Page 58 - Lindens Handbook of Batteries
P. 58
ELECTROCHEMICAL PRINCIPLES AND REACTIONS 2.15
where z and z are the charges (with sign) of the oxidized and reduced species, respectively.
R
O
Rearranging Eq. (2.28) and using
z -= z (2.30)
n
R
O
yields
-
i = exp (α nz ) Fφ e C exp -α nFE - - C exp (1 - )α nFE (2.31)
O
nFAk RT O RT R RT
In experimental determination, the use of Eq. (2.26) will provide an apparent rate constant k app ,
which does not take into account the effects of the electrical double layer. Taking into account the
effects appropriate to the approach of a species to the plane of nearest approach,
(α nz ) Fφ e
-
k app = k exp RT O (2.32)
For the exchange current the same applies,
-
α ( nz )Fφ e
i
() = i o exp RT O (2.33)
oapp
Corrections to the rate constant and the exchange current are not insignificant. Several calculated
7
examples are given in Bauer. The differences between apparent and true rate constants can be as
great as two orders of magnitude. The magnitude of the correction also is related to the magnitude
of the difference in potential between the electrocapillary maximum for the species and the potential
at which the electrode reaction occurs; the greater the potential difference, the greater the correction
to the exchange current or rate constant.
2.5 MASS TRANSPORT TO THE ELECTRODE SURFACE
We have considered the thermodynamics of electrochemical processes, studied the kinetics of elec-
trode processes, and investigated the effects of the electrical double layer on kinetic parameters. An
understanding of these relationships is an important ingredient in the repertoire of the researcher of
battery technology. Another very important area of study which has major impact on battery research
is the evaluation of mass transport processes to and from electrode surfaces.
Mass transport to or from an electrode can occur by three processes: (1) convection and stirring,
(2) electrical migration in an electric potential gradient, and (3) diffusion in a concentration gradient.
The first of these processes can be handled relatively easily both mathematically and experimentally.
If stirring is required, flow systems can be established, while if complete stagnation is an experimen-
tal necessity, this can also be imposed by careful design. In most cases, if stirring and convection are
present or imposed, they can be handled mathematically.
The migration component of mass transport can also be handled experimentally (reduced to
close to zero or occasionally increased in special cases) and described mathematically, provided
certain parameters such as transport number or migration current are known. Migration of electroac-
tive species in an electric potential gradient can be reduced to near zero by addition of an excess
of inert “supporting electrolyte,” which effectively reduces the potential gradient to zero and thus
eliminates the electric field that produces migration. Enhancement of migration is more difficult.
This requires that the electric field be increased so that movement of charged species is increased.
