14928
J. Phys. Chem. 1996, 100, 14928-14935
Rate Constants for the Relaxation of CH(X2Π,ν)1) by CO and N2 at Temperatures from 23 to 584 K Lee B. Herbert, Ian R. Sims, Ian W. M. Smith,* David W. A. Stewart, and Andrew C. Symonds The School of Chemistry, The UniVersity of Birmingham, Edgbaston, Birmingham B15 2TT, U.K.
Andre´ Canosa and Bertrand R. Rowe De´ partement de Physique Atomique et Mole´ culaire, U.A. 1203 du C.N.R.S., Campus de Beaulieu, UniVersite´ de Rennes I, 35042 Rennes Cedex, France ReceiVed: March 15, 1996; In Final Form: June 14, 1996X
Rate constants have been determined for the collisional relaxation of CH(X2Π,ν)1) by CO and N2 over a wide range of temperatures. Experiments between 584 and 86 K have been performed in heated and cryogenically cooled cells, and rate constants from 295 to 23 K have been measured in a CRESU (cine´tique de re´action en ecoulement supersonique uniforme) apparatus. In both series of experiments, pulsed laser photolysis was employed to generate CH radicals and the laser-induced fluorescence technique was used to observe the rate of removal of CH(ν)1). Vibrational relaxation is rapid, k298 ) 9.7 × 10-11 cm3 molecule-1 s-1 for CO and k298 ) 3.1 × 10-11 cm3 molecule-1 s-1 for N2, and the dependence of the rate constants on temperature is quite slight but complex. The results suggest that relaxation occurs via strongly bound complexes, and the implications of the results for the interpretation of the reactions between CH radicals and CO and N2 are discussed.
Introduction The methylidene radical CH is both widely found and highly reactive.1 There is interest in the kinetics of its reactions at high temperatures in view of its ubiquity in hydrocarbon combustion systems,2 where its reaction with N2 is especially important since it is probably the primary step in the mechanism responsible for the formation of “prompt” NO.3 Reactions of CH are also important in the chemistry of planetary atmospheres,4 especially in the nitrogen- and hydrocarbon-rich atmosphere of Titan5 and in the chemistry of interstellar clouds.6 For these purposes, knowledge of reaction rates at low and very low temperatures is required. Because of the interest in reactions of CH in the above complex environments and in order to understand better its high reactivity, we have launched a program of experiments to determine the rates of a large number of elementary reactions of CH over a temperature range from ∼600 K down to the ultralow temperatures achievable in a CRESU (cine´tique de re´action en ecoulement supersonique uniforme) apparatus.7 Our measurements apply the pulsed laser photolysis (PLP), laserinduced fluorescence (LIF) technique, with which we have successfully measured the rate constants for a number of reactions of CN and OH over similarly wide temperature ranges. To generate CH radicals, we used the method first employed by Lin,8 namely, the successive three-photon photolysis of CHBr3, in our case employing a frequency-quadrupled Nd:YAG laser or a KrF excimer laser:
CHBr3 + 3 hν (λ ) 266 or 248 nm) f CH + 3Br (1) Kinetic decays were obtained by tuning the output of either a dye laser or an optical parametric oscillator (OPO) to a line in the A2∆-X2Π electronic band system of CH to excite LIF signals at variable time delays after the pulse from the photolysis X
Abstract published in AdVance ACS Abstracts, August 15, 1996.
S0022-3654(96)00808-8 CCC: $12.00
laser, following the method first reported by Butler et al.9 Although the initial rovibrational state distribution of the CH (X2Π) produced by multiphoton photolysis of CHBr3 at 266 or 248 nm has not been measured, Okada et al.10 have determined the CH vibrational state distribution following photolysis at 193 nm. Our own experiments show that a significant fraction of the CH is produced in the first vibrationally excited level, ν ) 1, following photolysis at 266 or 248 nm, with smaller amounts (see below) being created in vibrational levels above ν ) 1. This is an ideal situation in which to measure the kinetics of species in ν ) 1. In this paper, we report the first measurements of this kind on CH(ν)1), namely, the relaxation of these species in collisions with N2 and CO:
CH(ν ) 1) + N2 f CH(ν)0) + N2
(2)
CH(ν ) 1) + CO f CH(ν)0) + CO
(3)
The results reported here and the mechanisms that are responsible for the remarkably rapid relaxation of CH(ν)1) in processes 2 and 3 are strongly related to the reactions of CH(ν)0) with N2 and CO. At the temperatures covered in the present experiments, these reactions of CH with the isoelectronic molecules N2 and CO undoubtedly occur by association; i.e., by collisional stabilization of the energetically excited adducts formed in collisions between CH and either N2 or CO:
CH + N2 + M f HCN2 + M; ∆rH°298 ) -(97 ( 10) kJ mol-1 11,12 (2a) CH + CO + M f HCCO + M: ∆rH°298 ) -(306 ( 10) kJ mol-1 12,13 (3a) The kinetics of these reactions have been the subject of an extensive study in Birmingham covering the temperature range between 202 and 584 K. The results of these experiments are © 1996 American Chemical Society
