Modeling of the Current Distribution in Aluminum Anodization
Rohan Akolkar and Uziel Landau Department of Chemical Engineering,
CWRU, Cleveland OH 44106.
205th Meeting of The Electrochemical Society, San Antonio, TX.
Yar-Ming Wang and Hong-Hsiang (Harry) KuoGeneral Motors R&D,
Warren MI 48090.
• 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
Outline
Aluminum Anodization • dc voltage = 12-20 V
• Alloy 6111
• 15 wt. % H2SO4
• time = 15-35 min
• oxide films ~ 5-25 μm
Introduction
Al metalAl2O3
barrier
Oxide pores
5-25 μm
~30 nm
Important Issues in Al Anodization
• Analyze and model the current distribution in anodizing systems, and compare with experimental measurements.
Objective
• 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 ?
Governing Equations
Net Flux = Diffusion + Migration + Convection
02
Boundary Conditions
• Insulator (zero current) :
• Electrode (Resistive Oxide) :
0
oEVBAe
+ _
H+zj
v
Assume :
• No concentration gradients
• Steady state
Potential Distribution
Mott Cabrera Kinetics
0 2 4 6 8 10 12 14 160
2
4
6
8
10
12
14
16
25 oC
20 oC 15 oC
Cu
rren
t D
ensi
ty (
mA
/cm
2 )
Anodization Potential (VSHE
)
Mott Cabrera Kinetics : i = A exp (B V) A, B: ionic transport parameters within the oxide film
Anodization kinetics
VERY HIGH SURFACE
RESISTANCE leads to
VERY HIGH SURFACE
OVER-POTENTIALS
Increasing temperature
Oxide Thickness Distribution
Current Density :
Faraday’s law :
+ _
i
0,2 zxi
tzxikh ),(
np1SFρ
Mεk
ox
ox
85.0
15.0p sA/cm104.4 35
current efficiency
oxide porosity
Analytical Modeling
e.g. analytical solution of
current balance equations
Numerical Modeling
e.g. CELL DESIGN*, FEM, FDM to solve Laplace equation
Scaling Analysis
e.g. Wagner number :
Current and Potential Distribution
Methods to compute current distribution
2avg
bRWa
i L
* CELL DESIGN, L-Chem Inc., Shaker Heights, Ohio 44120.
_ _+
Parallel plate anode assembly
0.8
43Cathode
30
Cathode
Anodes
Experimental setup
30
2.5
10
side shields
zyx
z
x
z
y
Numerical Modeling
Geometry
Electrode Properties e.g. kinetics
Electrolyte Properties
e.g. conductivity
Cell Design’s BEM* Solver
Potential Map
Current Distribution
Deposit Profile
* Boundary Element Method
Oxide Properties e.g. porosity
Simulation Results
Potential Distribution
Current Distribution
Significant potential
drop ONLY in the
interior of the parallel
plates
NON-UNIFORM oxide in
the interior
Anode
Cathode
0
43
86
43
Measurement of Oxide Distribution
Uniform Oxide
Non-Uniform Oxide
• Oxide thickness measured along the anode at ~5 cm intervals
for comparison with modeling results
0 10 20 30 40 50 60 70 80 900
2
4
6
8
10
12
14
16 experimental modeling
Experimental vs. Modeling
Ano
dic
Oxi
de T
hick
ness
(m
icro
ns)
Distance Along the Electrode (cm)
Uniform oxide thickness on the exterior
Non-uniform distribution in
the interior
0 10 20 30 40 50 60 70 80 900
2
4
6
8
10
12
14
16
18
20
Ano
dic
Oxi
de T
hick
ness
(m
icro
ns)
Distance Along the Electrode (cm)
Effect of Anodization Time
Constant oxide resistance
15 min
35 min
0 10 20 30 40 50 60 70 80 900
2
4
6
8
10
12
14
16
18
20
Ano
dic
Oxi
de T
hick
ness
(m
icro
ns)
Distance Along the Electrode (cm)
Effect of Anodization Time – Distributed resistance
Constant oxide resistance
Low growth rates for distributed
resistance within entire oxide
15 min
35 min
Effect of Anodization Voltage
0 10 20 30 40 50 60 70 80 900
2
4
6
8
10
12
14
16
18
20
Ano
dic
Oxi
de T
hick
ness
(m
icro
ns)
Distance Along the Electrode (cm)
14 V
18 V
Low oxide thickness inside
the interior
Uniform oxide
Effect of Anodization Temperature
Ano
dic
Oxi
de T
hick
ness
(m
icro
ns)
Distance Along the Electrode (cm)
0 10 20 30 40 50 60 70 80 900
2
4
6
8
10
12
14
16
18
20
22
24
15 oC
25 oC
Low oxide thickness inside the
interior
Uniform oxide
• 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.
Main Conclusions
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