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Low-index plane Pt single crystal electrodes modified by submonolayer deposition of Sn have been tested for ethanol oxidation in acidic media using cyclic voltammetry and chronoamperometry. The enhancement factor for ethanol oxidation depends on both substrate crystallography and Sn coverage. The optimum coverage was found to be around 0.2, 0.25 and 0.52 for (1 0 0), (1 1 1) and (1 1 0), respectively. The enhancement factor was found to decrease in the order: Sn/Pt (1 1 0) > Sn/Pt (1 0 0) > Sn/Pt (1 1 1). On the other hand, the current density obtained at 0.4 V after 15 min of electrolysis was found to decrease in the order: Sn/Pt (1 1 0) > Sn/Pt (1 1 1) > Sn/Pt (1 0 0).

Since the current density near the edges of ribbon and disk electrodes is enhanced, the resulting stationary and non-stationary double layer potential is generally inhomogeneous in all electrochemical reactions. We investigate the impact of this edge effect induced spatial inhomogeneity on the pattern formation of the oscillatory formic acid oxidation on thin Pt ribbon electrodes. In order to be able to theoretically describe the spatiotemporal behavior of the double layer potential distribution, we derive and discuss the properties of the electrochemical ribbon coupling function for various distances of the reference electrode. The resulting reaction–migration equation is analyzed in connection with a chemical model accounting for the specific reaction mechanism of the formic acid oxidation. The interaction of structural inhomogeneity, chemically induced temporal instability and nonlocal spatial coupling due to ion migration gives rise to novel types of spatiotemporal behavior. The results compare favorably with experiments conducted so far, which are presented as well and can be explained within the framework of reaction–migration equations.

We present a mathematical model for calcium oscillations in the cilia of olfactory sensory neurons. The underlying mechanism is based on direct negative regulation of cyclic nucleotide-gated channels by calcium/calmodulin and does not require any autocatalysis such as calcium-induced calcium release. The model is in quantitative agreement with available experimental data, both with respect to oscillations and to fast adaptation. We give predictions for the ranges of parameters in which oscillations should be observable. Relevance of the model to calcium oscillations in other systems is discussed.

A family of polynomial differential systems describing the behavior of a chemical reaction network with generalized mass action kinetics is investigated. The coefficients and monomials are given by graphs. The aim of this investigation is to clarify the algebraic-discrete aspects of a Hopf bifurcation in these special differential equations. We apply concepts from toric geometry and convex geometry. As usual in stoichiometric network analysis we consider the solution set as a convex polyhedral cone and we intersect it with the deformed toric variety of the monomials. Using Gröbner bases the polynomial entries of the Jacobian are expressed in different coordinate systems. Then the Hurwitz criterion is applied in order to determine parameter regions where a Hopf bifurcation occurs. Examples from chemistry illustrate the theoretical results.

Experimental observations of temporal dynamics in the electrocatalytic oxidation of methanol (CH3OH) on a polycrystalline platinum electrode are reported. Hidden negative differential resistance (HNDR) and instabilities of the system were investigated by means of an electrochemical impedance spectrum analysis and potential oscillations under galvanostatic control. This result could be applied for a direct methanol fuel cell (DMFC) with higher energy efficiency.

We report experimental observations on the temporal dynamics in the electrocatalytic oxidation of formic acid (HCOOH) on a polycrystalline Pt electrode modified by deposition of bismuth. Bismuth modification significantly enhanced the current density of HCOOH oxidation, since it suppressed the poisoning branch and increased the apparent direct oxidation rate. Impedance spectroscopy and the galvanostatic scan in HCOOH oxidation on Bi/Pt exhibited a hidden negative differential resistance and a Hopf bifurcation. The electrocatalytic oxidation of HCOOH on Bi/Pt spontaneously underwent transitions from homogeneous catalytic activity to spatiotemporally inhomogeneous distributions of the interfacial electrode potential, in the form of traveling pulses of the interfacial potential.

Oscillatory rotating activation pulses on a Pt ring electrode during formic acid oxidation were externally perturbed via a trigger electrode at one location of the ring. While usual phase resetting was obtained for small perturbation amplitudes, stronger perturbations resulted in reversal of the direction of pulse motion when applied behind the pulse over a wide phase interval. The results are in agreement with simulations carried out with a reaction–migration model and can be rationalized in terms of short-range positive and long-range negative coupling.

