Stochastic model of CO oxidation on platinum surfaces and deterministic limit

Emergence of Chemical Oscillations from Nanosized Target Patterns

This work investigates experimentally the mechanism by which chemical oscillations emerge in a nanometric system. We monitor the spatiotemporal dynamics of an oscillating reaction on the surface of a nanosized three-dimensional Pt model catalyst. Using high-resolution field emission techniques, we are able to show that the oscillations are generated by nanoscale chemical target patterns of much shorter characteristic time than the period with which the oscillations occur. Our observations are made for a specific reaction system-NO_{2} reduction with hydrogen-and represent the first experimental evidence for the presence of target patterns at the nanoscale. They can be seen as an experimental demonstration of reaction-diffusion mechanisms to hold at the nanoscale as they do at the macroscale. These results shed new light on the emergence of complexity through different time and length scales.

Effect of internal noise on the oscillation of N2O decomposition over Cu-ZSM-5 zeolites using a stochastic description

When considering stochastic oscillations of heterogeneous catalyst systems, most researches have focused on the surface of a metal or its oxide catalysts, but there have been few studies on porous catalysts. In this work, the effects of internal noise on oscillations of N2O decomposition over Cu-ZSM-5 zeolites are investigated, using the chemical Langevin equation and a mesoscopic stochastic model. Considering that Cu-ZSM-5 particles are finely divided particles, the number of Cu ions (Ns) is proportional to the particle size at a certain Cu/Al, and the internal noise is inversely proportional to Ns. Stochastic oscillations can be observed outside the deterministic oscillatory region. Furthermore, the performance of the oscillation characterized by the signal-to-noise ratio has a maximum within the optimal size range of 4-8 nm. This suggests that a nanometer-sized zeolite may be best for oscillations.

Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics

Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time-averaged entropy production P on the system size N in a parameter region close to the deterministic Hopf bifurcation (HB). In the large system size (weak noise) limit, we find that P ∼ N(β) with β = 0 or 1, when the system is below or above the HB, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly, P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the so-called CANARD point where the maximum disappears. This phenomenon could be qualitatively understood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.

Kinetic insights over a PEMFC operating on stationary and oscillatory states

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.

Fluctuation-induced phase transition in a spatially extended model for catalytic CO oxidation

A reaction-diffusion master equation has been introduced in order to model the bistable CO oxidation on single crystal metal surfaces at high pressure where the diffusion length becomes small and local fluctuations are important. Analytical solutions can be found in a reduced one-component nonlinear master equation after applying the Weiss mean-field approximation together with the adiabatic elimination of oxygen. It is shown that the Weiss mean-field approximation predicts a symmetry-breaking bifurcation associated with a phase transition. The corresponding stationary solutions of the nonlinear master equation are supported by Gillespie-type Monte Carlo simulations.

Internal Noise Coherent Resonance for Mesoscopic Chemical Oscillations: A Fundamental Study

The effect of internal noise for a mesoscopic chemical oscillator is studied analytically in a parameter region outside, but close to, the supercritical Hopf bifurcation. By normal form calculation and a stochastic averaging procedure, we obtain stochastic differential equations for the oscillation amplitude r and phase theta that is solvable. Noise-induced oscillation and internal noise coherent resonance, which has been observed in many numerical experiments, are reproduced well by the theory.

Theoretical analysis of internal fluctuations and bistability in CO oxidation on nanoscale surfaces

The bistable CO oxidation on a nanoscale surface is characterized by a limited number of reacting molecules on the catalytic area. Internal fluctuations due to finite-size effects are studied by the master equation with a Langmuir-Hinshelwood mechanism for CO oxidation. Analytical solutions can be found in a reduced one-component model after the adiabatic elimination of one variable which in our case is the oxygen coverage. It is shown that near the critical point, with decreasing surface area, one cannot distinguish between two macroscopically stable stationary states. This is a consequence of the large fluctuations in the coverage which occur on a fast time scale. Under these conditions, the transition times between the macroscopic states also are no longer separated from the short-time scale of the coverage fluctuations as is the case for large surface areas and far away from the critical point. The corresponding stationary solutions of the probability distribution and the mean first passage times calculated in the reduced model are supported by numerics of the full two-component model.

Effects of internal noise for rate oscillations during CO oxidation on platinum surfaces

We have studied the influence of internal noise on the reaction rate oscillation during carbon-monoxide oxidation on single crystal platinum surfaces using chemical Langevin equations. Considering that the surface is divided into small well-mixed cells, we have focused on the dynamic behavior inside a single cell. Internal noise can induce rate oscillations and the performance of the stochastic rate oscillations shows double maxima with the variation of the internal noise intensity, demonstrating the occurrence of internal noise coherent biresonance. The relationship between such a phenomenon with the deterministic bifurcation features of the system is also discussed.

Internal Noise Stochastic Resonance in NO Reduction by CO on Platinum Surfaces

We have studied the roles of internal noise in the oscillatory reaction kinetics during NO reduction by CO on low-index single crystal platinum surfaces using the chemical Langevin equation and the Poisson approximation algorithm. Considering that the surface is divided into small well-mixed cells, we have focused on the dynamical behavior inside a single cell. It is found that internal noise can induce rate oscillations and the performance of the stochastic rate oscillations undergoes a maximum with the variation of internal noise level for a given NO partial pressure, demonstrating the occurrence of internal noise stochastic resonance. Such a phenomenon is robust to the change of external parameters, such as NO pressures. Interestingly, it is also found that internal noise noticeably alters the oscillatory waveform and, hence, the reaction activity and oscillation signal intensity, but it nearly does not change the global reaction rate.

Realistic kinetic Monte Carlo study of the surface phase reconstruction

Reversible 1 x 1 <==> 1 x 2 reconstruction of Pt(110) surface is studied with the help of a kinetic Monte Carlo model. Activation energies of the allowed atomic steps are estimated using available computational and experimental data, and some discrepancies are reconciled to fit macroscopic data on surface reconstruction. Both energies of the various atomic configurations and activation energies depend on CO coverage and are estimated with the account of Pt-CO binding energies and repulsive interactions on adjacent sites. The model well reproduces both scanning tunneling microscopy results obtained for a clean 1 x 2 surface and available macroscopic data on 1 x 1 <==> 1 x 2 reconstruction.

A realistic kinetic Monte Carlo simulation of the faceting of a Pt(110) surface under reaction conditions

The faceting process on Pt(110) is studied with the help of a kinetic Monte Carlo model taking into account realistic Pt-Pt, Pt-CO, and Pt-O interactions. The activation energies of the allowed atomic steps are estimated using available computational and experimental data. The model well reproduces the region in the parameter space where faceting occurs. Under kinetic instability conditions, the simulated faceted pattern forms a periodic hill and valley structure with a lateral periodicity of approximately 140-170 A, which is comparable with experimental data. The simulations reproduce the development of faceting on a realistic time scale.