Polarization
What We Already Know…

Thermodynamics –



the equilibrium between metals and their
environment
Corrosion tendency of metals
Qualitative picture of what can happen at a given
pH and potential
But…

Considerations of equilibrium are irrelevant to
the study of corrosion

Some metals with pronounced tendency to
react (such as aluminum) react so slowly that
they meet the requirements of a structural
metal
Let us look at a Zn-H Cell





The Zn electrode moves away from equilibrium
by the removal of negative charges from the Zn
plate and positive ions are released from the Zn
plate to the liquid (a)
Zn is dissolved at the same rate as electrons are
transported to the Pt plate, where they are
consumed in the hydrogen reaction
The same cell process can be totally obtained on
a Zn plate submerged in a solution containing
hydrogen ions and Zn ions (b)
The reactions are accompanied by the same
changes in free enthalpy and have the same
equilibrium potentials as before
However, there is a higher resistance against the
hydrogen reaction on the Zn plate than on Pt,
and thus the reaction rate will be lower on the Zn
surface
(a)
(b)
So We Also Need to Know …

Electrode kinetics to predict the corrosion
rates for the actual conditions
Polarization and Overpotential

Electrode reactions are assumed to induce
deviations from equilibrium due to the passage of an
electrical current through an electrochemical cell
causing a change in the electrode potential. This
electrochemical phenomenon is referred to as
polarization.

The deviation from equilibrium causes an electrical
potential difference between the polarized and the
equilibrium (unpolarized) electrode potential known
as overpotential
Polarization and Overpotential
Equilibrium potential for cathodic reaction = Eoc
Equilibrium potential for anodic reaction = Eoa
Real potential = E
Cathodic Overpotential ηc = E – Eoc < 0
anodic Overpotential ηa = E – Eoa > 0
The Polarized Cell
Exchange Current Density




At the equilibrium potential of a reaction, a
reduction and an oxidation reaction occur,
both at the same rate.
For example, on the Zn electrode, Zn ions
are released from the metal and discharged
on the metal at the same rate
The reaction rate in each direction can also
be expressed by the transport rate of electric
charges, i.e. by current or current density,
called, respectively, exchange current, Io, and
(more frequently used) exchange current
density, io.
The net reaction rate and net current density
are zero
How Polarization is Measured
Causes of Polarization

Depending on the type of resistance that
limits the reaction rate, we are talking about
three different kinds of polarization



activation polarization
concentration polarization and
resistance (ohmic) polarization or IR Drop
Activation Polarization





When current flows through the anode and the
cathode electrodes, their shift in potential is partly
because of activation polarization
An electrochemical reaction may consist of several
steps
The slowest step determines the rate of the reaction
which requires activation energy to proceed
Subsequent shift in potential or polarization is
termed activation polarization
Most important example is that of hydrogen ion
reduction at a cathode, H+ + e- → ½ H2, the
polarization is termed as hydrogen overpotential
Hydrogen Overpotential


Hydrogen evaluation at
a platinum electrode:

H+ + e- → Hads

2Hads → H2
Step 2 is rate limiting
step and its rate
determines the value of
hydrogen overpotential
on platinum
Tafel Equation

Activation polarization (η) increases with
current density in accord with Tafel equation:
i
    log
io

The Tafel constant is given by:
2.3RT
β
αnF
Overpotential
Values
Concentration Polarization

Sometimes the mass transport within the
solution may be rate determining – in such
cases we have concentration polarization

Concentration polarization implies either
there is a shortage of reactants at the
electrode or that an accumulation of reaction
product occurs
Concentration Polarization: reduction of


O

4H

4e
 2H 2O
oxygen
2
Contd..

Fick’s Law:

dn
dc
  D 10 3
dt
dx
(1)
where dn/dt is the mass transport in x direction in
mol/cm2s, D is the diffusion coefficient in cm2/s, and c is
the concentration in mol/liter
w
I
i


At AnF nF

Faraday’s law:

Under steady state,
mass transfer rate = reaction rate
i  DnF
C B  C0

10 3
(2)
(3)
Contd..

Maximum transport and reaction rate are
attained when C0 approaches zero and the
current density approaches the limiting
current density:
iL  DnF
C

10 3
(4)
Contd..

