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An Experimental and Theoretical Study of the Thermal Decomposition of CH Isomers 4

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James Philip Andrew Lockhart, C. Franklin Goldsmith, John Batista Randazzo, Branko Ruscic, and Robert Simon Tranter J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 25 Apr 2017 Downloaded from http://pubs.acs.org on April 26, 2017

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The Journal of Physical Chemistry

An Experimental and Theoretical Study of the Thermal Decomposition of C4H6 Isomers James P. A. Lockhart,1 C. Franklin Goldsmith,2 John B. Randazzo,1 Branko Ruscic,1,3 and Robert S. Tranter1,* 1

Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Il, United States 2

3

School of Engineering, Brown University, Providence, RI, United States

Computational Institute, The University of Chicago, Chicago, IL, United States *Corresponding author: [email protected], 630-252-6505

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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

Abstract: The chemistry of small unsaturated hydrocarbons, such as 1,3– butadiene (1,3–C4H6), 1,2–butadiene (1,2–C4H6), 2–butyne (2–C4H6) and 1– butyne (1–C4H6), is of central importance to the modeling of combustion systems. These species are important intermediates in combustion processes, and yet their high-temperature chemistry remains poorly understood, with various dissociation and isomerization pathways proposed in the literature. Here we investigate the thermal decompositions of 1,3–C4H6, 1,2–C4H6, 2–C4H6 and 1–C4H6 inside a diaphragmless shock tube, at post shock total pressures of 26–261 Torr and temperatures ranging from 1428–2354 K, using laser schlieren densitometry. The experimental work has been complemented by high-level ab initio calculations, which collectively provide strong evidence that formally direct dissociation is the major channel for pyrolysis of 1,3–C4H6 and 2–C4H6; these paths have not been previously reported but are critical to reconciling the current work and disparate literature reports. The reaction mechanism presented here simulates the current experiments and experimental data from the literature very well. Pressure and temperature dependent rate coefficients are given for the isomerization, formally direct and direct dissociation paths.


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1. Introduction Small unsaturated hydrocarbons are an important class of species in combustion chemistry, as their thermal decomposition contributes to the radical pool that drives both ignition processes and particulate formation.1–5 For example, 1,3–butadiene (1,3–C4H6), 1,2–butadiene (1,2–C4H6), 1–butyne (1–C4H6) and 2–butyne (2–C4H6) are all secondary products of the pyrolysis of 2–methylfuran and 2,5–dimethyl furan,6–10 promising future biofuels with potential for large–scale production.11,12 There are conflicting reports as to the initial decomposition products and/or product branching fractions for the aforementioned C4H6 isomers, with radical13 and molecular products,14 as well as facile isomerizations15–21 between these species all proposed in the literature. If the rapid isomerization paths between 1,3–C4H6, 1,2–C4H6, 1–C4H6 and 2– C4H6 are correct, then no individual isomer can be treated in isolation. Instead a model is required that quantifies the competing isomerization and dissociation paths explicitly as a function of pressure and temperature. While ab initio calculations of the C4H6 potential energy surface (PES) have been previously reported by Lee et al.22 and Chambreau et al.,21 neither study used Rice-Ramsperger-Kassel-Marcus/Master Equation (RRKM/ME) theory to quantify pressure and temperature dependent rate coefficients associated with the surface. A summary of the experimental conditions, techniques, and major products reported following previous investigations of 1,3–C4H6, 1,2–C4H6, 1–C4H6 and 2–C4H6 decompositions are provided in Table 1. The conflicting conclusions drawn from these studies are summarized here. 1.1. 1,3–C4H6 1,3–C4H6 has been studied more extensively than the other C4H6 isomers due to its near ubiquitous nature in combustion chemistry.6,7,23–25 Kiefer et al. studied the decomposition of 1,3– 3 ACS Paragon Plus Environment


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C4H6 behind shock waves using laser schlieren (LS) densitometry to investigate the initial decomposition step, and time-of-flight mass spectrometry (TOF–MS) to detect reaction products.13 These authors developed a mechanism initiated by central C–C σ bond scission to give two C2H3 radicals (1a) and used the LS technique to quantify the heat of formation, ∆Hf, 298 K,

of C2H3, which at the time of their measurements was very uncertain; with reported values

ranging from 59.6–71.5 kcal mol-1.26,27 The analysis by Kiefer and co-workers reported a ∆Hf, 298 K

for C2H3 of 63.4 kcal mol-1,13 which while consistent with the range of values reported at the

time, has since been shown to have significantly underestimated the ∆Hf, 298 K of C2H3, currently determined as 71.0 ± 0.1 kcal mol-1,28 and led to a large error in their rate coefficient for the dissociation of C2H3.29 Moreover, Kiefer and co-workers were unable to simulate both their LS and TOF–MS experiments on 1,3–C4H6 using the same Arrhenius expression for C2H3 dissociation. 1,3–C4H6 + M → C2H3 + C2H3 + M

(1a)

Rao et al. studied the decomposition of 1,3–C4H6 behind reflected shock waves using atomic resonance absorption spectroscopy (ARAS) to monitor H-atom production directly,14 under conditions in which the C2H3 radical is known to promptly dissociate to H + C2H2.29 The H-atom profiles were inconsistent with the direct dissociation of 1,3–C4H6 to C2H3 (1a) proposed by Kiefer et al.,13 and Rao et al. concluded that the majority of 1,3–C4H6 decomposes to give the molecular products C2H2 + C2H4 (1b).14 1,3–C4H6 + M → C2H2 + C2H4 + M

(1b)

With a series of shock tubes Hidaka et al. investigated the decomposition of 1,3–C4H6 using UV absorption spectroscopy, quadrupole mass spectrometry or gas chromatography with


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thermal conductivity detection (GC–TCD) to detect the parent and stable reaction products.16 Hidaka and co-workers developed a mechanism initiated by rapid isomerizations from 1,3–C4H6 to 1,2–C4H6 (-2a) and 2–C4H6 (1c) to simulate their experimental reactant and product profiles. 1,3–C4H6 + M ⇌ 2–C4H6 + M

(1c)

1,2–C4H6 + M ⇌ 1,3–C4H6 + M

(2a)

More recently, Chambreau et al. studied the thermal decomposition of 1,3–C4H6, and its deuterated terminal carbon isotopologue 1,3–C4H2D4, using a flash pyrolysis silicon carbide reactor coupled to a TOF–MS, that allowed product formation to be observed on a tens of microsecond timescale.21 These authors reported CH3 and C3H3 as primary products of 1,3–C4H6 decomposition, and concluded that rapid isomerization from 1,3–C4H6 to 1,2–C4H6 (-2a) was likely the first step in the thermal decomposition of the conjugated diene. Finally, Peukert et al. studied the pyrolysis of 1,3–C4H6 behind reflected shock waves by measuring H-atom concentration profiles using ARAS.20 The model developed by these authors included the radical (1a) and molecular (1b) dissociation pathways proposed by Kiefer et al.13 and Rao et al.,14 respectively, as well as the facile isomerization channels (1c and -2a) proposed by Hidaka et al.16 Furthermore, satisfactory simulation of the experimental H-atom profiles measured by Peukert et al.20 were critically dependent on the inclusion of secondary H-atom eliminations from 2–C4H6 (3a’) and from the subsequent reactions of the products of direct dissociation of 1,2–C4H6 (2b) in their model. 1,2–C4H6 + M → CH3 + C3H3 + M

(2b)

2–C4H6 + M → 2–C4H5 + H + M

(3a’) 5 ACS Paragon Plus Environment


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Table 1: Summary of Previous Experimental Work on the Pyrolysis of 1,3–Butadiene (1,3– C4H6), 1,2–Butadiene (1,2–C4H6), 1–Butyne (1–C4H6) and 2–Butyne (2–C4H6) Reported in the Literature. Isomer

1,3–C4H6

1,2–C4H6

Technique/Authors

ST using LS densitometry, TOF– MS/Kiefer et al.13 ST using H–ARAS/ Rao et al.14 Single pulse ST using GC–TCD, and ST using UV absorption or quadrupole MS/ Hidaka et al.16 ST using H– ARAS/Peukert et al.20 Flash pyrolysis SiC reactor with TOF–MS/ Chambreau et al.21 ST using TOF–MS/ Kern et al.15

Single pulse ST using GC–TCD, and ST using UV or IR absorption/ Hidaka et al.17

Temperature Range (K) 1400–2200

Pressure Range (Torr)/ Bath Gas 200–500 / Ar, Kr, or Ne

Primary Reaction(s)/ (Product Branching)

1,3–C4H6 + M → C2H3 + C2H3 + M

1498–1771

2052 / Ar

1,3–C4H6 + M → C2H2 + C2H4 + M

1200–1700

972–3074 / Ar

1,3–C4H6 + M → C2H2 + C2H4 + M → 1,2–C4H6 + M → 1–C4H6 + M → 2–C4H6 + M

1500–1800

900–1425 / Ar

T ≤ 1520

Not reported / He

1,3–C4H6 + M → C2H2 + C2H4 + M → 1,2–C4H6 + M → 2–C4H6 + M 1,3–C4H6 + M → CH3 + C3H3 + M

1300–2000

152–418 / Ne

1,2–C4H6 + M → 1,3–C4H6 + M (2a) (k2a/k2, total = 0.39–0.66, increasing with T)

1100–1600

933–1746 / Ar

1,2–C4H6 + M → CH3 + C3H3 + M (2b) 1,2–C4H6 + M → 1,3–C4H6 + M (2a) (k2a/k2, total* = 0.5–0.25, decreasing with T)

→ CH3 + C3H3 + M (2b) (k2b/k2, total* = 0.17–0.47, increasing with T)

→ 2–C4H6 + M (2c) (k2c/k2, total* = 0.06–0.11, increasing with T)

→ 1–C4H6 + M (-4b) (k-4b/k2, total* = 0.27–0.16, decreasing with T)

2–C4H6

Flash pyrolysis SiC reactor with TOF–MS/ Chambreau et al.21 Single pulse ST using GC–TCD, and ST using UV or IR absorption/ Hidaka et al.18 ST using H–ARAS/ Peukert et al.20

T ≤ 1520

Not reported / He

1,2–C4H6 + M → CH3 + C3H3 + M

1100–1600

1100–2100 / Ar

2–C4H6 + M → 1,3–C4H6 + M (-1c) (k-1c/k3, total = 0.71–0.63, decreasing with T)

→ 1,2–C4H6 + M (-2c) (k-2c/k3, total = 0.29–0.34, increasing with T)

→ 2–C4H5 + H + M (3a) (k3a/k3, total = 0.002–0.03, increasing with T)

1500–1800

900–1425 / Ar

2–C4H6 + M → 1,3–C4H6 + M (-1c) (k-1c/k3, total = 0.27, independent of T)

→ 1,2–C4H6 + M (-2c) (k-2c/k3, total = 0.72–0.69, decreasing with T)

→ 2–C4H5 + H + M (3a) (k3a/k3, total = 0.01–0.04, increasing with T)


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Flash pyrolysis SiC T ≤ 1520 Not reported / 2–C4H6 + M → CH3 + C3H3 + M reactor with TOF–MS/ He Chambreau et al.21 1–C4H6 Single pulse ST using 1100–1600 933–1746 / Ar 1–C4H6 + M → CH3 + C3H3 + M (4a) GC–TCD, and ST → 1,2–C4H6 + M (4b) using IR absorption/ Hidaka et al.19 Note: The abbreviations are defined as follows: ST = shock tube, GC–TCD = gas chromatography thermal conductivity detection, ARAS = atomic resonance absorption spectroscopy and TOF–MS = time-of-flight mass spectrometry. Reactions are numbered as they are in the manuscript. Product branching fractions are included where comparisons between previous studies are informative, for the branching listed here the denominator terms are defined as follows: k2, total = k2a + k2b; k2, total* = k2a + k2b + k2c + k-4b; k3, total = k-1c + k-2c + k3a.

