Antonis Karantonis

Abstract: In the present paper the non-linear time evolution of the electrodissolution/passivation of iron in sulfuric acid-sodium chloride solution is explored. The working electrode is an assembly of two iron disk electrodes, interacting through the electrolyte, and the time evolution of the electric current has the form of spontaneous bursting oscillations. The main aim of this work is to characterize the modes of synchrony and more specifically the synchronization of electric bursts and the synchronization of electric spikes. The characterization is based on the calculation of the firing rates from the experimental time series and the extraction of the slow dynamics by lowpass filtering. The analysis is performed both for elliptic and square wave electrochemical bursting and the results are compared with neural oscillations. © Springer Science+Business Media B.V. 2009.

Abstract: In the present work the frequency response of the electrochemical interface is investigated during the electrodissolution of copper in trifluoroacetic acid (TFA). The instability of a stable steady state to periodic oscillations is characterized and thus the nature of the steady state close to the instability is revealed to be a stable focus. The frequency response of the stable focus is explored by electrochemical impedance spectroscopy and the impedance amplitude profile (ZAP) method. It is shown that the system resonates at a specific frequency of the input signal and thus acts as a resonator (band-pass filter) similarly to neural resonators. © 2010 Elsevier B.V. All rights reserved.

Abstract: The ability to produce bursting electrochemical oscillations via the slow external variation of the applied potential is investigated during the electrodissolution/passivation of iron in sulfuric acid. The results are compared with those concerning spontaneous electrochemical bursting in the presence of chloride ions. Moreover, an assembly of two electrochemical Fe/H₂SO₄bursters is studied experimentally. The effect of phase space topology on synchrony is explored by studying the coupled response for different types of electrochemical bursters. © 2009 Elsevier Ltd. All rights reserved.

Abstract: An experimental setup is designed in order to achieve unidirectional chemical coupling of an electrochemical oscillator and imitate neural synaptic transmission. The electrochemical oscillator is an iron electrode immersed in sulfuric acid solution and the chemical interaction is achieved via the flow of chloride ions towards the electrochemical interface, controlled by a peristaltic pump. The electrochemical interface responds to chemical pulses by producing periodic electric oscillations, electric bursts or electric spikes, depending on the interface potential. The type of electrical response to chemical interactions is determined by the topology of the phase space close to the bifurcation points. © 2008 Elsevier B.V. All rights reserved.

Abstract: The effect of halogen ions on the electrochemical oscillations of the Fe/H₂SO₄ system is studied experimentally. It is shown that the dynamic modification of the electrochemical interface transforms the periodic oscillator to a burster. The effect of the applied potential and the nature of halogen ions is investigated and bursting activity is classified according to the nonlinear characteristics of the oscillations. Different types of bursting are compared and interpreted according to the bifurcation characteristics of the periodic oscillator. © 2007 American Chemical Society.

Abstract: The electrocatalytic oxidation of formaldehyde on a polycrystalline platinum electrode is studied under potentiodynamic and galvanostatic conditions. It is shown that an extended dual path mechanism can reproduce the bistability, oscillations and bifurcation sequences observed experimentally. © 2006 Elsevier B.V. All rights reserved.

Abstract: Networks of weakly coupled discrete electrochemical oscillators have the ability of synchronizing rapidly in-phase or out-of-phase, depending on the network geometry. It is shown that a network consisting of N relaxation electrochemical oscillators, coupled through inhibitory connections, can have (N - 1)! coexisting out-of-phase states, each state being a permutation of a periodic spiking sequence. The out-of-phase states can be modified by shots of laser pulse perturbations and the phase relation is stored as a coded spatiotemporal pattern. The ability of the network to function as a re-writable memory of (N - 1)! different spatiotemporal patterns is demonstrated experimentally for N = 4. © World Scientific Publishing Company.

