Stereodynamics at the GasâLiquid Interface: Orientation and

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Stereodynamics at the Gas-Liquid Interface: Orientation and Alignment of CO2 Scattered from Perfluorinated Liquid Surfaces† Bradford G. Perkins, Jr. and David J. Nesbitt* JILA, UniVersity of Colorado and National Institute of Standards and Technology, and Department of Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309-0440 ReceiVed: July 23, 2009; ReVised Manuscript ReceiVed: October 29, 2009

Rotational orientation/alignment dynamics of CO2 scattered from a perfluorinated polyether (PFPE) liquid surface has been investigated via direct absorption experimental studies and theoretical molecular dynamics (MD) simulations. Experimentally, polarization modulation of a single mode diode laser is combined with lock-in detection to measure circular/linear IR polarizance due to CO2 scattering from the surface at θinc ) 60° and Einc ) 10.6(8) kcal/mol and probed over a series of final scattering angles. The differential absorption intensities are related through Fano-Macek theory to the three lowest multipole moments (A0, A2+, and O1-) which describe collisionally induced orientation and alignment at the liquid surface. The total scattering population reflects both trapping-desorption (TD) and impulsive scattering (IS) components, with a strong positiVe anisotropy in the MJ distribution that indicates preferential CO2 scattering from the surface with a forward (i.e., “topspin”) sense of end-over-end tumbling. Theoretical trajectory simulations provide 3D CO2 flux and J state distributions scattering from fluorinated self-assembled monolayers (F-SAMs) and are compared with experimental results as a function of final rotational state. Specifically, trends in the theoretical orientation/ alignment moments are in remarkable agreement over the full range of J states but with values consistently overpredicted by nearly 2-fold, which may reflect a higher level of local ordering for F-SAMS vs a gas-PFPE liquid interface. I. Introduction The interaction of isolated gas molecules at a liquid surface involves a dynamical series of collisions, which determines a path that may include direct impulsive scattering, surface trapping, desorption, or long-time solvation. The possibility of each of these events is dictated by a number of important chemical and physical properties where each interaction provides an avenue for energy transfer between the gas and liquid. While the trajectory of a gas is determined by properties such as mass,1,2 density,3,4 and electrostatic forces,4–11 dynamical motion of the surface directly influences the trapping probability of incident projectiles. Recent work in our laboratory has focused on molecular beam studies that involve scattering CO2 from a series of liquid surfaces,12–17 where the final translational, angular, and internal state distributions reflect the nature of the interface on the time scale of molecular collisions. Distributions for each of these degrees of freedom help elucidate the scattering mechanism, for example, whether it is dominated by impulsive collisions or a series of thermalizing interactions, or some combination of the two. In an effort to probe the collision dynamics in more detail, the current study focuses on the spatial distribution of angular momentum in CO2 as it scatters from a perfluorinated liquid surface. Specifically, we are interested in uncovering the lowest moments of the J, MJ distribution, where Table 1 lists the three lowest tensor elements corresponding to alignment (A0, A1+, and A2+) and orientation vector (O1-). Throughout this work, the z axis is parallel to the surface normal, with the incident molecular beam moving in the +x, -z direction and lying in the x-z plane. †

Part of the “W. Carl Lineberger Festschrift”. * Author to whom correspondence should be addressed. E-mail: [email protected].

We note that the alignment (A0, A1+, and A2+) contains only eVen moments and thus comments only on the magnitude but not the sign of the MJ distribution. Conversely, orientation (O1-) reflects an odd moment of the distribution and thus is sensitive to both the magnitude and sign of MJ. Such a vector-based characterization of the rotational excitation begins to provide a physical framework for understanding both equilibrium and nonequilibrium collision events at the gas-liquid interface. Motivation for the current work derives from earlier experiments probing the corresponding stereodynamics of collisions at gas-single crystal metal interfaces, for example, N2 and NO scattered from Ag(111) and Pt(111).18–24 In these pioneering studies, the lowest order orientation and alignment moments of the angular momentum are determined by probing final J, MJ state populations via polarized resonance enhanced multiphoton ionization (REMPI) methods.19,20 Orientation information for a given J state is obtained by right-hand/left-hand circular polarized excitation to reveal the net helicity associated with rotational excitation. Likewise, rotor alignment terms for the diatomic are extracted with horizontal/vertical linear polarized excitation, which provides information on the predominant plane of rotation.25,26 In the N2 + Ag(111) system,19,20 for example, the measurements clearly illustrate that J for the scattered species is oriented and points preferentially parallel to the surface and perpendicular to the scattering plane, i.e., corresponding to classical “cartwheel” motion. A predominant projection of J along the y axis is to be expected by symmetry. Interestingly, however, the sign of this projection for gas-single crystal metal scattering depends on the final scattering angle; for subspecular angles (i.e., θf < θspec), N2 molecules preferentially spin backward (i.e., “backspin”), whereas, for superspecular angles (θf > θspec), the N2 molecules preferentially spin forward (i.e., “topspin”). This result speaks to the close

10.1021/jp907022u  2010 American Chemical Society Published on Web 12/29/2009

Stereodynamics at the Gas-Liquid Interface

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TABLE 1: Lowest Order Orientation and Alignment Moments moment A0

A1+

A2+

O1-

expectation value of operator

〈〈Ji |3Jz2 - J2 |Ji〉〉 Ji(Ji + 1) 〈〈Ji |JxJz + JzJx |Ji〉〉 Ji(Ji + 1)

experimental expressiona 0° 0° 90° 90° + 2Plin Plin + Plin ) 2 · (Plin 0° 0° 90° 90° h(2)(Ji, Jf) · (3 + Plin - Plin Plin + Plin )

b

〈〈Ji |J2x - J2y |Ji〉〉 Ji(Ji + 1)

0° 90° - Plin ) 2 · (Plin 0° 0° 90° 90° h(2)(Ji, Jf) · (3 + Plin - Plin Plin + Plin )

〈〈Ji |Jy |Ji〉〉

0° 90° 2 · (1 + Plin )Pcir

√Ji(Ji + 1)

0° 0° 90° 90° h(1)(Ji, Jf) · (3 + Plin - Plin Plin + Plin )

a 90° 0° 90° 0° are linear polarizances Pcir and Pcir are circular polarizances for the φlaser ) 90° and 0° configurations, respectively. Likewise, Plin and Plin for the two experimental setups shown in Figure 3. b The A1+ moment is not accessible from the two laser probe configurations illustrated in Figure 3.

Figure 1. Dynamics at the gas-liquid interface involve a range of trajectory pathways that have nominally been classified as either trapping-desorption (TD) or impulsive scattering (IS). Nonequilibrium scattering distributions result in anisotropy in the spatial distribution of J for CO2 as it recoils from perfluorinated liquid surfaces. In terms of orientation and alignment, the stereodynamics provide details of the mechanism by which the forces at the surface cause significant torque on the scattered molecules.

