Bistable kinetics of simple reactions on solid surfaces: lateral interactions, chemical waves, and the equistability criterion

In heterogeneous reactions, the rate constants of desorption, diffusion and elementary reaction steps are usually strongly dependent on reactant coverages due to adsorbate-adsorbate lateral interactions. We analyze the effect of this factor on the bistable regime of the reaction kinetics. As an example, we consider CO oxidation on Pt(111). The equistability lines in the bistable region for this reaction are calculated by analyzing propagation of chemical waves and taking into account the coverage dependence of the CO diffusion coefficient. The results of simulations are compared with the available experimental data. We show that it is possible to obtain the relationship between various kinetic parameters, for example, between CO and oxygen sticking probabilities, by studying special features of the bistable kinetics.     

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.     

Stochastic aspects of pattern formation during the catalytic oxidation of CO on Pd(111) surfaces

We present experimental results on rare transitions between two states due to intrinsic noise between two states in a bistable surface reaction, namely the catalytic oxidation of CO on Pd(111) surfaces. The mean time scales involved are typically of order 10⁴ s and the probability distribution shows two peaks over a large part of the bistable regime of this surface reaction. We use measurements of the resulting CO₂ rate as well as photoelectron emission microscopy (PEEM) to characterize these rare transitions. From our dynamic data we can extract probability distributions for the CO₂ rate. We use x-t plots from PEEM measurements to describe the transitions, which are-as we demonstrate-characterized by one wall moving through the field of view in PEEM measurements. The resulting probability distributions for the CO₂ rate are shown to depend strongly on the value, Y, of the CO fraction in the reactant flux inside the bistable regime. We find that the probability distribution is strongly asymmetric indicating that the two basins of attraction are rather different in depth and width. This is also concluded from the PEEM measurements, which show in one case a rather sharp and narrow domain wall going one way, while it is rather wide and diffuse for the motion in the opposite direction. To have two basins of attraction in the bistable regime, which are rather different in nature is reminiscent of other bistable systems such as, for example, optical bistability, although the time scales involved in the present system are entirely different.     

Vanadium oxide nanostructures on Rh(1 1 1): Promotion effect of CO adsorption and oxidation

The adsorption of CO and the reaction of CO with pre-adsorbed oxygen at room temperature has been studied on the (2 × 1)ORh(1 1 1) surface and on vanadium oxideRh(1 1 1) “inverse model catalyst” surfaces using scanning tunnelling microscopy (STM) and core-level photoemission with synchrotron radiation. Two types of structurally well-defined model catalyst V₃O₉Rh(1 1 1) surfaces have been prepared, which consist of large (mean size of 50 nm, type I model catalyst) and small (mean size <15 nm, type II model catalyst) two-dimensional oxide islands and bare Rh areas in between; the latter are covered by chemisorbed oxygen. Adsorption of CO on the oxygen pre-covered (2 × 1)ORh(1 1 1) surface leads to fast CO uptake in on-top sites and to the removal of half (0.25 ML) of the initial oxygen coverage by an oxidation clean-off reaction and as a result to the formation of a coadsorbed (2 × 2)O + CO phase. Further removal of the adsorbed O with CO is kinetically hindered at room temperature. A similar kinetic behaviour has been found also for the CO adsorption and oxidation reaction on the type I “inverse model catalyst” surface. In contrast, on the type II inverse catalyst surface, containing small V-oxide islands, the rate of removal of the chemisorbed oxygen is significantly enhanced. In addition, a reduction of the V-oxide islands at their perimeter by CO has been observed, which is suggested to be the reason for the promotion of the CO oxidation reaction near the metal-oxide phase boundary.     

Oscillations, period doublings, and chaos in CO oxidation and catalytic mufflers

Early experimental observations of chaotic behavior arising via the period-doubling route for the CO catalytic oxidation both on Pt(110) and Ptgamma-Al(2)O(3) porous catalyst were reported more than 15 years ago. Recently, a detailed kinetic reaction scheme including over 20 reaction steps was proposed for the catalytic CO oxidation, NO(x) reduction, and hydrocarbon oxidation taking place in a three-way catalyst (TWC) converter, the most common reactor for detoxification of automobile exhaust gases. This reactor is typically operated with periodic variation of inlet oxygen concentration. For an unforced lumped model, we report results of the stoichiometric network analysis of a CO reaction subnetwork determining feedback loops, which cause the oscillations within certain regions of parameters in bifurcation diagrams constructed by numerical continuation techniques. For a forced system, numerical simulations of the CO oxidation reveal the existence of a period-doubling route to chaos. The dependence of the rotation number on the amplitude and period of forcing shows a typical bifurcation structure of Arnold tongues ordered according to Farey sequences, and positive Lyapunov exponents for sufficiently large forcing amplitudes indicate the presence of chaotic dynamics. Multiple periodic and aperiodic time courses of outlet concentrations were also found in simulations using the lumped model with the full TWC kinetics. Numerical solutions of the distributed model in two geometric coordinates with the CO oxidation subnetwork consisting of several tens of nonlinear partial differential equations show oscillations of the outlet reactor concentrations and, in the presence of forcing, multiple periodic and aperiodic oscillations. Spatiotemporal concentration patterns illustrate the complexity of processes within the reactor.     

