Determination Of Rate Coefficients Research Articles

Elaboration of collisional–radiative models for flows related to planetary entries into the Earth and Mars atmospheres

The most relevant way to predict the excited state number density in a nonequilibrium plasma is to elaborate a collisional–radiative (CR) model taking into account most of the collisional and radiative elementary processes. Three examples of such an elaboration are given in this paper in the case of various plasma flows related to planetary atmospheric entries. The case of theoretical determination of nitrogen atom ionization or recombination global rate coefficients under electron impact is addressed first. The global rate coefficient can be implemented in multidimensional computational fluid dynamics calculations. The case of relaxation after a shock front crossing a gas of N2 molecules treated in the framework of the Rankine–Hugoniot assumptions is also studied. The vibrational and electronic specific CR model elaborated in this case allows one to understand how the plasma reaches equilibrium and to estimate the role of the radiative losses. These radiative losses play a significant role at low pressure in the third case studied. This case concerns CO2 plasma jets inductively generated in high enthalpy wind tunnels used as ground test facilities. We focus our attention on the behaviour of CO and C2 electronic excited states, the radiative signature of which can be particularly significant in this type of plasma. These three cases illustrate the elaboration of CR models and their coupling with balance equations.

Gas Phase Kinetics and Equilibrium of Allyl Radical Reactions with NO and NO2

Allyl radical reactions with NO and NO(2) were studied in direct, time-resolved experiments in a temperature controlled tubular flow reactor connected to a laser photolysis/photoionization mass spectrometer (LP-PIMS). In the C(3)H(5) + NO reaction 1 , a dependence on the bath gas density was observed in the determined rate coefficients and pressure falloff parametrizations were performed. The obtained rate coefficients vary between 0.30-14.2 × 10(-12) cm(3) s(-1) (T = 188-363 K, p = 0.39-23.78 Torr He) and possess a negative temperature dependence. The rate coefficients of the C(3)H(5) + NO(2) reaction 2 did not show a dependence on the bath gas density in the range used (p = 0.47-3.38 Torr, T = 201-363 K), and they can be expressed as a function of temperature with k(C(3)H(5) + NO(2)) = (3.97 ± 0.84) × 10(-11) × (T/300 K) (-1.55±0.05) cm(3) s(-1). In the C(3)H(5) + NO reaction, above 410 K the observed C(3)H(5) radical signal did not decay to the signal background, indicating equilibrium between C(3)H(5) + NO and C(3)H(5)NO. This allowed the C(3)H(5) + NO ⇄ C(3)H(5)NO equilibrium to be studied and the equilibrium constants of the reaction between 414 and 500 K to be determined. With the standard second- and third-law analysis, the enthalpy and entropy of the C(3)H(5) + NO ⇄ C(3)H(5)NO reaction were obtained. Combined with the calculated standard entropy of reaction (ΔS°(298) = 137.2 J mol(-1)K(-1)), the third-law analysis resulted in ΔH°(298) = 102.4 ± 3.2 kJ mol(-1) for the C(3)H(5)-NO bond dissociation enthalpy.

Determining phenomenological rate coefficients from a time-dependent, multiple-well master equation: “species reduction” at high temperatures

In this article we discuss at length the determination of phenomenological rate coefficients from the solution to a time-dependent, multiple-well master equation. Both conservative and non-conservative formulations are considered. The emphasis is placed on how to handle the situation when a CSE (chemically significant eigenvalue of the transition matrix) merges with the quasi-continuum of IEREs (internal energy relaxation eigenvalues), indicating that one or more chemical reactions begin to take place on vibrational-rotational relaxation time scales. The methodology is illustrated with four examples.

Directly measuring reaction kinetics of ˙QOOH – a crucial but elusive intermediate in hydrocarbon autoignition

Hydrocarbon autoignition has long been an area of intense fundamental chemical interest, and is a key technological process for emerging clean and efficient combustion strategies. Carbon-centered radicals containing an -OOH group, commonly denoted ˙QOOH radicals, are produced by isomerization of the alkylperoxy radicals that are formed in the first stages of oxidation. These ˙QOOH radicals are among the most critical species for modeling autoignition, as their reactions with O2 are responsible for chain branching below 1000 K. Despite their importance, no ˙QOOH radicals have ever been observed by any means, and only computational and indirect experimental evidence has been available on their reactivity. Here, we directly produce a ˙QOOH radical, 2-hydroperoxy-2-methylprop-1-yl, and experimentally determine rate coefficients for its unimolecular decomposition and its association reaction with O2. The results are supported by high-level theoretical kinetics calculations. Our experimental strategy opens up a new avenue to study the chemistry of ˙QOOH radicals in isolation.

