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Reaction Rate and Isomer-Specific Product Branching Ratios of C2H + C4H8: 1‑Butene, cis-2-Butene, trans-2-Butene, and Isobutene at 79 K Jordy Bouwman,† Martin Fournier,‡ Ian R. Sims,‡ Stephen R. Leone,†,§ and Kevin R. Wilson*,§ †

Departments of Chemistry and Physics, University of California, Berkeley, California 94720, United States Institut de Physique de Rennes, UMR 6251 du CNRS, Université de Rennes 1, 263 Avenue du Général Leclerc, 35042 Rennes Cedex, France § Chemical Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, United States ‡

ABSTRACT: The reactions of C2H radicals with C4H8 isomers 1-butene, cis-2butene, trans-2-butene, and isobutene are studied by laser photolysis-vacuum ultraviolet mass spectrometry in a Laval nozzle expansion at 79 K. Bimolecularreaction rate constants are obtained by measuring the formation rate of the reaction product species as a function of the reactant density under pseudo-firstorder conditions. The rate constants are (1.9 ± 0.5) × 10−10, (1.7 ± 0.5) × 10−10, (2.1 ± 0.7) × 10−10, and (1.8 ± 0.9) × 10−10 cm3 s−1 for the reaction of C2H with 1-butene, cis-2-butene, trans-2-butene, and isobutene, respectively. Bimolecular rate constants for 1-butene and isobutene compare well to values measured previously at 103 K using C2H chemiluminescence. Photoionization spectra of the reaction products are measured and fitted to ionization spectra of the contributing isomers. In conjunction with absolute-ionization cross sections, these fits provide isomer-resolved product branching fractions. The reaction between C2H and 1-butene yields (65 ± 10)% C4H4 in the form of vinylacetylene and (35 ± 10)% C5H6 in the form of 4-penten-1-yne. The cis-2-butene and trans-2butene reactions yield solely 3-penten-1-yne, and no discrimination is made between cis- and trans-3-penten-1-yne. Last, the isobutene reaction yields (26 ± 15)% 3-penten-1-yne, (35 ± 15)% 2-methyl-1-buten-3-yne, and (39 ± 15)% 4-methyl-3-penten1-yne. The branching fractions reported for the C2H and butene reactions indicate that these reactions preferentially proceed via CH3 or C2H3 elimination rather than H-atom elimination. Within the experimental uncertainties, no evidence is found for the formation of cyclic species. CH + C4 H10 → C4 H8 + CH3

1. INTRODUCTION Reactions of the highly reactive ethynyl (C2H) radical are important in a large variety of environments, such as combustion engines, the interstellar medium, and planetary atmospheres. In the cold, dense atmosphere of Saturn’s largest moon, Titan, C2H radicals are efficiently formed through the photolysis of acetylene.1 Comprehensive chemical models,2−5 quantum-mechanical calculations,6,7 and laboratory experiments8−14 indicate that the reactions of C2H radicals with unsaturated hydrocarbons play an important role in the formation of larger hydrocarbons, such as polyynes, cyanopolyynes, and polycyclic aromatic hydrocarbons (PAHs), in Titan’s atmosphere. These species are thought to make up a large fraction of the characteristic yellow haze that shrouds the moon.14,15 C2H radicals are also present in the interstellar medium,16,17 where they are considered to play a crucial role in the formation of PAHs18 that are thought to be present along the line of sight of many objects.19,20 C2H radicals are also considered to be an important species in the formation of aromatics resulting from the combustion of hydrocarbons.21,22 Alkenes, such as butene isomers, are important as fuels23,24 and as intermediates in the oxidation of hydrocarbons.25,26 They are also considered to play a role in the photochemistry of Titan’s atmosphere. Lavvas et al.3,4 specifically included the production of C4H8 in their photochemical model via two formation routes:27 © XXXX American Chemical Society

1

CH 2 + C3H6 + M → C4 H8 + M

(R1a) (R1b)

3,4

In that model, Lavvas et al. considered the destruction of C4H8 to occur by its reactions with N atoms, C atoms, and a set of hydrocarbon radicals that includes C2H. They used a roomtemperature reaction rate of 2.6 × 10−10 cm3 s−1 for the C2H + butene reaction, and, because experimental data were lacking, they did not distinguish between the reactivity of the different C4H8 isomers. Moreover, because product branching ratios were also not available, no specific reaction products were included in the model.3,4 Synchrotron-photoionization mass spectrometry offers a sensitive technique for the mass-selective and isomer-specific disentanglement of the contents of gas mixtures.28,29 This technique is commonly used in conjunction with a reactor flow tube at the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory (LBNL) to study reactions of radicals with unsaturated hydrocarbons that are of interest in combustion chemistry.30−33 Photoionization spectra of reaction products are recorded by scanning the energy of the vacuum-ultraviolet (VUV) ionizing radiation from the synchrotron while Received: April 12, 2013 Revised: May 17, 2013

