Formation of Porous Anodic Alumina under Unstable

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Formation of Porous Anodic Alumina Under Unstable Electroconvection Flow Regimes: A Case Study of Tartronic Acid Electrolyte Mikhail Pashchanka, and Joerg J. Schneider J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06157 • Publication Date (Web): 26 Sep 2017 Downloaded from http://pubs.acs.org on September 26, 2017

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The Journal of Physical Chemistry

Formation of Porous Anodic Alumina under Unstable Electroconvection Flow Regimes: A Case Study of Tartronic Acid Electrolyte

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]

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ABSTRACT

This work focuses on the systematic study of porous anodic alumina films grown in novel moderately concentrated tartronic (2-hydroxymalonic) acid electrolyte. The morphological analysis enabled us to reveal new details of the alumina pore formation mechanism and to discover the processes responsible for such frequently occurring defects as branched pores and multiple pore openings within a single cell. The qualitatively new model developed herein explains satellite nanochannels formation from a colloidal electroconvection standpoint – namely, by the temporary change of the existing nanoconvective flows, which give rise to the cooperative cell pattern in porous alumina, from laminar to turbulent mode (such flow regimes are generally termed “transitional”, or in some recent literature also “laminar unstable”). Our theoretical discussion demonstrates that the morphological parameters of self-organized layers are strongly related to such properties of the liquid phase as the dielectric constant and the Debye length of the electrolyte solution. Additionally, we have conducted a detailed thermogravimetric study of the compositional and thermal properties of the new type of anodic alumina layers.


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1. Introduction Widening the range of suitable electrolytes for the synthesis of self-organized porous anodic aluminum oxide (PAOX) membranes is one of the current problems in contemporary synthetic electrochemistry.1-5 First of all, experimental data accumulation and discovery of similarities and regular dependences allow generalizing the principles of pore formation irrespective of the electrolyte chemical nature. From a practical point of view, different compositions enable to control the key morphological features of the alumina layers, like the inter-pore distances (or the cell sizes) Dint, and the pore diameters dp. These parameters determine such crucial property of PAOX as the porosity P, which can be calculated according to the following equation: =

√

(1)

where rp is the pore radius dp/2.6-7 Although PAOX systems always contain a certain number of irregular shaped cells and pores, they are all assumed in eq (1) to be idealized circles and hexagons. Nielsch et al. proposed that the optimal pore ordering in PAOX always results in 10% porosity and a constant rp/Dint ratio irrespective of the anodizing conditions (in fact, the actual porosities of the examined well-ordered anodic layers varied in this work between 8 and 12 percents).6 According to that work, any deviation from the optimal self-ordering conditions, i.e. a successful combination of the anodizing voltage and pH, will result in porosities significantly larger or smaller than 10%. However, there are a number of studies dealing with porosity modulation by different methods. For example, pore radii can be tuned while keeping Dint practically constant by addition of polyethylene glycol to the aqueous electrolyte solution in different proportions.7-8 Moyen et al. reported the decrease of porosity to 3.5% by using a galvanostatic pre-treatment of aluminum followed by potentiostatic porous alumina growth.9 The “10% porosity rule” can be also violated in single solute electrolytes (without additives) under


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simple classical oxidation conditions. For instance, the porosity of well-ordered layers formed in 0.3 M selenic acid at 48 V was only 0.8 %.10 All these examples suggest that the regularity in pore layout can be determined by some additional factors besides the tendency to 10% porosity. Thus, it would be interesting to find a working fluid where the assumed processes that control regular patterning are not entirely concurrent, but predominate within different ranges of anodization conditions. This would facilitate the investigation of their influence, and possibly even help to reconsider our current understanding of the favorable self-ordering conditions. In our previous work, we demonstrated the growth of disordered porous-type alumina thin films using the novel tartronic (2-hydroxymalonic, HOOC-CH(OH)-COOH) acid electrolyte.11 Herein, we conduct a detailed systematic research into the self-ordering behavior of layers formed in 0.3 M tartronic acid within a broad range of applied potentials (40-140 V). We analyze diverse morphological parameters of the resulting films (regularity of geometric shapes of cells, character of occurring defects, size distributions for dp and Dint, relationships between the applied voltage and dp/Dint or P), and show that the tendency to 10% porosity and to the best pore and cell uniformity are separated for this electrolyte in individual voltage ranges. We also obtain this new PAOX type as free-standing macroscopic films and thoroughly characterize their morphology and non-stoichiometric composition by electron microscopy and thermogravimetry methods. This experimental study allowed us to observe a new type of morphological features in PAOX, i.e. meander-shaped protuberances, which are oriented along the pore growth direction and accompany pore branching points close to the pore bottom. We explain these features using the concepts of the colloidal nanoconvection model, and propose a new universal formation mechanism of such frequently observed defects, as multiple pore openings within a single polygonal cell, or nanochannel branching. We were able to associate these two visually different


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types of imperfections with each other, and consider them both as resulting from the same underlying phenomena, which take place under non-optimal (transitional between self-ordering and chaotic) anodization regimes. These defects can thus be attributed to the occurrence of socalled transient “electroconvective turbulence” within growing nanochannels.12 We consider the ionic flows under non-optimal conditions as transitional, inherently unstable, and sensitive to small flow perturbations which can disrupt them and temporarily change the flow regime from laminar to partly turbulent. Since motions of the electrolyte-containing fluid trace out the shapes of formed nanochannels, such flow disruptions may result in irregular pore morphologies.

