1552
W. BRENNEN AND EDWARD C. SHANE
The Nitrogen Afterglow and the Rate of Recombination of Nitrogen Atoms in the Presence of Nitrogen, Argon, and Helium1
by W . Brennen* and Edward C. Shane Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (Received January 88, 1071) Publication costs assisted by the Advanced Research Projects Agency
Pressure jump experiments in static samples of decaying active nitrogen are used to determine the pressure dependence of the yellow Lewis-Rayleigh afterglow specific emission intensity. The form of the dependence is (I/[r\’lZ)= K [ X ] ( ~ T B [ M l)-l. ] Values of the apparent quenching constant, k , are reported for Nz, Ar, and He diluents. Describing N atom recombination by the equation -d[N]/dt = k,[N]2[M] k,[N]Z + T - ~ [ ? \ ’ ] , analysis of afterglow decays in a static system has been used to evaluate the homogeneous and heterogeneous recombination rate coefficients. The effect of impurity oxygen on 7-l is discussed. Our results on afterglow pressure dependence and atom recombination rate are combined with published measurements of the absolute afterglow intensity in pure nitrogen to evaluate the photon yield of recombination. The relative importance of the 52 and A82 afterglow mechanisms is discussed on the basis of existing evidence.
+
Introduction The lack of adequate means for sufficiently precise and accurate measurement of low light intensity and absolute atomic concentration has created a distressing situation in research on the kinetics and mechanism of nitrogen atom recombination and its attendant LewisRayleigh afterglow emission. After more than 50 years of effort it was not possible to write with confidence a tested rate law relating the relative (much less the absolute) intensity of a well defined portion of the afterglow spectrum to the atomic concentration and the concentration of diluent gas. I n addition to that, the factor of 8 disagreement existing in the literature about the value of the homogenous termolecular overall recombination rate coefficient in pure nitrogen seemed a poor reward for the large effort that had been expended. 2 , The important observation by Campbell and Thrushzd that [Nl2/I, the reciprocal of the specific intensity of the yellow portion of the visible afterglow, increases linearly with X(N2),the mole fraction of nitrogen, in N2-Ar and N2-He mixtures above X(iY2) 0.2 and at total pressures above 2 Torr led these workers to include in the afterglow mechanism strong quenching of the emitting iY2(B3rIIg, w’ = 10, 11, 12) molecules by nitrogen. Lifetime studies4 of the B311g state had previously given evidence of such a quenching process. This proposal has subsequently received support from the detailed work of Browns on the pressure and diluent composition dependence of the absolute intensity and spectral distribution of afterglow bands in the Aw = 3 sequence from levels w’ = 6 to 12 of iYz(B311g). The introduction of quenching of N2(B3rI,) by diluent gas, A I , into either the Berkowitz-Chupka-IGstiakowsky6 ( j 2 ) or Campbell-Thrushzd (A32) mechanisms The Journal of Physical Chemistry, Vol. 76, No. 10, 1071
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implies that the steady-state specific intensity of the afterglow from the highest populated levels of the B3TI, state in pure diluent XI should obey a rate law of the form
where K and k are constants for a particular diluent and T B is the radiative lifetime of the emitting state. Equation 1 shows that the specific intensity should be zero order with respect to diluent concentration, i.e., independent of pressure, a t sufficiently high pressure and first order a t sufficiently low pressure. The characteristic parameter in eq 1 is the half-quenching pressure, [11]1,2 = ( ~ T B ) - ~ . We have reported preliminary results confirming eq 1 with ;\I = N2.’ We report here the details of that work and extensions to 11 = Ar, He. Jonathan and Petty,* in an independent and simultaneous investigation of the afterglow pressure depen(1) Work supported by the Advanced Research Projects Agency in part under Contract DAHC15-67-C-0215 and in part under Contract F446320-67-C-0106 monitored by the Air Force Office of Scientific Research. (2) (a) A . N. Wright and C. A. Winlcler, “Active Nitrogen,” Academic Press, New York, ri. Y., 1968; (b) M. A. A. Clyne and D. H . Stedman, J . Phys. Chem., 71, 3071 (1967): (c) H. H . Bromer and W.Zwirner, 2. Naturforsch. A , 24, 118 (1969); (d) I. M. Campbell and B. A. Thrush, Proc. Roy. Soc., Ser. A , 296, 201 (1967). (3) K . H . Becker, W.Groth, and D . Kley, Z . Naturforsch. A , 24, 1840 (1969). (4) M. Jeunehomme and A. B. F. Duncan, J . Chem. Phys., 41, 1692 (1964). ( 5 ) R. L. Brown, ibid., 52, 4604 (1970). (6) (a) J. Berkowitz, W.A. Chupka, and G. B. Kistiakowsky, ibid., 25, 457 (1956); (b) K . D. Bayes and G. B. Kistiakowsky, ibid., 32, 992 (1960). (7) TV. Brennen and E. Shane, Chem. Phys. Lett., 2, 143 (1968). (8) N . Jonathan and R . Petty, J . Chem. Phys., 50, 3804 (1969).
1553
NITROGEN AFTERGLOW AND THE RATEOF RECOMBINATION OF NITROGEN ATOMS dence by a technique quite different from ours, have obtained data for 31 = Nz consistent with eq 1 which lead to a value of [M in fair agreement with ours. Becker, et have also independently studied the pressure dependence of the visible nitrogen afterglow in the 7.5-m diameter stainless steel sphere in Bonn by a technique similar to ours, and these workers also confirm the form of eq 1 and agree with our values for the half-quenching pressure. Knowing the pressure dependence of the specific afterglow intensity is important not only for understanding the afterglow mechanism but also for facilitating the study of total recombination rate by any method which relies on using the afterglow intensity to monitor the relative nitrogen atom concentration. We have used our findings on the pressure dependence of the afterglow in studying the total recombination rate of nitrogen atoms in nitrogen, argon, and helium diluents, and we have reported preliminary recombination results in the case of pure nitrogen.'O Our preliminary conclusions have been revised as ill be seen below. The present paper gives the details of this work and includes results in Ar and He diluents. One of the stimuli for our work was the surprising estimate made by Campbell and Thrushzd that half of all homogeneous nitrogen atom recombination events in pure nitrogen proceed by may of the emitting B3H, state. Our results on afterglow pressure dependence and total recombination rate, when combined with existing knowledge about the absolute emission intensity, clarify further this matter of the photon yield of recombination. This question is dealt with in the discussion.
