Effects of the solution flow rate on the growth of aluminum etch tunnels

Increasing the specific surface area of the anode foil of aluminum electrolytic capacitors is a research direction to improve the performance of capacitors. Industrial mass‐produced anode foil increases the specific surface area by electrochemical etching of the aluminum foil. However, the tunnels created by corrosion stop growing midway through this process. In this study, the effect of the solution flow rate on tunnel growth is investigated, and the growth of tunnels is analyzed using a new method of preparing oblique sections. Neater tunnels can be grown by increasing the solution flow rate to facilitate active tunnels.


INTRODUCTION
Electrochemical etching of aluminum foil has been used in the production of high surface area electrodes because the capacity of a capacitor is directly related to the surface area of the electrodes. Electrodes with high surface areas are key materials for aluminum electrolytic capacitors. Usually, the surface areas of electrodes are enhanced by local attack of aluminum surface in chloride-containing electrolytes. 1 The aluminum foil of high-voltage capacitors is etched by the direct current (DC) process, which produces crystallographic etch tunnels. The tunnels in aluminum foils are typically 1-2 μm wide, 40-50 μm long, and present at a density on the order of 10 7 cm −2. 2 The average length of tunnels determines the capacity of the anodic electrode. In addition to this method, scholars have prepared branch tunnels for capacity enhancement by depositing impurity elements. 3,4 The capacity is also increased by preparing composite oxide films to increase the dielectric constant. [5][6][7] However, the impurity elements used to prepare the branch tunnel can degrade the electrical properties of the capacitor. Usually the leakage current increases. When the dielectric constant of the composite oxide film prepared using valve metal oxide and alumina is increased, the voltage resistance of the oxide film decreases. This condition is fatal to capacitors. On the contrary, controlling the tunnel length to increase the capacity is a suitable method for capacitors. Longer length of tunnels are required to obtain higher capacity. However, longer the tunnels result in the worse bending resistance of the anode electrode. Therefore, the tunnel length needs to be controlled at a specific value. During the corrosion of aluminum foil, some tunnels will stop growing in the middle of the process, thereby reducing the capacity. Therefore, reducing the number of tunnels that stop growing midway is important for the preparation of high-capacity anodic electrode. Tunnel growth is difficult to study because it is accompanied by general crystallographic attack that masks tunnel initiation and confounds measurements of tunnel length. 8 Fortunately, we developed a polishing method enables counting the tunnel length. Many scholars have studied the effects of bath temperature, 8-10 current density, [10][11][12] and bath chemistry 3,13-17 on tunnel growth. These factors have a clear impact on tunnel growth and have guided industrial production. However, the corrosion fluid flow rate also significantly affects tunnel growth and studies on this subject are limited.
In the present study, we investigate the effect of corrosion fluid flow rate on tunnel growth by using a new preparation method. We also attempt to reveal the mechanism of corrosion fluid flow rate on tunnel growth. This article presents the results of the work by describing the experimental method and procedure, presenting the experimental results, discussing the experimental data, and summarizing the conclusions.

EXPERIMENT
The aluminum foil used in this study was 130 μm thick, 99.99 wt% pure, and fully annealed to obtain a high cubic texture (i.e., its {100} cubic texture fraction was greater than 95%). 18 The aluminum foil contained 55 × 10 −6 copper, 11 × 10 −6 silicon, 9 × 10 −6 iron, and 1.5 × 10 −6 lead by mass as the main impurities. 18 The foil was cut into a rectangular shape with dimensions of 20 cm × 8 cm and then mounted in a polypropylene holder with an area of 7 cm × 5 cm left exposed for etching. 14 First, specimens were cleaned by immersion for 1 min in 1 mol/dm 3 H 3 PO 4 at 60 • C. Second, specimens were rinsed and then immediately transferred to the electrochemical cell. The structure of the electrochemical cell with dimensions of 23 cm × 33 cm × 36 cm is shown in Figure 1, and the flow rate of the corrosion solution can be controlled by a flow meter. The current curve in Figure 2 was applied on the aluminum foil for etching in 1 mol/dm 3 HCl + 3.5 mol/dm 3 H 2 SO 4 at 68 • C under a fluid flow rate of 0, 1 (flow meter controlled at 0.0273m 3 /s), and 3 m/s (flow meter controlled at 0.082m 3 /s). The current curve was applied by a programmable power. As shown in Figure 2, the time of a single waveform is 22 s, followed by a 22 s interval, repeated four times. Third, specimens were rinsed and etched in 3 wt% HNO 3 solution at 50 mA/cm 2 for 300 s at 80 • C.
To observe tunnel growth, the sample was tilted 12 • , sealed in epoxy resin, and mechanically and electrochemically polished. After being sputter-coated with gold, the specimens were observed by scanning electron microscopy (SEM). According to the direction from the surface to the core of the aluminum foil, a series of pictures was obtained, and then the pictures were spliced into a long picture for analysis. Figure 3 shows the corrosion morphology of aluminum foil under solution flow rates of 0, 1, and 3 m/s. The erosion holes are square shapes, with a square side length close to 1 μm. Table 1 shows the statistics of the tunnels in Figure 3. The etched aluminum foil surface was analyzed using ImageJ software, which identifies etch tunnels by distinguishing between colors, thereby enabling the number, size, and shape of etch tunnel to be counted. Tunnels with circularity greater than 0.78 are defined as single tunnels. The tunnel generated at 0 m/s has a relatively large tunnel area percentage of 0.3, a large tunnel size of 0.94 for single tunnels, and a low single tunnel percentage of 0.4. No significant difference is found in the tunnels generated under 1 and 3 m/s. The total area of etch tunnels formed under the two conditions is approximately 29%. The average pore size is approximately 1.3 μm, and the single tunnel size is approximately 0.9 μm.

