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The Journal of Chemical Physics

Facile alignment of molecular rotation in supersonic beams

David P. Pullman, Břetislav Friedrich, Dudley R. Herschbach

Published Sep 1, 1990• 80 citations

Abstract

We have obtained substantial alignment of I2(X 1Σ+g;v″=0;J″=13,15) seeded in supersonic beams of light carrier gases. Laser-induced fluorescence and a variant of the magnetic precession technique were used to measure the ratio n⊥/n∥ of molecules with the rotational angular momentum vector J perpendicular to the beam axis z to those with J parallel (or antiparallel) to z. As the nozzle stagnation pressure P0 is increased, this ratio increases markedly, reaches a maximum, and then decreases steadily. At the maximum, n⊥/n∥=1.6, 1.7, and 2.2, respectively, for He, D2, and H2 as the carrier gases; this occurs at different pressures of the order of 103 Torr for nozzle diameter d=50 μm and temperature T0=315 K and corresponds to nearly the same rotational temperatures of about 6–8 K. We compare the observed dependence of alignment on P0⋅d with a J-dependent model that invokes two mechanisms for alignment, macroscopic gas transport, and anisotropic rotational cooling. The transport processes involve reorientation of J and give rise to alignment with n⊥/n∥>1; this dominates the initial increase with P0⋅d up to the maxima. The anisotropic cooling processes do not in our model involve reorientation of J but are fostered by the anisotropy of the rotational relaxation cross section; the alignment arises from different Boltzmann weights for molecules with J⊥z and J∥z due to their slightly different rotational temperatures (about 5%). At high P0⋅d the net alignment is dominated by the anisotropic cooling term. At the correspondingly low rotational temperatures, this term counteracts the effect of gaseous transport, so the net alignment can reverse. Indeed, at high P0⋅d we do observe n⊥/n∥<1. For a higher rotational state (J″=39,41) we find lower alignment that peaks at a higher rotational temperature (about 27 K), as predicted by the model.

DOI: 10.1063/1.458855

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We have obtained substantial alignment of I2(X 1Σ+g;v″=0;J″=13,15) seeded in supersonic beams of light carrier gases. Laser-induced fluorescence and a variant of the magnetic precession technique were used to measure the ratio n⊥/n∥ of molecules with the rotational angular momentum vector J perpendicular to the beam axis z to those with J parallel (or antiparallel) to z. As the nozzle stagnation pressure P0 is increased, this ratio increases markedly, reaches a maximum, and then decreases steadily. At the maximum, n⊥/n∥=1.6, 1.7, and 2.2, respectively, for He, D2, and H2 as the carrier gases; this occurs at different pressures of the order of 103 Torr for nozzle diameter d=50 μm and temperature T0=315 K and corresponds to nearly the same rotational temperatures of about 6–8 K. We compare the observed dependence of alignment on P0⋅d with a J-dependent model that invokes two mechanisms for alignment, macroscopic gas transport, and anisotropic rotational cooling. The transport processes involve reorientation of J and give rise to alignment with n⊥/n∥>1; this dominates the initial increase with P0⋅d up to the maxima. The anisotropic cooling processes do not in our model involve reorientation of J but are fostered by the anisotropy of the rotational relaxation cross section; the alignment arises from different Boltzmann weights for molecules with J⊥z and J∥z due to their slightly different rotational temperatures (about 5%). At high P0⋅d the net alignment is dominated by the anisotropic cooling term. At the correspondingly low rotational temperatures, this term counteracts the effect of gaseous transport, so the net alignment can reverse. Indeed, at high P0⋅d we do observe n⊥/n∥<1. For a higher rotational state (J″=39,41) we find lower alignment that peaks at a higher rotational temperature (about 27 K), as predicted by the model.

The mathematical term for the mean flow velocity in supersonic beams of ideal gases is extended to include real gas properties. This procedure yields an explicit dependence of the flow velocity on pressure, as observed in recent experiments of free jet expansions. Applied to stagnation conditions slightly above the critical point, the model suggests that seeded high-pressure jet expansions might be suitable for slowing down virtually any molecule with maximum efficiency. Moreover, we discuss the consequence of a pressure-dependent flow velocity

{v}_{0}

for the speed ratio $S={v}_{0}/\ensuremath{\Delta}{v}_{\ensuremath{\parallel}}$ with respect to collisional cooling and suggest to use the velocity spread $\ensuremath{\Delta}{v}_{\ensuremath{\parallel}}$ as a more nonambiguous measure of translational temperature in high-pressure jet expansions.

