High-Temperature Unimolecular Decomposition of Diethyl Ether

Subscriber access provided by UNIV OF SOUTHERN INDIANA

A: Kinetics, Dynamics, Photochemistry, and Excited States

High-Temperature Unimolecular Decomposition of Diethyl Ether: Shock-Tube and Theory Studies Paul Sela, Yasuyuki Sakai, Hang Seok Choi, Jürgen Herzler, Mustapha Fikri, Christof Schulz, and Sebastian Peukert J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b04186 • Publication Date (Web): 22 Jul 2019 Downloaded from pubs.acs.org on July 23, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

High-Temperature Unimolecular Decomposition of Diethyl Ether: Shock-Tube and Theory Studies

Paul Sela1, Yasuyuki Sakai2, Hang Seok Choi1, Jürgen Herzler1, Mustapha Fikri1, Christof Schulz1, Sebastian Peukert1*

1) IVG,

Institute for Combustion and Gas Dynamics – Reactive Fluids

and CENIDE, Center for Nanointegration Duisburg-Essen, University of Duisburg-Essen, 47048 Duisburg, Germany 2)

Graduate School of Engineering, University of Fukui, Fukui, Japan

Corresponding Author: Sebastian Peukert IVG, Institute for Combustion and Gas Dynamics – Reactive Fluids University of Duisburg-Essen 47048 Duisburg, Germany Phone: +49 202 3793511 Email: [email protected]

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 46

Abstract The unimolecular decomposition of diethyl ether (DEE; C2H5OC2H5) is considered to be initiated via a molecular elimination, a C–O, and a C–C bond fission step: C2H5OC2H5  C2H4 + C2H5OH (1), C2H5OC2H5  C2H5 + C2H5O (2), and C2H5OC2H5  CH3 + C2H5OCH2 (3). In this work, two shock-tube facilities were used to investigate these reactions via (a) time-resolved H-atom concentration measurements by H-ARAS (Atomic-Resonance Absorption Spectrometry), (b) time-resolved DEE-concentration measurements by high-repetition-rate time-of-flight mass spectrometry

(HRR-TOF-MS),

and

(c)

product-composition

measurements

via

gas

chromatography/mass spectrometry (GC/MS) after quenching the test gas. The experiments were conducted at temperatures ranging from 1054 to 1505 K and at pressures between 1.2 and 2.5 bar. Initial DEE mole fractions between 0.4–9300 ppm were used to perform the kinetics experiments by H-ARAS (0.4 ppm), GC/MS (200–500 ppm), and HRR-TOF-MS (7850–9300 ppm). The rate constants ktotal (ktotal = k1 + k2 + k3) derived from the GC/MS and HRR-TOF-MS experiments agree well with each other and can be described by the Arrhenius expression ktotal(1054–1467 K; 1.3–2.5 bar) = 1012.81±0.22 exp(–240.27±5.11 kJ mol1/RT) s−1.From H-ARAS experiments, overall rate constants for the bond fission channels k2+3 = k2 + k3 have been extracted. The k2+3 data can be well described by the Arrhenius equation k2+3(1299–1505 K; 1.3– 2.5 bar) = 1014.43±0.33 exp(–283.27±8.78 kJ mol1/RT) s1.

A

master-equation

analysis

was

performed using CCSD(T)/aug-cc-pvtz//B3LYP/aug-cc-pvtz and CASPT2/aug-cc-pvtz//B3LYP/augcc-pvtz molecular properties and energies for the three primary thermal decomposition processes in DEE. The derived experimental data is very well reproduced by the simulations with the mechanism of this work. Regarding the branching ratios between bond fissions and elimination channels, uncertainties remain.


Page 3 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. Introduction Ethers belong to the substance class of oxygenated hydrocarbons that are frequently used as additives in gasoline and Diesel fuels and that are under consideration as components in future biomass-derived fuels1. Dimethyl and tert-butyl methyl ether are prominent examples for additives and components of synthetic fuels2. Recently, test engine studies related to applying diethyl ether (DEE; C2H5OC2H5) as ignition improver have been performed. Mack et al.3 explored chemical pathways of combusting DEE and ethanol (C2H5OH) mixtures in homogeneous-charge compression-ignition (HCCI) engine combustion by tracing

14C

isotopes. The authors also

developed a numerical model of DEE/C2H5OH HCCI combustion to interpret the experimental data. According to their findings, fuel blends of C2H5OH and DEE showed higher reactivity than neat C2H5OH. Further studies on the influence of DEE in Diesel and HCCI engines on auto ignition as well as NOx and soot emissions have been conducted, e.g., by Cinar et al.4, Qi et al.5, Sivalakshmi and Balusamy6, and Rakopoulos et al.7. Autoignition properties were determined from shock-tube and rapid-compression machine (RCM) measurements by Werler et al.8. The kinetics of DEE pyrolysis was first studied for temperatures between 833 and 903 K by Laidler and McKenny9-10 at reduced pressures (20–430 mbar). At lower temperatures (697– 761 K), Seres and Huhn11 also studied DEE decomposition, similar to Laidler and McKenny9-10, by gas chromatography (GC). In another work, Miller et al.12 studied on the pyrolysis of 1,2,4,5hexatetraene in a shock tube in the context of the chemistry of important intermediates regarding the formation of first aromatics and soot. Miller et al.12 synthesized the 1,2,4,5hexatetraene by a Grignard reaction and in the synthesis, DEE was used as a solvent. They purified the raw product by atmospheric and vacuum distillation, but it was not possible to completely remove the solvent DEE. Therefore, DEE was part of the reactant gas mixtures. For verifying the thermal stability of DEE at the conditions of the 1,2,4,5-hexatetraene experiments, Miller et al.12 also determined overall rate constants for DEE decomposition in a high-pressure single-pulse shock tube at 613–1254 K at around 22 bar. Over reaction times of 1–2 ms, Miller et al.12 observed significant conversion of DEE at T > 1000 K. Assuming first-order kinetics,



Page 4 of 46

they derived an Arrhenius expression for the overall decomposition of DEE, i.e., DEE → products: ktotal(T) = 1010.91 exp(−181.33 kJ mol1/RT) s−1. The most detailed kinetics investigation on DEE pyrolysis and oxidation so far was conducted by Yasunaga et al.13 in the 900–1900 K and 1–4 bar range by combining three shock-tube facilities equipped with IR spectrometry at 3.39 µm for measuring DEE consumption, GC for measuring the composition of stable products, and chemiluminescence detection for the determination of ignition delay times. Yasunaga et al.13 derived a detailed reaction mechanism for DEE combustion and the calculated missing thermochemical data. Rate constants of important unimolecular and bimolecular reactions taken from literature are based on analogies to other oxygenated compounds and – where required – their pressure dependence was estimated based on Quantum RiceRamsperger-Kassel (QRRK) theory. A detailed quantum-chemical kinetics investigation on the low-temperature oxidation of DEE was reported by Sakai et al.14. From previous kinetics investigations on DEE pyrolysis it is known that DEE decomposes primarily by three unimolecular reactions: C2H5OC2H5 → C2H5OH + C2H4

(1)

C2H5OC2H5 → C2H5 + C2H5O

(2)

C2H5OC2H5 → CH3 + C2H5OCH2

(3)

In a previous investigation of the thermal decomposition of dimethoxymethane (DMM)15, we have equipped two shock tubes with three detection methods: H-ARAS (Atomic Resonance Absorption Spectrometry), high-repetition-rate time-of-flight mass spectrometry (HRR-TOF-MS), and GC/MS. Overall rate constant data on DMM decomposition obtained from these three experimental data sets were found to agree very well among each other. These results encouraged us to apply the same methodology for investigating the thermal decomposition of DEE. Even though Yasunaga et al.13 performed a comprehensive kinetics investigation on DEE combustion, their publication is the only detailed experimental and modeling kinetics study on


Page 5 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


DEE at T > 1000 K. Furthermore, while ignition delay time measurements are often used for model validation and development, they do not permit to extract rate constants of initial unimolecular reaction steps. By applying GC/MS and HRR-TOF-MS, we intend to directly determine overall DEE decomposition rate constants and by using toluene as a radical scavenger in the single-pulse GC/MS experiments, the influence of bimolecular reactions, in particular Hatom abstractions, can be suppressed and hence, these experiments permit to measure exclusively only the contribution of unimolecular reactions on DEE decomposition. In turn, applying H-ARAS permits to extract kinetics information on the two bond fissions (2) and (3). C2H5 radicals are a direct product of channel (2) and at T > 1000 K, C2H5 radicals rapidly dissociate to C2H4 + H. Channel (3) does not directly result in the formation of H atoms, however, the product radical C2H5OCH2 decomposes by a -bond fission to yield formaldehyde (CH2O) and again C2H5 radicals. A difficulty regarding the simulation of H-ARAS experiments is based on the subsequent dissociation channels of ethoxy radicals (C2H5O), which are a product of reaction (2). C2H5O radicals can dissociate by a C–C (reaction 4a) or C–H bond fission (reaction 4b): C2H5O → CH3 + CH2O

(4a)

C2H5O → H + CH3CHO

(4b)

According to Yasunaga et al.13 as well as to Curran16, channel (4a) is the major reaction: At 1100–1500 K, the branching ratio BR4a = k4a/(k4a+k4b), exhibits values between 0.81 (at 1100 K) and 0.70 (at 1500 K). Therefore, reaction (4a) can also contribute to a minor extent to the HARAS signal. The temperature and pressure dependence of C2H5O radical dissociation has also been studied experimentally by Caralp et al.17 by laser-induced fluorescence in flow reactors. The C2H5O dissociation branching ratios given in the Yasunaga et al.13 mechanism are in very good agreement with the branching ratios derived from the rate-constant expressions provided in the paper from Caralp et al.17. Relying on the branching ratio between channels (4a) and (4b), the H-ARAS experiments allow to extract kinetics data on the overall bond dissociation rate



constants k2+3, with k2+3 = k2 + k3. The experimentally based total rate constants ktotal and overall bond-dissociation rate constants k2+3 will be also complemented by an ab initio based RRKM/master equation analysis. By applying higher level quantum-chemical calculations and higher level unimolecular rate theory in combination with the present experimental data, we intend to further enhance confidence in the Yasunaga et al.13 DEE combustion chemistry model.

