
325Fuel Cell Characterization
where β
a
is the anodic beta coefcient in volts/decade and β
c
is the cathodic
beta coefcient in volts/decade. If a small signal approximation (η is small) is
applied to Equation 8.14, we get the following:
j
R
0
=
+
ββ
ββ
ac
acp
1
, (8.15)
where the new parameter, R
p
, is the polarization resistance. The polarization
resistance behaves like a resistor.
8.2.2.4 Charge Transfer Resistance
When the polarization depends only on the charge transfer kinetics, the
Butler–Volmer equation is given as (Equation 5.78)
j = j
0
(e
−αFη/RT
− e
(1−α)Fη/RT
). (8.16)
When the overpotential, η, is very small and the electrochemical system is ...