Kinetics of Gas Phase Electron-Ion Recombination by NO+ + e- + N+ 0 from Measurements in Flames BY NIGEL A. BURDETT AND ALLAN N. HAYHURST" Department of Chemical Engineering and Fuel Technology, University of Sheffield, Mappin Street, Sheffield, S1 3JD Received 25th March, 1977 Mass spectrometric measurements of ion concentrations in the burnt gases of flames of either CzH2 + O2 + N2 + occasionally trace amounts of NO or H2 + O2 + N2 with small additions of C2Hz and NO have enabled the rate coefficient, kl, for electron-ion recombination in reaction (I) NO++e- + N+O (1) to be determined. Such measurements have been made for a wide variety of flame conditions over the temperature range 1820 to 2650K and indicate that kl changes from 2.3xlO-' to 1 . 4 ~ lo-' ion-' cm3 s-l. At the lower temperatures kl varies as T-O*', but as at the hotter ones.There is evidence that circumstances can be devised in flames, when charged species are produced by chemi-ionization in the reverse of reaction (I), whose rate coefficient is found to be 6.7 x 10-l2 exp (- 31 9OO/T) atom-' cm3 s-l from 1820 to 2650 K. The NO+ ion is important in partially ionized systems containing nitrogen and oxygen, because of its stability and ease of formation from other ions. Thus ionization and recombination in hypersonic airflows or shock waves involve NO+ to a significant degree. In addition, NO+ plays an important role in the upper atmosphere and is sometimes present in hydrocarbon flames in amounts well above those for equilibrium. Measurements of the rate of dissociative recombination of NO+ with free electrons in reaction (I) NO++e- -+ N+O (1) have already been made and the results have been reviewed by Han~en.~ However, hardly any have been made under flame conditions, so that this work aims to remedy this and to check if the temperature dependence of k l , the recombination coefficient of (I), reported earlier ( k , varying as T-* for T > 2500K, but as T-% for T < 1000 K) holds in flames.Ions are produced in the reaction zone of a hydrocarbon-containing flame mainly by the primary chemi-ionization process : 5 CH+ 0 + CHO++e-, with CHO+ reacting rapidly by proton or charge transfer to a whole range of flame species, such as H20 and NO in reactions (11) and (111) : CHO++HzO 4 H,O++CO (W CHO++NO + NO++CO+H. (111) These H30+ and NO+ ions are, together with the free electron, the principal charged species to survive into the burnt gases of hydrocarbon The relatively small amount of natural neutral NO in the reaction zone means that the NO+ produced by reaction (111) is minimal, although this is not the case in C2H2/02/N2 flames7 or 5354 RECOMBINATION OF NO++e- ones of CO/O, with C2H2 and NO added.6 Another important source of NO+ is the forward step of which operates in the burnt gases of a flame.' This process can be sufficiently fast at the temperatures involved here to become balanced away from the reaction zone.Another possible route for the generation of NO+ is by chemi-ionization in the reverse of reaction (I). This occurs in shock tubes,2 but so far has not been established in flames.Ion recombination in the burnt gases of a flame containing H30+ and NO+ is by step (I), as well as reaction (V) whose kinetics have been m e a s ~ r e d . ~ ~ lo The study reported below aims to measure k, both directly and by comparison with the known rate coefficient k5 of reaction (V). H,O++NO + NO++H,O+H, (W H,O++e- -+ H+H+OH, 0') EXPERIMENTAL The flames were premixed ones of either H2 or CzH2 burnt at atmospheric pressure with O2 and Nz as diluent. The burner has been already described " 9 l2 and gave laminar cylindrical flames with an almost flat reaction zone. Flame compositions and temperatures are given in table 1, where it is seen that all those of H2 were fuel-rich, whereas the C2H2 ones had a wide range of unburnt stoichiometry and temperature for their burnt gases.Nitric oxide was occasionally added to the burner supplies from a N2 cylinder containing 1 % of NO, so that its maximum mole fraction in the unburnt gases was 0.007. Absolute measurements of hydrogen atom concentrations along the axis of each flame were made by the Sr+/SrOH+ technique.13 no 1 2 3 4 5 6 7 8 9 TABLE 1 .