Determination of the Rate Constant for the NH2 (X2B1)+ NH2 (X2B1

Article pubs.acs.org/JPCA

Determination of the Rate Constant for the NH2(X2B1) + NH2(X2B1) Recombination Reaction with Collision Partners He, Ne, Ar, and N2 at Low Pressures and 296 K. Part 1 Gokhan Altinay and R. Glen Macdonald* Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439-4831, United States

ABSTRACT: The recombination rate constant for the NH2(X2B1) + NH2(X2B1) → N2H4(X1A1) reaction in He, Ne, Ar, and N2 was measured over the pressure range 1−20 Torr at a temperature of 296 K. The NH2 radical was produced by 193 nm laser photolysis of NH3 dilute in the third-body gas. The production of NH2 and the loss of NH3 were monitored by high-resolution continuous-wave absorption spectroscopy: NH2 on the 1221 ← 1331 rotational transition of the (0,7,0)A2A1 ← (0,0,0) X2B1 vibronic band and NH3 on either inversion doublet of the qQ3(3) rotational transition of the ν1 fundamental. Both species were detected simultaneously following the photolysis laser pulse. The broader Doppler width of the NH2 spectral transition allowed temporal concentration measurements to be extended up to 20 Torr before pressure broadening effects became significant. Falloff behavior was identified and the bimolecular rate constants for each collision partner were fit to a simple Troe form defined by the parameters, k0, kinf, and Fcent. This work is the first part of a two part series in which part 2 will discuss the measurements with more efficient energy transfer collision partners CH4, C2H6, CO2, CF4, and SF6. The pressure range was too limited to extract any new information on kinf, and kinf was taken from the theoretical calculations of Klippenstein et al. (J. Phys. Chem A 2009, 113, 10241) as kinf = 7.9 × 10−11 cm3 molecule−1 s−1 at 296 K. The individual Troe parameters were: He, k0 = 2.8 × 10−29 and Fcent = 0.47; Ne, k0 = 2.7 × 10−29 and Fcent = 0.34; Ar, k0 = 4.4 × 10−29 and Fcent = 0.41; N2, k0 = 5.7 × 10−29 and Fcent = 0.61, with units cm6 molecule−2 s−1 for k0. In the case of N2 as the third body, it was possible to measure the recombination rate constant for the NH2 + H reaction near 20 Torr total pressure. The pure three-body recombination rate constant was (2.3 ± 0.55) × 10−30 cm6 molecule−2 s−1, where the uncertainty is the total experimental uncertainty including systematic errors at the 2σ level of confidence.

I. INTRODUCTION The amidogen radical, NH2, plays an important role in interstellar, environmental, and combustion chemistry. As the simplest amine, it is a fundamental building block in generating more complex nitrogen containing species in the interstellar medium.1 As well, it is a useful marker for understanding the chemical environment of comets.2 The NH2 radical is generated from NH3 by H atom abstraction reactions in the troposphere and UV photolysis in the stratosphere; thus, the active atmospheric N atom balance is intimately related to the fate of the NH2 radical.3 In combustion chemistry, NH2 is a key species in the formation of NOX pollutants from nitrogen containing compounds in fuels.4 Also, the NH2 radical is an intermediate in several noncatalytic NOX removal strategies © 2012 American Chemical Society

based on the injection of various chemicals into exhaust gases: ammonia, Thermal deNOX; cyanuric acid, RAPRENOX; urea, NOXOUT.5 In all these cases, one of the most important reactions is the NH2 + NO reaction.6,7 With the increased emphasis on the combustion of renewable biomass to reduce the global carbon footprint, more fuel-fixed nitrogen will be volatilized as NH3; thus, there is an increased desire to further understand NH3 pyrolysis8 and combustion chemistry.9 Although the reaction kinetics of the NH2 radical with stable molecular species has been studied by a number of Received: November 23, 2011 Revised: January 5, 2012 Published: January 9, 2012 1353

dx.doi.org/10.1021/jp211297x | J. Phys. Chem. A 2012, 116, 1353−1367

The Journal of Physical Chemistry A

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investigators, its chemistry involving transient species is not as well-known. However, there have been a number of experimental studies of the NH2 + NH2 reaction in the presence a number of third bodies.10−16 This laboratory has recently reported on the study of the NH2 self-recombination reaction17 with N2, Ar, and CF4 as third bodies and the reaction18 of NH2 with NH and H. This new measurement of the self-recombination reaction rate constant was found to be significantly larger than the previous results in the literature. The present work is an extension of these measurements using an upgraded laser system and an improved data acquisition system in both hardware and software. New measurements of NH2 self-recombination in the presence of weak colliders, He, Ne, Ar, and N2 will be presented in the present work. At higher pressures in N2, it was possible to measure the recombination rate constant for the elementary reaction, NH2 + H + (N2) → NH3 + (N2). In conjunction with the present study, experiments were also made involving strong colliders, CH4, C2H6, CO2, CF4, and SF6 in which both NH2 + NH2 + (M) → N2H4 + (M) and NH 2 + H + (M) → NH 3 + (M) could be measured for all collision partners. This work 19 will be presented in part 2. Recently, Klippenstein et al. 20 reported on a joint experimental and theoretical study of the thermal decomposition of hydroxylamine, NH2OH. They also provided theoretical estimates for rate constants for a number of reactions involved in secondary chemistry occurring in the NH3/NH2 system. The interaction of two NH2 radicals leads to singlet and triplet potential energy surfaces (PESs). Klippenstein et al.20 calculated the stationary points on both PESs at the CCSDT(T)/CBS//CCSD(T)/aug-cc-pvdz level of theory and augmented these calculations at the CASPT2(4e,4o) level of theory to improve the accuracy of the calculated barrier height on the triplet PES. These calculations clearly show that the barriers leading to H2 + N2H2(isomers) on the singlet surface are sufficiently high that these product channels will not contribute to products near room temperature. Thus the NH2 + NH2 reaction proceeds as

The NH2 + NH2 recombination reaction is an excellent candidate to compare theoretical calculations of radical association reactions to experimental values because the PESs for both spin manifolds have been explored at a high level of electronic structure theory.20 These calculations show that near 300 K only the recombination channel leading to a single product contributes significantly to the chemical removal of NH2. The NH2 radial can be detected with high sensitivity by high-resolution electronic absorption spectroscopy, and the NH3 molecule can be detected with modest sensitivity using rotational transitions of the v1 fundamental vibrational band with known line strengths. The 193 nm photolysis of NH3 produces NH2 + H with near unit quantum efficiency;18 thus, by monitoring the production of NH2 and the loss of NH3 simultaneously, the absorption coefficient for NH2 transition is directly determined.

II. EXPERIMENTAL SECTION The experimental reaction chamber has been slightly modified from previous work.17,18 The inner Teflon box was removed to increase the distance between the photolysis zone and the chamber walls. As described in previous studies,17,18 the absorption path length was increased using White cell optics contained in side chambers. The distance between the UV− IR dichroic mirror and a ZnS plate defined the base optical distance of the absorption path length. Power loss of the red diode laser radiation limited the number of passes through the photolysis region to twelve, giving a total path length of 1680 cm. The carrier gases were used directly from their cylinders and continuously flowed through the reaction chamber at flow rates varying from 300 to 1000 sccm. The flow rates were measured by in situ calibrated mass-flow meters. The gases used, with supplier and purity, were as follows: He, AGA 99.999%; Ne, Airgas 99.995%; Ar, AGA 99.9995%, N2; Airgas 99.995%; CF4, Linde 99.99%. The NH3 was supplied by AGA with a purity of 99.99% but was admitted to the reaction chamber from a 20 L storage bulb with a coldfinger kept at −50 °C. The NH3 partial pressure was measured directly by scanning the IR probe laser on and off the NH3 IR transition. The lasers used in the experiment were as follows: a Lambda Physik Compex model 205 excimer laser, operating at 193 nm, a Sacher Lasertechnik Lion 500 external cavity diode laser, operating from 665 to 677 nm, and a Linos model 4500 OPO system, operating from 2300 to 4000 nm. The IR laser was modified to operate in a dual-cavity mode. In this configuration, the pump and idler radiation are separated from the signal radiation, allowing the mode-hop free tuning range of the pump radiation (∼9 GHz) to be transferred to the desired IR radiation. As in previous work, both laser systems were continuously monitored by scanning the Fabry−Perot spectrum analyzers and wavemeters. Each probe laser beam was divided into two. A beam from each laser was spatially overlapped using a dichroic mirror and propagated through the multipass cell. Then, again separated by a dichroic mirror and directed to separate detectors, allowing the simultaneous detection of NH2 and NH3. The data acquisition hardware and LabView software have been improved form earlier work.17,18 The transient signals induced on both probe laser beams following the photolysis laser pulse were recorded by high-resolution, 14 bit and 16−22 flexible bit, A/D dual-channel transient recorders, providing direct measurement of the initial laser intensity and the digital resolution of small signals. The largest source of noise in the