competition between multiple torque contributions that arise from atomic corrugation of the single crystal surface, which is also consistent with the relatively small magnitude of these orientation/alignment effects. Gas-liquid interfaces, on the other hand, are thought to be intrinsically much rougher due to surface capillaries, phonons, and acoustic waves that arise from thermal excitation and define the interfacial boundary. This naturally raises the question of orientation/alignment stereodynamics of molecules due to collisions at the gas-liquid interface, which represents the major focus of this work. The current paradigm in gas-liquid collision dynamics is illustrated in Figure 1, for which the scattered gas molecules are grouped into two broad categories, historically labeled as trapping-desorption (TD) and impulsive scattering (IS).2,17 Gas molecules that scatter through the TD channel typically desorb from the surface after sufficient collisional interactions to result

in complete thermal accommodation; indeed, there is some incentive for TD being renamed as “thermalized desorption”. These molecules follow a cos(θf) desorption pattern, where θf is the final scattering angle, measured with respect to the normal, and translational and internal states reflect Maxwell-Boltzmann distributions characterized by the surface temperature (TS).6 By way of contrast, molecules in the IS category typically retain an appreciable fraction of the incident energy, in spite of significant inelastic interactions with the surface. Molecules that impinge at a finite incident angle (θinc > 0°) are more likely to scatter in the forward direction but with loss of parallel momentum due to surface corrugation, thus resulting in peak intensity at a subspecular angle.14 Though less is known about normal velocity component distributions (i.e., Vz), previous Doppler studies of CO2 and perfluorinated surfaces indicate that the rotational (J) and parallel (i.e., Vx, Vy) translational distributions from the IS channel are reasonably characterized by a temperature, TIS, which depends on incident energy and initial and final scattering angle.14 The ability of a single parameter to characterize impulsive scattering events would be consistent with multiple gas-surface collisional interactions, i.e., sufficient to scramble populations into a temperature-like distribution, albeit still with TIS . TS. In addition to these quantum state resolved studies, preliminary experiments from our group with circularly polarized light report that CO2 preferentially scatters from the surface with a positive sense of end-over-end tumbling, i.e., “topspin”.13 Furthermore, these orientation effects are strongly correlated with the magnitude of J, such that more rapidly rotating molecules are more highly oriented. Together, these measurements suggest a dynamically much rougher gas-liquid interface, for which local corrugation provides impact sites that preferentially torque CO2 into quantum states of both high J and 〈MJ〉 > 0 perpendicular to the scattering plane. Along with these quantum state resolved experimental studies, classical molecular dynamics (MD) simulations of CO2 + fluorinated self-assembled monolayers (F-SAMs) have been pursued, which provide considerable additional insight into the nature of the gas-liquid interaction.27–36 Prospects for meaning-

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Figure 2. Experimental configuration to probe orientation and alignment of CO2 with direct infrared absorption. Light from a narrow bandwidth Pb-salt diode laser is used to probe individual rovibrational transitions (0001 r 0000; J ) 0-50) for CO2 that scatters from a liquid surface. Orientation and alignment are determined from the differential absorption of two laser polarizations in a series of geometrical configurations. A photoelastic modulator (PEM) is used to rotate the polarization from right (RCP) to left (LCP) circularly polarized to determine orientation, or from parallel (|) to perpendicular (⊥) to the surface for alignment. The PEM crystal oscillates at 37.5 kHz, where any birefringence from the scattered CO2 leads to an oscillating absorption at that frequency. Standard lock-in techniques are used to demodulate the signal, which is directly proportional to either ARCP - ALCP or A|| - A⊥. The alignment tensors and orientation vector follow directly from these values through the details of Fano-Macek theory.

ful comparison of quantum states formed from CO2 + F-SAM versus CO2 + liquid PFPE surfaces stem from a similarity in physical properties. For example, liquid perfluoropolyether (PFPE) and F-SAM surfaces have nearly identical density (1.87 vs 1.93 g/cm3, respectively),12,37 thermal expansion (8.3 × 10-4 vs 1.0 × 10-3 K-1),12,37 and surface tension (17 vs ≈ 15 dyn/cm).12,38 Interestingly, both surfaces are characteristically rougher than single crystal metals, yet the root mean square (rms) surface deviations are nearly twice as large for PFPE (≈7 Å) compared to the F-SAMs (≈4 Å)39 under room temperature conditions. Indeed, results from these scattering simulations have been shown to be in remarkably quantitative agreement with experimental studies as a function of incident energy,27,28 surface temperature,12 and incident angle. Polarization studies on CO2 + perfluorinated liquids have also shown extensive end-overend “topspin” to be predicted in the molecular dynamics simulations.13 Both experimental and theoretical results reveal a J state dependent orientation, where the topspin magnitude systematically increases from nearly zero at low J to ≈20% at J ) 50. While the dominant stereodynamical effect is due to the collisional orientation of the rotor, alignment of the CO2 angular momentum also provides additional insights into the scattering mechanism. The focus of the present work is to systematically explore quantum state resolved orientation and alignment moments of the angular momentum distribution through experimental measurements with polarized laser light and theoretical simulations of the three-dimensional (3D) scattering distribution. These results may then be compared to previous quantum state resolved alignment/orientation studies of gas-single crystal systems, which serve to further illustrate the striking differences between liquid and solid metal surfaces. The organization of this paper is as follows. Section II describes the important details of the experiment and scattering geometries. Experimental results are presented in section III. Theoretical simulations are discussed in section IV, where results illustrate the full 3D flux and J distributions. Orientation/ alignment moments are extracted from analysis of the experimental and theoretical data in section V, followed by final remarks and conclusions in section VI. II. Experimental Methods A. Detection Scheme. The coordinate system for the scattering experiments is illustrated in Figure 1, where x and y define

the surface plane and z is parallel to the surface normal. Quantum state populations of scattered CO2 are measured with a high resolution Pb-salt diode laser spectrometer, as illustrated in the details of Figure 2. Spatial characterization of the angular moments (i.e., A0, O1-, A2+) requires measurements from at least two experimental configurations and with different laser polarizations.25 The choice of experimental configurations is based on the gas-surface scattering plane, with limiting cases dependent on the incident angle of the projectile. For example, the angular momentum and scattering distributions under normal incidence conditions (θinc ) 0°) will be symmetric due to the time averaging of interaction geometries at the interface. As a result, distributions of Jx and Jy parallel to the surface are equivalent and independent of the Jz component perpendicular to the surface. In this case, all of the odd (i.e., orientation) moments must vanish identically, due to the equal probability for torquing the molecule clockwise or counterclockwise with respect to the x and y axes. On the other hand, this is not true for any of the even moments. Thus, nonzero alignment is possible for any state with J > 0, and can be extracted from differential absorption of light linearly polarized parallel versus perpendicular to the surface. However, when θinc > 0°, the final angular patterns only retain a time averaged plane of symmetry defined by the surface normal (z) and the incident trajectory of the molecule in the x-z plane. Under these conditions, both even (alignment) and odd (orientation) moments can be nonzero for J > 0, which then require absorption measurements along multiple axes with both linearly and circularly polarized light. Geometries for the current study are illustrated in Figure 3, with the incident CO2 traveling at θinc ) 60° toward the surface in the x-z plane and the origin at the intersection of the molecular beam and the liquid surface. To detect the scattered flux of CO2, the laser beam is passed ∼2 cm above the liquid along one of two paths. In the φlaser ) 90° configuration, the laser propagates parallel to the y axis (k | y) and detects molecules that scatter at θscat ) 60°, which is the angle defined by the z axis, the origin, and the point at which the laser crosses the x-z scattering plane. The polarization vector (ε) is given by ε ) εx cos β + iεz sin β, where β ) 0° and 90° correspond to light polarized parallel (|) and perpendicular (⊥) to the surface, respectively. Similarly, β ) +45° and -45° indicate right (RCP) and left (LCP) circularly polarized radiation. Alternatively, for the φlaser ) 0° configuration, laser propagation is along the x axis (k | x), detecting mostly in-plane scattering trajectories but column-integrated over all final polar


J. Phys. Chem. A, Vol. 114, No. 3, 2010 1401 for linearly polarized light parallel (|) versus perpendicular (⊥) to the surface represents linear polarizance,

Plin )

Figure 3. Two experimental configurations are used to probe the scattering dynamics. In both setups, the liquid wheel assembly and laser multipass remain fixed in place while the position of the pulsed valve changes from parts a to b. In configuration a, the laser beam passes perpendicular to the scattering plane along the +y axis to capture inplane and out-of-plane scattering trajectories near the specular angle, (θinc ) θscat ≈ 60°). For configuration b, the origin of the molecular beam is moved so that the laser passes parallel to the +x axis above the liquid surface in the plane of the incident molecular beam. For both configurations, sample Doppler-broadened signals are plotted to illustrate absorption, circular polarizance, and linear polarizance for CO2 + PFPE.

