Biomedical Engineering Reference
In-Depth Information
with:
ı;corr
: loss in thickness (practical units mm or
m).
: density of the metal.
The standard hydrogen electrode of Fig.
3.5
consists of a platina rod immersed
in a solution under standard conditions:
T D 298
ı
K.
a
H
C
D 1
,
p
H
2
D 1
atm and
3.2.3.1
Anodic and Cathodic Currents
The anodic reaction we are interested in can be:
nC
e
M ! M
C n
(3.11)
and the cathodic ones:
H
C
C 2
e
!
2
H
2
(3.12)
or, in the presence of oxygen:
H
C
C 4
e
! 2
O
2
C 4
:
H
2
O
(3.13)
E
cell
D E
C
The overall driving force for reaction is the cell potential difference
E
A
. The individual polarizations or
overpotentials
are
A
D E
corr
E
A
relative to
(
3.11
) and,
are linked by
the exponential law of Tafel,
9
later theoretically underpinned by the Butler-Volmer
theory:
C
D E
corr
E
C
relative to (
3.12
)or(
3.13
). Current and
D a C b
log
i
(3.14)
with
the overpotential and a and b the Tafel coefficients. It is a very simplified
form of the Butler-Volmer equation and holds for
0.1 V.
Aplotof(
3.14
)isgiveninFig.
3.6
. In abscissa absolute current
E
i
,inordi-
nate potential
E
. In case the ordinate is expressed in overpotential,
is equal to
zero for
E
corr
. The corrosion cell stabilizes its potential at
E
corr
,where
ji
c
jD
jCi
a
E
corr
, the relation
current-potential is linear and from its slope the
polarization resistance
j
. Within a small interval of about 20 mV centered around
R
p
can be
calculated. Its determination is a method to quantify corrosion rate. It is performed
by a constrained modulation of the potential around
E
corr
and recording the resulting
current.
E
i
R
p
D
:
(3.15)
It is instructive to follow an anodic polarization curve over a wider potential inter-
val at a given pH and measuring the current, as a matter of fact a vertical promenade
9
Julius Tafel (1862-1918) Swiss chemist. He published his law in Z. phys. Chem.
50
, 641 (1905).
