Formation of nanoscale pore arrays during anodization of aluminum

Abstract

Abstract. -A theory of the spontaneous formation of spatially regular hexagonal arrays of nanopores in aluminum oxide film growing during aluminum anodization is presented. Linear stability analysis shows that, in certain ranges of the applied voltage and electrolyte pH, the oxide film is unstable with respect to perturbations with a well-defined wavelength. The instability is caused by a positive feedback between the oxidation-dissolution rates and variations of electric field caused by perturbations of the metal-oxide and oxide-electrolyte interfaces. The competition between this instability and the stabilizing effects of the Laplace pressure and elastic stress provides the wavelength selection mechanism. The hexagonal ordering of pores results from the resonant quadratic nonlinear interaction of unstable modes.Spatially regular, hexagonally ordered arrays of nanoscale pores in aluminum oxide can be formed by the anodization of aluminum in acidic electrolytes [1][2][3]. Nanoporous alumina has attracted renewed attention lately as a promising material for the fabrication of new magnetic storage devices, catalytic membranes, and as an inexpensive template for the production of nanoscale particles, wires, and photonic crystals [4].Despite many experimental studies and general understanding of the pore growth mechanism to be associated with electric-field-assisted dissolution of aluminum oxide, the mechanism of self-organization of regular pore arrays is not understood. A model for the steady growth of a single pore, based on the field-assisted dissolution, was proposed in [5]. A similar model was considered in [6] and a long-wave linear stability analysis of the interfaces was performed. It can be shown, however, that the model studied in [6] does not provide a physically justified short-wave cutoff and hence a regularization mechanism needs to be identified that would explain the selection of the pore diameter and interpore spacing. One such mechanism is the dependence of the activation energies of the interfacial reactions on the Laplace pressure at the curved interfaces due to surface energy [7]. An additional important factor may be the elastic stress caused by the volume expansion in the course of the Al → Al 2 O 3 reaction [8]. The presence of elastic stress can significantly affect the morphological stability of the surface [9].c EDP Sciences Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx

Dendritic-pattern formation in anodic aluminum oxide templates

“…At 20 V we see that the pores vary widely in diameter and they are not very well organized into rows. This disorder in pore growth was shown to be an unstable configuration in the papers by Singh et al 5,6 We can see that as the voltage increases, the pores become more ordered. At about 100 V the pores become fairly uniform in diameter and also self-organize themselves evenly.…”

“…But, their model does not account for dependence of morphology on the applied voltage. Perhaps the most successful model was published recently by Singh et al 5,6 In their model, the authors began from the same first principles as Parkhutik and Shershulsky, but note that there are various growth regimes which depend on the voltage. Also, they note definite instabilities in the growth mechanism.…”

Effect of Electrostriction on the Self-organization of Porous Nanostructures in Anodized Aluminum Oxide

“…In the absence of stress effects, the system can only yield long-wave instabilities which usually lead to the growth of irregular arrays of pores seen in other oxide materials such as titanium as well as AAO for certain parameter regimes [31,32]. Taking typical electrochemical [43,42,41,15,44], electrostrictive [38] and elastic [45,46,44,47] parameter values, we numerically obtain the roots of Eq.…”

“…In [29], the effects of interfacial diffusion at the metal-oxide interface were investigated, and in [30], the effects of a field-dependent oxide conductivity were explored. The model proposed by Singh et al in [31,32] included the contributions of elastic stress to the surface activation energies, and it was shown that these effects can result in a short-wave instability which can explain the formation of hexagonally ordered pores. The validity of this model was explored experimentally in [33,34,35,36].…”

“…In this work, we propose an alternative elastic effect to that studied in [31,32]. While Singh et al examined elastic effects resulting from epitaxial stress at the metal-oxide interface, we will instead consider the effect of electrostriction induced by the electric field as a possible mechanism for pattern formation.…”