Article pubs.acs.org/JPCA
Thermal Decomposition of 1,1,1-Trifluoroethane Revisited Akira Matsugi,*,† Kenji Yasunaga,‡ and Hiroumi Shiina† †
National Institute of Advanced Industrial Science and Technology (AIST), 16-1 Onogawa, Tsukuba, Ibaraki 305-8569, Japan Department of Applied Chemistry, National Defense Academy, Hashirimizu 1-10-20, Yokosuka, 239-8686, Japan
‡
ABSTRACT: 1,1,1-Trifluoroethane (CH3CF3) has been frequently used as a chemical thermometer or an internal standard in shock tube studies to determine relative rates of chemical reactions. The rate constants for the thermal decomposition of CH3CF3 were recently reported to have anomalous pressure dependence in the high-temperature falloff region. In the present study, the kinetics of the CH3CF3 decomposition were reinvestigated using shock tube/laser absorption (ST/LA) spectroscopy and single-pulse shock tube (SPST) methods over the temperature range 1163−1831 K at pressures from 95 to 290 kPa. The present rate constants are 2−3 times smaller than those reported in previous single-pulse experiments performed at near high-pressure limit conditions. The recommended rate constant expression, k = 5.71 × 1046T−9.341 exp(−47073 K/T) s−1, was obtained over the temperature range 1000−1600 K with uncertainties of ±40% at temperatures below 1300 K and ±32% at 1600 K. The rate constants at the hightemperature region showed clear falloff behavior and were in good agreement with recent high-temperature experiments. The falloff rate constants could not be reproduced by a standard RRKM/master-equation model; this study provides additional evidence for the unusual pressure dependence previously reported for this reaction. Additionally, the rate constants for the decomposition of 1,1-difluoroethylene (CH2CF2) were determined over the temperature range 1650− 2059 K at pressures of 100 and 205 kPa, and were reproduced by the RRKM/master-equation calculation with an average downward energy transfer of 900 cm−1.
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108 s−1. However, this interpretation has subsequently been questioned by Barker and co-workers on the basis of their statistical6 and classical trajectory7 calculations which proposed that IVR should not be as slow as suggested by the non-RRKM model. Another important motivation for studying the decomposition of CH3CF3 is that this reaction has been frequently used as a chemical thermometer or an internal standard in SPST experiments.8,9 Many of such studies employed the rate constants reported by Tsang and Lifshitz3 as a reference to determine the experimental temperature; however, recent kinetic studies on the pyrolysis of 2,5-dimethylfuran10,11 indicated that the reflected shock temperature specified in the study of Tsang and Lifshitz might be underestimated by a few tens of Kelvin. Therefore, reinvestigation of the rate constants for R1 is warranted to resolve this disparity. This study aims to provide additional experimental data on CH3CF3 decomposition using shock tube/laser absorption (ST/LA) and SPST methods. Laser absorption is one of the most sensitive and reliable methods for investigating the hightemperature chemical kinetics behind shock waves.12,13 Recently, the ST/LA technique has been applied to the measurement of the rate constants for the thermal decomposition of fluoroethane by utilizing the IR absorption of HF.14 The greatly improved sensitivity of the ST/LA method
INTRODUCTION Recent shock tube studies on the thermal unimolecular decomposition of 1,1,1-trifluoroethane (CH3CF3) CH3CF3 → CH 2CF2 + HF
(R1)
reported an anomalous pressure dependence of the rate constants that could not be accurately modeled by Rice− Ramsperger−Kassel−Marcus (RRKM) theory.1,2 The decomposition of CH3CF3 has been considered to dominantly proceed via a four-center transition state that produces 1,1difluoroethylene (CH2CF2) and hydrogen fluoride (HF), and the rate constants near the high-pressure limit were previously investigated using a single-pulse shock tube (SPST)3,4 and a turbulent flow reactor.5 As for the high-temperature falloff region, the shock tube/laser schlieren (ST/LS) measurements of Kiefer et al.1 showed that the high-temperature rate constants of R1 exhibit a distinct pressure dependence at pressures ranging from 2.0 to 13 kPa. However, their rate constant at pressures above 13 kPa (up to 73 kPa) showed surprisingly little pressure dependence, which was later reproduced by the shock tube/time-of-flight mass spectrometry (ST/TOF-MS) measurements of Giri and Tranter,2 performed at pressures of 80 and 160 kPa. The strange behavior described above could not be reproduced by the RRKM/master-equation model.1 Kiefer et al. attributed this anomaly to an intrinsic non-RRKM process due to slow intramolecular vibrational energy redistribution (IVR). Their non-RRKM model could reasonably model the experimental rate constants if the IVR rate was approximately © 2014 American Chemical Society
Received: October 10, 2014 Revised: November 18, 2014 Published: November 24, 2014 11688
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compared with previous ST/LS and ST/TOF-MS measurements enabled a kinetic study using highly diluted (a few tens of ppm) samples. The previous studies1,2 were conducted at CH3CF3 dilution ratios of more than 2%, which potentially affected the collisional energy transfer process during the decomposition. The data taken with a different experimental method and at significantly different dilution ratios should provide an additional cross-check of the validity of the rate constant data. In the present study, the rate constants for R1, k1, were measured using the ST/LA method over the temperature range 1221−1831 K at pressures of 95, 195, and 290 kPa. As HF produced from the subsequent decomposition of CH2CF2 affects the observed HF profiles, the rate constants (k2) for R2 CH 2CF2 → CHCF + HF
(R2)
were also determined at 1650−2059 K and 100 and 205 kPa. Measurement of the CH3CF3 decomposition was also performed using the SPST technique over the temperature range 1163−1574 K at pressures of 130−212 kPa to establish the consistency of the results.
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EXPERIMENT Shock Tube/Laser Absorption. The ST/LA experiments were performed using a double-piston-actuated diaphragm-less shock tube15 with a 5.0 cm i.d. test section. The details of the apparatus and method have been described elsewhere,14 and are only briefly presented here. HF produced from the thermal decomposition of CH3CF3 or CH2CF2 behind the reflected shock waves was detected by its IR absorption at the R(1) transition of the fundamental vibrational band near 2476 nm using a distributed-feedback laser. The HF concentration was calculated from Beer’s law using the absorption cross section parametrized in the previous study.14 Specifically, the temperature-dependent line strength of the R(1) transition was calculated from the known line strength at 295 K16 and the molecular partition function of HF evaluated using its molecular constants.17 The line shape was modeled using the hard collision profile of Rautian and Sobel’man,18 which is characterized by the collisional broadening (γ) and Dicke narrowing (β) coefficients. The coefficients parametrized in the previous study14 on the thermal decomposition of fluoroethane, γ(T) = 0.286(T/296 K)−0.68 cm−1 MPa−1 and β(T) = 0.153(T/ 296 K)−0.5 cm−1 MPa−1, were used to obtain the Rautian− Sobel’man profile and thus the peak absorption cross section. The uncertainty of the peak absorption cross sections was estimated to be 5%.14 The sample gases used in the ST/LA experiments were mixtures of 50−500 ppm of CH3CF3 (99% purity) or 50−100 ppm of CH2CF2 (99% purity) diluted in Ar (>99.9999% purity). The mixtures were prepared from pressure measurements using capacitance manometers. Helium (>99.995% purity) was used as the driver gas. The temperature (T5) and pressure (P5) behind the reflected shock waves were calculated from the incident shock velocity extrapolated to the end wall, as described in ref 14. The uncertainty of the measured shock velocity was estimated as ∼0.5%, corresponding to the uncertainty of ∼1% in the temperature. Examples of the HF time profiles observed following the decomposition of CH3CF3 and CH2CF2 are shown in Figure 1. As in the case of the C2H5F decomposition,14 the formation of HF was accompanied by a short incubation period caused by the relaxation of vibrationally excited HF14,19,20 produced from
Figure 1. Example of HF mole fraction profiles observed in the decomposition of (a) CH3CF3 and (b) CH2CF2 behind the reflected shock waves. The white lines represent the fitted profiles.
