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

Article pubs.acs.org/JPCA

Determination of the Rate Constants for the NH2(X2B1) + NH2(X2B1) and NH2(X2B1) + H Recombination Reactions in N2 as a Function of Temperature and Pressure Gokhan Altinay# and R. Glen Macdonald* Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439-4381, United States ABSTRACT: The recombination rate constants for the reactions NH2 + NH2 → N2H4 (reaction k1b) and NH2 + H → NH3 (reaction k2b) with N2 as a third-body have been measured as a function of temperature and pressure. The temperature range was from 292 to 533 K and the pressure range from a few Torr up to 300−400 Torr, well within the pressure falloff region. The NH2 radical was produced by 193 nm pulsed-laser photolysis of NH3 in a temperature controlled flow chamber. High-resolution time-resolved laser absorption spectroscopy was used to follow the temporal concentration profiles of both NH2 and NH3, simultaneously. The NH2 radical was monitored at 14800.65 cm−1 using the 1231 (0,7,0)Ã 2A1 ← 1331 (0,0,0)X̃ 2B1 ro-vibronic transition, and NH3 monitored at 3336.39 cm−1 on the qQ3(3)s (1,0,0,0) ← (0,0,0,0) ro-vibrational transition. The necessary collisional broadening parameters for each molecule were measured in separate experiments. The pressure and temperature dependence of k1b can be represented by the Troe parameters: k0, the low-pressure three-body recombination rate constant, k0(T) = (1.14 ± 0.59) × 10−19T−(3.41±0.28) cm6 molecule−2 s−1, and Fcent, the pressure broadening parameter, Fcent = 0.15 ± 0.12, independent of temperature. The data could not be fit by three-independent parameters, and the high-pressure limiting rate constant k∞(T) = 9.33 × 10−10T−0.414 e33/T cm3 molecule−1 s−1 was taken from the high-quality theoretical calculations of Klippenstein et al. (J. Phys. Chem A 2009, 113, 10241). The pressure and temperature dependence of k2b, can be represented by the Troe parameters: k0(T) = (9.95 ± 0.58) × 10−26T(−1.76±0.092) cm6 molecule−2 s−1, Fcent = 0.5 ± 0.2, k∞ = 2.6 × 10−10 cm3 molecule−1 s−1. Again, the data could not be fit with three independent parameters, and k2b∞ was chosen to be 2.6 × 10−10 cm3 molecule−1 s−1 and fixed in the analysis.

I. INTRODUCTION The amidogen radical, NH2, is an important intermediate in a number of chemical environments of fundamental importance, combustion chemistry, atmospheric chemistry, and astrochemistry. In combustion chemistry,1 the NH2 radical plays a key role in the chemistry of nitrogen containing molecules that are entrained in different fuel-feed stocks. This chemistry leads to the production of pollutants, NOX or the green-house gas N2O. At the same time, NH2 chemistry can be used as an abatement strategy for reducing these same species by the addition of various gases to combustion exhaust gases.2 In atmospheric chemistry,3 the NH2 radical is produced from the destruction of NH3 by photolysis and hydrogen abstraction reactions. Similarly, in astrochemistry, the fate of NH3 and NH2 are intimately rated in a number of environments4 from planetary atmospheres such as Titan, comets, and interstellar clouds5 It is important to note that NH2(X̃ 2B1) is isoelectronic with two other simple hydrogenated second row radicals, CH3(X̃ 2A1) and OH(X̃ 2Π), that are even of more fundamental interest especially in combustion6 and atmospheric chemistry. All three radicals are important fundamental building blocks in the production of many classes of different chemical compounds of related molecular structure. Furthermore, the self-recombination reactions of these three radicals have similar characteristics in that the interaction of two radicals with an © XXXX American Chemical Society

unpaired electron correlates to a singlet and triplet potential energy surfaces (PESs). On the singlet surface self-recombination results in the formation of stable products, while on the triplet PES an abstraction reaction can produce a stable molecular product and a radical or H atom. The interplay between these different product channels in these systems is receiving increasing scrutiny both experimentally7−12 and theoretically13−16 and with increasing accuracy. Similarly, the interaction of CH3(X̃ 2A1), NH2(X̃ 2B1), or OH(X̃ 2Π) with an H atom, again involving species with single unpaired electrons, likewise leads to the formation of stable products on the singlet surface and abstraction on the triplet surface. Studies of these relatively simple radical−radical reactions are a much more difficult experimental task than radical self-reactions because, in general, the temporal concentration profiles of two transient species must be monitored in order to determine the rate constant. Indeed, Special Issue: 100 Years of Combustion Kinetics at Argonne: A Festschrift for Lawrence B. Harding, Joe V. Michael, and Albert F. Wagner Received: January 28, 2015 Revised: April 9, 2015

A

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N2 at a backing pressure of 800 Torr and admitted to N2 flow through an ultrafine needle valve 2 m before reaching the reaction chamber offset by 5 cm from the center. The gases were injected perpendicular to the chamber axis through two concentric tubes. The inner tube was 0.125 in. in diameter and open at far end of the chamber. The outer tube was 0.313 in. in diameter and was sealed at the wall of the opposite conflate flange. Fine holes every 15 cm allowed the mixed and thermalized gases to be injected into the chamber. Flow rates of the N2 carrier gas of up to 5000 sccm were used so that chamber pressures of up to 400 Torr could be achieved and still refresh the gas in the photolysis zone between laser pulses. The laser systems used in the experiments have been discussed in detail in recent publications.9,11 The photolysis laser was a Lamda Physik Compex 205 excimer laser operating at 193 nm. The 675 nm laser used to monitor the NH2 radical was a Sacher Lasertechnik Lion 500 external-cavity laser. This laser could be fine-tuned over a range of over 0.5 cm−1 without mode hops. The IR laser was a Linos model 4500 OPO modified to operate in a dual-cavity configuration in which the idler (IR, wavelength) and pump radiation were resonant in the same laser cavity. In this configuration the mode-hop free tuning range of the IR radiation was about 0.25 cm.−1 The overlapped probe laser beams were multipassed through the photolysis zone using White cell optics with the notched mirror on the vertical axis so that the rectangular spot pattern had the same orientation as the long axis of the rectangular shaped photolysis zone. The number of passes that gave the most consistent signal-to-noise ratio was eight, giving an absorption path length of 1212 cm. Amplitude fluctuations of the probe laser beams passing through the photolysis zone are the largest source of noise in the experiments. As described previously,9,11 both laser beams were split into two optical paths, with I0 bypassing the reaction chamber and I passing through the photolysis zone, and carried the absorption signals. Common-mode noise is greatly suppressed by directly subtracting the balanced I0 and I signals in software. Both the I0 and I visible and infrared signals were digitized simultaneously by high-resolution (14 and 16 bit resolution, respectively) transient recorders. Both laser systems were continuously monitored by wavemeters and scanning Fabry− Perot spectrum analyzers to detect any deviation from singlemode behavior. At temperatures above 292 K, amplitude fluctuations, which increased rapidly with increasing temperature, were observed on the I channels of both laser systems. Under these circumstances, the red laser’s beam image was observed to shimmer causing movement across the detector. This effect was attributed to refractive index grades in the crystalline UV CaF2 windows induced by irregular temperature profiles. These fluctuations were largely suppressed but not entirely eliminated by internally water-cooling the window mounts. The kinetic data collection was conducted using a LabView program described in more detail in previous works.9,11 Briefly, temporal profiles of both NH3 and NH2 were recorded simultaneously, corrected for common-mode amplitude fluctuations and signal averaged. Tuning to the peak of an absorption feature was facilitated by recording and displaying the integrated absorption signal for each species along with a moving average of these signals. The wavemeter reading of each laser system was also recorded every second of data collection. A separate LabView program was written to measure the pressure broadening parameters for each of the spectral lines

there are significantly fewer low-temperature pressure-dependent experimental17,18,10,19 studies of the recombination of these three radicals with H atoms than the self-recombination reactions. On the theoretical side the situation is not much different; however, there have been important studies of the reaction20,21 CH3 + H and the reverse reaction.22 For OH + H, there has been one recent23 high-level electronic structure and kinetic investigation of this reaction as a function of temperature and pressure. The present work is a continuation of previous efforts9,10,24 from this laboratory to provide reliable rate constant information on these two classes of reactions involving NH2. The present work involves the measurement of the temperature and pressure dependence of reactions 1b and 2b: NH 2 + NH 2 + N2 → N2H4 + N2

(1b)

and NH 2 + H + N2 → NH3 + N2

(2b)