光学双稳态和混沌运动中的临界现象

本文以具有反馈时间延迟的非线性系统弛豫方程为出发点,讨论了双稳态临界点的临界现象。发现双稳区边沿的临界慢化与混沌运动中切分叉点附近阵发混沌时间间隔发散具有一致性,临界指数为1/2。在双稳区(尖顶突变模型)的尖顶处,与双稳区边沿临界点不同,它与混沌运动中倍周期分叉点及劈分叉点的临界慢化具有一致性,临界指数为1。上述结果具有普适性。以液晶混合光学双稳系统为例,进行了计算机实验,其结果与分析相一致。 关键词：     

Growth and Nonlinear Saturation of Fluctuations in a Nonlinear Oscillator at the Threshold of a Bifurcation of Spontaneous Symmetry Breaking

We consider the phenomenon of prebifurcation noise amplification in a nonlinear oscillator at the threshold of a bifurcation of spontaneous symmetry breaking. The studies are based on the model of a nonlinear oscillator in which the potential relief transforms from monostable to symmetric bistable and the noise acting on the system is assumed Gaussian and short-correlated. The fluctuation variance as a function of the regime of the system and the rate at which the bifurcation threshold is reached are examined. Our analytical estimates are in good agreement with the results of numerical simulation for both the linear growth and the nonlinear saturation of fluctuations. It is noted that in the case of fast bifurcation transitions, a loop of noise-dependent hysteresis and breaking of probability symmetry of stable final states are observed in the nonlinear oscillator. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 425–435, May 2005.     

Mechanistic study of the CO oxidation reaction on the CuO (111) surface during chemical looping combustion

Cu-based oxides oxygen carriers and catalysts are found to exhibit attractive activity for CO oxidation, but the dispute with respect to the reaction mechanism of CO and O₂ on the CuO surface still remains. This work reports the kinetic study of CO oxidation on the CuO (111) surface by considering the adsorption, reaction and desorption processes based on density functional theory calculations with dispersion correction (DFT-D). The Eley–Rideal (ER) CO oxidation mechanism was found to be more feasible than the Mars-van-Krevelen (MvK) and Langmuir–Hinshelwood (LH) mechanisms, which is quite different from previous knowledge. The energy barrier of ER, LH, and MvK mechanisms are 0.557, 0.965, and 0.999 eV respectively at 0 K. The energy barrier of CO reaction with the adsorbed O species on the surface is as low as 0.106 eV, which is much more active in reacting with CO molecules than the lattice O of CuO (111) surface (0.999 eV). A comparison with the catalytic activity of the perfect Cu₂O (111) surface shows that the ER mechanism dictates both the perfect Cu₂O (111) and the CuO (111) surface activity for CO oxidation. The activity of the perfect Cu₂O (111) surface is higher than that of the perfect CuO (111) surface at elevated temperatures. A micro-kinetic model of CO oxidation on the perfect CuO (111) surface is established by providing the rate constants of elementary reaction steps in the Arrhenius form, which could be helpful for the modeling work of CO catalytic oxidation.     

Ceria nanoformations in CO oxidation on Pt(1 1 1): Promotional effects and reversible redox behaviour

A well-defined CeO_x/Pt(1 1 1) model catalytic system has been fabricated using the self-assembling of Ce adatoms on a Pt(1 1 1) surface with a subsequent oxidation of the nucleating Ce submonolayer (0.3 ML). The resulting system of the “inverse supported catalyst” type consists of CeO_x nanoformations (2D islands of 5-15 nm size and ∼0.3 nm in height) more or less uniformly distributed over the Pt(1 1 1) surface. This CeO_x/Pt(1 1 1) system has been tested in the CO oxidation reaction where both the CO₂ production rate and the Ce oxidation state were monitored in situ. An enhanced reactivity and a remarkable shift of the bistable region of the reaction towards higher CO pressures were observed when compared to a clean Pt(1 1 1) surface. The CeO_x islands exhibit a pronounced redox behaviour that follows the hysteresis cycle of the reaction. The usefulness of such a type of the “inverse model catalyst” for studying the oxygen diffusion supply and the redox behaviour of ceria in the ceria-platinum catalysts is demonstrated.     