A

dx.doi.org/10.1021/jp403637t | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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2.1. Laval Expansion. A Laval nozzle designed to yield a mach 4 expansion is mounted in a vacuum chamber pumped by a 1200 m3/h Roots blower. The Laval nozzle is mounted on a reservoir block that is filled with a gas mixture by two solenoid valves. Gas pulses of 6 ms in duration are expanded through the nozzle into the vacuum chamber at a rate of 30 Hz. During Laval nozzle operation, the vacuum chamber is kept at 128 mTorr by means of a feedback-loop-controlled butterfly valve that is mounted on the blower. The temperature of the resulting collimated expansion is determined as described previously48 and is 79 ± 2 K. The gas mixture containing the bath gas (N2), reactant gas (C4H8), and radical precursor (C2H2) is prepared in a gas manifold by allowing the gases to flow through individually calibrated mass-flow controllers. A cylinder is mounted between the gas mixing manifold and the Laval nozzle to ensure a thorough mixing of the gases and to reduce pressure fluctuations in the gas supply. Ultra-high-purity nitrogen is used as the bath gas. The C2H radical precursor acetylene (C2H2, Airgas, stabilized by acetone) is passed through a Matheson-activated charcoal filter to remove residual acetone. The reactant molecules 1-butene (≥99%, Sigma-Aldrich), cis-2butene (≥99%, Sigma-Aldrich), trans-2-butene (≥99%, SigmaAldrich), and isobutene (≥99%, Matheson) are used without further purification. C5H6 isomer 2-methyl-1-buten-3-yne (99%, Sigma-Aldrich) is used as received and is diluted in nitrogen to measure its absolute photoionization spectrum. An unfocused ArF excimer laser operating at 193 nm is pulsed coaxially through the collimated expansion to generate C2H radicals from the C2H2 radical precursor. C2H radicals may be electronically and/or vibrationally excited, but the excited states are rapidly quenched in the expansion by collisions with the N2 bath gas.49 The number density of C2H2 is kept constant at 1.4 × 1014 cm−3, and the number density of C2H radicals produced by the photolysis of acetylene is calculated from the absorption cross section50 (2 × 10−19 cm−2) assuming a unity quantum yield51 for the formation of C2H radicals. A typical laser pulse fluence of 7 mJ cm−2 results in a number density of C2H radicals of 2 × 1011 cm−3. This value is small when compared to the number density of reactant molecules ([RH], ranging from ∼4.5 × 1013 to ∼2.0 × 1014 cm−3), ensuring that pseudo-first-order conditions ([C2H] ≪ [RH]) are fulfilled. 2.2. Product Detection. The collimated expansion is sampled through a 450 μm pinhole in a parabolically shaped airfoil, and the sampled part of the expansion enters the detection chamber, which is maintained at ∼10−7 Torr by two turbopumps during the operation of the pulsed Laval expansion. The sampled gas is ionized by quasi-continuous VUV light from the ALS, after which the resulting ions are detected in a quadrupole mass spectrometer (QMS). Undispersed synchrotron light with a photon energy of 11.25 eV and a full-width-at-half-maximum of 320 meV is used for the bimolecular rate constant measurements. The ion counts arising from 20 000 laser pulses are time-binned in a multichannel scaler to obtain a kinetic trace at a single [RH] density. Mass spectra of reaction products are recorded with 0.2 amu resolution. These species are sampled and subsequently ionized with 11.25 eV light that is dispersed by a 3 m monochromator with a slit width of 1 mm, which yields an energy resolution of ∼75 meV. For these measurements, ions are extracted and detected in the QMS, and ion counts are time-binned for 500

measuring the temporal formation of the products. Isomerspecific product branching ratios are derived by fitting the photoionization spectra with calculated or measured ionization spectra of possible reaction products. No isomer-specific product branching measurements have been reported for C2H + butene reactions. Over the past decades, Laval nozzle expansions have been employed by a number of groups to study a variety of reactions at low temperatures.34−39 Reaction rates involving the ethynyl radical are generally quantified under pseudo-first-order conditions using chemiluminescence to track the decay of the radical density.40−45 Using this technique, the bimolecular rate constants for C2H + 1-butene43,45 and C2H + isobutene45 were quantified and reported for discrete temperatures ranging from 103 to 296 K. The measured bimolecular-reaction rate constants for both reactions were found to be fast, suggesting that these reactions proceed via the barrierless formation of a complex followed by a unimolecular reaction to form the final products. To the best of our knowledge, no bimolecularreaction rate-constant measurements for C2H + cis-2-butene and C2H + trans-2-butene have been reported. The reactions between C2H and C4H8 isomers 1-butene, cis2-butene, and isobutene have been studied theoretically. Woon and Park46 found that these reactions proceed via the barrierless addition of C2H radical to the sp2 carbons of the C4H8 isomer, followed by isomerization of the energetic adduct. Their energetics are

The exothermicities relative to the reactants for R2a−R2e are in kcal/mol. The range of exothermicities accounts for the possibility of forming a set of different isomers within a single product channel, and a dash (−) denotes that the exit channel is inaccessible. In addition to the formation of the stable species listed above, Woon and Park46 also mentioned the formation of five- and six-membered C6H9 rings that would be formed without losing a fragment. These species are very energetic and would require significant stabilization to be formed. Here, we report the bimolecular-reaction rate constants and isomer-specific product branching ratios for the reactions of C2H radicals with C4H8 isomers 1-butene, cis-2-butene, trans-2butene, and isobutene measured in a Laval nozzle expansion at 79 K. The bimolecular-reaction rate constants are quantified by measuring the formation rate of the product species as a function of the reactant density. Photoionization spectra of the reaction products are measured, and isomer-specific branching ratios are derived from fitting the model to these spectra. The experimental results are compared to calculations, and the implications for combustion chemistry and the photochemistry of Titan’s atmosphere are highlighted.

2. EXPERIMENTAL SECTION The measurements are performed at the chemical dynamics beamline of the ALS at LBNL in an apparatus that combines a pulsed Laval nozzle reactor with time-resolved synchrotronphotoionization mass spectrometry. The experimental apparatus has been described in detail in a previous publication;47 therefore only a brief description is given here. B



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ionization energies are computed using the CBSQB3 basis set,54,55 which is found to yield reliable values. Ground-state geometries of the neutral and cation are optimized using the CBSB7 basis set,39 and Franck−Condon simulations are performed to simulate the shape of the ionization spectrum. Ionization cross sections are computed using a model by Bobeldijk et al.56 Within this model, the ionization cross section of a molecule at a photon energy of 11.8 eV can be estimated through the summation of the cross sections (σX−Y) of the number (n) of bonds X−Y within the molecule:

laser pulses for each mass-channel setting. This results in a 2D data set that contains ion counts as a function of both time and mass (Figure 1A). The mass-dependent sensitivity of the QMS

σtot =

∑ σX − YnX − Y

(1)

This model gives ionization cross sections that are generally accurate to within ∼20%.

