The influence of the internal state and translational energy of the molecular reactant upon the chemiluminescent reaction Ba + N2O → BaO* + N2

391

Chemical Physics 108 (1986) 391-402 North-Holland, Amsterdam

THE INFLUENCE OF THE INTERNAL STATE AND TRANSLATIONAL OF THE MOLECULAR REACTANT UPON THE CHEMILUMINESCENT Ba + N,O --, BaO* + N2 H. JALINK,

F. HARREN,

Fysisch Luboratorium,

Katholieke

D. VAN DEN ENDE Universiteit Nijmegen,

ENERGY REACTION

and S. STOLTE

Toernooivelrl, 6525 ED Nijmegen,

The Netherlands

Received 19 March 1986; in final form 14 July 1986

I=l)ofvariable Employing a hexapole focuser to produce a beam of state-selected N,O molecules ( n2 = 1, J=M=lor2, translational energy, E,, (0.08-0.16 eV), we have found the chemiluminescent cross section, o,,,, to be enhanced strongly, up to a factor of 4, upon excitation (n a = 1) of the bending mode of the N,O molecule. Revoking the commonly accepted ion-pan harpooning model we propose a revised mechanism in which the va-bending vibration provides the reaction-promoting coordinate for overcoming the symmetry barrier to the breaking of the NN-0 bond and the release of ground state 0 atoms to form the BaO product. A weak enhancement of o,,,(n, = 1) is observed for the J = 2 rotational state compared to the J = 1 state of the N,O reactant. Our results have been utilized successfully to explain the temperature dependence of the chemiluminescent rate observed earlier. Absolute cross sections have been extracted using a recent calibration.

1. Introduction Pioneering chemiluminescent experiments exploiting a molecular beam for the reaction Ba + N,O + BaO* + N, have been carried out by Ottinger and Zare [l]. The photon yield of its blue-green luminescence was found, unexpectedly, by Jones and Broida [2] not to quench but to increase when the rare gas background pressure was raised. To explain this intriguing phenomenon it was postulated 12-41 that the BaO product molecules are formed through an energetic metastable precursor (i.e. the so-called reservoir state) of a hitherto unknown character and are subsequently transferred by collisions to the light emitting A’Z+ state. Motivated by this interesting behaviour a large number of experiments, elucidating various aspects, have been carried out during the last 15 years leading to the “case study of the Ba + N,O reaction”. Reviews are given by refs. [2-51 and a survey of recent references can be found in refs. [6,7]. Although the detailed spectroscopy of relevant light emitting states of BaO still remains a formidable task [8,9], the nature of the predominant 0301-0104/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

states, in which the nascent BaO molecules are formed, has been revealed recently by Hsu and Pruett [lo] to be highly excited vibronic levels (u = 20-50) of the electronic ground state. This conclusion was reached by analyzing the excitation spectrum which was obtained under singlecollision conditions by laser-induced fluorescence. That almost all of the exothermicity (= 80%) of the reaction under study Ba + N,O + BaO + N, + (4.11 f. 0.09) eV,

(1)

was disposed into the internal energy of the product molecules was also the conclusion of an earlier study by Parr et al. [ll], in which the recoil velocity distribution of the BaO product was studied in a universal crossed-molecular beam machine. Moreover, since the BaO molecules were found to be scattered predominantly in the backward direction, a direct rebound reaction mechanism [12] was deduced. As an upper limit for the total reaction cross section uR, the Ba beam attenuation cross section for N,O gas u.,., was determined by monitoring the strength of the chemiluminescent signal [13-161. This yielded ur = 24 + 1 AZ as the most accurate value [6] in accorB.V.

392

H. Jalink et al. / The chemiluminescent

dance with a hard-wall type rebound reaction mechanism. The spectral distribution of the chemiluminescence produced under single-collision conditions was measured originally in the blue-green region [13] and recently in the far red [6]. The strong rotational excitation of BaO apparently suppresses the occurrence of sharp features such as bandheads. An accurate analysis and simulation is unfortunately still unavailable. Although a photographical observation [16] of the angular distribution of the chemiluminescence indicates that a considerable fraction of all the BaO* molecules is produced in the long-lived (7 = 9 f 1 ps [17]) A’ ‘II state, the chemiluminescence observed in other beam studies [1,6,13-151 is believed to originate predominantly from the shorter-lived (7 = 350 ns [18]) A’X+ state. This is due to loss out of the field of view of the optical light collection system before the occurrence of radiative decay of the long-lived state. Under these conditions, Cox and Dagdigian [6] were able to measure the absolute quantum yield for chemiluminescence, @ = u,,JuT = 9.3 f 3.4% (the total collision cross section for chemiluminescence is indicated by us as ah,), and to estimate moreover the vibrational distribution of the A’Z+ state, which is found to be peaked around u’ = 4-7. The dependence of u,,,, upon translational and internal reactant energy has been investigated by Wren and Menzinger [14,19,20] by using N,O/He beams with variable seeding fractions and nozzle stagnation temperatures, T,. The E,, dependence (0.1-0.4 eV) of u,,” for vibrationally cold N,O molecules (T, = 281 K) turned out to have a maximum at E,, = 0.15 eV followed by a monotonic decline. The influence of the reactant internal energy upon uhv was investigated by measuring the influence of raising T,. Especially at low E,, (= 0.15 eV), a strong increase of uhv at higher T, values was observed, i.e. uhv (T, = 499 K)/u,, (To = 281 K) = 3. At higher E,, these increases become appreciably smaller. This behaviour of course cannot be explained with the earliermentioned simple rebound reaction mechanism. Wren and Menzinger [14] explained the increase Of ‘hv with T, as being promoted by the vibrational bending mode (Ye = 589 cm-‘) of N,O,

