Direct Kinetics and Product Measurement of Phenyl Radical + Ethylene

The phenyl + ethylene (C6H5 + C2H4) reaction network was explored experimentally and theoretically to understand the temperature dependence of the reaction kinetics and product distribution under various temperature and pressure conditions. The flash photolysis apparatus combining laser absorbance spectroscopy (LAS) and time-resolved molecular beam mass spectrometry (MBMS) was used to study reactions on the C8H9 potential energy surface (PES). In LAS experiments, 505.3 nm laser light selectively probed C6H5 decay, and we measured the total C6H5 consumption rate coefficients in the intermediate temperature region (400–800 K), which connects previous experiments performed in high-temperature (pyrolysis) and low-temperature (cavity-ring-down methods) regions. From the quantum chemistry calculations by Tokmakov and Lin using the G2M(RCC5)//B3LYP method, we constructed a kinetic model and estimated phenomenological pressure-dependent rate coefficients, k(T, P), with the Arkane package in the reaction mechanism generator. The MBMS experiments, performed at 600–800 K and 10–50 Torr, revealed three major product peaks: m/z = 105 (adducts, mostly 2-phenylethyl radical, but also 1-phenylethyl radical, ortho-ethyl phenyl radical, and a spiro-fused ring radical), 104 (styrene, co-product with a H atom), and 78 (benzene, co-product with C2H3 radical). Product branching ratios were predicted by the model and validated by experiments for the first time. At 600 K and 10 Torr, the yield ratio of the H-abstraction reaction (forming benzene + C2H3) is measured to be 1.1% and the H-loss channel (styrene + H) has a 2.5% yield ratio. The model predicts 1.0% for H-abstraction and 2.3% for H-loss, which is within the experimental error bars. The branching ratio and formation of styrene increase at high temperature due to the favored formally direct channel (1.0% at 600 K and 10 Torr, 5.8% at 800 K and 10 Torr in the model prediction) and the faster β-scission reactions of C8H9 isomers. The importance of pressure dependence in kinetics is verified by the increase in the yield of the stabilized adduct from radical addition from 80.2% (800 K, 10 Torr) to 88.9% (800 K, 50 Torr), at the expense of styrene + H. The pressure-dependent model developed in this work is well validated by the LAS and MBMS measurements and gives a complete picture of the C6H5 + C2H4 reaction.


INTRODUCTION
In past decades, the formation of polycyclic aromatic hydrocarbons (PAHs) has attracted attention in astrochemical 1−4 and combustion 5−8 research. This chemistry is also important in processes for making coke, carbon black, and carbon nanotubes and in a variety of deposit formation mechanisms. 9−12 The simplest aromatic radical, phenyl radical (C 6 H 5 ), reacts with unsaturated hydrocarbons and forms a second ring through radical cyclization. PAHs in astrochemistry have been correlated with the unidentified infrared (UIR) emission band ranging from 3 to 14 μm 13−16 and recognized as a carrier of the diffuse interstellar bands (DIBs) in the lowwavelength visible (400 nm) to the near-infrared (1200 nm). 14,17,18 Due to their abundant existence in some carbonrich environments, PAHs are known to be important in the evolution of the interstellar medium (ISM). 19−21 While their existence is advantageous in the field of astronomy, PAHs as precursors to soot formation are normally undesired side products in chemical processing and combustion and contribute to air pollution 11,22 and global warming. 23 In efforts to minimize the yield of PAHs, numerous potential energy surfaces (PESs) involving PAH initiation and propagation have been calculated and applied to mechanisms used in industrial chemical processes, and species like styrene are important in PAH formation. 24−27 To validate the theoretical works, kinetics measurements and product quantification under different conditions have been designed and performed.
As one of the simplest unsaturated hydrocarbons, ethylene (C 2 H 4 ) and its reaction with C 6 H 5 and products on the corresponding PES have been recognized as important in various fields. The radical addition product, 2-phenylethyl radical, has been used as a carbon-centered radical interacting with DNA to study the metabolic activation of hydrazine derivatives. 28−31 Another radical adduct formed through 2phenylethyl radical isomerization is 1-phenylethyl radical, and it has been selected as a model species to react with various monomers to understand their reactivity toward the polystyrene radical. 32−35 In this reaction network, styrene can be generated through the well-skipping reaction from C 6 H 5 + C 2 H 4 and H-elimination from radical adducts.
To measure the kinetics of C 6 H 5 + C 2 H 4 , Fahr et al. performed low-pressure pyrolysis experiments from 1000 to 1330 K and styrene was proposed as a reaction product. 36,37 However, in this experiment, a large fraction of the carbon was deposited on the reactor wall, which caused C 6 H 5 loss and affected rate quantification. The cavity-ring-down (CRD) method was used by Yu and Lin 38,39 to measure total rate constants of C 6 H 5 + C 2 H 4 between 297 and 523 K; moreover, their multichannel RRKM analysis explained the discrepancy between the previous pyrolysis experiments and their CRD measurement. Zhang et al. investigated styrene formation with a crossed molecular beam setup under single-collision conditions. 40 The product styrene was found along with a H atom from a short-lived transient species after a collision between C 6 H 5 and C 2 H 4 . The experiment also found the reaction phenyl + ethene → styrene + H to be exoergic by 25 ± 12 kJ/mol (6.0 ± 2.9 kcal/mol). Using improved quantum chemical methods at the G2M level of theory, 41 Tokmakov and Lin completed a detailed analysis on the C 6 H 5 + C 2 H 4 PES including hindered rotor calculations. 42 Rate constants of all elementary reactions were computed using the transition state theory (TST), and the calculated rate for the initial addition step agreed well with the previous pyrolysis and CRD experiments. RRKM/ME calculations were performed as well to get k(T) at two different pressures. The energy released in styrene + H formation was calculated as 7.1 kcal/mol, consistent with the crossed molecular beam results. Product branching ratios were predicted at different T, P conditions; however, no experimental data was available at that time to provide direct validation. As suggested by Yu and Lin, 38 more experimental data on the product formation are needed to improve kinetic models.
