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.     

铂族金属氧化过程中的簇发振荡及其诱发机理

铂族金属表面氧化过程是典型的多相催化反应之一, 具有广泛的应用背景及丰富的振荡行为, 因此深入研究铂族金属的氧化中的物理及化学过程具有重要的理论意义及工程应用前景. 通过对铂族金属CO的氧化过程中实测数据的回归分析, 建立了不同尺度耦合解析动力学理论模型. 通过对平衡态的稳定性分析, 指出在一定条件下稳态解会由鞍-结同宿轨道分岔导致周期振荡. 当快子系统产生Hopf分岔时, 该周期振荡会进一步演化为两尺度耦合的周期簇发振荡, 即N^k振荡, 并由加周期分岔使得系统处于激发态的时间显著增加.在此基础上, 利用分岔理论进一步分析了周期簇发及加周期分岔的产生机理, 揭示了周期簇发中沉寂态和激发态相互转化时的不同分岔模式.     

高维广义蔡氏电路中的快慢动力学行为及其分岔分析

讨论了四阶广义蔡氏电路在两时间尺度下的动力学行为. 由数值模拟得到了系统在不同参数条件下的周期簇发解和混沌吸引子. 通过引入快慢分析法,从分岔的角度,以周期解为例, 对系统动力学行为产生的机理及其演化规律进行了理论分析和解释, 其结论与数值计算的结果基本符合.     

Bursting phenomena as well as the bifurcation mechanism in a coupled BVP oscillator with periodic excitation

We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system.By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency.Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples,in which different types of bursting oscillations such as sub Hopf/sub Hopf burster, sub Hopf/fold-cycle burster, and doublefold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states(QSs) and the repetitive spiking states(SPs) may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically.     

分段Filippov系统的簇发振荡及擦边运动机理

本文旨在揭示非光滑Filippov系统中由频域上不同尺度耦合导致的簇发振荡行为及其产生机理.以经典的周期激励Duffing振子为例,通过引入对状态变量的分段控制及适当选取参数,使得激励频率与系统固有频率之间存在量级差距,建立了频域两尺度耦合的Filippov系统.当激励频率远小于系统的固有频率时,可以将整个激励项视为慢变参数或慢变子系统,从而得到广义自治快子系统.分析了由非光滑分界面划分的不同区域中各快子系统的平衡点及其分岔特性随慢变参数变化的演化过程.考察了两种典型参数条件下系统的振荡行为及其动力学特性,指出参数变化不仅会引起其相应子系统平衡曲线及其分岔特性的改变,也会导致不同模式的簇发振荡.同时,轨迹穿越非光滑分界面时会产生不同的动力学行为,特别是在一定参数条件下,由于运动轨迹受不同子系统的交替控制,存在着擦边运动现象,从而导致特殊形式的非光滑簇发振荡.基于转换相图及各区域中快子系统的平衡曲线及其分岔特性,揭示了非光滑分界面对系统簇发振荡的影响规律及不同簇发振荡的分岔机理.     

多平衡态下簇发振荡产生机理及吸引子结构分析

以周期激励下受控Lorenz模型为例, 考察了多平衡态共存下激励频率与系统固有频率之间存在量级差距也即存在频域上的不同尺度时的耦合效应. 由于激励频率远小于系统的固有频率, 因此将整个激励项视为慢变参数, 分析随慢变参数变化下的各种分岔模式及其相应的分岔行为, 指出在一定条件下, 不同平衡点会产生Hopf分岔和fold分岔. 根据分岔条件的不同, 给出了两种典型情况下的簇发振荡, 并通过引入转换相图, 揭示了不同簇发的产生机理, 指出多平衡态和多种分岔共存不仅会导致沉寂态和激发态的多样性, 而且会使得不同沉寂态和激发态之间存在着不同的转换形式.     

Au_7团簇吸附O_2和CO及其对CO的催化反应机理研究

本文采用密度泛函理论,研究了Au_7团簇催化CO的氧化反应机理.研究发现,二维平面结构的Au_7团簇更容易吸附CO和O_2分子. Au_7团簇吸附一个O_2分子的吸附能为0.64 eV,但在吸附多个O_2分子时,平均吸附能有了明显的下降,表明Au_7团簇进行多吸附O_2分子的可能性不大. Au_7团簇吸附一个CO分子的吸附能为1.26 eV,且在吸附多个CO分子时,平均吸附能虽有减少,但减小的幅度不大,说明Au_7团簇有可能吸附多个CO分子.此外,在Au_7团簇催化CO的氧化反应过程中,整个反应克服的最高势垒仅为0.34 eV,说明Au_7团簇有望成为良好的CO氧化催化剂.     

