Transition state theory combustion

Thermodynamics and statistical mechanics deal with systems in equilibrium and are therefore applicable to phenomena involving flow and irreversible chemical reactions only when departures from complete equilibrium are small Fortunately this is often true in combustion problems, but occasionally thermodynamical concepts yield useful results even when their validity is questionable [for example, in the analysis of detonation structure (see Section 6.1.5) and in transition-state theory (see Section B.3.4)]. The presentation is restricted to chemical systems appropriate independent thermodynamic coordinates are pressure, p, volume, V, and the total number of moles of a chemical species in a given phase, N-, Moreover, results related to combustion theory are emphasized. 

Some of the continuing approaches to reaction-rate theory that differ from either the simple collisional theory or the transition-state theory discussed here are cited on pages 98-112 of [4]. Examples of differing approaches may be found in particular in theories for rates of three-body radical-recombination processes [61]. Advances in methods for calculating rate constants relevant to the Lindemann view of unimolecular processes also are providing new information relevant unimolecular and bimolecular rates. Future work may be expected to produce further results of use in combustion problems. 

The evaluations of Cohen and Westberg [28, 29] deal with a small number of reactions relevant to combustion (some reactions from the H2/O2 system, reactions of atomic oxygen and of OH with alkanes, NH2 and NH). The other reactions covered are mainly relevant to atmospheric chemistry. Their data sheets provide a much more detailed assessment of the primary data than most in some cases the original data are reanalysed in the light of advances since the original publication. They also make extensive use of transition state theory to interpolate between sets of data over a temperature range. 

D. G. Truhlar, K. Runge, and B. C. Garrett, Variational transition state theory and tunneling calculations of potential energy surface effects on the reaction of 0( P) with H2, Twentieth Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1984, p. 585. 

The kinetic parameters of each path are determined as a function of temperature and pressure using the bimolecular chemical activation analysis. High Pressure limit kinetic parameters from the calculation results are obtained with the canonical Transition State Theory. The multifrequency Quantum Rice-Ramsperger-Kassel analysis is utilized to obtain k(E) and Master Equation analysis is used for the evaluation of pressure fall-off in this complex bimolecular chemical activation reaction. Results are applicable to elementary experiments at low pressures, ambient combustion studies at one atmosphere, as well as higher-pressure turbine systems. 

These equations will allow us to predict the rate constants of the individual reaction steps in a complex mechanism, such as in combustion or in a catalytic reaction. We refer the curious reader to texts in physical chemistry or kinetics (e.g., Laidler, 1987) for detailed examples on how to apply the transition state theory (TST) for the kinetic parameter estimation. 

There have been a number of theoretical investigations on the CH -I- N2 HCN - - N system due, in part, to its importance in the production of NO in the combustion chemistry of hydrocarbons. It is also interesting from the perspective of electronic structure theory because it involves potential energy surfaces of the doublet and quartet states and spin-orbit coupling connecting these states, and because aspects of dynamics by a generalized transition state theory and a nonadiabatic RRKM theory can be used. 

For most combustion reactions at the temperatures characteristic of flames classical methods for treating the reaction dynamics — transition state theory (TST), statistical theory (ST), and classical trajectory (CT) methods — should be adequate. The TST method requires information about the potential energy surface only in the reactants and transition state regions and, so, can be readily applied to chemical reactions involving many nuclei. Semiempirical applications of TST have been surprisingly successful. We shall... 

B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Canonical variational calculations using the bond-energy-bond-order method for bimolecular reactions of combustion products, J. Amer. Chem. Soc. 101 5207 (1979). 

The term upconversion describes an effect [1] related to the emission of anti-Stokes fluorescence in the visible spectral range following excitation of certain (doped) luminophores in the near infrared (NIR). It mainly occurs with rare-earth doped solids, but also with doped transition-metal systems and combinations of both [2, 3], and relies on the sequential absorption of two or more NIR photons by the dopants. Following its discovery [1] it has been extensively studied for bulk materials both theoretically and in context with uses in solid-state lasers, infrared quantum counters, lighting or displays, and physical sensors, for example [4, 5]. Substantial efforts also have been made to prepare nanoscale materials that show more efficient upconversion emission. Meanwhile, numerous protocols are available for making nanoparticles, nanorods, nanoplates, and nanotubes. These include thermal decomposition, co-precipitation, solvothermal synthesis, combustion, and sol-gel processes [6], synthesis in liquid-solid-solutions [7, 8], and ionothermal synthesis [9]. Nanocrystal materials include oxides of zirconium and titanium, the fluorides, oxides, phosphates, oxysulfates, and oxyfluoiides of the trivalent lanthanides (Ln ), and similar compounds that may additionally contain alkaline earth ions. Wang and Liu [6] have recently reviewed the theory of upconversion and the common materials and methods used. 

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