Cellular structures in catalytic reactions with global coupling

Catalysis by Imaging: From Meso- to Nano-scale

In-situ imaging of catalytic reactions has provided insights into reaction front propagation, pattern formation and other spatio-temporal effects for decades. Most recently, analysis of the local image intensity opened a way towards evaluation of local reaction kinetics. Herein, our recent studies of catalytic CO oxidation on Pt(hkl) and Rh(hkl) via the kinetics by imaging approach, both on the meso- and nano-scale, are reviewed. Polycrystalline Pt and Rh foils and nanotips were used as µm- and nm-sized surface structure libraries as model systems for reactions in the 10–5–10–6 mbar pressure range. Isobaric light-off and isothermal kinetic transitions were visualized in-situ at µm-resolution by photoemission electron microscopy (PEEM), and at nm-resolution by field emission microscopy (FEM) and field ion microscopy (FIM). The local reaction kinetics of individual Pt(hkl) and Rh(hkl) domains and nanofacets of Pt and Rh nanotips were deduced from the local image intensity analysis. This revealed the structure-sensitivity of CO oxidation, both in the light-off and in the kinetic bistability: for different low-index Pt surfaces, differences of up to 60 K in the critical light-off temperatures and remarkable differences in the bistability ranges of differently oriented stepped Rh surfaces were observed. To prove the spatial coherence of light-off on nanotips, proper orthogonal decomposition (POD) as a spatial correlation analysis was applied to the FIM video-data. The influence of particular configurations of steps and kinks on kinetic transitions were analysed by using the average nearest neighbour number as a common descriptor. Perspectives of nanosized surface structure libraries for future model studies are discussed.

CO Oxidation on Stepped Rh Surfaces: μm-Scale Versus Nanoscale

Abstract

The catalytic CO oxidation reaction on stepped Rh surfaces in the 10−6 mbar pressure range was studied in situ on individual μm-sized high-Miller-index domains of a polycrystalline Rh foil and on nm-sized facets of a Rh tip, employing photoemission electron microscopy (PEEM) and field-ion/field-emission microscopy (FIM/FEM), respectively. Such approach permits a direct comparison of the reaction kinetics for crystallographically different regions under identical reaction conditions. The catalytic activity of the different Rh surfaces, particularly their tolerance towards poisoning by CO, was found to be strongly dependent on the density of steps and defects, as well as on the size (µm vs. nm) of the respective catalytically active surface.

Graphic Abstract

Catalytic CO oxidation on Pt under near ambient pressure: A NAP-LEEM study

A near ambient pressure low-energy electron microscope (NAP-LEEM) has recently been constructed, that allows in situ imaging of surfaces up to a pressure of 10^-1 mbar. Here we report on pattern formation in catalytic CO oxidation on a Pt(110) single crystal surface and on a polycrystalline Pt foil in the 10^-2 mbar range, operating the microscope in the mirror electron microscopy (MEM) and in the LEEM mode. Excitations localized at structural defects and spiral wave fragments have been observed.

Chemical diffusion of CO in mixed CO+O adlayers and reaction-front propagation in CO oxidation on Pd(100)

Within the framework of a realistic atomistic lattice-gas model, we present the theoretical formulation and simulation procedures for precise analysis of the chemical diffusion flux of highly mobile CO within a nonuniform interacting mixed CO + O adlayer on a Pd(100) surface. The approach applies in both regimes of relatively immobile unequilibrated and fairly mobile near-equilibrated O adlayer distributions. Spatiotemporal behavior in surface reactions is controlled by chemical diffusion in mixed adlayers. Thus, we naturally integrate the above analysis with a previously developed multiscale modeling strategy to describe mesoscale reaction front propagation in CO oxidation on Pd(100). This treatment avoids using a simplified prescription of chemical diffusion and reaction kinetics as in traditional mean-field reaction-diffusion equation approaches.