Cobalt-containing oxide layers on titanium, their composition, morphology, and catalytic activity in CO oxidation

In this study possibility to form the layered compositions CoO_x + SiO₂/TiO₂/Ti by plasma electrolytic oxidation (PEO) method was shown. Compositions have been obtained by both one-stage PEO method (Method I) with addition of Co(CH₃COO)₂ into silicate electrolyte and impregnation of preliminary obtained by the PEO method SiO₂/TiO₂/Ti systems in aqueous solutions containing cobalt salts with their following annealing (Method II). XRD, XPS and SEM/EDX were used to investigate the phase and element composition, microstructure of the coatings prepared by the two various methods. Catalytic activity of the cobalt-containing composites was investigated in the CO oxidation reaction. Under experimental conditions, the structures obtained by impregnation and annealing method were more active, than those obtained by one-stage PEO method. The surface structures of cobalt-containing coatings obtained by the PEO method and by impregnation and annealing differ in both quantitative and qualitative relation. The cobalt content on the surface of impregnating coatings is three times as much as that for those formed by one-stage PEO method. It is found that coatings obtained by the Method II have a more developed surface. The surface of CoO_x + SiO₂/TiO₂/Ti compositions obtained by the PEO method contains, presumably Co(OH)₂ and Co₃O₄. The surface of the similar compositions obtained by the Method II, possibly contains CoO, either Co₂O₃, or CoOOH. The combination of these factors, perhaps, also provides a higher activity of the compositions formed by the Method II.     

C20 fullerene and its boron- and nitrogen-doped counterparts as an efficient catalyst for CO oxidation

DFT calculations are utilised to investigate the CO oxidation on the C₂₀, BC₁₉, and NC₁₉ clusters. For CO oxidation over considered clusters, two continuous steps are proposed that in each step one CO₂ molecule is released from clusters surface. The calculations demonstrate that in the case of the C₂₀ cluster, the first step of CO oxidation takes place through the ER mechanism on two routes with a barrier height of 1.06?eV and 2.57?eV for the rate-limiting step. Also, in the cases of BC₁₉ and NC₁₉ clusters, both reaction paths occur via the ER mechanism. The activation energy of the first reaction step is about 0.53 and 0.46?eV, while it is negligible for the second step that is 0.04 and 0.18?eV for BC₁₉ and NC₁₉ clusters, respectively. Based on the present theoretical results, the catalytic activity of BC₁₉ and NC₁₉ clusters toward the CO oxidation is more than that of the C₂₀ cluster. These results show that the BC₁₉ and NC₁₉ clusters can be recommended as an efficient and metal-free catalyst for CO oxidation at near ambient temperatures.

Research Highlights

• CO oxidation over C₂₀ fullerene has been investigated.

• The effect of N/B-doing on the CO oxidation reaction is also studied.

• The N/B-doping increases the catalytic activity of C₂₀ fullerene.

• Boron/Nitrogen-doped C₂₀ fullerene can be applied as an efficient catalyst for CO oxidation.

     

Preparation of nanosized iron oxide and its application in low temperature CO oxidation

A method to prepare iron oxide material which has a higher surface area and nanosized particle was developed. It was used as a catalyst for CO oxidation at low temperature. Iron oxide materials were prepared by precipitation under constant pH value. The effects of preparation parameters, such as iron salt (FeCl₃, Fe(NO₃)₃ and FeCl₂), pH value (between 8 and 12), drying temperature (between 120°C and 300°C), and feeding rate of the aqueous solution of the iron salt, on the characteristics of iron oxide have been investigated. The materials were characterized by N₂ sorption, powder X-ray diffraction (XRD), transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). The surface area of iron oxide was greater than 400 m²/g using FeCl₃ as the starting material with very low feeding rate of 10 ml/min, the pH value of 11, and drying at 120°C. The XRD patterns indicated that the iron oxide samples heated at a temperature below 180°C was either amorphous or of a particle size too small (<4 nm) for the samples prepared with FeCl₃. Depending on the preparation conditions, the iron oxide samples showed a phase transition from amorphous to various crystalline phases. Large amount of hydroxyl groups were preserved if the drying temperature was below 200°C. TEM images showed that the particle diameters were less than 4 nm for the samples prepared with FeCl₃ at pH value of 11 with a low feeding rate of 10 ml/min, and heated below 200°C. XPS Fe 2p_3/2 spectra showed the phase transition of iron oxide from Fe₃O₄ to FeO. The feeding rate of starting material and pH value during precipitation played the important roles to obtain iron oxide with high surface area. The nanosized iron oxide demonstrated high activity for CO oxidation even at ambient condition. The higher activity of Fe _x O _y nanoparticles in CO oxidation was attributed to a small particle size, high surface area, high concentration of hydroxyl groups, and more densely populated surface coordination unsaturated sites.This revised version was published online in August 2005 with a corrected issue number.     