3. RESULTS The reactions between C2H radicals and 1-butene, cis-2-butene, trans-2-butene, and isobutene are studied in the low-temperature Laval nozzle expansion apparatus by photoionization mass spectrometry. Mass spectra of the reaction products are recorded, and biomolecular-reaction rate constants are measured for all four reactants by measuring the temporal formation of the main product species for a set of reactant densities under pseudo-first-order conditions. Subsequently, photoionization spectra of the reaction products are measured to obtain isomer-specific branching ratios. The results are described in detail in the following sections. 3.1. Mass Spectra. The formation of reaction products and photolysis products is recorded as a function of mass and time. Species in the expansion are ionized with monochromatized light at 11.25 eV prior to being extracted into the QMS. Mass information is obtained by stepping through the mass channels of the QMS with 0.2 amu resolution. Temporal information is obtained by time-binning ion counts for 500 photolysis laser pulses at each QMS mass channel. Shown in Figure 1A are the resulting ion counts that are detected (grayscale) as a function of the mass-to-charge ratio (m/z in amu on the x axis) and time (μs on the y axis) by the 193 nm photolysis of a mixture of 1.3 × 1014 cm−3 1-butene and 1.2 × 1014 cm−3 C2H2 in 1.4 × 1016 cm−3 N2. The horizontal line at t = 0 μs is an artifact caused by the photolysis laser and indicates the start time of the reaction. From Figure 1A it can be seen that, as is the case for time-offlight mass spectrometers, the arrival time of the ions after the photolysis laser pulse is proportional to the square root of the ion mass. The arrival time of the ions that are instantaneously formed from the photolysis of 1-butene and extracted into the QMS at a fixed potential (−10 V) is shown as a function of m/z in Figure 1B. Also shown in this figure is the fit to the arrival time based on

Figure 1. (A) Image of the ion counts formed by ionization at a synchrotron energy of 11.25 eV (grayscale) as a function of time (y axis) and m/z ratio (x axis) for the reaction between C2H radicals and 1-butene. (B) Arrival time of ions plotted against the mass-to-charge ratio together with a fit to the data.

detector is taken into account when determining the absolute branching ratio for reactions with multiple product channels, as described in detail in a previous publication.52 Photoionization spectra are measured by scanning the photon energy from ∼8.5 to ∼11.5 eV while detecting product ions. VUV light from the ALS is dispersed by the 3 m monochromator, and a part of the dispersed light is transmitted through a 600 μm slit, resulting in an energy resolution of ∼36 meV. Ionized product species are detected and typically timebinned for 2000 laser pulses at each photon energy. The ion counts are integrated over the duration of the cold expansion and normalized to the photon flux of the ALS measured with a NIST-calibrated photodiode. Error bars in the photoionization spectra display the shot-noise level, which is equal to the square root of the ion counts. 2.3. Computational Method. Measured photoionization spectra of the reaction products are modeled using measured absolute ionization spectra from the literature when available. Photoionization spectra are computed using Gaussian0953 when the spectra are unavailable from the literature and when the species cannot be purchased commercially. The

tarr = a + b(m /z)1/2

(2)

Ion counts are integrated for the first ∼150 μs after this arrival time (tarr) to obtain a mass spectrum that reflects the correct branching of the products formed in the cold expansion. Furthermore, integrated ion counts before the photolysis laser is pulsed are subtracted from the ion counts after the laser is pulsed to reflect only those species that are formed after the photolysis laser is pulsed. The resulting mass spectrum exhibits positive signals for species that are formed from photolysis and photochemical reactions and negative signals for species that are depleted. Although the synchrotron photon energy used for this measurement (11.25 eV) is below the ionization threshold C



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Figure 2. Mass spectra of the C2H + 1-butene reaction measured at an ionization energy of 11.25 eV. (A) Mass spectrum of 1-butene in N2 photolyzed at 193 nm. (B) Mass spectrum of acetylene and 1-butene in N2 photolyzed at 193 nm. (C) Reaction products formed from the reaction between C2H and 1-butene (spectrum B minus spectrum A).

of acetylene (I.E. = 11.4 eV), a negative signal that is caused by the photolysis of acetylene by the laser is observed at m/z = 26 (C2H2). The detection of the acetylene depletion at 11.25 eV is explained by the low photon-energy resolution used for this measurement because there is still some photon flux above the ionization threshold of acetylene. Depletion is also expected at the reactant’s mass, but saturation of the QMS detector causes the ion counts around this mass channel to be nonlinear with density. For this reason, data are omitted around the mass of the reactant species (from m/z = 55 to 57). Shown in Figure 2A is a mass spectrum of the products formed from the 193 nm photolysis of ∼1% 1-butene in nitrogen (total density 1.4 × 1016 cm−3). From this figure, it can be seen that strong features in mass channels m/z = 15 (CH3), 27 (C2H3), 29 (C2H5), 39 (C3H3), 41 (C3H5), and 53 (C4H6) appear upon the photolysis of 1-butene. The formation of these 1-butene photofragments, with the exception of C3H3, is in agreement with a previous study by Niedzielski et al.57 In Figure 2B, it can be seen that new products are detected at m/z = 50, 52, and 66 when ∼1% of the C2H radical precursor (C2H2) is added to the expansion. A mass spectrum showing only the reaction products is obtained by subtracting the trace in Figure 2A from the trace in Figure 2B and is displayed in Figure 2C after multiplication by a factor of 5. The product detected at m/z = 50 is identified as diacetylene (C4H2) formed from the reaction between C2H and C2H2, as described in previous publications.47,52 Bimolecular rate measurements confirm that the products at m/z = 52 and 66 originate from the reaction under investigation and are described in detail in the next section. The product signals detected at m/z = 50, 52, and 66 (Figure 2B) are small compared to the signals arising from the photolysis of the reactant species. This difference can be largely explained by the difference in the absorption cross section between 1-butene and C2H2 at 193 nm (Table 1). The fraction of the molecules that absorb a photolysis laser photon, γ, can be expressed as γ=

