Gas-Phase Boudouard Disproportionation Reaction Between Highly Vibrationally Excited CO Molecules

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Chemical Physics 330 (2006) 506–514 www.elsevier.com/locate/chemphys

Gas-phase Boudouard disproportionation reaction between highly vibrationally excited CO molecules

Katherine A. Essenhigh, Yurii G. Utkin, Chad Bernard, Igor V. Adamovich *, J. William Rich

Nonequilibrium Thermodynamics Laboratories, Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43202, USA

Received 3 September 2006; accepted 21 September 2006 Available online 30 September 2006

Abstract

The gas-phase Boudouard disproportionation reaction between two highly vibrationally excited CO molecules in the ground electronic state has been studied in optically pumped CO. The gas temperature and the CO vibrational level populations in the reaction region, as well as the CO2 concentration in the reaction products have been measured using FTIR emission and absorption spectroscopy. The results demonstrate that CO2 formation in the optically pumped reactor is controlled by the high CO vibrational level populations, rather than by CO partial pressure or by ﬂow temperature. The disproportionation reaction rate constant has been determined from the measured CO2 and CO concentrations using the perfectly stirred reactor (PSR) approximation. The reaction activation energy, 11.6 ± 0.3 eV (close to the CO dissociation energy of 11.09 eV), was evaluated using the statistical transition state theory, by comparing the dependence of the measured CO2 concentration and of the calculated reaction rate constant on helium partial pressure. The dispro- 18 3 portionation reaction rate constant measured at the present conditions is kf =(9±4)· 10 cm /s. The reaction rate constants obtained from the experimental measurements and from the transition state theory are in good agreement. 2006 Elsevier B.V. All rights reserved.

Keywords: CO disproportionation reaction; Vibrational excitation; Optical pumping

1. Introduction nario involves a reaction between a gas-phase CO molecule and an adsorbed CO molecule. In the surface reaction of The CO disproportionation reaction (Boudouard Eq. (1), the activation barrier is considerably reduced from reaction), the gas phase values, which appear to exceed at least CO þ CO ! CO þ C; ð1Þ 140 kcal/mole, although significant surface reaction still re- 2 quires rather high temperatures [1–13]. The theoretical is one of key free carbon formation processes occurring study of this disproportionation on surfaces of transition both in high-temperature gas flows and in non-equilibrium metal oxides by Cheng et al. [3] indicates that the second electric discharges. This reaction has long been observed at scenario is the totally dominant channel. Going beyond high temperatures on oxidized surfaces such as iron oxide near-thermal equilibrium reaction, the enhanced reactivity in the process known as metal dusting [1], which leads to of highly vibrationally excited molecules on metal surfaces corrosion of metal surfaces and has been of great concern is a well-known effect. There is evidence [4] that vibrational in various industrial processes. The mechanism of this reac- excitation of CO leads to production of CO2 on surfaces tion is still debated and includes two possible scenarios. In (primarily copper oxide) at significantly lower tempera- the first scenario, a reaction takes place between two CO tures, below 200 C. At these temperatures, thermal equi- molecules absorbed on the surface, while the second sce- librium reaction on the same surface shows no detectable CO2 production [4]. This suggests that vibrational excita- * Corresponding author. tion may contribute into overcoming the activation energy E-mail address: [email protected] (I.V. Adamovich). of the CO disproportionation reaction.