The experiments were conducted in a temperature controlled flow chamber designed to prevent any possibility of wall interactions affecting the chemistry. Both NH2 and NH3 were monitored simultaneously by high-resolution time-resolved laser absorption spectroscopy. The NH2 radical was produced by 193 nm laser photolysis of NH3. The present study significantly extends the pressure range from our previous work10,11 and provides the only experimental information on the temperature dependence of k1b and k2b around 300 K. The direct measurement of k2b in the present work shows that previous measurements25,26 of k1b as a function of N2 pressure near 300 K were actually a composite of both k1b and k2b and that k2b cannot be ignored in the data reduction as previously argued. The measurements of k1b will also be compared to the recent high-level electronic structure calculations and variablereaction-coordinate transition-state theory calculations of Klippenstein et al.16

II. EXPERIMENTAL SECTION The experimental apparatus was described11 recently and will only be briefly described here. The reaction chamber consisted of a 122 cm long 304 stainless-steel pipe 15.2 cm in diameter terminated with conflate flanges. Brewster angle UV grade CaF2 windows 50 mm in diameter were attached to the chamber on 15 cm long side arms. The ArF photolysis laser and the twoprobe laser beams were admitted to the reaction chamber along its central axis. The base optical path length was 151.5 cm. The chamber was heated by six 700 W Watlow barrel heaters, and the temperature was controlled by three PID Watlow controllers, dividing the heated regions into three symmetric zones, end, middle, and center. The side arms were wrapped with high temperature heating tape, and the temperature was controlled by simple intermittent controllers. The chamber and side arms were wrapped with ceramic wool. A thermocouple could be moved continuously along the length of stainless-steel cylinder through a sealed 1/4 in. tube, offset by 5 cm from the central axis. At the highest temperature the variation of the temperature along the axis was less than ±3 C. Both gases used in the experiment were supplied by AGA. The N2 carrier gas was 99.9995% pure and the NH3 was 99.99% pure. Both gases were used directly from their cylinders. The NH3 injection system was modified to accommodate the higher reaction chamber pressures. Two 20 L glass storage bulbs were filled with a 20% mixture of NH3 in B

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Figure 1. Typical scans over the line profiles of the NH2 (red crosses) and NH3 (red circles) transitions listed in Table 1 at different temperatures and pressures. The corresponding Voigt profiles with baseline offset are shown by the solid black lines. Figure 1a shows the NH2 transition at 292 K and 305 Torr of N2. The profile was fit with ṽ0 = 14800.656 cm−1 and bL = 0.0452 ± 0.00070 cm−1 (HWHM). The output from an etalon with a FSR of 2.0 GHz is shown at the top of the figure, with an arbitrary y-axis. Figure 1b shows the scan of the NH3 transition at 292 K and 155 Torr of N2. The Voigt parameters were ṽ0 = 3336.392 cm−1 and bL(N2) = 0.0217 ± 0.00024. Panel c is the same as panel b except at 422 K and 202 Torr of N2 with Voigt parameters ṽ0 = 3336.391 cm−1 and bL(N2) = 0.0212 ± 0.00036 cm.−1 Panel d is the same as panel b except for T = 533 K and 266 Torr of N2 with Voigt parameters ṽ0 = 3336.391 cm−1 and bL(N2) = 00242 ± 0.00019 cm.−1 The uncertainties in bL(N2) are at the 2σ level.

absorption spectroscopy has the potential to quantitatively measure the temporal concentration of transient species under a variety of experimental conditions; however, the appropriate collision broadening parameters need to be determined. The observed absorbance for a species X, AX, at wavenumber, ṽ, is given by the Beer−Lambert law27

chosen to monitor the NH3 and NH2 temporal concentration profiles. A continuous slow sawtooth ramp voltage, 0−10 V over 10 min, was applied to the fine-tuning controls of the laser used to probe the molecule of interest. For NH3, the line profile was sampled in a semicontinuous fashion by digitizing and averaging I0 and I every n seconds for a period of n/4, where 1/ n was the sampling frequency. For NH2, the ramp voltage was applied to the grating piezoelectric drive, and the photolysis laser was triggered with a frequency of 1/n. However, the temporal NH2 concentration profile was only sampled and averaged for a few hundred microseconds after a small delay following the photolysis laser pulse. For NH2 measurements, the signal from a nonscanning 2 GHz FSR Fabry−Perot etalon was also recorded.

3AX = Ln(3I0/3I ) = lσ (v )̃ X [X]

(1)

where l is the path length, σ(ṽ) is the absorption coefficient at ṽ of species X, and the brackets indicate its concentration in molecules cm−3. The temporal concentrations of NH2 and NH3 were calculated using eq 1 and a determination of σ(ṽ0), where ṽ0 is at the peak of the absorption feature. In turn, the absorption coefficient is related to molecular and environmental properties by

III. RESULTS AND DISCUSSION A. Pressure Broadening and Peak Absorption Coefficient Determination. High-resolution time-resolved laser

σ(v ̃ − v0̃ ) = Sjig (v ̃ − v0̃ ) C

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Figure 2. Determination of b0L(N2) for the NH2 and NH3 transitions used in the present experiments is shown. The slope of bL(N2) as a function of N2 pressure and temperature gives b0L(N2). Figure 2a shows the plot for bL(N2) measurements for the NH2 transition as a function of N2 pressure at 292 K. The slope of a linear fit to the data gives b0L(N2) = (1.14 ± 0.093) × 10−4 cm−1 Torr−1, where the uncertainty is at the 2σ level. Panels b−d show the same but for the determination of b0L(N2) for the NH3 transition at the three temperatures of the present work. The results of these measurements are summarized in Table 1

where Sji is the line strength of the observed transition from state i to j and g(ṽ − ṽ0) is the line shape function. The line strength depends on molecular properties and temperature of the absorber through a transition moment and thermal populations of quantum states i and j. On the other hand, the line shape function depends on the temperature, pressure, and nature of the gas mixture. A simple formulation to account for pressure broadening effects on g(ṽ) is given by a Voigt profile, a convolution of independent Doppler and Lorentz line profiles described by28 g (v ̃ − v0̃ ) =

P′a π

∞

of pressure. The peak Doppler broaden absorption coefficient is given by σD(ṽ0) is given by σD(ṽ0) = SjiP′. As outlined in section II, the line shape profiles for the NH3 infrared and NH2 visible transitions used in this work were recorded by slow wavenumber scans recording I0 and I values in small wavenumber increments so that a large number of points defined the line profiles. Typical scans over the NH2 and NH3 transitions are shown in Figure 1. Figure 1a shows a scan over the NH2 visible transition at the only temperature studied, 292 K. At higher temperatures, the loss in signal-to-noise due to increased Doppler width and smaller absorbance made direct measurements more problematic, and another avenue was used to determine σNH2(ṽ0), as will be discussed. The resolution of the wavemeter used to monitor the frequency of the diode laser radiation was 10 times poorer than that monitoring the infrared radiation. As a precaution about the accuracy of this wavenumber scale, the output of a nonscanning Fabry−Perot etalon with a FSR of 2.0 GHz was also recorded. This is also shown as the top trace in Figure 1a. The average FSR of the peaks in Figure 1a, determined using the wavenumber scale in the figure was 2.01 GHz, indicating good linearity and accuracy

−y 2

∫−∞ a2 + e(ζ − y)2 dy

(3)

where P′ is the normalization constant for a pure Doppler broaden line shape, P′ = {ln 2/π}1/2/bD, with bD = 3.581 × 10−7 ṽ0(T/M)1/2, the HWHM Doppler width, T is the temperature, and M is the mass of the absorber, a = bL/bD{ln 2}1/2, and ξ ={ln 2}1/2(ṽ − ṽ0)/bD. The pressure broadening parameter, bL, is the HWHM of the line at pressure P (Torr) given by bL = b0LP, where b0L is the slope of the line of bL plotted as a function D

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Table 1. Parameters to Describe the Calculation of the Voigt Line Profile for the qQ3(3)s (1000) ← (0000) Ro-vibrational Transition of NH3 in Collisions with N2 T (K)

ν0 (cm−1)

σD(ν0)a,b

bD (HWHM)c

bL0 (HWHM)d,e

292 ± 2 422 ± 5 533 ± 5

3336.39

(1.96 ± 0.059) × 10−18 (1.02 ± 0.03) × 10−18 (6.76 ± 0.2) × 10−18

4.96 × 10−3 5.95 × 10−3 6.79 × 10−3

(1.42 ± 0.019) × 10−4 (1.11 ± 0.057) × 10−4 (9.27 ± 0.028) × 10−5

Units = cm2 molecule−1. bUncertainty is estimated at the ±2σ level. cUnits = cm−1. dUnits = cm−1 Torr−1. eUncertainty is at the ±2σ confidence level, see text. a

