Self-Ordering Regimes of Porous Anodic Alumina Layers Formed in

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Self-Ordering Regimes of Porous Anodic Alumina Layers Formed in Highly Diluted Sulphuric Acid Electrolytes Mikhail Pashchanka, and Joerg J. Schneider J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11801 • Publication Date (Web): 14 Jun 2016 Downloaded from http://pubs.acs.org on June 20, 2016

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The Journal of Physical Chemistry

Self-Ordering Regimes of Porous Anodic Alumina Layers Formed in Highly Diluted Sulphuric Acid Electrolytes

Mikhail Pashchanka* and Jörg J. Schneider* Fachbereich Chemie, Eduard-Zintl-Institut, Fachgebiet Anorganische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 12, 64287, Darmstadt, Germany.

*E-Mail: [email protected], [email protected]

KEYWORDS porous anodic alumina, self-ordering, electrohydrodynamic convection, Rayleigh-Bénard convection, dissipative structures, sulphuric acid

ACS Paragon Plus Environment

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ABSTRACT

Nanoporous anodic alumina films with long-range hexagonal order have been obtained from a series of highly diluted sulphuric acid electrolytes. A simple linear relationship was established between the self-ordering voltages and acid concentrations (28 V, 29 V, and 30 V for 0.2 M, 0.1 M, and 0.05 M electrolytes, respectively). Besides establishing new self-ordering regimes, our experimental work sheds new light on some fundamental principles of honeycomb anodic alumina formation. It suggests that the spontaneous self-organisation of a stable nanoscale structure originates from the electrohydrodynamic (EHD) convection rather than from Marangoni-type instability at the anode surface. Theoretical analysis displays a decreasing exponential functional relationship between electrolyte concentration and the critical values of the earlier found electrochemical analogue of Rayleigh number, which can be used for prediction of hexagonal cell pattern in currently unexplored anodizing electrolytes.


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1. Introduction Porous anodic aluminum oxide (PAOX) layers have been intensively explored during the last decades because of their numerous scientific and technological applications.1 For example, they can be used for filtration, in nanofluidic systems,2-4 as templates for nanotechnology,5 or as periodic optical structures.6-7 For practical purposes, it is very important to control morphological parameters (like the inter-pore distances Dint, and the pore sizes dp) in PAOX, the degree of hexagonal ordering, as well as the non-stoichiometric chemical composition with variable content of anionic impurities.8 This could be achieved by increasing the number of suitable electrolytes for optimized aluminum anodization conditions. For instance, optical properties of 2D-photonic PAOX crystals (i.e. periodically arranged cylindrical mesopores in dielectric medium) strongly depend on morphological characteristics,9 and can be adjusted simply by changing the parameters of the aqueous electrolytes (oxalic acid, sulphuric acid, or mixture of both), or by subsequent use of etching solutions for pore widening.7, 10-11 However, only a few empirically

found

experimental

conditions

(temperatures,

voltages,

and

electrolyte

concentrations) have been currently investigated for obtaining well-organized arrays of uniform mesopores.12-14 Sulphuric acid is one of the most versatile known single-solute anodizing electrolytes. To date, formation of well-ordered 20-30 nm pores has been reported using 0.3-2.25 M (the latter corresponds to 20 wt.-%) concentrations of H2SO4 under moderate voltages at a low temperature (≈ 0 °C),12, 14-15 or using even higher 8-9.4 M concentrations at extraordinarily high solution temperatures (40-60 °C).16 The uniformity of pores and the degree of hexagonal ordering were optimized in all cases solely based on experimental grounds. However, much effort has also been put into developing a viable theoretical explanation of the self-ordering in PAOX. The early electrochemical models assumed pore formation by the simultaneous growth


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of dense alumina and its local field-assisted dissolution in the corrosive electrolyte medium, but the preferential etching in form of hexagons was still not explained.17 The recent studies suggested either the patterned field strength inhomogeneity18-20 or tensile stress distribution21 in alumina as possible factors assisting the pore ordering. However, the predicting ability of these theories has not been experimentally confirmed yet. Currently, many researchers share the opinion that the hexagonal pattern in PAOX is of convective origin.22-26 Indeed, PAOX bears similarities with numerous self-organized electrochemical systems where Rayleigh-Bénard convective flows are responsible for the hexagonal cell formation. For example, potentiostatically controlled PAOX growth displays periodic damped oscillations of electric current (I-t curves), which can be also observed during anodic dissolution of some other metals.27-28 Such oscillatory behaviour results from the interplay of so-called ‘positive and negative feedback loops’ in nonlinear dynamic electrochemical systems, which are generally necessary for the occurrence of spontaneous self-organization.25 As the possible driving forces for nano-convection, either Marangoni effect,25,