the decomposition of CH3CF3 and CH2CF2. The HF mole fraction profiles following CH2CF2 decomposition were found to reach steady asymptotes close to the initial mole fractions of CH2CF2, as shown in Figure 1b; therefore, the profiles were interpreted using the following two-step reaction model: CH 2CF2 → CHCF + HF*
(R2′)
HF* + Ar → HF + Ar
(R3)
where HF* indicates the vibrationally excited HF. The rate constant for the vibrational relaxation of HF, R3, was taken from ref 21, and those for the CH2CF2 decomposition were determined by least-squares fitting of the observed profile to a rate equation derived from the two-step model. Then, the HF profiles in the CH3CF3 experiments were modeled to derive the rate constants for the CH3CF3 decomposition using the following three-step mechanism: CH3CF3 → CH 2CF2 + HF*
(R1′)
CH 2CF2 → CHCF + HF*
(R2′)
HF* + Ar → HF + Ar
(R3)
with the rate constants for R2′ taken from the study on the CH2CF2 decomposition. The fitted profiles are also plotted in Figure 1 as white lines. Single-Pulse Shock Tube. The SPST measurements were performed using a magic-hole-type shock tube that has a 4.1 cm i.d. test section and has been described in detail by Hidaka et al.22−25 The reacted gas mixtures, quenched using the singlepulse method, were extracted into a pre-evacuated vessel (50 cm3) through a valve near the end plate. Subsequently, the concentrations of CH3CF3 and CH2CF2 in the mixtures were measured using three serially connected gas chromatographs (GCs) equipped with thermal conductivity detectors (TCDs)24,25 with accuracies of ±5%. 11689
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An effective reaction time, te, was defined as the time between heating of the mixture by the reflected shock wave and the time at which the reflected shock pressure had fallen by 20%.23,24 Assuming the adiabatic expansion of a nonreactive mixture, the temperature drops by ∼8.5% from its initial value at te. Given that the SPST has cooling rates of 6.6 × 105 K s−1,22 it can be assumed that the reaction was frozen at te. The validity of the effective heating time and cooling rate was previously tested in a study of the pyrolysis of N2O.22 The sample gases used in the SPST experiments were mixtures of 5000 ppm of CH3CF3 (99% purity) diluted in Ar (99.9999% purity) prepared from pressure measurements. The sample gas showed only one GC peak. The initial temperature and pressure behind the reflected shock waves were calculated from the incident shock velocity extrapolated to the end wall using the standard one-dimensional shock equations. The uncertainties in the reflected shock temperature and the effective reaction time are 1 and 5%, respectively.
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Figure 2. Arrhenius plot of the present and literature26 rate constants for the thermal decomposition of CH2CF2. The lines represent the result of the RRKM/master-equation calculation with ⟨ΔEdown⟩ = 900 cm−1.
RESULTS AND DISCUSSION CH2CF2 Decomposition. The rate constants for the decomposition of CH2CF2 are summarized in Table 1 and
position of fluoroethane (C2H5F, ⟨ΔEdown⟩ = 280−400 cm−1)14,28 and 1,1-difluoroethane (CH3CHF2, ⟨ΔEdown⟩ = 1600 cm−1).27 However, no rational explanation can be adduced for such an inconsistency from our current understanding of collisional energy transfer processes. The calculated rate constants for R2 over the temperature range 1200−2400 K were fitted to Troe’s formula29 as
Table 1. Experimental Conditions and Rate Constants for the ST/LA Measurements of CH2CF2 Decomposition
a
P5 (kPa)
T5 (K)
X(CH2CF2)a (ppm)
106 101 105 103 104 104 103 103 100 102 103 101 102 205 207 207 208 205 205 205 206
1698 1650 1768 1792 1803 1852 1890 1891 1909 1936 2000 2038 2059 1840 1902 1902 1962 1970 2004 2034 2042
100 100 100 50 100 50 100 50 100 50 100 50 100 50 50 100 50 50 100 50 50
k2 (s−1) 8.7 5.6 1.9 2.5 2.9 4.5 5.5 6.2 8.7 9.1 1.3 1.7 2.2 4.0 7.4 6.8 1.2 1.5 1.9 2.6 2.5
× × × × × × × × × × × × × × × × × × × × ×
102 102 103 103 103 103 103 103 103 103 104 104 104 103 103 103 104 104 104 104 104
k 2, ∞ = 5.19 × 1014 exp( − 43301 K/T ) s−1
k 2,0 = 1.48 × 1039T −12.852 exp( − 43859 K/T ) cm 3 molecule−1 s−1
Fcent = 0.083 exp( −T /1192) + 0.917 exp(−T /39) + exp( −6181/T )
where k2,∞ and k2,0 are the high- and low-pressure limiting rate constants, respectively, and Fcent is the broadening factor. The parametrized rate constants were used in the three-step reaction model to derive the rate constants for the CH3CF3 decomposition. CH3CF3 Decomposition at T < 1600 K. The present ST/ LA rate constants for R1 are summarized in Table 2. The rate constants at temperatures below 1600 K are plotted in Figure 3, together with the rate data reported by Tschuikow-Roux and Quiring4 and Tsang and Lifshitz3 using the SPST method and by Takahashi et al.5 using a turbulent flow reactor. The present rate constants are in good agreement with those obtained by Takahashi et al., but they are smaller than the previous SPST data by a factor of 2−3. This difference is slightly beyond the statistical uncertainty stated by Tsang and Lifshitz (a factor of 1.8).3 Because there is no apparent pressure dependence observed in the present rate constants at 95−290 kPa, it is unreasonable to attribute the difference between the present rate constants and the previous SPST data to the pressure dependence of the rate constants. A similar discrepancy was reported in recent kinetic studies on the pyrolysis of 2,5dimethylfuran,10,11 which suggested that the reflected shock temperature used in the study of Tsang and Lifshitz3 might be underestimated by a few tens of Kelvin. Indeed, temperature-
Initial mole fraction of CH2CF2.
plotted in Figure 2. A small pressure dependence was observed in the rate constants; k2 at 2000 K and 205 kPa was approximately 50% larger than that at 100 kPa. The rate constants reported by Tschuikow-Roux and Simmie,26 which were measured using a SPST method at a pressure of ∼440 kPa, are also plotted. Both the present and the previous rate constants were consistently reproduced by the RRKM/masterequation calculation (see the Appendix for details) when a barrier height of 349 kJ mol−1 and an average downward energy transfer, ⟨ΔEdown⟩, of 900 cm−1 were employed. It is interesting to note that this ⟨ΔEdown⟩ for the CH2CF2 decomposition is the same as that determined for vinyl fluoride (CH2CHF),27 despite the large difference observed between the decom11690
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Table 2. Experimental Conditions and Rate Constants for the ST/LA Measurements of CH3CF3 Decomposition P5 (kPa)
T5 (K)
X(CH3CF3)a (ppm)
94 99 107 97 94 92 94 95 91 95 93 93 99 93 89 100 98 92 99 101 101 107 101 92 100 111 93 98 188 191
1238 1254 1322 1331 1348 1355 1401 1435 1448 1457 1462 1499 1555 1559 1590 1606 1613 1620 1630 1654 1686 1713 1721 1746 1753 1759 1759 1831 1221 1247
200 500 500 200 100 100 100 100 50 100 100 100 100 50 50 100 100 50 100 100 100 100 100 100 100 100 50 100 500 500
k1 (s−1) 26 46 1.6 1.8 2.8 4.6 6.7 1.2 1.9 1.9 2.4 3.4 5.5 6.0 8.2 9.9 1.0 1.3 1.6 1.5 2.4 2.9 3.2 5.6 4.4 3.0 5.6 5.7 17 29
× × × × × × × × × × × × × × × × × × × × × × × × × ×
102 102 102 102 102 103 103 103 103 103 103 103 103 103 104 104 104 104 104 104 104 104 104 104 104 104 a
P5 (kPa)
T5 (K)
X(CH3CF3)a (ppm)
196 192 202 202 194 195 199 196 192 192 193 196 191 201 200 191 202 201 191 200 201 191 281 288 293 292 286 291
1347 1359 1429 1429 1456 1458 1507 1537 1562 1599 1601 1619 1630 1649 1677 1689 1708 1726 1729 1742 1789 1798 1469 1542 1619 1675 1722 1818
200 100 50 200 100 50 50 50 50 50 50 100 50 100 100 50 100 100 50 100 100 50 50 50 50 50 50 50
k1 (s−1) 2.0 3.0 5.9 7.3 1.4 1.4 2.8 4.1 7.3 1.2 1.1 1.2 1.7 1.5 2.5 3.1 3.2 3.3 4.7 4.8 7.2 6.4 2.0 5.0 1.4 2.1 3.3 7.4
× × × × × × × × × × × × × × × × × × × × × × × × × × × ×
102 102 102 102 103 103 103 103 103 104 104 104 104 104 104 104 104 104 104 104 104 104 103 103 104 104 104 104
Initial mole fraction of CH3CF3.
uncertainties in rate constants for reactions that they used as internal standards to determine the reaction temperatures. The solid line drawn in Figure 3 is the calculated highpressure limiting rate constant of R1 (see the Appendix for details). The results of the RRKM/master-equation calculation are also plotted. Analysis of the falloff behavior of the rate constants will be presented later in this paper. In the calculation, a reaction barrier height of 302 kJ mol−1 was chosen to reproduce the present rate constants at the low temperature region. This barrier height is close to that employed by Kiefer et al.;1 however, their high-pressure limiting rate constants are approximately 3−4 times larger than the present calculation, and are in agreement with the values reported by the previous SPST studies.3,4 This contradiction occurs from the invalid specification of the socalled “reaction path degeneracy”. As noted by Barker et al.,6 the reaction path degeneracy of the HF-elimination reaction from CH3CF3 should be three (due to the nine equivalent transition states and three reactant wells), instead of nine as assumed by Kiefer et al. In the present study, the reaction path degeneracy is taken into account as rotational symmetry numbers, which are an inherent property of molecules. Since the rotational symmetry number of CH3CF3 and the transition state of R1 are three and one, respectively, the reaction path degeneracy of three is implicitly given in the present calculation. The high-pressure limiting rate constants calculated for R1 in the temperature range 1000−2400 K can be represented with the following Arrhenius expression:
Figure 3. Arrhenius plot of the present and literature3−5 rate constants for the thermal decomposition of CH3CF3 at temperatures below 1600 K. The lines represent the result of RRKM/master-equation calculations. The solid line is the high-pressure limit, and the dotted and dashed lines are the rate constants at 95 kPa with ⟨ΔEdown⟩ = 1000 and 1600 cm−1, respectively.