In this work, time-resolved molecular beam mass spectrometry (MBMS) experiments of the C 6 H 5 + C 2 H 4 reaction are coupled with a pressure-dependent model derived from the complete molecular information reported by Tokmakov and Lin 42 to directly quantify product formation under a range of T, P (600−800 K, 10−50 Torr) conditions. Laser absorbance spectroscopy (LAS) experiments are conducted in the same apparatus to measure the total rate coefficients of C 6 H 5 + C 2 H 4 from 400 to 800 K.

EXPERIMENTAL METHODS
The experimental apparatus used in this work has been described in previous publications. 43 −46 Two types of experiments were performed in this apparatus. First, LAS was used to measure phenyl radical (C 6 H 5 ) consumption rates; second, time-resolved MBMS was used to evaluate the product formation and branching ratios.
All experiments were performed in a custom quartz flow reactor (1.6 cm inner diameter in the center section where the measurement takes place) sampled to a high vacuum chamber with a time-of-flight mass spectrometer (TOF-MS); the TOF-MS has the mass resolution, m/Δm, ∼400, which can easily distinguish chemical species with the mass-to-charge ratio (m/ z) values separated by 1 amu. 45 Gases were well-mixed before flowing into the reactor, which is pumped by a Roots blower. Pressure in the reactor was controlled between 4 and 50 Torr by throttling a butterfly valve at the reactor outlet. The reactor was wrapped with a nichrome ribbon wire to heat up the gas to desired temperatures (room temperature to 800 K) measured by two thermocouples located inside the reactor. Axial temperature profiles of the gas were measured in the previous work, 45 and temperatures with uncertainty for each experimental condition are reported in this work. For absorbance experiments, the temperature was evaluated from the region where the Herriott cell and photolysis overlap; for MBMS experiments, only the 5 cm section on the inlet side of the sampling pinhole was chosen to report average temperatures with uncertainties, corresponding to the distance traveled on the short reaction time scale (up to 2 ms) in this work.
A collimated 266 nm laser beam (fourth harmonic frequency of an Nd:YAG laser) was used to photolyze the radical precursor. The repetition rate was set at 1 Hz, except for a few control experiments at 2 Hz, and the total gas flow rate was controlled to maintain one flash-per-refresh (FPR) conditions. Before the laser beam entered the reactor, an adjustable iris was placed in the beam path to control the beam diameter. It was clipped from 1.8 to 1.5 cm, which is slightly smaller than the reactor's inner diameter, providing two main advantages: 1. Clipping the edges of the beam can decrease inhomogeneities in the radical concentration. 2. No direct contact was made between the reactor inner wall and the laser beam, but the beam was carefully aligned to minimize the gap between the irradiated volume and the reactor wall. This reduced the risetime of the MS signal after the photolysis flash, allowing us to measure product distribution with less interference from secondary reactions. In previous MBMS experiments, 46 we observed significant conversion of phenyl radical to benzene, but that was much less of a problem in the present work possibly because the improved alignment and faster risetime reduced wall reactions.
The wavelength of the probe laser in LAS experiments was 505.3 nm, which is close to the reported C 6 H 5 low-lying electronic transition at 504.8 nm. 38,47 At this wavelength, the main product radicals formed in the experiments (the phenylethyl radicals and vinyl radicals) are not expected to absorb and interfere with the kinetics evaluation. 39,48 In MBMS experiments, the photoionization laser beam at 118.2 nm (10.5 eV, ninth harmonic frequency of an Nd:YAG laser) intersected with the molecular beam produced by sampling from a 275 μm diameter pinhole in the center of the reactor. The ionized species were accelerated, focused, and guided to  the KORE TOF-MS detector (ETP electron multiplier, model  AF824). Iodobenzene (C 6 H 5 I; Sigma-Aldrich, 98%) was used as the photolytic precursor of phenyl radical (C 6 H 5 ). To remove oxygen and impurities, several freeze-pump-thaw cycles were performed on C 6 H 5 I in an air-tight bubbler. 46 Due to the high reactivity between C 6 H 5 and O 2 , a strong 505 nm absorbance signal from the product phenylperoxy (C 6 H 5 OO) can be observed when ≥100 ppm of O 2 remains in the bubbler. 49,50 Before each experimental condition, absorbance traces of C 6 H 5 without C 2 H 4 were taken to ensure that O 2 is eliminated. The co-product of photolysis from C 6 H 5 I, I atom, has the same initial concentration as C 6 H 5 ; therefore, the 1315 nm transition of the I atom was probed to determine the initial C 6 H 5 concentration. 46 Helium (He) was the bath gas for all experiments with UHP grade purity (≥99.999%) obtained from Airgas. Ethylene (C 2 H 4 ) had ≥99.5% purity (CP grade) and was purchased from Airgas.

