Transcript Slide 1

Modeling of the Current Distribution in
Aluminum Anodization
Rohan Akolkar and Uziel Landau
Department of Chemical Engineering,
CWRU, Cleveland OH 44106.
Yar-Ming Wang and Hong-Hsiang (Harry) Kuo
General Motors R&D,
Warren MI 48090.
205th Meeting of The Electrochemical Society,
San Antonio, TX.
Outline
• Anodic Oxide Films on Aluminum
• Current distribution – Significance
• Kinetics of oxide growth
• Modeling of Current and Potential Distribution
• Comparison with experiments
• Effect of operating conditions (t, V, T)
• Conclusions
Introduction
Aluminum Anodization
• dc voltage = 12-20 V
• Alloy 6111
• 15 wt. % H2SO4
5-25 μm
• time = 15-35 min
• oxide films ~ 5-25 μm
Oxide
pores
~30 nm
Al metal
Al2O3
barrier
Important Issues in Al Anodization
• Anodized parts with complex, non-accessible features
experience large oxide thickness variations.
• What are the current distribution characteristics inside
non-accessible cavities ?
• How are they affected by the operating conditions ?
Objective
• Analyze and model the current distribution in
anodizing systems, and compare with experimental
measurements.
Governing Equations
Net Flux = Diffusion + Migration + Convection
Assume :
• No concentration gradients
• Steady state
+
Potential
Distribution
  0
2
zj
_
H+
v
Boundary Conditions
   0

B V  E o  
• Electrode (Resistive Oxide) :    Ae
• Insulator (zero current) :
Mott Cabrera Kinetics
Anodization kinetics
Mott Cabrera Kinetics : i = A exp (B V)
A, B: ionic transport parameters within the oxide film
2
Current Density (mA/cm )
16
Increasing
temperature
14
12
VERY HIGH
SURFACE
RESISTANCE
leads to
VERY HIGH
o
SURFACE
15 C
OVERPOTENTIALS
o
25 C
10
8
o
20 C
6
4
2
0
0
2
4
6
8
10
12
14
Anodization Potential (VSHE)
16
Oxide Thickness Distribution
Current Density :
_
+
i  
  x, z   0
2
Faraday’s law :
i  
h  k  i( x, z )  t
ε  M ox
k
SFρox 1  p n
5
 4.4  10 cm / A  s
3
  0.85
current
efficiency
p  0.15
oxide
porosity
Current and Potential Distribution
Methods to compute
current distribution
Scaling
Analysis
e.g. Wagner
number :
 bR
Wa 
iavg L2
Numerical
Modeling
Analytical
Modeling
e.g. CELL DESIGN*,
FEM, FDM to solve
Laplace equation
e.g. analytical
solution of
current balance
equations
* CELL DESIGN, L-Chem Inc., Shaker Heights, Ohio 44120.
Experimental setup
_
_
+
Parallel plate
anode assembly
z
y
x
2.5
Anodes
43
Cathode
Cathode
z
30
10
z
0.8
x
30
y
side shields
Numerical Modeling
Geometry
Potential
Map
Electrode
Properties
e.g. kinetics
Electrolyte
Properties
Cell Design’s
BEM* Solver
Current
Distribution
e.g. conductivity
Oxide
Properties
e.g. porosity
* Boundary Element Method
Deposit
Profile
Simulation Results
Significant
potential
drop ONLY
in the
interior of
the parallel
plates
Potential
Distribution
Current
Distribution
NONUNIFORM
oxide in
the interior
Measurement of Oxide Distribution
for comparison with modeling results
0
86
Uniform
Oxide
Anode
Cathode
43
43
Non-Uniform
Oxide
• Oxide thickness measured along
the anode at ~5 cm intervals
Anodic Oxide Thickness (microns)
Experimental vs. Modeling
16
experimental
modeling
14
12
Non-uniform
distribution in
the interior
10
Uniform oxide
thickness on
the exterior
8
6
4
2
0
0
10
20
30
40
50
60
70
80
Distance Along the Electrode (cm)
90
Anodic Oxide Thickness (microns)
Effect of Anodization Time
20
18
16
35 min
14
12
Constant oxide
resistance
10
8
6
4
15 min
2
0
0
10
20
30
40
50
60
70
80
Distance Along the Electrode (cm)
90
Anodic Oxide Thickness (microns)
Effect of Anodization Time – Distributed resistance
20
18
Low growth rates
for distributed
resistance within
entire oxide
16
14
12
Constant oxide
resistance
10
8
35 min
6
4
2
15 min
0
0
10
20
30
40
50
60
70
80
Distance Along the Electrode (cm)
90
Anodic Oxide Thickness (microns)
Effect of Anodization Voltage
20
18
16
18 V
14
Uniform oxide
12
10
Low oxide
thickness
inside the
interior
8
6
4
14 V
2
0
0
10
20
30
40
50
60
70
80
Distance Along the Electrode (cm)
90
Anodic Oxide Thickness (microns)
Effect of Anodization Temperature
24
22
20
25 oC
18
16
Uniform oxide
14
12
Low oxide
thickness
inside the
interior
10
8
6
4
15 oC
2
0
0
10
20
30
40
50
60
70
80
Distance Along the Electrode (cm)
90
Main Conclusions
• An electrochemical CAD software used to model the
current distribution in anodizing.
• Excellent agreement between modeling and
experiments.
• The oxide growth rates are independent of time
indicating a porous oxide growth – the oxide
resistance resides in a compact barrier film at its
base.
• Current distribution was highly non-uniform in high
aspect ratio cavities due to dominance of ohmic
limitations over surface resistance.