Shock Tube Study on the Thermal Decomposition of Fluoroethane

the formation of HF by IR absorption at the R(1) transition in the fundamental vibrational band near 2476 nm using a distributed-feedback diode la...
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Shock Tube Study on the Thermal Decomposition of Fluoroethane Using Infrared Laser Absorption Detection of Hydrogen Fluoride Akira Matsugi* and Hiroumi Shiina Research Institute of Science for Safety and Sustainability, National Institute of Advanced Industrial Science and Technology, 16-1 Onogawa, Tsukuba, Ibaraki 305-8569, Japan ABSTRACT: Motivated by recent shock tube studies on the thermal unimolecular decomposition of fluoroethanes, in which unusual trends have been reported for collisional energy-transfer parameters, the rate constants for the thermal decomposition of fluoroethane were investigated using a shock tube/laser absorption spectroscopy technique. The rate constants were measured behind reflected shock waves by monitoring the formation of HF by IR absorption at the R(1) transition in the fundamental vibrational band near 2476 nm using a distributed-feedback diode laser. The peak absorption cross sections of this absorption line have also been determined and parametrized using the Rautian−Sobel’man line shape function. The rate constant measurements covered a wide temperature range of 1018−1710 K at pressures from 100 to 290 kPa, and the derived rate constants were successfully reproduced by the master equation calculation with an average downward energy transfer, ⟨ΔEdown⟩, of 400 cm−1.

1. INTRODUCTION There has been considerable experimental and theoretical interest in four-center HF elimination reactions from fluoroethanes.1−8 Earlier studies on the thermal decomposition of fluoroethanes1−4 were mostly performed using a single-pulse shock tube method at conditions close to the high-pressure limit, from which the derived rate constants could be well reproduced by transition-state theory.5,7,8 However, recent shock tube studies5−8 in the high-temperature falloff region have indicated unusual behavior of the pressure dependence of the rate constants. The anomaly was first reported by Kiefer et al. after investigation of the high-temperature decomposition kinetics of 1,1,1-trifluoroethane (CH3CF3) using the shock tube/laser schlieren (ST/LS) technique.5 The rate constants showed a deep falloff from the high-pressure limit but surprisingly little pressure dependence over the pressure range of 13−73 kPa. This behavior was later reproduced in the shock tube/time-of-flight mass spectrometry (ST/TOFMS) experiment reported by Giri and Tranter.6 Motivated by the anomaly observed for CH3CF3,5 Tranter and co-workers examined the falloff rate constants for the thermal decomposition of fluoroethane8 (C2H5F) and 1,1difluoroethane7 (CH3CHF2) using the ST/TOF-MS and ST/ LS methods, respectively. Unlike the case of CH3CF3, the pressure dependence of the rate constants for C2H5F and CH3CHF2 could be successfully modeled using the unimolecular master equation with a single exponential-down model employed for the collisional energy transfer. However, the average downward energy transfer ⟨ΔEdown⟩ was unusually large (1600 cm−1) for the CH3CHF2 decomposition and small (280 cm−1 at 1400 K) for C2H5F, when compared to the typical value for the decomposition of ethane.9,10 ⟨ΔEdown⟩ is a critical parameter for our understanding of the collisional energy transfer in unimolecular reactions; therefore, such deviation © 2014 American Chemical Society

potentially poses a significant problem for prediction of the kinetics for unimolecular reactions. In addition, the reported rate constants had a relatively large scatter, which may introduce some errors in ⟨ΔEdown⟩. Therefore, reexamination of the falloff rate constants, preferably using a different experimental method, is warranted. The present study is a reinvestigation of the thermal decomposition of C2H5F C2H5F → C2H4 + HF

(1)

in the falloff region using a shock tube/laser absorption (ST/ LA) technique. Laser absorption is one of the most sensitive and reliable methods for investigating high-temperature kinetics of radicals and molecules behind shock waves.11,12 Recent advances in tunable infrared (IR) diode lasers have enabled the sensitive and direct detection of hydrogen fluoride (HF) using its fundamental vibrational band and accurate measurements of the decomposition rates of fluoroethanes. In this study, this new technique is employed to refine the experimental data for reaction 1 over the extended temperature range of 1018−1710 K and at pressures of 100, 195, and 290 kPa.

