Ivonne Sgura

On worm-like chain models within the three-dimensional continuum mechanics framework

In this paper, we review critically some basic models derived from the statistics of long-chain molecules and then discuss the status of such models within the three-dimensional nonlinear theory of elasticity. We draw attention to some deficiencies of certain worm-like chain (WLC) models when viewed within the three-dimensional continuum mechanics framework. Modifications of the WLC models motivated by such considerations and avoiding these deficiencies are then discussed and shown to correspond well with data generated by the exact WLC model.

The relevance of nonlinear stacking interactions in simple models of double-stranded DNA

Single molecule DNA experiments provide interesting data that allow a better understanding of the mechanical interactions between the strands and the nucleotides of this molecule. In some sense, these experiments complement the classical ones about DNA thermal denaturation. It is well known that the original Peyrard–Bishop (PB) model by means of a harmonic stacking potential and a nonlinear substrate potential has been able to predict the existence of a critical temperature of full denaturation of the molecule. In the present paper, driven by the findings of single molecule experiments, we substitute the original harmonic intra-strand stacking potential with a Duffing type potential. By elementary and analytical arguments, we show that with this choice it is possible to obtain a sharp transition in the classical domain wall solution of the PB model and the compactification of the classical solitary wave solutions of other models for the dynamics of DNA. We discuss why these solutions may improve our knowledge of the DNA dynamics in several directions.

Spatio-temporal organization in alloy electrodeposition: a morphochemical mathematical model and its experimental validation

This paper proposes a novel mathematical model for the formation of spatio-temporal patterns in electrodeposition. At variance with classical modelling approaches that are based on systems of reaction–diffusion equations just for chemical species, this model accounts for the coupling between surface morphology and surface composition as a means of understanding the formation of morphological patterns found in electroplating. The innovative version of the model described in this work contains an original, flexible and physically straightforward electrochemical source term, able to account for charge transfer and mass transport: adsorbate-induced effects on kinetic parameters are naturally incorporated in the adopted formalism. The relevant non-linear dynamics is investigated from both the analytical and numerical points of view. Mathematical modelling work is accompanied by an extensive, critical review of the literature on spatio-temporal pattern formation in alloy electrodeposition: published morphologies have been used as a benchmark for the validation of our model. Moreover, original experimental data are presented—and simulated with our model—on the formation of broken spiral patterns in Ni–P–W–Bi electrodeposition.

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

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 codimension-two 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.

Metallic Plate Corrosion and Uptake of Corrosion Products by Nafion in Polymer Electrolyte Membrane Fuel Cells

Nafion contamination by ferrous-alloy corrosion products, resulting in dramatic drops of the Ohmic potential, is a suspected major failure mode of polymer electrolyte membrane fuel cells that make use of metallic bipolar plates. This study demonstrates the potential of scanning transmission X-ray microscopy combined with X-ray absorption and fluorescence microspectroscopy for exploring corrosion processes of Ni and Fe electrodes in contact with a hydrated Nafion film in a thin-layer cell. The imaged morphology changes of the Ni and Fe electrodes and surrounding Nafion film that result from relevant electrochemical processes are correlated to the spatial distribution, local concentration, and chemical state of Fe and Ni species. The X-ray fluorescence maps and absorption spectra, sampled at different locations, show diffusion of corrosion products within the Nafion film only in the case of the Fe electrodes, whereas the Ni electrodes appear corrosion resistant.

Numerical approximation of Turing patterns in electrodeposition by ADI methods

In this paper we study the numerical approximation of Turing patterns corresponding to steady state solutions of a PDE system of reaction-diffusion equations modeling an electrodeposition process. We apply the Method of Lines (MOL) and describe the semi-discretization by high order finite differences in space given by the Extended Central Difference Formulas (ECDFs) that approximate Neumann boundary conditions (BCs) with the same accuracy. We introduce a test equation to describe the interplay between the diffusion and the reaction time scales. We present a stability analysis of a selection of time-integrators (IMEX 2-SBDF method, Crank-Nicolson (CN), Alternating Direction Implicit (ADI) method) for the test equation as well as for the Schnakenberg model, prototype of nonlinear reaction-diffusion systems with Turing patterns. Eventually, we apply the ADI-ECDF schemes to solve the electrodeposition model until the stationary patterns (spots & worms and only spots) are reached. We validate the model by comparison with experiments on Cu film growth by electrodeposition.

