In a series of two papers, a mechanism is proposed to describe the initiation of organized arrays of nanopores and nanotubes formed via anodization of titanium. Part I describes the mechanism of initiation, based on the instability of the planar oxide/ electrolyte interface, and develops a criterion for the initiation of nanopores, while the present paper uses this planar interface instability criterion to calculate the size/spacing of nanopores. To facilitate the calculation, the destabilized interface is modeled by a series of sine waves, representing surface perturbations. Because the growth rates of the sine waves are a function of their wavelengths, the spacing of the ultimate array of nanopores and nanotubes is related to the wavelength of the fastest-growing perturbation. The proposed mechanism explains the transition from disorganized to organized and the influence of voltage on pore spacing and size.Nanoporous and nanotubular oxides of valve metals exhibit extremely high surface areas as well as electronic and electrochemical properties that strongly suggest applications in batteries, fuel cells, solar cells, and chemical sensors. [1][2][3] The size and spacing of nanopores and nanotubes are important parameters which govern the properties of the oxide nanostructures and, in our view, are established by the process of pore nucleation. The first of our two papers presented a mechanism of initiation of the nanopores in titanium oxide as well as equations expressing the criterion for pore initiation. In the present work, an expression is developed for the spacing of nanopore nuclei. The results provide estimates of pore spacing/size that are consistent with experimentally measured values of titanium oxide. In addition, the analysis explains three key experimental observations: ͑i͒ the simultaneous and homogeneous initiation of nanopores, ͑ii͒ the transition from disorganized to organized arrays of pores, and ͑iii͒ the increase in pore spacing/size with applied voltage. In the present study, scanning electron microscopic inspection of anodized titanium as a function of time of anodization confirms these three observations.
ExperimentalProcedure.-Anodization of Ti foils ͑0.125 mm, 99.6% ϩ purity, Goodfellow͒ was performed in a two-electrode cell, where Pt served as the counter electrode. Before anodization, the foils were sonicated in acetone and deionized ͑DI͒ water and then dried in a N 2 stream. Each foil sample was then immersed in an ethylene glycol solution containing 0.5 wt % NH 4 F and anodized at a constant potential of 20 V with a dc power supply. Different anodization times ͑30 s, 15 min, and 1 h͒ were applied to different foil samples. After the anodization step, the samples were again sonicated in DI water for 10 s and dried with N 2 before characterization. An FEI Strata 235 dual-beam scanning electron microscope was used to examine the morphology of the pores/tubes that formed on the surface of the foils.Results.-The influence of time of anodization on the appearance of the anodized surface of ...