reaction Ba + N,O + BaO* + N2

which is increasingly more populated at elevated T,. They proposed that the reaction occurs through an ionic intermediate: Ba + N,O + Ba+ + N,O-+ BaO* + N,. Since the vertical-electron affinity of N,O was found to increase strongly with the bending angle [21], v,-excitation was considered to be a specific promotor of reaction. In their attempt to relate quantitatively the observed To-dependence of a,,, to a specific dependence on vibrational reactant levels Wren and Menzinger [14] could not reach a satisfactory fit. Accepting the assumptions of absence of vibrational relaxation and no dependence of reactivity on the rotational state of N,O, the data imply that high levels of the v,-vibrational mode ( n2 = 2, 3, . ..) are responsible for the increase of u,,” with To. It is the goal of our study to elucidate the role of the n2 = 1 level in the To-dependence of a,,,, by employing state-selected beams of N,O molecules, and to discuss the implications for the studies mentioned above. The remainder of this paper is organized as follows. In section 2 the experimental arrangement is described. Section 3 presents the experimental methods and results. Finally in section 4 a discussion focused upon the interpretation of the measured specific energy dependence of the chemiluminescent cross SeCtiOn oh,,, concludes the paper.

2. Experimental arrangement 2.1. Outline of the machine Previously [22-251 our focusing and scattering apparatus has been described in detail. Here a short description concentrating on the modifications will suffice. As schematically shown in fig. 1, a supersonic beam of N,O molecules, emerging from a nozzle source, so, is state-selected by an electric hexapole field, ss. It focuses the beam trajectories of the desired state upon the entrance of one of the two extractable collimators, cs (0 = 2.0 mm) or cd (0 = 2.0 or 1.0 mm), which are situated in front of the scattering region and a home-built universal

H. Jalink et al. / The chemiluminescent reaction Ba + N,O + BaO’ + N2

393

Fig. 1. Schematic view of the molecular beam machine; sizes in mm. The following abbreviations have been used: so: N,O source; 0= 110 pm, sk: 2 skimmers; 0, =l.O mm; 0, = 1.75 mm, ss: electric hexapole state selector, ch: chopper; 30 Hz, vs: velocity selector; Au/u = 58, cs: collimator scattering chamber; 0 = 2.0 mm, o: barium oven; T = 1OOOK, c: 3 slit collimators; 2 X 10 mm’, wh: Woods horn, bd: barium detector, 1,1,: two aspherical lenses; 0,s = 60 mm; f,/lzr, = 0.65; fi/ 0, = 0.70, pmt: bialkali photomultiplier; 0= 9 mm, cd: collimator detector chamber; 0 -1.0 or 2.0 mm, io: ionizer, qmf: quadrupole mass filter.

detector, io, with an Extranuclear mass filter placed 2.7 m and 3.42 m downstream along the beam path, respectively. The inner radius, r,, of the hexapole state selector (as before equal to the diameter of the stainless steel rod-electrodes) has been enlarged to 7 mm, permitting a larger solid angle of selected N,O molecules to be focused. In this configuration a maximum voltage between neighbouring rods of = 50 kV can be maintained without sparking. As before [24], our 1.665 m long hexapole wobbles in a periodical motion (2.5 Hz), resembling, a square wave and modulating the center of the focused beam over a distance of displacement of 2.4 mm at the scattering collimator, cs, in front of the scattering region. Moreover, to modulate the full (unfocused) N,O beam for phase sensitive detection, a rotating blade chopper, ch (30 Hz), can be operated at the exit of the hexapole. A self-calibrating slotted-disk velocity selector [22], vs, can be lifted swiftly in or out of the beam path of the N,O molecules, without disrupting the measuring process, in a controlled motion regulated by compressed air.

2.2. Conditions of the N,O beam Because of the small deflection which can be exerted on the state-selected molecules by the hexapole focuser, the distance between the nozzle source and the scattering region has to be large (2.84 m). In order to produce an intense N,O beam to overcome the lack of strong chemiluminescence, the source-vacuum compartment is pumped by a baffled 3000 d/s (Leybold Di 3OOO/6) diffusion pump which is backed by a 500 m3/h rootspump and a 60 m3/h forepump in series. Under conditions similar to those of Wren and Menzinger [14], the N,O (seeded) supersonic beam emerges at room temperature through a quartz nozzle, so (0 = 110 pm), having a constant stagnation pressure, PO, of 300 mm Hg. In table 1 the compositions of six seeding mixtures employed in this study, covering a velocity range of 500 m/s < uNZo < 1000 m/s, are given together with the parameters of flow velocity u,, speed ratio S = u, (2k~,/m,20)-1’2, and translational beam temperature q,.

H. Jalink et al. / The chemiluminescent

394

reaction Ba + N,O --t BaO* + N2

Table 1 Conditions of the N,O beams. At stagnation temperature To = 296 K and pressure Pa = 300 mm Hg, the flow velocity us, speed ratio S, and beam temperature T,,, have been determined with the slotted-disk velocity selector. The values for T,, and the upper limit for Tvib have been obtained from focusing curves. The upper limit for Tvib of mixture (iv) has been obtained by assuming Tr,,, = T,,. In the case of mixture (v) no focusing curves have been taken, because the N,O molecules were too fast to state select with the hexapole installed No.

