Evidence for electrohydrodynamic convection as a source of spontaneous self-ordering in porous anodic alumina films

A comparative study of self-ordering behaviour of anodic alumina films fabricated in a series of diluted (down to 0.05 M) oxalic acid electrolytes allowed developing a relationship between the supporting electrolyte concentration and self-ordering voltages for the formation of porous oxide materials. Besides its practical importance, this work elucidates some fundamental principles of porous alumina formation, e.g. it suggests that the cell patterning arises from the electrohydrodynamic (EHD) convection process rather than the interfacial tension gradients near the anode surface (Marangoni-type instability).

Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2016 Morphological parameters of the porous alumina layers formed in 0.2 M oxalic acid electrolyte After anodic oxidation of aluminium at 30 V (the mean voltage from the confidence interval predicted by the eqn.(1) in the article text, using P = 0.057 ± 0.024), pore diameters d p averaged 18 ± 2 nm and interpore distances D int were in the range 75 ± 4 nm (see Fig. S1).The observed pore sizes d p after anodization at 42 V and 43 V (where 43 V is the critical ΔU, optimized for the best hexagonal ordering of practically flawless individual cells) are close to each other and lie within the interval 27 ± 2 nm.At the applied voltage of 45 V (the upper limit of the optimized process window for the best hexagonal arrangement), d p increases to 38 ± 3 nm.The interpore distances D int obtained at 42 V, 43 V, and 45 V are 103 ± 2 nm, 106 ± 4 nm, and 119 ± 5 nm, respectively.Note that the pore and cell dimensions at 45 V are characterized by a larger spread in values and higher d p /D int ratio (only parameters within ordered domains were measured, the disordered areas are excluded from our statistical treatment).
Fig. S2 SEM images of porous alumina films obtained from the classical 0.3 M oxalic acid electrolyte at 40 V (left) and 60 V (right) potential difference.When the voltage significantly exceeds optimal values, enlarged cells with double and triple pore openings are preferably formed.This feature was used in our work (in addition to other structural parameters) to determine the upper limit of the optimal process windows for smaller electrolyte concentrations (see the close-up images at 46 V in Fig. S1, at 45 V in Fig. S3, and at 48-50 V in Fig. S4).

Morphological parameters of the porous alumina layers formed in 0.1 M oxalic acid electrolyte
Oxidation at 14 V (the middle of the predicted process window 14 ± 6 V) resulted in 9 ± 1 nm pore sizes (see Fig. S3).The distance between the neighboring pores averaged 19 ± 2 nm.Although there was no regular hexagonal pattern, it is noteworthy that the spacing between adjacent holes was rather uniform.Interestingly, hexagonally ordered domains of the exceptionally large 0.7-1.1 µm size were sometimes observed on the sample formed at 40 V (see Fig. S3).However, this result could not be always reproducibly achieved, and thus, the voltage of 40 V cannot be regarded as the optimal one.The size of well-defined long range ordered domains at 44 V is up to 1.5 µm, the pore size d p = 24 ± 2 nm, and the interpore distance D int = 113 ± 3 nm (all parameters are measured within ordered areas).

Morphological parameters of the porous alumina layers formed in 0.05 M oxalic acid electrolyte
The pore sizes d p after oxidation at 5 V are within the confidence interval 6 ± 1 nm; the calculation of the interpore distance D int was difficult due to the stochastic pore arrangement, but the spacing between the nearest neighbouring pores can be roughly estimated as 26 ± 3 nm (see Fig. S4).It should be noted that reasonably large domains (up to ≈ 0.7 µm) composed of six-fold coordinated pores were formed at 40-42 V.This observation is consistent with the previous finding for PAOX films obtained from 0.1 M electrolyte at 40 V, where the long-range ordering could be also seen.However, both these cases are rather abnormal when compared to the self-ordering behavior of PAOX in more concentrated 0.3 M oxalic acid.For instance, extrapolation of this data suggests that the self-ordering in 0.3 M anodizing electrolyte should occur at a voltage below 40 V as well (more precisely at around 25 V, if we take into account 0.2-0.8µm large domains formed in 0.2 M solution at 32 V, and plot a line using three experimental points for 0.05 M, 0.1 M, and 0.2 M concentrations), but this does not happen in practice.The pore size d p at 45 V averaged 32 ± 2 nm, and the interpore distance D int was 117 ± 5 nm.

Fig. S1
Fig. S1 SEM analysis of porous anodic alumina films obtained from 0.2 M oxalic acid electrolyte at different anodization voltages.

Fig. S3
Fig. S3 Detailed SEM examination of porous alumina films formed in 0.1 M oxalic acid electrolyte at different tested voltages.The origin of the abnormal enlargement (out of the general trend) of the ordered domain size at 40 V is not entirely clear yet.

Fig. S4
Fig. S4 Morphologies of porous alumina films obtained from 0.05 M oxalic acid electrolyte at different voltages.