3402
J. Phys. Chem. 1996, 100, 3402-3413
State-to-State, Rotational Energy-Transfer Dynamics in Crossed Supersonic Jets: A High-Resolution IR Absorption Method Aram Schiffman,† William B. Chapman, and David J. Nesbitt* Joint Institute for Laboratory Astrophysics of the National Institute of Standards and Technology and UniVersity of Colorado, and Department of Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309 ReceiVed: September 15, 1995; In Final Form: NoVember 17, 1995X
A high-resolution IR absorption method is presented for the experimental determination of state-to-state, integral and differential cross sections for rotationally inelastic energy transfer. An infrared chromophore, cooled into its lowest rotational state(s) in a pulsed supersonic expansion, is rotationally excited with low collision probability by a gas pulse from a second supersonic jet. The initial and final populations of the infrared absorber are monitored as a function of J state and of Doppler detuning, via direct absorption of narrow bandwidth light from a continuously tunable, CW infrared laser. The scattered and unscattered species are detected with Doppler-limited spectral resolution (j0.01 cm-1), providing quantum-state selectivity not attainable with time-of-flight energy-loss methods. The infrared-based probe also permits study of a much wider class of absorbing species inaccessible to ultraviolet/visible laser-induced fluorescence (LIF) or resonanceenhanced multiphoton ionization (REMPI) methods. From fractional IR absorbances and Beer’s law, the column-integrated number densities in each jet are measured directly, which allows absolute, state-to-state, integral cross sections to be determined. Furthermore, the correspondence between the molecular velocity and the observed Doppler shift can be used to extract state-to-state differential cross sections from the highresolution line shapes. Details of the experimental technique are demonstrated via sample studies of stateto-state integral and differential scattering in rare-gas collisions with CH4.
I. Introduction The study of collisional energy transfer has been a focus of gas phase chemical physics with relevance to a broad range of areas. Knowledge of rotational energy transfer rates is necessary to model energy disposal in combustion processes,1 based on the rotational state distributions of burned and unburned constituents. In the earth’s atmosphere, rotationally inelastic collisions induce infrared pressure broadening in species such as H2O, CO2, CH4, etc., which impact on a detailed understanding of atmospheric “greenhouse” phenomena.2 In certain collision systems, highly state-selective, rotationally inelastic energy transfer can produce significant population inversions, such as that observed in the collisional pumping of the interstellar OH maser.3-5 Rotational state-changing collisions control the quenching of gain in chemical lasers and can be a dominant source of line broadening in spectroscopies such as four-wave mixing and laser-induced gratings.6-12 Of particular interest in this work, such collisional data provide valuable information on the topology of intermolecular potential surfaces, especially angular anisotropy in the repulsive wall region. The energy-transfer dynamics in such diverse systems can depend significantly on quantum state. For instance, steadystate concentrations of OH, formed from H + O3 chemistry in the mesosphere, have been observed with up to ∼23 000 cm-1 of rotational excitation.13,14 The metastability of OH in such rotationally energetic states implies relaxation rates that can vary as much as 1000-fold with J. In another limit, Andresen et al.15 have studied the rotational excitation of NO(N)0) by Ar and have observed strong oscillations in the final state populations as a function of end-over-end tumbling quantum number † Present address: Coherent Laser Group, 5100 Patrick Henry Drive, MSP33, Santa Clara, CA 95054. X Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-3402$12.00/0
N, due to the near forward/backward symmetry of the Ar + NO interaction potential energy surface. In yet another regime, strong correlations can exist between rotationally inelastic J and MJ changing collisions, which in seeded supersonic expansions can lead to macroscopic rotational alignment of molecules such as N2, I2, CO2, and Na2.16-19 Such examples underscore the importance of experimental methods by which cross sections for rotational energy transfer can be measured at the state-tostate level. A number of transient relaxation methods have been designed to probe the quantum state dependencies of rotational energy transfer rates.20 Typically, a target molecule in a gas cell is prepared in a single V, J state with a pulsed laser.21-27 Alternatively, a nonthermal distribution of initial states is created via laser photolysis,28 fast chemical reactions,29 or collisions with a translationally energetic atom.30-32 As the target molecules approach thermal equilibrium via collisions with a bath gas, the time evolution of the rotational state distribution is monitored with detection techniques such as infrared chemiluminescence,29 time-resolved Fourier transform spectroscopy,28,32 pulsed laser-induced fluorescence,24,33 or infrared laser absorption spectroscopy.30,31,34 The state-to-state cross sections, averaged over a spread in thermal velocity, can be inferred through detailed kinetic models of the time-dependent populations in each J state. These bath gas relaxation techniques have been used in determinations of state-to-state, rotational energy transfer cross sections for collision systems such as HF with rare gases,34 CH4 + CH4,21,25-27 CO2 with translationally hot H atoms, O(1D), and electronically excited Br*(2P1/2),30,31 selfrelaxation in D2CO,35 N2,36 and H237 and in the open-shell radical systems OH + rare gases, N2, and O2.33 By comparison of calculated and experimentally determined rotational energy transfer cross sections and their kinetic energy dependencies, the accuracy of ab initio and empirical potential energy surfaces © 1996 American Chemical Society
Energy-Transfer Dynamics in Crossed Supersonic Jets can be tested for a number of simple atom + molecule collision systems.8-10,20,38 In order to obtain detailed information on the shape of the potential surface, crossed atomic and molecular beam techniques have been developed to specify the single-collision event more precisely in terms of initial/final quantum states and center-ofmass collision energy.39 By supersonic cooling, the initial state J′′ of the target molecule can be prepared in the lowest rotational level. The use of two directed beams can lead to a narrow distribution of collision velocities and hence well-defined centerof-mass collision energies. By virtue of the inherently low number densities and short interaction path lengths in the beam environment, the influences of multiple collisions can be made negligible. The application of such crossed-beam methods to inelastic scattering measurements dates back well over a decade, with the earliest studies including those by Buck et al. of HD + Ne and D2,40-42 Gentry and Giese of HD + He,43 and Faubel et al. of N2 + He.44 A principal challenge in crossed-beam energy transfer studies has been state-resolved detection of the scattered molecules. In order to provide complete resolution of final scattering J states, spectroscopic detection schemes utilizing laser-induced fluorescence (LIF) or multiphoton ionization (MPI) have been implemented by several groups. In these laser-based methods, electronic transitions are pumped with light from a pulsed laser, and the J-dependent populations are monitored via emission from the excited state or LIF on a second transition. Parmenter and co-workers have utilized LIF to probe vibrational and rotational relaxation in electronically excited I2 by He45 and rovibrational energy transfer in glyoxal + H2.46 Bergmann and co-workers have performed a number of elegant crossed-beam studies of Na2 scattering by He, Ne, and Ar,47 in which supernumerary rotational rainbow features are observed via LIF detection as a function of laboratory angle. Meyer has recently employed REMPI with counterpropagating molecular beams to detect NH3 scattering by rare gases with final state resolution.48,49 Dagdigian and co-workers have used LIF to measure state-to-state cross sections in beam-gas and crossed-beam scattering experiments for closed-shell systems including LiH + HCl and DCl,50 as well as in the open-shell systems CO + CaCl,51 NH + Ar,52 and NH2 + He.53 Liu and co-workers have also employed LIF detection to measure rotational energy transfer cross sections for scattering systems with open-shell, free-radical species such as CH + He54 and OH + CO and N2.55 Recently, Suits et al. have introduced a novel modification to the REMPI technique, whereby a scattered molecule is stateselectively ionized with light from a pulsed laser and is spatially imaged onto a channel plate. With some approximations, the two-dimensional intensity pattern can be analyzed to obtain the three-dimensional, differential scattering distribution; this technique has been applied to determine the J-dependent, differential scattering distributions for NO + Ar.56,57 These laser-based methods hold great appeal due to their sensitivity and capability to resolve final J states. However, the methods are not generally applicable because relatively few molecules possess excited states suitable for such schemes. To probe molecular scattering systems inaccessible to LIF or REMPI techniques, several groups have exploited crossed beams of target and collider gases, with the scattered target flux detected as a function of laboratory angle in a rotatable timeof-flight mass spectrometer.39 Molecules in the target beam that are collisionally excited into different final J states can be distinguished by their velocities and hence by their respective arrival times into the mass spectrometer. The time-resolved signals map directly into an energy-loss spectrum from which
