Deductions from the master equation for chemical activation

Abstract

The master equation for unimolecular decomposition and collisional deactivation of an energetic species A formed by chemical reaction was investigated. Particular attention was paid to the validity of the approximation of neglecting upward transitions, i.e., collisional transitions in which energy is added to A. Calculations of κa , the collision frequency ω times the ratio of the rate of decomposition of A to that of deactivation, were performed for the stepladder model for very large and very small ω and for the separable model for small ω. Neglect of upward transitions reduces κa. For the stepladder model the amount by which κa is reduced is greater for large ω than it is for small ω. It was also found that κa is more sensitive to changes in 〈Δε〉−, the average internal energy loss from A in deactivating collisions, when ω is small than it is when ω is large. Thus, when fitting computational results to experimental data, one derives a 〈Δε〉− which is too small if one neglects upward transitions, and the amount by which 〈Δε〉− is too small is considerably greater for large ω than it is for small ω. This result explains both qualitatively and semiquantitatively the discrepancies in 〈Δε〉−’s derived from stepladder model calculations of low pressure and high pressure κa’s for sec-butyl radicals in the presence of rare gas diluents.

Consecutive Chemical Activation Steps in the OH‐Initiated Atmospheric Degradation of Isoprene: An Analysis with Coupled Master Equations

“…In general, for chemically activated intermediates two different steady-state regimes can be distinguished [31,32]: i. at earlier times, the so-called intermediate steady state, where only the concentration at high energies is constant, and the population at lower energies steadily grows (cf. Fig.…”

“…(1). The solution for the initial condition N(t = 0) = 0 and a constant input flux R a F switched on at t = 0 reads as [31][32][33] …”

Kinetics of the chemically activated HSO5 radical under atmospheric conditions – a master-equation study

“…In a time-dependent picture of chemical activation, the average thermal lifetime of the adduct characterizes the timescale on which the final or asymptotic steady state 59 is reached (see also the discussions in ref. 33,36,[60][61][62]. In contrast to the so called intermediate steady state, 59 which is characterized by the competition between decomposition and stabilization of the chemically activated adduct, the term final steady state implies that there is no more net stabilization; the stabilization reservoir is filled up, and time-independent energy distributions have been established.…”

On the role of bimolecular reactions in chemical activation systems

“…the thermal unimolecular rate coefficient, determines the rate of product formation. This time dependence of the branching between unimolecular decomposition and collisional stabilization under chemical activation conditions was first discussed by Snider 10 and by Pritchard and Vatsya 11 and investigated in more detail by Schranz and Nordholm. 12 General expressions for the temporal behaviour of the molecular populations in such systems were derived by Smith, McEwan, and Gilbert.…”