Confined anodic aluminum oxide nanopores on aluminum wires

Abstract

Anodic aluminum oxide (AAO) nanopores were grown on Al wire, 100 μm diameter in oxalic acid at 20, 40 and 70 V. Total charge passed and wire resistance were monitored as a function of anodization time providing precise Al consumption rates. Inductively coupled plasma optical emission spectroscopy was conducted on the used electrolyte to determine ejected Al³⁺ ion concentration. Reduced growth rates, lower interpore distances, thicker barrier layer Al₂O₃ and cracks in the AAO > 10 μm thick were observed. Compared to planar AAO at low current densities, at least 22% higher efficiencies and higher volume expansion factors were obtained. These results were explained on the basis of reduced ionic conductivity and increased viscosity of the barrier layer Al₂O₃ as a result of circumferential compressive stresses generated due to pore growth on convex surfaces.

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1. Introduction

Anodic aluminum oxide (AAO) nanoporous templates are an attractive platform for nanomaterial^1,2 and device synthesis.^3–7 The pores are separated by Al₂O₃ pore walls and possess hexagonal symmetry which provides the highest packing density for a given pore diameter and spacing. AAO films have been widely researched because of the intriguing property of the pores to self-assemble and form self-ordered nanostructures.^8,9 It has been suggested that pore formation and ordering is related to a combination of pore dissolution¹⁰ and viscous flow^11–14 of the barrier layer Al₂O₃.

Recently, Zhou et al.,¹⁵ have shown that these two mechanisms are current density dependent. At low current densities (<2 mA cm⁻²), low volume expansion is observed and field assisted dissolution of the barrier layer Al₂O₃ seems to be the primary mechanism of pore formation. Here, Al³⁺ ions are ejected from the barrier layer Al₂O₃ into the electrolyte resulting in low anodic efficiencies (i.e., ratio of Al³⁺ retained in the AAO to the total charge consumed for Al → Al³⁺ conversion).

For high current densities (>2 mA cm⁻²), a higher volume expansion is observed. Compressive stress gradients within the barrier layer Al₂O₃ are produced; from the oxide/electrolyte towards the metal/oxide interface, which drives viscous flow of the barrier layer Al₂O₃ along the metal/oxide interface and up along the pore walls.^16,17

On a planar Al substrate, the perpendicular z direction is the only free dimension along which the oxide can expand. Dynamic stress equilibration is achieved across adjoining pores as the pores grow parallel to one another. These pores are characterized by their pore radius, interpore distances (D_int) and the thickness of the barrier layer Al₂O₃. In turn, these parameters depend on fundamental material properties such as viscosity, electronic/ionic conductivity and stress state of the barrier layer Al₂O₃.

Since pore ordering on planar AAO is based on stress equilibration between adjoining pores,¹⁸ the stresses induced due to substrate curvature should play a role in determining pore ordering and morphology. Previous work on this includes AAO growth on concave Al films on Si substrates¹⁹ and on Al tubes.²⁰ Dendritic growth and crack formation characterize these nanoporous structures. These results imply that substrate curvature imparts non-equilibrium and high anisotropic stresses during pore growth which directly impact properties of the barrier layer Al₂O₃ and the morphology of AAO pores. Kopp²¹ and Lelonek²² have shown effects on AAO pores on both convex and concave surfaces providing empirical models on pore densities and growth rates. However, electrochemical and mechanochemical processes of AAO pore growth on curved surfaces is not well understood.

In this paper, we study the impact of convex Al substrates on AAO pore growth and morphology. In particular, we report the anodization of Al wires, 100 μm in diameter, in oxalic acid at 8 °C and under potentiostatic conditions. Pore kinetic and morphological parameters such as growth rates, barrier layer Al₂O₃ thickness and interpore distances are obtained. Ionic and anodic efficiencies are evaluated and AAO growth mechanisms on curved surfaces are discussed and compared with the current understanding of AAO pore growth on planar substrates.