2. Experiment The experimental equipment and the measurement procedure are described in detail in refs. 15, 18-20

and only a short overview is given here. The thermal decomposition of DEE was measured

in a helium-driven stainless-steel shock tube. The driver section (2.5 m length) and the driven section (6.3 m) are separated by 50–60-µm thick aluminum diaphragms; the inner diameter of the shock tube is 80 mm. The shock tube can be operated as a conventional as well as in a single-pulse mode, when the driver section is connected with a dump tank. The entire facility is pumped down to pressures of 3×10−3 mbar in between experiments. The shock velocity was determined from measuring the arrival of the incident shock wave at four subsequent pressure transducers and the measurement is extrapolated to the velocity at the end plate of the driven section using the observed shock attenuation of less than 1%/m. Gas temperatures and pressures behind the reflected shock waves (T5 and p5) were calculated from one-dimensional gas-dynamics with uncertainties in the calculated temperatures of ±1%. In other single-pulse shock-tube-facilities, temperatures have been determined by chemical thermometry21-22. In the study describing the details of our single-pulse shock-tube-apparatus18, the thermal decomposition of cyclohexene has been used to validate our facility. The temperatures determined from ideal shock-wave equations and the extracted cyclohexene decomposition rate constants were in very good agreement with literature values. Cyclohexene itself can be used as a compound for chemical thermometry in single-pulse shock-tubes. The inner diameter


Page 6 of 46

Page 7 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of 80 mm in our shock-tube-apparatus leads to more ideal shock-wave behavior and therefore we can apply ideal gas-dynamic equations equally well for temperature measurements. All gas mixtures were prepared manometrically in a 50000 cm3 stainless-steel mixing vessel. For GC/MS and HRR-TOF-MS experiments, Ar and Ne were used as diluent, respectively. To suppress bimolecular secondary reactions like H-atom abstractions, in two sets of single-pulse experiments, toluene was used as a radical scavenger. The filling pressure of the driven section (p1) depends on the desired value of p5. A gas chromatograph (GC/MS Agilent 7890A and MSD 5975C) was used for determining the product composition. The GC was equipped with a PLOT-Q column and combined with a quadrupole mass spectrometer (QMS). Gas samples were extracted from the shock tube via a solenoid valve (Balzers, EVI 005) with an opening time of 1 s triggered by the delayed signal from one pressure transducer and collected in a 55-cm3 sampling chamber. Sela et al.18 estimated the influence of boundary layer effects on uncertainties of reactant concentration measurements to be 0.1% of the initial concentration. To reduce uncertainties in the GC/MS measurements, each sample was analyzed three times within a time frame of 70 minutes. The results of three measurements for each sample were then averaged. The HRR-TOF-MS (Kaesdorf, Munich) enables time-resolved measurements of (mass-separated) species concentrations. The center position of the end plate contains a 60 µm nozzle that protrudes 1 mm into the shock tube and provides a continues gas jet into the ionization chamber of the mass spectrometer. The gas sample is ionized via pulsed electron ionization with an ionization energy of 45 eV and a repetition rate of 125 kHz. Between experiments, the ionization chamber and the drift section are pumped down to pressures of around 1×10−7 and 4×10−8 mbar, respectively. These settings yield full mass spectra with masses up to 120 u every 8 µs. Ne was used as bath gas in all HRR-TOF-MS experiments because of its small electronionization cross-section. Using Ne as bath gas therefore prevents overloading of the MCP detector. The signal of Ne at a mass-to-charge ratio (m/z) of 20 was further reduced by the



instrument’s mass filter. The arrival of the reflected shock wave causes an immediate increase in T5 and p5 which leads to an increased gas flow into the ion source (so-called gas-dynamic effects). To separate chemical kinetics from gas-dynamic effects in the detected timedependent signal intensities, all signals of species of interest were normalized to the peak area of the chemical-inert standard Kr that is added to the initial gas mixture at a mole fraction of 1%. For H-ARAS experiments, we used a different shock tube (inner diameter: 80 mm) with 3.0-m driver and 5.5-m driven sections separated by 50-µm thick aluminum diaphragms. Helium (Air Liquide, 99.999%) was used as driver gas. The driven section was pumped down to pressures of 1.0×10–6 mbar between experiments The reactant gas mixtures, which were filled into the driven section, consist of high-purity argon (Air Liquide, 99.9999%) with a trace amount of DEE (~0.4 ppm; Sigma Aldrich; purity ≥ 99.7%). The reason for the small reactant mole fractions used in ARAS experiments is related to the inherent sensitivity of this spectrometric method. To prepare gas mixtures with such small mole fractions we conducted four dilution steps in a stainless-steel mixing vessel manometrically. Between each dilution step, the gas mixtures in the vessel were allowed to homogenize for two hours. The velocities of the incident shock waves were measured in the same way as described above. The reflected shock wave arrival times were determined by a pressure transducer (Kistler 603A), mounted 20 mm apart from the end plate. Optical access was ensured by two VUV LiF windows. For quantitatively following the reaction progress behind reflected shock waves, H-ARAS at 121.6 nm (Lyman-α line) was employed. The Lyman-α radiation results from a helium/hydrogen plasma, which is ignited by a microwave discharge. The radiation passes through the shock tube through VUV (LiF) side-wall windows at a distance of 20 mm from the end plate. The transmitted radiation was detected by a photomultiplier (Hamamatsu R8487) located in a metal housing, which is purged by O2 at a pressure of 200 mbar. According to Appel and Appleton.23, O2 can be used to selectively transmit Lyman-α radiation. For each H-ARAS-experiment, the time resolution was 0.5 µs and the observation time was 1000 µs. A direct conversion of the


Page 8 of 46

Page 9 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


absorption profiles into H-atom concentration–time profiles is not possible via the BeerLambert law because the spectral emission of the ARAS lamp is not well enough characterized due to line-broadening as a consequence of self-absorption. To derive a functional relationship between the measured absorption and the absorber concentration, calibration experiments with N2O/H2 gas mixture were conducted. This reaction system provides a well-characterized source of H atoms; for details see Ref.15.



3. Reaction mechanism for DEE with toluene and theory From the single-pulse shock-tube experiments with GC/MS detection and toluene addition, the rate constants of the total unimolecular DEE decomposition were extracted by simulations using a DEE mechanism developed by Sakai et al.14, which was extended by a toluene sub-mechanism in a gasoline surrogate-fuel mechanism developed by Miyoshi et al.24 The species, reactions, and their Arrhenius parameters duplicated in both mechanisms were taken from the Sakai et al.14 DEE mechanism, which is primarily based on the Yasunaga et al.13 model. Major differences between the mechanisms from Sakai et al. and Yasunaga et al.13 are related to the lowtemperature oxidation chemistry, which is not relevant for DEE pyrolysis studied in the present work. The single-pulse experiments without toluene addition as well as the HRR-TOF-MS experiments were simulated with the Yasunaga et al.13 mechanism. To rationalize k(T,p) of the primary unimolecular reactions of DEE decomposition, an ab initio based RRKM (Rice-Ramsperger-Kassel-Marcus)/master equation (ME) analysis was carried out. Theoretical rate constants were calculated using the SSUMES code (steady-state unimolecular master-equation solver)25. Molecular properties of reactant, transition states and products were calculated at the B3LYP/aug-cc-pvtz level of theory with Gaussian0926. Optimized structures, vibrational frequencies, and rotational constants are given in table S1-S3 in supporting information. According to the recommendation by Sinha et al.27, the vibrational frequencies calculated by the B3LYP/aug-cc-pvtz method were scaled by 0.9867 for the zero-point energy calculation and by 0.9891 for the density of states in the RRKM calculations. For rate-constant calculations of bond fissions without pronounced energy barrier, a variational approach was applied. The geometries and frequencies along the reaction coordinate, approximated by the broken internuclear distance, were also obtained using B3LYP/aug-cc-pvtz. For C2H5OH elimination, single-point energies of optimized structures were calculated at the CCSD(T)/augcc-pvtz theory level, and for bond fissions, single-point energies of optimized structures were obtained by applying the CASPT2/aug-cc-pvtz method with minimal 2e/2o active space using


Page 10 of 46

Page 11 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the Molpro software (version 2012.1)28. The final energies along the reaction coordinate for rate constant calculations with SSUMES25 were normalized to the energies of CCSD(T)/aug-cc-pvtz. A tunneling correction was included for the calculation of the rate constants C2H5OH elimination, assuming the asymmetric Eckart potential29. Internal rotations along the single bond were treated as hindered rotations with the PitzerGwinn approximation30. The height of the sinusoidal potential in the Pitzer-Gwinn approximation was determined by comparing partition functions directly related to these motions, which are derived from the eigenstate energies by using the BEx1D program (basis-set expansion solver for 1-dimensional Schrödinger equation)31. Internal rotations around broken bonds for bond fission reactions were treated as free rotors. The density of states was calculated according to the equation of Knyazev32. In Figs. S1–S3 in the supporting material, the analysis of internal rotations is shown. Figure S1 shows internal rotation along C-C bond in DEE. Fig. S1a shows the potential energy (open circles) calculated at B3LYP/aug-cc-pvtz and its Fourier fitting curve (solid line) as a function of the O-C-C-H dihedral angle. Fig. S1b shows the exact partition function (Qexact) of the internal rotor obtained by using the BEx1D program. The partition function QHO was calculated with assumption of harmonic oscillator and QPG was calculated by Pitzer-Gwinn approximation with a potential height of 1000 cm1. From the comparison of these partition functions, it was concluded to use the Pitzer-Gwinn approximation with a potential height of 1000 cm−1 for the calculation of the density of states. We also applied this conclusion to the CH3 internal rotor in other species. Figure S2 shows internal rotation analysis along C-O bond in DEE and Fig. S3 shows internal rotation analysis along the C-O bond in the transition state of the C2H5OH elimination reaction. We concluded to approximate these internal rotations as Pitzer-Gwinn approximations with a potential height of 1900 cm1 in DEE and 900 cm1 in the transition state of C2H5OH elimination, respectively. Internal rotors along C-O bonds in other molecules were also approximated by Pitzer-Gwinn approximations with a potential height of 1900 cm−1.