2. Experimental section Anodic alumina was synthesized in a standard thermostatically controlled (0.5 ± 0.2 °C) and vigorously stirred potentiostatic electrochemical cell with parallel-plate aluminum electrodes, using a Sorensen XEL 250 DC power supply (∆Umax = 250 V, ∆Imax = 0.37 A) and a Lauda RM 6 cryostat. The electrolyte was prepared from tartronic acid (≥ 97.0 wt.-%, Sigma-Aldrich) and deionized water (σ ≈ 4 µS cm-1) using analytical volumetric flasks. The prior electropolishing step for commercial aluminum sheets was eliminated (Puralux®, purity 99.93%, thickness 1 mm). It was previously found that long preliminary oxidation in a two-stage anodization process (originally discovered by Masuda et al.13) is able to flatten natural defects on aluminum similarly to electropolishing; it was also reported by Ono et al. and Kikuchi et al. that electropolishing cannot be adapted in electrolytes with low dissociation constants and low concentrations because it retards the pore nucleation process and delays the formation of porous-type alumina.1, 5 For all tested voltages, aluminum was preliminary anodized for 8 hours, and the resulting alumina was then removed in an etching aqueous mixture (0.16 M K2Cr2O7 and 1.5 M H3PO4). The duration


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of the main anodization step was 20 hours in all cases, except for 72 hours for the preparation of mechanically stable free-standing films at 110 V. For scanning electron microscopy (SEM) and thermogravimetric analysis (TGA), these 110 V films were accurately detached from supporting metallic substrates using the polarity reversal method (the absence of Al residues on the basal side was confirmed by the high resolution HRSEM monitoring).14-15 In this method, alumina films are first separated from aluminum due to H2 gas generation at the metal/oxide boundary, and then mechanically lifted. All samples were afterwards thoroughly rinsed with deionized water and dried in a desiccator at 60 °C. Alumina layers were microscopically analyzed on a Philips XL30-FEG at the accelerating voltage of 20 kV and 5 mm working distance (selected spot size 3). For this purpose, they were mounted on a carbon-rich conductive polymeric film and coated with Pt/Pd alloy by magnetron sputtering (nominal coating thickness 4.5 nm). TGA data was obtained on a Netsch STA 449C Jupiter at a heating rate of 10 °C min-1 from ambient temperature to 1450 °C, using synthetic air atmosphere (flow rate 75 mL min-1). Statistical calculations were performed for 10 random dp or Dint measurements from HRSEM images. Confidence intervals for size distributions were defined by the significance leve α = 0.05 (all values were rounded up to whole numbers in nanometers to bring the calculated results to conformity with the microscope resolution). During the specific current density calculations (j, A m−2), the complete surface area of the anodes (the front side, the backside, and the lateral faces) was taken into account. The electric current values ∆I were estimated from multiple readings of the power supply in the middle and at the end of the main anodization step (equipment sensitivity is 0.1 mA).


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3. Results and discussion The results of the systematic microscopic investigation of the porous layers obtained from 0.3 M tartronic acid electrolyte in the voltage range between 40 and 140 V are demonstrated in Figure 1 (see Figure S1 of the Supporting Information file for the more detailed report with smaller voltage increments). It is evident from the micrographs that individual hexagonal cells can be found under practically all tested anodizing conditions. The definition of cell shapes visibly improves with the increase of the applied voltage, and the best results can be observed in the range between 80 and 120 V. The best pore uniformity can be also noticed at around 90 V (see the corresponding image in Figure S1). However, no ideal long-range ordering could be observed at any tested voltage, and the largest hexagonally arranged domains contained only about 10 pores. When the applied voltages exceed 120 V, the number of defects, such as multiple pores within a cell, or triangular pores instead of round, considerably increases. A similar change of pore shapes from circles to polygons has been previously reported upon application of longer anodization times.6 In our experiments, we observe a similar effect upon the increased anodization voltage, which suggests that there might be an equivalence of these two factors, and that some morphological features can be possibly tuned using different superposition of the anodizing voltages and durations. The preliminary comparison of SEM-images also shows that the dp/Dint ratio above the voltages of 90-95 V is noticeably small, which means a low pore density and extraordinarily low porosities at the increased process voltages. Figure 2 shows the dependency of steady-state current density j on the applied potential difference. Similarly to three most commonly used electrolytes (H2C2O4, H2SO4, H3PO4), 0.3 M tartronic acid exhibits a steep exponential curve within the range of the optimal self-ordering voltages.16 However, in contrast to the widely employed 0.3 M solution of dicarboxylic oxalic


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acid, tartronic acid yields remarkably lower current densities at identical voltages. The same values of j that are established in oxalic acid at around 30 V, could be reached in equally concentrated tartronic acid electrolyte only at 130-140 V. As can be concluded from the slope of the interpolation curve in Figure 2, the voltages above 140 V approach the critical voltage, after which the electrical breakdown may possibly occur. The resulting alumina coating acquired dark coppery-brown color at 150 V (see corresponding SEM images of the morphology at 150 V in Figure S1). Such drastic color changes at high current densities often manifest approaching to the critical maximum potential, where the phenomenon called “burning” takes place.17 As one can see in Figure 2, the experimental point at 140 V slightly deviates from the fitting curve towards lower values. This can be the effect of an increased PAOX growth rate and the resulting film thickness, and, consequently, a larger ohmic resistance of the coating. Another possible explanation of this deviation is based on the current density versus voltage (j-∆U) curves that cover the whole range of mild and hard anodization (MA and HA, respectively) potentials. According to Vega et al., the MA self-ordering interval (where current rises exponentially) is separated from the HA interval by a local maximum and a short plateau region due to some current-limiting mechanisms.18 Within this current plateau interval, no ordered domains can be microscopically observed due to the rearrangement of pores and their adjustment for the HA conditions. When the HA voltage is reached, j keeps on decreasing with the increased ∆U. This was associated with the fast enlargement of the nanochannels length, which imposes diffusive limitations for the electrolyte ions when they are transported towards the pore bases where the electrochemical reaction takes place.18 However, the progressively increased HA voltage finally results in a drastic amplification of the current density leading to so-called “dielectric breakdown” and damage of the anodic layer (“burning”). Thus, slowing down of the current


