Mystery of 1-Vinylpropargyl Formation from Acetylene Addition to the

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The Mystery of 1-Vinylpropargyl Formation from Acetylene Addition to the Propargyl Radical: An Open-and-Shut Case Gabriel da Silva J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b12996 • Publication Date (Web): 14 Feb 2017 Downloaded from http://pubs.acs.org on February 20, 2017

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The Journal of Physical Chemistry

The Mystery of 1-Vinylpropargyl Formation from Acetylene Addition to the Propargyl Radical: An Open-and-Shut Case

Gabriel da Silva*

Department of Chemical and Biomolecular Engineering, The University of Melbourne, Victoria 3010 Australia

*[email protected]

ABSTRACT The addition of acetylene (C2H2) to the propargyl radical (C3H3) initiates a cascade of molecular weight growth reactions that result in the production of polycyclic aromatic hydrocarbons (PAHs) in flames. Although it is well-established that the first reaction step produces the cyclic C5H5 radical cyclopentadienyl (c-C5H5), recent studies have also detected significant quantities of the open chain form, 1-vinylpropargyl (l-C5H5). This work presents a mechanism for the C3H3 + C2H2 reaction from ab initio calculations, which includes pathways for the formation of both the open and shut isomers as well as for their interconversion. Formation of both isomers proceeds from the initial HCCCH2CHCH• reaction adduct with similar barriers, both well-below the entrance channel energy. Subsequent isomerization of l-C5H5 with c-C5H5 also transpires at below the energy of the reactants, although this process connects two deep wells (being resonance stabilized radicals), and must compete with collisional energy transfer. An RRKM theory / master equation model is developed for the reported C5H5 reaction mechanism. Master equation simulations suggest that both cyclic and open-chain isomers are expected to form from the C3H3 + C2H2 reaction across a range of temperatures, although the lifetime of l-C5H5 is relatively short for rearrangement to cC5H5.

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Introduction Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous components of flames, where they are thought to lead to soot particle formation, a significant environmental concern.1-3 Describing the fundamental chemical processes that lead to the formation and growth of PAHs in flames has proven exceedingly challenging, although it is accepted that resonance stabilized radicals (RSRs) play a critical role, particularly with respect to formation of the first aromatic ring.4-5 Amongst the RSRs, propargyl (CH2=C=C•H, C3H3) is of particular importance, due to its propensity to react with itself to produce benzene.6,7 Following the formation of the first benzene unit, alternate growth mechanisms such as Hydrogen Abstraction C2H2 Addition (HACA) can take over.8,9 The reaction of RSRs with acetylene (C2H2) has been established as another mechanism for molecular weight growth in flames, which bypasses benzene formation altogether.10 This sequence is initiated by C2H2 addition to propargyl, a reaction that predominantly forms the cyclic RSR cyclopentadienyl (c-C5H5). Subsequent C2H2 additions generate the tropyl radical and then indene, a cyclopentafused PAH.10-13 A recent investigation of the C3H3 + nC2H2 cascade using isomer-resolved synchrotron VUV photionization mass spectrometry confirmed this reaction sequence, but also discovered that significant quantities of an openchain C5H5 isomer are produced in the initial reaction step, along with the cyclic form.14 This open-chain species is thought to be the 1-vinylpropargyl radical, CH2CHC•HCCH (l-C5H5). The l-C5H5 radical is an RSR, although it sits higher in energy than c-C5H5.15,16 Whereas both species have been detected in flames,17-19 only c-C5H5 is typically included in detailed chemical kinetic models of PAH formation. Importantly, trace amounts of an isomer attributed to l-C5H5 has also been seen in c-C5H5 pyrolysis at around 1000 K, suggesting that these species may be able to equilibrate below the decomposition threshold.20 The l-C5H5 radical has also been implicated in a number of astrochemical reaction mechanisms,21-23 and serves as an archetype for doubly-resonance-stabilized propargyl radical derivatives.24 In this study, computational chemistry techniques are used to revisit the C3H3 + C2H2 reaction, revealing the mechanism by which l-C5H5 is formed. Statistical reaction rate theory modelling is used to predict product branching ratios as a function of temperature and pressure, covering conditions relevant to previous experiments as well as to flames. In addition to solving the mystery of l-C5H5 formation, this work provides important insights into the isomerization and decomposition kinetics of the open-chain and cyclic C5H5 RSRs.

