Reaction Kinetics of CaOH with H and O2 and O2CaOH with O: Implications for the Atmospheric Chemistry of Meteoric Calcium.

The ablation of cosmic dust particles entering the Earth's upper atmosphere produces a layer of Ca atoms around 90 km. Here, we present a set of kinetic experiments designed to understand the nature of the Ca molecular reservoirs on the underside of the layer. CaOH was produced by laser ablation of a Ca target in the fast flow tube and detected by non-resonant laser-induced fluorescence, probing the D(2Σ+) ← X(2Σ1) transition at 346.9 nm. The following rate constants were measured (at 298 K): k(CaOH + H → Ca + H2O) = (1.04 ± 0.24) × 10-10 cm3 molecule-1 s-1, k(CaOH + O → CaO + OH) < 1 × 10-11 cm3 molecule-1 s-1, and k(CaOH + O2 → O2CaOH, 1 Torr) = (5.9 ± 1.8) × 10-11 cm3 molecule-1 s-1 (uncertainty at the 2σ level of confidence). The recycling of CaOH from reaction between O2CaOH and O proceeds with an effective rate constant of keff(O2CaOH + O → CaOH + products, 298 K) = 2.8-1.2+2.0 × 10-10 cm3 molecule-1 s-1. Master equation modeling of the CaOH + O2 kinetics is used to extrapolate to mesospheric temperatures and pressures. The results suggest that the formation of O2CaOH slows the conversion of CaOH to atomic Ca via reaction with atomic H, and O2CaOH is likely to be a long-lived reservoir species on the underside of the Ca layer and a building block of meteoric smoke particles.

Introduction

Layers of metal atoms occur in the mesosphere–lower thermosphere (MLT) region of the Earth’s atmosphere as a result of the ablation of cosmic dust particles. The total input of this dust has recently been estimated to be 43 ± 14 tonnes day–1, of which around 92% comes from comets and the rest comes from the asteroid belt between Mars and Jupiter.[1] The ablated metal atoms occur in layers between 80 and 105 km, which are global in extent. Four neutral metal atoms, Na, Fe, K, and Ca, can be observed from the Earth’s surface using the resonant lidar technique; uniquely for ground-based observations, the Ca+ ion layer can also be observed and occurs ∼5 km above the neutral Ca layer.[2] Although Ca has a similar elemental abundance to Na in meteorites, the Ca atom abundance in the MLT is roughly 2 orders of magnitude smaller than that of Na.[3−5] One reason for this Ca depletion is the highly refractory nature of CaO in molten meteoroids,[6] so that Ca ablates about 1 order of magnitude less efficiently than Na.[1] We have recently confirmed this differential ablation using a novel meteoric ablation simulator.[7]

A second reason for the Ca depletion may be that Ca is converted to very stable reservoir species, which are less easy to recycle back to atomic Ca than the corresponding Na reservoir, NaHCO3.[8] A good understanding of the cycling between elemental Ca and its reservoirs, including Ca-bearing ions, is emerging.[9−11] However, there is still a great deal of uncertainty about the nature of the stable Ca reservoirs. This is important because the formation of these reservoirs governs the lower ledge of meteoric atomic layers and, in some cases, may even determine the seasonal behavior of the layer as a whole.[12] Also, these processes determine the way in which metals incorporate into meteoric smoke particles (MSPs), which are nanometer-sized particles that form from the condensation of metallic species in the MLT.[2]

Figure is a schematic diagram of calcium chemistry in the MLT. Ca atoms react with O3 to produce CaO[13]which can then be recycled back to Ca by reaction with O(3P) or further react to yield reservoir molecules.[10,14]Although Ca(OH)2 is thermodynamically very stable, it reacts rapidly with H atoms to yield CaOH.[10]The role of the CaOH radical as a reservoir species is the focus of the present study. CaOH can recycle back to Ca via a reaction that is well-known in the field of metal-catalyzed flame chemistry[15,16]where the combination of reactions , R5, and R6b in essence catalyzes the recombination of 2H atoms to form H2.

Figure 1

Meteoric calcium chemistry in the MLT. Bold typescript and thick arrows highlight the reactions investigated in this study.

The reaction enthalpies at 0 K for reactions , R2a, R5, and R6 have been calculated using available heats of formation taken from data evaluations.[17−19] The preferred heats of formation of CaO and CaOH at 0 K (Figure S1 of the Supporting Information) are 26 ± 17 kJ mol–1 [19] and −170 ± 15 kJ mol–1,[17] respectively. Enthalpies of reaction for reactions and R4 were obtained from electronic structure calculations at the B3LYP/6-311+(2d,p) level of theory (estimated uncertainty of ±20 kJ mol–1).[10,14]

As shown in Figure , an unexplored and potentially important fate for CaOH could be its association with O2 [enthalpies of reaction from B3LYP/6-311+(2d,p) calculations can be found in the Supporting Information].The O2CaOH molecule can then recycle CaOH back by reaction with O(3P) in two stepsor associate with other metal-containing molecules to generate MSPs.