Table 2. Parameters To Describe the Calculation of the Voigt Line Profiles for the 1231 ← 1331 (070) A2A1 ← (000) X2B1 Rovibronic Transition of NH2 in Collisions with N2

a

T (K)

ν0 (cm−1)

σD(ν0)a,b

bD (HWHM)c

bL0 (HWHM)d,e

292 ± 2 422 ± 5 533 ± 5

14800.65

(1.22 ± 0.09) × 10−17 (7.58 ± 0.76) × 10−18 (5.38 ± 0.54) × 10−18

2.271 × 10−2 2.72 × 10−2 3.06 × 10−2

(1.04 ± 0.064) × 10−4 (6.30 ± 1.14) × 10−5 (3.77 ± 1.18) × 10−5

Units = cm2 molecule−1. bUncertainty is estimated at the ±2σ level. cUnits = cm−1. dUnits = cm−1 Torr−1. eUncertainty is at the ±2σ level, see text.

in the scan. The line profiles were all fit to Voigt function (eq 3) with a small baseline offset using the Origin graphic software package.29 All the fitting parameters, A(area), bD, bL, ṽ0, and offset, could not be determined independently with the quality of the data; however, by fixing bD and ṽ0, the other three parameters could be determined with statistical estimates of the errors involved in their determinations. As can be seen in Figure 1 the Voigt profiles fit the data for both NH2 and NH3 line profiles. The baseline offset shown in Figure 1 is small and attributed to the long interval time for the completion of a wavelength scan, and the manual adjustment to balance the I0 and I laser intensities for both laser systems as the lasers output power varies with wavelength. Figure 1a shows the scan over the 1231 ← 1331 (0,7,0)A2A1 ← (0,0,0)X2B1 ro-vibronic transition at 292 K and 305 Torr. The absorbance signal is time-averaged following the ArF photolysis pulse after a short delay to allow for ro-vibrational equilibration. Figure 1 panels b, c, and d show a typical scan over the NH3 qQ3(3)s(1,0,0,0) ← (0,0,0,0) ro-vibrational transition at temperatures of 292, 422, and 525 K and N2 pressures of 155, 202, and 266 Torr, respectively. The pressure of NH3 in each of these scans was approximately 0.018, 0.024, and 0.074 Torr, respectively. Figure 2a shows the plots of bL(N2) vs N2 pressure for the NH2 transition at 292 K; Figure 2 panels b−d show the same, except for the NH3 transition at the three temperatures used in the kinetic experiments. The uncertainties in measurements of bL(N2) returned by the fitting program at the 2σ level of uncertainty are approximately the size of the symbols in the figures. As is evident from all four panels the data are fit by a straight line forced to pass through the origin. The slope yields the pressure broadening parameters (HWHM) b0L(N2) for NH2 at 292 K and b0L(N2) for NH3 at the three temperatures. For NH2, b0L(N2) was found to be (1.14 ± 0.097) × 10−4 cm−1 Torr−1, where the uncertainty is at the 2σ level of uncertainty. The value used to calculate σNH2(ṽ0) for the determination of the temporal time dependence of the NH2 concentration was slightly lower than this value and will be discussed later. For the NH3 transition, the values for σNH3(ṽ0) and b0L(N2) are summarized in Table 1. The line strength of the NH3 q Q3(3)s transition was taken from the 295 K temperature data of Pine and Markov,30 and the Hitran31 data were taken for the temperature dependence of this transition. The measurement of b0L(N2) at 292 K is in excellent agreement with the detailed measurements of Pine and Markov for the collisional

broadening of the same NH3 transition. The temperature dependence of b0L(N2) can be represented by b0L(N2) = ATn. 4.75 ) × 10−3 cm−1 The results of this fit give, A = (8.38 ± 3.03 Torr−1 and n = (−0.718 ± 0.74), where the uncertainties are at the 2σ level. The temperature dependence of this collisional broadening parameter is in good agreement with the value of n = −0.72 for this NH3 band in the HITRAN30 database. It is evident from Figure 2 and summarized in Table 1 that the collisional broadening parameters for the NH3 molecule are well-established and in good agreement with literature values. A unique feature of the NH3/NH2 system and the experimental measurements is that the initial production of NH2 and the initial loss of NH3 are nearly equal; that is, Δ[NH3]0 = [NH2]0; hence, the radical concentration is directly calibrated from the known spectral properties of NH3. It has been demonstrated experimentally24 that the quantum yield for NH2 production is greater than 99%. Furthermore, both species were detected simultaneously following the photolysis laser pulse. As discussed previously,24 there is an initial rapid bleaching transient on the NH3 profile, which lasts for several hundred microseconds at the lowest pressures. Similarly, the NH2 radical is produced with substantial internal energy;32 however, rapid internal energy relaxation occurs in both species, and their initial concentrations can be determined by extrapolation back to t = 0 from regions past the transient occurrences. In turn, the concentration of [NH2]0 can be used to calculate σNH2(ṽ0) from σNH2(ṽ0) = A0NH2σNH3(ṽ0)/A0NH3, where A0X is the extrapolated t = 0 initial absorbance of species X. This is referred to as the σNH2(exp). A calculated peak absorption coefficient, σNH2(cal), was calculated as a function of b0L(N2), according to eq 3, for a range of b0L(N2) values separated by 0.2 × 10−4 cm−1 Torr−1 at each experimental pressure at given temperature. The optimal b0L(N2) value was determined by minimizing the sum of the squared residues between σNH2(cal) and σNH2(exp) over the whole pressure range. The results are summarized in Table 2. The temperature dependence of σNH2(ṽ0)D was calculated from a direct state count of the internal partition function33 and temperature dependent Doppler line width. These are summarized in the third column of Table 2. The reported errors in the Tables are an estimate of uncertainties in the determination of a parameter at the 2σ level. At 292 K, this optimal collision-broadening parameter was 10% smaller than the experimental measurement shown in Figure 2a. For each set E

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Figure 3. Results for the determination of the optimum value of b0L(N2) used to calculate the values of σNH2(ṽ0) over the whole pressure range for a given temperature. The σNH2(exp), was determined at each pressure as described in the text. The σNH2(cal) was determined using the value of b0L(N2) that minimized, in a least-squares sense the residuals (σNH2(cal) − σNH2(exp).2 The ratio σNH2(cal)/σNH2(exp) is plotted over the pressure range for each temperature. The dashed line in each figure gives the optimum average value at each temperature with the uncertainty of two standard deviations from the average. Each symbol in the figures is the average of at least three measurements under the same conditions but different initial NH2 concentrations. Note, at 292 K the line profile determination of b0L(N2) for NH2 was (1.14 ± 0.093) × 10−4 cm−1 Torr−1 (see Figure 2a), but the optimum value was found to be 1.04 ± 0.064) × 10−3 cm−1 Torr−1, as listed in Table 2

of experimental conditions the photolysis laser intensity was varied to change the initial radical concentration so each data point was the average of between three and five separate measurements. The ratio of calculated to experimental values of σNH2(ṽ0), σNH2(cal)/σNH2(exp), are plotted in Figure 3 for the three experimental temperatures. As is evident from the figure, there is scatter in the data. As noted earlier, amplitude fluctuations on both laser beams increase with increasing temperature, and the absorption cross sections also decrease with increasing temperature, all contributing to a loss of signal-

to-noise at higher temperatures. The temperature dependence 40 of b0L(N2) for the NH2 transition is given by ANH2 = 16.3 ± .07 and n = −1.70 ± 0.54, where the uncertainties are at the 2σ level. B. Reaction Mechanism. The reaction mechanism has been discussed in several recent publications9,24 and will only be briefly discussed here. An important point to note is that Klippenstein et al.16 have examined the PESs for the interaction of two NH2 radicals on the lowest energetic singlet and triplet PESs. On the singlet surface at the temperatures of the present F

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reactants

1a 1b 2a 2b 3a 3b 4 5 6 7 8 9a 9b 9c 10 11 a

NH2 NH2 NH2 NH2 NH2

+ + + + +

products −

NH(X ∑ ) + NH3 N2H4 + N2 NH(X3∑−) + H2 NH3 + N2 N2H2(cis) + H N2H2(trans) + H NH2 + H2 N2 + H 2 + H NH3 + N2 + H H2 + N2 N2H3 + H2 N2H2 + H2 NH2 + NH2 NH3 + NH NH3 + N2H3 X 3

