Model of porous aluminum oxide growth in the initial stage of anodization

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E. M. Aryslanova, A. V. Alfimov, S. A. Chivilikhin
St. Petersburg National Research University of Information Technologies, Mechanics and Optics, 49 Kronverkskiy, St. Petersburg, 197 101, Russia elizabeth. aryslanova@gmail. com
PACS 81. 05. Xj, 81. 15. Pq, 82. 45. Aa, 81. 07. Gf, 61. 46. Km
Currently, due to the development of nanotechnology and metamaterials, it has become important to obtain regular self-organized structures, with different parameters. Porous anodic alumina films are self-organizing structures, which can be represented in a hexagonal packing of cylindrical pores normal to the plane of the aluminum film and used as a template for synthesis of various nanocomposites. The diameter of pores and the distance between them can vary (pore diameter — from 2 to 350 nm, the distance between the pores — from 5 to 50 nm), using different electrolytes, voltage and anodizing time. Currently, there are various models that describe the growth of a porous film of aluminum oxide, but none take into account the influence of aluminum layers and electrolyte on the rate of aluminum oxide growth, as well as the effect of surface diffusion. In present work we consider those effects. Keywords: porous aluminum oxide, anodizing, anodized aluminum oxide.
1. Introduction
Currently the scope of anodic aluminum oxide (AAO) use has expanded beyond corrosion, electrical protection and thermal protection to the development of a template for the synthesis of various nanocomposites. Some examples are: the synthesis of nanotubes via the matrix method [1−4]: where in 50−60 nm thick films, with an ordered system of nanopores (diameter of 40−100 nm) are used for synthesizing oriented carbon nanotubes using pyrolysis of dichloromethane (CH2Cl2) under an inert atmosphere of argon at 500 °C, the synthesis of which varies from 6 minutes to 4 hours [5]- the ability to control parameters of the porous structure of Al2O3 can be used as filters, carriers for catalysts [1−4]- films with high regularity of the porous structure are increasingly used for creating nanoscale structures in electronic, magnetic, and photonic devices [6]- with sorption of silver ions in the matrix of porous alumina, followed by chemical deposition nanocomposites are synthesized with biochemical activity properties [7].
AAO films consist of a so-called honeycomb structure. This system has a dense hexagonal packing, which is oriented in a perpendicular manner to the substrate surface. In the center of each Al2O3 cell, nanoscale pores formed. The bottom surface of the pores is separated from the aluminum substrate by a thin barrier layer. The cells are separated by a so-called honey & quot-Skeleton"- [8−13].
The chemical composition of these regions varies and is dependent upon the an-odization conditions. The inner part of the cell may include electrolyte anions, where the & quot-skeleton"- is made of pure hydrated alumina [11]. The diameter and the distance between them can vary (pore diameter — from 2 to 350 nm, the distance between the pores — from 5 to 50 nm), using different electrolytes, voltage and anodizing times [2, 7].
Fig. 1. Hexagonal packing of the porous AAO
2. Anodization technique
On the surface of the aluminum, a non-conductive oxide film is formed that is fairly uniform in its coverage of the aluminum surface (Fig. 2). An electrochemical field is concentrated on surface irregularities of the oxide film and preferentially dissolves the oxide in places where the inhomogeneity is higher. Thus, in areas of inhomogeneity on the surface, pore-growth occurs, increasing with higher temperatures, and with electrical field amplification. Initially, a competition is occurring between adjacent pores, which, after some time, leads to a stabilization of the process and to orderly pore growth [10].
Electrode Electrolyte ^ AhOs
Fig. 2. The process of formation of the porous alumina
In the anodizing process, aqueous solutions of acids moderately dissolve Al2O3. The process is carried out in a vessel with an electrolyte, which houses the anode (aluminum) and a cathode (inert conductive material), which are respectively connected to the positive and negative outputs of the power supply (Fig. 2). Thus, the film is formed on the metal, the top layer of which is a micro-porous metal oxide partially hydrated, under which is the bottom layer — anhydrous microscopically thin film of vitreous oxide, featuring a considerable hardness [1−4].
3. Modeling
We considered the motion of the interfaces between the electrolyte-Al2O3 (dissolution), and between Al2O3-aluminum (oxidation), as well as the dynamics of moving boundaries and the change of small perturbations of these boundaries. Each area under Laplace'-s equation is solved for the potential of the electric field. The growth process of the porous alumina is described by the theory of small perturbations. In zero approximation boundaries are considered flat and the speed of their movements is proportional to the current density at these boundaries. In the first approximation, small perturbations of the interface are considered, which lead to small changes in the potential and the current on these boundaries. The evolution of small perturbations of the interface is defined as a disturbance of the current density at the borders, and the process of surface diffusion.
3.1. The evolution of perturbations of the film boundaries of Al2O3-layer model (Figure 3):
Fig. 3 shows the geometry of the area under consideration. Here hi and h2 are small perturbations of the Al-Al2O3 and Al2O3-electrolyte boundaries, respectively.