Methods A potential energy surface for the C3H3 + C2H2 reaction is developed using the composite G3X-K model chemistry,25 which has been designed specifically for thermochemical kinetics and provides average barrier heights at an accuracy of around 0.6 kcal mol-1. Geometries are optimized at the M06-2X/6-31G(2df,p) level of theory and demonstrate no imaginary 2 ACS Paragon Plus Environment

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frequencies for minima and one for transition states. Reported structures refer to the lowest energy conformation. Intrinsic reaction coordinate scans were used to further confirm transition state connectivity. All calculations were carried out within the Gaussian 09 software package.26 Reaction rate calculations were performed using the MultiWell-2012.1 suite27-29 in order to obtain phenomenological rate coefficient predictions, k(T,P), for C3H3 + C2H2 and related reactions. Sums and densities of state were from Stein-Rabinovitch-Beyer-Swinehart counts, assuming a rigid-rotor harmonic-oscillator model, with internal rotations in the initial addition products and the transition states leading to their formation treated as free rotors. Jahn-Teller distortion in c-C5H5 is treated as in ref 30. RRKM theory was used for microscopic rate coefficients, including Eckhart corrections for tunnelling in H-shift reactions. Collisional energy transfer was described using an energy-dependent bi-exponential model, ∆Ed = 65 + 0.0058E cm-1, using the energy transfer parameters measured for toluene.31 The bath gas was N2 and Lennard-Jones parameters for the C5H5 isomers were assumed to be σ = 5 Å and ε/kb = 300 K. The energy grained master equation was solved for 2000 grains of 10 cm-1, following which the quasi-continuum regime was extended up to 150 000 cm-1. For the chemically activated C3H3 + C2H2 reaction, master equation runs consisted of 106 independent trajectories, simulating a sufficient number of collisions to achieve steady-state or enter into the thermal decay regime.32 The PPM code was then used to extract k(T,P) values.31 For unimolecular reactions, 105 trials were employed (due to longer simulation times), and rate coefficients were fit following the initial relaxation phase.33

Results and Discussion Acetylene can add to both ends of the propargyl radical, corresponding to addition at the radical sites in the hypothetical localized acetylenic (•CH2–C≡CH) and allenic (CH2=C=C•H) forms. A potential energy diagram for the acetylenic addition mechanism is shown in Figure 1, with a corresponding diagram for allenic addition provided as Figure 2. Optimized structures for the C5H5 minima involved are depicted in Figure 3, with the transition state structures included in Figure 4. The main features of this surface were first reported by Roy et al.34 and by Moskaleva and Lin,35 with the steps leading to and from l-C5H5 described briefly in ref. 20. The mechanisms depicted in Figures 2 and 3 are connected by isomer 5, and all pathways are therefore available to both addition mechanisms and they are all incorporated into the final master equation model (they are separated into two energy diagrams only for clarity). The possible formation of 3-vinylpropargyl (CH2=C•H–C=C=CH2) was also considered, although no energetically competitive pathways were identified, including a direct H-shift in the initial reaction adduct 7. Addition of C2H2 to the acetylenic site of C3H3 requires a barrier of 12.2 kcal mol-1 (TS1) and is exothermic by almost 12 kcal mol-1. The resultant isomer can ring-close to 5 via TS3; the 3 ACS Paragon Plus Environment


