Environmental Engineering Reference
In-Depth Information
cells connected in series, with an active area of about 64 cm 2 each (one example of
its bipolar plate is shown in Fig. 3.4 )[ 45 ]. On the abscissa of Fig. 3.5 the current
delivered by the stack is reported, while the current density could be used to
compare stacks based on cells of different sizes, making the ratio between the
current delivered and the cell active area.
The parameter R reported in the legend of Fig. 3.5 (stoichiometric ratio) is
defined as R = R eff /R stoich , where R eff is the ratio between the air and hydrogen
mass flow rates, while R stoich is the same ratio as required by the stoichiometric
equation of H 2 oxidation (see Sects. 4.3 and 6.2 ).
It can be noticed that also in the absence of electric load, when gaseous reac-
tants are fed to the stack but the electric circuit is open (zero current) the total stack
voltage is lower than the theoretical or thermodynamic value
(OCV = 1.23 V 9 32 cells = 39.4 V at 25C and ambient pressure), and it cor-
responds to a voltage at zero current of about 0.96 V per cell (31 V/32 cells),
which cannot be explained by the slight shifting from standard conditions of
temperature and pressure (see Sect. 3.3.2 ). The terms polarization or overpotential
are used to describe the difference between the actual electrode potential and the
equilibrium potential, and represent the driving force for the electrochemical
reaction, i.e., the potential difference necessary to produce current. On the other
hand, the existence of overpotential in real systems evidences that also without
circulation of current in the external circuit some energy losses are present, which
of course are expected to increase when an electric load is applied. In fact, the
characteristic curve of Fig. 3.5 shows also that, for the real system considered,
after a voltage drop of about 5 V at lower current (up about 2 A), a slower and
linear voltage diminution occurs up to the maximum power (480 W at 30 A).
Starting from the energy supplied by a specific electrochemical reaction, all
voltage losses can be generally associated with the fraction of that energy which is
used by the cell to accomplish the electrode reactions at the desired speed, then
they are somehow correlated to the electrode kinetics, while the rest of the reaction
energy remains available for external use, such as production of useful work.
3.3.1.1 Losses Due to Activation Overpotential
The theoretical interpretation of the first voltage drop at low current is based on the
Butler-Volmer equation, which is derived by an analysis of electrode kinetics and
provides a general description of the relationship between current density and
surface overpotential for an electrochemical converter [ 46 ]:
exp
exp a Rd FE E
a Ox FE E
ð
Þ
ð
Þ
ð 3 : 23 Þ
i ¼ i 0
RT
RT
where i is the current density delivered by the cell and i 0 is the exchange current
density, which represents the continuous flow of electrons occurring at the
electrodes when reactants and products are in equilibrium conditions, i.e., when no
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