The role of viscous flow of oxide in the growth of self-ordered porous anodic. alumina films. Jerrod E. Houser and Kurt R. Hebert

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1 SUPPLEMENTARY INFORMATION The role of viscous flow of oxide in the growth of self-ordered porous anodic alumina films Jerrod E. Houser and Kurt R. Hebert Department of Chemical & Biological Engineering Iowa State University, Ames, IA 50011, USA 1. Temperature variation within the anodic film Anodic oxidation of aluminum can generate significant heat. 1,2 Temperature gradients on the length scale of the pore diameter, if they exist, could produce differential volume changes due to thermal expansion, and thereby influence the flow pattern under consideration in this paper. Here we present an estimate of the spatial temperature variation within our simulation domain (Figure 1 (b)). Heat is generated in the barrier layer of the anodic film primarily by ionic conduction, at a rate q s = iδφ per unit area, where i is the anodizing current density and Δφ is the potential drop through the film. 1,3 We assume that the dissipated heat flows primarily toward the solution, since the low heat transfer coefficient of air would block heat flow through the metal. The temperature drop through the barrier layer is ΔT b = ( q s L p )( 2k s ) 1, and that through the porous layer is ΔT p = q s L p ( ) 1 p ( ) 1, where L b and L p are the thicknesses of the barrier ( )k s + pk w and porous layers, p is the oxide porosity, and k s and k w are the thermal conductivities of oxide and water, respectively. 4 Of the PAA films in the calculations, those formed in phosphoric acid would have the largest power dissipation and temperature drop. Using the typical parameters of nature materials 1

2 supplementary information these films, i = 5 ma/cm 2, Δφ = 200 V, L b = 200 nm, L p = 10 µm, k s = 1.9 W/(m-K), 5 and p = 0.1, 6 we obtain ΔT b = 5 x 10-4 o C, and ΔT p = 0.06 o C. These very small temperature differences indicate that the barrier layer and the bottom 10 µm of the porous layer are nearly isothermal, in agreement with prior calculations. 1 This conclusion is supported by measurements of temperature increases during anodizing by De Graeve et al., who used electrolyte jets directed at the Al substrate to control convective heat transfer. 2 They found temperature increases of about 2 o C at the stagnation (i. e. impingement) point of the jet, for jet Reynolds numbers (Re) of 770 and For this range of Re, the expected range of heat transfer coefficient h of submerged liquid jets is W/(m 2 -K). 7 For the anodizing conditions used by De Graeve et al. (i = 80 ma/cm 2, Δφ = 18 V), the temperature drop through the solution is q s /h = o C, close to their measured values. Larger temperature increases of 8-10 o C found in unstirred cells are attributable to the smaller heat transfer coefficient associated with natural convection. These measurements are consistent with the view that the largest portion of the spatial temperature drop is located in the external solution, rather than the oxide. 2 nature MATERIALS

3 supplementary information 2. Figures Figure S1. Dependence of model geometric parameters on anodizing voltage, for film formation in sulfuric, oxalic and phosphoric acids. The parameters were deduced from measurements of film geometry. 6,8,9 Referring to symbol definitions in Fig. 1 (b), R 2 /R 1 is the ratio of inner to outer radii ; R 2 - R 1 is the barrier layer thickness; and θ 0 is the pore angle. nature materials 3

4 supplementary information Figure S2. Steady-state anodizing current density vs. voltage, for the three formation baths considered in this paper. Model fits (dashed lines) are compared to experimental data (solid lines). 6,8,9 (a) Anodic films formed in phosphoric acid solutions. (b) Anodic films formed in oxalic and sulfuric acid solutions. For sulfuric acid solutions, the three conduction parameters, u 0 O, u 0 M, and a (see Eq. (4)) were fit using three experimental values: the slope and intercept of plots of logarithm of current density vs. voltage, and the O -2 migration rate at the current density of 0.6 ma cm -2, at which the anodic film has been found to be stress-free. 10,11 Since no stress data were available for oxalic and phosphoric acids, the ratio u O 0 same as for sulfuric acid. u M 0 was assumed to be the 4 nature MATERIALS

5 supplementary information Figure S3. Comparisons of experimental and simulated tungsten tracer profiles. (a) Sulfuric acid after anodizing for 340 s (5 ma cm -2, 0.4 M H 2 SO 4, 293 K). Experimental image is taken from Ref. 12. (b) Oxalic acid after anodizing for 175 s (5 ma cm -2, 0.4 M H 2 (COO) 2, 293 K). Experimental image is taken from Ref. 13. nature materials 5

6 supplementary information References 1. Young, L. Temperature rise during formation of anodic oxide films. Trans. Faraday Soc. 53, (1957). 2. De Graeve, I., Terryn, H. & Thompson, G. E, Influence of local heat development on film thickness for anodizing aluminum in sulfuric acid. J. Electrochem. Soc. 150, B158- B165 (2003). 3. Nagayama, M. & Tamura, K., On the mechanism of dissolution of porous oxide films on aluminum during anodizing, Electrochim. Acta 13, (1968). 4. Incropera, F. P., DeWitt, D. P., Bergman, T. L. & Lavine, A. S., Fundamentals of heat and mass transfer. (Wiley, Hoboken, NJ 2007). 5. Borca-Tasciuc, D.-A. & Chen, G., Anisotropic thermal properties of nanochanneled alumina templates. J. Appl. Phys. 97, (2005). 6. Ono, S., Saito, M., Ishiguro, M. & Asoh, H., Controlling factor of self-ordering of anodic porous alumina. J. Electrochem. Soc. 151, B473-B478 (2004). 7. Bizzak, D. J. & Chyu, M. K. Use of a laser-induced fluorescence thermal imaging system for local jet impingement heat transfer measurement. Int. J. Heat Mass Transfer 38, (1995). 8. Ebihara, K., Takahashi, H. & Nagayama, M., Structure and density of anodic oxide films formed on aluminum in sulfuric acid solutions. J. Met. Finish. Soc. Jpn. 33, (1982). 9. Ebihara, K., Takahashi, H. & Nagayama, M., Structure and density of anodic oxide films formed on aluminum in oxalic acidsolutions. J. Met. Finish. Soc. Jpn. 34, (1983). 10. Nelson, J. C. & Oriani, R. A., Stress generation during anodic oxidation of titanium and aluminum. Corros. Sci. 34, (1993). 11. Bradhurst, D. H. & Leach, J. S. L., Mechanical properties of thin anodic films on aluminum. J. Electrochem. Soc. 113, Garcia-Vergera, S. J., Skeldon, P., Thompson, G. E. & Habazaki, H. Self generated porosity in anodic alumina formed in sulphuric acid electrolyte. Corros. Sci. 49, (2007). 13. Garcia-Vergera, S. J., Skeldon, P., Thompson, G. E. & Habazaki, H. Tracer studies of anodic films formed on aluminum in malonic and oxalic acids. Appl. Surf. Sci. 254, (2007). 6 nature MATERIALS