NH2 NH2 + N2 H H + N2 NH

NH3 + H N2H2 + H N2H2 + NH2 H + H + N2 N2H4 + H N2H3 + H

N2H4 +NH2 X

rate constanta,b,c

ref

9.36 × 10−24T3.53e278/T measured 7.70 × 10−15 measured k3a+3b = 9.6 × 10−11

16

1.21 × 10−10e6920/T 1.41 × 10−19T2.6e−112/T 1.46 × 1025T4.1e−811/T k0 = 1.8 × 10−30T−1.0b 1.17 × 10−11e−1260/T 1.70 × 10−11 8.30 × 10−11e1010/T 1.70 × 10−13 1.0 × 10−13 kdiff(X) (diffusion and flow)c

35 36 36 37 38 39 39 39 40

34 34

ki bimolecular rate constant, units = cm3 molecule−1 s−1. bk0 termolecular rate constant, units = cm6 molecule−2 s−1. cFirst-order, units = s−1.

zone has a rectangular geometry, and there are two diffusion time scales for motion along each axis of the rectangle. At low pressures (50 Torr), diffusion is too slow to be measured but can be calculated from the slope of a plot of kdiff(NH3) vs 1/P measured for the lower pressure data. C. Determination of k1b and k2b. Figure 4 shows the temporal concentration profiles of NH2 and NH3 measured at a pressure of 89.5 Torr and a temperature of 292 K. In each figure, the experimental data are represented by the black lines (actually recorded at one microsecond per point intervals for 10k points), and the model predicted concentration profiles for NH2 and NH3 by the open red circles and open red squares, respectively, using the optimum rate constant determinations for k1b and k2b. Although not completely clear, the NH2 profile shows a rapid rise and fall of about 50 microseconds, and similarly, there is initial increase in NH3 concentration at time 0, both features are due to rapid vibrational equilibration. The determination of the rate constants was initiated after this induction period. Figure 4b shows the NH3 profile on the same scale as the NH2 profile. The inset shows the complete profile and the initial NH3 concentration level. Figures 5 and 6 show temporal concentration profiles of NH2 and NH3 measured at the lowest and highest temperatures and near the highest pressures at these temperatures. These profiles reflect the poorest signal-to-noise in the present experiments at each temperature. The figure symbols and construction are the same as Figure 4. In both Figures 5 and 6, the initial NH2 concentrations are similar but the decay of NH2 and rise in NH3 are substantially faster in Figures 4a and 4b compared to that in Figures 5a and 5b. A comparison of the pretrigger baseline for both species, with the same number of records

experiment the only energetically accessible product channel is the recombination channel to form N2H4. The energy barriers leading to other product channels involving the N2H2 isomers + H2 are too high compared to the temperatures used in the present experiments, and these channels do not make any significant contribution. Similarly, the theoretically predicted rate constant for the abstraction channel occurring on the triplet surface, reaction 1a, is much smaller than the recombination rate constant over the experimental temperature range. Table 3 lists the complete reaction mechanism34−40 that was used in the data analysis; however, the following reactions account for 99% of the chemistry: 193nm

NH3 ⎯⎯⎯⎯⎯→ NH 2 + H −

NH 2 + NH 2 → NH(X3 ∑ ) + NH3 ΔH0r0 = −58 kJ mol−1

(1a)

NH 2 + NH 2 + (N2) → N2H4 + (N2) ΔH0r0 = −268 kJ mol−1

(1b)

−

NH 2 + H → NH(X3 ∑ ) + H 2 ΔH0r0 = −46 kJ mol−1

(2a)

NH 2 + H + (N2) → NH3 + (N2) ΔH0r0 = −444.1 kJ mol−1 NH 2 + NH → N2H 2(cis) + H →N2H 2(trans) + H

X → diffusion/flow

(2b) ΔH0r0 = −102 kJ mol−1 ΔH0r0

−1

= −124 kJ mol

(3a) (3b)

(11)

The enthalpies in the above reactions have been taken from Klippenstein et al.16 and Biczysko et al.41 All species are removed by diffusion and flow, reaction 11 in Table 3. As in a previous work, the binary diffusion coefficient for each species was calculated by the diffusion volume method developed by Fletcher et al.42 These were converted to firstorder rate constants by normalizing to the rate that NH3 was replenished following the photolysis laser pulse. The photolysis G

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Figure 4. Typical temporal concentration profiles of NH2 and NH3 for the simultaneous measurement of k1b and k2b at T = 292 K and PN2 = 89.5 Torr. In panel a, the solid black line is the experimental NH2 profile recorded every microsecond and signal averaged for 25 photolysis laser shots at a repetition rate of 0.33 Hz. The open red circles are the computer generate NH2 predictions using the model in Table 3. The optimum value of k1b was 2.17 × 10−11 cm3 molecule−1 s,−1 with a goodness-of-fit parameter of ±12% and for k2b, it was 7.06 × 10−12 cm3 molecule−1 s,−1 with a goodness-of-fit parameter of ±3%. The solid blue circles are the model predictions for the H atom concentration using an estimate of kdiff(H) of 35 s−1, as discussed in the text. At this pressure, the NH2 concentration is rate limiting, and the determination of k2b is almost independent of kdiff(H). Panel b is the simultaneously recorded NH3 profile shown by the black line. The computer generated NH3 profile is given by the red squares. The inset shows the complete NH3 profile with its baseline.

Figure 5. Same as Figure 4 except for the measurement of k1b and k2b at T = 292 K and PN2 = 342 Torr. The repetition rate of the photolysis laser was 0.2 Hz, and 50 pulses were signal averaged. The optimum value of k1b was 2.71 × 10−11 cm3 molecule−1 s,−1 and for k2b, it was 2.61 × 10−11 cm3 molecule−1 s,−1 with goodness-of-fit parameters of ±14% and 5%, respectively. The model predictions for the H atom concentration were calculated using an estimate of kdiff(H) of 10 s−1, as discussed in the text. Panel b is the simultaneously recorded NH3 profile shown by the black line. The computer generated NH3 profile is given by the red squares. The inset shows the complete NH3 profile with its baseline.

expected to ultimately produce NH3 but nothing is abnormal with the NH3 profile. The NH3 profiles are fit within the noise over the complete NH3 profile. A more likely possibility is a baseline shift of a few percent on the visible laser optical path, perhaps induced by refractive index gradients. These could be small at low pressure but increase in magnitude at higher ones. The broad wings of a Voigt line profile made it impractical to verify the exact cause of the presumed baseline shift. The profiles were fit by a variable step Runge−Kutta integration routine which takes many more steps in regions of rapid concentration changes than at times of small changes, as can be seen in Figures 4a, 5a, and 6a by the density of model generated points clustered around the initial portion of the profiles. Thus, the fitting procedure weights the initial portion of NH2 profile more than at later times, and the least-squared determination of k1b is largely determined by the initial portion. Over the whole profile, the value of k1b determined is reduced from a higher initial value in order to increase the NH2 concentration at long times and hence, reduce the chi-squared sum over the whole

signal-averaged, indicates the loss in signal-to-noise with increasing temperature, as mentioned in section II. It is noticed in Figures 4a, 5a, and 6a that the NH2 experimental profiles do not match the model generated profile, especially at long times. In all previous studies from this laboratory a similar observation was found for all species probed, transients or stable molecules, and was attributed to the diffusion process being governed by a fast and slow diffusional rate constant caused by the rectangular geometry of the photolysis zone.11 This is the case for Figure 4a but not the higher pressure experiments because NH2 can react further with excess H atoms and be removed from the system. The smaller diffusion rate constant is too small to influence the kinetics on the time scale of the profiles (9 ms observed reaction time). Several possibilities exist. First, the reaction mechanism is deficient and NH2 is produced at long times This seems unlikely as both NH2 and NH3 concentration profiles depend on k1b and processes producing NH2 would be H