Φλ (1 − exp(−Nσl)) hcNl

Table 1. Absorption Cross (σ) Sections at 193 nm, Ionization Energies (IE), and Fractional Absorption (Expressed as a Percentage of the Number Density) for the Radical Precursor and Reactant Species Under Typical Experimental Conditions

absorption path length. Under the experimental conditions typically used for the mass spectra in Figure 2 (∼1% reactant, ∼1% C2H2 in 1.4 × 1016 cm−3 N2, and ∼7 mJ/cm2 laser fluence), 1.2% of the 1-butene in the flow absorbs a photon compared to only 0.4% of the C2H2, yielding larger number densities for the 1-butene photolysis fragments than C2H radicals. An overview of the fractions of the reactant and radical precursor molecules that absorb a 193 nm photon is given in Table 1. Analyses similar to that described above for 1-butene are performed for the other reactant species to isolate reaction products from photofragments. The mass spectra of these reaction products are displayed in Figure 3. From this figure, it can be seen that products at m/z = 50 and 66 are formed from the reaction between C2H and cis-2-butene and trans-2-butene. The reaction between C2H and isobutene yields products at m/z = 50 and 66 and a weak product at m/z = 80. The product at m/z = 50, which is detected for all four reactions, is assigned to the C4H2 isomer diacetylene, which is a well-known product of the C2H + C2H2 reaction.32,37 Contributions of products to the observed mass channels formed by side reactions also need to be considered. Radicals that are formed from the photolysis of the reactant can potentially react with the reactant itself to form products that

(3)

where Φ is the laser fluence, λ is the photolysis laser wavelength, h is Planck’s constant, c is the speed of light, N is the number density of the reactant or radical precursor, σ is the absorption cross section at the laser wavelength, and l is the D



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Figure 4A. The fit routine described in Bouwman et al.52 is used to fit eq 4 to the measured data and is discussed briefly here.

Figure 3. Mass spectra of the reaction products of C2H reacting with isobutene, cis-2-butene, and trans-2-butene.

interfere with the C2H reaction products under investigation. No products are detected in the absence of the radical precursor (see Figure 2A for 1-butene), and such side reactions can thus be excluded. Also, side reactions of the radicals formed from the photolysis of the reactant can potentially react with acetylene to contribute to the detected product channels: C2H3 + C2H 2 → C4 H5⧧ → C4 H4 + H

(R3a)

C3H5 + C2H 2 → C5H 7 ⧧ → C4 H4 + CH3

(R3b)

C3H5 + C2H 2 → C5H 7 ⧧ → C5H6 + H

(R3c)

Figure 4. (A) Formation of a reaction product as a function of time at m/z = 66 (C5H6) measured at 11.25 eV for the C2H + cis-2-butene reaction at a reactant density of 2.1 × 1014 cm−3 plotted together with the best Gaussian convoluted fit to the data. (B) Gaussian with unit area that resembles the system-response function. (C) Fit function based on eq 4.

These reactions, however, have slow bimolecular rate constants (kR3a = 7.5 × 10−16 cm3 s−1 at 300 K,34 kR3b = kR3c = 4.5 × 10−19 cm3 s−1 at 300 K35). A chemical kinetics model is employed to investigate the contributions of these reactions. Under the experimental conditions used here, these side reactions were found to have negligible contributions to the product channels of all the reactions investigated. 3.2. Reaction Rate Determinations. Reaction rate constants for the reactions between C2H and C4H8 isomers are measured by recording the formation rates of product species as a function of reactant density. The experiments are performed under pseudo-first-order conditions (i.e., the density of the radical species [C2H] is much lower than that of the reactant [RH]). Under these conditions, the formation of product species [Pm] as a function of time can be expressed as described in detail in a previous publication:52 [Pm]t = Q m(1 − exp{−(k[RH] +

∑ kn[M n])t }) n

with Q m =

km[RH][C2H]0 k[RH] + ∑n kn[M n]

First, a value for Qm is determined by calculating the average of the ion counts for 130 < t < 150 μs. Subsequently, a fit based on eq 4 and an initial trial value for k1st is computed (Figure 4C). This trace is convoluted with a 16 μs-wide Gaussian shaped system-response function (Figure 4B) that is quantified from the instantaneous formation of radicals from the photolysis of 1-butene. The resulting fit function corrected for the system response is shown in Figure 4A. The difference between the resulting Gaussian convoluted fit and the measured data is quantified by calculating the sum of the residuals. This method is repeated for a large set of trial values of k1st. Finally, the value of k1st that yields the lowest sum of the residuals is selected and is displayed in Figure 4A. The analysis is repeated for the product formation at all densities, and the resulting values of k1st are displayed with an estimated error of ±3000 s−1 as a function of reactant density in Figure 5. The reactant density is corrected for losses due to the photolysis of the reactant. The analysis described above is performed for the strongest product channels of the reactions, and the resulting values of k1st are plotted as a function of calibrated reactant densities in Figure 5. Also shown in this figure are linear fits to the data. The intercepts are different for each reactant, and this is most striking for the isobutene data. The intercepts reflect additional loss processes of C2H radicals (eq 4). Possible loss processes are diffusion of radicals out of the expansion, reactions of C2H with background gases (e.g., oxygen), and reactions of C2H with radicals in the expansion that are formed from photolysis of the reactant. Hence, the large intercept for isobutene could

(4)

(5)

The bimolecular rate constant k is retrieved by measuring the first-order rate coefficient k1st = k[RH] + ∑nkn[Mn] for a set of reactant densities [RH]. The slope directly yields the bimolecular rate constant, and the intercept reflects the sum over the additional loss processes of the radical, for example, reactions with C2H2 and other radicals in the expansion. The prefactor Qm contains information on the product branching ratios, which will be described in more detail in the next section. A typical time trace for the formation of products from the reaction between C2H and cis-2-butene detected at m/z = 66 after being photoionized at 11.25 eV is displayed in black in E



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the isomers of the product species considered in this work together with their ionization energies is given in Table 2. Table 2. Product Isomers of the C4H4, C5H6, and C6H8 Species Considered in This Work Together with Their Structures, Ionization Energies, and Methods of Determining the Ionization Energies

Figure 5. Measured values of k1st as a function of the reactant density for the reaction between C2H and 1-butene (◊), cis-2-butene (○), trans-2-butene (Δ), and isobutene (□) displayed together with linear fits to the data.