2. Experiment

2.1 Experimental setup

Al wires of diameter ∼100 μm and 99.999% purity were purchased from Alfa Aesar®. Oxalic acid dihydrate (99.5–102.5%) was obtained from Alfa Aesar®. The Al wires were individually cut into strands 12 cm long and were first surface cleaned in ethanol and deionized water (DIW). Some wires underwent an electropolishing (EP) step for 5 seconds in perchloric acid + ethanol solution (1 : 5 vol%). This usually caused rapid, radially non-uniform, dissolution of Al. Hence, the data from the Al wires reported in this paper are without electropolishing (EP). Even though EP reduces surface nano-roughness, we find that for the thickness reported, surface preparation plays a minimal role in determining the various AAO growth parameters reported in this work. A single strand of wire was then dipped in 0.3 M oxalic acid solution maintained at 8 °C and allowed to thermally equilibrate with the oxalic acid solution. The wire was anodized at 40 V – conditions which have been optimized for ordered pore growth in planar Al foils.²³ The counter electrode was a cylindrical stainless steel tube providing a radially inwards electric field symmetric with the cross-sectional shape of the wire. The solution was stirred continuously while anodizing. Two Keithley® 2400 source measure units were used in the experiment – one for measuring the anodization current (meter 1) and another for measuring the Al wire resistance (meter 2). A customized Labview® program was used to control the two source meters using GPIB control. Fig. 1 shows the experimental setup used. The same setup was repeated for anodizing the wire at 20 V and 70 V.

Fig. 1 The experimental set-up uses meter 1 to apply the anodization voltage and measure the current between the anodized wire and the counter electrode while meter 2 is used to measure the resistance of the wire.

The current measurements from meter 1 were integrated to obtain the charge passed during anodization. Meter 2 was used to measure the Al wire resistance. As the wire anodized, Al was consumed and converted into AAO, resulting in the decrease in the Al wire cross section and an increase in the wire resistance. For our study, the initial Al wire resistances would have been ∼0.43 Ω given that the length of the wire was 12 cm, radius 50 μm and resistivity (ρ) 2.82 × 10⁻⁶ Ω cm. However, contact and lead resistance add to the total resistance and values from 0.8–1.0 Ω were usually obtained. Anodization was automatically stopped when the wire resistance crossed 20 Ω.

The anodized samples were extracted from the oxalic acid solution, washed in DIW and air dried. Cross sectional samples were prepared by mechanical cleavage of the samples. A Scanning Electron Microscope (FEI® Nova Nano-SEM 230) was then used to obtain multiple longitudinal and cross sectional images of the wire samples anodized for various times. Image J® software was used for making and recording statistical measurements on the SEM images.

For measuring the aluminum ion concentration in solution during anodization, ICP-OES measurements were made using a Perkin Elmer® Optima 7300 DV ICP-OES. Calibration standards for Al ion determination were prepared in the same blank oxalic acid from a Perkin Elmer® Multi-element mixed standard solution 4, with 200 mg L⁻¹ of Al. 0.02 mg L⁻¹, 0.2 mg L⁻¹, 2 mg L⁻¹ and 20 mg L⁻¹ calibration standards were prepared. The Al concentration was counted based on the intensity from Al emission wavelength 396.2 nm, since it showed the highest sensitivity as compared to the other emission wavelengths of Al (308.2 nm and 394.4 nm). The volume of the electrolyte was fixed at 688 mL. Before the onset of the experiment 12 mL of the solution was withdrawn to get the Al³⁺ concentration in the blank electrolyte. After the experiment was started, 12 mL of the electrolyte was withdrawn at time instants, 1, 2, 5, 9 and 22 hours. Each time the electrolyte was replenished with 12 mL of the blank solution. The resulting error from subsequent blank replenishments were calculated to be around 1.7% and is included in ESI Section S2.†

2.2 Analyses of measurements

2.2.1. Charge measurements. Using meter 1, current measurement from anodization is integrated to yield charge passed as a function of time. This is given as:

Q(t) = ∫Idt (1)

The anodization charge measures the sum of all reactions which lead to the generation of electrons including Al → Al³⁺ and other parasitic reactions such as O₂ generation. Here, we define ionic efficiency as ‘ξ_i’ where, ξ_i measures the ratio of Al → Al³⁺ consumed to the total charge passed. Assuming that the consumed Al is in the form of a cylindrical shell, the volume of Al consumed is given as:

V_shell = π(r_init² − r_Q(t)²)L (2)

where, a wire with initial radius r_init, after a time t, possesses a radius r_Q(t). Thus, using Faraday's law, the volume of Al consumed when a charge Q(t) has passed is given as (3)

Equating eqn (2) and (3), we get the radius of the Al wire at time ‘t’ as r_Q(t)

where, r_init is the initial radius (50 μm), mol wt of Al is 27 g mole⁻¹, z (effective charge number) is +3, F is the Faraday's constant (96 500 C), ρ_Al is the density of Al (2.7 g cm⁻³) and L is the length of the wire (8 cm).