In the gas phase, reaction of Eq. (1) has been observed also occur at low temperatures, in collisions of highly vib- in a glow discharge [5,6] and in experiments on isotopic rationally excited CO molecules in the ground electronic enrichment of 13C using ultraviolet photolysis of carbon state, monoxide [7–9]. In both cases, it has been concluded that COðvÞþCOðwÞ!CO2 þ C; ð4Þ the mechanism responsible for the CO2 production 3 involves metastable CO(a Pr) molecules produced by prepared by optical pumping of carbon monoxide by reso- either electron impact excitation of CO (in a glow dis- nance absorption of CO laser radiation, charge) or by resonance absorption of the 206.22 nm iodine COðvÞþhv ! COðv þ 1Þ: ð5Þ atom line generated by a flash lamp (in UV photolysis), However, the rate coefficient of reaction of Eq. (4) was esti- 3 15 3 COða PrÞþCO ! CO2 þ C: ð2Þ mated to be low, <10 cm /s. During optical pumping, 6 The activation energy of reaction of Eq. (2) is believed to only the low states of CO, v 10, are populated by reso- 3 nance absorption, while higher vibrational levels of CO, be close to the excitation energy of the a Pr electronic state, approximately 6 eV (140 kcal/mole) [5,9], and is v > 10, which are not directly coupled to the laser radia- about half of the CO dissociation energy of 11.09 eV. tion, are populated by the anharmonic vibration–vibration The rate constant of this reaction was estimated to be (V–V) exchange processes (Treanor pumping [15,16]), 3 12 3 kf(a P) = 1.3 · 10 cm /s, based on the concentration COðvÞþCOðwÞ!COðv 1ÞþCOðw þ 1Þ; w > v: ð6Þ of CO(a3P ) and the rate of CO production in a glow r 2 In previous CO optical pumping experiments [17–20], discharge [5]. The effect of vibrationally excited CO vibrational levels up to v 40 were detected, which corre- molecules, which were also present in the discharge, on sponds to a vibrational energy of up to 7.7 eV. Note that in the rate of the disproportionation reaction was not studied. electric discharges, where both electronically excited and A similar rate constant, k (a3P) = 1.9 · 1012 cm3/s, was f highly vibrationally excited CO molecules are created by reported in the UV photolysis experiments [9]. electron impact, the reaction channel of Eq. (4) may be ob- The gas-phase disproportionation reaction which does scured by reaction of Eq. (2). On the other hand, in the not involve electronically excited species may only occur optically pumped CO, in the absence of an externally ap- if the activation barrier is overcome at the expense of the plied electric field, direct excitation of electronic levels by translational or the vibrational energy of the reactants. electron impact is a minor factor compared to electric dis- The former channel would require extremely high gas charges. Although UV emission from electronically excited temperatures available only in shock tube experiments, CO has been observed in previous optical pumping exper- which is the main reason why Boudouard disproportion- iments, such as 4th positive bands CO(A1P X3R+) ation reaction is not commonly observed in the gas phase. ! [17,19,21,22] and 3rd positive bands CO(b3R+ a3P ) On the other hand, temperatures behind strong reflected ! r [21], the measured population of the electronically excited shocks are sufficiently high to induce chemical reactions CO(A1P) state was low, 1010 1011 cm3 [19]. Population in carbon monoxide [10–13]. In particular, Mick et al. of the metastable CO(a3P ) state in the optically pumped [13] have studied CO decomposition behind the reflected r CO, although never measured in the experiment, is also shock by monitoring the time-dependent concentrations likely to be low because of a very effective collisional of C and O atoms, assuming that CO dissociation quenching mechanism CO þ M ! C þ O þ M; ð3Þ 3 COða PrÞþCO ! COðwÞþCOðvÞ; ð7Þ (M = Ar or CO) is the dominant chemical reaction. We 10 3 note that the Arrhenius fit to the reaction rate constant with a rate coefficient of 10 cm /s [23]. This makes measured in Ref. [13], assuming the activation energy equal optically pumped CO an ideal environment to study reac- to the CO dissociation energy, 11.09 eV, yields a strong tion of Eq. (4). inverse temperature dependence of the pre-exponential fac- The main objective of the present work is to study kinet- tor, T3.1 This indicates that an alternative reaction chan- ics of reaction of Eq. (4) in optically pumped CO, to mea- nel, with a considerably lower activation energy, may sure its rate coefficient, and to determine whether CO affect the measured reaction rate. Interestingly enough, disproportionation may efficiently occur in a reaction the Arrhenius fit with the activation energy near 6.0 eV between two vibrationally excited CO molecules in the gives more reasonable pre-exponential factor temperature ground electronic state. dependence, near the collision-frequency dependence of T0.5 [4]. This result suggests that the disproportionation 2. Experimental setup reaction of Eq. (2), rather than CO dissociation reaction of Eq. (3), may in fact be the dominant reaction channel A schematic of the experimental setup is shown in during high-temperature CO decomposition behind shock Fig. 1. A carbon monoxide (CO) laser is used to vibration- waves. ally excite CO, initially at room temperature, in the flowing It has been previously suggested [14] that in the gas reactor (see Fig. 1). The CO laser used in the present exper- phase, the Boudouard disproportionation reaction may iments is a c.w. liquid nitrogen cooled, electric discharge 508 K.A. Essenhigh et al. / Chemical Physics 330 (2006) 506–514

