Weak Collision Effects Research Articles

Collisional stabilization of ion-molecule association complexes in He, H2, or N2 buffer gases

The role of collisional energy transfer in ion-molecule association reactions is analyzed. Rate constants for the formation of adducts between HCl and NO3−(HNO3)x (H2SO4)y or HSO4−(HNO3)x (H2SO4)y (with x = 0–2 and y = 0–2) in the buffer gases H2, He, and N2 and at temperatures between 150 and 300 K are considered. Quantum-chemical calculations of molecular parameters and statistical unimolecular rate theory are combined to model low-pressure rate constants whereas ion-molecule capture theory provides high-pressure rate constants. The comparison with experimental results indicates that energy transfer is dominated by overall collision numbers while weak-collision effects are only of minor importance. On the other hand, often neglected falloff effects between termolecular and bimolecular reaction behavior have to be taken into account.

The dissociation/recombination reaction CH4 (+M) ⇔ CH3 + H (+M): A case study for unimolecular rate theory

The dissociation/recombination reaction CH(4) (+M) ⇔ CH(3) + H (+M) is modeled by statistical unimolecular rate theory completely based on dynamical information using ab initio potentials. The results are compared with experimental data. Minor discrepancies are removed by fine-tuning theoretical energy transfer data. The treatment accounts for transitional mode dynamics, adequate centrifugal barriers, anharmonicity of vibrational densities of states, weak collision and other effects, thus being "complete" from a theoretical point of view. Equilibrium constants between 300 and 5000 K are expressed as K(c) = k(rec)/k(dis) = exp(52,044 K/T) [10(-24.65) (T/300 K)(-1.76) + 10(-26.38) (T/300 K)(0.67)] cm(3) molecule(-1), high pressure recombination rate constants between 130 and 3000 K as k(rec,∞) = 3.34 × 10(-10) (T/300 K)(0.186) exp(-T/25,200 K) cm(3) molecule(-1) s(-1). Low pressure recombination rate constants for M = Ar are represented by k(rec,0) = [Ar] 10(-26.19) exp[-(T/21.22 K)(0.5)] cm(6) molecule(-2) s(-1), for M = N(2) by k(rec,0) = [N(2)] 10(-26.04) exp[-(T/21.91 K)(0.5)] cm(6) molecule(-2) s(-1) between 100 and 5000 K. Weak collision falloff curves are approximated by asymmetric broadening factors [J. Troe and V. G. Ushakov, J. Chem. Phys. 135, 054304 (2011)] with center broadening factors of F(c) ≈ 0.262 + [(T - 2950 K)/6100 K](2) for M = Ar. Expressions for other bath gases can also be obtained.

Numerical solution methods for large, difficult kinetic master equations

The kinetics of gas-phase reactions, including pressure-dependent weak collision and non-equilibrium effects, can be modelled using a master equation. In this paper, we address the practical computational problem of finding solutions to such kinetic master equations. The mathematical structure of the master equation can be utilised to develop a number of specialised numerical techniques that are capable of solving the master equation in the presence of difficult numerics and for large problems. The former is important for modelling low temperature and pressure systems, and the latter is important for modelling the large networks of isomerising species common in combustion chemistry applications. We focus on numerical methods that exhibit particular practical use because of their robust nature or scalability to many isomers, or both. Recent developments in linear-scaling methods are highlighted.

HCO formation in the thermal unimolecular decomposition of glyoxal: rotational and weak collision effects

The multi-channel thermal unimolecular decomposition of glyoxal was experimentally investigated in the temperature range 1106 K < T < 2320 K and at total densities of 1.7 x 10(-6) mol cm(-3) < rho < 1.9 x 10(-5) mol cm(-3) by monitoring HCO (frequency modulation spectroscopy, FMS), (CHO)(2) (UV absorption), and H atom (atom resonance absorption spectroscopy, H-ARAS) concentration-time profiles behind shock waves. With a branching fraction of 48% at T = 2300 K and rho = 1.6 x 10(-5) mol cm(-3), the so-far-neglected, energetically unfavourable HCO-forming decomposition channel, (CHO)(2)--> 2HCO, was found to play a crucial role and in fact represents the major decomposition pathway at high temperatures and high total densities. A theoretical analysis of the experimental results in terms of Rice-Ramsperger-Kassel-Marcus theory (RRKM), the simplified statistical adiabatic channel model (SACM), and an energy-grained master equation (ME) was based on input parameters from ab initio calculations (G3 and MP2/6-311G(d,p)) and literature data on branching ratios from collision-free photolysis experiments. A consistent description of the temperature and density dependences was achieved, revealing that both rotational and weak collision effects are reflected in the measured branching ratios. Overall, a product channel switching occurs with the CH(2)O-forming channel, (CHO)(2)--> CH(2)O + CO, dominating at low temperatures/densities and the HCO-forming channel dominating at high temperatures/densities. Additionally, the so-called triple-whammy channel, (CHO)(2)--> 2CO + H(2), significantly contributes to the total decomposition rate at intermediate temperatures/densities whereas the HCOH-forming pathway, (CHO)(2)--> HCOH + CO, is predicted to be the least important one. The temperature and pressure dependences of the different decomposition channels are parametrized in terms of two-dimensional Chebyshev polynomials.