Abstract: The static and dynamic characteristics of the electrodissolution of steel covered with an organic layer as well as of plain steel are studied in aqueous solutions of various NaCl concentrations. Anodic polarization and electro-chemical impedance spectroscopy for plain steel indicate that active dissolution takes place in a potential region close to the open circuit potential where the current is less than 10^-4A. Similar experiments for coated steel suggest the adsorption of ionic species and the formation of a surface layer on the metal substrate. This layer results in a negative faradaic resistance, i.e. a potential region where the faradaic current is a decreasing function of the potential. This region of negative faradaic resistance is related to the occurrence of current oscillations. These oscillations, of a period ranging from 100 to 1200 s, might be attributed to the formation/dissolution of a salt precipitant within the pores of the organic layer.

Abstract: A network consisting of N relaxation electrochemical oscillators, mutually coupled by all-to-all inhibitory connections, can have (Nâ1)! coexisting out-of-phase states, each state being a permutation of a periodic spiking sequence. The modification of the out-of-phase states by shots of laser pulse perturbations is shown. In such networks the phase relation of the oscillators is stored as a coded pattern. The ability of the network to function as a rewritable memory of (Nâ1)! different spatiotemporal patterns is demonstrated experimentally for N=4. © 2005 The American Physical Society.

Abstract: Networks of relaxation electrochemical oscillators, coupled through the electrolytic medium, can synchronize into different synchronized states. Model calculations and experimental results suggest that the synchronized states can be manipulated by changing the geometry of the system and applying appropriate perturbations. © 2005 Elsevier Ltd. All rights reserved.

Abstract: The synchronization modes of coupled relaxation electrochemical oscillators are studied. The case of ring networks of discrete electrochemical oscillators is considered where boundaries are not present. A model of discrete coupled electrochemical oscillators is derived systematically from a continuous model and a discretization procedure. It is shown that, under specific conditions, the cells are coupled electrically and the connection is linear and symmetric. Also, the coupling strength is derived explicitly as a function of the geometric network characteristics, as well as the electric properties of the surrounding medium. The model equations are studied numerically, and the different modes of synchronization are discussed in detail. It is also shown that, because of fast transitions and the elimination of phase or period differences, networks of coupled relaxation electrochemical oscillators can perform some primitive information manipulation tasks.

Abstract: Experimentally observed effects of a spatially localised external laser forcing, on the oscillatory current of the electrodissolution of an iron ring electrode in sulfuric acid, can be reproduced qualitatively by means of a simple, spatially one-dimensional model, expressed by partial differential equations for the double layer potential drop and hydrogen ions concentration, coupled with an ordinary differential equation for the coverage fraction by the passivating hydroxide. These model equations can be solved efficiently and economically by means of the patch-adaptive finite-difference strategy, that automatically concentrates the spatial and temporal grids in the critical regions. The analysis of the model solutions reveals that activation caused by the forcing occurs via accelerating moving fronts, resulting in spatially non-homogeneous distributions of the dynamical variables. When the oscillator is predominantly in the passive state, then a one-dimensional discrete map can be constructed, based on single perturbation simulations, which predicts, with a good quantitative agreement, the temporal behaviour of the electric current simulated under conditions of periodic forcing. However, when the oscillator is not predominantly in the passive state, a more complex spatio-temporal behaviour is revealed by the simulations. The spatial non-homogeneity of the dynamic variables is observed in the most profound way for the concentration which lacks any relaxation characteristics. This suggests that it is not only the double layer potential drop, but also the ionic concentrations, which may play a role in the development of spatio-temporal patterns in electrochemical systems.

Abstract:

Abstract: The process of self-assembling of thiophene oligomers on gold substrate was studied in situ by optical second harmonic generation (SHG). It is shown that for thiophene both molecular and adsorption-modified nonlinear optical susceptibility of the substrate contribute to the SHG field. On the base of simultaneous consideration of nonlinear-optical and two-channel Langmuir-like kinetic models kinetic parameters of adsorption/self-assembling are estimated. © 2003 Elsevier B.V. All rights reserved.