J. Phys. Chem., Vol. 100, No. 9, 1996 3403 the J-dependent, differential cross sections may be inferred. This technique can provide extremely high angular resolution (J1°) for measurements of total (summed over all final J states) differential scattering cross sections. However, for typical flight times in the mass spectrometer (j10-3 s), the effective spectral resolution is limited typically to 10-100 cm-1, depending on the masses of the colliding species. For most molecular collision systems, this resolution is insufficient to allow the extraction of cross sections at the state-to-state level. Of considerable interest, therefore, would be a laser-based probe with the quantum state resolution of LIF and MPI methods and yet the molecular generality of the crossed beam, time-of-flight techniques. Since most molecules absorb in the infrared region of the spectrum, a direct absorption scheme based on tunable infrared light provides an important complement to these other methods and forms the focus of the present work. In this paper, we describe such an infrared method for study of state-resolved rotational energy transfer in crossed supersonic jets. The key ingredients are as follows. The infrared absorber, denoted the “target” molecule, is seeded in rare gas and cooled into its lowest rotational state via supersonic expansion through a pulsed pinhole valve. Rotational excitation occurs via collisions with a pulse of gas, denoted the “collider” atom or molecule, in a second supersonic expansion. The columnintegrated concentration of the target gas in the jet intersection region is monitored as a function of rotational level via the fractional absorption of a tunable, narrow-bandwidth infrared laser. The growth of the integrated infrared absorption strengths as a function of secondary jet stagnation pressure measures the rates for collisional energy transfer into each J state and hence the relatiVe integral cross sections for rotational energy transfer. From known infrared absorption line strengths and experimentally observed absorbances, absolute integral cross sections can also be measured with reasonable accuracy. Furthermore, the speed and direction of the absorber in initial and final scattering states can be inferred from the high-resolution infrared Doppler line shapes.58,59 Hence, with appropriate conversion between concentration and flux, this information can be used to infer differential scattering cross sections with full state-to-state resolution. The remainder of this paper is organized as follows. In section II, the crossed jet apparatus is described, with a number of experimental tests presented to characterize the nascent rotational populations, determine the jet speeds and collision energies, and ensure that rotational energy transfer occurs via single collisions with the collider gas. In section III, the determination of relative, state-to-state, inelastic scattering cross sections is discussed; sample data to illustrate this technique are provided for CH4 and HF scattering with rare gases. Additionally, methods for obtaining absolute inelastic cross sections from absolute absorbances are presented. Finally, examples of high-resolution IR Dopplerimetry are discussed from which state-to-state, differential scattering cross sections are derived. In section IV, the advantages and disadvantages of the infrared method are contrasted with other detection schemes, and extensions of the method into other areas are indicated. The paper is summarized in section V. II. Experimental Section A. Crossed-Jet Apparatus. The crossed-jet apparatus is shown schematically in Figure 1. The pulsed valves are housed in a vacuum chamber constructed from 3 cm thick aluminum. To provide sufficient room for infrared multipass optics inside the chamber and to allow the distance from each valve to the jet intersection region to be varied over e12 cm, the chamber
3404 J. Phys. Chem., Vol. 100, No. 9, 1996
Schiffman et al.
Figure 1. Schematic of the crossed jet/infrared laser spectrometer.
is 40 cm per side. A square hole is cut from each of the side and top faces, leaving a frame with a 5 cm border onto which Plexiglas flanges (3 cm thick) are mounted with O-ring seals. The transparent sides provide visual access to the inside of the chamber, thereby facilitating the alignment of the infrared laser multipass under vacuum. All pulsed-valve feedthroughs, CaF2 windows to pass the infrared laser beam, and vacuum gauges are on aluminum flanges mounted to the Plexiglas sides. The chamber is pumped through a liquid nitrogen-cooled baffle with an oil diffusion pump (4000 L/s) backed by a Roots blower (500 L/s). With no gas flow through either of the pulsed valves, the base chamber pressure is e3 × 10-6 Torr (1 Torr ) 133 Pa). With both valves pulsing at 10 Hz, the background pressure is still j10-5 Torr. This corresponds to mean free paths 1 or more orders of magnitude larger than the size of the chamber, ensuring that collisions with the background gas contribute negligibly to rotational excitation of the target molecule. The primary (“target”) and secondary (“collider”) jets are formed through pulsed, pinhole nozzles that enter the chamber via O-ring feedthroughs. Operation with two pulsed valves (e1% duty cycle) maintains a low average pressure and also allows the relative timing of the jets to be varied. The valves are mounted so that the jet center lines intersect at 90°, with a 10 cm distance between each nozzle and the jet intersection region. The gas pulse durations of the primary nozzle (diameter 520 µm) and the secondary nozzle (diameter 160 µm) are adjusted to ∼500 µs and ∼1 ms, respectively, allowing the target gas pulse to sample the uniform portion of flux in the longer, collider gas pulse. The valves are pulsed at a rate of e10 Hz, limited currently by the acquisition speed of the data collection system. The infrared beam from a color center laser is overlapped with light from a HeNe laser to establish a visible tracer spot and then is split into several beams. One fraction goes to a 10 cm long, reference gas absorption cell to aid in finding spectral transitions in the crossed-jet experiments. A second portion is sent to a traveling Michelson interferometer (“λ-meter”) after the design by Hall and Lee,60 which is used in conjunction with a polarization-stabilized HeNe laser61 to measure the infrared frequency with a precision of 0.0005 cm-1. This precision is limited currently by the number of digits in a fringe counter but is entirely adequate to locate and identify Doppler-broadened
lines with ≈0.01 cm-1 line widths. Another split-off of the infrared beam is sent to a confocal Fabry-Perot etalon (free spectral range 151 MHz), whose length is modulated via 30 Hz sawtooth modulation of a PZT controlled end mirror. The time delay from the beginning of each sawtooth cycle to the first interference fringe is measured and saved via time-toamplitude conversion (TAC), providing a linear frequency interpolation scale over each free spectral range of the etalon. Furthermore, any laser mode hops that might occur during a frequency scan are therefore readily identified as discontinuities in the TAC output. The remainder of the infrared light is split equally into signal and reference beams. To increase the absorption path length, the signal portion is first focused into the chamber with a CaF2 lens (f ) 50 cm) and then is multipassed up to 22 times through the jet intersection region with a 30 cm optical cell after the design by Herriot.62 For experimental ease of operation, the multipass geometry is perpendicular to the plane of two orthogonal jets. However, it is also possible to propagate the infrared beam in the plane of the crossed jets, a configuration that offers additional advantages for extraction of differential cross sections by direct inversion of Doppler profiles.58,59 On exiting the chamber, the infrared signal beam is collimated and focused onto a 0.5 mm diameter, 77 K InSb photovoltaic detector with a pair of CaF2 lenses (f ) 50 and 2.5 cm). The reference infrared beam is similarly collimated and focused onto a matched InSb detector. The infrared power on each InSb detector is maintained at e100 µW, a range over which the detector response is verified to be linear with respect to incident light power. The amplified voltage outputs of the signal and reference detectors are limited to 10 kHz bandwidths with electronic low-pass filters and subtracted with a fast differential amplifier to suppress common amplitude mode noise by g25fold. The resulting absorption signal is sent to a digital oscilloscope for signal averaging and transferred to the laboratory computer for storage and analysis. The infrared detection sensitivity in the crossed-jet apparatus is 1 × 10-6 Hz-1/2 or 1 × 10-4 in the 10 kHz detection bandwidth. For typical integrated absorption strengths of 10-17 cm/molecule and Doppler widths of ∼0.01 cm-1, the resulting detection limit is ∼5 × 108 molecules/(quantum state cm3) per gas pulse.
Energy-Transfer Dynamics in Crossed Supersonic Jets
J. Phys. Chem., Vol. 100, No. 9, 1996 3405
Figure 2. Time domain absorption in jet-cooled CH4 (10% CH4/Ar mix) for the primary and secondary jets. The 500 µs primary jet pulse (top trace) is delayed by 250 µs to sample the uniform temporal center of the 1 ms secondary jet pulse. The high S/N results from signal averaging the absorption signals for 500 valve pulses.