Study of Oscillations and Pattern Formation in the NO + CO Reaction on Pt(100) Surfaces through Dynamic Monte Carlo Simulation: Toward a Realistic Model

Oscillations and pattern formation driven by a surface reconstruction are studied for the catalytic reduction of NO by CO on Pt(100) single-crystal surfaces through dynamic Monte Carlo simulations at low pressure and relatively high temperatures conditions. This study incorporates recent experimental evidence obtained for the same reaction on a Rh(111) surface, which modifies the reaction scheme used in previous approaches. The main consequence of such experimental evidence is that the production of N(2) occurs through two parallel mechanisms: (a) the classical N + N recombination step; (b) the formation and subsequent decay of an (N-NO) intermediate species as the fastest pathway. Moreover, different factors influencing the NO dissociation rate, the key step in the whole reaction, such as the availability of neighboring vacant sites, the formation of N-islands, and the presence of other NO and CO adsorbed species in the neighborhood, are also taken into account and their effects discussed. Sustained, modulated, irregular, and damped oscillations are observed in our analysis as well as the formation of cellular structures and turbulent patterns. The effect and the importance of each elementary reaction step on the behavior of the system are discussed.

Turing instability mediated by voltage and calcium diffusion in paced cardiac cells

In cardiac cells, the coupling between the voltage across the cell membrane (V(m)) and the release of calcium (Ca) from intracellular stores is a crucial ingredient of heart function. Under abnormal conditions and/or rapid pacing, both the action potential duration and the peak Ca concentration in the cell can exhibit well known period-doubling oscillations referred to as "alternans," which have been linked to sudden cardiac death. Fast diffusion of V(m) keeps action potential duration alternans spatially synchronized over the approximately 150-mum-length scale of a cell, but slow diffusion of Ca ions allows Ca alternans within a cell to become spatially asynchronous, as observed in some experiments. This finding raises the question: When are Ca alternans spatially in-phase or out-of-phase on subcellular length scales? This question is investigated by using a spatially distributed model of Ca cycling coupled to V(m). Our main finding is the existence of a Turing-type symmetry breaking instability mediated by V(m) and Ca diffusion that causes Ca alternans to become spontaneously out-of-phase at opposite ends of a cardiac cell. Pattern formation is governed by the interplay of short-range activation of Ca alternans, because of a dynamical instability of Ca cycling, and long-range inhibition of Ca alternans by V(m) alternans through Ca-sensitive membrane ionic currents. These results provide a striking example of a Turing instability in a biological context where the morphogens can be clearly identified, as well as a potential link between dynamical instability on subcellular scales and life-threatening cardiac disorders.

Spatiotemporal oscillations and clustering in the Ziff-Gulari-Barshad model with surface reconstruction

We study the dynamics of the Ziff-Gulari-Barshad (ZGB) model on square (sq) and hexagonal-honeycomb (hex) lattices and when surface restructuring is introduced. We show that the ZGB model exhibits nonequilibrium phase transitions on the hex lattice similar to the ones already observed on the sq lattice, but the critical values of the kinetic parameters depend crucially on the substrate type. If surface reconstruction (sq<-->hex) is assumed for high lattice coverage of one of the reactive species then persistent spatiotemporal oscillations and clustering of homologous species are observed for kinetic parameter values 0.348<k1<0.393.

Pattern formation for NO+NH3 on Pt(100): two-dimensional numerical results

The Lombardo-Fink-Imbihl model of the NO+NH3 reaction on a Pt(100) surface consists of seven coupled ordinary differential equations (ODE) and shows stable relaxation oscillations with sharp transitions in the relevant temperature range. Here we study numerically the effect of coupling of these oscillators by surface diffusion in two dimensions. We find different types of patterns, in particular phase clusters and standing waves. In models of related surface reactions such clustered solutions are known to exist only under a global coupling through the gas phase. This global coupling is replaced here by relatively fast diffusion of two variables which are kinetically slaved in the ODE. We also compare our simulations with experimental results and discuss some shortcomings of the model.