Mixture

US (m s-‘)

S

?I (K)

T TO, (K)

Tvib (K) >

(9

10% 100% 50% 30% 20%

556$-4 619*4 75g*4 871*4 977+4

14.3 9.2 11.5 13.2 14.2

4.0 f 0.5 12.0* 1.0 10.5 f 1 .o 11.5*1.0 12.5 k 1.0

3.0 f 0.5 10.5 f 1.5 8.0 f 1.5 _

207f4 203 f 22 2og*11 244+23

(ii) (iii) (iv) (v)

N,O/Ar N,O N,O/He N,O/He N,O/He

2.3. The scattering region The oven orifice (2.5 x 5.0 mm2) from which the Ba beam effuses vertically upwards is located 5 cm below the intersection point (= scattering center) with the N,O beam (see fig. 1). The Ba oven itself consists of a top and a bottom chamber. To prevent clogging, the top chamber was always 50 K higher in temperature than the bottom-stock chamber which was kept at T = 1OOOK to provide sufficient vapour pressure (P,,(oven) = lop2 mm Hg). An operation time of typically 30 h (without clogging) could be achieved by loading the oven with 5 g Ba. Background light which could add large contributions to the weak chemiluminescent signal at the photomultiplier, was suppressed as much as possible. To avoid the usual .light emission produced by the heating elements, which are hotter than the oven, the cylindrical stainless steel oven was provided with a tapering groove around its outer surface in which, to ensure good thermal contact, a thermo-coax wire (0 = 1.0 mm, with cold ends) had been pressed and used as the heating element. A tight copper tube (1 mm wall thickness) was slid over the cylinder surface covering the thermo-coax windings to ensure a uniform temperature. Moreover the black body radiation, emitted from the oven orifice, was carefully collimated together with the Ba beam itself by three slit shaped collimators (2 x 10 nun2), mounted on top of a water-cooled copper screen surrounding the oven. The first collimator was mounted 17 mm from the oven and the distance between sequential collimators was

made equal to 7.5 mm. A divergence of 3’ x 18” resulted for the Ba beam at the scattering center which could be determined experimentally by inspection of the Ba deposit on the inner parts of the Woods horn located above the scattering region (see fig. 1). This horn, which also served to minimize the background light, had a small hole drilled in its. top to permit detection of the Ba beam flux by ‘means of a digital film thickness monitor (Kronos), bd, placed above it. The light of the chemiluminescence was collected by imaging the scattering center onto a diaphragm (10 x 32 mm2) enlarged two times by an aspherical lens (0, = 60 mm, f,/ 0, = 0.65) and afterwards again two times demagnified by imaging on the blue sensitive photomultiplier cathode (0 = 9 mm, EM1 9789 bialkali) by almost the same type of aspherical lens (0, = 60 mm, f2/ 0, = 0.70). In a typical experiment the background light turned out to have an intensity about an order of magnitude smaller than the chemiluminescent signals. The photon signals have been measured with a digital lock-in counting system (Ortec Brookdeal 5Cl) which is connected to an (Apple II) microcomputer to handle the data. 3. Experimental methods and resuks 3.1. Translational chemiluminescence molecules

energy dependence for non-state-selected

of

the N,O

From the measurement of the BaO* light yield (i.e. photomultiplier signal/mass spectrometer

H. Jalink et al, / The chemiluminescent

N,O beam signal) as a function of the N,O velocity (uNzo was tuned with the velocity selector) for a fixed seeding composition, the dependence of urahy upon z was obtained. To extend the range of translational energy, but to avoid measurements at the tails of the N,O velocity distribution (where intensities are low and velocity deconvolution through the velocity selector becomes necessary) several seeding mixtures [see table 1, (ii)-(v)] with overlapping velocity ranges have been used to span the full range of the dashed curve in fig. 2. Moreover, in fig. 2 a,,, has been plotted as a function of the averaged relative reactant velocity, 6,. As was shown by Bernstein [26] V, is calculated simply by the series expansion

395

reaction Ba + N,O + BaO* + N2

T,,leV1 Oh” .I

I

(arb. u.)

0.10 I

0.11

0.18 1

0.22 1

1

. . . . . . n2=1,J=2 -a-

n2=1,J=1

-

n,=O

-----

direct beam

3-

Ur=UNo2 [1+ 0.75(%/~,*o)2 2-0.0544(

ah/UN,0)3

-0.3115( agJuN,0)4

)I,

+0.1569( aBa/uNzO 5

(2)

where aBa = (2kT,Jm,,)‘/2 stands for the most probable velocity of the perpendicularly impinging effusive beam of Ba atoms (aBa = 348 m/s for our typical value of TBa = 1000 K). The average reactant translational energy, which has been indicated at the uppere horizontal axis of fig. 2, can be calculated in an even more straightforward way E, = tP( uzN,o+q,

(3)

with

and

Confirming the results at T, = 281 K of Wren and Menzinger [14] perfectly, a broad maximum for a,,, has been found at E,, = 0.16 eV. Moreover, again in agreement with ref. [14], u,,” (T, = 296 K) has been found to remain within 80% of its maximum value in our translational energy range (0.07-0.22 ev).

l-

O-

700

900

1100 _.

._

Fig. 2. The chemiluminescent cross section, q,,, as a function of the average relative velocity, Er [calculated with (Z)], and the average translational energy, E,, [calculated with (3)]. The (- - - - - -) line represents the a,,, of the non-state-selected direct beam. The (e-. - .) and (. . . . . -) lines are hand drawn curves of the e,, for N,O molecules in the (n,=l, J=l) and (n a = 1, J = 2) state, respectively. The () line is calculated by (5) and gives the a,,, dependence of N,O molecules in the ( n2 = 0, low J) state. The seeding mixtures used are indicated by the points as: + (i) (10% N,O/Ar), 0 (ii) (100% N,O), A (iii) (50% N,O/He), A (iv) (30% N,O/He), and W (v) (20% N,O/He).

