Chapter 5

Mechanism of complex electrode reaction

5.1.1 B-V equation for multi-electron process

For a di-electron reaction

Ox + 2e Red

Its mechanism can be described by

0

0

Ox 1e X

X+1e Red

a

b

i

i

At stable state d[X]

0dt

0 x0x

exp( ) exp( )2

a aa c c

F Fcii

RT RTc

0 x0x

exp( ) exp( )2

b ab c c

F Fcii

RT RTc

0 0

( ) ( )exp exp

1 12exp exp

a b a bc c

b ac c

a b

F F

i RT RTF F

RT RTi i

If 0 0a bi i

0 (1 )2 exp( ) exp( )b a

b c c

F Fi i

RT RT

0

0

Ox 1e X

X+1e Red

a

b

i

i

0 (1 )2 exp( ) exp( )b a

b c c

F Fi i

RT RT

Therefore 0 02 bi i

1

2b

2b

Consider a multi-step electrochemical process proceeding via the following mechanism

5.1.2 important consideration

Ox 'e Ox '

Ox ' e Red'

Red'+ ''e Red

n

n

Net result of steps preceding rds

(r.d.s.)

Net result of steps following rds

Note: n’+n’’+1 = n

0 0 ' 0 'O ' R '(0, ) exp( ( ) (0, ) exp( ( )rds rds rds

nF nFi nFAk c t c t

RT RT

Since preceding step is in equilibrium, one can write

'

'

ln'

o Opre

O

cRT

n F c

0 ''

'exp ( )O O pre

n Fc c

RT

Similarly, the succeeding reaction is also assumed to be

fast, i.e., at equilibrium

0 ' 'ln''

Rpost

R

cRT

n F c

0 '

'

'exp ( )O

preO

c n F

c RT

0 ''

''exp ( )R R post

n Fc c

RT

0 0 ' 0 'O ' R '(0, ) exp( ( ) (0, ) exp( ( )rds rds rds

nF nFi nFAk c t c t

RT RT

0 ''

''exp ( )R R post

n Fc c

RT

Replacing above

0 ' 0 'O

0

0 ' 0 'R

'exp ( ) exp( ( )

'' exp ( ) exp( ( )

pre rds

rds

post rds

n F nFc

RT RTi nFAk

n F nFc

RT RT

0 0 ' 0 'exp ' exp ( ' )c rds pre rds

F Fi k n n

RT RT

0 0 ' 0 'exp '' exp ( '' )a rds post rds

F Fi k n n

RT RT

O R(0, ) (0, )c ai nFA k c t k c t

0 ''

'exp ( )O O pre

n Fc c

RT

After very laborious algebra, one can show that

0 00

(0, ) (0, )( ' ) ( '' )exp expO R

O R

c t c ti n F n F

i RT RTc c

This equation correctly accounts for influence of redox pre-

equilibrium on measured value of Tafel slop for the reaction

scheme.

Tafel slope is not Tafel slope of rate determining step, ,

rather it is (n’+)

without considering concentration effects

0

( ' ) ( '' )exp exp

n F n Fi i

RT RT

By making comparison with

0 exp expnF nF

i iRT RT

The effect of potential change on activation energy of the

cathodic and anodic reaction differ from that of simple

electrochemical reaction

', '' 1n n

At small overpotentials, i.e., in the linear regime:

0

nFi i

RT

Therefore, charge transfer resistance for multi-step is:

0ct

RTR

nFi

The exchange current is n times that of the current of the r.d.s.