Fig. 1. Schematic of experimental setup. excited gas laser capable of lasing on multiple lines in cally reacting region is collected by an off-axis parabolic broadband mode. Typically, the gas mixture composition mirror and focused into an emission port of an IFS-66 Bru- and discharge conditions in the laser are optimized to pro- ker Fourier transform infrared spectrometer. The first duce a substantial fraction of its output on the v =1! 0 overtone CO emission spectra are used to infer the CO and v =2! 1 fundamental band transitions, which is nec- vibrational distribution function (VDF) and the transla- essary for the laser beam absorption by carbon monoxide tional/rotational temperature of the flow in the reaction in the reactor, initially at room temperature. The present zone. The response function of the FTIR detector and col- use of CO laser pumped absorption to study energy trans- lection optics was measured using a calibrated blackbody fer processes in molecular gases at conditions of extreme course (InfraRed Industries Inc, Model 201). First, the R vibrational disequilibrium is a further development of a branch of the 1 ! 0 band of the CO fundamental spectrum technique with a considerable literature [14–22,24]. was used to infer the translational–rotational temperature The continuous flow reactor is a six-arm glass cell with a in the reaction zone. Self-absorption may be a significant total volume of approximately 112 cm3. The reactor con- factor at relatively high CO partial pressures in the cell tains the gas mixture of CO, Ar, and He flowing at a very (3–12 Torr) and long optical path (10 cm). For this rea- slow flow rate, 24 cm3/s. The pressure inside the reactor is son, emission from high rotational levels, J0 = 30–40, was kept constant, P = 110 Torr. The flow rates of all the gases used to infer the rotational temperature. Then, the CO first are measured by rotameters upstream of the reactor. The overtone spectrum was used as an input in a computer code focused laser beam enters and exits the reactor through [20] to infer the VDF. Basically, the code infers relative 1 in. diameter CaF2 windows, as shown in Fig. 1. The populations of CO vibrational levels using the least squares arm used to let the CO laser beam into the reactor is fit of a synthetic infrared spectrum to a high-resolution purged by argon flow to prevent the laser beam absorption experimental spectrum, at a known temperature. by CO and resultant carbon deposit on the window. A The mixture of chemical reaction products flowing from cylindrical glass tube with a 5 mm diameter hole at one the reactor passes through an absorption cell mounted in a end blocks carbon monoxide in the reactor from entering sample compartment of the same FTIR. Infrared absorp- the purged region (see Fig. 1). The transmitted laser beam tion spectra of CO2 present in the product mixture are mea- power is measured by a power meter placed at the opposite sured by the FTIR using an internal infrared source arm of reactor (see Fig. 1). (globar) and calibrated using CO2-Ar mixtures of known Spontaneous infrared emission from carbon monoxide composition at the same pressure, P = 110 Torr. The cali- vibrationally excited by the CO laser beam absorption is brated CO2 absorption spectra are used to measure abso- collected at 90 through another CaF2 window, as shown lute concentrations of carbon dioxide produced in the in Fig. 1. The CO fundamental, first overtone, and second reactor. Since the FT spectrometer can only perform one overtone emission from the vibrationally excited, chemi- measurement (emission or absorption) at a time, the emis- K.A. Essenhigh et al. / Chemical Physics 330 (2006) 506–514 509 sion and absorption measurements were performed in a 9 Torr CO partial pressure quick succession one after the other and then repeated. 14 6.0x10 12 Torr CO partial pressure For the absorption measurements, a low spectral resolu- -3 tion of 2 cm1 was used, whereas high-resolution emission spectra (0.25 cm1) were used to infer the flow temperature and the VDF. Each measurement consisted of 24 FTIR 4.0x1014 scans to improve the signal to noise ratio. Small amounts of CO2 and water vapor present inside the absorption compartment of the FTIR presented a number density, cm 14 challenge. A commercial purge system (Puregas, model 2 2.0x10