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density growth at 140 V in Figure 2 may denote the end of the MA interval and transition to the current plateau. In fact, the observed structural coloration of the PAOX films at 150 V is in most cases a sign of the burning process initiation, but needs not necessarily be. It has to be mentioned that j-∆U curves strikingly similar to reported by Vega et al.18 are common for many electrochemical systems (e.g. dealing with electrolysis or electrodeposition) in which the electroconvection helps to overcome the diffusive transport limitations.12 Such systems also show characteristic current plateau regions where j does not increase with ∆U due to achieved transport saturation. However, upon further increase of the voltage above a certain critical value, the so-called “overlimiting current” is observed and j continues to increase owing to the electroconvective transport.12 This model explains why the PAOX system enters the disordered regime with pores rearrangement between two self-ordering modes: while the large vortices (corresponding to the larger HA cells in porous alumina) grow with the increased voltage, the initial MA nanoconvective cells shrink and become ineffective in charge transport. According to this model, controlling transport mechanisms under MA and HA regimes have to be qualitatively the same, but the current densities during hard anodization have to increase dramatically because large-scale electroconvective flows can drive much larger currents. In Figure 3, the variation of the pore sizes dp depending on the applied potential difference is presented. The early studies of PAOX formation posited that pore diameters increase linearly with higher applied voltage.19 This statement was based on the comparison between porous layers obtained at different voltages from different electrolytes and a misleading concept that the electrolyte type has only minor effect on dp, which depends mainly on the voltages applied. Later investigations showed that the aggressiveness of an electrolyte noticeably affects the alumina dissolution rates and the pore radii, which are determined by the pH-value.6 From this


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perspective, however, obtaining of the smallest pores from H2SO4 electrolytes with the lowest pH values should not be expected. Our experimentally obtained non-linear relationship resembles the earlier reported dependency between dp and ∆U, which was tested on different anodization conditions in 0.3 M oxalic acid electrolyte.20 Comparison of the data from both works confirms that similar rules can be applied for description of the relative changes in dp in a wide range of voltages regardless of the specific electrolyte type. Figure 4 illustrates the dependency of the interpore distance Dint on the applied anodization voltage. It has been earlier shown for a number of different electrolytes that the interpore distances Dint are linearly dependent on the applied voltage ∆U with the proportionality factor k ≈ 2.5 nm V-1.1-2,

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This regularity is also confirmed for the layers obtained in our work (see

Figure 4), however, the proportionality constant k slightly deviates from previously mentioned in literature towards smaller values and is equal to 2.227 nm V-1. Bearing in mind the trends demonstrated in Figures 3 and 4, dp does not undergo a proportional increase in size between 90-140 V, although Dint increases constantly across the whole range of tested voltages. Additionally, based on the previous observations from Figures 1 and S1, the layers obtained at the voltages above 90-95 V exhibited low pore density and low porosity P. Now, based on Figures 3 and 4, one can quantitatively establish relationships between dp/Dint and P (using the eq (1)) and applied voltages, and also determine the values of these both parameters corresponding to the best self-ordering conditions. It has been reported by Ono et al. that the dp/Dint ratio aims at 0.3 when the applied voltages approach the self-ordering voltage, regardless of the electrolyte type.16 According to this previous finding, the best self-ordering in 0.3 M tartronic acid should happen at 50-80 V (see Figure 5). However, the SEM monitoring of the samples (see Figures 1 and S1) points to the


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conclusion that the best self-ordering conditions are achieved at slightly higher voltages (90-110 V), where the dp/Dint ratio drops to 0.28-0.20. A similar mismatch with the earlier postulates can be noticed if a comparison of the film porosities P at the different applied voltages is made (Figure 6). Nielsch et al. established that 10% porosity leads to optimally ordered pore growth, irrespective of the specific anodization conditions.6 Later, it was shown that the porosity of 10% is not only the optimal one, but also the minimal one for the self-ordered films obtained from classical electrolytes.16 Taking into account these considerations and the data plotted in Figure 6, optimized pore ordering conditions can be expected for diluted tartronic acid between approximately 40 and 60 V. Nevertheless, the tendency to the best pore size uniformity and cell shape definition was observed in the range of voltages, where the porosities go down to 7.24.2%. Although we are not dealing with regular defect-free structures in this work, the foregoing observations still suggest that the self-ordering is possibly determined not only by the resulting porosity number. One of the other key influencing factors can be the current density j that reached stable measurable values in our experiments only starting from approximately 70 V. In our earlier work we proposed the idea that j characterizes the velocity of the electrochemical reaction, which is responsible for the smoothing of natural defects on aluminum surface and appearance of the regular cell pattern.11 Thus, a higher j can improve the pore ordering after the first long preliminary oxidation, although the layers may not match the “10% porosity rule” at higher voltages. The important role of high ∆U to induce high j while preventing the “burning effect” was also noticed by other researchers.5 Thus, tartronic acid can potentially serve as electrolyte where different controlling parameters are separated to some extent, and their influence on the self-organization process can be studied more independently than in the most commonly used acids.


