Kinetics of the Self Reaction of Cyclopentadienyl Radicals - The

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Kinetics of the Self Reaction of Cyclopentadienyl Radicals Vadim D. Knyazev* and Konstantin V. Popov Research Center for Chemical Kinetics, Department of Chemistry, The Catholic University of America, Washington, District of Columbia 20064, United States S Supporting Information *

ABSTRACT: The kinetics of the self-reaction of cyclopentadienyl radicals (cC5H5) was studied by laser photolysis/photoionization mass spectroscopy. Overall rate constants were obtained in direct real-time experiments in the temperature region 304−600 K and at bath gas densities of (3.00−12.0) × 1016 molecules cm−3. The room-temperature value of the rate constant, (3.98 ± 0.41) × 10−10 cm3 molecule−1 s−1, is significantly higher than the rate constants for most hydrocarbon radical−radical reactions and coincides with the estimated collision rate. The observed overall c-C5H5 + c-C5H5 rate constant demonstrates an unprecedented strong negative temperature dependence: k1 = 2.9 × 10−12 exp(+1489 K/T) cm3 molecule−1 s−1, with estimated uncertainty increasing with temperature, from 13% at 304 to 32% at 600 K. Formation of C10H10 as the primary product of cyclopentadienyl self-reaction was observed. In additional experiments performed at the temperature of 800 K, formation of C10H10, C10H9, and C10H8 was observed. Final product analysis by gas chromatography/mass spectrometry detected two isomers of C10H8 at 800 K: naphthalene (major) and azulene (minor).

1. INTRODUCTION Radical−radical reactions, including self-reactions of radicals, play important roles in the pyrolysis and combustion of hydrocarbon fuels.1,2 These reactions are integral parts of chemical models of the combustion of organic fuels; knowledge of the rate constants and product branching fractions of these reactions is required for success of such models. Information available on the rate constants of these reactions, however, is sparse and often controversial. Radical−radical reactions are difficult to study experimentally because of the high reactivity of radicals, as well as challenges encountered in creating desired radicals in known concentrations without at the same time producing other, interfering reactive species. Theoretical methods of evaluating and predicting rates of radical−radical reactions become ever more important, and recent advancement of theoretical methods holds great promise (e.g., refs 3 and 4 and references cited therein). Validation and further development of theoretical methods requires a database of accurately determined temperature-dependent experimental data on a variety of benchmark reactions, preferably obtained in direct experiments. Such a database is far from being complete, and in particular there is a scarcity of data on the kinetics of the reactions between hydrocarbon radicals with more than three carbon atoms. In many chemical models of combustion, radical−radical reactions are assumed to have no temperature dependences, or weak negative temperature dependences are used based on analogy with the few reactions of small radicals for which such temperature dependences are actually known from experiment. For example, rate constants of the self-reactions of methyl and ethyl radicals decrease with temperature approximately © XXXX American Chemical Society

following a power law with the rate constants proportional to the temperature raised to the power of negative 0.6−0.7.3,5 Thus, modeling studies frequently use a similar weak power law with the exponent between 0 and −1, or Arrhenius equations with negative activation energies of about 0.5 kcal mol−1, which gives a similar to T−0.5 decrease in the rate constant from 300 to 1000 K. Recently, we studied self-reactions of relatively large alkyl radicals, cyclohexyl6 and neopentyl.7 These studies demonstrated significantly stronger negative temperature dependences of the rate constants, corresponding to the negative activation energies of 1.0−1.1 kcal mol−1. The observed trend is in general agreements with the observation by Klippenstein et al.4 that additional substituents at the radical center and increasing steric bulk of radicals result in stronger negative temperature dependences of their theoretically calculated recombination rate constants. Radical−radical reactions generally contribute to molecular mass growth. Particularly interesting in that respect are the reactions of delocalized unsaturated radicals, with some of the reactions of this class implicated in formation of aromatics and polyaromatics and, ultimately, soot in combustion systems. For example, recombination of the propargyl radicals has been Special Issue: 100 Years of Combustion Kinetics at Argonne: A Festschrift for Lawrence B. Harding, Joe V. Michael, and Albert F. Wagner Received: January 21, 2015 Revised: March 9, 2015

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DOI: 10.1021/acs.jpca.5b00644 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A experimentally8 and theoretically9,10 proven to lead to the formation of the smallest aromatic compound, benzene. Reactions of larger delocalized radicals have been suggested as leading to formation of larger aromatics (e.g., a review in ref 11). Among the delocalized polyatomic radicals, the cyclopentadienyl radical (c-C5H5) generated significant interest, especially in the past decade, due to its propensity to accumulate in large amounts in combustion and pyrolysis systems, as well as its ability to react with itself and other radicals and unsaturated hydrocarbons and thus contribute to molecular mass and aromatics growth. Reviews of relevant literature can be found in refs 12−15 and are not repeated here. Despite the importance of the reactions of the cyclopentadienyl radical in combustion and pyrolysis systems, the only experimental study of its gas-phase kinetics prior to the current work was that of Roy et al.,16,17 who studied the reaction of hydrogen atom addition to c-C5H5 under shock tube conditions. One particular reaction of cyclopentadienyl radicals that generated substantial amount of discussion in the literature is the self-reaction of c-C5H5 radicals: c‐C5H5 + c‐C5H5 → Products

radicals. Reaction 1 was studied in direct real-time laser photolysis/photoionization mass spectrometry (LP/PIMS) experiments. Overall rate constants of reaction 1 were obtained in the temperature interval 304−600 K and bath gas (mostly helium) densities in the range (3.0−12.0) × 1016 molecules cm−3. Formation of C10H10 and (at high temperatures) C10H9 and C10H8 products was observed in real time experiments; C10H10 and C10H8 were also detected in a final product GC/ MS analysis.

2. EXPERIMENTAL SECTION 2.1. The LP/PIMS Apparatus. Details of the experimental apparatus have been described before,22 and only a brief description is given here. Pulsed 248 nm light from a Lumonics LX700 excimer laser was directed along the axis of a heated 50 cm-long tubular reactor with 1.05 cm i.d. The surface of the reactor was coated with boron oxide to reduce radical wall losses.23 The laser was operated at the fluence of 5−10 mJ pulse−1 cm−2 and the frequency of 4 Hz. The flow of the gas mixture containing the radical precursor (cyclopentadiene) and the bath gas (helium) was set at ∼4 m s−1 to ensure complete replacement of the photolyzed gas mixture with fresh reactants between laser pulses. The mixture was continuously sampled through a small tapered orifice in the wall of the reactor and formed into a beam by a conical skimmer before entering the vacuum chamber containing the photoionization mass spectrometer. As the gas beam traversed the ion source, a portion was photoionized by an atomic resonance lamp, mass selected by a quadrupole mass filter, and detected by a Daly detector. Temporal ion signal profiles were recorded from short time before the laser pulse (10−30 ms) to 15−35 ms following the pulse by a multichannel scaler interfaced to a PC computer. Typically, data from 500 to 10000 repetition of the experiment were accumulated before the data were analyzed. The sources of the photoionization radiation were chlorine (8.9−9.1 eV, CaF2 window, used to detect c-C5H5, c-C5H6, C10H10, C10H9, C10H8, C10H12, and C10H14) and hydrogen (10.2 eV, MgF2 window, used to search for all potentially imaginable photolysis products ranging from CH3 to C5H4) resonance lamps. 2.2. The Final Product Analysis Apparatus. The apparatus described earlier by Shafir et al.8 was used. Experiments were performed at three temperatures: 301, 600, and 800 K. Briefly, flow of the helium carrier gas ([He] = (12.6−27.2) × 1016 molecules cm−3) containing the cyclopentadiene radical precursor in concentrations of (1.7−1.8) × 1015 molecules cm−3 was directed through a heated tubular quartz reactor. The photolyzing laser beam was directed along the axis of the reactor. Small flows of helium were introduced through the inlets at the front and the rear ends of the reactor to create buffer zones next to the reactor window and at the rear end where no reaction takes place. The flow velocity (107−231 cm s−1) and the laser firing repetition rate (7−14 Hz) were selected to ensure that the mixture in the photolysis zone is completely replaced between the laser pulses. The flow of the photolyzed mixture exited the reactor through a heated side arm (postphotolysis zone). The final products were collected in a liquid nitrogen trap. The residence times were 65−140 ms in the heated photolysis zone of the reactor and additional 65−140 ms in the heated postphotolysis zone, to ensure that radicals created during photolysis decay due to recombination and heterogeneous loss before the reacting mixture reaches a cold zone.

