Kassel mechanism

Other radicals, in particular CH3, make a significant contribution in the kinetics of plasma pyrolysis. The Kassel mechanism is reduced and focuses only on CH2, which is sufficient for qualitative analysis. The CH2 radicals, according to the Kassel mechanism, lead to methane conversion into ethane ... 

To determine the upper limits of energy efficiency of this quasi-eqttilibritun process, kinetic specifics of the Kassel mechanism should be taken into accormt. The total endothermic process (9-1) of acetylene production from methane (CH4 I/2C2H2 -I- 3/2H2) under qttasi-eqttilibriiun conditions corresponds to the first kinetic order and can be characterized by the reaction rate coefficient... 

L. S. Kassel, Statistical mechanical treatment of the activated complex in chemical reactions, J. Chem. Phys. 3, 399 (1935). 

In addition, this mechanism was criticized on the basis of the Kassel-Rice theory of vibrationally excited ground states some time earlier by Zimmerman et alS3i)... 

Marcus developed a quantum mechanical formulation of Kassel-Rice-Ramsperger theories in which zero point energies have been taken into account (see flow chart). However, due to lack of data for individual molecules it is difficult to apply the theory of Rice-Ramsperger-Kassel-Marcus (RRKM)... 

Refs for this section 1) R.C. Tolman, Statistical Mechanics , NYChemCatalogCo, NY (1928) 2) L.S. Kassel, Kinetics of Homo-... 

A final possibility for a type of reaction resulting in acetylene formation which must be considered is that of combination of radicals. This is not likely to be significant in most systems, but in the case of methane reactions it becomes of particular interest. The production of ethylene, and acetylene in the thermal decomposition of methane requires some sort of combination reaction (40, 65). Kassel suggested a mechanism involving methylene radicals ... 

In more detail, our approach can be briefly summarized as follows gas-phase reactions, surface structures, and gas-surface reactions are treated at an ab initio level, using either cluster or periodic (plane-wave) calculations for surface structures, when appropriate. The results of these calculations are used to calculate reaction rate constants within the transition state (TS) or Rice-Ramsperger-Kassel-Marcus (RRKM) theory for bimolecular gas-phase reactions or unimolecular and surface reactions, respectively. The structure and energy characteristics of various surface groups can also be extracted from the results of ab initio calculations. Based on these results, a chemical mechanism can be constructed for both gas-phase reactions and surface growth. The film growth process is modeled within the kinetic Monte Carlo (KMC) approach, which provides an effective separation of fast and slow processes on an atomistic scale. The results of Monte Carlo (MC) simulations can be used in kinetic modeling based on formal chemical kinetics. 

Nowadays, the basic framework of our understanding of elementary processes is the transition state or activated complex theory. Formulations of this theory may be found in refs. 1—13. Recent achievements have been the Rice—Ramsperger—Kassel—Marcus (RRKM) theory of unimol-ecular reactions (see, for example, ref. 14 and Chap. 4 of this volume) and the so-called thermochemical kinetics developed by Benson and co-workers [15] for estimating thermodynamic and kinetic parameters of gas phase reactions. Computers are used in the theory of elementary processes for quantum mechanical and statistical mechanical computations. However, this theme will not be discussed further here. 

Sep. 3,1829, Kassel, Germany - Aug. 21,1901, Blanken-berghe, Belgium) Although Fick had an intense interest in mathematics as a schoolboy, he opted to study medicine on the advice of his brother. Flowever, Fick supplemented these studies by attending additional lectures on analytical mechanics , i.e., mathematics. Hav-ing studied in Marburg and Berlin, he received his M.D. 

Note The Lindemann mechanism was also suggested independently by Christiansen. Hence, it is also sometimes referred to as the Lindemann-Christiansen mechanism. The theory of unimolecular reactions was further developed by Hinshelwood and refined by Rice, Rampsberger, Kassel and Marcus. 

This standard mechanistic analysis has a long successful history. Organic chemistry textbooks are filled with PESs and discussions of the implication of single-step versus multiple-step mechanisms, concerted TSs, and so on. - Transition state theory (TST) and Rice-Ramsperger-Kassel-Marcus (RRKM) theory provide tools for predicting rates based upon simple assumptions built upon the notion of reaction on the PES following the reaction coordinate. " ... 

R. H. Fowler, Statistical Mechanics, Cambridge University Press, New York, 1936. See also L. Kassel, Kinetics of Homogeneous Gas Reactions, chaps. 2 and 5, Reinhold Publishing Corporation, New York, 1932. 

Another advantage of the quantum calculations is that they provide a rigorous test of approximate methods for calculating dissociation rates, namely classical trajectories and statistical models. Two commonly used statistical theories are the Rice-Ramsperger-Kassel-Marcus (RRKM) theory and the statistical adiabatic channel model (SACM). The first one is thoroughly discussed in Chapter 2, while the second one is briefly reviewed in the Introduction. Moreover, the quantum mechanical approach is indispensable in analyzing the reaction mechanisms. A resonance state is characterized not only by its position, width and the distribution of product states, but also by an individual wave function. Analysis of the nodal structure of resonance wave functions gives direct access to the mechanisms of state- and mode-selectivity. 

In contrast to the work of Hinshelwood et al., Kassel found the reaction order to be y and concluded that the mechanism is complex. It has been pointed out ° , however, that the treatment employed as well as the interpretation given by Kassel are both disputable. 

Modern unimolecular theory has its origins in the work of Rice, Ramsberger and Kassel [44] who investigated the rate of dissociation of a molecule as a function of energy. Marcus and Rice [44] subsequently extended the theory to take account of quantum mechanical features. This extended theory, referred to as RRKM theory, is currently the most widely used approach and is usually the point of departure for more sophisticated treatments of unimolecular reactions. The key result of RRKM theory is that the microcanonical rate coefficient can be expressed as... 

Kassel and Muskat1 were the first to attempt to calculate the surface energy after the quantum-mechanical theory of intermole-cular potential was completed in 1930. They assumed the distribution function of liquid in two alternative ways. First, they assumed that the radial distribution function g(R) is given by... 

A.R. Sanadi and D.F. Canfield. Interphase effects on the mechanical and physical behavior of natural fiber composites. In Second International Wood and Natural Fibre Composites Symposium, Kassel, Germany, June 28-29, 1999, pp. 9.1-9.18. 

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