29

or interaction of the electric field with the

ionic charge carriers are usually considered.24 The latter one is known for inducing the electrohydrodynamic (EHD) convection in homogeneous fluids and colloidal systems.25 Thus, the EHD convection can hypothetically be a part of the PAOX formation mechanism, especially if combined with the concept of colloidal alumina particles agglomeration proposed by Michelson.30 Recently, a theoretical model explaining the honeycomb oxide growth by in situ formation of colloidal alumina particles and their assembly assisted by Rayleigh-Bénard nanoconvection was suggested.22-23 In this theory, the required anodizing voltages for selfordering can be calculated using the empirically found electrochemical analogue of Rayleigh number P (the criterion for transition from dense to porous alumina):


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=

∆

(1)

where ∆U is the voltage, η – dynamic viscosity (cP), σ – specific electric conductivity (mS/cm), and qav is the average charge of supporting electrolyte anions (absolute value, qav = 10-pH/C, C is the known acid concentration). For the most widely used electrolytes, the critical value of P lies within the confidence interval 0.057 ± 0.024.22 While the Rayleigh number Ra determines the formation of convective flows in a viscous liquid under temperature gradient ∆T, the criterion number P determines the behavior of aqueous electrolyte in the same way, but is proportional to the potential difference ∆U. Correlation between the degree of hexagonal order in PAOX and the values of P calculated for new anodizing electrolytes with modulated properties (by systematic addition of glycerol in different proportions) was reported by Stepniowski et al.26 The best pore arrangement was observed in this work for systems where P approached the earlier reported ‘optimal criterion numbers’,22 and any deviation of P from these reference values inevitably led to hexagonal structure distortion. It still needs to be clarified, however, whether there is dependence between the systematically changed parameters of electrolytes and the new critical values of P for redetermination of new self-ordering conditions. Such relationship could eliminate the currently known limitations of the method. Since many properties of anodizing electrolytes are related to the amount of ionic species (such as conductivity, pH, and spatial charge in some parts of the electrochemical cell), the concentration of supporting electrolyte seems to be one of the most crucial influencing quantities for modulation. Recently, we have reported a detailed study employing oxalic acid with varying concentrations as a conventional electrolyte medium and its influential role in the formation of self-ordered porous anodic alumina films.31 In our present investigation, we focus on another widely used electrolyte type, sulphuric acid. We decrease its concentration in a broad interval


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(0.2-0.05 M), and search for new optimized anodization conditions, as well as a functional relationship between concentrations, self-ordering voltages, and the criterion P for the best hexagonal pore arrangement. Besides the practical importance of offering new self-ordering regimes in less aggressive acidic media with economical use of chemicals, our herein presented work solves several problems of theoretical interest. First, it provides the experimental test for the earlier suggestion that the hexagonal cell pattern can be formed in highly diluted electrolytes, close to deionized water (however, according to the general principles of PAOX formation, pH ≤ 4 must be assured).23 Second, it allows precise prediction of new self-ordering voltages in unexplored electrolytes and facilitates flexible design of future anodization experiments. Finally, the behavior of the criterion P in response to the changes of charge carriers’ concentration may indirectly clarify the nature of nano-convective pattern, and suggest the possible driving force of self-organization.

2. Experimental section Aqueous sulphuric acid electrolytes of different concentrations (0.2, 0.1, and 0.05 M) were prepared from H2SO4 (95-98 wt.%, purchased from Sigma-Aldrich) and distilled water (σ ≈ 2 µS/cm) using standard analytical volumetric flasks. The kinematic viscosities of solutions were measured with Schott Viscoclock Micro-Ubbelohde Viscometer (capillary diameter 0.53 mm). Samples’ temperature was controlled with Schott CT 1650 thermostat and CK 160 cooler. The densities of solutions at 0 °C were obtained on an Anton Paar DMA 5000 Density Meter. The specific conductivity was measured with WTW LF 538 Conductivity Meter using Lauda RM6 thermostat. pH values were determined using WTW Digital pH Meter pH 525. Aluminum sheets (PURALUX®, purity 99.5-99.93%) were anodized in the vigorously stirred electrolyte solutions