The reaction of CaOH and O may also be slightly exothermic and could potentially recycle reactive calcium.In this paper, we investigate the atmospheric fate of CaOH by studying experimentally the reactions of CaOH with H and O2 and the recycling of CaOH from O atom reactions.

Experiment

The laser ablation–fast flow tube–laser-induced fluorescence (LA–FFT–LIF) apparatus used in this study has been described in detail elsewhere.[20−22] Pulsed 532 nm Nd:YAG laser (Continuum Minilite) ablation of a rotating Ca cylindrical target was used to entrain Ca atoms and CaO molecules in a flow of a carrier gas, typically 3 standard liters per minute (slm) of N2 at 2 Torr. Under these conditions, the linear flow speed was ∼30 m s–1. A flow of H2O or H2 was added 2 cm downstream of the ablation source to generate CaOH (from electronically excited Ca species; see below). O2 was added further downstream via a movable injector. The concentration of O2 was changed by varying its flow while keeping the total flow constant by compensating with an extra flow of N2. H atoms were generated by a microwave discharge (Opthos, 2450 MHz, Evenson cavity) of a flow of H2 in He (1:5) and injected through a quartz tube at the midpoint between the ablation and the detection points, i.e., 10 cm downstream of the ablation point. The addition of He was essential to generate larger concentrations of H atoms. O atoms were generated by the microwave discharge of a flow of N2 followed by scavenging of the resulting N atoms by an excess of NO downstream of the plasma and before injection into the flow tube.

H and O atom concentrations as a function of the microwave power were calibrated by adding a known excess concentration of NO2 to the carrier flow upstream of the injector, to scavenge the corresponding atomic species via the well-known reactions:NO2 was monitored by electron impact–time-of-flight–mass spectrometry (EI–ToF–MS). The absolute difference in the NO concentration in the presence of atomic H or O, Δ[NO2], was calculated from the fractional change in the NO2 signal and the known concentration of NO2 added to the flow; Δ[NO2] = [H]0 or [O]0, their concentrations at the point of injection. The skimmer cone of the EI–ToF–MS was situated at the downstream end of the flow tube, 26 cm away from the microwave discharge. To measure the wall loss rate of H and O, NO2 was injected at different distances downstream of the microwave discharge port by changing the position of a movable injector. The residence time of the atoms in the tube could thus be varied before titration with NO2, so that the drop of the NO2 concentration observed is equal to the remaining concentration of H or O in the tube after a given flight time in the absence of reagents. The maximum concentrations of H and O atoms that were generated using this methodology were about 3 × 1013 atoms cm–3.

The relative CaOH concentration was measured 20 cm downstream of the ablation target by LIF between 336 and 356 nm, generated by directing a laser orthogonal to the flow tube axis. Pulsed laser radiation (pulse width, 6 ns; line width, 0.003 nm) was generated by a Nd:YAG-pumped dye laser (Continuum Surelite–Sirah Cobra Stretch) running on a solution of pyridine 1 in ethanol and frequency doubled with a KDP crystal. CaOH off-resonance fluorescence was collected perpendicular to the excitation beam through an orange high pass filter (Edmund Scientific, cuton at 550 nm) by a photomultiplier tube (Electron Tubes, 9816QB). Excitation of ro-vibrational bands of the D(2Σ+) ← X(2Σ1) transition was followed by green–orange fluorescence from the B(2Σ+) → X(2Σ+) and A(2Π) → X(2Σ1) transitions[23] (Figure a). In kinetic experiments, the CaOH concentration was monitored at the band head of the 100 ← 000 transition (346.88 nm vacuum or 28 848 cm–1; Figure b). The incident laser energy was monitored using a beamsplitter and photodiode, so that the LIF signal could be corrected for the pulse-to-pulse laser variability. A wavemeter (Bristol Instruments 871B) was used to monitor the wavelength of the excitation beam during spectral scans. The signals from the different detectors were recorded using a digital oscilloscope (LeCroy LT342) and transferred to a computer for further analysis. The laser triggering, oscilloscope data acquisition, and cycle repetition were synchronized using a delay generator (Quantum Composers 9815).

Figure 2

(a) Excitation spectrum showing ro-vibrational bands of the D–X transition of CaOH, with band assignments according to Pereira and Levy.[26] The red degraded band at 29 323 cm–1 fits well to the F(5)–X(0) transition of CaO, considering both the position of the band head and the spacing of the rotational lines. The prominent unassigned features (∗) also appear in the spectra by Pereira and Levy and show variable intensity with respect to the CaOH bands. (b) Detail of the D(000) ← X(000) band overlaid with a spectral simulation using molecular constants from Dick et al.[28] (T, 300 K; Doppler width, 1.1 cm–1).