angles. Now the x-y axis polarization labels are reversed (i.e., ε ) εy cos β + iεz sin β) but offer the same options for facile switching between parallel/perpendicular and right-hand/left-hand circularly polarized light with β.25 Scattered carbon dioxide is detected by direct absorption of infrared laser light, where the magnitude of the signal is determined by the given MJ distribution of the gas and the polarization of the laser light.40 Orientation and alignment moments are ascertained from the difference in the measured absorbance from two laser polarizations in a given configuration. Such differences arise from anisotropy in the scattered CO2 MJ distributions, which then impact the magnitude of the measurement based on Ho¨nl-London line strength factors and the polarization of light. In terms of experimentally determined quantities, the differential absorption of right (RCP) and left (LCP) circularly polarized light yields the circular polarizance, defined by

Pcir )

ARCP - ALCP ARCP + ALCP

(1)

where ARCP and ALCP are explicit absorbance intensities of the scattered CO2. In a similar fashion, the differential absorption

A|| - A⊥ A|| + A⊥

(2)

On the basis of the previous description, we note that Pcir determines the handedness of rotation, and thereby reflects the orientation of CO2 around a specific scattering axis. Likewise, Plin characterizes alignment with respect to the predominant plane of rotation. In order to relate these two polarizances to a given MJ distribution, the absorbances are expressed in terms of the appropriate J′,MJ′ r J′′,MJ′′ transition dipole moments. Explicit expressions for these relationships are listed in Table 2, with details further presented in section III. As first developed by Fano and Macek, this establishes a direct connection between (i) Pcir and Plin and (ii) the lowest dipole (O1-) and quadrupole (A0, A1+, and A2+) moments of the spatial distribution of J.25,26 These relationships are listed in Tables 1, 2, and 3, where the details of the theory are outlined in section V. B. Experimental Details. The fundamental experimental details have been described previously;13,14,17 we therefore focus on specifics relevant to the present measurements. A 10% mixture of CO2 in H2 passes through a 500 µm pinhole in a piezo-electric controlled pulsed valve,41 where the orifice is fixed 10 cm from the liquid surface. The molecular jet is then skimmed by a 3.0 mm aperture mounted 1.5 cm downstream along the expansion axis to limit angular beam divergence to (6°. Boltzmann analysis of the rotational distributions in the incident beam yields Trot ≈ 20 K for both the ground (0000) and first vibrationally excited state (0110).14,42 Translational kinetic energy is characterized by time-of-flight (TOF) measurements17 and high resolution Dopplerimetry of the absorption profiles, both of which confirm a beam energy of Einc ) 10.6(8) kcal/mol. The incident CO2 strikes a fresh liquid surface that is prepared according to methods first developed by Lednovich and Fenn.43 A 15 cm glass wheel rotates through a 300 mL reservoir of PFPE. As the submerged fraction of the wheel emerges from the liquid, a stainless steel razor blade scrapes away the top layer to reveal a fresh 0.5 mm thick film of PFPE, which then rotates into the path of the molecular beam. The valve, skimmer, and wheel assembly are housed inside a 60 L aluminum vacuum chamber, with a base pressure of 2 × 10-6 Torr and average pressure while pulsing of 3.0 × 10-5 Torr maintained by a 6” liquid nitrogen trapped diffusion pump. The scattered CO2 molecules are detected by direct absorption of polarization modulated infrared light from a Pb-salt diode laser. The laser beam is split several times within the spectrometer to simultaneously measure (i) the scattered CO2, (ii) the absolute frequency from a room temperature cell of CO2, and (iii) relative frequencies from the transmission fringes of a confocal etalon. To measure the scattered flux populations and polarizance, a linear MgF2 Rochon polarizer is used with a photoelastic modulator (PEM) to generate polarization states oscillating between RCP and LCP or | and ⊥. For example, the polarization state from the laser diode is first established by a linear polarizer (β ) 0°) before reaching the PEM, which is a ZnSe crystal driven resonantly by two piezoelectric bars to generate stress-induced birefringence. The polarization state of the desired RCP/LCP light is monitored by passing through a Babinet-Soleil compensator used as a λ/4 plate to convert back into | or ⊥ polarization, followed by a linear Rochon polarizer in a crossed configuration. The PEM amplitude is then increased until the transmission varies between zero (i.e., a true null) and a maximum value, which indicates that the polarization state

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TABLE 2: Experimentala Circular and Linear Polarizance Expressions

polarizanceb,c

φlaser Pcir

φlaser Plin

ARCP - ALCP ARCP + ALCP

A|| - A⊥ A|| + A⊥

(2J + 3) · 〈MJ〉

J(J + 1) - 3〈M2J 〉

(J + 1)(J + 2) + 〈M2J 〉

(J + 1)(3J + 4) - 〈M2J 〉

R-branch

(2J + 1) · 〈MJ〉

J(J - 1) - 3〈M2J 〉

J(J + 1) + 〈M2J 〉

J(3J + 1) - 〈M2J 〉

P-branch

6h(1)(Ji, Jf) · O1-

3h(2)(Ji, Jf) · (A0 - A2+)

4 + h(2)(Ji, Jf) · (A0 + 3A2+)

4 + h(2)(Ji, Jf) · (A0 + 3A2+)

φlaser ) 90°d

φlaser ) 0°

0

3h(2)(Ji, Jf) · (A0 + A2+) 4 + h(2)(Ji, Jf) · (A0 - 3A2+)

a φlaser φlaser Experimental configurations are illustrated in Figure 3. b Pcir and Plin are circular and linear polarizances for the specific experimental configuration defined by the laser detection geometry, φlaser ) 0° or 90°. c ARCP, ALCP, A|, and A⊥ are experimental CO2 absorbance intensities based on the given polarization of the laser light. d A0, A1+, and A2+ are the quadrupole moments of the angular momentum distribution. The labels for these quantities follow the historical precedence set in ref 25.

TABLE 3: h(1)(Ji, Jf) and h(2)(Ji, Jf) from ref 25 JF

absorption branch

h(1)(Ji, Jf)

h(2)(Ji, Jf)

Ji + 1

R

-Ji

-Ji 2Ji + 3

√Ji(Ji + 1) Ji

Q

Ji - 1

P

1

√Ji(Ji + 1) Ji + 1

√Ji(Ji + 1)

1

-(Ji + 1) 2Ji - 1

prior to the Babinet-Soleil λ/4 plate is correctly oscillating between RCP and LCP extrema once per cycle (37.5 kHz). For linear polarizance measurements, the Babinet-Soleil λ/4 plate is simply removed and the PEM amplitude further increased to reach the orthogonal linear polarization state (i.e., β ) 90°), once again to obtain modulation between a maximum transmission and a true null through the second Rochon crossed polarizer. In this case, the polarization state passes through linear twice per cycle, and therefore, the laser polarization is modulated between | and ⊥ at 75 kHz. Once the correct PEM amplitude has been achieved, the second Rochon polarizer is removed and the light passed above the liquid surface in a 14-fold multipass44 to detect the scattered CO2. Transmitted light after the multipass cell is measured on a liquid nitrogen cooled InSb photovoltaic, where the signal voltage is split to measure both (i) absorbance and (ii)