Abstract: A network of two coupled electrochemical oscillators is investigated theoretically and experimentally. It is shown that, if the network is controlled potentiostatically with a point reference electrode, the evolution of the system depends both on the uncompensated and solution resistances. As a result, the action of the connections between the two oscillators can be tuned to be either excitatory or inhibitory by changing the relative position of the working, counter, and point reference electrodes. The change of the connection's action induces different in-phase or out-of-phase stable synchronized states. The numerical predictions are qualitatively reproduced experimentally.

Abstract: Spatiotemporal patterns emerging through coupling of identical relaxation oscillatory electrode pairs are studied. Each pair, consisting of an iron anode and a copper cathode, oscillates periodically under fixed applied potential difference conditions. It is shown that the system synchronizes rapidly (within few oscillatory cycles) and differences of natural frequencies as well as boundary effects are compensated. The effect of the geometrical configuration on the dynamic modes is investigated for relatively large assemblies of such oscillatory pairs. When oscillators are coupled through neighboring electrodes, the response is synchronized by a simultaneous formation of groups. The formation of groups due to enhancement or inhibition of the oscillations depends on the relative position of interacting anodes and cathodes. The behavior of the system is compared with the response of coupled relaxation cells of neurophysiological interest. © 2002 The American Physical Society.

Abstract: A prediction method is proposed for one-step and multi-step forecasting of the chaotic response. The method is based on the determination of the transition matrix from experimental data by a linearization procedure. The procedure is applied to various chaotic time series obtained from the electrochemical oscillator Fe/H₂SO₄. The one-step prediction results are good in the case of smooth time series. Regions of poor prediction are analyzed and it is found that the forecasting is limited due to the presence of a high frequency component in the time series causing a virtual increase of the measuring interval, Δt. The method is also applied successfully for multi-step prediction. The performance is increased by implementing a false neighbors detection routine.

Abstract: We have studied the response of simple networks of relaxation oscillatory electrode pairs to inputs through external cells. Such networks are shown to respond to constant inputs by decreasing or increasing the period depending whether the connection with the external cell is excitatory or inhibitory. The response to pulse inputs is determined by the phase of the relaxation oscillations; within the refractory region the network remains unaffected whereas within the excitable region an increase in the period is observed accompanied by the induction of new peaks. © 2002 Elsevier Science B.V. All rights reserved.

Abstract: The electrocatalytic oxidation of formaldehyde on Pt(111) under potentiostatic conditions and periodic potential oscillations was studied by using optical second harmonic generation (SHG). Under potentiostatic conditions, order-disorder and order-order phase transitions were observed. Under galvanostatic conditions, oscillations of the SHG field occurred, corresponding to the potential oscillations. However, in the dynamic regime only the evidence of a structural order-disorder phase transition is present in SHG data. This might be due to a much higher time constant of the surface ordering in comparison to the oscillation period.

Abstract: The effect of spatially localized, time-periodic forcing on the Fe | 1 M H₂SO₄ system is studied experimentally within the oscillatory and excitable region. The electrode surface is perturbed locally or globally by a laser beam. The resulting response depends strongly on the period and phase of the external forcing. When periodic laser perturbations are applied to the excitable state, the resulting response is large excitations for a large forcing period and pairs of small and large excitations for a small forcing period. During autonomous oscillations the response is entrained either completely or by combinations of autonomous and excitable peaks. A systematic procedure is applied, based on single perturbation experiments, for the construction of one-dimensional maps for the periodically forced oscillator. A mathematical model is proposed for the description of the dynamical phenomena induced by the laser light. The model equations predict most of the experimental findings.

Abstract: Self-sustained current oscillations observed during iron electrodissolution are affected by laser pulse irradiation. One-dimensional discrete maps constructed by the response obtained under single laser pulse irradiation can predict the induced dynamical behavior under periodic laser irradiation conditions. © 2001 Elsevier Science B.V.

Abstract: A simple two-dimensional model of coupled electrochemical oscillators is studied, where linear diffusive coupling of the potential causes dephasing of the oscillators. It is shown that coherence breaks down due to a strong deformation of the phase flow near the limit cycle. When a large number of such oscillators is coupled, the temporal response is bursting oscillations. © 2001 Elsevier Science B.V.

