High-Temperature Measurements of the Reactions of OH with

Article pubs.acs.org/JPCA

High-Temperature Measurements of the Reactions of OH with Ethylamine and Dimethylamine Sijie Li,* Enoch Dames, David F. Davidson, and Ronald K. Hanson Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States S Supporting Information *

ABSTRACT: The overall rate constants of hydroxyl radicals (OH) with ethylamine (EA: CH3CH2NH2) and dimethylamine (DMA: CH3NHCH3) were investigated behind reflected shock waves using UV laser absorption of OH radicals near 306.7 nm. tert-Butyl hydroperoxide (TBHP) was used as the fast source of OH at elevated temperatures. Test gas mixtures of individual amines and TBHP, diluted in argon, were shock-heated to temperatures from 901 to 1368 K at pressures near 1.2 atm. The overall rate constants were determined by fitting the measured OH time-histories with the computed profiles using a detailed mechanism developed by Lucassen et al. (Combust. Flame 2012, 159, 2254−2279). Over the temperature range studied, the measured rate constants can be expressed as kEA+OH = 1.10 × 107·T1.93 exp(1450/T) cm3 mol−1 s−1, and kDMA+OH = 2.26 × 104·T2.69 exp(1797/T) cm3 mol−1 s−1. Detailed error analyses were performed to estimate the overall uncertainties of the measured reaction rate constants, and the estimated (2σ) uncertainties were found to be ±31% at 901 K and ±22% at 1368 K for kEA+OH, and ±29% at 925 K and ±21% at 1307 K for kDMA+OH. Variational transition state theory was used to compute the H-abstraction rates by OH for ethylamine and dimethylamine, with the potential energy surface, geometries, frequencies, and electronic energies calculated by Galano and Alvarez-Idaboy (J. Chem. Theory Comput. 2008, 4, 322−327) at CCSD(T)/6-311++G(2d,2p) level of theory. The calculated reaction rate constants are in good agreement with the experimental data.

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presence of H2 as a source of OH.12 Galano and Alvarez-Idaboy analyzed the different reaction channels of methylamine, dimethylamine, and ethylamine with OH, using variational transition-state theory.13 Geometry optimization and frequency calculations were performed at the BH&HLYP/6-311++G(2d,2p) level of theory, with electronic energy values improved by single-point calculations at the CCSD(T) level of theory and using the same basis set. The overall reaction rate constants and the branching ratios for reactions of amine with OH were reported within the temperature of 290−310 K.13 Recently, Lucassen et al. studied the laminar premixed flames of dimethylamine and ethylamine under one-dimensional lowpressure conditions.8 A detailed combustion model was developed to analyze the major pathways in those two flames, which successfully reproduced many trends observed in the flame experiments. To the authors’ best knowledge, there is no direct experimental or theoretical study of the reactions of aliphatic amines with OH under combustion conditions. The present work determines the reaction rate constants for the overall reaction of ethylamine (EA, CH3CH2NH2; CAS, 75−04−7)

INTRODUCTION The reaction kinetics of aliphatic amines is relevant to both atmospheric chemistry and combustion processes. In the context of atmospheric chemistry, aliphatic amines are potential precursors of HCN and stratospheric NOx.1−3 Additionally, the degradation of dimethylamine within the environment can lead to carcinogenic nitrosamines.4 In the context of combustion, the amino group is a common functional group to bioderived fuels.5−9 In previous studies, morpholine (C4H9NO, 1-oxa-4aza-cyclohexane), which is a 6-membered cyclic amine, was chosen as a representative candidate for a nitrogen-containing biofuel compound.6,7,9 More detailed investigation of smaller aliphatic amine is needed to aid understanding of the combustion chemistry of morpholine. Experimental and computational studies of the reactions between aliphatic amines and OH are scarce. Atkinson et al. investigated the reactions of methylamine (MA, CH3NH2; CAS, 74−89−5) with OH over the temperature range of 299− 426 K using a flash photolysis-resonance fluorescence technique.10 The same method was used to measure the rate constants for the reactions of dimethylamine, ethylamine, and trimethylamine with OH over the temperature range of 298− 426 K.11 Carl et al. studied the reaction rate constants of aliphatic amines with OH at 295 K, including those for methylamine, dimethylamine, ethylamine, and trimethylamine, using the sequential two-photon dissociation of NO2 in the © 2013 American Chemical Society

