1. Modeling of the Current Distribution in Aluminum Anodization Rohan Akolkar and Uziel Landau Department of Chemical Engineering, CWRU, Cleveland OH 44106. 205 th Meeting of The Electrochemical Society, San Antonio, TX. Yar-Ming Wang and Hong-Hsiang (Harry) Kuo General Motors R&D, Warren MI 48090.

2. 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

3. Aluminum Anodization dc voltage = 12-20 V Alloy 6111 15 wt. % H 2 SO 4 time = 15-35 min oxide films ~ 5-25 μm Introduction Al metal Al 2 O 3 barrier Oxide pores 5-25 μm ~30 nm

4. 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 ?

5. Governing Equations Net Flux = Diffusion + Migration + Convection Boundary Conditions Insulator (zero current) : Electrode (Resistive Oxide) : + _ H+H+ zjzj v Assume : No concentration gradients Steady state Potential Distribution Mott Cabrera Kinetics

6. 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

7. Oxide Thickness Distribution Current Density : Faraday ’ s law : + _ current efficiency oxide porosity

8. 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 * CELL DESIGN, L-Chem Inc., Shaker Heights, Ohio 44120.

9. _ _ + Parallel plate anode assembly 0.8 43 Cathode 30 Cathode Anodes Experimental setup 30 2.5 10 side shields z y x z x z y

10. 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

11. Simulation Results Potential Distribution Current Distribution Significant potential drop ONLY in the interior of the parallel plates NON- UNIFORM oxide in the interior

12. 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

13. Experimental vs. Modeling Anodic Oxide Thickness (microns)Distance Along the Electrode (cm) Uniform oxide thickness on the exterior Non-uniform distribution in the interior

14. Anodic Oxide Thickness (microns) Distance Along the Electrode (cm) Effect of Anodization Time Constant oxide resistance 15 min 35 min

15. Anodic Oxide Thickness (microns) 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

16. Effect of Anodization Voltage Anodic Oxide Thickness (microns) Distance Along the Electrode (cm) 14 V 18 V Low oxide thickness inside the interior Uniform oxide

17. Effect of Anodization Temperature Anodic Oxide Thickness (microns) Distance Along the Electrode (cm) 15 o C 25 o C Low oxide thickness inside the interior Uniform oxide

18. 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