NH2(X2 B2) + NH2(X2 B2) → NH(X3Σ−) + NH3

0 ΔH0r = −58 kJ mol−1

[M]

0 ΔH0r = − 268 kJ mol−1 (1b)

⎯⎯⎯→ N2H4

(1a)

where the exothermicities are from Klippenstein et al.20 There is an abstraction channel, (1a), on the triplet surface with a barrier of 22 kJ mole−1 and a barrierless recombination channel, (1b), on the singlet surface. Klippenstein et al.20 also provided theoretical estimates for k1a and k1b over the temperature range 300−2500 K. At 296 K, k1a was found to be 1.8 × 10−15 cm3 molecule−1 s,−1 in good agreement with a previous theoretical calculation.21 The theoretical calculation for k1b is more complicated, requiring a master equation analysis and highpressure limit, kinf, to account for the pressure dependence of the reaction. These theoretical calculations could describe earlier experimental measurements of Fargerström et al.16 with N2 as a collision partner using a value for the average energy transferred in a deactivating collision, ⟨ΔE⟩d, of 80 cm−1 but required an unreasonably large value for ⟨ΔE⟩d of ∼1000 cm−1 to fit the data of Bahng and Macdonald.17 In light of these conflicting experimental results, a compromise was chosen with ⟨ΔE⟩d = 150(T/300)0.85 cm.−1 1354



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Table 1. Summary of the Peak Doppler Broadened Absorption Coefficients for NH2 and NH3 Used in this Work molecule NH3 NH3 NH2 a

transition (1000) ← (0000) q Q3(3)s (1000) ← (0000) q Q3(3)a (070)A2A1 ← (000)X2B1 1 231 ← 1331

ν0 (cm−1)

Doppler width HWHM (cm−1)

σM(ν0) (cm2 molecule−1)

−3

(1.96 ± 0.059)b × 10−18 a

4.99 × 10

3336.390

(1.92 ± 0.058) × 10−18

3334.598 2.28 × 10−2

14800.59

(1.22 ± 0.09)b × 10−17

Kleiner et al.22 bUncertainty is ±2σ in the scatter.

pressure is over 20 Torr. Thus, the initial NH2 concentration can be used to calibrate the initial NH3 concentration. B. Reaction Mechanism. The detailed reaction mechanism has been described previously17 and will only be discussed briefly. Since this work, the rate constants for the NH2 + NH and NH2 + H have been measured and the yield18 of the NH(X3Σ−) from the 193 nm photolysis of NH3 has been established to be less than 1%. Klippenstein et al.20 have also provided theoretical estimates for rate constants of several important secondary reactions that occur in this system as well as for the NH2 self-recombination reaction in N2. As noted, near room temperature the only accessible product channel is N2H4. Recently, Asatryan et al.23 have reported another theoretical calculation on the singlet and triplet PESs for NH2 + NH2. These workers suggest alternate low energy pathways to N2H2 + H2 products, but these findings have not been verified by higher level multireference methods. The simplified reaction mechanism is

experiment is amplitude fluctuations of the probe laser intensity. Two strategies were taken to reduce this problem. First, the intensities of each split laser beam were equalized using polarizers. The signal from the beam passing through the photolysis zone was connected to one input of a dual channel high-resolution transient recorder and the signal from the unperturbed beam connected to the other. The two channels were subtracted in the data acquisition software, removing common-mode amplitude noise. The initial laser intensity (I0) for the signal channel recording the absorption transient was taken from the pretrigger portion of the captured trace. Second, the infrared laser intensity was kept at a constant value by controlling the current to the OPO pump laser using a Stanford Research model SIM960 PID controller. The data collection system was modified to greatly improve the ability to tune either laser system to the line center of an absorption feature. This was accomplished by also directing the detector signals from each laser system to a 200 kHz sampling 16 bit A/D digitizer board. Again, the appropriate signals were subtracted in computer memory to eliminate common-mode noise, and integrated for the length of the data record. The integrated absorption signals were then normalized for changes in I0 and photolysis laser power on each laser pulse. Moving averages of the normalized signals were monitored so that any drift in the absorption signal was directly apparent. This arrangement provided at least a factor of 100 improvement over the older technique of using the signal from a gated-boxcar averager to tune to the peak of an absorption feature. In the present version, the complete absorption signal is used instead of a narrow time slice.

193 nm

NH3 ⎯⎯⎯⎯⎯⎯⎯→ NH2 + H NH2 + NH2 → NH(X3Σ−) + NH3

0 ΔH0r = −58 kJ mol−1

(1a)

NH2 + NH2+(M) [M]

0 ΔH0r = −268 kJ mol−1 (1b)

⎯⎯⎯→ N2H4 + (M)

NH2 + H → NH(X3Σ−) + H2 0 ΔH0r = − 46 kJ mol−1

III. RESULTS AND DISCUSSION A. Concentration Measurements of NH2 and NH3. We have previously discussed the determination of molecular concentrations17 using absorption spectroscopy to monitor NH2 and NH3. In the present work, NH3 was monitored on either of the inversion doublets of the qQ3(3) rotational transition of the ν1 fundamental vibrational transition. The line strength of this transition is an order-of-magnitude stronger than that of the near-infrared (1010) ← (0000) combination band used in previous work. The line position and strength for the qQ3(3) transition was taken from Kleiner et al.22 The Doppler broadened line-center absorption coefficients for both NH2 and NH3 are summarized in Table 1. The determination of the peak absorption coefficient for NH2 reported in Table 1 is in excellent agreement with the previous measurement.17 Note that pressure broadening in NH3 becomes a concern for pressures over about 5 Torr for many collision partners. However, the Doppler width of the shorter wavelength NH2 transition is 4.5 times larger, and the peak absorption coefficient for NH2 will not be greatly reduced until the

(2a)

NH2 + H + (M) → NH3 + (M) 0 ΔH0r = − 444.1 kJ mol−1

(2b)

NH2 + NH → N2H2(cis) + H

0 ΔH0r = − 102 kJ mol−1 (3a)

N2H2(trans) + H

0 ΔH0r = − 124 kJ mol−1 (3b)

X → diffusion/flow

(4)

where the enthalpies were taken from Klippenstein et al.20 and Biczysko et al.,24 M is a collision partner for recombination, and X is any species in the system. This reaction sequence accounts for 99% of the removal of NH2 radicals. The two most important loss processes for NH2 radicals are reaction 1b and diffusion; however, reaction 2b does contribute to NH2 loss and NH3 production in the high-pressure experiments with N2 as third body. The complete reaction mechanism used in the data analysis consisted of 29 reactions and 12 species. 1355



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Figure 1. Typical NH2 and NH3 temporal concentration profiles showing the determination of k1b with He as a third body. (a) The experimental NH2 profile is shown by the solid red line, and the model calculated NH2 profile is shown every tenth point by the open circles using the optimum k1b. The nominal ArF laser fluence was 20 mJ cm.−2 The conditions of the experiment were PHe = 8.65, PCF4 = 0.249, and PNH3 = 0.091 Torr at 296 K. The CF4 was added to facilitate vibrational equilibration (see text). (b) Simultaneously measured NH3 profile for the NH2 profile in (a). The solid red line is the experimental profile, and open circles are the computed profile shown every tenth point. The profile is dominated by first-order recovery due to diffusion. (c) Same as (a) except the ArF laser fluence was about 10 mJ cm.−2 (d) Same as (a) except the ArF laser fluence was about 5 mJ cm.−2 A reaction path analysis shows that NH2 self-recombination accounts for 56% of the NH2 removal in (a) and is reduced to 36% for (d).

