Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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Revised Pages

16.4 Prediction of Corrosion Rates • 673

Current density

(logarithmic scale)

Overvoltage,

a

(V)

0.001

+0.1

0.01 0.1 1 10 100 1000

0

+0.2

• 0.1


• 0.2


• 0.3

i 0 (H 2 /H+)

H^2

2H

+ + 2

e–

H 2

2H+

+ 2

e–

• 

+

Figure 16.7 For a hydrogen

electrode, plot of activation

polarization overvoltage versus

logarithm of current density for

both oxidation and reduction

reactions. (Adapted from M. G.

Fontana,Corrosion Engineering,

3rd edition. Copyright©c 1986

by McGraw-Hill Book Company.

Reproduced with permission.)

Use of the term “current density” fori 0 is a little misleading inasmuch as there is no

net current. Furthermore, the value fori 0 is determined experimentally and will vary

from system to system.

According to Equation 16.25, when overvoltage is plotted as a function of the

logarithm of current density, straight-line segments result; these are shown in Figure

16.7 for the hydrogen electrode. The line segment with a slope of+βcorresponds to

the oxidation half-reaction, whereas the line with a−βslope is for reduction. Also

worth noting is that both line segments originate ati 0 (H 2 /H+), the exchange current

density, and at zero overvoltage, since at this point the system is at equilibrium and

there is no net reaction.

Concentration Polarization

concentration Concentration polarizationexists when the reaction rate is limited by diffusion in

polarization the solution. For example, consider again the hydrogen evolution reduction reaction.

When the reaction rate is low and/or the concentration of H+is high, there is always

an adequate supply of hydrogen ions available in the solution at the region near

the electrode interface (Figure 16.8a). On the other hand, at high rates and/or low

H+concentrations, a depletion zone may be formed in the vicinity of the interface,

inasmuch as the H+ions are not replenished at a rate sufficient to keep up with the

reaction (Figure 16.8b). Thus, diffusion of H+to the interface is rate controlling, and

the system is said to be concentration polarized.

Concentration polarization data are also normally plotted as overvoltage versus

the logarithm of current density; such a plot is represented schematically in Figure

16.9a.^2 It may be noted from this figure that overvoltage is independent of current

density untiliapproachesiL; at this point,ηcdecreases abruptly in magnitude.

(^2) The mathematical expression relating concentration polarization overvoltageηcand
current densityiis
ηc=
2. 3 RT
nf
log
(
1 −
i
iL
)
(16.27)
For concentration
polarization,
relationship between
overvoltage and
current density whereRandTare the gas constant and absolute temperature, respectively,nandfhave
the same meanings as above, andiLis the limiting diffusion current density.