Temperature dependence of vibrational energy transfer in the “low” pressure competitive two-channel 1,1-cyclopropane-d2 system

Intermolecular energy transfer has been studied in the two-channel competitive isomerization of 1,1-cyclopropane-d₂, both in the neat system and in the presence of helium bath gas at values of k/k^? centered around 0.02. The competing path ways differ in threshold energy by ≈ 0.6 kcal. The temperature range 773 K to 973 K was covered. Several methods of treating the data, whether by isotopic ratios of rate constants or by temperature dependence of fall off, are each independent of a knowledge of collision cross sections. Used in conjunction, they provide measurements of these quantities. Cyclopropane is an operationally strong collider (β_ω = 1) for itself at 773 K with an average down step size, <ΔE/s> >/ 10 kcal mole ^?1 (>/ 3500 cm^?1). At 973 K the substrate is no longer a strong collider; β_ω declines to ≈ 0.55 with <ΔE/s> ≈ 5.2 kcal mole^?1. For helium the corresponding quantities are β_ω ≈ 0.078 <ΔE/s> ≈ 1.1 kcal mole ^?1 declining to β_ω ≈ 0.010 and <ΔE/s> ≈ 0.53 kcal mole^?1. The several methods of measuring these quantities give excellent independent agreement. Comparison with the earlier theoretical formulation of Tardy and Rabinovitch gives good agreement, the temperature dependence of β_ω for the weak collider, helium, follows the relation β_ω ∝ T^?m, where m /s> 2.     

Collisional deactivation of highly vibrationally excited hexafluorobenzene molecules

The collisional deactivation of the internal energy of vibrationally highly excited hexafluorobenzene (HFB) molecules was examined by the analysis of ultraviolet absorption spectra of excited HFB molecules produced by excitation with an ArF(193 nm) laser. The decay time profile of the internal energy was calculated from the observed absorption decay profile of the hot molecule using the conversion relation between the absorbance by hot molecules and the internal energy. Thus the average energy 〈ΔE〉 transferred per collision was estimated by two different models; energy-independent and energy-dependent function for the decay of the internal energy. The obtained values of 〈ΔE〉 indicate that the energy-dependent model may give reasonable values for 〈ΔE〉, but as far as the value of 〈ΔE〉 is concerned, the energy-independent model is likely to be applicable to the analysis in this reaction system. The collisional deactivation mechanism of the hot HFB molecule and the heating-up effect observed at shorter wavelengths are discussed on the basis of the conversion curve.     

Vibrational energy transfer from chemically activated 1,4-cyclohexadiene

The thermal isomerization of cis, anti, cis-tricyclo[3.1.0.0^2,4] hexane was used to produce highly vibrationally excited 1,4-cyclohexadiene. The competition between unimolecular decomposition of the energized diene (to benzene and hydrogen) and collisional stabilization was studied using the parent compound, SF₆, CO₂, N₂, and He as quenching gases. Quenching efficiencies decreased in the order given above. By applying RRKM theory to the isomerization and decomposition reactions, it was possible to calculate the step size in a stepladder model of the deactivation of cyclohexadiene. The step sizes 〈ΔE〉 deduced (at 528 K and in units of kJ/mol) were: parent compound and SF₆, 7; CO₂, 5; N₂, 4; He, 2. The study confirmed the utility of this unimolecular chemical activation system for energy transfer studies.     

High-temperature collisional energy transfer in highly vibrationally excited molecules II: Isotope effects in isopropyl bromide systems