Relaxation Rate Constants of CH(X2Π,ν)1) reported elsewhere.12 The conclusion from that work and from other, relatively sparse, kinetics experiments on reaction 3a9,14 is that pressure-dependent association of CH with CO dominates over other possible reaction channels (e.g., that leading to H + C2O) and that the formation of strongly bound HCCO from CH + CO occurs over a potential energy surface without a barrier. The situation with respect to reaction between CH and N2 is more complex. There have been several investigations of the kinetics of this reaction, both at low and moderate temperatures (2300 K),21,22 where association is replaced by the slightly endothermic and spin-forbidden reaction yielding HCN and N atoms:
CH + N2 f HCN + N(4S); ∆rH°298 ) +(12 ( 9) kJ mol-1 (2b) which is generally thought to be so important in generating “prompt” NO in hydrocarbon flames.2,3 As well as being investigated in several experimental studies, the reaction between CH and N2 has been the subject of numerous theoretical calculations in recent years, again reflecting the likely importance of reaction 2b in hydrocarbon combustion. The calculations encompass both electronic structure calculations23-25 on the potential energy surfaces that are involved and rate calculations26-28 based on those surfaces. A fascinating picture has emerged, which demonstrates the contribution that ab initio calculations can make to understanding a problem of considerable technological importance. Two isomers of HCN2 are found to be stable (i.e., have lower potential energy) with respect to separated CH + N2. One is a trans, datively bonded structure, while the other is a C2V structure in which the CH bridges the N atoms. The minimum associated with the datively bonded isomer, which is calculated23,24 to have a potential energy ∼85-125 kJ mol-1 lower than CH + N2, can be accessed across a surface without any barrier. However, there is a high barrier (g300 kJ mol-1 24) separating this minimum from that associated with the C2V structure. Therefore, the datively bonded HCN2 appears to play no role in reaction 2b. Rather this reaction proceeds, across a barrier (∼76 kJ mol-1 high25), to the C2V adduct, and thence via an electronically nonadiabatic transition onto a quartet surface, before passing over a second barrier25 to HCN + N(4S), the products of reaction 2b. In short, reactions 2a and 2b proceed quite independently of one another across unconnected potential energy paths. In the present paper, we report rate constants for the relaxation of CH(ν)1) by N2 and CO, i.e., for processes 2 and 3. The measurements cover a very wide range of temperatures and constitute the first experiments involving vibrationally excited species that have been carried out in the ultracold environment provided in a CRESU apparatus. At all temperatures and at the relatively low total pressures of our experiments, removal of CH(ν)1) is much faster than that of CH(ν)0), and the measured rate constants, in contrast to those for reaction of CH(ν)0) with N2 and CO,12,14-20 are independent of total pressure. It seems at least very likely that vibrational relaxation of CH(ν)1) by N2 and CO is unusually facile because it takes place via the formation of strongly bound complexes in which intramolecular energy transfer is generally complete within the lifetime of the complex with respect to dissociation. Previous measurements of this kind have been made on the relaxation of OH(ν)1) by NO, NO2, and CO,29,30 of CN(ν)1) by NO31 and of NO(ν)1) by radical atoms.32 In each case, it has been argued that the rate constants for relaxation correspond to those for formation of the strongly bound collision complex and therefore provide a good estimate of the rate of the association
J. Phys. Chem., Vol. 100, No. 36, 1996 14929 reaction in the limit of high pressure, since the rate of this process is also controlled by the rate of formation of the energized adducts. The validity of this argument has now been demonstrated for several systems by direct measurements of the rate of association at total pressures of several hundred bars by Forster et al.33 If our hypothesis of relaxation via strongly bound complexes is correct, in the case of CH(ν)1) + N2, the complex involved must be the datively bonded HCNN species. The enthalpy of formation of this radical from CH + N2, given in eq 2b, is that derived by Fulle and Hippler11 from the results of recent experiments on the association of CH with N2 at pressures up to 150 bar. These results also allow us to compare the values of our rate constants for relaxation of CH(ν)1) by N2 with theirs for association of CH and N2 in the limit of high pressure. Although the results reported here give no direct information about the HC-N2 bond strength in datively bonded HCN2, in the Discussion section of this paper we take the opportunity to reassess the interpretation of kinetics experiments in the range 600-1075 K in the light of recent theoretical and experimental work. Experimental Section The techniques used in the present series of experiments, in particular the methods employed to achieve low and ultralow temperatures, have been described previously.7,34,35 Consequently, here we shall give only a brief, but self-contained, description of the apparatuses and of the procedures for obtaining rate constants for the removal of CH(ν)1) by CO and N2. In both sets of experiments, CH radicals in ν ) 0 and ν ) 1 were generated by pulsed laser photolysis of CHBr3. In the experiments performed in Birmingham, at temperatures between 86 and 584 K, the output at 266 nm from a frequencyquadrupled Nd:YAG laser (Spectron Lasers, Model SL404) was used to