Page 82 - Introduction to Transfer Phenomena in PEM Fuel Cells

Charge Transfer Phenomena 71
2.4.5. Current density
Since the electrochemical reaction taking place in the cell is a surface
reaction, the current density is therefore a characteristic variable of a fuel
cell. It is also expressed in amperes per square centimeter. On the physical
surface of the electrode, however, it is a function of many parameters (type
of fuel cell, fuel flow rate, etc.) [BLU 07]. Out of equilibrium, the current
density (j) is related to the activation overpotential (η act) by the Butler–
Volmer relation:

  α nF   (1−α )nF  
j = j exp η act  − exp − η act   [2.65]
0 
 
   RT   RT   
where (α) is the charge transfer coefficient which indicates the distribution
of the activation overpotential between the anode and the cathode. It gives
the proportion of the activation potential (η act) required for the activation
energy of anodic oxidation. The part of the activation energy required for the
reduction at the cathode is therefore (1-α). Its value is always between 0 and
1. For a symmetric reaction, α = 0.5. For electrochemical reactions, the value
of (α) is usually between 0.2 and 0.5 [BOU 07].

This equation, established by Butler and Volmer, describes, at the
macroscopic level, the transfer kinetics of electrons in a heterogeneous
medium. It is a simplified model of activation phenomena (assuming the
charge concentration at the surface of the electrode is equal to that in the
electrolyte, for example). It shows that the current density of a fuel cell
increases exponentially with the activation overpotential (η act) and that it is
important to have a high exchange current density value (j 0), as it decreases
the activation threshold by the use of a catalyst, by increasing the
temperature or the concentration of reagents. For large overpotentials,
|η act| >> (RT/F), usually greater than 50 or 100 mV, the term corresponding
to the opposite reaction is negligible (irreversible reaction) and we use the
simplified equation, established empirically, known as the Tafel equation,
which is a good approximation of the Butler–Volmer equation [BOU 07,
LAR 03]. It allows the values (j 0) and (α) of the Tafel equation to be
determined experimentally. This equation is as follows:

  α nF  
j = j exp  η act   [2.66]
0 
  RT  