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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 8313-8329 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Having elucidated a full theoretical analysis of the master equation for intermolecular and intramolecular energy transfer in multiple-well, multiple-channel chemically or thermally activated reactions [J. Chem. Phys. 107, 8904 (1997)], we now present efficient methods of numerical analysis for the computational examination of the dynamics of the master equation. We suggest the use of a Krylov-subspace method to determine the uppermost portions of the internal spectrum of the master equation kernel. Such a computation is pivotal in determining whether there exists a state of secular equilibrium for the population of the moieties and whether there exists within the possible state of secular equilibrium, a state wherein the dynamics are represented by an isolated dominating mode; for only in the state of secular equilibrium can one write rate equations for the dissociating processes that are local in time. And, if such a state is possible, we suggest the use of a Hermite–Laguerre orthogonal collocation method for obtaining highly accurate solutions to the population of the moieties. The theory and numerical analysis is then applied to study the dynamics of the chemically-activated reaction C2H5+O2. Comparison of the master equation treatment with modified strong-collision theory is also given for this system of multiple-well, multiple-channel reactions. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 8904-8916 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a full theoretical analysis of the master-equation formulation of the problem of intermolecular energy transfer in multiple-well, multiple-channel systems. It is shown that the master equation for chemical or thermal activation possesses a unique steady state, that corresponding to the trivial solution. Rate equations local in time and therefore time-independent rate coefficients for the dissociating processes may be obtained only if a state of secular equilibrium exists. For chemically-activated systems, a general state of secular equilibrium may exist which may contain within it a regime wherein there is a well-separated, nontrivial, least negative eigenvalue of the master equation kernel. The dynamics of thermally activated systems are similarly deduced by treating them as chemically activated systems with appropriate modifications to the inhomogeneous source term of the master equation. A degenerate and nondegenerate perturbation theory analysis of the case of rapid thermalization in the vicinity of the thermodynamic equilibrium state is also enunciated. The special case of negligible thermalization is analyzed. A classification of the ordering of the time scales of thermalization, isomerization, and dissociation is then given. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: It is now well confirmed that the influence of temperature on the fall-off behavior of dissociation, recombination and chemically-activated reactions can be dramatic. For single-well, single-product dissociation reactions, it is customary to approximate these fall-off surfaces using extensions of Lindemann's empirical expression. We consider here chemical-activation and dissociation reactions possessing multiple wells and multiple products. We show that direct approximation of the rate coefficients via Chebyshev expansions yields reliable and accurate representations of their pressure and temperature dependences, which are superior to those from a Lidemann approach to fit the form factor representing the fall-off surface. The superiority of the method is demonstrated in a study of seven channels corresponding to four different reactions important in combustion chemistry over the ranges 300-3,000 K and 0.02-200 atm.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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