J. CHEM. SOC. FARADAY TRANS., 1994, 90(21), 3221-3227 3221 Low-temperature Kinetics of Reactions between Neutral Free RadicaIs Rate Constants for the Reactions of OH Radicals with N Atoms (103 < T/K < 294) and with 0 Atoms (158 < T/K < 294) Ian W. M. Smith* and David W. A. Stewart School of Chemistry, The University of Birmingham, Edgbaston, Birmingham, UK B 15 2TT Rate constants have been determined for the reaction between OH radicals and N atoms at temperatures down to 103 K and for the reaction between OH and 0 atoms down to 158 K. Discharge-flow methods were used to generate known steady-state concentrations of N and 0 atoms in a cryogenically cooled flow of gas. OH radicals were produced, in concentrations much smaller than those of the atomic radicals, by pulsed laser photolysis of a small concentration of HNO, introduced into this gas flow, and their first-order kinetic decays were observed using the time-resolved laser-induced fluorescence technique.The rate constants for both reactions increase monotonically down to the lowest temperatures achievable in the present experiments but do not exhibit any simple functional dependence on temperature. It is suggested that expressions of the form: k(T) = Felec(T) (T/298)"k'(298) are used to fit the data on these reactions at temperatures d515 K. Here Fele,(T) is the temperature-dependent ratio of the electronic degeneracy of the lowest potential surface, leading adiabatically from reagents to products, to the product of the electronic partition functions for the reagents, n has the value -0.17 for the N + OH reaction and -0.24 for 0 + OH, and the values of k'(298) are 2.0 x lo-'' cm3 molecule-' s-' for N + OH and 3.7 x lo-'' cm3 molecule-' s-' for 0 + OH, and correspond to rate constants for reaction on the lowest potential-energy surface at 298 K.Because the value of Felec(T)for both reactions is essentially constant for T < 50 K, it is suggested that expressions of the form k(T) =ATB are used in chemical models of interstellar clouds with A = 2.0 x lo-'' cm3 molecule-' s-' and B = -0.17 for N + OH and A = 3.7x lo-'' cm3 molecule-' s-' and B = -0.24 for 0 + OH. This paper reports new kinetic measurements on the reac- laboratory measurements of k, and k, over a similarly wide tions of OH radicals with N and with 0 atoms: temperature range, not least because the factors controlling the temperature dependence of the rate constants of radical- N + OH +NO + H; A,H0(298 K) = -203.8 kJ mol-' radical reactions, especially those between reagents exhibiting (1) considerable electronic degeneracy and near-degeneracy, are 0 + OH -'02+ H; A,H0(298 K) = -70.7 kJ mol-' complex and only partially under~tood.'~ Reactions (1) and (2) are examples of the simplest kind of (2) non-associative reaction between free radicals and therefore Previous direct experiments 1-3 have established the rate con- serve as valuable prototypes of radical-radical reactions in stants for these reactions at temperatures between 220 and general.For this reason and because of their importance in a 515 K.Based on measurements made between 250 and 515 wide variety of environments, they have received considerable K, Howard and Smith' suggested that the temperature attention from theoreticians. There have been numerous cal- dependence of the rate constants of these reactions could be culations of the potential-energy surfaces that are involved in expressed by the functions : both reaction (1)'5-20and reaction (2).21-25 In addition, the dynamics of both reactions have been examined by a variety k,(T)= 5.3 x 10-"(T/298)-0.25 cm3 molecule-' s-' of theoretical methods26 including quasiclassical trajec-7-30k,(T)= 3.8, x 10-"(T/298)-0.50 cm3 molecule-' s-' t~ries,~ quantum scattering calculation^,^' transition state theories,32 statistical adiabatic channel models,33 and In evaluating these results, and those reported by Lewis and adiabatic capture Watson2 and Brune et ~l.,~ In our own laboratory, the for the purposes of atmospheric dynamics of reaction (1) have been investigatedchemistry, Baulch and co-workers have proposed the expres- e~perimentally~~by determining the nascent distribution of sions: the NO product over its energetically accessible vibrational k,(T)= 3.8 x lo-'' exp(85/T) cm3 molecule-' s-' levels.Although the distribution is close to that predicted by statistical phase-space theorie~,~~.~~ doubted if Smith etk2(T) = 2.3 x lo-'' exp(llO/T) cm3 molecule-' s-' this was evidence for reaction via a long-lived complex, and for the temperature ranges 220-500 K for reaction (1) and this conclusion appears to be confirmed by very recent trajec- 250-500 K for reaction (2).The experiments reported in this tory calculations by Guadagnin and S~hatz.'~ Rather, Smith paper extend the kinetic data base on these reactions down to et al. suggested that the tight angular-momentum constraints 103 K in the case of reaction (1) and to 158 K for reaction (2). present in this system might necessarily lead to a distribution The reactions between OH and nitrogen and oxygen atoms close to the phase-space prediction. and the reverse of these two reactions, particularly that A major motivation for the present low-temperature mea- between hydrogen atoms and 0,,play an important role in a surements on reactions (1) and (2) has been our wish to number of complex environments including combustion improve the kinetic data base for neutral-neutral reactions systems,' the atmospheres of the earth and other planets,6 used by those attempting to model the chemistry leading to and interstellar cloud^.