corrected rate constants suggested by Sirjean et al.10 are in better agreement with the present data. Sirjean et al. argued that there is a systematic uncertainty of a factor of 3 in the rate constant of Tsang and Lifshitz, which can be implied from 11691
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k1, ∞ = 3.33 × 1014 exp( − 37363 K/T ) s−1
Table 3. Experimental Conditions and Results for the SPST Measurements of CH3CF3 Decomposition
As noted in the Introduction, CH3CF3 is widely used as a chemical standard in SPST studies,8,9 and a number of experimental studies have been reported in which the evaluation of kinetic data depends on the reference rate constants of R1. The present study indicates that the rate constants used in those previous studies were overestimated by a factor of 2−3; therefore, it is desirable to reparameterize the rate constants. In general, SPST experiments are carried out at pressures higher than 100 kPa. Since no apparent pressure dependence was observed in the present experimental rate constants, the rate constants can be represented in a pressureindependent modified Arrhenius form. To derive the Arrhenius parameters, a data set of the rate constants was generated that is comprised of the experimental data obtained at temperatures below 1600 K in the present ST/LA measurements and the flow reactor experiments of Takahashi et al.5 The data set is augmented by the high-pressure limiting rate constants, k1,∞, calculated at 1000−1100 K with 10 K intervals to ensure a correct behavior at low temperature. This data set yields the recommendation
P5 (kPa)
T5 (K)
te (ms)
[CH3CF3]f/[CH3CF3]0
[CH2CF2]f/[CH3CF3]0
130 142 152 154 163 165 166 173 175 178 181 182 189 190 212 212
1163 1229 1278 1285 1333 1340 1352 1382 1392 1410 1422 1428 1460 1466 1573 1575
1.60 1.80 1.54 1.60 1.50 1.52 1.62 1.82 1.60 1.78 1.48 1.48 1.62 1.72 1.40 1.66
1.02 1.02 0.91 1.02 0.89 0.84 0.65 0.54 0.42 0.73 0.37 0.46 0.17 0.21 0.08 0.00
0.00 0.00 0.12 0.06 0.09 0.20 0.36 0.50 0.62 0.35 0.64 0.55 0.84 0.81 0.86 0.79
CH3CF3 and CH2CF2 in the postshock gas mixtures are shown in Figure 5 as a function of the temperature. These fractions are
k1 = 5.71 × 1046T −9.341 exp( −47073 K/T ) s−1
which is considered valid for the temperature range 1000−1600 K. This expression reproduces the rate constants in the experimental data set with a root-mean-squares deviation of 23%. Overall uncertainties of the rate constants are estimated to be ±40% at temperatures below 1300 K and ±32% at 1600 K. These values were calculated on the basis of the uncertainties in the fit, experimental temperatures, absorption cross sections of HF, and sample concentrations. The recommended rate constant and its uncertainty range are plotted in Figure 4,
Figure 5. Normalized fractions of CH3CF3 and CH2CF2 in the postshock mixture of the SPST measurements and the simulation results.
defined as [CH3CF3]f/[CH3CF3]0 and [CH2CF2]f/[CH3CF3]0, respectively, where [CH3CF3]0 is the initial concentration of CH3CF3 and [CH3CF3]f and [CH2CF2]f are the concentrations in the postshock mixtures. The results are compared to data obtained from kinetic simulations using the Cantera program.30 The simulations were performed under constant volume conditions with initial pressures of 170 kPa and reaction times of 1.6 ms. The kinetic model used consists of reactions R1 and R2 and the thermodynamic data31 of the species; the present recommended rate constant expression was used for R1, and the pressure-dependent expression given above was employed for R2. As seen, the experimental results are well reproduced by the kinetic simulation, thus corroborating the validity of the ST/LA results. Also, as described later, the rate constants determined in the ST/LA experiments are in good agreement with the earlier ST/ LS1 and ST/TOF-MS2 rate constants at higher temperatures.
Figure 4. Arrhenius plot of the experimental and recommended rate constants for the thermal decomposition of CH3CF3. The temperature-corrected rate constant of Tsang and Lifshitz3,10 is also plotted (see the text for details).
together with the experimental ones. Though the rate constants of Tsang and Lifshitz3 lie outside the present uncertainty band, they fall within the band if the temperature correction suggested by Sirjean et al.10 (marked as “corr.” in Figure 4) is applied. The present SPST data for the decomposition of CH3CF3 are summarized in Table 3. The normalized fractions of 11692
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⟨ΔEdown⟩. For example, the results with ⟨ΔEdown⟩ = 1600 cm−1 show reasonable agreements with the ST/LS data at 4.7 kPa, but they are unable to reproduce the pressure independence of the rate constants at 13−73 kPa. They are also overestimating the present 290 kPa data obtained at >1650 K. Therefore, though the present calculation with the revised high-pressure limiting rate constants provides an improved overall agreement with the experimental rate constants compared to the previous master-equation results,1,2,6 it still cannot resolve the strange pressure dependence of the experimental rate constants.
Therefore, the present ST/LA rate constants are considered to be consistent with the data obtained by the four other different experimental methods (the present SPST, the turbulent flow reactor,5 ST/LS,1 and ST/TOF-MS2). This provides additional confidence of the recommended rate constants. The present updated rate constant expression can be used to retroactively reanalyze previous kinetic measurements that employed CH3CF3 as a chemical thermometer or an internal standard. CH3CF3 Decomposition at the Falloff Region. Figure 6 shows the present ST/LA and the earlier ST/LS1 and ST/
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CONCLUSIONS The rate constants for the thermal decomposition of CH3CF3 were measured using the ST/LA method. The results indicate that the rate constants for this reaction previously used as a chemical thermometer or an internal standard in SPST experiments were overestimated by a factor of 2−3. The updated rate constant expression was derived on the basis of present and recent experimental data sets. The rate constants at the high-temperature region show clear falloff behavior and are in good agreement with the earlier ST/ LS and ST/TOF-MS results, which cannot be reproduced by the RRKM/master-equation calculation; this study provides additional support for the strange kinetics observed in the thermal decomposition of CH3CF3. The consistency of the results from the three different experimental methods with different dilution gases and ratios (2−10% in Kr for ST/LS,1 2−4% in Ne for ST/TOF-MS,2 and 50−200 ppm in Ar for ST/ LA) suggests that the anomalous pressure dependence of the rate constants originates neither from systematic errors in the experiments nor from the energy transfer in collisions with unexpected third bodies.
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APPENDIX
RRKM/Master-Equation Calculations
The RRKM/master-equation34 calculations were performed using the SSUMES program.35 The density of states and microscopic rate constants were calculated using a modified version of the UNIMOL program,36 based on the rovibrational properties and energies computed at the ωB97X-D37/6-311+ +G(d,p) level of theory using the Gaussian 09 program.38 The frequency and zero-point energy scaling factors of 0.950 and 0.975, respectively, were adopted.39,40 The rovibrational properties of the reactants and transition states are summarized in Table 4. The zero-point energy corrected barrier height and reaction energies were 285 and 127 kJ mol−1 for R1 and 353 and 188 kJ mol−1 for R2, respectively. The predicted barrier heights were modified to 302 and 349 kJ mol−1 in the RRKM calculations in order to reproduce the experimental rate constants as described in the text. Rigid-rotor and harmonic oscillator approximations were adopted except for the torsional mode of CH3CF3, which was treated as a sinusoidally hindered rotor with a barrier height1 of 1137 cm−1 and a symmetry number of 3. One-dimensional semiclassical tunneling corrections were included by assuming an asymmetric Eckart potential determined using the imaginary frequencies of transition state.41,42 The energy grain size used in the masterequation calculation was 20 cm−1. The collisional energy transfer probability was estimated by the exponential down model. The buffer gas was assumed to be Ar. The collision frequencies were calculated using Lennard-Jones collision parameters for CH2CF2 (σ = 4.5 Å and ε/kB = 250 K)
Figure 6. Arrhenius plot of the present and literature1,2 rate constants for the thermal decomposition of CH3CF3 in the falloff region. The lines represent the result of the RRKM/master-equation calculation with ⟨ΔEdown⟩ = 1000 (a) and 1600 (b) cm−1.
