An ab initio study of the molecular dynamics of the behavior of amorphous substances in anodic alumina under electric field

Influence of electric field strength

Figure 3A,B shows the mean square displacement (MSD) of amorphous alumina at different electric field strengths. The IDC of Al and O increases and then decreases rapidly as the electric field strength increases from 0.5 to 2 V/Å, reaching its maximum at 1 V. Table S1 shows the correlation between electric field strength and IDC (ion diffusion coefficient) and Ion mobility. For better understanding, we have included Fig. S5. The data suggest a nonlinear relationship between electric field strength and IDC, with a maximum value of ion diffusion rate as electric field strength increases. In addition, when the electric field strength was too high and the anhydrous amorphous alumina was not degraded, the IDC was low, indicating insulating properties. Under the above field strength, the IDCs of anhydrous amorphous alumina were very small due to the extreme stability of the Al-O bond. The stability of the Al-O bond makes it difficult for ions to move even in an electric field. This claim is supported by the slight structural change of the amorphous alumina over time in Fig. S2.

The MSD consists of three modules. (A, b) Al and O (anhydrous amorphous aluminum oxide), (C-E) Al, H, O (aluminum oxide monohydrate), (F–H) Al, H, O (aluminum oxide trihydrate).

In alumina monohydrate, the slope of the mean square displacement (MSD) increases monotonically as the field strength increases, as shown in Fig. 3C–E. The MSD did not change significantly at field strengths of 0.5 V/Å and 1 V/Å, but only when the field strength reached 2 V/Å did the slope of the MSD line increase significantly. This suggests the presence of a specific energy barrier for ion diffusion in alumina monohydrate. When the electric field strength is low, the energy barrier prevents significant ion diffusion. Only when the electric field strength is sufficient to overcome the diffusion energy barrier will the IDC be significantly improved. Figure S3 shows the structural changes of alumina monohydrate over time under an electric field of 2 V/Å. Under the influence of an electric field, H ions quickly break away from the bond. Some of the aluminum ions became isolated hydrogen ions and migrated freely in the aluminum oxide, while others remained associated with oxygen ions and migrated together. Table S1 and the inset image in Fig. S5 show that the ion diffusion coefficient (IDC) of aluminum and oxygen in alumina monohydrate is similar, while the IDC of hydrogen is an order of magnitude higher than that of other ions. This indicates that, except for the isolated hydrogen ion, the hydrogen ions of the bound oxygen ions induce and promote the migration of the oxygen ions. A separate study confirmed that H ions reduce the activation energy required for O ion migration in aluminum crystals³¹.

The IDC of alumina trihydrate gradually increased with increasing electric field strength (Fig. 3F–H). In addition, under the influence of an electric field, alumina trihydrate dissociated more H ions and bound HO ions, resulting in a higher IDC. Table S1 shows that at an electric field strength of 0.5 V/Å, the IDC of alumina trihydrate is an order of magnitude higher than that of alumina monohydrate (0.20 versus 0.0629). This is also shown in Fig. S5. However, it is important to note that the improvement effect is not infinite. The experiment³² showed a breakdown voltage, indicating that in the oxidation process of AAO formation, the electric field strength does not need to be maximized; rather, there seems to be a threshold. Our simulation also confirmed that if the field strength is too strong, the aluminum oxide trihydrate breaks down and is no longer able to maintain a stable structure. The electric field strength was set at 0.1 V/Å, 0.25 V/Å, and 0.5 V/Å. Figure S5 shows that the IDC peaks at an electric field strength of 0.25 V/Å. When the electric field is increased to 0.5 V/Å, the IDC begins to decrease. This is due to the excessive migration of H ions, which partially offsets the driving force of the electric field on Al and O ions.

The growth rate of the AAO film is typically proportional to the size of the IDC. Scientists have extensively studied the relationship between growth rate and tension^2,32,33,34. For porous AAO, the growth rate increases with higher voltage, which is directly related to the electric field strength. Previous experiments have maintained a consistent experimental system, except for the varying voltage magnitude^33.34. An increase in voltage can be interpreted as an increase in the electric field strength. The conclusions about trends in this chapter are consistent with those in previous experiments.

Influence of oxide composition

The oxide layer of the AAO oxidation process is not a single component. Based on Thompson’s model, it can be viewed as a hydrated oxide that varies along a gradient of water content between metal and electrolyte^15,16. The composition of hydrated oxides has a significant influence on ion diffusion.

Figure 3 shows that the ionic conductivity of anhydrous amorphous alumina remains low even at high voltage, while that of alumina monohydrate is significantly higher. Its peak value is almost 100 times higher than that of anhydrous alumina.