By modest signal averaging this can be further reduced to j108 molecules/(quantum state cm3). B. Doppler Profiles and Absolute, Integrated Column Densities. With the IR laser tuned to the peak of a molecular absorption, the temporal profile of both the primary and secondary jet pulses can be directly monitored in time (see Figure 2). The top trace in Figure 2 corresponds to 210 Torr stagnation pressure of 10% CH4 seeded in Ar, standard conditions for all the CH4 + rare gas data herein. Typical infrared absorbances for target molecules in the initial J state are A ≈ 1-10%. The corresponding scattered J state signals are down an additional 20-200-fold; with 10-4 absorbance sensitivity per pulse, however, these signals are still quite sufficient to observe with adequate signal-to-noise ratio (S/N). By doping the collider gas with a known concentration of an infrared absorbing species, the rare-gas densities and temporal profile of the secondary jet can also be monitored directly. Figure 2 also shows the time-resolved absorption signal observed when a CH4/Ar mix is run through the secondary nozzle, demonstrating the uniformity of the collider gas pulse for the full ∼1 ms open time of the valve. Since the infrared line strengths of the absorber are wellknown,63,64 the absolute column-integrated number densities in both the primary and secondary jets can be determined from fractional attenuation of the infrared light and Beer’s law. Specifically,
A(ν) ) ∫dν′ ∫dl F(ν′,l) σIR(ν-ν′)
(1)
where A(ν) is the absorbance, σIR(ν-ν′) is the homogeneous absorption profile at frequency ν for a center absorption frequency ν′, and F(ν′,l) is the spectral density of absorbers (in units of molecules/(cm3 cm-1)) along the IR probe laser coordinate (l) that have a Doppler-shifted center frequency of ν′. These homogeneous widths are 102 smaller than the inhomogeneous Doppler widths and thus the integral over ν′ can be readily evaluated to yield
A(ν) ) S0∫dl F(ν,l)
(2)
where S0 is the intrinsic line strength (cm/molecule) for a given transition. As will be exploited later, eq 2 provides a direct connection between experimental Doppler profiles and velocity distributions, column integrated over the full absorption path length. More typically, one is interested in the total column density irrespectiVe of final lab frame velocity, which is derived by summing over all Doppler shifts. Integrating eq 2 over the experimental absorption profile, one obtains
I ) ∫dν A(ν) ) S0∫dl ∫dν F(ν,l) ) S0∫dl N(l)
(3)
Figure 3. Scan over the CH4 [(V3 ) 1 r 0), 3028-3057 cm-1] R branch, demonstrating the efficient cooling of CH4 in the nascent, primary jet expansion as well as the complete spectral resolution of initial and final quantum states. Tick marks along the frequency axis denote 250 MHz spacings. More than 95% of the population in each CH4 nuclear spin symmetry modification is cooled into its ground rotational state. The line shapes for weak transitions out of “coolable” rotational levels (e.g., R(2)F2) are double-peaked due to slightly warmer beam conditions in the angular wings of the pinhole expansion.
where N(l) is the number density (molecules/cm3) of absorbers at a distance l along the laser probe axis. Here l ) 0 is defined to be the mutual intersection point of the two jet expansion axes, and therefore the integrals in eqs 1-3 run symmetrically over [-∞,∞]. From the dopant ratio of absorber to rare gas diluent, this yields the column-integrated collider gas density in absolute units (i.e., molecules/cm2). Since these column-integrated densities can be directly related to collision probability between target and collider species, the cross sections for state-to-state rotationally inelastic scattering can be inferred in absolute units, as will be described in section IV. C. Initial State Distributions. In order to measure the Doppler profiles of the scattered species, the infrared laser is scanned over absorption line shapes under computer control in 5 MHz (0.000 17 cm-1) steps. The transient absorption signal at each frequency is averaged for e32 pulses to increase S/N and integrated over the gated section of the target gas pulse. In order to determine the zero-absorption level and further eliminate fluctuations in the IR light, the two adjacent gates that flank the gas pulse are integrated, averaged together, and subtracted from the signal gate. During frequency scans the infrared light transmission through a 300 K absorption cell is monitored to provide reference spectral peaks. Interference fringes from a Fabry-Perot etalon (151 MHz FSR) are also acquired using the TAC to yield equally spaced frequency markers. This provides the necessary frequency ruler to extract lab frame velocity distributions from the infrared intensities as a function of Doppler shift. As one specific example, a series of high-resolution scans over individual R-branch transitions [(V3 ) 1 r 0), 3028-3057 cm-1] for CH4 cooled in the primary jet are shown in Figure 3. Tick marks along the frequency axis denote 250 MHz spacing; at j2 MHz laser resolution, the line shapes are completely Doppler limited. In each spectral scan, the infrared absorption intensities are scaled to the known Honl-London factors,63,64 so relative intensities are equivalent to relative initial J-state populations. It is worth noting that CH4 has three ground rotational states labeled by symmetry (A, E, or F) in the Td rotation group, because of the nuclear spin statistics of the four equivalent H atoms (nuclear spin IH ) 1/2). From Figure 3, states of A, F, and E symmetry are observed to be populated in
3406 J. Phys. Chem., Vol. 100, No. 9, 1996
Figure 4. Infrared absorption signal for the ground E symmetry state of CH4 seeded in 10% Ar as a function of primary jet stagnation pressure. From 150 to 500 Torr, the absorption grows linearly with stagnation pressure (solid line). At stagnation pressures j150 Torr, the growth is faster than linear because of increasingly efficient cooling of CH4 into the rotational state probed. At pressures J500 Torr, negative curvature is observed which can be attributed to clustering in the jet. Typical operating pressures (∼200-250 Torr) are chosen to be sufficiently high that CH4 is fully cooled but well below the observed onset of clustering.
the ratio of 4.9(2):9.2(3):2.1(1), in good agreement with the anticipated 5:9:2 ratio. The CH4 is efficiently cooled into each of these lowest rotational levels, with only e4% residual population summed over all rotionally excited states. The small fractional population in these excited (and therefore coolable) rotational states occurs preferentially in the slightly warmer edges of the supersonic expansion; this accounts for the weak “doublet” Doppler profiles structure seen in Figure 3, but which is completely absent for the lowest rotational levels. Trot is estimated to be j5 K, i.e., sufficiently low for hydrides (such as CH4, NH3, H2O, and HF) that the collisional events are dominated by excitation out of the lowest J state in each symmetry class. Since the different nuclear symmetry levels do not interact in the collision process (as verified experimentally), three independent collision experiments can be performed simultaneously on the A, F, and E manifolds, corresponding to J ) 0, 1, and 2, respectively. D. Primary Jet Characterization. In order to carry out these state-to-state scattering measurements, it is necessary to select a stagnation pressure for the primary jet that minimizes clustering, cools into the lowest rotational level(s), and provides a sufficiently low number density in the collision region. An optimum value is based on the following experimental considerations. For a cold jet of CH4 seeded in Ar, the columnintegrated number density of monomer CH4 should scale linearly with stagnation pressure.36 Figure 4 shows the infrared absorption signal for ground-state CH4 in the primary jet as a function of the pressure of CH4/Ar in the stagnation region. For intermediate pressures, the infrared signal rises linearly, as anticipated. At pressures J500 Torr, the infrared absorption signal for rovibrational ground-state CH4 begins to increase less rapidly and in fact eventually decreases with increasing pressure due to van der Waals clustering of the monomer. Indeed, Doppler line profiles measured for [CH4/Ar] J 500 Torr exhibit absorbance dips near the center frequency, revealing a decreased CH4 monomer concentration along the expansion axis where clustering occurs most readily. Conversely, at stagnation pressures j150 Torr the growth is also nonlinear, due to incomplete rotational cooling into the ground state. This dependence of jet temperature on backing pressures below 150 Torr is further corroborated by monitoring the population in the first rotationally excited state, which is quenched with increasing efficiency as the backing pressure is increased.
Schiffman et al.
Figure 5. Direct determination of terminal supersonic jet speeds via optical time-of-flight detection. Small concentrations of an IRabsorbing species are doped into the expansion gas. The nozzle-tolaser distance ∆x is varied from 0 to 90 mm, and the time ∆t is monitored from the valve trigger pulse to the peak of the infrared absorption signal. The speeds for Ar, Ne, and He agree within experimental uncertainty with the terminal expansion values predicted from eq 4.