2.2.2 Resistance measurements. Using meter 2, the time dependent resistance of a metallic wire whose radius changes over time is given as:where, R(t) is the resistance as function of time, ρ is the resistivity of the metal wire and r_Ω(t) is the radius at time ‘t’.

Thus, the net change in resistance as the radius of the wire decreases from r_Ω(t₁) to r_Ω(t₂) for a time interval Δt = t₂ − t₁ is given as:

where, ΔR is the increment in wire resistance measured while the anodization has proceeded from time t₁ → t₂. The boundary condition for the resistance measurements is then given as t = 0 s, r(0) = r_init = 50 μm and therefore R(0) = 0.44 Ω; the initial resistance of the Al wire before anodization. The advantage of using a difference method as given by eqn (4) is that this approach removes any parasitic series resistance originating from e.g., contact resistance of the alligator clips, which are effects extrinsic to the Al wire being anodized. Thus, successive readings in wire resistance can provide a real-time estimate of the change in radius of the metallic component of the wire as anodization proceeds.

2.2.3 Combining resistance and charge measurements. The Al wire radius obtained due to charge passed (r_Q(t)) and resistance measurements (r_Ω(t)) are two independent indicators of the same variable. By equating these two parameters ξ_i, the ionic efficiency can be easily obtained (see ESI Section S1†). In our case, we found ξ_i to ∼0.8 and independent of voltage and time. This indicates that 0.2 fraction of the charge is used in parasitic reactions such as oxygen evolution.

2.2.4 ICP-OES measurements. ICP-OES measurements provided Al³⁺ concentration ejected into the oxalic acid solution during AAO pore formation. These measurements were obtained at different anodization times (1, 2, 5, 9, 22 hours) and the amount of charge resulting from Al³⁺ in solution were calculated as Q_solution(t). The time dependency of anodic efficiency (ξ_a(t)) of oxide formation was calculated as the ratio of the charge retained within the oxide film to the charge consumed during the conversion of Al → Al³⁺, not all of which is retained in the oxide (i.e., ξ_iQ(t)). Thus,

2.2.5 Volume expansion factor. To calculate the volume expansion factor (VEF), i.e., the volume of AAO formed over volume of Al consumed, the radial thickness of metal consumed over time was computed as:

t_Al-consumed(t) = r_init − r(t) (8)

here r_init = 50 μm and r(t) can be r_Ω(t) or r_Q(t) since both refer to the inner Al wire radius.

The VEF for the case of a film with cylindrical cross section²⁴ was then given as:

3. Results

Current–time measurements for representative 100 μm diameter Al wires anodized at 20 V, 40 V and 70 V are shown in Fig. 2a. The current at the onset of anodization gradually drops over the entire course of anodization for all the three anodization voltages. This behavior is different than AAO grown on planar surfaces where the current, after an initial drop, rises to a steady state value.

Fig. 2 (a) Anodization current for the Al wires anodized at 20, 40 and 70 V as a function of anodization time. (b) Resistance increase for the Al wires anodized at 20, 40 and 70 V as a function of anodization time. (c) Active anodization area decreases linearly as anodization proceeds for the Al wires anodized at 20, 40 and 70 V as a function of anodization time. (d) Combining absolute current and area of anodization, current densities for various anodization voltages are obtained as a function of anodization time.

Fig. 2b shows the resistance of the Al wire as a function of anodization time. As expected, the resistance rises from an initial value ∼1 Ω to about 20 Ω in 63 hours, 33 hours and 5.5 hours for the 20, 40 and 70 V samples, respectively. However it can be seen that the increase in resistance to 20 Ω is faster for the wire anodized at 70 V as compared to that at 40 V and 20 V. The resistance increase gives us an indication of the rate at which Al is consumed to produce AAO and as expected, this increases with anodization voltage. Further, using eqn (4) one can estimate r_Ω(t) for the three wires as a function of anodization time. Using r_Ω(t), the effective metal/oxide interface area of the Al wire can be determined, which allows us to calculate the current density for the anodization.