A note on ion–dust streaming instability in a collisional dusty plasma

This note investigates an ion-dust streaming instability with frequency ω less than the dust collision frequency νd, in an unmagnetized collisional dusty plasma. Under certain conditions, a resistive instability can be excited by an ion drift on the order of the ion thermal speed, even when the dust acoustic wave is heavily damped. The effect of weak collisions on the usual dust acoustic instability in the regime ω &gt; νd is also considered. Applications to experimental observations of low-frequency fluctuations in laboratory d.c. glow discharge dusty plasmas are discussed.

The recombination of hydrogen atoms with nitric oxide at high temperatures

The rate constant for the H+NO+N2 reaction (R1,N2) has been determined in the temperature range 1000–1170K from flow-reactor experiments on the CO/O2/H2O/N2 system perturbed with different amounts of NO. The initiation temperature of this system is highly sensitive to reaction R1, which is the rate-controlling step in the nitric oxide catalyzed removal of hydrogen atoms. Based on the flow-reactor results and the limited amount of data reported in literature, a rate constant for the H+NO+N2 reaction of 4.0×1020T−1.75 cm6/(mol2s) was determined. This value is in good agreement with the recent result of Allen and Dryer at 1000K but significantly lower at high temperatures than the recommendation of Tsang and Herron. With the recently determined value of ΔHf,298 (HNO) of 26.0 kcal/mol, which is 2 kcal/mol higher than previous estimates, our results correspond to a rate constant of 1.7×1019T−1.5 exp(−23,400/T) cm3/(mol s) for the HNO+N2 dissociation reaction in the 1000–2500 K range. The sharp drop-off in the rate constant for H+NO+M at high temperatures suggested by the flow-reactor results are supported by reinterpretation of data reported in literature on H2/O2/N2 flames doped with NO. Theoretical considerations suggest that the effect can be attributed to weak-collision effects.

Weak Collision Effects on Broadening Factors for Unimolecular Reactions

Three models incorporating weak collision effects of thermal unimolecular reactions are used to obtain broadening factors as a function of u. The first model used the exponential formula for energy transfer and the Lindemann formula for the microcanonical rate constants. The second one used the same exponential formula with the extended Kassel formula. The third model also used the extended Kassel formula but the stepladder formula for the energy transfer. Weak collisions caused u{sub minimum} to decrease by no more than 0.25 for any of the three models. 14 refs., 3 tabs.

Kinetics of the unimolecular decomposition of isopropyl: weak collision effects in helium, argon, and nitrogen

Rate constants for the unimolecular decomposition of iso-C 3 H 7 have been determined by laser flash photolysis coupled with photoionization mass spectrometry, over the temperature range 720-910 K. The reaction was studied in He, at densities of (3-30)×10 6 atoms cm -3 . More limited measurements were made for Ar and N 2 . The reaction is in the falloff region under all conditions studied. Three methods of data analysis were employed: (i) A transition state model was constructed by reference to literature values of dissociation and association limiting high-pressure rate constants over the temperature range 177-910 K

