J. Phys. Chem. 1995,99, 13620-13626
13620
Rotational Alignment in Supersonic Seeded Beams of Molecular Oxygen Vincenzo Aquilanti,* Daniela Ascenzi, David Cappelletti, and Fernando Pirani Dipartimento di Chimica dell’Universitiz, Via Eke di Sotto, 8 I-06123 Perugia, Italy Received: March 29, 1995; In Final Form: May 17, 1 9 9 9
The “seeding” phenomenon associated with the supersonic expansion of gaseous mixtures into a vacuum leads to cooling of the molecular degrees of freedom and also to alignment of the rotational angular momentum. 2 from various gaseous mixtures with rare Exploiting magnetic analysis of supersonic seeded beams of 0 gases and from air near atmospheric pressure, we demonstrate that the phenomenon naturally leads to exclusive population of the ground rovibrational triplet state and also to strong rotational alignment. The observation is also made that the alignment depends on the final speed, so that within the same beam, molecules traveling faster show much greater alignment than slow ones. The dependence of the effect on the gas carrier and on pressure and composition of the mixtures has also been investigated.
served for other alkali metal dimersI4-l6 in the presence of free atoms. Alignment had also been studied for beams of molecular In this paper, we study the properties of molecular beams of More recently Pullman, Friedrich, and Herscha paramagnetic species, 0 2 , produced in supersonic seeded bachI8-*O have extended the study on supersonic beams of 12, expansions and exploit magnetic analysis to obtain information demonstrating the alignment to be facile by seeding the on the distribution of rotational levels. It is found-see ref 1 molecules with various gas carriers. They extensively invesfor a preliminary report-that conditions can easily be found tigated the phenomenon as a function of the nozzle stagnation for prominent cooling and alignment to occur and that the pressure: two distinct mechanisms were proposed to account alignment is strongly dependent on the final molecular velocities. for the dependence of the alignment on the experimental Elsewhere2a systematic investigation is reported on molecular conditions, and a model was developed to quantitativelyaccount oxygen beams in a lower stagnation pressure range, i.e. from for both effects (see also ref 21). All the observations of near effusive to moderately supersonic expansion (Mach number alignment effects reported so far involved probing the rotational I8). Under these conditions, moderate cooling was observed states by optical techniques. It appears that the availability of and the magnetic analysis indicated a rotational distribution suitable laser lines has limited the scope of these studies, which corresponding to an effective temperature. have often been restricted to some particular high rotational We study here a pressure range sufficiently high that, as has states of moderately cold beams with broad rotational distribubeen amply dem~nstrated,~-~ supersonic expansions involving tions. 0 2 may lead to very low rotational temperatures. In particular, Some evidence for alignment in the J = 1 rotational level of because of the large spacings among the rotational levels, the CO from high-pressure jets was reported in ref 22. A recent exclusive population of the ground K = 1 rotational state can extensive investigation of alignment in supersonic seeded beams be easily achieved (only odd K values are allowed for the 160t60 of COz has been carried out. The effect of seeded expansion molecules). characteristics (gas carrier, stagnation pressure, ...) has been The collisional alignment of molecules in a nozzle expansion For molecular ions reported for low rotational states (J 5 under supersonic conditions, qualitatively anticipated long ago’ (N2+ drifted in helium), see ref 24. in connection with a transport phenomenon, the SenftlebenAll the previous investigations, except a recent one on 1225 Beenakker effect,8 shows features which are similar to other which exhibits a slight dependence of rotational polarization alignment procedures commonly used in scattering or photoas a function of the distance transverse to the propagation fragmentation studies and may perhaps be of more general use. direction, focused on alignment properties of the full beam We mention (i) the focusing in electric fields through the Stark emerging out of the expansion. effect, either second order for linear moleculesg or first order In our experiments, a magnetic deflection technique and for symmetric top moleculesI0 (the latter stronger than the velocity selection are used to analyze seeded beams of oxygen former); (ii) the use of polarized absorption (limited to optically molecules from various gaseous mixtures. It has been found favorable transitions in the molecular manifold);” and (iii) the that the supersonic expansions of gas mixtures containing more recent bruteforceI2 techniques, which use strong electrical oxygen molecules with an excess of lighter carrier gas-such or magnetic fields and are limited to molecules with electric or as H2,He, Ne, N2 (but also Ar)-readily lead to the prominent magnetic dipole moments. features usually attributed to the seeding effect: acceleration Experimental evidence for collisional alignment in molecular and focusing of the heavier component, as well as its extreme beams under supersonic conditions was first noticed for I2 by cooling (Le. exclusive population of the ground rotovibrational Steinfeld and Korving (as reported in ref 13) by a laser-induced triplet state of 02). Strong rotational alignment also occurs: fluorescence technique; in 1975 Sinha et al.I3found a significant the important observation is made that such an alignment alignment of Na2 in supersonic beams of sodium atoms depends on the final speed-specifically it is found that, within containing dimer and interpreted the results in terms of a “hard the same beam, molecules traveling faster show much greater collisions” model. Later similar prominent effects were obalignment than slow ones. On the one hand, this dependence on final speed provides new insight on the collisional mechanism that induces the alignment. On the other hand, the possibility Abstract published in Advance ACS Abstracrs, July 15, 1995.