Travelling waves in a reaction-diffusion model for electrodeposition

In this paper we consider an analytical and numerical study of a reaction-diffusion system for describing the formation of transition front waves in some electrodeposition (ECD) experiments. Towards this aim, a model accounting for the coupling between morphology and composition of one chemical species adsorbed at the surface of the growing cathode is addressed. Through a phase-space analysis we prove the existence of travelling waves, moving with specific wave speed. The numerical approximation of the PDE system is performed by the Method of Lines (MOL) based on high order space semi-discretization by means of the Extended Central Difference Formulae (D2ECDF) introduced in [1]. First of all, to show the advantage of the proposed schemes, we solve the well-known Fisher scalar equation, focusing on the accurate approximation of the wave profile and of its speed. Hence, we provide numerical simulations for the electrochemical reaction-diffusion system and we show that the results obtained are qualitatively in good agreement with experiments for the electrodeposition of Au-Cu alloys.

Investigation into dynamics of Au electrodeposition based on analysis of SERS spectral time series

Abstract A considerable amount of electrochemical and structural information is available on Au electrodeposition, but its dynamic aspects are still largely ignored. In this paper, an investigation of the microscopic Au electrodeposition dynamics is presented. Extensive sets of SERS spectra during prolonged potentiostatic electrodeposition (∼3 h) are recorded. Two different spot sizes have been used, in order to also obtain some information on the coupling of temporal and spatial fluctuations at the cathodic surface. The time evolution of the SERS background and the intensity of the stretching band of adsorbed CN− have been used as markers of surface morphology and chemistry respectively. Statistical analyses of these quantities allowed extraction of detailed information at the coupled dynamics of SERS enhancement and surface concentration of CN−. The spectroelectrochemical investigation is complemented by SEM observations and mathematical modelling of the coupled dynamics of cathode morphology and CN− surface concentration.

A TWO-POINT BOUNDARY-VALUE PROBLEM FOR THE AXIAL SHEAR OF HARDENING ISOTROPIC INCOMPRESSIBLE NONLINEARLY ELASTIC MATERIALS ∗

The purpose of this research is to investigate a pure axial shear problem for the annular region between two concentric rigid cylinders occupied by an incompressible isotropic nonlinearly elastic material. Our main concern is with the subclass of these materials that exhibits hardening at large deformations. Such hardening at large strains is observed experimentally but is often not predicted by commonly used strain-energy densities. The particular axial shear problem that we investigate arises when the elastic material is perfectly bonded to an inner rigid circular core and to an outer rigid circular container. The deformation is driven by an axial pressure gradient. The problem is formulated as a two-point boundary-value problem for a second-order nonlinear ODE. For a broad class of incompressible isotropic hyperelastic materials, existence of smooth solutions is established on conversion to an initial value problem. We then specialize the material class to be of generalized neo-Hookean type, that is, w...

Morphological spatial patterns in a reaction diffusion model for metal growth.

In this paper a reaction-diffusion system modelling metal growth processes is considered, to investigate - within the electrodeposition context- the formation of morphological patterns in a finite two-dimensional spatial domain. Nonlinear dynamics of the system is studied from both the analytical and numerical points of view. Phase-space analysis is provided and initiation of spatial patterns induced by diffusion is shown to occur in a suitable region of the parameter space. Investigations aimed at establishing the role of some relevant chemical parameters on stability and selection of solutions are also provided. By the numerical approximation of the equations, simulations are presented which turn out to be in good agreement with experiments for the electrodeposition of Au-Cu and Au-Cu-Cd alloys.