Operating pressure between 150 and 500 Torr therefore provides optimum cooling into the lowest rotational levels but eliminates possible signal contamination by collisional fragmentation of larger clusters. Typical stagnation pressures are 200-250 Torr, i.e., at the low end of the linear region, to minimize gas flux into the vacuum chamber and maintain low background pressures. E. Jet Velocities and Center-of-Mass Collision Energies. The mean collision energies are determined by the masses and speeds of the constituents in each jet. The target molecule speed in the primary jet can be directly determined by monitoring the time delay ∆t from the valve trigger to the peak of the infrared absorption profile as a function of nozzle-to-laser distance ∆x. In the absence of velocity slip effects and for small dopant levels of absorber, the speed of the colliding rare gas species in the secondary jet can be similarly determined. From the slope of the linear plots of ∆x vs ∆t (Figure 5), the rare gas velocities for VAr, VNe, and VHe are found to be 5.6(2) × 104, 7.5(5) × 104, and 18(2) × 104 cm/s, respectively. We note that, in the region of the supersonic expansion probed by the infrared laser (i.e., g102 nozzle diameters downstream), the terminal velocity of the rare gas is approximately predicted to be39
Vrare gas )
x
2γkT (γ - 1)m
(4)
where γ ) Cp/CV is the ratio of the heat capacities at constant pressure and volume, respectively. The values predicted from eq 3 for a neat rare-gas expansion are 5.6 × 104, 7.9 × 104, and 17.7 × 104 cm/s, i.e., in good agreement with experimental measurement. Due to the finite angular width of the two jets, however, there is still a modest distribution in collision angles which leads to a corresponding spread in center-of-mass energies. This angular divergence can be estimated directly from the Doppler profiles observed for each expansion as follows. For a narrow supersonic jet distribution of speeds around V, the Doppler shift can be obtained geometrically from
ν - ν0 V ) sin θ ν0 c
(5)
where ν - ν0 is the Doppler detuning from the rest absorption frequency, and θ is the angle from the jet center line. A typical Doppler profile for the uncollided target gas jet (e.g., CH4, J )
Energy-Transfer Dynamics in Crossed Supersonic Jets
Figure 6. (a) Doppler profile for the ground CH4 Q(1)F1 transition, with a half-width at half-maximum of ∆νhwhm = 90 MHz. (b) Angular distribution ∆θhwhm = 22° of the CH4 in the free-jet expansion sampled at an angle θ by the IR laser, obtained from the Doppler profile in (a). Also shown (c, d) are the corresponding Doppler profile/angular distribution for beams skimmed with a 5 mm aperture diameter skimmer placed 3 cm from the jet (∆νhwhm = 16 MHz and ∆θhwhm = 5°, respectively).
0, A1) is shown in Figure 6a, which exhibits a half-width at half-maximum (hwhm) of 90 MHz. From eq 5 and the experimentally measured jet speed, this corresponds to an initial spread in θ of approximately (22°. If one also includes the quadratic density dependence as a function of distance downstream for the pinhole expansion, the angular distribution N(θ) shown in Figure 6b is obtained. Based on these divergences, the spread in center-of-mass collision energies E h com is conservatively estimated at (20% about the mean. This spread can be significantly reduced (J5-fold) by skimming the expansion (as shown in Figure 6c,d), but at the expense of collisional path length and excitation probability. Thus, from the measured jet velocities, the mean center-of-mass collision energies can be obtained and be “tuned” between 102 and 103 cm-1 for different mass combinations of collider, target, diluent gas, and jet intersection angle. For CH4 expanded in Ar and right angle scattering with He, Ne, and Ar, for example, E h com is calculated to be 460, 354, and 307 cm-1, respectively. F. Single-Collision Conditions. Of key importance to interpretation of the scattering data is the maintenance of singlecollision conditions. This is verified in a variety of ways, as described below. First of all, low background pressures (e10-5 Torr) are maintained in order to minimize the possibility of target molecules scattering from residual gas. At these pressures, the mean free path is g102 cm, i.e., already several times the length of the vacuum chamber. A related concern is reflection of target gas molecules off the 300 K chamber walls back into the viewing region. Indeed, if we look at later times (J1 ms), such reflected gas signals are weakly evident at the highest pressures. However, the time required to traverse this distance is well outside the duration of the primary jet pulse and readily isolated from the desired infrared signals by time gated detection. Second, by varying the relative timing of the two gas pulses, one may verify directly that rotational excitation occurs only
J. Phys. Chem., Vol. 100, No. 9, 1996 3407
Figure 7. Time-resolved infrared absorption signals as a function of the relative timing between the primary (10% CH4/Ar) and secondary (Ar) gas pulses. The trigger delay of the secondary jet is set to (i) precede, (ii) overlap, and (iii) follow the primary jet pulse. (a) Depletion signals demonstrating collisional loss of CH4(J)1,F1) only when the two pulses overlap. (b) Excitation signals demonstrating the collisional growth of CH4(J)5,F1(2)). The excited J ) 5 state is also observed only when the two pulses overlap, verifying that the excited state is populated only via collisions with the rare-gas atoms in the secondary jet. Small background population in J ) 5 is evident at the very beginning and end of the pulse, when the expansion is somewhat warmer, which can be readily discriminated against with a narrow (100 µs) detection time gate in the middle of the pulse.
via collisions with the secondary jet. Specifically, the populations of the target molecule in initial and excited J states can be monitored with the secondary pulse (i) prior, (ii) during, and (iii) immediately after the primary pulse. Typical results for CH4 scattering with Ar are shown in Figure 7, which shows the time-gated infrared absorption signals for the collisional process
CH4(J)1,F1) + Ar f CH4(J)5,F1(2)) + Ar
(6)
where F1 and F1(2) label the rotational symmetry of the CH4 wave function. As anticipated, the amplitude of the infrared absorption signal for CH4(J)1,F1) is depleted only when the two pulses are temporally coincident. Conversely, the excited J ) 5 state appears only in the presence of collider gas. Due to incomplete rotational cooling at the very beginning and end of the gas pulse, there is weak thermal population of J ) 5 evident in Figure 7. However, the use of gated detection in a 100 µs window near the peak of the gas pulse eliminates this component completely. Third, non-single-collision conditions can result from successive scattering of the target species with the rare-gas collider. The probabilities for N sequential collisions can be estimated from the Poisson distribution P(N):65
P(N) ) RNe-R/N!
(7)
where R is the single-collision probability given by
R ) 0.5σtot∫[M] dlcom
(8)
In eq 8, ∫[M] dlcom, is the column-integrated density of colliders evaluated from eq 3, and σtot is the total inelastic scattering cross section for excitation into all excited states. The factor of 0.5 arises from the fact that, for a mutually orthogonal jet and laser
3408 J. Phys. Chem., Vol. 100, No. 9, 1996 beam geometry, the full column-integrated density includes regions of the jet not yet sampled by the target molecules, which for an axisymmetric expansion overcounts the relevant column density by 2-fold. For CH4 + Ar, with σtot ∼ 50 Å2 and the measured values of ∫[M] dl, the single-collision probability is estimated to j10% over the range of Ar concentrations used. The probability for N > 1 collisional events is therefore j0.45% and j0.015% for N ) 2 and 3, respectively, indicating that multiple collisions for processes with comparable cross sections contribute j5% to the excited state signals observed. A more direct effect could arise from the rare-gas collider striking the rare-gas diluent in the primary jet, followed by secondary collisions with the target molecule. Since the diluent is present in excess, this could occur even though the singlecollision conditions for the target molecule are appropriately maintained. For a 10:1 dilution in the primary jet, the fraction of events where the collider has experienced a prior rare gasrare gas collision is estimated to be j25% at the highest primary and secondary jet stagnation pressures investigated. This would tend to modify the collider velocity distributions and broaden slightly the center-of-mass collision energy, Ecom. Since there is already a (20% spread in Ecom due to jet angular distributions, this incremental effect is not currently significant. This has been confirmed by (i) the linearity of the collisionally populated signals with the secondary jet stagnation pressure and (ii) the independence of the scattering results on primary jet backing pressure, as described in the next section. Finally, we note that a linear increase in final state distributions with stagnation pressure is not necessarily unambiguous evidence for lack of secondary collision effects. Specifically, secondary collision cross sections between excited states that are >20-fold larger than the initial excitation event can skew the observed final state distributions. Typically these effects contribute negligibly to the experimentally observed state-tostate ratios, though they are measurable for weak cross section transitions into near-resonant states such as J ) 0, A1 f 6, A1 and J ) 0, A1 f 6, A2 in CH4, where secondary collisional conversion between the degenerate 6, A1 and 6, A2 levels can occur via large cross sections characteristic of near-elastic scattering. In any detailed comparison between theory and experiment, however, corrections for scattering into the highest rotational levels can be taken perturbatively into account by master equation solutions with the full matrix of state-to-state cross sections. III. Sample Results and Analysis A. Total Inelastic Scattering Cross Sections. The simplest demonstration of the crossed-jet scattering method is monitoring of the loss of molecules out of the initial J state, which provides a measure of the total cross section for inelastic scattering. For example, Figure 8a shows a series of state-resolved signal profiles for CH4(J)0,A1) (monitored by absorption on the R(0) transition of V3 ) 1 r 0) as a function of He stagnation pressure behind the secondary jet. Three points are worth noting from the data. First of all, there is a clear decrease in peak and integrated absorption strength, as more CH4 molecules are inelastically scattered out of J ) 0 into J′ ) 3, 4, 6, 7, and 8 (i.e., up to the energetic limit at E h com = 460 cm-1). From eq 3, these absorption profiles provide the column-integrated densities of CH4(J)0,A1), integrated over the probe laser beam path. As a function of He collision density, there is a nearly exponential decay of the CH4(J)0,A1) population, which in the singlecollision regime is well approximated by its linear first term. As expected, a plot of these integrated densities (Figure 8b) exhibits a linear decrease with He stagnation pressure.