Dynamics of an ensemble of noisy bistable elements with global time delayed coupling

The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level, the system undergoes ordering transitions and demonstrates multistability. That is, for a strong enough positive feedback it exhibits a nonzero stationary mean-field,and a variety of stable oscillatory mean-field states are accessible for positive and negative feedback. The regularity of the oscillatory states is maximal for a certain noise level; i.e., the system demonstrates coherence resonance. While away from the transition points the system dynamics is well described by a Gaussian approximation, near the bifurcation points a description in terms of a dichotomous theory is more adequate.

Pattern formation on the edge of chaos: experiments with CO oxidation on a Pt(110) surface under global delayed feedback

Experiments with catalytic oxidation of carbon monoxide on Pt(110) show that chemical turbulence in this system can be suppressed by application of appropriate global delayed feedback. Different spatiotemporal patterns, seen near the transition from turbulence to uniform oscillations, are investigated. Such patterns include intermittent turbulence, oscillatory standing waves, cellular structures, and phase clusters. Using a method based on the Hilbert transform, spatial distributions of local phase and amplitude in these patterns are reconstructed from the experimental data.

Front instabilities in a forced oscillatory medium with global coupling

We study a two-dimensional, locally and globally coupled oscillatory system that is subjected to external forcing at a frequency equal to twice its natural frequency. It is shown that the onset of an Ising-Bloch transition is preceded by novel front instabilities: a pattern formation instability, wave trains along the front, and a weak turbulence in the frontal patterns.

Spatiotemporal patterns in CO oxidation on Pt(110): the role of nonlinear diffusion

Standing-wave patterns observed in the CO + O2 reaction on Pt(110) are described by a model that explicitly takes into account the coupling between the transport of adsorbed CO and the adsorbate-induced structural transformation of the substrate. We show that synchronization of the surface is achieved through nucleation and growth processes even in the absence of gas-phase coupling.

Breathing current domains in globally coupled electrochemical systems: a comparison with a semiconductor model

Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional domain. The results are compared with the dynamics and the bifurcation scenarios occurring in a closely related model which describes pattern formation in semiconductors. Under galvanostatic control both systems are unstable with respect to the formation of stationary large amplitude current domains. The current domains as well as the homogeneous steady state exhibit oscillatory instabilities for slow dynamics of the potential drop across the double layer, or across the semiconductor device, respectively. The interplay of the different instabilities leads to complex spatio-temporal behavior. We find breathing current domains and chaotic spatio-temporal dynamics in the electrochemical system. Comparing these findings with the results obtained earlier for the semiconductor system, we outline bifurcation scenarios leading to complex dynamics in globally coupled bistable systems with subcritical spatial bifurcations.

Controlling Chemical Turbulence by Global Delayed Feedback: Pattern Formation in Catalytic CO Oxidation on Pt(110)

Control of spatiotemporal chaos is one of the central problems of nonlinear dynamics. We report on suppression of chemical turbulence by global delayed feedback using, as an example, catalytic carbon monoxide oxidation on a platinum (110) single-crystal surface and carbon monoxide partial pressure as the controlled feedback variable. When feedback intensity was increased, spiral-wave turbulence was transformed into new intermittent chaotic regimes with cascades of reproducing and annihilating local structures on the background of uniform oscillations. The global feedback further led to the development of cluster patterns and standing waves and to the stabilization of uniform oscillations. These findings are reproduced by theoretical simulations.

Coupled maps with local and global interactions

A coupled map lattice model with both local and global couplings is studied as a simple example of hierarchical pattern dynamics with different length scales of interactions. Several phases are classified according to domain structures, degree of chaotic dynamics, distribution function, and power spectra. In particular, a cascade process of formation and collapse of bubbles is found in some parameter regime. The state is characterized by spatiotemporal power-law correlation and few positive Lyapunov exponents. In a two-dimensional case, the state leads to a characteristic spatiotemporal pattern that may be regarded as a dynamic extension of a Turing pattern. The possible relevance to natural patterns is also discussed. (c) 2000 American Institute of Physics.