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For the demonstration of mechanical stability and usability of the new type of PAOX layers, we have conducted anodic oxidation at 110 V, followed by separation of the samples from aluminum substrate using the polarity reversal technique (see Figure 7A). After the experiment of 72 hours duration, the resulting film thickness constituted 37.2 ± 0.1 µm (see Figure 7B), which means that the average growth rate under such conditions is slightly above 0.5 µm h-1. The top-side microscopic images (Figures 7C and 7D) show that the cells have only a moderate spread in sizes. However, a large fraction of cells contains irregular shaped pores and multiple pore openings, which imply an unstable pore formation mode at 110 V. Bottom-views under the SEM (Figures 7E and 7F) confirm the absence of metallic substrate residues after PAOX layer detachment, which makes the samples suitable for precise thermogravimetric compositional analysis. An interesting morphological feature can be seen in the cross-section SEM images (Figures 7G and 7H), namely the distinctive rounded protuberances at the pore splitting points (see Figure 7H, left). These protuberances typically accompany nucleation of new pore satellites on fracture side views, and suggest an ejection of a quickly setting material from the metal/oxide interface along to the pore growth direction. This new empirical evidence certainly needs to be explained, and may also update our knowledge about the pore deepening process and enable us to propose a new qualitative description of the pore branching mechanism. According to the earlier postulate of Nielsch et. al., the barrier layer thickness equal to one half of the Dint guarantees that no new pores nucleate between the existing pores.6 As one can see from Figure 7G, the barrier layer thickness is fairly uniform and reproducibly equals to approximately 130 nm, which is close, but slightly larger than expected according to the Dint = 222 ± 10 nm. This, probably, assures the constant instability and favorable conditions for pore satellites formation at the early stage of the growth (this can be microscopically observed on the top surface as multiple


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pore openings within a cell), and for pore branching at the later stages (this is observed on the film cross-sections), which makes our present PAOX sample formed in tartronic acid almost an ideal system for the study of these both phenomena. Pore branching is also attributed by some authors to the different longitudinal pore growth rates: deeper pores are considered to have the tendency to splitting and bring imperfections into the ordered structure.21 Deeper channels are supposed in this model to exhibit oxide growth in both the longitudinal and lateral directions, which can lead to the pore branching and termination of neighboring pores. Since the ion transport through branched nanochannels under the high voltage conditions is restricted by the pore total cross-sections ratio (before and after the splitting points), the branched pores cannot maintain the same growth rates as the neighboring straight pores and also tend to termination. The reduced number of pores then results in the increased average Dint. While the descriptive part of this model is quite accurate and touches upon numerous experimentally observed morphological features, the origin of pore branching still needs to be explained. For instance, the reasons for the lateral pore growth are not entirely clear, if the growth rates are supposed in this model to be determined by diffusion. Of course, local gradients of concentrations and the electrical field are known to give rise to the diffusion and migration transport components directed in parallel with the anode surface, but the relative contribution of such lateral diffusion components in self-organized electrochemical systems is usually only minor, and can be often neglected.22 In addition, if the aluminum electrode is treated as conductor, then it also needs to be isopotential.23 Thus, the contribution of local electric field variations can be only considered when special additional conditions for their appearance are accurately specified. Furthermore, according to the principles of electrostatics, the electric field just outside the perfect conductor is normal to the surface, and consequently there are no ionic currents tangential to the surface.23


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The components of the electric field tangential to the surface can exist outside the electrode either if we deal with an insulator23 (this supposition is inconsistent with the known PAOX formation models because they all imply electromigration of aluminum and hydroxide ions through the barrier layer), or if there exist some variations in geometric or chemical surface properties.12 In the latter case, however, electroconvective flows are induced, which have never been considered for the pore branching mechanism explanation so far. Recently, we have proposed a phenomenological model that explains the self-organization in PAOX from the electrohydrodynamic nanoconvection standpoint.11,

24-26

Briefly, this theory considers the

cooperative motion of hydrated electrolyte ions and charge-stabilized alumina particles, driven by a complex interplay between Coulomb attraction forces and the oppositely directed diffusion. The meander-shaped protuberances that we observe in this work at nanochannel splitting points (Figure 7H and SEM images in Figure 8) are in full agreement with the colloidal nanoconvection model, and can even elucidate the pore branching mechanism. As demonstrated in Figure 8A, the electrolyte anion fluxes, and the oppositely directed fluxes of charge-stabilized colloidal particles, self-organize into a ring-like system of cyclic currents, which is similar to the one that exists within a well-studied Rayleigh-Bénard convection cell. These cyclic flow systems underlie individual porous anodic alumina cells and are responsible for the spatial pattern formation. The highly mobile electrolyte ions (which do not participate in the reduction-oxidation reaction at the anode surface) are involved into the circular motion within the ring, while less mobile and heavier colloidal particles escape from the cyclic currents and are ejected at a tangent to them (ideally, in the direction of the regular pore walls growth, i.e. perpendicular to the anode surface). In the ideal case of laminar motion, when the „upstream“ and „downstream“ flows (see Figure 8A) are separated and parallel to each other, a single straight nanochannel with smooth


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walls is formed. However, smaller and lighter colloidal particles can be ejected at angles different from the right angle to the substrate surface, and thus intersect and disturb the “downstream” anion flows, also changing their direction. Under such conditions, if the streams are no more parallel and are mixed with each other, the flows will temporarily change to transitional (i.e. containing random vortex-type structures), which creates favorable conditions for satellite pores formation (Figure 8B). The number of channel branches after such bifurcation is determined by the number of protuberant “upstream” flows that are ejected from a threedimensional ring-like system at abnormal angles, and is therefore not necessarily restricted to two, as it may seem from the two-dimensional schematic projection in Figure 8B. This follows from the general properties of turbulent flows: they are always three-dimensional, even if confined within a symmetrical system like PAOX nanochannels.23 In the beginning of the anodizing process, before a steady-state oxidation regime is reached, ions and colloidal particles can move in complex unpredictable paths within the fluid. Since fluid flow is linked with ion flow, this creates favorable conditions for the occurrence of transient turbulence and nucleation of multiple pores within a single cell. Although the pattern regularity at the metal/oxide boundary improves with longer oxidation times, all the defects that appeared at the initial stage of the process remain microscopically visible on the top side of alumina layers. Thus, our proposed mechanism allows attributing two different types of frequently observed microscopic defects, i.e. multiple adjacent pore openings and branched nanochannels, to the same phenomena – namely, unstable transitional flow regime of the working fluid under unsteady anodizing conditions. Discovered meander-shaped protuberances also conform with the earlier proposed concept of alternate pH-regions in the vicinity of the working electrode.24 According to this model