Received: November 12, 2013 Revised: December 11, 2013 Published: December 13, 2013 70

dx.doi.org/10.1021/jp411141w | J. Phys. Chem. A 2014, 118, 70−77

The Journal of Physical Chemistry A

Article

Figure 1. Schematic of the shock tube/laser absorption diagnostic setup.

shock tube wall. Since each TBHP decomposes nearinstantaneously to form one OH, the TBHP concentrations were determined based on the peak OH value for each experiment. Before the experiment, controlled mixtures of fuel diluted in argon were made; the amine concentrations were then confirmed by sampling a portion of the mixture, after filling into the shock tube, from near the endwall to an external multipass cell with 29.9 m path length. The fuel concentration in the multipass cell was measured using a Jodon helium−neon laser at 3.39 μm, and Beer’s law was used to convert the measured absorption data to the fuel mole fraction. Further details about this laser diagnostic of fuel are reported elsewhere.16 The absorption cross-sections of ethylamine and dimethylamine from the PNNL database were used in the Beer’s law concentration calculation, and the measured fuel concentrations were consistent with the manometric values to within ±5%, which gave us more confidence in the manometric values. The manometric fuel concentrations were used for comparisons with simulations. The chosen wavelength for OH diagnostic was the peak of the well-characterized R1(5) absorption line near 306.7 nm in the OH A−X (0,0) band. Visible light near 613.4 nm was generated by pumping Rhodamine 6G dye in a Spectra Physics 380 laser cavity with the 5 W, continuous wave, output of a Coherent Verdi laser at 532 nm. The 613.4 nm visible light was intracavity frequency-doubled using a temperature-tuned AD*A nonlinear crystal to generate ∼1 mW of light near 306.7 nm. Using a common-mode rejection detection setup, a minimum OH detection sensitivity of ∼0.5 ppm could be achieved. Low TBHP and fuel concentrations were used for the experiment, and temperature changes during the test time were less than 0.5%; thus, a constant OH absorption cross-section throughout the entire test time was used for each shock tube experiment. The details of the OH laser diagnostic setup have been discussed previously,15,17 and a schematic for the OH diagnostic can be found in Figure 1.

and dimethylamine (DMA, CH3NHCH3; CAS, 124−40−3) with OH. EA + OH = products

(R1)

DMA + OH = products

(R2)

The OH radical was generated by near-instantaneous pyrolysis of tert-butyl hydroperoxide (TBHP; CAS, 75−91−2). The pseudo-first order decay of OH behind reflected shock waves was monitored using laser absorption at 306.7 nm, and the reaction rate constants of amine with OH were inferred from the measured OH time-histories. Variational transition state theory was used to compute the H-abstraction rates by OH for ethylamine and dimethylamine, with potential energy surface geometries, frequencies, and electronic energies calculated by Galano and Alvarez-Idaboy at CCSD(T)/6-311++G(2d,2p) level of theory.13 The calculated reaction rate constants are in good agreement with the experimental data. We believe the current work presents the first high-temperature measurements and theoretical study of the overall reaction rate constants for ethylamine and dimethylamine with OH.