Fig. 3. Inhomogeneous film with rough boundaries
We present the results of potentials perturbation calculations in each layer [14−16]: In the aluminum layer:
In the electrolyte layer:
i ii v i sh (kz)
1 =101 + MhiV Sh (H)
1 11 + v h sh (k (z — H3))
1 = (1 + -T h2fc 1
2V sh (k (H2 — Ha))'-
In the aluminum oxide layer:
k = ShJkHji + sh (k (z — H)) — fa + -^h-ik) sh (k (z — H2))) ,
where tk — the Fourier transform of the potential disturbance to the coordinates x, y:
oo oo
4& gt-k = / e-%kyy f te-ikxXdxdy, k2 = k% + k2y, t = t0z) + t, t0z) — stationary potential
-o -o
for the homogeneous problem, t — potential oscillations, ti — electrostatic potential of the aluminum layer on Al-Al2O3 interface, t2 — electrostatic potential of the aluminum layer on electrolyte-Al2O3 interface, ai — conductivity of the aluminum, a — conductivity
of aluminum-oxide, a2 — conductivity of the electrolyte, d = (jH + H +, v —
anodization voltage, H — thickness of aluminum oxide, Hi + hi — thickness of the aluminum
oo oo
layer, H3 — (H2 + h2)-thickness of the electrolyte layer, hi = / e-i (kyy) f e-i (kxx)hidxdy,
-o -o
oo oo
hk = / e-i (kyy) J e-i (kxx)h2dxdy.
-o -o
Using conditions of continuity of the current density at both interfaces, we obtain the system of equations relating the potential disturbance on the interfaces:
(-a2sh (kH) — ach (kH)) t2k + atlk = PekH — a -at2k + (aish (kH) + ach (kH)) tik = P — aekH
where a = | hik= § h2k.
We consider the solutions of the system (1) for different values kH: I. For kH"1,
'- ^ = 0
t = (a-l3)ai •
2k aia2kH+aia+a2^
II. For kH"1,
tik = 02 «•
t2k = ik {e^H —
3.2. Calculation of the evolution of alumina boundaries perturbations, without consideration of surface diffusion
The rate of change of small perturbations of the Al-Al2O3 and Al2O3-electrolyte boundaries without the influence of surface diffusion is proportional to the perturbation of the current density at these interfaces dh = aa '-dzz ¦ For Al-Al2O3 interface:
dtk- k (ti + ^ Ch (kz)
dz aid i kj sh (kHi)'-
-dtk = (^K cth (kHi), hik (t) = hik (0) • e*• (2)
For the Al2O3-electrolyte interface:
Is=k (t2+aVdhk i) cth (kH) (
We consider two cases: I. When kH"1,
Since the conductivity of the electrolyte and alumina is small compared with aluminum, we obtain from (3):
ai kv ¦ + f ankv_ +
«a? I / k ^ H Z-. I $ t
Kk = t (0) • e*1 + (h2t (0) — hi t (0) j e& quot-*1 (4)
II. When kH& gt->-1,
ai kv
h 2hik (0) a2e * t + (h (0) 2h! k (0) a2 a^vt (5)
h2k =, ^"kH + hot (0) ^J-^^ZkH Ie * • (5)
(a1 + a2) ekH 2 k w (ai + a2) ekH
From (4−5), we see that in this approximation, the perturbation on the Al2O3-electrolyte interface increases indefinitely with time.
3.3. Calculation of the evolution of alumina boundaries perturbations, with consideration of surface diffusion
The rate of change of small perturbations of the Al-Al2O3 and Al2O3-electrolyte boundaries with the influence of surface diffusion is described by the relation dh = V + DA2h, where D — is the surface diffusion coefficient.
For the Al-Al2O3 interface:
1/ (aivh Vl =(-hi kj& gt-
^ = hikk (a-f — Dk), hk = hikk (0) e (^ -4)t.
From (6), we get the value of spectral parameter corresponding to the limit of stability for the Al-Al2O3interface:
ki = (1/8 • (7)
All perturbations of this interface with k & lt- ki are unstable. Perturbations of the upper boundary in this spectral interval are the source of pore formation. We will estimate of distance between centers of aluminum oxide pores as 2n/ki.
For the Al2O3-electrolyte interface: For kH& lt-<-1,
t t vka2 /, aikv-cth (kHl) t
= ~jw i t (0) •e * t — h2 t) • (8)
For kH& gt->-1,
V2 =T, — l& gt-) +h2 t) — (9)
Then, as in (7−8), we obtain the expression, taking into account the surface diffusion: For kH& lt-<-1,
. (0) • e (^
For kH& gt->-1,
h2k = hit (0) • e (^-D2k4)t. (10)
2ht (0) a2e (^-D2k4)t
h — = *& quot- lkK& quot->- __(11)
h2k (ai + a2) ekH — (11)
From (10−11), we get the value of spectral parameter corresponding to the limit of stability for the Al2O3-electrolyte interface:
* = (D (12)
All perturbations of this interface with wavelength k & lt- k2 are unstable. The evolution of perturbations in this spectral interval determines the imperfection of the porous structure. This should be considered when preparing the aluminum plate used in this process.
4. Conclusion
i 1/3
As a result of the developed model, we obtained the minimum distance 2W ID) between centers of aluminum oxide pores in the beginning of anodizing process. The irreg-
ularities of the porous structure contains in the spectral interval k2 & lt- (¦
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