Fig. 2c shows the effective surface area through which the current flows and Fig. 2d shows the current density as it varies with the anodization time. The current density initially decreases but tends to gradually plateau and then rapidly increase towards the latter part of anodization. The current densities reported in this work are lower than those reported for AAO on planar Al substrates. For example, at 40 V a current density of ∼2.5 mA cm⁻² has been reported for AAO anodized at 1 °C and 0.3 M oxalic acid,²⁵ whereas in our study the current density was consistently lower than 2 mA cm⁻² throughout the anodization process, reaching a steady state value of 0.9 mA cm⁻². The increase in the current density at the end of the anodization can be attributed to the assumption that in the current density calculations, Al core is assumed to be cylindrical throughout the anodization process, whereas it will be shown next that the pore growth fronts planarize and the true area of anodization becomes higher.

Fig. 3 shows the sequence of SEM images corresponding to various anodization times ranging from 45 minutes to 17 hours for the Al wires anodized at 20, 40 and 70 V. For the wire anodized at 70 V, the anodization consumes almost the entire Al wire at the end of 6 hours, in line with the relatively rapid rise in electrical resistance. The AAO growth proceeds at a slower rate for the 20 and 40 V samples. Initially, the AAO growth is fairly symmetrical around the Al wire. However, cracks appear in the cross sections for AAO > 10 μm in thickness. These cracks are indicative of the high compressive stresses produced due to AAO growth on curved Al surfaces as adjacent pores grow inwards while competing for limited Al and volume necessary for expansion. Once cracks are formed, pore growth fronts are confined within ‘sectors’.

Fig. 3 Time sequence of SEM images of the wire cross sections, where row (a), (b) and (c) correspond to 20 V, 40 V and 70 V, respectively. All scale bars represent 20 μm. It can be seen that the Al core loses its circular symmetry over long anodization times. Cracks are observed in the wires for AAO > 10 μm thickness. Lower right image, (d) is a schematic of the wire cross section showing the various variables described in text.

We observe that in most samples tested, the number of cracks are limited to 3 or 4 only. The pore-growth fronts are affected by the presence of these cracks as the Al core cross sections change shape; from circular to triangular (for 3 cracks) or rectangular (for 4 cracks) with clear lines of symmetry. Fig. 4 shows this trend in a wire anodized at 40 V for 24 hours. In other words, cylindrical pore-growth fronts ‘straighten’ after the formation of cracks.

Fig. 4 The AAO growth on the cylindrical Al wire at 40 V, 24 hours shows that the surface eventually leads to formation of planar pore growth fronts. Crack formation occurs along the edge of adjacent fronts. Inset shows an enlarged image of the boxed section showing parallel growth of the pores.

Fig. 5a shows the AAO thickness as a function of anodization time as measured from the previous SEM images. The slope of the data provides an estimate of the growth rate. A growth rate of 15.5 nm min⁻¹, 41.9 nm min⁻¹ and 171.8 nm min⁻¹ was found for the wires anodized at 20, 40 and 70 V, respectively. The obtained growth rate for AAO on Al wire can be compared to the growth rate of 25.4 nm min⁻¹, 72 nm min⁻¹ and 372 nm min⁻¹ on planar foils anodized at 20, 40 and 70 V, respectively. Such a reduced growth rate on curved surfaces indicates a high degree of compressive stress in the AAO film throughout the growth process. Reduced growth rates have also been reported for AAO pores grown laterally on etched Al films with exposed sidewalls sandwiched between dielectric films.²⁶

Fig. 5 (a) AAO growth rates as a function of anodization voltage. The data points are measured from SEM images and growth rates are measured from linear best fits. (b) A good correlation is observed between the radius of Al core calculated from resistance measurements (solid lines) and those observed from SEM (data points) for all the three voltages, 20, 40 and 70 V.