photolyze CHBr3, whereas in the CRESU experiments in Rennes, at temperatures between 23 and 295 K, photolysis was effected with either an excimer laser operating on the KrF transition at 248 nm (Questek) or a frequency-quadrupled Nd: YAG laser (Spectra-Physics). In both sets of experiments, i.e., in Birmingham and in Rennes, the CH radicals in ν ) 1 were observed by LIF. Fluorescence was excited using a laser tuned to a line in the (1,1) band of the A2∆-X2Π system of CH at ∼431 nm and was observed at ∼490 nm in the (1,2), and possibly the (0,1) bands, through an interference filter centered at 490 nm (fwhm 10 nm). The advantages of working “offresonance”, and thereby reducing scattered laser light, off-set the effect of smaller Franck-Condon factors36 and emission coefficients37 for the (v′ - v′′) ) -1 bands compared with those for the (v′ - v′′) ) 0 bands. The probe lasers used in the two sets of experiments also differed. In Birmingham, LIF signals from CH were excited using a dye laser (JK Lasers, system 2000) pumped by a Nd: YAG laser (JK Lasers, DLPY4), whereas in Rennes an OPO employing BBO as the nonlinear component (Spectra-Physics, MOPO 730) was used in excite CH(ν)1). In Figure 1, we show LIF spectra of CH recorded in the CRESU apparatus at 295 and 23 K. The line in the (1,1) band used in the kinetic experiments is marked. In experiments in the CRESU apparatus it was relatively easy to tune the probe laser to a line in the (1,1) band. At higher temperatures, there was greater congestion of rotational lines from the two bands but there was little difficulty in distinguishing lines from the different bands, as the concentration of CH(ν)1) decayed much faster than that of CH(ν)0)12 under the conditions of the present experiments. At 23 K only two rotational levels in each vibrational state of CH are significantly populated, J ) 0.5, N ) 1 (F2e and F2f
14930 J. Phys. Chem., Vol. 100, No. 36, 1996
Figure 1. LIF spectrum of the ∆ν ) 0 bands in the A2∆-2Π system of CH recorded in the CRESU apparatus at two different temperatures: (a) 295 and (b) 23 K. In each case, the gas mixture contained only CHBr3 in Ar or He so that vibrational relaxation was minimal but the delay times were sufficiently long (40 and 80 µs, respectively) to allow complete rotational relaxation. In the lower panel, the few lines in each vibrational band (ν′, ν′′) are assigned. The arrow in the upper panel identifies the line used in the kinetic measurements.
components) and J ) 1.5, N ) 1 (F1e and F1f).38 Therefore, at this temperature and at the resolution of our experiments, very few lines in each vibrational band have measurable LIF intensity. These lines are assigned in the lower panel of Figure 1. From the intensity of these lines and the relative emission efficiencies37 of the observed transitions, it is possible to say that the relative CH(ν)0) populations are similar to those measured by Okada et al.10 for photolysis at 193 nm which were characterized by a temperature of ∼3000 K. This temperature corresponds to a population ratio Nν/Nν-1 of ∼0.3. The three cells employed in the experiments between 86 and 584 K were similar to those used in previous experiments above and below room temperature on reactions of CN and OH.34,35,39,40 To obtain temperatures above room temperature, the reaction cell was mounted in a high temperature oven.35 Temperatures below 298 K were achieved by passing various cryogens either through a coil mounted inside the low-temperature reaction cell40 or through the inner of two jackets to the reaction cell, the outer jacket being evacuated to provide good thermal insulation.34 In all cases, the actual temperatures achieved for particular conditions of heating or cooling were measured in separate, subsidiary experiments, using a thermocouple. The heated cell and that with an internally mounted cooling coil were cruciform and the beams from the photolysis and probe lasers counterpropagated along the side arms to the main reaction cell, intercepting the slow flow of gas at right angles. LIF signals were observed in the third perpendicular direction. With the doubly jacketed cell, the photolysis and probe lasers counterpropagated along the main longitudinal axis of the cell and LIF signals were observed through the Pyrex walls of the reaction vessel and its jackets. The principles of the CRESU technique and its adaptation to the measurement of rate constants for reactions between neutral species by the PLP-LIF technique have already been described
Herbert et al. in detail.6 Briefly, expansion through an axisymmetric Laval nozzle generates a supersonic flow of gas in which the Mach number, the temperature, the density of the gas, the mole fraction of the reagent in excess (here N2 or CO), and the velocity of the gas stream are constant along the axis of the flow. The temperature in the flow can be calculated from the Mach number and the reservoir temperature and checked by observing the relative intensities of rotational lines within the band of an LIF spectrum.7 Ar or He was used as the carrier in the present experiments. The laser beams from the photolysis and probe lasers were combined and copropagated along the axis of the supersonic gas flow. Fluorescence was gathered by an optically fast telescope-mirror combination mounted within the main vacuum chamber toward the downstream end of the uniform