TOF-MS2 rate constants for R1 at the falloff region. Although Cadman et al.32 also reported high-temperature rate constants at 1590−1865 K using a SPST method, they are not compared here, as there may be potential flaws in their data.33 The present results showed no clear pressure dependence from 95 to 290 kPa, but these results are in good agreement with the ST/LS results obtained at 13−73 kPa and the ST/TOF-MS results at 80 and 160 kPa. The pressure dependent rate constants evaluated by RRKM/ master-equation calculations with ⟨ΔEdown⟩ = 1000 and 1600 cm−1 are shown as lines in Figure 6. The RRKM/masterequation well reproduces the falloff behavior of the present rate constants if ⟨ΔEdown⟩ is in the range of approximately 800− 1200 cm−1. However, the low-pressure rate constants of Kiefer et al. were only approximately reproduced with larger values of 11693
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(12) Hanson, R. K. Applications of Quantitative Laser Sensors to Kinetics, Propulsion and Practical Energy Systems. Proc. Combust. Inst. 2011, 33, 1−40. (13) Hanson, R. K.; Davidson, D. F. Recent Advances in Laser Absorption and Shock Tube Methods for Studies of Combustion Chemistry. Prog. Energy Combust. Sci. 2014, 44, 103−114. (14) Matsugi, A.; Shiina, H. Shock Tube Study on the Thermal Decomposition of Fluoroethane using Infrared Laser Absorption Detection of Hydrogen Fluoride. J. Phys. Chem. A 2014, 118, 6832− 6837. (15) Yamauchi, M.; Matsui, H.; Koshi, M.; Tanaka, K.; Tamaki, S.; Tanaka, H. Shock Tube Studies on the Radical Emission Spectra by Use of an Imaging Spectrometer. Bunko Kenkyu 1987, 36, 388−394. (16) Pine, A. S.; Fried, A.; Elkins, J. W. Spectral Intensities in the Fundamental Bands of HF and HCl. J. Mol. Spectrosc. 1985, 109, 30− 45. (17) Webb, D. U.; Narahari Rao, K. Vibration Rotation Bands of Heated Hydrogen Halides. J. Mol. Spectrosc. 1968, 28, 121−124. (18) Rautian, S. G.; Sobel’man, I. I. The Effect of Collisions on the Doppler Broadening of Spectral Lines. Phys.-Usp. 1967, 9, 701. (19) Arunan, E.; Wategaonkar, S. J.; Setser, D. W. Hydrogen Fluoride/Hydrogen Chloride Vibrational and Rotational Distributions from Three- and Four-Centered Unimolecular Elimination Reactions. J. Phys. Chem. 1991, 95, 1539−1547. (20) Quick, C. R., Jr; Wittig, C. IR Multiple Photon Dissociation of Fluorinated Ethanes and Ethylenes: HF Vibrational Energy Distributions. J. Chem. Phys. 1980, 72, 1694−1700. (21) Bott, J. F.; Cohen, N. Shock-Tube Studies of HF Vibrational Relaxation. J. Chem. Phys. 1971, 55, 3698−3706. (22) Hidaka, Y.; Shiba, S.; Takuma, H.; Suga, M. Thermal Decomposition of Ethane in Shock Waves. Int. J. Chem. Kinet. 1985, 17, 441−453. (23) Hidaka, Y.; Nakamura, T.; Miyauchi, A.; Shiraishi, T.; Kawano, H. Thermal Decomposition of Propyne and Allene in Shock Waves. Int. J. Chem. Kinet. 1989, 21, 643−666. (24) Hidaka, Y.; Hattori, K.; Okuno, T.; Inami, K.; Abe, T.; Koike, T. Shock-Tube and Modeling Study of Acetylene Pyrolysis and Oxidation. Combust. Flame 1996, 107, 401−417. (25) Hidaka, Y.; Kimura, K.; Hattori, K.; Okuno, T. Shock Tube and Modeling Study of Ketene Oxidation. Combust. Flame 1996, 106, 155−167. (26) Tschuikow-Roux, E.; Simmie, J. M. Kinetics of the ShockInitiated Decomposition of 1,1-Difluoroethylene. J. Phys. Chem. 1970, 74, 4075−4079. (27) Xu, H.; Kiefer, J. H.; Sivaramakrishnan, R.; Giri, B. R.; Tranter, R. S. Shock Tube Study of Dissociation and Relaxation in 1,1Difluoroethane and Vinyl Fluoride. Phys. Chem. Chem. Phys. 2007, 9, 4164−4176. (28) Giri, B. R.; Kiefer, J. H.; Xu, H.; Klippenstein, S. J.; Tranter, R. S. An Experimental and Theoretical High Temperature Kinetic Study of the Thermal Unimolecular Dissociation of Fluoroethane. Phys. Chem. Chem. Phys. 2008, 10, 6266−6273. (29) Gilbert, R. G.; Luther, K.; Troe, J. Theory of Thermal Unimolecular Reactions in the Fall-Off Range. II. Weak Collision Rate Constants. Ber. Bunsen-Ges. 1983, 87, 169−177. (30) Goodwin, D. G.; Moffat, H. K.; Speth, R. L. Cantera: An objectoriented software toolkit for chemical kinetics, thermodynamics, and transport processes, version 2.1.1; Caltech: Pasadena, CA, 2014. (31) Goos, E.; Burcat, A.; Ruscic B. Ideal Gas Thermochemical Database with updates from Active Thermochemical Tables. http:// burcat.technion.ac.il/dir/ (accessed Nov 13, 2014), mirrored at http://garfield.chem.elte.hu/Burcat/burcat.html (accessed Nov 13, 2014). (32) Cadman, P.; Day, M.; Trotman-Dickenson, A. F. Static and Shock Tube Pyrolyses of Alkyl Fluorides. Part III. The Thermal Decomposition of 1-Chloro-2-Fluoroethane, 1,1-Difluoroethane, and 1,1,1-Trifluoroethane. J. Chem. Soc. A 1971, 1356−1360.
Table 4. Rovibrational Properties of the Reactants and Transition States species CH3CF3 TS(R1)
CH2CF2 TS(R2)
unscaled vibrational frequencies (cm−1) 240,a 368, 368, 544, 544, 605, 838, 977, 977, 1233, 1233, 1297, 1443, 1490, 1490, 3090, 3185, 3185 1725i, 240, 275, 402, 477, 491, 608, 765, 904, 961, 1021, 1314, 1419, 1429, 1587, 1784, 3172, 3278 445, 557, 643, 719, 844, 949, 969, 1317, 1416, 1802, 3214, 3321 1801i, 320, 444, 545, 621, 684, 744, 926, 1079, 1772, 2093, 3375
rotational constants (cm−1)
rotational symmetry number
0.173,b 0.183c
3
0.146,b 0.185c
1
0.368,b 0.250c
2
0.352,b 0.209c
1
a
Treated as a sinusoidally hindered rotor with a barrier height of 1137 cm−1 and a symmetry number of 3. bRotational constants for twodimensional inactive rotations. cRotational constants for active rotations.
(estimated), CH3CF3 (σ = 4.96 Å and ε/kB = 382 K),1 and Ar (σ = 3.5 Å and ε/kB = 93 K).43
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Kiefer, J. H.; Katopodis, C.; Santhanam, S.; Srinivasan, N. K.; Tranter, R. S. A Shock-Tube, Laser-Schlieren Study of the Dissociation of 1,1,1-Trifluoroethane: An Intrinsic Non-RRKM Process. J. Phys. Chem. A 2004, 108, 2443−2450. (2) Giri, B. R.; Tranter, R. S. Dissociation of 1,1,1-Trifluoroethane behind Reflected Shock Waves: Shock Tube/Time-of-Flight Mass Spectrometry Experiments. J. Phys. Chem. A 2007, 111, 1585−1592. (3) Tsang, W.; Lifshitz, A. Kinetic Stability of 1,1,1-Trifluoroethane. Int. J. Chem. Kinet. 1998, 30, 621−628. (4) Tschuikow-Roux, E.; Quiring, W. J. Kinetics of the Thermally Induced Dehydrofluorination of 1,1,1-Trifluoroethane in Shock Waves. J. Phys. Chem. 1971, 75, 295−300. (5) Takahashi, K.; Harada, A.; Horigome, S.; Cho, R.; Inomata, T. Thermal Decompositions of 1,1,1-Trifluoroethane and Pentafluoroethane in a Turbulent Flow Reactor. Combust. Sci. Technol. 2007, 179, 1417−1432. (6) Barker, J. R.; Stimac, P. J.; King, K. D.; Leitner, D. M. CF3CH3 → HF + CF2CH2: A Non-RRKM Reaction? J. Phys. Chem. A 2006, 110, 2944−2954. (7) Stimac, P. J.; Barker, J. R. Intramolecular Vibrational Energy Redistribution Involving the Torsion in CF3CH3: A Molecular Dynamics Study. J. Phys. Chem. A 2006, 110, 6851−6859. (8) Tranter, R. S.; Sivaramakrishnan, R.; Srinivasan, N.; Brezinsky, K. Calibration of Reaction Temperatures in a Very High Pressure Shock Tube Using Chemical Thermometers. Int. J. Chem. Kinet. 2001, 33, 722−731. (9) Tang, W.; Brezinsky, K. Chemical Kinetic Simulations behind Reflected Shock Waves. Int. J. Chem. Kinet. 2006, 38, 75−97. (10) Sirjean, B.; Fournet, R.; Glaude, P.-A.; Battin-Leclerc, F.; Wang, W.; Oehlschlaeger, M. A. Shock Tube and Chemical Kinetic Modeling Study of the Oxidation of 2,5-Dimethylfuran. J. Phys. Chem. A 2013, 117, 1371−1392. (11) Somers, K. P.; Simmie, J. M.; Gillespie, F.; Conroy, C.; Black, G.; Metcalfe, W. K.; Battin-Leclerc, F.; Dirrenberger, P.; Herbinet, O.; Glaude, P.-A.; et al. A Comprehensive Experimental and Detailed Chemical Kinetic Modelling Study of 2,5-Dimethylfuran Pyrolysis and Oxidation. Combust. Flame 2013, 160, 2291−2318. 11694
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(33) Tsang, W. Recalculation of Data on the Thermal Decomposition of 1,1-Difluoroethane and 1,1,1-Trifluoroethane. Int. J. Chem. Kinet. 1973, 5, 643−649. (34) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell: Oxford, U.K., 1990. (35) Miyoshi, A. SSUMES, revision 2010.05.23m2; The University of Tokyo: Tokyo, Japan, 2010. (36) Gilbert, R. G.; Smith, S. C.; Jordan, M. J. T. UNIMOL Program Suite; School of Chemistry, Sydney University: Sydney, Australia, 1993. (37) Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615−6620. (38) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision C.01; Gaussian, Inc.: Wallingford, CT, 2010. (39) Alecu, I. M.; Zheng, J.; Zhao, Y.; Truhlar, D. G. Computational Thermochemistry: Scale Factor Databases and Scale Factors for Vibrational Frequencies Obtained from Electronic Model Chemistries. J. Chem. Theory Comput. 2010, 6, 2872−2887. (40) Matsugi, A.; Shiina, H. Kinetics of Hydrogen Abstraction Reactions from Fluoromethanes and Fluoroethanes. Bull. Chem. Soc. Jpn. 2014, 87, 890−901. (41) Miller, W. H. Tunneling Corrections to Unimolecular Rate Constants, with Application to Formaldehyde. J. Am. Chem. Soc. 1979, 101, 6810−6814. (42) Garrett, B. C.; Truhlar, D. G. Semiclassical Tunneling Calculations. J. Phys. Chem. 1979, 83, 2921−2926. (43) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill Professional: Boston, MA, 2001.