Abstract: Spatio-temporal propagation of a reaction front along a ring electrode was observed during self-sustained iron dissolution current oscillations. The propagation was strongly related to the periodicity of the system, which depended on the cell geometry.

Abstract: The existence of stable and unstable attractors is investigated experimentally for an electrochemical system consisting of a ring iron electrode immersed in sulfuric acid solution. The applied potential is considered as the bifurcation parameter whereas an external resistance is considered as a second parameter of the system. The stable and unstable states of the system are revealed by combining steady state and laser perturbation experiments with the bifurcation characteristics. A structure of the steady state curve is proposed that can predict the experimental dynamical response. The system is modeled by considering the electrode potential and the concentration of one of the ionic species as dynamical variables. The resulting boundary value problem is studied numerically and a comparison between the experimental and theoretical results is performed. It is shown that the model can predict most of the experimental behavior in a good qualitative agreement.

Abstract: The spatio-temporal behavior during periodic current oscillations in the Fe|H₂SO₄ system is studied for a one-dimensional electrode surface. It is found that during the oscillatory response the electrode surface is never in the same state at the same time but the surface potential forms an accelerating front. The mode of communication between the individual regions of the reacting surface is explored by dividing the system into two identical coupled oscillators. The response is studied by either dividing the electrode surface with an insulating film of infinitesimal thickness or by a physical partition. The behavior of the coupled oscillators can be simple in-phase synchronization, k/n phase locking, out-of-phase locking or complex, depending on the length of the insulating film or the use of the partition and the applied potential. The results are compared with a model considering a simple coupling through the electrode potentials of the single oscillators. It is proposed that the coupling patterns can be attributed to the electrical coupling and the distribution of the frequency of the individual oscillators. © 2000 Elsevier Science B.V.

Abstract: The spatio-temporal behavior of an electrochemical oscillator during anodic dissolution is studied theoretically for a specific geometric configuration. The system consists of a metal disk electrode located at the bottom of a hollow cylinder with insulating walls. On the electrode surface a dissolution-precipitation mechanism is assumed to occur in the presence of a salt film. A model is formulated based on boundary value problem for Laplace equation and the equations of conservation of charge and mass balance. The boundary value problem is transformed to an infinite set of ordinary differential equations and solved numerically. The spatio-temporal response is presented for four different cases, namely, relaxation oscillations, complex oscillations, excitability and bistability. It is shown that during relaxation oscillations the whole electrode surface oscillates in a homogeneous manner while in the remaining cases non-homogeneities cause complex spatial behavior. Within the excitable and bistable regions under spatial perturbations located at the center of the disk, the electrode surface turns from the passive to an active state through a potential front. Once on an active state, the system returns to its final state via a potential front starting on the center of the disk and propagating along the electrode surface. © 2000 Elsevier Science Ltd. All rights reserved.

Abstract: Rayleigh-Bénard (RB) convection was observed in an electrolytic solution between two parallel copper wire electrodes. Electrochemically driven RB convection was achieved when the anode, where the electrodissolution of copper occurred, was placed above the cathode on which the reduction of ions took place. The motion of the solution was well controlled by the bias potential applied between the electrodes and the dissipation structure made by the flow of the fluid was visualized by using a laser interferometry. Under magnetic field normal to the plane of the convection the roll cells were found to travel horizontally along the wire electrode by the Lorentz force. It is shown that the electrochemically driven RB convection is controlled and monitored much simply than thermally induced conventional ones by adjusting electrochemical parameters and that the system has a wide variety in the structural regularity especially under magnetic field.

Abstract: Hydrodynamic instability analogous to Rayleigh-Bénard convection is observed in an electrolytic solution between two parallel copper wire electrodes. The laser interferometric technique can reveal the dissipation structure created by the motion of the fluid, which is controlled electrochemically. It is shown that under the presence of horizontal magnetic field the roll cells move horizontally along the electrodes. The electrochemically driven convection is simply controlled and monitored by setting and measuring the electrochemical parameters and forms many kinds of spatiotemporal patterns, especially under the magnetic field. The phenomenon is modeled by considering a Boussinesq fluid under a concentration gradient. The stability of the resulting equations is studied by linear stability analysis. The time dependent nonlinear system is investigated numerically and the main features of the experimental response are reproduced. ©1999 The American Physical Society.