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an iterative process. The kinetic equations corresponding to the model given in Table 3 were solved to find the best rate constant, either k1a or k2b, that minimized the difference between the calculated and experimental NH2 or NH3 concentration profile, respectively, in a least-squared sense. The other rate constant was fixed at its input value. The process was repeated for the other profile using the new optimized rate constant in the model calculations while the previously fixed rate was optimized. This sequence was repeated until successive iterations produced rate constants that agreed with the previous iteration within ±2%. Generally, convergence was reached after three or four compete cycles. As in previous work,43 a reaction path analysis was always conducted, and an integrated reaction contribution factor (IRCFX) was calculated for all the species in the computer model in Table 3. At low-pressures, less than 20 Torr, reaction 1b and diffusion dominate the removal of the NH2 radical, and diffusion dominates the recovery of NH3. As the pressure increases, between 20 and 100 Torr, the contribution of reaction 2b increases for both removal of NH2 and production of NH3, conversely diffusion rapidly becomes less important. At pressures greater than 100 Torr, the contribution of reaction 2b to the removal of NH2 increases almost linearly while reaction 1b enters the falloff region. At the highest pressure, the contribution of reaction 2b to NH2 removal approaches that of reaction 1b. This is illustrated in Figure 5 where the IRCFNH2 by NH2 is 0.523 and by H is 0.475 and in Figure 6 where IRCFNH2 by NH2 is 0.665 and by H is 0.323. The experimental conditions and determinations of k1b and k2b are summarized in Tables 4, 5, and 6 for each measurement temperature, 292, 422 and 533 K, respectively. As noted, multiple measurements of k1b and k2b were made under the same experimental conditions but different initial NH2 radical concentrations. The ranges of initial radical concentrations are given in column 4 of each of these tables. The concentration of NH3 was measured using absorption spectroscopy. The IR probe laser was manually tuned off and on line center, recording I 0 and I, respectively. Generally, the NH 3 concentration was high compared to that in previous work but sufficiently small to keep the transmission of the photolysis laser greater than 40%. There was no significant dependence on rate constant measurements with NH3 concentrations as can be seen from Tables 4, 5, and 6. It has been pointed out in a previous work44 that the radical gradient along the optical axis does not significantly influence the measurements of radical− radical recombination rate constants. This can be rationalized by noting that with modest attenuation of the photolysis beam the radical distribution along the photolysis length is to a good approximation linear because of the long-base path length. The absorption signal provides a measure of the average line-of-site radical concentration, which occurs at the midpoint of the optical path length. The near second-order rate constant is only a linear function of radical concentration. Thus, the higher radical concentrations near the entrance window are compensated by the lower radical concentrations near the exit window, and the measured second-order rate constant corresponds to that for the average radical concentration along the line-of-sight path. The rate constant measurements given in columns five and six of Tables 4−6 are the average of the different measurements for different initial NH2 concentrations, and the scatter in these measurements are at the ±2σ level of uncertainty.

Figure 6. Same as Figure 4 except for T = 533 K and P = 301 Torr. The repetition rate of the photolysis laser was 0.2 Hz, and 50 pulses were signal averaged. The solid black line is the experimental NH2 profile. The open red circles are the computer generated NH2 profile for the optimum value of k1b equal to 1.08 × 10−11 cm3 molecule−1 s−1, and for k2b, equal to 7.00 × 10−12 cm3 molecule−1 s−1, with goodnessof-fit parameters of ±18% and ±8%, respectively. The solid blue circles are the model predictions for the H atom concentration using an estimate of kdiff(H) of 27 s−1. Panel b is the simultaneously recorded NH3 profile shown by the black line. The computer generated NH3 profile is given by the red squares . The inset shows the complete NH3 profile with its baseline.

profile. Thus, the model slightly over predicts the initial NH2 concentration and under predicts the long time behavior, as observed in Figures 4a, 5a, and 6a. In any case, the results are only marginally affected by this baseline shift, whatever the cause. If the complete NH2 profiles were fit over the complete observation time of 9 ms, k1b would be further reduced by about 6%. The time interval to fit the data is a compromise between what is the cause of the baseline shift and the possibility of a model deficiency. It should also be pointed out that the highest pressure experiments showed the most deviation from the model predictions, and the fits between the model predictions and the NH2 profiles are in better agreement at low pressures, as shown in Figure 4a. The goodness-of-fit parameters for the determination of k1b and k2b are also summarized in each figure caption. The loss of H atoms (solid blue circles) predicted by the model calculations, is almost totally due to reaction 2b and flow. In all cases, the concentration of NH2 is the limiting reagent, and the rate constant determination of k2b had only a weak dependence on kdiff(H) decreasing with increasing pressures. The optimum rate constants were determined by I

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The Journal of Physical Chemistry A Table 4. Summary of Experimental Conditions and Measurements of k1b and k2b in N2 at 292 K partial pressure (Torr) [N2] (×10 )

P N2

PNH3

[NH2]0a,b (×1013)

k1bc,d (×10−11)

k2bc (×10−11)

0.180 0.221 0.272 0.454 0.480 0.652 0.998 1.49 1.72 2.26 2.96 4.48 4.86 6.51 8.35 10.3 11.3 13.7

5.44 6.66 8.24 13.7 14.5 19.7 30.1 45.1 52.1 68.2 89.5 135 147 197 251 310 342 414

0.0083 0.0087 0.014 0.15 0.0089 0.014 0.016 0.018 0.021 0.023 0.016 0.0228 0.015 0.019 0.01 0.012 0.0035 0.018

3.9−2.0 4.0−1.0 6.1−1.5 6.5−1.5 3.8−0.98 5.4−3.8 7.0−3.5 5.6−3.9 7.6−1.8 7.7−1.8 5.2−3.0 8.0−3.9 5.7−3.7 6.0−4.6 6.7−5.8 7.1−3.6 4.6−3.3 6.5−5.8

(0.471 ± 0.021) (0.538 ± 0.14) (0.697 ± 0.033) (0.967 ± 0.16) (1.01 ± 0.06) (1.10 ± 0.18) (1.44 ± 0.050) (1.65 ± 0.048) (1.96 ± 0.072) (1.95 ± 0.11) (2.20 ± 0.096) (2.40 ± 0.066) (2.53 ± 0.12) (2.35 ± 0.25) (2.39 ± 0.28) (2.26 ± 0.28) (2.76 ± 0.29) (2.80 ± 0.13)

(0.093 ± 0.038) (0.143 ± 0.082) (0.207 ± 0.18) (0.244 ± 0.19) (0.232 ± 0.041) (0.377 ± 0.048) (0.444 ± 0.16) (0.637 ± 0.091) (0.704 ± 0.066) (1.30 ± 0.062) (1.08 ± 0.11) (1.91 ± 0.19) (2.67 ± 0.391) (3.20 ± 0.18) (2.57 ± 0.38) (3.32 ± 0.62)

a

a

18

Units = molecules cm−1. bMultiple rate constants measurements were made under the same flow conditions. cUnits = cm3 molecule−1 s−1. Uncertainty is ±2σ in the scatter of the multiple measurements.

d

Table 5. Summary of Experimental Conditions and Measurements of k1b and k2b in N2 at 422 K ± 3 K partial pressure (Torr) [N2] (×10 )

PN2

PNH3

[NH2]0a,b (×10−13)

k1bc,d (×10−11)

k2bc (×10−11)

0.151 0.232 0.318 0.425 0.554 0.86 0.96 1.76 2.25 3.07 3.52 4.61 4.61 5.73 6.64

6.57 10.1 13.8 18.6 24.2 37.6 41.9 76.7 98.2 134 154 201 201 250 290

0.024 0.026 0.029 0.026 0.034 0.018 0.029 0.022 0.033 0.019 0.019 0.045 0.024 0.023 0.025

6.2−1.6 6.7−3.6 6.5−5.8 6.2−1.6 7.4−3.7 4.7−2.6 6.3−1.6 6.3−5.3 7.1−4.9 4.7−3.9 4.3−3.6 7.3−6.2 4.8−4.0 4.8−2.6 4.8−3.4

(0.155 ± 0.027) (0.267 ± 0.019) (0.338 ± 0.022) (0.377 ± 0.017) (0.468 ± 0.010) (0.622 ± 0.085) (0.692 ± 0.035) (0.954 ± 0.050) (1.08 ± 0.066) (1.18 ± 0.060) (1.28 ± 0.038) (1.52 ± 0.087) (1.38 ± 0.072) (1.49 ± 0.14) (1.50 ± 0.172)

(0.053 ± 0.060) (0.201 ± 0.019) (0.216 ± 0.11) (0.185 ± 0.087) (0.240 ± 0.066) (0.176 ± 0.030) (0.240 ± 0.020) (0.347 ± 0.024) (0.453 ± 0.066) (0.539 ± 0.009) (0.728 ± 0.075) (0.706 ± 0.25) (1.08 ± 0.16) (1.29 ± 0.290)

a

a

18

Units = molecules cm−1. bMultiple rate constant measurements were made under the same flow conditions. cUnits = cm3 molecule−1 s−1. Uncertainty is ±2σ in the scatter of the multiple measurements.

d

Figures 7 and 8, 9 and 10, and 11 and 12 show the results for the measurements of k1b and k2b as a function of pressure at the temperatures of 292, 422 and 533 K, respectively. The red circles with error bars are the average of the measurements with error bars at the 2σ uncertainty level in the scatter. Troe45−47 fits to the data for k1b and k2b as a function of pressure are shown by the solid blue lines. In this representation, the pressure dependence of the bimolecular rate constant describing the production of products, k, is expressed as a function of three parameters: k0, the low-pressure termolecular three-body rate constant; k∞, the pressure independent highpressure limiting rate constant; F, a function describing the pressure dependence in the falloff region. Thus, k is given by

k=

k 0[M]k∞ F k 0[M] + k∞

(4)

where F is given by F=

log(Fcent) 1 + {log(k 0[M]/k∞)}2 /N 2

(5)

with N = 0.75 − 1.27log(Fcent)