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electrochemically generated colloidal alumina particles are at first proton-stabilized and supported in mobile condition due to the following reaction: Al + 2H2O → Al(O)OH (boehmite) + 3H+ + 3e− As these particles migrate further from the anode surface – to the next stratum of fluid with an increased pH-value (protons are not generated there anymore and are neutralized by the attracted OH− ions from water solution), they start to coagulate and build solid pore walls. Protuberances with characteristic rounded tips suggest a rapid solidification of the ejected fluidized medium (e.g. coagulation of fine suspension), and thus can indirectly confirm the viability of this earlier hypothesis. It is worth mentioning that the concept of electroconvective flows also imposes an important limitation on the minimal achievable PAOX cell size, and can therefore explain numerous failed attempts at reducing Dint below approximately 50 nm under conventional long-term potentiostatic anodization conditions. The smallest high-aspect-ratio cells that can be achieved by spontaneous self-organization under constant DC-field have been reported using 10 wt.-% H2SO4 solutions at 19-20 V.8, 15 Significantly smaller Dint have been created either by artificial pre-patterning followed by short-term oxidation,27-30 or by applying unsteady AC-anodization conditions.31 Under normal potentiostatic conditions, the counterpropagating laminar flows of negatively charged electrolyte ions and positively charged stabilized particles have to be separated. This separation and prevention of intermingling (which is preferred by the system to maintain the local electroneutrality) can be achieved by the screening of the electrostatic attraction between the oppositely charged flows. This screening exists due to the response of solvent (dipole water molecules) and dissolved ions to the local electric fields, and is called Debye-Hückel screening. The flows in fluid are usually separated by a characteristic lengthscale


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comparable to the Debye-Hückel screening lenth λD, which is a property of the electrolyte solution, and is expressed as:

=

(2)

where ε is the electrical permittivity, R is the universal gas constant, T is thermodynamic temperature, F is the Faraday constant, and Ic is the ionic strength of the bulk solution. For most of electrolyte solutions, λD has a typical length between 1 and 100 nm,23 which is of the same order of magnitude as the nanopore dimensions in PAOX (unfortunately, the concentrationdependence of ε for tartronic acid electrolyte is currently unavailable in literature, which makes the more precise estimation of λD difficult). This idea also explains why higher electrolyte concentrations are usually needed for layers with reduced Dint and higher pore densities. For example, Masuda et al. reported the decrease of Dint to 25-30 nm in a highly concentrated 8-9.4 M H2SO4 solution at elevated temperatures (such aggressive electrolyte suited only for substrate pre-patterning, but not for a stable main anodization).27 Similar trend was observed during the experiments with etidronic acid CH3C(OH)[PO(OH)2]2, where the increase of concentration from 0.2 to 4.2 M resulted in the cells size shrinkage from 640 to 400 nm.4 According to eq (2),

λD (which determines Dint in our theory) is inversely related to the ionic strength of the solution, or, in other words, to the molar concentrations of the electrolyte ions. Therefore, it becomes clear why more concentrated electrolyte solutions are able to produce smaller PAOX cell sizes. Furthermore, solid experimental evidence reinforcing our ideas has been provided by Manzano et. al., who found that low dp is the consequence of the reduction of the electrical permittivity ε of the electrolyte.32 Since the Debye length λD is proportional to the dielectric constant ε according to eq (2), this earlier experimental observation directly confirms the validity of our theory (despite a different interpretation given by the authors).


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When increasing the electrolyte concentration, another important parameter needs to be considered as well – namely, the Bjerrum length λB. The Bjerrum length defines the spacing between ions in the solution, and therefore also their concentration, at which the electrostatic ionion interactions become important. For water at 25 °C, λB is equal to 0.7 nm, and spacing between ions in aqueous electrolytes shrinks down to this length when their concentrations exceed 1 M.23 From this standpoint, obtaining a stable self-ordered structure in PAOX with subnanometer periodicity seems to be absolutely impossible because at this scale the intermingling of nanoconvective flows is practically unavoidable. For the completion of our thorough study, we have also conducted the thermogravimetric (TGA) analysis of unsupported PAOX films obtained from tartronic acid at 110 V (see Figure 9) which reveals a multi-stage decomposition process, which is mainly similar to that of samples obtained earlier from oxalic and sulfuric acids.33 The first major mass loss event starts already at the ambient temperature and continues up to 730 °C, where a short plateau of thermal stability is reached. This first main stage can be divided into two minor steps (sections (1) and (2) in Figure 9). The first one is over at approximately 230 °C and results in a 3.05 % mass change (see region (1) in Figure 9). This minor decomposition step has been previously attributed to dehydration, which includes the loss of both absorbed and coordinated water.33 Our results are in full accordance with the earlier measurements, and demonstrate a clear systematic dependency between the pore sizes and sorption properties of porous alumina films: the previously detected absorbed water content was equal to 5.7 % for 24 nm pores (obtained from sulfuric acid electrolyte), 4.2 % for 31 nm pores (from oxalic acid), and is further decreased for larger pore sizes from this work.6,

33

Of course, the changes in hydrophilic character due to the more

acidified surface obtained from stronger electrolytes cannot be neglected as well. However, it


