16396
J. Phys. Chem. B 2005, 109, 16396-16405
Quantum State-Resolved Energy Transfer Dynamics at Gas-Liquid Interfaces: IR Laser Studies of CO2 Scattering from Perfluorinated Liquids Bradford G. Perkins, Jr., Thomas Ha1 ber,† 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: March 4, 2005; In Final Form: May 4, 2005
An apparatus for detailed study of quantum state-resolved inelastic energy transfer dynamics at the gasliquid interface is described. The approach relies on supersonic jet-cooled molecular beams impinging on a continuously renewable liquid surface in a vacuum and exploits sub-Doppler high-resolution laser absorption methods to probe rotational, vibrational, and translational distributions in the scattered flux. First results are presented for skimmed beams of jet-cooled CO2 (Tbeam ≈ 15 K) colliding at normal incidence with a liquid perfluoropolyether (PFPE) surface at Einc ) 10.6(8) kcal/mol. The experiment uses a tunable Pb-salt diode laser for direct absorption on the CO2 ν3 asymmetric stretch. Measured rotational distributions in both 0000 and 0110 vibrational manifolds indicate CO2 inelastically scatters from the liquid surface into a clearly nonBoltzmann distribution, revealing nonequilibrium dynamics with average rotational energies in excess of the liquid (Ts ) 300 K). Furthermore, high-resolution analysis of the absorption profiles reveals that Doppler widths correspond to temperatures significantly warmer than Ts and increase systematically with the J rotational state. These rotational and translational distributions are consistent with two distinct gas-liquid collision pathways: (i) a T ≈ 300 K component due to trapping-desorption (TD) and (ii) a much hotter distribution (T ≈ 750 K) due to “prompt” impulsive scattering (IS) from the gas-liquid interface. By way of contrast, vibrational populations in the CO2 bending mode are inefficiently excited by scattering from the liquid, presumably reflecting much slower T-V collisional energy transfer rates.
I. Introduction The role of collision dynamics at the gas-liquid interface has been a topic of considerable interest in recent years, stimulated in part by the overwhelming importance of such gasliquid interactions in areas such as aerosol chemistry, acid rain, tropospheric pollution, and hetereogeneous chemistry. The scattering process of a gas molecule from a liquid surface is also crucial for understanding surface interactions that range from high-energy radical impacts with supersonic aircraft and spacecraft1,2 to catalytic ozone-depleting reactions in the midlatitude stratosphere.3-5 Translational, rotational, and vibrational energy transfer phenomena clearly play a key role in the dynamics, controlling, for example, the rate of both accommodation of incident molecules on the liquid and the subsequent ejection of these species back into the gas phase. Indeed, a detailed understanding of the microscopic collision physics taking place at the gas-liquid interface requires information at the level of individual quantum states. Previous experimental studies of atom and molecule scattering at the gas-liquid interface have contributed to the development of a basic paradigm for gas-liquid collision dynamics. As schematically represented by the cartoon in Figure 1, some fraction (typically denoted 1 - R) of the incident molecules are thought to impulsively scatter (IS) promptly from the liquid surface back into the gas phase. In this case, the species can be rotationally, translationally, or even vibrationally excited by high-energy contact with the surface. Specifically, the time scale for such impulsive-scattering events is too fast to permit * Corresponding author. E-mail:
[email protected]. † Present address: Radiant Dyes Laser, Wermelskirchen, Germany.
Figure 1. A simple physical picture of the scattering pathways for a gas molecule from a liquid surface. The model includes (i) an impulsive scattering channel and (ii) a trapping pathway that leads to immediate desorption, surface residence, or long-time solvation. Channel selectivity depends on various gas and liquid parameters, which include energy transfer between translation, rotation, and vibration of the gas molecule.
equilibration between the projectile and the liquid surface (∆t , tequil), and thus the resulting translational and internal state distributions can contain information reflecting the microscopic collision dynamics. Alternatively, the remaining incident molecules (R) lose sufficient energy to remain on the surface long enough to lose memory of their incident velocities and rovibrational quantum states (∆t . tequil). Thus once in intimate contact with the surface, a given trapped gas molecule can either (i) desorb promptly back into the gas phase or (ii) diffuse further into the bulk liquid and eventually return to the surface and
10.1021/jp0511404 CCC: $30.25 © 2005 American Chemical Society Published on Web 08/05/2005
CO2 Scattering from Perfluorinated Liquids desorb. As both of these events reflect a loss of explicit knowledge of the incident dynamics, they are referred to as trapping-desorption (TD) events, even though there may be considerable dispersion in the experimental residence times. Provided there are no dynamical barriers in the desorption channel, the product distributions from this second scenario would reflect an equilibrium sampling of all states and thus at a temperature characteristic of the liquid, Ts. Several previous experimental efforts have probed the details of this energy transfer at the gas-liquid interface. The vast majority of these experiments have focused on kinetic energy transfer, using accelerated monatomic gases in molecular beams as incident projectiles to probe the translational dynamics of the gas-liquid scattering via time-of-flight mass spectrometry (TOFMS).6-13 Over the past decade, the Nathanson group, in particular, has developed and investigated the nonreactive scattering dynamics between high-energy molecular beams and liquid surfaces, including long chain hydrocarbons,7,9 perfluoropolyethers (PFPE),8,14,15 and liquid metals.16,17 Indeed, these mass spectrometry measurements and TOF velocity analyses have shown considerable support for this fundamental collision paradigm, i.e., gas molecules scatter from a liquid surface via two distinct channels: trapping-desorption (TD) and impulsive scattering (IS). Specifically, the TD channel consists of gas molecules that desorb from the surface with a MaxwellBoltzmann translational energy distribution consistent with the surface temperature, whereas the IS