(1) 18

It was suggested by Dean in 1990 that this reaction may produce naphthalene (C10H8) and molecular hydrogen. In 1996, Melius et al.19 performed a potential energy surface (PES) study of the adduct of this reaction (C10H10) and concluded that naphthalene can be produced by adduct rearrangements and successive elimination of two hydrogen atoms. Subsequent molecular orbital research12,14 into the properties of C10H10 PES studied various channels of isomerization and elimination of hydrogen atoms. The most recent work of Cavallotti and Polino12 included a PES study combined with master equation simulation of the C10H10 adduct isomerization and decomposition via two types of channels producing a hydrogen atom and either an azulyl or a fulvalenyl radical. Either channel is likely to result in the ultimate production of naphthalene in combustion environments. Kinetic modeling studies of cyclopentadiene pyrolysis20 and oxidation,21 as well as those of other combustion systems, include the naphthalene producing channels of reaction 1 in their chemical mechanisms, with estimated Arrhenius parameters. What remains unknown, however, is the rate constants of reaction 1, both that of the overall reaction as well as those of the individual channels. In the study of Cavallotti and Polino,12 the rate constant of reaction 1 forming the initial C10H10 adduct c‐C5H5 + c‐C5H5 → C10H10

(1a)

was evaluated using microscopic reversibility and the rate constant of the reverse reaction calculated using microcanonical variational transition state theory. The resultant k1a(T) increases from 1.4 × 10−12 to 5.6 × 10−12 cm3 molecule−1 s−1 in the 1000−2000 K temperature range used by these authors. The authors estimate the uncertainty in k1a(T) as greater than a factor of 2−3; however, they also demonstrate that the large uncertainty in the rate constant of reaction 1a only partially propagates to the rate constant of the channels producing azulyl and fulvalenyl radicals and the H atom: variations in the k1a by a factor of 4 at 1500 K resulted in up to 40% changes in the rates of these radical producing channels. In this work, we present the first experimental determination of the rate constant of the self-reaction of cyclopentadienyl B


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temperature continued to 800 K, where its peak’s intensity was already 51% of the C10H10 adduct of reaction 1, indicating that it is likely to be a product of chemically and/or thermally activated isomerization of the initial adduct. Cyclopentadiene was obtained by cracking the dimer, dicyclopentadiene (Aldrich, ≥ 96%), as described by Moffett27 and purified by vacuum distillation. Although liquid cyclopentadiene quickly dimerizes at room temperature, it can be stored in the gas phase at moderate pressures indefinitely: the Gibbs free energy of the dimer decomposition reaction in the gas phase is ΔGo298 = −29.8 kJ,28 which corresponds to the equilibrium constant KP = 1.67 × 105. Gaseous cyclopentadiene was stored in gas flasks at the pressure of ca. 100 Torr; the calculated equilibrium partial pressure of the dicyclopentadiene impurity under these conditions is 8 × 10−5 Torr. The helium carrier gas (99.999%, less than 0.0002% of oxygen) was obtained from Roberts Oxygen. 2.4. Kinetic Mechanism in the LP/PIMS System. The photolysis of cyclopentadiene produces c-C5H5 and an H atom. The following subsequent reactions are possible in the system:

Samples accumulated in the trap were defrosted, diluted with air to atmospheric pressure, and then analyzed using a HewlettPackard GC/MS (6890 Plus Gas Chromatograph with a 5973 Mass Spectrometer, 70 eV electron impact ion source) equipped with a FactorFour VF-5 capillary column (i.d. 0.25 mm, 20 m length, film thickness 0.25 μm). The temperature of the GC oven was kept at 70 °C for 30 min, with subsequent 5.0 °C min−1 increase to 200 °C, followed by 10 min at 200 °C. The GC injector port temperature trailed that of the oven. At first, analysis of the gas phase in the trap was performed, which resulted in no chromatographic peaks except for those of cyclopentadiene and trace amount of dicyclopentadiene. This lack of the detectable amounts of the expected products of radical recombination was attributed to low vapor pressures of such products at room temperature and adsorption on the walls of the trap. Therefore, in subsequent analyses, the trap was rinsed with ca. 0.5 mL of the cyclohexane solvent, which was then followed by the GC/MS analysis of the resultant solution. Analysis of thus obtained liquid samples demonstrated presence of the products of radical recombination, as described below. During defrosting, rinsing of the trap, and transfer to GC/MS syringe, samples were kept at 0 °C in an ice bath, to reduce the degree of polymerization of the nascent C5H5−C5H5 adduct24 (vide infra). 2.3. Generation of Radicals. The cyclopentadienyl radicals were generated by the 248 nm laser photolysis of cyclopentadiene. hv

C5H6 → c‐C5H5 + H

(2)

Cyclopentadiene photolysis has been used as a source of cyclopentadienyl radicals in numerous spectroscopic studies and is well documented (e.g., refs 25 and 26). However, none of these studies specifically investigated potential formation of other photolysis products. For a kinetic study of reaction 1, it was important to ensure that no other reactive photolysis products (free radicals) that could interfere with the kinetics of the reaction under study are produced. Therefore, temporal profiles of ion signals for masses corresponding to all potentially imaginable photolysis products ranging from CH3 to C5H4 were searched for using the LP/PIMS technique. The hydrogen lamp was used as the source of photoionizing radiation. Besides the c-C5H5 signal (m/z = 65), signals of C5H4 and C3H3 were detected. The intensities of these signals were negligible compared to that of the c-C5H5 ion signal (0.3% for C5H4 and 0.1% for C3H3). Thus, it was concluded that no polyatomic reactive species smaller than c-C5H5 were produced in the cyclopentadienyl photolysis in the amounts that would cause interference to c-C5H5 kinetics. The next important question is whether any isomers of C5H5 other than the cyclopentadienyl radical are produced in reaction 2. To address this concern, a final product analysis of cyclopentadiene photolysis was performed, as described below (section 2.6). The major result of the final product analysis study pertaining to radical generation was that C10H10 adduct attributed to reaction 1 was observed, and no other significantly structurally different isomers of C10H10 were found in any amounts that would present concern for the “purity” of the photolytic source of c-C5H5. One isomer of C10H10 different from the adduct of reaction 1 was observed but in very small amounts: 0.67% and 1.6% of the main C10H10 chromatographic peak at 301 and 600 K, respectively. The trend of increasing the relative yield of this C10H10 isomer with

c‐C5H5 + c‐C5H5 → Products (C10H10 or others)

(1)

c‐C5H5 → wall loss

(3)

H → wall loss

(4)

H + c‐C5H5 → c‐C5H6

(5)

H + c‐C5H6 → c‐C5H5 + H 2

(6)

H + c‐C5H6 → c‐C5H 7

(7)

c‐C5H 7 → wall loss

(8)

c‐C5H5 + c‐C5H 7 → C10H12

(9)

c‐C5H 7 + c‐C5H 7 → C10H14

(10)