Intense alkali beams containing up to 30% mole fraction of K2, Rb2, or Cs2 have been generated from a supersonic nozzle expansion, with oven temperatures up to ∼ 900°K (corresponding to alkali vapor pressures up to ∼ 350 torr) and nozzle temperatures ∼ 50–300°K higher. The total beam intensity obtained reached ∼ 5 × 1017 particles sec−1·sr−1. An inhomogeneous deflecting magnet was used to separate the dimer and atom components of the beam, and the variation of dimer concentration with oven pressure and nozzle temperature were studied for a variety of nozzle sizes (throat diameters 0.04–0.15 mm). The velocity distributions of the atom and dimer components were also measured and found to be quite similar; the peaks occur at velocities up to 70% higher than the most probable atom velocity in the oven, and the widths are very narrow, corresponding to random translational temperatures as low as ∼ 30°K, and Mach numbers up to ∼ 15. A simple one-dimensional theory of dimerization which takes into account vibrational relaxation and heat of condensation is found to be consistent with the data. It is shown that the observed velocity distributions and the variation of the dimer yield with pressure and nozzle diameter imply that most of the heat of condensation does not contribute to the beam acceleration but goes into vibrational excitation of the dimer molecules. A nominal value of ∼ 3 × 10−30 cm6 sec−1 at ∼ 600°K is obtained for the recombination rate constant for Cs+Cs+Cs→Cs2+Cs. A reduced variable plot is provided which enables the theory to be applied to nozzle expansions of any substance for which the chemical recombination is governed by three-body collisions.

By spectroscopically analyzing the white light and laser-induced fluorescence excited in a nozzle beam of Na2 molecules, we have measured the population distribution of the (v,J) levels of the ground state. The Na2 molecules are produced in nozzle beams with various stagnation pressures (50–240 torr) of alkali metal and with nozzles of different throat diameters (0.12–0.50 mm). We find at a stagnation pressure of 50 torr and a nozzle diameter of 0.5 mm a Boltzmann distribution characterized by a vibrational temperature of 153 ± 5°K and a rotational temperature of 55± 10°K. Beams under different stagnation conditions have essentially the same internal state distribution. Studies of K2 dimers produced in a nozzle beam with various stagnation pressures (20–300 torr) and a 0.25 mm nozzle throat diameter also show cooling in both vibrational and rotational modes. A search is made for atomic fluorescence arising from the photodissociation of dimers in high vibrational levels of the ground state. No evidence is found for the presence of vibrationally-excited dimers in the nozzle beam.

We have found recently that, in a supersonic expansion of a mixture of two monoatomic gases, the parallel temperatures of the two gases can be very different. This effect is large if the seeded gas is highly diluted and if its atomic mass is considerably smaller than the one of the carrier gas. In the present paper, we present a complete derivation of our theoretical analysis of this effect. Our calculation is a natural extension of the existing theory of supersonic cooling to the case of a gas mixture, in the high dilution limit. Finally, we describe a set of temperature measurements made on a beam of lithium seeded in argon. Our experimental results are in very good agreement with the results of our calculation.

We describe a pulsed rotating supersonic beam source, evolved from an ancestral device [M. Gupta and D. Herschbach, J. Phys. Chem. A 105, 1626 (2001)]. The beam emerges from a nozzle near the tip of a hollow rotor which can be spun at high-speed to shift the molecular velocity distribution downward or upward over a wide range. Here we consider mostly the slowing mode. Introducing a pulsed gas inlet system, cryocooling, and a shutter gate eliminated the main handicap of the original device in which continuous gas flow imposed high background pressure. The new version provides intense pulses, of duration 0.1-0.6 ms (depending on rotor speed) and containing ∼10(12) molecules at lab speeds as low as 35 m/s and ∼10(15) molecules at 400 m∕s. Beams of any molecule available as a gas can be slowed (or speeded); e.g., we have produced slow and fast beams of rare gases, O(2), Cl(2), NO(2), NH(3), and SF(6). For collision experiments, the ability to scan the beam speed by merely adjusting the rotor is especially advantageous when using two merged beams. By closely matching the beam speeds, very low relative collision energies can be attained without making either beam very slow.

Supersonic expansion is a very powerful tool to produce an atomic beam with a well defined velocity and, by seeding a test gas in such an expansion, the energy of the test gas can be transferred, at least partially, to the very-low-temperature carrier gas. The case usually studied is the one of a heavy gas seeded in a light carrier gas and, in this case, the parallel temperature of the seeded gas is always larger than the one of the carrier gas. In the present paper, we study the opposite case which has received less attention: when a light gas is seeded in a heavier carrier gas, the parallel temperature can be substantially lower for the seeded gas than for the carrier gas. This effect has been first observed by Campargue and co-workers in 2000, in the case of atomic oxygen seeded in argon. In the present paper, we develop a theoretical analysis of this effect, in the high dilution limit, and we compare our theoretical results to several experimental observations, including a set of measurements we have made on a beam of lithium seeded in argon. The agreement between theory and experiments is good.