Polarization curves are useful tools to predict electrochemical performance and diagnose system failures[1][2]. The construction of a reliable polarization curve requires a three-electrode system in which a reference electrode is used. In some systems, such as fuel cells, the use of a reference electrode is often impossible or impractical due the cell design[3][4]. We report a model that reliably predicts the behavior of well-characterized electrodes at temperatures up to 400 °C and 30 MPa without a reference electrode. We define well-characterized electrodes as those electrodes with reliable data for the charge transfer coefficient (α), the apparent activation energy (A_e), the resistance (R_Ω) and the exchange current density (j_0,ref) at a reference temperature (T_ref ) for the reaction system under consideration.

We report that the net reaction can be modeled by simply performing a linear combination of the total potential for the half-cell reactions at the anode and cathode, that is E_total,a+c = E_total,a + E_total,c, where E_total,a = E_rev,a + E_η,a + E_IR,a and E_total,c = E_rev,c + E_η,c + E_IR,c.

The net reaction being modelled by a simple linear combination of the half-cell reactions at the anode and cathode is not intuitive, as the potential due to ohmic losses appears to have been accounted for twice (E_IR,a + E_IR,c). In our cell design, the maximum variation in R is 4.76 Ω, which corresponds to a variation of about 0.4 Ω cm^-1 for the electrodes in our system, which have surface areas within 15% of each other.

Using this method, an estimated potential component breakdown can be found using only the net reaction data and the parameters obtained from the characterization of the electrodes.

References:

[1] Wang, L., Husar, A., Zhou, T., & Liu, H. (2003). A parametric study of PEM fuel cell performances. International journal of hydrogen energy, 28(11), 1263-1272.

[2] Serra, P. M. D., Espírito-Santo, A., & Magrinho, M. (2020). A steady-state electrical model of a microbial fuel cell through multiple-cycle polarization curves. Renewable and Sustainable Energy Reviews, 117, 109439.

[3] Winkler, J., Hendriksen, P. V., Bonanos, N., & Mogensen, M. (1998). Geometric requirements of solid electrolyte cells with a reference electrode. Journal of the Electrochemical Society, 145(4), 1184.

[4] Liu, Z., Wainright, J. S., Huang, W., & Savinell, R. F. (2004). Positioning the reference electrode in proton exchange membrane fuel cells: calculations of primary and secondary current distribution. Electrochimica Acta, 49(6), 923-935.

Figure caption:

A comparison of the raw data gathered from the two electrode system and values determined from the model using parameters obtained from characterizing the electrodes at room temperature. E_η,a, E_η,c, and E_η,total are the values for overpotential from the anode, cathode and net reaction respectively as calculated by the model. E_total,a, E_total,c, and E_total,net show the total potential for the anode, cathode, and net reaction, respectively. E_total,a + E_total,c is a linear combination of E_total,a and E_total,c which closely matches E_total,net.