Chapter 1. Introduction to Solid Oxide Fuel Cells and Perovskite Cathodes
1.5. Theoretical Background
1.5.4 Performance of fuel cell
Figure 1.14. A current-voltage (i-V) curve of a fuel cell [26]
A current-voltage (i-V) curve are used to evaluate the electrochemical performance of a fuel cell.
The i-V curves describe the voltage output of the devices for a given current output. The power density delivered by a fuel cell can be determined by multiplying the voltage at each point and the corresponding current density. It is obvious that the voltage output of fuel cell under operation is less than the voltage output thermodynamically predicted due to irreversible losses.[9] There are three major fuel cell losses with characteristic shape. Each of losses is derived by the basic fuel cell steps.
The real output voltage of the fuel cell could be calculated by given:
where V is real output-voltage of fuel cell, is predicted voltage output, is activation losses due to reaction kinetics, is ohmic losses derived from the ionic and electronic conduction, is concentration losses due to mass transport.
is overpotential consumed to activation energy for the reaction for the reactions. Current density can be expressed as the function of activation losses given by:
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where is the exchange current density, is known as the charge transfer coefficient. This equation is known as Butler-Volmer equation. With large , Butler-Volmer equation can be written as the Tafel equation as given by
Ohmic loss is derived by the resistance of electron flow through the electrode and ion flow in the electrolyte. On the other hands, surrounding material cannot maintain the initial state of the bulk fluid as the reactants are consumed at the electrode by the electrochemical reaction. Various processes my contribute are summarized as follow:
1. Slow diffusion in the gas phase within the electrode pore
2. Solution / Dissolution of reactants or products into and out of the electrolyte
3. Diffusion of reactants and products into the electrochemical reactions through the electrolyte.
At the practical densities, concentration polarization is mainly originated from the slow transport of reactants and products to/from electrochemical reaction site.
21 Reference
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