Troe Reaction#

Troe (fall-off) reaction rate constant equations take the form:

\[\frac{k_0[\mathrm{M}]}{1 + \frac{k_0[\mathrm{M}]}{k_{\infty}}} F_C^{\left(1 + \frac{1}{N} [\log_{10}(\frac{k_0[\mathrm{M}]}{k_{\infty}})]^2\right)^{-1}}\]

where:

  • \(k_0\) is the low-pressure limiting rate constant (\((\mbox{mol}\,\mathrm{m}^{-3})^{-(n-1)}\,\mathrm{s}^{-1}\)),

  • \(k_{\infty}\) is the high-pressure limiting rate constant (\((\mbox{mol}\,\mathrm{m}^{-3})^{-(n-1)}\,\mathrm{s}^{-1}\)),

  • \([\mathrm{M}]\) is the density of air (\(\mathrm{mol}\,\mathrm{m}^{-3}\)),

  • \(F_C\) and \(N\) are parameters that determine the shape of the fall-off curve, and are typically 0.6 and 1.0, respectively [FPJ99] [GY99].

\(k_0\) and \(k_{\infty}\) are calculated as Arrhenius rate constants with \(D=300\) and \(E=0\).

Input data for Troe reactions have the following format:

type: TROE
name: foo-troe
k0_A: 5.6e-12
k0_B: -1.8
k0_C: 180.0
kinf_A: 3.4e-12
kinf_B: -1.6
kinf_C: 104.1
Fc: 0.7
N: 0.9
gas phase: gas
reactants:
  - species name: foo
  - species name: bar
    coefficient: 2
products:
  - species name: baz
  - species name: qux
    coefficient: 0.65

{
    "type": "TROE",
    "k0_A": 5.6e-12,
    "k0_B": -1.8,
    "k0_C": 180.0,
    "kinf_A": 3.4e-12,
    "kinf_B": -1.6,
    "kinf_C": 104.1,
    "Fc": 0.7,
    "N": 0.9,
    "gas phase": "gas",
    "reactants": [
        {
            "species name": "foo"
        },
        {
            "species name": "bar",
            "coefficient": 2
        }
    ],
    "products": [
        {
            "species name": "baz"
        },
        {
            "species name": "qux",
            "coefficient": 0.65
        }
    ]
}

The key-value pairs reactants and products are required. Reactants without a coefficient value are assumed to appear once in the reaction equation. Products without a specified coefficient are assumed to have a coefficient of 1.0.

The gas phase key is required and must be set to the name of the phase the reaction takes place in. The reactants and products must be present in the specified phase.

The two sets of parameters beginning with k0_ and kinf_ are the Arrhenius parameters for the \(k_0\) and \(k_{\infty}\) rate constants, respectively. When not present, _A parameters are assumed to be 1.0, _B to be 0.0, _C to be 0.0, Fc to be 0.6, and N to be 1.0.

Rate constants are in units of \(\mathrm{(m^{3}\ mol^{-1})^{(n-1)}\ s^{-1}}\) where \(n\) is the total number of reactants.

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