1.2. 1,2–C4H6 Kern et al. studied the decomposition of 1,2–C4H6 behind reflected shock waves with both reactant and products detected using TOF–MS.15 These authors compiled a chemical model that included isomerization between 1,2–C4H6 and 1,3–C4H6 (2a), as well as dissociation of 1,2– C4H6 to CH3 + C3H3 (2b), to simulate their experimental product profiles. The analysis by Kern and co–workers concluded that branching through reaction 2b (defined here as k2b/k2, total, where k2, total = the sum of dissociation and isomerization channel rate coefficients considered by the authors) decreases from 0.61–0.34 as temperature increases from 1300–2000 K. Hidaka et al. investigated the pyrolysis of 1,2–C4H6 behind reflected shock waves using UV/IR absorption spectroscopy and GC–TCD to detect the parent and reaction products.17 The mechanism reported by these authors included the direct dissociations of 1,2–C4H6 to CH3 + C3H3 (2b) and H + C4H5, as well as isomerizations from 1,2–C4H6 to 1,3–C4H6, 2–C4H6 and 1– C4H6. Although contrary to the branching reported by Kern et al.,15 Hidaka and co-workers concluded that at higher pressures branching through reaction 2b (k2b/k2,

total)

increases from

0.17–0.47 as temperatures increase from 1100–1600 K, while branching through reaction 2a (k2a/k2, total) decreases from 0.50–0.25 with increasing temperature over the same range.17



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More recently, the flash pyrolysis study by Chambreau et al. detected CH3 + C3H3 as products of 1,2–C4H6 decomposition at temperatures greater than 1280 K, using TOF–MS.21 1.3. 2–C4H6 Hidaka and colleagues also investigated the thermal decomposition of 2–C4H6 behind reflected shock waves using UV/IR absorption spectroscopy and GC–TCD to detect the parent and reaction products.18 They concluded the high temperature chemistry was dominated by isomerization channels, with branching from 2–C4H6 to 1,3–C4H6 (-1c, defined here as k-1c/k3, total,

where k3, total = k-1c + k-2c + k3a’) decreasing from 0.71–0.63 as temperatures increase from

1100–1600 K, and branching from 2–C4H6 to 1,2–C4H6 (-2c, k-2c/k3, total) increasing from 0.29– 0.34 over the same temperature range. These authors concluded that H–atom elimination (3a’) was a minor loss channel for the symmetric alkyne. 1,3–C4H6 + M ⇌ 2–C4H6 + M

(1c)

1,2–C4H6 + M ⇌ 2–C4H6 + M

(2c)

More recently, Peukert et al.20 investigated the pyrolysis of 2–C4H6 behind reflected shock waves using H-ARAS under similar experimental conditions to the study by Hidaka et al.18 Both Peukert et al. and Hidaka et al. reported H-atom elimination from 2–C4H6 (4a) as a minor loss channel for the symmetric alkyne. However, unlike the study by Hidaka and coworkers, Peukert et al. concluded that isomerization from 2–C4H6 to 1,2–C4H6 (-2c) is the dominant reactive channel, with a branching fraction (k-2c/k3, total) of approximately 0.7, and that isomerization from 2–C4H6 to 1,3–C4H6 (-1c, k-1c/k3, total) is a relatively minor channel with a branching fraction of approximately 0.28, under their experimental conditions.


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Chambreau et al. investigated the decomposition of 2–C4H6 in a flash pyrolysis silicon carbide reactor and monitored products via TOF–MS.21 These authors reported CH3 + C3H3 as primary products of 2–C4H6 pyrolysis at temperatures greater than 1425 K. The experiments were complemented by theory that confirmed the lowest energy path from the parent alkyne to these radical products proceeds through the initial isomerization to 1,2–C4H6 (-2c) and subsequent dissociation of the diene (2b). 1.4. 1–C4H6 To the best of our knowledge, the only experimental investigation of 1–C4H6 pyrolysis is the shock tube study by Hidaka et al. using either IR absorption spectroscopy or GC–TCD to monitor the parent and reaction products.

19

These authors concluded that only two reactions

contribute to the high temperature chemistry of 1–C4H6, dissociation to CH3 + C3H3 (4a) and isomerization to 1,2–C4H6 (4b). Hidaka and colleagues reported that branching through reaction 4a, defined here as k4a/(k4a + k4b), increases from 0.46–0.8 as temperatures increase from 1100– 1600 K. 1–C4H6 + M → CH3 + C3H3 + M

(4a)

1–C4H6 + M ⇌ 1,2–C4H6 + M

(4b)

Despite the extensive experimental studies, using a broad range of techniques, there remains significant uncertainty as to the initiation processes involved in the thermal decompositions of 1,3–C4H6, 1,2–C4H6 and 2–C4H6. In this study, the initial decompositions of 1,3–C4H6, 1,2–C4H6, 2–C4H6, and 1–C4H6 are investigated over a broad range of pressures and temperatures using LS densitometry. An internally consistent model has been developed, that is informed by high level ab initio calculations and RRKM/ME theory. This model accounts for the 9 ACS Paragon Plus Environment


competing isomerization and dissociation pathways and successfully simulates the experimental density gradient profiles of all four C4H6 isomers over a broad range of pressures, temperatures and concentrations.

2. Experimental 2.1. Diaphragmless Shock Tube Laser Schlieren (LS) experiments were undertaken in a diaphragmless shock tube (DFST) that has been described in detail elsewhere.30,31 The driver section of the DFST consists of a stainless steel tube, which houses a bellows actuated valve that separates the driver and driven sections. When the valve is closed the driver and driven sections of the DFST can be filled to the desired loading conditions. A shock wave is then generated by rapidly opening the valve. A set of five evenly spaced pressure transducers, positioned around the LS windows, allow the incident shock wave velocity to be measured with an estimated uncertainty of 0.2%. Incident shock conditions (P2 and T2) were calculated from the loading conditions of the DFST, the shock wave velocity, and the heat capacities of the gases. The post shock conditions (P2 and T2) can be controlled within a narrow range (P2 ≤ 10%, T2 ≤ 0.5%) by varying the pressure in the driven (P1) and driver (P4) sections of the DFST. 2.2. Laser Schlieren (LS) Densitometry The LS technique has also been described in detail elsewhere.32,33 LS densitometry measures the angular deflection, θ, of a narrow laser beam traversing the shock tube perpendicular to the direction of propagation of the shock wave, to determine the axial density gradient behind the incident shock wave. The raw LS signal is converted to an axial density gradient, dρ/dx, using the shock tube diameter, W, and the mixture molar refractivity, KL (Eq. 1).33


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=

(Eq. 1)

The molar refractivities of the bath gases krypton, argon and xenon (6.367 cm3 mol-1, 4.198 cm3 mol-1 and 10.448 cm3 mol-1, respectively) were taken from Gardiner et al.34 The molar refractivities of each C4H6 isomer were calculated from their refractive index, n, and density, ρ, using the Lorenz–Lorentz equation34 (1,3–C4H6,35 n = 1.4292, ρ = 0.615 g cm-3; 1,2–C4H6,36 n = 1.4205, ρ = 0.676 g cm-3; 2–C4H6,37 n = 1.3930, ρ = 0.691 g cm-3 ; and 1–C4H6,38 n = 1.386, ρ = 0.7 g cm-3). The usual assumption is made that the mixture molar refractivity does not vary significantly throughout the observed reaction time. This approximation is valid for the dilute reagent mixtures used here. For example, during a 1,3–C4H6 experiment of relatively high initial concentration (2%), post-shock pressure (P2 = 125 Torr), and post-shock temperature (T2 = 2335 K), the mixture molar refractivity changes by approximately 3% over the first 12 µs of reaction. Changes in the mixture molar refractivity of this magnitude result in negligible changes to the experimental density gradient, particularly in the early portion which is dominated by the initial chemistry of the parent molecule. The majority of the experiments presented in this study used a Fabry–Perot diode laser (Newport model LQC635-08C) to generate a nominally circular beam (635 nm, 8 mW) of 1 mm diameter via a microlens attached to the laser exit. The output from the diode laser was either passed through an iris, or coupled to a fiber optic cable terminated at an aspheric lens to provide both a narrow and stable circular beam for LS measurements. Additional experiments were carried out using two alternate optical setups, the details of which are provided in the supplementary materials. Tests confirmed that experimental density gradient profiles measured under comparable conditions using each of these optical setups were effectively indistinguishable. As the shock wave propagates through the laser beam, the light is deflected, 11 ACS Paragon Plus Environment


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resulting in the characteristic valley and peak shown in the raw LS profiles presented in the inset of each panel in Figure 1. After the shock front passes through the laser beam, the axial density gradient resulting from the onset of non-isothermal chemistry in the shock heated gas also deflects the laser beam; this chemical signal is shown to the right of the large peaks in each panel inset of Figure 1. The axial density gradient is proportional to the rate, r, and heat of reaction, ∆H, with a small correction to account for the change in mole number, ∆N, summed over all reactions, j (Eq. 2).32,33

∆ − ∆

(Eq. 2)

The time signifying the onset of chemical reaction, t0, is obscured by the interaction of the shock front with the laser beam, but can be estimated to within 0.1–0.2 µs using a wellestablished method.33 Once a chemical kinetic model has been developed that satisfactorily simulates the experimental density gradient profile, the simulation can be extrapolated back to t0, at which time the only reactions contributing to the density gradient are unimolecular reactions of the parent molecule.


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Figure 1: Experimental density gradient profiles following the thermal decomposition of 1,3– C4H6 (a), 1,2–C4H6 (b), 2–C4H6 (c) and 1–C4H6 (d) dilute in krypton at ~123 Torr and temperatures ranging from 1664–2034 K, the corresponding raw LS signals are shown in the insets of each panel. The solid black lines show the simulated density gradient profile using an identical model.



2.3. Reagent Mixtures Reagent mixtures of 1,3–C4H6 (Aldrich, ≥ 99%), 1,2–C4H6 (ChemSampCo, research grade), 2–C4H6 (Aldrich, 99%) and 1–C4H6 (Aldrich, ≥ 98%) dilute in krypton (Airgas, 99.999%), argon (Airgas, ultra high purity) or xenon (AGA, 99.995%) were prepared manometrically in a 50 L glass vessel that was previously evacuated to < 10-3 Torr. Mixtures were stirred with a PTFE coated magnetic stirrer and allowed to homogenize for at least one hour before use. The identity of each reagent was confirmed by gas–chromatography–mass spectrometry (GC–MS), see Figure S4a and Figure S4b of the supplementary material. 1,3–C4H6, 1,2–C4H6 and 1–C4H6 were used direct from the cylinder. 2–C4H6, which is a liquid at room temperature, was degassed by repeat freeze/pump/thaw cycles prior to use. 2.4. Thermochemical Properties The thermochemical properties of nearly all species considered here were taken from Goos et al.,39 which includes periodic updates from the Active Thermochemical Tables (ATcT) approach.40,41 As opposed to traditional sequential thermochemistry (A begets B, B begets C etc.), ATcT constructs, statistically analyzes, adjusts to self-consistency, and solves a large Thermochemical Network (TN) that contains thermochemical determinations (both from experiment and theory), such as reaction enthalpies or free energies, bond dissociation energies, adiabatic ionization energies, adiabatic electron affinities, relative gas-phase acidities etc., that are relevant for defining the included chemical species.42–44 The current ATcT results are based on TN ver. 1.122, which contains ~1200 chemical species interlinked by more than 20,000 thermochemical determinations, the essential details of which were introduced previously.45,46 The 298.15 K enthalpy of formation of CH3 resulting from this version of ATcT, 34.98 ± 0.02 kcal mol-1,44,45 is significantly more accurate than the value recommended by IUPAC,47 which