channel population typically escapes the surface with a much higher fraction of its incident energy. As the simplest analysis procedure, detailed fits of these TOF signals to Maxwell-Boltzmann velocity distributions can be used to identify the fraction R of incident molecules that trap and desorb versus the (1 - R) fraction of molecules that scatter impulsively. R can be varied by tuning the collision energy, scattering angle, and the physical and chemical properties of the liquid. The analysis of such an experiment can be used to infer the microscopic collision physics at the gas-liquid interface. Additional studies have explored the interactions of gas molecules with a variety of liquidlike surfaces. In particular, extensive studies with self-assembled monolayers (SAMs) of alkanethiols have produced similar evidence for “two-channel” (TD/IS) dynamics when sampled for a variety of surface conditions, chain lengths, and type of incident gas molecules.18-26 Other systems investigated include nematic liquid crystals27 and amorphous ice.28 Scattering in each of these gas-surface collision systems reveals translational distributions in the scattered flux consistent with a two-component energy distribution, in close analogy with the work on gas-liquid interfaces. Such experiments have stimulated considerable theoretical simulation efforts16,24,29,30 that are beginning to successfully reproduce such two-channel translational energy exchange between a gas and a liquid surface. Although the microscopic collision physics of molecules at the liquid surface clearly involves rotational, vibrational, and translational degrees of freedom, only a handful of experiments have successfully explored internal energy distributions in the scattered gas molecules. Early measurements for Na2 evaporating from a liquid sodium surface31,32 revealed thermal distributions of rotational and vibrational states, which implied sticking coefficients are independent of quantum states for the reverse scattering process. McCaffery and co-workers explored aspects of nonequilibrium gas-liquid interactions with measurements of internal state populations of cold I2 gas molecules impinging upon liquid gallium and poly-siloxane oil.33,34 I2 scattering from
J. Phys. Chem. B, Vol. 109, No. 34, 2005 16397 liquid crystal surfaces27 was similarly investigated by Donaldson and co-workers. Both experiments revealed nonthermal energy transfer via IS and TD channels, resulting in internal state temperatures colder than the surface temperature, Ts. By way of contrast, Sagiv and co-workers found NO rotational distributions with temperatures hotter than Ts when scattered from longchain organic amphiphiles.35 Recently, McKendrick and coworkers studied the nascent quantum-state populations from reactive collisions of O(3P) with deuterated squalane (C30D62).36 They discovered that OD products are formed in both V′ ) 0, 1 vibrational states, i.e., clearly at a vibrational temperature much hotter than Ts, while the rotational states within each vibrational manifold are well characterized by a rotational temperature comparable Ts. These observations underscore the broader pallet of experimental results that can be observed by monitoring internal state distributions and indeed the very real possibility for fundamentally different collision dynamics in vibrational, rotational, and translational degrees of freedom. Furthermore, these previous studies have all been based on laser-induced fluorescence (LIF), which although quite sensitive, is nevertheless restricted to a relatively small class of scattering targets. This provides strong additional motivation to develop novel and more generally applicable methods to probe such gas-liquid interfacial dynamics, which serves as the primary focus of this work. In this paper, we report a simple yet powerful IR laser based method by which quantum-state resolved gas-liquid scattering dynamics may be studied via direct infrared laser absorption of gas molecules scattering from a liquid surface. A collection of individual rovibrational absorption profiles provides rotational, vibrational, and translational distributions of the scattered molecular flux. Measurements of the internal state distributions of the scattered gas flux provide complementary information about the energy transfer dynamics of polyatomic molecules probed in the TOFMS experiments. A complete account of the energy transferred to a scattered molecule provides insight into surface properties such as local surface corrugation and trapping probabilities. To demonstrate the feasibility of infrared detection, initial results are presented for high-energy carbon dioxide (Einc ) 10.6(8) kcal/mol, where the number in parentheses is one standard deviation from the average of multiple measurements) scattered upon a perfluorinated polyether (PFPE) liquid. The remainder of this paper is organized as follows. Section II describes the experimental details of the infrared absorption technique for detection of nascent quantum state populations of scattered gas molecules from a liquid surface. A sample system is presented, which includes a molecular beam of CO2 impinging upon a liquid PFPE surface. Section III presents a Boltzmann analysis to characterize rotational and vibrational populations, along with an introduction into the Dopplerimetry used to ascertain translational distributions. These methods are used to characterize the internal states and translational motion of CO2 in the incident and scattered flux. Section IV presents sample data of CO2 scattering from PFPE. In Section V, we present an analysis and discussion of the data to develop a simple two-channel scattering model that incorporates both TD and IS collision dynamics in the rotational and translational distributions. Major results and concluding remarks are summarized in Section VI. II. Experimental Section The apparatus for studying gas-liquid energy transfer exploits three essential components to access the detailed scattering dynamics of polyatomic molecules at the liquid interface. First,
16398 J. Phys. Chem. B, Vol. 109, No. 34, 2005
Figure 2. Schematic diagram illustrating the diode laser spectrometer that is used to measure the energy transfer between incident CO2 molecules and a liquid surface. Translational and internal state distributions of the scattered CO2 flux are probed by direct infrared absorption spectroscopy of the ν3 asymmetric stretch. The Pb-salt diode laser is scanned over 0.05 cm-1 to provide absorbance measurements and line shapes for individual rotational states.
