Conceptual Progress for Explaining and Predicting Self-Organization on Anodized Aluminum Surfaces

nanomaterials Review Conceptual Progress for Explaining and Predicting Self-Organization on Anodized Aluminum Surfaces Mikhail Pashchanka Department of Chemistry, Eduard-Zintl-Institute, Technical University of Darmstadt, Alarich-Weiss-Straße 12, 64287 Darmstadt, Germany; [email protected] Abstract: Over the past few years, researchers have made numerous breakthroughs in the field of aluminum anodizing and faced the problem of the lack of adequate theoretical models for the interpretation of some new experimental findings. For instance, spontaneously formed anodic alumina nanofibers and petal-like patterns, flower-like structures observed under AC anodizing conditions, and hierarchical pores whose diameters range from several nanometers to sub-millimeters could be explained neither by the classical field-assisted dissolution theory nor by the plastic flow model. In addition, difficulties arose in explaining the basic indicators of porous film growth, such as the nonlinear current–voltage characteristics of electrochemical cells or the evolution of hexagonal pore patterns at the early stages of anodizing experiments. Such a conceptual crisis resulted in new multidisciplinary investigations and the development of novel theoretical models, whose evolution is discussed at length in this review work. The particular focus of this paper is on the recently developed electroconvection-based theories that allowed making truly remarkable advances in understanding the porous anodic alumina formation process in the last 15 years. Some explanation of the synergy between electrode reactions and transport processes leading to self-organization is provided. Finally, future prospects for the synthesis of novel anodic architectures are discussed. Citation: Pashchanka, M. Conceptual Progress for Explaining Keywords: porous anodic alumina (PAA); chaos and self-organization theory; electroconvection; and Predicting Self-Organization on colloidal gel model; anion exchange; DLVO theory; fluid mechanics; surface chemistry; surface Anodized Aluminum Surfaces. Nanomaterials 2021, 11, 2271. https:// energy reduction; electrochemistry doi.org/10.3390/nano11092271 Academic Editor: Christophe Detavernier 1. Introduction It was the novelist Grace McCleen who once said: “Miracles do not have to be big, Received: 30 June 2021 and they can happen in the unlikeliest places.” This quote obviously did not have anything Accepted: 27 August 2021 to do with exact sciences or, specifically, with the stochastic nature of self-organization Published: 31 August 2021 in non-living matter. However, it certainly has a great metaphorical value that may help to explain some basic principles of such complex phenomena in a simpler manner. Publisher’s Note: MDPI stays neutral Indeed, for the miracle called “spontaneous self-organization” to occur, a system must with regard to jurisdictional claims in be stochastic. That is to say that such a system must always include different random, published maps and institutional affil- probabilistic processes because instabilities and accidental fluctuations are the necessary iations. factors leading to evolutionary patterns in the real-world systems. One vivid example of such “chaotic” evolution is the well-known sequence of “mild anodizing” (MA) [1,2] and “hard anodizing” (HA) [3,4] self-ordering regimes observed during honeycomb-like porous anodic alumina (PAA) formation under gradually increased anodizing voltages (Figure1A). Copyright: © 2021 by the author. The recent study by Vega et al. showed that the MA and the HA voltage ranges in which Licensee MDPI, Basel, Switzerland. self-ordering occurs are typically separated by a rather broad interval (that is recognizable This article is an open access article on a recorded linear sweep voltammogram) in which no formation of well-ordered pore distributed under the terms and arrays can be observed (see Figure1A–E) [ 5]. This experimental investigation confirms conditions of the Creative Commons that the new stable porous structure with a larger self-ordering periodicity which is formed Attribution (CC BY) license (https:// under the HA regime does not evolve from the previous array of smaller MA-generated creativecommons.org/licenses/by/ close-packed hexagonal cells after their continuous uniform expansion upon the gradual 4.0/). Nanomaterials 2021, 11, 2271. https://doi.org/10.3390/nano11092271 https://www.mdpi.com/journal/nanomaterials Nanomaterials 2021, 11, 2271 2 of 67 self-ordering periodicity which is formed under the HA regime does not evolve from the Nanomaterials 2021, 11, 2271 previous array of smaller MA-generated close-packed hexagonal cells after their2 of 67 continuous uniform expansion upon the gradual linear transition from “mild” to “hard” anodizing voltages. Instead, the new well-ordered textures emerge from an intermediate linearchaotic transition state. Thus, from “mild”the entire to “hard” evolution anodizing process voltages. where Instead, chaos theplays new its well-ordered constructive role texturesincludes emerge not only from gradual an intermediate quantitative chaotic chan state.ges but Thus, also the qualitative entire evolution transitions process and sharp wherequantitative chaos plays changes its constructive in between role due includes to the not complex only gradual interplay quantitative of different changes involved but fac- alsotors. qualitative This observation transitions leads and sharp us to quantitative the next important changes in betweenproperty due of toself the-organizing complex sys- interplay of different involved factors. This observation leads us to the next important tems—namely, their nonlinearity. Indeed, as demonstrated by voltammetry measure- property of self-organizing systems—namely, their nonlinearity. Indeed, as demonstrated byments voltammetry in the above measurements-mentioned in thework above-mentioned by Vega et al. work(Figure by Vega1A,B), et al.there (Figure is a 1nonlinearA,B), re- therelationship is a nonlinear between relationship electrical betweencurrent electricaldensity currentj and applied density jpotentialand applied difference potential ∆U in a differencetypical anodizingDU in a typical cell designed anodizing for cell PAA designed growth for PAA (in other growth words, (in other Ohm’s words, law Ohm’s is not met) law[5]. isThe not MA met) self [5].-ordering The MA self-orderinginterval (where interval current (where rises current exponentially rises exponentially;; see stage seeI in Figure stage1A) is I in separated Figure1A) from is separated the HA from self the-ordering HA self-ordering interval intervalby a local by amaximu local maximumm and a short andplateau a short region plateau (within region which, (within as which, discussed as discussed previously, previously, disordered disordered PAA is PAA formed is ; see formed;Figure see1C) Figuredue to1 C)some due current to some-limiting current-limiting mechanisms. mechanisms. Figure 1. (A) A typical nonlinear j−∆U curve for the formation of PAA divided into four stages la- Figure 1. (A) A typical nonlinear j−DU curve for the formation of PAA divided into four stages beled as I (“mild anodizing” regime, MA), II (“hard anodizing” regime, HA), II* (current plateau labeled as I (“mild anodizing” regime, MA), II (“hard anodizing” regime, HA), II* (current plateau region which corresponds to the HA self-ordering voltages and is preceded by an intermediate region which corresponds to the HA self-ordering voltages and is preceded by an intermediate “chaotic” state), III (dielectric breakdown), VHA (the beginning of II), and VBD (the beginning of III); “chaotic” state), III (dielectric breakdown), V (the beginning of II), and V (the beginning of III); (B) j–∆U curves obtained for 0.075–0.3 MHA oxalic acid electrolyte solutionsBD containing 5–10 vol % of (B) j–DU curves obtained for 0.075–0.3 M oxalic acid electrolyte solutions containing 5–10 vol % of ethanol; (C–E) SEM images demonstrating different degrees of pore ordering obtained at 100–150 V ethanol; (C–E) SEM images demonstrating different degrees of pore ordering obtained at 100–150 V anodizing voltages using a 0.3 M oxalic acid electrolyte solution (corresponds to the black j–∆U anodizing voltages using a 0.3 M oxalic acid electrolyte solution (corresponds to the black j–DU curve in (B), on which the tested voltages are shown by arrows and dashed lines). Adapted with curve in (B), on which the tested voltages are shown by arrows and dashed lines). Adapted with permission from [5]. Copyright 2015 American Chemical Society. permission from [5]. Copyright 2015 American Chemical Society. InIn general, general, the the nonlinearity nonlinearity in such in dynamic such dynamic self-organizing self-organizing systems (that syste is, inms which (that is, in spontaneouswhich spontaneous self-organization self-organization of matter intoof matter patterns into occurs patterns under occurs a certain under set of a condi-certain set of tions)conditions) means thatmeans the responsethat the ofresponse such a system of such has a tosystem be out has of proportion to be out toof theproportion external to the influenceexternal (ininfluence our case, (in to our the case, externally to the externally controlled gradualcontrolled increase gradual in theincrease applied in volt-the applied agevoltageDU). ∆ SuchU). Such rapid rapid exponential exponential amplification amplification of the electricalof the electrical current current followed followed by its by its inhibitioninhibition within within the the transitional

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