Electrochemical kinetics

§7.11 Polarization of electrode

Electrochemical kinetics

What are we going to learn?

Ideal vs. real electrochemical processes.

Concepts: overvoltage, polarization, overpotential; concentration/diffusion polarization,

electrochemical polarization

Method: overpotential measurement;

Rules: (1) polarization direction;

(2) Tafel equation;

Model: exchange equilibrium

Theoretical treatment: Master equation, Butler-Volmer equation

Applications: electrolysis, battery, corrosion protection


7.11.0 Introduction

Electrode process:

Fast equilibrium and rate-determining step

Diffusion—concentration polarization;

Electrochemical reaction – electrochemical

polarization


7.11.0 Introduction

Electrochemical kinetic parameters:

1/ mol s ni nFr nFkcj

A A A

−

= = =

,0

0exp( ) exp( )cB

G nFk T nFk k

h RT RT

+= − = −

Reaction rate: current density

Activation energy: overpotential


7.11.1. Decomposition voltage and overvoltage

Electrolysis of water Reversible decomposition

voltage Effective decomposition

voltage


The reversible electromotive force of the cell (Theoretical decomposition voltage) is

1.229 V. The effective decomposition voltage is 1.70 V. A discrepancy of ca. 0.5 V,

which is named as overvoltage, exist.

Decomposition voltage:

the minimum potential difference which

must be applied between electrodes before

decomposition occurs and a current flows.1.70 V

1.229 V

1.0 2.0 0.0 E / V

I/ A

Onset potential

7.11.1. Decomposition voltage and overvoltage


7.11. 2 Thermodynamics of irreversible cell

For reversible cell: Wre = nFEre For irreversible cell: Wir = nFEir

For electrolytic cell:

Ere < Eir ; E = Eir - Ere > 0

E = (a, ir-c, ir) - (a, re - c, re)

= (a, ir - a, re) + (c, re - c, ir)

(a, ir − a, re ) = a

E = c + a

(c, re − c, ir ) = c

c,ir c,re c = − a,ir a,re a = +

For galvanic cell:

Ere > Eir; E = Ere − Eir > 0

E = (c, re− a, re)−( c, ir − a, ir)

= (c, re−c, ir) + (a, ir−a,re)

E = c + a

(c, re − c, ir ) = c (a, ir − a, re ) = a

c,ir c,re c = − a,ir a,re a = +


Galvanic cell Electrolytic cell

c, ir = c, re − c

a, ir = a, re + a

c, ir = c, re − c

a, ir = a, re + a

Under irreversible conditions, electrode potential differs from its reversible value,

this phenomenon is defined as polarization.

The discrepancy between reversible potential and irreversible potential is termed

as overpotential ().

By definition, overpotential always has positive value.

7.11.2 Thermodynamics of irreversible cell


The irreversible potential and the irreversible electromotive force of cell depend on the

current density imposed. Polarization cause decrease in electromotive force of galvanic

cell and increase in decomposition voltage of electrolytic cell.

Galvanic cell Electrolytic cell

c, ir = c, re − c

a, ir = a, re + a

c, ir = c, re − c

a, ir = a, re + a

7.11.2 Thermodynamics of irreversible cell


7.11.3 Origin of overpotential

1) Resistance overpotential (R)

2) Concentration overpotential (C)

3) Activation overpotential (a)

1) Resistance overpotential (R)

Electrode, electrode/solution interface, solution and separator all have

resistance.

Elimination: How can we lower the inner resistance of a cell?

R = I R

= R + D + A


2) Concentration/diffusion overpotential (D)

i0 = ib = if

2+

0

Culn

RTa

nF = +


Exchange current

Electrochemical equilibrium

Surface concentration

Bulk concentration

2+Culn sRT

anF

= +2+

2+

Cu

0

Cu

ln

saRT

nF a =


elimination: 1) stir the solution in electroplating and in space battery; 2)

discharge the battery with intervals

2+

2+

Cu

0

Cu

ln

saRT

nF a =

2) Concentration/diffusion overpotential (D)



3) Activation/Electrochemical overpotential (A)

If the removal of electron from the electrode is not fast

enough, excess charge will accumulate on the electrode’s

surface, which results in shift of electrode potential i.e.,

electrochemical / activation polarization.e−

e−

e−

e−

e−

e−

e−

Fe3+

Fe2+

Depolarizer, depolarization: chemical species that can

undergo oxidation or reduction on the electrode surface can

slow the shift of electrode potential.