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Thermal Decomposition of 1,1,1-Trifluoroethane Revisited Akira Matsugi,*,† Kenji Yasunaga,‡ and Hiroumi Shiina† †
National Institute of Advanced Industrial Science and Technology (AIST), 16-1 Onogawa, Tsukuba, Ibaraki 305-8569, Japan Department of Applied Chemistry, National Defense Academy, Hashirimizu 1-10-20, Yokosuka, 239-8686, Japan
‡
ABSTRACT: 1,1,1-Trifluoroethane (CH3CF3) has been frequently used as a chemical thermometer or an internal standard in shock tube studies to determine relative rates of chemical reactions. The rate constants for the thermal decomposition of CH3CF3 were recently reported to have anomalous pressure dependence in the high-temperature falloff region. In the present study, the kinetics of the CH3CF3 decomposition were reinvestigated using shock tube/laser absorption (ST/LA) spectroscopy and single-pulse shock tube (SPST) methods over the temperature range 1163−1831 K at pressures from 95 to 290 kPa. The present rate constants are 2−3 times smaller than those reported in previous single-pulse experiments performed at near high-pressure limit conditions. The recommended rate constant expression, k = 5.71 × 1046T−9.341 exp(−47073 K/T) s−1, was obtained over the temperature range 1000−1600 K with uncertainties of ±40% at temperatures below 1300 K and ±32% at 1600 K. The rate constants at the hightemperature region showed clear falloff behavior and were in good agreement with recent high-temperature experiments. The falloff rate constants could not be reproduced by a standard RRKM/master-equation model; this study provides additional evidence for the unusual pressure dependence previously reported for this reaction. Additionally, the rate constants for the decomposition of 1,1-difluoroethylene (CH2CF2) were determined over the temperature range 1650− 2059 K at pressures of 100 and 205 kPa, and were reproduced by the RRKM/master-equation calculation with an average downward energy transfer of 900 cm−1.
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108 s−1. However, this interpretation has subsequently been questioned by Barker and co-workers on the basis of their statistical6 and classical trajectory7 calculations which proposed that IVR should not be as slow as suggested by the non-RRKM model. Another important motivation for studying the decomposition of CH3CF3 is that this reaction has been frequently used as a chemical thermometer or an internal standard in SPST experiments.8,9 Many of such studies employed the rate constants reported by Tsang and Lifshitz3 as a reference to determine the experimental temperature; however, recent kinetic studies on the pyrolysis of 2,5-dimethylfuran10,11 indicated that the reflected shock temperature specified in the study of Tsang and Lifshitz might be underestimated by a few tens of Kelvin. Therefore, reinvestigation of the rate constants for R1 is warranted to resolve this disparity. This study aims to provide additional experimental data on CH3CF3 decomposition using shock tube/laser absorption (ST/LA) and SPST methods. Laser absorption is one of the most sensitive and reliable methods for investigating the hightemperature chemical kinetics behind shock waves.12,13 Recently, the ST/LA technique has been applied to the measurement of the rate constants for the thermal decomposition of fluoroethane by utilizing the IR absorption of HF.14 The greatly improved sensitivity of the ST/LA method
INTRODUCTION Recent shock tube studies on the thermal unimolecular decomposition of 1,1,1-trifluoroethane (CH3CF3) CH3CF3 → CH 2CF2 + HF
(R1)
reported an anomalous pressure dependence of the rate constants that could not be accurately modeled by Rice− Ramsperger−Kassel−Marcus (RRKM) theory.1,2 The decomposition of CH3CF3 has been considered to dominantly proceed via a four-center transition state that produces 1,1difluoroethylene (CH2CF2) and hydrogen fluoride (HF), and the rate constants near the high-pressure limit were previously investigated using a single-pulse shock tube (SPST)3,4 and a turbulent flow reactor.5 As for the high-temperature falloff region, the shock tube/laser schlieren (ST/LS) measurements of Kiefer et al.1 showed that the high-temperature rate constants of R1 exhibit a distinct pressure dependence at pressures ranging from 2.0 to 13 kPa. However, their rate constant at pressures above 13 kPa (up to 73 kPa) showed surprisingly little pressure dependence, which was later reproduced by the shock tube/time-of-flight mass spectrometry (ST/TOF-MS) measurements of Giri and Tranter,2 performed at pressures of 80 and 160 kPa. The strange behavior described above could not be reproduced by the RRKM/master-equation model.1 Kiefer et al. attributed this anomaly to an intrinsic non-RRKM process due to slow intramolecular vibrational energy redistribution (IVR). Their non-RRKM model could reasonably model the experimental rate constants if the IVR rate was approximately © 2014 American Chemical Society
Received: October 10, 2014 Revised: November 18, 2014 Published: November 24, 2014 11688
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compared with previous ST/LS and ST/TOF-MS measurements enabled a kinetic study using highly diluted (a few tens of ppm) samples. The previous studies1,2 were conducted at CH3CF3 dilution ratios of more than 2%, which potentially affected the collisional energy transfer process during the decomposition. The data taken with a different experimental method and at significantly different dilution ratios should provide an additional cross-check of the validity of the rate constant data. In the present study, the rate constants for R1, k1, were measured using the ST/LA method over the temperature range 1221−1831 K at pressures of 95, 195, and 290 kPa. As HF produced from the subsequent decomposition of CH2CF2 affects the observed HF profiles, the rate constants (k2) for R2 CH 2CF2 → CHCF + HF
(R2)
were also determined at 1650−2059 K and 100 and 205 kPa. Measurement of the CH3CF3 decomposition was also performed using the SPST technique over the temperature range 1163−1574 K at pressures of 130−212 kPa to establish the consistency of the results.