Weak collision effects in the reaction ethyl radical .dblarw. ethene + hydrogen

The unimolecular decomposition of C[sub 2]H[sub 5] in helium has been investigated near the low-pressure limit (T = 876-1094 K; P =0.8-14.3 Torr). Rate constants (k[sub 1]) have been determined as a function of temperature and pressure in the indicated ranges in time-resolved experiments. The reaction was isolated for quantitative study in a heated tubular reactor coupled to a photoionization mass spectrometer. Weak collision effects (fall-off behavior) were analyzed using a master equation analysis. Values of [l angle][Delta]E[r angle][sub down] for the exponential down energyloss probability were obtained for each experiment performed. The microcanonical rate constants, k[sub 1](E), needed to solve the master equation were obtained from a transition state model for the reaction which is described. The temperature dependence of these [l angle][Delta]E[r angle][sub down] determinations was apparent and fits the expression [l angle][Delta]E[r angle][sub down] = 0.255T[sup 1.0([+-]0.1)] cm[sup [minus]1]. It is shown that this expression(derived from experiments conducted between 876 and 1094 K) provides a reasonable representation of observed weak collision effects in helium down to 285K. Values for [l angle][Delta]E[r angle][sub down]for C[sub 2]H[sub 5] decomposition in other bath gases were obtained by reexamining published data on the fall-off of the C[sub 2]H[sub 5] decomposition inmore » helium (200-1100 K); k[sub 1][sup 0]=6.63 [times] 10[sup 9]T[sup [minus]4.99] exp([minus]20,130 K/T) cm[sup 3]molecule[sup [minus]1]s[sup [minus]1]. Prior published experiments on both the forward and reverse reactions (C[sub 2]H[sub 5] +(M) [leftrightarrow] C[sub 2]H[sub 4] + H + (M)) in the fall-off region were reevaluated expression for the high-pressure limit rate constant for the temperature range 200-1100 K,k[sub 1][sup [infinity]] = 1.11 [times] 10[sup 10]T[sup 1.037] exp(-18,504/T) s[sup [minus]1]s. 49 refs., 12 figs., 5 tabs.« less

The relationship between recombination, chemical activation and unimolecular dissociation rate coefficients

A new solution to the master equation relating the rate coefficients for unimolecular, recombination (association) and chemical activation reactions, incorporating weak collision effects, is presented. The solution establishes conditions for the validity of the commonly used procedure of relating the recombination rate coefficient, throughout the falloff regime, to the reverse single-channel unimolecular rate coefficient via the equilibrium constant. In addition, a relationship between the rate coefficient for stabilization in a chemical activation reaction and the reverse multichannel unimolecular dissociation rate coefficient is derived. This result, in conjunction with recently developed methods for fully incorporating angular momentum conservation into the solution of the master equation for unimolecular dissociation, enables both angular momentum and weak collision effects to be accurately incorporated into the solution of the master equation for chemical activation reactions in the falloff regime. Application of this method to a typical ion/molecule chemical activation reaction, that of CH+3 with NH3, illustrates the importance of weak collision and angular momentum effects in this system.

Effects of collisions on the trapped particle mode in a linear machine

The effects of weak Coulomb and neutral collisions on the collisionless curvature driven trapped particle mode are studied in the Columbia Linear Machine [Phys. Rev. Lett. 57, 1729(1986)] by means of particle-conserving Krook and Fokker–Planck operators. Both types of collisionality are then combined, modeling neutral collisions with the conserving Krook and Coulomb collisions with a Lorentz model. The dispersion relation is then integrated over velocity space. Low Coulomb collisionality yields a small stabilizing correction to the magnetohydrodynamic collisionless mode, which scales as νe using the Krook model and ν1/2eC using a Lorentz pitch-angle operator. In higher collisionality regimes, both models tend to yield similar scalings.

Zur unimolekularen β‐Spaltung großer n‐Alkylradikale

AbstractThermal fall‐off curves for ethylen split‐off from higher alkyl radicals are calculated on the basis of RRKM theory and an empirical representation of weak collision effects. It is shown that rate constants under conditions of industrial pyrolysis do not reach their high pressure limit.

Energy transfer parameters from studies of unimolecular reactions induced by overtone excitation

Rates of cyclobutene isomerisation induced by excitation of the 6-0 CH stretching overtone at 16603 cm −1 have been measured as a function of the pressure of the bath gases He, Ar, CO 2, CH 4, SF 6 and cyclobutene. These data have been used to compare energy transfer parameters obtained from an approximate treatment of the effects of weak collisions with values from numerical solutions of the collisional master equation. Comparisons with data from previous photoactivation studies are also made. It is found that the combination of RRKM theory and an adequate treatment of inefficient intermolecular energy transfer can satisfactorily account for the observed results.

The role of electronically excited states in recombination reactions

AbstractMethods are described for including the participation of bound electronically excited states in calculations on radical recombination reactions. These methods are illustrated by applying them to the reactions For O2, accurate ab initio potentials are used in calculations which show that the electronic degeneracy and long‐range part of the potential are likely to be crucial in determining the contribution of a given electronic state to the overall reaction, as long as the state is not so weakly bound that it dissociates thermally before being electronically quenched. Weak collision effects are allowed for using a Monte Carlo technique and an assumed exponential form for the distribution of energies transferred in collisions with a third body. For larger systems it is evident that the role of bound excited states in the low‐pressure regime falls rapidly as the size of the system increases. As the high‐pressure limit is approached, however, the contribution of excited states is likely to come close to that expected simply on the basis of electronic degeneracy.