I. Introduction
@
0022-365419512099- 13620$09.00/0
0 1995 American Chemical Society
Supersonic Seeded Beams of Molecular Oxygen 110 cm
: skimmers
12 cm F
2,:
I
,
38 cm
32 cm ’ , I
gas inlet
molecular beam source
velocity selector
collimating slits
quadrupole mass filter
Figure 1. Sketch of the apparatus (not to scale) used in the present experiments. The diameters of the nozzle and first skimmer are 0.1 and 1.2 mm, respectively. The diameters of collimating slits are 0.7 mm for SI and 1.2 mm for S2. The acceptance angle to the detector is 2.7 x radians.
opens up of preparing beams of molecules with controlled alignment to study their collisions and to gather information on the anisotropy of intermolecular forces. For the latter aspect, see the preliminary report on the 02-Xe system.26 In the next section, we describe our apparatus and general properties of seeded supersonic expansions. In section 111, the procedure for extracting the degree of alignment from the magnetic analysis is outlined. Section IV is devoted to the presentation of results and to their analysis. A discussion and conclusions follow in section V.
11. Supersonic Seeding Beams of Molecular Oxygen The molecular beam apparatus used in the present experiments is the same as that previously employed for the magnetic analysis and for scattering studies of open-shell atoms (N, 0, F, C1)27-35 and of metastable nitrogen molecules.36 The characteristics of the apparatus which are of relevance to the present paper-in particular those associated with the SternGerlach magnetic deflection experiments, such as the geometrical features of the slits defining the beam profile and the acceptance angle to the detector (a mass spectrometer)-are detailed in Figure 1. With respect to the previous studies quoted above, an improved pumping system allows us to maintain a vacuum as low as Torr between the nozzle and the first skimmer and 10-5 Torr between the first and second skimmer-at least as long as the stagnation pressure PO in the source does not exceed 500 Torr for H2 and -900 Torr for the other carrier gases. In the present experiments, mixtures of oxygen molecules diluted in various gases enter through a sharp-edged nozzle of diameter -0.1 mm in the first vacuum chamber. It is in this chamber, between the nozzle and the first skimmer (of diameter -1.2 mm and conical angle -90°), that the oxygen molecules are translationally accelerated, rotationally cooled, and focused along the beam direction by the seeding phenomenon. The nozzle-skimmer distance is -10 mm and can be varied until the beam has maximum intensity and the signal increases approximately linearly with stagnation pressure-this linear dependence is usually taken as evidence of a “well behaved” supersonic expansion. For the gaseous mixtures used in these experiments, the supersonic characteristics of the seeded beams, such as the translational temperatures and Mach numbers,37 are obtained from the final velocity distributions by a high-resolution (5% fwhm) mechanical velocity selector. Typically an increase in speed ratio is accompanied by a relaxation in translational temperature and a cooling of the rotational degree of freedom. Extensive previous studies of both pure and seeded 0 2 beam^^-^ established a correlation between final rotational distributions and the translational temperature. In our seeded beams the
-
J. Phys. Chem., Vol. 99, No. 37, 1995 13621 relevant translational temperatures are found to be so low (between 2 and 7 K) that in the analysis only the ground K = 1 rotational state can be conceivably populated (the next level, K = 3, lies -20 K higher). A systematic investigation of the pressure dependence of the final translational temperature shows that down to -100 Torr the general trends appear to be qualitatively the same as those at higher stagnation pressure, although progressively attenuated; while at lower pressures the cooling is less extreme, and K = 3 and higher rotational levels can also be populated. The molecular beam source temperature is kept at TO 290 K by flowing water. In some experiments, liquid air cooling leads to To 230 K, with a negligible change in final translational temperatures for the lighter gas carriers, while in the case of beams seeded in Ar we got a broader velocity distribution and a larger population of higher internal degrees of freedom, presumably because of the heat release due to formation of Ar, (with n 2 2) clusters.