Materials

OFN N2 and UHP He (BOC) were used as carrier gases in the flow tube and the microwave discharge, respectively. Both N2 and He passed through liquid N2-cooled molecular sieve filters upstream of the experiment. UHP O2 and H2 (BOC) were used directly from the cylinder or from a glass bulb containing O2 diluted in N2 to a set partial pressure. NO2 (Air Products, 99.5%) was frozen at 77 K, pumped, thawed, and stored in a glass bulb, where it was diluted in N2 to make a 10% mixture. NO (99.95%, Air Products) was purified by freezing at 77 K, then warming the solid back to room temperature, and discarding the last 20% to vaporization. This process was repeated 3 times, and resulting NO was diluted in N2 to make a 3% mixture. A Ca ablation target (diameter = 6 mm) was prepared by compressing Ca pellets (99%, Sigma-Aldrich) into a cylindrical shape using a stainless-steel piston.

Results

Removal of Ca and CaO and Formation of CaOH

In the absence of reagents, laser ablation of the calcium target produced not only Ca atoms but also ground-state CaO and CaOH (both oxidation and hydration must occur during the preparation of samples under atmospheric conditions). Emission of blueish fluorescence around the ablation target indicated the formation of excited Ca. This emission was dispersed using a small monochromator, revealing many Ca lines between 300 and 600 nm, most of them connecting to the 3P° optically metastable state (181 kJ mol–1 above the ground 1S state[24]). The resonance line at 422.673 nm was not the strongest of these lines. At the LIF detection point, 20 cm downstream of the ablation target, fluorescence from the C(1Σ+) ← X(1Σ+) and F(1Π) ← X(1Σ+) band systems of CaO[25] and the D(2Σ+) ← X(2Σ+) band system of CaOH[26] was observed by scanning the dye laser wavelength. The ground-state CaO signals were greatly diminished or disappeared upon addition of H2 or H2O, while the signal at the peak of the CaOH D(100)–X(000) band increased correspondingly by about a factor of 6 (signal slightly larger with H2O than with H2). Figure a shows a spectral scan obtained using H2O as a reagent at 2 Torr. Figure b shows a comparison of the D(000) ← X(000) band of CaOH with a synthetic spectrum at 300 K calculated using the PGOPHER program,[27] with literature molecular constants.[28] The comparison demonstrates that the rotational state population is consistent with a rotational temperature of 300 K. The relative intensities of the (0, v2′, 0) ← (0, v2″, 0) vibrational bands in Figure a also indicate a vibrational temperature of 300 K.

Some experiments were carried out to investigate the source of CaO and CaOH. Figure shows the respective appearance and removal of ground-state CaOH (panel a) and CaO (panel b) with increasing H2. The LIF signal at the peak of the CaOH bands shows evidence of overlap with the CaO[F(5)–X(0)] bands when no reagent is added. As the concentration of H2 or H2O is increased, the CaO signal decays exponentially. The signal at the peak of the CaOH D(100)–X(000) band can be fitted using a bi-exponential expression (solid line), where the initial decay constant (k ∼ 1 × 10–10 cm3 molecule–1 s–1) is close to the decay constant of the single exponential fit of CaO in the bottom panel. This suggests that a fraction of CaOH originates initially from CaO. CaOH also shows a slower growth with increasing [H2] (k ∼ 2 × 10–10 cm3 molecule–1 s–1). This slower source is ultimately responsible for most of the CaOH signal observed under the usual experimental conditions, where [H2] was 10 times higher than the maximum [H2] in Figure (∼3 × 1013 molecules cm–3), i.e., the aforementioned factor of 6 increase. The decay of CaO (Figure b) in this set of low [H2] experiments was observed to depend upon the contact time, approaching the literature values of k(CaO + H2) and k(CaO + H2O)[10,14] when H2 and H2O are injected closer to the ablation target.

Figure 3

(a) Dependence of the CaOH LIF signals at the peak of three different bands of the D–X system on the concentration of [H2] (multiplied by a constant contact time t). (b) Same for the C–X and F–X systems of CaO. The CaOH traces show, in fact, an overlap of the CaO and CaOH signal. This spectral overlap can be appreciated in Figure c; λ = 693.3–693.8 nm. For very low [H2] (or [H2O]), the signal at the peak of the CaOH bands shows a decay with the same constant as the decay of CaO in panel b. The degree of overlap varies for the other two bands shown in panel a. The slower growth of CaOH that can be appreciated in panel a is ultimately responsible for the formation of most CaOH that is observed in experiments of CaOH reactions, where the concentration of H2 is 10 times higher.

Figure 4

Example of the sequence of experiments carried out to determine the rate constant of the CaOH + H reaction. (a) H atom calibration of the MW discharge, showing Δ[NO2] versus discharge power. (b) Loss of H atoms versus flight time, as determined by the distance between the MW port and the tip of the NO2 movable injector. (c) Excitation spectra in the absence of added reagent with and without discharge on He (blue and cyan, respectively), in the presence of H2O added downstream of the ablation point with and without discharge on He (black and green, respectively), and with H2O added and the maximum H atom concentration for these particular conditions (red). (d) Plot of the CaOH LIF signal at the D(100)–X(000) bandhead versus the product of the effective contact time τ (see the text for definition) and the initial H atom concentration [H]0.

