Direct Measurement of Radical-Catalyzed C6H6 Formation from Acetylene and Validation of Theoretical Rate Coefficients for C2H3 + C2H2 and C4H5 + C2H2 Reactions

1. Introduction

Polycyclic aromatic hydrocarbons (PAHs) formed during incomplete combustion are an important class of atmospheric pollutants and serve as precursors for soot.1−3 Understanding PAH chemistry, specifically the detailed chemical mechanisms and key radical reactions, is one of the most critical challenges for the development of efficient combustion engines with minimal environmental impact. It is thought that many PAHs are formed by hydrogen-abstraction-carbon-addition (HACA) mechanisms,4−7 wherein acetylene (C2H2) addition reactions play a key role. The present study focuses on simple analogues to the HACA reaction sequence, in which benzene, the simplest aromatic ring, is formed by acetylene addition to two different vinylic radicals, C2H3 and n-C4H5.

Observations of the chemical composition of sooting flames suggest that reactions involving unsaturated radicals dominate the formation of aromatics under combustion conditions.8−13 The reactions of several radicals (e.g., propargyl,14−18 cyclopentadienyl,19,20 and butadienyl21−25) implicated in benzene formation have been investigated. While the recombination of propargyl radicals has been identified as a primary route to benzene, it remains a matter of debate to what extent other radical reactions contribute to overall benzene yields.3,12,26−30 The addition of vinyl radical (C2H3) to C2H2 is a particularly interesting system because (1) it produces the butadienyl radicals n-C4H5 and i-C4H5, both of which can react with C2H2 to form benzene; and (2) it can produce high yields of vinylacetylene (C4H4) and H atoms, which can reform C2H3 via H addition to the C2H2 reactant, such that the reaction products are continuously generated as long as C2H2 is present. The reactions of C4H5 radicals with C2H2 are thought to play a role in the formation of aromatic compounds in flames;9,31,32 furthermore, vinylacetylene is expected to be an important source of radicals in acetylene pyrolysis at some conditions, as well as formation of larger PAHs.33−36 The high concentrations of C2H2 observed in sooting flames37,38 suggest that, in addition to the propargyl radical self-reaction, C2H3 addition to C2H2 may be a key step in the formation of aromatics, PAHs, and soot. These reactions also play a role in the exothermic polymerization of acetylene, which can create safety hazards in the use of compressed acetylene for various applications.

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To assess the relative importance of benzene formation channels, accurate reaction rate constants and product branching ratios are needed. The formation of products in the reaction of C2H3 with C2H2 has been investigated at various conditions in a few experimental works. Callear and Smith generated C2H3 radicals by photolyzing H2 in the presence of various concentrations of C2H2 and measured the yields of C2H4, C4H6, C6H6 (benzene), and C6H8 (trans-1,3,5-hexatriene) using gas chromatography.21 By assuming the steady-state approximation for radical intermediates and fitting to a complex mechanism, they indirectly estimated the reaction rate constant k1 of R1 relative to the reaction of C2H3 with H2 at 300 and 400 K and a pressure of 500 Torr, conditions for which R1 is likely in the high-pressure limit. Using their reported ratios along with temperature-dependent rate coefficients for C2H3 + H2 from a combined experimental and theoretical analysis39 gives values of ∼2 × 10-16 cm3 s-1 for k1 at 300 K and ∼3 × 10-15 cm3 s-1 at 400 K.

Fahr and Stein40 measured the rate constant of R2 in a Knudsen-cell pyrolysis flow reactor using mass spectrometry at 1023-1273 K and 1-10 mTorr and suggested a rate constant expression relative to the overall rate of the self-reaction of C2H3. Using a directly measured rate coefficient for the C2H3 self-reaction41 with the reported ratio at 1273 K yields an estimated value of ∼3 × 10-13 cm3 s-1 for k2; note that the measurements of ref (41) were conducted at a higher pressure and lower temperature range than Fahr and Stein’s measurements, which may affect the accuracy of this value of k2.