Experimental Section Studies of the pressure dependence of the afterglow and the rate of nitrogen atom recombination mere carried out with the apparatus shown schematically in Figure 1. Active nitrogen was produced in an aircooled, electrodeless discharge in a fused silica tube using a 2450-1IHz, 100-W Raytheon IIodel PGhl-10 microwave power generator coupled to a Type 5,11 '/4 wave cavity supplied by Ophthos Instruments. The per cent dissociation measured in the observation bulb was typically less than 0.25% in pure nitrogen and 1% for nitrogen diluted in He and Ar. A glass wool plug was inserted between the discharge and the light trap to remove vibrationally excited groundstate molecules formed in the discharge. l 2 Stopcocks permitted capture of a static sample of active nitrogen in either a 3.1-1. or a 5 1. Pyrex observation bulb which was housed in a wooden, light-tight box painted dead black inside. Light emitted by the gas in the bulb passed through the bulb wall, a filter, and an 18 cm long 2.5-cm i.d. blackened brass tube, and was detected by an uncooled EM1 6256-SA photomultiplier tube operated a t 1100 V from a Northeast Nodel RE-1602
,LIGHT
TO
MCLEOD GAUGE
VACUUM SYSTEM
TRAP
~
t
A F I E RGLO W
Figure 1. Schematic diagram of apparatus.
stabilized high-voltage power supply. The output of the photomultiplier tube was amplified by a Meithley Model 610-BR electrometer and displayed on a Leeds and Northrup Speedomax-G strip chart recorder. Experiments with nitrogen diluted in helium and argon employed a narrowband interference filter (G-5645800) from Oriel Optics Corp. which transmitted the nitrogen First Positive (11-7) and (10-6) bands. Some experiments with pure nitrogen employed a filter (G564-5800) and some a two-filter set (SOOW-6OOB) from Optics Technology, Inc. Experiments with nitrogen containing added oxygen impurity employed the filter set (600W-600B). The two-filter set (55OW-BOOB) was used for a number of preliminary experiments. Figure 2 shows the transmission curves of the filters obtained a t normal incidence on a Cary Model 14 spectrophotometer. All measurements were taken a t room temperature, whichwas21.0 f 1.5". The pressure dependence of the afterglow was studied using a pressure-increase technique. A steady flow of discharged gas was established through the observation bulb at the desired pressure. The bulb was then manually isolated by simultaneously closing stopcocks a t the entrance and exit of the bulb. The initial pressure in the bulb after isolation was measured with a tilting McLeod gauge, and then after the afterglow had been alloxed to decay for about 1 min the pressure was suddenly increased by opening a stopcock connecting the observation bulb to a 30-cc bulb containing gas at a higher pressure. For experiments with nitrogen diluted in argon or helium, pure diluent was added in the pressure increase. The afterg1oLv intensity was re(9) K . H. Becker, A. Elzer, W. Groth, and D. Kley, SHA/2, Institute ftir Physikalische Chemie der Universitat Bonn, 1968. We are grateful to Dr. Kley for making us aware of this work prior to publication. (10) E. Shane and W. Brennen, Chem. Phys. Lett., 4, 31 (1969). (11) F. C. Fehsenfeld, K. RI. Evenson, and H. P. Broida, Reb. Sci. Instrum., 3 6 , 294 (1965). (12) J. E. Morgan, L. F. Phillips, and H. I. Schiff, Discuss. Faraday Soc., 33, 119 (1962).
The Journal of Physical Chemistry, Vol. 7 6 , N o . IO, 1971
1554
W. BRENNEN AND EDWARD C. SHANE
‘
5000
5500
6000A‘
Figure 2. Filter transmission curves. Approximate positions of some afterglow bands [BW&’) + A%,+ ( v ” ) ] are shown.
corded until several minutes after the pressure jump. The final pressure was also measured with the McLeod gauge. Data on the rate of nitrogen atom recombination were extracted from static decay experiments. Discharged gas was passed through the observation bulb and the flow was adjusted to attain the desired conditions. The bulb was then isolated, and decay of the afterglow intensity in time was recorded. The pressure was measured a t the end of each run. The initial absolute nitrogen atom concentration in the decay bulb, [N],, corresponding to Io,the afterglow intensity a t the arbitrarily chosen zero of decay time-usually some seconds after the isoiation of the bulb-was determined with the help of eq 1. If the signal current, i, is assumed to be proportional to I , eq 1 can be rearranged as follows.