Ca was observed by EI–ToF–MS at m/z 40, 42, and 44 and decayed exponentially to a very small baseline (less than 10% of the initial Ca) upon the addition of increasing water concentrations, with a rate constant of k = (1.0 ± 0.2) × 10–11 cm3 molecule–1 s–1. CaOH was also detected in the mass spectra at m/z 57, exhibiting the formation and subsequent decay with increasing [H2O], although the signal was too noisy to allow for kinetic analysis. The addition of H2 did not remove the Ca signal. In the absence of any reagent, at pressures below 1 Torr and with the same total flow rate (and, therefore, flow speeds faster by a factor of 2 and reduced collisional quenching), fluorescence was observed at the LIF detection point without excitation, showing the characteristic time variation of the ablation pulse (see, e.g., the study by Broadley et al.[11]). This emission was spectrally bracketed using high pass filters between 600 and 700 nm.

CaOH + H

Reaction R6 (with H in excess over CaOH) and the first-order loss of CaOH and H to the flow tube wall can be described by the following set of differential equations:where k′H and k′CaOH are the wall loss rates of H and CaOH, respectively. The main assumption here is that no additional sources of CaOH exist, i.e., that CaOH is not recycled from the products of reaction R6. The time dependence of CaOH is then described by an analytical solution of eqs and E2where [H]0 is the initial concentration of H, i.e., the concentration at the injection point. Measurements were performed at a fixed contact time t defined by the mass flow rate of the carrier gas and the pressure in the flow tube. These experimental settings also determine the diffusional loss of H toward the wall, which was measured after the discharge calibration experiments and prior to the CaOH + H experiments. Therefore, eq can be rewritten aswhere SCaOH is the observed CaOH LIF signal, A is a constant, and τ is an effective time calculated from the contact time t and the measured k′H:Figure shows plots of SCaOH versus τ[H]0 for different combinations of pressure and carrier flow. The exponential fits yield the total rate constant of reaction R6 (k6 = k6a + k6b). Table is a summary of the experiments carried out with different CaOH precursors and contact times. Additional back-to-back experiments using H2O and H2 as precursor reagents yielded the same dependence of SCaOH upon [H]0, suggesting that there are no interferences derived from recycling of CaOH from Ca(OH)2 via reactions R2 and R5. The major sources of uncertainty are the microwave (MW) discharge H atom calibration (∼15%) and the H atom wall loss rate measurements (∼30%). Another important source of uncertainty is the baseline that appears in most decays, about 10% of the initial CaOH LIF signal (see Figure d), both using H2 and H2O in the CaOH source. Because the H atom concentration does not depend linearly upon the discharge power but levels off at ∼60 W (Figure a), it was not possible to increase [H] further to see whether CaOH would eventually disappear or the baseline would stay. In some cases, it was possible to fit the curves by fixing a zero baseline, and in these, the retrieved rate constant tends to hit the lower limit of the uncertainty range. It was found that discharging He without adding H2 to the flow passing through the MW cavity created a small additional source of CaO when no H2 or H2O were added downstream of the ablation target (blue and cyan spectra in Figure c) and CaOH if a reagent was added downstream (black and green spectra in Figure c). Therefore, the additional source of CaO/CaOH appears to be associated with reactions involving oxides of calcium ablated directly from the source and excited He atoms generated by the MW discharge. The weighted average of the measurements in Table yields a rate constant of k6(298 K) = (1.04 ± 0.24) × 10–10 cm3 molecule–1 s–1 (uncertainty at the 2σ level of confidence).

Table 1

Measured Rate Constants for the CaOH + H Reaction at 298 K

reactant	flow (slm)	P (Torr)	t (ms)	k′H (s–1)	k6a (×10–10, cm3 molecule–1 s–1)
H2O	2.5	2.0	4.0 ± 0.3	430 ± 80	2.2 ± 0.9
H2O	3.8	2.0	2.63 ± 0.17	430 ± 80	2.1 ± 0.9
H2O	4.7	2.0	2.13 ± 0.13	620 ± 40	1.0 ± 0.5
none	4.7	2.0	2.13 ± 0.13	620 ± 40	1.6 ± 0.6
H2O	4.7	2.0	2.13 ± 0.13	700 ± 100	1.2 ± 0.5
H2O	2.6	1.7	3.3 ± 0.3	703 ± 120	0.9 ± 0.3
H2O	2.3	2.0	4.2 ± 0.4	680 ± 50	0.8 ± 0.3
H2O	2.3	2.0	4.2 ± 0.4	680 ± 50	1.0 ± 0.3
H2O	2.3	1.0	2.13 ± 0.18	990 ± 120	0.9 ± 0.3
H2O	2.6	0.6	1.23 ± 0.10	980 ± 150	2.1 ± 1.3
H2	1.7	1.0	2.9 ± 0.3	950 ± 150	1.3 ± 0.4
weighted average					1.04 ± 0.12

Random uncertainty at the 1σ level of confidence.