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barrier for this reaction is 1.2 kcal mol-1 above the reactant energies but over 10 kcal mol-1 below the entrance transition state. An intramolecular 1,2 H-shift in 5 then provides c-C5H5 (6), with barrier over 23 kcal mol-1 below TS1. This is the conventionally accepted reaction mechanism for c-C5H5 formation from C2H2 + C3H3.34,35 Figure 1 reveals a further reaction pathway, however, that can proceed with competitive energetics. This involves ring-closing of 1 via TS2 to produce a four-membered ring compound (2), which then ring-opens to lC5H5 (3). This process is controlled by TS2, which sits at around 8 kcal mol-1 below the entrance transition state. We find that l-C5H5 is a locally deep well, with entrance and exit barriers greater than 35 kcal mol-1. The further rearrangement of l-C5H5 occurs via ringclosing to 4, a five-membered ring compound. This species is connected to isomer 5 via TS6, which sits over 20 kcal mol-1 below the entrance transition state energy. Interestingly, this reaction does not directly involve the radical centre, and instead proceeds via migration of a H atom from the methylene group around the ring; a H atom shift to the radical site, on the other hand, requires a prohibitively high barrier.36 Finally, it is important to observe that the l-C5H5 and c-C5H5 isomers are connected by a series of transition states (TS5, TS6, TS7) all with energies well below TS1 (or even TS3). Consequently, the equilibration of these isomers can be achieved at energies where their decomposition is slow. Following C2H2 addition to the allenic site in propargyl (Figure 2), the mechanism for c-C5H5 formation is similar to that described above, albeit with a higher entrance channel energy of 14.2 kcal mol-1 (TS8). Subsequently, it is expected to account for less of the overall reaction flux. Note that no energetically competitive reaction pathways were found connecting the initial reaction adduct to l-C5H5. A mechanism is available, however, which connects this adduct to isomer 5, via a ring-closing (TS9) ring-opening (TS11) sequence, although with relatively high barriers. Note, though, that the four-membered ring intermediate formed here (8) is around 20 kcal mol-1 more stable than that shown in Figure 1 (2), due to resonance stabilization. In an attempt to understand the experimental results of Savee et al.,14 master equation simulations were carried out for the acetylenic C3H3 + C2H2 reaction under conditions representative of their experiments: 0.01 atm and 800 K (Figure 5) / 1000 K (Figure 6). These calculations assume that reaction transpires via the initial production of isomer 1 in an internally excited state, following which it simultaneously chemically and vibrationally relaxes, with access to all of the pathways depicted in Figures 1 and 2. At 800 K the model predicts that the initial adduct rapidly redistributes itself amongst l-C5H5, c-C5H5, and C3H3 + C2H2, with similar yields of the two C5H5 RSRs. The C5H5 population is rapidly quenched to below the exit channel threshold, establishing the reverse (null) channel yield. Following this, however, slower isomerization of l-C5H5 to c-C5H5 continues, until these species are finally cooled down into their respective wells. The result is for around a 3:1 ratio of cyclic to open isomers, which is qualitatively consistent with the experimental findings. Interestingly, significant l-C5H5 formation is also predicted for the allenic addition mechanism (not shown), demonstrating the importance of c-C5H5 ↔ l-C5H5 isomerization. Similar results are obtained 4 ACS Paragon Plus Environment

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at 1000 K, but with lower yields of both C5H5 isomers. Note that Savee et al. saw almost no lC5H5 at 1000 K, which cannot be explained by the above simulations alone. The above calculations predict total C3H3 + C2H2 rate coefficients of 0.43×10-15 cm3 molecule1 -1 s at 800 K and 0.60×10-15 cm3 molecule-1 s-1 at 1000 K. By comparison, Savee et al. determined values of 1.8×10-15 and 2.4×10-15 cm3 molecule-1 s-1 at 800 K and 1000 K, respectively, whereas Knyazev and Slagle reported a value of 2.6×10-15 cm3 molecule-1 s-1 at 800 K. The predicted rate coefficients can be brought into good agreement with the experimental values by reducing the activation energy by 2 kcal mol-1, and this adjustment may be applied to the reported rate coefficient expressions provided below. However, the rate coefficient predictions are also very sensitive to the collisional energy transfer parameters, and reasonable agreement with experiment can also be obtained by quadrupling the ∆Ed values used in the model. It is likely that both factors contribute to the discrepancy, and experimental measurements obtained at various temperatures and pressures would be useful for benchmarking the master equation model, thus providing deeper insight into the reaction energetics and dynamics. In order to provide input data for chemical kinetic models, master equation simulations were carried out for the C3H3 + C2H2 reaction between 300 and 2000 K, at 1, 10, and 100 atm. Both addition mechanisms were simulated (although the C5H5 adducts have all pathways shown in Figures 1 and 2 available to them) and individual rate coefficients were summed to obtain the total. The chemically activated reaction process, which involves simultaneous vibrational and chemical relaxation, was complete on a timescale for which total C5H5 decomposition was insignificant, even at 2000 K. However, at intermediate to high temperatures the thermal rearrangement of l-C5H5 was found to compete with the true chemically activated process, and yields of the individual C5H5 isomers were assigned using the thermal decay approach of Pinches and da Silva,32 which corrects for this effect. Branching ratios between l-/c-C5H5 formation and reverse reaction are plotted in Figure 7 for 1 atm and 100 atm. An Arrhenius plot of overall k values compared to high pressure limit values and to previous experimental determinations is provided as Figure 8. Inverse log plots for the individual rate coefficients to the l-C5H5 and c-C5H5 isomers are shown in Figure 9, including three-parameter Arrhenius fits over the temperature range of 500 – 2000 K. Rate coefficient expressions are provided in Table 1 with numerical k(T,P) values listed in the Supporting Information. Figure 7 reveals that the C3H3 + C2H2 reaction is predicted to result in similar yields of both the l- and c-C5H5 isomers at temperatures and pressures relevant to combustion. At 1 atm there is a slight preference for the c-C5H5 isomer, but at higher pressures l-C5H5 becomes the dominant isomer, with the increased frequency of deactivating collisions working to trap C5H5 in this higher-energy form. At 100 atm collisional deactivation of the fragile addition adducts HCCCH2CHCH [1] and CH2CCHCHCH [7] is also important, dominating the total C5H5 population at 500 K and below (at 10 atm they are only significant at 300 K). Given that they 5 ACS Paragon Plus Environment


