Reverse Rate Coefficients Research Articles

An indirect approach to optimize the reaction rates of thermal NO formation for diesel engines

With stringent emission regulations, it has become more important for modern diesel engine manufacturers to accurately predict engine-out nitrogen oxide (NOx) emissions across a wide range of operating conditions. Thermal NO is the major source of engine-out NOx in modern diesel engines. For thermal NO formation, several earlier studies have recommended the forward and reverse reaction rate coefficients of the rate-limiting reaction (O + N2⇌ NO + N). However, due to deficiencies in sub-models and inadequacies of reduced chemical mechanisms to represent diesel combustion, these recommended values more often than not need to be adjusted in reduced order combustion models to accurately predict engine-out NOx. Hence, in this work a systematic and computationally efficient approach has been proposed to streamline the process of determining the optimum reaction rate coefficients. To develop the optimization approach, four different production diesel engines with different operating conditions in terms of speed, load, and exhaust-gas recirculation have been considered. Numerical simulations have been performed using a detailed zero-dimensional velocity-composition-frequency transported probability density function (0D-VCF-tPDF) model that uses hundreds of notional particles to capture in-cylinder stratification. Four different combinations of hydrocarbon and NOx chemical mechanisms were used to represent chemistry. It was found that for the rate-limiting reaction, the pre-exponent factors (Af1,Ar1) and activation energies (EA,f1,EA,r1) of the forward and reverse reaction rates follow a linear band in Af1−EA,f1 and Ar1−EA,r1 space where predicted engine-out NOx match the measured values closely. By encompassing such bands from different engines and considering constraints on activation energies, a reduced search domain of pre-exponent factors and activation energies was constructed that is expected to be applicable to any diesel engine. Eventually, computationally efficient three-line and one-line search approaches were proposed to determine the optimum values of the pre-exponent factors and activation energies that led to a minimum error between measured and predicted engine-out NOx. Finally, these three-line and one-line NOx optimization approaches were applied to a fifth production diesel engine for which the 0D-VCF-tPDF model showed a very good predictive performance in terms of predicting peak pressure, 50% burn rate, and engine-out NOx when compared to measured and 3D-CFD values.

Global Master Equation Analysis of Rate Data for the Reaction C2H4 + H ⇄ C2H5: ΔfH0⊖C2H5.

While forward and reverse rate constants are frequently used to determine enthalpies of reaction and formation, this process is more difficult for pressure-dependent association/dissociation reactions, especially since the forward and reverse reactions are usually studied at very different temperatures. The problems can be overcome by using a data-fitting procedure based on a master equation model. This approach has been applied to existing experimental pressure-dependent forward and reverse rate coefficients for the reaction C2H4 + H ⇄ C2H5 (k1, k-1) using the MESMER code to determine ΔfH0⊖C2H5 from the enthalpy of the reaction. New measurements of k1, k-1 were included in analysis. They are based on laser flash photolysis with direct observation of H atom time profiles by vacuum ultraviolet laser-induced fluorescence under conditions where the approach to equilibrium could be observed. Measurements were made over the temperature range 798-828 K and with [He] from 2.33 to 7.21 × 1018 molecule cm-3. These data were then combined with a wide range of existing experimental data with helium as the bath gas (112 measurements of k1 and k-1, covering the temperature range 285-1094 K, and [He] = 7.1 × 1015-1.9 × 1019 molecule cm-3) and fitted using the master equation solver MESMER. The required vibrational frequencies and rotational constants of the system were obtained from ab initio calculations, and the activation threshold for association (ΔEthresh), enthalpy of reaction (ΔrH0⊖), imaginary frequency (υimag), and helium energy-transfer parameters (⟨ΔE⟩d,298(T/298)n) were optimized. The resulting parameters (errors are 2σ) are ΔEthresh = 11.43 ± 0.34 kJ mol-1, ΔrH0⊖ = -145.34 ± 0.60 kJ mol-1, υimag = 730 ± 130 cm-1, ⟨ΔE⟩d,298 = 54.2 ± 7.6 cm-1, and n = 1.17 ± 0.12. A value of ΔfH298.15⊖(C2H5) = 120.49 ± 0.57 kJ mol-1 is obtained by combining ΔrH0⊖ with standard enthalpies of formation for H and C2H4 and making the appropriate temperature corrections. The dependence of these parameters on how the internal rotor and CH2 inversion modes are treated has been explored. The experimental data for other bath gases have been analyzed, and data sets compatible with the potential energy surface parameters determined above have been identified. The parameters are virtually identical but with slightly smaller error limits. Parameterization of k1, k-1 using the Troe formalization has been used to investigate competition between ethyl decomposition and reaction with oxygen under combustion conditions.