CaOH + O2

This reaction was studied by injecting O2 into the flow tube at the MW discharge port (with the MW off). CaOH was generated as described above, using H2O as the reagent. CaOH decayed upon the addition of increasing O2 concentrations (Figure a). The decays were exponential up to 2 Torr and started to become bi-exponential at higher pressures. We speculate that the bi-exponential decays are related to excited carrier gas atoms (metastable triplet He atoms) generated in the MW discharge. The bimolecular rate constants (i.e., krec,7 = k7[N2]) obtained from single-exponential fits at low pressures (0.5–2 Torr) or the fast component of the bi-exponential (2–5 Torr) fits increase with the pressure, as expected for reaction (Figure b). The resulting values of krec,7 are listed in Table .

Figure 5

(a) Decay of the CaOH LIF signal with increasing [O2] for two buffer gas pressures. (b) Dependence of the bimolecular rate constant of CaOH removal by O2 on the number density of the buffer gas (N2). Red circles, experimental data at 298 K; blue dots and black squares, master equation calculations at 298 and 200 K, respectively; and thin and thick lines, fits to the master equation results to the Troe expression for termolecular reactions, using the conventional broadening factor[39] and the new broadening factors proposed in ref (41), respectively.

Table 2

Measured Rate Constants for the CaOH + O2 + M Reaction at 298 K

flow (slm)	P (Torr)	t (ms)	krec,7a (×10–11, cm3 molecule–1 s–1)
0.7	0.5	4.0 ± 1.0	3.9 ± 1.0
1.1	1.0	4.5 ± 0.7	5.9 ± 0.9
2.5	2.0	4.0 ± 0.3	7.0 ± 0.9
3.8	3.0	4.0 ± 0.3	9.9 ± 0.8
5.6	4.0	3.58 ± 0.22	9.0 ± 0.9
7.0	5.0	3.86 ± 0.22	13.1 ± 1.9

Random uncertainty at the 1σ level of confidence.

O2CaOH + O

To study reactions and R9, O2CaOH was prepared by first injecting H2O and then O2 downstream of the ablation target (t = 0.3 and 1.6 ms after the ablation pulse, respectively) and upstream of the MW discharge port (t = 3.2 ms). The addition of O atom concentrations via the MW port resulted in the reappearance of a fraction of the CaOH LIF signal (detected at t = 6.4 ms) that had been lost by the addition of O2 upstream of the O atom injection. The CaOH recovery was stronger for lower [O2] concentrations (Figure ). This phenomenological growth of the CaOH signal with an increasing O concentration can be rationalized in terms of the chemical cycle formed by reactions –R9–R7. These reactions (with H in excess over O2CaOH and OCaOH) together with the first-order losses of O2CaOH, OCaOH, CaOH, and O to the walls of the flow tube are described by the following coupled differential equations:where k′O, k′O, and k′OCaOH are the wall loss rates of O, O2CaOH, and OCaOH, respectively. The wall loss rate of atomic O was found to be k′O = 250 ± 50 s–1. Theoretical estimates of the diffusion coefficients of Ca-containing molecules, such as CaOH, Ca(OH)2, or CaO3, in N2[10] justify using a common first-order loss rate k′CaX for CaOH, OCaOH, and O2CaOH, which greatly simplifies the modeling of eqs –E9; i.e., k′CaX = k′CaOH = k′OCaOH = k′O.

Figure 6

Reappearance of CaOH upon the addition of O atoms into a flow, where CaOH has been previously converted to O2CaOH by an excess of O2. Each panel (a–g) corresponds to a different O2 concentration, in decreasing order. The CaOH level in the absence of O2 and O (panel h) is placed at 3 units in the relative concentration scale shown. The solid lines are the optimal solution in the least squares sense of the system of differential eqs –E9, with keff = 5.5 × 10–11 cm3 molecule–1 s–1. Almost identical simulated curves are obtained by modeling explicitly reactions and R9, with k8 = 5.4 × 10–11 cm3 molecule–1 s–1 and k9 = 1.1 × 10–10 cm3 molecule–1 s–1.

In eq , a term has been included for reaction . It is likely that reaction cannot compete with reaction because [O2] ≫ [O], and reaction at 2 Torr is not far from the gas kinetic rate constant (see below); however, reaction might become competitive when [O2] ∼ [O]. To test this possibility, experiments were carried out where O atoms were added to the flow carrying CaOH in the absence of O2. Removal of CaOH was only observed beyond experimental uncertainty (Figure h) for the maximum O atom concentration that could be reached ([O] ∼ 1.3 × 1013 atom cm–3), implying an upper limit to the rate constant for reaction of k10 ≤ 1 × 10–11 cm3 molecule–1 s–1.