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EXPERIMENT Shock Tube/Laser Absorption. The ST/LA experiments were performed using a double-piston-actuated diaphragm-less shock tube15 with a 5.0 cm i.d. test section. The details of the apparatus and method have been described elsewhere,14 and are only briefly presented here. HF produced from the thermal decomposition of CH3CF3 or CH2CF2 behind the reflected shock waves was detected by its IR absorption at the R(1) transition of the fundamental vibrational band near 2476 nm using a distributed-feedback laser. The HF concentration was calculated from Beer’s law using the absorption cross section parametrized in the previous study.14 Specifically, the temperature-dependent line strength of the R(1) transition was calculated from the known line strength at 295 K16 and the molecular partition function of HF evaluated using its molecular constants.17 The line shape was modeled using the hard collision profile of Rautian and Sobel’man,18 which is characterized by the collisional broadening (γ) and Dicke narrowing (β) coefficients. The coefficients parametrized in the previous study14 on the thermal decomposition of fluoroethane, γ(T) = 0.286(T/296 K)−0.68 cm−1 MPa−1 and β(T) = 0.153(T/ 296 K)−0.5 cm−1 MPa−1, were used to obtain the Rautian− Sobel’man profile and thus the peak absorption cross section. The uncertainty of the peak absorption cross sections was estimated to be 5%.14 The sample gases used in the ST/LA experiments were mixtures of 50−500 ppm of CH3CF3 (99% purity) or 50−100 ppm of CH2CF2 (99% purity) diluted in Ar (>99.9999% purity). The mixtures were prepared from pressure measurements using capacitance manometers. Helium (>99.995% purity) was used as the driver gas. The temperature (T5) and pressure (P5) behind the reflected shock waves were calculated from the incident shock velocity extrapolated to the end wall, as described in ref 14. The uncertainty of the measured shock velocity was estimated as ∼0.5%, corresponding to the uncertainty of ∼1% in the temperature. Examples of the HF time profiles observed following the decomposition of CH3CF3 and CH2CF2 are shown in Figure 1. As in the case of the C2H5F decomposition,14 the formation of HF was accompanied by a short incubation period caused by the relaxation of vibrationally excited HF14,19,20 produced from
Figure 1. Example of HF mole fraction profiles observed in the decomposition of (a) CH3CF3 and (b) CH2CF2 behind the reflected shock waves. The white lines represent the fitted profiles.
the decomposition of CH3CF3 and CH2CF2. The HF mole fraction profiles following CH2CF2 decomposition were found to reach steady asymptotes close to the initial mole fractions of CH2CF2, as shown in Figure 1b; therefore, the profiles were interpreted using the following two-step reaction model: CH 2CF2 → CHCF + HF*
(R2′)
HF* + Ar → HF + Ar
(R3)
where HF* indicates the vibrationally excited HF. The rate constant for the vibrational relaxation of HF, R3, was taken from ref 21, and those for the CH2CF2 decomposition were determined by least-squares fitting of the observed profile to a rate equation derived from the two-step model. Then, the HF profiles in the CH3CF3 experiments were modeled to derive the rate constants for the CH3CF3 decomposition using the following three-step mechanism: CH3CF3 → CH 2CF2 + HF*
(R1′)
CH 2CF2 → CHCF + HF*
(R2′)
HF* + Ar → HF + Ar
(R3)
with the rate constants for R2′ taken from the study on the CH2CF2 decomposition. The fitted profiles are also plotted in Figure 1 as white lines. Single-Pulse Shock Tube. The SPST measurements were performed using a magic-hole-type shock tube that has a 4.1 cm i.d. test section and has been described in detail by Hidaka et al.22−25 The reacted gas mixtures, quenched using the singlepulse method, were extracted into a pre-evacuated vessel (50 cm3) through a valve near the end plate. Subsequently, the concentrations of CH3CF3 and CH2CF2 in the mixtures were measured using three serially connected gas chromatographs (GCs) equipped with thermal conductivity detectors (TCDs)24,25 with accuracies of ±5%. 11689
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An effective reaction time, te, was defined as the time between heating of the mixture by the reflected shock wave and the time at which the reflected shock pressure had fallen by 20%.23,24 Assuming the adiabatic expansion of a nonreactive mixture, the temperature drops by ∼8.5% from its initial value at te. Given that the SPST has cooling rates of 6.6 × 105 K s−1,22 it can be assumed that the reaction was frozen at te. The validity of the effective heating time and cooling rate was previously tested in a study of the pyrolysis of N2O.22 The sample gases used in the SPST experiments were mixtures of 5000 ppm of CH3CF3 (99% purity) diluted in Ar (99.9999% purity) prepared from pressure measurements. The sample gas showed only one GC peak. The initial temperature and pressure behind the reflected shock waves were calculated from the incident shock velocity extrapolated to the end wall using the standard one-dimensional shock equations. The uncertainties in the reflected shock temperature and the effective reaction time are 1 and 5%, respectively.
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Figure 2. Arrhenius plot of the present and literature26 rate constants for the thermal decomposition of CH2CF2. The lines represent the result of the RRKM/master-equation calculation with ⟨ΔEdown⟩ = 900 cm−1.
RESULTS AND DISCUSSION CH2CF2 Decomposition. The rate constants for the decomposition of CH2CF2 are summarized in Table 1 and
position of fluoroethane (C2H5F, ⟨ΔEdown⟩ = 280−400 cm−1)14,28 and 1,1-difluoroethane (CH3CHF2, ⟨ΔEdown⟩ = 1600 cm−1).27 However, no rational explanation can be adduced for such an inconsistency from our current understanding of collisional energy transfer processes. The calculated rate constants for R2 over the temperature range 1200−2400 K were fitted to Troe’s formula29 as
Table 1. Experimental Conditions and Rate Constants for the ST/LA Measurements of CH2CF2 Decomposition
a
P5 (kPa)
T5 (K)
X(CH2CF2)a (ppm)
106 101 105 103 104 104 103 103 100 102 103 101 102 205 207 207 208 205 205 205 206
1698 1650 1768 1792 1803 1852 1890 1891 1909 1936 2000 2038 2059 1840 1902 1902 1962 1970 2004 2034 2042
100 100 100 50 100 50 100 50 100 50 100 50 100 50 50 100 50 50 100 50 50
k2 (s−1) 8.7 5.6 1.9 2.5 2.9 4.5 5.5 6.2 8.7 9.1 1.3 1.7 2.2 4.0 7.4 6.8 1.2 1.5 1.9 2.6 2.5
× × × × × × × × × × × × × × × × × × × × ×
102 102 103 103 103 103 103 103 103 103 104 104 104 103 103 103 104 104 104 104 104
k 2, ∞ = 5.19 × 1014 exp( − 43301 K/T ) s−1
k 2,0 = 1.48 × 1039T −12.852 exp( − 43859 K/T ) cm 3 molecule−1 s−1
Fcent = 0.083 exp( −T /1192) + 0.917 exp(−T /39) + exp( −6181/T )
where k2,∞ and k2,0 are the high- and low-pressure limiting rate constants, respectively, and Fcent is the broadening factor. The parametrized rate constants were used in the three-step reaction model to derive the rate constants for the CH3CF3 decomposition. CH3CF3 Decomposition at T < 1600 K. The present ST/ LA rate constants for R1 are summarized in Table 2. The rate constants at temperatures below 1600 K are plotted in Figure 3, together with the rate data reported by Tschuikow-Roux and Quiring4 and Tsang and Lifshitz3 using the SPST method and by Takahashi et al.5 using a turbulent flow reactor. The present rate constants are in good agreement with those obtained by Takahashi et al., but they are smaller than the previous SPST data by a factor of 2−3. This difference is slightly beyond the statistical uncertainty stated by Tsang and Lifshitz (a factor of 1.8).3 Because there is no apparent pressure dependence observed in the present rate constants at 95−290 kPa, it is unreasonable to attribute the difference between the present rate constants and the previous SPST data to the pressure dependence of the rate constants. A similar discrepancy was reported in recent kinetic studies on the pyrolysis of 2,5dimethylfuran,10,11 which suggested that the reflected shock temperature used in the study of Tsang and Lifshitz3 might be underestimated by a few tens of Kelvin. Indeed, temperature-
Initial mole fraction of CH2CF2.
plotted in Figure 2. A small pressure dependence was observed in the rate constants; k2 at 2000 K and 205 kPa was approximately 50% larger than that at 100 kPa. The rate constants reported by Tschuikow-Roux and Simmie,26 which were measured using a SPST method at a pressure of ∼440 kPa, are also plotted. Both the present and the previous rate constants were consistently reproduced by the RRKM/masterequation calculation (see the Appendix for details) when a barrier height of 349 kJ mol−1 and an average downward energy transfer, ⟨ΔEdown⟩, of 900 cm−1 were employed. It is interesting to note that this ⟨ΔEdown⟩ for the CH2CF2 decomposition is the same as that determined for vinyl fluoride (CH2CHF),27 despite the large difference observed between the decom11690
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Table 2. Experimental Conditions and Rate Constants for the ST/LA Measurements of CH3CF3 Decomposition P5 (kPa)
T5 (K)
X(CH3CF3)a (ppm)
94 99 107 97 94 92 94 95 91 95 93 93 99 93 89 100 98 92 99 101 101 107 101 92 100 111 93 98 188 191
1238 1254 1322 1331 1348 1355 1401 1435 1448 1457 1462 1499 1555 1559 1590 1606 1613 1620 1630 1654 1686 1713 1721 1746 1753 1759 1759 1831 1221 1247
200 500 500 200 100 100 100 100 50 100 100 100 100 50 50 100 100 50 100 100 100 100 100 100 100 100 50 100 500 500
k1 (s−1) 26 46 1.6 1.8 2.8 4.6 6.7 1.2 1.9 1.9 2.4 3.4 5.5 6.0 8.2 9.9 1.0 1.3 1.6 1.5 2.4 2.9 3.2 5.6 4.4 3.0 5.6 5.7 17 29
× × × × × × × × × × × × × × × × × × × × × × × × × ×
102 102 102 102 102 103 103 103 103 103 103 103 103 103 104 104 104 104 104 104 104 104 104 104 104 104 a
P5 (kPa)
T5 (K)
X(CH3CF3)a (ppm)
196 192 202 202 194 195 199 196 192 192 193 196 191 201 200 191 202 201 191 200 201 191 281 288 293 292 286 291
1347 1359 1429 1429 1456 1458 1507 1537 1562 1599 1601 1619 1630 1649 1677 1689 1708 1726 1729 1742 1789 1798 1469 1542 1619 1675 1722 1818
200 100 50 200 100 50 50 50 50 50 50 100 50 100 100 50 100 100 50 100 100 50 50 50 50 50 50 50
k1 (s−1) 2.0 3.0 5.9 7.3 1.4 1.4 2.8 4.1 7.3 1.2 1.1 1.2 1.7 1.5 2.5 3.1 3.2 3.3 4.7 4.8 7.2 6.4 2.0 5.0 1.4 2.1 3.3 7.4
× × × × × × × × × × × × × × × × × × × × × × × × × × × ×
102 102 102 102 103 103 103 103 103 104 104 104 104 104 104 104 104 104 104 104 104 104 103 103 104 104 104 104
Initial mole fraction of CH3CF3.