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only form at high pressure / low temperature conditions these initial adducts can likely be ignored in combustion modelling. At all three pressures studied, reaction is dominated by C5H5 isomer stabilization up to 800 K, although at these temperatures reaction is relatively slow due to the substantial addition barrier. At higher temperatures the reverse dissociation back to the reactants begins to dominate, which results in significant falloff in the calculated rate coefficients. This can be observed more directly in Figure 8, where the calculated rate coefficients are seen to diverge significantly from the high pressure limit values from around 800 K onwards. This effect is particularly significant at 1 atm, where the 2000 K rate coefficient is markedly lower than even the 800 K value. At 2000 K there is over an order of magnitude difference between the 1 atm and 100 atm rate coefficients. In order to include l-C5H5 in combustion models, rate coefficients are also needed for its isomerization and decomposition. To obtain these, master equation runs initiated with thermally activated l-C5H5 were carried out at 1 atm. Conditions were chosen such that cC5H5 was thermally stable on the timescales considered, so as to avoid interference. Rate coefficients were fit for the decomposition reaction to C3H3 + C2H2 and for the isomerization reaction to c-C5H5; these are plotted in Figure 10, with Arrhenius parameters included in Table 1. Similarly, decomposition rate coefficients obtained starting as c-C5H5, at higher temperatures and longer timescales, are plotted in Figure 11. Figure 10 illustrates that isomerization to c-C5H5 dominates over decomposition, due to the lower reaction barriers. Even at the lowest temperature considered (1000 K), rearrangement is predicted to be relatively rapid, with a lifetime of ca. 200 µs. This likely explains the near-absence of l-C5H5 in the 1000 K experiments of Savee et al., where reaction was tracked for around 40 ms. On the other hand, at 800 K the l-C5H5 lifetime is predicted to be ca. 20 ms, which would allow it to accumulate to some extent. The present work describes a feasible mechanism by which l-C5H5 can form from acetylene addition to propargyl and from c-C5H5 rearrangement, and therefore in flames. The l-C5H5 isomer is produced in significant yields by the C3H3 + C2H2 reaction, although it rearranges to c-C5H5 relatively rapidly at temperatures relevant to combustion. Rate coefficient expressions are provided for key reactions of l-C5H5 so as to facilitate inclusion in detailed chemical kinetic models. However, bimolecular reactions such as those with acetylene and O2 will also need to be considered. Preliminary G3X-K calculations on the l-C5H5 + C2H2 reaction show that the initial addition barriers to the three radical sites are between 16 and 18 kcal mol-1. This is considerably larger than the C3H3 + C2H2 addition barriers, which can be attributed to the additional resonance stabilization in 1-vinylpropargyl vs. propargyl, which is lost upon addition of acetylene. Moreover, the l-C5H5 + C2H2 addition barriers are considerably larger than that for c-C5H5 + C2H2, which is predicted to be about 10 – 13 kcal mol-1.12,13,37,38 In the absence of any highly favorable rearrangement mechanisms, the addition of acetylene to the l-C5H5 isomer is expected to be slower than the corresponding 6 ACS Paragon Plus Environment

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reaction of c-C5H5. On the other hand, l-C5H5 may react with O2 more rapidly than the c-C5H5 isomer,39 if it follows the mechanism available to the parent propargyl radical.40 These and other processes may compete with unimolecular loss of l-C5H5 and will ultimately impact upon the extent to which the C3H3 + nC2H2 reaction cascade contributes to molecular weight growth chemistry in flames.

Acknowledgements: This work was supported by the Australian Research Council (ARC) through Future Fellowship project FT130101304.

Supporting Information Available: Optimized structures, vibrational frequencies, and rotational constants required for the master equation model. Calculated C3H3 + C2H2 rate coefficients, k(T,P).



