Modelling radical decomposition

In this section we shall concentrate on modelling the isopropyl data. Located as it is between the low and high pressure limits, data in this fall 

The great advantage of the Troe approach is that one can obtain good representations of the data using relatively simple analytic formulae, an important consideration in the modelling of combustion or atmospheric processes where rate coefficient determination has to be rapid. A disadvantage of this method is that it is not always possible to extract meaningful parameters from rate data or to assess the validity of theoretical models. 

Both of these corrections to the Lindemann model are embraced by the 

Furthermore, in the absence of reaction the system must approach the equilibrium Boltzmann distribution, f E), that is the system must obey detailed balance. 

From equation (2.30) it can be seen that p E, t) is dependent on cj, the form of P(EIE ) and k E). o is most often taken to be the Lennard-Jones collision frequency i.e., the hard sphere collision frequency which is rectified for the effects of intermolecular forces by the inclusion of a collision integral factor. 

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The tendency of the benzene combustion mechanism to substantially overestimate the formation of phenoxy radical suggested either flaws in the kinetic data involving C6H5O or incompleteness of the combustion mechanism. Subsequent work verified the kinetics and energetics used in modeling C6H5O decomposition. In separate studies, Liu et al. and Olivella et al. used ab initio and DFT models, along... 

Consequently, the benzene oxidation mechanism was further developed by considering additional decomposition and oxidation steps. Sethuraman et al. proposed that phenyl radical decomposition can occur by either of two key pathways (3-scission of phenyl radical or by breakdown of the phenylperoxy radical formed by the oxidation of phenyl radical (Fig. 9). Using PM3 calculations,which were ultimately verified by DFT studies,Carpenter predicted that another species, 2-oxepinoxy radical (3 in Fig. 9b), is an important intermediate due to its relative stability, formed via a spirodioxiranyl intermediate (2 in Fig. 9b) from phenylperoxy radical. Pathway A in Fig. 9b is the thermodynamically preferred pathway at temperatures increasing up to 432 K, while pathway B has an entropic benefit at higher temperatures. While pathway B essentially matched the traditional view of benzene combustion, pathway A introduced a new route for phenylperoxy radical, which could resolve discrepancies observed using previous models. 

R. Mereau, M. T. Rayez, J. C. Rayez, P. C. Hiberty, Phys. Chem. Chem. Phys. 3, 3650 (2001). Alkoxyl Radical Decomposition Explained by a Valence Bond Model. 

Calculated Rate Constants (Model II) for Ethyl Radical Decomposition C2H6 — C2H4 + H... 

These models were used to evaluate the necessary sums, densities, and moments of inertia, and eqs. (22) and (27) were integrated numerically to give k, (Fig. 12) and the calculated values of Table XVI. As was mentioned earlier in connection with ethane decomposition, we believe the thermally activated ethyl radical decomposition at 600°C. to be well into the fall-off region at pressures below atmospheric. In fact, comparison of Tables XII and XVI indicates that the fall-off behavior at 600°C. is very similar in its pressure dependence for ethyl and ethane, i.e., k, is a closely similar function of energy in both cases as shown explicitly... 

Section 2.5 examines addition reactions which are the reverse of the radical decomposition reactions considered in Section 2.4. These reactions in themselves are comparatively unimportant in hydrocarbon oxidation, but they have provided a good source of thermodynamic data on radicals. Thermodynamic parameters are central to the modelling of autoignition because of the importance of heat release, but also because of their use in determining the rate parameters for the reverse of well characterized reactions. Section 2.5 includes a brief review of the currently accepted alkyl radical heats of formation. This field has been in turmoil in recent years because of disagreements on the values, which largely derive from kinetic measurements. Consensus is emerging but controversy still remains. 

Radical decompositions are unimolecular reactions and show complex temperature and pressure dependence. Section 2.4.l(i) introduces the framework (the Lindemann mechanism) with which unimolecular reactions can be understood. Models of unimolecular reactions are vital to provide rate data under conditions where no experimental data exist and also to interpret and compare experimental results. We briefly examine one empirical method of modelling unimolecular reactions which is based on the Lindemann mechanism. We shall return to more detailed models which provide more physically realistic parameters (but may be unrealistically large for incorporation into combustion models) in Section 2.4.3. 

Y Huang, D Page, DDM Wayner, and P Mulder. Radical-Induced Degradation of a Lignin Model Compound Decomposition of l-phenyl-2-phenoxyethanol. Can. J. Chem. 73 2079-2085,1995. 

