Environmental Engineering Reference
In-Depth Information
The electrolyte concentration,
C
, can be expressed in Fick's law form as a
diffusion process having diffusion coefficient,
D
e
(cm
2
/s), and thickness of the
diffusion zone,
d
(cm), as
d
J
d
nFD
e
(mol
=
cm
3
)
C
¼
ð
10
:
9
Þ
In a one molal aqueous solution, the diffusion current density,
J
d
, or charge
transport, is limited to
J
~25mA/cm
2
with relatively slow time dynamics for build-up
and decay.
Ohmic polarization
results from resistance of electrode materials, electrode
current collectors, the terminals and contact resistance between the electrode active
mass and electrolyte diluents. Accurate representation of ohmic polarization is
modelled according to the cell geometry, material used and design of the current
collectors (surface finish, coatings, bosses on electrode plates etc.):
E
r
¼
I
ð
R
electrode
þ
R
collector
þ
R
surface
Þ
ð
10
:
10
Þ
Ohmic polarization has instantaneous time dynamics for build-up and decay.
Thermal effects also result from changes in the internal energy of the system
due to temperature variations. This effect can be explained by expanding (10.1) into
its thermodynamic equivalent expression relating to enthalpy and entropy change:
D
G
¼
nFE
¼ D
H
T
D
S
ð
10
:
11
Þ
D
G
¼ D
H
nFT
ð
dU
=
dT
Þ
ð
10
:
12
Þ
When the change in internal energy,
dU
/
dT
,is
>
0, the ideal cell will heat up
during charge and cool during discharge (Pb-acid is a representative case, and so
are electrochemical capacitors, ultra-capacitors). When the internal energy changes,
dU
/
dT
is
<
0, the ideal cell will cool during charge and heat up on discharge (NiCd
is representative of this behaviour). However, in practical cells this phenomena is
not fully observed because the heat flow,
Q
, absorbed or dissipated during charging/
discharging is always
>
0, meaning it is to be dissipated. This behaviour is explained
by the strong irreversible nature of the polarization phenomena of heat flux
Q
as a
function of entropy and Joule heating processes:
Q
¼
T
D
S
I
ð
E
oc
E
pol
-
total
Þ
ð
10
:
13
Þ
As a result of the combined effects of polarization, the voltage-current beha-
viour of any electrochemical cell can be described as having three phenomen-
ological regions as illustrated in Figure 10.4.
In Figure 10.4 the end of useful life of the cell is defined as the terminal
potential dropping to approximately 80% of its open circuit potential. This
boundary is marked E-discharged. Temperature moves the voltage-current curve as
shown by the diagonal trace. Lower ambient temperatures result in less useful