Reaction mechanism of spinel CuFe2O4 with CO during chemical-looping combustion: An experimental and theoretical study

Spinel CuFe₂O₄ is a promising oxygen carrier due to its synergistic enhanced performance. A fundamental understanding of the reaction mechanism between oxygen carrier and fuels is important for a rational design of highly efficient oxygen carrier. The reaction mechanism of spinel CuFe₂O₄ with CO during chemical-looping combustion (CLC) was studied based on thermogravimetric analyses (TGA) and density functional theory (DFT) calculations. Two distinct reaction stages were clearly observed. CuFe₂O₄ was mainly transformed into Cu and Fe₃O₄ with a rapid reaction rate in the initial stage, and then product Fe₃O₄ was slowly reduced to FeO or even to Fe. The reactivity of CuFe₂O₄ is much higher than that of Fe₂O₃, which is ascribed to the existence of Cu. The enhanced oxygen evolution activity of CuFe₂O₄ at low temperature is validated by both the experimental and theoretical methods. Three types of surface oxygen coordinated with different metal atoms show different reactivity. Two kinds of reaction pathways are involved in CO oxidation over CuFe₂O₄. In the one-step reaction pathway, CO directly reacts with the oxygen bonding to two octahedral Cu and one octahedral Fe atoms to form a CO₂ molecule without an energy barrier, which corresponds to the surface oxygen consumption observed in TGA experiments. In the possible two-step reaction pathway, CO first adsorbs on the surface, and then reacts with the oxygen bound to one octahedral Cu and two octahedral Fe atoms to generate CO₂ by surmounting an energy barrier of 10.84 kJ/mol, which is the most kinetically and thermodynamically favorable pathway.     

Fabrication of model Pt-ceria catalysts and an analysis of their performance for CO oxidation

Model Pt-ceria catalysts have been prepared by the evaporation of Pt onto ceria (CeO₂) films grown on Si(1 1 1) substrates. Photoelectron spectroscopy (XPS, UPS) data are used to characterise the surfaces and their adsorption characteristics, and CO oxidation has been used as a probe reaction to test the activity of the model catalysts.Pure ceria is catalytically-inactive under the test conditions employed, whereas the model Pt/ceria catalysts demonstrate high activity for CO oxidation. The model catalysts also reproduce many of the characteristics of their high-surface area analogues, including the possession of a characteristic light-off temperature, hysteresis in activity as a function of temperature and a negative-order dependence on the CO partial pressure.Many aspects of the behaviour of these catalysts are shown to be a direct result of the strong adsorption of CO. The sensitivity of the dispersed Pt towards oxidation is also experimentally-demonstrated and the importance of this phenomenon is discussed.     

CO and O coadsorption on Pt3Sn studied by DFT: Changes in the adsorptive properties of the surface with alloying and coverage

Adsorption of CO and coadsorption of O and CO on Pt₃Sn(1 1 1) was studied using periodic DFT calculations. Calculations were performed on Pt(1 1 1) by using the same set of parameters and their results were used as reference basis. The calculations showed that the most stable configuration with the minimum energy for coadsorption of CO and O is CO adsorbed atop Pt and O adsorbed on fcc Pt2Sn hollow site and that the decrease in the adsorption strength of the system at a total surface coverage of 0.5 ML is by 0.063 eV as a result of coadsorption, with respect to the adsorption of one species individually. Results show that the interaction between the adsorbed CO and O is short range on PtSn alloy, contrary to that on pure Pt, and this is mainly related to stronger Sn–O bonds compared to Pt–O bonds which eventually reduce the surface strain at the coadsorption structure. There is a pronounced effect of total surface concentration on the adsorption energy of coadsorbed species; the adsorption strength is not directly proportional to the surface coverage but is also related to the distribution of the coadsorbed species on the surface.     