2. EXPERIMENT The ST/LA experiment was performed using a diaphragm-less shock tube. The shock tube consists of a high-pressure driver section that is separated by a piston from the 4.2 m long and 5.0 cm i.d. stainless steel test section. Each shock wave was generated by pneumatically removing the piston using a double-piston system.13,14 The test section was evacuated Received: July 3, 2014 Revised: July 31, 2014 Published: August 4, 2014 6832

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with a 180 L/s turbomolecular pump to pressures less than 4 × 10−4 Pa between measurements. The velocities of the shock waves were measured with four miniature pressure transducers mounted at 30, 205, 405, and 605 mm upstream from the end plate of the test section. The temperature (T5) and pressure (P5) behind the reflected shock wave were calculated using the ideal shock wave theory with boundary layer corrections.15,16 Specifically, the incident shock velocity linearly extrapolated to the end wall (typical attenuation rates of the velocities were 0.5−2% per meter) was used to obtain uncorrected thermodynamic quantities. Then, the T5 and P5 at the observation zone used for kinetic measurements (30 mm from the end wall) were calculated using method (a) of ref 15. The pressure traces from the transducer located at 30 mm from the end wall were monitored using an oscilloscope and were found to be kept nearly constant over the time periods used for the kinetic measurements. The uncertainty of the measured shock velocity was estimated as ∼0.5%, corresponding to the uncertainty of ∼1% in the temperature. Sample gases used in this study were mixtures of 50−1000 ppm of C2H5F (>97% purity) diluted in Ar (>99.9999% purity). The mixtures were prepared from pressure measurements using capacitance manometers (±0.25% accuracy) in a glass vacuum line, stored in glass vessels, and allowed to homogenize for at least 12 h prior to the shock experiments. Helium (>99.995% purity) was used as the driver gas. HF produced from the thermal decomposition of C2H5F behind the reflected shock waves was detected using IR laser absorption spectroscopy. Figure 1 shows a schematic of the

system was limited by the beam width and was estimated from the reflected shock velocity to be ∼1 μs. The laser wavelength was controlled by tuning the laser temperature and injection current. The wavelength was set to the peak of the R(1) transition in the fundamental vibrational band of HF near 2476 nm.17 The line center was identified by scanning the absorption line of HF behind the reflected shock wave with modulation of the laser injection current at 5 kHz. The measured absorbance, −ln(I/I0), is related to the absorption cross section and the concentration of HF using Beer’s law, −ln(I/I0) = σHFCHFlabs, where I and I0 are the transmitted and initial laser intensities, respectively, σHF is the absorption cross section, CHF is the HF concentration, and labs is the absorption path length. The absorption time profile of HF following C2H5F decomposition was kinetically analyzed to derive the decomposition rate constant. The peak absorption cross section of HF was also determined.

3. RESULTS AND DISCUSSION HF Absorption Time Profile. Figure 2 shows representative examples of the HF absorption time profiles observed

Figure 1. Schematic of the experimental arrangement. A: aperture; L: lens; BS: beam splitter; F: band-pass filter; PD: InAs photovoltaic detector.

experimental setup. Continuous-wave laser radiation generated by a single-mode distributed-feedback (DFB) diode laser (∼1 mW, >35 dB side-mode suppression ratio) was split by a beam splitter into diagnostic and reference beams. The former beam was passed through the shock tube via MgF2 windows located 30 mm from the end plate. An aperture and plano-convex CaF2 lens (500 mm focal length) were placed in front of the DFB laser to constrain the beam diameter inside of the shock tube to less than 0.5 mm. Both the diagnostic and reference beams were collected by plano-convex CaF2 lenses (100 mm focal length), shielded by band-pass filters (2470 nm center wavelength, 50 nm halfwidth), and detected using liquid-N2cooled InAs photovoltaic detectors (0.1 μs rise time). The output signals from the two detectors were fed into a 10 MHz differential amplifier and recorded with a 20 MS/s digital oscilloscope. The differential amplifier subtracted the reference signal from the diagnostic beam signal, which substantially reduced the laser intensity fluctuation noise by common-mode rejection. The measurement time resolution of the present

Figure 2. Example of HF absorption profiles observed for the decomposition of C2H5F behind reflected shock waves at (a) 1380 and (b) 1120 K. White lines represent the fitted profiles.

behind the reflected shock waves. Time zero in the profiles indicates the passage of reflected shock waves, which causes a schlieren spike due to density deflection. The time resolution of the measurement can be deduced from the width of the spike, which is ∼1 μs and consistent with that estimated from the reflected shock velocity and the probe beam width. The formation of HF observed in Figure 2a is accompanied by a short incubation period. The vibrational relaxation of C2H5F is estimated to be too fast to be resolved8 under the present conditions; therefore, this incubation is attributed to the vibrational relaxation of HF. IR multiple photon dissociation18 and chemical activation19 experiments on fluoroethanes have indicated that the excess energy of this 6833

