Local forcing of a nonlinear surface reaction: CO oxidation on Pt(100)

A novel spatiotemporal perturbation method for nonlinear surface reactions is reported, thus allowing the creation of new spatially localized structures. Forcing was achieved by dosing reactant gases through a capillary positioned near the catalyst surface, providing control over the local surface coverage and reaction rate. The emergence of localized concentration patterns and oscillations in an otherwise stable system is attributed to a local modification of the catalytic properties of the surface due to external forcing. Based on the spatial orientation, the temporal and thermal stability of the modified surface, as well as the affinity of CO toward the perturbed surface, subsurface O is proposed as a possible source of the observed localized patterning and surface memory effect. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Influence of concentration waves on the fischer—tropsch reaction

Investigation of the hydrocarbon rate formation behaviour during the Fischer—Tropsch synthesis under periodic concentration forcing reveals the existence of resonance peaks for certain choices of cycle parameters. These peaks appeared under symmetrical cycling with a mean feed composition of 17–5% CO (balance H₂) at both low (less than 0-001 cps) and high (greater than 0-01 cps) frequencies for the alkanes. Although methane was more strongly stimulated under periodic operation than other hydrocarbons, the rate enhancement observed for C₂ to C₆ products signalled the potential for ‘tuning’ selectivity in this mode of operation.     

A linear algebraic approach to steady-state bifurcation of chemical reaction systems

A new linear algebraic method that makes use of the Carleman linearization procedure is given for determining the local multiplicity features of chemical reaction systems. The method requires no reduction of the original steady-state equations and gives exact multiplicity conditions in terms of the nullities of the successive Carleman matrices. The steady-state bifurcation problem of a general class of catalytic reaction systems is resolved using this method.     

Imaging and probing catalytic surface reactions on the nanoscale: Field Ion Microscopy and atom-probe studies of O2–H2/Rh and NO–H2/Pt

We present dynamic studies of surface reactions using video-Field Ion Microscopy (FIM) along with Pulsed Field Desorption Mass Spectrometry (PFDMS). Catalytic water formation is followed using rhodium and platinum 3D field emitter crystals for the oxidation of hydrogen with either oxygen (Rh) or NO (Pt). Strongly non-linear dynamics are observed with nanoscale spacial resolution. For both reactions quasi-oscillatory behaviour exists under certain conditions of temperatures and partial pressures. An influence of the probing electric field is observed and possibly essential in establishing oscillatory behaviour. Local chemical probing of selected surface areas with up to 400 atomic surface sites proves catalytic water formation to take place. Since water ions (H₂O⁺/H₃O⁺) cause image formation of the O₂–H₂ reaction on Rh, respective videos provide space-time resolved information on the catalytically active sites. Atom-probe data also reveal that the surface of the Rh sample reversibly switches from a metallic to an oxidized state during oscillations. As to the NO–H₂ reaction on Pt, fast ignition phenomena are observed to precede wave fronts. After catalytic water formation, NO molecules diffuse into emptied areas and cause high image brightness. Depending on the size of the Pt crystal, the reaction may ignite in planes or kinked ledges along the <100> zone lines. Thus FIM provides clear experimental evidence that kinks are more reactive than steps in the catalytic NO + H₂ reaction. Pt surface oxidation occurs and has probably been underestimated in previous FIM studies.     

Non-gaseous layer combustions: Part 1. Mechanism of the self-sustained reaction between iron and potassium dichromate

A detailed study of the mechanism of the self-sustained reaction between powdered iron and potassium dichromate, as a simple system for the simulation of rocket propulsion reactions, has been attempted. Temperature changes as the reaction front passes a point were measured; propagation velocities derived from these records by means of the Mallard-Le Chatelier theory agreed fairly well with the directly observed velocities. It was concluded that the thermal theory is a good representation of the behaviour of this particular composition. Kinetics at low density were found to differ greatly from those at high density. The difference may be explained on the hypothesis that reaction occurs at low density by means of the gas phase, and at high density, where contact is greater, by diffusion across solid—solid interfaces.     