3.2. State selection of N,O molecules excited Ieuel of the bending mode

in the first

The Stark effect of N,O molecules at the PZ~= 0 and n2= 1 vibrational levels of the bending mode (Y*= 589 cm-‘) has been investigated in detail by Reinartz et al. [27]. At practical field strengths, a

H. Jalink et al. / The chemiluminescent

396

linear (quadratic),Stark effect has been found for rotational states of the PZ~= 1 (n2 = 0) vibrational level. At the stagnation condition of room temperature = 10% of all the molecules are found to occupy the twofold degenerate n2 = 1 level thermally. The linear Stark energy of an N,O molecule is given by E Stark

reaction Ba + N,O * BaO* + N2

cos8

‘I2

AI/IO

I

2.5

‘h

‘14 ‘/5 ‘16 1

I

1

II

2.0 13,Vl

=

-dWJ(J+

I)]

E.

(4)

Here CL,_, is the electric dipole moment of N,O in the n = 1 state (p=, = 0.173 D [27]). The quantum number J indicates the total angular momentum, M the projection of J upon the direction of the external E field and I the vibrational angular momentum around the molecular axis. As explained in refs. [23,25], molecules in states with pLe,lM< 0 can be focused by a proper choice of the voltage, V, between the hexapole rods. The focused molecules are detected as the so-called “wobbled” beam intensity AI, which is a lock-in signal resulting from moving (at 2.5 Hz (see section 2.2) as an essential square wave modulation) the far end of the hexapole field axis back and forth through the detector orfice [22,23]. The on-axis position of the hexapole field yields detection of sharply focused molecules together with a background from weakly focused and unfocused molecules. The off-axis position yields only the background. Consequently the difference AI yields the signal due to sharply focused molecules. As a typical example of achieved state selection, in fig. 3 we have plotted AI/I, obtained for mixture (i) (see table 1) which was filtered through our velocity selector (Au/u = 0.05 fwhm at the peak velocity uNzo = 556 ms-’ as a function of the hexapole voltage V. As shown by dividing AI by I,, the unfocused intensity at V= 0, an appreciable enhancement, up to a factor 2.4 in fig. 3, due to focusing has been achieved. Because, according to eq. (4) the product E cos B with a= hU/J( J + 1) determines the Stark energy and since the electric field and its gradient inside the hexapole are all proportional to V, the focusing trajectories for a particular (J, I, M) state are determined solely by the value of V a, i.e. the focusing of the (J, I, M) = (2, 1, 2) state with a= l/3 will require V to be a factor 1.5 higher than for the focusing of the (J, I, M) = (1, 1, 1) state with ws 8= l/2. Thus after the

5

10

20

30

LO 50 VlkVl

Fig. 3. Focusing curve of beam (i) having a seeding composition of 10% N,O/Ar. The enhancement of the intensity on the detector, AI, by focusing with the hexapole divided by the intensity of the non-statsselected (V = 0 kV) direct beam, I,,, is displayed as a function of the hexapole voltage, V. At the upper horizontal axis the corresponding average cosine of the angle between the molecular axis of N,O and the electric field inside the hexapolk cos8= IM/J(J+l), has been indicated. The dots are experimental points while the solid line represents a focusing curve simulated by a computer program [28]. The individual resolved rotational states are given by (J, I, M).

(1, 1, 1) focusing peak has been identified in fig. 3, its accompanying peaks at cos8= l/3, l/4, l/6, can be attributed respectively to the focusing of the (2, 1, 2), the (3, 1, 3) and the pair (2, 1, 1) plus (3, 1, 2) states. Since the focusing force scales with V Case one expects in a plot of AI versus log V all focusing peaks belonging to a single value of cos to have the same width as has been observed indeed (e.g. fig. 3). Using a computer program (to be described in ref. [28]) the experimental focusing curve has been simulated. Hereto the earlier measured (see table 1) velocity distribution of mixture (i) had to be unfolded over the transmission function of the velocity selector. The resulting width of the focusing peaks, which has been found to be sensitive to the actual velocity width of N,O molecules, was

H. Jalink et al. / The chemiluminescent reaction Ba + N,O + BaO* + N,

calculated to be in perfect agreement with the observations in fig. 3. The relative height of the focusing peaks can be taken to be proportional to rotational state populations. From the ratio of the two strongest peaks, (1, 1, 1) and (2, 1, 2), a rotational temperature of 3.0 + 0.5 K has been deduced. The vibrational temperature is directly related to the fraction of nz = 1 molecules in the beam and can be estimated by comparing the absolute value of the focused intensity of the (1, 1, 1) peak with a theoretical prediction. The best fit to the experimental values of fig. 3 was obtained assuming Tvib= 207 f 4 K. However, this vibrational temperature has to be considered as a lower limit only. In this calculation the hexapole field has been assumed to have an ideal gradient up to rO, the geometrical inner radius. The nozzle source has been taken to have a virtual diameter [29] equal to zero. Non-ideal conditions tend to lower the maximum of a focused peak and it is for this reason that we consider the -fitted Tvib as a lower value. The mismatches with theoretical positions at the various values of cos in fig. 3 can possibly be brought about by a perturbing non-linear Stark effect [28,30]. The weak broadening of the focusing peak at cosB= l/6 however could also be induced by an effectively lagging behind of the actual hexapole voltage, V, due to leak currents between the hexapole rods near the limit of our high-voltage range. The small negative dip of AZ/Z0 at V= 9.5 kV has been caused by the fact that the optical and symmetry axes did not exactly coincide. When special care has been taken to make these two axes coincide, the negative dip has been found to disappear [28]. As described above for mixture (i), the state distributions of beam mixtures (ii)have also been analyzed with the hexapole and the results are displayed in table 1. T,,, = 1;, has been observed in all cases. 3.3. Comparison of the chemiluminescence for state-selected (nz = I, J = I) and non-state-selected (n1 = 0, low J) N,O molecules as a function of E,, During these experiments the velocity selector has been moved out of the beam path to allow the

