CAUSES OF POLARIZATION

5.4 CAUSES OF POLARIZATION

There are three types of electrode polarization: concentration polarization, acti- vation polarization, and IR drop.

1. Concentration Polarization (Diffusion Overpotential). If copper is made cathode in a solution of dilute CuSO 4 in which the activity of cupric ion is rep- resented by (Cu +2 ), then the potential φ 1 , in absence of external current, is given by the Nernst equation

log (Cu 2 + 1 ) (5.1)

When current fl ows, copper is deposited on the electrode, thereby decreasing surface concentration of copper ions to an activity (Cu 2+ ) s . The potential φ 2 of the electrode becomes

Since (Cu 2+ ) s is less than (Cu 2+ ), the potential of the polarized cathode is less noble, or more active, than in the absence of external current. The difference of

potential, φ 2 − φ 1 , is the concentration polarization , equal to

The larger the current, the smaller the surface concentration of copper ion, or the smaller the value of (Cu 2+ ) s , thus the larger the corresponding polarization. Infi nite concentration polarization is approached when (Cu 2+ ) s approaches zero

at the electrode surface; the corresponding current density that results in this limiting lower value of (Cu 2+ ) s is called the limiting current density . In practice,

CAUSES OF POL ARIZATION

polarization can never reach infi nity; instead, another electrode reaction estab- lishes itself at a more active potential than corresponds to the fi rst reaction. In the case of copper deposition, for example, the potential moves to that for hydro- gen evolution, 2H +

+ 2e − → H 2 , and hydrogen gas is liberated while copper is simultaneously plated out. If i L is the limiting current density for a cathodic process and i is the applied current density, it can be shown [3] that

As i approaches i L , φ 2 − φ 1 approaches − ∞ , that is, minus infi nity. This is shown by the plot of φ 2 − φ 1 versu s i in Fig. 5.4 . The limiting current density (A/cm 2 ) can be evaluated from the expression

DnF

c × 10 − 3 (5.5)

where D is the diffusion coeffi cient for the ion being reduced, n and F have their usual signifi cance, δ is the thickness of the stagnant layer of electrolyte next to the electrode surface (about 0.05 cm in an unstirred solution), t is the transference number of all ions in solution except the ion being reduced (equal to unity if

Figure 5.4. Dependence of concentration polarization at a cathode on applied current density.

60 KINETICS: POL ARIZATION AND CORROSION R ATES

many other ions are present), and c is the concentration of diffusing ion in moles/ liter. Since D for all ions at 25 o

C in dilute solution, except for H + and OH − , aver- ages about 1 × 10 −5 2 cm /s, the limiting current density is approximated by

i L = 0 02 . nc (5.6) For H + and OH − , D equals 9.3 × 10 −5 and 5.2 × 10 −5 2 cm /s, respectively (infi nite

dilution), so that the corresponding values of i L are higher. Should the copper electrode be polarized anodically, concentration of copper ion at the surface is larger than that in the body of solution. The ratio (Cu 2+ )/ (Cu 2+ ) s then becomes less than unity and φ 2 − φ 1 of (5.3) changes sign. In other words, concentration polarization at an anode polarizes the electrode in the cathodic or noble direction, opposite to the direction of potential change when the electrode is polarized as cathode. For a copper anode, the limiting upper value for concentration polarization corresponds to formation of saturated copper salts at the electrode surface. This limiting value is not as large as for cathodic polar- ization where the Cu 2+ activity approaches zero.

2. Activation Polarization. Activation polarization is caused by a slow elec- trode reaction. The reaction at the electrode requires an activation energy in order to proceed. The most important example is that of hydrogen ion reduction

2 H 2 . For this reaction, the polarization is called hydrogen overpotential .

at a cathode, H + − + e →

Overpotential is defi ned as the polarization (potential change) of an equilib- rium electrode that results from current fl ow across the electrode – solution inter- face. Overpotential, η , is the difference between the measured potential and the thermodynamic, or reversible, potential; * that is,

ηφ = meansured − φ reversible

At a platinum cathode, for example, the following reactions are thought to occur in sequence:

H + + − e → H ads

where H ads represents hydrogen atoms adsorbed on the metal surface. This rela- tively rapid reaction is followed by another reaction, namely, adsorbed hydrogen atoms combining to form hydrogen molecules and bubbles of gaseous hydrogen:

2 H ads → H 2

* Overvoltage , on the other hand, is defi ned as polarization (potential change) of a corroding electrode caused by fl ow of an applied current; that is, overvoltage, ε , is the difference between the measured potential and the corrosion (or mixed) potential; that is, ε = φ measured − φ corr .