THEORETICAL METHODS
3.1. Potential Energy Surface and Kinetics Calculation. The C 8 H 9 potential energy surface was calculated by Tokmakov and Lin using G2M(RCC5)//B3LYP. 42 Three pairs of bimolecular products were reported: phenyl + ethylene, vinyl + benzene, and H + styrene, along with five adducts on the PES, which is depicted in Figure 1. Four other C 8 H 9 isomers reported by Tokmakov and Lin 42 (i6−i9) have less significance in the conditions of this work; however, the corresponding reactions are included in our mechanism and presented in the expanded PES Figure S1. Other reactions were considered by Tokmakov and Lin; 42 however, those reactions were not included in their reported PES since the reaction barriers were too high. In previous works, total rate coefficients evaluated from the PES were validated by Fahr et al.'s experimental data (1000−1330 K) 36,37 and Yu and Lin's cavity-ring down experiments, 38,39 despite small systematic errors (1−2 kcal/mol) in the enthalpies and barriers for radical additions producing Π-radicals with a large degree of electron delocalization at the level of theory. 42 Tokmakov and Lin's prediction on product branching ratios had no experimental data to validate. The predicted rate coefficients and timedependent composition of the species on the C 8 H 9 PES were reported 42 at some T and P, but not at the conditions of our experiments.
In this work, we used Arkane, 51 a program in the opensource Reaction Mechanism Generator (RMG) 52 software package, to compute both high pressure and phenomenological pressure-dependent rate coefficients, k ∞ (T) and k(T, P), from the molecular information provided by Tokmakov and Lin with some modest extensions. At the high-pressure limit, canonical transition state theory (TST) was used with the rigid-rotor harmonic oscillator (RRHO) approximation to evaluate rate coefficients. The one-dimensional (1D) hindered rotor treatment was applied to replace the frequencies in square brackets in Tokmakov and Lin's Supporting Information, 42 which indicated internal rotations with low-energy barriers. 1D-asymmetric Eckart correction was chosen as the tunneling model. High-pressure limit rate coefficients of all elementary steps on the PES are reported in the Supporting Information.
When temperature increases, pressure decreases, or molecular size decreases, significant falloff or chemical activation effects may take place, and the pressure dependence of the kinetics should be considered. In our experiments, pressure ranged between 4 and 50 Torr, so many reactions were not in the high-pressure limit. Therefore, phenomenological pressure-dependent rate coefficients, k(T, P), were computed with Arkane and used in the model to compare with experimental results. Using the modified strong collision approximation, k(T, P) were fitted into the Chebyshev format by applying RRKM/ME from the ab initio data provided by Tokmakov and Lin. 51 Lennard-Jones parameters between He and the C 8 H 9 adducts (ϵ/cm −1 , σ/Å = 342, 6.83) were estimated by the Joback method 53 implemented in RMG. Collisional energy-transfer parameters (α(T) = 424*(T/300 K) 0.62 cm −1 ) were taken from Mebel et al. 54 for argon bath gas and scaled down for helium bath gas using the calculations of Jasper et al. 55 The pressure-dependent forward rate coefficients on the C 8 H 9 PES are from our master equation calculations based on Tokmakov and Lin's ab initio calculations at the stationary points. To ensure thermodynamic consistency, all of the reverse rate coefficients in the kinetic model are computed from the forward rate coefficients and equilibrium constants computed using the NASA polynomials for each species given in the Supporting Information. The database available in RMG has ∼40 libraries, which store thermochemistry properties from the literature or ab initio quantum chemistry calculation. Among these, the Narayanaswamy library 56 focuses on aromatics formation and contains accurate experimental data along with G3MP2//B3 calculations, so it was used to estimate thermochemical properties of dominant species (C 6 H 5 , C 2 H 4 , C 6 H 6 , C 2 H 3 , C 6 H 5 C 2 H 3 , i1) on the PES in Figure 1, except for the H atom, which was taken from primaryThermoLibrary. 52 The thermochemistry of 1-phenylethyl radical (species i2 in Figure 1) was found to sensitively affect the predicted adduct isomerization and styrene formation rates at some reaction conditions; however, its thermochemical properties were not available in any libraries. Therefore, ab initio calculation of 1phenylethyl radical was performed at the CCSD(T)-F12/cc-pVTZ-F12//wB97x-D3/def2-TZVP level of theory with 1D hindered rotors using MOLPRO 2015 57−67 and Q-Chem 4.4.0. 68 That species' enthalpy, entropy, and heat capacity were The Journal of Physical Chemistry A pubs.acs.org/JPCA Article then evaluated in Arkane and used in the mechanism. For the rest of the species containing aromatic rings, RMG was used to estimate their thermochemistry properties based on two improved algorithms: similarity matching and bicyclic decomposition, which extended the basic group additivity method. 69 Although the accuracy of the prediction is not as great as ab initio calculations or library values, a sensitivity analysis showed that the energy of those species have insignificant effect on the product formation, which will be thoroughly discussed in the Results and Discussion section. The full pressure-dependent mechanism including kinetics and species thermochemistry in the Chemkin format and the corresponding species dictionary with RMG-style adjacency lists of the species in the model are included in the Supporting Information. Although the Chebyshev format is recommended here to express pressure-dependent kinetics, the Plog format kinetics are also provided in the Supporting Information. Sensitivity analysis was performed using Arkane (sensitivity of reaction rate constants to species energy) and RMG (sensitivity of species concentration to reaction rate constants and species enthalpy), and rate of production (ROP) analysis was done using Chemical Workbench. 70 3.2. Modeling MBMS Experiments. The approach for modeling the MBMS experiments in this study is similar to what was described in Buras et al.'s work on phenyl radical + propene. 46 The main difference is the time scale studied; a short time scale up to 2 ms was used in this work to focus on the primary chemistry and minimize secondary reactions (product formation, which is not directly from C 6 H 5 + C 2 H 4 ) and side reactions (reactions not on the C 6 H 5 + C 2 H 4 PES). Scheme 1 shows the procedure for modeling MBMS experiments and converting predicted species concentrations obtained in the model into predicted signals, which can be compared with MBMS experimental data.
