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Estimation of Leakage Current in Proton Exchange Membrane Fuel Cells

^{-2}in PEM fuel cell modeling literature [1]. Unlike other types of fuel cells [2, 3], this current leakage has not been measured directly for PEM. The reactants (hydrogen and oxygen) crossover across the membrane, however, has been studied [4, 5]. It has been shown that the oxygen crossover is considerably less than that of hydrogen [5].

In this study, the amount of leakage current in a PEM fuel cell is estimated based on polarization curves and impedance measurements obtained for a 5-cm^{2} cell containing Nafion 212. The measurements were conducted with four different gas diffusion layers (GDLs) with different PTFE and MPL loadings. Although the polarization curves are different for different GDLs, it is expected to have the same amount of the leakage current as the same membrane has been used.

Considering the Tafel equation [1] for the anode and cathode, the activation loss in a PEM fuel cell can be presented as

*η _{act} = RT/*(

*nF*)

***(

*1/*)

*α*_{A}+1/*α*_{C}*ln(*

****j+*)

*j*_{leak}*(*

*- RT/**)*ln(*

*nF**j*

_{0,A}^{1/αA}

_{ }*)*

*j*_{0,C}^{1/αC}where *η _{act}*,

*j*,

*j*,

_{leak}*R*,

*T*,

*n*,

*F*,

*α*,

_{A}*α*,

_{C}*j*

_{0,A}_{ }and

*j*are the activation loss, current density, leakage current density, universal gas constant, temperature, number of electrons transferred due to the reaction, Faraday constant, anode and cathode charge transfer coefficients and anode and cathode exchange current densities, respectively. As the above equation shows, it is expected to have a linear relation between

_{0,C}*η*and ln(

_{act}*j+j*).

_{leak}To find the leakage current, the activation loss has to be determined from the polarization curves. By assuming negligible mass transport loss in the low current density region, the total overpotential can be determined based on the difference between the theoretical cell voltage (1.23 V) and the measured voltage. As a result, the activation loss can be calculated by subtracting the losses due to the contact resistance and proton transfer in the membrane (i.e., ohmic loss) from the total overpotential. This ohmic loss can be estimated from the high frequency resistance in the Nyquist plot as the intersection of the plot with the real impedance axis [6]. This loss can be considered as an ordinary resistance [6]. Thus, the corresponding overpotential becomes a linear function of the current density. To subtract this loss, it is necessary to rotate the polarization curve counter-clockwise with the same angle of the ohmic-loss line, as it is shown in Figure 1. Then, leakage current (*j _{leak}*) can be determined from the best linear fit to the

*η*versus ln(

_{act}*j+j*) graph.

_{leak}Using this methodology, the leakage current of the cell operated with the same membrane but four different GDLs are calculated and presented in Table 1. The polarization curves are shown in Figure 2. Although the polarization curves and Nyquist plots are different, the leakage currents are the same since the same membrane was utilized.

**References**

- R. O’hayre, S. Cha, W. Colella and F.B. Prinz,
*Fuel Cell Fundamentals*, Second ed., John Wiley & Sons (2009). - J.P. Meyers and J. Newman,
*J. Electrochem. Soc.*,**149**, A729 (2002) - D.J.L. Brett, A. Atkinson, N.P. Brandon and S.J. Skinner,
*Chem. Soc. Rev.*,**37**, 1568 (2008) - S.S. Kocha, J.D. Yang and J.S. Yi,
*AIChE Journal*,**52**, 1916 (2006) - B.T. Huang, Y. Chatillon, C. Bonnet, F. Lapicque, S. Leclerc and M. Hinaje,
*Fuel Cells*,**12**, 335 (2012) - S.M. Rezaei Niya, M. Hoorfar, Submitted to
*Electrochimica Acta*.