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under potentiostatic conditions at 0-0.5 °C using a Sorensen XEL 250 DC Power Supply at voltages in the range between 5 and 34 V. After the first oxidation for 20 hours, alumina was removed in an etching aqueous solution (0.16 M K2Cr2O7 and 1.5 M H3PO4). Then, the main oxidation step was performed for another 20 hours. The aluminum substrates were used ‘as is’, without prior electropolishing. Scanning electron microscopy (SEM) studies of the resulting porous films were performed using a Philips XL-30 FEG, operated at 20-25 kV. Samples were mounted on conductive carbon-rich polymer films and sputtered with Pt/Pd alloy. The pore sizes (dp) and interpore distances (Dint) were evaluated using measuring tools in the microscope control software or image processing programs. During the statistical treatment, confidence intervals were defined from 15 random measurements by the significance level α = 0.05; dp were measured in high resolution SEM images between the contrasting pore margins (without special visualization techniques), and Dint between centers of randomly chosen neighboring pores. To bring the confidence intervals to conformity with the electron-scan microscope resolution, the mean dp and Dint values were approximated to whole numbers.

3. Results and discussion Theoretical prediction of self-ordering voltages for new electrolyte concentrations using the earlier found value of P Before we start the empirical adjustment of self-ordering voltages, it is helpful to initially predict the process windows using eq 1. The empirical formula 1 suggests voltages appropriate for the transition from dense to porous alumina for all the solutions under study (see Table 1). Thus, our calculations show that the formation of PAOX film is possible in the whole range of selected concentrations. The theoretically predicted self-organization voltages from Table 1 are


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calculated for P = 0.057, i.e. for the centre of the confidence interval defined in Ref.[22] Since this confidence interval (0.057 ± 0.024) was broadened due to only three values used in statistical treatment, variations of the required voltages in a certain range are possible. Therefore, the initial experiments were followed by the empirical adjustment of the applied voltages to optimize the pore size uniformity and the degree of ordering. The specific electric conductivities of all tested H2SO4 solutions are high enough to expect acceptable reaction velocities and structurization of the aluminum substrates in form of hexagonal concaves within reasonable reaction times (the minimal requirement for self-ordering is around σ = 4-5 mS/cm).23 The average absolute anionic charge |qav|, which is derived from pH measurements, is decreasing with higher concentrations. This effect is entirely clear because the degree of dissociation is larger for diluted compositions. However, the value of |qav| for the most concentrated 0.3 M solution (is taken from the classical work of Masuda et al14 for comparison, but does not appear in our current experiments) slightly deviates from the general trend. This observation can be explained by the non-linear response of a glass pH electrode when approaching values 1.00 and below (so-called ‘acidic error range’, where the analytical equipment shows slightly overestimated pH-readings). Although this instrumental error cannot very largely influence the calculated values of |qav| and P, we must bear in mind this general shortcoming of a glass electrode. Nevertheless, all the measured pH values from Table 1 are noticeably below 4, which assures slight solubility of alumina in electrolyte solutions and enables formation of porous layers.32


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Experimental refinement of anodizing voltage in 0.2 M sulphuric acid electrolyte Eq 1 suggests a very broad process window for anodization in 0.2 M sulphuric acid (32 ± 13 V). The best self-ordering was achieved at 26-28 V, which is slightly lower than the mean predicted ∆U, but still in full accordance with the calculated interval. The ordered domain sizes at 26 and 28 V were about 0.5 and 2 µm, respectively (see Figure 1). The hexagonal pore arrangement was practically lost at all voltages increased above 28 V (see Figure S1 of the Supporting Information file). Therefore, 28 V can be considered as the new critical voltage for the best self-ordering using the concentration of 0.2 M. The pore size after oxidation at 28 V averaged 21 ± 1 nm, and the inter-pore distance Dint was equal to 74 ± 3 nm. Taking into account the new experimentally optimized ∆U, the earlier determined value of the criterion P is very likely underestimated for this new diluted electrolyte concentration and needs a correction. The readjusted value of P is equal to 0.051, which considerably exceeds P = 0.033 for the classical 0.3 M sulphuric acid solution (it should be mentioned here that P = 0.057 was originally estimated as the centre of the confidence interval for three commonly used electrolytes, while P calculated for 0.3M H2SO4 was lower).22 Thus, there is approximately a 54.5% enlargement in the critical value of the criterion P, when sulphuric acid concentration is decreased from 0.3 M to 0.2 M.