uncertainties in rate constants for reactions that they used as internal standards to determine the reaction temperatures. The solid line drawn in Figure 3 is the calculated highpressure limiting rate constant of R1 (see the Appendix for details). The results of the RRKM/master-equation calculation are also plotted. Analysis of the falloff behavior of the rate constants will be presented later in this paper. In the calculation, a reaction barrier height of 302 kJ mol−1 was chosen to reproduce the present rate constants at the low temperature region. This barrier height is close to that employed by Kiefer et al.;1 however, their high-pressure limiting rate constants are approximately 3−4 times larger than the present calculation, and are in agreement with the values reported by the previous SPST studies.3,4 This contradiction occurs from the invalid specification of the socalled “reaction path degeneracy”. As noted by Barker et al.,6 the reaction path degeneracy of the HF-elimination reaction from CH3CF3 should be three (due to the nine equivalent transition states and three reactant wells), instead of nine as assumed by Kiefer et al. In the present study, the reaction path degeneracy is taken into account as rotational symmetry numbers, which are an inherent property of molecules. Since the rotational symmetry number of CH3CF3 and the transition state of R1 are three and one, respectively, the reaction path degeneracy of three is implicitly given in the present calculation. The high-pressure limiting rate constants calculated for R1 in the temperature range 1000−2400 K can be represented with the following Arrhenius expression:
Figure 3. Arrhenius plot of the present and literature3−5 rate constants for the thermal decomposition of CH3CF3 at temperatures below 1600 K. The lines represent the result of RRKM/master-equation calculations. The solid line is the high-pressure limit, and the dotted and dashed lines are the rate constants at 95 kPa with ⟨ΔEdown⟩ = 1000 and 1600 cm−1, respectively.
corrected rate constants suggested by Sirjean et al.10 are in better agreement with the present data. Sirjean et al. argued that there is a systematic uncertainty of a factor of 3 in the rate constant of Tsang and Lifshitz, which can be implied from 11691
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k1, ∞ = 3.33 × 1014 exp( − 37363 K/T ) s−1
Table 3. Experimental Conditions and Results for the SPST Measurements of CH3CF3 Decomposition
As noted in the Introduction, CH3CF3 is widely used as a chemical standard in SPST studies,8,9 and a number of experimental studies have been reported in which the evaluation of kinetic data depends on the reference rate constants of R1. The present study indicates that the rate constants used in those previous studies were overestimated by a factor of 2−3; therefore, it is desirable to reparameterize the rate constants. In general, SPST experiments are carried out at pressures higher than 100 kPa. Since no apparent pressure dependence was observed in the present experimental rate constants, the rate constants can be represented in a pressureindependent modified Arrhenius form. To derive the Arrhenius parameters, a data set of the rate constants was generated that is comprised of the experimental data obtained at temperatures below 1600 K in the present ST/LA measurements and the flow reactor experiments of Takahashi et al.5 The data set is augmented by the high-pressure limiting rate constants, k1,∞, calculated at 1000−1100 K with 10 K intervals to ensure a correct behavior at low temperature. This data set yields the recommendation
P5 (kPa)
T5 (K)
te (ms)
[CH3CF3]f/[CH3CF3]0
[CH2CF2]f/[CH3CF3]0
130 142 152 154 163 165 166 173 175 178 181 182 189 190 212 212
1163 1229 1278 1285 1333 1340 1352 1382 1392 1410 1422 1428 1460 1466 1573 1575
1.60 1.80 1.54 1.60 1.50 1.52 1.62 1.82 1.60 1.78 1.48 1.48 1.62 1.72 1.40 1.66
1.02 1.02 0.91 1.02 0.89 0.84 0.65 0.54 0.42 0.73 0.37 0.46 0.17 0.21 0.08 0.00
0.00 0.00 0.12 0.06 0.09 0.20 0.36 0.50 0.62 0.35 0.64 0.55 0.84 0.81 0.86 0.79
CH3CF3 and CH2CF2 in the postshock gas mixtures are shown in Figure 5 as a function of the temperature. These fractions are
k1 = 5.71 × 1046T −9.341 exp( −47073 K/T ) s−1
which is considered valid for the temperature range 1000−1600 K. This expression reproduces the rate constants in the experimental data set with a root-mean-squares deviation of 23%. Overall uncertainties of the rate constants are estimated to be ±40% at temperatures below 1300 K and ±32% at 1600 K. These values were calculated on the basis of the uncertainties in the fit, experimental temperatures, absorption cross sections of HF, and sample concentrations. The recommended rate constant and its uncertainty range are plotted in Figure 4,
Figure 5. Normalized fractions of CH3CF3 and CH2CF2 in the postshock mixture of the SPST measurements and the simulation results.
defined as [CH3CF3]f/[CH3CF3]0 and [CH2CF2]f/[CH3CF3]0, respectively, where [CH3CF3]0 is the initial concentration of CH3CF3 and [CH3CF3]f and [CH2CF2]f are the concentrations in the postshock mixtures. The results are compared to data obtained from kinetic simulations using the Cantera program.30 The simulations were performed under constant volume conditions with initial pressures of 170 kPa and reaction times of 1.6 ms. The kinetic model used consists of reactions R1 and R2 and the thermodynamic data31 of the species; the present recommended rate constant expression was used for R1, and the pressure-dependent expression given above was employed for R2. As seen, the experimental results are well reproduced by the kinetic simulation, thus corroborating the validity of the ST/LA results. Also, as described later, the rate constants determined in the ST/LA experiments are in good agreement with the earlier ST/ LS1 and ST/TOF-MS2 rate constants at higher temperatures.
Figure 4. Arrhenius plot of the experimental and recommended rate constants for the thermal decomposition of CH3CF3. The temperature-corrected rate constant of Tsang and Lifshitz3,10 is also plotted (see the text for details).
together with the experimental ones. Though the rate constants of Tsang and Lifshitz3 lie outside the present uncertainty band, they fall within the band if the temperature correction suggested by Sirjean et al.10 (marked as “corr.” in Figure 4) is applied. The present SPST data for the decomposition of CH3CF3 are summarized in Table 3. The normalized fractions of 11692
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⟨ΔEdown⟩. For example, the results with ⟨ΔEdown⟩ = 1600 cm−1 show reasonable agreements with the ST/LS data at 4.7 kPa, but they are unable to reproduce the pressure independence of the rate constants at 13−73 kPa. They are also overestimating the present 290 kPa data obtained at >1650 K. Therefore, though the present calculation with the revised high-pressure limiting rate constants provides an improved overall agreement with the experimental rate constants compared to the previous master-equation results,1,2,6 it still cannot resolve the strange pressure dependence of the experimental rate constants.
Therefore, the present ST/LA rate constants are considered to be consistent with the data obtained by the four other different experimental methods (the present SPST, the turbulent flow reactor,5 ST/LS,1 and ST/TOF-MS2). This provides additional confidence of the recommended rate constants. The present updated rate constant expression can be used to retroactively reanalyze previous kinetic measurements that employed CH3CF3 as a chemical thermometer or an internal standard. CH3CF3 Decomposition at the Falloff Region. Figure 6 shows the present ST/LA and the earlier ST/LS1 and ST/
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CONCLUSIONS The rate constants for the thermal decomposition of CH3CF3 were measured using the ST/LA method. The results indicate that the rate constants for this reaction previously used as a chemical thermometer or an internal standard in SPST experiments were overestimated by a factor of 2−3. The updated rate constant expression was derived on the basis of present and recent experimental data sets. The rate constants at the high-temperature region show clear falloff behavior and are in good agreement with the earlier ST/ LS and ST/TOF-MS results, which cannot be reproduced by the RRKM/master-equation calculation; this study provides additional support for the strange kinetics observed in the thermal decomposition of CH3CF3. The consistency of the results from the three different experimental methods with different dilution gases and ratios (2−10% in Kr for ST/LS,1 2−4% in Ne for ST/TOF-MS,2 and 50−200 ppm in Ar for ST/ LA) suggests that the anomalous pressure dependence of the rate constants originates neither from systematic errors in the experiments nor from the energy transfer in collisions with unexpected third bodies.