Forced bursting and transition mechanism in CO oxidation with three time scales

The mathematical model of CO oxidation with three time scales on platinum group metals is investigated, in which order gaps between the time scales related to external perturbation and the rates associated with different chemical reaction steps exist. Forced bursters, such as point-point type forced bursting and point-cycle type forced bursting, are presented. The bifurcation mechanism of forced bursting is novel, and the phenomenon where two different kinds of spiking states coexist in point-cycle type forced bursting has not been reported in previous work. A double-parameter bifurcation set of the fast subsystem is explored to reveal the transition mechanisms of different forced bursters with parameter variation.     

Compatibility of field emitter studies of oscillating surface reactions with single crystal measurements: catalytic CO oxidation on Pt

Kinetic oscillations in catalytic CO oxidation on Pt have been studied on large (millimeter size) single crystal planes of Pt as well as on a Pt field emitter tip that exposes different crystal facets of nanometer size. In order to examine the compatibility of results from the two types of experiments, the regions of different dynamical behavior (bifurcation diagram) have been mapped out in p_CO,T-parameter space using a field electron microscope (FEM) and a field ion microscope (FIM). The comparison with the results of single crystal measurements shows that in the case of applied electrostatic fields less than 5 V nm⁻¹ (FEM), the field-induced effects are negligible, but they are significant for fields exceeding 12 V nm⁻¹ (FIM). The field-induced shift of the bifurcation diagram toward lower p_CO values, observed with FIM, is explained in terms of a field-modified interaction of CO and O₂ with Pt studied here with field ion appearance energy spectroscopy. With coadsorbed lithium (submonolayer coverage), the existence range for rate oscillations is shifted toward higher p_CO values. This shift is attributed to a redistribution of the electron density at the surface induced by alkali metal co-adsorption.     

非对称双稳耦合网络系统的尺度随机共振研究

研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象. 关键词： 尺度随机共振 非对称双稳耦合网络系统 余弦信号 矩形信号     

Wave initiation through spatiotemporally controllable perturbations

We study the initiation of pulses and fronts in a two-dimensional catalytic reaction-diffusion system: CO oxidation on Pt(110). Using a computer-controlled mobile focused laser beam, we impart various patterns (in space and time) of localized temperature "kicks" to the surface. We explore, and also rationalize through modeling, the cooperativity of such individually subcritical perturbations in both the excitable and the bistable regime.     

First passage times and minimum actions for a stochastic minimal bistable system

Bistability is an ubiquitous phenomenon in biological systems, and always plays important roles in cell division, differentiation, cancer onset, apoptosis and so on. However, stochastic fluctuations in bistable systems are still hard to understand. To address this issue, we propose a chemical master equation model for a minimal bistable system, which underlies generally bistable systems. For this master equation model, we mainly focus on the mean first passage times (MFPTs) by respectively using Gillespie algorithm and an approximation method of the large deviation theory, and does on minimum actions along optimal transition paths from OFF to ON states by the large deviation theory. Further, we find that for this stochastic system the MFPTs have different change tendencies compared to the corresponding minimum actions. Our results of this minimal stochastic model can also well understand more general bistable systems.     

Surface characterization of supported Pt,Rh, and alloy particles by CO chemisorption

Temperature programmed desorption (TPD) of CO is used to determine surface areas, binding states, and changes upon oxidation for 10–1000 Å particles of Pt, Rh, and Pt-Rh alloy on amorphous SiO₂. A low area sample configuration is used to obtain rapid and uniform heating and cooling in an ultra-high vacuum system. It is shown that both metals exhibit a higher CO binding state for small particles, but, as particle size increases, this state disappears and is replaced by a more weakly bound state. These states are suggested to be associated with (111) and higher surface free energy planes on these surfaces, heating Rh above 700 K in O₂ at 10^?6 Torr produces an oxide on which the CO saturation coverage is at least a factor of 10 lower than on the reduced surface. For Pt, oxidation produces only a small decrease in CO coverage, although the binding energy of CO increases on the oxygen treated surface. The difference in desorption temperatures for CO on Pt and Rh is consistent with previous experiments which show that an oxidation-reduction cycle produces a surface layer which is enriched in Rh and that the oxidized alloy contains no Pt atoms.     