PCDA), was used to remove water and carbon dioxide CO from the FTIR. Since it was found that some CO2 was still present in the system, the spectrometer was additionally 0.0 purged with nitrogen. Although we were unable to com- 01234 pletely remove CO2 leaking into the spectrometer from He partial pressure, Torr the atmosphere, background absorption (with the absorption cell pumped down below 0.1 Torr) was measured Fig. 3. CO2 number density vs. He partial pressure in the reactor. and then subtracted from each CO2 absorption spectrum. Absolute CO2 concentrations in the reactor were deter- function of helium partial pressure in the reactor at two dif- mined by comparing the integrated absorption of the asym- ferent CO partial pressures, 9 Torr and 12 Torr. From metric stretch band of carbon dioxide produced in the Fig. 3, one can see that the carbon dioxide number density reactor and that of the known amount of CO2. The calibra- significantly decreases as the helium partial pressure tion was performed using a mixture of 2.5% CO2 in Air. increases. At both CO partial pressures, adding approxi- Controlled amount of this mixture was diluted in Ar and mately 4 Torr of He to the mixture results in the CO2 con- flown through the reactor. The amount of CO2 added to centration reduction in the reaction products by about an the mixture during calibration was in the same range as order of magnitude, from 6 · 1014 cm3 to (2 4.0) · produced in the actual optical pumping experiments. 13 3 10 cm s (see Fig. 3). On the other hand, CO2 number density as a function of CO partial pressure remains nearly 3. Results and discussion constant (see Fig. 4), varying by only 10–20% as the CO partial pressure is increased by a factor of 4, from 3 Torr Fig. 2 shows a typical CO2 asymmetric stretch band to 12 Torr. 1 (2349.15 cm ) absorption spectrum measured in the flow Fig. 5 shows the flow temperature in the laser-excited of chemical reaction products generated in the optically reaction zone inferred from the CO fundamental spectra, pumped CO–Ar–He mixture. The CO2 number density cal- as discussed in Section 2. From Fig. 5, it can be seen that culated from the absorption spectra using the calibration the temperature significantly increases with CO partial procedure described in Section 2 is plotted in Fig. 3 as a pressure, from 750 K to 1000 K, mainly due to stronger CO laser beam absorption, and weakly decreases with He

0.04

8.0x1014

0.03 -3

/I)) 14 0 6.0x10

0.02

4.0x1014

0.01 number density, cm 2 Absorbance (ln(I 14

CO 2.0x10

0.00 2250 2300 2350 2400 2450 0.0 Frequency, cm-1 024681012 CO partial pressure, Torr Fig. 2. CO2 absorption band (asymmetric stretch band, resolution 1 2cm ); CO partial pressure 9 Torr. Fig. 4. CO2 number density vs. CO partial pressure in the reactor. 510 K.A. Essenhigh et al. / Chemical Physics 330 (2006) 506–514

1100 0 a 10 Amount of He added: 1000 0 Torr -1 1 Torr 10 900 1.6 Torr 2.4 Torr -2 3.6 Torr 800 10 4.5 Torr 700 5.5 Tor r 10 -3

600 Relative population

Temperature, K 3 Torr CO -4 500 6 Torr CO 10 400 9 Torr CO 12 Torr CO 10 -5 300 0 5 10 15 20 25 30 35 40 012345 Vibrational level He partial pressure, Torr 17 Fig. 5. Gas temperature in the plasma region vs. He partial pressure at b 10 diﬀerent CO partial pressures in the reactor. 6 Torr CO