^-'^ These environments span a wide molecular synthesis in interstellar clouds.Until very recently, range of temperature and it is therefore important to have there were very few measurements of rate constants for such J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 reactions below 200 K and none below 80 K. Consequently, personal computer signal amplifier modellers have had to rely on rough estimates of the required . rate constants or the results of untested theoretical calcu- lations. Within the last two years, a start has been made towards filling this experimental ~oid.~'*~' Rate constants have been determined for several reactions of CN;' OH41 and CH42 radicals at temperatures as low as 13 K, using a CRESU (Cinetique de Reactions en Ecoulement Super- sonique Uniforme) apparatus in which an ultra-cold gas mixture is prepared by its expansion through a Lava1 nozzle.As in the present experiments, the reaction is then initiated by creating radicals by pulsed laser photolysis (PLP) of a suitable radical precursor and the kinetic decays of the rad- icals are observed by time-resolved laser-induced fluorescence (LIF). Despite the success of this method it is clear that it will be difficult to apply it to those reactions, like (1) and (2), between two unstable free radicals.It is therefore important to obtain rate data for these prototypical radical-radical reactions down to as low a temperature as possible using more conventional techniques. The experimental method adopted for the present measure- ments is based on that employed by Howard and Smith.' The atomic radicals are produced and their steady-state con- centrations established employing standard discharge-flow techniques. The actual kinetic measurements are however made in 'real time'. A small concentration of HNO, is intro- duced into the gas flow downstream from the discharge and is partially dissociated to produce OH radicals by PLP at 266 nm.Subsequent decays in the concentration of OH are then observed using time-resolved LIF. In the experiments reported here, the flowing gas mixture could be cooled, using a variety of cryogens, to temperatures as low as 103 K. Although the design of the cell differed from those used in earlier experiments in our laboratory:' the general principle in the present experiments was the same as before. Experimental Fig. 1 shows a schematic diagram of the apparatus which was employed. The apparatus incorporates the following capabil- ities: (i) The generation of steady-state concentrations of N or 0 atoms in a flowing gas mixture and their estimation by standard discharge-flow techniques. (ii) The creation of a small concentration of OH radicals ([OHIO 4 [Nl or [O]) by PLP of HNO, which was added to the gas flow down- stream from the microwave discharge cavity.(iii) The obser- vation, by time-resolved LIF, of the decay with time of relative concentrations of OH following their creation by PLP of HNOJ. (iv) The variation of the temperature at which experiments were performed from room temperature down to ca. 100 K using a variety of cryogens. The central part of the apparatus was a reaction cell which was constructed from Pyrex. In contrast to the jacketed reac- tion vessels used in other low-temperature measurements in our lab~ratory,~, it was designed in the form of a cross and was similar to the cell used by Smith et a1." in their measure- ments of the NO vibrational state distribution from reaction (1).The main tube, id 40 mm and ca. 50 cm long, carried the gas flow and was evacuated by a high-speed rotary pump (Leybold, Trivac D40B). This tube incorporated a hollow insert through which refrigerant could flow. This insert extended for about 10 cm before and after the observation ,zone at the centre of the cross formed by the main flow tube and the side-arms through which the laser beams entered and left the apparatus. There was a gap of CQ. 3 cm between the two sections of the cooling insert before and after the obser- vation zone, allowing the beams from the photolysis and probe lasers unimpeded access to the gas flow. I W delay generator :!