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

Abstract

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.

High‐lateral resolution X‐ray fluorescence microspectroscopy and dynamic mathematical modelling as tools for the study of electrodeposited electrocatalysts

“…A comprehensive discussion of the physics underlying this model and an extensive experimental validation are expounded in the studies of Lacitignola et al [61,62] and Bozzini et al [63,66] Here, we briefly recall its basic factors, and in the Appendix, we propose an extension that allows to simulate XRF maps and i-t transients, which will be employed for the study of electrodeposited Mn-Mg-Cu/PPy composites.…”

“…The occurrence of a supercritical Hopf bifurcation for the local kinetics of the system has also been proved. [61] This feature has two main dynamical implications. (i) Complex spatio-temporal behaviour can occur for system Eqn (5) when the parameter values are chosen so that the local system kinetics exhibits an oscillatory regime.…”

“…This mechanism is referred to as TH instability of the Hopf limit cycle. The related phenomenology has been theoretically investigated in the study of Lacitignola et al [61] by using the analytical Ricard-Mischler approach, [69] which employs perturbation expansions to find conditions -expressed in terms of the system parameters -so that the TH instability of the Hopf limit cycle can occur. According to the specific choice of the parameter values, two kinds of TH instabilities are possible for the homogeneous periodic solution: weak TH or strong TH.…”

Coelectrodeposition of Ternary Mn-Oxide/Polypyrrole Composites for ORR Electrocatalysts: A Study Based on Micro-X-ray Absorption Spectroscopy and X-ray Fluorescence Mapping

“…Besides these common features, the individual materials are characterized by typical subpatterns consisting of aligned assemblies of micrometric grains. These patterns, as well as the morphochemically decoupled behavior of Cu, can be interpreted in terms of a dynamical electrodeposition model, recently developed by some of the authors [62,63] and validated experimentally with XRF maps [41]: a systematic analysis of this topic will be the object of a dedicated paper, but we can anticipate that it is possible to find a set of parameters within the Turing-Hopf region in which the observed patterns can be reconstructed theoretically.…”

Numerical Preservation of Velocity Induced Invariant Regions for Reaction–Diffusion Systems on Evolving Surfaces

“…It is worth remarking that, even though we consider two RD models for illustrative purposes, the following analysis can be easily extended to other types of RDSs. To mention two examples, for the well-known Hodgkin-Huxley model and for the DIB model for electrodeposition considered in [24,25], the invariant region study is carried out in [14].…”