flow and directed onto a photomultiplier tube. In both sets of experiments, CHBr3 was introduced into the gas mixture by bubbling a small flow of the carrier gas through a sample of liquid CHBr3 maintained at room temperature. This flow was adjusted to be the minimum consistent with obtaining good LIF signals from CH(ν)1) and was kept constant within each series of experiments. On the basis of the vapor pressure of CHBr3 at room temperature and the fraction of the total flow picking up CHBr3, we could estimate the concentration of CHBr3 in the reaction zone. It was always less than 5 × 1012 molecule cm-3 in the CRESU experiments, often appreciably less, but was up to a factor of 5 higher in the experiments in cooled and heated cells. These estimates are consistent with the first-order decays measured in the absence of N2 or CO (see below, Figures 2 and 3), if reaction of CH with CHBr3 has a large rate constant similar to those found for reaction of CH with simple unsubstituted alkanes.4 The rate of loss of CH(ν)1) was observed by scanning the delay time between the pulses from the photolysis and probe lasers. The signals were accumulated, processed, and analyzed by procedures we have used and described7,34,35 before. In every case, the variation of the LIF signals with time was well-fitted by a singleexponential decay (using a standard nonlinear least-squares algorithm), yielding a pseudo-first-order rate constant (k1st) for removal of CH(ν)1) under the particular conditions in that experiment. Results When free radicals are generated by photodissociation of a molecular precursor, the difference between the energy of the photon bringing about the dissociation and the dissociation energy of the molecule is distributed among the degrees of freedom of the separating products. In measuring rate constants for processes involving these radicals, it is necessary to allow time for the radicals to become thermally equilibrated. For the translational and rotational motions, relaxation generally takes only a few collisions, but the relaxation of vibrationally excited molecules can be extremely slow. The rates of rotational and vibrational relaxation can be followed via LIF, either by observing spectra with different delays set between the photolysis and probe lasers or by tuning the probe laser frequency to a transition from a particular rovibrational state and seeing how the intensity of the LIF signal changes as the time delay between the two laser pulses is varied. Previous experiments in the CRESU apparatus have been performed on CN7,39 and OH.41-43 CN radicals were generated by photolysis of NCNO at a wavelength close to threshold, so that vibrationally excited levels were energetically inaccessible and any necessary rotational relaxation was rapid. Spectra of the (0,0) band in the B2Σ+-X2Σ+ system of CN were used7 to confirm the temperatures in gas mixtures expanded through the Laval nozzle in the CRESU apparatus. OH radicals can be
Relaxation Rate Constants of CH(X2Π,ν)1)
J. Phys. Chem., Vol. 100, No. 36, 1996 14931
Figure 2. Typical data obtained in the CRESU apparatus: (a) firstorder decay of LIF signal from CH(ν)1) in the presence of 5.0 × 1013 molecule cm-3 CO at 44 K in Ar, fitted to a single-exponential decay, with residuals shown above; (b) first-order decay constants for CH(ν)1) at 44 K in Ar plotted against the concentration of CO.
Figure 3. Typical data obtained in the cryogenically cooled cell: (a) first-order decay of LIF signal from CH(ν)1) in the presence of 4.21 × 1014 molecule cm-3 CO at 146 K in Ar, fitted to a single-exponential decay, with residuals shown above; (b) first-order decay constants for CH(ν)1) at 146 K in Ar plotted against the concentration of CO.
generated35,41-43 by photolysis of HNO3 or H2O2 at 266 nm. Neither process generates significant quantities of vibrationally excited radicals, but they are produced in a “hot” distribution over rotational levels. In this situation, one must wait a few microseconds for the rotational state distribution to become thermalized41 before observing the kinetic decays resulting from removal of OH by chemical reaction. The situation with CH is different again. When CHBr3 is photolyzed to produce CH, a significant fraction of the CH is formed in levels with ν > 0 and the rotational distributions in each vibrational level are initially nonthermal. In addition, some short-lived chemiluminescence can be observed. As a result, particularly in the experiments at ultralow temperatures where the total gas densities were lower, it was necessary to start the exponential fit to the LIF signals some time after the photolysis pulse to allow the CH to equilibrate over rotational levels and to eliminate any interference from the chemiluminescence. Figure 2a presents a typical record of LIF signal from CH(ν)1) plotted against the time delay between the pulses from the photolysis and probe lasers. This experiment was performed in the CRESU apparatus and the diagram shows the fit of an exponential curve to the experimental points. Figure 3a shows similar data obtained in the cryogenically cooled cell. In mixtures of just CHBr3 and the noble gas (Ar or He), lines from CH(ν)1) persisted for the several hundred microseconds over which observations were made. With CHBr3, CO or N2, and inert gas in the gas mixture, CH(ν)0) was lost only slowly by diffusion from the observation zone, by reaction with undissociated CHBr3 (or its photodissociation products) and by slow three-body recombination with CO or N2.12 Under typical conditions, concentrations of CH(ν)1) decayed ∼2 orders of magnitude faster than CH(ν)0). In both sets of experiments, the traces of LIF signal from CH(ν)1) against time were well-fitted by single-exponential decays. There is no evidence in these decays for the effects of “cascading”; i.e., of population of the ν ) 1 level by relaxation from higher levels. This is not unexpected in view of the relatively small populations in higher levels and of the likely mechanism via strongly bounded complexes, which will tend