-
-
111. Distribution of the Spin-Rotational Sublevels from Magnetic Analysis As anticipated, the only rotational state appreciably populated after the expansion is the ground state K = 1 of the oxygen molecules. The 0 2 molecule belongs to Hund’s case (b): electronic spin S (with S = 1)-ultimately responsible of molecular paramagnetism-adds to the rotational angular momentum K to give three possible values for the total angular momentum J, according to the sequence J = 0, 2, and 1. The values of the magnetic fields used in these experiments (the average interaction energy of the molecules is on the order of K, Le. 2 orders of magnitude less than the splittings in the multiplet; see Figure 2) are not sufficiently strong to decouple K and S, so that J and mJ (where mJ is the projection of J along the magnetic field direction) are conserved as “good” quantum numbers. The magnetic field dependence of the Zeeman levels of the ground triplet state is reported in the upper part of Figure 2 and has been calculated as described in detail in the previous paper2 (for relevant literature, see ref 38). They are plotted up to magnetic field strengths higher than those used here (=10 kG) to show the onset of the Paschen-Bach effect, which occurs at fields larger than 20 kG. Effective magnetic moments p = - & W B are shown in the lower part of Figure 2-the sign of p being irrelevant for total deflection measurements. From Ipl and from the geometrical features of our apparatus, we can compute how molecules with given J, m ~and , velocity u are deflected at a given magnetic field strength, and thus their transmission factors to the detector s m J ( u).2732 Our measurables are beam intensities I and IO with and without the applied field, and the working equation for the beam transmittance I110 is
where w(JmJ)is the relative population of the JmJ sublevel. The beam transmittances are decreasing functions of the magnetic field, but they show different slopes corresponding to the selective deflection of different magnetic sublevels: at low field values, levels having larger p are deflected first while the ones presenting smaller p need a stronger magnetic field for the deflection. By comparison with the experimental data, information is obtained on the populations w(JmJ). Angular momentum algebra allows the computation, from these populations, of the relative weights wm for projections m of the rotational angular
Aquilanti et al.
13622 J. Phys. Chem., Vol. 99, No. 37, 1995
0.8
12
z
10
.-r
->
8 6
x
4 2
i2P
0.4
0.2
0
E o
6
8
~z,,,,
Figure 3. Transmission factors for sublevels JmJ calculated at the velocity v = 0.77 km * s-l. They are grouped in four families
-2
according to the magnetic moment values (see text).
-4
2.0
2
4
Magnetic field B , kG
Lu
0 c
2
-1
weights for M = 0 and 1 (which can be either +1 or -1 as a consequence of the axial symmetry of the expansion process). We define the degree of alignment p o l a r i ~ a t i o nas~ ~ ~ ~ ~
(3.4)
1.0
a, C
2m
0
0.0
L
c
0
m
.. -1.0
2
+1
-2.0 0
20 40 Magnetic field B , kG
60
Figure 2. Magnetic field dependence of Zeeman energy levels (in kelvin units, 1 K = 8.314 J * mol-') and magnetic moments (in Bohr magneton units, 1 p~ = 9.27 x J * G-I) for the rotational K = 1 level for the 02 molecule. Notice that the J = 0 level at zero magnetic field is taken as the origin of the energy scale.
momentum K = 1 along the magnetic field direction:
For an unpolarized beam, WO= WI = 0.33 and 4?= 0. In general, @'varies between 1 and -1, but in the following we will only encounter, within the limit of experimental error, 4? 2 0, corresponding to WdWl L 1. The ratio WdWl will be useful for comparison with previous work (see section V), although in our case the extreme quantum conditions make the assumption of a continuous angular distribution of the rotational angular momenta meaningless. However the difference WO WI represents the quadrupole m ~ m e n t of ~ ~the ~ ~distribution l and is the analog of the coefficient of the second term in a classical expansion in Legendre polynomials (the only other moment is the monopole term, WOf 2W1, which is equal to 1 according to our definitions). The nonstatistical behavior found for the population of the JmJ states is a manifestation of alignment effects on 02 molecules in supersonic seeded beams. It is important to remark that there are some contributions to eq 3.1 not distinguishable by the magnetic deflection technique, which only gives the sums w(2,kl) w(1,fl) and w(2,O) w(0,O) (see Figure 3): this does not affect our analysis in the former case, since the two mJ = f l states give exactly the same contribution to the relative populations wm because of the Clebsch-Gordan coefficients in eq 3.2. In the second case, the indistinguishability of the two mJ = 0 states introduces an uncertainty on w,; it has been estimated that such an uncertainty is lower than the overall experimental one, which is on the order of f5%.