Values for 〈ΔE_down〉, the average downward energy transferred from the reactant to the bath gas upon collision, have been obtained for highly vibrationally excited undeuterated and per-deuterated isopropyl bromide with the bath gases Ne, Xe, C₂H₄, and C₂D₄, at ca. 870 K. The technique of pressure-dependent very low-pressure pyrolysis (VLPP) was used to obtain the data. For C₃H₇Br, the 〈ΔE_down〉 values (cm^?1) are 490 (Ne), 540 (Xe), 820 (C₂H₄), and 740 (C₂D₄), and for C₃D₇Br, 440 (Ne), 570 (Xe), 730 (C₂H₄), and 810 (C₂D₄). The uncertainties in these values are ca. ±10%. The 〈ΔE_down〉 values for the inert bath gases Ne and Xe show excellent agreement with the theoretical predictions of the semi-empirical biased random walk model for monatomic/substrate collisional energy exchange [J. Chem. Phys., 80 , 5501 (1984)]. The relative effects of deuteration of the reactant molecule on 〈ΔE_down〉 also compare favorably with the predictions of this theoretical model. Extrapolated high-pressure rate coefficients (s^?1) for the thermal decomposition of reactant are 10^13.6±0.3 exp(?200 ± 8 kJ mol^?1/RT) for C₃H₇Br and 10^13.9±0.3 exp(?207 ± 8 kJ mol^±1/RT) for C₃D₇Br, which are consistent with previous studies and the expected isotope effect.     

The unimolecular dissociation of 3,4-dihydro-2H-pyran over a wide temperature range

The thermal decomposition of 3,4-dihydro-2H-pyran (DHP, C₅H₈O) has been investigated by two methods: in shock waves with the laser-schlieren technique using mixtures of 5 and 10% DHP in krypton over 900–1500 K, 110–560 torr; in a flow tube having a reaction pressure 0.5 torr above atmospheric using the decomposition of allylethyl ether as an internal standard, and covering 663–773 K. The retro-Diels-Alder dissociation to the stable acrolein and ethylene is the dominant channel for all conditions. Precise rate constants (rms deviation of 10%) were obtained for this process over the indicated temperature ranges. Unimolecular falloff is evident in the shock-tube results, and RRKM calculations also predict a slight falloff at the lower temperatures. These RRKM calculations use a routine vibration model transition state and agree closely with the high-temperature data when 〈ΔE〉_down is a fixed 400 cm^?1. Arrhenius expressions for k_∞ derived from the two measurements are in close accord and also consistent with most previous studies of this reaction. © 1995 John Wiley & Sons, Inc.     

High temperature collisional energy transfer in highly vibrationally excited molecules. III: Isotope effects in tert-butyl bromide systems

Changes in the magnitude of 〈ΔE_down〉, the average downward collisional energy transferred between a highly vibrationally excited reactant molecule and an inert bath gas, upon perdeuteration of the substrate are reported for tert-butyl bromide dilute in Ar, Kr, N₂, and CO₂. The technique of pressure-dependent very low-pressure pyrolysis (VLPP) was used to obtain the absolute values of 〈ΔE_down〉, which are for C₄H₉Br, 230 (Ar), 285 (Kr), 270 (N₂), and 365 (CO₂) while for C₄D₉Br, 200 (Ar), 250 (Kr), 220 (N₂), and 335 (CO₂), all in cm^?1 at ca. 720 K. The estimated uncertainties in these values are ca. ± 10%. These observed 〈ΔE_down〉, values and trends found with results from this series of isotope studies, are compared with current theoretical models. Extrapolated high-pressure temperature-dependent rate coefficients (s^?1) for the thermal decomposition of reactant are 10^13.8±0.3 exp(?175 ± 8 kJ mol^?1/RT) for C₄H₉Br and 10^14.3±0.3 exp(?183 ± 8 kJ mol^?1/RT) for C₄D₉Br. These results are in accord with other studies and the expected isotope effect.     

A shock tube,laser‐schlieren study of the pyrolysis of isobutene: Relaxation,incubation, and dissociation rates