to lead to relaxation of all vibrationally excited levels directly to ν ) 0. The first-order rate constants derived from a set of measurements at a particular temperature were plotted against the concentration of N2 or CO. Examples of such plots are given in Figures 2b and 3b. The gradients of the plots yield the second-order rate constants for removal of CH(ν)1). The measurements that have been carried out and the second-order rate constants that have been obtained for removal of CH(ν)1) by CO and N2 are summarized in Tables 1 and 2. The background rates, represented by the values of the intercepts in Figures 2b and 3b, are probably determined principally by reaction of CH with CHBr3 and its photolysis products, possibly with some small contribution from diffusion of radicals out of the observation zone. The errors quoted are (tσ, where σ is a single standard deviation and t is the Student’s t-factor reflecting 95% confidence limits. Only random errors are included in these estimates of errors. Systematic errors could arise from incorrect calibrations of the mass flow controllers or from incorrect estimates of the temperatures. The latter could not only introduce uncertainty in the temperature of a particular measurement but might also lead to errors in the derived second-order rate constants through the conversion of partial pressures to concentrations of CO or N2. We have assessed this latter source of error carefully, particularly in the case of experiments in the cryogenically cooled cells, where there are significant temperature gradients in the gas mixture as it flows through the cooled portion of the reaction cell. Based on thermocouple measurements within the flowing gas, we estimate that any error in the temperature, and hence in the derived rate constant, will not be greater than 5%. Errors from calibrations of the mass flow controllers are likely to be smaller still. Strong evidence that any systematic errors in our measurements are small is provided by the excellent agreement between the results obtained in the CRESU apparatus and in the cryogenically cooled cell in the temperature range (86-295 K) common to both sets of experiments. This agreement is displayed clearly in Figures 4 and 5, where the temperature dependence of the rate constants for relaxation of CH(ν)1) by
14932 J. Phys. Chem., Vol. 100, No. 36, 1996
Herbert et al.
TABLE 1: Second-Order Rate Constants for the Removal of CH(ν)1) by CO and N2 Measured in the CRESU Apparatus at Temperatures between 23 and 295 Ka (a) CH(ν)1) + CO T (K)
carrier gas
23 44 52.1 53.9 97.4 123 295
He Ar Ar Ar Ar He Ar
no. of exptsa
total gas density (1016 molecule cm-3)
range of [CO] (1014 molecule cm-3)
rate constant (10-10 cm3 molecule-1 s-1)
8 8 11 11 11 11 7
4.73 2.90 5.15 40.1 15.45 12.7 37.5
0.29-0.94 0.064-0.51 0.15-1.27 0.64-5.5 0.31-2.75 0.13-1.3 2.3-15.9
1.55 ( 0.13b 1.88 ( 0.08 1.82 ( 0.10 2.04 ( 0.07 1.53 ( 0.08 1.45 ( 0.10 0.86 ( 0.13
no. of exptsa
total gas density (1016 molecule cm-3)
range of [N2] (1014 molecule cm-3)
rate constant (10-10 cm3 molecule-1 s-1)
8 8 11 11 11 11 7
4.73 2.90 5.15 40.1 15.45 12.7 37.5
0.29-0.94 0.064-0.64 0.15-1.27 0.64-5.50 0.19-2.72 0.13-1.3 2.21-15.4
1.11 ( 0.17b 1.10 ( 0.09 1.14 ( 0.06 1.21 ( 0.05 0.72 ( 0.06 0.61 ( 0.09 0.32 ( 0.05
(b) CH(ν)1) + N2 T (K)
carrier gas
23 44 52.1 53.9 97.4 123 295
He Ar Ar Ar Ar He Ar
a Rate constants derived from measurements in the CRESU apparatus are the result of a single series of experiments with the number of individual measurements given in the third column of the table. b Errors quoted are (tσ statistical error, where t is the appropriate value of the Student’s t-distribution for the 95% point.
TABLE 2: Second-Order Rate Constants for the Removal of CH(ν)1) by CO and N2 Measured in Cryogenically Cooled and Heated cells at Temperatures between 86 and 584 Ka (a) CH(ν)1) + CO range of [CO] rate constant no. of T (K) exptl runsb (1014 molecule cm-3) (10-10 cm3 molecule-1 s-1) 86 108 146 202 294 364 484 584
4 2 3 2 2 2 1 3
2.6-9.5 1.5-8.3 0.4-4.2 1.13-9.15 0.80-8.6 0.78-10.0 0.58-11.3 0.49-8.9
2.17 ( 0.07c 1.52 ( 0.12 1.31 ( 0.05 1.17 ( 0.04 1.08 ( 0.12 0.87 ( 0.06 0.86 ( 0.38 0.94 ( 0.04
(b) CH(ν)1) + N2 range of [N2] no. of rate constant T (K) exptl runsb (1014 molecule cm-3) (10-10 cm3 molecule-1 s-1) 86 98 108 146 202 294 364 484 584
3 1 1 2 2 2 2 2 2
2.5-14.8 9.8-32.6 6.4-41.0 0.4-4.3 1.6-17.7 4.6-39.1 4.1-35.0 5.3-37.0 3.7-36.6
Figure 4. Rate coefficients for the relaxation of CH(ν)1) by CO as a function of temperature, displayed on a log-log scale. The filled circles show the results obtained in the CRESU apparatus while the open circles show those obtained in the heated/cryogenically cooled cell.