Modification of chemical-kinetic parameters for 11-air species in re-entry flows

The chemical-kinetic parameters for the two-temperature model for 11-air species are modified to increase the accuracy of the thermochemical nonequilibrium model for high temperature gases in Earth re-entry flows. In the present work, a set of modified chemical-kinetic parameters, for the vibrational relaxation time with high temperature correction, the Arrhenius rate coefficients for dissociation, the vibrational energy removal ratio due to chemical reaction, the equilibrium constant to evaluate the reverse rate coefficients, and collision integrals for high temperature gases are proposed, based on the results of recent state-to-state kinetic calculations and shock-tube experimental data. These modified chemical-kinetic parameters are utilized to reproduce the measured NO, N2, and N2+ VUV and UV spectrum of the high-enthalpy shock-tube experiments performed at the EAST facility, and the existing flight and ground experimental data from BSUV-2, the Mars-entry spacecraft model, RAM C-II, and FIRE-II. The proposed chemical-kinetic parameters more accurately reproduce the measured molecular spectra in the VUV and UV ranges, and the surface heat flux and electron number density on the surface of the re-entry modules, than the previous chemical-kinetic parameters in the Park model, except for the super orbital re-entry speed of the Fire-II experiments. In the Fire-II experimental case, the influence of the modified chemical-kinetic parameters in the present work are less effective because of the fast dissociation of the molecules.

Oxidation kinetics of n-pentanol: A theoretical study of the reactivity of the 1‑hydroxy‑1-peroxypentyl radical

n-Pentanol has been considered as a promising alternative fuel for compression-ignition engines due to its potential to reduce greenhouse gases and pollutant emissions. Engine performance is strongly dominated by fuel oxidation chemistry, and thus a more accurate determination of the coefficients of the reactions ruling its oxidation is essential for the utilization of n-pentanol in combustion engines. The reactions involving 1‑hydroxy‑1-pentyl and molecular oxygen were found to play an important role in controlling the low temperature oxidation chemistry, but have not been investigated experimentally or theoretically; this is also the case for the reactions of the 1‑hydroxy‑1-peroxypentyl radical, which is formed by the addition of oxygen to the radical center of 1‑hydroxy‑1-pentyl. This work presents a theoretical study with high level ab initio calculations at the CCSD(T)/aug-cc-pVTZ//M06-2X/cc-pVTZ level of theory to shed light on the fate of the 1‑hydroxy‑1-peroxypentyl radical. The rate coefficients of all the possible intra-molecular hydrogen shift reactions of that radical were computed using variational transition state theory with small curvature tunneling corrections. For certain reactions, tunneling and variational effects are very pronounced, proving the need for robust methodologies to account for these effects. The hydrogen shift reaction leading to a concerted HO2 elimination and formation of n-pentanal is the dominant pathway and governs the reactivity of 1‑hydroxy‑1-peroxypentyl radical at any temperature. The reverse of this reaction was thereby investigated as well. For this prominent pathway, the effects of multistructural (multiple conformers) torsional anharmonicity of the stationary points were taken into account in order to refine the forward and reverse rate coefficients. The rate coefficients calculated at room temperature are compared to those calculated using a previously developed cost-effective multi-conformer transition state theory approach. The system-specific quantum Rice-Ramsperger-Kassel (SS-QRRK) theory was used to compute the pressure-dependent rate coefficients, which indicate significant pressure dependence at intermediate and high temperatures. Implementation of the calculated reaction rate coefficients in chemical kinetics models of n-pentanol revealed that our computed rate coefficients enable better insights into the chemistry of n-pentanol, and help to understand how n-pentanal is formed.

Theoretical Study of the Kinetics of the Gas-Phase Reaction between Phenyl and Amino Radicals.