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Kubitza generated C2H3 using Na and vinyl iodide and measured the reaction rate of R2 at 623 K and 2 Torr, quantifying C2H3 and C4H4 concentrations using mass spectrometry and obtaining a value for k2 of ∼1 × 10-13 cm3 s-1.42 Knyazev et al. investigated the reaction kinetics of C2H3 + C2H2 using laser flash photolysis with time-resolved photoionization mass spectrometry at 630-980 K and 4-12 Torr, measuring the appearance of C4H4 only and assuming that the reaction proceeds solely via channel R2 under their conditions.43 Their reported Arrhenius expression yields k2 values ranging from 2.65 × 10-14 cm3 s-1 at 630 K to 1.47 × 10-13 cm3 s-1 at 980 K.

In addition to these experimental works, several theoretical studies have explored the C2H3 + C2H2 system. Weissman and Benson used a combination of the transition-state theory and the experimental measurements of Callear and Smith21 at 300 K to estimate pre-exponential factors and activation energies, which were then used to predict the temperature dependence of k1 at the high-pressure limit.44 They reported rate coefficients of 6.19 × 10-16 and 2.59 × 10-15 cm3 s-1 at 300 and 400 K, respectively. Wang and Frenklach used the Rice-Ramsperger-Kassel-Marcus (RRKM) theory to compute pressure-dependent rate constants for both R1 and R2 with a pseudo-strong-collider assumption, using molecular parameters corrected to reproduce experimental data.22 Later, Miller et al. used the electronic structure theory (DFT-B3LYP and a G2-like method) to calculate properties of stationary points on the C4H5 potential energy surface, an RRKM analysis to compute microcanonical rate constants, and solutions to the time-dependent, multiple-well master equation to extract information on the total rate constant and product distributions as a function of temperature and pressure.45 Their calculated rate coefficients agreed with previous experimental measurements21,40,43 within a factor of 2. They predicted that R1, R2, and the formation of the 4-membered ring cyclic isomer c-C4H5 (R3) all contribute to consumption of C2H3 at temperatures up to 800 K. Recent work by Ribeiro and Mebel treated the C4H5 surface at a higher level of theory, examining a comprehensive set of reactions including C2H3 + C2H2 using the CCSD(T)-F12//B2PLYPD3 method.46 The energies calculated by Ribeiro and Mebel46 for the C2H3 + C2H2 potential energy surface are shown in Figure ​Figure11.

The previous work indicates that under typical combustion conditions, R2 is the dominant channel for C2H3 + C2H2 and is relatively insensitive to pressure at those conditions. However, from 300 to 700 K, the conditions of most laboratory measurements, R1 and R3 also become important and all three rate coefficients are expected to be significant functions of pressure. (The channel leading to formation of i-C4H5, while possibly important under high-temperature and low-pressure conditions, is not expected to play a role in lower-temperature conditions due to the high barrier to isomerization from n-C4H5; see Figure ​Figure11.) Hence, measurements at one set of pressure and temperature conditions may not be applicable to other conditions, which might explain the discrepancy in reaction rates measured near 630 K at different pressures.42,43 A thorough understanding of the C4H5 potential energy surface, through validation of the theoretical calculations with direct experimental measurements at a variety of temperatures and pressures, is therefore needed to accurately describe the chemistry of C2H3 + C2H2.

The addition of n-C4H5 to C2H2 to form an aromatic ring has only been explored in a few studies, theoretically and through indirect measurements, despite its presumed importance in a variety of chemical mechanisms devised to model sooting flames.12,23,27,29 Callear and Smith reported rate constant ratios for R4 relative to C4H5 + H2 of 10.4 (9.2) at 300 (400) K; using rate parameters reported by Weissman and Benson44 for C4H5 + H2 yields k4 values of 2.4 × 10-15 cm3 s-1 (1.2 × 10-14 cm3 s-1).21 Wang and Frenklach performed semiempirical quantum mechanical calculations of several channels for the reaction of n-C4H5 with C2H2, including C6H7, acyclic C6H6, and benzene formation pathways, using molecular parameters corrected to match experimental data.22 Westmoreland et al. combined measurements of benzene production in C2H2/O2 flames with bimolecular quantum-RRK calculations of the pressure-dependent rate constants, which also used input parameters taken from previous measurements.23 Their Arrhenius expression for R4 yields 4.2 × 10-15 cm3 s-1 for k4 at 400 K and 1 atm, slightly lower than the value reported by Callear and Smith.

