Travelling waves in a reaction-diffusion model for electrodeposition

Bozzini, Benedetto; Lacitignola, Deborah; Sgura, Ivonne

doi:10.1016/j.matcom.2010.10.008

Cited by 16 publications

(5 citation statements)

References 18 publications

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“…In a series of recent papers [7][8][9][10][11][12][13][14][15] and [63] we used the reaction-diffusion modelling approach to rationalize the formation of morphological patterns in electrodeposition. The novelty of our approach was to consider more natural state variables: the morphology (surface profile) -that is the crucial observable -and the surface chemistry (composition) -that in fact controls the growth process -coupled through non-linear and physically straightforward electrochemical source terms.…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

2014

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In this paper, we investigate from a theoretical point of view the 2D reaction-diffusion system for electrodeposition coupling morphology and surface chemistry, presented and experimentally validated in Bozzini et al. (2013 J. Solid State Electr. 17, 467-479). We analyse the mechanisms responsible for spatio-temporal organization. As a first step, spatially uniform dynamics is discussed and the occurrence of a supercritical Hopf bifurcation for the local kinetics is proved. In the spatial case, initiation of morphological patterns induced by diffusion is shown to occur in a suitable region of the parameter space. The intriguing interplay between Hopf and Turing instability is also considered, by investigating the spatio-temporal behaviour of the system in the neighbourhood of the codimensiontwo Turing-Hopf bifurcation point. An ADI (Alternating Direction Implicit) scheme based on high-order finite differences in space is applied to obtain numerical approximations of Turing patterns at the steady state and for the simulation of the oscillating Turing-Hopf dynamics.

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Section: Introductionmentioning

confidence: 99%

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

2014

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“…4C). The low reproducibility obtained at À1 V can be attributed to the inherent non-stationarity of the electrocrystallisation processes [43][44][45]. It is well known that electrocrystallisation is in principle a non-stationary process, based on the formation of small particles (nuclei) and their successive growth [46][47][48].…”

Section: Impedance Spectramentioning

confidence: 99%

A study of external magnetic-field effects on nickel–iron alloy electrodeposition, based on linear and non-linear differential AC electrochemical response measurements

Ispas

Matsushima

Bund

et al. 2011

Journal of Electroanalytical Chemistry

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“…Az Az E J (10) where We recall that a reaction-diffusion system exhibits Turing or diffusion-driven instability, if a homogeneous steady state is stable to small perturbations in the absence of diffusion, but it is unstable to small spatial perturbations when diffusion is present [9]. By using standard linear theory (see e.g.…”

Section: Stability Analysismentioning

confidence: 99%

“…By using standard linear theory (see e.g. [9]), it can be shown that (η e , θ e ) can undergo Turing instability if the relationships in (12) and ( 13) are satisfied together with where J ij e are the entries of the Jacobian matrix in Eq. 9 or Eq.…”

Section: Stability Analysismentioning

confidence: 99%

“…Furthermore, metal electrodeposition has been proved to profoundly affect the RTIL adsorption behaviour [6]. Recently, we have developed a series of approaches to the analytical and numerical solution of these electrodeposition modelling issues, ultimately based on pure Butler-Volmer kinetics [8][9][10]. In this paper we describe the extension of our approach to systems, such as RTIL-based baths, in which mass-transport contributions are vital.…”

Section: Introductionmentioning

confidence: 99%

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Prediction of Morphological Properties of Smart-Coatings for Cr Replacement, Based on Mathematical Modelling

Bozzini

Sgura

Lacitignola

et al. 2010

AMR

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In this paper we present an extension of a mathematical model for the morphological evolution of metal electrodeposits – recently developed by some of the authors – accounting for mass-transport of electroactive species from the bulk of the bath to the cathode surface. The implementation of mass-transport effects is specially necessary for the quantitative rationalisation of electrodeposition processes from ionic liquids, since these electrolytes exhibit a viscosity that is notably higher than that of cognate aqueous solutions and consequently mass-transport control is active at all practically relevant plating rates. In this work we show that, if mass-transport is coupled to cathodic adsorption of ionic liquid species and surface diffusion of adatoms, it can lead to electrodeposit smoothing. This seemingly paradoxical theoretical result has been validated by a series of Mn electrodeposition experiments from aqueous baths and eutectic ionic liquids. The latter solutions have been shown to be able to form remarkably smoother coatings than the former ones. Mn electroplates have been proposed for Cd replacement and their corrosion protection performance seems comparable, but so far the required surface finish quality has not been achieved with aqueous electrolytes. Ionic liquids thus seem to provide a viable approach to aeronautic-grade Mn electroplating.

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Travelling waves in a reaction-diffusion model for electrodeposition

Cited by 16 publications

References 18 publications

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

A study of external magnetic-field effects on nickel–iron alloy electrodeposition, based on linear and non-linear differential AC electrochemical response measurements

Prediction of Morphological Properties of Smart-Coatings for Cr Replacement, Based on Mathematical Modelling

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