The potential energy surface (PES) of the C6H5 + NH2 reaction has been investigated by using ab initio CCSD(T)//B3LYP/6-311++G(3df,2p) calculations. The conventional transition-state theory (TST) and the variable reaction coordinate-TST (VRC-TST) have been used to predict the rate constants for the channels possessing tight and barrierless transition states, respectively. The Rice–Ramsperger–Kassel–Marcus/Master equation (RRKM/ME) theory has been utilized to determine the pressure-dependent rate constants for these reactions. The PES shows that the reaction begins with an exothermic barrierless addition of NH2 to C6H5 producing the vital intermediate state, namely, aniline (C6H5NH2, IS1). Once IS1 is generated, it can further isomerize to various intermediate states, which can give rise to different products, including PR4 (4,5,6-trihydro-1-amino phenyl + H2), PR5 (3,4,5,6-tetrahydro phenyl + NH3), PR6 (2,3,5,6-tetrahydro-1-imidogen phenyl + H2), PR9 (3,4,5,6-tetrahydro-1-imidogen phenyl + H2), and PR10 (2,5,6-trihydro-1-amino phenyl + H2), of which the most stable product, PR5, was formed by the most favorable channel going through the two advantageous transition states T1/11 (−28.9 kcal/mol) and T11P5 (−21.5 kcal/mol). The calculated rate constants for the low-energy channel, 1.37 × 10–9 and 2.16 × 10–11 cm3 molecule–1 s–1 at T = 300, P = 1 Torr and T = 2000 K, P = 760 Torr, respectively, show that the title reaction is almost pressure- and temperature-dependent. The negative temperature-dependent rate coefficients can be expressed in the modified Arrhenius form of k1 = 8.54 × 1013T–7.20 exp (−7.07 kcal·mol–1/RT) and k2 = 2.42 × 1015T–7.61 exp (−7.75 kcal·mol–1/RT) at 1 and 10 Torr, respectively, and in the temperature range of 300–2000 K. The forward and reverse rate coefficients as well as the high-pressure equilibrium constants of the C6H5 + NH2 ↔ IS1 process were also predicted; their values revealed that its kinetics do not depend on pressure at low temperature but strongly depend on pressure at high temperature. Moreover, the predicted formation enthalpies of reactants and the enthalpy changes of some channels are in good agreement with the experimental results.

Non-uniqueness of the multi-temperature law of mass action. Application to 2T plasma composition calculation by means of a collisional-radiative model

This work is devoted to the calculation of the composition for a monoatomic plasma (argon in the case presented) for which the assumption of thermal equilibrium is not realized. The plasma composition is obtained from a CR model, taking into account free electrons and a great number of electronic levels of Ar atoms and Ar+ ions. This model is based on a large set of transition probabilities and reaction rate coefficients for radiative processes (spontaneous emission and radiative recombination) and on an extended database of direct and reverse reaction rate coefficients for collisional processes (excitation/de-excitation and ionization/recombination mechanisms). Assuming Maxwellian energy distribution functions for electrons and heavy chemical species, detailed balance equations are determined for all kind of reactions in the frame of the micro reversibility principle. From these balance equations, reverse rate coefficients are calculated as a function of direct reaction rates and of electrons and heavy particles translation temperatures (T e and T h respectively). Particular attention is paid to problematic chemical reactions with electrons involved on one side and only heavy species on the other side such as: Ar + Ar → Ar + Ar+ + e. The detailed balance relations obtained for ionization/recombination processes demonstrate the non-uniqueness of the multi-temperature Saha-Eggert law (i.e. non-uniqueness of the multi-temperature law of mass action). Multi-temperature argon plasma compositions obtained in the present work exhibit abrupt density variations. These sharp variations are characteristic of the transition between the domination of heavy particle reactions (at low temperature) and the predominance of electron collisions (at high temperature).

Expansion of the equilibrium constants for the temperature range of 300K to 20,000K

Chemical-kinetic parameters of the equilibrium constants to evaluate the reverse rate coefficients in the shock layer of a blunt body and the expanding flows are derived for the temperature range from 300 K to 20,000 K. The expanded equilibrium constants for the chemical reactions of the dissociation, ionization, associative ionization, and neutral and charge exchange reactions of the atmospheric species and carbon materials are proposed in the present work. In evaluating the equilibrium constants, the inter-nuclear potential energies of the molecular species are calculated by the analytical potential function of the Hulburt-Hirschfelder model, and the parameters of the analytical model are determined from the semi-classically calculated RKR potentials. The electronic states and energies of the atoms are calculated by the electronic energy grouping model, and the rovibrational states and energies of each electronic states of the molecules are evaluated by the WKB method. The expanded equilibrium constants for 31 types of the reactions are provided for the best curve-fit functions, and the recombination reaction rate coefficients evaluated from the present equilibrium constants are compared with existing measured values.