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was 35.06 ± 0.07 kcal mol-1, though, disregarding the quoted uncertainty, its value at 298.15 K differs only marginally from the previous recommendation. However, at higher temperatures, the differences become significant: the new ATcT enthalpy of formation is lower than the corresponding IUPAC value by 0.41, 1.05, 1.95, 3.15, and 4.69 kcal mol-1 at 1000, 1500, 2000, 2500, and 3000 K, respectively. The primary reason for this difference is that – in contrast to the IUPAC recommendation, which relies on a standard rigid-rotor-harmonic-oscillator (RRHO) partition function for the extrapolation of thermochemical properties of CH3 beyond 298.15 K the current ATcT thermochemistry of CH3 relies on a newly constructed non-rigid-rotoranharmonic-oscillator (NRRAO) partition function. While the ubiquitous RRHO partition functions generally have a historical track record of providing an acceptable description of properties at higher temperatures for many chemical species, this is not quite the case for CH3. Namely, about a decade ago, a theoretical study of Medvedev et al.48 indicated that for this species the RRHO approximation overestimates the vibrational contributions to the partition function by a significant factor, primarily because of ignored anharmonic effects, which are particularly prominent in the umbrella vibrational motion of CH3. The NRRAO approach, as used in ATcT for CH3, commenced with an RRHO partition function, which was additionally corrected in first order for vibrational anharmonicity, centrifugal distortion, rotation-vibration interaction, resonances, as well as for low-temperature effects.49–52 The overall procedure is rather similar to the NRRAO approach applied by Gurvich et al.53 in select cases, such as, for example, methane. As mentioned above, the thermochemistry of 3CH2 and C2H6 was also taken from ATcT. The current ATcT enthalpy of formation of 3CH2 at 298 .15 K is 93.58 ± 0.03 kcal mol-1,44,45 to be compared with the slightly less accurate, but otherwise fully consistent IUPAC recommendation of 93.5 ± 0.4 kcal mol-1.47 Similarly, the current ATcT enthalpy of formation of



C2H6 is -20.05 ± 0.04 kcal mol-1,44,45 again slightly more accurate than previous values, such as 20.0 ± 0.1 kcal mol-1 that was recommended by Manion,54 based on the earlier recommendation by Gurvich et al.53 In ATcT, 3CH2 and C2H6 also use a NRRAO partition function, though for these two species the differences to previous partition functions are somewhat less pronounced at higher temperatures than in the case of CH3. The corresponding NASA polynomials describing the thermochemistry of CH3, 3CH2, and C2H6 were obtained by fitting a JANAF-style tabular output from ATcT using the McBride and Gordon NASA PAC program,55 and are supplied in the supplementary materials. The NASA polynomials for all other species were taken from Goos et al.39

3. Theoretical Methods 3.1. Electronic Structure Calculations The region of the C4H6 PES relevant to the thermal decompositions of 1,3–C4H6, 1,2– C4H6, 1–C4H6 and 2–C4H6 has been calculated at the UCCSD(T)/cc-pVTZ level of theory using a restricted Hartree-Fock reference wavefunction, as implemented in MOLPRO56 (Figure 2). The full C4H6 PES and corresponding stationary point energies relative to 1,3–C4H6 are provided in Figure S1a and Figure S1b, and Table S1a and Table S1b of the supplementary material. These methods provide barriers for the radical (1a) and molecular (1b) dissociation paths of 1,3–C4H6 proposed by Kiefer et al.13 and Rao et al.,14 respectively. Direct dissociation of 1,3–C4H6 to give two C2H3 radicals is strongly endothermic and corresponds to a zero point corrected energy loss of 112.2 kcal mol-1, in good quantitative agreement with the 113 kcal mol-1 value reported by Lee et al.22 at the G2M level of theory, and reasonable agreement with the current ATcT 0 K value of 114.0 ± 0.2 kcal mol-1.45,46 The direct dissociation of 1,3–C4H6 to C2H2 + C2H4 (1b) proceeds through a tight transition state with zero point corrected barrier height relative to 1,3– 16 ACS Paragon Plus Environment

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C4H6 of 92.7 kcal mol-1, that is again consistent with the 87.5 and kcal mol-1 barrier reported by Lee et al.22 The PES calculated here also provides quantitative evidence of the isomerization paths proposed by Kern et al.15 and Hidaka and co-workers.16–19 1,3–C4H6 can isomerize directly to 1,2–C4H6 with a barrier height of 81.2 kcal mol-1 relative to the conjugated diene, which is in excellent agreement with the 81.1 kcal mol-1 value calculated by Chambreau et al.21 at the G3X level of theory. However, an alternate indirect diene isomerization pathway has been identified that is more energetically favorable than the direct channel. This indirect pathway proceeds via the methyl-vinyl-carbene (CH3CCHCH2) intermediate with a barrier height relative to 1,3–C4H6 of 75.3 kcal mol-1, in excellent agreement with the values of 74.7 and 75.2 kcal mol-1 calculated by Lee et al.22 and Chambreau et al.,21 respectively. 1,2–C4H6 can in turn isomerize directly to both 1–C4H6 or 2–C4H6, both channels pass through tight transition states with barrier heights relative to 1,2–C4H6 of 85.4 and 87.8 kcal mol-1, respectively. However, lower energy, indirect isomerization paths from 1,2–C4H6 to both alkynes have been identified that again proceed via carbene intermediates. Indirect isomerization from 1,2–C4H6 to 2–C4H6 passes through CH3CCHCH2 and must surmount a barrier of 72.9 kcal mol-1 relative to the diene. This barrier height is consistent with the 73.7 kcal mol-1 value calculated by Chambreau et al.21 at the G3X level of theory, and the 78.9 kcal mol-1 value reported by Lee et al.22 at the G2M level. Indirect isomerization from 1,2–C4H6 to 1–C4H6 passes through propenyl carbene (CH3CHCHCH) with a barrier of 73.7 kcal mol-1 relative to the diene. 1,2–C4H6 and 1–C4H6 can dissociate directly to CH3 + C3H3, both of these endothermic processes are barrierless and correspond to an energy loss of 76.9 and 75.8 kcal mol-1, respectively.



Figure 2: A simplified potential energy surface of isomerization and dissociation pathways relevant to the pyrolysis of 1,3–C4H6, 1,2–C4H6, 2–C4H6 and 1–C4H6. All energies are relative to 1,3–C4H6. Formally direct dissociation channels, which are important for 1,3–C4H6 and 2–C4H6 (see text) are not shown. The dashed red box on the left highlights the reactions proposed by Kiefer et al.13 and Rao et al.14 for the dissociation of 1,3–C4H6. The thick solid blue lines to the right of 1,3–C4H6 represent the main isomerization channels between 1,3–C4H6, 1,2–C4H6 and 2– C4H6, a minor channel (thin blue line) also exists between 1,3–C4H6 and 1–C4H6. These mainly involve carbene intermediates. Alternative paths that involve higher energy 3-membered ring transition states are not shown for clarity, but are given in Figure S1a of the supplementary material. The thick black lines represent main pathways from 1,2–C4H6 and 1–C4H6 to CH3 + C3H3; the dashed lines represent the minor bond-fission pathways. The complete PES including intermediate species and transition state structures is given in the supplementary material.


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3.2. Master Equation Calculations RRKM/ME theory has been used to compute phenomenological rate coefficients for the competing isomerization and dissociation paths associated with this complex multi-well surface. Full RRKM/ME analysis of the C4H6 PES has been performed using the RRKM/ME code PAPR,57,58 recently developed at Argonne National Laboratory. A single exponential was used to model the collisional energy transfer, with a = 200 (T/298)0.85 cm-1, based upon previous work for molecules of this size.59,60 For the tight transition states in Table S1b, standard rigid-rotor harmonic-oscillator models were used to compute the microcanonical rate coefficients. For the bond scission channels – P3 through P9 of Table S1a – Phase Space Theory was used to compute the microcanonical rate coefficients.61–63 For each of these barrierless reactions, the coefficient of the interaction potential was adjusted so that the high pressure limit of the reverse reaction had a rate coefficient of approximately 3 × 10-10 cm3 molecule-1 s-1 for the seven C3H5 + H reactions (TS10-11, 18-20, 22, 24-25) and approximately 3 × 10-11 cm3 molecule-1 s-1 for the CH2CCH + CH3 and C2H3 + C2H3 reactions (TS12, 17, 24). No further adjustments were made to the PES. 3.3. Formally Direct Dissociation Pathways There is a growing awareness of the importance of formally direct reaction pathways in both combustion and atmospheric chemistry.64–70 The term “formally direct” describes a reaction in which reactants pass directly over more than one transition state to non-adjacent products on the PES in a single step. Critically for this study, the RRKM/ME analysis has identified formally direct dissociation paths for both 1,3–C4H6 and 2–C4H6 that have not been reported elsewhere. In these reactions the C4H6 species surmount an isomerization barrier with sufficient energy that



Page 20 of 99

collisional deactivation into the alternate C4H6 well is ineffective and instead both 1,3–C4H6 (1d) and 2–C4H6 (3b) dissociate directly to CH3 + C3H3 products. 1,3–C4H6 + M → CH3 + C3H3 + M

(1d)

2–C4H6 + M → CH3 + C3H3 + M

(3b)

4. Chemical Kinetic Mechanism Development The following section details the assumptions made in compiling the chemical mechanism used here, particular attention is given to formation and dissociation of C4H5 radicals, C4H4 species, and the fate of C3H3 radicals. Table 2: Key Reactions of the C4H6 Decomposition Mechanism Developed in This Study. For Reactions in which Arrhenius Parameters have been derived from both Experiment and Theory, the Experimental Values are presented in Bold. The Complete Reaction Mechanism is Available in Table S3 of the Supplementary Materials. Log (A)a

na

Eaa

∆Hr, 298 Ka

Source

1,3–C4H6 + M → C2H3 + C2H3 + M

73.64b

-17.13

142.9

115

P. W.e

1b

1,3–C6H4 + M → C2H2 + C2H4 + M

56.48b

-12.24

111.1

41

P. W.e

1c

1,3–C4H6 + M ⇌ 2–C4H6 + M

69.98b

-16.33

109.0

8

P. W.e

1d

1,3–C4H6 + M → CH3 + C3H3 + M

196.72c, (+0.18/-0.30)d

-50.0

243.6

93

P. W.e

75.95b

-17.29

129.8

74.85b

-17.71

103.0

-12

P. W.e

#

Reaction

1a

2a

1,2–C4H6 + M ⇌ 1,3–C4H6 + M


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2b


1,2–C4H6 + M → CH3 + C3H3 + M

2c

1,2–C4H6 + M ⇌ 2–C4H6 + M

3a

2–C4H6 + M → C4H4 + H + H + M

3b

2–C4H6 + M → CH3 + C3H3 + M

4a

1–C4H6 + M → CH3 + C3H3 + M

156.14c, (+0.18/-0.30)d

-36.93

180.2

75.6b

-17.53

108.9

75.88b

-18.24

65.01b

80

P. W.e

100.3

-4

P. W.e

-14.66

114.4

138

P. W.e

51.43c, (+0.18/-0.30)d

-11.05

87.9

84

P. W.e

74.29b

-17.06

116.3

116.13c, (+0.18/-0.30)d

-28.77

140.5

80

P. W.e

76.34b

-17.73

108.6

82.92b

-20.46

110.0

-1

P. W.e

68.57b

-16.45

101.7

-13

P. W.e

85.61b

-21.38

116.8

-5

P. W.e

4b

1–C4H6 + M ⇌ 1,2–C4H6 + M

4c

1–C4H6 + M ⇌ 1,3–C4H6 + M

4d

1–C4H6 + M ⇌ 2–C4H6 + M

5

C2H6 → CH3 + CH3

18.2

0

70.0

90

Yang et al.71

6a

C3H3 + C3H3 → C6H6, Bz

77.34

-18.68

44.5

-148

See Text

6b

C3H3 + C3H3 → C6H5 + H

61.17

-13.59

42.1

-35

See Text

6c

C3H3 + C3H3 → C6H6, other

67.51

-15.93

31.3

-88

See Text

a

Units: kcal, mol, cm, s. Rate coefficients are expressed in the form k = ATnexp(-Ea/RT) with T in K.

b

Arrhenius parameters derived from master equation theory from the present work (P. W.) valid for the

temperature range 1000–2200 K. cArrhenius parameters derived from experiment. dError in the assigned rate coefficient is estimated at ±50%. eReactions treated with pressure dependence. Note: C6H6,

Bz

refers to

benzene, C6H6, other refers to C6H6 isomers other than benzene. Except for reactions involving CH3 and C2H6



Page 22 of 99

(see text), standard enthalpies of reactions, ∆Hr, 298 K, were calculated using the thermochemical properties of Goos et al.39

In order to constrain the model the pressure and temperature dependent rate coefficients for the various C4H6 isomerization channels were fixed at the phenomenological values computed using RRKM/ME theory. The experimental density gradient is sensitive to the net rate of heat release due to chemical reactions occurring in the shock heated gases (Eq. 2). The standard heats of reaction, ∆Hr, 298 K, associated with the C4H6 isomerization channels considered here vary between ±13 kcal mol-1, corresponding to forward and reverse isomerization reactions between 1–C4H6 and 1,3–C4H6 (3c and -3c, respectively); the initial experimental density gradient is insensitive to the rate of reactions with ∆Hr,

298 K

of this relatively small magnitude.

