0581.5271 Electrochemistry for Engineers

LECTURE 5

Lecturer: Dr. Brian Rosen Office: 128 Wolfson

Office Hours: Sun 16:00

Forced Convection

Ideally polarizable electrodesDouble layer charging (if R ≠ infinity)

Kinetically controlled current flow - Reaction rate constant, k - Reaction rate law, (ex. r = kCO) - Exchange current (iO) - symmetry factor, α

Mass transport controlled - 1D diffusion model - Cottrell experiment - Mass transport limiting current

Mass transport + kinetic control

When in the “mixed control” regime, it is sometimes possible to separate the “activation” parameters from the “transport” parameters by operating with a system with well defined transport properties

= Rotating electrodes

Separate Contributions

Rotating Disc Electrodes

insulator

Laminar Flow at Electrode

22/12/351.0 xvx

rxvr2/12/351.0

Velocity(cm/s) Kinematic viscosity (cm2/s)

RotationRate(s-1)

Diffusion-Convection Layer • Systems with convection form diffusion-convection layers

of constant thickness adjacent to the electrode surface. This is due to the drag created at the interface. The thickness is function of convection rate and form.

Coexistence of diffusion and convection when x < δO

How to model Steady State Mass-Transport Limiting Current Density

• At the limiting current, the concentration of “O” at the electrode surface is zero (in a reduction) and the rate of convection and rate of diffusion are equal.

AB

x

x

A 2

x

CA O

xxBA

A xA

AO

0

21

B

x

A

A

O 3exp

3

B

x

x

C

x

C

x

OO

3exp

3

0

xB

x

x

CC

x

O

C

O

O

0

3

00 3exp

*

B

x

x

C

x

C

x

OO

3exp

3

0

separate and integrate

3/1

0

* 38943.0 Bx

CC

x

OO

0

x

Oo x

CnFADi

Recall..

*6/12/13/2, 62.0 OODiscl CnFADi

Levich Equation

PEM Fuel Cells

VEOHHeO

VEOHHeOO

O

7.022

23.144

222

22

Oxygen Reduction in Acid

Mass transport limiting current density at 3000 rpm

Linear Sweep Under Rotation

Kinetic current << mass transport limit KINETIC LIMITCurrent estimated by BUTLER-VOLMER

No dependence on ω

Kinetic current >> mass transport limit MASS TRANSPORT LIMITED

Current estimated by Levich EquationDependence on ω

Levich Plots

At exceptionally high speeds (generally >2500 rpm), reactions with slow kineticscannot keep up with the increasing speed of mass transport. These kinetic limitationscause the limiting current to fall BELOW the current predicted by the Levich equation

Mixed controlas kinetic limitationsset in at high ω

Lim

iting

cur

rent

(pla

teau

)

Mass transport control

*6/13/262.0 OO CnFADslope

Modeling Mixed Control

lim

111

iii K

Kinetically limiting current in the absence of mass transfer limitations

Mass transport limited current

Measured current under mixed control

Kouteckỳ-Levich Equation

lim

111

iii K

*6/12/13/262.0

111

OOK CnFADii

Kouteckỳ-Levich Equation

Where E2 < E1 (reduction) E2>E1 (oxidation)

As expected, iK grows larger (1/iK grows smaller) as the overpotentials is increased.

Plotting Mixed Control – f(E)Oxygen Reduction

E

(-)1/iK

*6/13/262.0

1

OO CnFADslope

Mixed Control Visualized Pt 1

Mass transport controlled

Mixed Control

Kinetic Control

ilim

iK

i

lim

111

iii K

Mixed Control Visualized Pt 2

Mechanistic Data on O2 Reduction

Mechanistic Information

▪

▲

●

Data from Eliran Hamo (EML-TAU)

Rotating Ring-Disc Electrodes (RRDE)

Recall convection pattern v(x,r)

Ring and disc are both WORKING ELECTRODES and are INDEPENDENTLY CONTROLLED

Operation

DISC RING r

O

OR RO

Scanning E (-) Constant E (+)

One can measure the extent a specific product is made at the disc by

reversing the reaction at the ring

Recall…

To what extent does the 2e- reaction occur at various potentials?

Example Operation or RRDE

DISC RING r

O2

O2 + 2H+ + 2e- H2O2

Scanning E (-) Constant E (+)

What is the practical limit for selecting the potential of the ring in this case?

O2 + 4H+ + 2e- H2OH2O2 O2 + 2H+ + 2e-

Ficks 2nd Law - RRDE

RDE:(from before)

RRDE:

Concentration is a function of radius due to depletion!

DISC RING r

Solving as before we get:

*6/12/13/232

3362.0 Oringl CrrnFi

……

RRDE Collection Efficiency

x = fraction of R that makes it to the ring electrodey = fraction of R that is flung back into solution1-x-y = fraction of R that is subjected to other processes (decomposition, conversion to non- electroactive species.

discl

ringl

i

iN

*6/12/13/2, 62.0 OODiscl CnFADi

3/2

31

32

31

33

r

r

r

r

i

iN

discl

ringl

*6/12/13/23/231, 62.0 OODiscl CDrnFi

*6/12/13/232

3362.0 Oringl CrrnFi