ATMOSPHERIC CHEMISTRY FOR ASTROPHYSICISTS: A SELF-CONSISTENT FORMALISM AND ANALYTICAL SOLUTIONS FOR ARBITRARY C/O

ABSTRACT We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients), and procedures associated with the Gibbs free energy (minimization, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen, and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.

Chemical Reaction Thermodynamics and Reaction Rate Theory

Chemical reactor modeling requires the formulation of Heat, Mass, and Chemical Species balances and depending on reactor configuration Computational Fluid Dynamic (CFD) to account for mixing effects. Thermochemical properties such as the species enthalpy have to be considered to account for heat of chemical reactions when conducting an overall or finite energy balance. To properly calculate the heat of reaction due to a reversible reaction, knowledge of the forward and reverse rate coefficients is required. Similarly, the species balance requires knowledge of the net rates of chemical reactions within the reactor to account for composition changes and the equilibrium constant is needed.

Communication: Equilibrium rate coefficients from atomistic simulations: The O((3)P) + NO((2)Π) → O2(X(3)Σg(-)) + N((4)S) reaction at temperatures relevant to the hypersonic flight regime.

The O((3)P) + NO((2)Π) → O2(X(3)Σg(-)) + N((4)S) reaction is among the N- and O- involving reactions that dominate the energetics of the reactive air flow around spacecraft during hypersonic atmospheric re-entry. In this regime, the temperature in the bow shock typically ranges from 1000 to 20,000 K. The forward and reverse rate coefficients for this reaction derived directly from trajectory calculations over this range of temperature are reported in this letter. Results compare well with the established equilibrium constants for the same reaction from thermodynamic quantities derived from spectroscopy in the gas phase which paves the way for large-scale in silico investigations of equilibrium rates under extreme conditions.

Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions

Simple bimolecular reactions $A_1+A_2\rightleftharpoons A_3+A_4$ are analyzed within the framework of the Boltzmann equation in the initial stage of a chemical reaction with the system far from chemical equilibrium. The Chapman-Enskog methodology is applied to determine the coefficients of the expansion of the distribution functions in terms of Sonine polynomials for peculiar molecular velocities. The results are applied to the reaction $H_2 +Cl\rightleftharpoons HCl+H$ , and the influence of the non-Maxwellian distribution and of the activation-energy dependent reactive cross sections upon the forward and reverse reaction rate coefficients are discussed.

QUENCHING OF CARBON MONOXIDE AND METHANE IN THE ATMOSPHERES OF COOL BROWN DWARFS AND HOT JUPITERS

We explore CO-CH4 quench kinetics in the atmospheres of substellar objects using updated time-scale arguments, as suggested by a thermochemical kinetics and diffusion model that transitions from the thermochemical-equilibrium regime in the deep atmosphere to a quench-chemical regime at higher altitudes. More specifically, we examine CO quench chemistry on the T dwarf Gliese 229B and CH4 quench chemistry on the hot-Jupiter HD 189733b. We describe a method for correctly calculating reverse rate coefficients for chemical reactions, discuss the predominant pathways for CO-CH4 interconversion as indicated by the model, and demonstrate that a simple time-scale approach can be used to accurately describe the behavior of quenched species when updated reaction kinetics and mixing-length-scale assumptions are used. Proper treatment of quench kinetics has important implications for estimates of molecular abundances and/or vertical mixing rates in the atmospheres of substellar objects. Our model results indicate significantly higher Kzz values than previously estimated near the CO quench level on Gliese 229B, whereas current model-data comparisons using CH4 permit a wide range of Kzz values on HD 189733b. We also use updated reaction kinetics to revise previous estimates of the Jovian water abundance, based upon the observed abundance and chemical behavior of carbon monoxide. The CO chemical/observational constraint, along with Galileo entry probe data, suggests a water abundance of approximately 0.51-2.6x solar (for a solar value of H2O/H2=9.61E-04) in Jupiter's troposphere, assuming vertical mixing from the deep atmosphere is the only source of tropospheric CO.