In the MBMS experiments, three main product peaks were observed: m/z = 105 (adducts, i1 and i2), m/z = 104 (H-loss product, styrene), and m/z = 78 (H-abstraction product, benzene). To validate the combined mechanism generated with pressure-dependent kinetics and species thermochemistry properties, simulations were performed with an isothermal and isobaric batch reactor at temperature and pressure conditions from each of the MBMS experiments. With the initial phenyl radical concentration (C C 6 H 5 ,0 ) taken from the I atom laser measurement, the simulation predicted time-dependent concentrations (C i ) of each species on the PES. Each product species was then weighted by its photoionization cross section (PICS, σ) at 10.5 eV. For stable products, PICS were taken from previously reported values: σ 10.5 eV, benzene = 31.8 ± 6.4 Megabarns (Mb), 71 σ 10.5 eV, styrene = 43.9 ± 4.4 Mb. 72 For radical products, some assumptions based on the literature were needed to estimate PICS as follows. Due to a

Scheme 1. Overall Approach to Predict Species Concentrations and Convert Them into MBMS Signals for Comparison With Experimental Data
The Journal of Physical Chemistry A pubs.acs.org/JPCA Article correspondingly lower occupancy of the highest occupied molecular orbital (HOMO) from which the electron is ejected in radicals, a decrease in PICS by a factor of 2−4 compared to their closed-shell analogues can be expected. 73 However, aromatic resonance-stabilized radicals (RSRs) may have PICS similar to their closed-shell counterparts, for example, the PICS of benzyl radical σ 10.5 eV, benzyl = 25.5 Mb 74 at 10.5 eV is close to that of the related closed-shell structure, toluene (32.0 Mb 72 ). Therefore, the PICS is estimated as 10 ± 5 Mb for the nonresonant 2-phenylethyl radical (i1) and 30 ± 6 Mb for the resonance-stabilized 1-phenylethyl radical (i2, RSR) in this work, given the PICS of 32.1 Mb 72 for ethylbenzene, the closed-shell analogue of i1 and i2. The above PICS is used with a response factor obtained from internal standards (present in the reactor at ∼1 × 10 11 molecule/cm −3 ) to calculate signals from the predicted time-dependent concentration for species i To account for the transport effects in the reactor and molecular beam sampling, a simple model with the first-order rate constant (k sampling ) was utilized, which was adapted from Baeza-Romero et al. 75 by Buras et al. 46 In this work, k sampling was fitted to the measured risetime of the m/z = 105 signal (initial adduct). The fitted k sampling is validated by the normalized signals of I atom at m/z = 127; Figure S2 presents an example at 700 K, 10 Torr. Finally, before summing all modeled species signals of the same m/z and comparing with the experiments, the impact of 13 C isotopes was assumed to contribute 1.1% x number of carbon atoms for each of the product. This is especially important for m/z = 105, where the adduct signal is overlapped by the 13 C satellite of styrene.

RESULTS AND DISCUSSION
4.1. Overall k(T) of C 6 H 5 + C 2 H 4 Measured by 505.3 nm Absorbance. In absorbance experiments, 505.3 nm absorbance was used to measure the total consumption rate coefficient, k total (T), of C 6 H 5 . The absorption cross section for C 6 H 5 was measured at 504.8 nm by Tonokura et al. 47 In our experiments, greater absorbance signals at 505.3 nm were observed compared to that measured at 504.8 nm, and other radicals formed on the C 8 H 9 PES, i.e., 1-phenylethyl, 2phenylethyl, and vinyl radicals, were not expected to have observable absorbance at this wavelength. At the high-pressure limit, k total (T) is composed of two channels: radical addition (forming i1) and H-abstraction (forming C 6 H 6 + C 2 H 3 ). In Figure 3, the predicted kinetics from Tokmakov and Lin shows that the H-abstraction channel has negligible rates at low temperatures (<1000 K) compared to the radical addition channel. From the barrier heights calculated and reported in Figure 1, the H-abstraction barrier (9.0 kcal/mol) is much higher than the radical addition barrier (2.3 kcal/mol), so the much slower H-abstraction kinetics and minor product branching of C 6 H 6 are expected.
