Kinetics for the reaction of phenyl radical with phenylacetylene and styrene

Proceedings of the

Proceedings of the Combustion Institute 31 (2007) 249–256

Combustion Institute www.elsevier.com/locate/proci

Kinetics for the reaction of phenyl radical with phenylacetylene and styrene q G. Nam a, I.V. Tokmakov b, J. Park c, M.C. Lin

c,*

a

b

Institute for Advanced Engineering, Yongin-si, Gyeonggi-do 449-863, South Korea Department of Chemistry, University of Missouri-Columbia, Columbia, MO 65211, USA c Department of Chemistry Emory University, Atlanta, GA 30322, USA

Abstract The kinetics for the reactions of C6H5 with phenylacetylene and styrene have been measured by CRDS in the temperature range 297–409 K under an Ar pressure of 3.6 Torr. The total rate constants can be given by the following Arrhenius expressions (in units of cm3 mol1 s1): k1(C6H5 + C6H5C2H) = 1013.0±0.1exp [(2430 ± 150)/RT] and k2(C6H5 + C6H5C2H3) = 1013.3±0.1 exp [(2570 ± 180)/T]. Additional DFT and MP2 calculations have been carried out to assist our interpretation of the measured kinetic data. The addition of C6H5 to the terminal CHx (x = 1 or 2) sites is predicted to be the dominant channel for both reactions. The calculated bimolecular rate constants are in reasonable agreement with experimental values for the temperature range studied.  2006 Published by Elsevier Inc. on behalf of The Combustion Institute. Keywords: Kinetics; Reaction rate; Phenyl radical; Phenylacetylene; Styrene

1. Introduction Comprehensive modeling and optimization of such important technological processes as hydrocarbon combustion, steam cracking, and radical polymerization require accurate kinetic and thermodynamic data for the reactions of hydrocarbon radicals. Aryl radicals play a key role in the mechanisms of formation and removal of polycyclic aromatic hydrocarbons (PAH) and soot in highT environments, such as hydrocarbon flames [1–4]. Reactions of aryl radicals with unsaturated hydrocarbons contribute to the molecular growth of the PAH, whereas the removal of aromatics is accomplished through oxidation and thermal q

Supplementary data for this article can be accessed online. See Appendix A. * Corresponding author. Fax: +1 404 727 6586. E-mail address: [email protected] (M.C. Lin).

decomposition of aryl radicals. Measuring or calculating accurate kinetic parameters for all relevant reactions of arbitrarily large polycyclic aromatic radicals would be a daunting and unrealistic task. Instead, kinetic parameters for the reactions of large aryl radicals can be inferred from the chemistry of smaller species. Phenyl (C6H5) is the simplest prototypical aryl radical, so building a kinetic database for its reactions is of particular importance. Our group [5–8] and others [9–11] devoted considerable efforts to studying the chemistry of this radical, using available experimental and computational tools. Recently, we have presented detailed accounts of the mechanism and kinetics for the reactions of phenyl radicals with C2Hx (x = 2, 4) [5,6] and C3H4 (allene and propyne) [7] unsaturated hydrocarbons. These studies indicate that, despite a slightly higher activation energy for the C6H5 + C2H2 reaction, the rate of phenyl addition

1540-7489/$ - see front matter  2006 Published by Elsevier Inc. on behalf of The Combustion Institute. doi:10.1016/j.proci.2006.07.140

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G. Nam et al. / Proceedings of the Combustion Institute 31 (2007) 249–256

to C2H2 is expected to be higher than those of the C2H4 and C3H4 addition reactions under combustion conditions, because the less negative activation entropy acts in favor of the C2H2-addition and becomes the dominant factor at high-T. Moreover, since C2H2 is present in higher concentrations than other unsaturated hydrocarbons under typical combustion conditions, it is expected to be the most efficient building block for the PAH molecular growth via radical-molecule addition reactions. Indeed, the standard kinetic models of hydrocarbon combustion and pyrolysis include sequential additions of the C2H2 blocks to aryl radicals, followed by cyclization and ring fusion, as the principal elementary steps in the PAH formation. However, the advanced stages of the PAH growth and soot inception are likely to involve aryl radical additions to heavier unsaturated hydrocarbons, particularly, to the more reactive mono-substituted aromatic hydrocarbons (MSAH), such as arylacetylenes and arylethylenes. The simplest prototypical reactions in the latter category are the reactions of phenyl radicals with phenylacetylene (C6H5C2H) and styrene (C6H5C2H3) which are, respectively, the addition/H-elimination products of C6H5 reactions with C2H2 and C2H4 under low-pressure conditions: C6 H5 þ C6 H5 C2 H ! products