The master-equation was calculated with a grain size of 100 cm−1. Lennard-Jones parameters (collision diameter (σ) and well depth (ε)) are σ = 3.54 Å and ε/kB = 93.3 K for Ar and σ = 5.68 Å and ε/kB = 313.8 K for DEE33. For the collisional energy transfer, a temperature-dependent expression was estimated: ⟨ΔEdown⟩ = 400(T/1000) cm−1. Due to much higher bond dissociation energies, C–H bond fissions have not been considered in the RRKM/ME calculation. All simulations were performed with the Chemical Workbench34 program (Version 4.1.15340) and. The data related to the GC/MS and HRR-TOF-MS experiments was simulated based on measured non-reactive pressure profiles.

4. Results and Discussion 4.1 Product species composition The GC/MS measurements presented in Fig. 1a–f show that in the pyrolysis of DEE at 1185– 1310 K and 1.2–2.4 bar, CH4, C2H4, C2H6, CH3CHO, and C2H5OH are main stable products. The most abundant stable product C2H4 is already formed at about 1075 K and its concentration increases continuously up to 1240 K (Fig. 1a). The formation of CH3CHO starts also around 1075 K and the concentration reaches its maximum value at around 1200 K (Fig. 1c). CH4, C2H6, and C2H5OH are formed at lower concentrations compared to C2H4, and C2H2 was only found in traces at temperatures above 1230 K (Fig. 1e).


Page 12 of 46

Page 13 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 1: Species-concentration–temperature profiles from single-pulse shock-tube measurements for various gas mixtures normalized to the initial concentration of DEE: (filled symbols) 500 ppm DEE, 500 ppm Kr in Ar; (open symbols) 200 ppm DEE, 200 ppm Kr in Ar; and (crossed symbols) 534 ppm DEE, 500 ppm Kr in Ar.

Fig. 2a–d shows the results of the GC/MS experiments with and without toluene. Unfortunately, with the GC/MS it was not possible to detect molecular hydrogen (H2) in this work. Fig. 2a shows that the concentration of C2H4 is not affected by toluene, because C2H4 is mainly formed by the four-center elimination of C2H5OH, reaction (1). Fig. 2b shows that the absolute concentration of CH4 drastically changed in the presence of toluene because CH3 radicals directly interact with the side chain of toluene and CH4 is formed. In addition, C2H2 and C2H6 were not detected since CH3 radical-recombination reactions were inhibited. The main sources of acetaldehyde (CH3CHO) are related to the formation of secondary DEE radicals (C2H5OCHCH3) and C2H5O radicals. C2H5OCHCH3 radicals are generated from H-atom abstraction from secondary C–H



bonds in DEE and these radials then decompose via -bond-fission to C2H5 and CH3CHO. C2H5O in turn is generated by the initial C– O bond fission (2) and CH3CHO is a result from the C–H bond fission channel (4b). As mentioned in the introduction, C2H5O primarily decomposes by channel (4a) to CH3 and CH2O. Even though the barrier for channel (4b) is almost 17 kJ mol1 higher than that for (4a)35, its branching fraction at temperatures between 1000 and 1400 K is approximately 20% and therefore its contribution to CH3CHO formation cannot be neglected. In presence of toluene, one can note that a larger amount of C2H5OH is formed (Fig. 2d). This can be explained by the inhibition of H + DEE and H + C2H5OH reactions. In the presence of toluene, DEE can only be consumed by unimolecular reactions and since C2H5OH is directly formed from unimolecular DEE decomposition, suppressing H + DEE and H + C2H5OH reactions at the same time leads to an enhanced extent of C2H5OH formation and to a lower extent of C2H5OH consumption. The argument of inhibited H + DEE reactions is also plausible to explain in part the observed lower extent of CH3CHO formation in the experiments with toluene addition. If H-atom abstraction from secondary C–H bonds in DEE is inhibited, no secondary DEE radicals are formed and therefore one possible source for CH3CHO molecules is excluded. In principle, it could be also possible to generate C2H5OH molecules by H-atom abstractions between C2H5O radicals and toluene molecules. However, at temperatures around 1000 K, the overall rate constants of C2H5O decomposition13, 16-17 is calculated to be in the order of 109 s1. Therefore, C2H5O basically decomposes instantaneously and it is not involved in bimolecular reactions with toluene. Some fraction of C2H5O radicals can also undergo H-atom abstraction from toluene, thereby leading to an enhanced C2H5OH formation. Since a significant fraction of C2H5O radicals react with toluene, the formation of CH3CHO is substantially reduced. This effect can be noted in Fig. 2c and d.


Page 14 of 46

Page 15 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 2: Species-concentration–temperature profiles of DEE, C2H4, CH3CHO, and C2H5OH for experiments with and without toluene, normalized to the initial concentration of DEE. Solid symbols represent experiments without toluene and the open and crossed symbols represent the ones with toluene. Open symbols: 185 ppm DEE, 200 ppm Kr, and 1.8% toluene in Ar. Crossed symbols: 214 ppm DEE, 200 ppm Kr,

and 1.8% toluene in Ar. The carbon balance is shown in Fig. 3. In the temperature range 1100–1275 K, we derived a carbon balance of roughly 90%. The missing carbon is probably bonded in CH2O and CO, since both species are formed during the pyrolysis of DEE. With the GC/MS used in this study, it is not possible to quantify CH2O and CO.



Fig. 3: Carbon balance of the single-pulse shock-tube experiments with GC/MS detection for varying initial mole fractions of DEE.

From the GC/MS experiments with added toluene, ktotal (k1 + k2 + k3) was derived by simulations with a reaction mechanism consisting of the DEE reaction mechanism of Yasunaga et al.13 and a toluene mechanism. During the modeling procedure of the GC/MS experiments with toluene addition, the branching ratios between reactions (1), (2), and (3) have been adopted from Yasunaga et al.13 Therefore, in this work, ktotal is the only parameter that was adjusted for each experiment in order to obtain best-fit rate constant data and by multiplying the adjusted ktotal values with the branching ratios of each primary unimolecular decomposition channel, rate constant data for k1, k2, and k3 have been obtained. The branching ratios for the respective channels are designated BR1 (BR1 = k1/ktotal), BR2 (BR2 = k2/ktotal), and BR3 (BR3 = k3/ktotal). According to Yasunaga et al.13, up to temperatures near 1180 K, the C2H5OH elimination (1) outweighs the bond fissions (2) and (3). From 1200 K and upwards, the bond fissions (2) and (3) prevail over channel (1). Among the bond fissions, channel (2), which leads to the formation of C2H5 radicals, clearly predominates over the other C–C bond fission (3): Within the 1000–1500 K temperature range, the branching fraction BR3 ranges from 1.7–5.9% whereas the other C–C fission (2) accounts for a branching fraction BR2 between 31 and 57% over the same


Page 16 of 46

Page 17 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


temperature range. At p = 2.0 bar and at temperatures between 1000–1500 K, the temperature dependence of BR1, BR2, and BR3 can be expressed by (T in K): BR1(T) = 34.7944  exp(–T/212.9460)) + 0.3534,

(Eq. 1)

BR2(T) = –7.19159 + (0.01636T) + (–1.1664510–5T2) + (2.8018710–9T3), (Eq. 2) BR3(T) = –0.0669 + 8.38510–5T.

(Eq. 3)

Since numeric values of the branching ratios are small and to avoid numeric errors due to the small values of calculated branching ratios, it is required to use a larger number of digits for the parameters in equations 1–3. For the modeling of all experimental data sets, we rely on the branching ratios BR1, BR2, and BR3, which are the outcome of rate constant data k1, k2, and k3, from the Yasunaga et al.13 mechanism. Table 1 shows a summary of experimental conditions and ktotal data derived from the present GC/MS experiments with toluene addition.

Table 1: Experimental conditions and ktotal data of the single-pulse GC/MS experiments with toluene addition. T5 and p5 refer to the conditions behind the reflected shock-wave. T5 / K

p5 / bar

ktotal / s–1

x0,DEE = 214 ppm, xKr = 200 ppm, xtoluene = 1.8% in Ne 1152 1188 1188 1212 1226 1239 1253 1264 1280 1308

2.36 2.17 2.36 2.18 2.09 2.20 2.17 2.28 2.10 2.00

70 137 138 270 345 397 585 715 925 1080

x0,DEE = 185 ppm, xKr = 200 ppm, xtoluene = 1.8% in Ne 1117 1127

2.22 2.37


45 38


1183 1185 1203 1227 1244 1260 1282

2.08 2.28 2.27 2.22 2.20 2.18 2.18

Page 18 of 46

158 157 200 320 580 780 875

The ktotal data presented in Table 1 have been used in the detailed DEE + toluene reaction mechanism in order to simulate the corresponding product compositions. These simulations along with the measured compositions are shown in Fig. 4.

Fig. 4: Product yields measured via GC/MS in the single-pulse shock-tube in presence of toluene compared with simulations as a function of temperature. All simulations were conducted with the DEE + toluene mechanism described in this work. Open symbols: 185 ppm DEE, 200 ppm Kr, and 1.8% toluene in Ar. Crossed symbols: 214 ppm DEE, 200 ppm Kr, and 1.8% toluene in Ar. Simulated DEE concentrations are represented by the solid black line and the concerning product species of each diagram are represented by the dashed lines.


Page 19 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


With the present ktotal data and the combination of the Yasunaga et al.13 DEE and the toluene mechanism, it was possible to reproduce measured product yields very well. Besides GC/MS experiments with toluene, we also carried out single-pulse experiments without adding toluene. For modeling these experiments, we applied the Yasunaga et al.13 mechanism only. in analogy to the experiments with toluene addition, we attempted to derive best-fit simulations by adjusting ktotal and by keeping the branching ratios BR1, BR2, and BR3 arising from the Yasunaga et al.13 model. As shown in Figs. 1 and 2, CH3CHO is one of the products of DEE pyrolysis. However, by adjusting ktotal only, it was not possible to fit the measured temperature dependence of the CH3CHO concentrations and since in these experiments no radical inhibitor was present, the simulations of product compositions also depend on the kinetics of bimolecular reactions.