be a result of the much larger absorption cross section of isobutene that causes 23% of this isomer to be photolyzed. Bimolecular-reaction rate constants are determined from the slopes of the linear fits to the data shown in Figure 5. The resulting bimolecular-reaction rate constants are (1.9 ± 0.5) × 10−10, (1.7 ± 0.5) × 10−10, (2.1 ± 0.7) × 10−10, and (1.8 ± 0.9) × 10−10 cm3 s−1 for the reactions of C2H with 1-butene, cis-2butene, trans-2-butene, and isobutene, respectively. The errors in the reaction rate constants are composed of 3σ in the linear fit together with a contribution of 10% to account for systematic errors. Furthermore, the uncertainty accounts for the fact that the derived rate constants are rather sensitive to the assumed starting point (t0) of the reaction, which is included in the model fit. The uncertainty in the bimolecular rate constant for isobutene is slightly larger because an additional uncertainty caused by the abundant isobutene photolysis fragments is introduced. The isobutene data seem to deviate from a linear dependence toward the higher reactant densities. This could be indicative of clustering in the expansion, but there is no further evidence for the formation of such clusters. The bimolecular-reaction rate constants reported here can be compared to those measured previously for C2H + 1butene43,45 and C2H + isobutene.45 These rate constants were measured for discrete temperatures ranging from 103 to 296 K and at 103 K are (2.6 ± 0.6) × 10−10 and (1.4 ± 0.3) × 10−10 cm3 s−1 for the 1-butene and isobutene reactions, respectively. The bimolecular rate constants reported here are in agreement with those measured previously and are consistent with the products being formed from the studied reactions rather than from side reactions. 3.3. Isomer-Specific Product Branching Ratios. Photoionization spectra of the reaction products are recorded to identify the isomers that are formed from the title reactions and to quantify their respective branching fractions. Product ion counts are measured as a function of the synchrotron photon energy and normalized to the photon flux, which is measured with a NIST-calibrated photodiode. The resulting photoionization spectra are modeled using contributions of absolute photoionization spectra of isomers that are expected to contribute to the overall spectrum. Computed spectra are used when measured spectra are unavailable. An overview of

3.3.1. C2H + 1-Butene. Figure 6 shows the photoionization spectrum of the product at m/z = 52 that is formed from the

Figure 6. Photoionization spectrum of the C4H4 (m/z = 52) product species formed from the reaction between C2H and 1-butene plotted together with a fit based on the vinylacetylene photoionization spectrum.

reaction between C2H and 1-butene. The sharp onset at ∼9.6 eV, the overall shape, and the characteristic resonances are consistent with a single predominant isomer, vinylacetylene. A fit is made using the measured absolute spectrum of vinylacetylene from Cool et al.58 and is also shown in Figure 6. An upper limit of 5% is derived for contributions of other C4H4 isomers by assuming a detection limit of twice the standard deviation in the baseline noise. A photoionization spectrum of the C5H6 species formed from the reaction between C2H and 1-butene and detected at m/z = 66 is shown in Figure 7. The ionization threshold of the C5H6 product species detected from the C2H + 1-butene reaction is around 9.8 eV. This ionization threshold is close to the calculated ionization threshold of 4-penten-1-yne (IE = 9.9 eV) and far from the thresholds of other possible C5H6 isomers52 (IE = 9.1, 9.2, and 9.3 eV, Table 2). The simulated ionization spectrum of C5H6 isomer 4-penten-1-yne is shown in Figure 7 and does not fully capture the measured spectrum. The simulated spectrum F



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The photoionization spectrum of this mass channel is shown in Figure 9. Also displayed in Figure 9 is the simulated photoionization spectrum of cis-3-penten-1-yne from Bouwman et al.52 The calculated ionization onset of cis-3-penten-1-yne resembles the ionization threshold that is measured experimentally. The vibrational structure at low energies is nicely captured by the calculated spectrum of cis-3-penten-1-yne, and a reasonable fit is obtained. There is a slight mismatch between the measurement and the calculation for energies exceeding 9.6 eV, but no clear secondary threshold at ∼9.9 eV is observed. Thus, no contribution of 2-methyl-1-buten-3-yne to the spectrum is apparent, and an upper limit of 5% is derived for this species. The slow rise could be caused by an artifact called chargetransfer ionization that is caused by inadequate pressure reduction in the mass spectrometer region.52 In this scenario, the charge of the ionized reactant, which is present in much larger abundance, is transferred to the reaction product. As a result, the shape of the ionization curve will exhibit some character of the reactant species, which in the case of cis-2butene exhibits a slow rise.59 Because the ionization thresholds of cis-3-penten-1-yne and trans-3-penten-1-yne is separated by less than 100 meV,52,60 an unambiguous identification of the exact geometrical isomers is difficult, if not impossible. Thus, although the fit to the data shown in Figure 9 exhibits very good agreement, the reaction products are identified as either cis-3-penten-1-yne, trans-3penten-1-yne, or a superposition of these geometrical isomers. Upper limits of 2 and 4% are derived for the formation of C6H8 from H loss and the formation of C4H4 from C2H3 loss, respectively. The detection of a product with m/z = 66 from the reaction between C2H and cis-2-butene can be understood from the reaction scheme shown in Figure 8. C2H radicals can add to either of the carbons in the CC bond of cis-2-butene, and by symmetry this forms a single-adduct species (Adduct 3 in Figure 8). This adduct can eject an H atom or a CH3 radical. Hydrogen shifts within adduct 3 could occur, but there is no experimental proof for such isomerization. The detection of geometrical isomers of 3-penten-1-yne as the only product species is in agreement with calculations by Woon and Park.46 3.3.3. C2H + trans-2-Butene. The photoionization spectrum of the C5H6 product that is formed from the C2H + trans-2butene reaction is measured and shown in Figure 10. Also shown in this figure is a fit to the data based on the simulated ionization spectrum of trans-3-penten-1-yne from Bouwman et al.52 The ionization threshold and vibrational structure are well represented, and an excellent fit is obtained for energies below ∼9.8 eV. At higher photon energies, there is a slight difference between the measured spectrum and the calculated spectrum, but no clear ionization threshold is observed. An upper limit of 5% is derived for contributions of 2-methyl-1-buten-3-yne. Although the ionization onset is captured very nicely by our simulated value, it is difficult to unambiguously assign the product to the geometrical isomer trans-3-penten-1-yne, as noted earlier for the cis-2-butene reaction product. Hence, the detected species is identified as cis- or trans-3-penten-1-yne or a superposition of the two. The reactions of C2H with cis- and trans-2-butene are very similar, and a possible reaction mechanism for trans-2-butene is also shown in Figure 8. The C2H radical adds to the π system of trans-2-butene to form adduct 4. This adduct subsequently ejects the largest possible fragment (CH3). Upper limits of 2