Before each absorbance experiment, background absorbance signals were recorded by flowing pure helium or helium + ethene with the same photolysis laser fluence as the kinetics experiments. Some nonzero background signals were observed, which may come from the slightly shifted probe laser beam caused by scattered photolysis light reflected by the Herriott cell optics. 46 Therefore, background subtraction was per-formed on all absorbance traces. The background-corrected signal traces were then fit to an exponential decay expression assuming pseudo-first-order kinetics Because of noise, imperfect background subtraction, and artifacts from AC-coupled detection electronics, a vertical shift factor (a) was used to account for the baseline offsets, which was normally within 10% and never exceeding 20% of the peak signal. Except for the gas-phase reaction of C 6 H 5 + C 2 H 4 measured, other reactions like wall reaction, selfrecombination, reaction with impurities like oxygen, and reaction with the precursor would lead to C 6 H 5 consumption and change in absorbance signals, and all of those reactions are collected in the term k wall . By increasing C 2 H 4 concentration at the same T, P condition, a faster decay of C 6 H 5 was observed with larger k′ fitted, which is shown in Figure 2. With at least five points on the plot of [C 2 H 4 ] versus k′, k total (slope) and k wall (y-intercept) were acquired from the fitted straight line. Table 1 summarizes the conditions and results of absorbance experiments from 400 to 800 K. Temperatures were measured for the region where the Herriott cell and the photolysis laser overlap, which was 20 cm long with 20% uncertainty. All experiments were performed at 10 Torr, except for Experiment 6 at 50 Torr. Experiments 7 and 8 were control experiments to test the effect of changing photolysis laser energy (20 to 35 mJ/pulse) and flash-per-refresh (FPR, 1 to 2). The rate coefficients measured in the control experiments fall within the uncertainty range of those measured at the standard conditions at 800 K (Experiment 5), which indicates that changing pressure, laser energy, and FPR have a negligible effect on the measured disappearance of C 6 H 5 due to C 6 H 5 + C 2 H 4 . The initial concentration of C 6 H 5 was determined by single-pass IR absorbance of the I atom (in the 2 P 1/2 ← 2 P 3/2 transition 76 ) generated simultaneously with C 6 H 5 after the photolysis pulse; this method was used in our previous works. 46,77 All experiments were carried out for at least five different concentrations of C 2 H 4 . In the Supporting Information, plots   Figure S3) and all k′ values in Experiment 1−8 are provided. The wall loss rate k wall accounts for a relatively small portion in the decay of C 6 H 5 , except for experiment 8 where k wall is larger than 1000 s −1 possibly due to the misaligned photolysis laser that generates radicals on the wall or reaction products from the prior flash since experiment 8 was operated with double flash-per-refresh; however, the contribution of k total was still more than a factor of three greater than k wall .
To compare with previous experiments on C 6 H 5 + C 2 H 4 kinetics, Figure 3 Figure 4 shows representative time-resolved mass spectra after the subtraction of prephotolysis background signals. These background signals mainly result from C 6 H 5 I with some impurity peaks and fragmentation; a representative background mass spectrum is shown in Figure S4. In addition All experiments were performed at a precursor concentration of 6.5 × 10 13 cm −3 (upper limit assuming that He exiting the bubbler is saturated with C 6 H 5 I at its room temperature and using a vapor pressure of 0.92 Torr for C 6 H 5 I 78 ). b Vertical shift in fits to normalized absorbance traces.    LAS provides a much better way to determine k total . The impurities mainly exist in ethylene (up to 1000 ppm of other hydrocarbons may be expected according to the stated purity) and the phenyl iodide precursor; however, no clear positive time dependence is observed for those impurities, so we conclude that the reaction of C 6 H 5 + C 2 H 4 is not affected. In addition to the impurities, the signal intensities of the calibration mixture have some fluctuation, which causes small peaks at those m/z values in the background-subtracted mass spectra in Figure 4. Vinyl radical, the co-product with benzene from the H-abstraction pathway, was observed at m/z = 27, but its small PICS made quantitative analysis impractical. The approach described in Section 3.2 was used to predict timedependent product distributions. Experimental conditions are summarized in Table 2.
To minimize recombination and other side reactions but also ensure that the reaction time scale was longer than the sampling time scale, the concentration of C 2 H 4 was controlled to achieve a reaction time of 1.5−2.0 ms. Similar to the absorbance experiments, the real temperature was determined by averaging over temperature measurements at different points in the reactor, in this case averaged over the 5 cm length on the upstream side of the center pinhole, which corresponds to the MBMS sampling region during the time after the flash. The pressure was 10 Torr for all experiments, except for experiments 15 and 16, which were performed at 50 Torr to understand the pressure dependence of product formation.