+
where (....I..) are Clebsch-Gordan coefficients. From the previous treatment we can obtain relevant information on the sublevel distribution and thus on the degree of alignment of molecules in the beam. During the supersonic expansion, the proper quantization axis for the description of collisions is the molecular beam velocity vector v. This means that, instead of m, the physically more interesting quantities are the rotational helicities M , which can be related unambiguously to possible alignment effects in the molecular beam: here the helicity quantum number M is defined as the absolute value of the projection of K along the velocity vector v (see later and Figure 8). Since the magnetic field gradients and velocity directions are orthogonal, a rotation by ni2 described by the elements of the appropriate Wigner rotation matrix39relates the measurable weights w m to the weights WM.
(3.3) All weights defined in this paper sum up to unity. The previous equation can easily be inverted to recover the relative
+
IV. Experimental Results and Analysis Typical results for the beam transmittance measured as a function of the applied magnetic field strength are reported in Figure 4. The case refers to beams of 0 2 seeded in He (2.5%) obtained with three values of the stagnation pressure PO in the source (100, 300, and 800 Torr). The transmittance measurements are shown for three different velocities u within each beam. Similar results, as a function of stagnation pressure and beam velocity, have been obtained for all the studied mixtures. Along the lines of ref 2 calculation of Ill0 has been done assuming a Boltzmann distribution for the relative weights w ( h J )corresponding to a spin-rotational temperature T,, equal to the translational temperature Ti, as suggested also from refs 3 and 4. This attempt fails to reproduce the experimental data although the agreement gets better at lower pressure (see the
J. Phys. Chem., Vol. 99, No. 37, 1995 13623
Supersonic Seeded Beams of Molecular Oxygen
0,(2.5%) seeded in He
I
I 2
4
6
2
8
4
6
8
2
4
6
8
Magnetic field B , kG
Figure 4. Transmittance Itlo of 02 supersonic beams seeded in He (2.5% in 0 2 ) at source temperature TO = 290 K and pressure PO = 800,300, and 100 Torr, measured as a function of B at different beam velocities u. The dashed lines are calculated assuming a statistical distribution for the relative weights w(Jm1) at a spin-rotation temperature T,, equal to the translational temperature Tf(see Table 2); the solid lines are the best fit calculations assuming a nonstatistical distribution of the Jmj sublevels of the K = 1 rotational level; and the dotted lines are calculated assuming a nonstatistical distribution according to the relative weights w(Jml), as appropriate for the higher velocity v = 1.73 k m * s - ’ (see Table 1).
.
-
0
0.8
s
.E 0.6
Ec
2 0.4
c
E
8
m
0.2
1 0
2
4
6
8
1
I 0
Magnetic field B , kG
Figure 5. Transmittance Ill0 of
0 2 supersonic beams seeded in He (2.5% in 0 2 ) at a source pressure PO = 800, measured as a function of B at two different beam velocities u = 1.73 and 1.35 km a s-I. The solid lines represent best fit calculations assuming nonstatistical distributions of the JmJ states. Dashed and dotted lines are calculations assuming a Boltzmann distribution at different spin-rotational temperatures.
dashed lines in all the panels of Figure 4). No satisfactory fit of the experimental data could be obtained by raising the assumed T,, above Tf, showing that the assumption of a statistical distribution of spin-rotational levels is not valid for pressures higher than 100 Torr. Two typical results are shown in Figure 5 for the case of a beam of 0 2 2.5% in He (source pressure PO 800 Torr) at the velocities 1.73 and 1.35 km-s-’ (corresponding respectively to the ‘head’ and ‘tail’ of the velocity distribution of the beam, which peaks at v = 1.60 km s-I).