Hydrogen atoms can decay on the wall of the reactor (reaction 4), recombine with c-C5H5 to regenerate cyclopentadiene (reaction 5), or react with cyclopentadiene via abstraction (thus generating c-C5H5, reaction 6) or addition (producing c-C5H7, 2-cyclopentenyl radical, via reaction 7). The rate constants of H atom reactions with cyclopentadiene (reactions 6 and 7) are unknown but can be estimated based on analogy with the reactions of H abstraction from propene and that of terminal H addition to 1,3-butadiene. H + CH3CHCH 2 → ·CH 2CHCH 2 + H 2

(11)

H + 1,3‐C4 H6 → ·CH 2CHCHCH3

(12)

In both reactions 11 and 12, like in reactions 6 and 7, electron delocalization in the product radical reduces the reaction energy barrier compared to similar reactions not affected by delocalization and resonance stabilization of the products. Using Tsang’s recommendation for reaction 11 (k11 = 2.87 × 10−19 T2.50 exp(−1250 K/T) cm3 molecule−1 s−1)29 and the room temperature value of k12 ≈ 8 × 10−12 cm3 molecule−1 s−1 30−32 and accounting for reaction path degeneracies, we can obtain for reactions 6 and 7 at 300 K: k6 ≈ 4.6 × 10−15 and k7 ≈ 8 × 10−12 cm3 molecule−1 s−1. At 600 K, the value of k6 ≈ 2.1 × 10−13 cm3 molecule−1 s−1 is obtained using the same approach. The temperature dependence of k7 can be estimated assuming the preexponential factor of 2.2 × 10−11 cm3 molecule−1 s−1 for an addition to the double bond29 and the reaction path C


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The Journal of Physical Chemistry A degeneracy of two, yielding k7 = 4.4 × 10−11exp(−511 K/T) cm3 molecule−1 s−1 and k7(600 K) = 1.9 × 10−11 cm3 molecule−1 s−1. The estimated k7/k6 ratio ranging from 1700 to 90 within the experimental temperature range of the current work (304−600 K) demonstrates that contribution of reaction 6 is negligible compared to that of reaction 7. The observed kinetics of the c-C5H5 radical is that of a nonexponential decay; the kinetics of the C10H10 product of reaction 1 exhibits a corresponding rise to saturation (Figure 1). The ion signal of cyclopentadiene exhibits a drop at the time

Figure 2. Ratio of the signals of c-C5H7 and c-C5H5 immediately after the laser photolysis as a function of c-C5H6 concentration obtained at 600 K. The solid line is the fit of the dependence with eq I. The vertical dashed lines indicate the range of c-C5H6 concentrations used in the experiments to determine the rate constant of reaction 1. The experimental details for the data presented in this plot are given in the Supporting Information, Table 1S.

for the ratio of the initial (i.e., after the laser pulse and H decay) concentrations of c-C5H7 and c-C5H5: [c‐C5H 7]0 k 7[c‐C5H6] [c‐C5H6] = = [c‐C5H5]0 k 7[c‐C5H6] + k4 [c‐C5H6] +

Figure 1. Typical ion signal of c-C5H5 (S(C5H5)), the corresponding reciprocal signal 1/S(C5H5), precursor (S(C5H6)), and product (S(C10H10)) profiles. Curvature of the 1/S(C5H5) plot indicates the presence of heterogeneous loss of radicals with the first-order constant k3. Values of the k1[c-C5H5]0 = 174 ± 8 s−1 product and k3 are obtained from fitting the S(C5H5) versus time profiles with eq II. Experimental conditions: T = 400 K; [He] = 12.0 × 1016 molecules cm−3, [c-C5H5]0 = 1.60 × 1012 molecules cm−3.

k4 k7

(I)

The dependence presented in Figure 2 was fitted to eq I using two adjustable parameters: the ratio of sensitivities of the detection system to c-C5H5 and c-C5H7 and the k4/k7 ratio. The resultant value (1.03 ± 0.06) of the sensitivities ratio indicates equal sensitivities to both radicals. The value of k4/k7 = (40 ± 5) × 1013 molecules cm−3, together with the estimated above k7 provides an estimate for the rate constant k4 of the wall loss of the hydrogen atoms: k4 = 7600 s−1, in agreement with the originally assumed fast decay of H on the reactor surface. The uncertainties quoted here are standard errors of the fit. The range of c-C5H6 concentrations used to obtain the data presented in Figure 2 greatly exceeds the range used in the experiments to determine the rate constant of reaction 1 at 600 K: (8.6−21.2) × 1013 molecules cm−3, indicated in Figure 2 with dashed vertical lines. The corresponding range of the [cC5H7]0/[c-C5H5]0 ratio is 0.18−0.35. Similar experiments to measure the dependences of the ratio of the initial signals of c-C5H7 and c-C5H5 as functions of cC5H6 concentration were performed at lower temperatures as well (305, 400, and 500 K). However, higher values of k1 at these temperatures (vide infra) required use of lower initial concentrations of c-C5H5 and, therefore, of c-C5H7. Since the signal of c-C5H7 was affected by the background ion signal from 13 C-containing fraction of c-C5H6, lower c-C5H6 concentrations had to be used to keep the signal of c-C5H7 within measurable range. As a result, the trend to saturation in the [c-C5H7]0/[cC5H5]0 versus [c-C5H6] dependences, clearly visible in Figure 2, could not be observed at the temperatures of 500 K and lower. At these temperatures, the obtained dependences were fitted using the ratio of sensitivities of the detection system to cC5H5 and c-C5H7 obtained in the 600 K experiments and the values of the k4/k7 ratio were obtained from the fits. These values were later used in the data analysis of the experiments to determine k1, as described below in Section 2.5. The value of k4/k7 at 350 K was obtained via interpolation using an Arrhenius equation for k4/k7. The corresponding [c-C5H7]0/[c-

of the photolysis with no subsequent changes. In addition to cC5H5 and C10H10, formation of c-C5H7, C10H12, and C10H14 was observed. The ion signal at the mass of c-C5H7 (m/z = 67) was affected by a large background from the c-C5H6 precursor (nominal mass of 66 Da but one 13C substitution results in the mass of 67 Da); thus, c-C5H7 temporal profiles were rather noisy. Nevertheless, it was clear that the kinetics of c-C5H7 exhibited an instantaneous (on the time scale of the experiment) production after the laser pulse and subsequent decay. The kinetics of C10H12 and C10H14 were those of growth to saturation. In several previous studies performed using the LP/PIMS experimental setup, the hydrogen atoms produced in the reactions studied therein have been shown to quickly decay on the boron oxide coated reactor walls.33−35 The kinetics of cC5H5, c-C5H7, c-C5H6, C10H10, C10H12, and C10H14 are consistent with the time scale of the H atom decay being orders of magnitude smaller than that of the decay or growth of these polyatomic species. In an attempt to approximately quantify the fast heterogeneous decay of hydrogen atoms, a series of experiments was performed to measure the ratio of the signals of c-C5H7 and c-C5H5 immediately after the laser photolysis at varying concentrations of c-C5H6. Figure 2 illustrates the results of this investigation at 600 K: the ratio of ion signals as a function of c-C5H6 concentration. Assuming that the decay of H atoms due to heterogeneous loss and reaction 7 occurs on the time scale that is shorter than the temporal resolution of the experiment (∼0.3 ms) and noting that c-C5H5 and H are produced in equal concentrations in the cyclopentadiene photolysis, one obtains the following equation D