Fig. 5: Local CH3CHO sensitivity analysis for an initial mole fraction of xDEE = 500 ppm in Ar. The local CH3CHO sensitivity SCH3CHO is defined as SCH3CHO = dxCH3CHO/dki. With: R5 (DEE + H = C2H5OCH2CH2 + H2), R1 (DEE = C2H5OH + C2H4), R7 (CH3CHO + H = CH3CO + H2), R8 (C2H4 + H + M = C2H5 + M), R9 (C2H5OH + H = SC2H4OH + H2), R10 (C3H8 + M = CH3 + C2H5 + M), R11 (CH3 + CH2O = C2H5O), R12 (CH3CHO + M = CH3 + HCO + M), R2 (DEE = C2H5O + C2H5), R6 (DEE + H = C2H5OCHCH3 + H2), R13 (DEE + CH3 = C2H5OCHCH3 + CH4), R14 (C2H5OCH2CH2 = C2H4 + C2H5O).



Page 20 of 46

Figure 5 shows a sensitivity analysis for the CH3CHO concentration, which indicates that the extent of CH3CHO formation strongly depends on the rate constants of the DEE + H abstraction reactions. By adjusting ktotal only, the simulations result in too high CH3CHO concentrations compared to the measurements. Another alternative for improving the performance of the mechanism would be to adjust the branching ratios between the bond fissions (2) and (3). This would, however, require to modify BR2 and BR3 in such a way that BR3 would be even larger than BR2. Since this would be a clear contradiction to theory and would also lead to contradictions to the DEE experiments with toluene addition, this approach was not further pursued. Instead, based on the findings of the sensitivity analysis, we increased the rate constant for H-atom abstraction from a primary H atom (5). C2H5OC2H5 + H → C2H5OCH2CH2 + H2

(5)

By increasing k5 by a factor of 1.8 and by adjusting ktotal, it is possible to fit all measured product compositions very well, without any contradiction to the DEE experiments with toluene addition. The other bimolecular reaction (6) between DEE and H atoms refers to the abstraction of a secondary H atom: C2H5OC2H5 + H → C2H5OCHCH3 + H2

(6)

Usually, H-atom abstractions from secondary C–H bonds are energetically preferred over those from primary C–H. Even by increasing k5 by a factor of 1.8, k6 is still larger than k5: At 1300 K, k6 ≈ 1.9k5, and at T = 1500 K, k6 ≈ 1.5k5. We think that adjusting k5 by a factor of 1.8 is plausible since at higher temperatures (T > 1000 K), energetic barrier heights of H-atom abstractions become less important than statistics: In case of DEE, there are 6 primary and four secondary C– H bonds and at temperatures above 1500 K, the total H-atom abstraction rate constant from primary C-H bonds can outweigh the total H-atom abstraction rate constant from secondary C– H bonds. This has been shown previously for instance in studies on H-atom abstractions of


Page 21 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


propane. Transition-state theory calculations on H + C3H8 abstractions that were in very good agreement with directly measured rate constant data from shock-tube experiments with H and D-ARAS36, indicate that at T = 1600 K, the calculated branching ratio of abstraction from primary C–H bonds is ≈ 0.52 and at 2000 K, this branching fraction increases to 0.56. For OH + C3H8 abstractions, at 2000 K the calculated branching ratios for abstraction from primary C–H bonds are near the statistically expected value of 0.637. Table S4 in the supporting material shows original and adjusted rate constant values of k5 and k6 used in modeling the present single-pulse shock-tube data. Therefore, adjusting k5 by a factor of 1.8 is regarded as a reasonable measure to simulate all experimentally determined product yields. Figure 6 shows a comparison between measured product compositions from GC/MS experiments without toluene addition and the corresponding calculated yields. By adjusting ktotal and k5, it was possible to gain very good agreement between measured yields and corresponding simulations. As described before: The branching ratios BR1, BR2, and BR3, were not adjusted. ktotal values derived from the measurements and the related T5 and p5 conditions of the GC/MS experiments without toluene are listed in table 2.



Page 22 of 46

Fig. 6: Product yields derived from single-pulse shock-tube experiments with GC/MS compared with simulations as a function of temperature. All simulations used the Yasunaga et al.13 mechanism applying the ktotal value obtained in this work. The product compositions from single-pulse shock-tube measurements for different mixtures are normalized to the initial concentration of DEE. Solid symbols: 500 ppm DEE, 500 ppm Kr in Ar. Open symbols: 200 ppm DEE, 200 ppm Kr in Ar. Crossed symbols: 534 ppm DEE, 500 ppm Kr in Ar. Solid line: simulated DEE concentration, dashed lines: simulations of the corresponding products. Table 2: Experimental conditions and ktotal data from the single-pulse GC/MS experiments without toluene addition. T5 and p5 refer to the conditions after passing of the reflected shock-wave. T5 / K

p5 / bar

ktotal / s−1

x0,DEE = 500 ppm, xKr = 500 ppm in Ne 1076 1117 1147 1189 1195 1223 1241 1276

2.50 2.49 2.42 2.37 2.29 2.28 2.23 2.22


12 31 80 171 282 401 813 528

Page 23 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



2.37 2.22 2.49 2.23 2.29 2.28 2.42 2.50

8 21 34 47 193 320 314 567


1.37 1.36 1.29 1.45 1.35 1.22 1.27 1.33

23 86 92 81 169 375 345 277

4.2 Time-resolved multi-species concentration measurements Simultaneous time-resolved concentration measurements of multiple species were performed between 1180–1470 K and 1.3–1.9 bar in the shock tube with HRR-TOF-MS detection. Figure 7 shows two mass spectra of one particular experiment. The data of the shown experiment is split into the region representing initial conditions at T1 = 295 K and p1 = 55 mbar (top-spectrum) and the region representing experimental conditions at T5 = 1391 K, and p5 = 1.6 bar (bottom spectrum). For better visualization, the top-spectrum was averaged over time of 0.26 ms and the bottom spectrum for 1.34 ms. With this procedure, we can easily attain qualitative information about the decomposition of DEE and the subsequent product formation by comparing these two mass spectra. The electron-impact ionization leads to a fragmentation of molecules. In case of DEE, not only the parent peak at m/z = 74 (C2H5OC2H5+) is detected. There are also stronger signals of fragments at m/z = 59 (C2H5OCH2+), 45 (C2H5O+), 31 (CH3O+) and many smaller signals are distributed over the entire mass spectrum.



The main peak (m/z = 31) is in a range where signals of oxygenated hydrocarbons can also be localized and thus overlap with the main peak. Therefore, the evaluation of the time dependent concentration of DEE was carried out with the signal at m/z = 59, so that a superposition with other species could be excluded. The signal multiplet at m/z = 78–86, with the main peak at m/z = 84 belong to the inert gas Kr (internal standard). In comparison, the mass spectrum behind the reflected shock wave (bottom spectrum) shows the signals of the products C2H4 and C2H6 at m/z = 26 (C2H2+), and of CH3CHO at m/z = 44 (CH2CHO+) formed during the decomposition of DEE. The signals of C2H4 and C2H6 are superimposed at m/z = 26 and it was not possible to clearly separate the signals of these hydrocarbon species. Therefore, the concentration–time profiles of C2H4 and C2H6 (see Fig. 8) are the summation of C2H4 and C2H6. This procedure can be applied because both species have very similar calibration parameters at m/z = 26 of 0.29750 and 0.29619, respectively. The signal of C2H6 at m/z = 30 is overlapping with the parent peak of CH2O. The signals at m/z = 27 and 28 are overlapping with signals of DEE and CO. The evaluation of the concentration–time profiles of CH3CHO was based on the parent peak at m/z = 44, since the main peak m/z = 29 with the highest intensity was superimposed by signals of species CH2O, DEE, C2H6, and C2H5OH. CO at m/z = 28 could not be determined due to the strong overlap of the fragmentation peaks of CH2O, C2H4 and C2H6. CH2O could not be detected because the signals at m/z = 28, 29, and 30 are overlapping with other species, see above. The calibration parameters of DEE and different products (C2H4, C2H6, CH3CHO) were determined in separate calibration experiments. Concentration–time profiles of DEE, CH3CHO, and C2H4 + C2H6 are depicted in Fig. 8. All concentrations were determined relative to the internal standard Kr, which was included both in the reactant and in calibration mixtures. Thus, mole fractions xi in mol% could be determined.

(

𝑥𝑖 = 𝑥i,products

𝑥Kr,educts

)=𝑥

𝑥Kr,products

(

)

𝑛total,products i,products 𝑛total,educts

(Eq. 4)


Page 24 of 46

Page 25 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 7: Mass spectra from an experiment with an initial mixture of 0.93% DEE, and 0.7% Kr in Ne representing pre-shock conditions (blue line; T1 = 295 K, p1 = 55 mbar, signal averaged for 0.26 ms) and post-shock conditions (red line, T5 = 1391 K, p5 = 1.6 bar, signal averaged for 1.34 ms and inverted).

Fig. 8: Post-shock concentration–time profiles of DEE, CH3CHO, and the summation of C2H4 and C2H6 from HRR-TOF-MS measurements. T5 = 1391 K, p5 = 1.4 bar, mixture: 0.93% DEE, and 0.7% Kr in Ne. xi represents mole fractions.

ktotal rate constant data of DEE decomposition were derived by modeling the measured DEEconcentration profiles with the Yasunaga et al.13 mechanism based on the measured pressure profiles of pure Ne. The thermal decomposition of DEE consumes heat, which can cause



temperature variation during the experiment. This effect is more pronounced with larger initial DEE reactant concentrations. Simulations with the Yasunaga et al.13 mechanism with accurate thermochemistry reflect these temperature variation. Figure 9 shows measured DEE as well as CH3CHO and (C2H4 + C2H6) concentration–time profiles and the corresponding best-fit simulations. The simulations were performed by adjusting ktotal only and the rate constants and the experimental conditions (T5 and p5) are listed in table 3. The brute-force sensitivity analysis for DEE illustrates how the simulated depletion of DEE is affected by increasing and decreasing the best fit ktotal rate constant by 2.0 and 0.5, respectively.

Fig. 9: Left: Concentration–time profiles of DEE (T5 = 1391 K, p5 = 1.6 bar, x0,DEE = 0.93%). The best-fit simulation was obtained by using the Yasunaga et al.13 mechanism (red solid curve). The blue dashed line and the green dotted line represent a brute-force sensitivity analysis, in which the best-fit rate constant ktotal was changed by factors of 0.5 and 2, respectively; Right: Experimental and simulated concentration– time profiles of DEE, CH3CHO, and the sum of C2H4 and C2H6 for the same experiment.