1.31 ( 0.05c 0.74 ( 0.05 0.64 ( 0.03 0.48 ( 0.03 0.40 ( 0.04 0.30 ( 0.02 0.26 ( 0.02 0.20 ( 0.02 0.17 ( 0.02
a All experiments in cooled and heated cells were performed in Ar diluent at a total pressure of 10 Torr. b Each experimental run consisted of 8-11 individual measurements of pseudo-first-order rate constants at different [CO] or [N2] within the range given in the third column of the table. c Errors quoted are (tσ statistical error, where t is the appropriate value of the Student’s t-distribution for the 95% point.
CO and N2 are shown in log-log plots of the rate constants against temperature. Unfortunately, it was impossible to obtain temperatures below 86 K in the cooled cell apparatus to reproduce the flattening-off of the rate constants to lower temperatures which is clearly observed in the experiments in the CRESU apparatus. The agreement between the two different sets of experiments not only demonstrates the reliability of both but also demonstrates that the rate constants for removal of CH(ν)1) by CO and N2 do not depend on the total gas density. To confirm this point, CRESU experiments at ∼53 K were
Figure 5. Rate coefficients for the relaxation of CH(ν)1) by N2 as a function of temperature, displayed on a log-log scale. The filled circles show the results obtained in the CRESU apparatus while the open circles show those obtained in the heated/cryogenically cooled cell.
performed at two gas densities differing by a factor of 8 with no significant change in the rate constants. Discussion There have been no previous systematic measurements of the collisional relaxation of CH(ν)1) by N2 and CO. The observation that CH(ν)1) is removed by these gases at rates that
Relaxation Rate Constants of CH(X2Π,ν)1) approach the collision efficiency and that are far faster than the removal of CH(ν)0) under similar conditions of temperature and total pressure substantiates the expectation that the vibrationally excited CH radicals undergo rapid relaxation facilitated by the formation of strongly bound complexes. As explained in the Introduction, this means that rate constants for relaxation in this kind of system are connected to those for reaction, especially the rate constants for association in the limit of high pressure, and therefore, we first discuss our results in the light of the kinetic data available for these reactions. At the temperatures of the present experiments, the chemical reactions of CH with N2 and CO occur predominantly by association; i.e., by reactions 2a and 3a and the former reaction yields the datively bonded HCNN species. The only extensive kinetic study of the reaction between CH and CO is that recently completed in Birmingham and reported by Brownsword et al.12 Their experiments cover the temperature range 202-584 K and the pressure range 2 or 4-400 Torr. Their data yield rate constants in the limit of low pressure which can be fitted to the expression: k°3a[Ar] ) 4.1 × 10-30 (T/298)-2.5 [Ar] cm3 molecule-1 s-1. The same fit gave12 an essentially temperatureindependent value of the rate constant in the limit of high pressure of k∞3a ) 1.3 × 10-11 cm3 molecule-1 s-1 but, as the experiments were performed at total pressures close to the lowpressure regime, the values of the limiting high-pressure rate constants were not well-defined by those experiments. Not surprisingly, in view of its importance in combustion, the reaction between CH and N2 has been studied rather extensively,12,14-22 notably by Brownsword et al.,12 Berman and Lin,16 Becker et al.,19 and Medhurst et al.20 Berman and Lin measured rate constants in 100 Torr Ar in the range 297-675 K. Becker et al. made similar measurements between 301 and 894 K in 20 Torr Ar19a and have very recently reported19b more extensive measurements covering the ranges 10-620 Torr and 298-1059 K. The strong negative temperature dependence of the rates below ∼600 K, similar to that found12,14 for CH + CO, confirms that, at low temperatures, reaction occurs by association according to eq 2a. This conclusion was confirmed by measurements of the pressure dependence of the reaction rate at 297 K by Berman and Lin.16 The experiments of Brownsword et al.12 covered the same ranges of temperature and pressure as those on CH + CO and yield k°2a[Ar] ) 1.7 × 10-31 (T/298)-2.3 [Ar] cm3 molecule-1 s-1. Again, their value of the high-pressure rate constants from the fit of the rate constants for association, k∞2a ) 2.2 × 10-11 cm3 molecule-1 s-1, is much smaller than that measured for relaxation in the present set of experiments. Very recently, Fulle and Hippler11 measured rate constants for CH(ν)0) + N2 at total pressures of up to 150 bar of helium and have thereby determined the limiting high-pressure rate constant for association in a more direct fashion, only a short extrapolation of the actual rate data being required. Between 200 and 500 K, they found values of k∞2a which can be expressed as (4.1 ( 0.8) × 10-11 (T/300)-0.15 cm3 molecule-1 s-1, in fairly good agreement (see below for further discussion) with the values we obtain for the relaxation of CH(ν)1) by N2 at the same temperatures. Furthermore, at higher temperatures, they observed the approach of reaction 2a to equilibrium and hence, from a van’t Hoff plot, have derived the value of the ∆rH°0 for the formation of HCN2 from CH + N2 which is quoted above in eq 2a. The observations of Fulle and Hippler and the relatively low value for the enthalpy of the association reaction to produce datively bonded HCN2, determined both from those experiments and from the theoretical calculations,23,24 calls into question the interpretation of other high-temperature (T g 600 K) measure-