The system of differential eqs –E9 was integrated numerically, and the resulting calculated curves of [CaOH] versus [O] for different [O2] were fitted to the observed SCaOH LIF versus [O] and [O2] by floating the rate constants k8 and k9 using a nonlinear least squares method.[10] However, Figure shows that the sum of squared residuals χ2 does not present a well-defined minimum for k8 and k9. These parameters are highly correlated, showing an empirical dependence (dashed line in Figure ) that can be approximated by the following equation:The asymptotes of this empirical dependence between the optimal values of k8 and k9 indicate a lower limit for both rate constants of 3 × 10–11 cm3 molecule–1 s–1. Alternatively, an effective reaction between O2CaOH and O, leading directly to the CaOH product, can be considered. The effective rate constant obtained from a global fit to the data shown in Figure using the latter approach is keff = 2.8–1.2+2.0 × 10–11 cm3 molecule–1 s–1, where the uncertainty at 95% confidence encompasses uncertainty propagated from k′O, k10, the contact time t, and the concentrations of reagents. The uncertainty limits of keff also apply to the rate-limiting step.

Figure 7

Contour plot of the sum of error-weighted squared residuals (χ2) (residuals calculated as the difference between the data in Figure and numerical solutions to the system of differential eqs –E9 with different values of k8 and k9) versus the free parameters k8 and k9. The dashed line indicates the empirical dependence of k9 versus k8 in the region with χ2 < 80, given by k9 = 3.5 × 10–11k8/(k8 – 3.0 × 10–11).

Discussion

Formation Mechanism of CaOH

The formation of CaOH from the evaporation[29] or ablation[26] of Ca within a carrier gas flow containing water vapor is well-known, but the actual mechanisms leading to CaOH have not been investigated in detail. In our LA–FFT–LIF experiments, the formation of CaOH in the gas phase requires the intervention of electronic excited states of Ca or CaO, because the reactions of Ca and CaO with H2O to make CaOH are endothermic.[17,30]The reaction of CaO and H2 (reaction R–6b) to make CaOH is probably endothermic (ΔHr = 20 ± 22 kJ mol–1), although the uncertainty is large because the uncertainties in the enthalpies of formation of CaO and CaOH are considerable (17 and 15 kJ mol–1, respectively). The blue emission around the ablation target shows that Ca-bearing species are vaporized in highly excited states. The low-lying excited states Ca(3P°, 3D, 1D2)[24] and CaO(A1Σ+, b3Σ+, a3Π, A′1Π)[31] have sufficient energy to form CaOH from these reactions. Some of these states are also optically metastable, which increases the probability of reaction. The radiative lifetime of Ca(3P) is 0.33 ms,[32] and the mean radiative lifetime of Ca(1D2) for emission to all lower states, including Ca(3P), is 1.7 ms.[32,33] The radiative lifetime of CaO(A′1Π) has not been measured but has been estimated to be on the order of 0.1 ms.[34]

The fact that similar amounts of CaOH are produced by the addition of H2O and H2 indicates that, in our experiments, the major precursor of CaOH must be an oxygen-bearing species: CaO* + H2O/H2. Minor contributions of Ca* + H2O and possibly of CaO + H2 depending upon the added reagent cannot be ruled out. Ground-state CaO is removed by H2O via reaction ,[14] and by H2[10] viaBecause the initial rate of formation of CaOH is compatible with the CaO loss rate (Figure ), it is possible that reaction R–6b does indeed occur (which supports the thermoneutrality of reaction ). However, this is a minor source of CaOH in our experiments, because when [H2] is increased by up to a factor of 10, the CaOH LIF signal still grows by up to a factor of 6, long after any CaO has been removed.

The removal of CaO by H2 has been seen to proceed with a slower rate constant (1 × 10–10 cm3 molecule–1 s–1) than the previously published result k13 = (3.4 ± 1.3) × 10–10 cm3 molecule–1 s–1[10] and to slow when H2 or H2O are injected further away from the ablation target. CaO* collisional and radiative relaxation is most likely the cause of this observation. In competition with collisional quenching and radiative decay, CaO* reacts with H2 or H2O to form CaOH with a relatively slow rate constant of the order of 2 × 10–12 cm3 molecule–1 s–1 (Figure ). When sufficient amounts of reagent are added, most CaO* is converted to CaOH.