Experimental refinement of anodizing voltage in 0.1 M sulphuric acid electrolyte The initially predicted self-ordering voltage in 0.1 M anodizing electrolyte lies within the interval 12 ± 5 V. Oxidation at 12 V resulted in entirely disordered pore layout (see Figure 2). No hexagonal structure was observed at the upper confidence limit as well (see the SEM images of the sample obtained at 17 V in Fig. 2). The first small fragments with hexagonal arrangement


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appear at 20 V and have dimensions up to 0.2-0.3 µm. As the voltage increases, the regularity in pore layout improves. The oxidation at 29 V resulted in ordered domains with the size of approximately 0.5 µm. Thus, hexagonal pore arrangement required voltages beyond the calculated potential window. Anodizing voltages exceeding 29 V produced films with deteriorated morphology. Although the size of ordered domains obtained at 30 V was still large (0.4-1 µm, see Fig. S2 of the Supporting Information file for details), the hexagonal shape of individual cells considerably worsened, and the number of such point defects as double or triple pores within a single cell increased. After oxidation at 31 and 32 V, ordered domains completely disappeared. Thus, the voltage of 29 V might be considered as the upper limit of the experimentally optimized process window and as the critical self-ordering voltage for 0.1 M concentration as well. The highly ordered PAOX membranes after oxidation at 29 V have an average pore size dp = 21 ± 3 nm and the inter-pore distance Dint = 73 ± 2 nm. The difference between the middle theoretically predicted critical voltage (using the value of P estimated for a higher H2SO4 concentration) and the experimentally optimized one now reached 17 V. Thus, the criterion P certainly needs a correction for the 0.1 M electrolyte. The new recalculated value of P is equal to 0.144, which is larger than both the previous values obtained for 0.3 M and 0.2 M concentrations. From this result, we can conclude that the critical values of P increase with decreased supporting electrolyte concentration progressively.

Experimental refinement of anodizing voltage in 0.05 M sulphuric acid electrolyte The difference in concentrations between the 0.05 M solution and the classical 0.3 M electrolyte used by Masuda et al.14 is the largest one in our series of experiments. Therefore, noticeable deviation of the experimentally optimized ∆U from the theoretically estimated values


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can be also expected. Indeed, although eq 1 has successfully predicted the transition from compact to porous films at 5-7 V (see Figure 3), the pores are randomly distributed, and films have a spongy structure without hexagonal cell definition. The first indications of the preferential formation of six-fold coordinated pores are visible only at 20 V, and long-range ordering with the size of domains approximately 0.5 µm was obtained at 30 V. The diameter of uniform pores at ∆U = 30 V was dp = 22 ± 4 nm, and the inter-pore distance was Dint = 82 ± 4 nm. Porous oxide growth was impracticable at voltages higher than 30 V due to the ‘aluminium burning effect’ and strong damage of substrates (i.e. local concentration of the electrical current and accelerated dissolution of metal, see Fig. S3 of the Supporting Information file).34 Although observation of this effect for the most diluted electrolyte (with the lowest electrical conductivity) may seem surprising, it can be explained by the presence of electrohydrodynamic (EHD) convection in the system. Generally, three possible types of charge carriers transport may contribute to the total faraday current: migration, diffusion, and convection. For instance, in low-voltage electrochemical cells containing abundant amount of supporting electrolyte (where no EHD convection occurs), electrical current mainly arises due to migration transport.25 In such systems, the Ohm’s law is met (i.e. current linearly depends on voltage). However, if high voltages are applied and concentration gradients are established, conductivity is enhanced due to the predominant contributions of diffusion and convective transport (fluid motion). It is claimed that a rapid (non-linear) increase of the electric current under applied voltage experimentally manifests the onset of EHD convection.25 It must also be noted that diffusion is related to the formation of nano-convective flows,22-23 and there is possibly a complex interplay between these two kinds of charge transport. A smaller concentration of H2SO4 in our work may result in increased concentration gradient between the region of the double layer and remote solution,


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which leads to the charge carriers acceleration by diffusion and convection. In other words, the local increase of the electrical current may depend not only on the total concentration of supporting electrolyte, but also on the existing concentration gradient, and is possibly concerned with the nonlinear phenomenon of self-organized EHD convection. Thus, ∆U = 30 V very likely has to be considered as the new optimized self-ordering voltage. The required critical voltage for 0.05 M sulphuric acid turned out to be several times larger, than could be theoretically expected using the earlier value of P in calculations. Thus, like in the previous cases with the 0.2 M and 0.1 M electrolyte solutions, the critical criterion number needs a correction, using the new experimentally established critical ∆U. The corrected new value of P is 0.334. It went up by a factor of 10 in comparison with the critical number for 0.3 M sulphuric acid electrolyte.