Fig. 5b shows a comparison of the Al core radius from electrical resistance measurements and those obtained from SEM. There is a good correlation between the two sets of data suggesting that the resistance measurements are a good indicator of the amount of aluminum consumed during the anodization. Starting from an initial 50 μm radius, the Al core is linearly reduced to 5 μm radius at the end of anodization for all the three wires.

In order to understand if the anodization on curved surface introduces any changes in the morphology and oxide parameters, the interpore distances were studied as a function of anodization time for all the three voltages. Fig. 6 shows the interpore distances for the Al wires anodized at 20, 40 and 70 V. The dotted lines indicate the theoretical interpore distances (D_int) for anodization on planar Al foils which scale at the rate of ∼2.75 nm V⁻¹.²⁷ It can be seen that the interpore distance for the 20 V sample is similar to the planar D_int value of 55 nm. The D_int is slightly lower than the planar D_int of 110 nm for 40 V sample. Finally, for the 70 V anodized wire, the D_int is 165 nm as compared to a planar value of 195 nm. Thus, for the same anodization voltages, curved surfaces have lower D_int as compared to planar substrates.

Fig. 6 The interpore distance (D_int) for the AAO on Al wire at anodization voltages of 20, 40 and 70 V. The dotted lines indicate the theoretical D_int for planar foils at those particular voltages following the linear relation of ∼2.75 nm V⁻¹. The scale bars indicate 500 nm.

Barrier layer thicknesses of the AAO can also be obtained from the SEM images shown in Fig. 6. These values are provided in Table 1. Similar to the trend observed in D_int, the barrier layer thickness on curved surfaces were 33, 74 and 82 nm for 20, 40 and 70 V, respectively. Barrier layer thicknesses on planar films have been empirically modeled,^25,27 varying as 1 nm V⁻¹ and thus, the expected barrier layer thickness on planar AAO would be 20, 40 and 70 nm, respectively. Thus, barrier layers grow thicker on curved Al surfaces than on planar substrates.

Table 1 Listing of pore parameters obtained during anodization of 100 μm Al wire as a function of anodization voltage. The measurement techniques are stated in parentheses. Where available, the value of pore parameters from planar Al foil are provided for comparison. The references for the planar Al foil have been taken from a = Alkire, 2007; b = Vrublevsky, 2003; c = Zhou, 2012; d = Li, 1998; e = Hebert, 2012.^27,31–34 In other instances, the values are obtained from the present study

	20 V		40 V		70 V
	Planar Al foil	100 μm Al wire	Planar Al foil	100 μm Al wire	Planar Al foil	100 μm Al wire
Growth rate in nm min^−1 (SEM, electrical)	25	16	72	42	372	171
Interpore distance Dint in nm (SEM)	54.5^d	50	110.7^d	85	195^d	165
Barrier layer thickness in nm (SEM)	20^d	33 ± 3	40^d	54 ± 7	70^d	82 ± 9
Anodic efficiency (ICP-OES)	—	0.52	0.6–0.7^e	0.60	—	0.71
Volume expansion (SEM)	1.22@20 °C^a	1.39@8 °C	1.42@1 °C^c	1.44@8 °C	1.46@16 °C	1.53@8 °C
			1.37@20 °C^a		1.51@20 °C^b

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Fig. 7 shows the anodic efficiency, ξ_a for different voltages as a function of anodization time based on the results from ICP-OES and using eqn (5). In general, ξ_a was found to gradually decrease with anodization time. Mercier et al.,²⁸ have reported ξ_a increase from a minima to a maximum and then reach steady values. This trend is usually observed in the first 200 seconds of anodization only. However, our anodization times and sampling rates for the ICP-OES measurements do not have the resolution to verify this trend. It was also found that at 20 V, the mean anodic efficiency was 0.52, while at an anodization voltage of 40 V, the mean anodic efficiency was 0.60. The mean anodic efficiency was 0.71 for the 70 V sample. It can also be noted that the 20 V sample shows a steeper slope of decrease in anodic efficiency compared to the 40 V and 70 V samples. This can be attributed to the dominance of field assisted dissolution over viscous flow in the pore walls at the significantly low current densities in the 20 V sample. Viscous flow dominates in the 40 V and 70 V samples and hence the decrease in anodic efficiency is not so steep.