391

full N,O beam for maximum signal and to permit rapid switching between various mixtures having different N,O velocities. Although the removal of the velocity selector has introduced some broadening of the velocity distribution, the focusing peaks of states, selected for reactive scattering remained separated. So the wobbling at appropriate V ensured complete on-off modulation of the selected state. As the first step, the wobble signals AZ of the (J, 1, M) = (1, 1, 1) and (2, 1, 2) states have been measured at the mass spectrometer detector and compared with the intensity of the unfocused direct beam, IO. As the next step, the collimator cs in front of the scattering center has been inserted exactly on the beam axis. Then the hexapole voltage V is raised by a factor 1.23, with respect to the original focusing value to move the sharp spot of the selected state from collimator cd towards cs (see fig. 1). Finally, the chemiluminescent signals, AZ,,“, obtained for the voltages focusing the (J, 1, M) = (1, 1, 1) and (2, 1, 2) states are measured and compared with those Z,,y,O for the unfocused (I’= 0 kV) N,O molecules. After this, similar ratios are again measured on the mass spectrometer when the collimator cs has been removed and the hexapole voltage lowered by a factor 1.23 etc. These measurements have been carried out for the mixtures (i)-(C) and the (1, 1, 1) selected state solely for mixture (iv). Since there are no electric guiding fields at the scattering region, nor homogeneous guiding fields near the hexapole exit (as seen by the N,O molecules) one cannot expect the N,O molecules to be oriented at the collision process. From the measured ratio of state-selected and non-state-selected beam fluxes passing through collimator cd, (AZ/I,),, one wants to calculate the similar quantity (AZ/Z,), which applies to the fluxes through cs into the zone of reaction. These two ratios are not identical because of geometrical differences in acceptance angles for (un)focused beam molecules transmitted through cd or cs. With our focusing computer program [28] this geometrical factor (and its estimated error) has been calculated, (AZ/Z,,),/ (AZ/Z,),, = 1.29 f 0.04 and was found to be insensitive for both the selected s&te and the velocity distribution of the employed beam mixture. From the ratios of photon (Z,JZhv,c) and mass

398

H. Jalink et al. / The chemiluminescenr

Table 2 The effect of state selection of the bending mode (n 2 = 1, J = 1 or 2) at various translational energies. Here e,,” stands for the chemiluminescent cross section for the indicated mixture in the absence of state selection. The chemiluminescent cross section of a state-selected beam is defined as u,J n2, J) No. (9

(ii) (iii) (iv)

Mixture

z

10% N,O/Ar 100% N,O 50% N,O/He 20% N,O/He

0.080 0.093 0.126 0.158

(ev)

akp(13

l)/akv

ukv(ly

3.27kO.2 3.50k0.2 1.98 f 0.1 1.70*0.1

2)/uku

3.7kO.2 4.2f0.3 2.15 kO.2 -

spectrometer signals (AZ/Z,,), one obtains di= 1.29 (AZhv/ rectly [23]: uhy(n, = 1, J)/a,, Z,,,,a)/(AZ/Z,), and after multiplying by the value obtained in section 3.1 one obtains the Of Ohv velocity dependence of u,,(n, = 1, J), plotted in fig. 2. A strong vibrational enhancement accompanied by a weaker rotational effect is observed. The velocity-dependence of uhv(n2 = 0), the chemiluminescent cross section for non-stateselected N,O molecules in the vibrational ground state has been estimated using the relation: uhvb2

=

O)

=

uhv

-fn2=1bhvb,

=

l)

-

uhvl

7

c5)

where fn2=,,the fraction of molecules in the n2 = 1 state, has been taken as the lower limit obtained from table 2, the rotational effects have been suppressed by setting uhv(n2 = 1) = max[u,,(l, l), uhv(l, 2)]. As fig. 2 shows, the difference between e,,v(n2 = 0) and uhv, assessing the effect of vibrational excitation of the unfocused beam turns out to be small.

4. Discussion We have found that the first excited state of the bending vibration of N,O, n2 = 1, enhances strongly the chemiluminescent yield. We conclude that our results (see fig. 2) are in qualitative agreement with the three-state model, 2c, of Wren and Menzinger [14] (dashed curve of their fig. 4). In hindsight the problems encountered by Wren and Menzinger [14] trying to obtain a reasonable fit for the T’,-dependence of uhu with vibrational-