& d flow Ik = 282.5 nm 12 NO Fig. 1 Schematic diagram of the apparatus The flow rate of the gas mixture could be adjusted by manipulating a large stopcock at the downstream end of the flow tube.A balance had to be struck between the require- ments: (i) to minimise atom loss (see below) and condensation of the HNO, on the cold surfaces of the inserts and (ii) to maximise the time for the gas to equilibrate at the tem- perature of the cryogen. In addition, in the present experi- ments where the beams from the photolysis and probe lasers are perpendicular to the gas flow, the linear flow could not be too fast, or transport of OH radicals past the region illumi- nated by the probe laser would contribute a major, non- exponential, loss term to the background decay of the LIF signals.This compromise led us to use linear flow speeds of ca. 2 m s-'. The temperatures which were achieved for par- ticular combinations of cryogen and gas flow at the centre of the cross, where kinetic observations were actually made, could be measured by inserting a thermocouple probe either down the length of the main tube, using the moveable injec- tor, or across the main tube, through one of the side-arms. These measurements indicated that the temperatures were constant to 1 K for & 1 cm about the central axis of the tube and for at least +_2 cm upstream and downstream of the point at which the laser beams crossed the gas flow. Using liquid nitrogen as the coolant, it was possible to reach 103 K, the lowest temperature in the present series of experiments. It is estimated that the temperatures which are cited below should be accurate to +4 K.All gas flows were controlled by mass flow controllers. Nitrogen atoms were generated by passing N2 through a microwave discharge applied in the side-arm leading to the main flow tube. A range of N atom concentrations was pro- duced by altering the power applied to the discharge in the J. CHEM.SOC. FARADAY TRANS., 1994, VOL. 90 range 25-120 W. The flow, and hence the concentration, of atomic nitrogen was determined by titration with NO.44NO could be added either at a fixed port (shown as point 1in Fig. 1) on the side-arm upstream of the main reaction cell but downstream of the discharge cavity, or through the injector (point 2 in Fig.1) which can be moved along the central axis of the main flow tube. The extent of the rapid titration reac- tion: N + NO -,N, + O(,P) (3) was followed by observing the chemiluminescent emissions from N,, up to the titration end-point, and from NOz, beyond the end-point, using a photomultiplier tube (EM1 9659QAM), placed on the main flow tube downstream from the observation point at the centre of the cross formed by the main flow tube and its side-arms. At the end-point, the emis- sions were extinguished. Reaction (3) was used not only to determine the steady-state concentration of N atoms, but also to convert those N atoms quantitatively to atomic oxygen. Once a known steady-state concentration of N or 0 atoms had been established in the flowing gas, a small flow of HNO, diluted in argon was added just upstream of the first cooled section of the main flow tube.Since these genuine flow tube experiments used quite large gas flows, rather than pre- preparing an HN0,-Ar mixture, a steady flow of argon was bubbled through a 1 :2 mixture of concentrated nitric and sulfuric acids maintained at room temperature. The argon flow was kept as low as possible consistent with obtaining acceptable LIF signals from the OH radicals produced by PLP of the HNO, . A cruciform shape was adopted for the reaction cell for two reasons. First, it means that the time for which the radical precursor and the radical atoms are mixed can be minimised. Although this was unimportant in the present series of experiments, since any reaction between HNO, and N or 0 atoms seems to be very slow, it may become a real difficulty in other radical-radical systems which we plan to study.The second reason is pertinent to the present experi- ments. The present design of the reaction cell incorporates a moveable injector so that atom concentrations can be mea- sured at various points along the flow tube. In the usual con- figuration for our low-temperature experiments:, the beams from the photolysis and probe lasers counterpropagate along the axis of the flow so that a moveable injector cannot be included in the apparatus. Measuring the concentrations of N and 0 atoms close to the reaction zone was important since they were found to decrease down the cooled section of the flow tube.The results of these experiments and visual inspec- tion of afterglows in similar cross-shaped vessels suggests that there is negligible loss of atoms into the essentially static gas occupying the side-arms. These measurements, and the esti- mation of concentrations of atoms in the observation zone, are described separately in the next section of this paper. The photolysis and probe laser beams entered the reaction cell in counterpropagating directions, and across the direc- tion of the gas flow, uia the two side-arms forming the cross. These side-arms were 30 mm id and ca. 30 cm long, and they carried bames to reduce scattered laser light and fluorescence from the Spectrosil windows mounted, at Brewsters angle, at the end of each side-arm.Photolysis of HNO, to produce OH radicals was effected by the frequency-quadrupled output at 266 nm of a Nd: YAG laser (Spectron Lasers, model SL404) which operated at 10 Hz and gave ca. 15-20 mJ per pulse. The probe radiation was provided by a frequency-doubled dye laser (JK Lasers, system 2000) pumped by a frequency-doubled Nd :YAG laser (JK Lasers, DLPY4) which was tuned at ca. 282.5 nm to a rotational line in the (1,O) band of the A ,X+-X,IT system of OH. Fluorescence in the (1, 1) and (0, 0) bands was observed through two filters: a filter which eliminated radiation below ca. 295 nm (UHQ, WG295), and a narrow band interference filter with a bandpass of 10 nm centred at 310 nm (Ealing Electro-Optics, 35-8044).The methods for controlling the delays between the pulses from the two lasers, for gathering and storing the LIF signals from OH and for fitting the decay traces were identical to those described in early papers from this lab~ratory.