a single-mode infrared diode laser (∆νlaser ≈ 0.0003 cm-1) directly measures the absorption of quantum state populations and Doppler shifts of the incident and scattered molecular flux. Second, a pulsed supersonic expansion is used to create a wellcharacterized molecular beam of molecules cooled into the lowest quantum states that is then scattered from a clean liquid surface. The third component is the generation of a continuously renewed liquid surface under vacuum, via methods developed by Lednovich and Fenn37 and used extensively by the Nathanson group.7 High-resolution Beer’s law absorption spectroscopy is employed to detect the flux of gas molecules scattered from the surface of a low vapor pressure liquid. Typical peak absorbances in this experiment range from 3% down to 0.03%. As illustrated in Figure 2, the spectrometer incorporates signal detection and frequency diagnostics by splitting the collimated laser light into several beams. To detect the scattered gas flux from the liquid surface, a signal beam is passed 1 cm above the surface in a modified Herriot cell configuration.38 After 10-20 passes above the liquid, the signal beam is directed onto a LN2-cooled InSb photovoltaic detector. The second laser beam is focused directly onto a reference InSb detector that allows common mode amplitude noise to be removed from the laser light by fast servoloop subtraction electronics. This subtraction scheme leads to an experimental absorption sensitivity of ∼2 × 10-6 Hz-1/2 over the 125 kHz detector bandwidth for 0.5 µW of λ ) 4.3 µm laser light. Two additional beams of the laser light are used for frequency diagnostics. Absolute frequencies are recorded from absorption profiles of a reference gas in a room temperature gas cell, while relative frequencies are obtained by interpolation between transmission fringes from a Fabry-Perot confocal cavity with 250 MHz free spectral range. The entire spectrometer is purged with dry N2 to eliminate frequency-dependent attenuation of the IR laser due to atmospheric water and CO2 absorption. The scattered J-state populations are measured from stepby-step tuning of the laser frequency over a single Dopplerlimited rovibrational transition, resulting in both quantum stateresolved populations as well as translational distributions along the laser probe axis. A computer-controlled data acquisition board records two millisecond time profiles of the transient gas pulse absorption at an infrared detuning frequency. The profile
Perkins et al.
Figure 3. Molecules in a skimmed supersonic jet impinging upon a renewed liquid surface to probe dynamics at the gas-liquid interface. Nascent distributions of scattered CO2 molecules are detected by direct infrared absorption with a single-mode IR laser, which is multipassed 10-20 times 1 cm above the liquid. A liquid surface is generated by a wheel that rotates through a reservoir. To generate a clean surface, the top layer of liquid is scraped away by a razor blade.
defines a window that incorporates a time before, during, and after the gas pulse collides with the surface. Integration over the duration of the transient absorption signal generates a single absorption value at the detuning frequency. Incident and scattered flux absorption profiles are generated by integrating the signal over the same 100 µs time window, which begins at the initial arrival of the scattered flux signal. Signal integration reduces the effective bandwidth and increases the sensitivity of the measurement. The results presented in this paper are one point per pulse measurements at a given detuning frequency, yet multiple gas pulses may be averaged to improve signal-tonoise. The incident gas molecules are formed into a molecular beam based on the pulsed valve designs of Proch and Trickl,39 thereby supersonically cooling the translational and internal states of the infrared absorber. A 400 µm diameter pinhole aperture is used in conjunction with an infrared active gas (e.g., CO2) reverse seeded into a carrier gas (e.g., H2, He, Ne) to tune the collision energies of the incident beam. The gas pulse operates with a pulse width that can be varied between 300 and 2000 µs and a repetition rate from 1 to 20 Hz. A 5.0 mm conical skimmer is placed 2.5 cm downstream along the centerline of the beam to reduce the angular velocity spread of incident molecules by ca. 5-fold. In the current experiment, the molecular beam source is fixed 11 cm from the surface and configured with the molecular beam axis normal to the surface. As depicted in Figure 3, a 12.7 cm diameter glass wheel is partially submersed in a 300 mL reservoir. The glass wheel rotates at 0.5 Hz through the viscous liquid and drags along a thick liquid layer. A 6 cm razor blade scrapes away the top layer of liquid from the surface to generate a fresh interface, leaving a 0.8 mm film on the rotating glass wheel. The pulsed valve and liquid surface assembly are mounted inside a 60 L vacuum chamber. The chamber is pumped through a LN2 cold trap with a 6 in. diffusion pump, which is capable of maintaining routine pressures 1000 cm-1. These absorption profiles are integrated over the Doppler profiles, corrected for minor contributions from the incident beam, and converted via known line strengths into J-state-dependent populations for each of the ground-state and bend-excited-state vibrational manifolds. The normalized results are summarized in Table 1, sampling a range of J ) 14-52 for 0000 and J ) 5-32 for the 0110. Values for the very lowest J states are not reported because of uncertainty in correcting for population in the incident beam. Note that only even J values are present for CO2 in the 0000 manifold, because of zero statistical weights for the nuclear spin-free oxygen atoms. Similar nuclear spin weight constraints also apply to the 011e/f0 state, however, yielding only J ) odd and even states for the nearly degenerate bending levels of e and f parity, respectively. Although they do not affect any of the Boltzmann analysis
