RATE COEFFICIENT FORMAT

BIMOLECULAR REACTIONS

The rate constant parameters for bimolecular reactions are set up in the form 
      k = A T^m exp(-E/RT)
with concentration units mol/cm3. The units of A are cm3/mol/s, T is in K, and E is in cal/mol. For termolecular recombination reactions, the units of A are cm6/mol2/s.

UNIMOLECULAR AND RECOMBINATION REACTIONS

The rate constant parameters for the high and low pressure limiting forms of the unimolecular decomposition or recombination reactions are given by 
      k = A T^m exp(-E/RT)
with concentration units mol/cm3. The units of A are 1/s, cm3/mol/s, cm6/mol2/s for first, second, and third order reactions, respectively; T is in K; and E is in cal/mol.

The low pressure limit rate constants and the rate constants of unimolecular reactions that are always near their low pressure limits for combustion conditions have been assigned 'enhanced efficiencies' in Chemkin format. From the model concentrations [M_i] and the efficiencies {f_i}, and effective concentration is computed through the formula 

      [M] = SUM{ f_i[M_i] },
where f_i = 1 for all species except those with enhanced efficiencies listed on the last line of the reaction input. If your program will not handle different efficiencies for different species automatically, then you will have to account for each of the colliders by writing separate reactions.

LINDEMANN FALLOFF FORM

This treatment applies if no specific falloff parameters are given. At pressures intermediate to the high and low pressure limits, the rate constant is given by the Lindemann formula: 
                    k_inf
         k = ----------------
             1  +  k_inf/k_o[M]
In cases where no high pressure limit rate constant parameters are given (i.e., the collider M as a reactant is not in parenthesis), the reaction is in the low pressure limit.

TROE FALLOFF FORM

A more refined treatment of pressure effects than Lindemann is employed using the TROE parameters. The falloff parameter F_cent for a unimolecular reaction is calculated from the values of a, b, c, and d by the formula of Troe 
      F_cent  =  (1-a) exp(-T/b)  +  a exp(-T/c)  +  exp(-d/T)
which gives the temperature dependence of F_cent, the factor by which the rate constant of a given unimolecular reaction at temperature T and reduced pressure P_r = k_o[M]/k_inf of 1.0 is less than the value k_inf/2 which it would have if unimolecular reactions behaved according to the Lindemann formula.

The broadening factor F, which is 1 for the Lindemann case where no parameters for F_cent are provided, is computed from F_cent by 

                                log F_cent
      log F = ---------------------------------------------
              1 + [(log P_r + C)/(N - 0.14{log P_r + C})]^2


      with N = 0.75 - 1.27log F_cent  and  C = -0.4 - 0.67log F_cent.
The rate coefficient, k, is then given by multiplying the Lindemann formula by F.
For more information about how these formulas work, consult pages 22 and 23 of 'Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics', Sandia Report SAND89-8009B UC-706, Reprinted January 1993, by R.J. Kee, F.M. Rupley and J.A. Miller. The person in charge of Chemkin is Fran Rupley, who can be reached via her Internet address fran@sandia.gov. The theory underlying the use of these formulas in combustion chemistry is described by W.C. Gardiner and J. Troe in Chapter 4 of Combustion Chemistry, Springer-Verlag, New York, 1984.