Theoretical analysis of the experimental data As can be concluded from Fig. 4, there is a simple linear relationship between the experimentally optimized critical voltages (presented by green circles) and electrolyte concentrations, which can be approximated as: ∆U = −10 × C + 30

(2)

Of course, scepticism regarding this linearity may arise from the narrow range of analysed concentrations and from the slight deviation of calculated ∆U for 0.05 M solution (29.5 V, while experimentally it was rounded up to 30 V). Sulphuric acid is miscible with water in any proportions, what allows a broad range of electrolyte compositions. For example, hexagonally ordered PAOX can be also formed in rather concentrated 10 wt% (corresponds to 1.07 M) H2SO4 at 0 °C and voltages of 19-20 V.12, 35 Such highly concentrated sulphuric acid solutions (above 0.3 M) were initially excluded from our experiments and statistical treatment because of their


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high electric conductivity, which was beyond the measuring range of our laboratory equipment. Thus, the 10 wt% electrolyte provides a new test for the eq 2 without recurrence. If we substitute C with 1.07 M, eq 2 yields ∆U = 19.3 V, which closely matches the earlier experimental values. Thus, eq 2 satisfactorily establishes proportionality between concentrations and critical voltages and can be extrapolated to a broader C-range, although some deviations from linearity are possible in the region of extremely diluted electrolytes. Fig. 4 also gives a visual picture of the discrepancy between the optimized critical voltages and initially predicted theoretical values using fixed P = 0.057 ± 0.024. From this comparison, it may seem that there is an inconsistency between the empirical eq 1 and the experimental data. In order to explain this difference, we can appeal to our recent study containing experiments with another type of electrolyte (oxalic acid) and featuring the electrohydrodynamic (EHD) convection as the possible source of the PAOX cell pattern formation.31 The analysis in this preceding work rests on the observation that there are similarities between the empirically found critical number P and the earlier theoretically derived electrical analogue of the Rayleigh number Rae, which determines the critical conditions for the self-ordering in other electrochemical systems, where the EHD convection sets in.25, 36 Moreover, the parameter qav from eq 1, which is defined as the ratio of the total negative charge of all anions in the solution to the supporting electrolyte concentration C,22 turned out to be closely related to another parameter from the earlier studies, called the excess space charge density qex.25 The latter interacts with the electric field in the fluid and is responsible for the appearance of volume electric forces, which lead to the onset of the EHD convection. Now, it is also important to note the following experimental fact about the critical parameters for self-organization, the required voltage ∆U for the appearance of the EHD convective pattern in a non-conducting non-electroactive organic fluid


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decreases from tens of kilovolts to a few volts after addition of even small amounts of conducting species.25 The initially experimentally confirmed critical value of the Rae = 99 for non-conducting fluids appeared to be invalid for the systems with symmetrical (so-called bipolar) charge carriers injection. In such electrochemical systems, lower critical voltages were needed for the onset of the EHD convection, and the new critical value of the Rae decreased to 46. A similar observation was made for the aqueous oxalic acid solution for PAOX formation, where P systematically decreased with higher electrolyte concentration.31 This situation is also consistent with our current experimental observations for PAOX cell formation in sulphuric acid electrolyte (see Table 1): the critical value of the criterion P drops from 0.334 to 0.033, as the supporting electrolyte concentration increases from 0.05 M to 0.3 M (also see Fig. 5 for graphic comparison). Unfortunately, in contrast to the previous studies of non-conducting organic liquids and determination of Rae, the estimation of P in the absolute absence of charge carriers in an aqueous system remains elusive for a number of reasons. First, the electrochemical cell will never be completely ion-free due to the dissociation of water molecules and participation of water in redox-reactions. Second, although water is the electro-active substance for alumina synthesis, aqueous systems with pH ≥ 4 (i.e. at extremely low acid concentrations) are incompatible with pore formation, what makes the ex situ microscopic analysis impossible. Thus, the PAOX electrochemical cell always includes a complex combination of many interrelated parameters, which are difficult to isolate and study separately. The interpolated dependence of the criterion for self-ordering P on the supporting electrolyte concentration can be expressed as:

= 0.824 . + 0.033


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where 0.033 is equal to the critical value of P for 0.3 M anodizing electrolyte. Although the physical meaning of the concentration-dependent increment still needs to be clarified, all experimentally observed points obtained for the critical values of the criterion P coincide with the exponential fitting curve with practically no scattering. Thus, there is obviously a strong functional correlation between the critical parameter P for cell pattern appearance and the electrolyte concentration. This evidence is consonant with the previously obtained results for the PAOX growth in oxalic acid electrolytes of different concentrations (see Fig. S4 of the Supporting Information file for the comparison of P-C curves from both studies).31 Thus, our present report gives convincing reason to think that the EHD nano-convection model can be generalized to self-ordering in porous alumina films irrespective of the chemical nature of electrolyte.