CO2 Scattering from Perfluorinated Liquids
J. Phys. Chem. B, Vol. 109, No. 34, 2005 16401
TABLE 1: Experimental Dataa for CO2 Scattering from PFPE with Einc ) 10.6(8) kcal/mol at Normal Incidence 0000 vibrational manifold
0110 vibrational manifold f
Jb,c,d
fractional populatione
∆υD (MHz)
Ttrans (K)
∆υD(IS) (MHz)
14 16 18 20 22 24 26 28 30 32 36 38 40 42 44 46 52
0.058(1) 0.0568(8) 0.058(1) 0.056(1) 0.055(1) 0.052(2) 0.048(1) 0.0452(4) 0.0414(8) 0.0374(8) 0.0303(9) 0.0263(3) 0.0233(4) 0.0199(3) 0.0179(5) 0.0149(3) 0.0092(2)
143(6) 160(10) 160(10) 160(9) 165(4) 162(4) 169(5) 168(4) 173(5) 174(1) 182(5) 183(3) 189(8) 188(3) 190(4) 194(6) 199(6)
360(20) 460(30) 470(30) 450(30) 480(10) 460(10) 500(20) 500(10) 530(10) 535(5) 590(20) 600(10) 640(30) 630(10) 640(20) 680(20) 710(20)
180(20) 183(8) 200(20) 216(3) 222(5) 213(9) 232(4) 216(7) 220(9) 214(3) 220(10) 214(2) 214(7) 211(3) 208(6) 212(5) 213(8)
Jb,d
fractional populatione
∆υD (MHz)
Ttrans (K)
5 8 10 13 15 16 17 18 23 24 27 28 29 32
0.0003(1) 0.00063(6) 0.00069(8) 0.00089(9) 0.00102(2) 0.00101(2) 0.00090(9) 0.00096(9) 0.00109(3) 0.00084(5) 0.00077(6) 0.00075(2) 0.00075(1) 0.00064(5)
140(4) 100(10) 100(20) 120(20) 140(20) 147(6) 130(30) 130(30) 178(7) 160(7) 180(20) 180(50) 160(30) 192(6)
340(10) 180(10) 190(40) 280(40) 360(40) 380(20) 290(70) 320(60) 560(20) 460(20) 560(50) 600(200) 480(90) 660(20)
a Uncertainties listed in parentheses are one standard deviation from the average of multiple (∼6) measurements. b Nuclear spin statistics establish that only even rotational levels are populated in the 0000 and 011f0 states, while only odd rotational levels are populated in the 011e0 state. c All populations have been corrected for incident beam contributions. Values for J ) 0-12 are not reported because of uncertainties in the population subtractions. d Frequency coverage with the Pb-salt diode laser currently includes ∼90% of the transitions from P(54)-R(20) in the 0000 state and P(40)-R(40) in the 0110 state. Unlisted values of J correspond to inaccessible frequencies for these transitions (e.g., J ) 34, 48, 50 in the 0000 state). e Populations are generated from integrated absorbances and scaled by the appropriate Ho¨nl-London factor described in Section III. Populations are normalized by a sum over the predicted populations in the 0000 and 0110 manifolds. The Boltzmann analysis described in Sections IV and V allows populations to be predicted for all rotational states. f Doppler component of the IS channel from a two-temperature Voigt fit. See Section V for details.
presented below, the populations in Table 1 are additionally normalized to unity by summing over all rovibrational states in both vibrational manifolds. Populations for the 0000 state are predicted from an improved two-temperature fit to the observed data, as described in Section V, while 0110 state populations are predicted from a single temperature fit. Scattered populations in the 0000 state are scaled by Ho¨nlLondon factors and logarithmically plotted in a standard Boltzmann format in Figure 6. A comparison between the J-state populations of the incident (Trot ≈ 19K) and scattered flux indicates a dramatic change in the rotational energy content during the gas-liquid scattering event. This rotational excitation is, in fact, superthermal. By way of example, Figure 6 also shows a line corresponding to a Boltzmann distribution at Ts ) 298 K, providing evidence that CO2 molecules scatter from the surface clearly in excess of the surface temperature. This immediately implies that collisions at the gas-liquid interface are not simply dominated by thermal accommodation and desorption, and that nonequilibrium dynamics must be taking place. A least-squares Boltzmann fit of these 0000 populations to a straight line yields an approximate rotational temperature of Trot ) 456(8) K. A corresponding Boltzmann analysis for rotational distributions in the 0110 manifold yields a quite similar result, with an effective rotational temperature of Trot ) 435(30) K, which is within the experimental uncertainty of the 0000 fits. Nevertheless, there is no a priori reason to expect data in either of these vibrational manifolds to exhibit properties characteristic of a thermal distribution. In fact, a closer examination of the 0000 nascent rotational populations in Figure 6 reveals subtle but clear evidence of upward curvature in these Boltzmann plots. As will be addressed later in the discussion, these results prove to be quite well described with a two-temperature model for the rotational populations, where the two components reflect distributions resulting from separate trapping-desorption (TD) and impulsive scattering (IS) events. Measurements of scattered flux in the 0110 state reveal not only the extent of rotational energy transfer, but also the degree
Figure 7. Sample absorption profiles contrasting the hot band and ground-state populations in the scattered molecular flux, which illustrates an idea of a vibrational temperature. Note that the hot band absorption profile has been magnified by a factor of 10.