The Effect of Radiogenic Heating on the Amino Acid Content of an Early Cometary Body

This study compares the rates for the formation and destruction of amino acids in the liquid cometary core subjected to radiogenic heating by the β+ decay of the cosmogenic nuclide 26Al. The evolution of the temperature and mass of the comet were computed along with the dynamics of relatively complex organic species such as amino acids. Given the experimentally determined rate coefficient for the radiolysis of amino acids in water solution, the destruction of amino acids is virtually completed after an absorbed radiation dose of ~1 kGy. The calculations suggest that the liquid water core in comets with an initial radionuclide abundance that is sufficient to crystallize and melt the original amorphous ice is subjected to a dose of 100 - 1500 kGy. Any amino acid concentration formed in water either by radiolysis of simpler compounds or by thermal processes such as the synthesis of Strecker could not survive the irradiation delivered by the decay of 26Al.

Gas-phase reactivity study of (E)-3-pentenenitrile and 4-pentenenitrile towards OH radicals and Cl atoms at atmospheric pressure

The relative-rate technique has been used to obtain rates coefficients for the reactions of (E)-3-pentenenitrile (CH3CHCHCHCN) and 4-pentenenitrile (CH2CHCH2CH2CN) with OH radicals and Cl atoms at 298 K and (760 ± 10) Torr total pressure of synthetic air using different reference compounds. The experiments were performed in an environmental chamber with “in situ” FTIR spectroscopy to monitor the reactants concentrations. The following room temperature rate coefficients (in cm3 molecule−1 s−1) were obtained: k1 (OH + CH3CHCHCHCN) = (5.05 ± 1.10) × 10−11, k2 (Cl + CH3CHCHCHCN) = (2.60 ± 0.26) × 10−10, k3 (OH + CH2CHCH2CH2CN) = (2.90 ± 0.64) × 10−11 and k4 (Cl + CH2CHCH2CH2CN) = (2.56 ± 0.26) × 10−10. This is the first kinetic study for all of these reactions. The effect of atom or group substituent on the overall rate coefficients is analyzed and the reactivity of nitriles is compared with those of other unsaturated compounds in the literature. In addition, a comparison between the experimentally determined rate coefficients from this work and the kOH and kCl predicted from k vs EHOMO correlations is presented.The atmospheric lifetimes at room temperature of these compounds has been estimated using the rate coefficients determined in this work.

Collisional excitation of interstellar HCl by He

Modelling of molecular emission from interstellar clouds requires the calculation of rate coefficients for excitation by collisions with the most abundant species. This paper deals with the determination of rate coefficients for the rotational and hyperfine excitation of the HCl molecule in its ground vibrational state due to collisions with He. Calculations of pure rotational (de-)excitation cross-sections of HCl by He were performed using the essentially exact close-coupling method. The calculations are based on a new potential energy surface obtained from highly correlated ab initio calculations. Cross-sections for transitions among the 11 first rotational levels of HCl were calculated for total energies up to 3000 cm−1. The hyperfine cross-sections are then obtained using a recoupling technique. The rotational and hyperfine cross-sections are used to determine collisional rate coefficients for temperatures ranging from 5 to 300 K. A clear propensity rule in favour of odd Δj rotational transitions is observed. The usual Δj=ΔF propensity rule is observed for the hyperfine transitions. The new rate coefficients are compared with the previous results obtained for the HCl molecule. Significant differences are found, mainly due to the use of a new potential energy surface. The new rate coefficients will significantly help in interpreting HCl emission lines observed with current and future telescopes.