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EXPERIMENTAL SETUP The overall rate constants of hydroxyl radicals (OH) with ethylamine and dimethylamine were studied behind reflected shock waves in a shock tube that has a 3.35 m driver section and an 8.54 m driven section, both with an inner diameter of 14.13 cm. The incident shock speeds were measured using five piezoelectric pressure transducers near the driven section endwall. Temperature and pressure behind shocks were calculated based on one-dimensional shock relations. More details concerning this shock tube can be found in refs 14 and 15. Between experiments, the shock tube was routinely evacuated to ∼5 μTorr to ensure purity of the test mixtures. The chemicals used in the experiments include 97% ethylamine, anhydrous ≥99% dimethylamine, and a solution of 70%, by weight, tert-butyl hydroperoxide (TBHP) in water, all supplied by Sigma-Aldrich with no further purification. Research grade argon (99.99%) supplied by Praxair was employed as the bath gas. All the mixtures were prepared manometrically using a double-dilution method in a 12 L electro-polished stainless steel tank, and mixed with a magnetically driven stirring vane for at least one hour prior to the experiments. The double-dilution method was employed to allow for more accurate pressure measurements in the manometric preparation of mixtures, especially for the current mixtures with low fuel concentrations. Before each experiment, the shock tube was passivated to avoid loss of amine to the

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KINETIC MEASUREMENTS

Experiments were performed behind reflected shock waves over the temperature range of 901−1368 K and pressures near 1.2 atm. tert-Butyl hydroperoxide (TBHP) was used as the OH radical precursor. At temperatures greater than 1000 K, TBHP dissociates near-instantaneously to form an OH radical and a tert-butoxy radical. The tert-butoxy radical, (CH3)3CO, further dissociates into acetone and a methyl radical. TBHP also reacts with OH radical to form other products. The TBHP chemistry set can be describe as follows: 71



Article

Table 1. Reactions Describing EA and DMA + OH Experiments rate constant (cm3 mol−1 s−1) number

reaction

1 2 3 4 5 6 7 8

EA + OH = products DMA + OH = products TBHP = (CH3)3CO + OH (CH3)3CO = CH3COCH3 + CH3 TBHP + OH = H2O + O2 + tert-C4H9 TBHP + OH = H2O + HO2 + iso-C4H8 CH3 + OH + M = CH3OH + M CH3 + OH = CH2(s) + H2O

TBHP = (CH3)3 CO + OH

3.57 1.26 2.30 2.49 1.73 1.65

A

m

× × × × × ×

see text see text 0 0 0 0 1.41 0

1013 1014 1013 1013 108 1013

E

ref

3.575 × 104 1.530 × 104 5.223 × 103 2.655 × 103 −3.32 × 104 0

this work this work 15 15 15 15 24 15

EA + OH = CH 2CH 2NH 2 + H 2O

(R3)

(R1c)

8

(CH3)3 CO = CH3COCH3 + CH3

(R4)

TBHP + OH = H 2O + O2 + tert ‐C4 H 9

(R5)

TBHP + OH = H 2O + HO2 + iso‐C4H8

(R6)

In the Lucassen et al. mechanism, the reaction rate constant for reaction R1a was estimated by analogy to methylamine + OH, with k1a = 2.4× 106 T2 exp(−447[cal/mol]/RT) cm3 mol−1 s−1 from Dean and Bozzelli.29 The theoretical study by Galano and Alvarez-Idaboy shows that channel R1b contributes ∼98% of the total ethylamine + OH rate within the temperature range 290−310 K13 and was assumed to be the dominant channel by Lucassen et al. Thus, the overall reaction rate constant measured by Carl et al. at 295 K12 was used by Lucassen et al. for this channel with k1b = 1.4× 1013 cm3 mol−1 s−1. For, reaction R1c, Lucassen et al. estimated the reaction rate constant to be k1c = 1.6× 1012 exp(−1300[cal/mol]/RT) cm3 mol−1 s−1, by analogy to CH3CH2OH + OH.30 A sensitivity analysis for OH radical, using the Lucassen et al. mechanism with the TBHP chemistry set as in Table 1, in the mixture of 470 ppm ethylamine with 50 ppm TBHP and 140 ppm water in argon at 1067 K and 0.83 atm, is shown in Figure 2. The OH sensitivity is defined as SOH = (∂XOH/∂ki) × (ki/