of vibrational accommodation with the surface. By way of example, the data illustrated in Figure 7 compare sample absorption profiles for transitions out of J ) 26 and J ) 12 rotational levels in the 0000 and 0110 manifolds, respectively, where the latter profile has been scaled by 10-fold for visual clarity. To aid in this comparison, the specific pair of J levels have been chosen for their nearly comparable rotational populations at Trot ≈ 456 K. The experimentally observed intensity ratio is ca. 25:1, which is more than 2-fold larger than would be expected for complete equilibration between rotational and vibrational degrees of freedom. More quantitatively, Figure 8 displays rotational Boltzmann plots on the same scale for both ground and bend-excited vibrational states. First, the data confirm that collisional excitation at the gas-liquid interface yields, within experimental uncertainty, superthermal and equivalent rotational temperatures for both manifolds. Second, by summing over all J states in these fits, these Boltzmann plots can be used to estimate a ratio of 0.0311 for populations in the 0000 to 0110 manifolds. Based on a 667 cm-1 energy gap, this
16402 J. Phys. Chem. B, Vol. 109, No. 34, 2005
Figure 8. A Boltzmann plot showing scattered flux populations in both the 0000 and 0110 vibrational states. The hot band populations are fit to a rotational temperature of 435(30) K. A comparison of 0000 and 0110 populations reveals a sub-Ts vibrational temperature (Tvib ≈ 230 K) in the scattered flux.
Perkins et al. Absorption profiles for scattered CO2 molecules can be similarly fit with a Voigt line shape function, using the same algorithm outlined in the characterization of the incident molecular beam. By way of example, sample data in Figure 9b illustrate a Doppler-broadened P(22) profile for CO2 flux scattered into J ) 22 of the 0000 manifold. The measured Doppler component is ∆νD ) 165(4) MHz, i.e., ca. 2.5-fold larger and signaling significant momentum transfer from the liquid to the projectile in the plane parallel to the surface. Interestingly, these measured translational distributions also exceed predictions based simply on thermal equilibration to the surface temperature, which would yield a Doppler width of only ∆νD(298 K) ) 130 MHz. This unambiguously implies a nonequilibrium component to the gasliquid collision dynamics, as was indeed observed in the rotational populations. Even more intriguingly, analysis of all the Doppler profiles reveals a clear J-dependence in these translational distributions, specifically increasing with increasing final rotational excitation. By way of example, a sample Doppler profile for P(46) in the 0000 manifold is displayed in Figure 9c, which is well fit to a Voigt line shape with a Gaussian width of ∆νD ) 194(4) MHz, i.e., significantly broader than for J ) 22. This novel and unexpected correlation between translational and rotational distributions reveals additional evidence for the nonequilibrium nature of the gas-liquid scattering events. Although these correlations could reflect a dynamical coupling between torque and transverse momentum transfer to the projectile, a much simpler picture proves sufficient to rationalize the data, as presented in the following section. V. Analysis and Discussion
Figure 9. Representative Doppler profiles illustrating translational energy transfer during the gas-liquid collision. The absorption profiles are fit with a Voigt function, which convolves the laser line width (∆νlaser ≈ 20-30 MHz) with a single temperature Doppler component (∆νD). (a) A sample profile and fit for a low-J state in the incident molecular beam illustrates ∆νD(J) < 131 MHz, which is the Doppler width for the surface temperature of 298 K. Sub-Ts Doppler widths provide the opportunity to investigate translational energy transfer during the collision. (b and c) Two sample profiles show state-dependent translational distributions in the scattered flux.
ratio would be consistent with a “two-point” vibrational temperature of Tvib ≈ 230 K in the scattered flux, indeed, only slightly warmer than similar estimates of vibrational temperature (Tvib ≈ 190 K) in the incident flux. This remarkably simple yet clear result indicates a dramatic difference in efficiency for vibrational versus rotational energy transfer efficiency because of collisions at the gas-liquid interface. Investigation of the translational energy transfer employs high-resolution Dopplerimetry analysis of the measured line shapes. The plot in Figure 9 displays sample absorption profiles and nonlinear least-squares fits of typical J-state transitions for both incident and scattered fluxes. Figure 9a illustrates the typical fit of an individual J-state in the incident flux of carbon dioxide, with skimmed line widths of ∆νD ) 63(2) MHz.
Further analysis of the internal state populations and translational distributions suggests a physical picture that is consistent with the two-channel scattering dynamics seen experimentally by TOFMS studies2,8,22,25,36 and theoretically by modeling simulations.16,24,29,30 Nonlinearity in the Boltzmann distributions first suggested the presence of a multiple channel-scattering process. To keep the analysis simple, a two-temperature model is constructed to analyze the internal state populations and translational distributions. The model assumes that the measured J-state populations reflect the sum of TD and IS components. Molecules that scatter via the TD channel have sufficient time to thermally accommodate on the surface, yet escape from the surface within the experimental observation window. As the CO2 molecules desorb through the TD channel, each degree of freedom is characterized by a surface temperature distribution at 298 K. This supposition is entirely consistent with similar assumptions made in fitting TOF profiles to a thermal TD component in other gas-liquid experiments.8,11 With the temperature of the TD fraction constrained at Trot(TD) ) 298 K, the observed rotational populations can be fit to a simple sum of two Boltzmann curves, where the second channel reflects the IS fraction of carbon dioxide scattering at the gas-liquid interface with different rotational temperature, Trot(IS). Such a simple yet physically motivated two-temperature model is applied to the rotational populations in Table 1 for the ground vibrational state, with the results plotted in Figure 10. The J-state populations for J ) 14-52 in 0000 have been least-squares fit to the sum of two Boltzmann populations, which consists of a rotational temperature and relative fraction for each component. The results in Figure 10 now indicate a much improved fit to the experimental data, nicely accounting for the upward curvature in the previous Boltzmann plots. More quantitatively, the model fit suggests an ∼46(2)% component
CO2 Scattering from Perfluorinated Liquids
Figure 10. Illustration of a two-temperature Boltzmann fit to populations for J ) 14-52 in the 0000 state. The Boltzmann function is constructed to model two-channel (TD/IS) scattering dynamics, which includes two temperatures and a relative fraction in each channel. A constraint is imposed that fixes Trot(TD) ) 298 K. The result of the fit indicates 46(2)% of the molecules scatter through the IS channel with Trot(IS) ) 715(36) K. Numbers from this fit are used to determine the trapping-desorption fraction, R ) 0.54(3).