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23. Dangi, B. B.; Maity, S.; Kaiser, R. I. A Combined Crossed Bean and Ab Initio Investigation of the Gas 1 + 3 1 Phase Reaction of Dicarbon Molecules (C2; X Σg /a Πu) with Propene (C3H6; X A'): Identification of the Resonantly Stabilized Free Radicals 1- and 3-Vinylpropargyl. J. Phys. Chem. A 2013, 117, 11783-11793. 24. Reilly, N. J.; Kokkin, D. L.; Nakajima, M.; Nauta, K.; Kable, S. H.; Schmidt, T. W. Spectroscopic Observation of the Resonance-Stabilized 1-Phenylpropargyl Raidcal. J. Amer. Chem. Soc. 2008, 130, 3137-3142. 25. da Silva, G. G3X-K Theory: A Composite Theoretical Method for Thermochemical Kinetics. Chem. Phys. Lett. 2013, 558, 109-113. 26. Gaussian 09, Revision B.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al., Gaussian, Inc., Wallingford CT, 2010. 27. MultiWell-2012.1 Software, 2012, designed and maintained by John R. Barker with contributors Nicholas F. Ortiz, Jack M. Preses, Lawrence L. Lohr, Andrea Maranzana, Philip J. Stimac, T. Lam Nguyen, and T. J. Dhilip Kumar; University of Michigan, Ann Arbor, MI; http://aoss.engin.umich.edu/multiwell/. 28. Barker, J. R. Multiple-Well, Multiple-Path Unimolecular Reaction Systems. I. MultiWell Computer Program Suite. Int. J. Chem. Kinet. 2001, 33, 232-245. 29. Barker, J. R. Energy Transfer in Master Equation Simulations: A New Approach. Int. J. Chem. Kinet. 2009, 41, 748-763. 30. da Silva, G.; Cole, J. A.; Bozzelli, J. W. Kinetics of the Cyclopentadienyl + Acetylene, Fulvenallene + H, and 1-Ethynylcyclopentadiene + H Reactions. J. Phys. Chem. A 2010, 114, 2275-2283. 31. Lenzer, T.; Luther, K.; Reihs, K.; Symonds, A. C. Collisional energy Transfer Probabilities of Highly Excited Molecules from Kinetically Controlled Selective Ionization (KCSI). II. The Collisional Relaxation -1 of Toluene: P(E',E) and Moments of Energy Transfer for energies up to 50 000 cm . J. Chem. Phys. 2000, 112, 4090-4110. 32. Pinches, S. J.; da Silva, G. On the Separation of Timescales in Chemically Activated Reactions. Int. J. Chem. Kinet. 2013, 45, 387-396. 33. da Silva, G.; Trevitt, A. J.; Steinbauer, M.; Hemberger, P. Pyrolysis of Fulvenallene (C7H6) and Fulvenallenyl (C7H5): Theoretical Kinetics and Experimental Product Detection. Chem. Phys. Lett. 2011, 517, 144-148. 34. Roy, K.; Horn, C.; Frank, P.; Slutsky, V. G.; Just, T. High-Temperature Investigations on the Pyrolysis of Cyclopentadiene. Symp. (Int.) Comb. 1998, 329-336. 35. Moskaleva, L. V.; Lin, M. C. Unimolecular Isomerization/Decomposition of Cyclopentadienyl and Related Bimolecular Reverse Process: Ab Initio MO/Statistical Theory Study. J. Comp. Chem. 2000, 21, 415-425. 36. Stahl, F.; Schleyer, P. v. R.; Bettinger, H. F.; Kaiser, R. I.; Lee, Y. T.; Schaefer, H. F., III. Reaction of the Ethynyl Radical, C2H, with Methylacetylene, CH3CCH, Under Single Collision Conditions: Implications for Astrochemistry. J. Chem. Phys. 2001, 114, 3476-3487. 37. Cavallotti, C.; Derudi, M.; Rota, R. On the Mechanism of Decomposition of the Benzyl Radical. Proc. Comb. Inst. 2009, 32, 115-121. 38. da Silva, G.; Cole, J. A.; Bozzelli, J. W. Thermal Decomposition of the Benzyl Radical to Fulvenallene (C7H6) + H. J. Phys. Chem. A 2009, 113, 6111-6120. 39. Robinson, R. K.; Lindstedt, R. P. On the Chemical Kinetics of Cyclopentadiene Oxidation. Combust. Flame. 2011, 158, 666-686. 40. Hahn, D. K.; Klippenstein, S. J.; Miller, J. A. A Theoretical Analysis of the Reaction between Propargyl and Molecular Oxygen. Faraday Discuss. 2001, 119, 79-100.



