We present efficient algorithmic methods to detect Hopf bifurcation fixed points in chemical reaction networks with symbolic rate constants, thereby yielding information about the oscillatory behavior of the networks. Our methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of our methods then reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can be solved using computational logic packages. The second method uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the examples that we have attempted; we have shown it to be able to handle systems involving more than 20 species.

In the present review, we consider the transformations of molecular catalysts, leaching, aggregation and various interconversions of metal complexes, clusters and nanoparticles that occur during catalytic processes. The role of catalyst evolution and the mechanistic picture of “Cocktail”-type systems are considered from the perspective of the development of a new generation of efficient, selective and re-usable catalysts for synthetic applications. Rational catalyst development and the improvement of catalyst performance cannot be achieved without an understanding of the dynamic nature of catalytic systems.

Herein, oscillatory formic acid (FA) electrooxidation on polycrystalline palladium is investigated and compared with the one on polycrystalline platinum; major differences between both are attributed to differences on the kinetics of sub-set chemical network as well as to preferential routes admitted on palladium surface. To presume the kinetic rate of poison accumulation on palladium, FA oxidation was accomplished in presence of occluded hydrogen and hydrogen-free electrodes. The preferential routes were presumed from the temporal pattern. Markedly, oscillations during FA electrooxidation have minimum potential at 0.2 V, which is linked to the fast rate of direct dehydrogenation; moreover, it has one of the largest induction period (ca. 60 min) and oscillatory period (20 min) observed in electrochemistry, since subsurface hydrogen slows down the rate of CO accumulation on the surface.

The co-existence of disparate time scales is pervasive in many systems. In particular for surface reactions, it has been shown that the long-term evolution of the core oscillator is decisively influenced by slow surface changes, such as progressing deactivation. Here we present an in-depth numerical investigation of the coupled slow and fast surface dynamics in an electrocatalytic oscillator. The model consists of four nonlinear coupled ordinary differential equations, investigated over a wide parameter range. Besides the conventional bifurcation analysis, the system was studied by means of high-resolution period and Lyapunov diagrams. It was observed that the bifurcation diagram changes considerably as the irreversible surface poisoning evolves, and the oscillatory region shrinks. The qualitative dynamics changes accordingly and the chaotic oscillations are dramatically suppressed. Nevertheless, periodic cascades are preserved in a confined region of the resistance vs. voltage diagram. Numerical results are compared to experiments published earlier and the latter reinterpreted. Finally, the comprehensive description of the time-evolution in the period and Lyapunov diagrams suggests further experimental studies correlating the evolution of the system's dynamics with changes of the catalyst structure.

We build on our previous work to compute Hopf bifurcation fixed points for chemical reaction systems on the basis of reaction coordinates. For determining the existence of Hopf bifurcations the main algorithmic problem is to determine whether a single multivariate polynomial has a zero for positive coordinates. For this purpose we provide heuristics on the basis of the Newton polytope that ensure the existence of positive and negative values of the polynomial for positive coordinates. We apply our method to the example of the Methylene Blue Oscillator (MBO).

Electrochemical reactions exhibit autosustained oscillatory states once the appropriate parameters are applied. As shown herein, the main impact of operating a reaction in an oscillatory state is the increased efficiency. The electroxidation of CO-containing hydrogen is analyzed because its oscillating mechanism mimics the oscillator known as hidden negative differential resistance (HNDR). With that, experimental results and the thermodynamic calculations of this contribution could be extended for other HNDR oscillators such as ethanol and methanol electroxidation. The enlarged efficiency results from a smaller chemical dissipation.

The problem of non-stationarity in experimentally recorded time-series is common in many (electro)chemical systems. Underlying this non-stationarity is the slow drift in some uncontrollable parameter, and it occurs in spite of the fact that all controllable parameters are kept constant. Particularly for electrochemical systems, some of us have recently suggested [J. Phys. Chem. C, 144, (2010), 22262-22268] an empirical method to stabilize experimental time-series. The method was exemplified for the electro-oxidation of methanol and different patterns were satisfactorily stabilized. In this paper we further elaborate some mechanistic aspects of this method and test it for the electro-oxidation of formaldehyde, a system that has some resemblance with the electro-oxidation of methanol, but produces a richer dynamics. In terms of the reaction mechanism, we were able to describe the coupling and to separate the surface processes of the two sub-systems: the fast one (or the core-oscillator) and the slow one, responsible for the drift.

