Course notes
53
MX is inserted between two metallic electrodes Me (1) and (2) where the
chemical potential μ X of species X is fixed. The following equilibrium holds
in each electrode:
X + e m X
−
Given the potential difference ΔE measured at the terminals of the chain, we
can determine the average ionic transport number t i in the domain μ X
(1) −μ X
(2)
by
applying the Wagner model
t
E
E
th
Δ
Δ
=
i
ΔE th is the theoretical electromotive force (emf) that we calculate by applying
the Nernst equation:
E
F
th
X
(1)
X
(2)
μ
μ
Δ
=
−
When the electrode electrochemical equilibria are ensured by fixing the partial
pressures P
( )
X
1
2
and P
( )
X
2
2
at the electrodes, ΔE th is given by
E
2F
RT
ln P
P
th
X
(2)
X
(1)
2
2
Δ
=
The measurement of ΔE can be distorted by the existence of an electrochemical semipermeability flux, which, in particular, polarizes the electrodes and/or
introduces a slow mechanism of adsorption-desorption of the gaseous species
at the electrodes.
Note – An identical approach can be developed for the case where a chemicalpotential gradient is imposed on the metallic species M at the electrodes.
2.2.2 – Using the results of total conductivity
This method exploits the variation of the total conductivity σ t of a mixed conductor MX as a function of the partial pressure of X 2 . The range of pressure
under study must be sufficiently large to lead to the appearance of
2 a plateau of constant ionic conduction σ i (t i = 1) and
2 a zone where the total conductivity varies. Under these conditions, we have
σ t = σ i + σ e
from which we deduce the electronic transport number t e
53
MX is inserted between two metallic electrodes Me (1) and (2) where the
chemical potential μ X of species X is fixed. The following equilibrium holds
in each electrode:
X + e m X
−
Given the potential difference ΔE measured at the terminals of the chain, we
can determine the average ionic transport number t i in the domain μ X
(1) −μ X
(2)
by
applying the Wagner model
t
E
E
th
Δ
Δ
=
i
ΔE th is the theoretical electromotive force (emf) that we calculate by applying
the Nernst equation:
E
F
th
X
(1)
X
(2)
μ
μ
Δ
=
−
When the electrode electrochemical equilibria are ensured by fixing the partial
pressures P
( )
X
1
2
and P
( )
X
2
2
at the electrodes, ΔE th is given by
E
2F
RT
ln P
P
th
X
(2)
X
(1)
2
2
Δ
=
The measurement of ΔE can be distorted by the existence of an electrochemical semipermeability flux, which, in particular, polarizes the electrodes and/or
introduces a slow mechanism of adsorption-desorption of the gaseous species
at the electrodes.
Note – An identical approach can be developed for the case where a chemicalpotential gradient is imposed on the metallic species M at the electrodes.
2.2.2 – Using the results of total conductivity
This method exploits the variation of the total conductivity σ t of a mixed conductor MX as a function of the partial pressure of X 2 . The range of pressure
under study must be sufficiently large to lead to the appearance of
2 a plateau of constant ionic conduction σ i (t i = 1) and
2 a zone where the total conductivity varies. Under these conditions, we have
σ t = σ i + σ e
from which we deduce the electronic transport number t e