of CO2 scattering through the IS channel with a rotational temperature of Trot(IS) ) 715(36) K, with the remaining ∼54(3)% desorbing via the TD pathway. The results of the fit indicate that the lower J-states are predominantly populated by the TD events while higher J-states are populated nearly exclusively by the IS channel. As will be seen later, this has important consequences for the resulting Doppler profiles, and indeed can nicely account for the observed J-dependent trends in the experimental data. The TD fraction includes the molecules that desorb from the surface within the experimental observation window, i.e., several 1000 µs or so. As illustrated in Figure 1, a trapped CO2 on the surface or in the bulk could potentially remain trapped beyond the given experimental observation window, which would skew the measured value of the TD fraction. Surface residence times observed in similar systems provide support for the assumption that CO2 desorbs from the surface within a time regime that is several orders of magnitude shorter than our experimental observation window.50 Furthermore, the TD fraction contains a small, yet negligible uncertainty from long time solvation of CO2 into the liquid. For the given pulsed valve duration, Henry’s law coefficient for CO2 in perfluorinated liquids, and typical diffusion constants, approximately one in 104 incident CO2 molecules will dissolve into the liquid, which is far less than our uncertainty in the TD fraction. The results of this two-channel model can be compared with the TOFMS studies by the Nathanson group.8 Specifically, for nonpolar gases (e.g., methane) on PFPE, the trapping-desorption fractions have been found to be R ) 0.31 (Einc ) 5.3 kcal/mol) and R ) 0.11 (Einc ) 12.2 kcal/mol),8 which are lower than values observed in our fits. However, these previous TOFMS scattering studies have been performed at an incident angle of 45°, when the trapping-desorption probability is known to increase severalfold as the incident angle of the molecular beam approaches normal incidence.11,14,51,52 In the current scattering studies at normal incidence, the CO2 molecule is therefore much more likely to transfer incident energy to the surface, which would be consistent with the higher trapping-desorption fractions (R ) 0.54) observed. In addition to TOFMS studies, the nonthermal collision dynamics of CO2 scattering from PFPE can also be qualitatively compared to the state-resolved distributions of NO scattered from an organized amphiphilic monolayer.35 Sagiv and coworkers probed the interaction between NO and self-assembled monolayers (SAM) of perfluorinated acid ester, HOOC-(CH2)8-
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Figure 11. A sample plot showing a single translational temperature of the measured state-dependent Doppler widths reported in Table 1. In addition, each profile is fit by a two-temperature Voigt function, which extracts Ttrans(IS) ) 770(60) K while Ttrans(TD) is constrained to 298 K. The solid line is a prediction of the Doppler width described in Section V.
C(dO)-O-(CH2)2(CF2)9CF3. These systems also present a terminal CF3 group at the gas-surface interface and therefore may be expected to mimic some of the local surface properties of PFPE. Indeed, Boltzmann plots for incident energies ranging from Einc ) 3.3 to 10.6 kcal/mol show a similar nonlinear, hyperthermal progression of rotational populations in the scattered NO flux. Specifically, for J > 10.5 and comparable collision energies of 10.6 kcal/mol, simple linear Boltzmann fits to their data reveal the NO rotational temperatures to be Trot ≈ 650 K, which is remarkably similar to the Trot ≈ 715 K results demonstrated herein. This comparison provides clear motivation for performing these CO2 scattering studies on PFPE at a series of incident collision energies, efforts which are currently in progress. We can take this two-component TD/IS analysis one step further by examining the J dependence of the translational Doppler profiles, and thereby provide independent validation of the proposed model. Specifically, the Doppler widths in Table 1 are plotted in Figure 11 and indicate a clear dependence on the final J rotational state. However, the relative fractional contributions to TD and IS scattering channels also vary with rotational state, as cleanly summarized by the least-squares fit in Figure 10. Thus, based on reasonable expectations for translational distributions into both TD and IS channels, one should, in principle, be able to predict the experimental Doppler profiles as a function of J state. In fact, the only a priori expectation we have is for the TD distributions, which presumably have accommodated to the surface temperature, and thus, in the absence of any exit barriers, emerge with Doppler widths characteristic of Ts. However, we can exploit this constraint along with the experimentally determined TD and IS fractions in Figure 10 and thereby investigate J-dependent Doppler width contributions purely for the IS channel. The analysis proceeds as follows. All J-state absorption profiles are considered as a sum of both TD and IS populations, where the TD component desorbs with a surface-temperature velocity distribution (Ts) and the IS population scatters with an unknown translational distribution also presumed to be Maxwellian. To isolate these two populations, the measured absorption profiles are then refit as a J state-dependent sum of two Voigt functions:
gJ(ν - ν0) ) RJ ‚gTD(ν - ν0) + (1 - RJ)‚gIS(ν - ν0) (1) where gTD(ν - ν0) and gIS(ν - ν0) reflect the TD and IS line shapes and RJ is the trapping desorption fraction calculated from the two-temperature Boltzmann fit in Figure 10.