Knowing the value of k r from ~ measurements on the pressure dependence of I / [N12,we established a value for K’ by carrying out a series of KO titrations a t a known and experimentally convenient pressure. The value of K’ of course depended on the filter used and on the nature of R4. Once K’ had been established, the absolute nitrogen atom concentration could be calculated from eq 2 a t any pressure by measuring the signal current and the pressure. The reliability of this procedure was actually confirmed by doing KO titrations a t several pressures and noting the constancy of K’ and also by remeasuring K’ from time to time to detect possible changes in the sensitivity of the photomultiplier. Our use of eq 2 to measure [Nl0 made it possible to study recombination a t very low pressures where the direct use of the NO titration is difficult. The NO titrations were carried out under steadyflow conditions in the exit tube leading from the observation bulb. The NO inlet was located about 2 cm The Journal of Physical Chemistry, Vol. 76,No. IO, 1971
away from the bulb and the end point was detected with an auxiliary RCA 1P21 photomultiplier tube equipped with a filter transmitting from 5200 to 6100 8 and located 45 cm downstream of the NO inlet. Under the conditions prevailing during the NO titrations with the 3.1-1. bulb, the mean residence time of the active nitrogen in the observation bulb was about 10 sec, while the time of flow from the NO inlet to the end point detector was 0.3 sec. Also, under the same conditions, the time required for a nitrogen atom to diffuse a root mean square distance of one bulb diameter was 0.5 sec and the pseudo-first-order half-life for disappearance of atoms was about 40 sec. The observation bulb clearly satisfied the conditions for a stirred reactor,I3 and the concentration of atoms in the efflux was the same as the uniform concentration of atoms in the bulb. Prepurified nitrogen, ultrahigh purity helium, argon, oxygen, and hydrogen, and technical grade (98.5%) NO were obtained from the Matheson Co. For experiments with nitrogen diluted in argon and helium, mixtures containing 5% Nz were prepared in a 12-1. bulb and flowed from there through the discharge. For experiments in which oxygen impurity was added after the discharge, a measured amount of oxygen was introduced into the observation bulb from the 30-cc appended bulb after the observation bulb had been isolated. All gas mixtures were passed through two spiral liquid nitrogen cooled traps before entering the discharge with the exception of iY2-Ar mixtures, which were passed through the same traps cooled with Dry Ice in acetone. Gases were always conducted from the tanks in glass or copper tubing. Glass-metal connections were all made either with soldered IZovar seals or with epoxy adhesive. NO was purified by vacuum distillation from a trap maintained a t 113°K to one cooled with liquid nitrogen, with initial and final fractions being discarded. Diluent and NO flow rates had to be measured to carry out the KO titrations, Diluent flow rates were measured using a Poiseuille f l o ~ m e t e r ’made ~ with a 29.70 =k 0.02 cm long piece of Fisher-Porter precision bore capillary tubing (0.500 mm nominal id.). The bore diameter was determined experimentally by repeated weighing of mercury threads of known length a t a known temperature and found to be 0.6028 i= 0.0004 mm. The ends of the capillary were snapped off cleanly using a glass knife and sealed into larger tubes with epoxy adhesive. With this capillary under the flow conditions used, corrections for end effects and slip flow were negligible. Flows were calculated from the measured pressures a t the ends of the capillary, (13) K. G. Denbigh, “Chemical Reactor Theory,” Cambridge University Press, New York, N. Y., 1966. (14) H. Melville and B. G. Gowenlock, “Experimental Methods in Gas Reactions,” MacMillan and Co., Ltd., London, 1964.
NITROGEN AFTERGLOW AND THE RATEOF RECOMBINATION OF NITROGEN ATOMS literature values for the gas viscosities,16 the capillary geometry, and the temperature. We estimate the accuracy of these flow rates to be *5%. Diluent flow rates were typically mol/sec. For experiments in which oxygen impurity was added to the nitrogen before the discharge, flows were measured with less accurate (f10%) ball float flowmeters. Added NO flow rates were measured by timing a pressure drop in a calibrated volume16 using DowCorning DC-704 silicone oil ( p = 1.063 g/cc a t 25’) as the working fluid in the differential manometer. The 3-1. observation bulb was ritually poisoned against wall recombination by rinsing with fuming red nitric acid, distilled water, 10% aqueous HF, and again with distilled water. N atom recombination studies with a n IT2buffer used both the 3-1. bulb and a 5-1. bulb whose walls were coated with syrupy phosphoric acid. The syrupy phosphoric acid was prepared by saturating 85% aqueous orthophosphoric acid with Pz0~.
Results Pressure Dependence of the Afterglow Intensity. Equation 1 is used as the starting point for the analysis of the pressure jump experiments. The main assumption on which this technique rests is that the sudden addition of diluent to a sample of afterglowing gas does not significantly alter the volume density of nitrogen atoms in the observation bulb in a time comparable to the mixing time. If this assumption is correct, the experiment measures the ratio of specific intensities a t two pressures, which is to say it samples values of the function [nI](km[M] l)-l a t two pressures as long as K (see eq 1) is not itself pressure dependent. Letting I1and I , be the intensities before and after the pressure increase, respectively, and [MI1 and [h4I2be the corresponding pressures, it follows from eq 1 that a single pressure increase experiment can be used to calculate a value for JGTB from the equation
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(3) For the most accurate results it is advantageous to choose the conditions of the experiment so that [MI1 < [iM]1,2 < [ M ] 2 . If [MI1 and [MI, are both smaller than [MI,/,, then the numerator of eq 3 is small and inaccurately determined; if [XI11 and [MI2 are both much larger than [iM]l/2, then the denominator of eq 3 is small and inaccurately determined. Figure 3 shows the record of a typical pressure increase experiment in pure nitrogen. A slight momentary overshoot in the intensity trace after the pressure jump, visible in Figure 3 , was common, especially in runs with large pressure increases. This effect was not due to underdamping of the recording system. We attribute this effect to momentary enhancement of the rate of recombination of atoms resulting from the introduction of gas which has
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1555
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I
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2 T I M E (rninufes)
I
3
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4
Figure 3. Typical pressure inrrease record. Nitrogen buffer with initial and final pressures of 0.046 and 0.48 Torr, respectively.