Two reactions could complicate the data analysis: NH2 + N2H4 → NH3 + N2H3 and H + N2H4 → H2 + N2H3. The former cannot account for the NH3 production observed in these studies because of the collision partner dependence on NH3 production. Model studies on NH3 pyrolysis by Konnov et al.8 provided an estimate of this rate constant to be 1.0 × 10−14 cm3 molecule−1 s−1 at 300 K. The latter rate constant has been measured by Vaghjiani25 to be 1.5 × 10−13 cm3 molecule−1 s−1 at 300 K and is too small to contribute significantly to the kinetics. The first-order rate for replenishment of the NH3 concentration following the photolysis laser pulse determined the rate constant for diffusion. Typical NH3 concentration profiles are shown in Figures 1b, 2b, 3b, and 4b for He, Ne, Ar, and N2 carrier gases, respectively. Although not clear from these figures, the diffusion process is described by two exponential

terms with rate constants differing by about a factor of 6−10. This is roughly the ratio of the long to short sides of the rectangular cross section of the photolysis laser beam. To simplify the data analysis, the NH3 profile was fit to a single exponential term for a fixed time interval, chosen to adequately describe the initial portion of the NH3 profile, as shown in Figures 1b, 2b, 3b, and 4b. For a dilute species, X, in a gas mixture, the diffusion rate constant (kdiff(X)) is given by the product of the binary diffusion constant (D12(X)) and a geometrical factor determined by the boundary conditions. The D12(X) in carrier gas, M, was calculated using the diffusion-volume procedure of Fuller et al.26 In this method each atom is assigned a diffusion volume and the diffusion volume for a molecule is summed from its constituent atoms. Some species are unique and Fuller et al.26 assigned them a separate 1356



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Figure 2. Same as Figure 1 except Ne is the third body. The conditions of the experiment were PNe =10.46, PCF4 = 0.176, and PNH3 = 0.0057 Torr at 296 K. The CF4 was added to facilitate vibrational equilibration (see text). (a) The nominal ArF laser fluence was 19 mJ cm.−2 (b) Simultaneously measured NH3 profile. (c) Same as (a) except the nominal ArF laser fluence was 15 mJ cm.−2 (d) Same as (a) except the nominal ArF laser fluence was 4.6 mJ cm.−2 A reaction path analysis shows that reaction 1b accounts for 61% of NH2 removal in (a) and is reduced to 37% in (d).

molecular diffusion volume, such was the case with NH3. Using this method, the calculated D12(NH2) was 1.3 times larger than D12(NH3). The diffusion volume for H atoms was determined from the D12(H) measured by Lynch and Michael27 in several inert gases. This D12(H) differed from Fuller et al.’s estimate by only 10%. The geometrical factor for the experiment was calculated from the measured value of kdiff(NH3) and the calculated D12(NH3). The difficulty in determining transport properties for use in combustion modeling has recently been addressed by Brown et al.28 These workers note the uncertainty in calculating binary diffusion constants for transient species and compare various theoretical treatments to the available experimental values for OH, HO2, and O3 in a He bath gas. The diffusion-volume model provides binary diffusion constants that are in reasonable agreement with the experimental values: D12(OH) = 686 (650), D12(HO2) = 538 (430), and D12(O3) = 467 (410) (units Torr cm2 s−1), where the terms in parentheses are the experimental measurements.29

As is evident from Figures 1−4, the model fits to the NH2 and NH3 concentration profiles slightly under predict the NH2 experimental profiles and slightly over predict the NH3 experimental profiles at the end of the plotted trace. This deviation has been noted before17 and is due to the rectangular cross section geometry of the photolysis zone. As discussed above, the two exponential terms were approximated by a single exponential term, allowing the diffusion process to be described by a first-order process. This procedure is a compromise and cannot completely account for the contribution of the smaller exponential diffusion rate constant term at long times. Thus at long times, the model predicts less NH2 (faster decay) and more NH3 (faster replenishment) as observed in the figures. C. Determination of NH2 Self-Recombination Rate Constant, k1b. Typical experimental profiles for the temporal concentration profiles of NH2 and NH3 are shown in Figures 1−4 with He, Ne, Ar, and N2, as third bodies, respectively, at pressures near 10 Torr. In each figure, the solid red lines are the 1357



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Figure 3. Same as Figure 1 except Ar is the third body. The conditions of the experiment were PAr = 11.06, PCF4 = 0.244, and PNH3 = 0.010 Torr at 295 K. CF4 was added to facilitate vibrational equilibration (see text). (a) The nominal ArF laser fluence was 29 mJ cm.−2 (b) Simultaneously measured NH3 profile. (c) Same as (a) except the nominal ArF laser fluence was 15 mJ cm.−2 (d) Same as (a) except the nominal ArF laser fluence was 6 mJ cm.−2 A reaction path analysis shows that reaction 1b accounts for 76% of NH2 removal in (a) and is reduced to 62% in (d).

laser power has been attenuated, either by the insertion of finemesh stainless screens into the laser beam or by reducing the excimer laser charging voltage. On each of the NH3 profiles, Figures 1b, 2b, 3b, and 4b, sharp spikes are present at time zero, especially the positive spike. These are due to electronic ringing from the high flexible bit resolution A/D transient recorder used to monitor the NH3 signal. As discussed in previous work,17 a small amount of CF4 was added to the gas mixture to facilitate vibrational relaxation in both NH2 and NH3.30 This was not done in the experiment with N2 as third body shown in Figure 4. In this case, the positive spike in Figure 4b is electronic but the downward spike has a large component created by rapid repopulation of the NH3 ground vibrational level. Evidence of the influence of vibrational relaxation on the NH2 profile is provided in Figures 4a, 4c, and 4d. No CF4 was added in this experiment, and the rise to the maximum in NH2 concentration occurred over several hundred microseconds following the photolysis laser pulse unlike in Figures 1−3 in

experimental profiles and the open circles are the model fits using the optimum bimolecular rate constant, k1b. The kinetic equations describing the model chemistry were integrated with the initial concentrations for NH 3 ([NH 3 ] 0 ) and NH 2 ([NH2]0) determined from the appropriate profile. The optimum k1b was determined by finding the value of k1b that minimizing the sum-of-the-squares of the difference between the experimental and model NH2 concentration profiles (χ2). Except for N2 as a third body at high pressure, there is little chemistry affecting the NH3 concentration; its recovery following the photolysis laser pulse is due to diffusion from the surrounding environment. As noted in section IIIB, the initial portion of the NH3 profile was fit to a single exponential term to determine kdiff(NH3). Both NH2 and NH3 were detected simultaneously following the photolysis laser pulse, as shown in panels a and b for Figures 1−4. The other panels (c) and (d) show only the NH2 profile obtained under the same experimental conditions as panels a and b except the photolysis 1358



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Figure 4. Same as Figure 1 except N2 is the third body. Note also, without CF4 added, the rise in NH2 occurs over several 100s of μs (see text). The conditions of the experiment were PN2 = 10.51 and PNH3 = 0.0080 Torr at 296 K. (a) The nominal ArF laser fluence was about 17 mJ cm.−2 (b) Simultaneously measured NH3 profile. The initial negative spike is due to vibrational relaxation in NH3. (c) Same as (a) except the nominal ArF laser fluence was 7.5 mJ cm.−2 (d) Same as (a) except the nominal ArF laser fluence was 3 mJ cm.−2 A reaction path analysis shows that reaction 1b accounts for 79% of NH2 removal in (a) and is reduced to 66% in (d).