(6)

Each data set was fit to the Troe representation using a commercial program, IGOR.48 This program could also fit weighted input data and return estimates of the statistical uncertainties in the fit parameters. Unfortunately the data were not of sufficient quality to independently return statistically J

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The Journal of Physical Chemistry A Table 6. Summary of Experimental Conditions and Measurements of k1b and k2b in N2 at 533 K ± 3 K partial pressure (Torr) [N2] (×10 )

PN2

PNH3

[NH2]0a,b (×1013)

k1bc,d (×10−11)

k2bc (×10−12)

0.145 0.148 0.185 0.242 0.423 0.609 0.755 0.86 1.27 1.62 1.85 1.94 2.47 2.49 2.89 3.74 4.74 5.44

8.02 8.17 10.2 13.4 23.4 33.6 41.7 46.6 70.1 89.9 102.5 107 137 137 160 207 262 301

0.036 0.037 0.034 0.035 0.018 0.021 0.025 0.026 0.024 0.017 0.022 0.036 0.029 0.041 0.027 0.033 0.047 0.031

7.9−3.7 6.7−2.6 7.8−1.9 7.0−4.8 6.2−1.4 4.8−3.1 5.4−2.3 2.7−1.2 4.9−2.3 2.0−1.6 5.5−2.5 6.4−3.1 6.1−2.5 7.1−3.3 5.3−2.2 5.3−2.5 7.0−4.9 6.1−4.0

(0.173 ± 0.048) (0.246 ± 0.049) (0.224 ± 0.063) (0.2404 ± 0.062) (0.289 ± 0.066) (0.328 ± 0.046 (0.354 ± 0.058) (0.470 ± 0.049) (0.453 ± 0.053) (0.581 ± 0.039) (0.571 ± 0.102) (0.572 ± 0.083) (0.677 ± 0.13) (0.698 ± 0.063) (0.763 ± 0.10) (0.869 ± 0.12) (1.06 ± 0.089) (1.07 ± 0.18)

(0.113 ± 0.043) (0.144 ± 0.16) (0.220 ± 0.074) (0.140 ± 0.11) (0.236 ± 0.059) (0.207 ± 0.049 (0.2613 ± 0.035) (0.274 ± 0.058) (0.324 ± 0.074) (0.313 ± 0.033) (0.353 ± 0.097) (0.468 ± 0.077) (0.489 ± 0.11) (0.634 ± 0.26)

a

a

18

Units = molecules cm−1. bMultiple rate constants measurements were made under the same flow conditions. cUnits = cm3 molecule−1 s−1. Uncertainty is ±2σ in the scatter of the multiple measurements.

d

experimental artifact such as the baseline shift shown in Figures 5 and 6 apparent on the NH2 concentration profile (but not present on the NH3 profile) could be present but not detected. The experimental measurements of k2b as a function of pressure for temperatures 292, 422, and 533 K, summarized in Tables 4, 5, and 6 are shown in Figures 8, 10, and 12. Troe fits to the data are also given, and the parameters are summarized in Table 8. A comparison between the data for k1b and k2b at each temperature clearly shows that the measurements of k2b are more uncertain than those for k1b. The Troe fits for k2b summarized in Table 8 are even more uncertain than those for k1b in Table 7. There are no reliable theoretical predictions for any of these parameters. The value of k∞2b was estimated to be the average of a high-level theoretical calculation of k∞2b for the reactions20,23 CH3 + H and OH + H involving the CH3 and OH radicals isoelectronic with NH2. The k∞2b rate constant was assumed temperature independent. A weighted fit to the data for k02b and Fcent2b did not converge unless Fcent2b was constrained. The value listed in Table 8 fell within this range and was also assumed to be temperature independent. The value of k02b was determined with the stated 2σ uncertainties with k∞2b and Fcent2b fixed at the values in Table 8. These fits are shown in Figures 8, 10, and 12 by the solid blue lines. The approximate Troe fits are a better representation of the data for an estimate of k02b than the low-pressure limit of eq 4, given by kNH3 = k0NH3[N2]. A plot of k02b[N2] against [N2] is linear through the origin with slope equal to k02b. The results for k2b shown in Figures 8, 10, and 12 can be analyzed in this fashion but the values for k0NH3 are all about a factor of 2 larger than the values given in Table 8. As long as k∞2b is large, >2.0 × 10−10 cm3 molecule−1 s−1, the results for k02b are not too sensitive to the exact value of k∞2b. The temperature dependence of k01b can be determined from the data in Table 7 by representing the temperature dependence as ATn. A plot of log(k01b) vs log(T) gives n equal to −3.41 ± 0.12 and A equals (1.14 ± 0.59 × 10−19) cm6

significant values for the three independent parameters. Two strategies were adopted: for both reaction systems k∞ was taken or estimated from other data, and Fcent was assumed to be temperature independent. The results are summarized in Tables 7 and 8. Fortunately, Klippenstein et al.16 have investigated reactions 1a and 1b with high-levels of electronic structure theory and kinetic rate constant theory and have made predictions on the pressure and temperature dependence of the Troe parameters for reaction 1b in a N2 bath gas. These are shown by the dotted black line in Figures 7, 9, and 11. The agreement between theory and experiment is very good. The theoretical predictions of Klippenstein et al. were optimized to fit the available data24−26 to them, not the present work. The parameters determined by Klippenstein et al. are also summarized in Table 7. In the Troe fits to the experimental data, k∞1b was fixed to the theoretical predictions of Klippenstein et al.16 given in Table 7. The data sets for k1b as a function of temperature, Tables 4, 5, and 6, shown in Figures 7, 9, and 11, were fit with k01b and Fcent1b as parameters. The values of Fcent1b had a large uncertainty and were averaged. With the use of Fcent1b fixed to the average value, new values of k01b were determine and are shown in Table 7. The uncertainty is an estimate at the 2σ level in these two fit parameters. The results for k1b and k2b at all temperatures have the largest scatter at the highest pressures, perhaps most clearly seen at 292 K, comparing Figures 8 and 9. This is in part due the increasing importance of k2b in the removal of NH2 as discussed above, and the decrease in signal-to-noise as the absorption coefficients decrease with increasing pressure. Pressure broadening has a much more detrimental effect on the peak absorption coefficient of NH3 than NH2, as can be seen from comparing Tables 1 and 2. This is important for monitoring the NH3 molecule and the determination of k2b. For example, at 292 K σNH3(ṽ0) decreases by a factor of 17.7 from the Doppler peak to the peak at a pressure of 414 Torr while σNH2(ṽ0) decreases by a factor of 3.21. However, some other K

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Figure 8. Same as Figure 7 except that k2b in Table 4 is plotted. As noted, k1b and k2b were determined simultaneously. Table 8 summarizes estimates of Troe fit parameters for k2b and these are shown by the solid blue line.

Figure 7. Summary of the measurements for k1b in Table 4 as a function of the N2 concentration at a temperature of 292 K are shown by the red circles. The average of 3 to 5 measurements of k1b at different [N2]0 concentrations are indicated by the error bars at the 2σ uncertainty level. The Troe fit to these results is given in Table 7 and is shown by the solid blue line along the theoretical calculations of k1b by Klippenstein et al.,16 also listed in Table 7.