J. Phys. Chem., Vol. 100, No. 36, 1996 14933 ments19,20 on the reaction between CH and N2 which has been assumed to occur by collisionally assisted association at temperatures up to and beyond 1000 K. Medhurst et al.,20 for example, to interpret their kinetic measurements, performed RRKM calculations on the association reaction using a HCN2 bond energy of 122 kJ mol-1 based on the calculated value of Martin and Taylor.24 To illustrate our doubts about the validity of this interpretation, we consider experiments performed by Medhurst et al.20 at 750 K, where the rate constants they report (see Figure 7 of their paper) show a surprising and unexplained dependence on total pressure. The standard entropy change for CH + N2 f HCN2(dative) can be estimated using the standard entropy of HCNO in place of the unknown value for datively bonded HCN2. Combining the resultant value of ∆rS°(750K) ) -141 J K-1 mol-1 with ∆rH°(750K) ) -122 kJ mol-1 yields ∆rG°(750K) ≈ -16 kJ mol-1 and an equilibrium constant of 13.5 atm-1. It is then easy to show that, with the partial pressures of N2 present in the experiments, the conversion of CH to HCN2 would be far from complete, even at a temperature well below the maximum values employed in the experiments of Becker et al.19 (1059 K) and Medhurst et al.20 (1075 K). Using the value of ∆rH° inferred by Fulle and Hippler makes the equilibrium even less favorable for a simple interpretation of kinetics experiments between 600 and 1100 K. Of course, at very high temperatures, the association reaction 2a is replaced by reaction 2b, forming HCN and N atoms. It is now accepted23-28 that these reactions proceed independently, association via the dative complex, reaction 2b via the complex with C2V structure. The importance of the present results is that they serve to constrain the values of the rate constant for formation of the datively bonded complex that can be used in any attempt to model the kinetics of the reaction between CH and N2. The absolute and relative values of the rate constants for relaxation of CH(ν)1) by CO and N2 and their dependence on temperature all merit some discussion. Qualitatively, the results are consistent with a process in which the rate-determining step is determined by the ability of the lowest intermolecular potential acting between CH and CO or N2 to capture the two species.43,44 Although the magnitudes of the rate constants at room temperature are similar to those for relaxation found in radical-radical systems, for example OH(ν)1) + NO, NO229,30 and CN(ν)1) + NO,31 it should be remembered that there are fewer potential energy surfaces correlating with CH(X2Π) + CO(1Σ+) or N2(1Σg+), than in the radical-radical systems investigated previously. The rates at which CO and N2 relax CH(ν)1) differ by factors of between 1.4 and 5.5 over the range of temperatures covered in the present experiments, with CO being the more effective collision partner, especially at higher temperatures. The negative temperature dependences of the rate constants for relaxation of CH(ν)1) by CO and N2 below room temperature may, at least in part, reflect changes in the distribution of CH over rotational levels associated with different spin-orbit components of the 2Π electronic ground state, but such an effect should be the same in the cases of CH + CO and CH + N2. Although CO and N2 are isoelectronic, the polarizability, the quadrupole moment and, of course, the dipole moment are all greater for CO than for N2. Consequently, the long-range electrostatic attraction between CH and CO must be somewhat larger than that between CH and N2. As the HC-CO bond strength is so much greater than that between CH and N2, the chemical interaction between CH and CO is also likely to be much stronger than that between CH and N2 at the large reagent
14934 J. Phys. Chem., Vol. 100, No. 36, 1996 separations that determine the rates of adiabatic capture. These differences are probably responsible for the difference between the rate constants for relaxation at low temperatures, since these rate constants almost certainly correspond to those for adiabatic capture by a combination of the long-range (electrostatic) and medium-range (chemical) forces acting between the reagents. However, the similarity of the temperature dependence of the rate constants for the two systems below room temperature is somewhat surprising. The larger difference between the rate constants for relaxation by CO and N2 at higher temperatures could have a different, and interesting, origin. Under these conditions, the thermal translational and rotational energy in collisions between CH and N2 begins to become a substantial fraction of the HC-N2 bond energy. Consequently, the lifetime of the collision complex with respect to redissociation may be so short that there is insufficient time for energy to flow from the high-frequency CH vibration into the low-frequency modes of HCN2. If this intramolecular energy transfer is incomplete, then the assumption that the rate constant for relaxation is the same as that for formation of the collision complex is invalid. Some support for this notion comes from a comparison of the rate constants, given in Table 2, for relaxation of CH(ν)1) by N2 at temperatures above 300 K with Fulle and Hippler’s measurements of k2∞, the high-pressure rate constant for association of CH with N2, in the range 200-500 K. They reported values of k2∞ (see above) that are almost independent of temperature, whereas the rate constants for relaxation fall from (3.0 ( 0.2) × 10-11 cm3 molecule-1 s-1 at 294 K to (1.7 ( 0.2) × 10-11 cm3 molecule-1 s-1 at 584 K. The magnitude of the rate constants for both the relaxation processes that have been studied in the present work and the fact that they increase as the temperature is lowered