Tables 2−5, the rate constant determinations show no detectable trend on the initial NH3 concentration. This is in agreement with expectations of the uncertainty introduced in secondorder rate constant measurements due to nonuniform radical column density.31 Pressure broadening causes the line center absorption cross section to be reduced from its Doppler value because the integrated line shape function equals the line strength. The influence of pressure broadening on the peak absorption cross section for NH3 is included in Tables 2−5 by tabulating the ratio [NH3]0/[NH2]0, calculated using peak Doppler absorption coefficients in Table 1, defined as prbd, in column five. These quantities were determined by the time-zero intercept of multiple exponential fits to the appropriate temporal concentration profile, usually two exponential terms for NH3 and three terms for NH2. For NH3, the fitting procedure was delayed by several hundred microseconds to suppress the

which the maximum in the NH2 concentration required only a few tens of microseconds. However, the time scale of the recombination is substantially longer than this vibrational induction period and the rate constant measurements are not affected, as seen in Table 5 where experiments are summarized with and without CF4 addition in N2 carrier gas. The experimental conditions and results for the determination of k1b are given in Tables 2−5 for each collision partner, He, Ne, Ar, and N2, respectively. At least four measurements of k1b for a range of initial NH2 concentrations were averaged to obtain the final value for a given set of experimental conditions and are tabulated in the last columns of Tables 2−5. Unlike previous experiments, the concentration of NH3 was determined in situ using IR absorption spectroscopy. The absorbance of the IR laser radiation by the steady-state NH3 concentration was measured by manually scanning the IR laser frequency over the NH3 transition listed in Table 1. As can be seen from 1359



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Table 2. Summary of Experimental Conditions and Measurements of k1b in He at 296 ±2 K partial pressure (Torr) PHe 1.457 1.901 1.984 2.474 3.114 3.309 3.868 5.91 6.014 7.102 8.365 8.651 10.1 10.11 12.29 12.817 13.77 15.33 16.24 17.08 20.49

PCF4 0.0957 0.0899 0.0972 0.137 0.147 0.154 0.172 0.219 0.315 0.354 0.317 0.249 0.421 0.256 0.268 0.263 0.205 0.252 0.224 0.252 0.332

PNH3 0.0084 0.0075 0.0072 0.0087 0.0098 0.0052 0.0066 0.0098 0.011 0.0084 0.0040 0.0091 0.0078 0.0044 0.0059 0.0057 0.0061 0.0052 0.0098 0.012 0.011

range [NH2]0 (1013 molecules cm−3) b

2.99−1.51 4.24−1.28 3.97−1.20 5.23−1.56 5.48−1.72 3.57−1.14 4.42−1.38 5.36−1.65 4.73−0.854 5.26−1.57 2.64−0.917 4.24−1.31 4.02−1.10 2.54−0.724 3.21−0.903 4.22−1.53 4.50−1.70 3.45−1.44 5.84−1.82 6.20−1.92 5.72−3.49

prbda

v (10−12 cm3 molecule−1 s−1)

0.888 0.931 0.914 0.897 0.938 0.865 0.865 0.883 0.954 0.862 0.946 0.850 0.839 0.943 0.817 0.828 0.826 0.967 0.817 0.841 0.984

0.14 (±0.30)c 0.64 (±0.56) 1.63 (±1.62) 1.94 (±0.98) 1.96 (±0.86) 2.34 (±1.76) 3.09 (±1.94) 3.66 (±0.94) 3.53 (±1.02) 4.07 (±0.84) 5.06(±0.88) 4.48 (±0.80) 5.06 (±0.98) 5.51 (±1.04) 5.63 (±0.92) 5.80 (±0.42) 6.31 (±0.28) 7.69 (±0.44) 6.55 (±0.24) 6.92 (±0.36) 9.28 (±0.42)

a

Pressure broadening parameter, prbd = [NH3]0 /[NH2]0, calculated using peak Doppler absorption coefficients measurements were made under the same flow conditions. cUncertainty is ±2σ in the scatter of the measurements.

b

Multiple rate constant

Table 3. Summary of Experimental Conditions and Measurements of k1b in Ne at 296 ± 2 K partial pressure (Torr) PNe 1.322 1.397 1.509 1.55 1.851 1.956 2.463 2.497 2.684 2.756 3.962 4.007 4.359 4.473 7.196 7.339 8.025 8.178 10.46 10.84 11.78 11.92 12.28 13.06 13.99 17.04 18.12

PCF4 0.15 0.114 0.13 0.109 0.0687 0.139 0.183 0.204 0.231 0.196 0.264 0.331 0.312 0.318 0.246 0.597 0.362 0.578 0.176 0.879 0.421 0.839 0.203 1.051 0.355 0.432 0.299

PNH3 0.0056 0.0081 0.0078 0.0082 0.0096 0.0085 0.0098 0.010 0.0079 0.0087 0.0091 0.0090 0.0084 0.0067 0.0065 0.013 0.0096 0.0062 0.0057 0.0089 0.0058 0.0056 0.0048 0.0079 0.0066 0.012 0.0087

range [NH2] (1013molecules cm−3) b

3.44−1.05 4.21−0.502 4.40−1.36 4.58−0.582 5.08−0.768 4.71−0.62 5.76−1.68 6.40−0.513 4.73−1.40 4.87−0.589 5.59−1.84 5.52−0.803 5.88−1.91 4.11−0.561 3.35−0.994 5.81−4.79 3.63−1.07 3.15−0.377 3.04−0.817 3.81−0.306 2.35−0.641 2.49−0.384 2.72−1.08 3.67−0.534 4.24−1.689 5.57−1.56 4.43−1.42

a

Prbda

k1b (10−12cm3 molecule−1 s−1)

0.930 0.995 1.001 1.029 1.018 0.990 0.995 1.091 0.990 0.965 0.967 1.011 0.995 0.909 0.872 0.881 0.872 0.835 0.842 0.810 0.832 0.820 0.842 0.779 0.857 0.825 0.827

1.13 (±2.44)c 0.60 (±0.98) 1.21 (±1.40) 0.65 (±0.76) 1.08 (±0.10) 0.86 (±0.62) 1.66 (±0.94) 1.78 (±1.12) 1.49 (±0.92) 1.20 (±1.60) 2.41 (±0.82) 2.13 (±0.12) 2.36 (±0.78) 1.95 (±1.06) 3.24 (±0.50) 2.97 (±0.36) 3.23 (±0.38) 3.26 (±0.90) 4.17 (±0.48) 3.14 (±0.88) 4.20 (±0.60) 3.93 (±1.40) 4.65 (±0.38) 4.25 (±0.88) 5.25 (±0.18) 5.80 (±0.54) 6.06 (±0.26)

Pressure broadening parameter, prbd = [NH3]0 /[NH2]0, calculated using peak Doppler absorption coefficients measurements were made under the same flow conditions. cUncertainty is ±2σ in the scatter of the measurements. 1360

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Table 4. Summary of Experimental Conditions and Measurements of k1b in Ar at 296 ± 2 K partial pressure (Torr) PAr 1.3 1.351 1.446 1.546 2.502 2.659 2.66 2.864 3.983 4.098 4.414 4.79 5.624 6.666 8.01 8.083 8.408 9.044 10.26 11.06 11.97 13.15 14.69 15.64 15.87 16.97 19.28 20.06 20.36

PCF4 0.0817 0.13 0.129 0.12 0.153 0.206 0.237 0.274 0.321 0.248 0.271 0.288 0.213 0.188 0.188 0.263 0.248 0.16 0.14 0.244 0.386 0.232 0.266 0.276 0.227 0.201 0.195 0.237 0.175

PNH3 0.0072 0.0084 0.011 0.0066 0.0091 0.010 0.0088 0.011 0.0084 0.011 0.0083 0.0089 0.0098 0.0082 0.0076 0.0081 0.0096 0.0092 0.010 0.010 0.010 0.011 0.010 0.015 0.0089 0.013 0.0095 0.0098 0.014

[NH2]0 (1013molecules cm−3) b

4.13−1.21 4.30−1.26 5.33−1.56 5.12−1.53 4.75−1.40 5.81−1.68 6.31−1.30 5.35−1.32 4.50−1.34 5.76−1.59 4.43−1.30 4.24−1.20 4.41−1.22 3.78−1.10 3.68−1.12 3.63−1.05 3.46−0.963 4.45−1.31 4.55−1.34 2.99−1.01 6.20−2.02 5.50−1.69 4.18−1.16 5.96−1.13 4.82−1.53 5.19−1.40 3.62−0.963 4.18−1.08 5.08−1.34

Prbda


1.145 1.082 1.284 1.089 1.042 1.043 1.035 1.010 0.985 0.984 0.942 0.943 0.924 0.917 0.873 0.847 0.879 0.917 0.844 0.836 0.865 0.859 0.797 0.798 0.840 0.837 0.759 0.796 0.806