Dissociation, vibrational relaxation, and unimolecular incubation have all been observed in shock waves in isobutene with the laser‐schlieren technique. Experiments covered a wide range of high‐temperature conditions: 900–2300 K, and post‐incident shock pressures from 7 to 400 torr in 2, 5, and 10% mixtures with krypton. The surprising observation is that of vibrational relaxation, well resolved over the full temperature range. The resolved process is completely exponential, with relaxation times in the range 20–120 ns atm. Relaxation and dissociation are clearly separated for T > 1850 K, with estimated incubation times near 200 ns atm. Incubation is essential for modeling of the very low‐pressure decomposition. Modeling of gradients with a chain mechanism initiated by CH fission produces an excellent fit and accurate dissociation rates that show severe falloff. A restricted‐rotor, Gorin‐model RRKM analysis fits these rates quite well with the known bond‐energy as barrier and 〈ΔE〉_down = 680 cm^?1. The extrapolated k_∞ is log k_∞(s^?1) = 19.187–0.865 log T ?87.337 (kcal/mol)/RT, in good agreement with previous work. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 381–390, 2003     

What,Methane Again?!

A combination of an error discovered in the Multiwell code and some more recent examinations of the system CH₃ + H = CH₄ prompted a reexamination of earlier work by this author. Values of the energy transfer parameter, 〈ΔE_d〉, are considerably different from the previous study. It is suggested that the Baulch et al. parameters for this system can be improved by replacing the values for k_rec,₀ and k_rec,_∞ with values suggested by Troe and Ushakov. k_rec,₀ = [Ar] 10^?26.19 exp[–(T/21.22 K)^0.5] cm⁶ molecule^?2 s^?1, k_rec,_∞ = 3.34 × 10^?10 (T/25200 K)^0.186 cm³ molecule^?1 s^?1 while keeping their value for F_c = 0.63 exp(–T/3315) + 0.37 exp(–T/61).     

Collisional energy transfer in highly vibrationally excited molecules: A very low-pressure pyrolysis study of acetyl chloride

The average downward energy transfer (〈Δ E_down〉) is obtained for highly vibrationally excited acetyl chloride with Ne and C₂H₄ bath gases at ca. 870 K. Data are obtained by the technique of very low-pressure pyrolysis (VLPP). Fitting these data by solution of the appropriate reaction-diffusion integrodifferential master equation yields the gas/gas collisional energy transfer parameters: 〈Δ E_down〉 values are 220 ± 10 cm^?1 (Ne bath gas) and 330 ± 20 cm^?1 (C₂H₄). These energy transfer quantities are much less than those predicted by statistical theories, or those observed for similar sized molecules such as CH₃CH₂Cl. These results are explained by the qualitative predictions of the biased random walk model wherein the fundamental mechanism of energy transfer is the multiple interactions between the bath gas and the individual atoms of the reactant molecule, during the course of the collision event. The charge distribution of acetyl chloride decreases the number of such interactions, thereby reducing the amount of energy transferred per collision.     

Incubation in cyclohexene decomposition at high temperatures

A detailed master equation simulation has been carried out for the thermal unimolecular decomposition of C₆H₁₀ in a shock tube. At the highest temperatures studied experimentally [J. H. Kiefer and J. N. Shah, J. Phys. Chem., 91, 3024 (1987)], the average thermal vibrational energy is greater than the reaction threshold and therefore 〈ΔE〉 (up and down steps) is positive for molecules at that energy, rather than negative; the converse is true at lower temperatures. The calculated incubation time, in which the decomposition rate constant rises to 1/e of its steady state value, is found to be only weakly dependent on temperature (at constant pressure) between 1500 K and 2000 K and to depend almost exclusively on 〈ΔE〉_d (down steps, only), and not on collision probability model. Simulations of the experimental data show the magnitude of 〈ΔE〉_d depends weakly on assumed collision probability model, but is nearly independent of temperature. The second moment 〈ΔE〉^½ is found to be independent of both temperature and transition probability model. The experimental data are not very sensitive to the possible energy-dependence of 〈ΔE〉_d for a wide range of assumptions. It is concluded that the observed experimental “delay times” probably can be identified with the incubation time; further experiments are desirable to test this possibility and obtain more direct measures of the incubation time.     