reaction Ba + N,O --* BaO * + N2

state-dependent cross sections, can be attributed to the unanticipated J-dependence of uhv(n2 = 1) observed by us, and to a possible enhanced vibrational relaxation at the low temperatures present in a nozzle expansion (e.g. refs. [31,32]). The rather weak dependence of uhv(n2 = 1) upon J, as presented in fig. 2, is not uncommon for other chemical reactions [33,34]. Similar effects could also be present for uhv( n, = 0). Since the rotational states occupied in the unfocused n, = 0 beam are also low ( Jmax - 2.5), we conclude that the main source of enhancement of a,, is due to vibrational excitation. At this stage of investigation we will refrain from interpretations of the J-dependence of uh y. Wren and Menzinger [20,14] explained the strong enhancement of uhv by excitation of the bending mode, n2 = 1, 2,. . . , by proposing that the reaction mechanism is initiated by an electron jump: Ba + N,O --, Ba+ + N,O- + BaO* + N,. Invoking this mechanism a potential surface for the resembling reaction between Mg + N,O has been constructed [35]. The v,-vibration was argued to be a reaction-promoting coordinate because of the increase of the N,O electron affinity, EA, with the bending angle [21]. A striking demonstration of this phenomenon was given by Chantry [36] who observed an increase by three orders of magnitude of the dissociative attachment rate of thermal electrons (e + N,O + N, + O-) upon raising the vibrational temperature from 350 to 1000 K. The crossing radius at which an electron jump will occu! can be estimated [12] simply by R, = 14.35 eV A/AEO with AE, = IP - EA, where IP = 5.2 eV is the ionization potential of Ba. Substituting EA = -2.2 eV for the vertical electron affinity of N,O (n2 =0) yields R, = 1.7 A. To obtain an increase of the electron jump cross section by a factor of 2 (i.e. R, with 2’12), one has to raise the vertical electron affinity with 2.7 eV to a value EA = 0.5 eV. Such an increase can be achieved by bending the N,O molecule over more than 45” into its state of maximum EA [14]. The classical amplitude of the bending motion yields and BN,O (n,= l)= 13.3”, e N,O (n,=0)=7.7’ so that the electron jump mechanism is deemed to be inadequate in explaining the observed increase of uhy from n2 = 0 to n2 = 1.

H. Jalink ut al. / The chemiluminescent reaction Ba + N,O + Boo*

Gt

(eV)

products

-V

(rtbd

I

I

+ N,

~,,+ADo(eV) reactants

1 I

399

,/

.. .. . . . . . . . . . . < -.-.-.-.I.,

_..

-.-.-... . .. . . . . . . . . ‘LO 35 30 25 20 15 \

1.5

2.0

2.5

3.0

3.5 r0a-0 (1)

Fig. 4. Energy diagram for the Ba+N,O + BaO + N, reaction. The representative reactant energies [ll] Et, = 0.11 eV (.-. - .) and 0.38 eV (. . . . . . ) have been drawn in the right panel of the figure and are indicated with the addition of the exothermicity AD, = 4.11 eV (also plotted) as the energies totally available for products. In the panel in the middle, RKR-potential curves [8] of BaO, assigned vibrationally, have been plotted to show possible final electronical and vibrational product states. Of all the electronic states displayed only the A’ ‘II and b 311 states correlate for a large internuclear distance rBa_o to the separated ground state atoms Ba(‘S) andO(3P).TheenergyoftheA’1IIandb3IIpotentialcurvesatr as _o 2 2.8 A is the lowest and it is this surface which is proposed to intermediate the release of the 0 atom from N, to form the product bond with Ba already at large ( 2 3.5 A) distances between the reactants. The perturbations of the BaO molecule itself [8] in combination with the avoided curve crossings between the potential surfaces [4] are responsible among all possible electronic states as indicated in the figure. The average energy released as internal energy of product molecules &, has been found to decrease for increasing reactant energy: Et’“,= 3.61 eV (. -. - .) for EC,,= 0.11 eV and E;,,, = 3.28 eV (. . . . . .) for Err = 0.38 eV [ll].

Consider the potential energy curves of the various electronic states of BaO as determined by Gottscho et al. [S] together with the energies of the Ba + N,O reaction in fig. 4. At the interatomic distance rBaO= 3.4 A the attraction of the b 311, A’ ‘II potential curves overcomes the binding energy of the NN-0 bond and reaction becomes possible without an electron jump. However, by

dissociating the NN-0 bond of a free linear N,O(X ‘I: ’ ) molecule one produces an 0 atom in an excited S state instead of the ground P state, which is lower by 4 eV. This barrier can be broken by disturbing the cylindrical symmetry around the molecular axis by the bending motion, allowing direct coupling to the dissociation channel of the 0 atom in the ground P state. It is just the P state

400

H. Jalink et al. / The chemiluminescent

of 0 which correlates with the attractive potential curves of the (b 311, A’ ‘II) BaO states (see fig. 4) and could form possibly the so-called reservoir state. Even a rather small increase of the bending amplitude might possibly lower the symmetry barrier to break the NN-0 bond to yield the P state of the 0 atom and thereby enhance the reaction probability confirming the observations. The presence of a high density of excited vibrational levels for the electronically excited a3Z+ and A’Zf states and for the ground X iZf state, which are practically degenerate with those of the intermediating b ‘II, A’ ‘II reservoir states (see fig 4), will induce an effective scrambling of the electronic signature of the nascent product due to the collisional perturbation by the outgoing N, molecule. Moreover, the results of fig. 2 show that after a maximum at low Et,, uhV decreases with E,, both for n2 = 1 and n2 = 0. Parr et al. [ll], measuring the translational recoil energy of all BaO product molecules for different collision energies by seeding and heating the N,O molecules, observed that increasing E,, tends to decrease the average energy disposed into the internal degrees of freedom of product molecules. Two typical examples are displayed in fig. 4. Since the value of Ei’,, is expected to reflect the level of excitation of the new formed bond Ba-0, the lowering of EL, decreases the ratio of state density for available electronically excited vibrational states to ground vibrational states, i.e. the branching fraction towards chemiluminescence is expected to decrease for increasing E,, and can be held (partly) responsible for the decrease of u,,” in fig. 2 at increasing E,,. In a beam-gas experiment Wren and Menzinger [14] also measured the dependence of the rate constant for chemiluminescence, khv, together with the rate constant for Ba beam removal, k,, as a function of the temperature (TN,o = 298-591 K) of the N,O gas. In fig. 5c we have replotted their results as a function of TN,o and J?,,. Apparently the similar dependence of k,, and k, upon TN2,(&,) suggests that (at least qualitatively) at low Et,, u,,,, can be considered to reflect ur( = ua). When the smaller rotational energy dependence of uhV is ignored it becomes possible to calculate the observations of ref. [14] for khv(TNIO) using the

reaction Ba + N,O + BaO* + Nz

010

0

0.30

0.20

O.LO

Et,i eV1 IlEt,) (arb.u.)