0.77 1.59 1.33 2.04 2.31 2.71 2.58 2.79 3.22 3.57 3.40 3.85 4.47 4.36 5.87 5.03 5.47 5.41 6.66 6.88 6.89 7.29 7.97 7.90 8.77 8.73 9.36 9.54 9.91

a


b

(±0.78)c (±2.1) (±0.64) (±1.30) (±0.84) (±0.60) (±0.88) (±0.80) (±0.28) (±0.72) (±0.66) (±0.76) (±0.92) (±0.40) (±0.60) (±0.38) (±0.64) (±0.50) (±0.78) (±0.38) (±0.24) (±0.38) (±0.48) (±0.50) (±0.60) (±0.60) (±0.46) (±0.32) (±0.64)


Table 5. Summary of Experimental Conditions and Measurements of k1b in N2 at 296 ± 2 K partial pressure (Torr) PN2 1.281 1.720 1.951 2.450 3.904 4.342 4.354 6.210 7.138 7.403 9.260 10.51 11.93 12.35 13.45 15.15 15.32 16.46 19.39 19.60 20.58

PCF4 0.122 0.000 0.000 0.213 0.000 0.000 0.317 0.000 0.000 0.314 0.000 0.000 0.169 0.000 0.000 0.107 0.000 0.000 0.000 0.0127 0.000

PNH3 0.0083 0.012 0.010 0.011 0.014 0.013 0.013 0.0086 0.0088 0.014 0.0085 0.0080 0.011 0.0094 0.0109 0.0069 0.0014 0.016 0.0085 0.0094 0.0088

range [NH2]0 (1013molecules cm3) 3.55−0.958 4.77−1.29 4.65−1.25 1.13−0.413 4.98−1.30 3.39−0.925 4.43−1.21 3.10−0.815 2.95−0.816 4.09−1.08 3.50−1.02 2.71−0.828 3.24−0.846 4.13−1.19 4.62−1.47 2.83−0.865 3.03−0.807 5.02−1.30 4.31−1.13 3.61−0.979 3.09−0.899

a

b

Prbda


1.179 1.219 1.206 1.093 1.018 0.921 0.976 0.842 0.821 0.868 0.788 0.764 0.789 0.768 0.771 0.757 0.705 0.716 0.672 0.702 0.646

0.12 (±0.082)c 0.32 (±0.12) 0.33 (±0.10) 0.35 (±0.096) 0.52 (±0.13) 0.61 (±0.12) 0.56 (±0.11) 0.72 (±0.070) 0.87 (±0.10) 0.80 (±0.078) 0.98 (±0.052) 1.12 (±0.062) 1.10 (±0.072) 1.16 (±0.056) 1.28 (±0.044) 1.36 (±0.082) 1.36 (±0.16) 1.44 (±0.16) 1.63 (±0.14) 1.61 (±0.062) 1.69 (±0.11)

Pressure broadening parameter, prbd = [NH3]0 /[NH2]0, calculated using peak Doppler absorption coefficients measurements were made under the same flow conditions. cUncertainty is ±2σ in the scatter of the measurements. 1361

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A variation of ±50% in kdiff(H) results in change of ∓11% in k2b at each pressure in Figure 5b,d. It is clear from Figure 5b,d that reaction 2b does not contribute a great deal to the production of NH3. A reaction path analysis shows that reaction 2b contributed 2.35 × 1012 molecules cm−3 to the flux of NH3 and accounted for 21% of the NH3 production at a pressure of 16.46 Torr. At 19.39 Torr, reaction 2b contributed a flux of NH3 of 2.19 × 1012 molecules cm−3 and accounted for 22% of the NH3 production. The experimental conditions and results under which k2b could be measured are summarized in Table 6. Although the results are scattered and obtained over a narrow pressure range, the reaction was assumed to be in the low-pressure recombination regime and k2b, with k2b = k02b(N2)[N2] (see eq 6), where k02b(N 2) is the three body recombination rate constant with N2 as a third body. A linear least-squares plot through the origin gives k02b(N2) to be (2.3 ± 0.25) × 10−30 cm6 molecule−2 s,−1 where the uncertainty is ±2σ in the standard error in the fit. E. Pressure Broadening. The parameter (prbd) in column 5 of Tables 2−5 has been defined above. Although the pressure range of the measurements is not large, these results can be used to provide estimates of the pressurebroadening parameters for the NH 3 (ν 1 ) fundamental q Q 3 (3) transition. The convolution of independent Doppler and pressure-broadened line shapes, with HWHM line widths bD and bL, respectively, is described by a Voigt line shape function 34 g(υ), at frequency ν, which is given by

obvious perturbations from vibrational relaxation, as illustrated for NH3 in N2 (Figure 4b), and for NH2 a delay of only several 10s μs was needed when CF4 was present. At pressures less than 3 Torr, the measurements of both kdiff(NH3) and k1b systematically increased as the initial concentration of NH2 decreased due to the attenuation of the photolysis laser radiation. This is reflected in Tables 2−5 as increased scatter in the measurements of k1b at low pressures and values of prbd exceeding 1. There is little chemistry influencing the NH3 concentration profile, and kdiff(NH3) should be independent of laser photolysis fluence. However, if vibrational equilibration is not complete, part of the recovery of NH3 could be due to relaxation kinetics. It is difficult to predict the nature of this signal because only the degeneracy weighted population difference in the levels connected by the optical transition is actually measured. On the other hand, more uncertainty is expected in determining kdiff(NH3) at low pressures because it has an inverse pressure dependence, and part of this systematic behavior in k1b is due to the increasing importance of diffusion to the loss of NH2 rather than recombination, as the initial NH2 concentration decreases. But it may also be a manifestation that vibrational equilibration was not complete at the low pressures of these experiments in both NH3 and NH2 vibrational manifolds. The 193 nm laser photolysis of NH3 generates NH2 with considerable internal excitation32 and is degraded by collisions into excited vibrational modes of NH2, which ultimately equilibrate. Although CF4 is efficient at relaxing the NH2 bending mode,33 at low pressures the initial NH2 concentration may be still be underestimated, causing prbd to be greater than 1. At pressures above about 3 Torr, the uncertainty in k1b is reduced and vibrational relaxation is sufficiently fast that these problems are greatly reduced or eliminated. D. Determination of k2b in N2. At pressures near 20 Torr and with N2 as the carrier gas, the NH3 recovery was faster than that dictated by diffusion alone. The most likely reaction producing NH 3 is reaction 2b, and the NH 3 temporal concentration profiles were analyzed by treating k2b as a variable. The final optimum values of k1b and k2b were determined by iterating between fitting the NH2 and NH3 profiles with new values of k1b and/or k2b until the values converged. Typical experimental NH2 and NH3 temporal concentration profiles at 16.46 and 19.39 Torr are shown in Figure 5. In Figure 5, the red lines are the experimental NH2 or NH3 concentration profiles, and the open black circles are the model determination using the optimum k1b or k2b rate constants, respectively. In Figure 5a,c, the solid green circles are the model predictions for the H atom profile using the optimum value of k1b. The black dash-dot curves are the calculated H atom profiles if kdiff(H) was decreased by 50%, and the blue dash-dash curves are the calculated H atom profiles if kdiff(H) was increased by 50%. Panels c and d of Figure 5 are identical to panels a and b except they were recorded at 19.39 Torr pressure. The value of kdiff(NH3) was determined by fitting the experimental NH3 profile to a single exponential starting 5 ms after the photolysis laser pulse. As can be seen in Figure 5a,c, after this length of a delay the NH2 concentration has decayed significantly, reducing the importance of reaction 2b to the production of NH3. Under the conditions of the experiment, high pressure and high initial NH2 concentration, NH2 is the rate limiting reagent, as shown by the H atom profiles in Figure 5a,c.