The value of k sampling was consistent (3500 s −1 ) over the range of temperatures and pressures operated in most of the MBMS experiments. In experiment 14, the high photolysis energy or a shifted laser alignment may have caused an inhomogeneous concentration of the phenyl radical after the photolysis pulse and more diffusion, leading to a slightly slower sampling risetime of the MBMS signals (k sampling = 2500 s −1 ). From previous experiments, the upper limit for time taken for transport via supersonic expansion to the ionization region due to effusive and supersonic sampling has been determined to be 100 μs. 75,79 The measured sampling time constant is slower than this, due to the time required to diffuse from the photolyzed region to the pinhole. In the present work, the sampling rate k sampling is higher than previous experiments 46 in the same apparatus (for which k sampling = 80−2000 s −1 ) possibly because the photolysis laser beam was better aligned inside the reactor. With faster k sampling , signals on a shorter time scale become observable and enable the quantification of the initial product distribution, even if they have sub-millisecond lifetimes. Figure 5 shows time profiles of measured product peaks in MBMS experiments and the model prediction for experiments 9 (600 K, 10 Torr), 10 (700 K, 10 Torr), 12 (800 K, 10 Torr), and 15 (800 K, 50 Torr) up to ∼2 ms reaction time; other control experiments to test the effect of changing C 2 H 4 concentration (reaction time ∼1.5 ms) and photolysis energy (20−30 mJ/pulse) are shown in the Supporting Information. In Figure 5, the model predictions are plotted with the MBMS experimental data, and uncertainty ranges of the model predictions due to uncertainties in PICS are shown as error bars. Due to the estimated PICS of radical species, large uncertainties can be found in the model prediction of m/z = 105 signals. To ensure that 2 ms was a reasonable time scale for C 6 H 5 decay, absorbance traces at the same conditions were measured. The traces plotted in Figure 5, which are the average value of every 20 data points, and t 90% in Table 2 show that the C 6 H 5 absorbance decays to less than 10% of its initial value within 2 ms, which indicates that the C 2 H 4 concentration was sufficient. Detailed comparison of mass spectra and laser absorbance traces show the rate of product formation matches the rate of phenyl decay, though some noise can be observed in the traces. When we quantified the kinetics from the absorbance data described in Section 4.1, at least five C 2 H 4 concentrations were used at a single T, P condition to minimize noise.
At 600 K, the experiment showed that the signal at m/z = 105 is dominant at early times due to the depletion of C 6 H 5 , while signals at m/z = 104 and 78 were very small. The modeled curve successfully predicts this behavior and attributes the adduct signals mostly to i1. This result suggests that once C 6 H 5 + C 2 H 4 crosses the radical addition barrier (2.3 kcal/mol) as seen in Figure 1, most of the addition products are thermalized to i1. When the temperature is increased to 700 K, the formation of styrene started to appear along with a All experiments were performed at a precursor concentration of 6.5 × 10 13 cm −3 (upper limit assuming that He exiting the bubbler is saturated with C 6 H 5 I at its room temperature and using a vapor pressure of 0.92 Torr for C 6 H 5 I 78 ). b Time at which 90% of phenyl radicals has been consumed, obtained from the absorbance traces at the same reaction conditions using eq 2.
The Journal of Physical Chemistry A pubs.acs.org/JPCA Article slight increase in benzene formation. The model again captures the product distribution from t = 0−2.0 ms and predicts that the formation of i2 increases gradually, whereas the formation of i1 reaches a plateau after 1.0 ms. In Figure 5b, the formation of styrene and i2 is predicted to occur on a similar time scale, such that the concentration of styrene and i2 is nearly the same at any given condition considering their PICS are close. This can be explained by their similar barrier heights (35.1 kcal/mol for styrene versus 33.1 kcal/mol for i2), which will be discussed more in the next section. At 800 K (Figure 5c,d), the highest temperature in this work, the signals of styrene were comparable to the sum of adduct signals dominated by i2. However, the benzene signals are still limited because the Habstraction barrier is much higher than the radical-addition barrier, see Figure 3. Unlike k total (T), which is pressure-independent, the product distributions and branching ratios are affected by pressure. From the analysis by Wong et al., 80 for species on the C 8 H 9 Experiments cannot distinguish i1 and i2, but the predicted signals of i1 and i2 from the model are shown as dashed lines. At 600 K, i1 dominates over the time scale measured; at 700 K, i1 is produced rapidly, while i2 increases slowly (almost overlapping with the styrene model line) and becomes similar to i1 at 2 ms; at 800 K, i2 dominates over i1 after 0.5 ms.
The Journal of Physical Chemistry A pubs.acs.org/JPCA Article PES at 800 K, the switchover pressure (the pressure below which pressure dependence should not be neglected) falls within 0.01−0.1 atm (7.6−76 Torr). Therefore, increasing pressure from 10 to 50 Torr was considered a good strategy to validate the pressure dependence of the model. One can clearly see that when pressure increased, styrene formation was less significant, and at early times, the initial adduct (i1) was preferred; this pressure dependence was observed in both the experiments and the model. Overall, the model predictions agree well with the MBMS measurement in the range of T, P studied in this work. Styrene formation is overestimated by the model by ∼20−30% after 1.0 ms in the 800 K, 50 torr MBMS experiments, Figure 5d; a sensitivity analysis to address this discrepancy is presented in the next section. 4.3. Product Branching and Sensitivity Analysis. From the results of the absorbance and MBMS experiments, a kinetic model derived from the C 8 H 9 PES calculated by Tokmakov and Lin has been validated. With the validated model, direct product branching ratios for the primary reaction channels can be determined. Some clarification of the relevant reaction pathways is needed to avoid confusion. In Figure 6, the major products corresponding to masses observed in the MBMS experiments are shown along with their formation pathways. The formation of i3 appears in the model with some amount at 600 K and becomes less important than that of i1 and i2 at higher temperatures. Therefore, i3 is not included in Figure 6. Solid lines represent "mechanistically direct pathways", which have one transition state connecting reactant and products, like the radical addition of C 6 H 5 on C 2 H 4 forming i1 and the Habstraction reaction forming benzene + C 2 H 3 . Dashed lines, on the other hand, are reactions traversing more than one transition state and defined as "formally direct" pathways 81−84 including C 6 H 5 + C 2 H 4 (+M) → i2 (+M) and C 6 H 5 + C 2 H 4 (+M) → styrene + H (+M). In the k(T, P) model generated from Arkane, both formally direct and mechanistically direct pathways are included. The competition between formally direct and mechanistically direct pathways consuming C 6 H 5 is illustrated in Table 3 from the ROP analysis at t = 0. The product branching ratio can be related to the MBMS experiments as time-resolved product signal ratios, i.e., the signal of 104/signal of 105 and the signal of 78/signal of 105.