-DESCRIPTION OF FLAMES STUDIED unburnt composition ratios burnt gas C2H2 H2 0 2 Nz temp/K velocity/m s-1 1 .o 1.5 4.5 2630 22.9 1 .o 2.0 6.0 2650 23.1 1 .o 2.5 7.5 2590 22.6 1 .o 3.0 9.0 2490 21.7 1 .o 3.5 10.5 2380 20.7 1 .o 4.0 12.0 2200 19.2 3.12 1.0 5.77 1820 8.4 3.09 1.0 4.74 1980 11.4 3.18 1.0 4.07 2080 15.6 Concentrations of positive and negative ions were measured at various points along each flame by direct and continuous sampling into a quadrupole mass spectrometer.11* l4 Calibration techniques to arrive at absolute ion concentrations have been described before.ll Since the burnt gases of each flame have well characterised axial velocities, any distance from the reaction zone can be transformed into a time.Most observations were made in the region 5-25 mm from the reaction zone, to avoid disturbances of the flame by the sampling system l5 and the surrounding atmosphere. One difficulty with this work is that the process of sampling introduces cooling and a consequent falsification of mass spectra. This arises through ions reacting in the sample in the time of -1 ,us before all collisions cease.16- l7 For instance, hydrates of H30+ with up to four water molecules attached can be detected.They were assumed to be formed from the genuine flame ion 5 3 l6 H30+ during sample cooling, so that their concentrations were simply added to that of their parent, H30+. When NO was added to H2 flames, both NO+ and NO+.HzO were observed. For instance, [NO+]/[NO+.HzO] was measured to be 15N . A. BWRDETT AND A. N . HAYHURST 55 when sampling 10 mm downstream of the reaction zone of flame 7 using a chromium sampling nozzle l2 of diameter 0.06 mm. Under these conditions [H30+]/[H30+.HzO] was 2.9, with the lower value probably arising from the hydration of H30+ being faster than that of NO+. In any event, [NO+] was always corrected for hydrate formation. The other possible sampling disturbance is a shift in reaction (IV) for systems containing H30+ and NO+.This does not happen in CzHz flames without added NO, since reaction rates are then too slow.' However, it can occur in the hottest H2 flames (T > 2400 K) with NO as an additive: because [HI and [H,O] are much larger than in CzHz flames of similar temperature. This matter is referred to again below, but it should be noted here that only if the relative abundance of an ion does not depend on the nature of the sampling system (e.g. on the inIet orifice diameter), can it be assumed to be unaffected by sampling. RESULTS In CzH2 flames with no NO added, the principal positive ions in the burnt gases were H,O+ and NO+, with the free electron being by far the major negatively charged species. This is in striking contrast to H2 flames, where NO+ nearly always has a negligible concentration.The difference presumably arises from neutral NO being formed only by the Zel'dovich scheme l 8 in H2 flames, but by the " prompt " one as well in hydrocarbon systems." 19* 2o Typical ion profiles for H30+ and NO+ along the burnt gases are shown in fig. 1 for flame 5 (see table 1 for details). I \k 0 distance from reaction zone/= FIG. 1.