Photoexcitation of an autoionizing resonance in the presence of off-diagonal relaxation

We discuss the theory of photoexcitation of an autoionizing resonance. We solve a set of coupled stochastic integrodifferential equations which are based on the Fano model for autoionization, but which include the effects of weak elastic collisions, weak or strong laser excitation, and finite laser bandwidth. We determine the exact photoelectron spectrum and give formulas for spectral peak positions and widths. Redistributive scattering is evident, as are various effects normally associated only with transitions between discrete levels. Under certain conditions symmetries and fixed points of the electron spectrum can be predicted.

Density drift instabilities and weak collisions

This paper describes the effects of weak collisions on the linear kinetic theory of electrostatic density drift instabilities. The model assumes a weak, uniform density gradient, a uniform magnetic field and the BGK collision operator with a modification of the local approximation to derive a dispersion equation valid at all frequencies and wave numbers. The properties of the universal and collisional density drift instabilities at maximum growth rates are presented in detail. Their thresholds in an ionospheric model, which includes ion‐neutral, electron‐neutral, and electron‐ion collisions, are discussed and compared with the threshold of the lower hybrid density drift instability. In particular, the ionospheric conditions (plasma density ≲105 cm−3, altitude ≳250 km) and maximum scale lengths necessary to excite the universal at wavelengths of the order of the ion gyroradius are presented. We conclude that the k−5 short wavelength density power spectra observed above 280 km in the PLUMEX experiment are due to the effects of the universal density drift instability.

An efficient solution of weak-collision master equations in thermal unimolecular reaction rate theory

A new finite-basis-set method of solving the weak-collision master equation of thermal unimolecular reactions in the general pressure regime is presented. Consecutive sections of the equilibrium probability density are used as basis functions. Significant advantages in terms of efficiency and applicability are obtained. Representative calculations are performed to illustrate the method's convergence properties and storage requirements. Calculations of collisional efficiency factors in the low-pressure limit β 0 and weak-collision broadening factors F W C (ω) are performed to offer a simple concise representation of weak-collision effects. It is noted that weak-collision effects can be incorporated into fall-off curves with an accuracy of within an order of magnitude by simple scaling of the strong-collision fall-off curves. However, for accurate representation of weak-collision effects the weak-collision broadening must be taken into account.

Fall-off behavior of models of thermal unimolecular reactions

Aspects of fall-off behavior for thermal unimolecular reactions were investigated theoretically. The starting point for this investigation was the master equation which describes the generally accepted picture of collisional excitation and reaction. Deviations from simple Lindemann behavior were analyzed in terms of deviations from linearity of the reciprocal of the rate coefficient as a function of reciprocal concentration (or pressure) of collider gas. This function was shown to be always either linear or concave downward under conditions for which the rate of chemical reaction is slow compared to the rate of relaxation of the internal state distribution of the reacting molecules. Analytic results were obtained for two collision models of interest, the stepladder model and the separable exponential model. The strong collision limits for these models were carefully defined, and it was shown that the fall-off behavior becomes more Lindemann-like as the strong collision limit is approached. It was further shown how this characteristic of the approach to the strong collision limit is related to the pressure dependence of weak collision effects.

A numerical method for extending ray trace calculations of radio fields into strong focusing regions

This paper presents a practical method for computing radio fields in regions of strong focusing, using ray intercept data provided by a standard ray‐tracing program. The procedure extends the usefulness of the ray trace by allowing fields to be computed near caustics and cusps where ray density calculations fail. Using a plane wave decomposition of the field components, phase integrals are computed by curve‐fitting intercepts of rays traced through ionospheric or tropospheric media whose refractive indices vary arbitrarily with altitude. A numerical algorithm is described for performing the plane wave angular spectral integrations. This procedure avoids the complications associated with higher‐order asymptotic techniques, allowing a broad range of refractive‐index profiles to be analyzed by a single method. It is applied to two sample profiles, and the results agree very closely with higher‐order stationary‐phase estimates in caustic regions. Moreover, the computer code runs efficiently, despite the presence of highly oscillatory integrands. The method is capable of including the effects of weak collisions, the spherical earth, and azimuthally dependent transmitter configurations.

Internal energy randomisation in weak-collision unimolecular reaction systems

We examine the conjecture that the principal difference between weak-collision and strong-collision behaviour in thermal unimolecular reaction systems arises from a difference in internal energy randomisation rates. To do this, we solve analytically the strong-collision master equation for a thermal unimolecular reaction including explicit allowance for the randomisation processes, and we show that all weak-collision effects so far observed in thermal systems can be accommodated within this framework.In an appendix, we give the extension of this analytic solution for reactions yielding two (or more) distinct sets of products.