8
respectively. According to the transition state theory from chemical kinetics, rate
constants are related to the free energies of activation, which are related to the
potential. From these relations, the basic equation is derived, which describes how
the overall current on an electrode depends on the applied potential.
1.3.1 Current-Potential Curves
The equation which describes the fundamental relationship between the electrical
current on an electrode and the electrode potential, assuming that both a cathodic
and an anodic reaction occur on the same electrode, is called the Butler–Volmer
equation:
j j
nF
RT
nF
RT
−
−
(
)
−
−
0
1
exp
e xp
α
η
α η
(1.9)
where j 0 is the exchange current density, T is absolute temperature, R is universal
gas constant, α is the so-called symmetry factor or charge-transfer coefficient, and
η is the overpotential. Overpotential is the extent to which the reaction is driven
beyond the equilibrium potential, E eq :
η = −
E E eq
(1.10)
At high anodic overpotential, partial cathodic current can be excluded compared
to the anodic, meaning that the Butler–Volmer Eq. (1.9) simplifies to:
j j
j
nF
RT
= =
−
(
)
a
0
1
exp
α
η
(1.11)
Partial anodic currents can be excluded from Butler–Volmer equation at high
cathodic overpotential:
j j
j
nF
RT
= = −
−
c
0 exp
α η
(1.12)
The current-overpotential plot has the shape as in Fig. 1.5, where coefficient b
includes all constants and the symmetry factor α. From the Eqs. (1.5) and (1.6) for
the high anodic or cathodic overpotential, the corresponding Tafel equations can be
derived:
η
α
α
= −
−
(
)
+
−
(
)
2 303 1
2 303 1
0
.
l og
.
l og
RT
nF
j
RT
nF
j a
(1.13)
1 Short Introduction to the Science of Electrocatalysis
respectively. According to the transition state theory from chemical kinetics, rate
constants are related to the free energies of activation, which are related to the
potential. From these relations, the basic equation is derived, which describes how
the overall current on an electrode depends on the applied potential.
1.3.1 Current-Potential Curves
The equation which describes the fundamental relationship between the electrical
current on an electrode and the electrode potential, assuming that both a cathodic
and an anodic reaction occur on the same electrode, is called the Butler–Volmer
equation:
j j
nF
RT
nF
RT
−
−
(
)
−
−
0
1
exp
e xp
α
η
α η
(1.9)
where j 0 is the exchange current density, T is absolute temperature, R is universal
gas constant, α is the so-called symmetry factor or charge-transfer coefficient, and
η is the overpotential. Overpotential is the extent to which the reaction is driven
beyond the equilibrium potential, E eq :
η = −
E E eq
(1.10)
At high anodic overpotential, partial cathodic current can be excluded compared
to the anodic, meaning that the Butler–Volmer Eq. (1.9) simplifies to:
j j
j
nF
RT
= =
−
(
)
a
0
1
exp
α
η
(1.11)
Partial anodic currents can be excluded from Butler–Volmer equation at high
cathodic overpotential:
j j
j
nF
RT
= = −
−
c
0 exp
α η
(1.12)
The current-overpotential plot has the shape as in Fig. 1.5, where coefficient b
includes all constants and the symmetry factor α. From the Eqs. (1.5) and (1.6) for
the high anodic or cathodic overpotential, the corresponding Tafel equations can be
derived:
η
α
α
= −
−
(
)
+
−
(
)
2 303 1
2 303 1
0
.
l og
.
l og
RT
nF
j
RT
nF
j a
(1.13)
1 Short Introduction to the Science of Electrocatalysis