Cours of analytical electrochemistry

Mn+ + ne- M0

E / V

i / A

13th October 2003, Université de Toulon et du Var. La Garde, France

Polarography is a method that provoces and analyses the passage of electrones from or to an electrode because of reduction or oxidation of ions at the solution/electrode interface.

ChemistryElectrochemistry, spectroscopy,...Concerned with the interrelation of electrical

and chemical effects. It deals with- the study of chemical changes caused by the passage of an electric current, and

- the production of the electrical energy by chemical reaction.

The field of electrochemistry encompasses different

phenomena: electrophoresis, corrosion

Devices: electrochromic displays, electroanalytical sensors, batteries, fuel cells

Technologies: the electroplating of metals, large-scale production of aluminum and chlorine

All this is covered by the main principles. We shall focus ourselves to application of electrochemical methods to the study of chemical systems.

Electrochemical measurements are done on chemical systems for different reasons:

-interest may be in obtaining thermodynamic dataabout the reaction

-Generate an unstable intermediate such as a radical ion and study its rate of decay

-Analyze a solution for trace amounts of metal ionsor organic species.

-Electrochemical properties of the systems themselves are of primary interest (as a new power source or for the electrosynthesis of some products).

+

+

+ + +

Electronic conductorPt, Ir, Au, Ag

Hg

Electrochemical cells and reactions

Ionic conductorH+, Na+, Cl-

H2O or nonaqueous solvent

low resistance

+

+

-

-

-

-

-

-

-

-

metal electrolyte

How and why charge is transported accros the interface?

H2

PtAg

Excess AgCl

Pt/H2/H+, Cl-/AgBr/Ag

NHE Ag/AgCl SCE

0 V 0.197 V 0.242 V

NO single interface-

At least two –electrochemical cell: two el. separated by at least one electrolyte

Working el. and reference el.

NHE

+Po

tent

ial

|

Electrode Solution

Vacant moleculara orbitals

Occupied molecular orbitals

Energy level of electrons

The critical potentials at which these processes occur are related to the standard potentials, E0, for the specific chemical substances in the system.

reduction current

oxidation current

number of electrons is related to the amount of chemical reactant

1 C is equivalent to 6.24 x 1018 electrons

96,485.4 C is equivalent to 1 mol in a one-electron reaction – F. l.

1 ampere (A) is equivalent to 1 C/s.

Current – potential (i vs. E) curve can have information aboutthe nature of the solutionthe nataure of the electrodesthe reactions that occur at the interfaces

Pt Ag

VA

Power Suppl.

AgBr

Pt/H+, Br- (1M) / AgBr/Ag

Open-circuit potential:

From standard potentials of half-reactions at both electr.

When there is no thermodinamic equilibrium – the OCP is not defined

1.5 0.5 -0.5 -1.5

Pt/H+, Br-(1 M)/AgBr/Ag Cathodic

Anodic

potential

curr

ent

start of Br-

oxidation on Pt

start of H+

reduction on Pt

Hg drop e.

Ag

VA

Power Suppl.

AgBr

Hg/H+, Br- (1M) / AgBr/Ag

1.5 0.5 -0.5 -1.5

Pt/H+, Br-(1 M)/AgBr/Ag Cathodic

Anodic

potential

curr

ent

Hg/H+, Br-(1 M)/AgBr/Ag

start of Hg oxidation

start of H+

reduction

heterogeneous rate constant of hydrogen evolution reaction is much lower at mercury than at Pt

1.5 0.5 -0.5 -1.5

Pt/H+, Br-(1 M)/AgBr/Ag Cathodic

Anodic

potential

curr

ent

Hg/H+, Br-(1 M)/AgBr/Ag

start of Hg oxidation

start of H+

reduction

Hg/H+, Br-(1M), Cd2+(1mM)/AgBr/Ag

start of Cd2+

reduction

Faradaic and nonfaradaic processes

-------

Metal MetalSolution Solution

-

-

-

-

+

+

+

+

+

Nonfaradaic processes

-

+

Batery Capacitor- - - -

+ + + +

e

e

i

E

i

E

Ideal polarizable electrode

(ideal working electrode)

Ideal nonpolarizable electrode

(ideal reference electrode)

Electrical double layer

Metal Solution-

-

IHP OHP

+

+

+

+

+

= solvent molecule

Solvated cationHelmholtz (1879)

Gouy –Chapman

Stern (1924)

Graham (1947)

Parsons (1954)

Bokris (1963)

Diffuse layer

Charge density: σS = σi + σd = - σMσi σd

σM

Metal Solution-

-

IHP OHP

+

+

+

+

+

x

φ

x1 x2

φs

φ2

φΜ

Reference electrode

Counter electrode

Working electrode

Cd Rf

Ru

RΩ

Eref

Etrue

t

i

t

E

sRE

sRE37.0

dsCR=τ

E

dsCRt

s

eREi /−=

i

Rs Cd

An example:

For Rs = 1 Ω

Cd = 20 µF

τ = 20 µs

Voltage step

After 3 tau, current diminishes to 5% of its initial value

t

i

t

E

Applied E(t)

Resultant i

vCd [ ])/(1 dsCRtd evCi −−=

v/2Cd

Voltage ramp

i

Rs Cd

v = dE/dt

steady state current can be used to estimate Cd

t

i

t

E

Ei

Applied E(t)

Resultant i = f(t)Resultant i = f(E)

Triangular wave

vCd

-vCd -vCd

vCd

Faradaic processesNow we deal with processes where charge passes from the electrode-solution boundary.