Dynamic Methanation of CO2 – Effect of Concentration Forcing

Investigating the effect of concentration forcing of the CO₂ methanation is not only relevant for power‐to‐gas plants but also for the study of dynamic phenomena of this reaction. In this study a Ni/Al₂O₃ catalyst is investigated under concentration forcing at industrially relevant conditions. The dynamic experiments allow an evaluation in terms of the reaction rate and enable the study of the reaction mechanism. The experiments show that no methane is formed in the CO₂‐rich part of the cycle, whereas a fast hydrogenation of carbonaceous species to methane takes place upon switching to H₂.     

Oscillatory behaviour during the oxidation of methane over palladium metal catalysts

Oscillatory reactions over palladium foil and wire catalysts during the oxidation of methane have been investigated over a wide range of reaction temperatures and argon/methane/oxygen feed gas compositions. Characterisation of the catalyst has also been carried out using scanning electron microscopy (SEM) techniques, which revealed the presence of a porous surface. This suggested that the metal surface has undergone a change since the reaction commenced, and using X-ray powder diffraction (XRD) techniques the palladium phase was shown to be the dominant phase present. Hysteresis phenomena were observed in the activity of the reaction as the temperature was cycled up and down, showing that the metal surface was continually changing throughout the reaction. The activation energies of the reaction during the high reactivity mode, PdO, and low reactivity mode, Pd, were also calculated. Oscillation rates were observed to depend on the dominant surface. Oscillations were frequent when the high reactivity mode was dominant while the activation energy of this mode was found to be low. When the low reactivity mode was dominant, the oscillations were slower and the activation energy was three times larger. The results obtained imply that the behaviour of the palladium surface, switching back and forth from the reduced state to the oxidised state, is responsible for the oscillatory behaviour seen in this system.     

Real and Ideal Relationships between Selectivity,Reactivity and Equilibrium

Reactivity and selectivity are discussed in terms of quadratic rate—equilibrium relationships for reaction series sharing a common intrinsic barrier, notably Marcus' equation. R.D. Levine's emphasis on such reactions as forming a “Brønsted Series” is suggested as a basis for defining “ideal” reactivity behavior. Ideal relationships between selectivity and reactivity and selectivity and equilibrium are derived based on reaction schemes drawing a formal distinction between reagent and substrate. In a simple Brønsted relationship, the reagent varies and the substrate is held constant. In an extended relationship, in which both substrate and reagent vary, the Brønsted series becomes a selectivity “network” or matrix characterized by direct and cross quadratic coefficients reflecting curvature of a free energy relationship and the dependence of selectivity upon rate or equilibrium respectively. In the ideal case, the quadratic coefficients are equal but, in practice, they generally differ. Inspection of the relevant reaction schemes shows that in evaluating the coefficients, there is greater cancellation of experimental and chemical scatter arising from non-systematic variations in reagent structure for the cross than the direct coefficient; this phenomenon accounts in part for the wider observation of reactivity—selectivity than non-linear free energy relationships. New measurements are reported for reactions of carboxylic acids with enolate and imine substrates. The results are combined with literature data and plotted as reactivity—selectivity and extended Brønsted relationships. The correlations are satisfactorily considered in the context of departures of real from ideal behaviour.     

A finite element solution of coupled heat and mass transfer with chemical reaction

A finite element method is presented for solving the coupled non-linear parabolic differential equations describing transient transport of heat and mass in chemically reacting systems. The method appears to be a useful approximation for a wide variety of problems. Typical numerical results are reported for non isothermal catalytic solid—fluid reactions. Applications to other fields such as absorption accompanied by reaction and non-catalytic solid—fluid reaction models are also formulated.     

Zur Pyrolyse von 3-Ethylpent-2-en – Ein weiterer Hinweis auf eine Homoallyl-Umlagerung

Pyrolysis of 3-Ethylpent-2-ene — a Further Evidence for a Homoallylic-Rearrangement The pyrolysis of 3-ethylpent-2-ene has been studied under conditions of steam cracking in the temperature range 600—700°C in a laboratory scale tubular reactor. The main products of decomposition were methane, 2-ethylbutadiene and isoprene. The majority of products obviously arose from H abstraction and radical addition, typical for radical chain reactions in olefins decomposition including phenomena resulting from allylic resonance. The formation of isoprene, however, could only be explained by a reaction network including a homoallylic rearrangement.     