been cooled by sonic flow’l through the nozzle formed by the bore of the stopcock through which the gas is added. Since the amount of gas introduced in a typical pressure increase experiment is greater than the amount of afterglowing gas present in the bulb before the increase, the relaxation of the cooling effect ought to require a small multiple of the diffusional mixing time. This is consistent with the appearance of the effect on the traces. A rough calculation of the magnitude of the excess recombination resulting from momentary cooling revealed it to be sufficiently small so as not to invalidate the assumption that the concentration of atoms is the same before and after the pressure increase. To measure I z / I l , the slow decay following the pressure increase was smoothly extrapolated back to the moment of mixing, effectively cutting the overshoot off the trace. Results of the pressure increase experiments with &/I = N2,Ar, and He are given in Table I.lS (See also footnote e in Table I.) For the He and Ar experiments the gas composition changes during the pressure increase. The initial 5% N2-He or 5% N2-Ar mixture is diluted with pure He and Ar. If, using He to illustrate, the contributions of the third bodies are considered to be of the form, k = k(He)X(He) Ic(IY2)X(S2), where X is the mole fraction of the gas, then the apparent quenching constant for pure He, k(He), may be calculated from the equation
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(15) J. Kestin and W. Leidenfrost, Physica (Utrecht), 25, 1033 (1959). (16) W. R . Brennen and R. L. Brown, Rev. Sci. Instrum., 39, 608 (1968). (17) L. D. Landau and E. M. Lifshite, “Fluid Mechanics,” AddisonWesley, Reading, Mass., 1959. (18) M. Jeunehomme, J . Chem. Phys., 45, 1805 (1966). The Journal o j Physical Chemistry, Vol. 76,No. IO, 1971
W. BRENNEN AND EDWARD C. SHANE
1556
Table I: Recent Results of Studies on the Pressure Dependence of the Nitrogen Afterglow Intensity M
k7Ba
NZ NZ
8.6 i1.3 7.7 5.8” 8.3
N2
NZ NZ Nz
2.0
He He He He Ar Ar Ar Ar Ar Ar
0.6 f0.1 0.5 1 . 5 =I= 0.2 2.6 1.5 0.7
Comment
kb
66 60 45 63 27 16 4 . 6 [2.4d] 4.0 0.8 2.2 12 [ 1 . P ] 1.1 20 12 6 1.6
u = 12, 11, 10
v not given v = 12, 11, 10 v = 2 v < 10 Determined from pressure dependence of the lifetime of the Kz(B)state; v = 4-12 v = 11, 10 u and gas composition not given u < 10; gas composition not given v = 6-12; 1% Nz u = 11, 10 v = 6-12; 1%Nz v and gas composition not given u = 12, 11, 10; 11.5%Nz u = 2; ll.?i%Nz u < 10; gas composition not given
Ref
This work 3 8 8 e 4 This work 3 e 5 This work 5 3 8 8 e
a In units of Torr+. * In units of 10-12 cm3 molec-1 sec-1. When a value of ~ T was B reported, k was evaluated using 7 8 = 4 X lop6sec for v = 12, 11, and 10 and T B = 9 X 10+ see for u = 2.’8 A temperature of 21’ was assumed in making unit conversions. Average of two sets of results, one observing the Av = 5 sequence emission and one the Av = 4 sequence emission. Corrected using Brown’s5intensity distribution to represent quenching of levels v = 6-12. R. A. Young, G. Black, and T. G. Slanger, J . Chem. Phys., 50, 303 (1969).
and likewise for Ar. The value of mk(N2)comes from the pure nitrogen experiments. Typically the second term amounts to a few per cent of the first term in our experiments. Equation 3’ was derived using the assumption that K in eq 1 is independent of gas composition. This assumption is not really a good one as Brown’s results Until we know more about the detailed mechanistic effects of third-body substitution, any procedure for dealing with the effects of composition on the afterglow intensity must needs be someldiat ad hoc and unsatisfactory. Nitrogen Atom Recombination. Decay Experiments. The afterglow decays were analyzed in terms of the following differential equation, which was assumed to govern the rate of disappearance of nitrogen atoms -d[nT]/dt
=
{k,[;lI]
+ k,}[N]2+ 7-’[S](4)
where k , is the termolecular, homogeneous recombination rate coefficient, IC, is the sum of a homogeneous radiative recombination rate coefficient and a recently proposed second-order wall recombination rate coefficient,2d and 7-l is the apparent first-order r a l l recombination rate coefficient. Since eq 4 is taken to represent the disappearance of nitrogen atoms by all possible processes, it is important to recognize that k r must be a composite rate coefficient which includes contributions of unknown relative magnitudes from recombination into the three bound states which correlate with normal atoms, i e . , 52, A3&+, and X1.Zg+. The solution of eq 4, when combined with eq 1, gives the following equation governing the decay of light intensity a t constant pressure The Journal of Physical Chemistry, Vol. 76, KO.I O , 1972
x
= ( I ~ / I ) ”=~ (1 + A ) exp(t/T)
-A
(5)
+
where I o is the intensity at t = 0, A = [N]O~(kr[I\I] kg), and [IT],is the atom concentration at t = 0. Two different methods can be used to extract values of the rate coefficients from the intensity-time relationship described by eq 5. One approach is to determine 7 and A graphically by approximating dx/dt by Ax/At and plotting In ( A x / A t ) against t. The slope of such a graph is 7-l and the intercept is In { [K]o(kr[;\I] kd 7-1). An alternative procedure is to graph x against 2. Where only processes which are second order in [N] are present such a graph is linear with a slope of (kr[M] k,) [N],. The introduction of first-order N atom recombination causes a deviation from linearity in the x us. t graph. It can be seen from eq 5 that such a graph will have a limiting initial slope equal to { (k,[Rl] k,) [NIO 7-1). Traditionally, in studies of K atom recombination the value for the k , is derived from x us. t graph^.*^^^^'^-^^ Decays in a 5-1. bulb coated with syrupy phosphoric acid were analyzed using z YS. t graphs for which the zero of time was taken to be a few seconds after isolation. These graphs deviated significantly from linearity after 20-30 sec. Such a graph is shown in Figure 4b. The initial
+
+
+
+
+
(19) J. T. Herron, J. L. Franklin, P. Bradt, and V. H. Dibeler, J . Chem. Phys., 30, 879 (1959). (20) P. Harteck, R. R. Reeves, and G. G. Mannella, ibid., 29, 608 (1958). (21) K. M . Evenson and D. 8 . Buroh, ibid., 45, 2450 (1966).