~, Results Corrections for Atomic Recombination Preliminary experiments, both in the present series and earlier,45 showed that the concentrations of N and 0 atoms decreased as the gas mixture containing them flowed through the reaction cell. This effect increased as the tem- perature was lowered, was greater for 0 atoms than N atoms and could be affected by deposition of HNO, on the cold walls of the inserts carrying the cryogens. As has already been mentioned, to counter this last effect the flow of HNO, was kept to a minimum.Under our experimental conditions, there was no noticeable change in the rate constants for removal of OH which could be attributed to build-up of HNO, on the cold surfaces of the reactor. To illustrate the need to guard against, or allow for, atom losses, the results of two series of experiments exploring such losses between titration point 1 and the reaction zone are shown in Fig. 2. Fig. 2(a) compares the N and 0 atom con- centrations at these points at room temperature and 4 Torr total pressure, with a linear flow speed in the main flow tube of 1.1 m s-'. The greater loss of 0 atoms is clearly evident. Fig. 2(b)compares the loss of 0 atoms in experiments at dif- ferent temperatures using the same mass flow and total pres- sure in each case.The loss of atoms clearly increases as the temperature is lowered. The rate constants for the gas-phase recombinations of N and of 0 and their temperature depen- dence throughout most of the temperature range employed in our experiments, are well established, and hence the extent of atom loss by homogeneous, as distinct from heterogeneous, association could be estimated. Comparison with the mea- sured losses (see below) suggests that gas-phase recombi- nation was insignificant at room temperature, but that it could play a significant role at the lowest temperatures of our experiments. . . 7 E45-y-3,1I / r-----7 -0iii4 01234 [atom] at 1/10i4 molecule ~m-~ [OJat 1/1014 molecute ~m-~ Fig.2 Examples of curves showing the loss of N and 0 atoms between the first titration point (1 on Fig. 1) and the reaction zone. (a) Losses for (a)N atoms and (A) 0 atoms at 294 K and a total pressure of 4 Torr, with a linear velocity in the main flow tube of 1.1 m s-'. (b)Losses of 0 atoms at different temperatures: (a),294 (A), 227 (m) 190 and (V)158 K. The mass flow rate and the total pressure (2.5 Torr) was the same in each case. It should be emphasised that the experimental conditions leading to the results shown in Fig. 2 were chosen to illus- trate that atom losses occurred, not to minimise the effects of those losses. In the 'real' experiments, where OH decays.were measured, conditions were chosen to reduce the effects of atom losses between the discharge and the LIF observation zone below those shown in Fig.2. Thus, to minimise the time for homogeneous and heterogeneous reactions to occur, the linear flow rate was made as large as possible. Despite this precaution, atom losses were still significant. For N atoms, no correction for such loss was strictly necessary, as N + NO titrations could be performed by adding NO, via the move- able injector, directly into the zone where the side-arms cross the main flow tube, as well as at the fixed point 1, a few centimetres downstream from the discharge cavity. In both cases, the chemiluminescent emissions were observed using the photomultiplier tube near the downstream end of the main flow tube.In this way, a comparison could be made, for wide ranges of total pressure and temperature, between the concentrations of N atoms estimated by titration at point 1 and those actually present at the point where time-resolved experiments were carried out. Experiments like these were conducted with the moveable injector in the same position as in the LIF measurements on OH radical decays which are described in the next section of this paper. They enabled the required N atom concentrations to be determined from titra- tions carried out at the fixed titration point 1. The results for N + OH quoted in Table 1 include the results of experiments in which the concentrations of N atoms were estimated by both methods: 'direct' titration in the reaction zone, and titration at point 1 with subsequent correction for atom loss.In only four out of the 36 sets of experiments was the maximum correction for loss of N atoms greater than 16%. In the case of experiments at 103 K, where the losses of N atoms were quite extensive, their concentrations were assessed only by titration with NO added through the injector directly into the reaction zone. The situation in respect of 0 atoms was rather different, and less favourable, partly because the losses were greater and partly because it was less straightfoward to estimate their concentration in the reaction zone. The latter difficulty arose because, in order to ensure complete mixing and hence quan- titative conversion of N to 0 atoms by the reaction zone, it was necessary to add NO to the gas flow several centimetres upstream.