0

( ' )expc c

n Fi i

RT

At higher negative polarization

At higher negative polarization0

( '' )expa a

n Fi i

RT

0

( ' )expc c

n Fi i

RT

0 c= log +- log( ' ) ( ' )c

RT RTi i

n F n F

For a multi-electron reaction

Ox + ne Red

Its mechanism can be described by 0

0

0

0

0

0

0

1

1 2

2 1

1

1

2 1

1

Ox 1e X

X +1e X

X +1e X

X +1e X (rds)

X +1e X

X +1e X

X +1e Red

a

b

b

b

b

b

b

i

i

i

j j

i

j j

i

j j

i

n n

i

n

Steps before rds, with higher i0 at equilibrium

Steps after rds, with higher i0 at equilibrium

0( 1) ( )

exp( ) exp( )j jj c c

j F n j Fi ni

RT RT

Therefore 0 0ji ni

1j j

n

j n j

n

0( 1) ( )

exp( ) exp( )j jj c c

j F n j Fi ni

RT RT

2 0j c

Fi n i

RTAt small overpotential

2 00 ji n i

At higher overpotential

0( 1)

exp jc j c

ji ni

RT

For cathodic current

0( 1)

exp ja j a

ni ni

RT

For anodic current

5.1.3 Stoichiometric number multi-electron process

5.2 surface transitions reactions:

Ob

Surface region

Bulk solution

Os

Mass transfer

O*Chem. rxn

O* Desorption/ adsorption

R*

EC rxn

R*

Desorption/ adsorption

RbRsMass transfer

Chem. rxn

5.2 Homogeneous proceding surface reactions

place

homogeneous ( region close to electrode surface)

heterogeneous ( adsorption, desorption, new phase formation )

time

Foregoing / preceding

Post, succeeding

parallel

Electrochemical -chemical (EC)

Chemical-Electrochemical (CE)

Classification of couple electrode homogeneous :1) Mechanism with single electrochemical step

(1) CE – preceding reaction

e.g. Reduction of formaldehyde on mercury

Dominant, no EC rxn.

2 2

2

CdX Cd X

Cd 2e Cd(Hg)

f

b

k

k

A difficult to be reduced CE A H HA Pne

1) Mechanism with single electrochemical step

(2) EC – following reaction

NH2HO NHO + 2H+ + 2e

NHO + H2O OO + NH3

O

O

e-

O

O

H2OO

O

EC

H+ + M +e M H2 M H 2M + H2

H+ + M H + e M + H2

Possible proceeding/succeeding reactions:

dissociation, complexities, dimerization, isomerization ,

formation of new phase (gas bubble, metal plating, conversion

layer).

EC

EE

For evolution of hydrogen

1) Mechanism with single electrochemical step

(3) ECcat – catalytic reaction

Fe3+ + 1e- Fe2+

2Fe2+ + H2O2 Fe3+ + 2H2O+ 2H+ 2

*

*

O O

O + R

f

b

k

k

ne

For CreEre reaction as f

b

kK

k

If K <1, then O is the main reactant which can be reduced at potential 2, while O* is easier to be reduced at potential 1 than O. This means at 2, both O and O* can be reduced.

* ,d O dI I

At 1, For fast chemical kinetics, O* can be replenished in time:

* ,,d O dO dI I I

Limiting kinetic current Ik

5.2 Reaction mechanism-proceeding reaction

At 1, For slow chemical kinetics:

1 2

At 2, For slow chemical kinetics:

* ,,d O dO dI I I

Curves I and II can be described by normal diffusion current when O and O* become totally depleted, respectively.

Curve III is different.

At electrode surface, the concentration gradient of O and O* can be described as:

*

2

2O O

O f O b O

c cD k c k c

t x

* *

* *

2

2O O

f O bO O

c CD k C k C

t x

At stable state: 0Oc

t

*

0Oc

t

*O Oc cIf: At 1

*

2

20O

O f O b O

cD k c k c

x

Very small

No concentration polarization of O at electrode surface.

* *

* *

2

02

O Of O bO O

c CD k C k C

t x

For O* at complete concentration polarization, its boundary conditions are:

* (0, ) 0O

c t At x = 0, At x = , *

0( , ) OOc t Kc

* *

*

0 1 exp b

O OO

kc c x

D

*

*

*

0

0

O b

OOx

c kc x

x D

Therefore, the concentration gradient at electrode surface is:

surface concentration:

*

*

*

0

0

O b

OOx

c kc x

x D

The thickness of reaction region

* *

*

0

0

O O

bO

x

c D

kc

x

* *

*

0

0

O O

bO

x

c D

kc

x

Less than the effective thickness diffusion layer, why?