However, secondary reactions started to affect the product distribution after t = 0 and were more significant at longer time scales and higher temperatures. For example, thermalized i1 formed by radical addition can isomerize into i2 or eliminate H atom generating styrene. Time-resolved product signal ratios from the MBMS experiments and the model are summarized in Figures 7 and 8.
At 600 K, the formation of i1 dominates over the formation of other products, and the model predicts 93.2% of C 6 H 5 reacting to form i1 through the radical addition pathway, 1.9% forming i2, and 1.6% forming i3 (for Experiment 9). As shown in Figure 5a, m/z = 105 signals are contributed predominantly by i1 at this relatively low temperature. Therefore, both the signal ratios of 104/105 and 78/105 were small, as seen in The results are in good agreement with the branching predicted in Table 3, where the relative yield of adducts (i1 + i2 + i3):H-loss:H-abstraction is predicted as 96.7% : 1.0% : 2.3%. When the temperature was increased to 700 K, the predicted branching of C 6 H 5 to i2 and styrene + H increased, due to the increased importance of well-skipping reactions over adduct stabilization. Also, the predicted branching to benzene + C 2 H 3 increased because higher temperature enables the reactants to cross the relatively high H-abstraction barrier. At higher temperature, secondary reactions also become faster, causing the product distribution to vary with time even at relatively short times. As shown in Figure 7b, the predicted 104/105 ratio increased by a factor of three from time 0 to 2.0 ms. Therefore, it is more challenging to determine the rate coefficient ratios from the product signals. However, given that  The Journal of Physical Chemistry A pubs.acs.org/JPCA Article the time dependence of the experimental data is consistent with the model prediction in Figures 7 and 8, we conclude that the model is well validated for both direct pathways and secondary reactions. At 700 and 800 K, the H-elimination from i1 to styrene + H plays an important role. With more i1 being converted into styrene, the 104/105 ratio increased. For the product channel of benzene + C 2 H 3 , the measured 78/105 signal ratio slightly decreased at 700 K between t = 0 and 2.0 ms. Although benzene + C 2 H 3 formed by the mechanistically direct pathway, C 6 H 5 + C 2 H 4 → benzene + C 2 H 3 , was not affected by secondary reactions, the isomerization of i1 into i2 changed the time dependence of the 78/105 signal ratio. For each i1 isomerized into i2, the total concentration of mass 105 adducts was fixed, but the 105 signal increased because the PICS of i2 is larger than that of i1. At 800 K and 10 Torr, the predicted t = 0 branching fraction to i1 further decreased to 80.2% and secondary reactions became more important, which is supported by the fact that the 104/105 ratio increased by more than a factor of 4, and most styrene is formed by βscission reactions from thermalized i1 and i2.  The change in the observed 104/105 signal ratio shown in Figure 7c,d is due to the pressure dependence of C 6 H 5 + C 2 H 4 → styrene + H and i1 → styrene + H. As explained by Tokmakov and Lin, 42 the effective total rate constants of the C 6 H 5 -addition are independent of pressure, as is the rate of the H-abstraction. The sum of branching fractions is always 100%, like the sum i1, i2, i3, styrene + H, and benzene + H in Table  3. When pressure increases, the y-axis intercept at t = 0 observed in Figure 7c,d at short times shows that the formally direct pathway of styrene + H is preferred at lower pressure over the adduct formation.
To understand how the uncertainty in quantum chemistry calculations affects the pressure-dependent kinetics in the C 8 H 9 PES and the predicted MBMS signals, a sensitivity analysis was performed using Arkane to study how the kinetics on the C 8 H 9 PES are affected by perturbing the zero-point energies of species (E 0 ) relative to C 6 H 5 + C 2 H 4 used in the pressure-dependent kinetics calculations. For the sensitivities to the zero-point energies of the saddle points, see the Supporting Information. Using the chain rule, the Arkane sensitivity of rate constants to E 0 was coupled with the sensitivity of species concentration to reaction rate constants and species enthalpy evaluated by RMG, and the sensitivity coefficients (d ln S m/z /dE 0,i ) of predicted MBMS signals of m/z = 78, 104, and 105 to E 0 were evaluated. The results of d ln S m/z /dE 0,i are presented in Figure 9, which shows only the sensitivity coefficients of the reactants (C 6 H 5 + C 2 H 4 ), i1, i2, and i3; for all other species on the C 8 H 9 PES, the predicted signals under the studied conditions showed negligible sensitivity to varying the species E 0 .