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cyclopentadienyl precursor. An example of the c-C5H6 profile illustrating a sharp drop in the signal due to the photolyzing laser pulse is presented in the lower left inset in Figure 1. The precursor depletion fraction δ was determined, and the initial radical concentration was obtained as

C5H5]0 ratios ranged from 0.051 to 0.105 at 500 K and were below 0.10, 0.042, and 0.025 at 400, 350, and 304 K, respectively. Contributions of c-C5H7 at temperatures below 600 K were lower than at 600 K because the values of the reaction 1 rate constant are higher (vide infra), and thus lower concentrations of cyclopentadienyl radicals and the cyclopentadiene precursor had to be used. Details of the k4/k7 determinations and interpolation are presented in the Supporting Information. 2.5. Determination of the Rate Constant of Reaction 1. The kinetics of the cyclopentadienyl radical decay was monitored in real-time. Rate constant measurements were performed using a technique similar to that applied by us earlier to the studies of the self-reactions of ethyl,5 propargyl,8 cyclohexyl,6 and neopentyl7 radicals, which, in turn, is based on the method used by Slagle and co-workers36 in their study of the CH3 + CH3 reaction. As follows from the discussion of the kinetic mechanism in Section 2.4 above, after the photolyzing laser pulse, a mixture of c-C5H5 and c-C5H7 radicals is produced, with the [c-C5H7]0/[cC5H5]0 ratio ranging from 0.009 to 0.35, with less c-C5H7 interference at lower temperatures. If the presence of c-C5H7 can be ignored and the self-reaction of c-C5H5 is unperturbed by any side processes other than the wall loss, the only two reactions affecting the decay of cyclopentadienyl are c‐C5H5 + c‐C5H5 → Products (C10H10 or others)

(1)

c‐C5H5 → walls loss

(3)

[R]0 = δ[c‐C5H6]

In each experiment to determine k′ = k1[R]0, the photolytic precursor depletion fraction δ was measured two times (before and after the kinetics of the radical decay was recorded). For each experimental temperature, the initial radical concentration was varied by changing the concentration of cyclopentadiene and/or the laser fluence. The values of the k1[R]0 product obtained from the data fits were plotted as a function of the initial concentration of radicals obtained from the measurements of the photolytic depletion of cyclopentadiene ([R]0 obtained via eq III). The values of the radical self-reaction rate constant were determined from the slopes of the linear k1[R]0 versus [R]0 dependences. Even though at low temperatures (304 and 350 K) interference due to the presence of c-C5H7 can be neglected ([c-C5H7] is 4% of [c-C5H5] or less), at higher temperatures it must be accounted for. Therefore, corrections due to the effects of c-C5H7 were introduced into the results of all experiments. According to the mechanism of reactions 1 and 3−10 and taking into account that all H atom reactions (reactions 4−7) occur instantaneously on the time scale of the experiment, the kinetics of c-C5H5 and c-C5H7 is determined by the following differential equations:

For this simple kinetic mechanism, the corresponding first order differential equations can be solved analytically: S(t ) =

d[c‐C5H5] = −2k1[c‐C5H5]2 − k 3[c‐C5H5] dt

S0 · k 3 (2k′ + k 3) ·e k3t − 2k′

(III)

− k 9[c‐C5H5][c‐C5H 7]

(IV)

(II)

d[c‐C5H 7] = −2k10[c‐C5H 7]2 − k 8[c‐C5H 7] dt

Here, k′ = k1[R]0, k1 and k3 are the rate constants of reactions 1 and 3, respectively, [R]0 is the initial radical concentration ([cC5H5]0), S(t) is the c-C5H5 ion signal, and S0 is the signal amplitude (i.e., the signal corresponding to zero reaction time). A derivation of eq II is given in the Supporting Information to ref 7. In each experiment, the values of the signal amplitude S0, the wall loss rate k3, and the k1[R]0 product were obtained from the fits of the real-time radical decay profiles (i.e., c-C5H5 signal vs time dependences) with eq II. A typical signal profile of the cyclopentadienyl radical decay is shown in Figure 1. Different parts of the radical decay profiles exhibit different sensitivities to the fitting parameters. The initial part of the signal profile is most sensitive to the rate constant of the radical self-reaction, whereas the end part is most sensitive to k3, the rate constant of the wall loss. These sensitivities are illustrated in the upper right inset in Figure 1, where the reciprocal of the radical signal (with the baseline subtracted) is plotted as a function of time. In the absence of any heterogeneous wall loss of radicals (pure second order decay) the reciprocal signal is directly proportional to time and forms a straight line; the self-reaction rate constant can be obtained from the slope of the line. In the presence of heterogeneous loss, the line is curved, the initial slope is proportional to (2k′ + k3), and the deviation from a straight line can serve as a measure of the contribution from the heterogeneous wall loss. In each experiment, the initial concentration of radicals was determined by measuring the photolytic depletion of the

− k 9[c‐C5H5][c‐C5H 7]

(V)

Using notation α for the ratio of the initial concentrations of cC5H7 and c-C5H5 (i.e., concentrations of the radicals formed after reactions 4−7 proceed to completions following the photolyzing laser pulse, α = [c-C5H7]0/[c-C5H5]0) and δ defined above as the measured precursor depletion fraction after the laser pulse, we still obtain eq III, where [R]0 now means the total concentration of radicals, both c-C5H7 and cC5H5. This equation can be rewritten as [R]0 = [c‐C5H5]0 + [c‐C5H 7]0 = (1 + α)[c‐C5H5]0 = δ[c‐C5H6]

(VI)

The measured depletion of c-C5H6 after the photolyzing laser pulse and completion of reactions 4−7 provides the total concentration of radicals because reactions 5 and 6 produce or deplete c-C5H6 as they deplete or produce c-C5H5, respectively, and reaction 7 producing c-C5H7 also depletes c-C5H6. The rate constants of reactions 8−10 are unknown. It is highly unlikely that the rate constant of reaction 10 is greater than that of reaction 1. First, as will be seen later, k1 has unusually high values at low temperatures, greater than those of most other polyatomic radical self-reactions for which data are available. Second, cyclopentadienyl radical has radical character on each of the five carbon atoms due to electron delocalization; E


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still given by eq II where k′ = k1[c-C5H5]0. However, eqs III and VI give the total radical concentration and not the desired initial concentration of c-C5H5 only. The latter can be obtained as follows:

c-C5H7, although also delocalized, is expected to have radical character on only two of the five carbon atoms. Thus, it can be reasonably expected that k9 is lower in value than k1. However, since exact values of the rate constants are unknown, data analysis was performed using two limiting models, with opposite estimates placed on the reactivity of c-C5H7. Both models are, most likely, unrealistic; however, they were chosen to encompass all possible situations and thus place upper and lower limits on the effect of c-C5H7 contribution to the observed kinetics of c-C5H5. In the first limiting model, reactivity of c-C5H7 is assumed to be exactly the same as that of c-C5H5. Thus, k10 = k1, k8 = k3, and k9 = 2(k1k10)1/2 = 2k1. Here, the “Geometric Mean Rule”37,38 approximation is used to estimate k9; it should be kept in mind that although this approximation has support from both experiments and theory for alkyl radicals (e.g., refs 39 and 4), it has not been well tested for delocalized radicals. Now, denoting the total concentration of radicals as [R] ([R] = [cC5H7] + [c-C5H5]) and combining eqs IV and V, we obtain

[c‐C5H5]0 =

(VIII)