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was reported that the absorbed water content in films with ≈ 160 nm pores (formed in H3PO4) was reduced to only 1.2 %.33 Thus, the pore dimensions very likely belong here to the main contributing factors. Interestingly, the elimination of absorbed water from the porous alumina formed in tartronic acid also required a significantly lower temperature than the earlier studied samples from classical electrolytes, which denotes a less hydrophilic character of the new material. The onset point of the second minor decomposition step, which is marked in Figure 9 as region (2) and corresponds to the slow dehydroxylation process, is located at 238 °C. Although alumina can be normally converted into practically anhydrous adsorbent at 300-400 °C, the IR-spectroscopy investigation has revealed that approximately 10 % of the oxide surface are still covered by the residual OH-groups even at the temperature of 650 °C.34 Thus, our experiment is in a good agreement with the earlier obtained data for alumina samples, which have a composition close to boehmite Al(O)OH · nH2O. The mass loss resulting from the complete removal of the surface hydroxyl groups equals to 1.97 %. The plateau of thermal stability, region (3) in Figure 9, is followed by the second major decomposition stage (4), which has the onset point at 920 °C and is finished by 1270 °C. This last event represents the decomposition of incorporated 2-hydroxymalonate anions, and the corresponding mass loss amounts to 4.93 %. This result is practically equal to the earlier reported 4.92 % mass loss due to the decomposition of oxalate-anions in alumina obtained from the classical oxalic acid electrolyte.33 If we assume that all the negative charges in both compared alumina types are balanced with Al3+ cations at this temperature (at lower temperatures, amorphous alumina has a complex polymeric non-stoichiometric composition with fractional charges on aluminium ions), and that the anionic impurities are contained in form of stoichiometric salts and undergo decomposition into Al2O3, the calculation using the experimentally obtained mass losses yields


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5.7 wt.-% of 2-hydroxymalonate anions in our initial anodic alumina, and 6.0 wt.-% of oxalate anions in the layers obtained from the widely used oxalic acid. Although the mass fractions of anionic impurities from both dicarboxylic acids are fairly close to each other, the molar content of 2-hydroxymalonate anions is approximately 1.4 times smaller than was reported for oxalate anions. Thus, despite a higher applied voltage and a larger expected ionic migration towards the deposited solid anodic films, tartronic acid has a slightly lower tendency to the inclusion into formed alumina than the previously studied oxalic acid. After the complete thermal evolution path, the residual mass of the ‘tartronic’ alumina is 90.05 %. In order to specify characteristic temperatures of the mass loss events more precisely, and to identify the thermal processes which are not necessarily associated with the mass changes, DTG and DTA characterization curves were plotted as well (Figure 10). For the first dehydration step, the DTG peak maximum (which corresponds to the temperature of the largest mass percentage change d∆m/dT = −0.1 % min−1 at the predetermined heating rate of 10 °C min−1) is located at 145 °C. There are also two peak temperatures for the main step between 920-1270 °C: at 1017 and 1217 °C (mass percentage changes −0.4% min−1 and −0.1% min−1, respectively). This confirms a complex multi-stage decomposition character of the 2-hydroxymalonate anions in the alumina matrix. The broad structureless curvature of the DTA plot before 610 °C corresponds to the endothermal dehydration and dehydroxylation processes and is followed by another minor endothermal signal centered at 636 °C. Further, there is a very prominent endothermal signal with the maximum at 893 °C, which corresponds to the plateau (3) in TGA (Figure 9) and thus cannot be associated with composition changes. It is well known that a number of intermediate phases (such as γ, δ, θ) are formed in the sequence of thermal dehydration of boehmite before the final transformation into α-corundum occurs.35 Thus, the peak at 893 °C very likely corresponds


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to the restructuring of the crystal lattice into another polymorph modification, which is more stable at the elevated temperatures. The following broad exothermal signal of low intensity centered at 1008 °C matches the 2-hydroxymalonate decomposition region in Figure 9. The last narrow peak with the maximum at 1221 °C is related to the final phase transformation into αAl2O3. It should be noted that the intermediate γ-alumina is known to be metastable and thus has excess energy. Given this fact, the interpretation of the sharp exothermal peak at 1221 °C as belonging to the final polymorphic phase transition into stable corundum is completely justified. Interestingly, the reported onset points of this final transformation for the alumina obtained from sulfuric, oxalic, and phosphoric acid electrolytes are at 1223, 1209, and 1368 °C, respectively.33 In our measurements, the onset point of this final exothermal peak is at 1201 °C. Thus, the transformation of the alumina layers from this work into α-Al2O3 begins at the lowest temperature in comparison with the earlier studied types of alumina from the most typical electrolytes.

4. Conclusions The progress in understanding the nature of self-organization in PAOX has often been limited by the frontiers of in situ analysis techniques. The details of formation mechanism are hidden from direct observation because of the complexity of anodization conditions: the nanoscale dynamic PAOX system is surrounded by corrosive aqueous electrolyte medium under applied potential on the order of tens of volts. However, the working fluid flows are known to be linked with ionic flows in the electrochemical systems where irreversible dissipative self-organization processes occur.23 The shapes of nanochannels in PAOX are thus traced out by the electrolyte solution flows during the electrochemical oxidation, which makes them very informative for the