parameters necessary to determine the concentrations of NH3 and NH2 are summarized in Tables 1 and 2, respectively. For NH3, the agreement between the measurements of b0L(N2) in this work and literature values suggests the uncertainty in determination of σNH3(ṽ0) as a function of pressure is small and estimated to be less than ±5% over the temperature and pressure range of the experiments, at the 2σ confidence level. As is evident from Table 2, there is more uncertainty associated with the determination of σNH2(ṽ0), especially the pressure broadening parameters at higher temperatures. As discussed in section IIIA, the pressure broadening parameters for NH2 were determined by finding the b0L(N2) that minimized the square of the residuals, (Δ[NH3]0 − [NH2])2, over the pressure range at each temperature. At 292 K, b0L(N2) determined by the leastsquared-minimization technique was 10% smaller than that determined by scanning the NH2 probe laser across the line profile and provided a better estimate of b0L(N2) to use in the data reduction at 292 K. At the highest pressure of 414 Torr at 292 K, the use of b0L(N2) given in Table 2 increased σNH2(ṽ0) by 3% compared to that determined by scanning over the line shape. Figure 3 illustrates the agreement between individual pressure measurements of σNH2(ṽ0), and the values determined using the value of b0L(N2) that provided the best fit over the complete pressure at each temperature.. An estimate of ±10%

molecule−2 s−1, where the uncertainties are at the 2σ level. Expressing the theoretical representation of k01b in the same form as used for the experimental k01b the theoretical expression is n equals −2.89 and A equals 5.85 × 10−22 cm6 molecule−1 s.−1 Similarly, the summary of the k02b measurements in Table 8 can be fit in the same form as k01b. The results for the temperature dependence of k02b gives n equals −1.76 ± 0.092 and A equals (9.95 ± 0.58) × 10−26 cm6 molecule−1 s.−1 The decrease in k0 with increasing temperature is much more rapid for reaction 1b than for 2b. D. Uncertainty in the Determination of k1b and k2b. The uncertainties in the determination of k1b and k2b have been discussed in recent work.9,10 As in all studies of radical−radical reactions the determination of radical concentration is one of the most important factors in the accuracy of the rate constant measurements. As noted in the introduction, high-resolution time-resolved laser-absorption spectroscopy offers the advantage of a direct connection of the radical concentration to the observed absorption signal by eqs 1, 2, and 3. Thus, uncertainty in the determination of the peak absorption coefficient is directly reflected in the radical concentration and hence the measured rate constant. The uncertainties in the spectroscopic L

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Figure 9. Same as Figure 7, except the results for k1b summarized in Table 5 for 422 K are plotted.

Figure 10. Same as Figure 8 except the results for k2b at 422 K in Table 5 are plotted.

in the determination of the NH2 concentration, at the 2σ confidence level, can be conservatively applied to the complete data set. The experimental conditions and measurements of k1b and k2b are summarized in Tables 4, 5, and 6. Also shown in columns 5 and 6 is the scatter, at the 2σ confidence level, from multiple measurements of these rate constants under the same experimental conditions but different initial radical concentrations. The pressure averaged values of the fractional experimental uncertainties for a given temperature are similar for each temperature, approximately ±0.08 and ±0.28, for k1b and k2b, respectively. These uncertainties provide a reasonable estimate of experimental uncertainty for the complete data set. Combining these estimates with those for the systematic fractional uncertainty in concentration measurements for NH2 as ±0.10 provides a fractional error estimate of ±0.13 and ±0.29 for k1b and k2b, respectively, including experimental and systematic uncertainties, assuming they are uncorrelated. It is important to note that the NH2 radical pool is influenced by both k1b and k2b in an anticorrelated fashion. If k2b is larger than the true value the NH2 radical pool is not depleted as quickly as it should be to match the NH3 profile, and the value of k1b found to match the NH2 profile will be smaller. Similarly, if k1b is larger than the true value than the NH2 radical pool will be larger than it should be, and the value of k2b determined in the fit of the NH3 profile will be smaller than it should be. This

effect can be seen in the high pressure ends of the plots of the rate constants plotted against pressure, Figures 7− 12. If one of the pairs of the rate constants k1b and k2b is lower or higher the other is higher or lower. E. Comparison with Previous Work. There are only five previous studies of reaction 1b as a function of N2 pressure, and this laboratory has conducted three of them with increasing sophistication in the reaction chamber design and laser diagnostics. The comparison of experimental and theoretical values for the measurement of k1b as a function of N2 concentration at 295 K is shown in Figure 13. Figure 13a shows the low concentration region and Figure 13b shows the complete concentration range of previous measurements. Khe et al.25 studied reaction 1b in N2 and Ar bath gases over the pressure range from 0.3 to 1000 Torr near 300 K. These workers used kinetic flash photolysis of NH3 to generate NH2 and H atoms and followed the NH2 decay using several rovibronic transitions grouped near 597.7 nm of the (090)A2A1← (000)X2B1 band using a Xe lamp and monochromator in a multipass cell. The NH2 absorption signal was calibrated by titrating the H atoms produced in the photolysis step with isobutane and measuring the resulting H2 quantitatively by mass spectrometry. They checked this calibration against a kinetic measurement based on the rapid NH2 + NO reaction. Both provided similar results for the apparatus-dependent NH2 absorption coefficient. The second-order decay rate constants of NH2 measured by Khe et al.25 in a N2 carrier gas are shown M

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Figure 11. Same as Figure 7 except the results for k1b from Table 6 for 533 K are plotted.

Figure 12. Same as Figure 8 except for the results for k2b at 533 K are plotted.

by the open blue squares in Figure 13 panels a and b. Their reported measurements consisted of simple second-order rate constants for the removal of NH2 comprising undistinguished contributions from reactions 1b and 2b. As shown in Figures 7 and 8 of the present work, reaction 1b makes a significant contribution to the removal of NH2, and at 400 Torr the contributions are almost equal. Khe et al. attempted to try and estimate this contribution using the data of Gordon et al.19 but were unsuccessful and concentrated on analyzing their data near the extremes of the pressure range. The only other pressure dependent study of reaction k1b with N2 as the bath gas, outside of this laboratory, was by Lozovskii et al.26 Their measurements are shown by the solid triangles in both panels a and b of Figure 13. These workers used intracavity laserabsorption spectroscopy to monitor the temporal dependence of NH2 following flash photolysis of NH3/N2 mixtures. These workers calibrated the observed NH2 absorption signal to concentration measurements using NH 2 + NO kinetic measurements similar to Khe et al. They also used the same rovibronic transition (0,9,0)A2A1 ← (0,0,0)X2B1 centered near 597.9 nm. These workers also reported on the total secondorder loss rate constant for NH2 as a function of N2 pressure, and did not separately identify the contributions that reactions 1b and 2b made to the removal of NH2. Lozovskii et al. attempted to estimate the contribution k2b relative to k1b at 570 Torr by varying the initially equal NH2 and H concentrations over a large range. They concluded from their measurements

that k1b/k2b must be 12 or greater and that reaction 2b had little influence on their measurements over the pressure range of their experiments. They attributed the second-order decay rate constants of NH2 to only reaction 1b. However, as noted above, the results of the present work for the direct determination of k2b by monitoring of the temporal dependence of the NH3 concentration profiles, Tables 4, 5, and 6 shown in Figures 7, 9, and 11, clearly indicate that k2b makes a significant contribution to the removal of NH2, almost equal at 400 Torr and 292 K, and cannot be ignored in the data reduction. Figure 13a also shows the rate constant data for k1b as a function of pressure at low-pressure determined by Bahng and Macdonald24 (plus-centered red circles), Altinay and Macdonald9 (open red circles), and this work (solid red circles). Figure 13b shows the experimental results for k1b from this work, Table 4, and Figure 6 over the complete range of N2 concentrations as the solid red circles. The results of Bahng and Macdonald are clearly higher than the other two measurements from this laboratory. In these experiments the NH3 was probed on an isolated feature of (1,0,1,0) ← (0,0,0,0) overtone transition. The σNH3(ṽ0) for this transition is a factor of 10 smaller than the σNH3(ṽ0) for the ν1 fundamental stretching vibrational transition used in the present work. Bahng and Macdonald used the same NH2 transition as listed in Table 2 and found σNH2(ṽ0) to be 1.19 × 10−17 cm2 molecule−1, similar to the value listed in Table 2 and given N

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Table 7. Summary of Troe Parameter Fits for the Pressure Dependent Rate Constant, k1b, for the NH2 + NH2 → N2H4 Reaction in N2 as a Function of Temperature k01ba,b

k∞1bd

Fcent1be

T (K)

exp (×10−28)

theoryc (×10−29)

theoryc (×10−11)

exp

theoryc

292 422 533

(4.62 ± 0.28) (1.28 ± 0.11) (0.598 ± 0046)

4.26 1.69 0.736

7.94 7.06 6.52

(0.148 ± 0.12) (0.148 ± 0.12) (0.148 ± 0.12)

0.31 0.31 0.31

a Units = cm6 molecule−2 s−1. bUncertainty at the ±2σ level. cKlippenstein et al.16 dUnits = cm3 moleule−1 s−1. eFcent1b was assumed independent of temperature and the average value of Fcent1b was used for all temperatures.

