Simplest model of catalytic oscillator

The simplest mathematical model for self-oscillations in catalytic reactions whose mechanism includes the steps: 1)ZX; 2) X+2Z3Z; 3) ZQ, is described.

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, : 1. ZX; 2. X+2Z3Z; 3. ZQ.

     

Mathematical simulation of self-oscillations in methane oxidation on nickel: An isothermal model

The dynamics of methane oxidation on nickel was studied by mathematical modeling within the framework of an 18-step microkinetic scheme. The model examined predicts the appearance of self-oscillations caused by the periodic oxidation-reduction of nickel in the reaction proceeding under isothermal conditions.     

Modelling of self-oscillations in the combustion of n-heptane-isooctane mixtures

A mathematical model has been constructed to describe the self-oscillation regime of the cool-flame combustion of an n-heptane-isooctane mixture. The character of the dependence of the amplitude and oscillation period on the temperature and mixture composition is in a qualitative agreement with the similar experimental data.

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Mathematical modeling of self-oscillations in ethane oxidation over nickel

The methodology of constructing a phenomenological model for complex heterogeneous catalytic reactions is described in detail. The proposed approach is applicable to development of mathematical models describing the onset of self-oscillations in hydrocarbon oxidation on the transition metal surface. The approach is based on construction of a microkinetic scheme taking into account the formation of main reaction products and intermediates, on estimation of the heat of reaction, activation energy, and preexponential factor for elementary steps and includes development and a subsequent analysis of the corresponding mathematical model. Catalytic reactions are considered in the ideal adsorption layer approximation without taking into account the relationship between coverages and spatial coordinates. Accordingly, the mathematical model is an independent system of ordinary differential equations. This methodology is used to develop a point (lumped) model for ethane oxidation over nickel, which is based on a 36-step microkinetic scheme taking into account the oxidation and reduction of nickel and the formation of total (CO₂ and H₂O) or partial (CO and H₂) ethane oxidation products, as well as the dehydrogenation of ethane into ethylene. The proposed model predicts the onset of self-oscillations in this reaction at atmospheric pressure in the temperature range from 850 to 1400 K. The kinetic oscillations are caused by the cyclic oxidation and reduction of nickel. The self-oscillations of the reaction rate are accompanied by oscillations of the catalyst temperature. The results of modeling are compared with experimental data.     

Properties of variational transition states for association reactions

The relationships between the structures of microcanonical variational transition states for association reactions and potential energy surface properties are analyzed. The analysis is facilitated by the recent finding that in many cases the vibrational frequencies for the transitional modes in the association reaction vary exponentially with the reaction coordinate. An increase in the attenuation of the transitional mode frequencies results in a tighter transition state. Long-range minimum energy path potentials of the form −c/r″ have only one transition state at each energy. Certain types of association reactions may not have transition states.     

Cluster approach to ion association reactions in electrolyte solutions

Ionic chemical reactions in liquid solutions can be described by association processes between oppositely charged particles and treated by classical statistical mechanics. Previous attempts to derive explicit microscopic expressions for the cluster densities were not completely adequate. In this paper we fill this gap. The average evolution of cluster densities then yields the usual time-correlation function expression for the phenomenological rate constants. As an application we describe the case of pair formation reactions in an electrolyte solution.     

Monte-Carlo studies of trigger self-oscillations in a bimolecular heterogeneous catalytic reaction

Dynamics of processes on metal surfaces and conditions for rate oscillations taking into account reconstruction of the catalyst are investigated using the Monte-Carlo method for a catalytic reaction following the Langmuir-Hinshelwood mechanism. Different regions of the oscillations were found, particularly the region where the oscillations are governed by the formation of a steady compact cluster which controls the frequency and amplitude of oscillations.     

Kinetic model for laser-assisted reactions

A bimolecular expression has been developed for the prediction of reactive rate constants and cross sections in non-resonant laser fields. The result is a function of the laser power density, the electronic transition moment, the spectral detuning and the parameters which define the internuclear potential. The final form is based on a phenomenological model and is the result of treating the reaction as a unimolecular process. Available data are discussed in terms of a van der Waals potential and are correlated as a function of the long-range attraction. Agreement with published results is very good. The model is used to make predictions of branching ratios in several systems and a discussion of the molecular properties requisite to successful experiments is presented.     

A model for free-radical reactions

Using an EHT type Hamiltonian the Heitler-London-VB treatment of the three-centre three-electron problem is simplified such that the interesting features of the potential hypersurfaces of arbitrary three-centre three-electron systems can be obtained simply from the knowledge of atomic orbital energies and overlap integrals. The method is applied to the hypersurfaces of the H₃ system and extensions of the discussion of general radical reactions are indicated.     