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Perkins et al.
Most importantly, this trapping-desorption fraction is explicitly dependent on the final J state,
RJ ) R‚PTD(J)/(R‚PTD(J) + (1 - R)‚PIS(J))
(2)
where the probabilities are defined by
PTD/IS(J) ) (2J + 1) exp(-Erot/kTTD/IS)/QTD/IS
(3)
As a result, the low-energy J states are dominated by molecules in the TD channel while J states at very high energies are exclusively formed by scattering in the IS channel. With fitted values of RJ and a fixed Doppler distribution for the TD channel, the least-squares fit for each absorption profile reduces to a single parameter, specifically the Doppler width for the IS channel, denoted in Table 1 as ∆νD(IS). Each high-resolution absorption profile for J > 14 has been fit to the two-temperature line shape function with the appropriate values of RJ. The extracted Doppler widths for the IS channel are listed in Table 1; these prove to be surprisingly independent of J. Indeed, this remarkable result would be consistent with an even simpler model than imposed in the least-squares fit, specifically that all IS scattering events into all J final states can be adequately represented by a single Doppler width of 213(7) MHz. Interestingly, this average width would correspond to a translational temperature of Ttrans(IS) ≈ 770(60) K, which is in fact within the experimental uncertainty of the Trot(IS) ≈ 715(36) K temperature obtained for the rotational distributions. As a final test of the model, we return to the earlier J-state progression of experimental Doppler widths and attempt to predict these from the parameters determined above. For fixed values of Ttrans(IS) ) 770 K, Ttrans(TD) ) 298 K, and trappingdesorption fraction RJ, the absorption profiles can now be explicitly predicted and least-squares fit to yield an effective Doppler translational “temperature” as a function of J. The predicted temperatures are plotted in Figure 11, which indicates remarkable agreement with the corresponding experimentally observed values. This level of agreement is obtained with only a single parameter to characterize the common translational temperature for the IS channel. Indeed, if one were to interpret the apparent empirical equivalence between translational and rotational temperatures for the IS channel as a robust feature of the dynamics, the results in Figure 11 reflect confirmation of this simple two-channel model, with no adjustable parameters. The observation of energy transfer beyond thermal speeds parallel to the liquid surface suggests a gas-surface collision where the liquid surface is locally “rough”. Local corrugation provides a mechanism for momentum transfer from normal incidence to parallel scattering. Simple models such as the “washboard hard cube” model provide a physical description of momentum transfer into parallel surface directions.53 Surface corrugation has shown to drastically affect the trapping probabilities of incident molecules.51 Similar effects may also be responsible for exciting the translation of the scattered flux. A number of dynamical scattering models29,53-55 may also help describe these physical observations. One might also consider the possibility of local warming of the surface throughout the duration of the gas pulse. Based upon the properties of the gas pulse, however, the total incident energy per pulse on the liquid film is roughly 1.7 × 10-6 cal/cm2, which for typical heat capacities and 1 mm thick liquid would result in a 2 × 10-5 K temperature rise, i.e., totally negligible. As a parting comment, the subthermal vibrational temperature (Tvib ≈ 230 K) of the scattered gas molecules offers evidence of contrasting energy transfer into the vibrational modes of CO2.
Additional development in the two-channel-scattering model provides the opportunity to describe the anomalous energy transfer in the vibrations of CO2. As with rotations and translations, the vibrations are allowed to thermally accommodate on the surface through the TD channel. Dynamics through the IS channel are constrained in the following manner. The impulsive interaction of the incident CO2 with the PFPE structure involves a single collision or, at most, several collisions before rebounding into the vacuum above the surface. Transfer of translational and rotational energy into vibrational modes often requires orders of magnitude more collisions56 than the number assumed to occur through the IS channel at the surface. Therefore, a collision through the IS channel provides little opportunity to excite the bending modes in CO2. Such a model would constrain Tvib(TD) to 298 K and Tvib(IS) to the temperature of the incident flux (∼190 K). If 54% of the molecules scatter through the TD channel with Tvib(TD) ) 298 K, the characteristic vibrational temperature is expected to be ∼220 K, which is close to the estimated value in the scattered flux. The two-channel model would therefore be consistent with no energy transferred to the bending modes of carbon dioxide via the IS channel, perhaps because of the greatly limited number of collisional interactions in such a prompt scattering event. VI. Summary and Conclusion The results presented in this paper demonstrate the feasibility of the investigation of gas-liquid surface scattering with direct infrared absorption. Quantum