Rate coefficients for the dissociations of 1,3–C4H6 to give two C2H3 radicals (k1a) and C2H2 + C2H4 (k1b), and H-atom eliminations from all C4H6 isomers were also fixed at the pressure and/or temperature dependent values calculated from RRKM/ME theory. Analysis of the density gradient profiles has shown that these reactions contribute less than 5% of the total C4H6 loss rate under the conditions considered in this study, and consequently do not contribute significantly to the observed density gradient. Indeed, sensitivity analysis demonstrated that increasing the k1a value derived from RRKM/ME theory by an order of magnitude had a negligible effect on the density gradient profile simulated here following 1,3–C4H6 decomposition at temperatures ranging from 1800–2350 K. Similarly, the simulations of 1,3–C4H6 are insensitive to the exact value of k1b. To produce noticeable effects at the extremes of the experimental temperature range, k1b had to be increased by a factor of 10 at 1850 K and a factor of 3 at 2350 K.


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4.1. C4H5 Radicals The theoretical methods employed here have shown that under the conditions of the current work scission of the various C–H bonds in the C4H6 isomers lead to four distinct C4H5 radicals (Figure 3). These radicals dissociate rapidly at the temperatures relevant to this study as discussed below. H–atom loss from either terminal carbon of 1,3–C4H6 results in formation of n– 1,3–C4H5. H atom loss from either of the central carbon atoms of 1,3–C4H6 or from the methyl group of 1,2–C4H6 result in formation of i–1,3–C4H5 radicals. The loss of an H–atom from carbon three of 1,2–C4H6 or from either methyl group of 2–C4H6 result in formation of 2–C4H5 radicals. Finally, H-atom loss from carbon one of 1,2–C4H6 or from carbon three of 1–C4H6 result in formation of n–1,2–C4H5 radicals.

Figure 3: Schematic of the four C4H5 radicals, and their resonant structures, that form following the various C–H bond scissions in the C4H6 isomers considered here. The bond C–H scission



Page 24 of 99

reactions should be read from left to center, or right to center. Resonant C4H5 structures for i– 1,3–C4H5, n–1,2–C4H5 and 2–C4H5 are separated by a double headed arrow.

The thermal dissociation of n–1,3–C4H5 results in formation of C2H2 + C2H3,72 with C2H3 promptly dissociating further to C2H2 + H at temperatures greater than 800 K.29 The thermal dissociations of i–1,3–C4H5 and n–1,2–C4H5 result in formation of vinylacetylene + H,73 whereas the decomposition of 2–C4H5 leads to 1,2,3–butatriene + H products.74 Battin-Leclerc and coworkers reported rate coefficients for the dissociations of n–1,3–C4H5, i–1,3–C4H5, n–1,2–C4H5, and 2–C4H5 radicals ranging from 5 × 105 to 4 × 1010 s-1 as temperatures increase from 1428– 2354 K.73,74 Consequently, in this study all C4H5 radicals are assumed to dissociate rapidly upon formation, and the C–H bond scission step has been combined with the radical dissociation step to give one effective reaction (1e, 1f, 2d, 3a, and 4e) with the initial rate coefficient for C4H5 formation determining the overall reaction rate. At temperatures below 1750 K the C–H bond scission reactions are generally not competitive with C4H5 production by bimolecular H–atom abstraction reactions with H, CH3 and C3H3 radicals produced through secondary processes. As above, the reactions forming a C4H5 radical via H–atom abstraction and the rapid dissociation of that radical are combined in one step with the initial reaction being rate controlling. Rate coefficients for H–abstractions from the central and terminal carbons of 1,3–C4H6 by CH3 and H–atom have been calculated from RRKM/ME theory (reactions 7 and 8, respectively). 1,3–C4H6 + H → C2H2 + H2 + C2H3

(7a)

→ C4H4 + H2 + H

(7b) 24 ACS Paragon Plus Environment

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1,3–C4H6 + CH3 → C2H2 + CH4 + C2H3

(8a)

→ C4H4 + CH4 + H

(8b)

The rate of reaction of C3H3 with 1,3–C4H6 (9) is slower than reactions 7 and 8 due to the C3H3 radicals resonant stability, but leads to the production of C2H2 + C2H3 + allene (aC3H4). The rate coefficient expression used here for k9 was taken from Kern et al.15 1,3–C4H6 + C3H3 → C2H2 + aC3H4 + C2H3

(9)

The rate coefficients and products formed following H–atom abstraction reactions from all remaining C4H6 isomers by CH3, C3H3 and H were taken from the literature.16–19,74 1,2–C4H6 + H → C4H4 + H2 + H

(10a)

1,2–C4H6 + CH3 → C4H4 + CH4 + H

(11)

1,2–C4H6 + C3H3 → C4H4 + aC3H4 + H

(12)

2–C4H6 + H → C4H4 + H2 + H

(13a)

2–C4H6 + CH3 → C4H4 + CH4 + H

(14)

2–C4H6 + C3H3 → C4H4 + aC3H4 + H

(15)

1–C4H6 + H

→ C4H4 + H2 + H

(16a)

→ C2H2 + C2H5

(16b)

1–C4H6 + CH3 → C4H4 + CH4 + H

(17)

1–C4H6 + C3H3 → C4H4 + aC3H4 + H

(18)



Page 26 of 99

H-atom addition-elimination reactions are also important during the pyrolysis of unsaturated hydrocarbons.75–77 Hidaka and co-workers included addition-elimination channels for the 1,3– C4H6 + H reaction that produce C2H3 + C2H4 (7c), for the 1,2–C4H6 + H reaction that produce CH3 + aC3H4 (10b), and for the reactions of H-atoms with 1–C4H6 that yield C2H2 + C2H5 (16b) and CH3 + aC3H4 (16c), in their experimental C4H6 studies.16–19 More recently, ab initio calculations by Miller reported pathways for reactions 7b, 10b and 16c on the C4H7 potential energy surface at the G3/B3LYP level of theory.78 The model presented here includes reactions 7c, 10b, 16b and 16c, and uses the Arrhenius parameters for k7c, k10b, k16b and k16c reported by Hidaka et al.16 The theoretical study by Miller78 also identified an addition-elimination pathway for the 2-C4H6 + H reaction that yields CH3 + pC3H4 (propyne) (13b), and reported barrier heights for reactions 13b and 16c of 2.7 and 1.5 kcal mol-1, respectively, relative to the reactants. In the model presented here we also include reaction 13b, with Arrhenius parameters for k13b estimated to equal those reported by Hidaka et al. for k16c.16 1,3–C4H6 + H → C2H4 + C2H3

(7c)

1,2–C4H6 + H → CH3 + aC3H4

(10b)

2–C4H6 + H → CH3 + pC3H4

(13b)

1–C4H6 + H → CH3 + aC3H4

(16c)

These addition-elimination reactions influence the relative concentrations of the parent and products of C4H6 pyrolysis simulated using the model developed here over millisecond timescales and at higher total pressures. However, brute force sensitivity analysis has demonstrated that increasing or decreasing rate coefficients k7c, k10b, k13b, k16b and k16c by a factor of five has only a minor effect on the consumption rate of the parent C4H6 isomer, and alters the 26 ACS Paragon Plus Environment

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relative concentrations of the minor products of C4H6 pyrolysis reported here over millisecond timescales by less than 25%. With respect to simulation of the LS experiments, the additionelimination reactions of H-atoms with C4H6 isomers are only of minor importance, particularly early in reaction, because there are never simultaneously high concentrations of H and C4H6. 4.2. C4H4 Species The above reactions of C4H6 isomers (7b, 8b, 10a, 11, 12, 13a, 14–16a, 17 and 18) lead to the formation of C4H4 species vinylacetylene and 1,2,3–butatriene. Cremer et al. calculated stationary points along the C4H4 potential using quantum chemical methods.79 These authors reported vinylacetylene as the most stable closed shell species on the potential, and calculated that 1,2,3–butatriene lies between 7.6 and 11.5 kcal mol-1 higher in energy, depending on the level of theory. In addition, Cremer and co-workers identified a path connecting 1,2,3–butatriene with vinylacetylene that proceeds via an allenyl carbene intermediate, with a barrier height of 69–78 kcal mol-1 relative to 1,2,3–butatriene, depending on the level of theory.79 Furthermore, in the C4H6 shock tube studies by Hidaka and co-workers 1,2,3–butatriene was not observed, leading these authors to conclude that 1,2,3–butatriene rapidly isomerizes to vinylacetylene under their experimental conditions.16–19 Here we invoke the same assumption as Hidaka and coworkers and treat H-atom eliminations from 2–C4H6 (3a) and from carbon three of 1,2–C4H6 to both proceed directly to vinylacetylene (C4H4) + H + H products. Site-specific phenomenological rate expressions for H–atom eliminations from the terminal and central carbons of 1,3–C4H6 that lead to formation of C4H4 + H + H (1e) and C2H2 + C2H3 (1f), respectively, have been calculated from RRKM/ME theory. Phenomenological rate expressions for H–atom eliminations from carbons one, three and four of 1,2–C4H6 were also calculated from theory. The sum of these site-specific rate coefficients gave the overall rate 27 ACS Paragon Plus Environment


Page 28 of 99

coefficient for C4H4 + H + H formation from 1,2–C4H6, k2d. The computed k2d values were fit to a non-Arrhenius expression at each pressure. The site-specific and overall k2d rate coefficient expressions are listed in Table S3 of the supplementary material. 1,3–C4H6 + M → C2H2 + C2H3 + H + M

(1e)

→ C4H4 + H + H + M

(1f)

1,2–C4H6 + M → C4H4 + H + H + M

(2d)

At the conditions relevant to this study the only significant H-atom elimination site from 1–C4H6 is from the central carbon to give the resonantly stabilized n–1,2–C4H6 radical.74 Similarly, the only possible H–atom elimination sites from 2–C4H6 are from either methyl group. The computed rate coefficients for these reactions were used to quantify the rates of C4H4 + H + H formation from 2–C4H6 (k3a) and 1–C4H6 (k4e). 2–C4H6 + M → C4H4 + H + H + M

(3a)

