Experimental and theoretical studies of ion-molecule reactions (1989)
AuthorsSmith, Sean Campbellshow all
The present work deals with the development of a coherent and accurate means of modelling unimolecular decomposition, association and chemical activation reactions, particularly those involving ions, by the use of RRKM theory in conjunction with solution of the master equation. A new solution of the chemical activation master equation (which includes association as a special case) is derived which reveals a very simple relationship between the non-equilibrium rate coefficient for association and that for the reverse unimolecular dissociation. It is shown that the non-equilibrium association rate coefficient is related to the reverse non-equilibrium unimolecular dissociation rate coefficient by the equilibrium constant and a non-equilibrium factor that is calculated from solution of the unimolecular master equation. Hence separate solution of the chemical activation or association master equations to obtain the stabilisation rate coefficient is not necessary: both solutions are implicit in the solution of the single or multichannel unimolecular master equation. Solutions to the two-dimensional unimolecular master equation are developed which allow full incorporation of the constraint of angular momentum conservation into single and multi-channel unimolecular master equation calculations at any pressure for the first time. In conjunction with the solution to the chemical activation and association master equations, this allows ion/molecule association and chemical activation reactions, predictions for which are very sensitive to the effects of angular momentum conservation, to be modelled by accurate master equation calculations for the first time. Two extensions to RRKM theory, necessary for the accurate prediction of microscopic rate coefficients k(ɛ,J) in ion/molecule reactions, are identified. (1) Correct incorporation of the hindrance to dipole rotation, produced by the non-central ion/dipole potential, into the determination of the density of states in the loose transition state. An exact semiclassical means of incorporating this effect is derived and implemented. (2) Adiabatic effects, i.e., the absence of coupling of many degrees of freedom with the reaction coordinate at large separation of an ion/dipole pair, are shown to significantly reduce the predicted capture rate from that obtained by normal microcanonical variational implementation of RRKM theory. A variant of the normal RRKM expression for k(ɛ,J) is derived which enables exact accounting for this non-coupling. The theory is applied to three well-studied ion/molecule reactions: (1) the association of CH₃⁺and HCN in a helium bath gas, (2) the chemical activation reaction between CH/ and NH₃ in helium, and (3) the chemical activation reaction between CH₃⁺ and CH₃CN in both helium and CH₃CN bath gases. In the case of the reaction between CH₃⁺and HCN, RRKM parameters are sufficiently well known to allow the average downward transfer of internal and (external) rotational energies in collisions to be estimated as 150cm⁻¹ ± 50%. The results of modelling of the other reactions are consistent with similar sized average energy transfer parameters. Illustrative calculations for two neutral reactions, the recombination of methyl radicals and the two-channel dissociation of 1-iodopropane, are also presented. An experimental study involving unimolecular dissociation of the CH₃CH₂OH² ⁺ ion, induced in the drift field of a Variable-Temperature, Selected-Ion-Flow-Drift Tube, is presented. The theoretical interpretation of this experiment is discussed. It is found that (1) the induction time for approach to steady state of the vibrational and rotational degrees of freedom of the CH₃CH₂OH₂⁺ ion in the helium carrier gas is negligible on the experimental timescale for motion of the ions through the drift region, and (2) the unimolecular dissociation rate coefficients do not correspond directly to thermal data at an elevated temperature with mean energy equal to the ion centre-of-mass energy. This implies that the steady-state ion translational-energy distribution is not sufficiently close to a Maxwellian distribution to enable simple interpretation of the results as pseudo-thermal data. The form of interpolation to zero field required to obtain thermal data is not yet clear. A simple extension to the Langevin capture model is derived which allows an improved estimate of the total non-reactive ion/induced-dipole collision frequency (necessary for master equation modelling of ion/molecule reactions) by including steric effects due to the finite size of the species involved.