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