Kinetic (T = 201–298 K) and Equilibrium (T = 320–420 K) Measurements of the C3H5 + O2 ⇆ C3H5O2 Reaction

The kinetics and equilibrium of the allyl radical reaction with molecular oxygen have been studied in direct measurements using temperature-controlled tubular flow reactor coupled to a laser photolysis/photoionization mass spectrometer. In low-temperature experiments (T = 201-298 K), association kinetics were observed, and the measured time-resolved C(3)H(5) radical signals decayed exponentially to the signal background. In this range, the determined rate coefficients exhibited a negative temperature dependence and were observed to depend on the carrier-gas (He) pressure {p = 0.4-36 Torr, [He] = (1.7-118.0) × 10(16) cm(-3)}. The bimolecular rate coefficients obtained vary in the range (0.88-11.6) × 10(-13) cm(3) s(-1). In higher-temperature experiments (T = 320-420 K), the C(3)H(5) radical signal did not decay to the signal background, indicating equilibration of the reaction. By measuring the radical decay rate under these conditions as a function of temperature and following typical second- and third-law procedures, plotting the resulting ln K(p) values versus 1/T in a modified van't Hoff plot, the thermochemical parameters of the reaction were extracted. The second-law treatment resulted in values of ΔH(298)° = -78.3 ± 1.1 kJ mol(-1) and ΔS(298)° = -129.9 ± 3.1 J mol(-1) K(-1), with the uncertainties given as one standard error. When results from a previous investigation were taken into account and the third-law method was applied, the reaction enthalpy was determined as ΔH(298)° = -75.6 ± 2.3 kJ mol(-1).

Reaction of Hydroxyl Radicals with C4H5N (Pyrrole): Temperature and Pressure Dependent Rate Coefficients

Absolute (pulsed laser photolysis, 4-639 Torr N(2) or air, 240-357 K) and relative rate methods (50 and 760 Torr air, 296 K) were used to measure rate coefficients k(1) for the title reaction, OH + C(4)H(5)N → products (R1). Although the pressure and temperature dependent rate coefficient is adequately represented by a falloff parametrization, calculations of the potential energy surface indicate a complex reaction system with multiple reaction paths (addition only) in the falloff regime. At 298 K and 760 Torr (1 Torr = 1.33 mbar) the rate coefficient obtained from the parametrization is k(1) = (1.28 ± 0.1) × 10(-10) cm(3) molecule(-1) s(-1), in good agreement with the value of (1.10 ± 0.27) × 10(-10) cm(3) molecule(-1) s(-1) obtained in the relative rate study (relative to C(5)H(8), isoprene) at this temperature and pressure. The accuracy of the absolute rate coefficient determination was enhanced by online optical absorption measurements of the C(4)H(5)N concentration at 184.95 nm using a value σ(184.95nm) = (1.26 ± 0.02) × 10(-17) cm(2) molecule(-1), which was determined in this work.

Multiscale Modeling of Reaction and Diffusion in Zeolites: From the Molecular Level to the Reactor

A hierarchical multiscale approach is presented to calculate effective rates of reaction for zeolite catalyzed reaction systems. The first step in this approach involves the determination of intrinsic rate coefficients for all elementary reactions by means of quantum chemical calculations combined with transition state theory. The second step is the calculation of adsorption isotherms and diffusion coefficients of all species by means of Monte Carlo and molecular dynamics simulations. The third step comprises a continuum description of a zeolite crystal based on the reaction-diffusion equation. For coupling the intrinsic rate coefficients obtained in the first step to the continuum variables, a model is proposed that calculates the local concentration of reactants at the catalytically active centers from the total concentrations of adsorbed species. The adsorption isotherms and diffusivities are coupled to the continuum variables by analytical theories such as the ideal adsorbed solution theory and the Maxwell-Stefan formulation of multicomponent diffusion. The fourth step involves fixed-bed reactor simulations based on the continuum description of single zeolite crystals. The approach is illustrated by means of the alkylation of benzene with ethene over zeolite H-ZSM-5.

Determination of gas-phase ozonolysis rate coefficients of a number of sesquiterpenes at elevated temperatures using the relative rate method

The rates of ozonolysis of four sesquiterpenes, β-caryophyllene, α-humulene, isolongifolene and α-cedrene, are determined in the gas phase at an elevated temperature of 366 ± 3 K and a pressure of ~780 Torr using the EXTreme RAnge chamber (EXTRA). The experimentally obtained rate coefficients agree with extrapolated room temperature rate coefficients for isolongifolene and α-cedrene but not for β-caryophyllene and α-humulene, which were found to be three orders of magnitude slower than this in the literature. These new measurements support the hypothesis that operating under ambient conditions, kinetic measurements of condensable species can be influenced adversely by heterogeneous processes and should therefore be treated with caution.