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The temperature-dependent line strength of the R(1) transition was calculated from the value at 295 K,21 2.38 × 10−18 cm−1 molecule−2 cm2, and the molecular constants of HF.17 Because the Dicke narrowing effect22 significantly contributes to the absorption line shape of HF,23 the line shape was modeled using the hard collision profile of Rautian and Sobel’man,22 which is characterized by the collisional broadening (γ) and Dicke narrowing (β) coefficients. The line shape asymmetry23 was not taken into account here because the peak absorption cross section was found to be insensitive to the asymmetry parameter. The Dicke narrowing coefficient may be compared with the dynamic friction coefficient deduced from the diffusion coefficient24 and is expected to have a temperature dependence25 of ∼T−0.5. The room-temperature (296 K) Dicke narrowing coefficient for Ar has been reported23 to be 0.153 cm−1 MPa−1. Therefore, in this study, the Dicke narrowing coefficient was assumed to be β(T) = 0.153(T/296 K)−0.5 cm−1 MPa−1. The collisional broadening coefficients for the R(1) transition of Ar were derived by matching the peak absorption cross sections shown in Figure 3 to those calculated from the line strength and Rautian−Sobel’man line shape function. They are plotted in Figure 4 as a function of temperature. The

four-center elimination reaction is preferably distributed to the HF vibrational energy and a significant portion of the HF is produced in its vibrationally excited state. In this study, the following two-step reaction model was considered for interpretation of the observed profiles C2H5F → C2H4 + HF*

(1′)

HF* + Ar → HF + Ar

(2)

where HF* indicates the vibrationally excited HF. The vibrational relaxation rate of HF* by Ar was obtained from the shock tube study reported by Bott and Cohen.20 Although this is a rather primitive model, the incubation behavior could be well reproduced using the reported relaxation rate;20 therefore, it is postulated that the correct rate constants for C2H5F decomposition can be obtained with this two-step model. As the HF elimination is considered to be a sole reaction channel from C2H5F decomposition,8 the absorption cross section of HF and the rate constant for reaction 1 can be determined from a rate equation derived from the model. At temperatures above 1250 K, the rate constant and the absorption cross section were simultaneously determined by a nonlinear least-squares fitting of the absorption time profile to the rate equation. The fitted profile is presented as a white line in Figure 2a. At temperatures below 1250 K, however, they cannot be determined at the same time because only a small fraction of C2H5F is decomposed within the observation time period (typically 1 ms), as shown in Figure 2b. Instead, the rate constants in the low-temperature region were obtained using the fixed absorption cross section values that were extrapolated from the high-temperature data, as described below. Absorption Cross Section of HF. The peak absorption cross sections of HF at the R(1) transition are plotted in Figure 3. The measurements were performed over the temperature range from 1250 to 2135 K at pressures of 100, 195, and 290 kPa. The absorption cross section is the product of the line strength and line shape function and is thus represented using pressure-independent line shape parameters.

Figure 4. Collisional broadening coefficients for the R(1) transition in the fundamental vibrational band of HF in Ar buffer gas as a function of temperature measured at pressures of 100 (circles), 195 (squares), and 290 (diamonds) kPa. The value at 296 K23 (solid triangle) is also indicated for reference. The solid line represents the fitted γ(T).

collisional broadening coefficients showed no variation with respect to the pressure, which indicates the applicability of the presumed Dicke narrowing coefficient. The temperature dependence of the collisional broadening coefficient can be expressed as γ(T) = γ(T0)(T/T0)n, where T0 is a reference temperature and the exponent n is the temperature-dependent coefficient. The reference value of the coefficient, γ(T0), is 0.286 cm−1 MPa−1 at T0 = 296 K.23 The temperaturedependent coefficient, n = −0.68, was obtained by a leastsquares fit, and the resultant γ(T) is plotted in Figure 4 as a solid line. The absorption cross sections at the R(1) line center calculated from the line strength and Rautian−Sobel’man line shape function using these parameters are also plotted in Figure 3. The peak absorption cross sections were reproduced with a relative root-mean-squares deviation of 2.6%. The overall

Figure 3. Peak absorption cross sections for HF at the R(1) transition in the fundamental vibrational band as a function of temperature at pressures of 100 (circles), 195 (squares), and 290 (diamonds) kPa in Ar buffer gas. Lines represent the peak absorption cross sections calculated from the line strength and Rautian−Sobel’man line shape function (see the text for details). 6834

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Table 1. Experimental Conditions and Rate Constants (k) for C2H5F Decomposition P5/kPa

T5/K

100 99 97 101 97 105 104 105 98 104 103 99 100 102 106 106 107 105 102 102 101 102 102 105 105 106 102 99 103 100 102 105 102