Studies on the Cl + C2H5I reaction; site specific abstraction reactions and thermodynamics of adduct formation studied by observation of HCL product

The reaction of chlorine atoms with alkyl iodides can play a role in the chemistry of the marine boundary layer. Previous studies have shown that at room temperature the reaction takes place via a complex mechanism including adduct formation. For the Cl + ethyl iodide reaction results on the thermodynamics of adduct formation and on the product yields are inconsistent. The kinetics of the reaction Cl + C(2)H(5)I have been studied by the direct observation of the HCl product in real time flash photolysis/IR absorption experiments as a function of temperature from 273 to 450 K. At temperatures above 375 K kinetic measurements confirm a direct process and the rate coefficient determined (4.85 +/- 0.55) x 10(-11) exp((-363 +/- 51)/T) cm(3) molecule(-1) s(-1) is in good agreement with previous direct determinations. Product yield studies have also been undertaken by comparing the HCl signal from Cl + C(2)H(5)I with that from a calibration reaction which shows that HCl is the sole product of the reaction at these temperatures. Yield studies with selectively deuterated ethyl iodide demonstrate that abstraction occurs predominantly from the alpha site, with the selectivity decreasing with temperature. Extrapolation of the yield data to 298 K predicts an alpha:beta ratio of 0.68:0.32. At temperatures between 273 and 325 K a biexponential growth was observed for the HCl signal consistent with adduct formation. Analysis of the HCl time profiles allowed the extractions of the forward and reverse rate coefficients for adduct formation and hence the calculations of the thermodynamic properties of adduct formation. A third law analysis yields a value of Delta(r)H = (-54 +/- 4) kJ mol(-1). The value of Delta(r)H is in good agreement with a previous third law determination (J. J. Orlando, C. A. Piety, J. M. Nicovich, M. L. McKee, P. H. Wine, J. Phys. Chem. A, 2005, 109, 6659).

Kinetics, mechanism, and thermochemistry of the gas-phase reaction of atomic chlorine with pyridine

A laser flash photolysis-resonance fluorescence technique has been employed to study the kinetics of the reaction of atomic chlorine with pyridine (C(5)H(5)N) as a function of temperature (215-435 K) and pressure (25-250 Torr) in nitrogen bath gas. At T> or = 299 K, measured rate coefficients are pressure independent and a significant H/D kinetic isotope effect is observed, suggesting that hydrogen abstraction is the dominant reaction pathway. The following Arrhenius expression adequately describes all kinetic data at 299-435 K for C(5)H(5)N: k(1a) = (2.08 +/- 0.47) x 10(-11) exp[-(1410 +/- 80)/T] cm(3) molecule(-1) s(-1) (uncertainties are 2sigma, precision only). At 216 K < or =T< or = 270 K, measured rate coefficients are pressure dependent and are much faster than computed from the above Arrhenius expression for the H-abstraction pathway, suggesting that the dominant reaction pathway at low temperature is formation of a stable adduct. Over the ranges of temperature, pressure, and pyridine concentration investigated, the adduct undergoes dissociation on the time scale of our experiments (10(-5)-10(-2) s) and establishes an equilibrium with Cl and pyridine. Equilibrium constants for adduct formation and dissociation are determined from the forward and reverse rate coefficients. Second- and third-law analyses of the equilibrium data lead to the following thermochemical parameters for the addition reaction: Delta(r)H = -47.2 +/- 2.8 kJ mol(-1), Delta(r)H = -46.7 +/- 3.2 kJ mol(-1), and Delta(r)S = -98.7 +/- 6.5 J mol(-1) K(-1). The enthalpy changes derived from our data are in good agreement with ab initio calculations reported in the literature (which suggest that the adduct structure is planar and involves formation of an N-Cl sigma-bond). In conjunction with the well-known heats of formation of atomic chlorine and pyridine, the above Delta(r)H values lead to the following heats of formation for C(5)H(5)N-Cl at 298 K and 0 K: Delta(f)H = 216.0 +/- 4.1 kJ mol(-1), Delta(f)H = 233.4 +/- 4.6 kJ mol(-1). Addition of Cl to pyridine could be an important atmospheric loss process for pyridine if the C(5)H(5)N-Cl product is chemically degraded by processes that do not regenerate pyridine with high yield.