RESULTS
The cross-sectional morphology in Figure 4 shows that the tunnels grow at an uneven length under a flow velocity of 0 and 1 m/s. On the contrary, at a flow rate of 3 m/s, the tunnels grow with slightly more uniform lengths. The average TA B L E 1 Analytical data of corrosion tunnels on the surface of aluminum foil in Figure 3  tunnel length is approximately 50 μm, but the length of the tunnel grown at 0 m/s is low by about 47 μm. However, many of the tunnels shown in Figures 4A and Figure 4B stopped growing in the middle. Quantitative analysis the tunnel growth from the cross-sectional morphology is impossible. Therefore, the tunnel growth process can be judged by preparing oblique sections and observing the number of tunnels at different depths. Figure 5 shows an oblique cross-sectional image. This figure is stitched together from multiple SEM images, which can systematically show the growth of tunnels at different depths. Figure 5 shows that the tunnels decrease gradually from the surface of the aluminum foil toward depth. This finding implies that some factors cause the tunnel to stop growing during the growth process. Figure 5A-C were compared, and results showed that the number of tunnels growing to depth is higher in Figure 5B. The number of tunnels in the deepest part of Figure 1 is significantly lower than the two other tunnels. This result indicates that the increase in the solution flow rate is conducive to the growth of tunnels to a greater depth.
In Figure 6, the percentage of active tunnels at different depths is shown, where the active tunnels are those that can continue to grow. Tunnels observed at a specific depth are considered to be tunnels that continue to growing at this depth and are defined as active tunnels. The data in Figure 6 are obtained by counting the number of tunnels at different depths in Figure 5. At a flow rate of 0 and 1 m/s, about 40% of the tunnels stop growing at 25 μm, whereas at a flow rate of 3 m/s, the tunnels remain active at the same depth. At depths of 35 and 45 μm, the percentage of active tunnel at 0 m/s is the lowest. This result indicates that increasing the flow rate of corrosion fluid is conducive to the growth of small pores to a deeper depth.

DISCUSSION
Capacitance is a key evaluation parameter for capacitor quality. 19 The capacitance formula of the plate capacitor is C = (εε 0 S)/d, where the vacuum permittivity ε 0 is 8.85 × 10 −12 F m −1 , S is the specific surface area of the electrode, and d is the thickness of the oxide film. 19 For aluminum electrolytic capacitors, the relative dielectric constant of Al 2 O 3 is fixed at approximately 8 −10.19 Thus, increasing S (the specific surface area) is essential to obtain high capacitance. 19 The surface area of aluminum foil increases after corrosion. To further increase the surface area of the etched foil, the number or length of tunnels needs to be increased. The average tunnel length can be increased by reducing the number of tunnels that stops growing in the middle.
Generally, corrosion products accumulate at the bottom of the tunnel during the growth process. [20][21][22] The corrosion products are Al 2 (SO 4 ) 3 and AlCl 3 . Tunnels can maintain growth because of rapid dissolution of these corrosion products. 20 Once the corrosion product at the tip of the tunnel reaches saturation, the tunnel will stop growing. The mass transfer resistance increases with pit depth, making ion transport in and out of pits difficult. 19 Deficiency of Cl − leads to reduced aggressiveness to salt films. In addition, when there is no excess anion pairing of Al from electrolysis, the following hydrolysis reaction will occur: H 2 O + 2e − → H 2 + O 2− . O 2− reacts with Al 3+ to form a passivation film and prevents the growth of small pores. [22][23][24][25] Jong 26 investigated the effect of Al 3+ concentration on the growth of tunnel pits. The results showed that as the concentration of Al 3+ increased, the Cl − activity decreased, and the axial growth of the tunnel pit was suppressed. Cl − is the key element to maintain the growth of tunnels. 27 The ultimate length of corrosion tunnels increases with increasing Cl − concentration, indicating that tunnels are more likely to remain active in environments with high Cl − concentrations. 13 Timely replenishment of Cl − in the tunnel and timely diffusion of Al 3+ out of the tunnel are prerequisites to ensure that the tunnel continues growing.
According to convective diffusion theory, ∝ u − 1 2. where is the thickness of the diffusion layer and u is the convection velocity. 19 Therefore, increasing the flow rate will reduce the thickness of the diffusion layer. 19 According to Fick's first law equation, J = −D C 0 −C 1 , where J is the diffusion flux, D is the diffusion coefficient, and C 0 and C 1 are the concentrations of substances at the two ends of the diffusion layer. Generally, reducing the thickness of the diffusion layer is conducive to increasing the diffusion flux J. In this study, the mass transfer process was accelerated by increasing the solution flow rate so that more tunnels could remain active.
As shown in the schematic in Figure 7, when the solution flows through the tunnel, it drives the solution flow at the mouth of the tunnel. This effect promotes the convection of material in the tunnel. Therefore, at faster flow rates, ions in the tunnels are more easily transported. Therefor the lifetime of the tunnel in Figure 4C is longer.

CONCLUSION
In this study, anode materials for aluminum electrolytic capacitors were prepared by DC electrolysis of aluminum foil in a mixture of HCl and H 2 SO 4 . The effect of three flow rates, 0, 1, and 3 m/s, on the growth of tunnel holes was investigated.
The results show that the lifetime of the tunnel is longer at a 3 m/s flow rate and still close to 100% active at a 25 μm depth. Preparing oblique sections is an effective method to observe and analyze the tunnel growth pattern.

ACKNOWLEDGMENT
This research was supported by Xinjiang Joinworld Company limited.

CONFLICT OF INTEREST
The authors declare no potential conflict of interest.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.