The approach to hydrocarbon cracking taken by the Froment school is to model the actual elementary steps of radicals at the various molecular configurations [38]. These are relatively few initiation hydrogen abstraction from a primary, secondary, or tertiary carbon and radical decomposition by scission of a carbon-carbon bond in /3-position to the unpaired electron. Boolean relation matrices are used to reflect the structures of the hydrocarbon reactants by indicating the existence and location of all their carbon-carbon bonds. Computer software generates reaction networks on the basis of known rate coefficients and activation energies at the various positions. Froment states the number of components in naphtha cracking as around 200, that of radicals as 40, and that of elementary radical steps... 

Mechanism of Nonoxidative Thermal Dehydrochlorination. This subject is still very controversial, with various workers being in favor of radical, ionic, or molecular (concerted) paths. Recent evidence for a radical mechanism has been provided by studies of decomposition energetics (52), the degradation behavior of PVC-polystyrene (53) or PVC-polypropylene (54) mixtures, and the effects of radical traps (54). Evidence for an ionic mechanism comes from solvent effects (55) and studies of the solution decomposition behavior of a model allylic chloride (56). Theoretical considerations (57,58) also suggest that an ionic (El) path is not unreasonable. Other model compound decompositions have been interpreted in terms of a concerted process (59), but differences in solvent effects led the authors to conclude that PVC degrades via a different route (59). 

Mode-specific decomposition has been illustrated for the H—C—C — H -f C==C model Hamiltonian (Swamy et al., 1986). Lifetimes for different resonance states are given in table 8.2. The states are listed according to the quantum numbers for the HC and CC stretch modes. The CC stretch progression of resonance states with zero quantum in the HC stretch has the longest lifetimes, while the progression with two quanta in the HC stretch has the shortest lifetimes. Such a finding is characteristic of mode-specific decomposition. A similar mode-specific decomposition is observed for formyl radical decomposition, HCO —> H + CO (Wang and Bowman, 1994 Werner et... 

Modeling the decomposition mechanism of artemisinin at Hartree-Fock (HF) and DFT theoretical levels supported the current hypothesis that some of the stable neutral intermediates and radical anions could be responsible for the antimalarial activity of artemisinin derivatives <2006BMC1546, 2006PCA7144, 2006JME6065>. 

Spin trapping with PMNB was applied to the radicals derived from initiator decomposition (formula 3) and their subsequent reactions with the model compounds (formula 5). Both initiator radicals could be trapped and identified. When model compounds were present during UV-irradiation, new radicals were identified from the ESR spectra. For dihydrocyclopentadiene (DHCPD) only one trapped radical was found and for ethylidene norbornane (ENB) two radicals. By comparison with computer simulated ESR spectra, it is concluded that the radicals of these model compounds are all allyl radicals (formula 8 and 9) formed by hydrogen abstraction from the models. Radical (8 a) has two stereoisomers but they have closely the same ESR spectra when trapped and cannot be separated. Radical (8 b) has two resonance structures (shift of double bond in the ethylidene group) but only one radical (8 b) is trapped, probably due to steric hinderance for trapping the methin radical. The DHCPD radical (formula 9) has two steric forms because the two allylic hydrogens are not identical. Once they are formed, the spin trap can only approach from one side and only one of the steric forms is trapped as shown in the ESR spectrum. 

Alkoxy Radical Decomposition Explained by a Valence Bond Model. 

Kinetic Models Used for Designs. Numerous free-radical reactions occur during cracking therefore, many simplified models have been used. For example, the reaction order for overall feed decomposition based on simple reactions for alkanes has been generalized (37). 

The ultrahigh vacuum STM was used to investigate the addition of the 2,2,6,6-tetramethyI-l-piperidinyloxy (TEMPO) radical to the dangling bond of Si(l 0 0)-2 X 1 surface. ° ° The TEMPO can bond with a single dangling bond to form stable Si-O coupling products, in contrast to the thermal decomposition of TEMPO-silicon compounds. Semiempiiical and DFT calculations of TEMPO bound to a three-dimer silicon cluster model yielded... 

However, the biochemical significance of the latter studies is challenged by the fact that the transformation of transient purine and pyrimidine radicals into diamagnetic decomposition products is oxygen-independent in the solid state. Therefore, it is necessary to study the chemistry of one-electron nucleobase intermediates in aerated aqueous solutions in order to investigate the role of oxygen in the course of reactions that give rise to oxidation products within DNA and model compounds. In this respect, type I photo-... 

The accepted kinetic scheme for free radical polymerization reactions (equations 1-M1) has been used as basis for the development of the mathematical equations for the estimation of both, the efficiencies and the rate constants. Induced decomposition reactions (equations 3 and 10) have been Included to generalize the model for initiators such as Benzoyl Peroxide for... 

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