Free radicals trapped in polyethylene matrix: 2. Decay in single crystals and diffusion

The kinetics of the decay of main chain free radicals trapped in polymer matrix in vacuum was investigated. The decay behaviour of alkyl radicals trapped in the lamellar surface of the crystallites of solution grown polyethylene should be different from that of the same radicals trapped in the inner part of the crystallite, and this difference was clearly observed. The analysis of the data of the decay reaction was made, based on three-dimensional diffusion-controlled reaction theory, and reasonable interpretation of the data was made. Alkyl radicals were also observed in an irradiated urea—polyethylene complex and the decay rate of these radicals were very slow in spite of the large mobility. According to these occurrences, it was concluded that the mechanism of three-dimensional diffusion of the free radicals across the chain may occur in the inner part of the crystallites via hydrogen abstraction reactions.     

Etude de la reaction du carbone avec le sulfure d'hydrogene H2S a hautes temperatures et sous basses pressions

Reaction of carbon with hydrogen sulfide at high temperature (1000–2000°C) and low pressure (10^?4–10^?2 Torr) exhibits the following features:—carbon disulfide CS₂ is the only carbonaceous reaction product. There is no indication that CS₂ would originate from a secondary reaction of the unstable carbon monosulfide CS. Some decomposition of H₂S into its elements is also observed (Figs. 1–3).—as already observed in other high temperature carbon gasification reactions, the intrinsic reactivity of the sample surface is temperature and pressure dependent. Consequently, transitory or stationary rates are observed, depending respectively upon a changing or a stationary surface state of the carbon sample (Fig. 4). The changes in the surface state are more marked for amorphous than for graphitized samples (Fig. 5).—below 1700°C, the true reaction order is smaller than one, as a consequence of the high stability of the carbon-sulfur surface complexes.—for ungraphitized samples, the carbon surface loses slowly and irreversibly its ability to change with changes in pressure and temperature.All these features were previously observed in the reaction of carbon with sulfur vapor: consequently hydrogen sulfide appears to behave simply as a gaseous sulfur carrier. The kinetic behaviour is in agreement with former interpretations assuming presence of peculiar reactive sites, which originate from chemical attack of the solid but disappear due to a surface thermal heating process.Confirming also previous assumptions, sulfur chemisorption strongly affects the reaction kinetics, as shown by the influence of H₂S traces on the kinetics of the C-O₂ reaction (Fig. 10):—at lower temperatures (< 1300°C) there is an important inhibiting effect on the CO production: H₂S is adsorbed strongly on the reactive sites which become inaccessible to O₂ molecules.—in the intermediate temperature range an enhancing effect is observed which is attributed to a hindrance of thermal healing (caused by chemisorption still present).Finally, the kinetic features as a whole are tentatively summarized in a comprehensive diagram where the consistency of experimental results appears clearly.     

A computer model for the regenerative bed

The transient behavior of a packed bed of uniform spheres is considered, where heat (or mass) transfer inside the sphere is described by a linear parabolic second order partial differential equation — the standard diffusivity equation. One dimenisonal plug flow is assumed; hence, the fluid behavior is given by a set of first order partial differential equations, with bed axial position and time as the independent variables. The existence of chemical reaction in the fluid makes these equations non-linear. The two systems of equations describing the solid and the gas are coupled by the equations for heat (or mass) transfer at the surface. Numerical methods for solving both the linear (no reaction) and non-linear (with reaction) cases are presented. In the former, the implicit Crank-Nicholson method is used; in the latter the two systems of equations are first decoupled and then solved separately.     