Direct comparison of the reactivity of the non-oxidic phase of Ru(0 0 0 1) and the RuO2 phase in the CO oxidation reaction

Applying in situ surface X-ray diffraction (SXRD) together with on-line mass spectrometry during the CO oxidation over Ru(0 0 0 1) allows a direct comparison of the reactivity of the non-oxidic state with that of the RuO₂(1 1 0) covered surface. This comparison reveals that the RuO₂(1 1 0) surface is a catalytically active phase at least as active as the non-oxidic phase. At high CO and O₂ pressures of 200 mbar and temperatures above 550 K, the CO oxidation reaction does not proceed isothermally on the RuO₂(1 1 0) surface. The released reaction heat leads rather to an increase of the sample temperature of up to 130 K accompanied by a self-acceleration of the CO oxidation reaction.     

Study of the state of Ag and Pd in silver-palladium catalysts on a titanium dioxide substrate by IR spectroscopy of adsorbed CO

We have used IR spectroscopy of adsorbed CO to study the effect of the method for preparation of silver-palladium catalysts on a TiO₂ substrate and exposure to an oxidizing or reducing gaseous atmosphere on the state of Ag and Pd centers. We have shown that as a result of the metal-support interaction, the reducibility of the Ag and Pd particles is increased, which leads to a change in their adsorption and catalytic properties. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 1, pp. 16–20, January–February, 2007.     

一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型的Hopf分岔与周期解问题

研究了一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型. 给出了产生Hopf分岔的临界时滞条件, 利用Mawhin重合度理论,探讨了该模型的周期解问题. 关键词： 时滞 厄尔尼诺-南方涛动模型 Hopf分岔 周期解     

CO2在气体水合物结构特性的固体核磁共振波谱与拉曼光谱实验研究

天然气水合物是蕴含着巨大能源潜力的非常规能源,2017年和2020年两次我国南海探索性试采的成功,加快了天然气水合物项目的进展。二氧化碳置换开采法,既能开发CH₄,又能封存CO₂。同时水合物法分离烟气中CO₂具有很好的应用前景,而CO₂在气体水合物的微观结构和特性尚不明确,实际应用存在一定的未知影响。为了考察其特性,利用13C固体核磁技术（NMR）和拉曼光谱（Raman）进行CO₂置换CH₄水合物、合成13CO₂-H₂-CP混合水合物实验表征,讨论CO₂在水合物中的定量问题,研究CO₂分子在笼型结构中的分布,探讨CO₂分子在气体水合物中的结构类型和特性。结果表明：（1）利用Raman费米低频共振1 277.5 cm-1峰积分得到CO₂在I型大笼（51262笼）的占有率为0.978 2,CH₄在Ⅰ型小笼（512笼）和大笼（51262笼）的占有率为0.059 3和0.009 5,水合数7.61,Raman费米高频共振1 381.3 m-1峰积分得到CO₂在51262笼的占有率为0.984 3,CH₄在512笼和51262笼的占有率为0.023 7和0.003 3,水合数7.70,CO₂几乎占满了大笼,CO₂气体的加入会导致水合物中,CH₄的大、小笼占有率均大幅度降低,置换后水合数略低于纯甲烷水合物,未标记的CO₂水合物在核磁中较难测出信号,CO₂气体置换后CH₄在小笼的占有率仅0.097 5,大笼占有率为0.317 2,两种方法差异主要原因为核磁的CO₂未出峰。（2）利用拉曼费米低频共振1 273.4 cm-1峰积分得到H₂、CO₂在512笼、CP在51262的占有率分别为0.124 8,0.304 2和0.997 8,水合数9.16;Raman费米高频共振1 380.6 cm-1峰积分得到H₂、CO₂在512笼、CP在51262的占有率分别为0.123 6,0.577 1和0.985 1,水合数7.12。13C标记CO₂分子在水合物中达到较好的固体核磁分辨率,首次确认CO₂在Ⅱ型小笼中的化学位移为124.8 ppm,计算得到CO₂的小笼占有率为0.783 1,CP的大笼占有率为0.971 8,水合数6.70,Raman高频频费米共振峰（1 380.6 cm-1）定量计算与13C NMR结果更接近。（3）对CO₂的13C NMR化学位移进行了归属,并结合Raman与13C NMR的对比分析,为CO₂水合物的13C NMR研究和拉曼定量提供参考。     

Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity

In this Letter, we investigate the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.