Figure 7. Photoionization spectrum of C5H6 product species formed from the reaction between C2H and 1-butene plotted together with a simulated ionization spectrum of 4-penten-1-yne.

exhibits a sharp onset, whereas the measured spectrum rises more slowly. The mismatch of the shape can be attributed to large structural differences between the optimized geometries of the 4-penten-1-yne neutral and cation ground state. The resulting poor Franck−Condon overlap can translate into a slow rise in the measured photoionization spectrum that is not well captured by the Franck−Condon simulation. Product species with the general formula C6H8 (m/z = 80) are accessible on C6H9 potential-energy surface (R2a). The mass spectrum displayed in Figure 2C, however, shows no evidence for the formation of this species. From eq 1, an ionization cross section of 51 MB is computed for C6H8. With this ionization cross section and a detection limit of 2σ of the baseline noise, we derived an upper limit of 6% for the contribution of these species. A product branching fraction is derived for the formation of the product at m/z = 52 (vinylacetylene) and m/z = 66 (4penten-1-yne) for C2H + 1-butene. The absolute energydependent ionization cross section of vinylacetylene is available from the literature.58 The absolute ionization cross section of 4penten-1-yne (45 MB) was computed in a previous study.52 After correcting for the mass-dependent sensitivity of the QMS,52 the reaction between C2H and 1-butene is found to yield (65 ± 10)% vinylacetylene and (35 ± 10)% 4-penten-1yne. The errors in the branching fractions are indicated at the 1σ level and mainly result from the uncertainty in the computed ionization cross section of 4-penten-1-yne. A possible reaction mechanism for the C2H + 1-butene reaction is displayed in Figure 8. C2H radical can add to either of the sp2 carbons of 1-butene, giving rise to two distinct adducts. Possible pathways from adduct 1 (Figure 8) are H or CH3 loss to form 3-hexen-1-yne or 4-penten-1-yne, respectively. Adduct 2 can lose an H atom or C2H3 radical to form 3ethyl-but-3-en-1-yne or vinylacetylene, respectively. The most prominent product found experimentally is vinylacetylene with a branching of 65 ± 10%. This is in excellent agreement with the computed branching fraction value of ∼58%.46 The quantity of 4-penten-1-yne amounts to 35 ± 10% and is also in excellent agreement with the computed value of ∼42%.46 An upper limit of 6% is put on the detection of signal at m/z = 80. Within this channel, the cyclic C6H8 molecule methylcyclopentadiene is accessible by a double H shift followed by a ring closure, but this route is very unlikely. 3.3.2. C2H + cis-2-Butene. The reaction between cis-2butene and C2H yields a reaction product at m/z = 66 (C5H6). G



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Figure 8. Possible reaction mechanisms for the reaction between C2H and 1-butene, cis-2-butene, trans-2-butene, and isobutene (u.l. denotes an upper limit).

photolysis of the reactant forms deposits on the MgF2 window through which the photolysis laser enters the Laval flow. Over the course of an experiment, this reduces the laser power in the expansion and hence reduces the number density of C2H radicals that are formed. Further investigations have shown that these soot deposits indeed cause the laser power in the system to decay exponentially over time for the isobutene experiments. C5H6 isomer 2-methyl-1-buten-3-yne is a likely contributor to the m/z = 66 ionization spectrum in Figure 11. The ionization spectrum of the commercially available 2-methyl-1buten-3-yne is measured in the Laval nozzle expansion relative to that of isobutene. Subsequently, the spectra are scaled to the absolute ionization spectrum of isobutene measured by Wang

and 4% are derived for the formation of C6H8 from H loss and the formation of C4H4 from C2H3 loss, respectively. These findings are expected on the basis of the cis-2-butene measurements and calculations reported above. 3.3.4. C2H + Isobutene. The reaction between C2H and isobutene exhibits two product channels (m/z = 66 and 80, Figure 3), and ionization spectra have been acquired for both reaction products. The photoionization spectrum of the C5H6 species at m/z = 66 is displayed in Figure 11. The signal-tonoise ratio for this measurement is significantly lower than that for the other reactions. This is caused by the large absorption cross section of the reactant, which results in the photolysis of one-quarter of the reactant species before they react. Moreover, H



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Figure 12. Absolute photoionization spectrum of 2-methyl-1-buten-3yne measured in the Laval nozzle expansion (1 MB = 10−18 cm2).

Figure 9. Photoionization spectrum of the C5H6 reaction product formed from the C2H + cis-2-butene reaction plotted together with a fit based on a calculated cis-3-penten-1-yne ionization spectrum.