demonstrate that there is no electronic potential energy barrier to the addition of CH radicals to either CO or N2. In these circumstances, the factors that lead to the observed, quite slight, variations of rate constants with temperature are rather subtle.44,45 In part, the negative temperature dependence may be caused by a redistribution of the CH radicals between separate spin-orbit states as the temperature changes,45 if reaction proceeds only on a single surface that correlates with the lower of the spin-orbit components of CH(X2Π). However, the spin-orbit splitting in CH is small, only 28.15 cm-1 38 (equivalent to 40.5 K), so such an effect will probably become appreciable only at very low temperatures. As our previous low-temperature studies have shown,46 although negative temperature dependences, of the kind exhibited by CH(ν)1) + CO between ∼100 and 600 K and by CH(ν)1) + N2 between ∼100 and 400 K, may differ quantitatively for different chemical systems, they are apparently the norm when there is no electronic energy barrier on the long- and medium-range potentials between the chemical reagents so that the collision dynamics are controlled by adiabatic capture.44,45 In these cases, as the temperature is increased, so on average are the energies and the rotational and orbital angular momenta associated with the reagents. This leads to the participation of an increasing number of adiabatic potentials that have maxima at decreasing interreagent separations, as a result, for example, of the need to conserve total angular momentum and of the transformation of free rotations of the molecular reagents to restricted vibrational motions (hindered rotations, torsions, and finally bending modes) as the separation between the reagents becomes less. As a consequence, the rate constant for capture and the formation of strongly bound complexes such as HCCO and HCN2 falls as the temperature increases and as a greater fraction of collisions fail to surmount the maxima on the longand medium-range adiabatic potentials.
Herbert et al. The observation that the rate constants for relaxation of CH(ν)1) by both CO and N2 reach maximum values at ∼100 K and then at lower temperatures remain constant or slightly decrease is unusual but not unprecedented.39,43,45,46 This kind of behavior has been attributed45 to the collision dynamics reaching a limit where capture is determined by the long-range electrostatic potential. In the case of simple attraction between two particles a distance r apart where the potential energy varies as r-6, the rate constant for capture would vary as T1/6. What is surprising in the cases of CH(ν)1) + CO and CH(ν)1) + N2 is that the limiting behavior is reached at a temperature as high as 100 K. More detailed explanation of the temperature dependence of the rate constants determined in the present work must await detailed calculations using quantum capture,44 microcanonical variational, and other forms of transition state theory,44,47 or statistical adiabatic channel model methods.48 Summary and Conclusions This paper reports the first kinetic experiments on the vibrational relaxation of a diatomic species, CH(ν)1), to temperatures as low as 23 K. Rate constants for relaxation by N2 and CO are reported for temperatures ranging from 23 to 584 K. In view of (a) the fact that CH is known to associate with N2 (to form datively bonded HCN2) and with CO (to produce HCCO) in reactions without activation energies and (b) the magnitude and temperature dependence of the rate constants for relaxation of CH(ν)1) measured in the present work, it is proposed that relaxation occurs via the formation of chemically bound complexes in which intramolecular energy redistribution is facile. The factors leading to the observed temperature dependence of the rate constants have been discussed. In the case of CH(ν)1) + N2, our results at room temperature and above can be compared with the limiting high-pressure rate constants for the association of CH(ν)0) with N2 inferred from experiments at total pressures up to 150 bar.11 The agreement is satisfactory, lending weight to our proposal for the relaxation mechanism and demonstrating again that relaxation measurements of this kind can provide a means of obtaining an estimate of limiting high-pressure rate constants in appropriate systems. Finally, we draw attention to our suggestion, based on simple and approximate thermodynamic arguments as well as on the results of Fulle and Hippler,11 that it may be necessary to reexamine the interpretation of experiments on the kinetics of CH(ν)0) + N2 in the range 600-1100 K, since it does not appear that collisionally assisted association to the datively bonded structure of HCN2 can provide a satisfactory explanation for the rate constants that have been reported.19,20 Acknowledgment. We thank Simon Gatenby for assistance with some of the experiments performed in the cryogenically cooled cells. We acknowledge funding from the EPSRC and from the CEC under the Science Plan (Contract SC*CT890261). The experiments carried out in the CRESU apparatus in Rennes were also supported by the GDR’s ‘Physicochimie des Mole´cules et des Grains Interstellaires’ and ‘Dynamique des Re´actions Mole´culaires’ programmes. Some of the lasers for these experiments were borrowed from the EPSRC Laser Loan Pool at the Rutherford-Appleton Laboratory, for which we express thanks. D.W.A.S. is also grateful to SERC for the award of research studentship. We are also most grateful to Professor Dr. H. Hippler for permission to cite some of his results prior to their publication and I.W.M.S. acknowledges useful discussions with Drs. J. A. Miller and G. P. Smith.
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