-3 16 9 Torr CO 10 12 Torr CO partial pressure (by approximately 10% with the addition 1015 of 4 Torr of He). Summarizing the results of Figs. 3–5, one can see that adding helium to the CO–Ar mixture sub- 1014 stantially reduces the resultant CO2 concentration, Number density, cm although the flow temperature remains nearly constant. 13 On the other hand, adding CO to the mixture does not 10 affect the CO2 concentration although in this case both the flow temperature and the reactant (CO) concentration 1012 0 5 10 15 20 25 30 35 40 increase. This behavior clearly demonstrates that CO for- 2 Vibrational level mation in the optically pumped cell is controlled by a non- thermal chemical reaction, with a non-Arrhenius rate coef- Fig. 6. (a) CO VDFs at PCO = 6 Torr, at different helium partial ficient dependence. pressures, (b) CO VDFs at different CO partial pressures, without helium. Fig. 6 shows CO vibrational distribution functions (VDFs) in optically pumped CO–Ar–He mixtures at different He and CO partial pressures, inferred from the first the CO2 concentration in the reactor is primarily controlled overtone CO spectra, as discussed in Section 2. Note that by the high CO vibrational level populations, rather than Fig. 6(a) plots relative (normalized) CO vibrational level by flow temperature or by CO partial pressure. populations at different He partial pressures, while To infer the rate constant of the CO disproportionation Fig. 6(b) plots absolute CO vibrational level populations reaction (reaction of Eq. (4)) from the results of measure- at different CO partial pressures. It can be seen that vibra- ments presented in Figs. 3–6, we have used a perfectly stir- tional levels as high as v = 37 are detected. From Fig. 6(a), red reactor (PSR) approximation [25]. This approximation it is apparent that adding He to the CO–Ar mixture affects assumes that the chemical composition of the mixture at only high vibrational level populations (v > 15), while the any point in the reactor is the same. Indeed, since the flow low level populations remain very nearly the same as with- rate of the mixture through the reactor is very small out helium. The effect of high CO vibrational level depop- (24 cm3/s), the flow residence time in the reactor is several ulation by helium (helium titration) is due to rapid seconds. The excitation of the vibrationally excited CO vibrational relaxation of CO in collisions with He atoms, reactants, by absorption of the c.w. laser pump beam and and has been previously observed in optical pumping subsequent Treanor up-pumping is extremely rapid, on a experiments [17–19]. On the other hand, Fig. 6(b) shows much shorter time scale than the residence time in the reac- that although adding CO to the mixture does increase tor; we have very rapid and spatially uniform excitation of absolute populations of low vibrational levels, up to the reactants. The residence time is sufficient to complete v = 15–20, the high level populations (v > 25) remain mixing of the reaction products before the flow exits the nearly unchanged. reactor, so that at steady state the CO2 produced within Comparing the results of Fig. 6 with the measurements the reaction zone is distributed uniformly over the entire of the CO2 concentration, which decreases with helium par- volume of the reactor. tial pressure and does not change with CO partial pressure Using the PSR model, the rate constant of reaction of (see Figs. 3 and 4) suggests a straightforward conclusion: Eq. (4), kf, can be determined from the following equation: K.A. Essenhigh et al. / Chemical Physics 330 (2006) 506–514 511 d½CO2V reactor To infer the reaction activation energy from the present ¼½CO F þ k ½CO½COV ; ð8Þ dt 2 f RZ experimental results, we have used the statistical transition 3 state theory [28,29], which assumes that two vibrationally where [CO2] and [CO] are the number densities [cm ]of carbon dioxide and of carbon monoxide in the reactor, F excited CO molecules form a transition complex, with the 3 total vibrational energy randomly distributed among all is the volumetric flow rate [cm /s]; VRZ is the volume of available vibrational modes of the complex. Then the over- the reaction zone (optically pumped plasma), and Vreactor is the total volume of the reactor. The volume of the reac- all rate constant of reaction of Eq. (4) can be expressed as tion zone was determined from the visible emission from follows: the vibrationally excited region, which is almost entirely Xvmax Xvmax vw 3 03 k k ; 11 due to the C2 Swan bands emission (A Pg ! X Pu transi- f ¼ f ð Þ v0 w0 tion). Electronically excited C2, with a radiative lifetime of vw 3.16 ls, is also