Laser Experiments and Theoretical Modeling for the Diagnosis of bifurcation Sequences of an oscillating Electrode reaction

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.

[1]  Z. Noszticzius,et al.  Bifurcation from excitability to limit cycle oscillations at the end of the induction period in the classical Belousov–Zhabotinsky reaction , 1987 .

[2]  H. Degn.  Theory of electrochemical oscillations , 1968 .

[3]  James P. Keener,et al.  Waves in Excitable Media , 1980 .

[4]  M. Kleinke.  Chaotic Behavior of Current Oscillations during Iron Electrodissolution in Sulfuric Acid , 1995 .

[5]  J. Maselko.  Determination of bifurcation in chemical systems. An experimental method , 1982 .

[6]  John Newman,et al.  Experimental Determination of the Passive‐Active Transition for Iron in 1M Sulfuric Acid , 1983 .

[7]  A. Bard,et al.  Semiconductor Electrodes: V. The Application of Chemically Vapor Deposited Iron Oxide Films to Photosensitized Electrolysis , 1976 .

[8]  H. Swinney,et al.  Interrupted separatrix excitability in a chemical system , 1991 .

[9]  S. Nakabayashi,et al.  Spatiotemporal propagation of a non-linear electrochemical reaction over an iron electrode , 1998 .

[10]  M. Koper,et al.  A simplified approach to the modeling of wave propagation at electrode/electrolyte interfaces , 1993 .

[11]  A. Arvia,et al.  The Potentiostatic Current Oscillations at Iron/Sulfuric Acid Solution Interfaces , 1979 .

[12]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[13]  Katharina Krischer,et al.  SYNCHRONIZATION AND PATTERN FORMATION IN ELECTROCHEMICAL OSCILLATORS : MODEL CALCULATIONS , 1997 .

[14]  K. Uosaki,et al.  Nonlinear Iron Electrochemical Oscillator: Coupling and Photo Effects , 1996 .

[15]  Ioannis G. Kevrekidis,et al.  Spatiotemporal period doubling during the electrodissolution of iron , 1993 .

[16]  John L. Hudson,et al.  Negative coupling during oscillatory pattern formation on a ring electrode , 1999 .

[17]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .

[18]  Shenhao Chen,et al.  The nature of the potentiostatic current oscillations at iron/sulfuric acid solution interfaces , 1994 .

[19]  M. Koper,et al.  A mathematical model for current oscillations at the active-passive transition in metal electrodissolution , 1993 .

[20]  J. Newman,et al.  Current oscillations observed within the limiting current plateau for iron in sulfuric acid , 1986 .

[21]  J. Newman,et al.  Anodic Dissolution of Iron in Acidic Sulfate Electrolytes II . Mathematical Model of Current Oscillations Observed under Potentiostatic Conditions , 1986 .

[22]  I. Kevrekidis,et al.  The Impact of the Operation Mode on Pattern Formation in Electrode Reactions From Potentiostatic to Galvanostatic Control , 1998 .

[23]  J. L. Hudson,et al.  Electrochemical Reaction Dynamics - A Review , 1994 .

[24]  K. Krischer,et al.  A general model for pattern formation in electrode reactions , 1995 .

[25]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[26]  M. Koper,et al.  Electrochemical oscillators: their description through a mathematical model , 1991 .

[27]  M. Pagitsas,et al.  Generalized Hopf, saddle-node infinite period bifurcations and excitability during the electrodissolution and passivation of iron in a sulfuric acid solution , 1993 .

[28]  John L. Hudson,et al.  Chaos during the electrodissolution of iron , 1987 .

[29]  I Z Kiss,et al.  Stabilization of unstable steady states and periodic orbits in an electrochemical system using delayed-feedback control. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  Meron,et al.  Model for spiral wave formation in excitable media. , 1988, Physical review letters.