-Measured ion profiles along the axis of flame 5 for 0.7 vol % of NO added (0, A) to the burner supplies and for none added (e, A). Some concentrations have been multiplied by the factors shown for clarity. e H30+( x 3), 0 H30+( x loo), A NO+, A NO+( x 3). H,O+ without NO added has a maximum concentration in the reaction zone and subsequently decays in the burnt gases by recombination with electrons in reaction (V) and by charge transfer in reaction (IV).Under these conditions [NO+] is initially small, but away from the reaction zone rises to a maximum, with subsequent dis- appearance by recombination with electrons in reaction (I) and possibly also in the reverse of reaction (IV). The initial rise in [NO+] is caused7 principally by its formation from H30+ in reaction (IV). Fig. 2 shows the profiles for H30+ and NO+ along the hotter C2Hz flame 3 at56 RECOMBINATION OF NO k+e- 2590 K. Here the maximum [NO+] has shifted into the reaction zone and also is larger than that for H30+, suggesting that increases in temperature and [NO] make a reaction such as (111) more effective than (11) in competing for the many available distance from reaction zone/mm FIG.2.-Concentrations of A, NO+ and 0, H30+ along the axis of flame 3 at 2590 K for no NO added. hydrocarbon In this flame the ratio [NQ-t-]/[H,Q+] is so high (at least 10) that, except very close to the reaction zone, the principal reaction is a loss of NO+ through dissociative recombination in reaction (1). This is described by with [e-] equalling [NO+] to within -5 %. Integration of eqn (1) yields the usual recombination expression : 1 1 + k i t [NO'] = for [NO+] = [NO+lo at time t = 0. Fig. 3 is a plot of l/[NO+] against distance along flame 3 using the data of fig. 2. As predicted by eqn (2), a good straight line can be fitted, enabling an estimate of kl to be made from the slope. The alternative recombination scheme in reactions (VI) and (VII) : NO++HzO = NO+.H20 (VI) NO+.H,O+e- -+ NQ+H,O will be considered below and rejected, mainly because the measured kl values are inconsistent with a two-step process involving the hydrate as intermediate.A more accurate way of arriving at kl is to take the measurements of [NO+] at various times from fig. 1 and, after an initial smoothing,21 numerically differentiate [NO+] with respect to time. The resulting values of d[NQ+]/dt at successive points along a Aame may then be combined with the measured [NO+] and [e-] (from [H30+] + [NQ+]) and substituted in eqn (1) to give kl at various distances along the bwnt gases. However, the increased computation time did not yield a significant improvement in accuracy, so that a simple measurement of the slope of a recombina-N. A .BURDETT AND A . N. HAYHURST 57 tion plot was preferred. Complications arose when [H,O+] was large compared with [NO+], because the charge transfer process (IV) affected the decay of NO+ and eqn (2) did not apply. This is especially true in the coolest C2H2 flame and all the H2 ones. To overcome this, NO was added to the C2H2 flames and the H, ones too, but here together with a small amount (<+ % by vol.) of C2H2 to increase primary ionization. 1 1 I 10 20 30 LO distance from reaction zone/mm FIG. 3.-Plot of l/[NO+] against axial distance along flame 3 using the data of fig. 2. The effect of this is shown in fig. 1 for the C2H2 flame 5 at 2380 K. Concentrations of [NO+] now very much exceed those of [H,O+] and the maximum [NO+] is now moved to the reaction zone.There appears to be no evidence for the operation of reaction (IV), since the [NO+] profile fits well to eqn (2), thereby establishing that (I) is the main reaction for NO+. In this case the above procedure for arriving at kl TABLE 2.-MEASURED VALUES OF kl FROM THE DIRECT METHOD AND FROM THE COMPARISON k5/kl. UNITS ARE cm3 ions-1 s-l 1 2630 1.2 2 2650 1.6 3 2590 1.4 4 2490 1.5 5 2380 1.7 6 2200 2.1 2.0 2.1 7 1820 1.7 2.4 8 1980 2.0 2.0 9 2080 2.0 2.0 flame temp/K 107k1 kslkl 107k1 may be used with confidence for all the C2Hz flames. The results of these measure- ments are given in the third column of table 2, these deriving from the average slope of the recombination plot in the region 5-25mm from the reaction zone. It was found that the measured kl did not vary at all with the diameter of the sampling hole, establishing