Table 8. Summary of Troe Parameter Fits that Describe the Pressure Dependent Rate Constant, k2b, for the NH2 + H → NH3 Reaction in N2 as a Function of Temperature T (K) 292 422 533

k2b0a,b

k2b∞c,d −30

(4.49 ± 0.66) × 10 (1.40 ± 0.28) × 10−30 (1.55 ± 0.15) × 10−30

Fcente −10

2.60 × 10 2.60 × 10−10 2.60 × 10−10

0.5 ± 0.2 0.5 ± 0.2 0.5 ± 0.2

a Units = cm6 molecule−2 s−1. bUncertainty at the ±2σ level, determined with fixed kb∞ and fe. cUnits = cm3 moleule−1 s−1. dk2b∞ chosen, see text. efe was assumed independent of temperature, see text.

by Altinay and Macdonald.9 However, the reaction cell was substantially different than the current chamber; the inner height of a 100 cm × 100 cm Teflon box was 5 cm, slightly larger than the height of the rectangular photolysis laser beam profile. No explanation as to the divergence of these measurements from the current ones can be offered except the signal-to-noise ratio was reduced in the low-pressure region because of the smaller σNH3(ṽ0), and there may have been some undetected wall chemistry occurring because of the close proximity of the walls to the photolysis zone. In the experiments of Altinay and Macdonald the inner Teflon box was removed reducing the possibility of wall interference, and the NH3 probe laser was replaced by a tunable OPO laser system allowing the (1,0,0,0) ← (0,0,0,0) fundamental vibration to be used to monitor NH3. The measurements of Altinay and Macdonald are within the ±2σ uncertainty of the combined uncertainties with those of the present experiments but are still unexpectedly higher than those of this work. The improvement in the reaction chamber design could be a possible factor in the difference in these measurements. The reaction chamber of the present experiments has been designed to reduce the volume by a factor of 4, increasing the gas throughput over the old design. Also, in the new chamber, the photolysis zone is 5 cm from the chamber walls and greatly reduces the possibility of wall effects influencing the chemistry. Also shown in Figure 13 panels a and b are the results of a statistical adiabatic channel model calculation49,50 by Fagerström et al.51 for reaction 1b. These are indicated by the black dotted lines in the figures. Fagerström et al. used pulse radiolysis of NH3/SF6 mixtures to generate NH2 radicals by the F atoms abstraction of an H atom from NH3. They also monitored NH2 by using a white-light monochromator combination, as Khe et al., again using the same NH2 spectral band at 597.7 nm. They calibrated the initial F atom concentration using CH3 UV absorption at 216.4 nm produced in the F + CH4 abstraction reaction. Fagerström et al. measured the pressure dependence of k1b in SF6 from 300 to 1000 Torr at 298 K. There was no H atom production in these experiments so that reaction 2b is not a complicating issue. Using the semiempirical theory of Troe and co-workers,44,48,49 the SF6

Figure 13. Comparison of the available experimental and theoretical data for k1b as a function of N2 concentration at T = 295 ± 3 K. Panel a shows k1b in the low-concentration range of N2 and panel b shows k1b over the complete experimental range. For both panels: this work, solid red circles; Altinay and Macdonald,9 open red circles; Bahng and Macdonald,24 centered-plus sign red circles; Khe et al.,25 open blue squares; Lovovskii et al.,26 solid black triangles. The theoretical description of k1b by Fagerström et al.50 is shown by the black dotted line, and the high-level theoretical calculations of Klippenstein et al.,16 summarized in Table 7, are plotted as the dashed blue line. As discussed in the text, Khe et al. and Lovovskii et al. underestimated the impact of k2b on the measurements of k1b, especially at high-pressures, and the measurements are a composite of both k1b and k2b.

data was fit using appropriate model parameters. This analysis yielded a determination of the k∞ for reaction 1b of 1.2 × 10−10 cm3 molecule−1 s−1. Using this information, Fagerstrom et al. repeated the analysis for the available data on k1b as a function of N2 pressure, that is, the data of Khe et al.25 and Lozovskii et al.26 As can be seen from Figure 13b, the apparent highpressure limit for k1b from Lozovskii et al. was in better agreement with their estimate than that of Khe et al. In Figure 13b, there is agreement between the semiempirical calculations O

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The Journal of Physical Chemistry A for k1b by Fagerström et al. and the present work in the intermediate concentration region. However, this is probably coincidental because even in this region reaction k2b contributes to the removal of NH2, but their predictions were based on the data of Lozovskii et al. in which the contribution of k2b to the kinetics was ignored. For completeness, the high-level theoretical description of reaction 1b in a N2 bath gas by Klippenstein et al.16 is again shown in Figure 13 panels a and b by the blue dashed line. The agreement with the present measurements over the concentration range of the experiments is quite good. As is evident from Figure 13, the experimental results from this work rise more rapidly than the calculations of Klipperstein et al. The disagreement is outside the expected uncertainty in the k1b in this region. Unfortunately, given the discrepancies in the experimental data from this laboratory, it is not clear if this difference is real or not. The first credible study of reactions 1b and 2b as a function of pressure was the work of Gordon et al.19 These workers studied reactions 1b and 2b in NH3 over the pressure range of 250 to 1520 Torr. They used pulse radiolysis to effectively generate NH2 with an equal concentration of H atoms, and quantified the concentration of NH2 using the known G value for the radiation chemistry of NH3. They monitored NH2 using the same procedure as Khe et al. Gordon et al. attempted to separate the effects of reactions 1b and 2b. They noted that because of the asymmetry in the number of NH2 radicals loss compared to H atoms, the second-order plots will become pseudo-first-order and become distorted at long times. A simple three reaction model was generated in which k1b and k2b were varied to give agreement with the observed distorted secondorder plots. They determined that k1b was independent of pressure and equal to 1.0 × 10−10 cm3 molecule−1 s−1. They also found k2b to be linearly dependent on NH3 pressure with a slope of 5.4 × 10−30 cm6 molecule−1 s−1 but plateauing at 1000 Torr to a value of 2.0 × 10−10 cm3 molecule−1 s−1. Recently, Altinay and Macdonald10 studied reaction 2b in a number of different third bodies, CH4, C2H6, CO2, CF4, and SF6, and found k2b to be linearly dependent on third-body pressure but with slopes larger than that found for NH3 by Gordon et al. Altinay and Macdonald also reported an estimate of linear pressure dependence of reaction 2b in N2 to be (2.3 ± 0.9) × 10−30 cm6 molecule−1 s−1. If measurements of k2b reported in Table 4 and plotted in Figure7 were treated as a linear function of N2 pressure the slope would be (2.5 ± 0.12) × 10−30 cm3 molecule−1 s−1, in good agreement with Altinay’s and Macdonald’s earlier estimates.

The agreement or disagreement between previous studies of the NH2 + NH2 system may be a sign of undetected experimental artifacts or simply the experimental challenge of making quantitative temporal measurements of transient species. Nevertheless, there is remarkable agreement between the experimental measurements of this work, illustrated in Figures 7, 9, 11, and 12, and the high-level electronic structure and kinetic analysis of Klippenstein et al.16 The importance of reaction 2b to the net loss of NH2 radicals in experiments where UV photolysis of NH3 is used to generate the NH2 radical has been clearly demonstrated in this work, as summarized in Table 4 and illustrated in Figure 8. In section III D, it was shown that previous studies of reaction 1b underestimated the possible influence of k2b in the data reduction, and the reported rate constant measurements of k1b, even at modest pressures are a combination of k1b and k2b. The data for the pressure and temperature dependence of k1a were fit to the usual Troe form by fixing the high-pressure limiting rate constant to the theoretical value, and assuming Fcent was temperature independent. The results are summarized in Table 7. For k2b, a high-pressure limiting rate constant was estimated from the average of k∞ for the recombination CH3 + H and OH + H reactions. Again, Fcent was assumed to be temperature independent and was constrained in the fit. These results are summarized in Table 8. The measurements of this work provide the first investigation of the pressure and temperature dependence of reactions k1b and k2b. They illustrate the utility of high-resolution timeresolved laser absorption spectroscopy to the study of radical− radical reactions over a broad range of both pressure and temperature.

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AUTHOR INFORMATION

Corresponding Author

*Phone 630 252 7742. E-mail: [email protected] or [email protected]. Present Address

# G.A.: Intel, 2501 Northwest 229th Avenue, Hillsboro, Oregon, 97124.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Chemical Sciences, Geosciences, and Biosciences, US. Department of Energy under Contract No. DE-AC0206CH11357.

IV. CONCLUSION The recombination reactions NH2 + NH2 → N2H4 and NH2 + H → NH3 in a N2 bath gas have been investigated as a function of both pressure and temperature. The simultaneous detection of NH2 and NH3 following initiation of the reaction sequence have allowed for the clear separation of these individual rate processes. This was not previously accomplished in investigating the kinetics of these reactions. The present work is the only low-temperature study that provides a realistic description of the pressure and temperature dependences of these rate processes. As noted in the Introduction the NH2 radical is isoelectronic with CH3 and OH radicals and the decreasing molecular complexity for the self-recombination and the recombination of these radicals with H atoms with increasing atomic number may be useful in the further study of radical− radical reactions.

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REFERENCES

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