Schiffman et al.
Figure 8. Determination of total inelastic scattering cross section for He + CH4(J)0,A1) at a mean collision energy of 460 cm-1. (a) Doppler scans showing the depletion of CH4(J)0,A1) at a series of He stagnation pressures. The subtle broadening observable at high He concentrations results from elastic scattering. (b) Plot of column integrated CH4(J)0,A1) density, determined by summing over all Doppler subgroups for each line shape in (a), as a function of integrated He density. The loss is a linear function of ∫[He(l)] dl, corroborating that collision energy transfer is dominated by single collisions. The slope of the best fit line through the data, scaled by eq 10 for the velocity Jacobian transformation, gives the total loss cross section out of the J ) 0, A1 manifold in absolute units.
Second, on careful inspection there is a subtle broadening of the Doppler profiles with increasing He collider density. This effect is quite pronounced for heavier rare gas colliders and is due to elastic scattering of CH4(J)0,A1) molecules, which redistributes the velocities in the center-of-mass frame. Analysis of these Doppler profiles permits both the uncollided and elastically collided contributions to be separated. With appropriate treatment of the density to flux transformation, this allows a detailed investigation of elastic differential scattering, free from interference by inelastic processes occurring simultaneously. Third, the linear slopes in plots such as Figure 8b can be used to calculate the total inelastic cross section in absolute units in the following manner. After interaction through a collisional path length l in the lab frame, the fractional depletion of the target molecule concentration in a differential distance dlcom in the center-of-mass frame is given approximately by
d[CH4(J)0);l] [CH4(J)0);l]
) -σinelastic[He(l)] dlcom
(9)
In eq 9, σinelastic is the sum over all cross sections depopulating the initial state, and dlcom is scattering path length in the centerof-mass frame. Due to the relative motion of the two jets in the laboratory frame, the center-of-mass frame scattering path length (dlcom) differs from the lab frame path length (dl) of the CH4 by the Jacobian transformation Vrel/VCH4, where Vrel is the
Energy-Transfer Dynamics in Crossed Supersonic Jets
J. Phys. Chem., Vol. 100, No. 9, 1996 3409
TABLE 1: Absolute Total Inelastic Cross Sections for He + CH4 at E h com ) 460 cm-1 nuclear spin manifold
experiment (Å2)
close coupling QMa (Å2)
J r 0, A1 J r 1, F1 J r 2, E
21(4) 23(5) 17(4)
24.8 24.7 17.3
a Based on full close coupling calculations on the He + CH4 potential energy surface of Buck and co-workers.76
relative collision speed. For the current right angle geometry, this kinematic transformation is
dlcom )
x
dl VHe2 + VCH42 VCH4
) dl
x1 + (V
2 He/VCH4)
(10)
This expression neglects small density to flux transformation corrections for the elastically scattered components remaining in CH4(J)0,A1). Inserting eq 10 into eq 9, integrating from the CH4 nozzle (l , 0) to the center line (l ) 0), and taking the exponential of both sides, one obtains
[CH4(J)0)]l)0 )
{
[CH4(J)0)l)-∞] exp -σinelastic
}
Vrel ∫∞ [He] dl 2VCH4 -∞
(11)
where, as in eq 8, the 1/2 reflects that the CH4 has traveled through only half of the full column-integrated density of He prior to IR detection. As described previously, the absolute value of the columnintegrated He density, i.e., [He(l)] dl, can be obtained from absolute absorbances measured for dopant levels of IR chromophores in the secondary jet. Thus, eq 11 predicts an absolute fractional depletion of CH4(J)0) that is linearly proportional ∞ [He] dl, as experimentally observed in Figure 8b. to ∫-∞ Furthermore, the slope of this plot is (σinelastic/2)(Vrel/VCH4) from which the absolute total inelastic cross sections can be determined. The value obtained for He + CH4(J)0,A1) total inelastic scattering (see Figure 8b) is 21(4) Å2, where the uncertainty reflects scatter in the fractional loss slope, the ∼20% spread in collision energies, and the neglect of density to flux transformation for the elastic component. Due to conservation of nuclear spin statistics in the inelastic collision event, the corresponding data for scattering out of J ) 1 (i.e., F symmetry) and J ) 2 (i.e., E symmetry) rotational levels can also be investigated. Similar plots for total inelastic scattering in the F and E nuclear spin manifolds yield 23(5) and 17(4) Å2, respectively (see Table 1). In order to compare state-resolved experimental cross sections rigorously with theory requires an equivalent high level of quantum state-resolved scattering calculation, ideally with few or no dynamical approximations. This level of rigor can be achieved by full close coupled quantum scattering calculations, as described previously. At the thermal energies sampled in these studies, the number of open rotational channels is significant (approximately 15-20 for the F nuclear spin manifold) but still manageable with close-coupled methods. We have performed such close coupling calculations on the He + CH4 potential surface of Buck and co-workers, with the results for total inelastic cross sections reported in Table 1. The theoretical values of 24.8, 24.7, and 17.3 Å2 for A, F, and E manifolds, respectively, are in excellent agreement with the current experimental results (see Table 1). It is worth reiterating that these experimental values are internally calibrated by direct absorption measurements in the secondary jet and thus require
Figure 9. Relative column integrated density scattered from CH4(J)1,F1) into J ) 2, 3, 4, ..., 7 final rotational states by collisions with He at 460 cm-1. Note the linear dependence on column integrated Ar scattering density. For a constant density to flux transformation, these fractional slopes yield state-to-state inelastic cross sections in absolute units, when multiplied by the total inelastic cross sections in Table 1. A more rigorous density to flux transformation can be obtained from analysis of the high-resolution Doppler profiles.