Further details about the TBHP chemistry set can be found in the literature.15,17−21 The rate constants for reactions R3, R5, and R6 were adopted from Pang et al.,15 and the reaction rate constant for reaction R4 was obtained from Choo and Benson.22 The thermodynamic parameters for TBHP and tert-butoxy radical were taken from the thermodynamic database by Goos et al.23 Methyl radical is formed in reaction R4, and previous works15,17 have shown that the accuracy of the CH3 + OH rate constant around 1.5 atm is important for accurate determination of the fuel + OH reaction rate constant. There are two channels for CH3 + OH: CH3 + OH + M = CH3OH + M

(R7)

CH3 + OH = CH 2(s) + H 2O

(R8)

Reaction R7 was updated using the results from Srinivasan et al.24 at ∼0.3−1.1 atm, and their values agree well with the theoretical study by Jasper et al.25 and the measured values from Vasudevan et al. at 1.3 atm.18 The rate constant for reaction R8 was updated with the value measured by Pang et al.,15 which agrees well with the values by Srinivasan et al.24 and Vasudevan et al.18 Sangwan et al. recently measured the reaction rate for reaction R8 over the temperature range of 294−714 K.26 The rate constant for reaction R8 by Pang et al. also agrees with extrapolation of the Sangwan et al. results, within the uncertainty limit used for error analysis in the following sections. The rate constants for reactions R3−R8 are provided in Table 1. The same set of reaction rate constants for TBHP chemistry has been used before by Lam et al.21,27 The above TBHP chemistry set was implemented into the base ethylamine and dimethylamine mechanism developed by Lucassen et al.8 and was used for the current study. The CHEMKIN PRO28 package was used to simulate the OH timehistories, with the standard constant energy and volume assumption. Ethylamine (EA) + OH. The reaction of ethylamine with OH consists of 3 different channels: EA + OH = CH3CH 2NH + H 2O

(R1a)

EA + OH = CH3CHNH 2 + H 2O

(R1b)

Figure 2. Sensitivity analysis of OH using the Lucassen et al. mechanism8 with inclusion of TBHP chemistry, in a mixture of 470 ppm EA, 50 ppm TBHP, and 190 ppm H2O, in Ar at 1067 K and 0.83 atm.

XOH), where XOH is the local OH mole fraction and ki is the rate constant for reaction i. As can be seen in Figure 1, the fast formation of OH is controlled by TBHP decomposition, reaction R3, and the ethylamine + OH reaction dominants the OH removal process. Reaction R8 is the most important secondary reaction that affects OH time-histories at the later times, with smaller contributions from OH + H 2 = H + H 2O 72

(R9)


The Journal of Physical Chemistry A CH3OH + H = CH 2OH + H 2

Article

(R10)

The effects of the secondary reactions are included in the error analysis, and no modification to reactions R9 and R10 in the Lucassen et al. mechanism was made. Illustrated in Figure 3 is a sample measured OH time-history in the mixture of 470 ppm ethylamine with 50 ppm TBHP and

Figure 4. Error analysis for measured k1 in 470 ppm EA/Ar with 50 ppm TBHP and 190 ppm H2O, at 1067 K and 0.83 atm.

in a root-sum-squared method to yield a total uncertainty of ±26% for the rate constant k1 at 1067 K. Similar experiments were carried out over the temperature range of 901−1368 K and pressures of 0.83−1.64 atm, with the measured overall rate constant summarized in Table 2. Different initial ethylamine concentrations were implemented to confirm the pseudo-first order kinetics in OH.

Figure 3. Sample OH trace in a mixture of 470 ppm EA, 50 ppm TBHP, and 190 ppm H2O, in Ar at 1067 K and 0.83 atm.