-
The inadequacy of the statistical assumption appears larger at the higher velocity, and therefore a nonstatistical distribution of the spin-rotational substates must be assumed for the levels of the oxygen molecules as emerging from these expansions. To obtain information on the relative population from the experiments at PO 2 100 Torr, we note again that at these pressures our measured Tfvalues are so low compared to the 0 2 rotational splitting (see Figure 2) that only the rotational K = 1 ground state can conceivably be populated under these conditions. In the investigated range of magnetic field strengths (B 5 10 kG),there are four well separated groups of sublevels associated with the K = 1 rotational level; the corresponding transmission factors, GmJ(v)’s(see eq 3.1), of the four groups =. %*I, u 7 0 , and 550 = .5&,, as can be seen are u57L2, from Figure 3 for a particular beam velocity v. This facilitates the analysis needed to obtain proper combinations of relative populations w(JmJ)of substates from fits of measured beam transmittance as a function of the magnetic field. So, in the example of Figure 3, the observed deflection at the velocity investigated is mainly due to the states with mJ = &2 for B I 1 kG,while states with mJ = 0 are only deflected for B 1 3
kG. To fit the experimental data (Ill0 versus E ) , we carried out a linear regression on the weights of the four different groups of sublevels; estimates of the uncertainties have been obtained by modifying the best fit weights within the limit of the experimental errors. For the case of beams seeded in He the results of these calculations are shown in Figures 4 and 5 as solid lines. In this way it has been possible to establish that the main deviation from statistical weights consists in an increase of the populations of both the 2 iz 2 and 1 0 sublevels. This effect has been observed for all the studied systems: it is more pronounced for H2 and He as seeding gases and decreases in going from Ne to Ar. It also decreases, in all cases, as the source pressure is lowered. A most prominent feature of the observed nonstatistical behavior is its dependence on velocity within the same molecular beam emerging out of the supersonic seeded expansion. This feature is evident when the calculation made with the nonstatistical population obtained at the higher velocity is compared in Figure 4 (as dotted lines) with the data measured at the two lower velocities, showing considerable deviations. Results of the quantitative determination of the weights w(JmJ),obtained from this analysis for the case of He-seeded beams, are shown in Table 1 and compared with the statistical values expected assuming a spin-rotational temperature T,, = Tf.These results show some minor deviations from statistical results in the distribution over the J states of the triplet. The relative weights get close to the statistical ones only as the stagnation pressure PO is lowered: this has been demonstrated by further experiments* carried out with a partially supersonic beam at about PO = 60 and 30 Torr, using the same source conditions (temperature and nozzle diameter) for the production of supersonic beams. A systematic study of the dependence of the degree of alignment polarization on the source pressure POhas been done specifically for the case of beams seeded in He, although general trends have been controlled for other mixtures as well. In general (see Figure 6) gincreases with pressure, up to -800 Torr, which is the maximum pressure used for nearly all mixtures in our experiments. The pressure dependence has been found to be stronger for those molecules which, within each beam, have higher speeds, while, for velocities lower than about 10% of v,,, (see Table 2), 4?is practically negligible at all pressures investigated.
Aquilanti et al.
13624 J. Phys. Chem., Vol. 99, No. 37, 1995
TABLE 1: Weights of the Magnetic Sublevels Associated with the Rotational Level K = 1 of 0 2 in Supersonic Beams Seeded in He (2.5% of 0 2 ) at Different Molecular Velocities Po= 8 W Po = 3006 Po = lOOb W(JmJ)a u = 1.73' u = 1.6W u = 1.35' Ts,=1.8d u = 1.73' T,,= 3d u = 1.73' T,,=7.0d w(2,f2) 0.50 0.17 0.05 (0.18) 0.42 (0.22) 0.25 (0.22) 0.38 0.40 (0.22) 0.16 (0.30) 0.30 (0.36) w ( 2 , f l ) w(1,fl) 0.10 0.10 (0.43) 0.07 (0.29) 0.19 0.35 (0.58) w(2.0) + W(0,O) 0.15 0.32 (0.04) 0.38 (0.07) 0.26 0.20 (0.02) 0.25 w( 1,O)
+
a Relative weights of the magnetic sublevels JmJ (see section In). Source stagnation pressure (Torr). Molecular velocity (km-s-I). In parentheses are reported the statistical weights corresponding to spin-rotational temperatures T,, as deduced from fits of the velocity distributions (see text).