The evolution of the oxide structure in Fig. S3 suggests that the dissociated hydrogen ions in the hydrate contribute significantly to conducting an electric field. The H ion is the smallest element and can easily migrate in the oxide under the influence of an electric field. As a result, the diffusion rate of the H ion is significantly higher than that of other ions, as shown in Table S1 and the purple and brown lines in Fig. S5. In addition, some H ions have combined with O, which can trigger and “delay” the migration of O ions. And these H ions can also reduce the migration energy barrier of O ions.

Alumina trihydrate can achieve the same IDC as alumina monohydrate obtained at high voltage when subjected to a lower voltage. However, increasing the electric field strength does not increase the IDC of alumina trihydrate; Instead, it starts to decrease. This suggests that the presence of H ions in the hydrate does not consistently promote ion diffusion and excess H ions can consume a significant amount of electric field energy. Although the IDC of hydrogen still increased, the IDC of aluminum and oxygen ions in the oxide decreased. Therefore, only the hydrogen ions that have combined with oxygen ions can facilitate ion migration in alumina. It is concluded that the role of hydrogen ions in hydration in the oxidation process of AAO mainly includes: (a) providing an ion channel; (b) the resistance effect in the migration process; (c) Reducing the activation energy of ions.

The influence of hydrate content on the structure of alumina was observed in the radial distribution functions of alumina monohydrate at 2 V/Å and alumina trihydrate at 0.5 V/Å, as shown in Fig. 4. The electric field strength increased the Al ion distance, resulting in a change in the Al-Al distance of alumina monohydrate from 2.85 to 3.15 Å and of alumina trihydrate from 2.75 to 3.25 Å. Hydration loosened the structure of the aluminum oxide.

RDF of Al–Al in hydrated alumina, green line shows no electric field, yellow line is under electric field. (A) 2 V/Å aluminum oxide monohydrate, (b) 0.5 V/Å aluminum oxide trihydrate.

Influence of the electrolyte environment

The electrolyte plays a crucial role in the AAO process. In general, anodic aluminum oxide forms a dense protective layer in neutral environments and a vertically porous structure with uniform distribution in acidic environments. In this article, H ions are used instead of O ions to give the system a positive charge and create an acidic environment suitable for simulating anodic oxidation. This ion exchange method is often used to simulate charged systems²⁹. Table S2 shows the correlation between IDC, ion mobility of ions in hydrated alumina, and acidity at an electric field strength of 0.1 V/Å.

Figure 5 shows the MSD of hydrous alumina in an acidic environment. The IDC of H ions increased with increasing acidity, while the IDC of Al and O ions were significantly decreased in both alumina monohydrate and alumina trihydrate. Table S2 and the blue and yellow lines in Fig. S6 show that the IDC of H is much higher than that of Al and O. Combined with the electric field strength effect discussed in the “Influence of electric field strength” section, the system would do would collapse if the electric field was too strong. When the system malfunctioned, the charge (mainly in the form of H and electrons) moved rapidly along the breakdown channel, resulting in a decrease in the IDC of the remaining ions rather than an increase. Trihydrate alumina has a higher water content, lower density and looser structure compared to monohydrate alumina, resulting in a lower breakdown electric field. Therefore at a concentration of 3.513 MH⁺The alumina monohydrate remained intact, resulting in the highest diffusion rate. Conversely, alumina trihydrate was degraded, resulting in a much lower diffusion rate than that of alumina monohydrate. Unless otherwise stated, the diffusivity rate refers to the IDC of Al ions with changes in H and O ion content. At an H ion concentration of 7.026 M, the diffusion rate decreased sharply due to the degradation of alumina monohydrate. The IDC of H was about 20 times higher than that of Al (or O) when the system collapsed, as shown by voltage influence data. This information is a crucial reference for analyzing the oxidation process of anodic aluminum oxide (AAO). It can be concluded that the IDC in the oxide layer is enhanced by the acidic environment, resulting in an increased oxidation rate. Higher acidity can lead to the degradation of water-containing compounds, preventing the oxide thickness from increasing.

MSD in the electric field of Al, H, O. (A) Al, (b) H, (C) O of aluminum oxide monohydrate under acidic conditions. (D) Al, (E) H, (F) O of aluminum oxide trihydrate under acidic conditions.

Existing experimental results suggest that the film growth rate increases with acid concentration^34,35,36,37. This is similar to our conclusion as growth rate is positively correlated with IDC and ion mobility.