We use nonlinear signal processing techniques, based on artificial neural networks, to construct a continuous-time model (set of ordinary differential equations, ODEs) from experimental observations of mixed-mode oscillations during the galvanostatic oxidation of hydrogen on platinum in the presence of bismuth and chloride ions. The data was in the form of time-series of the potential for different values of the applied current and chloride ion concentration. We use the model to reconstruct the experimental dynamics and to explore the associated bifurcation structures in phase-space. Using numerical bifurcation techniques we locate stable and unstable periodic solutions, calculate eigenvalues, and identify bifurcation points. This approach constitutes a promising data post-processing procedure for investigating phase-space and parameter space of real experimental systems; it allows us to infer phase-space structures which the experiments can only probe with limited measurement precision and only at a discrete number of operating parameter settings. For example, the fitted model suggests the existence of a sub-critical Hopf bifurcation near the range of parameters probed in the experiments; this might explain the experimental difficulty in locating small amplitude simple oscillations.

We consider a comprehensive classification scheme of oscillatory electrochemical systems with respect to the mechanistic basis of their kinetic instability. Four principal oscillator categories are distinguished depending on the mechanistic role of the potential drop across the electrode ∣ electrolyte interface (double layer potential) and of the chemical species involved. In a comparative characterization, the typical experimental behavior of the four oscillator categories is described when subjected to various identification tests such as stationary and scanned cyclic voltammetric profiles, bifurcation behavior, impedance spectra and feedback control methods. It is shown that each category corresponds to a specific class of kinetic prototype models. Experimental example systems as well as numerical models taken from the literature are discussed in the context of their corresponding oscillator class. Moreover, an operational experimental procedure for a systematic mechanistic categorization of an unknown electrochemical oscillator is proposed. It is argued that an initial mechanistic categorization significantly facilitates the subsequent clarification of the relevant chemical steps of the unknown electrochemical oscillator.

Turing-like patterns formed during the polymerization of acrylamide in the presence of sulfide, methylene blue and molecular oxygen are presented. We propose a chemical model of the polymerization of acrylamide in the presence of sulfide and oxygen. The model explains the formation of Turing patterns in this system. The experimental process of pattern formation becomes light sensitive if methylene blue is added. A space-periodic perturbation may thus be introduced into the system and spatial entrainment effects can be studied. The perturbation was realized by imposing an illumination pattern upon the reactive layer: after mixing the gel components and the MBO system in a Petri dish, a mask made of transparent film was placed between the light source and the dish. At different perturbation wavelengths we observed synchronization with the perturbation as well as irregular responses.

An experimental and theoretical description of the oscillatory electrocatalytic iodate reduction system in alkaline solution is presented. Experimental measurements suggested the crucial role of a negative differential resistance as well as the presence of hydrogen evolution in the oscillatory instability. A simple kinetic model with one chemical species was developed which involved: (i) an iodate reduction current with N-shaped potential dependence due to a Frumkin repulsion effect; and (ii) an additional ‘iodate-independent’ current providing process. The dynamical behavior of the model compares favorably with experiments as far as voltammetric profiles, stirring effects and bifurcations between stable and oscillatory states are concerned. It is further shown that the model can account for oscillatory states in a number of related electrocatalytic systems.

The underpotential deposition (UPD) of copper on to Pt(111) in the presence of chloride anions was studied by full-dynamical LEED-intensity analyses. A deformed (4×4) LEED pattern was observed at an emersion potential of 0.36 V vs. Ag/AgCl, right in between the two characteristic and well-separated peaks of the cyclic voltammogram (CV). Corresponding LEED intensity measurements and simulations of the integral-order beams indicate that the UPD of Cu forms a single pseudomorphic Cu layer on Pt(111).

We address the stability of solitary pulses as well as some other traveling structures near the onset of spatiotemporal chaos in a two-species reaction-diffusion model describing the oxidation of C ...