NITROGEN AFTERFLOWAND THE RATEOF RECOMBINATION OF NITROGEN ATOMS 1
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1
4a. The same effect is present for all decays in a clean Pyrex bulb above 0.4 Torr. I n a preliminary reportlo for the clean Pyrex system the initial curvature was overlooked and results were reported based on long-time decay data. It can be seen in Figure 4a that beyond the first minute of the decay the data, within scatter, follow a straight line. Typical decays were long enough (1-Torr decays lasted 1 hr) that 1-min time intervals were used in the In ( A x l A t ) graphs. Thus long-time decay data were weighted most heavily and the initial curvature was obscured. The (k,[nl] k,) against [MI graph genI I I I IP erated with long-time decay data is represented by the 2 4 6 8 TlMEimini upper curve in Figure 6. Higher values of (k,[AI] Figure 4. (a) In ( A z l A t ) against time for a pure Nt decay at 5 IC,) were obtained and the k , values were found to be Torr. The bulb and inlet tube were coated with syrupy pressure dependent. At this point the meaning of the phosphoric acid. (b) z against time graph for the initial results obtained from long-time decays with curved In portion of the decay. The arbitrary time zero for both plots is about 3 sec after isolation of the bulb. ( A x l A t ) graphs is not clear. Integration of eq 4 to give eq 5, which is used to derive the In ( A x l A t ) relationship, assumed that the rate coefficients are constant. Figure 5 shows clearly that a t least one of the terms is changing in time. This invalidates the integration of eq 4 and obscures the meaning of the In ( A x l A t ) graph. The cause of the curvature in the In ( A x l A t ) graphs is unknown, but we think it is probably an impurity problem. Weak CN violet and NO@ emission is observed in our system. Experiments with added 02, to be discussed below, suggest that the small oxygen concentration responsible for NO@emission does not produce curvature in the In ( A x l A t ) graphs. The C N radical may be involved in reactions that are first and possibly second order in [N]. A change in [CN] in the course of a run would then produce curvature in the In PRESSURE(torr) ( A x l A t ) graph as the slope, reflecting first-order proFigure 5. @,[MI k.) against pressure for pure nitrogen. cesses, and the intercept, reflecting second-order proThe filled-in circles represent runs in which the bulb was coated cesses, change. The question of impurity contribution with syrupy phosphoric acid. The open circles represent runs in which the discharged gas passed through a trap containing will be investigated in future experiments. syrupy phosphoric acid located just before the observation Limited initial decay data from our preliminary bulb; the observation bulb was not coated. experiments'O with a clean Pyrex bulb were analyzed k,) against with x us. t graphs. A graph of (kr[n!I] slope of the x us. t graph was corrected for the T-' con[AI]is shown in Figure 6. The results are significantly tribution to give a value of (IC, [AI] k,) [NIo. 7-l was lower than those we previously obtained using longdetermined from the slope of a In ( A x l A t ) graph of the time data from the same experiments and within scatter initial decay data and amounted typically to a 20% described a straight line. A least-squares fit of the correction. Using the absolute value of [SI, derived molec-2 data gave JCr(S2) = (1.1 0.4) X k,) was calculated. A graph of from Io, (k, [MI 0.04) X 10-l6 cm3 molec-' sec-l and k , = (0.39 ( k , [AI] k,) against pressure is shown in Figure 5. sec-l. Within scatter the kr(X2) value overlaps that The slope gives k,(N2) = (0.79 f 0.10) X (em6 obtained with phosphoric acid poisoning of the bulb. molec-2 sec-'), and the intercept gives k , = (0.13 f Decays in which nitrogen was diluted in Ar and He 0.05) X cma molec-'sec-'. buffers were not plagued with the difficulties just deThe same information that is derived from x vs. t scribed for pure nitrogen; In ( A x l A t ) graphs were linear graphs of initial data should be available in In ( A Z ~ A ~ )for the duration of the decay. x us. t graphs for the vs. t graphs for the duration of the decay. With syrupy first 20-30 sec of the decay gave the same results as In phosphoric acid poisoning decays below 1.?I Torr gave ( A x l A t ) graphs for long-time decay data. Graphs of identical results with both procedures. Above 1.5 (kr[hI] IC,) against [hI] are shown for Ar and He Torr the In ( A z l A t ) graph is not linear, as expected, but buffers in Figures 7a and 7b, respectively. Values for develops curvature. Such a graph is shown in Figure the slopes and intercepts gave IC, (Ar) = (2.3 f 0.5) X I
+
+
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+
+
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* *
+
+
The Journal of Physical Chemistry, Vol. 76, No. 10, 1071
1558
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W. BRENNEN AND EDWARD C. SHANE I
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1
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1
+
Figure 6. @,[MI k,) against pressure for pure nitrogen in a clean Pyrex bulb. The filled-in circles represent the results of initial decay data analysis. The upper curve represents the results of long-time decay data analysis for the same experiments. For the open circles 0.07y002 was added to the decay bulb after isolation.
1
I
1
I 4
2
PRESSURE(torr)
+
Figure 7. (k,[M] k,) against pressure for (a) Ar buffer and (b) He buffer in a clean Pyrex bulb.