Abstract: A two-dimensional metal film localized at the interface between 4-methyl-2-pentanone and aqueous electrolyte solution, was formed by an electrochemical deposition of zinc. The shape of this film changed as a function of the electrode potential. In the large overpotential region where the deposition was restricted by the transport of the zinc ion, a fractal pattern was formed. However, a disk pattern was made under the potential region where the electron transfer was the rate-determining step. Under a magnetic field, a spiral distortion of the two-dimensional and quasi-two-dimensional fractal pattern was observed at an air|liquid interface and in a thin layer electrolyte solution, respectively. The pattern produced at the liquid|liquid interface showed no distortion under the magnetic field.

Abstract: A method is proposed for the construction of normal forms from experimental observations which describe the dynamics of a system close to the bifurcation points. The method is applied for the bifurcation of the Fe/2 M H₂SO₄ electrochemical system from a steady state to a chaotic attractor by considering the applied potential and the external ohmic resistance as bifurcation parameters. Steady state and time evolution curves of the response function are recorded. Perturbation experiments, time delay reconstruction of the attractors and calculation of power and Lyapunov spectra are performed. From the above experimental procedure the linear part of the normal form is constructed. The nonlinear part of the normal form is derived only from the knowledge of the linear part. Perturbations of the derived normal form on the bifurcation point are considered through the versal deformation of the normal form and the construction of the versal family of the normal form. The resulting normal form equations reproduce the dynamic characteristics and the bifurcation diagram of the electrochemical system.

Abstract: A uniform formalism is introduced for the description and comparison of the algorithms of Sano and Sawada [M. Sano and Y. Sawada, Phys. Rev. Lett. 55, 1082 (1985)] and Eckmann et al. [J.-P. Eckmann, S. O. Kamphorst, D. Ruelle, and S. Cilibert, Phys. Rev. A 34, 4971 (1986)], for the calculation of the Lyapunov spectrum from experimental data. It is shown that both algorithms coincide for the calculation of the maximum Lyapunov exponent and differ for the other exponents. A numerical application is carried out which confirms the above result. A detailed investigation of the dependence of the Sano and Sawada and the Eckmann et al. algorithms on the parameters of the algorithms, the signal and the reconstruction of the attractor, for the calculation of the whole Lyapunov spectrum is presented. Calculations are performed for three kinds of signals: (a) the noise-free dynamical variable x(t) of the Lorenz system, (b) the stiff and long duration time evolution of the total current of the electrochemical oscillator Fe-2M H₂SO₄ in the presence of external Ohmic resistance R, and (c) the smooth variation and short duration signal of the same experimental system for a different set of parameters. A comparison between the results of the two algorithms is attempted as well as an investigation of the trends of the Lyapunov spectrum by varying the algorithm, signal, and reconstruction parameters.

Abstract: The iron/sulfuric acid (Fe/2 M H₂SO₄) system exhibits periodic current oscillations of relaxation type within the potential transition region formed between the active and passive states of the iron electrode when it is polarized in the 2 M sulfuric acid solution. In the present work the dynamical response of the Fe/2 M H₂SO₄ electrochemical oscillator is investigated when the applied potential at the iron electrode is sinusoidally perturbed. The behavior of the periodically perturbed Fe/2 M H₂SO₄ oscillator differs significantly from the response of other forced oscillators, as the potential amplitude E _p and the frequency ratio ω_p/ω₀ vary. The ω_p and ω₀ are the angular frequencies of the perturbed applied potential and the unperturbed oscillator, respectively. A special feature of its response is the appearance of a number of spikes, generated within the passive section of a periodic oscillatory cycle for ω_p/ω₀ < 2.9, for periods of the autonomous oscillator T₀ > 3 s. The number of the generated spikes depends on the amplitude and frequency of the perturbed applied potential as well as on the period of the autonomous oscillator. Spikes are not generated for ω_p/ω₀=1 and the system is harmonically entrained by the forcing frequency. However, when the system is subharmonically entrained for ω_p/ω₀ close to 2, spike generation does occur. By increasing the perturbation frequency for ω_p/ω₀ > 2.9 and T₀ > 3 s, or by decreasing the autonomous period for T₀ < 3 s and all the ω_p/ω₀ < 2.9 ratios, the spike generation pattern, is replaced by a quasiperiodic pattern. The dynamical response of the perturbed Fe/2 M H₂SO₄ electrochemical oscillator is characterized by using time-delay reconstructions of the attractors, Poincaré maps, and Fourier power spectra. © 1993 American Institute of Physics.