The values of k1 can then be obtained from the slopes of the k′ vs [c-C5H5]0 obtained from the measured c-C5H6 photolytic depletion δ via eq VIII. For each experimental temperature, the value of k1 was determined using both of the limiting models, and the average was calculated. The differences between the average and the limiting model values were used as an additional systematic component of the uncertainty in the rate constant determination. This uncertainty component increased with temperature, from 0.8% at 304 K to 13.0% at 600 K, due to the decrease in the rate constant of reaction 1 and the corresponding increase in the concentrations of c-C5H6 that had to be used to obtain concentrations of c-C5H5 that are sufficiently high to observe the second-order self-reaction. Experiments to determine k1 were not performed at temperatures higher than 600 K because of the expected further increase in the effects of c-C5H7 production via reaction 7 and in the associated uncertainties in k1. The bath gas densities (helium with 0.01−0.29% of radical precursors) of 3.0 × 1016 and 12.0 × 1016 molecules cm−3 were used in the experiments. Experimental parameters such as the photolyzing laser intensity and the concentrations of cyclopentadiene were varied for individual experiments. For each temperature, the values of the k1[R]0 product obtained under different experimental conditions are shown on the same k1[R]0 versus [R]0 plots in Figure 3. These plots correspond to the analysis performed under the first limiting model, the one

d[R] = − 2k1[c‐C5H5]2 − k 3[c‐C5H5] dt − 4k1[c‐C5H5][c‐C5H 7] − 2k1[c‐C5H 7]2 − k 3[c‐C5H 7]

and d[R] = −2k1[R]2 − k 3[R] dt

δ[cC5H6] [R]0 = 1+α 1+α

(VII)

It can also be shown that the ratio of the concentrations of cC5H7 and c-C5H5 stays constant. If one denotes β = [c-C5H7]/ [c-C5H5] (note that at time zero β0 = α), one obtains the following differential equation for ln(β): d ln[c‐C5H 7] d ln[c‐C5H5] d ln β = − dt dt dt d[c‐C5H 7] d[c‐C5H5] 1 1 = − dt [c‐C5H 7] dt [c‐C5H5]

Substituting eqs IV and V for the derivatives of concentrations and using the above relationships between rate constants, we obtain d ln β = −2k1[c‐C5H 7] − k 3 − 2k1[c‐C5H5] dt + 2k1[c‐C5H5] + k 3 + 2k1[c‐C5H 7] = 0

Thus, β stays constant and equal to α, or, in other words, the ratio of [c-C5H7] to [c-C5H5] does not change. Therefore, [R] = (1 + α)[c-C5H5] at any time. Equation VII is the kinetic equation corresponding to a combination of the second order self-reaction and a first order loss, like in reactions 1 and 3 above; the solution is given by eq II, where signal S is proportional to [R] and therefore to [cC5H5]. Analysis of c-C5H5 decay based on eq II provides the value of k′ = k1[R]0, where [R]0 now is the sum of the initial concentrations of c-C5H5 and c-C5H7, determined from the photolytic depletion of c-C5H6 (eqs 3 and VI). Thus, in the case of the first limiting model, the procedure to determine k1 does not need to be modified compared with the case where production of c-C5H7 is negligible. In the second limiting model, reactivity of c-C5H7 toward cC5H5 is assumed to be negligible, and the third term in eq IV can be neglected. Then the solution for the decay of c-C5H5 is

Figure 3. k1[R]0 versus [R]0 dependences obtained in the study of reaction 1. Filled symbols represent data obtained with the bath gas (helium) density of 3.0 × 1016 molecules cm−3; all other data were obtained with [He] = 12.0 × 1016 molecules cm−3. F


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The Journal of Physical Chemistry A Table 1. Conditions and Results of Experiments to Determine k1 [M]a

Ib

[c-C5H6]c

αe

[R]0d

12.0 12.0 12.0 12.0 3.0 3.0

7.8 7.8 7.8 7.8 10.4 5.2

12.0 12.0 12.0 12.0 3.0 3.0

7.8 7.8 7.8 7.8 10.4 5.2

12.0 12.0 12.0 12.0 12.0 12.0

10.4 10.4 5.2 7.8 10.4 10.4

12.0 12.0 12.0 3.0 3.0

10.4 6.5 7.8 6.2 10.4

12.0 12.0 12.0 12.0 12.0

6.5 10.4 6.5 5.2 9.1

−10

k1[R]0f −1

3

k3g

−1

Experiments at 304 ± 2 K. k1(304 K) = (3.98 ± 0.41 ) × 10 cm molecule s 0.148 0.283 ± 0.014 0.010 112.5 ± 6.1 0.222 0.412 ± 0.021 0.015 153.1 ± 5.3 0.349 0.594 ± 0.051 0.024 247.3 ± 11.0 0.123 0.191 ± 0.012 0.009 85.6 ± 5.6 0.258 0.531 ± 0.033 0.018 203.4 ± 10.5 0.257 0.309 ± 0.025 0.018 122.5 ± 7.4 Experiments at 350 K. k1(350 K) = (2.09 ± 0.22h) × 10−10 cm3 molecule−1 s−1 0.148 0.283 ± 0.014 0.010 112.5 ± 6.1 0.222 0.412 ± 0.021 0.015 153.1 ± 5.3 0.349 0.594 ± 0.051 0.024 247.3 ± 11.0 0.123 0.191 ± 0.012 0.009 85.6 ± 5.6 0.258 0.531 ± 0.033 0.018 203.4 ± 10.5 0.257 0.309 ± 0.025 0.018 122.5 ± 7.4 Experiments at 400 K. k1(400 K) = (1.15 ± 0.16h) × 10−10 cm3 molecule−1 s−1 0.303 0.656 ± 0.082 0.033 85.7 ± 4.2 0.434 1.01 ± 0.14 0.046 110.4 ± 4.4 0.431 0.547 ± 0.061 0.046 64.4 ± 5.0 0.977 1.51 ± 0.09 0.098 166.5 ± 7.7 0.966 2.11 ± 0.09 0.097 222.4 ± 10.2 0.303 0.656 ± 0.082 0.033 85.7 ± 4.2 Experiments at 500 K. k1(500 K) = (5.26 ± 0.76h) × 10−11 cm3 molecule−1 s−1 1.03 2.72 ± 0.12 0.105 130.9 ± 7.2 0.942 1.61 ± 0.14 0.097 90.7 ± 5.5 0.475 0.886 ± 0.052 0.051 42.8 ± 2.4 0.881 1.25 ± 0.09 0.091 63.1 ± 4.0 0.846 2.00 ± 0.38 0.088 113.2 ± 5.2 Experiments at 600 K. k1(600 K) = (3.76 ± 0.84h) × 10−11 cm3 molecule−1 s−1 0.86 1.74 ± 0.21 0.178 66.1 ± 4.3 1.42 3.58 ± 0.40 0.264 125.0 ± 8.3 1.39 2.48 ± 0.19 0.259 75.5 ± 3.1 2.12 3.07 ± 0.33 0.347 101.9 ± 4.4 2.00 5.00 ± 0.20 0.334 162.1 ± 5.6 h

8.9 ± 2.5 11.5 ± 1.6 1.1 ± 2.0 41 ± 2.5 22.3 ± 2.3 23.4 ± 2.7 8.9 ± 2.5 11.5 ± 1.6 1.1 ± 2.0 41.0 ± 2.5 22.3 ± 2.3 23.4 ± 2.7 46.5 ± 1.9 6.5 ± 2.0 29.9 ± 3.1 21.5 ± 2.2 39.5 ± 2.0 46.5 ± 1.9 47.3 33.4 38.9 43.5 46.4

± ± ± ± ±

2.3 2.5 1.7 2.2 1.8

21.6 25.7 16.7 11.0 13.9

± ± ± ± ±

2.6 3.1 1.7 2.0 1.6

a Concentration of the bath gas (helium with up to 0.29% of radical precursor) in units of 1016 molecules cm−3. bEstimated laser fluence in units of mJ pulse−1 cm−2. cIn units of 1014 molecules cm−3. dNascent concentration of radicals in units of 1012 molecules cm−3 determined from the measured photolytic depletion of c-C5H6. eCalculated ratio of the initial concentrations of c-C5H7 and c-C5H5 (see text). fObtained from the fits of the kinetics of the cyclopentadienyl decay with eq II. The quoted uncertainty is one standard error of the fit. gRate constant of the heterogeneous wall loss obtained from the fits of the kinetics of the c-C5H5 decay with eq II. The quoted uncertainty is one standard error of the fit. hUncertainties are twice the standard error (statistical) + systematic, with the latter including the uncertainty due to c-C5H7 interference (0.8%, 1.6%, 3.9%, 4.1%, and 13.0% of k1 value at 304, 350, 400, 500, and 600 K, respectively).