that observations are not being falsified by sample cooling.It was necessary to adopt another approach for H2 flames, even with traces of C2H2 and NO added, because [H,O+] is significant compared with [NO+], the ratio58 RECOMBINATION OF NO++e- [H30+]/[NO+] being in the range 0.5 to 2. In this case the fall in the total positive ion concentration [P+] was observed, since --- d[p'l - (kl[NO'] + k5[H30'])[Pf] dt for [P+] = [NO+]+[H30+]. This leads to Thus in a flame in which [H,O+] and [NO+] are comparable, it should be possible to arrive at k5 and k l . Since any measurement of k5 is known lo to be affected by sampling, the following procedure was adopted here for H2 flames and the coolest flame of C2H2. The differential d[P+]/dt was obtained using the numerical procedures 10 0 I I 0.5 I .o I ;5 [HJO+I/"O+] FIG.4.-Experimental plots of - V(dlP+]/dz)/p+]WO+] against [H30+]/[NO+] for a range of flames as labelled. [P+] is the total positive ion concentration. mentioned above, using the fact that it equals Vd[P+]/dz, where V is the velocity of the burnt gases at distance z downstream of the reaction zone. Plots of the left hand side of eqn (3) against [H30+]/[NO+] are given in fig. 4 for flames 6-9. They are all fair approximations to straight lines. The value of kl was obtained from the ratio of the slope to intercept (= k5/kl) and the known lo k5 of 4.1 x ions-I mls-l for the flame temperatures used here. Such a procedure avoids a direct calibration of the mass spectrometer and the sampling difficulties occasionally lo associated with H30+.Table 2 lists both k,/kl and the kl values resulting from this approach in the third column. Once again these kl values were found not to vary with the size of the sampling inlet orifice. DISCUSSION The recombination coefficient kl has been measured using two methods : a direct one necessitating a calibration of the mass spectrometer and an indirect one involving a comparison with the already known k5. All the results from both approaches areN. A . BURDETT AND A . N. HAYHURST 59 plotted in fig. 5 as In kl against In T. First, it is seen from fig. 5 that results from the two approaches are in agreement with each other. This is encouraging both as far as the validity of the adopted calibration procedure is concerned and the assumption that k5 is constant at 4.1 x !O-7 ions-I cm3 s-l over this temperature range.Closer examination shows that In kl is not linear in In T, the best fit being curved, so that at 2650 K we have kl varying as T-195i,0*8, but as T-0-7i0-8 at 1800 K. The only other values of kl reported from flame work are 1.6rfrO.l x ions-' cm3 s-l, measured22 at 2500K from the decay of NO+ in a C0/02/N2 flame with small amounts of C2Nz added and 4.2f2.5 x ions-l cm3 s-l from a C2H2 flame at 2600 K. These independent observations are thus in agreement with the kl from this study, considering that the final kl values in table 2 each have an associated error of 60 %. The alternative recombination scheme to (I), involving steps (VI) and (VII), can now be considered.If the measured kl values are interpreted on the assumption that processes (VI) and (VII) are the relevant ones, we have kl = K6k7[H20], where K6 is the equilibrium constant of reaction (VI) and k7 is the rate constant of (VII). 16.0 * * - I ! I I I Now the C2H2 flames burnt have much smaller [H,O] in their burnt gases (by up to a factor of 10) than the H2 ones. That this is the case is manifested by NO+.H20 being hardly detectable in C2H2 flames. We conclude that the continuous curve of fig. 5, which covers measurements of kl in both types of flames, indicates that reaction (I), rather than (VI) and (VII), is operating, since otherwise a discontinuity arising from the dependence of kl on [H,O] should be apparent.In addition, the variation with temperature of the observed kl value has contributions from Ks and