1.5.1 Influence of Impedances to the Transport of Ionic
and Atomic Species within the Cell
In practical electrochemical cells Eout is not always equal to Eth. There are several
reasons for this disparity. Impedance always exist to the transport of electroactive
ions and related atomic species across the cell e.g. resistance of electrolyte to
ionic transport, or at one or both of the two electrolyte/electrode interfaces. Further,
impedance to the progress of the cell reaction in some cases is related to the timedependent
solid state diffusion of the atomic species into, or out of, the electrode
microstructure.
‘Impedances’ are used in this discussion instead of ‘resistances’, since they can
be time-dependent if time-dependent changes in structure or composition are occurring
in the system. The impedance is the instantaneous ratio of the applied force
(e.g. voltage) Eappl and the response (e.g. current) across any circuit element. As
an example, if a voltage Eappl is imposed across a material that conducts electronic
current Ie, the electronic impedance Ze is given by
Ze = Eappl/Ie (1.18)
The inverse of the impedance is admittance, which is the ratio current/voltage. Under
steady state (time-independent) DC conditions, the impedance and resistance of
a circuit element are equivalent.
If current is flowing through the cell, there will be a voltage drop related to each
impedance to the flow of ionic current within the cell. Thus, if the sum of these
internal impedances is Zi the output voltage can be written as
Eout = Eth−IoutZi (1.19)
This relationship can be modeled by the simple circuit in Fig. 1.11.
1.5.2 Influence of Electronic Leakage within the Electrolyte
The output voltage Eout can also be different from the theoretical electrical equivalent
of the thermodynamic driving force of the reaction between the neutral species
1.5.1 Influence of Impedances to the Transport of Ionicand Atomic Species within the CellIn practical electrochemical cells Eout is not always equal to Eth. There are severalreasons for this disparity. Impedance always exist to the transport of electroactiveions and related atomic species across the cell e.g. resistance of electrolyte toionic transport, or at one or both of the two electrolyte/electrode interfaces. Further,impedance to the progress of the cell reaction in some cases is related to the timedependentsolid state diffusion of the atomic species into, or out of, the electrodemicrostructure.‘Impedances’ are used in this discussion instead of ‘resistances’, since they canbe time-dependent if time-dependent changes in structure or composition are occurringin the system. The impedance is the instantaneous ratio of the applied force(e.g. voltage) Eappl and the response (e.g. current) across any circuit element. Asan example, if a voltage Eappl is imposed across a material that conducts electroniccurrent Ie, the electronic impedance Ze is given byZe = Eappl/Ie (1.18)The inverse of the impedance is admittance, which is the ratio current/voltage. Understeady state (time-independent) DC conditions, the impedance and resistance ofa circuit element are equivalent.If current is flowing through the cell, there will be a voltage drop related to eachimpedance to the flow of ionic current within the cell. Thus, if the sum of theseinternal impedances is Zi the output voltage can be written as
Eout = Eth−IoutZi (1.19)
This relationship can be modeled by the simple circuit in Fig. 1.11.
1.5.2 Influence of Electronic Leakage within the Electrolyte
The output voltage Eout can also be different from the theoretical electrical equivalent
of the thermodynamic driving force of the reaction between the neutral species
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