only the infrared absorption strengths for the dopant species to obtain absolute collision cross sections. B. Relative State-to-State Cross Sections. A more detailed picture of the collision dynamics can be obtained by monitoring the states into which the target IR chromophore is inelastically excited. To obtain this, the IR absorption signals for transitions out of the rotationally excited states are first integrated over all Doppler detunings for each transition. By eq 3, this rigorously provides the total, column-integrated concentration of stateresolved species in a given final J, irrespective of final-state velocity. Next, these column-integrated concentrations are plotted as a function of the secondary jet stagnation pressure, Pcollider. Since the scattering probabilities are small, the fraction of target gas scattered into a given J scales linearly with columnintegrated collider gas concentration. In the single-collision regime, these plots must therefore be linear with Pcollider, with the relative slopes reflecting the propensity for state-resolved excitation into different final rotational states. This behavior is demonstrated in Figure 9 for CH4 + He scattering out of the lowest F manifold (J′′ ) 1) into J′ ) 2, 3, 4, .... The data indicate several points worth noting. First of all, the anticipated linear dependence of the integrated signals with Pcollider is corroborated over the full range of sampled crossing-jet densities. This provides important additional confirmation that the inelastic events predominantly reflect single collisions. Second, although decreasing in magnitude, final rotational states are observed up to very nearly the centerof-mass energetic limit. The ability to detect even small populations with high J′ reflects the IR detection sensitivity and further underscores the near-single-collision nature of the crossed-beam experimental conditions. Finally, there is a clear trend in relative scattering propensity, rapidly decreasing with increasing rotational inelasticity. For example, the column-integrated number density for J ) 7 r 1 scattering is down by 40-fold from J ) 2 r 1, with a roughly monotonic dropoff for intermediate ∆J values. Such behavior is qualitatively consistent with conventional energy and quantum gap models for rotationally inelastic processes.66-69 Indeed, the F-manifold data in Figure 9 can be roughly fit to an exponential form, i.e., P(∆E) ∝ exp{-β∆E}, with an average energy
3410 J. Phys. Chem., Vol. 100, No. 9, 1996 transfer per collision of 100 cm-1. However, clear discrepancies with these simple models are also evident. For example, the relative cross sections are neither monotonic in J (e.g., 4,F2 vs 3,F1) nor necessarily close for different fine structure states with the same J (e.g., 3,F2, vs 3,F1, 4,F2 vs 4,F1, 5,F1(2) vs 5,F1(1)). Furthermore, detailed comparison between A, E, and F nuclear spin symmetry manifolds shows these simple energy and angular momentum gap trends often to be dramatically violated; for example, the ∆J ) 3 r 0 (∆E ≈ 60 cm-1) transition in the A manifold is roughly 4 times more probable than the ∆J ) 3 r 1 (∆E ≈ 50 cm-1) transition in the F manifold. Thus, the energy-transfer dynamics exhibit a clear sensitivity to the initial and final rotational state wave functions, which experimentally access different features of the potential surface angular anisotropy. Results for CH4 scattering in each of the nuclear spin manifolds with Ar, Ne, and He, along with a more detailed comparison with full quantum theoretical predictions for trial potential energy surfaces, will be presented elsewhere.70 Obtaining quantitative state-to-state cross sections from these plots requires additional considerations. To first order, the relative slopes of these plots can simply be scaled to the total inelastic cross section, measured in absolute units (e.g., see Figure 8) by loss of the initial state. However, this neglects any quantum state dependence to the lab frame velocity distribution, which can exert a small influence on the conversion between column-integrated density (i.e., the result of any absorption measurement) and flux (i.e., the defining quantity in a cross-section measurement). These are linearly related but differ by the ratio of components of the scattered velocities perpendicular to the laser probe axis in the lab frame. This result is true both for molecules scattered from outside into the probe region, as well as for collisions that occur inside the laser column and scatter out of the probe region. Since the species are predominantly forward scattered in the lab frame, then to a good first approximation this effect can be taken into account by scaling the measured density inversely by the final state speed. The magnitude of these corrections are generally small (i.e., j10%) and decrease with decreasing collider mass but can be significant for scattering into the highest rotational level energetically accessible. A more rigorous extraction of the absolute state-to-state cross sections can be obtained by direct measurement of the final-state angular distributions, which permits the exact density to flux conversion to be performed. These state-resolved angular distributions can be obtained via Doppler analysis of the high-resolution line profiles, as demonstrated in the next section. C. State-to-State Angular Distributions from HighResolution Dopplerimetry. The use of high-resolution, direct absorption IR laser sources offers substantially more power than simply labeling the initial and final rotational quantum states in the collision event. Specifically, the inelastic (or elastic) event redistributes the center-of-mass velocities symmetrically around the relative velocity vector, which leads to a distribution of lab frame velocity projections along the laser probe axis. By highresolution Doppler analysis of the molecular frequency shifts, this distribution of velocities for a given initial to final quantum state scattering event can be obtained. From the lab (and centerof-mass) frame velocity distributions, the state-to-state differential cross sections can be directly inferred. The details of this Dopplerimetry procedure have been described elsewhere for hot atom inelastic scattering in the open-shell Cl + HCl system;71 we focus in this section simply on one example to indicate the potential for obtaining state-resolved inelastic angular distributions in the crossed-jet apparatus. An example of high-resolution Dopplerimetry is shown in
Schiffman et al.
Figure 10. Doppler profiles for CH4 F levels following scattering by Ar at E h com ) 307 cm-1). The top trace is the ground rotational state (J ) 1, F1); the traces below it all represent states populated via collisional energy transfer. The Doppler profiles clearly broaden with increasing ∆J, indicating a propensity for increased side scattering with increasing rotational inelasticity.
Figure 10, which displays line profiles for CH4 (F manifold) molecules scattered from J′′ ) 1 into J′ ) 2-7 by collisions with Ar. Several points are worth noting. The J′′ ) 1 initial state exhibits a narrow, roughly Gaussian profile, with a fwhm of 130 MHz. This is somewhat narrower than shown in Figure 6 due to nozzle aperture and expansion conditions. The inelastically populated J′ states, on the other hand, show a systematic increase in Doppler line widths with increasing inelasticity, rising more than 2-fold for J ) 7 r 1 transitions. For reference, the initial CH4 center-of-mass velocity, if directed along the laser, would correspond to approximately a 400 MHz Doppler width, so substantial redistribution of lab frame velocities out in the wings of the Doppler profile is clearly occurring. Due to the mutually perpendicular geometry of the probe laser and intersection plane of the two jets, this increase in Doppler width reflects a propensity for side scattering in the center-of-mass frame that grows with ∆J. Hence, the line shapes indicate a systematic increase in average center-of-mass scattering angle with increasing rotational inelasticity. The differential cross section for each J′ can be extracted as a histogram of flux into a series of angular bins in the centerof-mass frame.71 The key expression is eq 2, which rigorously equates the absorbance at some Doppler-shifted frequency ν to the spectral density of absorbers integrated over the full laser absorption column. For a known rotational inelasticity, initial and final Ar and CH4 velocities, the Doppler profile for molecules scattered into each angular bin can be readily predicted. This profile is first averaged over the initial velocity distributions of Ar and CH4, obtained from the unscattered Doppler profiles in primary and secondary jets. Second, this profile is averaged (via Monte Carlo integration) over the range of collision events inside and outside of the laser volume, which lead to final state population in the laser probe column during the time gate of the gas pulse. Furthermore, this provides the opportunity to correct explicitly for final-state velocity in the
Energy-Transfer Dynamics in Crossed Supersonic Jets
J. Phys. Chem., Vol. 100, No. 9, 1996 3411 worthy of note is the nonmonotonic behavior for inelastically scattered flux into the higher J levels, which is reminiscent of rotational rainbow72 effects in atom + diatom systems. There are relatively few fully state-resolved studies of inelastic differential scattering with which to make a comparison; however, a quite similar phenomenon is observed in stateresolved inelastic scattering of Ar + HF in experiments of Keil and co-workers.73 Specifically, these previous studies reported a systematic shift from forward to side/backward scattering as the final state J′HF varies from 0 to Jmax ) 5. Furthermore, their results for J′HF J 3 indicated a nonmonotonic dip in angular flux for intermediate scattering angles with essentially zero forward scattering flux observed for the J′HF ) 5 state, in good agreement with the currently reported results for Ar + CH4 angular distributions. Further studies with quantum close coupling calculations and/or classical trajectory calculations in such atom + spherical top systems would be extremely useful in interpreting the relevant collision dynamics responsible for this behavior. IV. Discussion
Figure 11. Differential cross section information for CH4 (J ) 3, F1 and 5, F1(2)), excited from CH4 (J ) 1, F1). These plots, presented as differential angular flux into a series of angular bins, are derived from the corresponding Doppler profiles via singular value decomposition methods (ref 71). Unscattered CH4 defines forward scattering, as shown in the top plot. Note the increased propensity for side scattering with rotational inelasticity, and the clear peaking at large center-of-mass deflection angles for the higher J states. This trend is in good qualitative agreement with final state-resolved differential scattering measurements of Ar + HF by Keil and co-workers (ref 73), as well as theoretical predictions for atom and diatom inelastic scattering by Schinke and co-workers (ref 72).