Types and definitions of electrochemical cellsGalvanic cells – reactions occur spontaneously at the electrodes when they are connected externally by a conductor. These cells are often employed in converting chemical energy into electricalenergy – all kinds of batteries and fuel cellsElectrolytic cell - reactions are effected by the imposition of an external voltage greater than the open-circuit potential of the cell. Commercial processes include electrolytic syntheses, electroplating..

Faradaic processesNomenclature: the electrode at which reduction occurs is called cathode, and the electrode at which oxidation occurs is called anode.A current in which electrons cross the interface from the electrode to a species in solution is a cathodic current, while electron flow from a solution species into the electrode is an anodic current.

In an electrolytic cell, the cathode is negative with respect to the anode, but in a galvanic cell it is just opposite.

Here we should repeat that we shall be mostly concerned about the reactions that occur at one electrode – working electrode.

Faradaic processesVariables affecting the rate of an electrode reaction:

Electrode variabales materialsurface areageometrysurface condition

Mass transfer variables mode (diffusion, convection)adsorption

Solution variables bulk concentration of electroactive speciesconcentrations of the speciessolvent

Electrical variables potential (E)current (i)quantity of electricity (Q)

External variables temperature (T)pressure (P)time (t)

)/()( scoulombsdtdQampersi =

Nmolcoulombs

coulombsnFQ =

)/()(

where n is number of electrons consumed in a electrode reaction

Rate (mol/s) = =

It is a heterogeneous reaction occurring only at the electrode – electrolyte interface. It is usually described in units of mol/s per unit area, that is

Rate (mol s-1 cm-2) = ,

where j is the current density (A/cm2)

dtdN

nFi

nFj

nFAi =

(mol electrolyzed)

The following relation demonstrates the direct proportionality between faradaic current and electrolysis rate:

Mass-transfer-controlled reactionsModes of mass transfer

Migration (a gradient of electrical potential)Diffusion (a concentration gradient)Convection (natural – by density gradient, forced – by stirring (stagnant

regions, laminar flow, turbulent flow)

Expression for one-dimensional mass transfer:

)()()()( xvC

xxCD

RTFz

xxC

DxJ iiiii

ii +∂Φ∂−

∂∂

−=

Rigorous solution is generally not very easy to obtain.

Electrochemical systems are frequently designed so that one or two contributions are negligible.Supporting electrolyte is introduced to reduce a migration component, and stirring is suppressed at the time of measurement.

Nernst – Planck equation

When the mass transport is proportional only to the concentration gradient:

If we assume linear concentration gradient within the diffusion layer:

00000 )/()/( == =∝ xxmt dxdCDdxdCv

)]0([/)]0([ 0*0000

*00 =−==−= xCCmxCCDvmt δ nFA

i=

C0(x = 0)

C0*

C0

C0 δ0 x

1

2

[mol l-1 cm-2]

Fick’s laws of diffusion

First law: flux is proportional to the concentration gradient

xtxCDtxJ

∂∂=− ),(),( 0

00

Second law: defines the concentration of ions at certain time at a certain distance

∂

∂=∂

∂2

02

00 ),(),(

xtxCD

ttxC

General formulation for Fick’s second law:

02

00 CD

tC ∇=∂∂

For spherical electrode such as hanging mercury drop electrode (HMDE):

∂

∂+∂

∂=∂

∂r

trCrr

trCDt

trC ),(2),(),( 02

02

00

For the situation where O is an electroactive species transported purely by diffusion to an electrode, where it undergoes the electrode reaction O + ne ! R and if no other reaction occurs, then the current is related to the flux of O at the electrode surface:

0

000

),(),0(=

∂∂==−

xxtxCD

nFAitJ

il – limiting current, when C0(x=0) = 0

by rearranging:

[ ])0(0*00 =−= xCCnFAmi

*00nFACmil =

00 )0(

nFAmiixC l −==

If the kinetics of electron transfer is rapid, the concentration of O and R at the electrode surface can be assumed to be at equilibrium with the electrode potential, as governed by the Nernst equation for the half reaction

)0()0(

ln 00

==

+=xCxC

nFRTEE

R

When R is initially absent

rR nFAm

ixC == )0(

−

+−=i

iinFRT

mm

nFRTEE l

r

o lnln'0

When 2lii =

r

o

mm

nFRTEEE ln'0

2/1 −==

E1/2 is independent of reactant concentration and so is characteristic of the redox system