ð1Þ

C6 H5 þ C6 H5 C2 H3 ! products

ð2Þ

These simple C6H5C2Hx (x = 1, 3) monosubstituted aromatic hydrocarbons and their radical precursors (C8H7 and C8H9) are important intermediates in the mass growth sequences leading to the fused aromatic rings (e.g. naphthalene and indene). Various derivatives of naphthalene, indene, and larger PAH have been identified [12] among the main products of the phenylacetylene pyrolysis. With increasing temperature, product formation is found to be controlled by reactions of phenyl-type radicals, such as reaction (1). Kinetic modeling of benzene and butadiene flames [3] indicates that phenylacetylene and styrene can be formed under combustion conditions by cracking of ethylbenzene, the recombination product of benzyl and methyl radicals, or by phenylation of acetylene and ethylene as aforementioned. Styrene has also been identified as the major initial oxidation product of the small amounts of ethylbenzene in the mixture with H2 + O2 + N2 [13]. These observations show that MSAH can be produced in notable concentrations under combustion conditions and that their reactions with hydrocarbon radicals, including reactions (1) and (2), could contribute to the PAH growth. Therefore, the rate constants for these reactions are required to better model the formation of larger PAH in sooting hydrocarbon flames, especially those featuring aromatic fuel components.

The kinetics for the C6H5 reactions with styrene and 1,1-diphenylethylene (DPE), a close derivative of styrene, have been studied in Freon 113 solution by Scaiano et al., [10] using laser flash photolysis. The room-T rate constant has been measured for reaction (2), k2 = (1.1 ± 0.1) · 10 [11] cm3 mol1 s1. Thermal rate constants and activation parameters have been determined for the reaction of C6H5 with DPE. At room-T the latter reaction is 4 times faster than reaction (2), with a rate constant expressed as kC6H5+DPE = 1012.2exp(709/RT) cm3 mol1 s1 in the range of T = 240–314 K. It is worth noting that the apparent activation energy, Ea(C6H5+ DPE) = 0.7 kcal/mol, is much smaller than that determined in the same study [10] for the reaction of C6H5 with cyclohexene, Ea(C6H5 + c-C6H10) = 2.3 kcal/mol, which can be compared to our predicted barrier for the C6H5-addition to ethylene, E0(C6H5 + C2H4) = 2.3 kcal/mol [6]. No further experimental kinetic data are available for reactions (1) and (2). The absence of experimental and theoretical kinetic data for reactions (1) and (2) in the gas phase was the motivation for this work. Furthermore, a comparative study of the C6H5 + C2H2/ C6H5C2H and C6H5 + C2H4/C6H5C2H3 reactions presents an opportunity to look into the effect of aromatic substitution on the reactivity of double and triple CC bonds. In the following section, we report the absolute total rate constants for reactions (1) and (2) measured by the cavityring-down spectrometry coupled with pulsed laser photolysis (PLP-CRDS). Then the mechanistic interpretation of the experimental results is given on the basis of density functional and higher level electronic structure computations. 2. Kinetic measurements by CRDS The details of the experiment using the cavity ringdown (CRD) technique have been described in our previous works [5–8] and only brief description will be given here. All experiments were performed under slow-flow conditions using Ar as the carrier gas. The flow reactor consists of a heatable Pyrex glass tube attached with two pairs of laser windows opposite of each other, permitting the two-split photolysis laser beams to cross at the center of the reactor at a 30 angle. The reactor was vacuum-sealed at the ends with a pair of highly reflective mirrors (R = 0.9999 at 500 nm, radius curvature 6 m), which form a high quality optical cavity, approximately 50 cm in length. The quality of the cavity can effectively increase the lifetime of a probing laser pulse from FWHM 10 ns to 35–40 ls, providing an effective optical path of 6 · 105 cm. Two pulsed lasers were employed, one for the generation of the C6H5 radical and the other for