CAUSES OF POL ARIZATION

This reaction is relatively slow, and its rate determines the value of hydrogen overpotential on platinum. The controlling slow step of H + discharge is not always the same, but varies with metal, current density, and environment.

Pronounced activation polarization also occurs with discharge of OH − at an anode accompanied by oxygen evolution:

2 OH − → O 2 + HO

2 +e 2

The polarization corresponding to this reaction is called oxygen overpotential . Overpotential may also occur with Cl − or Br − discharge, but the values at a given current density are much smaller than those for O 2 or H 2 evolution. Activation polarization is also characteristic of metal - ion deposition or dis- solution. The value may be small for nontransition metals, such as silver, copper, and zinc, but it is larger for the transition metals, such as iron, cobalt, nickel, and chromium (see Table 5.1 ). The anion associated with the metal ion infl uences metal overpotential values more than in the case of hydrogen overpotential. The controlling step in the reaction is not known precisely, but, in some cases, it is probably a slow rate of hydration of the metal ion as it leaves the metal lattice, or dehydration of the hydrated ion as it enters the lattice.

Activation polarization, η , increases with current density, i , in accord with the Tafel equation * :

i ηβ = log

where β and i 0 are constants for a given metal and environment and are both dependent on temperature. The exchange current density, i 0 , represents the current density equivalent to the equal forward and reverse reactions at the electrode at equilibrium. The larger the value of i 0 and the smaller the value of β , the smaller the corresponding overpotential.

A typical plot of activation polarization or overpotential for H + discharge is shown in Fig. 5.5 . At the equilibrium potential for the hydrogen electrode ( − 0.059pH), for example, overpotential is zero. At applied current density, i 1 , it is given by η , the difference between measured and equilibrium potentials. Although usually listed as positive, hydrogen overpotential values are negative and, corre- spondingly, oxygen overpotential values are positive on the φ scale.

3. IR Drop. Polarization measurements include a so - called ohmic potential drop through a portion of the electrolyte surrounding the electrode, through a metal - reaction product fi lm on the surface, or both. An ohmic potential drop always occurs between the working electrode and the capillary tip of the refer- ence electrode. This contribution to polarization is equal to iR , where I is the

* Named after J. Tafel [ Z. Phys. Chem. 50 , 641 (1904)], who fi rst proposed a similar equation to express hydrogen overpotential as a function of current density.

62 KINETICS: POL ARIZATION AND CORROSION R ATES

T A B L E 5.1. Overpotential Values

ηβ i = log

0 i η at 1 mA/cm 2 Metal

(A/m 2 ) (V) a

Hydrogen Overpotential

Pt (smooth)

25 0.1 N NaOH

20 0.12 N NaOH

0.10 −3 10 0.40 (Stern) Cu

25 4% NaCl pH 1 – 4

20 0.15 N NaOH

20 2 SO 2 N H 4 0.10 10 −5 0.60 Al

20 2 SO 2 N H 4 0.10 −6 10 0.70

20 2 SO 1 N H 4 0.12 1.6 × 10 −7 0.94

Hg 20 0.1 N HCl

0.12 × 10 7 −9 1.10 20 2 SO 4 0.1 N H 0.12 × 10 2 −9 1.16

0.10 × 10 3 − 11 1.15 Pb

20 0.1 N NaOH

20 0.01 – 8 N HCl

Oxygen Overpotential

Pt (smooth) 20 2 SO 4 0.1 N H 0.10 × 10 9 −8 0.81

0.05 × 10 4 −9 0.47 Au

20 0.1 N NaOH

20 0.1 N NaOH

Metal Overpotential (Deposition)

Zn 25 1 M ZnSO 4 0.12 0.2 0.20(Bockris) Cu

25 1 M CuSO 4 0.12 0.2 0.20(Bockris) Fe 25 1 M FeSO 4 0.12 10 −4 0.60(Bockris)

Ni 25 1 M NiSO 4 0.12 × 10 2 −5 0.68(Bockris) a 1 mA/cm 2 = 10 A/m 2 . Source : Data from B. E. Conway, Electrochemical Data , Elsevier, New York, 1952; Modern Aspects

HYDROGEN OVERPOTENTIAL

Figure 5.5. Hydrogen overvoltage as a function of current density.

current density, and R , equal to l / κ , represents the value in ohms of the resistance path of length l cm and specifi c conductivity κ . The product, iR , decays simultane- ously with shutting off the current, whereas concentration polarization and acti- vation polarization usually decay at measurable rates. The iR contribution can be calculated as described in Section 5.3.1 .

Note : Concentration polarization decreases with stirring, whereas activation polarization and iR drop are not affected signifi cantly.