A recently proposed model to describe the galvanostatic oscillating oxidation of hydrogen on Pt in the presence of copper and chloride is also able to explain the potentiostatic behaviour of the experimental system. For sufficiently high series resistance it exhibits current oscillations on a branch where the stationary current-voltage curve has a positive polarization slope. This is in contrast to most of the potentiostatic oscillators examined and described previously, where the oscillations are caused by an interplay between the IR drop and a region of negative polarization slope. The mechanism is discussed and compared with other models which describe potentiostatic oscillators. The main difference is shown to lie in the existence of a hidden negative impedance, which is detected experimentally by impedance spectroscopy.

The dynamics of a large number of heterogeneously catalyzed reactions have been studied under a variety of conditions using different catalysts and reactor designs. Experiments with single crystal surfaces at low pressure are required in order to elucidate the underlying elementary chemical steps. Here we present a case study of such an approach using the isothermal CO oxidation on a Pt(110) surface. Surface science experiments allow to construct a simple but realistic reaction-diffusion model capable of reproducing the experimentally observed spatiotemporal patterns, representative examples of which are described.

A simple model of the galvanostatic oscillations that occur during the oxidation of hydrogen at platinum electrodes in the presence of electrosorbing metal ions and specifically adsorbing anions is presented. It consists of three ordinary differential equations describing the degree of coverage of the electrode with underpotential-deposited metal and with specifically adsorbed anions; the third variable is the potential drop across the double layer. This model is able to reproduce the potentiostatic experiments of the system. The galvanostatic behavior is examined by integration of the equations and by bifurcation analysis. The experimental dependence on the control parameters is reproduced in all main features. The parameters were altered to check the model for robustness and to determine the essential processes leading to oscillations. Mixed-mode and period-doubled oscillations were also found. Inclusion of a fourth variable, the concentration of metal ions in front of the electrode, leads to a better quantitative description of oscillations at low metal ion concentrations.

Rigidly rotating spiral waves under constant external parameters, drifting spirals under the influence of a periodic perturbation as well as turbulent patterns have been observed in the isothermal CO oxidation on a Pt(1 1 0) single crystal surface. A simple reaction-diffusion model can reproduce these findings. It is pointed out that the spiral resonances depend on the symmetry of the surface. The mechanism leading to turbulence is briefly described.

We studied the oscillatory galvanostatic Hg-oxidation on the three low-index Pt surfaces in the presence of Cu 2+ and different electrolytes: H 2 SO 4 , H 2 SO 4 +Cl - and H 2 SO 4 +Br - . It was found that both surface orientation of the Pt-electrode as well as the nature of the anions strongly influence the dynamics. Halide ion adsorption plays an essential role for the occurrence of oscillations; their binding strengths on the different single-crystal electrodes correlate with the dynamic behaviour of the respective system. The reaction was further investigated using ring-disk electrodes (Pt/Pt and Pt/Au). This allowed the quantitative determination of the change of the copper coverage and the Hg-current during oscillations as well as their phases relative to the electrode potential. From these studies a simple three-variable model (taking into account the coverages of copper and anions as well as the potential) was deduced, based on competitive adsorption of halides and Cu. The model explains the occurrence of oscillations and predicts the correct phase relationships of the oscillating variables

A refined version of the Sano-Sawada algorithm to compute Lyapunov spectra has been implemented and tested with several models, which include periodic, chaotic and hyperchaotic attractors, under conditions designed to mimic experimental situations. It was found that reliable Lyapunov exponents can be obtained for time series of moderate length and point density, also in the presence of interactive noise as long as its amplitude does not exceed ≈ 1% of the oscillation amplitude. The algorithm was then applied to experimental data from the CO oxidation on Pt(110), clearly showing the occurrence of chaos as well as hyperchaos.

The dynamic behavior of the electrocatalytic oxidation of hydrogen on a platinum anode in the presence of Cu 2+ and Cl − ions under galvanostatic conditions has been studied experimentally in two control parameters: current density and copper ion concentration. This parameter plane can roughly be divided into three broad regions: A steady state is found at low values of the current density, at medium values the system shows small amplitude oscillations, whereas at high current densities typical mixed mode oscillations (MMOs) are found. Depending on the Cu 2+ concentration, the transition from the small amplitude to the mixed mode regime takes place from a simple periodic, period doubled, or chaotic attractor arising from a Feigenbaum route. In this paper we focus on the characteristics of these different transitions to MMOs and try to construct a bifurcation diagram. The bifurcation from the small chaotic attractor to MMOs very likely constitutes an interior crisis (a bifurcation at which the small chaotic attractor is destroyed by colliding with a stable manifold of a saddle type limit set). At lower copper ion concentrations, the transition to MMOs moved through the period-double cascade. We compile different properties of the bifurcation diagram and discuss a scenario which fits the observations in a consistent way.