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Therefore, in order to estimate the loss of 0 atoms between titration point 1 and the reaction zone, a method was adopted which was based on observing the NO, afterglow emission at the photomultiplier downstream from the reaction zone in two series of experiments. In each of the first set of measure- ments, the N atoms in the flowing gas were titrated against NO which was admitted to the reaction zone through the moveable injector. Then a known, small, excess of NO was added and the intensity of the NO, chemiluminescence was measured, By repeating this process for a number of atom concentrations and with the same excess [NO], a plot was obtained of the concentration of 0 atoms in the reaction zone against the intensity of the NO, emission.Experiments in the second series were similar but now NO was added at the fixed titration point 1, just downstream of the discharge cavity. The titration end-point gave [O] at point 1, whilst the intensity of the NO, afterglow with the same excess [NO] present as before, by reference to the earlier graph of intensity against concentration, gave the con- centration of 0 atoms in the reaction zone. The two sets of experiments enabled us to construct graphs of [O] at point 1 us. [O] in the reaction zone for the ranges of total pressure and temperature used in the kinetics experiments. Only in one case (at 158 K) did the maximum correction for 0 atom loss exceed 35%.At 103 K, the loss of atomic oxygen was too great to make an acceptably accurate correction. Kinetic Measurements on the Reactions of OH with N and 0 Atoms A typical example of the LIF signal decays obtained in the present experiments is shown in Fig. 3. These observed signals were fitted to an exponential decay using a non-linear least-squares fitting program. Inspection of the residuals and autocorrelations, also provided by the computer program, confirmed that the experimental signals were accurately matched by a single-exponential decay function. The pseudo-first-order rate constants (kist) obtained at a given temperature by fitting the experimental LIF signals in the manner just described were plotted against the concentra- tions of the radical atom making due allowance for atom loss. Examples of plots of klst us.[N] and kist us. [O] are given in Fig. 4. The gradients of these plots yield second- order rate constants for reactions (1) and (2). The number of runs and the conditions used for each combination of tem- Table 1 Summary of experimental conditions and rate constants for N + OH and 0 + OH reactions' no. of expts. PI or COl/loi4molecule p/Torr /lo-" k, or k, cm3 molecule-' s-I N+OH 294 14 0.5-3.5 2.5-6.0 5.2& 0.3' 227 5 0.5-2.4 2.0-2.5 6.0& 0.4 190 9 0.6-2.2 1.5-2.5 6.4f0.5 158 5 0.6-2.6 1.5-2.5 7.0 0.6 103 3 0.25-1.5 1 .o 8.0 & 0.8 50 10 -- -- -- (14.0) (10.2)" O+OH 294 11 0.5-2.9 2.5-4.0 4.2& 0.2 227 5 0.5-2.1 2.0-2.5 4.5& 0.3 190 9 0.5-2.0 1.5-2.5 5.2& 0.3 158 3 0.5-2.5 1.5-2.0 6.1 f0.6 103 50 10 --- --- --- (8.O)ll (11.1) (16.0) ~___~ a Values given in brackets are estimated, using the method described in the text.'Weighted average of the individual determinations with errors quoted as single standard deviations. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 01 I1 I I I I 0 60 120 180 240 300 360 time/lO-* s Fig. 3 Example of the decay of LIF signals from OH as the delay time between the pulses from the photolysis and probe lasers was increased. Temperature 103 K, total pressure 1.0 Torr and the con- centration of N atoms 1.2 x loi4molecule perature and radical atom are summarised in Table 1, which also lists the average values of k, and k, at each temperature.The average values of the rate constants at each temperature were obtained by taking a weighted average of the individual values of k,(T) and k,(T) determined from plots of k,,, us. 20 18-16 I-7 14-II,," 12-m 0 z17 10-I:r cc 8--Y.?u 2 , ,"v, ji-", 10.O.O 0.5 1.0 1.5 0 1 2 3 [N]/1014molecule cm-' [O]/lO'" molecule ~rn-~ Fig. 4 Examples of the plots from which values of the second-order rate constants k, and ki were determined. Each panel shows the variation of the pseudo-first-order rate constants for decay in the LIF signal from OH: (a) with the concentration of N atoms, T = 103 K and p = 1.0 Torr; (b) with the concentration of 0 atoms, T = 158 K and p = 1.5 Torr.60 708090100 200 300 400 5001600700 TIK Fig. 5 log-log plot showing the variation of the rate constants for reaction between OH and N atoms with temperature. (0)Experi-mental rate constants observed in the present work and (A)by Howard and Smith,' the line is their recommended fit. (H)Corre-spond to values of the hypothetical rate constants for reaction on the lowest potential-energy surface correlating with reagents and pro- ducts (see text). o&-------- J 100 200 300 400 500 600700 T/K Fig. 6 log-log plot showing the variation of the rate constants for reaction between OH and 0 atoms with temperature. (0)Experi-mental rate constants observed in the present work and (A)by Howard and Smith,' the line is their recommended fit.