V → R,T energy transfer processes in vibrationally excited pentafluorobenzene using a Hg tracer absorption method

A new technique based upon the Doppler and Lorentz broadening of the isotopic and hyperfine Hg multiplet lines near 254 nm was used to monitor the translational equilibration of vibrationally excited pentafluorobenzene (PFB). Excitation was achieved with a pulsed CO₂ infrared laser focused into a cell containing PFB and a trace amount of Hg. Rates of V→ R, T energy transfer were found to be linearly dependent on both the excitation energy and the pressure of PFB. Excitation energies were independently determined by the Hg absorption technique and by measuring the change in absorption by the PFB at 254 nm. For PFB¹-PFB¹ collisions, the average energy transferred per collision divided by the average excitation energy of the colliding pair, 〈Δ〉/ 〈E〉, is0.0133±0.0016.     

Modified statistical theory of energy transfer in ion-molecule collisions

The modified statistical theory developed previously for potentials appropriate to interactions in neutral-neutral collisions, is now extended to more strongly attractive potentials involved in ion-neutral collisions. The model system is the collisional deactivation of C₅H₉⁺ by a variety of both polar and non-polar neutral molecules. A 12 - 6 - 4 potential is used for ion interaction with non-polar neutrals, and a 12 - 6 - 4 - 2 potential, as modified by Su and Bowers to take into account the rotational energy of the neutral, for interaction with polar neutrals. Calculated is (ΔE), the average energy lost by the ion in a collision, and compared with experiment. For C₅H₉⁺-CH₄ collisions, the calculated (ΔE) agrees with experiment within 5%. Predictions of the theory, namely that (ΔE) should increase with excitation energy and should decrease with the size of the excited reactant, are found to be in fair agreement with the somewhat ambiguous experimental evidence.     

Excimer formation mechanism in gaseous krypton and Kr/N2 mixtures

A new approach for the understanding of the energy relaxation dynamics of excited atoms involving a long-lived molecular precursor is presented here for krypton. Excitation of the gas close to the 5s[3/2]₂ metastable atomic level (E _at. ?E _exc.<kT) is achieved with an intense VUV laser source (I ≈ 10¹² photon/pulse) realized by resonantly enhanced 4-wave mixing (2ω₁ + ω₂) in room temperature mercury vapor (N _Hg ≈ 10¹³ at./cm³). The decay of the II. continuum luminescence (145 nm) is studied. In the pressure range 200–500 mbar, decay rates depend linearly on pressure but have a negative zero-pressure intersect. We show here that this result can be understood as an effect of the exchange of energy between two different “reservoirs” of atomic (5s[3/2]₂) and molecular (1_g) nature, and can be an inherent peculiarity of the recombination kinetics of excited atoms with several product channels. The efficiency of the model is checked for the Kr/N₂ system. Rate constants for relaxation processes are determined in pure krypton and in Kr/N₂ mixtures.     

Competitive collisional activation in vibrational energy transfer with cyclopropane-1t1-2,2d2. A three-channel system

Vibrational energy transfer has been studied in a reacting system by the method of competitive collisional reaction “spectroscopy.” Cyclopropane-1t₁-2,2d₂ provides a three-channel competitive system which has several advantages relative to conventional absolute rate techniques for the study of collisional transition probabilities. It is found in the range 823–1123 K that both collisional efficiency and the amount of energy transferred from the hot molecule to helium bath gas molecule decline with rise temperature. This is of great importance for high temperature shock tube and laser decomposition systems.     

Collisional relaxation of transient vibrational energy distributions in a thermal unimolecular system. The variable encounter method

A method has been developed, called the Variable Encounter Method, for the study of the relaxation of an initial vibrationally cold ensemble of molecules into a vibrationally hot distribution by a known and variable number of successive collisions with a hot wall. The theory of the experiment is presented. The system studied was the isomerization of 1,1-cyclopropane-d₂ with a fused quartz wall temperature of 800 K to 1175 K, and average number of collisions from 2.3 to 22.3. Various modified gaussian and exponential models of energy transfer were found to give agreement with the data. The average down-step size was found to decline from ≤ 3500 cm^?1 at the lowest temperature to ≈ 2500 cm^? at the highest on the basis of a gaussian model. A mathematical analysis of the relation between mean first passage times and incubation times is given. Incubation times increase from ≈ 7 to ≈ 12 collisions with increasing temperature. Transient population distributions and the sequential reaction probabilities as a function of collision number are calculated.     