Concepts from algebraic geometry (polynomial rings) can be used to determine analytically the stationary solutions in chemical reactions systems, more generally, systems of ordinary differential equations of polynomial form. The stability analysis via the Jacobian matrix often leads to complicated expressions which can hardly be analyzed. It is shown that these expressions can be simplified by forming quotient rings of the corresponding polynomial ring. The coefficients in the characteristic equation of the Jacobian can be represented by the normal forms obtained by generating the quotient rings so that their sign changes in dependence of a kinetic parameter and, hence, the stability can be determined. The procedure is illustrated using a well-known surface reaction.

Kinetic investigations in the oscillatory state have been carried out in order to shed light on the interplay between the complex kinetics exhibited by a proton exchange membrane fuel cell fed with poisoned H(2) (108 ppm of CO) and the other in serie process. The apparent activation energy (E(a)) in the stationary state was investigated in order to clarify the E(a) observed in the oscillatory state. The apparent activation energy in the stationary state, under potentiostatic control, rendered (a) E(a) ≈ 50-60 kJ mol(-1) over 0.8 V < E < 0.6 V and (b) E(a) ≈ 10 kJ mol(-1) at E = 0.3 V. The former is related to the H(2) adsorption in the vacancies of the surface poisoned by CO and the latter is correlated to the process of proton conductivity in the membrane. The dependence of the period-one oscillations on the temperature yielded a genuine Arrhenius dependence with two E(a) values: (a) E(a) around 70 kJ mol(-1), at high temperatures, and (b) E(a) around 10-15 kJ mol(-1), at lower temperatures. The latter E(a) indicates the presence of protonic mass transport coupled to the essential oscillatory mechanism. These insights point in the right direction to predict spatial couplings between anode and cathode as having the highest strength as well as to speculate the most likely candidates to promote spatial inhomogeneities.

A mechanism for the kinetic instabilities observed in the galvanostatic electro-oxidation of methanol is suggested and a model developed. The model is investigated using stoichiometric network analysis as well as concepts from algebraic geometry (polynomial rings and ideal theory) revealing the occurrence of a Hopf and a saddle-node bifurcation. These analytical solutions are confirmed by numerical integration of the system of differential equations. (C) 2010 American Institute of Physics

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 (100), (111) and (110), respectively. The enhancement factor was found to decrease in the order: Sn/Pt (110)>Sn/Pt (100)>Sn/Pt (111). On the other hand, the current density obtained at 0.4V after 15min of electrolysis was found to decrease in the order: Sn/Pt (110)>Sn/Pt (111)>Sn/Pt (100).

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.

For the description of complex dynamics of open systems, an approach is given by different concepts of majorization (order structure). Discrete diffusion processes with both invariant object number and sink or source can be represented by the development of Young diagrams on lattices. As an experimental example, we investigated foam decay, dominated by sinks. The relevance of order structures for the characterization of certain processes is discussed.

We studied the open circuit interaction of methanol and ethanol with oxidized platinum electrodes using in situ infrared spectroscopy. For methanol, it was found that formic acid is the main species formed in the initial region of the transient and that the steep decrease of the open circuit potential coincides with an explosive increase in the CO2 production, which is followed by an increase in the coverage of adsorbed CO. For ethanol, acetaldehyde was the main product detected and only traces of dissolved CO2 and adsorbed CO were found after the steep potential decay. In both cases, the transients were interpreted in terms of (a) the emergence of sub-surface oxygen in the beginning of the transient, where the oxide content is high, and (b) the autocatalytic production of free platinum sites for lower oxide content during the steep decay of the open circuit potential.

The use of a ribbon-shaped Pt electrode gives rise to edge effects of the interfacial potential, as is predicted from the potential theory in the form of the corresponding reaction-migration equation. They are studied in the bistable region of formic acid oxidation. Essentially, the edges tend to be more passive than the bulk of the electrode, which also causes a passivation (activation) transition to originate from the edges (center) of the ribbon. The experimental results are in agreement with simulations of the reaction-migration system.

In the present work the electrochemical pattern formation was investigated during electro-oxidation of formic acid on platinum electrode. The working electrode is quasi-one-dimensional ribbon polycrystalline platinum. The stationary domains (sDs) have been successfully captured after an external pulse was triggered. At a relatively high conductivity a new kind of electrochemical pattern was found and it is named as cyclopean pattern. In a nonlinear electrochemical system with an N-type negative differential resistance, the theoretical simulation of the spatial temporal structure is able to predict the existence of stationary domains. Increasing the electrolyte conductivity promotes the formation of stationary domains and cyclopean pattern. The difference of the potential amplitudes in two phases (domains) becomes smaller in an electrolyte with a higher conductivity.