* * * *

1/2 1/2 0 1/2 1/2 0( )k b fO O O OI nFD k c nFD Kk c

* * *

1/2 1/2 0( )sk bO O O

I nFD k c c

At incomplete polarization:

The limiting current resulted for CE mechanism is usually much larger than that of merely diffusion control kinetics, Why?

When = 0 V, c0 = 1 mM , A= 1cm2, DA = DB = DC = 10-5 cm2

/s, K =103, kf = 10-2 s-1, kb =10 s-1, T =25 , at scan rates ,℃ v of

(1) 10 V/s; (2) 1 V/s; (3) 0.1 V/s; (4) 0.01 V/s.

Cyclic voltammograms for the CE case.

A B;

B + e - C

When K=10-3, kf =10-2 s-1 kb = 10 s-1, v=0.01~10 V s-1, = 26 ~ 0.026.

v / Vs-1 lg control effect of preceding

10 -1.6 DP Less effect (1)

1 -0.6 KI

0.01 1.6 KP Depends on cre not on diffusion

0 2 4 6 8 10

0.5

1.0

1.5

2.0

v

,

,

p a

p c

i

i

1/ 2 1( )K

Some diagnostic criteria for a CE situation .

1) ip /v1/2 will decrease as v increases

2) ipa /ipc will become large for small K or for large v

The first wave The first wave corresponds the reduction corresponds the reduction of Cdof Cd2+2+ which is governed which is governed electrochemically, while electrochemically, while the second wave the second wave corresponds to reduction of corresponds to reduction of CdXCdX--. Wave III is oxidation . Wave III is oxidation of Cd(Hg) which is of Cd(Hg) which is governed by diffusion. governed by diffusion.

2 2

2

CdX Cd X

Cd 2e Cd(Hg)

f

b

k

k

Both O and O* can be reduced

O e Rn R S O Pk

Assuming [S] >> [O]

Electrocatalysis

5.3 Reaction mechanism-succeeding/parallel reaction

3 2Fe e Fe

2 32 2

1Fe + H O == Fe OH

2

5.3.1 For EreCcat

Catalytic decomposition of hydrogen peroxide

S is the substrate whose concentration is usually much higher than that of O and R. Therefore, I mainly depends on Id, O.

3 2Fe e Fe 2 32 2

1Fe + H O == Fe OH

2

O e Rn R S O Pk

Assuming [S] >> [O]

0O RO R O O

c cJ J D D

x x

2

20O

O f b O f total

cD k k c k c

x

2

20O

O f b O f total

cD k k c k c

x

Solution is

0 1 expO total

O

f b

xc c

D

k k

0

0

total O O

O f b f

x

c D Dc k k kx

When Concentration of R is very low

1/ 21/ 2 0,c d O f b OI nFD k k c

Catalytic current at complete concentration polarization

Catalytic current at other polarization

1/ 21/ 2 0,

sc d O f b O OI nFD k k c c

1/ 2/i

Increasing

i

1/ 2

diffusionECcat

Here both behaviors going on: we are consuming Red with rate constant k, this will shift the ratio [Red]/[Ox]. So we expect the half wave potential to shift. But, we also are generating Ox with rate k. So we expect the wave to get bigger.

5.3.2 For EreCir reaction

EC

- *

k*

E O + e R

C R R

*

2O O

O R2 Rt f b

c cD k c k c

x

* *

* *

2

R RR2R Rt f b

c cD k c k c

x

For ECir mechanism:

* * *

1/ 2 1/ 2 0

R R R

sk fI nFD k c c

If is negligible

The kinetic current is

*

0

Rc

* *

1/ 2 1/ 2

R R

sk fI nFD k c

The thickness of the reactive layer *R

f

D

k

for the EC reaction when the electron transfer reaction is reversible and the chemical rate constant kEC is extremely large

EreCir

The reduction in size of the reverse peak occurs since much of the R produced electrochemically is destroyed by the chemical step.

