Cleaner Combustion pp 549-576

Part of the Green Energy and Technology book series (GREEN)

Statistical Rate Theory in Combustion: An Operational Approach

Chapter

Abstract

Statistical rate theory is a valuable tool to rationalize the microscopic mechanisms of elementary chemical steps in the gas phase, to analyze results of kinetic experiments, and to adequately parameterize the temperature and pressure dependence of rate coefficients. We briefly describe the essential elements of statistical rate theory that are relevant for the kinetic characterization of reactions under combustion conditions, emphasizing application aspects. The calculation of rate coefficients for reactions over potential energy barriers and potential energy wells is elucidated. In the former case conventional transition state theory is used, in the latter case the temperature and pressure dependence is described by means of master equations with specific rate coefficients from RRKM theory and the simplified statistical adiabatic channel model. Examples for the different types of reaction are given, and crucial quantities are discussed. The article primarily aims at readers on an intermediate level between graduate students and junior scientists, who are interested in performing practical calculations, and who are looking for a compact presentation of the topic as a guide to the extensive literature.

List of Important Symbols and Abbreviations

<X>

Average of quantity X

A

Vector/matrix containing elements a(Ei)/a(Ei, Ej)

B

Rotational constant

Bcent(q)

Rotational constant for centrifugal motion in SACM

D

Morse parameter

Ei

ith eigenvector of the matrix J

ΔESL

Energy transfer parameter of the stepladder model

E>

Average energy transferred per collision (all, up and down)

E>d

Average energy transferred per down collision

E>u

Average energy transferred per up collision

ΔEz

Zero-point energy correction in SACM

E0(i)

Threshold energy of reaction i

f(E)

Initial distribution of the intermediate in a complex-forming bimolecular reaction

FAM

Angular momentum coupling factor in SACM

FE

Density of states correction factor

h

Planck′s constant

HO

Harmonic oscillator

J

Total angular momentum quantum number

J

Matrix of the master equation, for definition see Eq. 21.3

ki

Rate coefficient of reaction i

ki

High-pressure limiting value of the rate coefficient for reaction i

kB

Boltzmann′s constant

Li

Reaction path degeneracy for reaction i

n(E)

Distribution of a reacting species

ns(E)

Steady-state distribution of a reacting species

ñs(E)

Normalized steady-state distribution of a reacting species

P

Pressure

P(E′,E)

Collisional transition probability (density) for a collision EE

PST

Phase space theory

q

Reaction coordinate/interfragment distance

qe

Equilibrium distance

q*HIR

Partition function for hindered internal rotor (local coordinate)

qHO

Partition function for harmonic oscillator (normal coordinate)

q*HO

Partition function for harmonic oscillator (local coordinate)

Q

Partition function

R

Gas constant

R1

Rate of reaction of a complex-forming bimolecular reaction

RRKM

Rice, Ramsperger, Kassel, Marcus

SACM

Statistical adiabatic channel model

T

Temperature

TST

Transition state theory

V

Volume

V(q)

Classical interfragment potential

Wi

Cumulative reaction probability/sum of states for reaction/transition state i

α

Interpolation parameter of simplified SACM or energy transfer parameter of the exponential down model

β

Morse parameter

γc

Collision efficiency in a chemically activated reaction

ε(q)

Vibrational or rotational quantum in SACM

λi

ith eigenvalue of the matrix J

ρ

Density of states

σ

Symmetry number

ω

Collision frequency (unit: s−1)

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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Institut für Physikalische ChemieKarlsruher Institut für Technologie (KIT)KarlsruheGermany

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