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APPENDIX
RRKM/Master-Equation Calculations
The RRKM/master-equation34 calculations were performed using the SSUMES program.35 The density of states and microscopic rate constants were calculated using a modified version of the UNIMOL program,36 based on the rovibrational properties and energies computed at the ωB97X-D37/6-311+ +G(d,p) level of theory using the Gaussian 09 program.38 The frequency and zero-point energy scaling factors of 0.950 and 0.975, respectively, were adopted.39,40 The rovibrational properties of the reactants and transition states are summarized in Table 4. The zero-point energy corrected barrier height and reaction energies were 285 and 127 kJ mol−1 for R1 and 353 and 188 kJ mol−1 for R2, respectively. The predicted barrier heights were modified to 302 and 349 kJ mol−1 in the RRKM calculations in order to reproduce the experimental rate constants as described in the text. Rigid-rotor and harmonic oscillator approximations were adopted except for the torsional mode of CH3CF3, which was treated as a sinusoidally hindered rotor with a barrier height1 of 1137 cm−1 and a symmetry number of 3. One-dimensional semiclassical tunneling corrections were included by assuming an asymmetric Eckart potential determined using the imaginary frequencies of transition state.41,42 The energy grain size used in the masterequation calculation was 20 cm−1. The collisional energy transfer probability was estimated by the exponential down model. The buffer gas was assumed to be Ar. The collision frequencies were calculated using Lennard-Jones collision parameters for CH2CF2 (σ = 4.5 Å and ε/kB = 250 K)
Figure 6. Arrhenius plot of the present and literature1,2 rate constants for the thermal decomposition of CH3CF3 in the falloff region. The lines represent the result of the RRKM/master-equation calculation with ⟨ΔEdown⟩ = 1000 (a) and 1600 (b) cm−1.
TOF-MS2 rate constants for R1 at the falloff region. Although Cadman et al.32 also reported high-temperature rate constants at 1590−1865 K using a SPST method, they are not compared here, as there may be potential flaws in their data.33 The present results showed no clear pressure dependence from 95 to 290 kPa, but these results are in good agreement with the ST/LS results obtained at 13−73 kPa and the ST/TOF-MS results at 80 and 160 kPa. The pressure dependent rate constants evaluated by RRKM/ master-equation calculations with ⟨ΔEdown⟩ = 1000 and 1600 cm−1 are shown as lines in Figure 6. The RRKM/masterequation well reproduces the falloff behavior of the present rate constants if ⟨ΔEdown⟩ is in the range of approximately 800− 1200 cm−1. However, the low-pressure rate constants of Kiefer et al. were only approximately reproduced with larger values of 11693
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(12) Hanson, R. K. Applications of Quantitative Laser Sensors to Kinetics, Propulsion and Practical Energy Systems. Proc. Combust. Inst. 2011, 33, 1−40. (13) Hanson, R. K.; Davidson, D. F. Recent Advances in Laser Absorption and Shock Tube Methods for Studies of Combustion Chemistry. Prog. Energy Combust. Sci. 2014, 44, 103−114. (14) Matsugi, A.; Shiina, H. Shock Tube Study on the Thermal Decomposition of Fluoroethane using Infrared Laser Absorption Detection of Hydrogen Fluoride. J. Phys. Chem. A 2014, 118, 6832− 6837. (15) Yamauchi, M.; Matsui, H.; Koshi, M.; Tanaka, K.; Tamaki, S.; Tanaka, H. Shock Tube Studies on the Radical Emission Spectra by Use of an Imaging Spectrometer. Bunko Kenkyu 1987, 36, 388−394. (16) Pine, A. S.; Fried, A.; Elkins, J. W. Spectral Intensities in the Fundamental Bands of HF and HCl. J. Mol. Spectrosc. 1985, 109, 30− 45. (17) Webb, D. U.; Narahari Rao, K. Vibration Rotation Bands of Heated Hydrogen Halides. J. Mol. Spectrosc. 1968, 28, 121−124. (18) Rautian, S. G.; Sobel’man, I. I. The Effect of Collisions on the Doppler Broadening of Spectral Lines. Phys.-Usp. 1967, 9, 701. (19) Arunan, E.; Wategaonkar, S. J.; Setser, D. W. Hydrogen Fluoride/Hydrogen Chloride Vibrational and Rotational Distributions from Three- and Four-Centered Unimolecular Elimination Reactions. J. Phys. Chem. 1991, 95, 1539−1547. (20) Quick, C. R., Jr; Wittig, C. IR Multiple Photon Dissociation of Fluorinated Ethanes and Ethylenes: HF Vibrational Energy Distributions. J. Chem. Phys. 1980, 72, 1694−1700. (21) Bott, J. F.; Cohen, N. Shock-Tube Studies of HF Vibrational Relaxation. J. Chem. Phys. 1971, 55, 3698−3706. (22) Hidaka, Y.; Shiba, S.; Takuma, H.; Suga, M. Thermal Decomposition of Ethane in Shock Waves. Int. J. Chem. Kinet. 1985, 17, 441−453. (23) Hidaka, Y.; Nakamura, T.; Miyauchi, A.; Shiraishi, T.; Kawano, H. Thermal Decomposition of Propyne and Allene in Shock Waves. Int. J. Chem. Kinet. 1989, 21, 643−666. (24) Hidaka, Y.; Hattori, K.; Okuno, T.; Inami, K.; Abe, T.; Koike, T. Shock-Tube and Modeling Study of Acetylene Pyrolysis and Oxidation. Combust. Flame 1996, 107, 401−417. (25) Hidaka, Y.; Kimura, K.; Hattori, K.; Okuno, T. Shock Tube and Modeling Study of Ketene Oxidation. Combust. Flame 1996, 106, 155−167. (26) Tschuikow-Roux, E.; Simmie, J. M. Kinetics of the ShockInitiated Decomposition of 1,1-Difluoroethylene. J. Phys. Chem. 1970, 74, 4075−4079. (27) Xu, H.; Kiefer, J. H.; Sivaramakrishnan, R.; Giri, B. R.; Tranter, R. S. Shock Tube Study of Dissociation and Relaxation in 1,1Difluoroethane and Vinyl Fluoride. Phys. Chem. Chem. Phys. 2007, 9, 4164−4176. (28) Giri, B. R.; Kiefer, J. H.; Xu, H.; Klippenstein, S. J.; Tranter, R. S. An Experimental and Theoretical High Temperature Kinetic Study of the Thermal Unimolecular Dissociation of Fluoroethane. Phys. Chem. Chem. Phys. 2008, 10, 6266−6273. (29) Gilbert, R. G.; Luther, K.; Troe, J. Theory of Thermal Unimolecular Reactions in the Fall-Off Range. II. Weak Collision Rate Constants. Ber. Bunsen-Ges. 1983, 87, 169−177. (30) Goodwin, D. G.; Moffat, H. K.; Speth, R. L. Cantera: An objectoriented software toolkit for chemical kinetics, thermodynamics, and transport processes, version 2.1.1; Caltech: Pasadena, CA, 2014. (31) Goos, E.; Burcat, A.; Ruscic B. Ideal Gas Thermochemical Database with updates from Active Thermochemical Tables. http:// burcat.technion.ac.il/dir/ (accessed Nov 13, 2014), mirrored at http://garfield.chem.elte.hu/Burcat/burcat.html (accessed Nov 13, 2014). (32) Cadman, P.; Day, M.; Trotman-Dickenson, A. F. Static and Shock Tube Pyrolyses of Alkyl Fluorides. Part III. The Thermal Decomposition of 1-Chloro-2-Fluoroethane, 1,1-Difluoroethane, and 1,1,1-Trifluoroethane. J. Chem. Soc. A 1971, 1356−1360.
Table 4. Rovibrational Properties of the Reactants and Transition States species CH3CF3 TS(R1)
CH2CF2 TS(R2)
unscaled vibrational frequencies (cm−1) 240,a 368, 368, 544, 544, 605, 838, 977, 977, 1233, 1233, 1297, 1443, 1490, 1490, 3090, 3185, 3185 1725i, 240, 275, 402, 477, 491, 608, 765, 904, 961, 1021, 1314, 1419, 1429, 1587, 1784, 3172, 3278 445, 557, 643, 719, 844, 949, 969, 1317, 1416, 1802, 3214, 3321 1801i, 320, 444, 545, 621, 684, 744, 926, 1079, 1772, 2093, 3375
rotational constants (cm−1)
rotational symmetry number
0.173,b 0.183c
3
0.146,b 0.185c
1
0.368,b 0.250c
2
0.352,b 0.209c
1
a
Treated as a sinusoidally hindered rotor with a barrier height of 1137 cm−1 and a symmetry number of 3. bRotational constants for twodimensional inactive rotations. cRotational constants for active rotations.
(estimated), CH3CF3 (σ = 4.96 Å and ε/kB = 382 K),1 and Ar (σ = 3.5 Å and ε/kB = 93 K).43
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
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