k7. The hydration energy 23 of NO+ is -82 kJ mol-1 and gives a significant change in K6 over the temperature range employed here. Admittedly, [H20] increases with temperature (as well as depending on the composition of the unburnt gases and the nature of the fuel) but the product Ksk,[H20] is not expected to vary as modestly and smoothly with temperature as fig. 5 indicates. Perhaps the most persuasive evidence against reactions (VI) and (VII) is that the low [NO+. H20] in CzHz flames would require k , to take values as unacceptably large as ions-' cm3 s-l at flame temperatures. We thus conclude that these measurements refer only to process (I), with free N and 0 atoms as the only conceivable products from energy transfer considerations.60 RECOMBINATION OF NO++e- Hansen has investigated other previous determinations of kl and fitted them to the expression : 4.8 x lo-* (kT)-* [l -exp (-0.27/kT)] ions-l cm3 s-l, where kT is in eV.This gives a room temperature dependence of T-3, changing to T-3 at high temperatures. This change is attributed to the participation of higher vibrational levels of the molecular ion. The temperature dependence of kl found from our work is in line with Hansen's conclusion. However, his correlation gives kl varying from 1.0 to 0.7 x ions-l cm3 s-1 at temperatures from 1820 to 2650 K, which is about a factor of 2 lower than the k l values determined here. The percentage temperature variations are about the same though.The measured kl values in fig. 5 have been taken together with the equilibrium constant of (I), as calculated from statistical mechanical considerations, to give I C - ~ , the rate coefficient for N+O --+ NO++e-. The results fit well to the expression k-l = 6.7 x 10-l2 exp (- 31 9OO/T) atoms-l cm3 s-l over the temperature range (1820 to 2650 K) of this work. The activation energy for this, the reverse of (I), 1.0 0.8 3 0;6 > .3 Y - 2 0;4 Oi2 I I I I 0 0; 2 0 : 4 0 ; 6 % volume NO in burner supplies FIG. 6.-Variation of kl with the amount of NO added to flame 5. is thus its endothermicity. The pre-exponential factor is roughly twice that given by Hansen at 2400 K and six times that from the work of kin and Teare at the same temperature.These authors give the pre-exponential factor varying as T4 and T-3, respectively, whereas our observations are more in line with it having no temperature dependence. The above expression for corresponds to a steric factor of 5 x All the results above have been arrived at on the basis of the reverse of (I) being unimportant in determining [NO+] in our flames. The rate coefficient, Ll, at 2500 K is 1.9 x lo-" cm3 atom-l s-l according to the above expression. It is thus possible to estimate the concentration of free nitrogen atoms necessary for the chemi- ionization rate k-,[N][O] to equal the recombination rate kl[NO+][e-1. Taking [NO+] = [e-] = lo1* ions ~ m - ~ , [O] = 1015 and kl = 1.5 x ions-l cm3 s-l requires CN] = 8 x 1014 atoms ~ r n - ~ , corresponding to a mole fraction of 3 x This is high for a flame without nitrogenous additives, because the natural [NO] in which reflects the inefficiency of chemi-ionization in this case.N.A . BURDETT AND A . N. HAYHURST 61 a C2H2/02/N2 flame at 2500 K is ’ -7 x 1015 molecules ~ r n - ~ and is very much less in H2 flames. However, there is evidence 2 o s 24 that when NO is added to a hydro- carbon-containing flame as above, a large fraction of it is converted in the reaction zone to substances such as HCN and possibly also a pool of N, NH, NH2 and NH3, with their concentrations linked by balanced reactions. For instance, it appears 24 that if NO is added to a flame of H2 + O2 + N2 with C2H2 also in the burner supplies, then significant fractions of the NO disappear in the reaction zone.In fact, the loss of NO is proportional to the amount of C2H2 present.24 Even so, the NO does reappear in the