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FIGURES

TS1 [12.2] + HCCH HC

C

TS2 [3.8]

CH2

TS3 [1.2]

CH

[0.0] HC

TS4 [-6.9]

C

TS5 [-8.5]

TS6 [-11.4]

2 [-17.5]

1 [-11.6]

TS7 [-11.3]

C HC CH2 HC

4 [-39.8]

C C

3 [-44.8]

5 [-39.0] H C

6 [-71.9]

Figure 1. Energy diagram for acetylene addition to propargyl (acetylenic site). Energies are 0 K enthalpies in kcal mol-1, calculated at the G3X-K level of theory.

10

ACS Paragon Plus Environment

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TS11 [15.2]

TS8 [14.2] TS9 [7.1]

+ HCCH

H2C

C

TS10 [0.3]

CH

[0.0]

TS7 [-11.3]

CH H2C

C

7 [-17.8]

C H2C

8 [-37.8]

5 [-39.0] H C

6 [-71.9]

Figure 2. Energy diagram for acetylene addition to propargyl (allenic site). Energies are 0 K enthalpies in kcal mol-1, calculated at the G3X-K level of theory.

11



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1

2

3

4

5

6

7

8

Figure 3. Optimized structures for C5H5 intermediates shown in Figures 1 and 2. Calculated at the M06-2X/6-31G(2df,p) level of theory.

12


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TS1

TS4

TS8

TS2

TS3

TS5

TS9

TS6

TS7

TS10

TS11

Figure 4. Optimized structures for C5H5 transition states shown in Figures 1 and 2. Calculated at the M06-2X/6-31G(2df,p) level of theory. Displacement vectors for imaginary frequencies are indicated. 13



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Figure 5. Calculated yields (top) and vibrational energy (bottom) as a function of time in the addition of acetylene to propargyl (acetylenic mechanism, Figure 1), from energy grained master equation simulations at 0.01 atm and 800 K.


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Figure 6. Calculated yields (top) and vibrational energy (bottom) as a function of time in the addition of acetylene to propargyl (acetylenic mechanism, Figure 1), from energy grained master equation simulations at 0.01 atm and 1000 K.



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Figure 7. Calculated branching fractions in the overall propargyl + acetylene reaction as a function of temperature at 1 atm (top) and 100 atm (bottom).


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Figure 8. Phenomenological rate coefficients in the propargyl + acetylene reaction, calculated at 1, 10, and 100 atm and in the high pressure limit (HPL).



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Figure 9. Calculated rate coefficients (dot points) and model fits (solid lines) for C3H3 + C2H2 → c-C5C5 (top) and C3H3 + C2H2 → l-C5C5 (bottom). From master equation simulations at 1, 10, and 100 atm and 500 – 2000 K.


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Figure 10. Calculated rate coefficients for isomerization and decomposition of l-C5H5, from master equation simulations at 1 atm.



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Figure 11. Calculated rate coefficients for decomposition of c-C5H5 to C3H3 + C2H2, from master equation simulations at 1 atm.


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TABLES

Table 1. Rate coefficient expressions determined in this study, in the form k = A'Tnexp(Ea/RT). Pre-exponential factors (A'Tn) in cm3 molecule-1 s-1 or s-1, activation energies (Ea) in kcal mol-1.

C3H3 + C2H2 → c-C5H5 (1 atm) C3H3 + C2H2 → l-C5H5 (1 atm) C3H3 + C2H2 → c-C5H5 (10 atm) C3H3 + C2H2 → l-C5H5 (10 atm) C3H3 + C2H2 → c-C5H5 (100 atm) C3H3 + C2H2 → l-C5H5 (100 atm) l-C5H5 → c-C5H5 (1 atm) l-C5H5 → C3H3 + C2H2 (1 atm) c-C5H5 → C3H3 + C2H2 (1 atm)

A' 5.95×1034 4.45×1021 5.31×1020 7.67×1012 3.36×1018 2.51×108 1.84×1094 1.01×1068 7.55×1099

n -14.2 -10.3 -9.9 -7.5 -9.1 -6. 0 -24.4 -16.1 -24.4

Ea 31.7 25.6 26.2 22.8 27.0 22.6 79.3 83.0 128.2



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TOC Graphic


Mystery of 1-Vinylpropargyl Formation from Acetylene Addition to the

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