TABLE 2: Values of the Degree of Alignment Polarization and of the Alignment Ratio Observed for Various Gas Carriers and at Selected Molecular Velocities
A
g 0.8
seeding gas"
0) 0)
0
HZ
C 0.6
T j b(K)
3.0
.-0 m .-N 4-
-50 0.4
He
P
1.8
e
6 0.2
5 .-
2.28r 2.44 1.35 1.52 I .6@
0)
7
tc (kms-I) 2.11
0.0
~~
0
200
~
400
600
800
1000
Total stagnation pressure Po, torr
Figure 6. Pressure dependence of the degree of polarization Y(as defined in the text) measured for different beams at three molecular velocities (lower than, equal to, and higher than umaX). Curves connecting experimental points are visual aids to exhibit the pressure dependence. The one for u = umaxfollows the empirical formula JP= 0.0045Pd(l + O.OlPo), where PO IS in Torr, see refs 19 and 20 and section V. The unexpected dependence of the rotational alignment on the speeds of molecules within each beam is illustrated in Figure 7 for three oxygen beams (respectively seeded in He, Ne, and a 1:l mixture of the two at a total pressure of 800 Torr). Values of &?and of the ratio WdWl are reported in Table 2 for the same mixtures at different velocities. We record that, although less spectacular, the effects also occur in air: after expansion of a 20% mixture of 0 2 in NZ at -1 atm of pressure, oxygen molecules are found to be accelerated from thermal to supersonic, with a final translational temperature Tfof -7.0 K (peak velocities umaxfrom 0.48 to 0.77 km. s-I), and polarization crises from zero (WdWl = 1) at the peak speed and to to 0.26 f 0.10 (Le. WdWl = 1.7:;:;) 0.50 f 0.10 (Le. WdWl 9 3.O:b:f) for molecules traveling in front of the beam of 0.85 km s- . We also carried out measurements as a function of the composition of the mixtures. Results are obtained for 1%, 2.5%, and 5% 0 2 in H2 at a total pressure of 500 Torr and for 2.5% and 5% 0 2 in Ne at a total pressure of 800 Torr, but we found no significant differences in all cases in changing the composition of the mixtures within the range of a few percent 0 2 . V. Discussion Although the main unexpected feature emerging from this work has been the observation of the dependence of the rotational alignment on the molecular speed, we first discuss our results with reference to the effect on alignment of the nature of the seeding gas carrier and of the stagnation pressure in the source. All our observations consistently show that alignment is larger for the lighter carrier gases. This is in agreement with a large
He:Ne = 1:l
2.8
1.68 1.73 1.79 1.08 1.14f 1.20 1.25 0.71 0.74 0.77f 0.81 0.83
_'pd
0.06 & 0.06 0.40 i 0. IO 0.75 i 0.10 0.00 i 0.05 0.23 & 0.05
0.40 f 0.10 0.59 i0.10 0.74 f 0.08 0.82 f 0.07 0.19 f 0.06 0.32 i.0.10 0.54 f 0.10 0.73 +C 0.10
Wdwi' 1.1 i 0.1 2.3:;: t5.3 7.0-2.3 1.0 +C 0.1 1.6 f 0.2 2.3::
3.9:;:; 6.7!:,: 10.45::; 1.5 f 0.2 +0.5
1.9-0.4 3.4:::; 6.4:::; Ne 3.0 0.00 5 0.05 1.0 i 0.1 '0.2 0.18 f 0.05 1.4-0.1 0.30 i 0.10 1.9 +C 0.4 0.47 f 0.08 2.8:::; 0.57 +C 0.09 3.71;:; -1.6 0.62 +C 0.09 0.85 4.3- I .O The composition of all the mixtures is 2.5% 02, and the total source stagnation pressure is 500 Torr for H2 and 800 Torr for all other seeding gases. Translational temperature, as obtained from the velocity distributions. Molecular velocity. Degree of alignment polarization, see section 111. e Alignment ratio, see section 111. f Peak velocity umax. amount of i n f ~ r m a t i o n ' ~ ~that ' * -all ~ ~properties associated with the seeding phenomenon-acceleration and focusing in the forward direction and cooling of the internal degrees of freedom of the heavier component-appear to increase with the so-called 'velocity slip' factor. Figure 7 illustrates that alignment effects indeed are stronger for He than for Ne and that a mixture of the two leads to intermediate behavior. A comparison with previous measurements for other systems in other laboratories, which have provided information on properties of the 'full' beam, requires that we integrate our results obtained at selected speeds over the velocity distributions (it turns out that this averaging in most cases is very close to the alignment ratio as measured at peak velocity). Typical numbers, for 0 2 mixtures at 2.5%, are Wn/W, = 2.3 in H2 at 500 Torr, 2.3 in He, 1.9 in a 1:l He-Ne mixture, and 1.8 in Ne-the latter three cases for a total pressure of 800 Torr. These average WdWl values can be considered (see section 111) the quantum counterparts of the classical anisotropy ratio between populations for perpendicular and parallel alignment of rotational angular momentum. The present numbers are then found to be close to e.g. those reported for Na2,I3Ir,'8-20 and C02.23 The main mechanism to explain the observed pressure increase is discussed as "bulk alignment" in refs 18-21 (a second mechanism-anisotropic rotational cooling, responsible
J. Phys. Chem., Vol. 99, No. 37, 1995 13625
Supersonic Seeded Beams of Molecular Oxygen
o2 2.5% -
0 2 2.5% in He:Ne=l:1
inNe
O2 2.5% in He
0.0 0.6
0.8
1.0 1.2 1.4 Velocity , km s-'
1.6
(D
d
1.8
Figure 7. In this figure, where typical results are shown for seeded beams of oxygen molecules in (from left to right) Ne, a He-Ne mixture, and He at a total pressure of 800 Torr, open dots are relative beam intensites and black squares are alignment polarization fractions Q(as defined in the text). The continuous curves are best fit velocity distributions obtained using the formulas in ref 37. The dotted curves are a visual aid to describe the velocity dependence of the alignment polarization fractions obtained from the w, defined in section 111. The observed positive values of g a r e an indication that WO> Wl, Le. that the molecules aligned along the direction of flight prevail in front of the beam, while the slower ones are more randomly distributed.