Page 26 of 46

Page 27 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3: Rate constants and experimental conditions (T5 and p5) of the thermal decomposition experiments of DEE measured with HRR-TOF-MS. T5 and p5 refer to the thermodynamic state behind reflected shock-waves. T5 / K

p5 / bar

ktotal / s–1

x0,DEE = 0.785%, xKr = 0.7% in Ne 1182 1230 1239 1266 1325 1378 1390 1414 1467

1.65 1.65 1.55 1.61 1.47 1.43 1.30 1.34 1.27

120 327 244 660 2422 5925 7191 10497 23225

x0,DEE = 0.93%, xKr = 0.7% in Ne 1182 1198 1204 1217 1240 1276 1284 1286 1334 1347 1351 1391

1.91 1.90 1.86 1.89 1.83 1.80 1.69 1.63 1.59 1.69 1.59 1.64

150 211 144 314 249 997 1157 1801 2833 2477 5681 7307

4.3 Time-resolved H-atom concentration H-atom concentrations were measured as a function of time with H-ARAS. Because of its high sensitivity, very low reactant concentrations, i.e., initial mole fractions lower than 1 ppm can be used. Therefore, the effects of exo- or endothermicities during the gas-phase reactions as well as the impact of consecutive reactions are strongly suppressed. As a consequence, the H-ARAS experiments can be modeled with a reduced reaction mechanism containing only the most



Page 28 of 46

important elementary reactions. The mechanism used to model the H-ARAS experiments is presented in table 4 and contains 23 elementary reactions. Table 4: Elementary kinetics reaction mechanism for the simulation of the time-dependent H-atomconcentration profiles obtained via H-ARAS during the decomposition of DEE. All Arrhenius equations given in the table are valid over the 1000–1800 K temperature range. Reaction C2H5OC2H5 = C2H5OH + C2H4

Rate constant To be adjusted

Reference See text and ref. 13

C2H5OC2H5 = C2H5 + C2H5O

To be fitted

See text

C2H5OC2H5 = CH3 + CH3CH2OCH2

To be fitted

See text

C2H5O = CH3 + CH2O

k(T) = 1.321020 T−2.018 exp(-10442 K/T) s−1

[16]

C2H5O = H + CH3CHO

k(T) = 5.431020 T−0.687 exp(-11187 K/T) s−1

[16]

CH3CH2OCH2 = C2H5 + CH2O

k(T) = 4.131015 T−0.880 exp(-8203 K/T) s−1

[13] [13]

C2H4 + H (+M) = C2H5 (+M)

k∞(T) = 1.08×1012 T0.454 exp(-917 K/T) s–1 k0(T) = 1.201042 T–7.62 exp(3508 K/T) cm3mol–1s–1  = 0.975/T*** = 210/T* = 984/T** = 4374

[13]

CO + H2 (+M) = CH2O (+M)

k∞(T) = 4.30×107 T1.50 exp(-40059 K/T) s–1 k0(T) = 5.071027 T–3.42 exp(42448 K/T) cm3mol–1s–1  = 0.932/T*** = 197/T* = 1540/T** = 10300

[13]

HCO + H (+M) = CH2O (+M)

k∞(T) = 1.09×1012 T0.48 exp(131 K/T) s–1 k0(T) = 1.351024 T–2.57 exp(717 K/T) cm3mol–1s–1  = 0.782/T*** = 271/T* = 2755/T** = 6570

CH3CHO = CH3 + HCO

k(T) = 6.001014 exp(-39757 K/T) s-1

[13]

HCO + M = H + CO + M

k(T) = 4.751011 T0.66 exp(-7485 K/T) cm3mol–1s–1

[13] [38]

C2H5OH = C2H4 + H2O

PLOG / 0.001 k0.001(T) = 3.41×1059 T−14.20 exp(-42108 K/T) s–1 PLOG / 0.010 k0.010(T) = 2.62×1057 T−13.30 exp(-42908 K/T) s–1 PLOG / 0.100 k0.100(T) = 1.65×1052 T−11.50 exp(-42648 K/T) s–1 PLOG / 1.000 k1.000(T) = 5.23×1043 T−8.90 exp(-41018 K/T) s–1 PLOG / 10.00 k10.00(T) = 4.59×1032 T−5.60 exp(-38278 K/T) s–1 PLOG / 100.0 k100.0(T) = 3.84×1020 T−2.06 exp(-34958 K/T) s–1

[38]

C2H5OH = CH3 + CH2OH

PLOG / 0.001 k0.001(T) = 1.20×1054 T−12.90 exp(-50328 K/T) s–1 PLOG / 0.010 k0.010(T) = 5.18×1059 T−14.00 exp(-50278 K/T) s–1 PLOG / 0.100 k0.100(T) = 1.62×1066 T−15.30 exp(-53038 K/T) s–1 PLOG / 1.000 k1.000(T) = 5.55×1064 T−14.50 exp(-53436 K/T) s–1


Page 29 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


PLOG / 10.00 k10.00(T) = 1.55×1058 T−12.30 exp(-53227 K/T) s–1 PLOG / 100.0 k100.0(T) = 1.78×1047 T−8.96 exp(-50858 K/T) s–1 [38]

C2H5OH = C2H5 + OH

PLOG / 0.001 k0.001(T) = 8.10×1046 T−11.30 exp(-55887 K/T) s–1 PLOG / 0.010 k0.010(T) = 1.86×1056 T−13.50 exp(-53967 K/T) s–1 PLOG / 0.100 k0.100(T) = 4.65×1063 T−15.00 exp(-55167 K/T) s–1 PLOG / 1.000 k1.000(T) = 4.46×1065 T−14.90 exp(-56537 K/T) s–1 PLOG / 10.00 k10.00(T) = 2.79×1061 T−13.40 exp(-56907 K/T) s–1 PLOG / 100.0 k100.0(T) = 6.17×1051 T−10.30 exp(-55327 K/T) s–1

[38]

CH2O + H (+M) = CH2OH (+M)

k∞(T) = 5.40×1011 T0.454 exp(−1812 K/T) s–1 k0(T) = 1.271032 T–4.82 exp(3286 K/T) cm3mol–1s–1  = 0.719/T*** = 103/T* = 1291/T** = 4160

C2H6(+M) = CH3 + CH3 (+M)

k∞ = 8.031028 T–3.52 exp(47983 K/T) s–1 k0 =2.801072 T–15.10 exp(54222 K/T) cm3mol–1s–1 α = 0.21/T*** = 1.00×10–30/T* = 1.00×1030

[39]

CH3 + CH3 = 2H + C2H4

k(T) = 3.21013 exp(-7395 K/T) cm3mol–1s–1

[40]

CH3 + H (+M) = CH4 (+M)

[41]

C2H6 + CH3 = C2H5 + CH4

k∞ = 7.2 × 1013 T0.19 exp(T/25200 K) cm3mol1s1 k0 = [M] 2.31021 exp[(T/21.22 K)0.5] cm6 mol–2s–1 Fc = 0.262 + [(T  2950 K)/6100 K]2 F(x)=1−(1 − Fc) exp(−[log(1.5x)/N]2/N*)a) k(T) = 34.5 T3.44 exp(-5237 K/T) cm3mol–1s–1

C2H6 + H = C2H5 + H2

k(T) = 8553 T3.06 exp(-2559 K/T) cm3mol–1s–1

[36]

CH4 + H = CH3 + H2

k(T) = 1.81014 exp(-6945 K/T) cm3mol–1s–1

[43]

CH3 + H = CH2 + H2

k(T) = 6.01013 exp(-7610 K/T) cm3mol–1s–1

[44]

H2 + M = H + H + M

k(T) = 2.21014 exp(48352 K/T) cm3mol–1s–1

[44]

a)

[42]

x = k0/k∞; N = 0.75−1.27 × log(Fc); N* = 2 for log(1.5x) > 0; N* = 2 × [1 − 0.15 log(1.5x)] for log(1.5x) < 0.

For the analysis of H-ARAS experiments, only unimolecular reactions will be discussed, but one might wonder if, once H atoms are formed, the [H](t) profile can be also affected by the reaction of H atoms with DEE. H-atom abstraction from a secondary C-H bond (6) yields C2H5OCHCH3 radicals, which decompose to CH3CHO molecules and C2H5 radicals, thereby rapidly regenerating H atoms through C2H5 → C2H4 + H. Therefore, the present H-ARAS experiments are not sensitive to H abstraction (6), since H atoms consumed by reaction (6) are rapidly regenerated. H abstraction from a primary C–H bond (reaction 5), could potentially influence [H](t), since C2H5OCH2CH2 radicals decompose to C2H5O and C2H4. In this case, H atoms consumed by reaction (5) are not regenerated. However, due to the highly diluted conditions, i.e., initial



reactant mole fractions near 0.4 ppm, the influence of bimolecular reactions is strongly suppressed. Even by considering H + DEE H-atom abstraction channels and corresponding decomposition processes of primary and secondary DEE radicals with Arrhenius parameters from the Yasunaga et al. mechanism, the best fit simulations do not change. Therefore, H + DEE reactions are not listed in the table 4 mechanism. In principle, the present H-ARAS experiments allow to directly determine the sum of bondfission rate constants k2+3 (k2+3 = k2 + k3). The evaluation of the H-ARAS experiments, however, strongly depends on the branching ratios between DEE bond fissions (2) and (3) on the one side and C2H5OH elimination from DEE (1) on the other side. For consistency with the GC/MS and HRR-TOF-MS experiments, the temperature- and pressure-dependent branching ratios BR1, BR2, and BR3 were not changed in comparison to the Yasunaga et al.13 mechanism. In the modeling procedure, k2+3 was adjusted for each experiment until the simulated H-atom concentration profile matched the measured H-atom profile. Keeping the branching ratios as provided in the Yasunaga et al.13 mechanism, adjusting k2+3 during modeling also requires to simultaneously adjust k1, and hence, also to modify ktotal. Therefore, relying on the Yasunaga et al.13 branching ratios, the H-ARAS experiments also allowed to extract an estimate for ktotal and to compare it with the results of the GC/MS and HRR-TOF-MS experiments.