polarizance. The voltage is first sent directly to an analog-todigital converter, which stores time traces of the transmitted signal as a function of frequency across a rovibrational transition. To determine the differential absorption for the polarizance, the signal voltage is then heterodyned against the PEM crystal oscillation using standard lock-in techniques, where the reference frequency is either f ) 37.5 or 75 kHz for the orientation or alignment experiments, respectively. As the frequency of the light is tuned over a Doppler-broadened absorption profile, the demodulated signal reflects the birefringence caused by an anisotropic MJ distribution in the scattered flux of CO2. This signal passes through a six-pole low-pass Bessel filter to eliminate the 2f component, after which the DC value is linearly proportional to the desired polarizance. The demodulated and absorbance signals are stored in real time, with both traces later processed with adjustable time gates to generate frequencydependent absorption and polarizance profiles, respectively. III. Experimental Results A. Rotational State Populations. Sample absorption profiles are illustrated in Figure 3a and b for scattered CO2 (J ) 40) measured in the φlaser ) 90° and 0° configurations, respectively. The Doppler-broadened line shape reflects the coupled translational and angular distributions of the scattered flux, while the integrated area (AV,J) of these profiles samples the fractional population in the given J state. In terms of the measured polarizance, AV,J is equal to either 1/2(ARCP + ALCP) or 1/2(A|| + A⊥). A previous report from our group featured a detailed analysis of the rotational, translational, and angular scattering distributions, where these populations were characterized surprisingly well by TD and IS components at different temperatures.13–15 Specifically, the TD component is assumed to desorb from the surface with rotational and translation distributions that cor-



respond to Trot(TD) ≈ Ttrans(TD) ≈ TS ) 298 K. In addition, the final angular distribution is assumed to follow a cos(θf) pattern that reflects the effusive nature of desorption. The twotemperature model extracts both the relative fraction of TD (R) in each scattering configuration as well as an IS rotational temperature. The final angular distributions for this incident angle are broad lobular patterns that preferentially peak in the forward, slightly subspecular direction. In the context of this model, we expect little or no contribution to the alignment/ orientation dynamics from the accommodated TD fraction, with only the nonequilibrated IS population contributing significantly to the spatial anisotropy of J. B. Circular Polarizance. From the outline in section IIA, orientation is primarily obtained from the differential absorption of RCP and LCP light. A sample demodulated signal (ARCP ALCP) for J ) 40 is plotted in Figure 3a for φlaser ) 90°. On the basis of the geometry of the scattering system and laser beam, these absorption measurements characterize CO2 that has been scattered in the specular direction. The demodulated signal for this geometry (k | y) reveals a nonzero orientation across the Doppler-broadened profile, where ARCP - ALCP > 0 indicates a preferential absorption of RCP (∆MJ ) +1) versus LCP (∆MJ ) -1). It is important to remember throughout the following analysis that MJ refers to quantization of J along the laser propagation direction, which therefore depends on probe geometry from (i) y axis for φlaser ) 90° to (ii) x axis for φlaser ) 0°, and indeed never refers to the z axis surface normal. Explicit details of the MJ distribution are evident from the Ho¨nl-London transition dipole moment (µ) expressions. Specifically, the MJ dependent absorbance for a given J state is

ARCP/LCP ∝

µ2 (J ( MJ + 2)(J ( MJ + 1) 2 (2J + 1)(2J + 3)

(3)

where (+) and (-) correspond to the absorbance of RCP and LCP, respectively. These values can be combined to yield an expression for circular polarizance

Pcir ∝ ARCP - ALCP ∝ µ2

〈MJ〉 2J + 1

(4)

where the brackets around MJ indicate an average value over the 2J + 1 individual states. From eq 4, we note that the preferential absorption of RCP indicates that 〈MJ〉 > 0, which reveals that the rotational states are oriented with J, on average, pointed along the +y axis. In other words, Jy/|J| > 0 and reflects a classical picture of “topspin”. In clear contrast, the demodulated signals for φlaser ) 0° reveal no differential absorption between RCP and LCP across the Doppler profile in Figure 3b, as indeed expected from the planar detection symmetry of the system. In this configuration, the laser propagates in the plane of the incident molecular beam (k|x), where the absorbance expressions in eq 3 now reflect the MJ distribution along the x axis. The natural time-averaged symmetry of the liquid surface provides an equal probability for CO2 to scatter from the surface with Jx/|J| < 0 and Jx/|J| > 0, which immediately predicts a null measurement for differential absorption of RCP versus LCP laser radiation. From these profiles, circular polarizance is calculated for each J state from the integrated area of the demodulated signal, which is then normalized to the column densities described in section IIIA. The polarizance for each nonzero J state is determined from P-branch transitions, i.e., J′ - 1 r J′′. While the magnitude of Pcir is dominated by the given MJ distribution, the expressions listed in Table 2 show that the measured polarizance also depends upon either R- or P-branch transitions. Importantly,

Figure 4. Circular polarizance versus J for (a) φlaser ) 90° and (b) 0°.

these small differences lead to the same moments through the geometrical factors listed in Table 3. Values for Pcir are plotted in Figure 4 and listed in Table S1 in the Supporting Information for a series of measured J states in the two experimental configurations. In terms of the φlaser ) 90° measurements, the circular polarizance shows a clear dependence on J, where values start near zero at low J and systematically increase with the degree of rotational excitation. The sign of Pcir is positive, which indicates that, in general, the scattered CO2 tends to rotate with 〈MJ〉 > 0, where the magnitude depends on the J state. The corresponding Pcir values for φlaser ) 0° are zero within uncertainty for all J states, as consistent with the probe geometry symmetry and thus a vanishing mean component of J along the x axis. C. Linear Polarizance. In addition to Pcir measurements, we also require the linear polarizance, Plin. Sample profiles are plotted at the bottom of Figure 3a to illustrate differential absorbance between parallel and perpendicular linear polarizations. The sign of A|| - A⊥ is positive, which indicates preferential absorption of linearly polarized light parallel to the surface. It is worth noting, however, that the overall polarizance signals are ≈0.1 of the ARCP - ALCP values seen in the φlaser ) 90° configuration, which means that CO2 alignment effects are an order of magnitude weaker than orientation. Such a difference indicates that the dominant feature in the scattering mechanism preferentially torques the molecule with a sense of spin, yet no favored plane of alignment. In terms of the angular momentum, the transition dipole moment for the ν3 asymmetric stretch vibration is parallel to the OdCdO molecular axis, and therefore always orthogonal to J. Thus, the positive sign of the polarizance signal shows a small preference for J not to point along the polarization x axis for parallel excitation. Ho¨nl-London transition strengths for parallel (∆MJ ) 0) and perpendicular (∆MJ ) (1) polarizations permit further analysis of Plin from a quantum mechanical perspective. Explicitly, the contributing MJ dependent terms are

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(J + 1)2 - M2J A|| ∝ µ (2J + 1)(2J + 3) 2

(5)

and

A⊥ ∝

[

µ2 (J + MJ + 2)(J + MJ + 1) + 4 (2J + 1)(2J + 3) (J - MJ + 2)(J - MJ + 1) (2J + 1)(2J + 3)

]

(6)

The linear polarizance can then be expressed as the difference between eqs 5 and 6 to yield

Plin ∝ A|| - A⊥ ∝ µ2

J(J + 1) - 3〈M2J 〉 2(2J + 1)(2J + 3)

(7)

where MJ quantization again refers to the y axis and x axis for φlaser ) 90° and φlaser ) 0°, respectively. Two limiting cases are (i) 〈MJ〉 ≈ 0 and (ii) 〈|MJ|〉 ≈ J that would lead to Plin . 0 and Plin , 0, respectively. In the present case of k | y (φlaser ) 90°) and relatively small values of Plin g 0, the preferential absorption of parallel light indicates a nearly balanced distribution of angular momentum projections along the y axis but with 〈M2J 〉/[J(J + 1)] g 1/3. The linear polarizance is extracted from the integrated demodulated Doppler line shape, and then appropriately normalized by Ho¨nl-London factors for the desired J state transition. Values for Plin are plotted in Figure 5a to illustrate the J state dependence in the φlaser ) 90° configuration. The trend shows that the linear polarizance is essentially zero at J ≈ 0 and increases superlinearly with increasing J, reaching a maximum positive value of Plin ≈ +3% near the highest CO2 J values accessible at our experimental sensitivity (J ≈ 50). Again, Plin > 0 at φlaser ) 90° implies a propensity for moderate, nonzero angular momentum projections along the y axis direction and a classical limit of 〈J2y 〉/[J(J + 1)] g 1/3. This is consistent with, for example, the CO2 recoiling from the surface in a preferential “cartwheel” (i.e., y axis) fashion but does not support a predominance of “helicopter” (i.e., z axis) or “corkscrew” (i.e., x axis) rotational motion. This would be in agreement with the