140 ppm water in argon at 1067 K and 0.83 atm. Under the current pseudo first-order conditions, the OH removal process is close to be an exponential decay and nearly linear on a semilog plot. The Lucassen et al. mechanism with the TBHP chemistry set was used to simulate the experimental data, and a best-fit overall rate constant for reaction R1 of 1.8 × 1013 cm3 mol−1 s−1 was obtained between the experiment and the simulation, as is presented in Figure 3. Also shown in Figure 3 are the simulations for the perturbations of ±50% in the best-fit overall rate constant. No discernible effect, due to the branching ratio of reaction R1, on the overall reaction rate determination was observed, and the branching ratios proposed by Lucassen et al. were kept in the simulations. It is worth noting that the presence of H2O in the test mixture has no noticeable influence on the simulated OH profiles. A detailed error analysis was conducted to evaluate the overall uncertainty of the measured rate constant for reaction R1 in the mixture of 470 ppm ethylamine with 50 ppm TBHP and 140 ppm water in argon at 1067 K and 0.83 atm. The primary sources of uncertainty for the rate constant determination include 2σ uncertainties in (a) pressure (±1%), (b) temperature (±1%), (c) mixture composition (±5%), (d) OH absorption cross-section (±3%), (e) fitting data (±5%), (f) the rate constant for TBHP = tert-butoxy + OH (reaction R3, ± 30%), (g) the rate constant for CH3 + OH = CH2(s) + H2O (reaction R8, uncertainty factor used = 2), (h) the rate constant for OH + H2 = H + H2O (reaction R9, ± 25%), and (i) the rate constant for CH3OH + H = CH2OH + H2 (reaction R10, ± 50%). Figure 4 shows the contributions from each source of uncertainty, which were obtained by perturbing each uncertainty source to its error limits and refitting an overall rate constant for reaction R1. The uncertainty in reaction R8 is the major contributor to the measured rate constant k1, and no noticeable influence on k1 determination due to the known uncertainties in reactions R3, R9, and R10 was observed. All the uncertainties were combined

Table 2. Measured Rate Constants for EA + OH = Products T (K) 901 946 959 1067 1082 1154 1178 1288 1295 1368 910 960 1017 1126 1165 1259

P (atm)

k1 × 10−13 (cm3 mol−1 s−1)

50 ppm TBHP, 470 ppm EA, Ar 1.00 1.50 0.92 1.55 0.83 1.60 0.83 1.80 1.64 1.83 1.64 1.88 1.48 1.95 1.38 2.20 1.29 2.20 1.22 2.40 27 ppm TBHP, 670 ppm EA, Ar 1.12 1.52 1.13 1.60 1.11 1.70 1.07 1.85 1.00 1.90 0.98 2.05

Figure 5 presents an Arrhenius plot for the overall rate constant k1 over the temperature range of 901−1368 K and pressures of 0.83−1.64 atm. Similar error analyses as in Figure 4 were carried out for 901 and 1368 K, and the uncertainties were estimated to be ±31% and ±22%, respectively. Also shown in Figure 5 is the estimated overall rate constant by Lucassen et al., which underpredicts the observed activation energy. On the basis of extrapolation of the current study to higher temperatures, the reaction rates for EA + OH = products used in Lucassen et al. might be lower than the actual values at flame temperatures. 73



Article

Figure 5. Measured overall reaction rates for EA + OH = products, in comparison with the estimation by Lucassen et al.8

Figure 7. Sample OH trace in 320 ppm DMA/Ar with 22 ppm TBHP and 134 ppm H2O, at 1176 K and 0.9 atm.

Dimethylamine (DMA) + OH. The reaction of dimethylamine with OH consists of 2 different channels:

the simulation. Also shown in Figure 7 are the simulations for the perturbations of ±50% in the best-fit overall rate constant. Note in this figure that nonkinetic effects, i.e., laser beam steering by the shock passage, contribute to the measured absorption profiles at times before t = 0. As was done for the ethylamine with OH reactions, the branching ratios by Lucassen et al. were kept the same in the simulations. Under the current pseudo first-order conditions, OH decays exponentially and is close to a straight line in the semilog plot of Figure 7. A detailed error analysis was conducted to evaluate the overall uncertainty of the measured rate constant for reaction R2 in the mixture of 320 ppm dimethylamine with 22 ppm TBHP and 140 ppm water in argon at 1176 K and 0.9 atm. The primary sources of uncertainty for the rate constant determination include 2σ uncertainties in (a) pressure (±1%), (b) temperature (±1%), (c) mixture composition (±5%), (d) OH cross-section (±3%), (e) fitting data (±7%), (f) the rate constant for TBHP = tert-butoxy + OH (reaction R3, ± 30%), (g) the rate constant for CH3 + OH = CH2(s) + H2O (reaction R8, uncertainty factor used = 2), (h) the rate constant for CH3 + CH2 = C2H4 + H (uncertainty factor used = 2), and (i) the rate constant for CH3NHCH2 = CH3 + CH2NH (uncertainty factor used = 2). Figure 8 presents the contributions from each source of uncertainty, which were obtained by perturbing each uncertainty source to its error limits and refitting an overall rate constant for reaction R2. The uncertainty in reaction R8 is the major contributor to the measured rate constant k2, and no significant influence on k2 determination was observed due to the uncertainties in other secondary reactions. All the uncertainties were combined in a root-sum-squared method to yield a total uncertainty of ±26% in the rate constant k2 at 1176 K. Similar tests were carried out for the reaction of DMA with OH, over the temperature range of 925−1307 K and pressures of 0.89−1.24 atm, with the measured overall rate constants summarized in Table 3. Different initial dimethylamine concentrations were implemented to confirm the pseudo-first order kinetics in OH. Figure 9 presents the Arrhenius plot for the overall rate constant k2 over the temperature range of 925−1307 K and pressures of 0.89−1.24 atm, together with the estimation by Lucassen et al.8 Lucassen et al. assumed a constant reaction rate, and this value overpredicts the measured reaction rate

DMA + OH = CH3NHCH 2 + H 2O

(R2a)

DMA + OH = CH3NCH3 + H 2O

(R2b)

In the Lucassen et al. mechanism, the total rate constant of DMA with OH at 295 K measured by Carl et al.,12 and the branching ratio by Galano and Alvarez-Idaboy at 295 K13 was used for all temperatures, with k2a = 2 × 1013 cm3 mol−1 s−1 and k2b = 1.9 × 1013 cm3 mol−1 s−1. An OH sensitivity analysis was carried out for the overall rate constant determination of reaction R2 (k2 = k2a + k2b) in the mixture of 320 ppm DMA with 22 ppm TBHP (and 140 ppm water) diluted in argon, at 1176 K and 0.9 atm. As illustrated in Figure 6, the sensitivity analysis shows that reaction 2 is the

Figure 6. Sensitivity analysis of OH using the Lucassen et al. mechanism8 with TBHP chemistry set, in the mixture of 320 ppm DMA/Ar with 22 ppm TBHP and 140 ppm H2O, at 1176 K and 0.9 atm.

dominant reaction with minor interferences from secondary reactions. The measured OH time-history under the same conditions is shown in Figure 7. The Lucassen et al. mechanism with the TBHP chemistry set was used to simulate the experimental data, and a best-fit overall rate constant of k2 = 3 × 1013 cm3 mol−1 s−1 was obtained between the experiment and 74



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Table 3. Measured Rate Constants for DMA + OH = Products

925 995 1016 1170 926 1141 1176 1278 1307 978 1010 1088 1187 1218 1276

P (atm)