1–C4H6 + M → C4H4 + H + H + M

(4e)

4.3. C3H3 Chemistry Analysis of the experimental LS density gradient profiles of all of the C4H6 isomers considered here has shown that a significant portion of the later density gradient can be attributed to the exothermic reactions associated with the complex recombination of C3H3 radicals (6), and their reactions with H–atoms and CH3 radicals. Theoretical80,81 and experimental studies82–84 have shown that at the temperatures of the current work C3H3 recombination (6) leads to formation of eight C6H6 isomers which can subsequently interconvert ultimately leading to


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benzene. The theoretical work of Georgievskii et al.81 also showed that at high temperatures the initial C6H6 complex can dissociate to phenyl radical, C6H5, and an H-atom. The total rate coefficient for C3H3 recombination, k6, was recently measured, in the same apparatus used in the current work, by the LS technique at pressures of 130 Torr and temperatures ranging from 1023– 1446 K,85 and the experimental density gradients were simulated using the theoretical product distributions reported by Miller et al.80 As the current work is concerned with the early stages of C4H6 pyrolysis we take advantage of the LS technique’s sensitivity to ∆Hr and simplify C3H3 recombination into three reactions (6a–6c), where C6H6, Bz is benzene and C6H6, other represents a combined surrogate for the remaining seven C6H6 isomers. (∆Hr, 298 K = -148.1 kcal mol-1)

(6a)

→ C6H5 + H

(∆Hr, 298 K = -35.3 kcal mol-1)

(6b)

→ C6H6, other

(∆Hr, 298 K = -87.6 kcal mol-1)

(6c)

C3H3 + C3H3 → C6H6, Bz

The benzene and C6H5 + H production rate coefficients, k6a and k6b respectively, were calculated using the theoretical product branching fractions reported by Miller et al.80 and the k6 value measured by Tranter et al.85 The product distributions of the remaining C6H6 isomers were obtained from Miller et al.80 and used to weight the standard heat of reaction, ∆Hr, of each remaining C6H6 product channel. Subsequently, the net enthalpy of reaction associated with formation of the alternate C6H6 isomers was estimated at temperatures in the range 1400–2360 K. Under these conditions ∆Hr varies from -89.4 to -88.8 kcal mol-1.39 For simulation purposes the thermochemical properties of the C6H6 isomer 3,4–dimethylenecyclobutene (3,4–DMCB) are used for C6H6,

other

as the ∆Hr for formation of 3,4–DMCB by C3H3 recombination closely

approximates the combined reaction enthalpy. The validity of this approximation has been tested



by simulating density gradient profiles following C3H3 recombination using the full mechanism reported by Miller et al.,80 and using the three product channel mechanism described here. These tests confirmed that the density gradients simulated using the full and approximate mechanisms are effectively indistinguishable at temperatures ranging from 1400–2360 K. The rate coefficient, k6c, is defined as k6c = k6 - k6a - k6b. Another important reaction of propargyl is H + C3H3 (19). This reaction can proceed along several product paths depending both on the relative orientation of the reactants at the point of reaction, and whether the reaction occurs via an addition, addition-elimination or direct abstraction process.86,87 H atom addition to C3H3 can result in formation of either propyne (pC3H4, 19a) or allene (aC3H4, 19b). The addition-elimination reaction proceeds via initial complex formation followed by subsequent elimination of H2, and yield either singlet propadienylidene (1H2CCC), or singlet propargylene (1C3H2) as co-product; whereas direct H atom abstraction from C3H3 produces triplet propargylene (3C3H2). The VARIFLEX code88 was used to compute phenomenological rate coefficients for the various product channels (over the pressure and temperature ranges of the present experimental study) following reaction 19 using the C3H4 potential reported by Miller et al.86 The direct H atom abstraction channel is the dominant source of C3H2 under the conditions of this study and accounts for more than 60% of the total C3H2 (1C3H2 + 3C3H2 + 1H2CCC) formed through reaction 19. At the experimental temperatures of this work these various forms of C3H2 can rapidly interconvert,89 and consequently here we treat 3C3H2 as the sole product of reaction 19. The computed rate coefficients for each of the pressure dependent addition-elimination channels were summed with the rate coefficient for direct H-atom abstraction, to give the total rate coefficient for 3C3H2 formation following reaction 19 as a function of temperature and pressure. The sum of these


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computed rate coefficients were fit using a non-Arrhenius expression to provide temperature dependent k19c values at 30, 60, 120 and 240 Torr. The kinetics and branching associated with the CH3 + C3H3 association reaction are treated explicitly by the code used to simulate the experimental density gradient profiles. H + C3H3 + M → pC3H4 + M

(∆Hr, 298 K = -91.9 kcal mol-1)

(19a)

→ aC3H4 + M

(∆Hr, 298 K = -90.5 kcal mol-1)

(19b)

→ 3C3H2 + H2 + M

(∆Hr, 298 K = 44.4 kcal mol-1)

(19c)

The dominant C4H6 dissociation channels reported here yield both C3H3 and CH3 radical products. The CH3 chemistry used in the current work was taken from previous experimental work,71 the details of which are provided in Table S3 of the supplementary material.

5. Results and Discussion A total of 502 laser schlieren (LS) experiments have been carried out that span all four C4H6 isomers. The loading and postshock experimental conditions, as well as the dissociation rate coefficient of the parent molecule to CH3 + C3H3 (k1d, k2b, k3b or k4a) are listed in Tables S2a–p of the supplementary material. Each of the LS density gradient profiles can been successfully simulated using an internally consistent model that incorporates the 83 reactions listed in Table S3 of the supplementary material, the key reactions used to simulate LS experimental density gradient profiles at ~120 Torr are listed in Table 2. In the remainder of this section the experimental and modeling results for each isomer along with a comparison to selected experiments from the literature are discussed.



5.1. Pyrolysis of 1,3–butadiene A total of 189 experiments were performed behind incident shock waves at P2 of 29 ± 3, 60 ± 4, 123 ± 9, and 249 ± 20 Torr and temperatures ranging from 1739–2354 K using reagent mixtures of 1, 2, and 4% 1,3–C4H6 dilute in either krypton, argon or xenon. Representative experimental density gradient profiles over a range of conditions are presented in Figures 4a–d, with the corresponding raw LS signals included in the insets of each panel. Each of the experimental density gradient profiles measured following thermal decomposition of 1,3–C4H6 can be successfully simulated using the mechanism listed in Table S3 (solid black lines). In Figure 4d the start of the simulation has been delayed by 0.4 µs as shown by the vertical dashed line to account for incubation delay, ti. This behavior been reported in other LS studies at high temperatures and low pressures and accounts for vibrational relaxation of the parent species prior to dissociation.90–92


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Figure 4: Semi-log experimental absolute density gradient plots for the pyrolysis of 1,3–C4H6 dilute in krypton over a range of temperatures, pressures and concentrations. The corresponding raw LS signals are included in the inset of each panel. The solid black lines show the simulated density gradients for comparison. Included in Figure 4a are simulated density gradients using k1d × 1.5 (red dashed line) and k1d × 0.5 (blue dotted line). The vertical dashed line in panel 4d



indicate the incubation delay time, ti. Open and filled circles represent positive and negative density gradients, respectively. Accurate simulation of the experimental density gradient profiles following decomposition of 1,3–C4H6 necessitates a model that includes the formally direct dissociation path to CH3 + C3H3 (1d). Reaction 1d is the dominant product channel during 1,3–C4H6 pyrolysis at temperatures ranging from 1739–2354 K, with branching fractions (defined here as k1d/k1, where k1 = k1a + k1b + k1c + k1d + k1e + k1f + k-2a + k-4c) ranging from 0.62–0.78 with greatest yields at the lowest temperatures, independent of pressure. Molecular fragmentation of 1,3–C4H6 to C2H2 + C2H4 (1b) is a relatively minor loss channel with branching fractions (k1b/k1) ranging from 0.04–0.15, independent of pressure but that increase with temperature from 1739–2354 K. Isomerization from 1,3–C4H6 to 2–C4H6 (1c) is the most significant isomerization channel with a branching fraction (k1c/k1) of ~ 0.12 independent of temperature and pressure. Branching for isomerization from 1,3–C4H6 to 1,2–C4H6 (k-2a/k1) ranges from 0.05–0.1, independent of temperature and pressure. Direct H-atom elimination from the central 1,3–C4H6 carbons (1f) is also a minor channel, with branching fractions (k1f/k1) of less than 0.05 under all conditions, but with greater yields at higher temperatures and pressures. The contributions of direct dissociation to vinyl (C2H3) radicals (1a), H-atom elimination from the terminal carbons (1e), and isomerization to 1–C4H6 (-4c) to the total removal of 1,3–C4H6 are negligible under all experimental conditions. The simulated density gradient profiles are highly sensitive to the rate of formally direct dissociation of 1,3–C4H6, k1d, as demonstrated by Figure 4a, which includes the density gradient simulations with k1d both increased (red dashed line) and decreased by 50% (blue dotted line). Increasing k1d by 50% results in a simulation that underestimates the experimental density 34 ACS Paragon Plus Environment

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gradient profile at time greater than 4 µs, alternatively, decreasing k1d by 50% results in a simulation that significantly underestimates the initial gradient. The pressure and temperature dependent experimental k1d values measured here are plotted in Arrhenius form in Figure 5. The experimental k1d values show non-Arrhenius behavior and are in the falloff regime under the conditions of this study. The data set at each pressure was fit using a non-Arrhenius expression (solid lines). The k1d values calculated from RRKM/ME theory at pressures of 30, 60, 120 and 240 Torr are included in Figure 5 for comparison. The k1d values derived from RRKM/ME analysis generally underestimate the experimental rate coefficients under the conditions of this study, with disparity between theory and experiment increasing as pressures increase and temperatures decrease; for example at 249 Torr and 1739 K the theoretical value for k1d underestimate the experimentally measured rate coefficient by more than a factor of 4.

Figure 5: Arrhenius plot of the temperature and pressure dependent rate coefficients, k1d, for the 1,3–C4H6 + M → CH3 + C3H3 + M reaction in krypton, argon or xenon bath gas. The solid lines 35 ACS Paragon Plus Environment


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show the least squares fit through the data set at each experimental pressure, the corresponding non-Arrhenius parameters are listed in Table 2. The error in the experimental rate coefficients is estimated at ±50%. The dotted, dashed, dot-dashed, and dot-dot-dashed lines show the temperature dependent k1d values calculated from RRKM/ME analysis at 30, 60, 120 and 240 Torr, respectively. The corresponding non-Arrhenius parameters are listed in Table 2.