EC

O+ R

R Pk

ne

A/B * = 0 V, c0=1 mM, A =1 cm2, D = 10-5 cm2 /s, and kf = 10 s-1. The vertical

scale changes from panel to panel.

Scan rates on voltammograms

Conversion rate constant on Conversion rate constant on voltammogramsvoltammograms

http://www.nuigalway.ie/chem/Donal/Surfaces11.ppt#274,13,Catalytic

180 120 60 600

0.2

0.0

0.2

0.4

(e)

Nor

mal

ized

cur

rent

( 1/2) n / mV

= 10 0.1

0.01

0.1

0.01

Normalized current for several values of .

For small , reversible by nature. For large , no reverse current can be observed, i.e., irreversible.

k RT

v nF

0.2

0.4

0.6

0.8

1.0

lgv

I p,c/ I p,c

1) ipa / ipc will approach 1 as v

increases

2) ipc proportional to v1/2

3) pc will be displaced in the anodic direction as v decreases

(30/n mV per 10 in v)180 120 60 600

0.2

0.0

0.2

0.4

(e)

Nor

mal

ized

cur

rent

( 1/2) n / mV

= 10 0.10.01

0.1

0.01

Diagnostic Criteria for EreCir mechanism:

Electrochemical dimerizationElectrochemical dimerization

5.4.1 Conversion involving adsorption

Osol Oads

RadsRsol

solads

sol ads y y

rad 10* 0 coverage

rde 0* maximum coverage 0

* at equilibrium

0 00 0

1

1o o

pe pe

o o

i i i

1 1o at large negative polarization : rxn, fast

0o

So 01

ope

d

o

ii

When 0 1o make adsorption .id = io

0lnre o

RTconst

nF lnir o

RTconst

nF

0

ln ore ir

o

RT

nF

0, 1oo

00

(1 )ope

o

i i

0 0

1 o d

dpe o

i ii

ii

ln( )d

d

IRT

nF I I

For proceeding reaction, its polarization curves is similar to that of diffusion-control kinetics.

post kinetic :0

Repostine

Ox d R

0 0Re0, 0Re

1

1d R

post postd R

i i i

Using similar treatment : ln 1post

RT i

nF i

so ln lnopost

RT RTi i

nF nF

For succeeding reaction, its polarization curves is similar to that of electrochemistry-control kinetics.

Since R and O are confined, no diffusion

If we use the Langmuir isotherm to describe the coverages of O and R

make use of the Nernstian criterion

5.4.2 Conversion of surface species

When bO bR,

Reversible, Nernstian, Langmuir, Monolayer

Electrochemistry of LB film

Dynamics of Br electrosorption on single-crystal Ag(100)

Journal of Electroanalytical ChemistryVolume 493, Issues 1-2, 10 November 2000, Pages 68-74

* *( / ) ln Op re ad ad

R

bRTO R

nF b

y

If bR >>bOIf bO >> bR

Pre-wave post-wave

Dash line: without adsorption

Solid line: with adsorption

1

2

O+ B

B+ P

e

e

1 2

12

0

1 2

0

1 2

0

5.5 Other mechanisms

5.5.1 EreEre mechanism

Changing shapes of cyclic voltammograms for the Er Er reaction scheme at different values of E0

When > 125 mV, two peaks becomes distinguishable

Shoulder

CVs for the reduction of di-anthrylalkanes (An-(CH2)n-An) in 1:1 benzene/acetonitrile containing 0.1 M tetrabutylammonium perchlorate at a Pt electrode.

A Be 01

B Cb

f

k

k /f bK k k

C De 02

0 02 1

It is much easier for C to be reduced than A

180mV

5.5.2 EreCreEre mechanism

The figure shows the voltammogram for an ECE mechanism where the product (S) is more difficult to reduce than the starting material (O).