THEORETICAL STUDY

To the authors’ best knowledge, there are no theoretical studies for the reaction rates of methylamine and ethylamine + OH at high temperature. Galano and Alvarez-Idaboy performed CCSD(T)/6-311++G(2d,2p) single-point calculations along the internal reaction coordinates corresponding to various Habstraction pathways for DMA and EA + OH.13 They initially explored the potential energy surface through DFT calculations at the BH&HLYP/6-311++G(2d,2p) level of theory and then used refined CCSD(T)/ energies for both conventional and variational transition state theory (VTST) to compute Habstraction rates by OH for various channels in DMA and EA for the temperature range of 298−310 K. In this work, analogous calculations were performed for the temperature range of 800−1300 K, with all geometries, frequencies, and electronic energies adopted from the work of Galano and Alvarez-Idaboy.13 Eckart tunneling corrections were included but are expected to be negligible at the temperatures of this work. Multiwell 201331−33 was used for all calculations. For DMA + OH, internal degrees of freedom corresponding to CH3 and OH rotations were treated as internal hindered rotors. For EA + OH, internal degrees of freedom corresponding to NH2, CH3, and OH rotations were treated as internal hindered rotors. Because not all possible pathways were explored at the CCSD(T) level of theory, stereochemical and symmetry information required for calculation of reaction path degeneracy was not available for all reaction pathways. Thus, reaction path degeneracy was determined by multiplying the rate for a specific channel by the number of equivalent H-atoms. The electronic energies at 0 K, relative to corresponding reactants, and rotational data used in the VTST calculations can be found in Table 4. The transition states for EA + OH (R1) are referred to as TS_1a, TS_1b, and TS_1c for three channels, and the transition states for DMA + OH (R2) are referred to as TS_2a and TS_2b for two channels, respectively. The vibrational frequencies computed at the BH&HLYP/6-311+ +G(2d,2p) level of theory, previously computed by Galano and Alvarez-Idaboy,13 are provided as the Supporting Information. For the three abstraction channels in EA + OH treated by VTST, each corresponding transition state is geometrically fixed over the temperature range of 800−1300 K, corresponding to HO−H distances of 1.284 Å (R1a), 1.493 Å (R1b), and 1.279 Å (R1c). The same observation was made for the two abstraction channels of DMA + OH that were treated with VTST, each corresponding transition state is geometrically fixed over the temperature range of 800−1300 K, corresponding to HO−H distances of 1.559 Å (R2a) and 1.485 Å (R2b). The resulted reaction rate constants using VTST are presented in Table 5. The authors note that it is more appropriate to compute the rates for these systems using modern comprehensive methods like multistructural and multipath VTST while accounting for torsional anharmonicity,35 or with direct trajectory simulations. However, there is evidently a fortuitous cancellation of errors for the VTST calculations performed here, as total rate constants R1 and R2 only need to be slightly changed in order to bring the predictions into good agreement with the experimental data. Compared in Figure 10 are the computed results with the experimental data, for the overall reaction rates of DMA and EA + OH, with the calculated total rate constants R1 and R2 slightly changed (increase of 13% for R1 and a decrease of 20% for R2).

Figure 8. Error analysis for measured k2 in 320 ppm DMA/Ar with 22 ppm TBHP and 134 ppm H2O, at 1176 K and 0.9 atm.

T (K)

Article

k2 × 10−13 (cm3 mol−1 s−1)

60 ppm TBHP, 440 ppm DMA, Ar 0.99 2.80 1.24 2.90 0.93 3.00 1.16 3.15 22 ppm TBHP, 320 ppm DMA, Ar 1.16 2.80 1.16 3.15 0.89 3.20 1.17 3.40 1.04 3.50 30 ppm TBHP, 570 ppm DMA, Ar 1.14 2.90 1.08 2.95 1.09 3.10 1.02 3.20 0.99 3.30 0.98 3.46

Figure 9. Measured overall reaction rate for k2: DMA + OH = products, in comparison with the estimation by Lucassen et al.8

constant. Similar error analyses as in Figure 8 were carried out for 925 and 1307 K, and the uncertainties were estimated to be ±29% and ±21%, respectively. 75



Article

Table 4. Summary of the Zero Kelvin Electronic Energies and Rotational Data Used for VTST Calculations external rotorsb species EA TS_1a TS_1b TS_1c DMA TS_2a TS_2b OH

a

E (kcal/mol)

inactive

c

0.283 0.090 0.115 0.082 0.296 0.104 0.136 19.24

−1.26 −1.62 3.54 −0.393 −2.39

internal rotorse d

active

V0,1

sym

V0,2

sym

1.112 0.842 0.276 0.821 1.181 0.354 0.289

1050 40.1 8.91 12.7 1155 10.6 3.4

3 1 1 1 3 1 1

700 1050 1050 1050 1155 1155 1155

1 3 3 3 3 3 3

V0,3

sym

700 700 700

1 1 1

1155 1155

3 3

a

Relative to reactants; all geometries, frequencies, and electronic energies were adopted from the work of Galano and Alvarez-Idaboy.13 bUnits of all rotational data are in cm−1. cTwo-dimensional (all symmetry number σ = 1). dOne-dimensional (all symmetry number σ = 1). eRotor barriers for CH3 and NH2 are estimated from Benson;34 internal rotational barriers for OH estimated as B = 420 cm−1 and the potential calculated as V = v2/B,31 where v is the vibrational frequency associated with the OH rotation and B is its estimated rotational constant.