(m) Corre-spond to values of the hypothetical rate constants for reaction on the lowest potential-energy surface correlating with reagents and pro- ducts (see text). [N] or [O],like those shown in Fig. 4,the weighting factors being inversely proportional to the variances of the individ- ual values. The errors quoted in Table 1 correspond to single standard deviations calculated from the weighted variance of the individual results.48 The unweighted averages of the indi- vidual results and the standard deviations of these results about that mean value are very similar to the results sum- marked in Table 1. Errors in the corrections for atom loss were judged to be small relative to other errors.Moreover, they would show up in differences between the various values of the second-order rate constants determined at a particular temperature but under different flow conditions. Finally, Fig. 5 and 6 display the temperature dependence of the observed rate constants. Where the present results overlap those obtained by Howard and Smith,' the agree- ment is excellent. The dashed lines represent the functions derived by Howard and Smith to match their experimental rate constants and given in the Introduction of the present paper. It is evident that k, and k, continue to increase as the temperature is lowered through the range covered in the present experiments and that the rates of these increases appear to be greater than predicted by the expressions given by Howard and Smith.Discussion The variation with temperature of the rate constants for reac- tions (1) and (2) can be considered to result from two effects. One factor arises from the temperature dependence of the reagent populations in different spin-orbit states, which changes the fraction of collisions which occur on the poten- tial surface across which reaction takes place. In addition, there will be some temperature dependence resulting from the dynamics of the collisions on the reactive potential. Quantum-chemical calculations suggest that, for both (1) and (2), reaction takes place over the lowest potential-energy surface which correlates adiabatically with reagents and pro- ducts.In the case of reaction (1),24 the symmetry of the surface is 3A'';for reaction (2)," the lowest energy surface has 'A'' symmetry. In the absence of non-adiabatic effects, an assumption which appears to be supported by the detailed study of the O(3P)+ OH reaction by Graff and the effect of electronic degeneracy and near-degeneracy in the reagents can be calculated by elementary statistical mecha- nics and allowed for by a factor (FJ,which is simply the ratio of the electronic degeneracy of the surface over which J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 reaction occurs to the product of the electronic partition functions of the reagents; i.e. F,, = gz/ng,,, i. Consequently, the effect of changes in this factor as the temperature is changed can be allowed for by dividing the observed rate constants by the appropriate value of F,, .? This procedure yields rate constants (k; and k;) relating only to those collisions whose dynamics are controlled by the lowest potential-energy surface.We have calculated values of these rate constants and examined their temperature depen- dence as shown in Fig. 5 and 6. Within experimental error these log-log plots are linear so that one can derive the fol- lowing expressions for k, and k,: k,(T)= F,,(T)(T/298)-0.'72.0 x lo-'' cm3 molecule-' s-' k2(T)= F,,(T)(T/298)-0.243.7 x lo-'' cm3 molecule-' s-' Our present results confirm that the rate constants for the reactions between the OH radical and the atomic radicals N(4S) and O(3P) continue to increase as the temperature is lowered, to 103 K in the case of reaction (1) between N atoms and OH, and to 158 K for 0 +OH, and that this tem- perature dependence is not due entirely to variations in the electronic factors F,, .The 'negative temperature dependences' which are observed for k;(T)and k;(T)are con- sistent with rate constants or cross-sections for reaction which are determined by the ability of the intermolecular potential at long and medium range to 'capture' the reagents and bring them into close collisions. It seems likely that, in keeping with other radical-radical system^,^^.