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0581.5271 Electrochemistry for Engineers
LECTURE 5
Lecturer: Dr. Brian Rosen Office: 128 Wolfson
Office Hours: Sun 16:00
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Forced Convection
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Ideally polarizable electrodesDouble layer charging (if R ≠ infinity)
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Kinetically controlled current flow - Reaction rate constant, k - Reaction rate law, (ex. r = kCO) - Exchange current (iO) - symmetry factor, α
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Mass transport controlled - 1D diffusion model - Cottrell experiment - Mass transport limiting current
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Mass transport + kinetic control
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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
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Rotating Disc Electrodes
insulator
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Laminar Flow at Electrode
22/12/351.0 xvx
rxvr2/12/351.0
Velocity(cm/s) Kinematic viscosity (cm2/s)
RotationRate(s-1)
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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
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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.
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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
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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
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PEM Fuel Cells
VEOHHeO
VEOHHeOO
O
7.022
23.144
222
22
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Oxygen Reduction in Acid
Mass transport limiting current density at 3000 rpm
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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
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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
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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
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Kouteckỳ-Levich Equation
lim
111
iii K
*6/12/13/262.0
111
OOK CnFADii
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Kouteckỳ-Levich Equation
Where E2 < E1 (reduction) E2>E1 (oxidation)
As expected, iK grows larger (1/iK grows smaller) as the overpotentials is increased.
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Plotting Mixed Control – f(E)Oxygen Reduction
E
(-)1/iK
*6/13/262.0
1
OO CnFADslope
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Mixed Control Visualized Pt 1
Mass transport controlled
Mixed Control
Kinetic Control
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ilim
iK
i
lim
111
iii K
Mixed Control Visualized Pt 2
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Mechanistic Data on O2 Reduction
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Mechanistic Information
▪
▲
●
Data from Eliran Hamo (EML-TAU)
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Rotating Ring-Disc Electrodes (RRDE)
Recall convection pattern v(x,r)
Ring and disc are both WORKING ELECTRODES and are INDEPENDENTLY CONTROLLED
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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
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Recall…
To what extent does the 2e- reaction occur at various potentials?
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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-
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Ficks 2nd Law - RRDE
RDE:(from before)
RRDE:
Concentration is a function of radius due to depletion!
DISC RING r
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Solving as before we get:
*6/12/13/232
3362.0 Oringl CrrnFi
……
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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
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*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