G. Nam et al. / Proceedings of the Combustion Institute 31 (2007) 249–256

0 0

1=tc ¼ 1=toc þ B½Ao ek t

ð1aÞ

or
o

ln 1=tc  1=tc ¼ C  k 0 t0

3000 2700

-1

2400

k' / sec

its detection. For radical generation, we employed Lambda Physik LPX 100 excimer laser at 248 nm with C6H5NO as the precursor and for the probing of the C6H5 radical at 504.8 nm, Lambda Physik excimer laser (EMG 102) pumped tunable dye laser (FL 3002, Coumarin 307) was used. The probing laser was injected directly into the reactor cavity through one of the mirrors along the axis of the reactor tube. A fraction of the photon pulse transmitted through the second mirror was filtered and detected with a Hamamatsu photomultiplier tube (PMT, Hamamatsu R955). Photoelectric signal from the PMT was amplified with a fast pre-amplifier (SR445) and acquired and averaged with a multichannel digital oscilloscope (LeCroy 9310 M). The averaged signal was stored in a computer for future data analysis. A pulse-delay generator (SR DG 535) interfaced with the computer was employed to control the firing of the two lasers as well as the triggering of the data acquisition system. C6H5NO (Aldrich, 97%) was recrystallized from ethanol and vacuum-dried. Then it was placed on a sintered glass fritted disk inside a sealed mixing tube and carried into the reactor by a through flow of Ar gas (Specialty Gases, 99.995% UHP grade). Phenylacetylene (C6H5C2H) and styrene (C6H5C2H3) were placed in the sealed bubbler and degassed by several freeze-pump-thaw cycles in liquid nitrogen. Then their vapor was diluted by a continuous flow of Ar gas over the liquid reactants and carried into the reaction zone. The gas flows were regulated by calibrated MKS mass flow controllers. For kinetic measurements, the CRD method measures the decay times of the injected probing photons in the absence (toc ) and the presence (tc) of absorbing species. These photon decay times can be related to the concentration of the species at time t 0 after its generation by the equation

2100

2k 2

1800 k2

1500

2k 1

0.5k 2

1200

k1

900

0.5k 1

600 0.0

0.4

0.8

1.2

1.6

2.0

-9

2.4

2.8

3.2

3.6

3

[X] / 10 mol/cm

Fig. 1. k 0 versus [C6H5C2H] at 297 K (s) and [C6H5C2H3] 396 K (D). Linear least-squares fit yields the second-order rate constants (k) for the C6H5 + C6H5C2Hx (x = 1,3) reaction. Lines are kinetically modeled results using different k values. (Inset) Typical pseudo-first order decay plots for the C6H5 + C6H5C2H reaction at 352 K. The slopes of these plots give the first-order decay constants k 0 . The concentration unit in mol/cm3.

k 0 ¼ k o þ k 00x ½X 

ðIIÞ

o

where k is the radical decay constant in the absence of the molecular reactant X due to the loss of the radical by diffusion away from the probing beam and recombination reactions (e.g., C6H5 + NO and C6H5 + C6H5). The slopes of these plots give the bimolecular rate constant k(T) for the C6H5 + C6H5C2Hx (x = 1, 3) reactions. The experimental rate constants for two reactions measured at 3.62 Torr Ar carrier gas pressure are summarized on Table 1. They can be represented by the following Arrhenius

Table 1 Measured bimolecular rate constantsa C6H5 + C6H5C2Hx (x = 1,3) reactions

for

the

HC

T (K)

[HC]/109 mol cm3

k/1011 cm3 mol1 s1

C6H5C2H

297 318 335 352 375 409

0–2.32 0–2.17 0–2.06 0–1.96 0–1.84 0–1.69

1.76 ± 0.13 2.43 ± 0.13 2.59 ± 0.14 3.45 ± 0.38 3.96 ± 0.69 5.62 ± 0.36

C6H5C2H3

297 314 327 353 374 396

0–2.04 0–1.93 0–1.85 0–1.71 0–1.62 0–1.53

2.52 ± 0.17 2.83 ± 0.25 3.44 ± 0.31 4.42 ± 0.29 6.00 ± 0.62 7.43 ± 0.55

ð1bÞ

where [A]o is the initial concentration of the radical species of interest, C6H5, B is a constant which contains experimental parameters such as the cavity length (50 cm), the refractive index of the absorbing medium, etc. and C = ln(B[A]o). The slopes of the lnð1=tc  1=toc Þ vs. t 0 plots as illustrated in Fig. 1 as an inset for the reactions of C6H5 with C6H5C2H yield the pseudo-first-order rate coefficients, k 0 , for the decay of C6H5 in the presence of known, excess C6H5C2H concentrations as specified. A standard plot of k 0 vs. reagent concentration is shown in Fig. 1, which gives the averaged second-order rate constant k00 from its slope according to the relationship

251

a Cited errors represent one-standard deviation; total pressure 3.62 Torr.