transformation from flux, which is generated by the scattering event, to density, which is experimentally measured via the absorption process. This set of Doppler profiles forms a complete (but highly linearly dependent) basis set, into which the experimental line shape can be expanded. The coefficients of this expansion are determined by singular value decomposition (SVD) methods, where linear dependence in the basis set is systematically taken into account by restricting the degree of freedom of the linear least-squares fit. The angular resolution of such a fitting procedure is currently limited to ∆(cos θcom) ≈ 0.1 by the initial spread of perpendicular velocity components in the primary jet. Sample results for angular flux distributions in the centerof-mass frame from such a fit are shown in Figure 11 for the initial state, J ) 1, and two inelastically populated states, J′ ) 3 and J′ ) 5. Since forward and backward scattering are not distinguished for a perpendicular probe geometry, the plots are presented as a function of |cos θcom|. The trend from purely forward flux for the unscattered state (Figure 11a) to progressively sideways scattered flux for the inelastically excited species is clearly evident. This qualitative trend to larger scattering angle with increasing rotational inelasticity is common with many other systems and classically reflects scattering off the hard repulsive core of the potential energy surface.72 Also
It is worth briefly discussing the relative advantages and disadvantages of the infrared detection method, particularly in comparison with crossed-beam, time-of-flight experimental methods. The major strength of the present infrared laser absorption method is its high quantum state resolution of initial and final states, which thereby permits relatively facile determination of integral state-to-state cross sections for rotationally inelastic scattering. The time-of-flight method has been used principally to establish total differential cross sections, typically summed over all J states. In favorable cases where the molecular rotational constant is large and the colliding atom is light (e.g., CH4 + He), individual state-to-state cross sections can be determined from the amplitudes of successive peaks in the time-resolved mass spectrum. In general, however, the peaks in the time-of-flight spectrum are not sufficiently resolved. For example, even in the best-case scenario of CH4 + He scattering, different fine-structure states in the A, E, and F nuclear spin manifolds (0.1 cm-1) are completely overlapped via time-of-flight methods. For non-hydrides, the situation is even more problematic; in the He + CO2 (BCO2 ) 0.39 cm-1) studies of Beneventi et al.,74 the final scattering states of CO2 appear as one unresolved peak. By comparison, the Doppler widths (∼0.004 cm-1 for CO2) and laser bandwidth in the infrared would be sufficient to resolve all final J scattering states by 2 or more orders of magnitude. Aside from its generality, a principal strength of the timeof-flight technique has been the superb angular resolution offered by the narrow solid angle intercepted by the mass spectrometer. As a result, diffraction oscillations in the angular scattering amplitude have been well resolved for a number of atom + molecule systems including CH4 + He, Ne, Ar,75-77 and CO2 + He.74 In contrast, the current infrared laser technique offers a substantially more modest angular resolution, currently on the order of ∆(cos θ) ≈ 0.1 and limited by velocity spread in the initial jet. Even for perfectly collimated beams, the Jacobian for velocity-to-frequency space transformation in the current right angle geometry is unfavorable; for a nominally 2 MHz laser bandwidth, the resolution would still be g5°,58 which is already substantially inferior to the best angular resolution in the time-of-flight experiments. However, since the time-offlight method samples molecules scattered far from the crossing region, the detected flux is low and decreases quadratically with increasing flight path length and energy resolution.76 In contrast, the infrared laser exploits high-resolution spectroscopy to
3412 J. Phys. Chem., Vol. 100, No. 9, 1996 distinguish the final scattered states and therefore can probe directly in the scattering volume where densities are highest. Another clear advantage of direct infrared absorption methods is the capability to measure absolute state-to-state cross sections directly, which proves to be difficult with other detection schemes. For example, differential cross sections reported from time-of-flight studies have been scaled to theoretically determined cross sections, due to lack of absolute intensity calibration. Similar problems exist for LIF and MPI methods, where the calibration issues involving absolute fluorescence quantum yields, ionization, and photomultiplier detection efficiencies can make extraction of absolute number densities in the scattering region challenging. In the present direct absorption experiments, however, the absolute integrated number densities can be determined directly from absolute integrated absorbances, based simply on line strengths determined from previous spectroscopic studies. This novel capability facilitates particularly rigorous comparison of state-to-state experimental results with predictions from ab initio and empirical potential energy surfaces,74-76 as demonstrated71 for He + CH4 in Table 1. Finally, one can use skimmers to reduce the angular and velocity divergences in the primary and secondary jets. As shown in Figure 6c,d the Doppler fwhm (30 MHz) observed in this configuration is 5-6-fold narrower than obtained in the unskimmed jets and additionally reduces the spread in centerof-mass collision energies. With this modification, the collision energy may also be continuously “tuned” by varying the angle with which the beams intersect. In principle, this could allow direct studies of scattering resonances and of the onset of rotationally inelastic scattering channels near their energetic thresholds. Furthermore, by orienting the infrared laser beam parallel to the relative velocity vector, it becomes possible to distinguish forward and backward scattering collision events via high-resolution Dopplerimetry. This scattering geometry would also take advantage of the elegant mathematical schemes of Serri et al.58 and Taatjes et al.59 for direct inversion of Doppler profiles to obtain center-of-mass scattering distributions. V. Summary A general method for measurements of state-to-state, integral and differential cross sections for rotational energy transfer in crossed jets is presented, based on direct absorption of tunable, narrow bandwidth, infrared laser light. An infrared chromophore target gas, seeded in rare gas and cooled into its lowest J state via supersonic expansion in a pulsed pinhole nozzle, is rotationally excited in single collisions with a second pulsed jet of collider gas. The populations of the target molecule are monitored via time-resolved absorption of infrared laser light in the jet intersection region, as a function of J state and Doppler detuning. Total inelastic scattering cross sections can be obtained by measuring the loss of initial quantum state, while state-to-state cross sections can be obtained by monitoring growth into the collisionally excited final states. Angular information on the center-of-mass frame flux can be extracted from the observed Doppler profiles, which reflect the speed and direction of the scattered species for each J state. Furthermore, absolute column-integrated number densities of gases in the jet intersection region can be determined from the fractional infrared attenuations via Beer’s law, which permits absolute state-tostate scattering cross sections to be measured. This method provides high-resolution experimental access to information on the angular anisotropy of the potential surface at energies above the van der Waals dissociation limit (E J D0). As such, these studies are quite complementary to the extensive investigations of potential surfaces in the bound state region (E j D0) made