3. The error limits of the rate constant values reported in this work represent a sum of twice the standard error random uncertainty and the estimated systematic uncertainty, with the latter including the uncertainty due to c-C5H7 interference. The temperature dependence of k1 is presented in Figure 4 in two formats: the usual Arrhenius format (Figure 4a) and the semilogarithmic plot of k1 versus temperature (Figure 4b). The latter is shown to facilitate the discussion of the temperature dependence in comparison with other self-reactions of polyatomic radicals. An unusually strong negative temperature dependence is observed, which can be represented with the following Arrhenius expression:

where c-C5H7 is assumed to have the same reactivity as c-C5H5, as described above. The differences between the plots of k1[R]0 versus [R]0 obtained with the first limiting model and k1[R]0 vs [c-C5H5]0 obtained using the second limiting model are presented in the Supporting Information (Figure 1S) for the temperatures of 500 and 600 K, where such differences are most pronounced. The rate constant of the cyclopentadienyl radical self-reaction does not demonstrate any dependence on the varied parameters, including pressure, within the experimental uncertainties. The conditions and the results of individual experiments are presented in Table 1, together with the values of k1 for all experimental temperatures used. The sources of error in the measured experimental parameters such as temperature, pressure, flow rate, signal count, etc. were subdivided into random and systematic and propagated to the final values of the rate constants using different mathematical procedures for propagating systematic and random uncertainties.40 The same systematic and random sources of error contributed to the individual uncertainties in k1[R]0 and [R]0 values given in Table 1 and shown on the linear plots in Figure

k1 = 2.9 × 10−12 exp(+ 1489 K/T ) cm3 molecule−1 s−1 (304−600 K)

(IX)

The estimated uncertainty associated with this expression increases with temperature, from 13% at 304 and 350 K to 17% at 400 K, 21% at 500 K, and 32% at 600 K. G


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Figure 5. Temporal profiles of c-C5H5, C10H10, C10H9, and C10H8 obtained in the LP/PIMS experiment at 800 K. [He] = 6.0 × 1016 molecules cm−3, [c-C5H6] = 4.70 × 1014 molecules cm−3; [c-C5H5]0 = 7.7 × 1012 molecules cm−3.

Figure 4. Temperature dependence of k1. (a) The Arrhenius plot. (b) Comparison with several strong negative temperature dependences of self-reaction rate constants of polyatomic hydrocarbon radicals, on a semilogarithmic k1 versus T plot. Data for c-C6H11, neo-C5H11, and tC4H9 radicals are from refs 6, 7, and 4, respectively. Cyclopentadienyl radical demonstrates the strongest negative temperature dependence.

A final product analysis was also performed at three temperatures: 301, 600, and 800 K. A description of the apparatus and the procedures used is given above, in Section 2.2. The main goal of the 301 K and the 600 K experiments was to determine the “purity” of the photolytic source of the cyclopentadienyl radicals, i.e., whether c-C5H5 isomers other than cyclopentadienyl are formed in the photolysis of cyclopentadiene, as discussed in Section 2.3. The purpose of the 800 K experiment was to identify the isomer(s) of C10H8 formed at this temperature, as observed in the real-time LP/ PIMS experiment. As described above in Section 2.2, samples accumulated in the liquid nitrogen trap were defrosted to the temperature of 0 °C and diluted with air to atmospheric pressure; then the trap was rinsed with ca. 0.5 mL of cyclohexane, and the resultant solutions were analyzed using GC/MS. According to Hedaya et al.,24 the nascent c-C5H5−C5H5 adduct readily polymerizes at ambient temperatures but “can be manipulated at low temperatures”. An experimental confirmation of this effect was observed in the current study. Chromatograms contained peaks with retention times longer than 40 min and mass spectra with masses above 134 Da (C10H14). The contribution of these peaks increases if the samples obtained in the final product analysis were not handled at 0 °C upon defrosting but were kept at room temperature for 5−20 min. Therefore, these peaks were attributed to products of thermal polymerization of the C10H10 and possibly other radical adducts, and were not analyzed any further. The most prominent feature in all chromatograms was that at 18.5 min, which appeared as an unresolved combination of two or more peaks. Even though this combined peak was significantly nonsymmetric, the mass spectrum within the peak did not depend on the retention time. The mass spectrum has the base peak of m/z = 129 and the most likely nominal mass of the corresponding chemical compound is 130 Da (C10H10). No matches to this mass spectrum could be found in

2.6. Detection of the Products of Reaction 1. Formation of C10H10 (m/z = 130) was observed in real-time experiments at both ends of the experimental temperature range. The characteristic rise times of the C10H10 profiles matched those of the c-C5H5 decay due to reaction 1. An example of a C10H10 rising signal profile is given in the upper left inset in Figure 1. Since the issue of potential formation of naphthalene in reaction 1 presents a particular interest, as discussed in the Introduction, ion signal profiles at the m/z = 128 (C10H8) and m/z = 129 (C10H9) were monitored in search of any signs of growth. At all experimental temperatures below 600 K, no formation of either C10H8 or C10H9 was observed. However, at 600 K, a trace signal at m/z = 129 appeared following the laser pulse. The signal-to-noise ratio of the signal was too low to allow for a determination of the shape of the profile to compare it with that of the c-C5H5 decay. Thus, an extra experiment was performed using the LP/PIMS apparatus at a higher temperature, 800 K. Figure 5 presents the temporal profiles of c-C5H5, C10H10, C10H9, and C10H8 obtained in this experiment. The C10H9 signal intensity is significantly stronger than at 600 K but still weaker than that of C10H10 by approximately 2 orders of magnitude; the shape of the signal is that of growth to saturation, with the characteristic rising time matching that of the decay of c-C5H5. The signal profile of C10H8 is significantly different from that of C10H10 and C10H9, demonstrating an approximately linear growth with time. The signal intensity is comparable to that of C10H9. Since sensitivities of the detection system to these species are unknown, signal intensities may serve, at best, only as very approximate indicators of abundances. H


