(Invited) Growth of Self-Ordered Anodic Oxide Nanomaterials By Coupled Ion Migration and Viscous Flow
Authors: Mishra Pratyush , Hebert Kurt 
Published: February 2020

Porous anodic alumina films are self-organized porous oxides nanomaterials formed by electrochemical oxidation. Pores initiate after an initial stage of barrier oxide growth at the oxide-solution interface. The porous film eventually evolves into a hexagonally-ordered array of parallel cylindrical pores of order 100 nm diameter with a characteristic spacing that scales directly with the cell voltage. The spacing also depends on the type of oxyacid comprising the cell solution, e. g. sulfuric, oxalic or phosphoric acid. This presentation describes our efforts to understand the instability mechanism during anodization of Al in acidic aqueous solutions through a combination of experimental and modeling methods.
The process of self-ordering of porous alumina films is characterized by evolution of an irregular distribution of incipient pores into the steady-state pore array. We explore the roles of mechanical stress and oxide flow in self-ordering, through a modeling analysis of stress-driven viscous flow of oxide (1-3). The model is based on coupled viscous flow of oxide and stress- and electric field-driven migration of Al+3 and O-2 ions (1). The present version of the model includes boundary conditions that include surface stress at the oxide-solution interface. These boundary conditions provide the ability to predict morphology evolution and stress distributions. Surface stress arises from incorporation of O-2 ions and electrolyte anions during anodizing. The calculation results depict the buildup of compressive stress within a layer of a few nanometers thickness at the oxide surface, as inferred previously from in situ stress measurements (4). Additionally, the model predictions are consistent with observations of tensile bulk stress in the oxide accompanying inward oxide flow during the transition to the steady-state pore array (5). This transition is due to competitive growth of the initially nonuniform distribution of incipient pores until a monodisperse steady-state distribution is attained.
We present linear stability analysis incorporating the surface stress boundary conditions in the coupled oxide flow-electrical migration model of Houser and Hebert (1). The calculations reveal steady-state pore spacing-voltage scaling ratios that compare favorably to those found experimentally. This result is independent of oxide viscosity or uncertainty in the values of any other model parameters.
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Figure 1. Comparison of predicted and experimental evolution of stress depth profiles near the oxide surface (3). Anodic oxidation in 0.4 M phosphoric acid at 4.5 mA/cm2. (a) Model predictions vs. depth from solution interface. (b) Experimental stress-depth profiles from Ref. (4).

Figure 1