burnt gases with -97 % doing so after 1 ms for [C2H2] = 1 vol. %. This contrasts with the situation where NO is added to a H2/02/N2 flame without hydrocarbon present, when all the NO passes through the reaction zone unchanged and exists as such in the burnt gases.25 All this suggests that there might be situations when NO+ is formed by the reverse of (I), particularly when NO is added to C2H2 flames, thereby possibly liberating free N atoms in and close to the reaction zone. This has been tested by measuring kl in the C2H2 flame 5 with various amounts of NO added. On each occasion linear recombination plots were obtained and the results are plotted in fig.6 as kl (normalised on that for no added NO) against [NO] in the burner supplies. It is clear that kl is reduced on the addition of NO, which is in accord with N atoms being formed under these circumstances. In this case the equation governing [NO+] is The constancy of the observed effective recombination coefficient with time indicates that the ratio [r\sl[0]/[NO+J2 is only a weak function of time. These conclusions do not have any effect on the above determinations of k , in C2H2 flames, because NO was only added to the coolest ones and in amounts <O. 1 %, so that the k , values in table 2 are really for zero [NO]. As for H2 flames with the small amounts of additives used here (<0.7 vol. % of NO and <+ % of C2H2) the reappearance of NO from HCN and the pool of nitrogenous radicals N, NH, etc.is completed in the first 10 mm of the burnt gases.23 So, provided observations are made after this initial region and with small amounts of C2H2, as above, there is no reason to suspect the validity of the resulting kl. This work was financed by the S.R.C., whose support is gratefully acknowledged. A. Q. Eschenroeder and T. Chen, Amer. Inst. Aeronautics Astronautics J., 1966, 4, 2149. S. C. Lin and J. D. Teare, Phys. Fluids, 1963, 6,355. L. Thomas, J. Atmos. Terrestrial. Phys., 1976, 38, 61. C. F. Hansen, Phys. Fluid., 1968, 11, 904. J. A. Green and T. M. Sugden, 9th Int. Symp. Combustion (Academic Press, New York, 1963), p. 607 ; H. F. Calcote and D. E. Jensen, Adv. in Chemistry Ser., No. 58 (Amer.Chem. SOC., 1966), p. 291. I R. Hurle, T. M. Sugden and G. B. Nutt, 12th Int. Symp. Combustion (The Combustion Institute, Pittsburgh, 1969), p. 387. ’ N. A. Burdett and A. N. Hayhurst, 16th Int. Symp. Combustion (The Combustion Institute, Pittsburgh, 1977), p. 903. A. N. Hayhurst and D. B. Kittelson, Combustion and Flame, to be published. R. Kelly and P. J. Padley, Trans. Faraday Soc., 1970, 66, 1127. A. N. Hayhurst and N. R. Telford, J C S Faruday I, 1974,70, 1999. A. N. Hayhurst and N. R. TeIford, Combustion and Flame, 1977,28, 67. l 2 N. A. Burdett and A. N. Hayhurst, Proc. Roy. SOC. A , 1977, 355, 377. A. N. Hayhurst and D. B. Kittelson, Proc. Roy. Soc. A, 1974, 338, 155.62 RECOMBINATION OF NO++e- l4 A. N. Hayhurst, F. R. G. Mitchell and N. R. Telford, Int. J. Muss Spectr. Ion Phys , 1971, l5 A. N. Hayhurst, D. B. Kittelson and N. R. Telford, Combustion and Flame, 1977, 28, 123. l6 A. N. Hayhurst and N. R. Telford, Proc. Roy. SOC. A, 1971,322,483. l7 A. N. Hayhurst and D. B. Kittelson, Combustion and Flame, 1977,28,137. l8 Y. B. Zel'dovich, Acta Phys. Chim. U.S.S.R., 1946,21, 577. l9 A. N. Hayhurst and H.-A. G. McLean, Natlrre, 1974, 251, 303 ; A. N. Hayhurst and I. M. 2o C. Morley, Combustion and Flame, 1976, 27, 189. 21 H. C. Hershey, J. L. Zakin and R. Sirnha, Ind. and Eng. Chem. (Fundamentals), 1967, 6, 413. 22 A. Van Tiggelen, J. Peeters and C. Vinckier, 13th. Int. Symp. Combustion (The Combustion 23 F. C. Fehsenfeld, M. Mosesman and E. E. Ferguson, J. Chem. Phys., 1971,55,2115. 24 A. N. Hayhurst and I. M. Vince, unpublished work. 2 5 E. M. Bulewicz and T. M. Sugden, Proc. Roy. Soc. A , 1964, 277, 143. 7, 177. 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