The spontaneous emission between 600 and 700 nm observed at a low pressure in the absence of reagents must correspond to a species with a radiative lifetime commensurate with ∼2.4 ms required to travel from the ablation target to the detection region (at the minimum pressure of 0.7 Torr in our experiments). The 3P → 1S transition of Ca occurs at 657.278 nm, and the radiative lifetimes of Ca(3P) and Ca(1D2) are of the order of 1 ms. CaO(A′1Π) is also expected to be long-lived and to give rise to chemiluminescence in the observed range.[35]

Our observations indicate that, shortly after ablation, highly excited Ca atoms decay predominantly to the metastable 3P state, which is long-lived enough not to undergo complete radiative relaxation (or collisional quenching) within 0.3 ms of flight time between ablation and the point where water was injected. Thus, the removal process observed by EI–ToF–MS is likely to be the following reaction:with k14 = (1.0 ± 0.2) × 10–11 cm3 molecule–1 s–1.

CaOH + H

We have determined a rate constant of reaction R6 at room temperature of k6(298 K) = (1.04 ± 0.24) × 10–10 cm3 molecule–1 s–1. A summary of previous determinations of k6 is presented in Figure . Our value is consistent with the lower limit reported by Broadley and Plane:[10]k6(298 K) ≥ 1.1 × 10–11 cm3 molecule–1 s–1. Cotton and Jenkins[15] carried out a study of alkaline-earth-catalyzed radical recombination reactions in flames and found k6(1570–1800 K) = 4.48 × 10–12 cm3 molecule–1 s–1 (no uncertainty reported). In a subsequent flame study, Jensen and Jones[16] reported an Arrhenius expression k6(1800–2615 K) = 1 × 10–9 exp(−1400/T) cm3 molecule–1 s–1, with an estimated uncertainty of a factor of 3. This expression is clearly at odds with the results of the earlier flame study. Extrapolation to room temperature yields k6(298 K) ∼ 9 × 10–12 cm3 molecule–1 s–1, which is consistent with the lower limit reported by Broadley and Plane, within the uncertainty of the extrapolated flame data. Also, an Arrhenius type of expression may be fitted to the average of the temperature range of Jensen and Jones and the room-temperature value reported in this work: k6(300–2615 K) = 6.78 × 10–10 exp(−560/T) cm3 molecule–1 s–1.

Figure 8

Literature values for the CaOH + H reaction and possible extrapolations toward low temperature. The dashed line is an extrapolation of the temperature-dependent expression reported by Jensen and Jones[16] between 1800 and 2615 K. The dotted line results from an Arrhenius fit to the 1978 flame data combined with the room-temperature determination reported in the present work. The thin solid line illustrates a long-range-type temperature dependence of T1/6 to the room-temperature result of the present work.

The calculated potential energy surface (PES) for this reaction (Figure S1 of the Supporting Information) shows that the barrier leading to channel reaction is submerged well below the entrance channel. Therefore, the reaction can always proceed via reaction , which would rule out a significant activation energy. The overall rate constant k6 = k6a + k6b is more likely to show a very weak temperature dependence, for example, a T1/6 type of dependence characteristic of long-range interaction. Only a temperature-dependent branching ratio would result from the endothermicity of reaction , with k6b increasing at the expense of k6a as the temperature increases.

It is possible that the higher rate constant at 1800–2615 K determined by Jensen and Jones[16] results from systematic errors in the data analysis. The quoted uncertainty of the flame results is large, not least because several reactions with unknown rate coefficients and equilibrium constants needed to be included in the mechanism to fit the emission spectroscopy observations; also, important reactions may have been ignored, and several catalytic cycles can potentially fit the observations. Furthermore, the uncertainty in the rate constants may be too large to fit a temperature dependence in a relatively reduced temperature range (1800–2615 K), which then needs to be extrapolated toward much lower temperatures. We note that Jensen and Jones also reported the rate constants of reaction [k2a(1800–2615 K) = 8 × 10–10 cm3 molecule–1 s–1, factor of 2.3 uncertainty] and reaction [k5(1800–2615 K) = 1.4 × 10–11 exp(−600/T) cm3 molecule–1 s–1, factor of 2.3 uncertainty]. Both rate constants have been determined for 278 < T < 513 K in previous PLP–LIF and LA–FFT–LIF studies in our laboratory,[10,14] producing the following results: k2a(298 K, 760 Torr) = 5.8 × 10–10 cm3 molecule–1 s–1 (20% uncertainty) and k5(298 K) ≥ 1.1 × 10–11 cm3 molecule–1 s–1. Therefore, the flame and flow tube determinations of k2a are consistent, but extrapolating k5 of Jensen and Jones to room temperature results in k5(298 K) = 1.9 × 10–12 cm3 molecule–1 s–1, which is inconsistent with the flow tube data. This seems to indicate that the flame study by Jensen and Jones produced high-temperature rate constants, which are, within uncertainty, consistent with the lower temperature results, but the Arrhenius temperature dependences are most likely wrong or not applicable below 1800 K.

