Electrochemical characterization: iV-Curve and EIS technique

The polarization curve is the most used method for the characterization of PEM water electrolyser because it allows to estimate the effects of many parameters such as temperature, pressure, composition, relative humidity on the cell performance. In general, the polarization curve has three characteristic regions, as depicted in Figure 8, related to the major internal irreversibilities of the cell.

Figure 8 Experimental polarization curve of a PEM electrolyser [26]

The shape of the polarization curve is dictated by the several loss mechanisms aforementioned. At low current density, it assumes a logarithmic behaviour due to charge-transfer phenomena at the anode and the cathode; moreover, the anodic overvoltage is outweighed with respect to the cathodic one because the kinetics of the OER is lower than that of the HER. With increasing current densities, the shape becomes linear because activation losses are less relevant with respect to ohmic losses. Meanwhile, at high current densities the mass transfer processes are dominant giving to the cell voltage a non-linear behaviour. The polarization curve enables the identification of the overall loss of the cell making difficult to separate the different contributions of the loss mechanisms to the cell performance. In contrast to the I-V curves, the electrochemical impedance spectroscopy (EIS) is a very promising technique to analyse complex electrochemical systems like PEM water electrolysers.

Electrochemical impedance spectroscopy (EIS) is a powerful and non-invasive in-situ diagnostic method for the characterization of electrochemical processes and devices. It is mainly used to study and evaluate the different phenomena in a separate way, taking

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advantage from the fact that the polarization losses occurring within the cell exhibit different characteristic time constants and frequency response.

The measurement approach consists of applying a sinusoidal current (galvanostatic mode) or voltage (potentiostatic mode) of a certain amplitude and frequency superimposed on the normal operating DC current/voltage and measuring the amplitude and phase shift of the output voltage-in case of current control mode- or current when a voltage control mode is applied. This procedure is repeated for a discrete quantity of frequency values over kHz-mHz range, thereby generating a characteristic impedance spectrum. The impedance or the admittance (inverse of impedance), for galvanostatic and potentiostatic modes respectively, is obtained by the ratio between the response (output) and the perturbation (input) according to Eq. 2.11 and Eq. 2.12 [23].

𝑍(𝑓) =𝑈_𝐴𝐶(𝑓)

𝐼_𝐴𝐶(𝑓) = |𝑍(𝑓)| ∗ 𝑒^{𝑖𝜃(𝑓)} (𝐸𝑞. 2.11) 𝑌(𝑓) = 𝑍(𝑓)⁻¹= 𝐼_𝐴𝐶(𝑓)

𝑈_𝐴𝐶(𝑓)= |𝑍(𝑓)|⁻¹∗ 𝑒^{−𝑖𝜃(𝑓)} (𝐸𝑞. 2.12)

Generally, the impedance spectrum can be presented in Nyquist and Bode plots, which are representations of the impedance as a function of frequency. Nyquist plot- where imaginary part is plotted against the real part- consists of two or more (depressed) semicircles representing the different processes taking place in the WE cell such as charge transfer, electronic and ionic conduction, diffusion and transport processes [23]. In particular, it is possible to identify three domains as in the polarization curve.

Figure 9 Characteristic impedance spectrum [26].

In the Bode graph each semicircle of the Nyquist representation- characterized by a specific time constant- is represented by a peak of the phase angle as function of frequency. When

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semicircles merge, it means that processes have time constants with same order of magnitude and this, translated to the Bode plot, is graphically shown by merging peaks as well, but these are still pronounced and distinguishable even if merged. In these cases, the individuation and separation of the phenomena becomes challenging and troublesome.

The Nyquist plot is the most used graphical representation of the impedance data since from a visual inspection it allows to individuate some important features- high frequency, mid frequency and low frequency features- directly correlated to the main sources of losses in the cell. The high frequency intercept with the real axis corresponds to the sum of the internal ohmic resistances, including the electrolyte, active material, current collectors and electrical contacts. Hence, it gives an insight of the ohmic losses within the cell. The arcs appearing in the mid-frequency region- which can be more or less defined and usually it appears as two merged semicircles- are primarily due to the electrochemical processes occurring at the electrolyte/electrode interfaces inside the cell, which combine resistive and capacitive effects.

These are OER at the anode and HER at the cathode, but mostly of the time the charge transfer reaction of the anode dominates due to its sluggish kinetics. Finally, the low-frequency range reflects mainly mass transport limitations in the active material of the cell electrodes.

It is important to point out that the impedance is defined for those systems that are compliant with the condition of causality, linearity and time-invariance. These are the conditions to get good impedances. Although PEM electrolysers, and in general electrochemical systems, are non-linear, the condition of linearity can be achieved if the amplitude of the perturbating signal is small enough to determine a linear response from the system under study [23]. As a consequence, the impedance data obtained are numerically validated through the use of the Kramers-Kroning relations which describe the correlation between the real and imaginary parts of the impedance. More details will be discussed in the next sections.

The analysis of the impedance spectrum is made by fitting the experimental data with a suitable equivalent electrical circuit (EEC) model composed of a combination of resistances, capacitors, inductors, Warburg elements and constant phase elements. These impedance elements are connected in parallel and/or in series to closely simulate the impedance spectrum and thus for describing the different processes characterized by different time constant.

For PEM electrolyser a common ECM used for the fitting procedure is shown in the figure below.

Figure 10 General ECM to simulate the impedance spectrum of a PEMWE [23].

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The resistor 𝑅_Ω in series with the inductor 𝐿_𝐶 represent the resistance of the electrolyte membrane and the inductance of cables/wires used in the test, respectively. Thereafter, the subsequent two impedance elements consist of an ideal capacitor 𝐶_𝑑𝑙 in parallel with an ideal resistor 𝑅_𝑐𝑡. These parallel connections account for the electrode/electrolyte interface at the anode and the cathode; the capacitance represents the double layer charging at the electrode interface whereas the resistance, commonly called charge-transfer resistance, accounts for the effective resistance for the electrode reaction. More elaborate models substitute the capacitance with constant phase element (CPE) to simulate the fractal and porous nature of the electrodes and add a Warburg element to consider the diffusive processes occurring in both electrodes [23].

Finally, the unknown values of the ECM, such as 𝑅_𝑐𝑡, 𝑅_Ω, 𝐶𝑃𝐸, are evaluated by a Non-linear Least Squares (CNLS) analysis. The CNLS-fit of the impedance data is carried out with commercially available software. It is an iterative process so once that good initial values of the parameters are estimated, the software will adjust them until the goodness of the fit is satisfactory. When the fit looks inappropriate, i.e. the simulation of the impedance spectrum results poorly close to the experimental data, the reason may be the wrong choice of the ECM or incorrect estimation of the initial values. Therefore, in these cases the procedure should be repeated [27].