252

G. Nam et al. / Proceedings of the Combustion Institute 31 (2007) 249–256

-1 -1

11.8 11.6

Log(k"/cm mol sec )

12.0

3

12.2

a P=3.62 torr

0.02 301 K

0.00

C6H5 Sensitivity Coefficients (arbitray units)

-0.02

11.4 11.2 11.0 2.1

C6 H5C2H3 C6H5C2H 2.4

2.7

3.0

3.3

3.6

1000/T

Fig. 2. Arrhenius plots of the C6H5 + C6H5C2H and C6H5 + C6H5C2H3 reactions.

expressions (in units of cm3 mol1 s1) as shown in Fig. 2:

4

-0.04 -0.06

6

-0.08 5

-0.10 -0.12 -0.14

1

-0.16

b

421 K

0.00 6 -0.05

5

-0.10 -0.15 -0.20

k 1 ðC6 H5 þ C6 H5 C2 HÞ

-0.25

1

¼ 1013:00:1 exp½ð2430  150Þ=RT  -0.30 0.0

0.2

0.4

k 2 ðC6 H5 þ C6 H5 C2 H3 Þ

0.6

0.8

1.0

time (msec)

¼ 1013:30:1 exp½ð2570  180Þ=RT 

Fig. 3. Sensitivity analysis for the C6H5 + C6H5C2H reaction at P = 40 Torr. The conditions are [C6H5]0 = 4.3 · 1012 mol/cm3, [C6H5NO] = 4.1 · 1011 mol/cm3, [C6H5C2H] = 3.32 · 109 mol/cm3 at 297 K and [C6H5]0 = 3.4 · 1012 mol/cm3, [C6H5NO] = 5.1 · 1011 mol/cm3, [C6H5C2H] = 1.69 · 109 mol/cm3 at 409 K. The reaction numbers are given in Table 2.

The kinetics for the decay of C6H5 radicals in the range of 5–20% of the initial C6H5NO concentration of 1–8 · 1011 mol/cm3, determined by UV/ Vis spectrometry (SHIMADZU, UV-2401 PC) in the downstream of the reaction cell using standard calibration mixtures, have also been simulated by chemical kinetic modeling using CHEMKIN program [14] with the mechanism summarized in Table 2. The sensitivity of the decay of C6H5 radicals in the second order plot is also illustrated in Fig. 1. Our sensitivity analyses on C6H5 illustrated in Fig. 3 clearly indicate that

the decay of C6H5 radical is predominantly affected by the C6H5 + C6H5C2H reaction. Our value of k2 = (2.5 ± 0.2) · 1011 cm3mol1 s1 measured at room temperature in the gas phase is a factor

Table 2 Reactions and rate constants used in the modeling of the C6H5 + C6H5CHx (x = 1, 3) reactions in the CRD experiment at 3.62 Torr Ar carrier-gas pressurea Reactions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

C6H5 + C6H5C2H ) C6H5C8H6 C6H5 + C6H5C2H3 ) C6H5C8H8 C6H5NO ) C6H5 + NO C6H5 + NO ) C6H5NO C6H5 + C6H5NO ) C12H10NO C6H5 + C6H5 ) C12H10 C6H5 + C6H5O ) C12H10O C6H5 + C12H10N ) C18H15N C6H5 + C6H5NO ) C12H10 + NO C12H10NO + C6H5 ) C12H10N + C6H5O C12H10N + NO ) C12H10NNO C12H10NO ) C6H5NO + C6H5 a

A 13

1.0 · 10 2.0 · 1013 1.4 · 1017 3.0 · 1012 4.9 · 1012 2.4 · 1013 1.0 · 1013 1.0 · 1013 5.0 · 1012 1.0 · 1013 1.0 · 1013 5.0 · 1014