formed in chemical reactions of the optically where kf is the state-specific rate constant, rffiffiffiffiffiffiffiffi pumped CO. The short radiative lifetime precludes signifi- 2 2 vw T Ea xeCO cant diffusion of electronically excited C2 out of the reac- k ¼ k S A f f 1 f g 300 vw v w E E x tion volume, so that the size of the visible emission v þ w eCO2 region is close to the volume of the vibrationally excited re- ð12Þ gion. The emission region is a long slender cylinder approx- 10 3 1 imately 10 cm length. The plasma diameter was also In Eq. (12), kg =3· 10 cm s is the gas kinetic rate measured using a probe (a thin wire) inserted into the plas- at room temperature, T is the temperature in the reaction 6 ma. The probe was moved perpendicular to the plasma to zone (optically pumped plasma), S 1 is the steric factor, find the positions where it clips the visible emission region Avw is the step function, Avw =1 if Ev + Ew P Ea and from two opposite sides. The distance between these two Avw =0 if Ev + Ew < Ea,Ev and Ew are the vibrational positions turned out to be d = (1.74 ± 0.1) mm. A very sim- energies of two CO molecules, CO(v) and CO(w), Ea is the reaction activation energy, fv and fw are normalized ilar result, d = (1.67 ± 0.08) mm, was obtained by photo- 1 graphing the plasma and the CaF window from a large CO vibrational level populations, xeCO = 2214.24 cm 2 and x = 2226.85 cm1 are the vibrational quanta of distance and then comparing the size of the emission region eCO2 with the diameter of the window. The emission volume re- CO and of CO2 asymmetric stretch mode, respectively. mained approximately constant in all experiments reported Basically, the state-specific rate coefficient given by Eq. here, although diminishing in radiative intensity with the (12) is a product of the gas kinetic collision frequency, addition of helium. These dimensions give a reaction vol- the steric factor (i.e. the probability of the transition state 3 complex formation in a collision), and the probability of ume VRZ = (0.23 ± 0.03) cm . Note that the reverse reaction of Eq. (4) is not included the vibrational energy pooling into one of the CO vibra- in the present analysis. Indeed, nascent C product of the tional modes (with the C–O bond breaking energy Ea). Boudouard reaction is rapidly removed by a subsequent The steric factor in Eq. (12) accounts for the orientation reaction with the most abundant reactive species in the of the colliding partners and is the probability that the col- mixture, carbon monoxide, lision geometry will favor the transition state complex formation. The double summation in Eq. (11) is over all CO C þ CO þ M ! C2O þ M; ð9Þ vibrational levels populated at the present experimental conditions (vmax = 37, see Fig. 6). producing C2O and other carbon suboxide products detected in previous CO optical pumping experiments Since both the vibrational level populations and the [14,26,27]. Therefore, at steady state Eq. (8) gives: temperature in the reaction zone are measured in the present experiments, Eqs. (10)–(12) allow evaluating the reac- ½CO F tion activation energy, Ea. Specifically, since the rate k ¼ 2 ð10Þ f coefficient of the reaction is proportional to the CO2 con- ½CO½COV RZ centration (see Eq. (10)), one can compare the behavior Thus, the reaction rate constant predicted by the PSR of the measured CO2 number density and of the rate con- model is proportional to the CO2 concentration in the reac- stant predicted by Eqs. (11) and (12), both as functions tor, and inversely proportional to the square of the CO of He partial pressure. For the comparison, we have used concentration, which are both measured in the present the CO vibrational level populations, fv and fw, measured experiments. Note that the rate constant given by Eq. at different He partial pressures (see Fig. 6(a)) in Eq. (10) does not explicitly depend on the high CO vibrational (12), while the activation energy Ea in Eq. (12) was consid- level populations, which control the CO2 production rate in ered a parameter. the optically pumped plasma (see Figs. 3,4 and 6 and the The results of the comparison for three different CO par- discussion above). Therefore, while Eq. (10) allows infer- tial pressures are shown in Fig. 7(a–c). For each case, the ence of the rate constant from the CO2 and CO concentra- results are plotted for two activation energies, Ea =6eV tion measurements, it cannot help determining the (the activation energy for the reaction of Eq. (2)), and activation energy of the reaction of Eq. (4). the one that provides the best fit with the experimentally 512 K.A. Essenhigh et al. / Chemical Physics 330 (2006) 506–514