7.11.4 Measurement of overpotential

W.E.: Working electrode

R.E.: Reference electrode

C.E.: Counter/auxiliary electrode

Conventional three-electrode cell

potentiostat

C.E. W.E. R.E.

H2SO4

potentiostat

Polarization circuit

Measurement circuit


7.11.4 Measurement of overpotential


7.11.5. Hydrogen overpotential

If H+ acts as depolarizer

e−

e−

e−

e−

e−

e−

e−

H+

H 2000

6000

10000

0.00.40.81.2

Black Pt

bright PtAu

Ag

HgC

/ V

j / Am-2

Polarization curve

2H+ + 2e− → H2

1) Hydrogen polarization and Tafel plot


In 1905, Tafel reported the log J ~ curves

of hydrogen evolution on different metal

surfaces.

Tafel equation

a and b are empirical constant, which can

be obtained from the Tafel plot.

jba log+=

At higher polarization > 118 mV, a linear

relation exists:



Metal a / V b / V

black Platinum 0.0

bright Platinum 0.1 0.03

nickel 0.63 0.11

silver 0.95 0.10

zinc 1.24 0.12

mercury 1.40 0.11

Values of a and b of different metals



Categories a Metals

Metal with high hydrogen

overpotential 1.0-1.5

Hg(1.41), Pb(1.56), Zn(1.24),

Sn(1.20)

Metal with medium hydrogen

overpotential 0.5-0.7 Fe(0.7), Ni(0.63), Cu(0.87)

Metal with low hydrogen

overpotential 0.1-0.3 Pt(0.05), Pd(0.24)

2) Classification of metal according to a value



7.11.6. Theories of hydrogen overpotential

The discharge of protons on metal

surface comprises five steps.

1) diffusion: H+ diffuses from bulk

solution to the vicinity of the double

layer

2) Foregoing step: H+ transfers across

the double layer and undergoes

configuration changes such as

dehydration etc.

3) Electrochemical step:

H3O+ + M + e− ⎯→ M-Had + H2O

Volmer reaction, forms adsorbed H

atomThe slowest step will control the overall

rate of the electrochemical reaction.


Electrochemical desorption:

M-H + H3O+ + e- ⎯→ H2 + M

(Heyrovsky reaction)

4) Desorption of H atom:

Combination desorption (catalytic reaction):

2 M-H ⎯→ 2M + H2 (Tafel reaction)

5) Succeeding step: diffusion, evolution.

The theories of hydrogen overpotential:

1) The slow discharge theory

2) the slow combination theory

7.11.6. Theories of hydrogen overpotential


According to Tafel equation, how can

we lower hydrogen overpotential ?

jba log+=

Discussion:

1) The Way to reduce hydrogen overpotential

7.11.7. Application of hydrogen overpotential


(1) Use materials with low a as electrode

Now, Ni-S alloy is used for evolution of

hydrogen.

For evolution of oxygen, we now use

RuO2 as anodic catalyst.

Electrocatalysis and electrocatalyst

Pt nanoparticles loaded on carbon.

For electrolysis of water, in laboratory,

we use Pt (a = 0.05) as cathode, while in

industry, we use iron (a = 0.7).



(2) Enlarge effective surface area:

porous electrode 1) Why do we use platinized platinum

electrode?

Its effective area is more than 1000~3000

times larger than that of bright platinum.

2) Powder/Porous electrode. In lead-acid

battery, porous lead electrode and porous

lead dioxide electrode is adopted.

SEM image of porous electrode. The particle is in fact

aggregate of nanoparticles.



1) Electroplating of active metal from aqueous solution (Pb, Zn, Sn). Why

Zn/Zn2+ is a reversible electrode?

2) Corrosion protection: zinc- or tin-plated iron

3) In battery: Pb negative electrode; amalgamated zinc negative electrode in

dry-battery. (homogeneity, tension, overpotential)

4) Use lead or lead alloy as cathode materials in electrosynthesis to improve

current efficiency.

(3) Take advantage of hydrogen overpotential



Electrochemical kinetics

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