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More recently, Senosiain and Miller performed rQCISD(T) calculations and used the RRKM theory to predict pressure-dependent rate coefficients for n-C4H5 addition to C2H2; their calculations are summarized in Figure ​Figure11.24 In contrast to earlier studies, their calculations indicated that aromatic ring formation in R4 proceeds via two distinct channels producing benzene and fulvene. At 300 (400) K and 1 atm, their Arrhenius expression predicts a roughly 2:1 ratio of benzene to fulvene with a combined rate constant k4 of 3.6 × 10-17 cm3 s-1 (1.2 × 10-15 cm3 s-1). Their calculations indicate that stabilized C6H7 may also be formed under some conditions. There are several different acyclic isomers and conformers of C6H7, which would be expected to react and interconvert at different rates. Senosiain and Miller considered a species CH2CHCHCHCHCH (referred to as n-C6H7 in Figure ​Figure11), which may exist in cis or trans conformers with varying reactivities. Other C6H7 isomers may also play a role in the n-C4H5 + C2H2 reaction; e.g., investigations of the hydrogen-assisted isomerization of fulvene to benzene identify a two-step isomerization pathway connecting C6H7-2 to C6H7-6.47−49 A detailed consideration of the C6H7 potential energy surface, while outside the scope of this work, would be worthwhile to more accurately describe the pressure dependence of benzene and fulvene formation in this system.

The value of k4 calculated by Senosiain and Miller is insensitive to pressure below 1 atm, similar to the results of Westmoreland et al. The k4 values derived from the experiments of Callear and Smith21 are at least a factor of 2 larger than the theoretical predictions of Senosiain and Miller, although it should be noted that the temperatures of these experiments (300 and 400 K) fall outside the range of Senosiain and Miller’s Arrhenius fit. A possible explanation for the difference is that Callear and Smith did not consider the C2H3 self-reaction in their reaction mechanism; instead, they assumed that all of the C4H6 they measured was formed by the reaction of C4H5 with H2. Since the self-reaction can also form C4H6, this omission would affect their interpretation of the measured [C4H6]/[C6H6] and lead to an artificially large k4. Furthermore, since these values are derived from rate ratios relative to the rate constant of n-C4H5 + H2, uncertainty in the latter value (which in this work was taken from Weissman and Benson44 who also based their calculations on indirect experimental measurements) could contribute to the discrepancy. For these reasons, we recommend against the use of the k4 value provided by Callear and Smith.21

The temperature-dependent rate coefficients for R1, R2, and R4 reported in previous experimental and theoretical works are summarized in Figure ​Figure22. The scarcity of direct measurements for the above reactions, variations up to an order of magnitude or more in calculated values of k1 and k4, and the lack of experimental validation of the pressure-dependent rate constants for R1 and R4 at temperatures above 400 K indicate that further investigation is needed to properly characterize these reactions. Moreover, the regeneration of C2H3 due to H addition to C2H2, though significantly reversible at typical combustion temperatures, is sensitive to pressure and may affect the formation of products under laboratory conditions. Due to the relative complexity of the C2H3 + C2H2 system, relying on a combination of uncertain rate estimates for elementary steps within a larger mechanism will lead to large uncertainties in predicted benzene and PAH yields.

In this work, reaction kinetics and product branching for C2H3 + C2H2 were directly measured at temperatures of 500 and 700 K and pressures ranging from 5 to 50 Torr using time-resolved photoionization time-of-flight mass spectrometry. We report time-resolved concentration profiles of C2H3, C4H4, C4H5, C6H6, and other key reaction products, as well as the sensitivity of product yields and branching ratios to temperature and pressure. The experimental time profiles are compared with the predictions of a kinetic model constructed using previous theoretical and experimental rate parameters24,41,46,50 to assess the validity of these calculated values for describing PAH formation. The results provide detailed validation of theoretical rate coefficients, which can be used to extrapolate to combustion-relevant conditions in kinetic mechanisms to better understand the production of soot in a wide range of combustion processes.

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