Experimental investigation of acoustically enhanced colloid transport in water-saturated packed columns

The effects of acoustic wave propagation on the transport of colloids in saturated porous media were investigated by injecting Uranine (conservative tracer) as well as blue and red polystyrene microspheres (colloids of different diameters; 0.10 and 0.028 μm, respectively) into a column packed with glass beads. Experiments were conducted by maintaining the acoustic pressure at the influent at 23.0 kPa with acoustic frequencies ranging from 30 to 150 Hz. The experimental results suggested that colloid size did not affect the forward and reverse attachment rate coefficients. The acoustic pressure caused an increase in the effective interstitial velocity at all frequencies for the conservative tracer and colloids of both sizes, with maximum increase at 30 Hz. Furthermore, acoustics enhanced the dispersion process at all frequencies, with a maximum at 30 Hz.

Quantum Chemical Study of the Mechanism of Reaction between NH (X 3Σ-) and H2, H2O, and CO2 under Combustion Conditions

Reactions of ground-state NH (3sigma-) radicals with H2, H2O, and CO2 have been investigated quantum chemically, whereby the stationary points of the appropriate reaction potential energy surfaces, that is, reactants, products, intermediates, and transition states, have been identified at the G3//B3LYP level of theory. Reaction between NH and H2 takes place via a simple abstraction transition state, and the rate coefficient for this reaction as derived from the quantum chemical calculations, k(NH + H2) = (1.1 x 10(14)) exp(-20.9 kcal mol(-1)/RT) cm3 mol(-1) s(-1) between 1000 and 2000 K, is found to be in good agreement with experiment. For reaction between triplet NH and H2O, no stable intermediates were located on the triplet reaction surface although several stable species were found on the singlet surface. No intersystem crossing seam between triplet NH + H2O and singlet HNO + H2 (the products of lowest energy) was found; hence there is no evidence to support the existence of a low-energy pathway to these products. A rate coefficient of k(NH + H2O) = (6.1 x 10(13)) exp(-32.8 kcal mol(-1)/RT) cm3 mol(-1) s(-1) between 1000 and 2000 K for the reaction NH (3sigma-) + H2O --> NH2 (2B) + OH (2pi) was derived from the quantum chemical results. The reverse rate coefficient, calculated via the equilibrium constant, is in agreement with values used in modeling the thermal de-NO(x) process. For the reaction between triplet NH and CO2, several stable intermediates on both triplet and singlet reaction surfaces were located. Although a pathway from triplet NH + CO2 to singlet HNO + CO involving intersystem crossing in an HN-CO2 adduct was discovered, no pathway of sufficiently low activation energy was discovered to compare with that found in an earlier experiment [Rohrig, M.; Wagner, H. G. Proc. Combust. Inst. 1994, 25, 993.].

The Kinetics of Addition and Fragmentation in Reversible Addition Fragmentation Chain Transfer Polymerization: An ab Initio Study

High-level ab initio calculations of the forward and reverse rate coefficients have been performed for a series of prototypical reversible addition fragmentation chain transfer (RAFT) reactions: R* + S=C(Z)SCH3 --> R-SC*(Z)SCH3, for R = CH3, with Z = CH3, Ph, and CH2Ph; and Z = CH3, with R = (CH3), CH2COOCH3, CH2Ph, and C(CH3)2CN. The addition reactions are fast (ca. 10(6)-10(8) L mol(-1) s(-1)), typically around three orders of magnitude faster than addition to the C=C bonds of alkenes. The fragmentation rate coefficients are much more sensitive to the nature of the substituents and vary from 10(-4) to 10(7) s(-1). In both directions, the qualitative effects of substituents on the rate coefficients largely follow those on the equilibrium constants of the reactions, with fragmentation being favored by bulky and radical-stabilizing R-groups and addition being favored by bulky and radical-stabilizing Z-groups. However, there is evidence for additional polar and hydrogen-bonding interactions in the transition structures of some of the reactions. Ab initio calculations were performed at the G3(MP2)-RAD//B3-LYP/6-31G(d) level of theory, and rates were obtained via variational transition state theory in conjunction with a hindered-rotor treatment of the low-frequency torsional modes. Various simplifications to this methodology were investigated with a view to identifying reliable procedures for the study of larger polymer-related systems. It appears that reasonable results may be achievable using standard transition state theory, in conjunction with ab initio calculations at the RMP2/6-311+G(3df,2p) level, provided the results for delocalized systems are corrected to the G3(MP2)-RAD level using an ONIOM-based procedure. The harmonic oscillator (HO) model may be suitable for qualitative "order-of-magnitude" studies of the kinetics of the individual reactions, but the hindered-rotor (HR) model is advisable for quantitative studies.

