The rate coefficients of unimolecular reactions in the systems with power-law distributions

Yin, Cangtao; Guo, Ran; Du, Jiulin

doi:10.1016/j.physa.2014.04.021

Cited by 16 publications

(12 citation statements)

References 36 publications

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“…In high pressure limit, by generalizing the energy distribution function P(E), the generalized unimolecular reaction theory rate formula for the nonequilibrium system presenting power-law behavior was obtained [26],…”

Section: Generalized Unimolecular Reaction Theorymentioning

confidence: 99%

“…If there are s degrees of freedom in the reactant with frequencies vi, there are s−1 degrees of freedom in the transition state with frequencies v i ≠ when the reaction coordinate is excluded. In the same way, the unimolecular reaction theory rate in the low pressure limit was also generalized in the framework of nonextensive statistical mechanics [26], where Z AM is the collision number between reactant molecule A and M per unit volume per unit time. (M is a insert/buffer gas, or any molecule that does not react with the molecule A, which could be A itself.)…”

Section: Generalized Unimolecular Reaction Theorymentioning

confidence: 99%

“…Two unimolecular reactions, the dissociation of CH3CO and the isomerization of CH3NC, were taken as application examples to calculate their reaction rates [26]. It should be mentioned that the famous RRKM (after Rice, Ramsperger, Kassel, and Marcus) theory is in fact the high pressure limit of unimolecular reaction theory.…”

Section: Applicationsmentioning

confidence: 99%

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The Generalized Reaction Rate Theories in the Systems with Power-Law Distributions

Yin

2015

Rev. Proc. Q.

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The calculations of reaction rate are important in studying the different processes in physics, chemistry, biology, engineering etc. There exist many theories of reaction rate, such as transition state theory, collision theory, and unimolecular reaction theory. One key assumption in these theories is that thermodynamic equilibrium prevails throughout the entire system studied for all degrees of freedom. According to the Boltzmann-Gibbs statistical mechanics, a Maxwell-Boltzmann distribution whose form is exponential law holds in the whole time. This exponential law form of reaction rate is usually called Arrhenius behavior in chemistry. However, plenty of experimental results show non-Arrhenius behavior, such as power-law behavior. Besides, in reacting systems, the processes of evolution from one meta-stable state to another neighboring metastable state happen all the time, therefore the equilibrium assumption would be quite far-fetched. In these cases, current theories are no longer valid, and they can not even serve as a conceptual guide for understanding the critical factors that determine rates. Therefore, providing corresponding theoretical description for non-Arrhenius behavior or power-law behavior becomes urgent. In this general paper, generalized reaction rate theories with power-law distributions in the framework of nonextensive statistical mechanics were discussed based on experimental and observing facts.

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Section: Generalized Unimolecular Reaction Theorymentioning

confidence: 99%

Section: Generalized Unimolecular Reaction Theorymentioning

confidence: 99%

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The Generalized Reaction Rate Theories in the Systems with Power-Law Distributions

Yin

2015

Rev. Proc. Q.

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“…Unimolecular decompositions are commonly the first step in the conversion of a fuel in combustion systems. Correspondingly, the accurate determination of rate coefficients for unimolecular reactions has attracted a great deal of attention from combustion kinetics researchers [1][2][3][4][5][6][7][8][9]. The RRKM/master equation (ME) method is the preferred approach for computing the temperature-and pressure-dependent rate coefficients for unimolecular reactions [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Global uncertainty analysis for RRKM/master equation based kinetic predictions: A case study of ethanol decomposition

Xing

Wang

et al. 2015

Combustion and Flame

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A precise understanding of the accuracy of reaction rate constants, whether determined experimentally or theoretically, is of considerable importance to kinetic modelers. While the uncertainties of experimentally measured rate constants are commonly provided, the "error bars" of computed (temperature-and pressure-dependent) rate constants are rarely evaluated rigorously. In this work, global uncertainty and sensitivity analysis is applied to the propagation of the uncertainties in the input parameters (e.g. barrier heights, frequencies and collisional energy transfer parameters et al.) to those in the rate constants computed by the RRKM/master equation method for the decomposition of ethanol. This case study provides a systematic exploration of the effect of temperature and pressure on the parametric uncertainties in RRKM/master equation calculations for a prototypical single-well multiple-channel dissociation. In the high pressure limit, the uncertainties in the theoretical predictions are controlled by the uncertainties in the input parameters involved in the transition state theory calculations, with the most important ones being those describing the energetics of the decomposition. At lower pressures, where fall-off is important, the uncertainties in the collisional energy transfer parameters play a significant role, particularly for the higher energy of

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“…Non-Gaussian or non-MB/power-law distributions have been noted prevalently in physical, chemical, biological and even social systems. In recent years, theoretical and experimental researches of these distributions have attracted great attention in the various fields of science, such as astronomy and astrophysics [25][26][27][28][29], plasmas and space physics [10,14,[30][31][32][33][34], and reaction rate theory in chemistry [35][36][37][38][39] etc. In terms of the above studies, the power-law distributions often link to the complex systems involving long-range interactions, inhomogeneity and non-equilibrium dissipation processes.…”

Section: Introductionmentioning

confidence: 99%

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

Guo

2015

Annals of Physics

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We study the time behavior of the Fokker-Planck equation in Zwanzig's rule (the backward-Ito's rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation-dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker-Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution.

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The rate coefficients of unimolecular reactions in the systems with power-law distributions

Cited by 16 publications

References 36 publications

The Generalized Reaction Rate Theories in the Systems with Power-Law Distributions

The Generalized Reaction Rate Theories in the Systems with Power-Law Distributions

Global uncertainty analysis for RRKM/master equation based kinetic predictions: A case study of ethanol decomposition

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

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