O R S T

If the product (S) is more easy to reduce, slightly different behaviour is seen

0.00 0.60

0.00

4.00

3.00

2.00

1.00

3.00

2.00

1.00

Cur

rent

=

0

(a)E

0.10

II

I

Cur

rent

=

0.4

0

0.00 0.60

0.00

4.00

3.00

2.00

1.00

2.00

1.00

(c)E

0.10 III

I

IV

Cur

rent

=

0.0

5

0.00 0.60

0.00

3.00

2.00

1.00

2.00

1.00

(b)E

0.10 III

I

IV

II

0.00 0.60

1.00

5.00

4.00

3.00

2.00

2.00

1.00

0.00C

urre

nt

= 0

(d)E

0.10III

I

IV

CVs for the EreCirEre case obtained by digital simulation for E10

= 0.44 V, E20 =

0.20 V for different values of =(kb/v)(RT/F); n1=n2=1.(a) =0 (unperturbed

Nernstian reaction ); (b) 0.05 ;(c) 0.40 ;(d) 2.

The ECE mechanismThe ECE mechanism

Figure 5.5 – CV of sample B67 in 3 10-3 mol dm-3 4-aminophenol & 0.5 mol dm-3 H2SO4

Various scan rates, Ag dag contact, geometric area of working electrode = 20 mm2

CV of 4-Aminophenol

 

cyclic voltammograms recorded

using a highly doped diamond

electrode in an aqueous solution

containing 3  10-3 mol dm‑3 4-

aminophenol ( C6H4(OH)(NH2) ),

and 0.5 mol dm‑3 sulphuric acid

(H2SO4).4-aminophenol is an

aromatic organic molecule, which

may undergo a two step oxidation.

The cyclic voltammograms show

two oxidation peaks and two

reduction peaks per scan

http://www.chm.bris.ac.uk/pt/diamond/mattthesis/chapter5.htm

CCrere E Erere

(as above)(as above)

CCrere E Eirir

Diffusion equation (all Diffusion equation (all xx and and tt))ReactionReactionCaseCase

Y Of

b

k

k

O Rne

2Y Y

Y f Y b O

c cD k c k c

t x

2

O OO f Y b O

c CD k C k C

t x

2

2R R

R

c cD

t x

Y Of

b

k

k

O Rne

Summarization

(as above, with (as above, with kkbb = 0) = 0)

(equation for (equation for ccYY not required ) not required )

EEre re CCirir

EEre re CCrere O Rne

R Yf

b

k

k

2

2O O

O

c cD

t x

2

R RR f R b Y

c cD k c k c

t x

2

Y YY f R b Y

c cD k c k c

t x

O Rne

R Yfk

EEre re CC2ir2ir O Rne

2R Xfk

2

2O O

O

c cD

t x

22

2R R

R f R

c cD k c

t x

The zones are DP, pure diffusion: DM, diffusion modified by equilibrium constant of preceding reaction: KP pure kinetics: and KI, intermediate kinetics.

Here,

f bk k RT

v nF

CreEre reaction diagram with zones for different types of

electrochemical behavior as a function of K and (defined in

the following table).

Treatment depend on scan rate and on particular technique :

Dimensionless Parameters for Voltammetric Methods

Technique TimeParameter (s)

Dimensionless Kinetic parameter, , for

CE EC EC

Chronoamperometryand polarography

t (kf +kb ) t k t k Cz* t

Linear sweep and cyclic voltammetry

1/ [(kf +kb )/v] (RT/nF)

(k/v )(RT/nF)

[(kcz* )/v]

(RT/nF)

Chronopotentiometry (kf +kb ) k k Cz*

Rotating disk electrode 1/ (kf +kb )/ k/ k cz* /

for large kf and kb, p will be displaced as a function of v .