非线性液位系统的反馈线性化控制

为了更好地研究非线性液位系统在工作点大范围变化时的控制问题,对A3000过程控制装置中非线性单容水箱的液位控制进行了研究。建立了精确的单容水箱模型,提出了一套基于传统PID控制的反馈线性化控制方案,并在Freelance 800F DCS中成功进行了组态和调试,验证了反馈线性化控制方案在非线性液位系统中的可行性和优越性。     

Kinetically induced unstable behaviour in heterogeneously catalyzed reactions

Evidence has appeared in the literature that ignition-extinction phenomena in heterogeneously catalyzed reactions can be induced by pure kinetic effects. This paper presents an elegant and simple analytical reasoning based upon elementary properties of polynomials to derive explicit necessary and sufficient conditions for this behaviour for various reaction mechanisms, including Langmuir as well as non-Langmuir-type of adsorption. It is inspired on geometric arguments on the steady state equation, involving tangent adsorption and surface reaction rate curves as a function of surface coverage, which represent the limiting cases of rate multiplicity. The approach is particularly attractive for Langmuir-type adsorption as the adsorption rate equations are linear in this case. The technique is also applicable with the same ease in most situations of nonlinear adsorption characteristics and is to be preferred over a number of more intricate alternatives, because of its simplicity and its ability of defining explicit maximal bounds on the fundamental parameters.     

The kinetics of thin film polyesterification

The goal of this work was to investigate the increase in the rate of polyesterification that takes place as surface-to-volume ratio is increased. The polymer used in this reaction was derived from the esterification of adipic acid (hexanedioic acid) and propylene glycol (1,2-propanediol). The effect of three variables—film thickness, water concentration of the nitrogen atmosphere, and temperature—was studied to determine their effect on the reaction rate. The water content of the atmosphere was found to severely retard the progress of the esterification and this fact reaffirms that the reverse reaction, hydrolysis, is much more important than was realized by earlier investigators. The reaction in the film was found to have an activation energy of 22,600 cal/mole compared to 12,600 cal/mole in the batch reaction, indicating a possible change in controlling rate from the batch to the film system. New evidence was found which illustrates the possible role of reactant mobility at high conversions. It is suggested that a possible explanation for the change in controlling rate may be due to a complex surface phenomenon such as the alignment of reactive groups at the surface or the orientation of water molecules at the gas–liquid interface.     

An application of the self-ignition method of polymers: Anti-smoke additive induced glowing effect in the combustion of poly(vinylchloride)

The effect of anti-smoke additives in poly(vinylchloride) (PVC) has been studied using self-ignition methods. The self-ignition reaction was followed thermally, visually and by gas—liquid chromatography of the gaseous phase around the sample. Particular emphasis was palced on the determination of the CO, CO₂ and aromatic species. It is shown that ferrocence, among similar additives, considerably modifies the self-ignition behaviour of PVC by inducing glowing phenomena of various kinds. In some cases this incandescence can lead to self-ignition. From the analysis of carbon oxids and aromatic species as a function of time and temperature, it is possible to deduce that the anti-smoke reaction is associated, at least partially, with reactions which lead to incandescence. These reactions transform the carbon into carbon oxides instead of producing, in the gaseous phase, molecules which on further condensation lead to aromatic species at the origin of the soot. In short, the anit-smoke reaction appears to proceed mainly through a competing mechanism.     

Simulation,model‐reduction,and state estimation of a two‐component coagulation process

The issue of state estimation of an aggregation process through (1) using model reduction to obtain a tractable approximation of the governing dynamics and (2) designing a fast moving‐horizon estimator for the reduced‐order model is addressed. The method of moments is first used to reduce the governing integro‐differential equation down to a nonlinear ordinary differential equation. This reduced‐order model is then simulated for both batch and continuous processes and the results are shown to agree with constant Number Monte Carlo simulation results of the original model. Next, the states of the reduced order model are estimated in a moving horizon estimation approach. For this purpose, Carleman linearization is first employed and the nonlinear system is represented in a bilinear form. This representation lessens the computation burden of the estimation problem by allowing for analytical solution of the state variables as well as sensitivities with respect to decision variables. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1557–1567, 2016     

持续振荡行为的动力学模拟

作者已经研究了甲醇在 KY 分子筛上催化氧化的振荡行为。本文进一步探讨反应的机理,对表面覆盖度、表面温度和产物浓度随时间变化的非线性方程组进行稳定性分析。证明了极限环和周期解的存在性。数值计算模拟了实验得到的振荡行为,结果与实验现象和分析较好吻合。