9
η
α
α
=
−
2 303
2 303
0
.
l og
.
l og
RT
nF
j
RT
nF
j c
(1.14)
Since the partial cathodic current is negative under the convention and a logarithm of a negative number is undefined, it is assumed in Eq. (1.14) that value j c is
in fact absolute value, |j c |.
Logarithmic dependence of η on j given by Eqs. (1.13) and (1.14) can be simplified to:
η = +
a b
j
log
(1.15)
where a and b are constants. In its graphical presentation (Fig. 1.6), the value of a is
the intercept and b is a slope. From the intercept, one can calculate the exchange
current density, j 0 , by the extrapolation of the potential to the equilibrium potential.
Slope b is called the Tafel slope.
For anodic reaction, Tafel slope is positive, while for the cathodic reaction, it is
negative. This value is important in electrochemical kinetics, because it allows the
calculation of the symmetry factors for elementary reactions and serves as a diagnostic criterion to predict the reaction mechanism of complex reactions. The linear
dependence takes place at η ≈ 50–100 mV. Tafel slope value also indicates the
number of electrons exchanged in the electrochemical reaction. For a reaction,
where the number of electrons exchanged equals 1 and the charge-transfer coefficient is 0.5, the theoretical Tafel slope at 25 °C is ±118 mV per decade. Thus, Tafel
slopes provide valuable information regarding the mechanism of a reaction and
indicate the identity of a rate-determining step of the overall reaction. This was the
way of using electrochemical data to derive criteria from current-potential relations
to obtain a molecular-level information on reaction mechanisms. In a number of
cases, the procedure with limited possibilities resulted in a remarkable success.
Recent development of in situ spectroscopies for studies of electrochemical reactions opened a new era in the electrocatalysis and the studies of electrochemical
reaction mechanisms (vide infra).
Fig. 1.5 Current-potential
curves
1.3 Charge-Transfer Reactions
η
α
α
=
−
2 303
2 303
0
.
l og
.
l og
RT
nF
j
RT
nF
j c
(1.14)
Since the partial cathodic current is negative under the convention and a logarithm of a negative number is undefined, it is assumed in Eq. (1.14) that value j c is
in fact absolute value, |j c |.
Logarithmic dependence of η on j given by Eqs. (1.13) and (1.14) can be simplified to:
η = +
a b
j
log
(1.15)
where a and b are constants. In its graphical presentation (Fig. 1.6), the value of a is
the intercept and b is a slope. From the intercept, one can calculate the exchange
current density, j 0 , by the extrapolation of the potential to the equilibrium potential.
Slope b is called the Tafel slope.
For anodic reaction, Tafel slope is positive, while for the cathodic reaction, it is
negative. This value is important in electrochemical kinetics, because it allows the
calculation of the symmetry factors for elementary reactions and serves as a diagnostic criterion to predict the reaction mechanism of complex reactions. The linear
dependence takes place at η ≈ 50–100 mV. Tafel slope value also indicates the
number of electrons exchanged in the electrochemical reaction. For a reaction,
where the number of electrons exchanged equals 1 and the charge-transfer coefficient is 0.5, the theoretical Tafel slope at 25 °C is ±118 mV per decade. Thus, Tafel
slopes provide valuable information regarding the mechanism of a reaction and
indicate the identity of a rate-determining step of the overall reaction. This was the
way of using electrochemical data to derive criteria from current-potential relations
to obtain a molecular-level information on reaction mechanisms. In a number of
cases, the procedure with limited possibilities resulted in a remarkable success.
Recent development of in situ spectroscopies for studies of electrochemical reactions opened a new era in the electrocatalysis and the studies of electrochemical
reaction mechanisms (vide infra).
Fig. 1.5 Current-potential
curves
1.3 Charge-Transfer Reactions