Selected ion flow tube study of NH4+ association and of product switching reactions with a series of organic molecules

A study has been made of the association reactions of NH4+ with a series of organic molecules, CH3OH, C2H5OH, (CH3)2O, CH3CHO, CH3CO2H and (CH3)2CO, at 300K using a Selected Ion Flow Tube (SIFT). Ternary association rate coefficients have been determined and the product ions of several of the reactions have been probed by their further reactivities. The reaction with CH3NH2 was also studied, but this proceeds by proton transfer, being the only case in the study where this is energetically possible. The association reactions are generally rapid, and are pressure saturated in some cases, indicating strong bonding. Probing of the reactivity of the product ions of the (CH3)2O, CH3CHO, CH3CO2H and (CH3)2CO associations with the same set of molecules has shown that the reactions occur exclusively by switching, where one associated molecule is replaced by another. These switching reactions, when exothermic, can be very efficient, but the efficiency is strongly dependent on energetics. The study enabled both forward and reverse rate coefficients to be determined, and hence equilibrium constants, K, at 300K; from these K’s relative bond energies were estimated. Relative bond energies for NH4+ bound to the neutral are (CH3)2CO>CH3CO2H>CH3CHO>(CH3)2O, with the bond to (CH3)2CO being substantially stronger than the others. The reaction mechanism is suggestive of a strong cluster bond, although a chemically reactive alternative is possible and is discussed. Interstellar implications are mentioned.

Rate coefficient calculation for diffusion-influenced reversible reactions with longer-range reactivities

The chemically relevant so-called phenomenological forward and reverse rate coefficients of reversible bimolecular solution reactions, for nonlocal reactivities defined via attributed irreversible diffusion-kinetic schemes [W. Naumann and A. Molski, J. Chem. Phys. 103, 3474 (1995)], are exactly expressed by formal operator expressions. It is shown that this rate coefficient definition corresponds to the so-called integral encounter theory by Gopich, Kipriyanov, and Doktorov [J. Chem. Phys. 110, 10888 (1999)], an isolated reactive pair approximation. Assuming detailed balance, for the bimolecular isomerization A+B⇌B+C the operator expressions lead to exact relations with the rate coefficients of the irreversible partial reactions A+B→B+C and A+B←B+C. Generalizations of the well-known Noyes formula to reversible reactions result when the corresponding Wilemski-Fixman closure approximations of the irreversible and reversible rate coefficients are inserted.

Potential energy surface, thermal, and state-selected rate coefficients, and kinetic isotope effects for Cl+CH4→HCl+CH3

A new potential energy surface is reported for the gas-phase reaction Cl+CH4→HCl+CH3. It is based on the analytical function of Jordan and Gilbert for the analog reaction H+CH4→H2+CH3, and it is calibrated by using the experimental thermal rate coefficients and kinetic isotope effects. The forward and reverse thermal rate coefficients were calculated using variational transition state theory with semiclassical transmission coefficients over a wide temperature range, 200–2500 K. This surface is also used to analyze dynamical features, such as reaction-path curvature, the coupling between the reaction coordinate and vibrational modes, and the effect of vibrational excitation on the rate coefficients. We find that excitation of C–H stretching modes and Cl–H stretching modes enhances the rate of both the forward and the reverse reactions, and excitation of the lowest frequency bending mode in the CH4 reactant also enhances the rate coefficient for the forward reaction. However, the vibrational excitation of the CH3 umbrella mode (lowest frequency mode in products) slows the reaction at temperatures below 1000 K, while above 1000 K it also accelerates the reaction.