1018 1039 1051 1075 1099 1120 1138 1169 1173 1188 1208 1256 1265 1296 1314 1314 1322 1338 1338 1359 1368 1375 1380 1399 1403 1411 1425 1475 1482 1483 1502 1531 1560

X(C2H5F)a/ppm P5 ≈ 100 kPa 1000 1000 1000 1000 1000 200 200 200 1000 200 200 200 200 50 50 50 100 50 50 50 200 200 50 50 100 50 50 200 50 200 50 100 50

k/s−1 8.9 14 23 32 99 80 1.1 2.5 4.7 4.6 8.1 2.0 2.0 3.3 3.5 3.7 3.7 4.5 5.7 5.3 7.0 8.1 7.7 1.1 1.1 1.2 1.9 2.6 2.6 2.8 3.6 4.0 4.3

× × × × × × × × × × × × × × × × × × × × × × × × × × ×

102 102 102 102 102 103 103 103 103 103 103 103 103 103 103 103 103 104 104 104 104 104 104 104 104 104 104

a

uncertainty of the calculated peak absorption cross sections was estimated to be 5% based on the statistical error and uncertainties in the line strength21 and sample purity. C2H5F Decomposition Rate Constant. The rate constants for C2H5F decomposition are summarized in Table 1 and plotted in Figure 5 with the ST/TOF-MS data reported by Giri et al.8 and an earlier single-pulse shock tube measurement reported by Okada et al.1 Cadman et al.26 also reported hightemperature rate constants using a single-pulse shock tube method; however, the reliability of their data has been questioned due to the physical infeasibility of the measurement1,27 and thus are not plotted in Figure 5. The present rate constants in the low-temperature range below 1150 K are in excellent agreement with those reported by Okada et al.1 The pressure independence of the low-temperature rate constants (P5 = 100 kPa in this study and 330−1170 kPa in Okada et al.1) indicates that these rate constants are close to the high-pressure limit. Falloff behavior is clearly observed at higher temperatures. A small but appreciable pressure dependence is also visible at temperatures above 1500 K. The rate constants were found to be systematically larger, by a factor of ∼2, than the ST/TOFMS data8 that were obtained at pressures of ∼67 and ∼160 kPa (Ne buffer). However, such deviation is within the scatter and the experimental uncertainties of the rate constants specified in Figure 6 of ref 8.

P5/kPa

T5/K

102 101 97

1592 1644 1679

186 188 191 191 199 196 196 203 204 198 198 196 196 194 195 199 195 193

1106 1146 1194 1233 1310 1345 1347 1374 1380 1409 1475 1535 1539 1610 1616 1634 1648 1698

298 295 286 288 292 296 280 283

1360 1425 1487 1544 1615 1629 1697 1710

X(C2H5F)a/ppm P5 ≈ 100 kPa 50 100 50 P5 ≈ 195 kPa 200 200 200 50 50 50 100 200 200 50 50 100 50 50 100 200 50 50 P5 ≈ 290 kPa 100 100 100 100 100 50 100 50

k/s−1 5.5 × 104 7.9 × 104 9.7 × 104 74 1.7 4.2 9.8 2.6 5.3 5.5 8.2 8.4 1.2 2.5 4.9 4.9 8.7 9.2 1.2 8.6 1.3

× × × × × × × × × × × × × × × × ×

102 102 102 103 103 103 103 103 104 104 104 104 104 104 105 104 105

7.3 1.5 3.5 6.6 1.0 1.1 1.7 1.6

× × × × × × × ×

103 104 104 104 105 105 105 105

Initial mole fraction of C2H5F.

Figure 5. Arrhenius plot for the present and literature1,8 rate constants for the thermal decomposition of C2H5F. The solid line denotes the theoretical high-pressure limiting rate constant.8 Dotted, dashed, and dashed−dotted lines are the results from master equation calculations at pressures of 290, 195, and 100 kPa, respectively.