and &(He) = (2.22 f 0.12) X cm6 molec-2 sec-' and ks(Ar) = (0.22 f 0.06) X and k,(He) = (0.65 f '0.13) X 10-l6 cm3 molec-' sec-'. The results with Ar and He suggest that the difficulty with pure nitrogen decays may be an impurity that is present in the prepurified nitrogen. When the Nzis sufficiently The Journal of Physical Chemistry, Vol. 76,N o . 10,1971
diluted in Ar or He the impurity concentration is lowered enough so as to be ineffective. Stirred Flow Reactor Experiments. A completely independent measurement of k r is possible when the observation bulb is treated as a stirred flow r e a ~ t o r . ' ~ ~ ~ ~ Neglecting any contribution by k,, stirred flow reactor theory gives the result
where 7-l is the first-order rate coefficient, fv is the volume flow rate of the gas a t pressure [MI in the bulb, I' is the volume of the bulb, and [N]&and [ K ] b are the atomic concentrations at the entrance and exit of the bulb, respectively. NO titrations were performed at the entrance and exit of the bulb under constant flow and discharge conditions to give [N], and [N]b. Titrations with A 1 = Nz,Ar, and He performed at 0.8, 1.6, and 1.6 Torr, 0.4) X cm6 respectively, gave ICr(N2) = (1.2 moIec-2 sec-l, k,(Ar) = (2.7 1.0) X cm6 molec-2 sec-l, and k,(He) = (3.2 f 1.1) x cmo molec-2 sec-l. These results are in reasonable agreement with the more accurate determination of IC, from decay experiments. The main reason the stirred flow reactor calculations are inherently less accurate than the decay results is that three different flow rates must be measured to evaluate IC, from eq 6. These flow rates enter eq 6 in such a way that we expect an error of 20-30% in a single k , determination by this method. For experiments with Ar and He buffer the term which is first order in [N] reduces the calculated IC, by less than 5%. With a Nz buffer the first-order correction is large, amounting to approximately 50%. The value of 7-l was estimated from the data for the first 10 sec of a decay at the pressure at which the stirred flow reaction calculation was performed. For 11 = Nz the inaccuracy in estimating the effective value of T-' introduces an additional 20% error in k,. E$ect of Added Oxygen on 16,. Decays of N2 with 0.07% Oz added after the discharge did not show the peculiar features of pure nitrogen decays; In (AzlAt) graphs were linear for the duration of the decay. IC, values derived from these graphs are represented by the open circles in Figure 6. Within experimental scatter they agree with the results of initial decay calculations for pure K2. Only lower pressure decays were taken with added oxygen because at higher pressures firstorder removal of N atoms by atomic and molecular oxygen dominates the decay. Real and Apparent First-Order Surface Recombination. Were the first-order recombination coefficient, T - ~ ,due entirely to wall recombination, it should be independent
* *
(22) (a) A. A. Frost and R. G. Pearson, "Kinetics and Mechanism," 2nd ed, Wiley, New York, N. Y . , 1961, p 265; (b) G. B. Kistialtowsky and G. G. Volpi, J . Chem. Phys., 27, 1141 (1957).
NITROGEN AFTERGLOW AND
THE
of the total pressure and equal to 3dy/4R, where d is the average speed of the nitrogen atoms, y is the wall recombination probability, and R is the radius of the spherical vessel. We observed, however, that 7-l increased with increasing pressure as shown in Figure 8. These results forced us to consider the possibility that experimental 7-1 values arose partly from wall recombination and partly from homogeneous processes involving impurities, the latter appearing kinetically to be quasi-first order in [XI. The addition of only 0.07% oxygen impurity after the discharge, Figure 8, drastically increased the slope of the 7-l vs. [MI graph.23 The quantity 7-1 may be decomposed as follows 7-l
= k,
1559
RATEOF RECOMBINATION OF NITROGEN ATOMS
+ ki[M]
I
I
1
l o
(7)
where k, is the true surface recombination rate coefficient and Ici contains the effects of impurity oxygen. We viewed the effect of added oxygen on the basis of the reaction scheme
+ 02 --+NO + 0 IS+ o + n1:--.+No + n4 N + NO +Nz + 0 0+0 +M +M N
--t 0 2
Using this mechanism, the quantity
ki
= 2kax(02)
ki
(8%) (8b) (84
(84
in eq 7 becomes
+ 2kb[o]
(9)
where X(02)is the mole fraction of molecular oxygen. The factors of 2 enter eq 9 because the removal of a nitrogen atoms by reactions 8a or 8b guarantees the removal of another in each case by the subsequent very rapid reaction 8c. When molecular oxygen is added to afterglowing nitrogen the value of [0]is initially zero. As reactions 8 proceed, [02] decreases and [O] increases. Using literature values of the rate constantsz4for reactions 8 and our results for the time dependence of [N] we have made step-by-step calculations of the time dependence of ki for our runs with 0.07% added 02. It appears that after 1-2 min of decay history, the value of k i remains essentially constant for a long time. These limiting values of k i were used to draw the upper curve in Figure 8. The agreement with experiment is good, which supports our interpretation of the effect of oxygen impurity. Very slight pressure dependence of 7 - l for the helium mixture is consistent with the low oxygen impurity level claimed for the helium we used. The results for the argon mixture lead us to conjecture that we did not exhaust the air from our mixing bulb with sufficient care prior to making the mixture. From extrapolations to zero pressure we derived an average value of k , = 3 X 10-1sec-’, which yields a value of y = 5.0 X for the wall recombination probability. This is the lowest value of y for nitrogen atom recombination ever reported for any surface. The literature contains numerous reports of widely
Figure 8. 7-1 against pressure for Ar buffer (filled-in circles), He buffer ( x ), and pure nitrogen with 0.07y0 0 2 added after the discharge (open circles). The upper curve is a calculated curve based on eq 8 (see text).
