Collisional Transition Probabilities for Vibrational Deactivation of Chemically Activated sec-Butyl Radicals. The Rare Gases

Vibrationally excited sec-butyl radicals, having a narrow range of energies above 40 kcal mole−1, were produced in a heat bath of cis-butene-2-rare-gas mixtures by H addition to cis-butene-2. He, Ne, Ar, and Kr were used. Two competing reactions of the chemically activated radicals, decomposition by C–C rupture with critical energy of 33 kcal mole−1 and collisional stabilization, were studied as a function of pressure. Apparent rate constants for decomposition ka were obtained at three temperatures over a range of bath pressures by analysis of the decomposition and stabilization products. Strong and weak multistep collisional deactivation processes, corresponding to transfer of all or only part of the initial excess vibration energy (≥7 kcal mole−1) of the radicals, were considered. Multistep models of various step sizes (ΔE) give a family of calculated curves of ka as a function of p, each of which turns up from a quasi-constant value at higher pressures to higher values at low pressures. Comparison with the low-pressure experimental ``turnup'' yielded information on ΔE, independent of the assumed collision cross section. Comparison of relative rates in the higher-pressure region gave minimum estimates of ΔE or, alternatively, conventional ``efficiency'' factors, βmin; these conclusions are somewhat dependent on the assumed cross section. Values of ΔE from the lower-pressure turnup data bunch at 2.5–3.5 kcal mole−1 on an assumed stepladder model of transition probabilities. Such a model corresponds only formally to harmonic oscillator restrictions, and encompasses the characteristics of models in which small steps are less probable than large ones. Values of 〈ΔE〉exp for an exponential weighting of transition probabilities group at 1.2–1.8 kcal mole−1; this distribution describes the characteristics of models in which small steps are more probable than large ones and seems to be the preferred description of the rare-gas behavior here. He and Ne appear to transfer less energy than Kr and Ar. ΔE for cis-butene itself was confirmed to be ≥9 kcal, as derived in a previous study of deactivation of sec-butyl-d1 radicals by Harrington, Rabinovitch, and Hoare; and by contrast, the stepladder model is more appropriate here. From the higher-pressure data, values of βmin which varied from 0.16 for He at 100°C to 0.62 for Kr at −78°C were found. The efficiencies increase with increasing atomic weight of the rare gas and with decreasing bath temperature. Energy transfer between rare-gas atoms and butyl radicals is thus surprisingly efficient, with relatively large amounts of energy transferred per collision (〈ΔE〉kT). The findings provide further detailed evidence concerning the inapplicability of the Landau-Teller theory and related models to polyatomic molecules at high vibrational energies (cf. Herzfeld and Litovitz). The possible role of rotational degrees of freedom is considered.