,

b

1.0

tA

0

a30

O.?O

0.10

Et,ltVl II lerb. u.)

0.01

LltVl 0.00

0.09 ,

I

2.0 -

-khv.&.Ifth=O

eVI

0 300

LOO

500

600

‘n2010 Fig. 5. In the upper panel (a), the extrapolated (- - - - - -) and ) cross sections ehv(n2 = 0) and interpolated (~ a,,(n, = 1) are plotted as a function of E,, for two threshold energies, Eth = 0 eV and E,, = 0.04 eV. In the middle panel (b), the Boltzmann translational energy distribution of reactants is shown for the lowest and highest N,O temperature: T N,O = 300 K + T,,f = 470 K and TNlo = 600 K + T,,, = 697 K (TBa = 1000 K). In the lowest panel (c). experimental points of the rate constant for chemiluminescence, k,, and the rate constant for barium removal k,, as measured by Wren and Menninger [14] are plotted as a function of TNzo and E,, (lower and upper horizontal scales). The solid and dashed lines are the calculated k,, [from eq. (7)] from our measurements for Et,, = 0 eV and E,,, = 0.04 eV, respectively. All the rate constants have been “normalixed” equal to 1 at TN+,.= 298 K.

H. Jalink et al. / The chemiluminescent reaction Ba + N,O + BaO * + N2

extrapolated uhv(n2 = 1, J = 2) and u,,“(n2 = 0) of fig. 2 as input. In fig. 5a we have displayed these cross sections together with the analytical extrapolation for E,, 4 0.08 eV according to the modified line-of-centers model, uhv= (E,, - Eth)*/E,, generalized by Levine and Bernstein [37] and with the graphical extrapolation of E,, > 0.22 eV following the trends measured in refs. [14,20]. Since a unique value for the threshold energy, El,,, does not follow from the extrapolation, two extreme (and possible) values of E,, have been selected for the calculation of khv(TNZO), Et,, = 0 eV and 0.04 eV. These values are in agreement with E,, = 0.01 eV fitted empirically in a recent model calculation

1381.

In fig. 5b we have plotted the Boltzmann energy distributions of reactant translation f&)

= 2(kT,,,)-3’2(Etr/n)1’2 xexp( -E,,/&r

(6)

),

for an effusive beam of Ba atoms (Tsa = loo0 K) colliding in a cell filled with N,O gas at its lowest (TN,0 = 300 K) and highest (TNzo = 600 K) temperatures [14]. The effective translational temperature of the collision process is simply given by [39]

The marginal contribution of the region of E,, > 0.25 eV in fig. 5b to f(E,,) shows immediately the insignificance of the behaviour of the extrapolated u,,“(E,,) at this region for the calculation of khp(TNzO). The rate constant khv(TNzO) is obtained by numerical integration as khY( TN*o) = /,*dE,, x

[

+

(1

f&r)

fnp=o%v(~2

-fn+l)%b*

(2E&))“* =

401

nicely confirmed by the calculation. The domination of the bending mode dependence of u,,” (see fig. 5a) explains why the data are reproduced equally well by the slopes of khu(TNzO) with Et,, = 0 eV (fig. 5c, -) or with Et,, = 0.04 eV (fig. 5c, - - -). The absence of an actual observation of a finite threshold energy and the slightly better fit of the solid curve to the data favor the more simple choice of Et,, = 0 eV, which was also taken by us elsewhere [40]. After combining the absolute value of k, at T = 300 K [14] with the best relative value of th:&antum yield k,,/k, = 9.3 f 3.4% [6] an absolute calibration for khv(TNzO = 300 K) = (1.37 f 0.58) X 10-l’ m3/s results. This value also calibrates the vertical uhv-axis as is indicated in fig. 5a. Assuming the quantum yield to be independent of E,,, the total reaction cross section us is obtained directly after multiplying u,,, with k,/k,, = l/0.093. At its maximum a (surprizingly) large value for ua is found, 32 A2 (130 A*) for n2 = 0 ( n2 = 1) at E,, = 0.14 eV (0.10 ev). When this calibration is done with Et,, = 0.04 eV instead of E,, = 0 eV, all absolute values of uh,, (ua) have to be multiplied by 1.43. In this procedure the fact that Et, was somewhat higher in ref. [6] than in ref. [14] was ignored because of the earlier mentioned insensitivity of k,,/k, at low Z,.

Experimental work [40] studying the effect of the orientation of N,O is in progress. An investigation of the polarization of the emission, found to be anisotropic and dependent on reactant orientation carried out in relation to E,,, is promising in also providing more data on the mechanism in the course of the intriguing and prolonged “case study” of the Ba + N,O reaction.

0)

=

I)].