-17 Table 1 a 8.0x1014 3.0x10 CO 2 number density Rate constants of reaction of Eq. (4) obtained from the experiment and -4 k f ·8·10 (Ea = 6 eV) calculated from the transition state theory using the experimental VDFs exp 3 calc 3 -3 k f (Ea = 11.6 eV) CO partial pressure, Torr k ,cm /s k ,cm /s S 14 f f -1 6.0x10 17 17 -17 6 1.3 · 10 2.5 · 10 0.5

2.0x10 sec 9 4.5 · 1018 7.1 · 1018 0.6 3 12 9.6 · 1018 1.4 · 1017 1.4 14 4.0x10 , cm f k

1.0x10-17 agreement with the experiment. Such high value of the acti- number density, cm 14 vation energy suggests that the gas-phase Boudouard reac- 2 2.0x10 tion of Eq. (4) can occur only in collisions of two highly CO vibrationally excited CO molecules by pooling their vibra- 0.0 0.0 tional energies together. Note that the inferred activation 0 1 2 3 4 5 6 energy of Ea = 11.6 ± 0.3 eV is close to the CO dissociation He partial pressure, Torr energy, 11.09 eV, which also suggests that the reaction pro- ceeds via breaking one of the C–O bonds in the transition b 7x1014 CO number density -18 state complex. 2 8.0x10 - 4 14 ·3·10 Having determined the activation energy of the Boudou- 6x10 kf (Ea = 6 eV) -3 ard reaction from the CO2 concentration dependence on He kf (Ea = 11.9 eV) 14 5x10 6.0x10-18 partial pressure (see Fig. 7), we can now evaluate the value -1 of the steric factor, S,inEq.(12) by comparing the rate con- 14 exp 4x10 sec stants given by Eq. (10) (kf , from direct measurements of 3 -18 4.0x10 the CO and CO2 concentrations) and by Eqs. (11) and 3x1014

, cm calc f (12) (k , using the statistical theory at S = 1). The results

k f

number density, cm 14 are summarized in Table 1. The uncertainty in the Ay is 2 2x10 2.0x10-18 about factor of 2 and is mostly due to the uncertainty in CO 1x1014 determining the reaction region volume, V RZ The uncertainty in the kcalc is primarily determined by the uncertainty 0 0.0 f 0 1 2 3 4 in the activation energy determined from the data ﬁts in He partial pressure, Torr Fig. 7, and is also about a factor of two. From Table 1, one can see that the values of the rate constants are of the order of k 1017 cm3/s, which is well below the estimates c -17 f 6x1014 CO2 number density 1.5x10 15 - 4 indirectly inferred from previous data of 10 cm/s [4].It k f ·6·10 (Ea = 6 eV)

-3 14 can also be seen that the two rate coeﬃcients are in rather 5x10 k f (Ea = 11.4 eV)

-1 close agreement, within the accuracy of the present experi-

14 -17 4x10 1.0x10 sec mental results. From the comparison of the experimental 3 and the calculated rate constants, it can be concluded that 14

3x10 , cm the steric factor for the rate constant of reaction of Eq. (4) f k is of the order of one, S 1. Qualitatively, this suggests that 2x1014 5.0x10-18

number density, cm nearly every collision between two CO molecules results in 2 14 formation of a transition state complex, regardless of the

CO 1x10 collision geometry, and that at Ev + Ew Ea the reaction 0 0.0 occurs an a near gas kinetic rate. 0 1 2 3 4 Fig. 8 shows relative contributions of state-specific reac- He partial pressure, Torr tion channels into the overall reaction rate coefficient, vw kf =kf , as functions of vibrational quantum numbers, cal- Fig. 7. CO2 concentration and reaction rate constant, kf, vs. helium partial pressure for two different activation energies; (a) 6 Torr CO, (b) culated from Eq. (12) using experimental VDFs at a CO 9 Torr CO, (c) 12 Torr CO in Ar, at 110 Torr total pressure. partial pressure of 12 Torr. In Fig. 8, vibrational quantum numbers w and v are defined as follows:

COðvÞþCOðv þ wÞ!CO2 þ C: ð13Þ measured CO2 concentrations. From Fig. 7, it can be seen that the activation energy of Ea) = 6 eV predicts a much Each curve in Fig. 8 corresponds to a diﬀerent value of slower CO2 concentration reduction as a function of w =0,2,4,...,18 (indicated in the plot), with v being var- helium partial pressure, compared with the experiment. ied from v =0tov = 37. From Fig. 8, it can be seen that However, in all three cases, the activation energy near although vibrational levels as low as v = 16 can participate Ea = 11 eV (11.6 eV at Pco = 6 Torr, 11.9 eV at Pco = in the reaction of Eq. (4), the main contribution comes 9 Torr, and 11.4 eV at Pco = 12 Torr) provides very good from the levels from v =22tov = 32. One can also see that K.A. Essenhigh et al. / Chemical Physics 330 (2006) 506–514 513

0.016 ond, there is the rapid quenching mechanism of Eq. (7), which becomes dominant at high CO partial pressures. 3 Also, the estimated minimum CO(a Pr) concentration 0.012 would have to exceed the measured electron density in opti- 10 3 cally pumped CO–Ar plasmas, ne 10 cm , by about f two orders of magnitude [22,30]. Finally, the inferred reac- / k tion activation energy, about 11 eV, considerably exceeds

vw 0.008 f

k the activation energy of the reaction of Eq. (2). All this indicates that the gas-phase Boudouard reaction in high- 12 10 pressure optically pumped plasmas occurs by collisions of 14 8 0.004 16 6 two highly vibrationally excited CO molecules in the