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CONCLUSIONS The overall rate constants of hydroxyl radicals (OH) with ethylamine (EA, CH3CH2NH2) and dimethylamine (DMA, CH3NHCH3) were investigated using UV laser absorption of OH radicals near 306.7 nm, behind reflected shock waves over the temperature range of 901 to 1368 K and at pressures near 1.2 atm. Over the temperature range studied, the measured values can be expressed as kEA+OH = 1.10 × 107·T1.93 exp(1450/ T) cm3 mol−1 s−1, and kDMA+OH = 2.26 × 104·T2.69 exp(1797/T) cm3 mol−1 s−1. Detailed error analyses were performed to estimate the overall uncertainties of these reactions, and the estimated (2σ) uncertainties were found to be ±31% at 901 K and ±22% at 1368 K for kEA+OH, and ±29% at 925 K and ±21% at 1307 K for kDMA+OH. Variational transition state theory was used to compute the H-abstraction rates by OH for ethylamine and dimethylamine, with potential energy surface geometries, frequencies, and electronic energies calculated by Galano and Alvarez-Idaboy13 at CCSD(T)/6-311++G(2d,2p) level of theory. The calculated reaction rate constants are in good agreement with the experimental data. To the authors’ best knowledge, the current work presents the first direct hightemperature measurements and theoretical study of the overall rate constants for ethylamine and dimethylamine with OH.

Table 5. VTST Reaction Rate Constants of Individual Channels for EA and DMA + OH rate constant (cm3 mol−1 s−1) number 1a 1b 1c 2a 2b

reaction

A

m

E

5

EA + OH = CH3CH2NH + H2O EA + OH = CH3CHNH2 + H2O EA + OH = CH2CH2NH2 + H2O DMA + OH = CH3NHCH2 + H2O DMA + OH = CH3NCH3 + H2O

1.12 × 10

2.36

−2.86 × 103

3.28 × 105

2.24

−3.04 × 103

7.94 × 102

2.97

−1.04 × 102

5.73 × 106

2.09

−1.37 × 103

6.07 × 105

2.11

−3.21 × 103

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ASSOCIATED CONTENT

S Supporting Information *

Vibrational frequencies computed at the BH&HLYP/6-311+ +G(2d,2p) level of theory by Galano and Alvarez-Idaboy.13 This material is available free of charge via the Internet at http://pubs.acs.org.

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Figure 10. Comparison of the measured reaction rates and theoretical study results for DMA + OH and EA + OH.

AUTHOR INFORMATION

Corresponding Author

*(S.L.) E-mail: [email protected]. The authors also note this change in total rate is justified considering the relatively large uncertainty in the overall predicted rate constants. The largest potential sources of errors lie in the fact that only one 1-D potential surface was employed per reaction channel, that internal rotor barrier heights are estimated or obtained from group additivity contributions, and that reaction path degeneracy cannot be rigorously defined, as has been outlined in a previous work,36 without further ab initio calculations. Considering all this, the uncertainty in the computed rate constants is likely a factor of 2 or larger.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The experimental work was supported by the Army Research Office/Multidisciplinary University Research Initiative (ARO/ MURI) with Dr. Ralph A. Anthenien as the contract monitor. The VTST calculation work was supported by the Combustion Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Basic Energy Sciences under Award Number DE-SC0001198. We would like to thank Annia 76



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Galano and J. Raul Alvarez-Idaboy for providing information necessary to carry out the VTST calculations.

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High-Temperature Measurements of the Reactions of OH with

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