Page 83 - Introduction to Transfer Phenomena in PEM Fuel Cells

72 Introduction to Transfer Phenomena in PEM Fuel Cells
be simplified to a linear equation:
 For overpotential values below 10 mV, the Butler–Volmer equation can
nF

j ≅ j 0  η act  [2.67]
 RT 
2.5. Polarization phenomena
When the terminals of the fuel cell are connected to the charge traversed
by a current of intensity (j), the voltage at the terminals of the fuel cell
decreases with respect to the theoretical voltage due to polarization
phenomena, of which there are three forms: activation, ohmic and
concentration polarization.

2.5.1. Activation polarization

The activation polarization is greater at the cathode due to the kinetics of
oxygen reduction, which is slower than the reduction of hydrogen at the
anode.

This polarization is due to the activation energy of the reactions at the
electrodes. The chemical kinetics at the electrodes is the result of complex
reaction steps each with its own kinetics.

This activation polarization can be estimated using the empirical Tafel
equation in its detailed form as follows [BLU 07, BOU 07, LAR 03, OHA 09]:

RT RT
η = − ln j + ln j [2.68]
act
α nF 0 α nF
This equation gives the decrease in voltage at an electrode. In order to
know the voltage decrease in a fuel cell, it is necessary to know the voltage
decrease at the cathode and at the anode. Noting respectively (J o_a) and (J 0_C),
the exchange currents at the anode and at the cathode, and (A a) and (A c) the
coefficients of the Tafel equation at the anode and at the cathode, the
expression of the voltage decrease in the cell is:

 j   j 
η act = Aln a  + A ln C  [2.69]
  j 0_ a     j 0 _ C  