2

P′a ∞ e− y g (υ) = dy = P′K (ξ,a) π −∞ a2 + (ξ − y)2

∫

(5)

where P′ is the normalization constant for a pure Doppler broaden line shape, P′ = {ln 2/π} 1/2/bD with bD = 3.581 × 10−7ν 0(T/M) 1/2 and T is the temperature and M the mass of the absorber, a = bL/bD{ln 2}1/2, and ξ = {ln 2}1/2(ν − ν0)/bD. The pressure broadening parameter (bL) is given by bL = bL0 P, where bL0 is defined for a given standard pressure and P is the pressure of the collision partner. At line center frequency, ν 0, the peak absorption coefficient g(ν 0) is reduced from the Doppler peak by the factor K(0,a), which is equal to prbd. For each collision partner prbd was plotted against pressure and fit to a straight line. Data below 3 Torr were neglected in the fits because of difficulties with attaining vibrational equilibrium at low pressure, as discussed earlier. The prbd linear fit parameters were used to calculate K(0,a) at 5, 10, 15, and 20 Torr pressure for each collision partner. Equation 5 was integrated at each pressure as a function of b L0 until agreement was found with the experimental value at that pressure. The results of the determination of bL0 are summarized in Table 7. The second last row is the average of the three highest pressure determinations of bL0 for each collision partner, and the uncertainty is one standard deviation in these measurements. The last row summarizes the detailed measurements of Pine and Markov 35 on the line broadening parameters for the rotational lines of the NH 3 ν 1 fundamental vibration for He, Ar, and N 2 as collision partners. These measurements are much more extensive than those reported here, but the results overlap at the ±2σ level of uncertainty. 1362



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Figure 5. Determination of k2b in N2 is shown at two pressures. (a) The experimental NH2 temporal concentration profile is shown by the solid red line, the model predicted NH2 profile by the open circles, and the H atom profile by the solid green circles using the model-predicted rate constant for the H atom diffusion constant, kdiff(H). A change in kdiff of ±50% is shown by the black dash-dot line and by the blue dashed line. The corresponding changes in k2b were ∓12%. The experimental conditions were PN2 = 16.46 and PNH3 = 0.017 (Torr) at a nominal ArF laser fluence of 25 mJ cm.−2 (b) Same as (a) except the simultaneously determined NH3 profile is shown. kdiff(NH3) was determined by fitting the NH3 profile at times longer than 5 ms. The blue dashed lines shows the calculated NH3 profile for k2b = 0. (c) The same as (a) except a change in kdiff of ±50% produced changes in k2b of ∓12%. (d) Same as (b) except PN2 = 19.39 and PNH3 = 0.014 Torr at a nominal laser fluence of 23 mJ cm−2.

Table 6. Summary of Experimental Conditions and Measurements for the Determination of k2b in N2 at 296 ± 2 K partial pressure P N2 13.45 15.15 15.32 16.46 19.39 19.72 20.5

PCF4 0 0.107 0 0 0 0.127 0

PNH3 0.011 0.0070 0.0087 0.017 0.014 0.0095 0.0088

range [NH2] (1013molecules cm−3) 4.62−2.95 2.17−1.70 3.03−2.43 3.56−2.60 2.94−2.30 2.54−1.95 3.10−2.58

a

b

Prbda

k2b (10−12cm3 molecule−1 cm−1)

0.771 0.757 0.705 0.716 0.672 0.702 0.646

0.72 (±1.2)c 1.45 (±1.5) 1.16 (±0.42) 1.38 (±1.5) 1.41 (±1.6) 1.46 (±1.5) 1.73 (±1.0)


F. Determination of Troe Parameters: k0, kinf, and Fcent. It is common practice to report the pressure dependence of

b


recombination reaction rate constants using the formulation of Troe.36−38 In this representation, the bimolecular rate constant 1363



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was varied to minimize the χ2 between the experimental pressure dependence of k1b and that predicted by eq 6. The k0 values were varied from 4.0 × 10−29 to 3 × 10−28 in steps of 1.0 × 10−30 cm6 molecule−2 s−1, kinf from 8 × 10−11 to 1.6 × 10−10 in steps of 2 × 10−11 cm3 molecule−1 s−1, and Fcent from 0 to 1 in steps of 0.01. As expected, the variation in kinf had little effect on the optimum values of k0 and Fcent and the values reported were with kinf fixed at the theoretical20 value of 7.9 × 10−11 cm3 molecule−1 s−1 for 296 K. For the collision partners of this work, the minimum in the χ2 vs k0 plane was relatively shallow, resulting in a large range in the pairs of k0 and Fcent values that adequately fit the data. On the other hand in the χ2 vs Fcent plane, there was always a sharp well-defined minimum for a k0, kinf pair. The results of this optimum search for the collision partners studied in this work are presented in Figures 6−9 for He, Ne,

Table 7. Summary of the Determination of bL0 for the NH3 Q 3(3) ν1 Fundamental Transition

q

bL0 a collision partner pressure (Torr) 5 10 15 20 avb bL0 Pine and Markovd bL0

He (×105)

Ne (×105)

Ar (×105)

N2 (×104)

10.3 6.1 4.8 4.05 5.0 ± 0.22c 3.77e

7.15 7.40 8.30 9.11 8.3 ± 0.18

8.20 7.12 7.02 7.15 7.1 ± 0.14 6.31e

1.02 1.08 1.16 1.27 1.2 ± 0.20 1.42e

Units cm−1 Torr−1. bThe average of the three highest pressures. Uncertainty is ±2σ in the average. dReference 35. eUncertainty ±1%.

a c

describing the production of products, k, is expressed in the form

k=

k 0[M]k inf F k 0[M] + k inf

(6)

where F is determined from

Log(F ) =

Log(Fcent) 1 + {Log(k 0[M]/k inf )}2 /N2

(7)

with N defined by

N = 0.75 − 1.27 Log(Fcent)

(8)

The value of kinf depends only on the properties of the energized product molecule and can be evaluated using variational transition-state theory39 and electronic structure theory to describe the recombining fragment’s interaction potential. The value of k0 depends on the nature of the third body and in principle can be determined from the limiting pure recombination region, where k is given by k0[M]. The Fcent parameter accounts for broadening of the falloff curve that deviates from the simple Lindemann−Hinshelwood expression. The determination of k0 and kinf provides challenges for their direct experimental determination because it is difficult to make rate constant measurements under conditions where either clearly dominates the recombination process. The most complete description of the pressure dependence of a recombination rate constant is a full master equation treatment of the collision process over a range of pressures using quantum chemistry and variational reaction rate theory to calculate kinf. As noted in the Introduction, Klippenstein et al.20 conducted a detailed theoretical study of reaction 1b with N2 as a collision partner using variational transition-state theory based on quantum chemistry evaluation of the NH2−NH2 PES and a master equation analysis to determine the pressure dependence. The ⟨ΔE⟩d for N2 was estimated to be 150 cm−1 in light of the conflicting rate constant measurements for reaction 1b in the literature. They fit their results to the Troe parametrization scheme, eqs 6−8 to provide theoretical estimates of k0, kinf, and Fcent with N2 as the third body. Even for strong collision partners considered in part 2, the pressure range 1−20 Torr was too small to provide any information on kinf; however, to determine the influence a variation in kinf would have on the determinations of k0 and Fcent, kinf was treated as a variable for completeness. A grid search was implemented to determine the optimum set of Troe parameters to fit the pressure dependence of k1b for each collision partner. For each pair, (k0, kinf), Fcent

Figure 6. Comparison of the experimental pressure dependence of k1b with the optimum Troe parameters for k1b for He as a collision partner. The limiting high-pressure rate constant,20 kinf, was taken to be 7.9 × 10−11 cm3 molecule−1 s.−1 The solid red circles are the experimental measurements summarized in Table 2, and the solid blue line is the best fit to the data yielding k0 = 2.8 × 10−29 cm6 molecule−2 s−1 and Fcent = 0.47.

Ar, and N2, respectively. For each collision partner, the experimental rate constants summarized in the appropriate Tables 2−5 are plotted as a function of partial pressure of the collision partner, given by the solid red circles. The contribution of CF4 to the NH2 kinetics was accounted for in the model calculations for the optimum value of k1b. The blue solid line is the optimized fit to the pressure dependence of k1b. The parameters found for the fits are summarized in Table 8. Also shown in Figures 8 and 9 by the open red circles are the previous measurements from this laboratory for Ar and N2 as collision partners, respectively. As can be seen from these two figures, at 10 Torr pressure the previous results are about 50% larger than the present measurements and have larger uncertainties. Although this disagreement is within the uncertainties in the two measurements at the 2σ level, it might suggest some systematic experimental problem with the previous measurements from this laboratory. In the present experiments, the concentration of NH3 was measured directly by IR absorption spectroscopy, allowing higher partial pressures 1364



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Figure 7. Same as Figure 6 except the comparison is for Ne as the third body. The experimental measurements are summarized in Table 3. The optimum Troe parameter values were k0 = 2.7 × 10−29 cm6 molecule−2 s−1 and Fcent = 0.34.