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The Journal of Physical Chemistry A the NIST Mass Spectral Database.41 A minor dicyclopentadiene impurity (7.6 min retention time) was also observed in all chromatograms. All other chromatographic peaks with peak integrals of at least 1% of the most prominent peak were analyzed for their mass spectra. Cyclopentadiene was not observed as its retention time (1.2 min) is shorter than that of the cyclohexane solvent (1.5 min) and was thus within the set solvent delay of 2.2 min. At 301 K, peaks with the mass spectra corresponding to the nominal masses of 132 (four peaks, 9.3−10.3 min) and 134 (two peaks, 8.7−9.1 min) Da were observed. These peaks were only partially resolved. The corresponding mass spectra also had no matches in the NIST database. These peaks were attributed to C10H12 and C10H14 adducts of the c-C5H7 + cC5H5 and c-C5H7 + c-C5H7 reactions and products of their isomerization. In addition, one minor peak with the retention time of 31.4 min was observed, with the peak integral of 1.5% relative to that of the main C10H10 peak. This peak has a mass spectrum with the base peak of 67, and the largest observed m/ z =169. It was therefore attributed to one of the products of thermal polymerization of the C10H10. No corresponding peaks were observed at experiments performed at higher temperatures, which serves as an indirect confirmation of the secondary nature of the responsible compound, as the amounts of polymerization products are sensitive to handling of the samples and time spent between sample collection and analysis. In addition, a search was performed for more minor peaks that may correspond to compounds with the nominal mass of 130 Da (C10H10). One such peak was revealed at the retention time of 34.9 min, with the peak integral of 0.67% relative to that of the main C10H10 peak. Its mass spectrum is very similar to that of the main C10H10 peak. This peak also appears at highertemperature experiments in increased quantities (vide infra), suggesting that it may be either the product of the original cC5H5 + c-C5H5 reaction or that of the isomerization of the nascent C10H10 adduct. The main result of the final product analysis performed under the room-temperature conditions is that two kinds of C10H10 products are produced. One kind is characterized by two or more compounds with very similar retention times (unresolved combination peak at 18.5 min) and indistinguishable mass spectra. The other kind present in a small amount (ion current integral is 0.67% relative to that of the main C10H10 peak) likely has a significantly different skeletal structure, as manifested by a very different retention time (34.9 min), but a very similar mass spectrum. These results are consistent with the theoretical predictions of Cavallotti and Polino.12 These authors obtained the potential energy surface (PES) of reaction 1 and performed master equation simulations of the sequence of reactive steps that follow the initial addition of two c-C5H5 radicals. Although master equation simulations were performed in ref 12 only for the temperature of 1100 K and above, the C10H10 PES demonstrates that the addition of two cyclopentadienyl radicals (potential energy well depth of 51.3 kcal mol−1) is followed by a sequence of fast and reversible chemically activated isomerizations via H atom transfer along the carbon skeleton of the adduct. The energy barriers for these isomerizations are between 17.7 and 25.1 kcal mol−1, much lower than the vibrational energy of the nascent C10H10 adduct. It is therefore expected that the thermalized products of the cC5H5 + c-C5H5 reaction at low temperatures should consist of a mixture of C10H10 isomers, which have the same carbon skeletal structure but differ in the numbers of hydrogen atoms bonded

to individual carbons within that structure. It can be reasonably expected that these isomers will have very similar chromatographic retention times, in agreement with the observations of the current study. The second kind of C10H10 product of the c-C5H5 + c-C5H5 reaction, with a retention time of 34.9 min, may be a product of one of the further isomerization steps involving changes to the carbon skeleton, which would explain the very different retention time. Alternatively, it may be a product of recombination of the cyclopentadienyl radical with a different c-C5H5 product of the photolysis of cyclopentadiene. In any case, the very small amount of this C10H10 product observed in the room temperature experiments (less than 1% of the ion count corresponding to the main C10H10 product) indicates that at least ∼99% of the 248 nm photolysis of cyclopentadiene is the production of the cyclopentadienyl radical and the hydrogen atom. At a temperature of 600 K, the final product analysis revealed the presence of two additional chromatographic peaks (5.17 and 8.32 min), with the nominal masses of 132 and 134 Da, which exceeded the threshold of 1% of the main C10H10 peak. Also, a new peak (2%) appeared at the retention time of 4.96 min. The corresponding mass spectrum is similar to that of 3(2-Propenyl)cyclopentene, C8H12.41 Investigation of the chromatograms obtained in the 301 and 800 K experiments demonstrated that peaks with the same retention time and similar mass spectra appear on these chromatograms but are minor, below the 1% threshold. The minor C10H10 peak at 34.9 min increased in intensity at 600 K, reaching 1.6% of the main C10H10 peak. The experiment performed at 800 K produced a chromatogram with more C10H12 peaks, at longer retention times (13.2− 27.7 min). Two more minor C10H10 peaks appeared, at 18.8 and 22.6 min (intensities of 1.8% and 1.1% of the main C10H10 peak). The intensity of the C10H10 peak at 35.0 min increased dramatically, to 50.7% of the main C10H10 peak. In addition, an unresolved compound peak was observed at 21.5 min, with the intensity of 3.6%. Application of the AMDIS42,43 peak deconvolution system revealed the presence of two main components of the peak, with nominal masses of 132 and 128 Da. The mass spectrum of the latter matches the database41 spectra of naphthalene and azulene, which are very similar to each other. Since the question of the presence of C10H8 compounds among the products of reaction 1 presents particular interest, further search of the chromatogram for components matching C10H8 nominal mass of 128 was performed. This search revealed the presence of a minor peak (0.23% of the main C10H10 peak) at the retention time of 37.2 min, with the mass spectrum identical to that of the mass 128 component of the 21.5 min peak and thus matching the naphthalene/azulene database mass spectra. Pure samples of naphthalene and azulene dissolved in cyclohexane were analyzed with the GC/MS using the same temperature program settings. The retention times of pure naphthalene and azulene matched those of the peaks at 21.5 and 37.2 min, respectively. Mass spectra of the compounds detected in the final product analysis experiments are presented in the Supporting Information.

3. DISCUSSION 3.1. Rate Constant Values. The room-temperature value of the rate constant of the reaction of cyclopentadienyl radical recombination, (3.98 ± 0.41) × 10−10 cm3 molecule−1 s−1, is I


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skeleton of the nascent C5H5−C5H5 adduct (dihydrofulvalenes), and those with the skeleton of azulene (i.e., bicyclic structures with five-member and seven-member rings, dihydroazulenes). The energy barrier for the reactive pathway between these two groups is larger than those for isomerizations within a group. One can speculate that these dihydroazulenes produced through isomerization involving a tricyclic transitional structure12 may be responsible for the minor C10H10 peak. The retention time of this peak (35 min) is similar to that of azulene (37 min) and is very different from that of the main C10H10 peak (18.5 min). The other product of reaction 1, C10H9, detected only at high temperatures (800 K plus a trace signal at 600 K), is likely to be an 1-H-azulyl or a 2-H-azulyl radical, or a mixture of both. However, it should be kept in mind that it is impossible to exclude the possibility that the C10H9+ signal observed in the current study is caused by the fragmentation of the C10H10+ ions at high temperatures (the temporal profiles of C10H10 and C10H9 match); the discussion below assumes that this signal is produced by the photoionization of an actual C10H9 radical. Cavallotti and Polino12 predict that at temperatures below 1500 K the major channel of further reaction of the nascent C10H10 adduct and its isomers is the formation of 1-H-azulyl or 2-Hazulyl C10H9 radical and a hydrogen atom. Although these authors performed master equation calculations only for the temperatures of 1100 K and above, the trends in their results indicate that at 800 K the second channel producing a variety of fulvalenyl C10H9 radical isomers and H atoms is likely to be ca. 2 orders of magnitude weaker. The final product analysis detects the presence of naphthalene at 800 K, as well as of azulene in minor amount. As can be seen from the plot in Figure 5, the C10H8 product growth does not match the decay of c-C5H5 but appears to be approximately linear in time. This result may have an explanation within the framework of the theoretical PES and kinetic studies of Cavallotti and Polino12 and Kislov and Mebel.13 The quantum chemical study of Kislov and Mebel,13 among other results, reports the PES and some of the kinetic properties of the reactive pathway from 1-H-azulyl radical to naphthalene + H. The pathway follows that presented earlier by Alder et al.,50 who used a lower-level density functional theory (DFT) method in their detailed PES study of azulene to naphthalene direct and radical-promoted isomerization pathways. The sequence of individual steps is as follows: 1-H-azulyl radical → 9-H-azulyl radical → tricyclyl intermediate radical → 9-H-naphtyl radical → naphthalene + H. The limiting step with the highest energy barrier (34.4 kcal mol−1 relative to 1-Hazulyl13) is that between the tricyclyl intermediate and the 9-Hnaphtyl radical. The authors of refs 13 and 50 did not calculate the thermal rate constant for this reactive pathway as a whole; however, Kislov and Mebel report the high-pressure-limit values of rate constant obtained in transition state theory calculations for all individual steps. Using the reported rate constant values at 800 K and assuming fast equilibration in the steps of the reactive sequence preceding the limiting step, one can estimate the 800 K rate constant for the overall 1-H-azulyl to naphthalene + H reaction as 2.8 × 103 s−1. Such a high value would predict that this reaction should be instantaneous on the time scale of the LP/PIMS experiment, where the temporal resolution of the equipment is ca. 0.3 ms, and thus the naphthalene signal profile should be synchronous with that of C10H10. However, considering potential uncertainty in the G3level energy of the transition state and in the preexponential

