Elsevier

Electrochemistry Communications

Volume 12, Issue 9, September 2010, Pages 1174-1176
Electrochemistry Communications

What controls the pore spacing in porous anodic oxides?

https://doi.org/10.1016/j.elecom.2010.06.010Get rights and content

Abstract

In this paper, we use energy-based perturbation criteria to examine whether strain or electrostatic energy acts as a driving force for porosity initiation in anodic oxides. By doing so, we also succeeded to rationalise the dependence of pore spacing on anodising conditions. Our experimental approach consists of measuring in-situ the internal stress in anodic oxide films grown galvanostatically on aluminium in phosphoric acid, and to correlate these data with the measured pore spacing of the obtained porous films. Our results indicate that the possibility of a strain energy-induced surface instability is unlikely, as for this case the constitutive dependence of pore spacing on internal stress was not verified. Instead, the measured pore spacing, electric field and barrier oxide thickness obtained on our anodic alumina films indicate that electrostatic energy is the main driving force for pore initiation, as well as the factor controlling the pore spacing. Corroborative quantitative evidence for this novel electrostatic-based scaling law is provided by data compiled from the literature for a range of other anodic oxide systems, including nanoporous alumina and nanotubular titania films.

Introduction

Despite the routine or potential use of porous anodic oxides in many technological applications, no mechanistic insights have been made available yet to explain the observed systematic dependence of pore dimensions, including pore spacing, on anodising conditions. For instance, it is found experimentally that the anodising parameter that predominantly controls the pore spacing is the anodising voltage. For anodic alumina, a constant ratio between pore spacing and anodising voltage of about 2.5 to 2.8 nm/V has been reported [1], [2], [3], [4], [5]. Such a direct proportionality with anodising voltage has also been observed for nanotubular anodic oxides on titanium [6], [7]. However, the anodising voltage cannot be the only parameter that controls the pore spacing in anodic oxides. Indeed, the ratio between pore spacing and anodising voltage has been reported to depend also on the composition of the anodised metal [7]. Moreover, even at fixed alloy composition, different ratios are obtained depending on the anodising conditions [5]. For instance, anodic alumina obtained by hard anodisation has a lower pore spacing/voltage ratio than that obtained by conventional anodising [8]. A dependence of this ratio on electrolyte composition has also been observed for nanotubular anodic titania, for which the tube spacing has been reported to depend on the water content of the electrolyte [9]. A mechanistic model describing the dependence of pore or tube spacing on anodising conditions would definitely allow to improve our understanding of the processes involved in the well-established systematic selection of pore morphologies. Such a model could also shed a light on the origin of porosity initiation, and hence in the transition from a dense to a porous oxide, since the associated increase in oxide surface area alone is energetically not favourable.

An attempt for such a model has recently been proposed by Raja et al. [10], who suggested, based on earlier seminal work by Asaro and Tiller [11], that internal stresses in anodic oxides are responsible for the initiation of porosity and the associated selection of pore spacing. Their suggestion is based on the well-documented observation that in several cases, an initially flat growing thin film may start to develop surface roughness, the lengthscale of which being selected by the internal stress in the layer [12]. In such a case, the initially flat surface of the solid is energetically unstable against perturbations if the characteristic wavelength of the perturbation is greater than a critical value λc, the latter being defined as the wavelength at which the total (surface plus strain) energy is the same in the flat and the perturbed state. By balancing the increase in surface area with the resulting decrease in strain energy, the critical perturbation wavelength λc can be expressed for an isotropic solid as [11], [13]:λc=πMγσ2where M is the biaxial modulus of the solid, γ its surface energy, and σ its internal biaxial stress.

Besides strain energy, other energy terms can stabilise a perturbed surface as well, leading to a different expression for the critical wavelength λc than the one predicted by Eq. (1). For instance, in the case of a parallel plate capacitor in vacuum over which an electric field E is present, the following expression was derived for λc [14]:λc=4π2hγεoE2where h is the distance between the capacitor plates and εo is the vacuum permittivity. In the specific case of anodic oxide growth, during which relatively high electric fields on the order of 109 V/m are present, we therefore anticipate that surface perturbations may be stabilised as well by the associated decrease in electrostatic energy. In such a case, the relevant critical perturbation wavelength for an oxide dielectric with relative permittivity εr should then be equal to:λc=4π2hoxγεoεrE2where hox is the oxide thickness upon perturbation, corresponding to the thickness of the dense barrier layer (further denoted as hox,b).

The objective of this paper is to verify whether the selection of pore spacing during the growth of anodic oxide films can be rationalised by either of the two generic model Eqs. (1), (3) that are known from literature to govern stabilisation of surface perturbations. This was done by combining internal stress data, taken in-situ at different current densities during galvanostatic anodising of aluminium in phosphoric acid, with morphological data on pore spacing and barrier oxide thickness obtained from cross-sectional electron microscopy.

Section snippets

Experimental

Aluminium films were deposited 800 nm thick by electron-beam evaporation onto double-side polished oxidised silicon substrates. The preparation of the samples and the in-situ curvature measurement setup have already been described elsewhere [15]. Anodising was performed galvanostatically in 0.4 mol L1 phosphoric acid. The mean internal stress in the oxide < σox> is calculated from the curvature change of the sample ΔK through a multilayer version of Stoney's equation [16]:<σox>hox=Mshs26ΔK+<σAl>PBR

Results and discussion

The dependencies of the barrier layer thickness, pore spacing, steady-state voltage, electric field and internal stress on current density are shown in Fig. 1. The electric field, calculated as the ratio between the steady-state voltage and barrier layer thickness observed at the end of anodising, increased from 0.8 to 1.0 V/nm when the current density increased from 2.0 to 50 mA/cm2. The electric field values are consistent with typical values for Al anodising [17]. As to the internal stress in

Conclusions

Energy-based perturbation criteria were examined to explain the appearance of porosity and the dependence of pore spacing on anodising conditions. Internal stress data, measured in-situ during galvanostatic aluminium anodising, indicate that a strain-induced surface instability is unlikely to be the controlling factor for pore initiation and pore spacing selection in anodic oxides. Instead, the observed pore spacing in anodic oxides of both aluminium and titanium, compiled for a wide range of

Acknowledgements

QVO acknowledges financial support of the Fonds pour la Recherche dans l'Industrie et l'Agriculture through a fellowship. The authors would like to thank Prof. Joost Vlassak from Harvard University for pointing out relevant references for performing the appropriate perturbation analyses.

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