Figure 5. Linear polarizance versus J for (a) φlaser ) 90° and (b) 0°.

above-mentioned circular polarizance data, which at φlaser ) 90° already suggests a strong propensity for “cartwheel” behavior upon scattering from the gas-liquid interface. To complete the total polarization data set, we have also obtained Plin as a function of J in the φlaser ) 0° configuration. It is worth noting that, unlike Pcir, the linear polarizance is not required to vanish for φlaser ) 0° by time averaged symmetry of the liquid surface with respect to the scattering plane. However, as shown in the profile in Figure 3b, the experimental polarizance seen from this probe geometry is indeed even smaller than that for φlaser ) 90°, with signal-to-noise ≈ 1 or smaller for these measurements. Integration over the full Doppler profiles improves this signal-to-noise ratio considerably to reveal a small but positive linear polarizance, with values ranging between Plin ≈ 0.3 and 1.0% and possibly also indicating a superlinear increase with J. The small magnitude of such polarizance data indicates nearly balanced parallel and perpendicular light absorption with respect to propagation along the x axis, or, in other words, 〈J2x 〉/[J(J + 1)] ≈ 1/3 in the classical limit. As discussed in more detail in section V, these linear and circular polarizance data for φlaser ) 0° and 90° provide sufficient information to calculate the lowest order moments of the orientation and alignment tensor, which therefore help provide a physical picture for the spatial distribution of J. IV. Theoretical Simulations A. CO2 + F-SAM Scattering. Details of the theoretical molecular dynamics (MD) simulations using VENUS05 have been outlined in previous papers.12,27,28 Therefore, we only provide the essential components of the model to help understand the correlation between PFPE and F-SAM surfaces. The surface consists of 48 chains of CF3(CF2)7S chemisorbed onto a slab of Au(111) atoms. The simulation involves integrating CO2 trajectories through interactions with the surface where the incident conditions match those in the experiment (i.e., Einc ) 10.6 kcal/mol, θinc ) 60°, and TS ) 300 K). Additionally, the incident azimuthal angle is selected randomly to average over the effects of the ∼12° tilt angle of the thiol chain. Motion of the surface atoms is governed by atom-atom potentials that have been previously published for fluorinated hydrocarbons by Borodin et al.45 Similarly, the CO2 surface potential is extracted from high level ab initio calculations of Hase and coworkers and discussed elsewhere.27 Position and momenta for CO2 are recorded throughout the duration of the trajectory, where final values are used to determine velocity and angular momentum along the x, y, and z directions. As illustrated in Figure 6a, the coordinate system definition is identical to our experiment, with the incident gas molecule traveling through the x-z plane toward the surface. Rotational state, translational, and angular scattering distributions have been previously reported in a series of studies, where the two-temperature analysis scheme reveals nearly quantitative agreement between the simulated and experimental results. The total number of trajectories involved in this investigation is 32 029, which is responsible for the high statistical quality of the results. By way of illustrating 3D angular effects, scattered distributions are plotted in Figure 6a, where the distance from the origin reflects the magnitude of the CO2 flux and reveals a broad, lobular pattern due to a superposition of both TD and IS trajectories. This flux magnitude is generated by counting the number of trajectories that pass within a 10° half angle cone (∆Ω ≈ 0.0955 steradians) for a set of (θf, φf) grid points and normalizing with respect to the 2π scattering hemisphere. The 3D representation immediately underscores the tendency for IS


Figure 6. CO2 + F-SAMs molecular dynamics (MD) simulations provide a theoretical system to model the gas-liquid experimental results with PFPE. (a) Scattered flux distribution for θinc ) 60° with Einc ) 10.6 kcal/mol, where 32 029 trajectories have been integrated in VENUS05. The color bar indicates 〈J〉 for the molecules that pass with 10° of a given (θf, φf) grid point on the hemispherical scattering volume. (b) Sample P(Jy/|J|) for trajectories with J ) 40 -50. (c) Additional parsing by final scattering angle, θscat ) tan-1(Vx/Vz), matches the experimental system where θscat ) 60°. P(Jy/|J|) distributions are generated for both flux- and density-based weighting schemes.

scattering in the forward direction, though there is also significant azimuthally symmetric cos(θf) flux from TD trajectories, as well as out-of-plane IS scattering contributions due to corrugation at the liquid interface. As an additional degree of information, this angular flux surface is also color-coded to reveal the average 〈J〉 for molecules scattering into a given differential area, where J is obtained from a trajectory by equating the classical angular momentum j with [J(J + 1)]1/2p. In general, molecules that scatter in the forward direction have greater rotational energy than those scattering backward. However, average rotational energies for forward versus backward scattering are 460 and 230 cm-1, respectively, i.e., both higher than the surface energy of kTS ≈ 208 cm-1. In order to analyze this distribution in a way that parallels experiment, the total set of trajectories is binned by final J into groups of J ) 0-10, 10-20, etc., which provides the opportunity to compare low, middle, and high J scattering behavior from both systems. To obtain information on the stereodynamics, individual Jx, Jy, and Jz components for each trajectory are also sorted and normalized by |J|, so that the abscissae Jx,y,z/|J| can be binned from -1 to 1. For trajectories into a given window of final J states, this allows us to generate a set of normalized probability distributions, P(Ji/|J|) for i ) x,y,z. By way of illustration, P(Jy/|J|) is plotted in Figure 6b for trajectories that scatter into J ) 40-50 and 〈J〉 ≈ 44, which clearly reflects the preferential tendency for CO2 to spin with forward (Jy/|J| > 0) versus backward (Jy/|J| < 0) end-over-end tumbling. To facilitate rigorous comparison with any laser-based absorption experiment, however, we must take this one step further and obtain column integrated densities, which necessitates (i) sorting by projection along the laser propagation direction (θscat ) tan-1(Vx/Vz)) and (ii) performing a flux-todensity transformation. Our trajectory set was therefore binned

J. Phys. Chem. A, Vol. 114, No. 3, 2010 1405 in J and θscat with two different distributions generated based on (i) flux through or (ii) density in the detection region. For any laser-based absorption scheme, the signal is rigorously proportional to the density, which reflects the flux weighted by the time spent in the probe region. For a fixed detection geometry, the time weighting factor is inversely proportional to V⊥ ) (V2x + Vz2)1/2. These effects are illustrated in Figure 6c, where P(Jy/|J|) for J ) 40-50 is plotted against histograms sorted by θscat ≈ 60° ( 10° and weighted by either flux or density. The differences between the three distributions are in fact negligible compared to the shot noise associated with the counting statistics. This motivates a presentation of final flux and J distributions for the entire ensemble of trajectories, as shown below. B. 3D Angular Momentum Component Distributions. The three angular momentum components (Jx,Jy,Jz) provide a complete characterization of the J distribution for CO2 as it scatters from a perfluorinated liquid surface. Probability distributions for each projection are generated as a function of J, and plotted in Figure 7 alongside a cartoon that illustrates the scattering geometry. As for the general trends, projection distributions for the lowest J values (Figure 7b-d) all appear to be nearly constant, which indicates no orientation or alignment in this fraction of the population. At least in the limit of J ) 0, this is required quantum mechanically, since the spatial distribution for the MJ ) 0 level must be spherically symmetric. However, the fact that the trajectory distributions smoothly recapitulate this limiting quantum behavior at low J is not required and suggests a more physically motivated picture described below. The spatial distribution of J evolves with J, with Jx and Jz developing nonequilibrium components symmetrically distributed around zero, while Jy histograms illustrate a systematic shift with J toward +Jy/|J|. A strong correlation between the three angular momentum directions is evident in any given subset of trajectories. For example, the probability that CO2 scatters with Jy > 0 at high J indicates that J is preferentially pointed along the y axis. In addition, the probability density for |Jz| also exhibits some increase near Jz/|J| ≈ (1. The consequence of these two effects results in a smaller net contribution of J along the x axis, which thereby increases the probability density of Jx/|J| ≈ 0. To help visualize the final CO2 scattering distributions, both the flux and J distributions are plotted in Figures 8 and 9, respectively, as a function of J. The angular flux patterns in Figure 8 are generated from the same sorting algorithm used to generate the total flux distribution in Figure 6a, where the plotting angle is the same as Figure 6a to clearly illustrate the important spatial components of the flux. The number of trajectories for each grid point (〈J〉, θf, φf) is normalized to the total number and the differential area (∆Ω ) 0.0955 steradians), with the color code in Figure 8 reflecting the probability per unit area of scattering with a particular direction and rotational state. The vector J distribution patterns in Figure 9 are generated in a similar fashion, where the space is defined in spherical coordinates by J, θJ, and φJ. Both angles are calculated directly from the projections of J, where explicitly θJ ) cos-1(Jz/|J|) and φJ ) tan-1(Jx/Jy). The 3D distributions are then constructed by simply counting the number of trajectories that fall within 10° of a given (θf,φf) grid point on the full 4π-steradian sphere. Once again, these values are normalized to the total number of trajectories and differential area due to binning in a 10° angular cone. Together, the 3D flux and angular momentum distributions provide insight into the correlated nature of the scattering