4. Conclusions To sum up, we introduced some new principles of honeycomb anodic alumina formation and demonstrated that the growth of highly ordered porous films is possible in H2SO4 electrolyte solutions with very low concentrations (6-45 times smaller, than previously known for mild anodization conditions).12, 14-15 The criterion number for self-organization P appears to be nonconstant for different supporting electrolyte concentrations, namely, there is a clear damped exponential functional relationship. This finding explains the earlier difficulties with prediction of new self-ordering voltages for different electrolyte compositions with modulated properties (with large deviations of such parameters as viscosity, electric conductivity, and pH from classical solutions), when P was kept unchanged.26 For the first time, the found exponential relationship helps to adjust P correctly for new unexplored diluted sulphuric acid electrolyte


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compositions, and thus facilitates the design and optimization of future anodization experiments. The explanation for the observed behavior of P is based on the concept of self-organized electrohydrodynamic (EHD) convection. As our results indicate, there is ample experimental evidence to support this idea. For example, a drastic decrease of the criterion number P with increased supporting electrolyte concentration is similar to the response of the electrical analogue of Rayleigh number Rae, which determines the conditions for the onset of the EHD convection in other systems, to the changes of charge carriers amount in the liquid. The rapid non-linear increase of the electrical current (so-called ‘aluminum burning effect’) under certain critical applied voltage can be also explained by the onset of the EHD convection, which leads to variable electrical resistance of the solution. In a certain way, our new results challenge current thinking about the origin of self-organization in porous alumina. Although the idea of EHD nano-convection has been expressed before,24,

31

another hypothesis based on the existence of

local interfacial tension gradients (Bénard-Marangoni instability) is still prevailing in contemporary literature.25 Supported by the previous study of the self-organization process in oxalic acid solutions,31 our present work gives the clue to the role of the EHD nano-convection in the formation of the honeycomb PAOX pattern irrespective of the type of electrolyte. Results from this work cast a new light on the self-ordering process, and can help turn the study of structure-forming role of the EHD nano-convection in PAOX layers into an experimental science.


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AUTHOR INFORMATION Corresponding Author * [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The contribution of Dorian Müller-Borges into the experimental part of this work is gratefully acknowledged. ASSOCIATED CONTENT Supporting information available: SEM images and photographs of aluminum foils anodized at voltages above the optimized ones for the best hexagonal pore ordering. This material is available free of charge via Internet at http://pubs.acs.org.


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REFERENCES 1.

Jani, A. M. M.; Losic, D.; Voelcker, N. H., Nanoporous Anodic Aluminium Oxide:

Advances in Surface Engineering and Emerging Applications. Prog. Mater. Sci. 2013, 58, 636704. 2.

Fu, J. P.; Mao, P.; Han, J., Artificial Molecular Sieves and Filters: A New Paradigm for

Biomolecule Separation. Trends Biotechnol. 2008, 26, 311-320. 3.

Bohn, P. W., Nanoscale Control and Manipulation of Molecular Transport in Chemical

Analysis. Annu. Rev. Anal. Chem. 2009, 2, 279-296. 4.

Wu, S. M.; Wildhaber, F.; Vazquez-Mena, O.; Bertsch, A.; Brugger, J.; Renaud, P.,

Facile Fabrication of Nanofluidic Diode Membranes Using Anodic Aluminium Oxide. Nanoscale 2012, 4, 5718-5723. 5.

Pashchanka, M., Engstler, J., Schneider, J. J., Siozios, V, Fasel, C., Hauser, R., Kinski, I.,

Riedel, R., Lauterbach, S., Kleebe, H. J. et al., Polymer-Derived Sioc Nanotubes and Nanorods via a Template Approach. Eur. J. Inorg. Chem. 2009, 23, 3496-3506. 6.

Masuda, H.; Ohya, M.; Asoh, H.; Nishio, K., Photonic Band Gap in Naturally Occurring

Ordered Anodic Porous Alumina. Jpn. J. Appl. Phys. Part 2-Lett. 2001, 40, L1217-L1219. 7.

Zhang, Y.; Son, S. J.; Ju, H., Anodized Aluminum Oxide Membranes of Tunable

Porosity with Platinum Nanoscale-Coating for Photonic Application. Curr. Appl. Phys. 2012, 12, 1561-1565. 8.

Mata-Zamora, M. E.; Saniger, J. M., Thermal Evolution of Porous Anodic Aluminas: A

Comparative Study. Rev. Mex. Fis. 2005, 51, 502-509.


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Page 19 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


9.