6 @+
I
I1
I11
Figure 8. Schematic blowup of the supersonic molecular beam source (upper part). Molecules emerging from gaseous mixtures through the nozzle are accelerated, focused in the forward direction, rotationally cooled, and aligned in the encircled region immediately outside of the nozzle. Here, collisions with the seeding gas produce the sequence of events illustrated in the lower part of the figure and detailed in section V.
for an eventual decrease of alignment at high pressures-is not operative for the rotational ground state under focus here). Results and empirical fits according to the formula @= (a$o)/ (1 alPo) (analogous to the one given in ref 19) are shown in Figure 6, selecting three velocities for the same beam. The high alignment measured for molecules traveling faster (i.e. in front of the beam) has to be contrasted with the fact that practically no polarization is observed for molecules traveling in the tail. The u u, case can be taken as representative of the behavior of the full beam (see above), and as such the corresponding fitting parameters can be of use for comparison with previous work. To qualitatively understand the strong velocity dependence of the observed effects, consider Figure 8, where a classical view of acceleration, rotational cooling, and alignment in expansions of diatomic molecules seeded in a lighter gas is presented. A diatomic molecule (as in I in the figure) rotating in a plane randomly oriented with respect to the flight direction v expands into vacuum at sufficiently high pressure that it
+
experiences several collisions (the number of collisions can be estimated to be in the range lo2- IO3 under our conditions) with faster atoms of the lighter seeding gas. During a collision, the intermolecular potential is strong enough to decouple K and S, so K and M can be considered as good quantum numbers. Three ranges of impact parameters can be found. Collisions with impact parameters b on the order of molecular dimensions or smaller (e.g.by atoms 3 and 4 in the figure) lead to acceleration (i.e. exchange of linear momentum and increase in v) while those with intermediate b (as by atoms 2 and 5 ) may also bend the rotational plane, the net average effect being a decrease in the helicities M (this is a bottleneck that requires several collisions); those with large b (as by atoms 1 and 6) will only elastically deflect the molecules, with a net average effect of focusing them in the forward direction. After a great number of collisions, most molecules (as in 11) will have low helicity, i.e. will fly edge-on, offering a target to collisional removal of rotational angular momentum: those which have suffered a sufficiently high number of collisions will be as in 111; i.e. fast, very slowly rotating, and with such a low helicity as to be mainly aligned along v [as can be seen by imagining the (now small) vector K distributed uniformly on a plane orthogonal to VI. In a quantum mechanical picture, which is more appropriate to the description of the present results, the classical illustration of Figure 8 modifies only slightly: to low, intermediate, and large impact parameters, the correspondence is with the orbital angular momentum and with the collisions falling into cases (y), (a), and (E), respectively (we are using a classification reminiscent of Hund's cases of s p e c t r o ~ c o p y ~ ~ -For ~ ) .room temperature 0 2 , rotational states are distributed over a range of K values (most probable being K = 9) and random helicities M: they will be collisionally deactivated to lower K states only when the helicity is sufficiently low. A substantial variation in the helicity quantum number is a very slow process which requires many collisions: in fact M is a "good" quantum number in case (y), and its decrease requires case (6) (Le. intermediate angular momentum) collisions. The cooling and alignment of molecular rotations are the results of several collisions with the seed gas and depend on the cross-sectional area that a particular rotational state presents perpendicular to the flow direction. It is therefore reasonable to attribute the preferential alignment of molecules emerging with higher speed to the fact that they are those which have experienced a larger number of accelerating and focusing collisions at short and intermediate impact parameters. It should be noted that the measured alignment might