At 800 K, 50 torr, 2.0 ms, the modeled styrene signals overestimated the experimental signals by ∼20−30%, as seen in Figure 5d. The sensitivity coefficients of the styrene (m/z = 104) signal to the assumed E 0 values are shown in Figure 9b. The styrene signal is sensitive to the energy of the reactants C 6 H 5 + C 2 H 4 and also to the energy of i1. If the zero-point energy of C 6 H 5 + C 2 H 4 varies by 1 kcal/mol, Figure 9b indicates a change of 30% in the m/z = 104 signal at 800 K, 50 Torr. At the G2M(RCC5)//B3LYP level of theory used in the model, an uncertainty in E 0 of about 1−2 kcal/mol is expected, 42 which is responsible for ∼30−60% uncertainty in the absolute value of signals at m/z = 104. In addition to the uncertainty in E 0 , there may be uncertainty due to the faster rate of side reactions such as adduct radicals reacting with the I atom at high temperatures, which compete with i1 → styrene + H and i2 → styrene + H. Some signals of m/z = 232 (C 8 H 9 adduct + I atom) were observed in experiments 15 and 16.
Kinetics of these side reactions are significantly uncertain, and the signals of styrene were only affected after 1.0 ms at 800 K, 50 torr; thus, the model in this work does not include these side reactions. Considering the uncertainty due to E 0 and side reactions, the difference in styrene signals between the measurement and the model can reasonably fall within the model uncertainty.
The absolute values of the sensitivity coefficients in Figure 9 indicate that product formation is only sensitive to the energies of C 6 H 5 , C 2 H 4 , i1, and i2. The species with the next highest sensitivity is i3, which has negligible values in all experimental conditions. Given the low sensitivity coefficients of the other species, the extended group additivity method, which has a 3− 5 kcal/mol mean absolute error for cyclic species, is sufficient for estimating the energy and thermochemical properties of these insensitive species. 69 In summary, both the temperature and pressure dependence of the model developed from the C 8 H 9 PES were validated by MBMS experiments. The full pressure-dependent mechanism is given in the Supporting Information.

CONCLUSIONS
The C 6 H 5 + C 2 H 4 reaction network was investigated experimentally with laser absorbance and MBMS experiments combined in a unique apparatus and theoretically with a pressure-dependent model developed using Tokmakov and Lin's C 8 H 9 PES. The total consumption rate coefficients, k total (T), of C 6 H 5 were measured from 400 to 800 K using laser absorption at 505.3 nm and showed satisfactory agreement with the calculated values. In the previous experimental work, the rate coefficients of C 6 H 5 + C 2 H 4 were determined experimentally at low (297−523 K) and high (1000−1300 K) temperatures. With our new measurements performed at intermediate temperatures, the Arrhenius expression k total (T) = k R-addition + k H-abstraction = (4.41 × 10 5 )T 1.96 exp(−971/T) + (9.45 × 10 −3 )T 4.47 exp(−2250/T) has been fully verified over a wide temperature range as well as the barrier heights calculated by the G2M(RCC5)//B3LYP method.
The MBMS experiments provide direct product quantification on the C 6 H 5 + C 2 H 4 reaction network, which has never been reported before. Careful alignment of the photolysis laser enabled a faster rate of molecular beam sampling, allowing us to measure reaction chemistry at shorter times after the flash. Within the time scale of C 6 H 5 decay, signals from adducts, Helimination products, and H-abstraction products were observed and quantified. Predicted time profiles for the signals at m/z = 105, 104, and 78 peaks were obtained using a model The Journal of Physical Chemistry A pubs.acs.org/JPCA Article consisting of phenomenological pressure-dependent rate coefficients, k(T, P), and accurate thermochemical properties both derived from the quantum chemistry calculations of Tokmakov and Lin. The experimental measurements under different T, P conditions verified the accuracy of the model. Increasing the temperature from 600 to 800 K clearly increased styrene formation, which is an important polymer precursor and significant in HACA pathways leading to PAHs. Sensitivity analysis suggested the importance of accurate C 6 H 5 , C 2 H 4 , i1, and i2 thermochemistry, which were carefully considered in the model. At higher pressures of 50 Torr, more adducts were observed relative to experiments at 10 Torr, in agreement with the pressure dependence predicted by the model. A known disadvantage of mass spectrometry experiments is the inability to distinguish isomers; here, the validated model was used to understand the formation of two adducts with the same mass-to-charge ratio, i1 and i2. Since their total signals in the model agreed with the MBMS experiments, individual signals of i1 and i2 can be obtained from the model prediction. A ROP analysis was performed and showed that the i1 formation channel dominates the consumption of C 6 H 5 at 600 K 10 Torr (93.2%) but is less important at 800 K 10 Torr (80.2%). At 600 K, the branching ratio of the H-loss channel forming styrene + H was directly measured using a high C 2 H 4 concentration to minimize secondary reactions and agrees well with the model, which predicts that formation of i1 is the main contribution to the m/z = 105 signal. As pressure increases, the predicted branching to the formally direct products, i2 and styrene + H, decreases due to the higher collisional stabilization of i1. The effects of secondary reactions such as i1 isomerization and i1 H-elimination are important at high temperatures and longer times, which can be seen in the timeresolved 104/105 signal ratio. Given its complete validation by the experiment, the pressure-dependent rate coefficients developed in this work are recommended for modeling systems including the C 6 H 5 + C 2 H 4 reaction network.
High-pressure-limit kinetics from the model and the additional results from the LAS and MBMS experiments are reported; pressure-dependent kinetics in Plog format (PDF) Chemkin mechanism and species dictionary (ZIP) Quantum calculation output files for 1-phenylethyl radical (ZIP) Results of sensitivity analysis (XLSX)