Abstract: We consider that the electrode potential in the simplified Franck-FitzHugh (F-F) model is externally forced by a periodic modulation. The F-F model is a two-dimensional model and describes the potential or current oscillations which are observed during the electrodissolution of iron in sulphuric acid solutions, under galvanostatic or potentiostatic conditions, respectively. The potential and the fraction of the surface coverage are the dynamical variables in the F-F model which reproduces the electrochemical oscillations of the system Fe/0.5 M H₂SO₄. By applying an external sinusoidal forcing potential, the two-dimensional system of F-F model becomes a three-dimensional one of non-linear equations which was integrated numerically for a wide range of forcing amplitude and frequency. The results of these integrations were interpreted by using various methods of the non-linear dynamics like phase plane, stroboscopic maps, time-delay reconstructions and Liapunov characteristic exponents. The forced F-F model shows different types of behaviour which depends on the frequency and amplitude of the forcing potential. For small forcing amplitude we observed a wide zone of quasi-periodic response interrupted by harmonic entrainment bands. For higher amplitudes the behaviour of the system consists of multi-periodic (subharmonic, harmonic) and quasi-periodic oscillations. The response of the forced F-F model is compared with the response of other forced systems. © 1992.

Abstract: The effects of a periodically perturbed applied potential on the potentiostatic current oscillations observed during the transition of an iron electrode between the active and passive states in 2 M sulphuric acid solutions is studied experimentally in this work. Autonomous current oscillations appear during the electrodissolution of iron in sulphuric acid solutions when the iron electrode turns from the active to the passive state and vice versa. After the application of a potential perturbation the forced oscillations are conducted in a region with such a parameter space that the autonomous limit cycle is observed. The overall study was limited to the hysteresis region. The response of the oscillatory system Fe/2 M H₂SO₄ to an external perturbation of the potential was studied as a function of two parameters, the frequency, ω_p, and the amplitude, E_p, of the forcing potential and it was characterized with the aid of time-delay reconstructions. The various types of response are presented in the phase diagram E_p-ω_p/ω₀. For low amplitudes of the potential perturbation and for both ω_p/ω₀ < 1 and ω_p/ω₀ > 1 the response of the perturbed system exhibits wide zones of quasi-periodicity interrupted by entrainment bands which are harmonic or subharmonic. For higher amplitudes the entrainment bands become broad and as the forcing amplitude increases the system tends to be driven by the forcing frequency. From this experimental study on forced electrochemical oscillations of the system Fe/2 M H₂SO₄ it is seen that at very positive potentials for sustained periodic current oscillations to occur under stationary conditions, periodic or quasi-periodic current oscillations could be triggered by the local dissolution of the passive film with a potential pulse of a sufficient amplitude in order for the transition to the active state to be feasible. The resulting small uncovered part of the electrode surface allows metal electrodissolution and its propagation along the surface. © 1992.

Abstract: A network of coupled relaxation type electrochemical oscillators was investigated. It was also shown that if the network was controlled potentiostatically with a point reference electrode, the action of connections between oscillators can be turned to be either excitatory or inhibitory by changing the cell geometry. It was observed that globally coupled inhibitory network of electrochemical oscillators have a large capability to stored information the form of spatially and temporally patterned pulse train. The experimental tool was self-sustained current oscillations during Fe electrodissolution in 1M H₂SO₄ solution.