Schiffman et al. possible by high-resolution near-IR, far-IR, and microwave spectroscopic studies of the corresponding molecular complexes. Detailed application of these methods to state-to-state scattering of rare gases with CH4, HF, and H2O, as well as rigorous comparison with full quantum close coupling predictions from currently available intermolecular potential surfaces, will be presented elsewhere.70,78 Acknowledgment. This work has been supported by funds from the Air Force Office of Scientific Research. References and Notes (1) Hucknall, D. J. Chemistry of Hydrocarbon Combustion; Chapman and Hall: New York, 1985. (2) Brasseur, G.; Solomon, S. Aeronomy of the Middle Atmosphere; Reidel: Dordrecht, 1986. (3) Andresen, P.; Aristov, N.; Beushausen, V.; Ha¨usler, D.; Lu¨lf, H. W. J. Chem. Phys. 1991, 95, 5763. (4) Bertojo, M.; Cheung, A. C.; Townes, C. H. Astrophys. J. 1970, 208, 914. (5) Kosloff, R.; Kafri, A.; Levine, R. D. Astrophys. J. 1977, 215, 497. (6) Yelle, R. V. Astrophys. J. 1991, 383, 380. (7) Schiffman, A.; Nesbitt, D. J. J. Chem. Phys. 1993, 100, 2677. (8) Pine, A. S.; Looney, J. P. J. Mol. Spectrosc. 1987, 122, 41. (9) Pine, A. S. J. Chem. Phys. 1944, 101, 3444. (10) Roche, C. F.; Hutson, J. M.; Dickerson, A. S. J. Quant. Spectrosc. Radiat. Transfer 1955, 53, 153. (11) Rahn, L.; Palmer, R. E. J. Opt. Soc. B 1986, 3, 1164. (12) Williams, S.; Zare, R. N.; Rahn, L. A. J. Chem. Phys. 1994, 101, 1072. (13) Pendleton, W., Jr.; Espy, P.; Baker, D.; Steed, A.; Fetrow, M. F. J. Geophys. Res. 1989, 94, 505. (14) Smith, D. R.; Blumberg, W. A. M.; Nadile, R. M.; Lipson, S. J.; Huppi, E. R.; Wheeler, N. B. Geophys. Res. Lett. 1992, 19, 593. (15) Andresen, P.; Joswig, H.; Pauly, H.; Schinke, R. J. Chem. Phys. 1982, 77, 2204. (16) Sitz, G. O.; Farrow, R. L. J. Chem. Phys. 1994, 101, 4682. (17) Clark, R.; McCaffery, A. J. Mol. Phys. 1978, 35, 617. (18) Mattheus, A.; Fischer, A.; Ziegler, G.; Gottwald, E.; Bergmann, K. Phys. ReV. Lett. 1986, 56, 712. (19) Weida, M. J.; Nesbitt, D. J. J. Chem. Phys. 1994, 100, 6372. (20) Schiffman, A.; Chandler, D. W. Int. ReV. Phys. Chem., in press. (21) Foy, B.; Hetzler, J.; Millot, G.; Steinfeld, J. I. J. Chem. Phys. 1988, 88, 6838. (22) Chen, H.-L.; Moore, C. B. J. Chem. Phys. 1971, 54, 4072. (23) Kurzel, R.; Steinfeld, J. I. J. Chem. Phys. 1977, 53, 3293. (24) Bergmann, K.; Demtroder, W. Z. Phys. 1971, 243, 1. (25) Hetzler, J.; Millot, G.; Steinfeld, J. I. J. Chem. Phys. 1989, 90, 5434. (26) Hetzler, J.; Steinfeld, J. I. J. Chem. Phys. 1990, 92, 7135. (27) Klaassen, J. I.; Coy, S. L.; Steinfeld, J. I.; Roche, C. J. Chem. Phys. 1994, 100, 5519. (28) Fletcher, T. R.; Leone, S. R. J. Chem. Phys. 1988, 88, 6838. (29) Sung, J. P.; Setser, D. W. J. Chem. Phys. 1978, 69, 3868. (30) Kreutz, T. G.; Kahn, F. A.; Flynn, G. W. J. Chem. Phys. 1990, 92, 347. (31) Zhu, L.; Kreutz, T. G.; Hewitt, S. A.; Flynn, G. W. J. Chem. Phys. 1990, 93, 3277. (32) Lovejoy, C. M.; Goldfarb, L.; Leone, S. R. J. Chem. Phys. 1992, 96, 7180. (33) Lengel, R. K.; Crosley, D. J. J. Chem. Phys. 1977, 68, 5309. (34) Taatjes, C. A.; Leone, S. R. J. Chem. Phys. 1988, 89, 302. (35) Bewick, C. P.; Haub, J. G.; Hynes, R. G.; Martins, J. F.; Orr, B. J. J. Chem. Phys. 1988, 88, 6350. (36) Sitz, G. O.; Farrow, R. L. J. Chem. Phys. 1990, 93, 7883. (37) Farrow, R. L.; Chandler, D. W. J. Chem. Phys. 1988, 89, 1994. (38) Green, S.; Hutson, J. M. J. Chem. Phys. 1994, 100, 891. (39) Scoles, G. Atomic and Molecular Beam Methods; Oxford University Press: New York, 1988. (40) Buck, U.; Huisken, F.; Schleusener, J. J. Chem. Phys. 1978, 68, 5654. (41) Buck, U.; Huisken, F.; Schleusener, J.; Schafer, J. J. Chem. Phys. 1980, 72, 1512. (42) Andres, J.; Buck, U.; Huisken, F.; Schleusener, J.; Torello, F. J. Chem. Phys. 1980, 73, 5620. (43) Gentry, W. R.; Giese, C. G. J. Chem. Phys. 1977, 67, 5389. (44) Faubel, M.; Kohl, K.-H.; Toennies, J. R.; Tang, K. T.; Yung, Y. Y. Faraday Discuss. Chem. Soc. 1982, 73, 205. (45) Krajnovich, D. J.; Butz, K. W.; Du, H.; Parmenter, C. S. J. Chem. Phys. 1989, 91, 7725.
Energy-Transfer Dynamics in Crossed Supersonic Jets (46) Butz, K. W.; Du, H.; Krajnovich, D. J.; Parmenter, C. S. J. Chem. Phys. 1988, 89, 4680. (47) Gottwald, E.; Bergmann, K.; Schinke, R. S. J. Chem. Phys. 1987, 86, 2685. (48) Meyer, H. J. Chem. Phys. 1994, 101, 6686. (49) Meyer, H. J. Chem. Phys. 1994, 101, 6697. (50) Dagdigian, P. J.; Wilcomb, B. E.; Alexander, M. H. J. Chem. Phys. 1979, 71, 1670. (51) Corey, G. C.; Alexander, M. H.; Dagdigian, P. J. J. Chem. Phys. 1986, 84, 1547. (52) Dagdigian, P. J. J. Chem. Phys. 1989, 90, 6110. (53) Dagdigian, P. J. J. Chem. Phys. 1989, 90, 2617. (54) Macdonald, R. G.; Liu, K. J. Chem. Phys. 1989, 91, 821. (55) Sonnenfroh, D. M.; Macdonald, R. G.; Liu, K. J. Chem. Phys. 1991, 94, 6508. (56) Suits, A. G.; Bontuyan, L. S.; Houston, P. L.; Whitaker, B. J. J. Chem. Phys. 1992, 96, 8618. (57) Bontuyan, L. S.; Suits, A. G.; Houston, P. L.; Whitaker, B. J. J. Phys. Chem. 1993, 97, 6342. (58) Serri, J. A.; Becker, C. H.; Elbel, M. B.; Kinsey, J. L.; Moskowitz, W. P.; Pritchard, D. E. J. Chem. Phys. 1980, 74, 5116. (59) Taatjes, C. A.; Cline, J. I.; Leone, S. R. J. Chem. Phys. 1990, 93, 6554. (60) Hall, J. L.; Lee, S. A. Appl. Phys. Lett. 1976, 29, 367. (61) Balhorn, R.; Kunzman, H.; Lebowsky, F. Appl. Opt. 1972, 4, 742. (62) Herriot, D.; Kogelnik, H.; Kompfner, R. Appl. Opt. 1965, 4, 25. (63) Dang-Nhu, M.; Pine, A. S.; Robiette, A. G. J. Mol. Spectrosc. 1979, 77, 57. (64) Pine, A. S.; Fried, A.; Elkins, J. W. J. Mol. Spectrosc. 1985, 109, 30.
J. Phys. Chem., Vol. 100, No. 9, 1996 3413 (65) Hogg, R. V.; Tanis, E. A. Probability and Statistical Inference; Macmillan: New York, 1977. (66) Polanyi, J. C.; Woodall, K. B. J. Chem. Phys. 1972, 56, 1563. (67) Brunner, T. A.; Pritchard, D. AdV. Chem. Phys. 1982, 50, 589. (68) McCaffery, A. J.; Proctor, M. J.; Whitaker, B. J. Annu. ReV. Phys. Chem. 1986, 37, 223. (69) McCaffery, A. J.; Alwahabi, Z. T.; Osborne, M. A.; Williams, C. J. J. Chem. Phys. 1993, 98, 4586. (70) Chapman, W. B.; Schiffman, A.; Nesbitt, D. J. Manuscript in preparation. (71) Zhao, Z.-Q.; Chapman, W. B.; Nesbitt, D. J. J. Chem. Phys., in press. (72) Schinke, R.; Korsch, H. J.; Pappe, D. J. Chem. Phys. 1982, 77, 6005. (73) Rawluk, L. J.; Fan, Y. B.; Apelblat, Y.; Keil, M. J. Chem. Phys. 1991, 94, 4205. (74) Beneventi, L.; Casevecchia, P.; Vecchiocattivi, F.; Volpi, G. G.; Buck, U.; Lauenstein, C.; Schinke, R. J. Chem. Phys. 1988, 89, 4671. (75) Buck, U.; Kohlhase, A.; Phillips, T.; Secrest, D. Chem. Phys. Lett. 1983, 98, 199. (76) Buck, U.; Kohl, K.-H.; Kohlhase, A.; Faubel, M.; Staemmler, V. Mol. Phys. 1985, 55, 1255. (77) Malik, D. J.; Secrest, D.; Buck, U. Chem. Phys. Lett. 1980, 75, 465. (78) Chapman, W. B.; Kulke, A.; Nesbitt, D. J. Manuscript in preparation.
JP952708J