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Figure 8. 3D flux distributions versus 〈J〉 for CO2 + F-SAM MD simulations.

Figure 7. J state dependent probability distributions for the x, y, and z projections of J. The coordinate system for the MD simulations is illustrated in panel a.

mechanism at the gas-liquid interface. For example, the flux at low J appears to be slightly shifted in the forward direction. At the same time, J samples all directions with nearly equal probability. These patterns reflect not only the isotropically scattered TD component but also the fraction of the IS population that lacks significant rotational excitation, and any appreciable alignment or orientation. As J increases, however, the flux distributions systematically progress toward a lobular scattering pattern, with the intensity peaking at subspecular scattering angles. In parallel with these changes, the angular momentum also evolves from nearly isotropic to highly directional. Details of this structure are most clearly evident in the highest 〈J〉 ) 55 distributions, where the projection of J

Figure 9. 3D angular momentum distributions versus 〈J〉 for CO2 + F-SAM MD simulations. The contours plotted in the x-z plane reflect the values at Jz ≈ 0.

predominantly points along the +y axis. Specifically, additional subtle structure in x and z is also apparent; (Jx appears to be positively correlated with (Jz. The illustrations in Figure 9 clearly show the highly anisotropic nature of the scattering distribution, where interactions at the surface predominantly torque the molecule to induce positive topspin. Additionally,



these forces tend to spin CO2 in either the right- or left-handed direction, which leads to the alignment of J in the plane that includes y and approximately bisects x and z. V. Orientation and Alignment Characterization of a vector J involves expanding its spatial distribution in terms of multipole moments. The entire distribution for a given J state is fully characterized by 2J + 1 multipole elements, with a one-photon laser-based detection providing access to the lowest four anisotropy moments based on the scattering symmetry. To extract lowest order multipole elements from the above linear and circular polarizance measurements, we turn to the seminal work of Fano and Macek25,26 relating the anisotropy of the J distribution of a gas to the polarization of emitted radiation. Previous studies in our laboratory have shown that the same Fano-Macek theories may also be directly applied to direct absorption measurements.46,47 Specifically, for propagation (i) parallel to the interface and (ii) at an arbitrary angle with respect to the scattering plane, the absorbance (A) for any laser polarization can be cast in terms of lowest multipole moments, A0, A2+, and O1, as

1 1 A ) C 1 + h(2)(Ji, Jf) · A0 · (3 cos 2β + 1) + 3 4 3 (2) h (Ji, Jf) · A2+ · cos 2φlaser · (cos 2β - 1) + 4 3 (1) h (Ji, Jf) · O1- · sin φlaser sin 2β 2

[

]

(8)

where C is a constant, φlaser and β are defined by the probe geometry/polarization, and h(k)(Ji,Jf) (k ) 1 or 2) are geometrical factors25 for a given Jf r Ji transition (see Table 3). For example, by inserting β ) +45° (RCP) and β ) -45° (LCP) into eq 8 to yield ARCP and ALCP, respectively, one can easily re-express Pcir for φlaser ) 90° in terms of O1-, A0, and A2+. The corresponding results for all four combinations of polarizances and laser probe geometries are summarized in Table 2, though there are only three independent predictions, since Pcir (φlaser ) 0°) vanishes due to time averaged reflection symmetry with respect to the scattering plane. Extension of this treatment to include nonparallel laser probe angles with respect to the interface would generate information on A1+, which has thus far not been pursued. However, the parallel probe geometry data alone generates three linearly independent expressions for three unknowns, which can then be inverted to yield A0, A2+, and O1-. Closed form expressions for these tensor components in terms of polarizance and probe geometry are tabulated along with the expectation values of the multipole moment operators in Table 1. Results for A0, A2+, and O1- are summarized as a function of J in Table S2 of the Supporting Information, and plotted in Figure 10a, which shows a clear dependence upon the degree of rotational excitation. The first point worth noting is that all three tensor moments vanish at J ) 0, which is as expected due to the presence of only a single MJ ) 0 state. Interestingly, however, these magnitudes remain nearly zero for many low J values, in spite of the fact that the above argument requires the tensor moments to be zero strictly only at J ) 0. One simple classical picture for this observation is that the low J states exhibit less gyroscopic stability throughout any gas-liquid collision event, which thus can result in large fluctuations in the alignment and/or orientation in the final state distributions. In addition to this instability of low J states, previous Dopplerimetry studies have shown that the rotation and translation of the scattered CO2 are positively correlated, where final velocities

Figure 10. Orientation and alignment moments for (a) the CO2 + PFPE experiment and (b) the CO2 + F-SAM simulation.

increase with rotational excitation. On the basis of these results, the small degree of orientation and alignment at low J is consistent with a physical picture in which the slower molecules tend to spend more time near the interface, which then increases the probability for additional collisions that tend to randomize the direction of J. Furthermore, these tensor moments all increase (or decrease) in magnitude in a way that grows roughly superlinearly with J. A simple picture consistent with such monotonic increases in A0, A2+, and O1- tensor components is that enhanced orientation/alignment requires stronger torques exerted on molecules at the surface, which in turn can result in higher J values. The orientation and alignment is preserved, since the CO2 in these high J states scatters away from the interface more quickly due to the higher average translational speeds. For example, in terms of the individual components, O1- indicates that the average value of 〈Jy〉/|J| is ∼0.20 at the highest J states, which reveals that the distribution is dominated by topspin over backspin by nearly 3:2. The A0 value isolates the relative alignment of the scattering distribution with respect to the z axis, where values above zero indicate a preferential component of J perpendicular to the surface, i.e., a helicopterlike behavior. Finally, A2+ reflects the difference between second moments of Jx and Jy, and therefore provides a measure of the relative width of the two distributions. The negative sign of A2+ arises from a significantly broader Jy rather than Jx distribution, which is also consistent with the large orientation associated with the scattered distribution. For most rigorous comparisons with the experiment, orientation and alignment in the simulated CO2 + F-SAM trajectories have been calculated directly from the expectation values listed in Table 1 and the distributions in Figure 7. From the 3D distribution, all four moments are obtainable, which now even provides insight into the A1+ parameter. These values are plotted in Figure 10b and listed in Table S3 of the Supporting Information, where the moments have been calculated for groups of J binned by 5 up to J ) 70+. Interestingly, the trends in A0,