Figure 9. Same as Figure 6 except the comparison is for N2 as the third body. The experimental results are summarized in Table 5. The optimum Troe parameter values were k0 = 5.7 × 10−29 cm6 molecule−2 s−1 and Fcent = 0.61. The blue dashed line are the theoretical predictions by Klippenstein et al.20 for the pressure dependence of k1b from a consideration of all the available experimental data.10−17 The Troe fit parameters at 296 K are k0 = 4.1 × 10−29 cm6 molecule−2 s−1 and Fcent = 0.31 for a ⟨ΔE⟩d parameter of 150 cm−1 at 296 K. The open red circles are the experimental measurements from Bahng and Macdonald17 obtained using a preliminary version of the experimental apparatus.

Figure 8. Same as Figure 6 except the comparison is for Ar as the third body. The experimental results are summarized in Table 4. The optimum Troe parameter values were k0 = 4.4 × 10−29 cm6 molecule−2 s−1 and Fcent = 0.41. The open red circles are the experimental measurements from Bahn and Macdonald17 obtained using a preliminary version of the experimental apparatus.

Table 8. Summary of the Troe Paramaterized Fits to the Experimental Data for k1b for each Third Body, at 296 K

of NH3 for each experimental run and, hence, larger initial concentrations of NH2. Also, NH3 was monitored on the much stronger ν1 fundamental band providing much better signal-tonoise for the NH3 temporal concentration profiles and a more reliable determination of kdiff(NH3). Both factors contributed to a better determination of k1b in the present experiment by increasing the importance of reaction 1b over diffusion and a more accurate determination of the contribution made by diffusion to the removal of NH2. Another possibility is the production of an unknown reactive species by photolysis of reaction products. The 193 nm absorption coefficient for N2H4 has been measured by Vaghjiani25 to be 4.50 × 10−18 cm2 molecule−1 with a quantum yield of 1.0 for the production of H + N2H3. Although the steady-state concentration of N2H4 will be much smaller than the initial NH2 concentration, this is a relatively strong absorption and its influence on the results should be minimized. Thus, in the present experiments, the

kinfa = 7.9 × 10−11 b k0

third body He Ne Ar N2

(2.8 (2.7 (4.4 (5.7

± ± ± ±

c

1.2) 1.4) 1.4) 1.4)

Fcent × × × ×

10−29 d 10−29 10−29 10−29

0.47 0.34 0.41 0.61

± ± ± ±

0.8 0.6/0.0 0.28 0.22

a Klippenstein et al. 20 b Units cm 3 molecule−1 s−1 . c Units cm6 molecule−2 s−1. dUncertainty is ±2σ in the goodness of the fit.

inner Teflon box was removed by increasing the volume of the reaction chamber directly accessible to the reaction products from the photolysis zone and providing a possible sink for reactive species on the stainless steel walls. With the box in place, its top and bottom were only a centimeter from the photolysis zone, and the gas flow was restricted to only the direction perpendicular to the propagation direction of the 1365



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collision partners and the range of pressures covered in these experiments. H. Estimated Uncertainty in k2b. As shown in Figure 5 and summarized in Table 6, at high pressure and large initial concentrations of NH2, it was possible to measure k2b with N2 as a collision partner. The same considerations apply to the uncertainties in the measurement of k2b as to those for the measurement of k1b discussed in the previous section. However, there is now the additional uncertainties due to the direct NH3 concentration measurement and the contribution the uncertainty in kdiff(H) adds to the determination of k2b. As summarized in Table 7, the pressure broadening parameters measured in this work are not significantly different from the refined measurements of Pine and Markov,35 and the peak absorption coefficient is only perturbed by a few percent at 20 Torr pressure. This was added to the uncertainty in σNH3(ν0) and it is increased to ±5%. The uncertainties in both the NH2 and NH3 concentration measurements contribute to the determination of k2b and combine to give a total uncertainty of ±9%. As shown in Figure 5a,c, the H atom concentration is not rate limiting, and a variation of ±50% in kdiff(H) only perturbed the value of k2b by an additional ∓11%, The reaction path analysis for the two experiments illustrated in Figure 5 was discussed in section IIID. The scatter in the measurements of kdiff(NH3) was reduced to about 10% because of the higher pressure and longer time scale for diffusion. However, diffusion still accounts for roughly 80% to the recovery of the NH3 concentration and hence introduces ±8% error into the uncertainty in the determination of k2b. The standard error in the slope of the linear least-squares fit through the origin is k2b ± 11%. Combing the above-mentioned uncertainties in concentration measurements, kdiff(H), kdiff(NH3), and the error slope of the line results in a total experimental uncertainty of ±25% at the 2σ confidence level. I. Comparison with Previous Work. The present work is an extension of previous work from this laboratory17 on the determination of the NH2 self-recombination in Ar, N2, and CF4. A detailed comparison with previous work in the literature was given there. A comparison with our previous measurements for Ar and N2 as third bodies is shown in Figures 8 and 9, respectively, and is discussed in section IIIF. There is only one previous measurement of k2b by Gordon et al.11 with NH3 as a collision partner. These workers used pulse radiolysis and white-light absorption spectroscopy to monitor the temporal dependence of NH2 using a partially resolved (0,8,0)A2A1 ← (0,0,0)X2B1 vibronic band. The radical concentration was calibrated using the known G value for the yield NH2 radicals from the radiolysis of NH3. The rate constant, k2b, was measured over the pressure range 250−1520 Torr and was assumed to be in the pure three-body recombination range 250−760 Torr. The rate constant, k2b, was found to be 5.4 × 10−30 cm6 molecule−2 s−1 at 295 K, in reasonable agreement with values found in part 2 for collision partners more efficient than N2. In the same experiments, these workers found the high-pressure limit for k1b to be 1.0 × 10−10 cm3 molecule−1 s.−1 Again, this result is in good agreement with the theoretical estimate of Klippenstein et al.20

excimer laser. However, in both experiments the measurements of k1b were independent of the photolysis laser repletion rate from 3 to 0.5 Hz so that it is difficult to attribute the difference in the two sets of measurements to the presence of the inner Teflon box. G. Estimated Uncertainty in k1b. The experimental uncertainties in the measurement of k1b have been discussed previously17 and much of that discussion pertains to this work. However, the present work extends these measurements to both lower and higher pressures as well as to nine different collision partners, encompassing parts 1 and 2. As noted in section II, the new data acquisition software greatly facilitated in tuning both probe lasers to the line centers of the absorption features. For NH3, it was instantaneously noted when the IR laser frequency drifted because the laser frequency was already placed on line center using the background NH3 steady-state concentration. The measurement of k1b does not depend on σNH3(ν0) but σNH3(ν0) does contribute about ±3% (Table 1) at the 2σ level of uncertainty to the determination of σNH2(ν0). (Note, the uncertainties quoted in this and the following section will all be expressed at the ±2σ confidence level.) The combined uncertainty in the absorption coefficient measurements contributes ±8% in the determination of the NH2 concentration. The results in Tables 2−5 were reported as the time zero value of multiple exponential fits to the absorbance profiles and are in agreement with the results in Table 1. The theoretical work of Klippenstein et al.20 shows that at room temperature reactions 1a and 1b are the only reaction paths accessible to the NH2 + NH2 product manifold, with reaction 1a contributing less than 1% to the product channels. Thus, recombination and diffusion are the only significant processes removing NH2 radicals. A reaction path analysis was always conducted with each optimization fit. Typical results are given in the figure captions for Figures 1−5. The contribution to NH2 removal by diffusion and flow increases as the pressure decreases and vice versa. An estimate of the contribution that the uncertainty in kdiff(NH2) makes to the overall uncertainty in k1b was taken to be the average scatter of ±20% in kdiff(NH3) in Ne at 10 Torr pressure. As discussed previously,40 a good estimate of the error introduced into a rate constant involving a given species by an error in a rate constant for a process contributing to the species concentration is given by the integrated fractional reaction contribution factor of that process times the error in the contributing rate constant. At 10 Torr pressure of Ne, reaction accounts for about 60% of the removal NH2 and diffusion the remainder; thus, the uncertainty in k1b from uncertainty in kdiff(NH3) can be calculated to be ±8%. An estimate in the scatter for individual experimental determination of k1b can be estimated from the average of the uncertainties in Tables 2−5 after removing some of the more scattered low-pressure measurements. The result in the experimental scatter at the 2σ level is as follows: He, 24%; Ne, 35%; Ar, 20%; and N2, 18%. The average over all four different bath gases is 24%. This is taken as representative of the experimental scatter in the measurements. Assuming the uncertainties are uncorrelated, the combined uncertainty in the measurement of k1b is ±8% from σNH2(ν0), ± 8% from kdiff(NH2), and ±24% from experimental scatter, resulting in a total uncertainty of ±27% in the uncertainty in k1b. Of course, this is just a rough estimate because of the number of different