18 4 ground electron state (reaction of Eq. (4)). On the other 2 0 hand, in low-pressure CO glow discharges the alternative 3 0.000 channel with participation of CO(a Pr) molecules pro- 10 15 20 25 30 35 duced by electron impact is likely to be the dominant chan- v nel, because of low absolute populations of highly vibrationally excited CO molecules at low pressures. Fig. 8. Relative contributions of different reaction channels into the vw overall reaction rate coefficient ðkf =kf Þ as functions of v and w at a 12 Torr CO partial pressure (values of w are indicated in the plot). 4. Summary above the activation energy threshold, the state-specific The gas-phase Boudouard disproportionation reaction rate coefficients plotted in Fig. 8 first increase because of between two highly vibrationally excited CO molecules in 2 the energy factor in Eq. (12),1 [(Ea/(Ev + Ew))] , and the ground electronic state has been studied in optically then gradually fall off because of the reduction of the vibra- pumped CO. The gas temperature and the CO vibrational tional level populations, fv and fw, at higher vibrational lev- level populations in the reaction region, as well as the CO2 els. According to the statistical reaction rate model, the concentration in the reaction products have been measured near resonant collisions (at small values of w) provide using FTIR emission and absorption spectroscopy. The greater contribution to the overall reaction rate compared results demonstrate that CO2 formation in the optically to collisions with a large vibrational energy difference pumped reactor is controlled by a non-thermal chemical between the collision partners (see Fig. 8). reaction, with a non-Arrhenius rate coefficient dependence. As discussed in Section 1, there is no evidence of pres- The CO2 concentration in the reactor is primarily con- 3 ence of electronically excited CO(a Pr) molecules in the trolled by the high CO vibrational level populations, rather optically pumped plasma at the present conditions. than by flow temperature or by CO partial pressure. The However, this electronic level might be excited by the same disproportionation reaction rate constant has been deter- vibration-to-electronic (V–E) energy transfer mechanism, mined from the measured CO2 and CO concentrations mediated by low-energy electrons, which results in using the perfectly stirred reactor (PSR) approximation. production of CO(A1P) molecules at similar experimental The reaction activation energy, 11.6 ± 0.3 eV (close to the conditions [17,19,20]. Associative ionization in optically CO dissociation energy of 11.09 eV), was evaluated using pumped CO–Ar–He mixtures occurs in collisions of highly the statistical transition state theory, by comparing the vibrationally excited CO molecules [18,30]. Using Eq. (10), dependence of the measured CO2 concentration and of 3 the lower bound CO(a Pr) number density necessary to the calculated reaction rate constant on helium partial produce the amount of CO2 detected in the present exper- pressure. This suggests that the gas-phase Boudouard reac- iments can be estimated as follows: tion occurs in collisions of two highly vibrationally excited CO molecules by pooling their vibrational energies ½CO2F ½COða3PÞ ¼ ; ð14Þ together. Finally, the reaction rate constants obtained from k ða3PÞ½COV f RZ the experimental measurements and from the transition 3 12 3 where kf(a P) 10 cm /s is the rate constant of reac- state theory are in good agreement. This suggests that tion of Eq. (2) [5,9], and other notations are the same as nearly every collision between two CO molecules results in Eq. (10). From Eq. (14), the minimum number density in formation of a transition state complex (steric factor 3 of CO(a Pr) molecules in the optically pumped mixture of 1), and that the reaction occurs an a near gas kinetic 11 3 3 should be 5 · 10 cm . Although such CO(a Pr)EQ rate if the combined vibrational energy of the reactants concentrations are somewhat high, they are attainable in exceeds the activation energy. The disproportionation reac- 3 low-pressure CO glow discharges where CO(a Pr) mole- tion rate constant measured at the present conditions is 18 3 cules are produced by electron impact excitation. However, kf =(9±4)· 10 cm /s. To the best of our knowledge, they are unlikely to be achieved in the optically pumped this is the first direct measurement of the rate constant of plasma, for two reasons. First, there is no direct electron the gas phase Boudouard reaction in vibrationally excited, impact excitation in the absence of electric field, and sec- ground electronic state CO. 514 K.A. Essenhigh et al. / Chemical Physics 330 (2006) 506–514

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