For certain conditions: reversibility, but also ratio of Dr1/2/Do

1/2 and ionic strength we have

Heyrovský – Ilkovič equation for polarographic wave

and for current explicitly

( )2/11EE

RTnF

l

e

ii

−+

=

iii

nEE l −+= log059.0

2/1

-E / V

i / A

E1/2

il

E1/2

iiil −log

E

Slope 59/n mV

Potential Step Methods

t0

E(-) E1

τ

E1

E2

capacitive

Faradaic

time

curr

ent

Potential Sweep Methods

Linear Scan

Ep

Ep/2 ip

E

Et

i

Cyclic voltammetryE

t

i

E

Ep/2

Ep, c

Ep, a

Randles-Ševčik equation:

2/1*0

2/12/12/1

2/32/3

443.0 vCADTRFnip =

nEnFRTEEp /0285.01.1 2/12/1 −=−= for 25°C

( ) ( ) nEEkpap /057.0=−

Reversible reaction

Ireversible reaction

2/1*0

2/12/12/12/1

2/1

)(496.0 vCADnnTR

Fi ap α=

−

+−= 000 ln

21780.0 e

a

ap k

RTFvnD

FnRTEE αα

nEE pp /0565.02/ =− for 25°C

for 25°Ca

pp nEE

α04771.0

2/ =−

i

E

Polarographic and voltammetric techniques

Polarography – term reserved for DME

Direct current polarography (DCP)

Voltammetry – all that is preformed on one drop, or at the solide electrode

t

DMEdropping mercury electrode

SMDEstatic

mercury drop electrode

Drop fall

Different types of mercury drop electrodes

Ilkovič equation for DME

6/13/2*0

2/10708 tmCnDid =

A cm2/s mol/cm3 mg/s s

Cotrell equation, SMDE equivalent to the Ilkovič equation

2/12/1

*0

2/10)(τπ

τ CnFADid =

Direct current (DC) polarography

t

Eb

E(-)

Drop 1 Drop 2 Drop 3

-E / V

i / A

E1/2

id

Reversible reactions

i iE E nF RT

d=− +exp ( ) //1 2 1

i nFCA Dtd

m

=π

General case

Φ ΨDC L t= ( ) /τ λ π

L kD

es

ox

= −αϕ τ λ= t

Ψ( ) ( )τ πτ ττ= e erfc2

λ α ϕ= + −L kD

es

red

( )1

ϕ = −nF E E RT( ) /0

Normal pulse voltammetry

≈ ≈ ≈

t

Eb

E(-)

Drop 1 Drop 2 Drop 3

The shape od the i vs E curve and the expressions are the same as for DC polarography

≈≈

t

t

Eb

E

i

Waiting period(0.5 – 5 s)

Pulsed electrolyis (1 – 100 ms)

Drop dislodged

Current sampled

≈

Differential pulse polarography and voltammetry

≈

≈

≈

5 – 100 ms

0.5 – 4 s10 – 100 mV

Drop fall

Drop fallDrop fall

t

E

First current sample Second current sample

i E A A( ) / ( exp( )) ( / ( exp( )) / ( exp( )))= + + + − +1 1 2 2 11 1 1 1 1ϕ ϕ ϕ

Reversible reactions

A t T1 1 1= −/ / A t T2 1= −/

ϕ1 0= −nF RT E E/ ( ) ϕ 2 0= + −nF RT E E Eh/ ( )

General case

Φ Φ Φ= +DC P

ΦPrev L

t Te

e L L=

−−

+ −

−

−λ π λ

ε

ε( ) / ( )1

Ψ( ) ( )τ πτ ττ= e erfc2

L kD

es

ox

= −αϕ λ α ϕ= + −L kD

es

red

( )1

τ p H t T= − ε = nF E RT∆ / H L e Le= − +− −( ) ( )λ α ε αε1

Φ ΦP prev= ( ) ( )t pΨ τF

( ) ( ) / ( ) ( ) /( )( )t L e L e t

e e= + − − + −

−− −

− −1 1 11

1αε α ε

αε α ελ τ πλΨF

t / s

E /

V

∆E

ESW

-ESW

if

ib

τEdep

Square wave voltammetry – shape of applied potential

∆i nFSC Dt

Q Q Qj mj

ox

p

m m m

m

j

= − +− +

− +

=∑

*

π β1 1

0

2 j = 1, 3, 5, . . .

Qmm

m

=+εε1

β = t ts p/ εmm

rnF E ERT

= −exp( ( ) )/1 2

E E m E Em i sm

sw= − + + −( ) / ( )1 2 1∆ for m ≥ 1

Current is presented as a function of middle potential: Ej=Ei-(j/2)Es

SWV - Reversible reaction

Ag

AgCl(s)

Cl-

Reference electrode – why its potential is constant?

When the current passes:

Ag0 ! Ag+ + e- ion-transfer reactionAg+ + Cl- ! AgCl" precipitation/dissolutionAg0 + Cl- ! AgCl + e- net reaction

The electrode potential:

Activity of the silver ions from the solubility constant:0

ln),(0

Ag

AgAgAg

a

a

FRTEE

++ +=

−+= ClAgs aaK−

+ =Cl

sAg a

Ka

−+ −+= ClsAgAg a

FRTK

FRTEE lnln),(

0

=1