Airfoil sampling of a pulsed Laval beam with tunable vacuum ultraviolet synchrotron ionization quadrupole mass spectrometry: Application to low-temperature kinetics and product detection

A new pulsed Laval nozzle apparatus with vacuum ultraviolet (VUV) synchrotron photoionization quadrupole mass spectrometry is constructed to study low-temperature radical-neutral chemical reactions of importance for modeling the atmosphere of Titan and the outer planets. A design for the sampling geometry of a pulsed Laval nozzle expansion has been developed that operates successfully for the determination of rate coefficients by time-resolved mass spectrometry. The new concept employs airfoil sampling of the collimated expansion with excellent sampling throughput. Time-resolved profiles of the high Mach number gas flow obtained by photoionization signals show that perturbation of the collimated expansion by the airfoil is negligible. The reaction of C(2)H with C(2)H(2) is studied at 70 K as a proof-of-principle result for both low-temperature rate coefficient measurements and product identification based on the photoionization spectrum of the reaction product versus VUV photon energy. This approach can be used to provide new insights into reaction mechanisms occurring at kinetic rates close to the collision-determined limit.

RAFT kinetics revisited: Revival of the RAFT debate

AbstractRecently, two electron spin resonance (ESR)‐based methods for the determination of addition and fragmentation rate coefficients in dithiobenzoate‐mediated reversible addition fragmentation transfer (RAFT) polymerization were introduced, one being based on a spin‐trapping method and the other on single‐laser pulse initiation in conjunction with ESR detection at microsecond time resolution. For the RAFT‐intermediate radical fragmentation rate, coefficient data differing by six orders of magnitude were obtained, which cannot be explained by the usual model dependencies, that is the so‐called cross‐termination versus stable intermediate model. Even under consideration of fast cross‐termination in both cases, the large difference persists. Both the experimental designs are thus critically reviewed to identify potential error sources and to explain the vast difference in the individual results. Both techniques appear to be robust and only small interferences could be identified. Finally, recommendations for the refinement of the individual techniques are given to achieve a consistent kinetic picture of the underpinning reaction equilibria. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011

A Rapid Electrochemical Method for Determining Rate Coefficients for Copper-Catalyzed Polymerizations

Copper(I) polyamine complexes have emerged as excellent atom-transfer radical polymerization catalysts. The rate of their reaction with organic halide initiators (the so-called activation step) varies across a broad range, depending on both the structure of the copper complex and the initiator. Herein, we report a new technique for determining the rate of copper-catalyzed activation (k(act)) using cyclic voltammetry coupled with electrochemical simulation. This method is applied to measuring k(act) for one of the most active catalysts, [Cu(I)(Me(6)tren)](+) (Me(6)tren = N,N,N-tris-(2-(dimethylamino)ethyl)amine), in reaction with ethyl bromoisobutyrate.

Determination of gas-phase ozonolysis rate coefficients of C8–14 terminal alkenes at elevated temperatures using the relative rate method

The rates of ozonolysis of a suite of terminal alkenes ranging from C(8-14) are determined in the gas phase at an elevated temperature of 395.9 ± 1.2 K and a pressure of ∼650 Torr using the EXTreme RAnge chamber (EXTRA). Rates are found to be invariant with carbon number, whilst literature measurements conducted under ambient conditions exhibited an increase in rate coefficient after 10 carbon atoms. These earlier findings appear to contradict the intuitive notion that the inductive effect is a short-range process operating over a maximum distance of a few carbon atoms. These new measurements support the hypothesis that operating under ambient conditions, kinetic measurements of condensable species can be influenced adversely by heterogeneous processes and should therefore be treated with caution.