Fig. 7 Current efficiency during anodization at 20, 40 and 70 V on an Al wire as a function of anodization time. The lines are guide to the eye. The error bars represent standard deviation of 3 samples of electrolyte tested.

Table 1 summarizes all the results reported above. The pore parameters (growth rate, D_int and barrier layer thickness), mean anodic efficiencies and mean VEFs for the Al wires obtained at the three anodization voltages are provided and comparisons between curved and planar substrates (where possible, from literature) are made. We note that the mean VEFs obtained in our experiments were slightly higher than those reported in literature, though the exact anodization temperature could not be matched to the experimental conditions.

4. Discussion

Our results indicate that AAO growth on convex surfaces affect the growth and morphology of the individual pore as well as induce macroscopic effects such as crack formation. We discuss our results pertaining to these two different length scales.

4.1 Effect on pore morphology

AAO growth on convex Al surfaces is a dynamic process where the pores are forced to compete for limited Al and volume for expansion. This creates circumferential compressive stresses (see Fig. 8a), the effects of which are seen in reduced D_int (Fig. 6) and slower growth rates (Fig. 5a). This stress is in addition to the stresses produced within the barrier layer Al₂O₃ at the oxide/electrolyte and metal/oxide interfaces as a result of anodization.

Fig. 8 (a) Schematic of a sector of AAO growth on Al wire showing the generation of circumferential compressive stresses on the orange colored pore, prior to crack initiation. (b) Graph of anodic efficiency as a function of current density, where current density is obtained from Fig. 2d. At low current densities (<2 mA cm⁻²), the trend line lies above the one predicted by Houser and Hebert¹⁷ and the raw data obtained by Zhou et al.,¹⁵ both for planar AAO. At higher current densities, the values match those obtained by Zhou et al.¹⁵

Stresses affect barrier layer Al₂O₃ conductivity and viscosity. First, the presence of additional compressive stress increases the energetic barrier to ionic hopping and hence the conductivity of the barrier layer Al₂O₃ is reduced. This has been found to be true for O²⁻ diffusion in metal oxides.²⁹ In our case, the observation of lower current densities (as shown in Fig. 2d) during anodization is in line with this fact. Further, increased compressive stress drives O²⁻ adsorption and subsequent diffusion from the oxide/electrolyte interface into the barrier layer Al₂O₃ and reduces cationic transport numbers (t_c).¹⁷ Thus, the larger O²⁻ ion (140 pm as opposed to 39 pm of Al³⁺) carries the majority of the ionic current. This leads to lower overall net ionic mobility and therefore, lower conductivity.

Second, compressive stresses increase the viscosity of the barrier layer Al₂O₃. The relation between viscosity (η_oxide) and compressive stress (σ) is approximated as³⁰

where, t_BL is the barrier layer Al₂O₃ thickness and dt_pore/dτ is the pore growth rate. Further, we find that t_BL is thicker (Table 1) and the growth rates are reduced (Fig. 5a) when compared to t_BL and growth rates of planar AAO thus, contributing to higher η_oxide. Finally, as a matter of consistency, we note that Houser and Hebert¹⁶ have shown the product of conductivity and viscosity is empirically a constant for the AAO system and thus, reduced conductivity should lead to a corresponding increase in viscosity and vice versa.

The effect of compressive stress on conductivity (i.e., lower current density) and viscosity (i.e., thicker t_BL and lower growth rates) of the barrier layer Al₂O₃ point to a reduction in t_c through the barrier layer Al₂O₃. Both t_c and ξ_a are related as t_c = 1 − ξ_a and thus, for AAO on convex surfaces where lower t_c is obtained, ξ_a should be higher than for planar AAO.¹¹