A kinetic model of the catalytic CO oxidation on a Pt(110) surface is used to describe effects of spatiotemporal self-organization, which have been observed experimentally with this system. After some simplification and taking advantage of the strong separation of fast and slow variables the model can be used to obtain analytical expressions for front and pulse velocities, pulse width and the dispersion relation, as well as for the dependency of pinned spiral rotation on the core size. Comparison with experimentally observed wave velocities and spiral rotation allows to draw conclusions about defects on the surface. Possible extensions of the model in order to explain more complex spatiotemporal behavior are briefly discussed.

A set of coupled nonlinear reaction-diffusion equations was formulated for the oxidation of CO on low-index plane Pt surfaces and solved for their spatiotemporal behaviour using continuation techniques and the method of global connections. A 2-variable model for Pt(111), consisting of the CO and O coverages as a function of time and space, gave rise to reaction fronts. In order to model the behaviour of Pt(111) or Pt(100) a third equation describing the respective adsorbate-driven phase transition had to be added. The resulting 3-variable system predicts extended regions of excitability, where pulses can be triggered. The front — respectively pulse — velocities as well as the critical radii for the nucleation were computed and compared to experimental data where available.

The electrocatalytic oxidation of hydrogen in the presence of Cu2+ and Cl− ions under galvanostatic conditions has been studied on the three low-index plane surfaces of platinum. Over the parameter ranges investigated and with the electrode pretreatment used, no oscillations were observed on Pt(110), whereas only simple periodic oscillations were seen with Pt(111). The Pt(100) surface, on the other hand, exhibited a variety of oscillation types, including simple periodic oscillations, period-doubling, chaos and mixed-mode behavior as two parameters, copper ion concentration and current density, were varied. The dynamics on Pt(100) turned out qualitatively very similar to that observed previously on polycrystalline platinum electrodes.

Time series from the oscillatory CO oxidation on a Pt(110) surface, which exhibit a period-doubling transition to chaos, have been analyzed using an algorithm to compute all Lyapunov exponents. Near the onset of chaos one positive exponent is obtained, while two positive exponents were obtained farther away from the onset, demonstrating the occurrence of hyperchaos in this reaction.

In the CO oxidation on a Pt(110) surface under isothermal gradientless conditions at low pressures, kinetic oscillations occur which have been studied in detail experimentally. A simple 3-variable model, based on the classical Langmuir-Hinshelwood mechanism and the adsorbate-driven 1 × 1 → 1 × 2 phase transition of the Pt(110) surface, has been developed and analysed with the help of bifurcation theory. It explains the bistability and the occurrence of simple limit cycles. Extensions of the model in order to reproduce the more complex dynamics found in experiment are briefly discussed. With appropriate modifications the equations can model the dynamical behaviour of the Pt(100) and (111) surfaces, respectively.

The isothermal catalytic oxidation of CO on a Pt(110) surface in a gradientless flow reactor at low pressure ( −4 Torr) exhibits under properly chosen conditions ( P co , P o 2 , T ) sustained temporal oscillations of the reaction rate as monitored through the variation of the work function Δφ. Experimental data are presented in which by small, stepwise changes of the CO partial pressure the time series undergo a transition from simple periodic via a sequence of period doublings to aperiodic behavior as characteristic for the Feigenbaum route to chaos. Analysis of the data was performed by evaluating the power spectra, autocorrelation functions, three-dimensional attractors, correlation integrals, the Lyapunov exponents, as well as the lower limit for the Kolmogorov entropy. These results allow clear identification of deterministic chaos (including its embedding dimension n = 5 which agrees with the minimum number of variables determining the physical properties of the investigated system) as well as its distinction from periodic or random (noise) behavior.