9.1 eV. The simulated spectra of C5H6 isomers cis-3-penten-1yne and trans-3-penten-1-yne exhibit a sharp onset around this photon energy and these species are also expected to contribute to the measured ionization spectrum. The simulated spectrum and cross section of trans-3-penten-1-yne taken from Bouwman et al.52 are used for the analysis. No further attempt is made to distinguish the two geometrical isomers, and it is concluded that one or both of the geometrical isomers contribute to this channel. Contributions of 2-methyl-1-buten-3-yne and cis- and trans-3penten-1-yne to the m/z = 66 spectrum are computed from fits to the measured data. The fact that the radical density, and inherently the product signal, decreases because of deposits on the MgF2 laser entrance window needs to be taken into account in the fit procedure. To do so, the computed spectrum of trans3-penten-1-yne and the acquired spectrum of the 2-methyl-1buten-3-yne that are used for the fit are multiplied by an exponential function that accounts for the measured decay of the laser power. The resulting fit to the measured ionization spectrum and the individual contributions of the two scaled C5H6 isomers are shown in Figure 11. The fit to the data nicely agrees with the resonances in the measured spectrum that arise from 2-methyl-1-buten-3-yne. Contributions of (57 ± 15)% for 2-methyl-1-buten-3-yne and (43 ± 15)% for geometrical isomers cis- and trans-3-penten-1-yne are derived for the m/z = 66 mass channel of the C2H + isobutene reaction. The errors in the branching fractions are displayed at the 1σ level and are dominated by the computed ionization cross section of cis- and trans-3-penten-1-yne. A photoionization spectrum is recorded for the C6H8 (m/z = 80) product formed from the reaction between C2H and isobutene and is displayed in Figure 13. Also displayed in Figure 13 is the simulated spectrum of C6H8 isomer 4-methyl3-penten-1-yne that is likely formed from the reaction. There is good agreement between the measured and calculated ionization onsets. Furthermore, the shape of the measured spectrum is captured by the calculated spectrum, and this signal is assigned to 4-methyl-3-penten-1-yne. The branching ratio between the m/z = 66 and 80 channels for the reaction between isobutene and C2H is also determined. As described above, because the window is covered by deposits very rapidly when running isobutene at 193 nm, the time-trace measurements are performed for both mass channels in quick succession in the absence and presence of the C2H precursor at a single photon-energy value. The integrated ion counts resulting from these traces are subsequently corrected for the

Figure 10. Photoionization spectrum of the C5H6 product species formed from the reaction between C2H and trans-2-butene plotted together with a fit to the data based on a calculated ionization spectrum of trans-3-penten-1-yne.

Figure 11. Photoionization spectrum of the C5H6 species formed from the reaction between C2H and isobutene plotted together with a simulated spectrum of trans-3-penten-1-yne and a measured spectrum of 2-methyl-1-buten-3-yne that are corrected for the decay of the photolysis laser (see text).

et al.59 The measured absolute photoionization spectrum of 2methyl-1-buten-3-yne is displayed in Figure 12. The decrease in signal beyond a photon energy of 11.2 eV is presumably caused by dissociative ionization, as is common for hydrocarbons. The ionization spectrum of 2-methyl-1-buten-3-yne matches the resonances in the acquired spectrum (Figure 11), but it does not explain the rather sharp ionization threshold at around I



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Figure 13. Photoionization spectrum of the product formed from the reaction between C2H and isobutene and detected at m/z = 80.

mass-dependent QMS sensitivity and the ionization cross sections of the C5H6 and C6H8 species. The ionization cross section of C6H8 is computed using eq 1 and is 51 MB. The branching fractions derived from these signals are (61 ± 15)% for the m/z = 66 product and (39 ± 15)% for the m/z = 80 product. The errors in the branching fractions are displayed at the 1σ level and are dominated by the uncertainty in the computed ionization cross sections. A schematic of a possible reaction network for the reaction between C2H and isobutene is shown in Figure 8. The C2H radical adds to either carbon of the π system of the reactant to form adduct species 5 and 6. Adduct 5 undergoes direct CH3 elimination to form the stable product 2-methyl-1-buten-3-yne. Adduct 6 can lose an H atom to form the stable product 4methyl-3-penten-1-yne. A hydrogen from 6 to form adduct 7 needs to be included to explain the detection of cis- and/or trans-3-penten-1-yne. H-atom shifts followed by H-atom or CH3-radical elimination could lead to the formation of ring structures, but no experimental evidence is currently found for these reaction pathways and an upper limit of 10% is derived for the formation these species. The branching fractions reported here for the C2H + isobutene reaction can be compared to calculated values reported in the literature.46 From the measurements presented here, we find that (26 ± 15)% is in the form of cis- and trans-3penten-1-yne, (35 ± 15)% is in the form of 2-methyl-1-buten-3yne, and (39 ± 15)% is in the form of 4-methyl-3-penten-1-yne. These values qualitatively agree with calculated branching fractions of 24% for 4-methyl-3-penten-1-yne, 64% 2-methyl-1buten-3-yne (C5H6), and 12% trans-3-penten-1-yne reported by Woon and Park.46 The difference between the measurements and calculations are possibly caused by the assumption that is made in the computations that addition to the carbon atoms in the π system has equal probability. Steric effects may become more dominant for larger molecular systems, possibly causing larger discrepancies between the computations and experiments.

Figure 14. Overview of the product branching fractions for C2H reacting with alkenes up to C4. Only product fractions larger than 15% are depicted.

the previous study, it was found that the C2H + ethene reaction yields solely vinylacetylene (C4H4) through H elimination. For this reaction, this is the only accessible elimination pathway that leads to the formation of a stable species. For the C2H + propene reaction, it was found that methyl loss from the initial adduct is the dominant channel and only a small fraction (15%) of the product is in the form of various C5H6 isomers that are formed through H-atom elimination. It was suggested that the prevalence of the methyl elimination channel is caused by either a steric effect in the formation of the adduct or by a Hatom shift after the adduct is formed.51,52 The dominant exit channel of the C2H + 1-butene reaction is found to be the loss of the vinyl radical to form (65 ± 10)% vinylacetylene. The other observed channel for the C2H + 1butene reaction is the formation of 4-penten-1-yne through methyl loss and accounts for (35 ± 10)%. The preferred formation of vinylacetylene over 4-penten-1-yne can have a similar origin as in propene reaction. Addition to the nonterminal carbon of the π system can be preferred, forming adduct 1 (Figure 8) in larger abundance. Alternatively, an H shift can occur within adduct 1, giving rise to the preferred formation of vinylacetylene. Although direct H elimination from the adduct species is accessible, it is not detected. The cis- and trans-2-butene reactions could proceed via H elimination, but the data show that methyl elimination is the only observed pathway. The methyl-loss channel is also dominant for the C2H + isobutene reaction, but for this reaction, a significant fraction proceeds via H elimination. This is likely caused by the fact that H elimination is the only pathway to a stable product that is directly accessible from adduct 6 in Figure 8. The direct H-loss pathway competes with an H shift that exhibits a barrier that is lower by only 1 kcal/ mol.46 The branching fractions reported here can be compared to theoretical work. From a multiple-well treatment, Woon and Park46 derived branching ratios for the C2H + C4H8 reactions over a range of temperatures (50−300 K) and pressures (10−2 mbar to 1 bar). For the reaction between C2H and 1-butene