Page 30 of 46

Page 31 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 10: Left: Measured H-atom concentration–time profile at T5 = 1384 K and p5 = 1.37 bar with x0,DEE = 0.35 ppm, compared with simulations using the table 4 mechanism. The best-fit simulation is depicted by the red solid line. The green dashed curves are discussed in the text. Right: Local H-atom sensitivity (SH = dxH/dki) is analyzed for the table 4 mechanism and the derived k2+3 value. For the branching ratios BR1, BR2, and BR3 values from the Yasunaga et al.13 mechanism are used.

Figure 10 shows a measured H-atom-concentrationtime [H](t) profile and the corresponding best-fit simulation for a mixture with an initial DEE mole fraction x0,DEE = 0.35 ppm. Due to the large sensitivity of H-ARAS, even small variations in x0,DEE affect the simulated [H](t) curves at later observation times (in Fig. 9: t > 600 µs). But because of the low reactant mole fraction and thus operation under highly diluted conditions, the exact DEE mole fraction does not influence the measured unimolecular kinetics, which controls the raise of the experimental [H](t) profile at earlier observation up to 400 µs. To get best-fit profiles over the entire time range, x0,DEE was varied within ±0.03 ppm along with the overall bond dissociation rate constant k2+3 and the total DEE decomposition rate constant ktotal. The red solid curve in Fig. 9 represents the best-fit simulation with k2+3 = 4800 s1. The green dashed curves represent the results of a brute-force sensitivity analysis, in which the best fit for k2+3 was increased and decreased by a factor of 2. This simple analysis illustrates that the [H](t) measurements are strongly influenced by the kinetics of the DEE bond-fission channels. The local H-atom sensitivity analysis in Fig. 10 indicates that the reactions (1) and (2) have the largest impact on [H](t). The other DEE C–C bond fission reaction (3) has only minor influence on [H](t), because of its low branching ratio BR3, in comparison to BR1 and BR2. As outlined in section 4.1, even at 1500 K, BR3 is not



Page 32 of 46

exceeding 6%. Besides the initial DEE decomposition channels, few unimolecular secondary reactions show an impact on the H-atom formation. In particular, the two C2H5O dissociation reactions (4a and 4b) have a significant influence on the generation of H atoms. At longer reaction times (approximately at t > 500 µs), also the C–C bond fission in C2H5OH, C2H5OH = CH3 + CH2OH, slightly contributes to [H](t), because CH2OH radicals decompose to CH2O + H. Table 5 lists the derived best-fit overall bond dissociation rate constants k2+3, the estimated rate constants ktotal, and the experimental conditions (T5 and p5) of the H-ARAS experiments. Table 5: Rate constants and experimental conditions (T5 and p5) of the thermal decomposition of DEE measured via H-ARAS.

T5 / K

p5 / bar

k2 + k3 / s–1

ktotal / s–1

x0,DEE = 0.35±0.03 ppm in Ar 1321 1353 1384 1415 1427 1497

1.34 1.36 1.37 1.30 1.35 1.37

1.4103 3.4103 4.8103 1.0104 1.3104 3.8104

2493 5940 8242 17023 21880 61672

x0,DEE = 0.42±0.03 ppm in Ar 1299 1341 1349 1366 1368 1393 1491 1505

1.18 1.27 1.29 1.20 1.33 1.28 1.34 1.35

1.4103 2.2103 3.0103 4.1103 3.8103 6.5103 2.8104 4.2104

2581 3911 5296 7253 6609 11220 45686 68041

Figure 11 shows the comparison between experimentally based k2+3 rate constant data and the k2+3 data as provided by the Yasunaga et al.13 mechanism along with theoretical predictions for


Page 33 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


k2+3 at p = 1.0 bar. The experimentally-determined bond-dissociation rate constants k2+3 can be reproduced very well by the following Arrhenius equation: k2+3(T) = 1014.43±0.33 exp(283.27±8.78 kJ mol1/RT) s1.

(Eq. 5)

Fig. 11: Measured k2+3 rate constants (symbols) related two-parameter Arrhenius fit (dashed orange curve). The red dotted and the solid green curves refer to k2+3 provided by Yasunaga et al.13 and the present theoretical prediction for k2+3 at p = 1.0 bar, respectively.

The uncertainties of the k2+3 data were estimated to be ±38%. For the H-ARAS data, the primary source of experimental error lies in uncertainties of determining post-reflected-shock temperatures due to uncertainties in measuring the incident shock-wave velocities. Concerning temperatures, the uncertainties are estimated to be ±1%. For H-ARAS as well as the other experimental methods, temperature errors of ±1% result in rate constant deviations of up to ±26%. For the experiments with DEE, the simulations of the H-ARAS data are potentially affected by the ratio of secondary unimolecular C2H5O dissociation channels (4a) and (4b). Assuming uncertainties in the rate constants k4a and k4b by a factor of 2 or 0.5 leads to deviations of k2+3 by around ±20% in each case.



Uncertainties in initial DEE reactant mole fractions are in the range of ±0.03 ppm. However, these uncertainties influence the plateau of the H-atom density, which is reached at longer reaction times, but not the rate-constant values being necessary to fit the increase of the measured H-atom profiles. Based on the root-sum-square method, the uncertainty for H-ARAS experiments is estimated to be (0.262 + 0.22 + 0.22)0.5, i.e., the combined uncertainty is approximately ±38%. 4.4 Comparison of experimental data and theory Figure 12 depicts all experimentally derived ktotal rate constants including those extracted from the H-ARAS measurements. The rate constants derived from the three independent measurements (GC/MS, HRR-TOF-MS, H-ARAS) agree well among each other with deviations below ±40%.

Fig. 12: Comparison of measured high-temperature ktotal (symbols) and the ktotal rate constants of Yasunaga et al.13 (green dashed line) and Miller et al.12 (black solid and black dashed curves). The cyan solid curve refers to the RRKM/ME-calculated ktotal data at 2.0 bar.


Page 34 of 46

Page 35 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The rate constants ktotal derived from GC/MS and HRR-TOF-MS measurements can be well reproduced by the following Arrhenius equation: ktotal(T) = 1012.81±0.22 exp(–240.27±5.11 kJ mol1/RT) s1.

(Eq. 6)

The estimated overall uncertainty of ktotal is ±38%. With respect to reflected shock-wave temperatures, uncertainties of ±1% result in ktotal deviations of up to ±23%. In case of the GC/MS experiments, uncertainties of initial DEE mole fractions of ±5% can lead to deviations of ktotal by ca. ±5%. We assumed deviations of the initial DEE mole fractions of ±5%, and with the Yasunaga et al.13 mechanism we tested how much the best-fit rate constant ktotal needed to be adjusted to obtain the measured DEE mole fraction. The modeling of GC/MS experiments is also influenced by the rate constants of the two possible H-atom abstraction reactions (5) and (6). Uncertainties in k5 by factors of 2 and 0.5 lead to errors in ktotal of ±10%, whereas uncertainties in k6 by factors of 2 and 0.5 yield ktotal errors of up to ±25%. In a similar way, also uncertainties in the HRR-TOFMS experiments can be evaluated. However, in case of HRR-TOF-MS experiments, it is not possible to quantify the uncertainty of ktotal assuming ±5% uncertainties in x0,DEE. Simulated [DEE](t) profiles, in which x0,DEE are varied by ±5%, are within the scatter of the measured HRRTOF-MS signals. Analog to GC/MS, also simulations of HRR-TOF-MS measurements are influenced by the rate constant values used for k5 and k6. Assuming again uncertainties in k5 and k6 by factors of 2 and 0.5 results in ktotal errors of ±10% and ±16%. Applying the root-sum-square method, we obtain (0.232 + 0.052 + 0.12 + 0.252)0.5 ≈ 35% for GC/MS and (0.232 + 0.12 + 0.162)0.5 ≈ 30% for HRR-TOF-MS experiments. The estimated uncertainties of H-ARAS experiments were approximately 38%. Altogether, the present ktotal data are in excellent agreement with the experimentally-based ktotal provided by Yasunaga et al.13, i.e., ktotal-this work ≈ 1.4  ktotal-Yasunaga et al. (for 1054–1505 K). Regarding the Miller et al.12 data, we observe discrepancies at lower temperatures, i.e., between 1000 and 1100 K. At T = 1100 K, ktotal-this work ≈ 4.0  ktotal-Miller et al.. However, extrapolating the ktotal data from Miller et al.12 to higher temperatures lead to lower variations. At temperatures between 1300 and 1500 K, the Miller et al. ktotal data match the



present ktotal estimates derived from the present H-ARAS experiments, i.e., the deviations are lower than a factor of two. One should keep in mind that Miller et al.12 evaluated their highpressure single-pulse GC/MS data by assuming a simple first-order kinetics in order to estimate the thermal stability of DEE at a certain temperature range. At the time of their publication, no detailed DEE mechanism has been available and it was not the primary purpose of their work to investigate DEE pyrolysis in detail. We also conducted a theoretical analysis on DEE decomposition and attempted to derive data for ktotal(T,p) and to predict branching ratios. Figure 12 also includes the present RRKM/ME prediction for ktotal at p = 2.0 bar. Due to the high bond dissociation energies of C–H bonds, C–H bond fissions have not been considered in the RRKM/ME analysis. At lower temperatures, i.e., between 1000 and 1180 K, the experimental data are around three to four times larger than the calculated values. But at temperatures above 1200 K, the calculation for ktotal agrees quite well with measured ktotal data. Between 1200 and 1300 K, the deviation between ktotal,exp. and ktotal,theory is within a factor of 2 and above 1300 K, theoretical ktotal values are within less than 40% of experimental ktotal data. This is also confirmed by inspection of Fig. 11, which contains a comparison between calculated k2+3 data at p = 1.0 bar and H-ARAS measured k2+3 values. Figure 13 shows the potential energy surface (PES) of DEE decomposition channels. Besides C2H5OH elimination, one could also envision a four-center elimination forming CH3CHO and C2H6 and another four-center H2 elimination, but we did not obtain converged transition state structures for these potentially occurring reactions. Therefore the PES shown in Fig. 13 includes only one molecular channel. According to the PES, C2H5OH elimination is expected to be the major unimolecular reaction at lower temperatures. Figure 14 shows RRKM/ME-predicted branching ratios BR1, BR2, and BR3 at 10, 100, and 1000 mbar and branching ratios BR1 to BR3 from the Yasunaga et al. mechanism at p = 1 bar.