Temperature dependence of the exciton—phonon coupling in the strong coupling limit: Results for solid nitrogen

High resolution (ΔE = 0.75 meV) absorption profiles of the vibronic bands in the range of the w¹Δ_u ← X¹Σ⁺_g and a¹II_g ← X¹Σ⁺_g exciton progressions at hv ≈ 8.9 eV in solid N₂ have been measured in the temperature range between 6 K and 30 K. These excitations are strongly localized so that the observed temperature dependence of the fine structure, consisting of a zero phonon line and a phonon side band, can be described very well in the model of strong exciton—phonon coupling at point defects. The experimental results for the w¹Δ_u transition are found to be consistent with the assumption of a Debye spectrum for the phonon density of states and we derive a value for the Debye temperature of θ = 78 K, which is in very good agreement with that derived from other measurements.     

Molecular beam chemiluminescence. Collisional dissociation of tetramethyldioxetane by a fast xenon beam

The chemiluminescence arising from collisional dissociation of tetramethyldioxetane (TMD) by a supersonic xenon beam is recorded as function of collision energy (1–4.6 eV) and of TMD pressure. At TMD pressures as low as 5 × 10^?5 torr a third-order process is prominent, demonstrating the importance of secondary collisions which enhance the light yield. The energy dependence shows a threshold at E_O ≈ 30 ± 3 kcal/mol. Structure in the energy dependence is interpreted in terms of a rise with energy of the singlet/triplet acetone branching ratio.     

Quasi-resonant energy transfer in collisions: Na2(A1Σ u + )+K(4S)

Cross sections for electron energy transfer from the initial rotational stateJ′of the two lowest vibrational levelsv′=0 andv′=1 of excited dimers Na₂(A) to potassium atoms as described by Na₂(A¹Σ _u ⁺ ,v′J′)+K(4S)→Na₂ (X¹Σ _g ⁺ ,v″J″)+K(4P)+ΔE have been examined by laser-induced fluorescence. A strong increase of the cross section by as much as an order of magnitude has been observed for those dimerv′J′-levels for which the dipole transitions are close to resonance of the 4S-4P transitions in the atom (ΔE<4 cm^?1). The absolute cross sections for energy transfer have been calculated by the Rabitz approximation of first-order perturbation theory. In the case of closest energy resonance (ΔE=0.9 cm^?1) the cross section is Q=7.8×10^?13 cm².     

On the density of states for two-level systems in amorphous solids

Recently proposed distribution functions for the asymmetry (Δ) and tunnel (λ) parameters are used to explore the density of states, ρ(E), for two-level systems (TLS). For intrinsic TLS it is shown that ρ(E) is a slowly increasing function of the tunnel splitting E (∝ E^μ) with 0.2 ≲ μ ≲ 0.5 over a broad energy range as recently predicted. For the distribution parameters believed to be appropriate for the more slowly relaxing extrinsic TLS, TLS_ext, μ ≈ 0 over a comparable energy range. In addition, the results demonstrate that a gap (at low E) in ρ(E) emerges in a natural way from the model. At much higher tunnel splittings, the DOS is shown to turn over yielding a negative slope with the turn over point related to a distribution function parameter for Δ. Comparison of the calculated results with experiment is provided.     

Autocollimation spectroscopy for fast hydrogenic ions

We propose a new experimental method (Autocollimation Spectroscopy), which provides a strong suppression of systematic error contributions in the laser resonance spectroscopy of broad resonances. Using a bidirectional laser beam with a fixed wavelength in connection with high current pulsed ion beams an accuracy ofΔE _Exp/Γ≈5·10^?5 (Γ: resonance width) for the resonance energy seems to be achievable. Applying this technique to 2S-Lamb shift (LS) measurements on medium heavy ions would yield a precision ofΔE _Exp/E _LS≈1·10^?5, i.e. an improvement by a factor up to 100 as compared to present experiments.