There is poor quantitative agreement between experiment and theory regarding the formally direct rate coefficient for 1,3–C4H6 dissociation, k1d. However, the error in the phase space theory used to compute microcanonical rate coefficients associated with bond scission processes such as this are estimated at a factor of 5. Furthermore, the effect of varying the energy transfer parameter, , typically treated as an adjustable fitting parameter, has not been explored. More refined theoretical calculations will be the subject of future work. 5.1.1. Comparison with Previous 1,3–butadiene Experiments To the best of our knowledge, this is the first investigation of 1,3–C4H6 pyrolysis to consider a formally direct dissociation pathway (1d). Analysis of the experimental LS density gradient profiles has assigned reaction 1d as the dominant product channel during the decomposition of 1,3–C4H6. Molecular dissociation (1b) and isomerizations to alternative C4H6 species represent relatively minor product channels of 1,3–C4H6 decomposition at pressures of 29–254 Torr and temperatures ranging from 1739–2354 K. This mechanism is consistent with the flash pyrolysis experiments using a heated silicon carbide tube by Chambreau et al.,

21

that

detected CH3 + C3H3 as initial products of 1,3–C4H6 decomposition at temperatures ~1500 K, but inconsistent with the facile isomerization channel proposed by Hidaka et al. at total pressures of


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1.3–4.1 bar and temperatures ranging from 1200–1700 K using off-line diagnostics.16 Chambreau and co-workers used TOF–MS to detect the initial products of 1,3–C4H6 decomposition with tens of microsecond time resolution, while the mechanism proposed by Hidaka et al.16 was based largely on stable reaction products detected on millisecond timescales. Hidaka et al. developed a mechanism initiated by facile isomerization from 1,3–C4H6 to 1,2– C4H6 (-2a), followed by dissociation of 1,2–C4H6 to CH3 + C3H3 (2b) to explain their detection of CH4 and 1,2–C4H6 as products. It is worthwhile to consider the magnitudes of the isomerization (2a) and dissociation (2b) rate coefficients required to simulate the LS density gradient profiles reported here using a mechanism that does not include the formally direct dissociation of 1,3–C4H6 (1d) and 2–C4H6 (3b) as shown in Figure 6. The black solid line (model A) in Figure 6 represents the simulated density gradient profile using the model developed here. The blue line (model B) shows the simulated density gradient with formally direct dissociation channels 1d and 3b omitted from the mechanism, and with the isomerization rate from 1,2–C4H6 to 1,3–C4H6 (k2a) and the direct dissociation rate for 1,2–C4H6 to CH3 + C3H3 (k2b) fixed at the values reported here. This simulation clearly demonstrates that without reactions 1d and 3b the model does not come close to replicating the experimental density gradient profile. The green line (model C) shows the simulated density gradient profile again without reactions 1d and 3b, but using the k2a and k2b values reported by Hidaka et al.16 Even using the higher pressure experimental k2a and k2b values reported by Hidaka and co-workers, the model significantly underestimates the early experimental density gradient without including the formally direct dissociation channels. The red line (model D) shows that a satisfactory simulation of this experimental LS density gradient profile is possible without the formally direct dissociation channels included in the mechanism,



but requires dissociation (k2b) and isomerization rate coefficients (k2a) for 1,2–C4H6 that are factors of ~4 and ~80 faster than those derived from RRKM/ME theory, respectively.

Figure 6: Semi-log experimental absolute density gradient plots for the pyrolysis of 1% 1,3–C4H6 dilute in krypton at 244 Torr and 1860 K. Model A (black solid line) shows the density gradient profile simulated using the mechanism developed in this study. Simulated density gradient profiles are included with the formally direct channels 1d and 3b omitted from the mechanism and with the isomerization (k2a) and direct dissociation rate coefficients for 1,2–C4H6 (k2b) fixed at the RRKM/ME values (Model B, blue dotted line), using the k2a and k2b values reported by Hidaka et al.16 (Model C, green dash-dot line), and with k2a and k2b adjusted to simulate the experimental density gradient profile (Model D, red dashed line).

The model proposed by Hidaka et al. required rapid isomerization from 1,3–C4H6 to 1,2– C4H6 to rationalize the products observed during their experiments.16 Here we provide strong evidence for the importance of a formally direct dissociation path from 1,3–C4H6 to CH3 + C3H3 38 ACS Paragon Plus Environment

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(1d). The mechanism proposed here removes the need for the facile isomerization channel suggested by Hidaka et al.,16 as CH3 + C3H3 are produced directly from 1,3–C4H6 (1d). Hidaka et al.16 observed 1,2–C4H6 in their products, however, instead of being formed from 1,3–C4H6 isomerization, 1,2–C4H6 could be formed, at least in part, by the CH3 + C3H3 (-2b) reaction in the shock heated gases and in the quenching phase of their single-pulse experiments. Hidaka et al. reported C2H2, C2H4, C4H4, and CH4 as major products of reaction 1.16 The product distributions reported by Hidaka et al. following pyrolysis of a 0.5% 1,3–C4H6, 99.5% argon mixture are plotted in Figure 7, together with the product distributions simulated using the model developed during this study. The model compiled here captures the general product distribution trends of both the major and minor products reported by Hidaka and co-workers, despite their measurements being made at higher total pressures, over significantly longer timescales, and using a different detection technique, than the present study.



Figure 7: Relative parent and product concentration profiles reported by Hidaka et al.16 following pyrolysis of a 0.5% 1,3–C4H6, 99.5% argon gas mixture using off-line GC–TCD, at pressures ranging from 1.36 (1200 K) to 2.17 (1600 K) bar. All concentrations are plotted relative to the initial 1,3–C4H6 concentration. Effective heating times are 2400 µs (1200 K), 2050 µs (1300 K), 1760 µs (1400 K), 1520 µs (1500 K), and 1300 µs (1600 K). The solid curves show the simulated product distributions using the mechanism developed in this study.

Kiefer et al. investigated the decomposition of 1,3–C4H6 behind shock waves using LS densitometry to extract kinetics and TOF–MS to monitor the decay of the parent and formation 40 ACS Paragon Plus Environment

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of stable products at pressures of 200–500 Torr and temperatures ranging from 1400–2200 K.13 Sample LS density gradient profiles reported by Kiefer and co-workers13 following decomposition of 4% 1,3–C4H6 dilute in argon are plotted in Figure 8, measured at post-shock pressures and temperatures of 180 Torr and 1853 K (Figure 8c), and 190 Torr and 1766 K (Figure 8d). Also included in Figure 8 are LS density gradient profiles of 4% 1,3–C4H6 dilute in krypton measured during this study under comparable post-shock conditions (Figure 8a and Figure 8b). The solid lines show the simulated density gradient profiles using the 124 Torr mechanism developed in this study, but with the rate coefficient for the formally direct dissociation of 1,3–C4H6 (k1d) increased by approximately 26% to account for the increase in P2. The model developed in this study simulates the first 5 µs of the experimental density gradient profile measured here very well (solid black lines, Figure 8a and Figure 8b). However, the same model does not capture the early experimental density gradient profiles reported by Kiefer and co-workers (solid red lines, Figure 8c and Figure 8d), and significantly overestimates their density gradient at times greater than 1.5 µs. It is difficult to ascertain the reason for the discrepancy between the density gradient profiles reported here and those measured by Kiefer et al. without access to the corresponding raw LS signals measured by those authors. The DFST experiments required the use of krypton bath gas to generate post-shock conditions comparable with the measurements made by Kiefer et al.13 Additional LS experiments following decomposition of 1,3–C4H6 were carried out using both argon and xenon bath gases. The experimental rate coefficients derived from these density gradient profiles for the formally direct dissociation of 1,3–C4H6 (k1d) are plotted in Arrhenius form in Figure 5., and demonstrate that no third body kinetic effects were observed through using different bath gases.



Figure 8: Semi-log experimental absolute density gradient plots for the pyrolysis of 4% 1,3–C4H6 dilute in krypton (8a and 8b), with corresponding raw LS signals included in the inset. The black solid lines show the simulated density gradient using the mechanism developed here (see text for details). Semi-log experimental absolute density gradient plots following pyrolysis of 4% 1,3– C4H6 dilute in argon (8c and 8d) reported by Kiefer et al.13 Solid red lines show the simulated density gradient profiles using the mechanism developed here (see text for details).


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The TOF–MS experiments by Kiefer et al. reported C2H2 and C2H4 as major products of 1,3–C4H6 decomposition dilute in neon at pressures of ~300 Torr and temperatures ranging from 1400–2000 K.13 The concentration profiles for 1,3–C4H6, C2H2 and C2H4 derived from those experiments are presented in Figure 9. Also included are the corresponding concentrations simulated using the model developed by Kiefer et al. (dashed lines, Figure 9) that clearly demonstrate the mechanism proposed by those authors overestimates the experimental C2H4 profile at high temperatures. The solid lines in Figure 9 show the concentration profiles simulated using the model developed here at 249 Torr. The simulations capture the shape of the experimental profiles well, and, given the scatter in the experimental profiles, the agreement between this model and the concentration profiles reported by Kiefer et al. is very good.



Figure 9: Time-of-flight mass spectrometry concentration profiles for C4H6, C2H2 and C2H4 following the thermal decomposition of 3% 1,3–C4H6, dilute in neon, behind reflected shock waves reported by Kiefer et al.,13 under comparable experimental conditions to those considered in this study. The solid lines represent simulation results using the model developed in this study. The dashed lines show the C2H2 and C2H4 concentration profiles simulated by Kiefer et al.13


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5.2. Pyrolysis of 1,2–butadiene A total of 117 experiments were performed behind incident shock waves at P2 of 29 ± 4, 60 ± 2, 123 ± 8, and 237 ± 23 Torr and temperatures ranging from 1452–2113 K, using reagent mixtures of 1, 2 and 4% 1,2–C4H6 dilute in krypton. Representative experimental density gradient profiles and simulations, that cover a range of initial and post shock conditions, are presented in Figures 10a– d; the corresponding raw LS signals are included in the insets of each panel. Direct dissociation to CH3 + C3H3 (2b) is the dominant loss process for 1,2–C4H6 under the conditions considered in this study, with branching fractions (defined here as k2b/k2, where k2 = k2a + k2b + k2c + k2d + k-4b) ranging from 0.63–0.75 that increase with both temperature and pressure. The simulated density gradient profiles are sensitive to the dissociation rate coefficient of 1,2–C4H6 to CH3 + C3H3 (k2b), as demonstrated in Figure 10a. Isomerization from 1,2–C4H6 to 1,3–C4H6 (2a) is the second most important process during the thermal decomposition of 1,2– C4H6, with branching fractions (k2a/k2) that range from 0.17–0.26, independent of temperature, that are most significant at lowest pressures. Branching fractions for isomerization from 1,2– C4H6 to 2–C4H6 (k2c/k2) range from 0.09–0.13, independent of pressure but with greater flux at lower temperatures. Isomerization from 1,2–C4H6 to 1–C4H6 (–4b) is negligible under all conditions considered in this study. A common feature of all the C4H6 isomers studied here is that the exothermic recombination of CH3 (-5) and C3H3 radicals (6) dominate the secondary chemistry. These reactions generate negative density gradients (Eq. 2), although the change in sign is not always distinguishable from the experimental noise. C2H6 + M → CH3 + CH3 + M

(∆Hr, 298 K = 90.0 kcal mol-1) 45 ACS Paragon Plus Environment

(5)


Figure 10: Semi-log experimental absolute density gradient plots for the pyrolysis of 1,2–C4H6 dilute in krypton over a range of temperatures, pressures and concentrations. The corresponding raw LS signal is included in the inset of each panel. The solid black lines show the simulated density gradients for comparison. Included in panel 10a are simulated density gradients using k2b


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× 1.5 (red dashed line) and k2b × 0.5 (blue dotted line). Open and filled circles represent positive and negative density gradient, respectively. The experimental pressure and temperature dependent k2b values derived from LS experiments are plotted in Arrhenius form in Figure 11. At each pressure the data set has been fit using a non-Arrhenius expression (solid lines). The rate coefficients calculated from RRKM/ME analysis (dashed lines) at comparable pressures are included for comparison. The agreement between the experimental and theoretical k2b values are excellent at all pressures for temperatures below ~1800 K. Both the experimental and theoretical k2b values presented here show Arrhenius curvature. However, the experimental falloff behavior is not fully captured by the theory and consequently at pressures of 29, 60 and 123 Torr the theory overestimates the experimental k2b values by as much as 53% at temperatures of ~2000 K. Despite the disparity between the theoretical and experimental k2b values at higher temperatures, these disagreements are all well within the combined uncertainties.

Figure 11: Arrhenius plot of the temperature and pressure dependent rate coefficients, k2b, for the 1,2–C4H6 + M → CH3 + C3H3 + M reaction. The solid lines show the least squares fit through



the data sets at each experimental pressure, the corresponding non-Arrhenius parameters are listed in Table 2. The error in the experimental rate coefficients is estimated at ±50%. The dotted, dashed, dot-dashed, and dot-dot-dashed lines show the temperature dependent k2b values calculated from RRKM/ME analysis at 30, 60, 120 and 240 Torr, respectively. The corresponding non-Arrhenius parameters are listed in Table 2.

