Pattern Formation in Anodic Aluminum Oxide Growth by Flow Instability and Dynamic Restabilization

Abstract

The viscous flow of oxide driven by the electrostriction force during the growth of anodic aluminum oxide is treated by linear stability and scale analysis. A uniform oxide film is unstable to a periodic deformation. The restabilization of pore growth is examined by scale analysis of the steady pore diameter. The pattern spatial period and pore radius predicted by the analysis are compared with experimental observations reported in the literature.Anodizing is an electrochemical process technology that imparts an integral oxide coating to the surface of aluminum and its alloys. The metal is immersed in acid solution and an anodic current is passed through the metal-solution interface. An oxide coating is formed on the metal surface as the metal is consumed by electrochemical oxidation. The driving force in anodizing is enormous, ranging from 10 to more than 100 V. In a phase-growth process driven so far from equilibrium, we expect instability, dynamic restabilization, and pattern formation. On a scale of tens to hundreds of nanometers, the anodic aluminum oxide ͑AAO͒ coating is in fact highly ordered, with an array of high aspect ratio pores centered within hexagonal cells.The emergence of a pore array in AAO has been attributed to locally accelerated dissolution, 1 mechanical stresses originating with mismatches in a specific volume between the metal substrate and the oxide film, 2 and electrokinetic forces. 3 Stability analyses have been formulated based on these driving forces. 2-7 However, the most recent experimental and computational results make it clear that oxide flow is an important element of the process. 8-10 Based on these developments and on an electrochemical and fluid mechanical model of oxide growth described below, we propose that anodizing be viewed as a pattern formation process governed by a flow instability of the oxide film and its dynamic restabilization into cellular growth. 11,12 Pattern formation growth or deposition processes are characterized by high driving force, rapid entropy generation, and the emergence of structures that have no obvious relationship to the microstructure of the component material. 13 They typically progress through stages of compact growth, instability, and dynamic restabilization. The patterns are generated dynamically in the sense that they depend not on equilibrium properties of the material but on dissipative rate processes such as heat transfer, diffusion, or viscous flow. These characteristics are in contrast to self-assembly processes in which highly structured molecules aggregate into equilibrium structures.The hexagonal cell structure of the thicker oxide layers produced in anodizing is the signature of a flow process. The notion that oxide deformation induced by electrostatic forces could account for a breakdown of passive films was introduced by Sato 14 and a tracer study by Skeldon et al. 8 found evidence for flow in the AAO layer. Skeldon et al. considered the possibility that the flow is driven by electrostriction and reasoned that if the oxide laye...

Role of Oxide Stress in the Initial Growth of Self-Organized Porous Aluminum Oxide

“…Thus, peaks would grow and valleys deepen. A flow instability mechanism of porous anodic oxide formation was also presented by Barkey and McHugh [27]; however, flow in their model was driven by electrostriction stress, which according to our experiments is small compared to the oxide stress [21].…”

“…Thus, stress-driven ionic transport toward the pore walls is envisioned to assist pore formation. Various investigators have suggested transport mechanisms by elastic displacement [22][23][24], stress-affected ion migration [8], or oxide flow [16,[25][26][27][28].…”

Mathematical Modeling of Self‐Organized Porous Anodic Oxide Films

“…Their calculations revealed increasingly tensile stress at higher anodizing current density, consistent with some but not all experiments [114]. The morphological instability study by Barkey and McHugh incorporated bulk oxide motion as an essential feature of the instability mechanism driving pattern formation [113]. This model treated oxide motion as Newtonian viscous flow generated by electrostriction stress at the oxide-solution interface.…”

“…Such motion has been interpreted differently as either plastic flow, or rigid body motion due to elastic forces [53,64,73]. In mathematical models, oxide motion has been treated as viscous flow [65,87,113]. Houser and Hebert tested the interpretation of bulk oxide motion as plastic flow, in a simulation of steady-state growth of porous anodic alumina [65].…”

“…Barkey and McHugh considered a model of barrier oxide growth in which the rate of oxide-solution interface motion was entirely determined by the flow velocity [113]. Flow was driven by pressure due to the combined effects of electrostriction and capillary forces.…”