IV. CONCLUSION The rate constant for the NH2 self-recombination reaction, k1b, has been measured with four different bath gases, He, Ne, Ar, and N2, at 296 ± 2 K and over a pressure range from 1366



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(19) Altinay, G.; Macdonald, R. G. Part 2, manuscript in preparation. (20) Klippenstein, S. J.; Harding, L. B.; Rusic, B.; Sivaramakrishnan, R.; Srinivasan, N. K.; Su, M.-C.; Michael, J. V. J. Phys. Chem. A 2009, 113, 10241−10259. (21) Xu, Z.-F; Fang, D.-C.; Fu, X.-Y. Int. J. Quantum Chem. 1998, 70, 321−329. (22) Kleiner, I.; Brown, L. R.; Tarrago, G.; Kou, Q.-L.; Picque, N.; Guelachvili, G.; Dana, V.; Mandin, J.-Y. J. Mol. Spectrosc. 1999, 193, 46−71. (23) Asatryan, R.; Bozzelli, J. W.; da Silva, G.; Swinnen, S.; Nguyen, M. T. J. Phys. Chem. A 2010, 114, 6235−6249. (24) Biczysko, M.; Poveda, L. A.; Varandas, A. J. C. Chem. Phys. Let. 2006, 424, 46−53. (25) Vaghjiani, G. L. Int. J Chem. Kinet. 1995, 27, 777−790. (26) Fuller, E. N.; Ensley, K.; Giddings, J. C. J. Phys. Chem. 1969, 73, 3679−3685. (27) Lynch, K. P.; Michael, J. V. Int. J. Chem. Kinet. 1978, 10, 233− 248. (28) Brown, N. J.; Bastien, L. A. J.; Price, P. N. Prog. Eng. Combust. Sci. 2011, 37, 565−582. (29) Ivanov, A. V.; Trakhtenberg, S.; Bertram, A. K.; Gershenzon, Y. M.; Molina, M. J. J. Phys. Chem. A 2007, 111, 1632−1637. (30) Yamasaki, K.; Watanabe, A.; Tanaka, A.; Sato, M.; Tokue, I. J. Phys. Chem. A. 2002, 106, 6563−6569. (31) Bahng, M.-K.; Macdonald, R. G. J. Phys. Chem. A 2007, 111, 3850−3861. (32) Loomis, R. A.; Reid, J. P.; Leone, S. R. J. Chem. Phys. 2000, 112, 658−669. (33) Yamasaki, K.; Watanabe, A.; Kakuda, T.; Fukushima, H.; Endo, M.; Maruyama, C.; Tokue, I. J. Phys. Chem. A. 2002, 106, 7728−7735. (34) Smith, M. A. H.; Rinsland, C. P; Fridovich, B.; Rao, K. N. In MolecularSpectroscopy: Modern Research Vol III; Rao, K. N., Ed.; Academic Press: Orlando, FL, 1985; Chapter 3. (35) Pine, A. S.; Markov, V. N. J. Mol. Spectrosc. 2004, 228, 121−142. (36) Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 161−169. (37) Gilbert, R. G.; Luther, K.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 169−177. (38) Troe, J; Ushakov, V. G. J. Chem. Phys. 2011, 135, 054304− 054304-10. (39) Fernández-Ramos, A.; Miller, J. A.; Klippenstein, S. J.; Truhlar, D. G. Chem. Rev. 2006, 106, 4518−4584. (40) Gao, Y.; Macdonald, R. G. J. Phys. Chem. A 2005, 109, 5388− 5397.

1 to 20 Torr. The results of this work were fit to the Troe parameters, k0, kinf, and Fcent, according to eqs 6−8. The value of kinf was taken to be the theoretical value at 296 K calculated by Klippenstein et al.,20 kinf = 7.9 × 10−11 cm3 molecule−1 s.−1 The optimum fit parameters k0 and Fcent are summarized in Table 8. The relative collision efficiencies for He:Ne:Ar:N2 are 1.0:0.96:1.6:2.0, respectively. The individual Troe parameters were: He, k0 = 2.8 × 10−29 and Fcent = 0.47; Ne, k0 = 2.7 × 10−29 and Fcent = 0.34; Ar, k0 = 4.4 × 10−29 and Fcent = 0.41; N2, k0 = 5.7 × 10−29 and Fcent = 0.61, with units cm6 molecule−2 s−1 for k0. The optimum parameters found in the Troe fits are not well-defined. There was a large range of k0, Fcent pairs that could fit the data reasonably well. Further effort is needed to extend these measurements over a more extensive pressure range and theoretical analysis using a master equation analysis. The rate constant for the NH2 + H reaction, k2b, was measured with N2 as a collision partner to be (2.3 ± 0.45) × 10−30 cm6 molecule−1 s−1, where the uncertainty is at the 2σ confidence level and includes all experimental contributions.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

ACKNOWLEDGMENTS This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, U.S. Department of Energy under Contract Number DE-AC02-06CH11357.

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REFERENCES

(1) Lis, D. C.; Goldsmith, P. F.; BerginE. A.FalgaroneE.Gerin, M.; Roueff, E. In ASP Conference Series; Scoville, N. Z., Zmuidzinas, J., Eds.; ASP: San Francisco, 2009; Vol. 417, pp 23−35. (2) Kawakita, H.; Mumma, M. J. Astrophys. J. 2011, 727, 1−11. (3) Dentener, F. J.; Crutzen, P. J. J. Atmos. Chem. 1994, 19, 331−369. (4) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. 1989, 15, 287−338. (5) Gardner, W. C., Jr. Gas-Phase Combustion Chemistry; SpringerVerlag: New York, 1999. (6) Miller, J. A.; Klippenstein, S., J. J. Phys. Chem. A 2000, 104, 2061− 2069. (7) Klippenstein, S. J.; Harding, L. B.; Glarborg, P.; Miller, J. A. Combsut. Flame 2011, 158, 774−789. (8) Konnov, A. A.; De Ruyck, J. Combust. Sci. Technol. 2000, 152, 23−37. (9) Skreiberg, Ø.; Kilpinen, P.; Glarborg, P. Combust. Flame 2004, 136, 501−508. (10) Dransfeld, P.; Hack, H.; Kurzke, H.; Temps, F.; Wagner, H. GG. Twentieth Symposium (International) on Combustion; The Combustion Institute: Pittsburg, PA, 1984; pp 655−663. (11) Gordon, S.; Mulac, W.; Nangia, P. J. Phys. Chem. 1971, 75, 2087−2093. (12) Khe, P. V.; Soullgnac, J. C.; Lesclaux, R. J. Phys. Chem. 1977, 81, 210−214. (13) Lozovskii, V. A.; Nadtochenko, V. A.; Sarkisov, O. M.; Cheskis, S. G. Kinet. Katal. 1979, 20, 918−922. (14) Patrick, R.; Golden, D. M. J. Phys. Chem. 1984, 88, 491−495. (15) Stothard, N.; Humpfer, R.; Grotheer, H.-H. Chem. Phys. Lett. 1995, 240, 474−480. (16) Fagerström, K.; Jodkowski, J. T.; Lund, A.; Ratajczak, E. Chem. Phys. Lett. 1995, 236, 103−110. (17) Bahng, M.-K.; Macdonald, R. G. J. Phys. Chem. 2008, 112, 13432−13443. (18) Bahng, M.-K.; Macdonald, R. G. J. Phys. Chem. 2009, 113, 2415−2423. 1367


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