^' the crucial part of the intermolecular potential only becomes that arising from the dispersion forces and the non-symmetric charge dis- tributions on the reagents, at very low temperatures indeed. At higher temperatures, the crucial transition-state region moves to shorter inter-reagent separations, where chemical forces start to act and this change contributes to the decrease in the rate constants as the temperature is increased.A major motivation for the present work has been the wish to provide a basis on which reasonably accurate estimates could be made of the rate constants for reactions (1) and (2) under the conditions prevailing in interstellar clouds. We believe that the analysis given above, in which the tem-perature effects due to changes in the fine structure popu- lations are separated from those resulting from the dynamics on the potential-energy surface for reaction, provides such a basis.At Td 50 K, both O(3P)atoms and OH(X 'II) radicals will be predominantly (> 99% and >98%, respectively) in their lowest spin-orbit state, if the populations are thermally equilibrated, so that the factors F,, become temperature inde- pendent and equal to 0.375 for reaction (1) and 0.2 for reac- tion (2) under interstellar conditions (10 < T/K d 50). Therefore, for the purposes of modelling interstellar cloud chemistry, the rate constant can be expressed in the form: k(T)= AT', with A= 2.0 x lo-'' cm3 molecule-' s-', B = -0.17 for the reaction between N atoms and OH, and A= 3.7 x lo-'' cm3 molecule-' s-', B = -0.24 for the 0 + OH reaction. The effect that revised rate constants for neutral-neutral reactions can have on models of interstellar cloud chemistry can be dramatic. Until the mid-l980s, modellers used expres- sions for k,(T) and k,(T) with a positive (T'") temperature dependen~e,'.~which yielded rate constants at 10 K roughly 1/20th of the estimated values which are given in Table 1.~~ ~~ ~ -~ t For OH, g,, is calculated by summing the populations in the rotational levels of the two spin-orbit states and evaluating gel as 2(1 +f')where f' is the ratio of the populations in the upper and lower sets of levels. Since then, values of k,(T) and k2(T)based on the rate expressions given by Howard and Smith' have been incorp- orated into a number of model^.^-'^ Here, we cite three examples of the results of such revised calculations. First, based on Howard and Smith's rate constant for reac- tion (l), Tarafdar and Dalgarno' argue that the reaction between N atoms and OH is the principal source of NO in diffuse interstellar clouds, although they note that the con- centrations of NO estimated on this basis are in poor agree- ment with those inferred from observations on the Ophiuchi cloud.Secondly, Nercessian et ~1.'~have estimated that the number density of OH in a molecular cloud near the star HD-29647 drops by an order of magnitude when rate constants are used for reaction (1) based on the expression of Howard and Smith.' This change improves the agreement with observation. Finally, we point to a paper by Davidsson and Stenh~lm.~~ In addition to using classical trajectory methods, an extended Langevin model and Howard and Smith's experimental results in order to estimate values of k2(T) in the temperature range appropriate to interstellar clouds, they discussed the implications for interstellar chem- istry of larger low-temperature rates for the 0 + OH reac-tion, particularly problems associated with the non-detection of 0, in interstellar clouds.Although the present experimental results and the pro- posed method of extrapolation provide a reasonable basis for the estimated rate constants which are given in Table 1, there is, of course, no substitute for direct laboratory measure- ments at the ultra-low temperatures of interstellar clouds.At present, the best hope for such measurements would seem to lie with the CRESU rneth~d.~'However, application of this technique to reactions involving two unstable radical species is likely to prove very difficult, as it will be necessary to gen- erate one of the radicals in a large known concentration. Until such time as results from direct measurements at ultra- low temperatures become available, we suggest that the rate constants estimated in this paper should be employed in astrochemical models. Summary Using a combination of pulsed laser photolysis and discharge-flow techniques in a cryogenically cooled reaction vessel, it has proved possible to obtain rate constants for the reactions of OH radicals with N atoms down to 103 K and with 0 atoms down to 158 K.These experiments significantly increase the temperature range for which direct kinetic data for these reactions have been measured. The rate constants for both reactions increase monotonically as the temperature is lowered. By factorising out effects due to the temperature dependence of the reagent populations in different fine struc- ture states, the rate constants for both reactions obtained in the present work and in the experiments of Howard and Smith' can be fitted to a relatively simple expression. It is suggested that this fit can be used to make accurate estimates of the rate constants for reactions (1) and (2) at ultra-low temperatures and hence provide values of k,(T) and k,(T) which can be used in chemical models of molecular synthesis in interstellar clouds.We thank SERC and CEC, under its Science Plan pro- gramme, for support of our work on gas-phase kinetics at low temperature. D.W.A.S. is also grateful to SERC for the award of a research studentship. We acknowledge the assist- ance of Ken Boyle with some of the experimental measure- ments reported in this paper. We thank Professor George Schatz for preprints of his papers, ref. 20 and 27. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 3227 References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 (a) M. J. Howard and I. W. M. Smith, Chem. Phys. Lett., 1980, 69, 40;(b) M. J. Howard and I. W. M. Smith, J. Chem. SOC., Faraday 2, 1981,77,997.R. S. Lewis and R. T. Watson, J. Phys. Chem., 1980,84,3495. W. H. Brune, J. J. Schwab and J. G. Anderson, J. Phys. Chem., 1983,87,4503. (a) R. Atkinson, D. L. Baulch, R. A. Cox, R. F. Hampson Jr., J. A. Kerr and J. Troe, J. Phys. Chem. Ref:Data, 1989, 18, 881; (b) R. Atkinson, D. L. Baulch, R. A. Cox, R. F. Hampson Jr., J. A. Kerr and J. Troe, J. Phys. Chem. Ref. Data, 1992,21, 1125. J. A. Miller, R. J. Kee and C. Westbrook, Annu. Rev. Phys. Chem., 1990,41,345. R. P. Wayne, Chemistry of Atmospheres, Clarendon Press, Oxford, 2nd edn., 1991. S. Prasad and W. T. Huntress Jr., Astrophys. J. Suppl. Ser., 1980, 43, 1. T. E. Graedel, W. D. Langer and M. A. Frerking, Astrophys. J. Suppl. Ser., 1982,48, 321. Y. P. Viala, Astron. Astrophys. Suppl. Ser., 1986, 64, 391.G. Pineau des ForQts, E. Roueff and D. R. Flower, Mon. Not. Roy. Astron. Soc., 1990,244,668. S. P. Tarafdar and A. Dalgarno, Astron. Astrophys., 1990, 232, 239. E. Nercessian, J. J. Benayoun and V. P. Viala, Astron. Astro- phys., 1988, 195, 245. R. D. Brown and E. H. N. Rice, Mon. Not. Roy. Astron. SOC., 1986,223,405. I. W. M. Smith, J. Chem. SOC., Faraday Trans., 1991,87,2271. G. A. Gallup, Inorg. Chem., 1975,14,563. (a) P. J. Bruna and C. M. Marian, Chem. Phys. Lett., 1979, 67, 109; (b) P. J. Bruna, Chem. Phys., 1980,49,39. (a) S. P. Walch and C. M. Rohlfing, J. Chem. Phys., 1989, 91, 2939. T. J. Lee, J. Chem. Phys., 1993,99,9783. F. Pauzat, Y. Ellinger, G. Berthier, M. Gerin and Y. Viala, Chem. Phys., 1993,174,71. R. Guadagnin, G. C. Schatz and S. P. Walch, J.Chem. Phys., 1994, in the press. C. F. Melius and R. J. Blint, Chem. Phys. Lett., 1979,64, 183. S. R. Langhoff and R. L. Jaffe, J. Chem. Phys., 1979,71,1475. T. H. Dunning, Jr., S. P. Walch and M. M. Goodgame, J. Chem. Phys., 1981, 74, 3482. S. P. Walch, C. M. Rohlfing, C. F. Melius and C. W. Bauschli- cher Jr., J. Chem. Phys., 1988,88,6273. A. J. C. Varandas, J. Brandgo and L. A. M. Quintales, J. Phys. Chem., 1988,92,3732. D. C. Clary, Annu. Rev. Phys. Chem., 1990,41,61. R. Guadagnin and G. C. Schatz, J. Chem. Phys., 1994, in the 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 (a) N. Markovic, G. Nyman and S. Nordholm, Chem. Phys. Lett., 1989, 159, 435; (b) G. Nyman and J. Davidsson, J. Chem. Phys., 1990,92,2415. D. C. Clary and H-J. Werner, Chem.Phys. Lett., 1984,112,346. S. N. Rai and D. G. Truhlar, J. Chem. Phys., 1983,79,6046. J. Troe, J. Phys. Chem., 1986,90,3485. D. C.Clary, Mol. Phys., 1984,53, 3. (a) L. F. Phillips, Chem. Phys. Lett., 1990, 165, 545; (b) L. F. Phillips, J. Phys. Chem., 1990,94, 7482. J. Davidsson and L. G. Stenholm, Astron. Astrophys., 1990, 230, 504. I. W. M. Smith, R. P. Tuckett and C. J. Whitham, J. Chem. Phys., 1993,98,6267. M. Quack and J. Troe, Ber Bunsenges, Phys. Chem., 1976, 80, 1140. (a)P. Pechukas, J. C. Light and C. Rankin, J. Chem. Phys., 1966, 44,794; (b)J. C. Light, Discuss. Faraday SOC., 1967,44, 14. (a)I. R. Sims, J-L. Queffelec, A. Defrance, C. Rebrion-Rowe, D. Travers, B. R. Rowe and I. W. M. Smith, J. Chem. Phys., 1992, 97, 8798; (b) I. R. Sims, J-L. Queffelec, A.Defrance, C. Rebrion-Rowe, D. Travers, P. Bocherel, B. R. Rowe and I. W. M. Smith, J. Chem. Phys., 1994, 100, 4229; (c) I. R. Sims, J-L. Queffelec, A. Defrance, D. Travers, B. R. Rowe, L. Herbert, J. Karthauser and I. W. M. Smith, Chem. Phys. Lett., 1993,211,461. (a) I. R. Sims,P. Bocherel, A. Defrance, D. Travers, B. R. Rowe and I. W. M. Smith, J. Chem. SOC., Faraday Trans., 1994, 90, 1473; (b) I. R. Sims, I. W. M. Smith, D. C. Clary, P. Bocherel and B. R. Rowe, J. Chem. Phys., 1994,101, 1748. B. R. Rowe, I. R. Sims, P. Bocherel and I. W. M. Smith, Am. Inst. Phys. Conf: Proc., 1994, in the press. (a)M. J. Frost, P. Sharkey and I. W. M. Smith, Faraday Discuss. Chern. SOC., 1991,91, 305; (b)P. Sharkey and I. W. M. Smith, J. Chem. SOC., Faraday Trans., 1993, 89, 631; (c) M. J. Frost, P. Sharkey and 1. W. M. Smith, J. Phys. Chem., 1993,9, 12254; (d) C. M. Moore, I. W. M. Smith and D. W. A. Stewart, Znt. J. Chem. Kinet., 1994, 26,813. M. A. A. Clyne in Reactive Intermediates in the Gas Phase, ed. D. W. Setser, Academic Press, 1979, ch. 1. M. J. Frost, P. Sharkey and I. W. M.Smith, unpublished results. W. Brennen and E. C. Shane, J. Phys. Chem., 1971,75,1552. I. M. Campbell and C. N. Gray, Chem. Phys. Lett., 1973,18,607. M. J. Pilling in Modern Gas Kinetics: Theory, Experiment and Applications, ed. M. J. Pilling and I. W. M. Smith, Blackwells, Oxford, 1987. M. M. Graff and A. F. Wagner, J. Chem. Phys., 1990,92,2423. S. J. Klippenstein and Y-W. Kim, J. Chem. Phys., 1993,99,5790. I. W. M. Smith in The Chemical Kinetics and Dynamics of Small Radicals, ed. K. Liu and A. Wagner, World Scientific, Singapore, 1994, in the press. 28 press. (a)J. A. Miller, J. Chem. Phys., 1981,74, 5120; 1981, 75, 5349; (b) J. A. Miller, J. Chem. Phys., 1986,84,6170. 29 (a) L. A. M. Quintales, A. J. C. Varandas and J. M. Alvarino, J. Phys. Chem., 1988, 92, 4552; (b) A. J. C. Varandas, J. Brandao and M. R. Pastrana, J. Chem. Phys., 1992, 96,5137; (c)A. J. C. Varandas, J. Chem. Phys., 1992,97,4050. Paper 4/04127E; Received 6th July, 1994