(30/n mV per 10 times v)

'1

2

0.277 ln2

RT RT

nF nF y

1

2

ln

dRT

d v nF

10.471

1.02d

i

iK

5.5 Methods for mechanism study

Tafel Equation - “Simple” Electron Transfer

0

2.3 2.3lg lg

RT RTi i

nF nF

For a simple 1 electron process

slope = 1 / 120 mV

For a simple 2 electron process

slope = 1 / 60 mV

Assuming that ==0.5

Using the Butler-Volmer and Tafel Equation to Determine Multistep Reaction Mechanisms

Mechanism (A): Cu2+ + 2e = Cu orMechanism (B): Cu2+ + e = Cu+

Cu+ + e = Cu

For mechanism (A): n = 2 , = 0.5

Plotting logi against gives a straight line with a gradient of - [60 mV]-1.Similar arguments for reverse reaction: Cu Cu2+ + 2e, gives a straight line with a gradient of [60 mV]-1.

Mechanism B (Forward Reaction)

assume (1) is rate determining step (r.d.s.):

For mechanism (B): n = 1 , = 0.5

Hence, for Cu deposition with Cu2+ + e Cu+ (r.d.s.)

Cathodic section of Tafel plot (logi vs. )

gives a slope of - 1 / 120 [mV]

Mechanism (B): Cu2+ + e = Cu+

Cu+ + e = Cu

Mechanism B : Reverse Reaction

Reverse: Cu+ Cu2+ + e also r.d.s.

rapid step (2) in equilibrium. Can use Nernst eq. to find [Cu+]:

Tafel slope = 1 / 40 [mV]

Mechanism (B): Cu2+ + e = Cu+

Cu+ + e = Cu

5.7 determination of intermediate

Rotating Ring-Disk Electrodes

Reversal techniques are obviously not available with the

RDE, since the product of the electrode reaction, R, is

continuously swept away from the surface of the disk.

addition of an independent ring electrode surrounding the disk.

By measuring the current at the ring electrode with the potential maintained at a given value, some knowledge about what is occurring at the disk electrode surface can be obtained. For example, if the potential of the ring is held at a value at the foot of the O+ ne → R wave, product R formed at the disk will be swept over to the ring by the radial flow streams where it will be oxidized back to O (or “collected”).

The theoretical treatment of ring electrodes is more complicated than that of the RDE, since the radial mass transfer term must be included in the convective-diffusion equation.

The current at the ring electrode is given by

3

20

2r

OO r

y

ci nFD rdr

y

The solution to these equations yields the limiting ring current:

3 3 2 / 3 2 / 3 1/ 6 1/ 2 03 20.620 ( ) O Oi nF r r D v c

Levich equation for disk electrode:

2 / 3 1/ 6 1/ 2 00.620 O Oi nFAD v c

3 3 2 / 33 2

21

( )R D

r ri i

r

Notice that for given reaction conditions (co0 and ) a ring electrode

will produce a larger current than a disk electrode of the same area. Thus the analytical sensitivity of a ring electrode (i.e., the current caused by a mass-transfer-controlled reaction of an electroactive species divided by the residual current) is better than that of a disk electrode, and this is especially true of a thin ring electrode. However, constructing a rotating ring electrode is usually more difficult than an RDE.

RRDE experiments are usually carried out with a bipotentiostat,which allows separate adjustment of ED and ER.

Several different types of experiments are possible at the RRDE:

Collection experiments, where the disk-generated species is observed at the ring

Shielding experiments, where the flow of bulk electroactive species to the ring is perturbed because of the disk reaction, are the most frequent.

Example for a collection experiment: the ring (b) measures the reduction of peroxide produced at the disk (a) during the electroreduction of oxygen.

the ring current is related to the disk current by a quantity N,

the collection efficiency ; this can be calculated from the

electrode geometry, since it depends only on r1, r2, and r3 and is

independent of c, , DR,DO

R

D

iN

i

5.6.3 detection of intermediates using the same electrode (CV)

5.6.4 detection of intermediates using thin-layer cell and spectroscopy