significantly higher than the rate constants for most hydrocarbon radical−radical reactions. Within the uncertainty limits, it coincides with the collision rate of 3.7 × 10−10 cm3 molecule−1 s−1 estimated using Lennard-Jones parameters of ref 44, which translates into an effective steric factor of unity, meaning that virtually every collision at room temperature results in the formation of an adduct. A likely explanation for this fact is the unique electron delocalization in c-C5H5, where each carbon atom possesses a radical character. The few existing sets of experimental data on the rate constants of radical self-reactions confirm the trend that electron delocalization increases the probability of adduct formation, most likely due to larger values of the reaction degeneracy and, consequently, of the steric factor. The room-temperature rate constant for the recombination of n-C3H7 radicals is (1.66 ± 0.41) × 10−11 cm3 molecule−1 s−1 45 whereas those of delocalized C3H5 (allyl) and C3H3 (propargyl) are (2.65 ± 0.20) × 10−11 46 and ca. 4 × 10−11,47−49 respectively. The temperature dependence of the rate constant is also unprecedented. The values of k1 decrease by a factor of 3.5 from room temperature to 400 K, and by another factor of 3 from 400 to 600 K. The corresponding effective negative activation energy is −1489 K, or −2.96 kcal mol−1. This is a much stronger negative temperature dependence than those of other hydrocarbon radicals, which are briefly discussed in the Introduction. Figure 4b presents the k1(T) dependence obtained in the current study in comparison with several strong negative temperature dependences of self-reaction rate constants of polyatomic hydrocarbon radicals. Experimental data are shown for two radicals (cyclohexyl6 and neopentyl7), which belong to a category of relatively large radicals (at least when compared with other radicals for which data obtained in direct experiments are available). A theoretical study by Klippenstein et al.4 observed stronger negative temperature dependences of the rate constants of recombination reactions of larger radicals. Correspondingly, the third temperature dependence shown is that of the calculated recombination rate constant of the t-butyl (t-C4H9) radical, the largest radical considered by Klippenstein et al. As can be seen from the plot, temperature dependences of of the rate constants of t-C4H9, cC6H11, and neo-C5H11 exhibit similar trends, whereas cyclopentadienyl radical demonstrates a much stronger negative temperature dependence. 3.2. Products of Reaction 1. The product of the cyclopentadienyl radical self-reaction detected in the real-time LP/PIMS experiments at all experimental temperatures has the chemical formula C10H10, and its rise time matches that of the c-C5H5 decay (Figure 1). As discussed above, in Section 2.6., the quantum chemical study of Cavallotti and Polino12 demonstrates that the nascent C10H10 is expected to quickly undergo a series of chemically activated H-shift isomerization reactions, which do not change the carbon skeleton of the adduct. An earlier PES study of Melius et al.19 also predicted the existence of some of the isomers of the C10H10 adduct with easy isomerizations via H atom shift between them. The final product analysis appears to be in agreement with this expectation: the major detected C10H10 chromatographic peak corresponds to two or more compounds with very similar retention times and indistinguishable mass spectra. The identity of the compound(s) responsible for the other, much weaker C10H10 peak detected at 301 and 600 K, is unknown. The study of ref 12 involves many isomers of C10H10, most of which can be subdivided into two major groups: isomers with the carbon J


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pages). This material is available free of charge via the Internet at http://pubs.acs.org.

factor, one can easily conceive of a lower value for the rate of 1H-azulyl to naphthalene + H conversion. For example, a 2 kcal mol−1 higher barrier and a factor of 5 lower preexponential factor would reduce this rate constant to 160 s−1, in which case naphthalene growth profile will not match those of either C10H10 or C10H9. Also, the rate of 2-H-azulyl radical isomerization and decay into naphthalene + H is unknown; if in the range of ca. 20−100 s−1, it is likely to explain the qualitative shape of the overall C10H8 versus time signal profile. Formation of naphthalene in the self-reaction of cyclopentadienyl radicals has been observed before, although not in time-resolved experiments. Filley and McKinnon51 pyrolyzed triphenylmethylcyclopentadiene, a precursor of cyclopentadienyl radicals, at the temperatures between 500 and 700 °C in a flow reactor and analyzed the final products using GC/MS. These authors observed the formation of products with the masses of 130 and 128 Da. The 128 Da product was identified as naphthalene; the authors also suggested that the 130 Da products are likely to be two of the dihydrofulvalene isomers predicted by Melius et al.19 Sheer et al.52 studied the pyrolysis of three precursors of cyclopentadienyl radicals (anisole, cyclopentadiene, and methylcyclopentadiene) between 1100 and 1225 °C using a hyperthermal tubular reactor and photoionization reflectron time-of-flight mass spectrometer, under conditions that allowed the detection of radical intermediates as well as final products. These authors also observed the formation of species with masses of 130 and 128 Da, the latter identified as naphthalene. In addition, species with the mass of 129 Da were observed and identified as C10H9 radicals. The results of the current study are in qualitative agreement with these earlier observations, to which the above discussion of the pathways of C10H9 and C10H8 formation also applies. Formation of the minor amount of azulene observed in the final product analysis can be potentially explained by the decomposition of 1-H-azulyl to azulene + H (rate constant of 95 s−1 calculated by Kislov and Mebel13 at 800 K). The detailed PES study of ref 13 did not include reactions of the 2-H-azulyl radical, one of the products of reaction 1 predicted by Cavallotti and Polino. Therefore, no estimates of the rates of azulene or naphthalene formation from this radical are available. However, the results of Alder et al.50 indicate that isomerization of 2-Hazulyl to 1-H-azulyl and vice versa is likely to occur at 800 K, with the DFT-calculated energy barrier of 32 kcal mol−1. In the final product study, it is impossible to completely exclude unknown potential effects of heterogeneous chemistry. Mechanisms of radical decay on the reactor walls, generally, are unknown; products of these wall reactions can remain adsorbed or become released into the gas phase. Moreover, heterogeneous thermal isomerization of products or intermediates may occur with rates that are different from those of similar reactions in the gas phase. Only a small fraction of radicals decayed on the wall in this study; therefore, caution is advised in interpreting, particularly, reactive pathways leading to the formation of minor products.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Tel: +1-202-319-6742. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by U.S. National Science Foundation, Combustion, Fire, and Plasma Systems Program under Grant No CBET-0853706.

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REFERENCES

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S Supporting Information *

A supplement, including detailed information on the determinations and interpolation k4/k7 values, differences between the results obtained using two kinetic models of cC5H7 reactivity, and mass spectra of final reaction products (13 K


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Kinetics of the Self Reaction of Cyclopentadienyl Radicals - The

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