A modified model of diffusion-controlled reactions

The treatment used for diffusion-controlled reactions is extended to the case when the final jumplike step of the reagent approach differs essentially from the preceding diffusion. In terms of the model proposed it is possible to take into account, in a simple way, chemical inhomogeneity of the reagents when the in-cage reaction rate depends on the pair state (for example, on the molecular orientation). In this connection the reaction can be controlled either by the reagent intrusion into the solvation shell of the partner, or by the in-cage relaxation.     

The Structure of the Elusive Simplest Dipeptide Gly-Gly

Among the hundreds of peptide compounds for which conformations have been determined by using different spectroscopic techniques, the structure of the simplest dipeptide glycylglycine (Gly-Gly) is conspicuously absent. Herein, for the first time, solid samples of Gly-Gly have been vaporized by laser ablation and three different structures have been revealed in a supersonic expansion by Fourier transform microwave spectroscopy. The intramolecular hydrogen bonding interactions that stabilize the observed forms have been established based on the ¹⁴N nuclear quadrupole hyperfine structure. We have illustrated how conformer interconversion distorts the equilibrium conformational distribution, giving rise to missing conformers in the conformational landscape.     

Binding of gaseous Fe(III)-heme cation to model biological molecules: Direct association and ligand transfer reactions

The binding of a variety of ligands with Fe(III)-heme(+) ion, prosthetic group of heme proteins, has been studied in the gas phase by ESI-FT-ICR mass spectrometry. The ligands have been selected among substrate molecules of heme proteins (e.g., NO, nitroso compounds) or among model compounds acting for the functional groups that are present in the protein backbone (e.g., amines, thioethers, nitriles, ketones, amides, etc.). Both the kinetic and the thermodynamic features of the addition reactions are reported. Fe(III)-heme(+) ions react faster with lone pair donor ligands as the reaction becomes increasingly thermodynamically favored (higher heme cation basicity of the ligand, HCB, namely -DeltaG degrees for the ligand addition reaction). In turn HCBs correlate in general with the gas phase basicity toward the proton of the various ligands. A ligand addition equilibrium is established with weaker ligands, methanol, acetonitrile and acetone, yielding absolute HCB values, whereas ligand transfer equilibriums allowed a scale of relative (and absolute) HCBs to be constructed. NO displays exceptional binding properties towards Fe(III)-heme(+), unrelated to the low gas phase basicity toward the proton of this molecule, which is clearly the basis for the paramount role of heme proteins in NO binding and regulation.     

The entropy term in isodesmic,association, and conformational equilibration reactions

Isodesmic reactions involving methyl, phenyl, and vinyl species are shown to be accompanied by small entropy changes. In contrast, the association≓ reaction of methane with vinyl species has a large entropy change that is quite well estimated by approximate translational entropy differences. The effect of neglecting multiple species on conformational equilibrium returns us to small but still predictable changes.     

Nonlinear coupling model for reactions in dense media

A reaction rate theory for dense‐phase reactions, based on the assumption of nonlinear coupling between reactant and medium, is proposed. The relations between the exact dynamic theory, the stochastic rate theory, and the transition state theory is discussed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 1–3, 2001     

Acceleration mechanisms in curing reactions involving model systems

The mechanisms involving some of the most common accelerators in the curing reactions of epoxy resins have been investigated by use of model systems. Phenyl glycidyl ether was used as a model compound. The characterization of the reaction products was mainly carried out by High-Performance-Liquid-Chromatography and by preparative methods. Special attention was paid to the oligomerization reactions of the oxirane ring in the presence of tertiary amines. Three different types of oligomers depending on phenyl glycidyl ethers are discussed. The mechanisms of multifunctional accelerators such as imidazoles or phenol-MANNICH-base-compounds are much more difficult. The extraordinary interaction of imidazoles depends on the formation of different oligomers. Furthermore, the cleavage of the imidazole ring was observed. It is possible that the glycidyl ether oligomerization plays an important role in understanding the network structure. Some aspects of the accelerating effect of tertiary amines in the curing of glycidyl ethers with acid anhydrides were likewise discussed. The results obtained using these model reactions may be applied to influence the curing process in commercial epoxy resin systems.     

An optical model for exchange reactions

An optical model or complex potential has been used in a relatively simple fashion to provide an interpretation of several molecular dynamics experiments. Rather than attempting a quantitative curve fit to the available data using a phenomenological optical potential (which is certainly possible) we have correlated certain physically reasonable features of the complex potential with general trends in the reaction dynamics. As an explicit example, the relationship between the range characteristics of the optical potential and the dependence of the reaction probability upon the kinetic energy of the reactants is derived. Other correlations are also presented, such as the dependence of the reaction probability upon impact parameter and degree of rotational excitation. The power of such a treatment obviously lies in its general applicability to complex systems as well as in its ability to often provide a simple physical understanding of some rather anomalous features of the reaction dynamics.