Finally, in view of the discussion above, we recommend an overall rate constant for reaction R6 under mesospheric conditions of k6(200 K) = (1.0 ± 0.3) × 10–10 cm3 molecule–1 s–1. The question whether reaction is endothermic or not remains open. However, this would not be very relevant in the MLT, because any CaO produced via reaction would mostly be converted into Ca by reaction with atomic O (reaction below), because this species occurs at significant concentrations throughout a full diurnal cycle at altitudes above 82 km.[2]

CaOH + O2

The Master Equation Solver for Multi-Energy Well Reactions (MESMER)[36,37] was used to extrapolate k7 toward the lower end of the range of mesospheric temperatures and pressures (T ∼ 120 K, and P ∼ 10–4 Torr). The required molecular parameters of the species of interest and the zero-point-corrected energies at 0 K of the stationary points on the PES were calculated at the B3LYP/6-311+g(2d,p) level using the Gaussian 09 package[38] (Table S1 of the Supporting Information). This level of theory compares well to results obtained with more accurate methods (Tables S1 and S2 of the Supporting Information). In MESMER, the internal energies of the stationary points on the PES are divided into a contiguous set of grains (width of 100 cm–1), each containing a bundle of rovibrational states. The density of these states is calculated using the ab initio vibrational frequencies and rotational constants. Each grain was then assigned a set of microcanonical rate coefficients for dissociation, which were determined using inverse Laplace transformation to link them directly to the high-pressure limiting recombination coefficient, which, here, we set to the gas kinetic rate constant with an assumed temperature dependence: k7rec,∞ = 1.5 × 10–10 × (T/298 K)1/6 cm3 molecule–1 s–1. The microcanonical dissociation rate coefficients are then determined by a detailed balance. The exponential down model is used for describing collisional energy transfer probabilities. The energy transfer parameter ΔEdown is set to a typical value for N2 of 300 cm–1.

The results of these calculations are shown in Figure b. Although we have not attempted floating the parameters to fit the experimental data, it can be seen that the agreement is quite satisfactory. The calculated rate constants were then fitted to the Lindemann expression modified by a broadening factor Fc(39) to derive an analytical expression for k7 ready to use in atmospheric modeling, as we have done in a previous work.[14] The low-pressure limiting rate coefficient, log10(k7rec,0, cm6 molecule–2 s–1) = −(12.70 ± 0.04) – (4.986 ± 0.016)log T is obtained from the MESMER calculation. The best fit yields Fc = 0.136 ± 0.005, which is smaller than the value of 0.6 often assumed.[40] The O2CaOH adduct has a relatively large number of low-frequency vibrational modes (see Table S1 of the Supporting Information), which tends to cause Fc in the conventional falloff expression to be less than 0.2, resulting in unphysical inflection points in the falloff curves[41] (thin lines in Figure b). We have therefore used the modified broadening factor expression of Troe (eqs 7 and 8 in ref (41), with parameters x0 = 0.9, b = 0.25, and Fc = 0.2), which produces a better fit to the master equation data, as shown by the thick lines in Figure b.

The rate-determining reaction of the sequence reaction –R9 proceeds with a rate constant of 3 × 10–11 cm3 molecule–1 s–1, but from the modeling of the available data, it is not possible to tell whether the rate-limiting step is reaction or R9. A possible solution to the ambiguity in the assignment of values to the rate constants k8 and k9 is suggested by comparing reactions and R9 to the analogous reactions.[10]CaO2 has C2 symmetry, and therefore, the terminal O2 is arranged in a similar manner to O2CaOH.[10] The rate constants of these reactions have been reported by Broadley and Plane:[10]k15(298 K) = 3.1–1.5+2.0 × 10–10 cm3 molecule–1 s–1, and k16(298 K) = 2.2–1.4+7.0 × 10–11 cm3 molecule–1 s–1. Thus, it is possible that, by analogy and following eq , k9(298 K) = 2.4 × 10–10 cm3 molecule–1 s–1 and k8(298 K) = 3.5 × 10–11 cm3 molecule–1 s–1. In any case, for atmospheric modeling purposes, it is always possible to choose one of the rate constants and use eq to derive the other. Reactions and R16 show weak temperature dependences,[10] owing to the absence of barriers and the potential wells of the adducts not being deep enough with respect to the exit channels to allow for stabilization. For reactions and R9, we have a similar situation and therefore would expect the rate constants k8 and k9 to show a weak temperature dependence.

Conclusion

In this work, we report rate constants of important Ca-bearing molecules with species relevant in the MLT region, which have not been measured before or have only been measured in flame chemistry studies, i.e., within a range of temperatures far from the atmospheric range. We provide recommended values of these rate constants under MLT conditions. We have identified an important Ca reservoir, O2CaOH, which forms quickly as a result of the fast recombination of CaOH with O2 and the high atmospheric abundance of O2. Above 82 km, where there are significant concentrations of atomic O, even during the night,[2] the formation of O2CaOH will provide a holding cycle, which slows the conversion of CaOH back to active Ca via a reaction with H. Below 82 km, where the atomic O concentration falls off by orders of magnitude, O2CaOH will become the major sink for Ca and the likely form in which it is incorporated into MSPs.