Page 36 of 46

Page 37 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 13: Potential-energy surface of DEE decomposition. For details of theory: See text (section 3). The energies are relative to the reactant and include zero-point-energy correction.

Fig. 14: Calculated branching ratios BR1, BR2, and BR3 based on the present RRKM/ME analysis for p = 10 mbar (top left), 100 mbar (top right), 1.0 bar (bottom left) and branching ratios based on Yasunaga et al. mechanism at p = 1.0 bar (bottom right).



According to Fig. 14, one can note that at p = 10 , 100, and 1000 mbar, BR1 is the primary channel until T ≈ 1440, 1145, and 1075 K, respectively, and above these temperatures, the bond-fission channels are predicted to prevail over C2H5OH elimination. RRKM/ME-predicted branching ratios at p ≥ 1.0 bar do not substantially differ anymore among each other. According to the Yasunaga et al.13 mechanism, at 1.0 bar, C2H5OH elimination is the major channel up to 1220 K. In addition, the C–C bond fission (reaction 3) has only a minor contribution to the overall DEE decomposition. Therefore, the present predictions for branching ratios and those that can be extracted from the Yasunaga et al.13 mechanism contradict each other. When we apply the present RRKM/ME-predicted branching ratios in the Yasunaga et al.13 mechanism to simulate the present GC/MS experiments, the mechanism predicts C2H5OH mole fractions that are too low in comparison to the measured C2H5OH mole fractions. This is illustrated in Fig. 15.

Fig. 15: Measured mole fractions from GC/MS experiments with toluene addition (see Fig. 4) as a function of temperature. The dashed colored curves (green, red, magenta, and orange) refer to simulations using the branching ratios BR1–BR3 from the DEE/toluene mechanism.13-14, 24 The blue solid curve (top left; simulation of DEE) and the blue dotted curves represent simulated species concentrations using the RRKM/ME-predicted branching ratios.


Page 38 of 46

Page 39 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 15 shows that by using the branching ratio of the RRKM/ME analysis, most species profiles could be modeled equally well. In case of CH4, we can see even a slight improvement. For all simulations, in which we used RRKM/ME-based branching ratios from this work, it was necessary to increase ktotal (Eq. 6) by 1.5 in order to reproduce measured DEE decomposition. Deviations for C2H5OH are too large to be within the error of the GC/MS measurements. The prediction of too low C2H5OH mole fractions cannot be avoided by adjusting rate constants of other unimolecular secondary reactions without being in contradiction to measurements of other species mole fractions such as for example CH3CHO. There might be a possibility that C2H5OH formation and consumption can be subject of other reaction paths that are not considered in the Yasunaga et al.13 mechanism. However, the evidence so far is that the Yasunaga et al.13 DEE base-mechanism is working very well in describing the high-temperature gas-phase chemistry of DEE pyrolysis. Based on the comparison between experiment and theory, it is preferable to rely on the BR1–BR3 branching ratios from the Yasunaga et al.13 model. However, the present predictions for ktotal(T,p) agree well with the experimental data from this work and in order to derive expressions for k1(T,p), k2(T,p), and k3(T,p) that can be used for combustion modeling at temperatures above 1100 K, we extracted pressure- and temperature-dependent rate constants k1, k2, and k3 by multiplying our RRKM/ME-based ktotal(T,p) data with the corresponding predictions for BR1(T,p), BR2(T,p), and BR3(T,p) from the Yasunaga et al.13 model. The resulting rate constant data k1(T,p), k2(T,p), and k3(T,p) can be described by the Arrhenius expressions that are summarized in table 6. Table 6: Three-parameter fits, k(T) = A  Tn  exp(-Ea/RT), for the k1, k2, and k3 rate constants obtained from multiplying RRKM/ME predictions for ktotal(T,p) with BR1(T,p), BR2(T,p), and BR3(T,p) from the Yasunaga et al.13 mechanism. These modified Arrhenius fits are recommended to be used for combustion modeling over the 1100–1800 K temperature range.

k1(T,p); C2H5OC2H5 = C2H5OH + C2H4 p / bar 110–6 110–5

A / s–1 8.192  1081 3.470  1088

n –21.425 –22.901


Ea/(kJ mol−1) 378.305 411.665


110–4 110–3 0.01 0.1 1.0 10.0 100.0 1000.0 10000.0

9.587  1093 8.385  1098 1.485  10103 1.153  1098 1.562  1079 3.208  1043 6.182  1019 3.328  1021 1.766  1025

–24.031 –25.014 –25.808 –23.997 –18.382 –8.172 –1.469 –1.984 –3.052

Page 40 of 46

444.380 477.952 510.753 515.578 477.178 380.315 310.788 314.507 324.575

k2(T,p); C2H5OC2H5 = C2H5 + C2H5O 110–6 110–5 110–4 110–3 0.01 0.1 1.0 10.0 100.0 1000.0 10000.0

4.638  1071 3.554  1095 1.278  10107 5.231  1093 7.239  1093 2.679  1094 5.549  1092 4.971  1083 4.323  1060 7.923  1042 4.379  1038

–18.177 –24.550 –27.420 –23.305 –23.305 –22.775 –21.924 –19.028 –12.304 –7.212 –5.994

421.019 498.247 541.824 507.568 507.568 528.815 539.442 530.744 474.844 427.276 415.590

k3(T,p); C2H5OC2H5 = CH3 + C2H5OCH2 110–6 110–5 110–4 110–3 0.01 0.1 1.0 10.0 100.0 1000.0 10000.0

1.221  1067 5.155  1090 3.488  10101 1.950  1086 1.521  1080 2.346  1097 1.736  1094 7.152  1077 1.440  1062 1.246  1044 7.306  1036

–16.982 –23.286 –25.960 –21.338 –19.299 –23.746 –22.467 –17.498 –12.828 –7.613 –5.542


431.740 507.739 548.204 506.295 491.574 555.176 561.944 530.356 497.302 450.599 430.849

Page 41 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5. Conclusions In this study, we investigated the thermal decomposition of DEE with two shock tubes and a set of three detection techniques and determined high-temperature rate constants of the total thermal decomposition of DEE. Thermal decomposition of DEE is initiated by three unimolecular reactions: C2H5OC2H5 → C2H5OH + C2H4 (reaction 1), C2H5OC2H5 → C2H5 + C2H5O (reaction 2), and C2H5OC2H5 → CH3 + C2H5OCH2 (reaction 3). The depletion of DEE and the formation of major products (i.e., C2H5OH, CH3CHO, CH4, C2H4, and C2H6) were measured: (i) as a function of temperature in a single-pulse shock tube by GC/MS (1054–1308 K and 1.2–2.5 bar) and (ii) as a function of time by HRR-TOF-MS at 1195–1424 K and 1.3–1.9 bar. The rate constants ktotal for DEE decomposition were derived from the GC/MS and the HRR-TOF-MS experiments using simulations based on the Yasunaga et al.13 mechanism. The ktotal rate constants are the sum of the individual rate constants k1, k2, and k3: ktotal = k1 + k2 + k3. In some GC/MS experiments, toluene was added to the reactant gas mixtures to suppress bimolecular reactions. For modeling these experiments, the Yasunaga DEE mechanism was merged with a detailed toluene reaction mechanism. With the Arrhenius equation of ktotal from this study and the branching ratios of the initial unimolecular DEE channels from the Yasunaga et al.13 mechanism, it was possible to reproduce the product compositions measured by GC/MS and the time-resolved speciesconcentration profiles measured by HRR-TOF-MS. The quasi-instantaneous dissociation of secondary radicals, the C–O and C–C bond fissions (reactions (2) and (3)) lead to H-atom formation. Therefore, ARAS was used for time-resolved Hatom measurements ([H](t)). Modeling experimental [H](t) profiles made it possible to obtain quantitative estimates for the overall bond-dissociation rate constant k2+3 = k2 + k3. Relying again on the branching ratios for C2H5OH elimination (reaction (1)) and bond fissions (reactions (2) and (3)) provided by Yasunaga et al.13, modeling the H-ARAS data yielded k2+3 estimates that agree very well with the k2+3 values given by Yasunaga et al.13.



In an attempt to rationalize ktotal(p,T), a RRKM/ME analysis was carried out, using properties ab initio calculated at the CCSD(T)/aug-cc-pvtz//B3LYP/aug-cc-pvtz theory level for C2H5OH elimination and CASPT2/aug-cc-pvtz//B3LYP/aug-cc-pvtz theory level for C–C- and C–O-bond fissions. At T ≥ 1200 K, the predictions for ktotal agreed very well with the experimental data. The theory-based branching rations for the three initial DEE decomposition reactions (BR1 = k1/ktotal, BR2 = k2/ktotal, and BR3 = k3/ktotal), however, were in conflict with the measurements. The RRKM/ME analysis predicts BR1 to be too low and consequently, simulated C2H5OH mole fractions relying on the RRKM/ME prediction would be too low in comparison to the measurements. The present experiments suggest to rely on the branching ratios BR1–BR3 that can be extracted from the Yasunaga et al.13 mechanism. By combining the present ktotal(T,p) predictions with branching ratios BR1–BR3 from the Yasunaga et al.13 mechanism, we can extract expressions for k1(T,p), k2(T,p), and k3(T,p) that are applicable for combustion simulation at high temperatures (between 1100 and 1800 K). Altogether, our results indicate that the Yasunaga et al.13 mechanism is able to predict product compositions and the formation of reactive intermediates during pyrolysis of DEE very well.

Acknowledgement This work was supported by the German Research Foundation (DFG) within the framework of the research unit FOR 1993 ‘Multi-functional conversion of chemical species and energy’ (SCHU 1369/19) and the DFG research project FI 1712/1.

References 1. 2.

Sarathy, S. M.; Oßwald, P.; Hansen, N.; Kohse-Höinghaus, K., Alcohol Combustion Chemistry. Progr. Energy Combust. Sci. 2014, 44, 40-102. Boehman, A. L., Developments in Production and Utilization of Dimethyl Ether for Fuel Applications. Fuel Process. Technol. 2008, 89 (12), 1243.


Page 42 of 46

Page 43 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3. 4. 5. 6. 7.