(7)

In eq. (7) the practical assumption has been made that all vibrationally excited levels of N,O have the same reactivity as the dominantly occupied n2 = 1 state of the bending mode. As fig. 5c displays so gratifyingly (all rate constants have been “normalized” equal to unity at TNzo = 298 K) the experimental dependence of k,, on TN+ [14] is

Acknowledgement Stimulating communications with several researchers and especially with Professor R.B. Bernstein and Professor M. Menzinger are very much appreciated. We thank Professor A. Dymanus and Professor J. Reuss for support, J. Holtkamp, F. van Rijn and C. S&kens for technical advice and contributions and Professor D.B.

402

H. Jalink et al. / The chemiluminescent

McLay for critical remarks. This work is partially supported by Stichting voor Fundamenteel Onderzoek der Materie (FOM).

References Ill Ch. Ottinger and R.N. Zare, Chem. Phys. Letters 5 (1980) 243. 121C.R. Jones and H.P. Broida, J. Chem. Phys. 59 (1973) 6677. modern research, 131 R.W. Field, in: Molecular spectroscopy, Vol. 2., ed. K.N Rao (Academic Press, New York 1976) p. 261. 141 M. Menzinger, Advan. Chem. Phys. 42 (1980) 1; in: Gas phase chemiluminescence and chemi-ionization, ed. A. Fontijn (North-Holland, Amsterdam, 1985) p. 25. chemical kinetics, Vol. 151 J.C. Whitehead, in: Comprehensive 24., eds. C.H. Bamford and C.S.H. Tipper (Elsevier, Amsterdam, 1983) p. 357. J. Chem. Phys. 79 (1983) 161 J.W. Cox and P.J. Dagdigian, 5353. ]71 J.J. Reuther and H.B. Palmer, J. Chem. Phys. 77 (1982) 83. ]81 R.A. Gottscho, P.S. Weiss, R.W. Field and J.G. Pruett, J. Mol. Spectry. 82 (1980) 283. J. Brooke Koffend and R.W. Field, J. 191 R.A. Gottscho, Mol. Spectry. 82 (1980) 310. 1101 Y.C. Hsu and J.G. Pruett, J. Chem. Phys. 76 (1982) 5864. R. Behrens and R. Herm, J. 1111 T.P. Parr, A. Freedman, Chem. Phys. 67 (1977) 2181. 1121 R.D. Levine and R.B. Bernstein, Molecular reaction dynamics (Oxford Univ. Press, London, 1974). 1131 C.D. Jonah, R.N. Zare and Ch. Ottinger, J. Chem. Phys. 56 (1972) 263. ]141 D.J. Wren and M. Menzinger, Faraday Discussions Chem. Sot. 67 (1979) 97. 1151 C.R. Dickson, S.M. George and R.N. Zare, J. Chem. Phys. 67 (1977) 1024. 1161 A. Siegel and A. Schultz, Chem. Phys. 28 (1978) 265. H71 J.G. Pruett and R.N. Zare, J. Chem. Phys. 62 (1975) 2050. ]I81 S.E. Johnson, J. Chem. Phys. 56 (1972) 149.

reaction Ba + NJ0 --f BaO* + Nz Chem. Phys. Letters 25 1191 D.J. Wren and M. Menzinger, (1974) 378. 1201 D.J. Wren and M. Menzinger, J. Chem. Phys. 63 (1975) 4557. ]211 R.J. Buenker and S.D. Peyerimhoff, Chem. Rev. 74 (1974) 127; D.G. Hopper, A.C. Wahl, R.L.C. Wu and T.O. Tierman, J. Chem. Phys. 65 (1976) 5474, ]221 D. van den Ende and S. Stolte, Chem. Phys. 89 (1984) 121. ]231 D. van den Ende and S. Stolte, Chem. Phys. Letters 76 (1980) 13. 1241 H. Thuis, S. Stolte and J. Reuss, Chem. Phys. 43 (1979) 35. 1251 D. van den Ende and S. Stolte, Chem. Phys. 45 (1980) 55. [261 R.B. Bernstein, Comments At. Mol. Phys. 4 (1973) 43. 1271 J.M.L.J. Reinartz, W.L. Meerts and A. Dymanus, Chem. Phys. 31 (1978) 19. 1281 F. Harren, H. Jalink, K.H. Meiwes Broer and S. Stolte, in preparation. (291 H.C.W. Beyerinck and N.F. Verster, Physica C 111 (1981) 327. and A.L. Schawlow, Microwave spec1301 C.H. Townes troscopy (McGraw-Hill, New York, 1955); S.M. Freund, G. Duxbury, M. Riimheld, J.T. Tiedje and T. Oka, J. Mol. Spectry. 52 (1974) 38. Vibrational and rotational relaxation in 1311 J.D. Lambert, gases, ed. J.S. Rowlison (Clarendon Press, Oxford, 1977). 1321 G. Luijks, S. Stolte and J. Reuss, Chem. Phys. Letters 94 (1983) 48. [33] N. Sathyamurty, Chem. Rev. 83 (1983) 601. [34] M. Hofmeister, L. Potthast and H.J. Loesch, Chem. Phys. 78 (1983) 369. [35] D.R. Yarkoni, J. Chem. Phys. 78 (1983) 6763. [36] P.J. Chantry, J. Chem. Phys. 51 (1969) 3369. [37] R.D. Levine and R.B. Bernstein, Chem. Phys. Letters 105 (1984) 467. [38] A. Gonzalez Ureha and M. Menzinger, Chem. Phys. 99 (1985) 437. [39] P.J. Dagdigian, H.W. Cruze and R.N. Zare, J. Chem. Phys. 62 (1975) 1824. [40] H. Jalink, D.H. Parker, K.H. Meiwes Broer and S. Stolte, J. Phys. Chem. 90 (1986) 552.