On the validity of the capillarity approximation in the rate theory of homogeneous nucleation

An Einstein model is used to calculate the internal vibrational free energy of approximately spherical fcc crystallites as a function of crystallite size at T/θ = 1. It is found that the free energy per surface atom does not become convergent until a size of about 3 × 10⁷ atoms is reached. The excess free energy at convergence is used to define the macroscopic surface tension for use in the capillarity approximation. The internal free energy of microcrystallites containing of the order of 100 atoms is fortuitously well described by the capillarity approximation. A good estimate of the total free energy of the microcrystallite (nucleus) is obtained from the capillarity approximation only by adding the contributions from free translation and rotation and the replacement partition function.     

The effect of potassium bromide and sodium carbonate on coal char combustion reactivity

The addition of halogens, particularly iodine, to the gas during coal char oxidation has been used in previous studies to quench gas-phase chemistry, thereby allowing one to separate the effects of homogeneous and heterogeneous reactions. Halogen addition suppresses the gas-phase radicals to near-equilibrium levels. A similar effect can be expected from other compounds with high efficiency as fire suppressants, such as alkali metals. The effectiveness of the use of additives in distinguishing homogeneous and heterogeneous reactions during char oxidation relies on the assumption that radicals are suppressed while heterogeneous reactions occurring on the char surface are not affected. The present work tests this assumption for potassium bromide (KBr) and sodium carbonate (Na₂CO₃) reacting with a pulverized eastern bituminous coal char during oxidation. An increase in CO and a slight reduction in particle temperature were observed with the addition of KBr, consistent with known effects of halogens on gas-phase chemistry. An increase in particle size was also observed with the KBr addition. This observation and the results of model calculations suggest that there is significant incorporation of liquid KBr on the char surface under the conditions examined. With Na₂CO₃ addition, the particle temperature did not change, the particle size showed a slight decrease, and CO production increased. Although the mechanisms for Na interaction with radicals at combustion conditions are not well established, char oxidation modeling suggests that a decrease in OH concentration in the particle boundary layer is the cause for the observed increase in CO production. It is concluded that Na₂CO₃ has clear advantages over KBr for inhibiting gas-phase chemistry without affecting char oxidation for the conditions investigated here.     

Dynamic characteristics of nonlinear Bragg gratings in photonic crystal fibres

We study numerically the temporal and spatial dynamics of light in Bragg gratings in highly nonlinear photonic crystal fibre for a CW input signal. Our numerical model is based on the plane wave mode solver and a set of nonlinear coupled-mode equations which we solve using a variation of implicit fourth order Runge-Kutta method. We observe not only bistability of the intensity versus transmitted and reflected light but also complex dynamics. We demonstrate that for values of input intensity above the bistable region the steady state may undergo a supercritical Hopf bifurcation. For some ranges of the input intensity we also observe a coexistence of two periodic attractors. The dynamics found, in particular the features in the bifurcation diagram, strongly depend on the parameters of the fibre. Consequently, we suggest that by proper design of the photonic crystal in the cladding we can adjust such nonlinear features of the Bragg gratings as the width of the bistable region, the intensity at which the bifurcation occurs and also the characteristics of the dynamics at high values of input intensity.     

Transient yielding of CO2 over oxidized ruthenium surfaces: Monte Carlo simulations

We develop Monte Carlo simulations to study the catalytic oxidation of CO over a surface of ruthenium. The catalyst is exposed to a continuous flux of CO molecules and its surface is pre-covered with an amount of oxygen atoms. Recent experiments performed on this system [R. Blume, W. Christen, H. Niehus, J. Phys. Chem. B 110 (2006) 13912] have shown that three different reaction mechanisms can account for the experimental results. Two of them are based on the Langmuir-Hinshelwood mechanism, where CO molecules are adsorbed at oxygen-free defect sites before reactions take place. The third one proceeds via the Eley-Rideal mechanism, which is almost time independent, and reactions occur at non-defect sites. In our model, we consider a semi-infinite cubic lattice to mimic the surface of the catalyst and oxygen atoms are incorporated into the layers below the surface. A fraction of defects is created at the topmost layer and at the first subsurface layer. Oxygen atoms can diffuse over the surface as well as between adjacent layers of the system. We also assumed a temperature dependent reaction rate that is related to the residence time of CO at the surface. Comparisons are made between the CO₂ yielding at defect-rich and smooth surfaces as a function of temperature.