Ea

Referenceb

2430 2570 55100 860 68 111 0 0 4500 0 0 45000

This work This work

Rate constants are defined by k = A exp (Ea/RT) and in units cm3, mol, and s; Ea is in the units of cal mol1. [8] Otherwise noted.

b

G. Nam et al. / Proceedings of the Combustion Institute 31 (2007) 249–256

of two higher than that determined by Scaiano et al. [10] in Freon solution. 3. Computational methods All electronic structure calculations described herein were carried out with Gaussian 03 [15] program package. Molecular structures of the reactants, products, and transition states were optimized by the B3LYP/6-31G(d,p) method [16] and refined with the 6-311++G(d,p) basis set. The assignment of the transition states to the elementary reactions was routinely done by a visual inspection of atomic movements in the vibrational modes associated with imaginary frequencies. Harmonic vibrational frequencies calculated at the same levels of theory were used without any adjustments for ZPE corrections, characterization of the stationary points as minima or saddle points, and rate constant calculations by canonical transition state theory [17] with unsymmetric Eckart tunneling corrections [18,19] performed with the ChemRate program [20]. The partition functions for large amplitude (low frequency) torsional modes were evaluated using a 1D hindered/ free rotor model. Reduced moments of inertia for internal rotations were calculated by the method of Pitzer and Gwinn [21], including a correction for rotor-rotor coupling. The calculated and available experimental [22–24] molecular parameters are summarized in the Supplementary Document. Among a limited number of higher level theoretical methods that could be employed for open-shell systems containing 14 carbon atoms, we have chosen the RMP2 [25] method with the 6-311G(d,p) basis set for single point calculations

253

of the barriers for reactions (1) and (2), because this method performed reasonably well in predicting the barriers and enthalpies for the phenyl radical additions to C2H2, C2H4, CH3CCH, and CH3CHCH2. In particular, the deviations of the RMP2 barriers from the more reliable G2M values were less than 1 kcal mol1 for six previously studied phenyl radical addition reactions (see Table 3). A frozen core approximation was used in the RMP2 calculations. 4. Rate constant calculations Reactions (1) and (2) may, in principle, proceed via C6H5-addition or H-abstraction channels. In our previous computational study [6] of the C6H5 + C2H4/C2H2 reactions, the barrier for the olephinic H-abstraction by the C6H5 radical (9.0 kcal/mol) was found to be considerably higher than the C6H5-addition barriers to the double and triple CC bonds (2.3–3.8 kcal/mol) predicted at the same G2M level of theory. These estimates should be accurate to within 1–2 kcal/mol. The aromatic C–H bond in benzene is 2 kcal/mol stronger than the C–H bond in ethylene, and we estimate that the aromatic and vinylic C–H bonds in phenylacetylene and styrene should have similar bond strengths and similar magnitude of the H-abstraction barriers as those calculated for the C–H bond in ethylene. On the other hand, the C6H5 substitution at the double and triple CC bonds increases their reactivity towards radical addition (see below). Under our low-T experimental conditions, the total rates of the C6H5 + C6H5C2Hx (x = 1, 3) reactions are expected to be almost entirely due to the low-barrier C6H5-addition channels with a very

Table 3 Energetic parameters for a series of C6H5-addition reactions to unsaturated HC calculated by the B3LYP/6311++G(d, p) and RMP2/6-311G(d, p) methods Reaction

B3LYP

RMP2

Best value

Ea (0 K)/kcal/mol C6H5 + C2H2 fi C6H5CHCH C6H5 + C2H4 fi C6H5CH2CH2 C6H5 + CH3CCH fi C6H5CHCCH3 C6H5 + CH3CCH fi C6H5(CH3)CCH C6H5 + CH3CHCH2 fi C6H5CH2CHCH3 C6H5 + CH3CHCH2 fi C6H5(CH3)CHCH2 C6H5 + C6H5C2H fi C6H5CCHC6H5 C6H5 + C6H5C2H3 fi C6H5CHCH2C6H5

4.42 3.31 3.97 6.67 2.96 5.31 2.51 1.26

3.28 2.24 2.22 3.13 1.31 2.33 0.50 1.43

3.7a 2.3a 3.0a 3.9a 1.2b 2.2b (—) (—)

DH (0 K)/kcal/mol C6H5 + C2H2 fi C6H5CHCH C6H5 + C2H4 fi C6H5CH2CH2 C6H5 + C6H5C2H fi C6H5CCHC6H5 C6H5 + C6H5C2H3 fi C6H5CHCH2C6H5 a b c

G2M(RCC5,RMP2) predictions from Refs. [5–7]. G2M(RCC6,RMP2) predictions from [26]. From isodesmic analysis.