5.2.1. Comparison with Previous 1,2–butadiene Experiments The only previous investigations of 1,2–C4H6 pyrolysis that included isomerization channels in their reaction mechanisms are the shock tube studies by Hidaka et al.17 and Kern et al.15 Hidaka and co-workers reported 1,3–C4H6, 2–C4H6, 1–C4H6, C2H2, C2H4, C4H4 and CH4 as major products, and concluded that the dominant processes responsible for 1,2–C4H6 removal were direct dissociation to CH3 + C3H3 (2b) and isomerization to 1,3–C4H6 (2a).17 Hidaka and co-workers reported that branching through reaction 2b increases from 0.39–0.47 as temperatures increase from 1450–1600 K, while branching from 1,2–C4H6 to 1,3–C4H6 (2a) decreases with temperature from 0.31–0.25 over the same range. In addition, Hidaka and colleagues reported that isomerization from 1,2–C4H6 to 2–C4H6 (2c) was a relatively minor channel, with a branching fraction of ~0.1 independent of temperature between 1450–1600 K. These reaction paths and branching fractions reported by Hidaka et al. are consistent with those reported here. However, the analysis by Hidaka et al. concluded branching from 1,2–C4H6 to 1– C4H6 (-4b) of ~0.17 at temperatures ranging from 1450–1600 K, whereas the model developed here has shown branching through reaction -4b (k-4b/k2) is nearly negligible under these conditions. The theoretical methods used here have calculated 0 K barrier heights for reactions 2c and -4b relative to 1,2–C4H6 of 72.9 and 73.7 kcal mol-1, respectively (Figure 2). Both 48 ACS Paragon Plus Environment

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isomerization paths from 1,2–C4H6 to alkyne products pass through carbene intermediates. However, 1,2–C4H6 passes through a relatively tight transition state to form propenyl carbene (CH3CHCHCH), on the path to produce 1–C4H6 (-4b), compared to the loose transition state path required to form methyl vinyl carbene (CH3CCHCH2) on route to 2–C4H6 (2c). Furthermore, the 2–C4H6 well lies 3.7 kcal mol-1 lower in energy than 1,2–C4H6, whereas 1–C4H6 sits 1.1 kcal mol-1 higher in energy than 1,2–C4H6 (Figure 2). Consequently, isomerization from 1,2–C4H6 to 2–C4H6 is expected to be a more facile process than isomerization to 1–C4H6. The product distributions reported by Hidaka et al.17 are plotted in Figure 12, with the corresponding simulations using the mechanism developed in this study (solid lines) included for comparison. The agreement between the experimental measurements by Hidaka and co-workers and the profiles simulated using the mechanism developed here is excellent for almost all species, and well within the combined experimental uncertainties. Significantly, the model developed here, based on relatively low pressure measurements, simulates the relative yields of 1,3–C4H6 and 2–C4H6 reported following higher pressure measurements by Hidaka et al. well, given the scatter in these experimental data. The production of 1,3–C4H6 and 2–C4H6 at temperatures relevant to the experiments by Hidaka et al. occurs primarily through direct isomerization from 1,2–C4H6 (2a and 2c), with relatively minor contributions from CH3 + C3H3 cross-combination reactions (-1d and -3b). There is a significant discrepancy between the simulated 1–C4H6 concentrations and the experimental profile reported by Hidaka et al. (Figure 12). We cannot attribute this to a particular source, however, a possibility is that 1–C4H6 is being formed by the combination of CH3 and C3H3 radicals (-4a) during the quenching phase of Hidaka and co-workers single pulse shock tube experiments. A similar issue was noted with single pulse shock tube studies of the allyl radical.93



Figure 12: Relative parent and product concentration profiles reported by Hidaka et al.17 following pyrolysis of a 1% 1,2–butadiene, 99% argon gas mixture using off-line GC–TCD, at pressures ranging from 1.23 (1200 K) to 2.3 (1600 K) bar. All concentrations are plotted relative to the initial 1,2–C4H6 concentration. Effective heating times are 2700 µs (1100 K), 2400 µs (1200 K), 2250 µs (1300 K), 2150 µs (1400 K), 2000 µs (1500 K), and 1800 µs (1600 K). The solid curves show the simulated product distributions using the mechanism developed in this study.


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Kern et al. studied the decomposition of 1,2–C4H6 using TOF–MS to detect both reactant and products, and were able to simulate their product profiles using a mechanism that included isomerization from 1,2–C4H6 to 1,3–C4H6 (2a), and fragmentation of 1,2–C4H6 to CH3 + C3H3 (2b).15 These authors reported branching fractions through reaction 2a that range from 0.49–0.6 and increase with temperature from 1500–2000 K. Kern et al. adopted the 1,3–C4H6 decomposition mechanism proposed by Kiefer et al.,13 with chemistry initiated by dissociation of the conjugated diene to give two C2H3 radicals (1a). However, as previously discussed, both the thermochemistry and kinetics relating to the C2H3 radical reported by Kiefer et al. have since been proven inaccurate.29,39 Furthermore, the experimental and theoretical methods used here have concluded that the decomposition of 1,3–C4H6 to C2H3 radicals under the conditions of Kern and co-workers experiments is negligible. It is worthwhile to consider the investigations of 1,2–C4H6 and 1,3–C4H6 pyrolysis reported by Kern et al.15 and Kiefer et al.,13 respectively, using TOF–MS; studies for which mass spectra were recorded in the same laboratory. As implemented in these experiments, TOF–MS cannot distinguish between the various C4H6 isomers. Instead the total 54 m/z signal was monitored with respect to time, and attributed to all C4H6 isomers. In Figure 13 the time-resolved total C4H6 decay profile reported by Kern et al.15 is shown for 3% 1,2–C4H6 dilute in neon at 1716 K and 272 Torr. The solid line in Figure 13 shows the total C4H6 concentration simulated using the model developed in this study at 1716 K and 272 Torr, and clearly shows the model predicts a much faster rate of total C4H6 consumption than was reported by Kern et al.15 Also included in Figure 13 is the total C4H6 decay profile reported by Kiefer et al.13 following the decomposition of a 3% mixture of 1,3–C4H6 dilute in neon at 1734 K and 280 Torr (open black squares). The total C4H6 signal decays are near identical for the 1,2–C4H6 and 1,3–C4H6



experiments under comparable conditions. This would suggest one of three scenarios: 1.) 1,2– C4H6 and 1,3–C4H6 dissociate at similar rates; 2.) rapid isomerization between 1,2–C4H6 and 1,3–C4H6 occurs before one of these species dissociate to smaller mass species; 3.) both 1,2– C4H6 and 1,3–C4H6 isomerize to a common species at low temperatures prior to dissociation. However, the C4H6 profiles are inconsistent with the product distributions reported by Hidaka and co-workers following shock heating mixtures of 1,2–C4H6 and 1,3–C4H6 dilute in argon that showed 1,2–C4H6 decomposition occurs more rapidly, and at lower temperatures than 1,3–C4H6, under comparable pressures.16,17 The single pulse shock tube study by Hidaka et al. reported that at 1300 K, after an effective heating time of 2250 µs, approximately 90% of the initial 1,2–C4H6 concentration is consumed (Figure 12).17 A subsequent single pulse shock tube study by Hidaka et al.16 reported that at 1300 K, after an effective heating time of 2050 µs, only around 10% of the initial 1,3–C4H6 concentration had been consumed (Figure 7). The modest difference in effective heating times cannot account for the relative rates of 1,2–C4H6 and 1,3–C4H6 consumption reported by Hidaka and co-workers at 1300 K. Significantly, the experimental product distributions reported by Hidaka et al. following 1,2–C4H6 decomposition quantified a 1,3–C4H6 yield of only 25% at 1300 K, with approximately 90% of the parent molecule consumed (Figure 12).17 Consequently, it is concluded that the TOF–MS measurements by Kiefer et al.13 and Kern et al.15 are inconsistent with both the Hidaka et al. experiments,16,17 and the work presented here.


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Figure 13: Time-of-flight mass spectrometry concentration profile for total C4H6 concentration reported by Kern et al.15 following the thermal decomposition of 3% 1,2–C4H6, dilute in neon. The solid line shows the corresponding concentration profile simulated using the model developed in this study. Included for comparison is a time-of-flight mass spectrometry concentration profile for total C4H6 concentration reported by Kiefer et al.13 following thermal decomposition of 3% 1,3–C4H6 dilute in neon. 5.3. Pyrolysis of 2–butyne A total of 109 experiments were performed behind incident shock waves at P2 of 29 ± 3, 59 ± 2, 122 ± 7, 252 ± 7 Torr, and temperatures ranging from 1637–2268 K, using reagent mixtures of 1, 2 and 4% 2–C4H6 dilute in krypton. Representative experimental density gradient profiles and simulations, that cover a range of initial and post shock conditions, are presented in Figures 14a–d.



Figure 14: Semi-log experimental absolute density gradient plots for the pyrolysis of 2–C4H6 dilute in krypton over a range of temperatures, pressures and concentrations. The corresponding raw LS signals are included in the inset of each panel. The solid black lines show the simulated density gradients for comparison. Included in panel 14a are simulated density gradients using k3b × 1.5 (red dashed line) and k3b × 0.5 (blue dotted line). The vertical dashed lines in panel 14d indicate the incubation delay time, ti.


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Successful simulation of the experimental density gradients presented here requires a model that includes the formally direct dissociation of 2–C4H6 to CH3 + C3H3 (3b), with branching fractions through reaction 3b (defined here as k3b/k3, where k3 = k3a + k3b + k-1c + k-2c + k-4d) that range from 0.48–0.6, and increase with temperature, independent of pressure. The simulated density gradient profiles are sensitive to the rate coefficient k3b, as demonstrated in Figure 14a. Isomerization from 2–C4H6 to 1,3–C4H6 (-1c) is the second most important channel during 2–C4H6 pyrolysis with branching fractions (k-1d/k3) that vary from 0.3–0.41, independent of pressure but with greater flux at lower temperatures. Isomerization from 2–C4H6 to 1,2–C4H6 (-2c) and H-atom elimination (3a) are relatively minor loss channels for 2–C4H6 under the conditions of this study, with branching fractions through reactions -2c (k-2c/k3) and 3a (k3a/k3) of less than 0.1 and 0.05, respectively. The pressure and temperature dependencies of the formally direct 2–C4H6 dissociation rate coefficient, k3b, derived from LS experiments are plotted in Arrhenius form in Figure 15. The data set at each pressure have been fit using a non-Arrhenius expression (solid lines). The k3b values calculated using RRKM/ME theory at total pressures of 30, 60, 120 and 240 Torr are included for comparison. Both experiment and theory suggest that k3b is in the falloff regime, and demonstrates non-Arrhenius behavior, under the conditions of this study. However, the theory does not capture the falloff curvature observed experimentally, and consequently underestimates the experimental k3b values at low temperatures and overestimates the rates at high temperature; for example, the theory overestimates the experimental k3b value by 31% at 29 Torr and 2268 K, but underestimates the rate coefficient by 57% at 253 Torr and 1651 K. These discrepancies are all well within the combined uncertainties of experiment and theory.



Figure 15: Arrhenius plot of k3b values derived from LS experiments. The solid lines show the least squares fits through the data sets at each experimental pressure, the corresponding nonArrhenius parameters are listed in Table 2. The error in the experimental rate coefficients is estimated at ±50%. The dotted, dashed, dot-dashed, and dot-dot-dashed lines show the temperature dependent k3b values calculated from RRKM/ME analysis at pressures of 30, 60, 120 and 240 Torr, respectively, the corresponding non-Arrhenius parameters are listed in Table 2.