varying y values for nitrogen atom recombination a t ostensibly similar surfaces (ref 2a and Table 11); however, it is hard to assess the significance of these values because, with one exception,$ no 7-1 vs. [fill data have previously been published. It is very likely that some published y values are measures of gas impurity instead of effective surface characteristics. As far as our value of y is concerned, we cannot confidently say this is a characteristic of clean Pyrex because of the possibility that tiny areas of stopcock grease or other material exposed to the afterglowing gas in our bulb may be very effective in destroying atoms. If such active regions of area X’ have a wall recombination probability y’, then it is sufficient that y’Sl = 0.52 X om2 for our calculation of the apparent y for the entire surface to come out as it did. Obviously a very small active surface area could account for all the first-order heterogeneous recombination which, by calculating as we did, we attempt to attribute to the large interior surface area of the entire bulb. It is entirely possible that y = 0 for clean Pyrex. Carefully designed experiments with pure gas in bulbs (23) The value of 7 - 1 was taken from the slope of In ( A z / A t ) graphs. Due to the ambiguity associated with In (Az/At) graphs for an Nz buffer, only results for Ar and He buffers are reported. When Nz was poisoned with 0.07% 02 the In ( A r / At) graphs were normal and 7 - 1 values obtained from the slopes could be used with confidence. (24) (a) J. E. Morgan and H. I. Schiff, J . Chem. Phys., 38, 1495 (1963); (b) I. M . Campbell and B. A. Thrush, Proc. Roy. SOC.Ser. A , 296,222 (1967); (c) M.A. A. Clyne and B. A. Thrush, ibid., 261, 259 (1961); (d) K. Schofield, Planet. Space Sci., 15, 643 (1967); (e) W.E. Wilson, J . Chem. Phys., 46, 2017 (1967); (f) C. Mavroyrtnnis and C. A. Winkler, Can. J . Chem., 39, 1601 (1961). The Journal of Physical Chemistry, Vol. 76, No. 10, 1971
W. BRENNEN AND EDWARD C. SHANE
1560
to about 10%. Limited data by Young, et ~ l . , ~for 1 a 1% N2-He mixture indicated the specific intensity was pressure dependent between 1 and 4 Torr. Our results indicate that the specific intensity has reached 71% of its maximum value a t 4 Torr. Our value of k r ~ for Ar and He, as corrected with Brown’s5 intensity distribution, is in good agreement with Brown’s apparent quenching constant for v = 6-12. For an Ar buffer Becker, et U Z . , ~ report a higher k r B but again the N2 contribution is unknown. Jonathan and Petty8 report an uncorrected k m value identical with ours but for an 11.5% Nz-Ar mixture. This value is not influenced by the distribution shift because JP used a direct titration technique to measure atom concentrations, but it does include an Nzcontribution. Using the apIc(N2)X(K2),JP’s proximation the IC = k(Ar)X(Ar) data suggest I C A ~ T B = 0.23 Torr-’. The contribution to ~ T ofB the small amounts of Y2 present in the inert gas mixtures need clarification. Our experiments and other s t ~ d i e ofs the ~ ~pressure ~ ~ ~ dependence of the afterglow have determined the intensity-pressure relationship to be that represented in eq 1. The experiments of Jonathan and Petty8 suggest that the form of this equation is valid not only for the highest levels of N2(B),v = 12, 11, and 10, but also for lower levels, v = 6, 5 , and 2. The pressure dependence of the afterglow is rooted in the mechanism of the afterglow-. We will now consider the predictions of several proposed mechanisms and their agreement with experiment. Berkowitz, Chupka, and Kistiakowskyaa (BCK) have proposed that the mechanism for population of the topmost vibrational levels of Kz(B) involves nitrogen atom recombination into the Nz(Q) state followed by collisionally induced transfer from N&Z) to Nz(B311,). Introduction of the quenching reaction, Nz(B) M -% quench, into the BCK mechanism gives an intensity-pressure relationship of the form of eq 1 where lc = 1 ~ For . the lower vibrational levels of NZ (B) BCK suggest that Sz(A3Z,+) is involved as an intermediate. Campbell and Thrushzd (CT) suggest that Kz(A3Z1,+) is the sole intermediate in the recombination. See Figure 9a. Steady-state analysis of the C T mechanism gives an intensity-pressure relationship of the form of eq 1 where k = k-.l(kk,)(lc_ k, k1)-‘ k ~ . k is identified as a quenching constant plus a complex combination of rate constants. In the CT mechanism k no longer simply represents electronic quenching of the KZ(B)d a t e . The model shown in Figure 9b schematically represents an obvious elaboration of the simple CT scheme,
of different surface-to-volume ratios would help to clarify this point.
Discussion Pressure Dependence of the Afterglow and the Afterglow Mechanism. Values of the apparent quenching constant, k , for pure Nz are summarized in Table I. Pressure increase experiments reported here and by Becker, et u L . , ~ and an entirely independent experimental approach by Jonathan and Petty8 give similar values of k X 3 . Jeunehomme and Duncan’s k r B value is calculated from the pressure dependence of the lifetime of the N2(B) state. Later, Jeunehomme’* reported more accurate data on the lifetime, but new data on the pressure dependence of the lifetime in pure Szbuffer B not be calcuwere not reported, so a revised ~ T could lated. The results of Young, et al. (see Table I, footnote e ) , are low but they are difficult to compare with our experiments due to their different method of formation of Nz(B) and their observation of lower vibrational levels. For pure nitrogen the pressure dependence of the afterglow for the topmost emitting levels of the B311 state seems firmly established with k 7 = ~ (8.0 1.2) Torrp1. The pressure dependence of the afterglow varies with the third body. For an XZbuffer the pressure at which the specific intensity, 1/[Kl2, reaches 50% of its maximum value-the so-called half quenching pressure-is 0.12 Torr. Above 1 Torr little pressure dependence is detected, in agreement with higher pressure studieszdJ*25~26 which found the specific intensity to be pressure independent above about 2 Torr. With Ar and He buffers there is much less apparent quenching than in pure Nz;consequently the specific intensity depends significantly on pressure to higher pressures. The interpretation of pressure increase experiments in Ar and He is complicated by the fact that the vibrational distribution in B311 is, especially in Ar, rather strongly dependent on pressure and gas composition as Brown5 has shown. Since we observe emission from levels 11 and 10 in the pressure increase experiments and the distribution shifts to lower levels a t higher pressure, failure to correct for the distribution shift gives values of ~ T in B Ar and He which are too high. We used Brown’s vibrational distributions to correct our data for levels 11 and 10 to represent apparent quenching of the top seven vibrational levels of Nz(B). I n Table I we have shown both our uncorrected and corrected values of ~ T in B Ar and He. As can be seen in Table I there is only fair agreement on the value of krB for the inert gases. Becker, et u Z . , ~ r e p x t a preliminary k R e 7 B value similar to ours, but since they did not report the gas composition it is not clear whether Nz made a contribution to the observed value. An XZcontribution will raise the observed ~ T value. I n our experiments the nitrogen contribution was less than the scatter in the data, which amounted The Journal of Physical Chemistry, VoZ. 76,N o . IO, 1971
+
+
+
B
+ +
+
(25) R. W. Gross, J . Chem. Phys., 48, 1302 (1968). (26) R. A. Young and R. L. Sharpless, ibid., 39, 1071 (1963). (27) R. A. Young, R. L. Sharpless, and R. Stringham, ibid., 41, 1497 (1964).