8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Mack, J. H.; Flowers, D. L.; Buchholz, B. A.; Dibble, R. W., Investigation of HCCI Combustion of Diethyl Ether and Ethanol Mixtures Using Carbon 14 Tracing and Numerical Simulations. Proc. Combust. Inst. 2005, 30 (2), 2693-2700. Cinar, C.; Can, Ö.; Sahin, F.; Yucesu, H. S., Effects of Premixed Diethyl Ether (DEE) on Combustion and Exhaust Emissions in a HCCI-DI Diesel Engine. Appl. Therm. Eng. 2010, 30 (4), 360-365. Qi, D. H.; Chen, H.; Geng, L. M.; Bian, Y. Z., Effect of Diethyl Ether and Ethanol Additives on the Combustion and Emission Characteristics of Biodiesel-Diesel Blended Fuel Engine. Renewable Energy 2011, 36 (4), 1252-1258. Sivalakshmi, S.; Balusamy, T., Effect of Biodiesel and its Blends with Diethyl Ether on the Combustion, Performance and Emissions from a Diesel Engine. Fuel 2013, 106, 106-110. Rakopoulos, D. C.; Rakopoulos, C. D.; Giakoumis, E. G.; Papagiannakis, R. G.; Kyritsis, D. C., Influence of Properties of Various Common Bio-fuels on the Combustion and Emission Characteristics of High-Speed DI (Direct Injection) Diesel Engine: Vegetable Oil, Bio-Diesel, Ethanol, n-Butanol, Diethyl Ether. Energy 2014, 73, 354-366. Werler, M.; Cancino, L. R.; Schiessl, R.; Maas, U.; Schulz, C.; Fikri, M., Ignition Delay Times of Diethyl Ether Measured in a High-Pressure Shock Tube and a Rapid Compression Machine. Proc. Combust. Inst. 2015, 35 (1), 259-266. Laidler, K. J.; McKenney, D. J., Kinetics and Mechanisms of the Pyrolysis of Diethyl Ether I. The Uninhibited Reaction. Proc. Royal Soc. A 1964, 278 (1375), 505-516. Laidler, K. J.; McKenney, D. J., Kinetics and Mechanisms of the Pyrolysis of Diethyl Ether II. The Reaction Inhibited by Nitric Oxide. Proc. Royal Soc. A 1964, 278 (1375), 517-526. Seres, I.; Huhn, P., Radical Steps in Diethyl Ether Decomposition. Int. J. Chem. Kinet. 1986, 18 (8), 829-836. Miller, C. H.; Tang, W.; Tranter, R. S.; Brezinsky, K., Shock Tube Pyrolysis of 1,2,4,5-Hexatetraene. J. Phys. Chem. A 2006, 110 (10), 3605-3613. Yasunaga, K.; Gillespie, F.; Simmie, J. M.; Curran, H. J.; Kuraguchi, Y.; Hoshikawa, H.; Yamane, M.; Hidaka, Y., A Multiple Shock Tube and Chemical Kinetic Modeling Study of Diethyl Ether Pyrolysis and Oxidation. J Phys Chem A 2010, 114 (34), 9098-9109. Sakai, Y.; Herzler, J.; Werler, M.; Schulz, C.; Fikri, M., A Quantum Chemical and Kinetics Modeling Study on the Autoignition Mechanism of Diethyl Ether. Proc. Combust. Inst. 2017, 36 (1), 195202. Peukert, S.; Sela, P.; Nativel, D.; Herzler, J.; Fikri, M.; Schulz, C. Direct Measurement of HighTemperature Rate Constants of the Thermal Decomposition of Dimethoxymethane, a Shock Tube and Modeling Study. J. Phys. Chem. A 2018, 122 (38), 7559-7571. Curran, H. J., Rate constant estimation for C1 to C4 Alkyl and Alkoxyl Radical Decomposition. Int. J. Chem. Kinet. 2006, 38 (4), 250-275. Caralp, F.; Devolder, P.; Fittschen, C.; Gomez, N.; Hippler, H.; Me′reau, R.; T. Rayez, M.; Striebel, F.; Viskolcz, B. l., The Thermal Unimolecular Decomposition Rate Constants of Ethoxy Radicals. Phys. Chem. Chem. Phys. 1999, 1 (12), 2935-2944. Sela, P.; Shu, B.; Aghsaee, M.; Herzler, J.; Welz, O.; Fikri, M.; Schulz, C., A Single-Pulse Shock Tube Coupled with High-Repetition-Rate Time-of-Flight Mass Spectrometry and Gas Chromatography for High-Temperature Gas-Phase Kinetics Studies. Rev. Sci. Instrum. 2016, 87 (10), 105103. Dürrstein, S. H.; Aghsaee, M.; Jerig, L.; Fikri, M.; Schulz, C., A Shock Tube with a High-RepetitionRate Time-of-Flight Mass Spectrometer for Investigations of Complex Reaction Systems. Rev. Sci. Instrum. 2011, 82 (8), 084103.



20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

Tranter, R. S.; Giri, B. R.; Kiefer, J. H., Shock Tube/Time-of-Flight Mass Spectrometer for High Temperature Kinetic Studies. Rev. Sci. Instrum. 2007, 78 (3), 034101. Lifshitz, A.; Bauer, S. H.; Resler, E. L., Jr., Studies with a Single-Pulse Shock Tube. I. The Cis—Trans Isomerization of Butene-2. J. Chem. Phys. 1963, 38 (9), 2056-2063. Tsang, W.; Lifshitz, A., Kinetic Stability of 1,1,1-Trifluoroethane. Int. J. Chem. Kinet. 1998, 30 (9), 621-628. Appel, D.; Appleton, J. P., Shock Tube Studies of Deuterium Dissociation and Oxidation by Atomic Resonance Absorption Spectrophotometry. Proc. Combust. Inst. 1975, 15 (1), 701-715. Miyoshi, A.; Sakai, Y., Construction of a Detailed Kinetic Model for Gasoline Surrogate Mixtures. Transactions of Society of Automotive Engineers of Japan 2017, 48 (5), 1021-1026. Miyoshi, A. SSUMES: Collection of Programs to Obtain Steady-State Solutions to Master-Equation for Unimolecular Decompositions, Recombination, and Complex-Forming Reactions. http://akrmys.com/ssumes/. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Gaussian 09; Gaussian. Inc.: Wallingford, CT., 2009. Sinha, P.; Boesch, S. E.; Gu, C.; Wheeler, R. A.; Wilson, A. K., Harmonic Vibrational Frequencies: Scaling Factors for HF, B3LYP, and MP2 Methods in Combination with Correlation Consistent Basis Sets. J. Phys. Chem. A 2004, 108 (42), 9213-9217. Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P.; Györffy, W.; Kats, D.; Korona, T.; Lindh, R.; et al. Molpro Quantum Chemistry Software. Garrett, B. C.; Truhlar, D. G., Semiclassical Tunneling Calculations. J. Phys. Chem. 1979, 83 (22), 2921-2926. Pitzer, K. S.; Gwinn, W. D., Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops. J. Chem. Phys. 1942, 10 (7), 428-440. Miyoshi, A. BEx1D program, Revision 2008.10.0. http://akrmys.com/bex1d/. Knyazev, V. D., Density of States of One-Dimensional Hindered Internal Rotors and Separability of Rotational Degrees of Freedom. J. Phys. Chem. A 1998, 102 (22), 3916-3922. Poling, B. E.; Prausnitz, J. M.; O´Connel, J. P., The Properties of Gases and Liquids. 5th edition ed.; McGraw-Hill: Boston, MA, 2001. Deminsky, M.; Chorkov, V.; Belov, G.; Cheshigin, I.; Knizhnik, A.; Shulakova, E.; Shulakov, M.; Iskandarova, I.; Alexandrov, V.; Petrusev, A.; et al. Chemical Workbench–Integrated Environment for Materials Science. Comput. Mater. Sci. 2003, 28 (2), 169-178. Senosiain, J. P.; Klippenstein, S. J.; Miller, J. A., Reaction of Ethylene with Hydroxyl Radicals: A Theoretical Study. J. Phys. Chem. A 2006, 110 (21), 6960-6970. Sivaramakrishnan, R.; Michael, J. V.; Ruscic, B., High-Temperature Rate Constants for H/D + C2H6 and C3H8. Int. J. Chem. Kinet. 2012, 44 (3), 194-205. Sivaramakrishnan, R.; Srinivasan, N. K.; Su, M. C.; Michael, J. V., High Temperature Rate Constants for OH+ Alkanes. Proc. Combust. Inst. 2009, 32 (1), 107-114. Mittal, G.; Burke, S. M.; Davies, V. A.; Parajuli, B.; Metcalfe, W. K.; Curran, H. J., Autoignition of Ethanol in a Rapid Compression Machine. Combust. Flame 2014, 161 (5), 1164-1171. Kiefer, J. H.; Santhanam, S.; Srinivasan, N. K.; Tranter, R. S.; Klippenstein, S. J.; Oehlschlaeger, M. A., Dissociation, Relaxation, and Incubation in the High-Temperature Pyrolysis of Ethane, and a Successful RRKM Modeling. Proc. Combust. Inst. 2005, 30 (1), 1129-1135. Lim, K. P.; Michael, J. V., The Thermal Reactions of CH3. Proc. Combust. Inst. 1994, 25, 713 – 719.


Page 44 of 46

Page 45 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


41. 42. 43. 44.

Troe, J.; Ushakov, V. G., The Dissociation/Recombination Reaction CH4 (+M) ⇔ CH3 + H (+M): A Case Study for Unimolecular Rate Theory. J. Chem. Phys. 2012, 136 (21), 214309. Peukert, S. L.; Labbe, N. J.; Sivaramakrishnan, R.; Michael, J. V., Direct Measurements of Rate Constants for the Reactions of CH3 Radicals with C2H6, C2H4, and C2H2 at High Temperatures. J. Phys. Chem. A 2013, 117 (40), 10228-10238. Sutherland, J. W.; Su, M. C.; Michael, J. V., Rate Constants for H + CH4, CH3 + H2, and CH4 Dissociation at High Temperature. Int. J. Chem. Kinet. 2001, 33 (11), 669-684. Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Esser, C.; Frank, P.; Just, T.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker, R. W.; et al. Evaluated Kinetic Data for Combustion Modelling. J. Phys. Chem. Ref. Data 1992, 21, 411 – 429.



TOC Graphic


Page 46 of 46

High-Temperature Unimolecular Decomposition of Diethyl Ether

Recommend Documents