Indeed, when ξ_a is plotted as a function of current density, we see this effect clearly. This is shown in Fig. 8b, where ξ_a at low current densities (<2 mA cm⁻²) for AAO on convex substrates is parallel to, and at least 22% higher than ξ_a of AAO on planar substrates. On the other hand, at higher current densities (>2 mA cm⁻²), our data matches well with Zhou et al.¹⁵ indicating that viscous flow of the barrier layer is the prevailing mechanism for pore growth for both convex and planar substrates. Both Zhou et al.¹⁵ and the predicted model from Houser and Hebert¹⁷ are obtained for planar AAO. While our data is obtained in oxalic acid at 8 °C, we note that Zhou's data pertains to anodization in oxalic acid at 20 °C and Houser and Hebert's data is independent of the electrolyte. The temperature effect on chemical dissolution is assumed to be minimal.¹⁵ Additionally, chemical dissolution during very long anodization times employed in our experiments can only lead to lower ξ_a, which is not the case here. Thus, the presence of additional compressive stress causes field assisted dissolution to be suppressed in favor of viscous flow of barrier layer Al₂O₃. Our work suggests that current density based transition regimes (such as the ∼2 mA cm⁻² reported by Zhou et al.) between field assisted dissolution and viscous flow may not be a hard demarcation, but will depend on the overall stress state of the barrier layer Al₂O₃ and can be tailored by a suitable choice of substrate geometry.

Higher ξ_a should lead to higher VEF. VEF data (Table 1) indicates this to be the case however, direct comparison with available literature on planar AAO is difficult since most of the reported VEF is from samples anodized at different temperatures. Additionally, crack formation will relax stresses in the AAO, thereby masking the true VEF on convex surfaces. Notwithstanding this, VEFs obtained are higher than those reported in literature.

4.2 Macroscopic effects

AAO pores on convex surfaces attempt to achieve minimal energy by two type of processes. Pore merging occurs, reducing the pore densities and hence volume expansion associated with the AAO growth. Alternately, pore branching occurs, reducing radially inward growth rates since the pores now grow in an angled direction. When adjacent growth fronts meet, they create weakened interfaces which ultimately are regions from which cracks nucleate and propagate.

Cracks release built-up stresses. In our experiments, we find that the AAO films are crack free for up to 10 μm thickness for all anodization voltages. This thickness therefore, provides an upper limit for creating viable AAO structures on curved surfaces of 100 μm diameter Al wires. Once the cracks originate, independent ‘sectors’ of growth are formed. A gradual planarization of the curved AAO fronts is observed and for long anodization, fully planar growth fronts of ordered nanopores are observed. Planarization of the growth front is also an effective way to reduce volume expansion as the number of pores per unit area is reduced and this reduces volume expansion and associated stresses.¹⁹ When these growth fronts meet, triangular or rectangular Al cores are produced as shown in Fig. 4. The pores are well-ordered at this point but have several of their key morphological parameters different including barrier layers, electrical conductivity, D_int and efficiencies. Thus, for long anodization times, AAO on curved surfaces resort to ‘self-planarizing’ of growth front as means of minimizing compressive stresses.

5. Conclusions

AAO pore growth was studied on 100 μm Al wires subjected to different anodization voltages. The wire, by virtue of its geometry, afforded us to measure total charge passed as well as resistance of the metal remaining, simultaneously. AAO pore growth rates and ionic efficiencies of the process could be obtained in real time. Through a time-series of SEM and ICP-OES measurements, we obtained parameters for pore structure, anodic efficiency and volume expansion factor.

Circumferential compressive stresses generated as a result of AAO growth on curved surfaces leads to lower ionic conductivity and higher viscosity of the barrier layer Al₂O₃. This causes slower AAO growth rates, lower interpore distances and thicker barrier layer. Additionally, efficiency of anodization is at least 22% higher than those reported for planar substrates at low (<2 mA cm⁻²) current densities. These results suggest that the presence of additional compressive stresses suppresses field assisted dissolution in AAO in favor of viscous flow of the barrier layer. Volume expansion factors are found to be slightly higher. An upper limit for crack free AAO on curved surface of a 100 μm wire seems to be ∼10 μm and is found to be independent of anodization voltage. Beyond this thickness, cracks propagate radially inwards and cause self-planarization of pore growth fronts.

Acknowledgements

The authors wish to thank the McDonnell Academy for Global Energy and Environment Partnership (MAGEEP) for providing seed funding for this work. This work was performed in part at the Nano Research Facility (NRF), a member of the National Nanotechnology Infrastructure Network (NNIN), which is supported by the National Science Foundation under Grant no. ECS-0335765. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. NRF is part of the School of Engineering and Applied Science at Washington University in St. Louis.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3ra47283c

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