NITROGEN AFTERGLOW AND THE RATEOF RECOMBINATION OF NITROGEN ATOMS
I
I
FREE ATOMS
FREE ATOMS
Figure 9. (a) Campbell-Thrush model and (b) expanded Camp bell-Thr ush model,
1561
sured the intensity distribution of the nitrogen first positive bands in the Av = 3 sequence, coming from upper levels v = 6-12, in the range from 0.06 to 4.5 Torr with nitrogen, argon, and helium buffers. He attempted to fit the results for an Ar buffer to a model involving vibrational relaxation and electronic quenching in K2(B). The levels of Nz(B) were assumed to be populated from an unidentified precursor. I n order to obtain a reasonable fit to the observed NZ(B) vibrational distributions it was necessary to use unreasonably high vibrational relaxation rate coefficients, corresponding to one transfer for every ten gas kinetic collisions. Brown concluded that vibrational relaxation in Nz(B) was not adequate to explain the observed vibrational distributions. He suggested it was most likely that the vibrational relaxation occurs mainly in the precursor state. Estimates of the depth of the 5Z potential \Tell based on observed predissociations in other statesz8and on the effect of temperature on the vibrational distribution in the B311 stateBbsuggest that the 2 state could be a direct precursor, if not the only one, of the v = 12 and possibly also the v = 11 and 10 levels of N2(B3n[). For Nz(B311)levels below v = 10 the A 3 2state is a more reasonable direct precursor than on the grounds that amounts of electronic energy large compared to kT are unlikely to be dissipated into other degrees of freedom in simple collision events. Providing that molecules in the B311and A311states can be easily interconverted by collision, it is possible for the 5Z state to be the ultimate supplier of population in levels of the B3n[state well below the topmost emitting ones as indicated by the sequence
which shows the vibrational structure of the A and B states and suggests the possibility of crossover between A and B at various energies. If the quenching and radiative rate constants are assumed to be independent of level, the steady-state solution for the intensity of emission from level n of B, though algebraically messy, can be written down. The expression for the intensity from the top level of B is naturally identical with that from the CT mechanism. For lower levels the intensity-pressure relationship becomes more complicated in appearance, and it seems odd that eq 1 should apply hI M M M atoms + 52+B 3 n ( u k ) 4A32(v,) + to any but the topmost level. Simplifications are possiM ble, however, when assumptions are made about the A3Z(vJ < v,) +B311(v1< vk) +emission relative magnitudes of various rate constants. Consider two extreme examples. If quenching of KZ(B) Our pressure dependence studies and those of others is always much more efficient that back-transfer to cannot be used to assess the relative importance of the K*(A), i e . , if ~ C Q>> k-,, for all n, then the intensity several possible pathways by which molecules in various from each level of N2(B) obeys an equation of the form levels of B311are formed. of eq 1, and the apparent quenching constant is k ~ . Nitrogen Atom Recombination. Values for the homoIf, on the other hand, vibrational relaxation in NZ(A) geneous termolecular rate coefficient for nitrogen atom is always more efficient than crossing to S2(B),i.e., recombination are summarized in Table 11. Recent kn,n+l >> k , for all n, then the intensity from each level s t ~ d i e s ~are ~ in * ~agreement j ~ ~ ~ ~that for RI = IY2, k, of IVZ(B)is again of the form of eq 1, but the apparent = (1.0 f 0.2) X cm6 molec-2 sec-' at room temquenching constant for each level is k~ k+ I n this perature. I n our experiments the inconsistencies, apinstance if k-, >> kQ for all n then 12-, would have to parently involving impurity reactions, that are assodepend weakly on "IZ for the same formula to apply to ciated \Tith long time pure nitrogen decays have been all levels. avoided by using initial decay data. Initial decays on Until more precise level-by-level measurements of a clean Pyrex surface and on a surface coated with the pressure dependence of the intensity are available, syrupy phosphoric acid give consistent results within it will not be possible to make a firm decision about the experimental scatter. Experiments with added 0 2 mechanistic significance of the apparent quenching further suggested that impurity reactions are involved constant. in N-atom removal and that Oz is acting to quench An important contribution to the evaluation of mechanistic models has been made by He mea(28) P. K. Carroll, J . Chem. Phys., 37, 805 (1962).
+
The Journal of Physical Chemistry, Vol. 76, No. 10, I971
W. BRENNEN AND EDWARD C. SHANE
1562 Table 11: Summary Results of Nitrogen Atom Recombination Studies M
h a
ksb
Wall material or coating; method
Y
Nz
0.79 f 0.1
0.13 f 0.05
Nz Ar He Nz, Ar He Nz
1.1 i 0 . 4 2.3 f0.5 2.2 =t0.2 0.76 f 0.06 1.05 f 0.2 0.96 f 0 . 3 0.75 f 0.05 1.05 0.91 1.4 f0.5 0.6 f 0 . 3 2.3 f 0.9 2.25 f 0 . 2 1.57 f 0.2 0.78 f 0.08 0.23 3.3 f0.8 3.44 f 0 . 4 2.9 f 0 . 5
0.4 f0.1 0.22 f 0.06 0.06 f 0.01 1.44 1.44 1.7