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A2+, and O1- over the entire range of J closely parallel the values obtained in the experiment of CO2 + PFPE. For example, these values all vanish at J ) 0 as well as remain near zero for low J, rising superlinearly from zero at the highest J values observed. The signs and relative ordering of the A2+ and O1- tensor moments as a function of J are in remarkable agreement with experiment. Qualitative agreement with the A0 data is also quite strong, with both data sets reaching a maximum near J ) 40-50 and decreasing to higher J values. Indeed, the MD simulations even indicate a change in A0 from positive to negative at J ≈ 60-70, though this is already beyond where the experiment can currently scan. However, while the qualitatiVe trends in moments for the experiment and simulations are very nearly identical, closer inspection reveals the importance of quantitatiVe differences in the magnitudes of these values. Specifically, the theoretical MD simulations lead to alignment/orientation tensor parameters that are nearly ≈2 times larger than the extracted experimental parameters. This discrepancy is somewhat remarkable, indeed revealing the first appreciable difference noted between experimental results for CO2 scattered from PFPE versus theoretical simulations of an F-SAM surface.12,27,28 From the above analysis in section IVA, we now know that flux-to-density effects play a negligible role, in essence due to the relatively constant average recoil velocity achieved for any final J state. We can speculate that some differences may arise from the relative surface roughness values, which are estimated to be ≈7 Å for PFPE but only 3-4 Å for an F-SAM. However, one could argue that a decrease in surface roughness might correlate with a decreased alignment, rather than the presently observed increase with respect to experiment. A possibility for further theoretical exploration is that there is intrinsically higher chemical covalency and spatial order in our F-SAM model vs a true liquid such as PFPE, due to the more highly ordered attachment via thiol linkages to the Au lattice undersurface. On the basis of these differences, the decreased order in the PFPE surface may effectively attenuate the magnitude of the orientation and alignment effects by exposing collision sites that lead to further randomization of J. As a final point, the results from the gas-liquid studies provide another opportunity to compare and contrast the differences between (i) liquid and (ii) single crystal metal surfaces. Our previous studies have shown important qualitative differences that arise in the sticking coefficients,15 where the probability for trapping on a liquid surface decreases with incident angle. Such phenomena indicate a dynamically rough liquid surface where the local interaction geometries sample a wide variety of angles, compared to the relatively flat metal surfaces. As for the stereodynamics, previous N2 + Ag(111) studies have shown that the scattered molecules tend to be aligned with J pointing parallel to the surface,19,20 where values for A0 reach nearly -0.8 at high J. In direct contrast, A0 in the current gas-liquid study is much smaller and positiVe, peaking at ≈0.05 for J ) 50. The smaller overall magnitude and change in sign indicate significant contributions from interactions that torque the CO2 with topspin yet also sample a wide range of forces that induce more helicopter-like trajectories. As for the orientation of a metal crystal, the sense of the N2 cartwheel spin depends upon the final scattering direction, where (i) subspecular directions reveal backspin, (ii) specular angles show small positive topspin, and (iii) superspecular trajectories reveal a J-dependent orientation that changes sign from backward to forward. By way of direct comparison with experimental CO2 + PFPE values, one observes O1- ≈ 0.05 for N2 (J ) 10-20)

Perkins and Nesbitt

Figure 11. Angle dependence of O1- for 〈J〉 ) 50. Trajectories are sorted by scattering angle, θscat, which leads to distributions that include both in-plane and out-of-plane directions.

scattering in the specular direction and O1- ≈ 0.10 (i.e., 2× larger) for CO2 (J ) 50). The 2× larger orientation magnitude indicates that the liquid surface provides additional sites for surface torques to generate topspin in the scattered molecule prior to leaving the surface. As for the angular dependence of the sign of O1- for gas-metal scattering, the MD simulations provide evidence that the sense of topspin in gas-liquid scattering is relatively independent of the final scattering direction. To show this effect, O1- is plotted in Figure 11 for 〈J〉 ) 50 as a function of θinc and θscat. The curves in the plot illustrate several important points about the stereodynamics of the collision. First, normal incidence leads to no net orientation, which is expected based on an azimuthally symmetric collision geometry with equal probability to torque CO2 clockwise and counterclockwise. Other than normal incidence, the general trend in the plot shows that O1remains positive as a function of θscat. Such a result shows that the surface corrugation provides impact geometries that torque the CO2 into states with topspin independent of the final scattering direction. In other words, molecules that scatter either forward or backward have topspin. Interestingly, the magnitude of O1- increases with 〈θscat〉, which suggests a larger fraction of the normal momentum is converted into rotational tumbling as the molecules scatter from the surface. VI. Summary and Conclusion The orientation and alignment of scattered CO2 has been probed with high resolution infrared spectroscopy, where differential absorption of two laser polarizations in various geometrical configurations uncovers the anisotropy in the spatial distribution of J. Specifically, absorption of RCP versus LCP is used to characterize the sense of rotation either for end-overend tumbling or for left- versus right-handed spin. Likewise, parallel and perpendicular linear polarizations are used to determine the favored plane of rotation. Through the theories of Fano and Macek, these absorption measurements uncover three of the four lowest moments of the J distribution (A0, A2+, and O1-), which shows the final distribution is characterized by a strong sense of rotational topspin along with subtle torques to the left or right. In parallel with previous studies of CO2 + perfluorinated liquids, we compare the experimental scattering results to MD simulations, where the fluorinated surface is

Stereodynamics at the Gas-Liquid Interface modeled by an F-SAM. Trajectories are integrated from initial conditions that match the experimental studies. From the final scattering distribution, the projections of J along x, y, and z are characterized as a function of J to show the anisotropy associated with the gas-liquid interaction. To help visualize the final distribution, flux and J distributions illustrate the strong correlation between impulsive forces and torques that lead to preferential forward scattering with considerable forward endover-end tumbling. The four lowest moments are directly calculated from the expectation values and the probability distributions. Experimental and theoretical results are compared through the lowest moments (A0, A2+, and O1-) to illustrate the similarities and differences associated with a PFPE and F-SAM surface. Surprisingly, results for the two systems show qualitative similarities over a range of J states, yet quantitatively, the effects are nearly twice as large for the theoretical CO2 + F-SAM simulations. While the qualitative agreement is remarkable, these quantitative discrepancies are somewhat unexpected on the basis of the high level of agreement in previous comparisons of the scattering dynamics. Possible explanations involve the relative stiffness of the two surfaces, differences in roughness, or perhaps the increased mobility associated with the liquid. Additional work may address these points, specifically, where experiments with F-SAMs and simulations of a true PFPE liquid surface would provide additional insight into the subtle differences in dynamics. Such a comparison may be especially useful to help understand the time scale of the interactions, especially to characterize the differences between the interactions of CO2 with a F-SAM vs PFPE surface. Presumably, the dynamic nature of the surface may be an important cause for the quantitative differences between our current experimental and theoretical results. The qualitative agreement between the PFPE and F-SAM systems is valuable, however, in terms of visualizing the final flux and J distributions. The strong end-over-end forward tumbling suggests the interactions consist of one to several collisions where the linear momentum of the incident molecule is converted into angular momentum through impulsive torques between the gas and surface. The result of these interactions leads to forces that act as friction to cause the forward tumbling. The subtle structure in the distributions along Jx and Jz also reveals evidence of significant interactions that torque the CO2 to the left or right as it scatters from the surface. These types of impulsive torques are a result of the high degree of local surface corrugations, which provide a diverse range of impact sites that lead to forces on the CO2 that are both parallel and perpendicular to the surface normal. In addition to this static surface structure, the stereodynamics are affected by the dynamic motion of the surface, which is able to respond to the incident CO2 on time scales that match the rotational periods of CO2 and the low frequency vibrational modes of the perfluorinated interface. These types of active interactions may tend to diminish the orientation and alignment at low J yet preserve the effects for high rotational states. These two 3D representations are directly compared to results for N2 + Ag(111), where the sign of alignment differs with the gas-liquid results. Specifically, N2 preferentially spins from the surface with J aligned parallel to the surface, whereas CO2 scatters with J pointed perpendicular to the liquid. Such a result illustrates the considerable roughness of the liquid, especially when the alignment is combined with the large orientation that reflects forward tumbling from the surface. These results once again reveal the qualitative differences between scattering from