37.85 31.19 44.91 40.21

38.96 40.22 45.56 47.85

39.6c 36.2c (—) (—)

G. Nam et al. / Proceedings of the Combustion Institute 31 (2007) 249–256

collected in Table 3. For smaller systems, accurate energetics are available from our previous investigations [5–7,26]. The RMP2/6-311G(d,p) barriers are within 1 kcal/mol from the available benchmark values, whereas the B3LYP/6311++G(d,p) calculations tend to overestimate the barriers for all reactions in Table 3. Assuming that this trend extends to reactions (1) and (2), their barriers are expected to be lower than the B3LYP values of 2.5 and 1.3 kcal/mol, respectively. The RMP2 barriers amount to 0.5 kcal/mol for reaction (1) and 1.4 kcal/mol for reaction (2), with a tentatively assumed accuracy of ±2 kcal/ mol. The rate constants for reactions (1) and (2) calculated using the B3LYP molecular parameters (see Supplementary Document) are shown together with experimental data in Figs. 5 and 6 and can 13.0

-1 -1

12.0

11.0

3

minor contribution from the H-abstraction channels. Therefore, we have only considered the addition pathways in the computational part of this work. Both phenylacetylene and styrene have six different sites where phenyl radical can add: a- and b-C atoms of the side chain and ipso(i)-, ortho(o)-, meta(m)-, and para(p)-positions of the aromatic ring. The corresponding branching pathways are shown in Fig. 4 for the reaction of C6H5 with C6H5C2H. Our survey calculations at the B3LYP/6-31G(d,p) level confirm that the barrier for b-addition is more than 3 kcal mol1 lower than the barriers for C6H5-additions at any other site. Figure 4 also shows that the b-addition pathway produces the most stable addition product, b-C6H5C8H6 radical. At higher levels of theory, we have shown in the earlier studies [5,6] that H atoms preferably add to both phenylacetylene and styrene at the b-position with high regioselectivity, so that other pathways account for less than 10% of the total rate. Therefore, only b-addition pathways were considered for reactions (1) and (2) in our higher level calculations. The choice of affordable theoretical methodologies for open shell systems containing 14 carbon atoms is rather limited. Calculations at the B3LYP/6-311++G(d,p) and RMP2/6-311G(d,p) levels based on the geometries optimized by the first method may not be able to provide chemically accurate energetic parameters for reactions (1) and (2). We can get an idea about the level of accuracy of these calculations by analyzing their performance for similar reactions, which have been studied at the higher levels of theory. Energetic parameters for a series of C6H5-addition reactions to unsaturated hydrocarbons are

Log(k /cm mol s )

254

k (RMP2) 1

10.0

k (B3LYP) 1

9.0

k C6H5+C2H2 8.0 2.4

2.6

2.8

3.0

3.2

3.4

1000 K / T

Fig. 5. Rate constants for the C6H5 + C6H5C2H reaction: (solid line) k1 calculated from the B3LYP barrier of 2.5 kcal/mol; (dotted line) k1 calculated from the RMP2 barrier of 0.5 kcal/mol; (dashed line) rate constant of phenyl addition to C2H2; (j) k1 measured by PLPCRDS.

TS1(i) 9.9

C6H5 + C6H5C2H

TS1(p) 4.2

0.0 i-C6H5C8H6 -10.7

TS1(o) 4.4

TS1(m) 5.6

p-C6H5C8H6 -23.8 o-C6H5C8H6 -22.5

-1

β-C6H5C8H6 -49.7

k 2(RMP2)

12.0

-1

TS1(β) 0.9

11.0

3

α-C6H5C8H6 -35.0 TS1(α) 5.8

Log(k/cm mol s )

13.0

m-C6H5C8H6 -18.8

Fig. 4. Branching channels for the C6H5 + C6H5C2H addition reaction. Energies (ZPE-corrected, T = 0 K) are given relative to the reactants as calculated by the B3LYP/6-31G(d,p) method.

k 2(B3LYP) 10.0

9.0

k C6H5+C2H4

8.0 2.4

2 .6

2.8

3 .0

3.2

3 .4

1000 K / T

Fig. 6. Rate constants for the C6H5 + C6H5C2H3 reaction: (solid line) k2 calculated from the B3LYP barrier of 1.3 kcal/mol; (dotted line) k2 calculated from the RMP2 barrier of 1.4 kcal/mol; (dashed line) rate constant of phenyl addition to C2H4; (j) k2 measured by PLPCRDS; (s) k2 measured in solution, from [10].