Temperature‐dependent kinetics for the ozonolysis of selected chlorinated alkenes in the gas phase

AbstractThe ozonolysis of olefinic species is an important tropospheric process impacting on climate and human health. However, few studies have investigated these reactions as a function of temperature and even less information is available upon the effects of alkene heteroatomic substitution on the Arrhenius parameters. The electron‐withdrawing capacity of substituents about the olefinic bond strongly influences the rate of alkene ozonolysis. To understand better the effect of these substitutions, the temperature‐dependence of a series of ozone–chloroalkene reactions is investigated. Experiments were conducted in the EXTreme RAnge (EXTRA) chamber, over the range of 292–409 K and 760 Torr. The experimentally determined rate coefficients were fitted using an Arrhenius‐type analysis to yield the following activation energies: 30.80 ± 0.79, 23.18 ± 0.59, 65.2 ± 2.8, 116.9 ± 5.6, 29.5 ± 1.8, and 18.67 ± 0.96 kJ mol−1 and preexponential A‐factors 1.22+0.39−0.29×10−15, 9.3+6.7−5.4×10−16, 1.6+2.5−1.0×10−10, 6+22−3.9×10−4, 1.7+1.6−0.8×10−14, and 4.2+1.9−1.3×10−15 cm3 molecule−1 s−1 for cis‐1,2‐dichloroethene, trans‐1,2‐dichloroethene, trichloroethene, tetrachloroethene, 2‐chloropropene, and 3‐chloro‐1‐butene, respectively. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 43: 120–129, 2011

Determination of Propagation Rate Coefficients for Methyl and 2-Ethylhexyl Acrylate via High Frequency PLP−SEC under Consideration of the Impact of Chain Branching

The radical propagation rate coefficients, kp, of methyl acrylate (MA) and 2-ethylhexyl acrylate (EHA) have been determined in bulk via high frequency (500 Hz) pulsed laser polymerization coupled to size exclusion chromatography (PLP−SEC) up to elevated temperatures (20 ≤ T/°C ≤ 80). Prior to the analysis of the generated polymeric material, an investigation into the branching behavior of the generated polymers has been undertaken, employing the concept of local dispersity, D(Ve). In addition, the Mark-Houwkink-Kuhn-Sakurada parameters for both poly(MA) and polyEHA were determined at each studied reaction temperature. The temperature averaged values read (K = 10.2 × 10−5 dL g−1; α = 0.741) and (K = 9.85 × 10−5 dL g−1; α = 0.719) for poly(MA) and polyEHA, respectively. The local dispersity data indicate that branching in polyEHA may be considerably more prevalent than in poly(MA), as with increasing temperature polymer microinhomogeneities are observed. Consequently, the Arrhenius parameters for kp of EHA ...

A generalized Fisher equation and its utility in chemical kinetics.

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The GFE is an exact mathematical result that has been widely used in population dynamics and genetics, where it originated. Here we demonstrate that the GFE can also be useful in other fields, specifically in chemistry, with models of two chemical reaction systems for which the mechanisms and rate coefficients correspond reasonably well to experiments. A bad fit of the GFE can be a sign of high levels of measurement noise; for low or moderate levels of noise, fulfillment of the GFE is not degraded. Hence, the GFE presents a noise threshold that may be used to test the validity of experimental measurements without requiring any additional information. In a different approach information about the system (model) is included in the calculations. In that case, the discrepancy with the GFE can be used as an optimization criterion for the determination of rate coefficients in a given reaction mechanism.

Determination of rate coefficients for fusion-relevant atoms and molecules by modelling and measurement in the boundary layer of TEXTOR

Rate coefficients for the excitation and ionization of neutral as well as singly ionized particles and-–predominantly-–their ratios S(D)/XB, which are important for the conversion of photon into particle fluxes in ionizing fusion boundary plasma, have been modelled and experimentally determined in boundary plasmas for fusion-relevant species such as He I, Li I, C I, B I&II, O I&II, Si I&II, Mo I, W I&II, H2, CH(D), C2.

Online Low-Field 1H NMR Spectroscopy: Monitoring of Emulsion Polymerization of Butyl Acrylate

The emulsion polymerization of butyl acrylate was monitored by online nuclear magnetic resonance spectroscopy at 20 MHz 1H frequency. The reaction progress could be followed, monitoring the conversion of the reactant time-resolved without any need of sample preparation. Experimental data were analyzed with kinetic models for free-radical polymerization. The data comprised the polymerization rate in seeded batch emulsion polymerizations of butyl acrylate with doubly deionized water and D2O as solvent. The polymerization rate versus conversion curve behaves compatible with the three rate intervals model, typically observed in emulsion polymerizations. Zero−one kinetics explains the experimental results appropriately, leading to the determination of entry and termination rate coefficients.