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following detailed ex situ microscopic study of the formation mechanism. A very large (and constantly growing) number of empirical facts that can be successfully explained in the framework of electrohydrodynamic convection model give sufficient reason to think that this theory is valid. This model provides an understanding of the influence of multicomponent electrolyte parameters, such as concentrations and temperature (which determine the electric permittivity, Debye length, or Bjerrum length of the solution) on the porous alumina cell dimensions and character and number of morphological imperfections. The electroconvective flows model explains the complex shape of the j-∆U curves within the mild anodization and hard anodization voltage ranges, as well as the presence of the intermediate “chaotic” regime in between due to the rearrangement of the convective cell pattern for more effective charge transport under high voltage conditions. It also provides a completely new physical insight into the formation of such defects as multiple pore openings within a single cell or nanochannel branching, offering an explanation based on the presence of instable transitional (no longer laminar, but also not fully turbulent) flows under non-optimal anodization conditions. The development of this mechanism was possible after the discovery of new morphological features in PAOX layers formed in tartronic (2-hydroxymalonic) acid electrolyte – namely, the meandershaped protuberances at pore bifurcation points. These features possibly could not be observed for conventional electrolytes with higher dissociation constants (which are more aggressive towards amorphous alumina) because of the partial dissolution shortly after their formation. Therefore, moderately concentrated solution of comparatively weak tartronic acid appeared to be very useful for the detailed investigation of the pore branching mechanism. The flows in microscale channels are generally considered to be laminar with slow mixing, and turbulence is usually difficult to achieve, but the situation can be different for less studied nanoscale channels,


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which have diameters comparable to the molecular sizes or the Debye length of the employed electrolyte solution. Nevertheless, several factors increase the chances of turbulence occurrence within PAOX nanochannels during their growth. First, the fluid at pore bottoms is constantly stirred due to the electroconvection, and the convection is known to make mixing occurring much more quickly.23 Second, the transition between different fluid flow modes is characterized by the Reynolds number Re, which is a function of the dynamic viscosity (the Reynolds numbers corresponding to fully laminar and fully turbulent flows differ by a factor of only 1.74). In the nanoconvective model, the bottom layer of PAOX is presented during the formation as a fluidlike colloidal suspension, and rheological properties of colloidal systems are rarely described with the Newtonian model.23 The bottom layer can thus be a “shear-thinnig” fluid (i.e., the viscosity decreases upon the increase of the strain rate or, in other words, the velocity of deformation) or can have viscoelastic properties. Such nonlinear behavior can increase the mobility of the migrating colloidal alumina particles within nanochannels or even make an impact on the fluid flow regime. Of course, the electrohydrodynamic convection model of PAOX formation is currently more qualitative, than quantitative, and awaits formalization. We believe that a collective endeavor of specialists in Fluid Mechanics and Electrochemistry can make this theory a very powerful instrument in further studies of the self-organized PAOX system.


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ASSOCIATED CONTENT Supporting Information: SEM images of aluminum foils anodized at progressively increased voltages in the range between 40 and 150 V with small (5-10 V) increments are available free of charge via Internet at http://pubs.acs.org. 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 M.P. acknowledges the German Research Foundation (DFG) for the financial assistance for the conduct of this research through the grant PA 2713/1-1


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Akiya, S.; Kikuchi, T.; Natsui, S.; Sakaguchi, N.; Suzuki, R. O. Self-Ordered Porous

Alumina Fabricated via Phosphonic Acid Anodizing. Electrochim. Acta 2016, 190, 471-479. 3.

Kikuchi, T.; Nishinaga, O.; Natsui, S.; Suzuki, R. O. Self-Ordering Behavior of Anodic

Porous Alumina via Selenic Acid Anodizing. Electrochim. Acta 2014, 137, 728-735. 4.

Takenaga, A.; Kikuchi, T.; Natsui, S.; Suzuki, R. O. Exploration for the Self-Ordering of

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of Porous Alumina: The 10% Porosity Rule. Nano Lett. 2002, 2, 677-680. 7.

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Martin, J.; Manzano, C. V.; Caballero-Calero, O.; Martin-Gonzalez, M. High-Aspect-

Ratio and Highly Ordered 15-nm Porous Alumina Templates. ACS Appl. Mater. Interfaces 2013, 5, 72-79.


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Ordered Sub-10 nm Nanopore Template for Nanotechnology. Adv. Mater. 2012, 24, 5094-5098. 10. Nishinaga, O.; Kikuchi, T.; Natsui, S.; Suzuki, R. O. Rapid Fabrication of Self-Ordered Porous Alumina with 10-/Sub-10-nm-Scale Nanostructures by Selenic Acid Anodizing Sci. Rep. 2013, 3, 02748. 11. 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. 12. Davidson, S. M.; Wessling, M.; Mani, A. On the Dynamical Regimes of PatternAccelerated Electroconvection. Sci. Rep. 2016, 6, 22505. 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. Kyotani, T.; Xu, W. H.; Yokoyama, Y.; Inahara, J.; Touhara, H.; Tomita, A. Chemical Modification of Carbon-Coated Anodic Alumina Films and Their Application to Membrane Filter. J. Membr. Sci. 2002, 196, 231-239. 15. 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. 16. Ono, S.; Saito, M.; Ishiguro, M.; Asoh, H. Controlling Factor of Self-Ordering of Anodic Porous Alumina. J. Electrochem. Soc. 2004, 151, B473-B478.


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17. Aerts, T.; De Graeve, I.; Terryn, H., Study of Initiation and Development of Local Burning Phenomena During Anodizing of Aluminium under Controlled Convection. Electrochim. Acta 2008, 54, 270-279. 18. Vega, V.; Garcia, J.; Montero-Moreno, J. M.; Hernando, B.; Bachmann, J.; Prida, V. M.; Nielsch, K. Unveiling the Hard Anodization Regime of Aluminum: Insight into Nanopores SelfOrganization and Growth Mechanism. ACS Appl. Mater. Interfaces 2015, 7, 28682-28692. 19. O'Sullivan, J. P.; Wood, G. C. Morphology and Mechanism of Formation of Porous Anodic Films on Aluminium. Proc. R. Soc. London, Ser. A 1970, 317, 511-543. 20. Su, Z.; Zhou, W. Pore Diameter Control in Anodic Titanium and Aluminium Oxides. J. Mater. Chem. 2011, 21, 357-362. 21. Napolskii, K. S.; Roslyakov, I. V.; Eliseev, A. A.; Byelov, D. V.; Petukhov, A. V.; Grigoryeva, N. A.; Bouwman, W. G.; Lukashin, A. V.; Chumakov, A. P.; Grigoriev, S. V. The Kinetics and Mechanism of Long-Range Pore Ordering in Anodic Films on Aluminum. J. Phys. Chem. C 2011, 115, 23726-23731. 22. Orlik, M. Self-Organization in Electrochemical Systems II; Springer-Verlag: Berlin, 2012. 23. Kirby, B. H. Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices; Cambridge University Press: New York, 2013. 24. 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.