G. Nam et al. / Proceedings of the Combustion Institute 31 (2007) 249–256

be given by the following expressions (in units of cm3 mol1 s1) in the temperature interval from 300 to 2500 K: k 1 ðB3LYPÞ ¼ 1:03  106 T 2:14 expð536=RT Þ k 1 ðRMP2Þ ¼ 1:05  106 T 2:14 expð2543=RT Þ k 2 ðB3LYPÞ ¼ 6:34  103 T 2:70 expð2066=RT Þ k 2 ðRMP2Þ ¼ 5:46  103 T 2:70 expð616=RT Þ: Solid and dotted lines represent theoretical values based on the B3LYP and RMP2 estimates of the reaction barriers, respectively. The k1(RMP2) rate constant is slightly below the experimental values, but the deviation is well within a factor of 2. On the other hand, the k2(RMP2) rate constant appears to be overestimated. The B3LYP rate constants are systematically too low. At least partially, this is due to the overestimated barriers at the B3LYP/6-311++G(d,p) level of theory. Additional uncertainty in the calculated rate constants is introduced by the treatment of low frequency modes in the transition states TS1(b) and TS2(b). Five transitional modes with frequencies below 100 cm1 are present in both TS1(b) and TS2(b). The lowest frequency modes in both transition states correspond to the virtually unhindered torsional motion of the phenyl radical. They were treated as free 1D internal rotors in our rate constant calculations. The second lowest frequency in TS1(b) corresponds to the rotation of phenylacetylene about its axis of symmetry, or equivalently, the phenyl radical rotation about the same axis. The partition function for this degree of freedom was calculated assuming a hindered 1D rotor model. Other transitional frequencies in TS1(b) and TS2(b) can not be assigned to the torsion-like modes. They were treated as harmonic oscillators. This model underestimates partition functions for very low frequency anharmonic modes of TS1(b) and TS2(b), which is partially responsible for underestimation of k1 and k2 by the conventional TST. Also shown in Figs. 5 and 6 are the rate constants for the C6H5-addition to C2H2 and C2H4. As follows from their comparison with k1 and k2, the C6H5-for-H substitution strongly enhances the reactivity of unsaturated CC bonds towards C6H5.

5. Conclusions The reactions of C6H5 with phenylacetylene and styrene have been studied experimentally by PLP-CRDS and theoretically by DFT and RMP2 methods. Both reactions predominantly produce b-adducts, stabilized by p-conjugation. Such resonantly stabilized radicals may have rela-

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tively long lifetimes in combustions regimes and may be involved in the mechanism of PAH formation. The calculated 0 K barriers fall in the range from 0.5 to 2.5 kcal/mol for reaction (1), and from 1.4 to 1.3 kcal/mol for reaction (2). The rate constants calculated by conventional TST exhibit substantial deviations from the experimental values, which we attribute in part to the errors in the theoretical barriers and in part to the limited accuracy of the harmonic oscillator treatment of several low frequency vibrational modes. Our experimental k2 is in good agreement with the room-T rate constant of Scaiano et al. [10] measured in Freon solution. A comparison of the k1 and k2 rate constants with those for the C6H5-addition to ethylene and acetylene shows that C6H5-substitution increases the reactivity of unsaturated CC bonds. The following reactivity scale can be suggested based on the trapping efficiency of phenyl radical by selected HC at room-T: C2 H2 : C2 H4 : C6 H5 C2 H : C6 H5 C2 H3  1 : 1:8 : 240 : 380:

Acknowledgments The authors are grateful for the support of this work from the Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences through Contract DE-FGO2-97ER14784. Also, we are thankful to the Cherry L. Emerson Center of Emory University for the use of its resources, which is in part supported by National Science Foundation grant (CHE-0079627) and an IBM Shared University Research Award.

Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/ j.proci.2006.07.140.

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