5.3.1. Comparison with Previous 2–butyne Experiments To the best of our knowledge, this is the first investigation of 2–C4H6 pyrolysis to consider a formally direct dissociation path. Hidaka et al. reported C2H2, C2H4, CH4, 1,3–C4H6, 1,2–C4H6 and pC3H4 as major products of reaction 3 and developed a mechanism based on fast isomerizations from the parent alkyne to 1,3–C4H6 (-1c) and 1,2–C4H6 (-2c) to account for these products.18 The experimental product distributions reported by Hidaka and co-workers are


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plotted in Figure 16, with the corresponding product distributions simulated using the mechanism developed here (solid lines) included for comparison.

Figure 16: Relative parent and product concentration profiles reported by Hidaka et al.18 following pyrolysis of a 2.5% 2–C4H6, 97.5% argon gas mixture using off-line GC–TCD, at pressures ranging from 1.46 (1100 K) to 2.79 (1500 K) bar. All concentrations are plotted relative to the initial 2–C4H6 concentration. Effective heating times are 2010 µs (1100 K), 1920 µs (1200 K), 1820 µs (1300 K), 1730 µs (1400 K), and 1630 µs (1500 K). The solid curves show the simulated product distributions using the mechanism developed in this study.



The experimental parent and lower mass product profiles reported by Hidaka et al.18 are in good agreement with the corresponding profiles simulated using the model developed in this study, taking into account the differences in experimental pressure, observation time, and diagnostic technique used in these studies. The model does underestimate the 1,3–C4H6 and 1,2–C4H6 product profiles reported by Hidaka et al.,18 and this may suggest that either C4H6 isomerization channels are more significant at higher pressures, or that 1,3–C4H6 and 1,2–C4H6 were produced in the quenching wave of the single pulse experiments by Hidaka et al. Nonetheless, the development of an internally consistent model, that successfully simulates the LS density gradient profiles of all four C4H6 isomers considered in this study, necessitates inclusion of the formally direct dissociation paths of 1,3–C4H6 (-1d) and 2–C4H6 (3b). Furthermore, the mechanism developed here is consistent with the flash pyrolysis experiments by Chambreau et al. that detected CH3 + C3H3 as initial products of both 1,3–C4H6 and 2–C4H6 decomposition at temperatures greater than 1425 K via TOF–MS.21 5.4. Pyrolysis of 1–butyne A total of 87 experiments were performed behind incident shock waves at P2 of 30 ± 4, 61 ± 5, 123 ± 11, and 247 ± 25 Torr and temperatures ranging from 1428–2113 K using reagent mixtures of 1, 2, and 4% 1–C4H6 dilute in krypton. Representative experimental density gradient profiles and simulations (solid black lines), that cover a range of initial and post shock conditions, are presented in Figures 17a–d; the corresponding raw LS signal is included in the inset of each panel.


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Figure 17: Semi-log experimental absolute density gradient profiles for the pyrolysis of 1–C4H6 dilute in krypton over a range of temperatures, pressures and concentrations. The corresponding raw LS signals are included in the inset of each panel. The solid black lines show the simulated density gradients for comparison. Included in panel 17a are simulated density gradients using k4a × 1.5 (red dashed line) and k4a × 0.5 (blue dotted line). Open and filled circles represent positive and negative density gradient, respectively. The vertical dashed line in panel 17d indicates the incubation delay time, ti. 59 ACS Paragon Plus Environment


The simulations have shown that the only significant product channel associated with 1– C4H6 pyrolysis under the conditions of this work is direct dissociation to CH3 + C3H3 (4a); the sensitivity of the simulations to variations in k4a are demonstrated in Figure 17a. At temperatures greater than 1800 K and under all experimental pressures considered here the density gradients measured following thermal decomposition of 1–C4H6 became negative during the course of the experimental observation time, due to the exothermic secondary chemistry of CH3 and C3H3 radicals. The temperature and pressure dependent k4a values derived from LS experiments are plotted in Arrhenius form in Figure 18. At each pressure the data set has been fit using a nonArrhenius expression (solid lines). The k4a values calculated from RRKM/ME theory at 30, 60, 120 and 240 Torr are included for comparison.

Figure 18: Arrhenius plot of k4a values derived from LS experiments. The solid lines show the least squares fit through the data sets at each experimental pressure, the corresponding nonArrhenius parameters are listed in Table 2. The error in the experimental rate coefficients is 60 ACS Paragon Plus Environment

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estimated at ±50%. The dotted, dashed, dot-dashed, and dot-dot-dashed lines show the temperature dependent k4a values calculated from RRKM/ME analysis at 30, 60, 120 and 240 Torr, respectively. The corresponding non-Arrhenius parameters are listed in Table 2.

The theoretical k4a values underestimate the experimental rate coefficients at 247 Torr at all temperatures, with the strongest disagreement at lowest temperatures; for example, at 1428 K the computed k4a value underestimates the experimental rate coefficient by 37%. Both the experimental and theoretical k4a values shown non-Arrhenius curvature, but the experimental falloff behavior is not fully captured by the theory. Consequently, at pressures of 30, 60 and 123 Torr the calculated k4a values underestimate the experimental rate coefficient at highest temperatures and overestimate the rate coefficient at lower temperatures. At these pressures the disagreement between the experimental and theoretical k4a values is most evident at 30 Torr, where the calculations overestimate the experimental rate coefficient by 35% at 2113 K and underestimate the experimental rate coefficient by 33% at 1496 K. Despite the aforementioned differences, the agreement between the experimental and theoretical k4a values reported here are satisfactory and well within the combined uncertainties. 5.4.1. Comparison with Previous 1–butyne Experiments The only previous experimental investigation of 1–C4H6 decomposition at temperatures greater than 1400 K was the shock tube study by Hidaka et al.,19 in which experiments were performed at higher pressures (1.23–2.3 bar) than were considered here. Hidaka and co-workers reported C2H2, C2H4, C4H4, CH4, 1,2–C4H6 and 1,3–C4H6 as products of reaction 4, and concluded the majority of 1–C4H6 was lost through direct fragmentation to CH3 + C3H3 (4a), and that the remainder isomerizes to 1,2–C4H6 (4b). These authors reported branching fractions 61 ACS Paragon Plus Environment


through reaction 4a ranging from 0.73–0.80 at temperatures ranging from 1430–1600 K. The product distributions reported by Hidaka et al. are plotted in Figure 19, with the corresponding product distributions simulated using the mechanism developed here (solid lines) included for comparison.

Figure 19: Relative parent and product concentration profiles reported by Hidaka et al.19 following pyrolysis of a 1% 1–C4H6, 99% argon gas mixture using off-line GC–TCD, at pressures ranging from 1.23 (1100 K) to 2.3 (1600 K) bar. All concentrations are plotted relative to the initial 1–C4H6 concentration. Effective heating times are 2400 µs (1100 K), 2240 µs (1200 62 ACS Paragon Plus Environment

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K), 2070 µs (1300 K), 1920 µs (1400 K), 1750 µs (1500 K) and 1590 µs (1600 K). The solid curves show the simulated product distributions using the mechanism developed in this study. The agreement between the experimental 1–C4H6 decay profile reported by Hidaka et al.19 and corresponding decay profile simulated using the model developed in this study is overall very good. The product distributions simulated using the model developed here for C2H2, C2H4, pC3H4, CH4 and C4H4 are also in good agreement with the experimental measurements by Hidaka et al. (Figure 19), given the scatter in these data. However, the simulation fails to capture the experimental product distributions of 1,2–C4H6 or 1,3–C4H6 reported by Hidaka et al. These differences suggest that either the rate of isomerization from 1–C4H6 to 1,2–C4H6 (k4b) is further into falloff than the rate of dissociation of 1–C4H6 to CH3 + C3H3 (k4a), and consequently at higher pressures reaction 4b becomes increasingly competitive with reaction 4a, or that C4H6 species are formed in the quenching wave of the single pulse shock tube experiments by Hidaka et al.

6. Conclusions The dissociation of small unsaturated hydrocarbons contributes to the growth of the radical pool that drive ignition processes and particulate formation,1–5 and a detailed understanding of the rates and product branching associated with small molecule decomposition is required to model combustion processes. The thermal decompositions of 1,3–C4H6, 1,2–C4H6, 2–C4H6 and 1–C4H6 have been studied over a broad range of temperatures (1428–2354 K) and pressures (26–261 Torr) using the LS technique. The results presented here greatly extend the range of experimental conditions under which decomposition of these C4H6 isomers have been reported in the literature.13–21 The entire C4H6 experimental density gradient data set has been



successfully simulated at each pressure using an internally consistent model which incorporates direct dissociations of 1–C4H6 and 1,2–C4H6, and formally direct dissociations of 1,3–C4H6 and 2–C4H6, to CH3 + C3H3. 1,3–C4H6 decomposition paths to C2H3 + C2H3 (1a) and C2H2 + C2H4 (1b) are included in the model, as are the various C4H6 isomerization pathways and H-atom elimination channels, with pressure dependent rate coefficients either calculated from RRKM/ME theory or taken from the literature. Under the conditions of this study the dominant product path for each of these C4H6 isomers is dissociation to CH3 + C3H3. The agreement between the experimental rate coefficients for the direct dissociations of 1–C4H6 (k4a) and 1,2– C4H6 (k2b), and the formally direct dissociation of 2–C4H6 to CH3 + C3H3 (k3b) and the values calculated using RRKM/ME theory are good under all conditions. However, the theoretical methods employed here underestimate the experimentally measured formally direct rate coefficient for dissociation of 1,3–C4H6 to CH3 + C3H3 (k1d). This may indicate that isomerization from 1,3–C4H6 to 1,2–C4H6 is a more facile process than the theory suggests, or point to an alternate lower energy path from 1,3–C4H6 to CH3 + C3H3 products on the C4H6 potential. Representative simulations of experimental density gradient profiles for each of the C4H6 isomers considered here using the identical model are presented in Figure 1, and demonstrate the quality of the simulations achievable using the identical model developed here at temperatures ranging from 1664–2034 K. The mechanism developed here is consistent with the products reported elsewhere on both microsecond and millisecond timescales.13,16–19 This study has identified for the first time the importance of formally direct dissociation channels in the thermal decompositions of 1,3–C4H6 and 2–C4H6. Formally direct dissociation channels are rarely treated systematically in combustion models, and the rates of these reactions typically exhibit strong


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pressure dependencies due to the redistribution of internal energy within the reactant species that follow gas-phase collisions. The work presented here highlights the need for the concerted efforts of theory and experiment to quantify the pressure dependencies of formally direct processes relevant to combustion chemistry.

7. Supporting Information Details of the theoretical methods employed in constructing and analyzing the C4H6 potential energy surface, a full list of pre and postshock conditions for all the shock tube experiments (including experimental rate coefficients for the dissociations of 1,3–C4H6, 1,2– C4H6, 2–C4H6 and 1–C4H6 to CH3 + C3H3), the full mechanism and Arrhenius parameters used in experimental analysis, the NASA polynomial used to calculate the thermochemical properties of CH3, gas chromatograms and mass spectra for each C4H6 species, and details of the alternate optical setups used here are provided in the supplementary materials. This material is available free of charge via the Internet at http://pubs.acs.org.

8. Acknowledgements This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, U.S. Department of Energy. The work at ANL was supported under contract No. DE-AC02-2006CH11357. CFG gratefully acknowledges support from Brown University and from the National Science Foundation through Award #1553366. The authors are grateful to Dr. Raghu Sivaramakrishnan for useful discussions and calculating the channel specific, temperature and pressure dependent rate coefficients for the H + C3H3 + M reaction using the VARIFLEX code.



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Figure 1 170x162mm (300 x 300 DPI)

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