Wehrspohn, R. B., Schilling, J., Choi, J, Luo, Y, Matthias, S., Schweizer, S. L., Müller,

F., Gösele, U., Lölkes, S., Langa, S. et al., Electrochemically-Prepared 2d and 3d Photonic Crystals. In Photonic Crystals: Advances in Design, Fabrication, and Characterization., Busch, K., Ed. Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, 2004; pp 63-84. 10. Wang, C. C.; Lu, H. C.; Liu, C. C.; Jenq, F. L.; Wang, Y. H.; Houng, M. P., Improved Extraction Efficiency of Light-Emitting Diodes by Modifying Surface Roughness with Anodic Aluminum Oxide Film. IEEE Photon. Tech. Lett. 2008, 20, 428-430. 11. Zhao, L. R.; Wang, J.; Li, Y.; Wang, C. W.; Zhou, F.; Liu, W. M., Anodic Aluminum Oxide Films Formed in Mixed Electrolytes of Oxalic and Sulfuric Acid and Their Optical Constants. Physica B 2010, 405, 456-460. 12. Schneider, J. J.; Engstler, N.; Budna, K. P.; Teichert, C.; Franzka, S., Freestanding, Highly Flexible, Large Area, Nanoporous Alumina Membranes with Complete through-Hole Pore Morphology. Eur. J. Inorg. Chem. 2005, 12, 2352-2359. 13. Masuda, H.; Fukuda, K., Ordered Metal Nanohole Arrays Made by a 2-Step Replication of Honeycomb Structures of Anodic Alumina. Science 1995, 268, 1466-1468. 14. Masuda, H.; Hasegwa, F.; Ono, S., Self-Ordering of Cell Arrangement of Anodic Porous Alumina Formed in Sulfuric Acid Solution. J. Electrochem. Soc. 1997, 144, L127-L130. 15. Sulka, G. D.; Parkola, K. G., Anodising Potential Influence on Well-Ordered Nanostructures Formed by Anodisation of Aluminium in Sulphuric Acid. Thin Solid Films 2006, 515, 338-345.


19


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 29

16. Masuda, H.; Takenaka, K.; Ishii, T.; Nishio, K., Long-Range-Ordered Anodic Porous Alumina with Less-Than-30 Nm Hole Interval. Jpn. J. Appl. Phys. Part 2-Lett. & Express Lett. 2006, 45, L1165-L1167. 17. Thompson, G. E., Porous Anodic Alumina: Fabrication, Characterization and Applications, Thin Solid Films, 1997, 297, 192-201 18. Singh, G. K., Golovin A. A., Aranson, I. S., Formation of Self-Organized Nanoscale Porous Structures in Anodic Aluminum Oxide, Phys. Rev. B, 2006, 73, 205422 19. Zhou, W. Z., Su, Z. X., Hahner, G., Investigation of the Pore Formation in Anodic Aluminium Oxide, J. Mater. Chem,, 2008, 18, 5787-5795 20. Zhou, W. Z., Su, Z. X., Formation Mechanism of Porous Anodic Aluminium and Titanium Oxides, Adv. Mater., 2008, 20, 3663-3667 21. Houser, J. E., Hebert, K. R., The Role of Viscous Flow of Oxide in the Growth of Selfordered Porous Anodic Alumina Films, Nat. Mater., 2009, 8, 415-420 22. Pashchanka, M.; Schneider, J. J., Origin of Self-Organisation in Porous Anodic Alumina Films Derived from Analogy with Rayleigh-Benard Convection Cells. J. Mater. Chem. 2011, 21, 18761-18767. 23. Pashchanka, M.; Schneider, J. J., Experimental Validation of the Novel Theory Explaining Self-Organization in Porous Anodic Alumina Films. Phys. Chem. Chem. Phys. 2013, 15, 7070-7074. 24. Sha, J.; Lu, S. J.; Su, Z. S.; Zhou, W. Z., Ionic Nano-Convection in Anodisation of Aluminium Plate. Chem. Commun. 2009, 37,5639-5641.


