-sustaining reaction. This process takes time and limits the current flow.
5. ηohm (ohmic loss). ηohm is mainly caused by proton flow across the membrane and the ionomer inside the catalyst layers. It also includes resistance originating from the non-ideal electrodes and the electrode interconnections.
6. ηconc (concentration loss or mass transport loss). ηconc is related to the reactant concentration gradients in the gas channels within the catalyst layers. This loss mainly occurs in the high current density range where reactant gas supply becomes the limitation.
The voltage–current curve is a simple and efficient way to evaluate a fuel cell’s properties. However, the underlying mechanisms are difficult to analyze by this method because the contributions from different processes overlap. Figure 3.14 shows the percentages of the cell voltage drop caused by membrane, charge transfer, and mass transfer resistances, obtained through EIS measurements [21]. It indicates that at a given current density, the potential loss is the sum of these resistances. At low, medium, and high current density ranges, the dominant processes are kinetic, ohmic, and mass transfer, respectively. For example, the activation loss depends on current density; therefore, it affects the cell voltage not only at low but also at intermediate and high currents, which is not clearly shown from the polarization curve.
126 X-Z. Yuan, C. Song, H. Wang and J. Zhang
Figure 3.14. Percentage of cell individual voltage drop caused by charger transfer, membrane, and mass transfer resistances at different current densities and 80ºC [21].
(Reproduced by permission of ECS—The Electrochemical Society, from Tang Y, Zhang J, Song C, Liu H, Zhang J, Wang H, Mackinnon S, Peckham T, Li J, McDermid S, Kozak P.
Temperature dependent performance and in situ AC impedance of high-temperature PEM fuel cells using the Nafion-112 membrane.)
EIS has the ability to distinguish between influences from different processes, especially when the system involves multiple-step reactions, parallel reactions, or additional processes such as adsorption. Generally speaking, the measurements and analysis of the EIS for a PEMFC are complicated compared with those of the polarization curve. However, the results from both methods are not insular, and some relationships exist between the complicated impedance spectrum and the simple polarization curve [22].
The correlation between the EIS measurements and polarization curves is that the polarization resistance of the cell measured at a certain voltage corresponds to the tangent to the polarization curve at that voltage [23], i.e., a negative slope in the polarization curve equals the polarization resistance in the impedance spectrum.
The polarization resistance is the AC impedance when the frequency approaches zero, where only ohmic components attract attention. Obtaining the polarization resistance of a fuel cell requires extrapolation from the simulated EIS impedance at a very low frequency (e.g., 1 nHz) or summing the individual resistances, which are obtained by fitting the measured spectra with an equivalent circuit. The correlation between impedance measurements and polarization curves is illustrated in Figure 3.15.
0 10 20 30 40 50 60 70 80 90 100
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Current Density (A/cm2)
Cell Voltage Drop Percentage (%)
Mass Transfer Portion Charge Transfer Portion Membrane Resistance Portion
Figure 3.15. Schematic representation of the correlation between fuel cell impedance and polarization curve. (Modified from [23], with kind permission from Springer Science+Business Media: Journal of Applied Electrochemistry, Characterization of membrane electrode assemblies in polymer electrolyte fuel cells using a.c. impedance spectroscopy, 32(8), 2002, 859–63, Wagner N. Figure 4.)
Figure 3.16. Schematic representation of the correlation between polarization resistances (anode, cathode, and cell) and polarization curves [23]. (With kind permission from Springer Science+Business Media: Journal of Applied Electrochemistry, Characterization of membrane electrode assemblies in polymer electrolyte fuel cells using a.c. impedance spectroscopy, 32(8), 2002, 859–63, Wagner N. Figure 6.)
128 X-Z. Yuan, C. Song, H. Wang and J. Zhang
Perry et al. [24] and Jaouen et al. [25] have provided useful diagnostic criteria.
They concluded that cathodes controlled by either Tafel kinetics and oxygen diffusion in the agglomerate regions, or by Tafel kinetics and proton transport in the catalyst layer could result in double Tafel slopes. If the cathode was controlled by Tafel kinetics, oxygen diffusion, and proton transport all together, quadruple Tafel slopes would appear.
Using the electrode resistances (Ranode and Rcath) gained from simulation with an equivalent circuit, the individual cathode and anode polarization curves can be determined, as shown schematically in Figure 3.16 [23].