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25. 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. 26. Pashchanka, M.; Schneider, J. J. Self-Ordering Regimes of Porous Anodic Alumina Layers Formed in Highly Diluted Sulfuric Acid Electrolytes. J. Phys. Chem. C 2016, 120, 14590–14596. 27. 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. 28. Matsui, Y.; Nishio, K.; Masuda, H. Highly Ordered Anodic Porous Alumina with 13-nm Hole Intervals Using a 2D Array of Monodisperse Nanoparticles as a Template. Small 2006, 2, 522-525. 29. Asoh, H.; Nishio, K.; Nakao, M.; Tamamura, T.; Masuda, H. Conditions for Fabrication of Ideally Ordered Anodic Porous Alumina Using Pretextured Al. J. Electrochem. Soc. 2001, 148, B152-B156. 30. Asoh, H.; Nishio, K.; Nakao, M.; Yokoo, A.; Tamamura, T.; Masuda, H. Fabrication of Ideally Ordered Anodic Porous Alumina with 63 nm Hole Periodicity Using Sulfuric Acid. J. Vac. Sci. Technol. B 2001, 19, 569-572. 31. Pashchanka, M.; Schneider, J. J. Uniform Contraction of High-Aspect-Ratio Nanochannels in Hexagonally Patterned Anodic Alumina Films by Pulsed Voltage Oxidation. Electrochem. Commun. 2013, 34, 263-265.


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32. Manzano, C. V.; Martin, J.; Martin-Gonzalez, M. S. Ultra-Narrow 12 nm Pore Diameter Self-Ordered Anodic Alumina Templates. Microporous Mesoporous Mater. 2014, 184, 177-183. 33. Mata-Zamora, M. E.; Saniger, J. M. Thermal Evolution of Porous Anodic Aluminas: A Comparative Study. Rev. Mex. Fis. 2005, 51, 502-509. 34. Little, L. H. Infrared Spectra of Adsorbed Species; Academic Press: London, 1966. 35. Cai, S. H.; Rashkeev, S. N.; Pantelides, S. T.; Sohlberg, K. Phase Transformation Mechanism between Gamma- and Theta-Alumina. Phys. Rev. B 2003, 67, 224104


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Figure 1. Comparison of the upper side topography of PAOX films synthesized at progressively increased voltages in the 40-140 V range. All images are taken at consistent magnifications of 350 000× and 100 000×. Further microscopic analysis including additional tested voltages with smaller increments of ∆U is demonstrated in Figure S1 of the Supporting Information file.


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Figure 2. Dependence of the steady-state current density on the applied voltage during the potentiostatic oxidation of aluminium in tartronic acid electrolyte.

Figure 3. The variation of pore diameter dp with anodizing voltage for films formed in 0.3 M tartronic acid (40 to 140 V).


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Figure 4. Linear relationship between the applied potential difference ∆U and the interpore distance Dint observed during anodic alumina formation in 0.3 M aqueous tartronic acid electrolyte.

Figure 5. Dependency of dp/Dint ratio on the anodizing voltage, calculated using the mean statistical values of the pore and cell diameters.


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Figure 6. Dependency of the anodic layer porosities P, calculated using eq. (1), on the applied anodizing voltages.


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Figure 7. Photograph of an unsupported macroscopic PAOX sample obtained from 0.3 M tartronic acid solution at 110 V (A). A HRSEM cross-sectional view demonstrates the resulting film thickness after 72 h of anodic oxidation (B). Top-views (C and D) and bottom-views (E, F) of the free-standing film, obtained at 350 000× and 100 000× magnifications. High resolution cross-sectional view (G) allows comparing the barrier layer thickness and the interpore distance Dint. New morphological features are observed for the first time (H) – meander shaped spacers at points where electrolyte ion flows separate from each other and initiate pore branching (see discussion in the text and Fig. 8 for the details of the proposed mechanism).


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Figure 8. Schematic drawing of the change from laminar to transitional flow mode, which takes place upon small flow perturbations due to coupling between the electric fields and fluid motions (A), and the mechanism of pore branching, or satellite nanochannels formation (B). The colored arrows symbolize pathlines of the multiphase flow: the inflow of negatively charged ions (acid electrolyte, hydroxyls) and the linked flow of entrained water from top is depicted in red, and the flows containing electrochemically generated proton-stabilized colloidal alumina particles are in blue. Figures (C) and (D) demonstrate the same fragment of the layer cross-section. The short white arrows in (C) point at the arising meander-shaped protuberances at the bifurcation points, which serve as obstacles for the oncoming electrolyte flows. Arrows in (D) demonstrate the aforementioned flow pathlines in the real (non-idealized) system.


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Figure 9. TGA curve of porous anodic alumina obtained from tartronic acid electrolyte at 110 V with marked regions corresponding to individual decomposition steps.

Figure 10. DTG and DTA traces of porous alumina layers obtained from tartronic acid at 110 V.


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Formation of Porous Anodic Alumina under Unstable

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