J. Phys. Chem. A, Vol. 114, No. 3, 2010 1409 a solid metal vs liquid surface, where the dynamics of the latter can be strongly influenced in addition by surface roughness and molecular motion on the time scale of incident CO2 rotational and translational degrees of freedom. Acknowledgment. Primary support for this research has been provided by the Air Force Office of Scientific Reports, with additional equipment and computer funds provided by the National Science Foundation. Additionally, we would like to thank Professors William Hase and Emilio Martinez-Nunez for their help and exceptional insight into the MD simulations, Dr. Michael Deskevich for help with the 3D visualization of the scattering distributions, and Professor Chris Greene for useful discussions regarding the details of Fano-Macek theory. Supporting Information Available: Detailed tables of experimentally determined linear and circular polarizances for CO2 + PFPE are listed in Table S1. From these values, the lowest moments of the angular momentum distribution are calculated and listed in Table S2. Similar moments are calculated for the MD simulations of CO2 + F-SAMs, which are tabulated in Table S3. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Saecker, M. E.; Govoni, S. T.; Kowalski, D. V.; King, M. E.; Nathanson, G. M. Science 1991, 252, 1421. (2) Nathanson, G. M. Annu. ReV. Phys. Chem. 2004, 55, 231. (3) Saecker, M. E.; Nathanson, G. M. J. Chem. Phys. 1994, 100, 3999. (4) Saecker, M. E.; Nathanson, G. M. J. Chem. Phys. 1993, 99, 7056. (5) Zhang, J. M.; Garton, D. J.; Minton, T. K. J. Chem. Phys. 2002, 117, 6239. (6) Minton, T. K.; Garton, D. J. Dynamics of Atomic-Oxygen-Induced Polymer Degradation in Low Earth Orbit. In Chemical Dynamics in Extreme EnVironments; Dressler, R. A., Ed.; World Scientific Publishing Co.: Singapore, 2001; p 420. (7) Garton, D. J.; Minton, T. K.; Alagia, M.; Balucani, N.; Casavecchia, P.; Volpi, G. G. J. Chem. Phys. 2000, 112, 5975. (8) Kelso, H.; Kohler, S. P. K.; Henderson, D. A.; McKendrick, K. G. J. Chem. Phys. 2003, 119, 9985. (9) Bagot, P. A. J.; Waring, C.; Costen, M. L.; McKendrick, K. G. J. Phys. Chem. C 2008, 112, 10868. (10) Allan, M.; Bagot, P. A. J.; Westacott, R. E.; Costen, M. L.; McKendrick, K. G. J. Phys. Chem. C 2008, 112, 1524. (11) Allan, M.; Bagot, P. A. J.; Costen, M. L.; McKendrick, K. G. J. Phys. Chem. C 2007, 111, 14833. (12) Perkins, B. G.; Nesbitt, D. J. J. Phys. Chem. B 2008, 112, 507. (13) Perkins, B. G.; Nesbitt, D. J. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 12684. (14) Perkins, B. G.; Nesbitt, D. J. J. Phys. Chem. A 2008, 112, 9324. (15) Perkins, B. G.; Nesbitt, D. J. J. Phys. Chem. A 2007, 111, 7420. (16) Perkins, B. G.; Nesbitt, D. J. J. Phys. Chem. B 2006, 110, 17126. (17) Perkins, B. G.; Haber, T.; Nesbitt, D. J. J. Phys. Chem. B 2005, 109, 16396. (18) Lahaye, R.; Stolte, S.; Holloway, S.; Kleyn, A. W. J. Chem. Phys. 1996, 104, 8301. (19) Sitz, G. O.; Kummel, A. C.; Zare, R. N. J. Chem. Phys. 1988, 89, 2558. (20) Sitz, G. O.; Kummel, A. C.; Zare, R. N.; Tully, J. C. J. Chem. Phys. 1988, 89, 2572. (21) Jacobs, D. C.; Kolasinski, K. W.; Shane, S. F.; Zare, R. N. J. Chem. Phys. 1989, 91, 3182. (22) Jacobs, D. C.; Kolasinski, K. W.; Madix, R. J.; Zare, R. N. J. Chem. Phys. 1987, 87, 5038. (23) Corey, G. C.; Alexander, M. H. J. Chem. Phys. 1987, 87, 4937. (24) Luntz, A. C.; Kleyn, A. W.; Auerbach, D. J. Phys. ReV. B 1982, 25, 4273. (25) Greene, C. H.; Zare, R. N. Annu. ReV. Phys. Chem. 1982, 33, 119. (26) Fano, U.; Macek, J. H. ReV. Mod. Phys. 1973, 45, 553. (27) Martinez-Nunez, E.; Rahaman, A.; Hase, W. L. J. Phys. Chem. C 2007, 111, 354. (28) Nogueira, J. J.; Vasquez, S. A.; Mazyar, O.; Hase, W. L.; Perkins, B. G.; Nesbitt, D. J.; Martinez-Nunez, E. J. Phys. Chem. A 2009, 113, 3850. (29) Yan, T. Y.; Hase, W. L.; Barker, J. R. Chem. Phys. Lett. 2000, 329, 84. (30) Yan, T. Y.; Hase, W. L. Phys. Chem. Chem. Phys. 2000, 2, 901.

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(31) Isa, N.; Gibson, K. D.; Yan, T.; Hase, W.; Sibener, S. J. J. Chem. Phys. 2004, 120, 2417. (32) Alexander, W. A.; Morris, J. R.; Troya, D. J. Phys. Chem. A 2009, 113, 24061. (33) Alexander, W. A.; Day, B. S.; Moore, H. J.; Lee, T. R.; Morris, J. R.; Troya, D. J. Chem. Phys. 2008, 128, 014713. (34) Day, B. S.; Morris, J. R.; Alexander, W. A.; Troya, D. J. Phys. Chem. A 2006, 110, 1319. (35) Scott Day, B.; Morris, J. R.; Troya, D. J. Chem. Phys. 2005, 122, 214712. (36) Troya, D.; Schatz, G. C. J. Chem. Phys. 2004, 120, 7696. (37) DuPont “Krytox Fluid Performance Sheets”, 2003. (38) Colorado, R.; Lee, T. R. Langmuir 2003, 19, 3288. (39) Alves, C. A.; Porter, M. D. Langmuir 1993, 9, 3507. (40) Townes, C. H.; Schawlow, A. L. MicrowaVe Spectroscopy, 1st ed.; McGraw-Hill Book Company: New York, 1955.

Perkins and Nesbitt (41) Proch, D.; Trickl, T. ReV. Sci. Instrum. 1989, 60, 713. (42) The notation (ν1 ν2 lν3) characterizes the vibrational state of CO2; the quantum numbers ν1, ν2, and ν3 describe the symmetric stretch, bend, and antisymmetric stretch, and l is the vibrational angular momentum quantum number. (43) Lednovich, S. L.; Fenn, J. B. AIChE J. 1977, 23, 454. (44) Kaur, D.; Desouza, A. M.; Wanna, J.; Hammad, S. A.; Mercorelli, L.; Perry, D. S. Appl. Opt. 1990, 29, 119. (45) Borodin, O.; Smith, G. D.; Bedrov, D. J. Phys. Chem. B 2002, 106, 9912. (46) Weida, M. J.; Sperhac, J. M.; Nesbitt, D. J. J. Chem. Phys. 1996, 105, 749. (47) Weida, M. J.; Nesbitt, D. J. J. Chem. Phys. 1994, 100, 6372.

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