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Page 21 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25. Orlik, M., Self-Organization in Electrochemical Systems II; Springer-Verlag: Berlin Heidelberg, 2012, p 448. 26. Stepniowski, W. J.; Norek, M.; Michalska-Domanska, M.; Forbot, D.; Krol, A., Study on the Correlation between Criterion Number Derived from Rayleigh-Benard Convective Cells and Arrangement of Nanoporous Anodic Aluminum Oxide. Mater. Lett. 2014, 125, 124-127. 27. Wang, H.; Wang, H. W., Analysis on Porous Aluminum Anodic Oxide Film Formed in Re-OA-H3PO4 Solution. Mater. Chem. Phys. 2006, 97, 213-218. 28. Baranowski, B., The Electrochemical Analogon of the Bénard Instability Studied at Isothermal and Potentiostatic Conditions. J. Non-Equilib. Thermodyn. 1980, 5, 67-72. 29. Li, F. Y.; Zhang, L.; Metzger, R. M., On the Growth of Highly Ordered Pores in Anodized Aluminum Oxide. Chem. Mater. 1998, 10, 2470-2480. 30. Michelson, C. E., Current-Voltage Characteristics of Porous Anodic Oxides on Aluminum. J. Electrochem. Soc. 1968, 115, 213-219. 31. Pashchanka, M.; Schneider, J. J., Evidence for Electrohydrodynamic Convection as a Source of Spontaneous Self-Ordering in Porous Anodic Alumina Films. Phys. Chem. Chem. Phys. 2016, 18, 6946-6953. 32. Diggle, J. W.; Downie, T. C.; Goulding, C. W., Dissolution of Anodic Oxide Film on Aluminium in a Sulphuric Acid Solution. Comment on Paper by Nagayama and Tamura. J. Electroanal. Chem. 1968, 18, 192-193. 33. Zhang, X. Y.; Zhang, L. D.; Zheng, M. J.; Li, G. H.; Zhao, L. X., Template Synthesis of High-Density Carbon Nanotube Arrays. J. Cryst. Growth 2001, 223, 306-310


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34. Ono, S.; Saito, M.; Asoh, H., Self-Ordering of Anodic Porous Alumina Induced by Local Current Concentration: Burning. Electrochem. Solid State 2004, 7, B21-B24. 35. Martin, J.; Manzano, C. V.; Caballero-Calero, O.; Martin-Gonzalez, M., High-AspectRatio and Highly Ordered 15-nm Porous Alumina Templates. ACS Appl. Mater. Interfaces 2013, 5, 72-79. 36. Schneider, J. M.; Watson, P. K., Electrohydrodynamic Stability of Space-Charge-Limited Currents in Dielectric Liquids 1. Theoretical Study. Phys. Fluids 1970, 13, 1948-1954.


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Table 1. Measured parameters of H2SO4 solutions at 0 °C, calculated and experimentally refined voltages, observed pore diameters dp, and revised values of the criterion P Concentration Measured macroscopic solution parameters

0.3 Ma 0.2 M 0.1 M 0.05 M a

η (cP)

σ (mS/ pH cm)

|qav|

Critical ∆U Initial d / Dint Calculated (V) refined p dp (nm) after b ∆U (V) by (nm) optimization experimentc

Specific numerical values of P

1.88

192

0.88

0.44

-

-

27a

22a

1.85

127

1.07

0.43

32 ± 13

-

28

21 ± 1 / 74 0.051 ±3

1.83

68

1.21

0.62

12 ± 5

6±1

29

21 ± 3 / 73 0.144 ±2

1.81

36

1.44

0.73

5±2

7±1

30

22 ± 4 / 82 0.334 ±4

0.033

Solution properties are taken from Ref. [22], optimized ∆U and corresponding dp from

Ref. [14, 33]. b

Approximated to whole numbers.

c

Determined by the optimal combination of such morphological features as the size of long-

range ordered domains and regular hexagonal shape of defect-free cells containing single pores.


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Figure 1. SEM micrographs of porous anodic alumina films formed in 0.2 M sulphuric acid electrolyte at 26 V and 28 V anodization voltages. All images are taken at consistent 500 000x and 150 000x magnifications. The samples, synthesized at voltages exceeding 28 V, are depicted in Fig. S1 of the electronic Supporting information file.


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Figure 2. SEM examination of the PAOX films obtained from 0.1 M sulphuric acid electrolyte at different anodization voltages (close-up images are taken at 500 000x magnification, and overall views at 150 000x). Further microscopic analysis including tested voltages above 29 V is demonstrated in the Fig. S2 of the Supporting information file.


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Figure 3. SEM micrographs of the PAOX films formed in 0.05 M sulphuric acid electrolyte at different anodizing voltages. The best hexagonal structure could be achieved at 30 V. Porous oxide formation at voltages above 30 V was disturbed by ‘aluminium burning effect’ and damage of substrate due to intensive anodic dissolution (see Fig. S3 of the Supporting information file).


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Figure 4. Comparison of initially expected process windows (calculated using P = 0.057 ± 0.024) and experimentally optimized ∆U for different electrolyte concentrations.


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Figure 5. Damped exponential dependence of the critical number P on the sulphuric acid supporting electrolyte concentration.


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TOC graphic


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Self-Ordering Regimes of Porous Anodic Alumina Layers Formed in

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