be a lower limit to the true collisional one emerging out of the supersonic expansion. Recoupling of K and S to give J occurs (as estimated from relative precession times) in -lo-" s, leading to a natural depolarization e f f e ~ e ~ -in~the ' -lo-* which typically elapse between two successive collisions. The flight time from the skimmer to the magnetic analyzer is on the order of s, so the magnetic analyzer samples the polarization downstream, where the molecular beam can be exploited for scattering or photofragmentation studies. Indeed, the effects discussed in this paper stimulate the quantum mechanical extension of previous classical models. They also prove that collisional alignment in seeded expansions provides a flexible and powerful tool to produce stereodirected states4 to study steric effects in collisions of molecules in gases and on surfaces. By varying the nature and partial pressure of mixtures, beams can be generated where important molecules such as oxygen fly at a given speed with an alignment that can be varied in a controlled way from random to the pure edge-on mode (we continue to use a classical analogy). This allows the realization
13626 J. Phys. Chem., Vol. 99, No. 37, 1995 of collisional configurations for which an interesting phenomenology and nomenclature is already being introduced: the ‘broadside’ or ‘edge-on’ molecules will give ‘helicopter’ or ‘cartwheel’ states impinging on surface^^*-^^ and ‘airplane’ or ‘pinwheel’ states colliding on other molecules.44 Experiments of the latter type will be described elsewhere (for the system 02-Xe, see ref 26): from ‘‘glory” scattering, information on the anisotropy of intermolecular forces is obtained. It has also been shown that scattering can be an effective probe of alignment for diatomic molecules (such as for example N2) for which we may suspect a velocity dependence of the alignment in gaseous expansions similar to that demonstrated here for oxygen molecules but for which a direct measurement by the present technique is barred because of lack of magnetic moment. Acknowledgment. We thank Dr. Simona Cavalli for helpful discussions. This work is supported by the Italian Consiglio Nazionale delle Ricerche and Minister0 per 1’Universith and by European Union contracts. References and Notes (1) Aquilanti, V.; Ascenzi, D.; Cappelletti, D.; Pirani, F. Nature 1994, 371, 399. (2) Aquilanti, V.; Ascenzi, D.; Cappelletti, D.; Pirani, F. lnt. J . Mass Spectrom. Ion Phys., in press. (3) Amirav, A.; Even, U.; Jortner, J.; Kleinman, L. Chem. Phys. 1980, 73, 4217. (4) Mettes, J.; Heijmen, B.; Reuss, J.; Lain*, D. C. Chem. Phys. 1984, 87, 1. (5) Kuebler, N. A,; Robin, M. B.; Yang, J. J.; Gedanken, A,; Hemck, D. R. Phys. Rev. A 1988, 38, 737. (6) Matsumoto, T.; Kuwata, K. Chem. Phys. Lett. 1990, 171, 314. (7) Gorter, C. J. Naturwissenschafren 1938, 26, 140. (8) Beenakker, J. J. M.; McCourt, F. R. Annu. Rev. Phys. Chem. 1970, 21, 47 and references therein. (9) Toennies, J. P. Faraday Discuss. Chem. Soc. 1962, 33, 96. Bennewitz, H. G.; Kramer, K. H.; Paul, W.; Toennies, J. P. Z. Phys. 1964, 84, 177. Luben, A.; Rotzoll, G.; Giinther, F. J . Chem. Phys. 1978, 69, 5174. (10) Kramer, K. H.; Bemstein, R. B. J . Chem. Phys. 1964, 40, 200. Parker, D. H.; Bemstein, R. B. Annu. Rev. Phys. Chem. 1989, 40, 561. Brooks, P. R.; Jones, E. M. J. Chem. Phys. 1966,45, 3449. Stolte, S. Ber. Bunsen-Ges. Phys. Chem. 1982,86,413. Kasai, T.; Fukawa, T.; Matsunami, T.; Che. D.-C.; Ohashi, K.; Fukunishi, Y.; Ohoyama, H.; Kuwata, K. Rev. Sci. lnstrum. 1993, 64, 1150. (1 1) Kamy, Z.; Estler, R. C.; Zare, R. N. J . Chem. Phys. 1978,69,5 199. Treffers, M. A.; Korving, J. Chem. Phys. Lett. 1983, 97, 342. Hoffmeister, M.; Schleysing, R.; Loesch, H. J. J. Phys. Chem. 1987, 91, 5441. Mattheus, A.; Fischer, A.; Ziegler, G.; Gottwald, E.; Bergmann, K. Phys. Rev. Lett. 1986,56,712. Hefter, U.; Ziegler, G.; Mattheus, A,; Fischer, A.; Bergmann, K. J . Chem. Phys. 1986, 85, 286. McCaffery, A. J.; Reid, K. L.; Whitaker, B. J. Phys. Rev. Lett. 1988, 61, 2085. (12) Loesch, H. J.; Remscheid, A. J . Chem. Phys. 1990, 93, 4779. Friedrich, B.; Herschbach, D. R. Nature 1991, 353, 412. Friedrich, B.; Herschbach. D. R. Z. Phvs. D 1991. 18. 153. Friedrich. B.: Herschbach. D. R. Z. Phys. D 1992, 24, 25. (13) Sinha, M. P.; Caldwell, C. D.; Zare, R. N. J. Chem. Phys. 1975, 61, 491.
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