4. DISCUSSION The experimental results presented here provide pivotal information for understanding the chemistry in combustion environments and the photochemistry in cold regions, such as Titan’s atmosphere. This work adds to previously published work on the C2H + C2H4 and C2H + C3H6 reactions.52 An overview of the product branching fractions from the previous study and the work presented here is shown in Figure 14. From J



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C2H and 1-butene is found to yield (65 ± 10)% vinylacetylene and (35 ± 10)% 4-penten-1-yne. The cis-2-butene and trans-2butene reactions yield purely cis-3-penten-1-yne, trans-3penten-1-yne, or a combination of these two geometrical isomers. Finally, the isobutene reaction yields (26 ± 15)% cisand trans-3-penten-1-yne, (35 ± 15)% 2-methyl-1-buten-3-yne, and (39 ± 15)% 4-methyl-3-penten-1-yne. The bimolecular-reaction rate constants and product branching ratios reported here provide important input for chemical models that aim to understand hydrocarbon chemistries, such as combustion chemistry and the chemistry in the atmosphere of Saturn’s largest moon, Titan. In Titan’s atmosphere, reactions between unsaturated hydrocarbons and hydrocarbon radicals are thought to lead eventually to the formation of the yellow haze that shrouds the moon. This haze is composed of large, possibly cyclic and/or aromatic hydrocarbons. Similarly, in combustion environments the reactions of C2H radicals are considered to play an important role in the formation of aromatic species. In the work presented here, no evidence is found for the formation of cyclic molecules from butenes reacting with C2H, and an upper limit of 10% is put on this channel. The feedback of CH3 and C2H5 radicals indicates that subsequent reactions of these radicals may play a more prominent role in the overall chemistry in these environments.

under temperature and pressure conditions where no adduct stabilization occurs (e.g., for 50−100 K at ca. 10 mbar and below), they calculate that 58% is in the form of vinylacetylene (C4H4) formed by C2H5 elimination with the remaining 42% 4penten-1-yne formed by CH3 elimination. For C2H + cis-2butene, they predict that the only product is trans-3-penten-1yne formed by CH3 elimination from the adduct species. Finally, from their calculations they predict that the reaction between C2H and isobutene forms 24% 4-methyl-3-penten-1yne (C6H8), 64% 2-methyl-1-buten-3-yne (C5H6), and 12% trans-3-penten-1-yne (C5H6). They report significant stabilization of the adduct species toward higher pressures (e.g., for 50− 100 K at ca. 1 mbar and above). The measured product branching ratios reported in this work agree qualitatively with these calculated values. For the reactions of alkenes of up to C4 with C2H, there is a propensity to proceed via the elimination of the largest possible radical fragment from the initially formed adduct. The loss of a vinyl or methyl radical is thus preferred over the loss of an H atom, and this is likely caused by the larger bond strength of the C−H bond compared to that of the C−C bond. These results imply that molecular growth via C2H is fairly inefficient, and an important consequence of these reactions is the production of CH3 and C2H5 radicals. Reactions of these radicals may thus play a more prominent role in the overall chemistry on Titan. The C2H + C2H4, C3H6, and C4H8 reactions are included in the latest comprehensive chemical model describing Titan’s atmospheric chemistry.3 The C2H + propene reaction was assumed to proceed via H elimination, but experimentally it was found to occur via CH3 elimination instead.52 In current photochemical models, no specific products were assigned to the C2H + C4H8 reactions. The data presented here can be directly used in refining chemical models that aim to understand the photochemistry that occurs in Titan’s atmosphere. Calculations predict that the branching ratios do not change significantly toward higher temperatures (300 K),46 and this is likely caused by the fact that the reactions exhibit no entrance barrier. Hence, the branching fractions reported here can be cautiously used in models describing combustion reactions. At higher pressures, as predicted by calculations, significant stabilization of the adduct may occur.46

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +1-510-495-2474. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

The Advanced Light Source and Chemical Sciences Division (K.R.W. and S.R.L.) are supported by the Director, Office of Science, Office of Basic Energy Sciences of the U.S. Department of Energy under contract no. DE-AC0205CH11231 at the Lawrence Berkeley National Laboratory. K.R.W. and S.R.L. are supported in part by NASA grant no. NNH13AV43I. Support for J.B. was obtained from the National Science Foundation Engineering Research Center for Extreme Ultraviolet Science and Technology. Construction of this Laval instrument was made possible by a National Aeronautics and Space Administration Planetary Major Equipment grant. I.R.S. thanks the CNRS for the award of sabbatical funding during the period of this research and the French Programme National de Planétologie for financial support. M.F. thanks the French Ministère de l’Enseignement Supérieur et de la Recherche for a doctoral grant. We thank the FranceBerkeley Fund for financial support.

5. CONCLUSIONS Low-temperature bimolecular-reaction rate constants are measured for the C2H + 1-butene, cis-2-butene, trans-2-butene, and isobutene reactions. The rates are quantified at 79 K in a Laval nozzle expansion by measuring the formation of product species as a function of time for a set of reactant densities under pseudo-first-order conditions. The rate constants amount to (1.9 ± 0.5) × 10−10, (1.7 ± 0.5) × 10−10, (2.1 ± 0.7) × 10−10, and (1.8 ± 0.9) × 10−10 cm3 s−1 for the reactions between C2H and 1-butene, cis-2-butene, trans-2-butene, and isobutene, respectively. The rate constants of 1-butene and isobutene compare well to those measured previously, and the rate constants for cis- and trans-2-butene are reported for the first time. Mass spectra of the products that are formed from the lowtemperature reactions in the Laval expansion are recorded. Photoionization spectra are recorded for each of the detected product channels. The spectra are modeled with measured ionization spectra when available or simulated ionization spectra when unavailable to derive low-temperature isomerresolved product branching fractions. The reaction between

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