The most typical concentration polarization occurs
when there is a lack of reactants, and (in corroding
systems) therefore most often for reduction
reactions

This is the case because reduction usually implies
that ions or molecules are transported from the bulk
of the liquid to the electrode surface, while for the
anodic (dissolution) reaction, mass is transported
from the metal, where there is a large reservoir of
the actual reactant
Contd..

Equations (1) to (4) are valid for uncharged
particles, as for instance oxygen molecules

If charged particles are considered migration will
occur in addition to the diffusion and the previous
equation must be replaced by
iL  DnF
C
10 3
t
(5)
where t is the transference number of all ions in
solution except the ion getting reduced
Overpotential due to concentration polarization

If copper is made cathode in a solution of
dilute CuSO4 in which the activity of cupric
ion is represented by (Cu+2 ), then the
potential φ1 , in absence of external current,
is given by the Nernst equation:
2.3RT
1
2.3RT
2
1  0.337 
log

0.337

log(Cu
)
2
nF
(Cu )
nF
Contd..

When current flows, copper is deposited on
the electrode, thereby decreasing surface
concentration of copper ions to an activity
(Cu2+ )s . The potential φ2 of the electrode
becomes:
2.3RT
1
2.3RT
2
2  0.337 
log

0.337

log(Cu
)S
2
nF
(Cu )S
nF
Contd..

Since (Cu2+ )s is less than (Cu2+ ), the
potential of the polarized cathode is less
noble, or more active, than in the absence of
external current. The difference of potential,
φ2 − φ1 , is the concentration polarization ,
equal to:
(Cu 2 )S
2.3RT
2  1 
log
nF
(Cu 2 )
Contd..
(Cu 2 ) S  (Cu 2 ) 
iLt
(Cu ) 
DzF
it
DzF
2
 Conc   2  1 

2.3RT
i 
log 1  
nF
 iL 
il
k
IR Drop

When polarization is measured with a potentiometer and a
reference electrode-Luggin probe combination, the measured
potential includes the potential drop due to the electrolyte
resistance and possible film formation on the electrode surface

The drop in potential between the electrode and the tip of Luggin
probe equals iR.

If l is the length of the electrode path of cross sectional area s, k
is the specific conductivity, and i is the current density then
resistance
l
R
k
il
iR drop in volts =
k

Combined Polarization

Total polarization of an electrode is the sum
of the individual contributions,
ηT  ηa  ηc  ηr

If neglect IR drop or resistance polarization is
neglected then:
ηT  ηa  ηc
Combined Polarization

Effect of temperature,
concentration and
velocity of the aqueous
environment on combined
polarization is shown in
the figure
Combined Polarization

During anodic dissolution of a metal
concentration polarization is not important:
ηdiss  β log

i
io
During reduction reaction at an electrode
both types of polarization have to be taken
into account:
ηred

i
RT
i
  β log  2.3
log 1  
io
nF
 iL 
Anodic and Cathodic Combined Polarization
Polarization Data and Rates of Corrosion

The corrosion current can be calculated from
the corrosion potential and the equilibrium
potential if


the equation expressing polarization of the anode
or cathode is known, and
if the anode – cathode area ratio can be
estimated
Contd..

If an active metal M is corroding in a
deaerated acid, the metal surface is usually
covered with Hads atoms thus acting mostly
as cathode. The open circuit potential is 0.059pH and if icorr >> i0 for 2H+ + 2e- → H2
Tafel equation can be used for cathodic
polarization
Contd..

Stern-Gray Equation:
icorr
Δ iappl  βc βa 



2.3 Δφ  βc  βa 
The Area Effect
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Usually cathodic reactions are slower than anodic
reactions
For a cathodic reaction to occur, there must be
available sites on the metal surface. Corrosion cells
will not work when the cathodic area is too small for
surface sites
In a galvanic cell, the anode/cathode area ratio is an
important factor for severity of corrosion attack
A large cathode causes severe attack on a small
anode
If we cannot avoid situations for galvanic corrosion, we
may reduce thinning by making the anode material of
large surface area and cathode of smaller area.
The Area Effect
Copper plates with steel rivets in
seawater
Steel plates with copper rivets in
seawater
Steel rivets severely attacked
Tolerable corrosion of steel plate
Large cathode/small anode
Small cathode/large anode
Influence of Polarization on Corrosion Rate
Zinc in H2SO4
Lead immersed in H2SO4
Iron exposed to natural
waters
Magnesium exposed to
natural waters
Iron immersed in a
chromate solution
Porous insulating covering
a metal surface