The lines in Figure 5 represent results from the master equation calculation28 performed using the SSUMES pro6835

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gram.29 In this calculation, the density of states of C2H5F was calculated from the rovibrational properties taken from Table 2 of ref 8, and the microscopic rate constant for the C2H5F decomposition was estimated by the inverse Laplace transform method30 using the high-pressure limiting rate constant parametrized in ref 8, which was based on the variational transition-state theory calculation. The collision frequencies are calculated using the Lennard-Jones collision parameters for C2H5F (σ = 4.4 Å and ε/kB = 300 K),8 Ar (σ = 3.5 Å and ε/kB = 93 K),31 and Ne (σ = 2.8 Å and ε/kB = 33 K).31 The difference of the buffer gas (Ar or Ne) was found to be negligible; therefore, only the results for Ar buffer are presented here. The collisional energy-transfer probability was estimated by the exponential-down model. The experimental rate constants are well reproduced with ⟨ΔEdown⟩ = 400 cm−1, as shown in Figure 5, the value of which is somewhat larger than that reported in ref 8 (280 cm−1 at 1400 K), which reflects the difference between the present and their experimental rate constants. However, considering that the present rate constants cover the broad temperature range from the near-high-pressure limit to the falloff region, they are considered to correctly describe the falloff behavior in the C2H5F decomposition. The rate constant calculated using the master equation calculation with ⟨ΔEdown⟩ = 400 cm−1 over the temperature range of 900−2000 K was fitted to the Troe formula32 as

(3) 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. (4) Tsang, W.; Lifshitz, A. Kinetic Stability of 1,1,1-Trifluoroethane. Int. J. Chem. Kinet. 1998, 30, 621−628. (5) 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. (6) 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. (7) 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. (8) 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. (9) Kiefer, J. H.; Santhanam, S.; Srinivasan, N. K.; Tranter, R. S.; Klippenstein, S. J.; Oehlschlaeger, M. A. Dissociation, Relaxation, and Incubation in the High-Temperature Pyrolysis of Ethane, and a Successful RRKM Modeling. Proc. Combust. Inst. 2005, 30, 1129− 1135. (10) Oehlschlaeger, M. A.; Davidson, D. F.; Hanson, R. K. HighTemperature Ethane and Propane Decomposition. Proc. Combust. Inst. 2005, 30, 1119−1127. (11) Hanson, R. K. Applications of Quantitative Laser Sensors to Kinetics, Propulsion and Practical Energy Systems. Proc. Combust. Inst. 2011, 33, 1−40. (12) 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, DOI: 10.1016/ j.pecs.2014.05.001. (13) 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. (14) Koshi, M.; Yoshimura, M.; Fukuda, K.; Matsui, H.; Saito, K.; Watanabe, M.; Imamura, A.; Chen, C. Reactions of Nitrogen (N(4S)) Atoms with Nitric Oxide and Hydrogen. J. Chem. Phys. 1990, 93, 8703−8708. (15) Michael, J. V.; Sutherland, J. W. The Thermodynamic Dtate of the Hot Gas behind Reflected Shock Waves: Implication to Chemical Kinetics. Int. J. Chem. Kinet. 1986, 18, 409−436. (16) Michael, J. V. Rate Constants for the Reaction O+D2 → OD+D by the Flash Photolysis-Shock Tube Technique over the Temperature range 825−2487 K: The H2 to D2 Isotope Effect. J. Chem. Phys. 1989, 90, 189. (17) Webb, D. U.; Narahari Rao, K. Vibration Rotation Bands of Heated Hydrogen Halides. J. Mol. Spectrosc. 1968, 28, 121−124. (18) 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. (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) Bott, J. F.; Cohen, N. Shock-Tube Studies of HF Vibrational Relaxation. J. Chem. Phys. 1971, 55, 3698−3706. (21) 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. (22) Rautian, S. G.; Sobel’man, I. I. The Effect of Collisions on the Doppler Broadening of Spectral Lines. Phys.-Usp. 1967, 9, 701. (23) Pine, A. S. Line Shape Asymmetries in Ar-Broadened HF (ν = 1−0) in the Dicke-Narrowing Regime. J. Chem. Phys. 1994, 101, 3444−3452.

k∞ = 5.50 × 1013 exp( − 30068 K/T ) s−1 k 0 = 3.04 × 1045T −14.94 exp(− 38096 K/T ) cm3 molecule−1 s−1

Fcent = 0.651 exp( −T /1496)

where k∞ and k0 are the high-8 and low-pressure limiting rate constants and Fcent is the broadening factor.

4. CONCLUSION The rate constants for the thermal unimolecular decomposition of C2H5F were measured over the temperature range of 1018− 1710 K at pressures of 100, 195, and 290 kPa behind reflected shock waves by the sensitive laser absorption detection of HF. The measurements covered both the low-temperature regime, where the rate constants are close to the high-pressure limit, and the high-temperature regime, where the falloff effect is significant. The derived rate constants were well reproduced by the master equation calculation with ⟨ΔEdown⟩ = 400 cm−1. The peak absorption cross section of the R(1) transition in the fundamental vibrational band of HF was also determined and parametrized using the Rautian−Sobel’man line shape function, which will enable future quantitative studies on the thermal decomposition of a variety of hydrofluorocarbons.

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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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