state-resolved detection capabilities in this experimental approach offer a new window into correlated translational, rotational, and vibrational degrees of freedom in the scattered flux, and thereby probing energy transfer dynamics at the gas-liquid interface with unprecedented detail. Our first investigation of jet-cooled CO2 scattering on PFPE liquid interfaces has shown clear evidence of nonequilibrium dynamics that is consistent with a simple two-channel model of trapping-desorption (TD) and impulsive scattering (IS). Two-temperature Boltzmann analysis of the rotationally resolved data by fixing Trot(TD) ≈ Ts ≈ 298 K and adjusting Trot(IS) in a least-squares fit provides a simple, but excellent, description of the rotational distributions, with Trot(IS) ≈ 715(36) K. This analysis is further tested by detailed examination of the highresolution Doppler profiles, whose explicit J-dependence can be simply and accurately modeled by assuming that the IS translational distributions are all determined by a single temperature, Ttrans (IS) ≈ 770(60) K. Indeed, the empirical observation that Ttrans(IS) is essentially equal to Trot(IS), within experimental uncertainty, provides for a remarkably simple yet faithful reproduction of the J-dependent Doppler profiles, with no adjustable parameters. Analysis of hot band transitions out of the vibrationally excited 0110 manifold indicate similarly “hot” rotational temperatures as observed in the ground 0000 state, but with a vibrational temperature of only Tvib ≈ 230 K, i.e., much colder than Trot, only slightly warmer than present in the incident molecule beam, and yet not as warm as the liquid surface temperature. The inefficient warming of vibrational modes is in accordance with standard theories of energy transfer among different degrees of freedom, whereby impulsive collisions can impart considerable additional energy into translation and rotation, while the vibrational states with much larger energy spacings remain largely unpopulated. The results presented in this paper build intellectually on pioneering TOFMS experiments for gas-liquid scattering, adding to this suite of tools the capability for internal state
CO2 Scattering from Perfluorinated Liquids detection. Although these attempts represent a promising beginning, clearly much more work will need to be done to substantiate these models as a function of collision energy and angle of incidence. Additional efforts will also test these models by varying physical and chemical properties of both liquid interface and molecular projectile. Also of interest will be efforts to extract information on local surface corrugation and trappingdesorption residence dynamics from time- and frequencyresolved direct absorption traces, as elucidated by detailed Monte Carlo simulations of the scattering process. In future experimental directions, this direct absorption IR approach also offers the possibility of polarization modulation of the laser source, thereby probing mJ-dependent orientational and alignment effects,46 for example, gas molecules preferentially scattering from the liquid surface in a “cartwheel” versus “helicopter” type of rotational motion. Acknowledgment. Work presented in this paper was supported by grants from the Air Force Office of Scientific Research and the National Science Foundation. References and Notes (1) Minton, T. K.; Tagawa, M.; Nathanson, G. M. J. Spacecr. Rockets 2004, 41, 389. (2) Zhang, J.; Garton, D. J.; Minton, T. K. J. Chem. Phys. 2002, 117, 6239. (3) Hanson, D. R.; Lovejoy, E. R. J. Phys. Chem. 1996, 100, 6397. (4) Solomon, S. ReV. Geophys. 1999, 37, 275. (5) Barnes, G. T. Colloids Surf. A 1997, 126, 149. (6) Hurlbut, F.; Beck, D. E. U.C. Eng. Proj. Report HE-150-166, University of California, 1959. (7) Saecker, M. E.; Govoni, S. T.; Kowalski, D. V.; King, M. E.; Nathanson, G. M. Science 1991, 252, 1421. (8) Saecker, M. E.; Nathanson, G. M. J. Chem. Phys. 1994, 100, 3999. (9) Saecker, M. E.; Nathanson, G. M. J. Chem. Phys. 1993, 99, 7056. (10) Sinha, M.; Fenn, J., 1975, Nice. (11) Nathanson, G. M. Annu. ReV. Phys. Chem. 2004, 55, 231. (12) Goodman, F. O.; Wachman, H. Y. Dynamics of Gas-Surface Scattering; Academic Press: New York, 1976. (13) Nathanson, G. M.; Davidovits, P.; Worsnop, D. R.; Kolb, C. E. J. Phys. Chem. 1996, 100, 13007. (14) King, M. E.; Nathanson, G. M.; Hanninglee, M. A.; Minton, T. K. Phys. ReV. Lett. 1993, 70, 1026. (15) King, M. E.; Saecker, M. E.; Nathanson, G. M. J. Chem. Phys. 1994, 101, 2539. (16) Chase, D.; Manning, M.; Morgan, J. A.; Nathanson, G. M.; Gerber, R. B. J. Chem. Phys. 2000, 113, 9279. (17) Manning, M.; Morgan, J. A.; Castro, D. J.; Nathanson, G. M. J. Chem. Phys. 2003, 119, 12593. (18) Shuler, S. F.; Davis, G. M.; Morris, J. R. J. Chem. Phys. 2002, 116, 9147. (19) Ferguson, M. K.; Lohr, J. R.; Day, B. S.; Morris, J. R. Phys. ReV. Lett. 2004, 92. (20) Ferguson, M. K.; Low, E. R.; Morris, J. R. Langmuir 2004, 20, 3319. (21) Day, B. S.; Morris, J. R. J. Phys. Chem. B 2003, 107, 7120.
J. Phys. Chem. B, Vol. 109, No. 34, 2005 16405 (22) Day, B. S.; Shuler, S. F.; Ducre, A.; Morris, J. R. J. Chem. Phys. 2003, 119, 8084. (23) Rosenbaum, A. W.; Freedman, M. A.; Darling, S. B.; Popova, I.; Sibener, S. J. J. Chem. Phys. 2004, 120, 3880. (24) Isa, N.; Gibson, K. D.; Yan, T.; Hase, W.; Sibener, S. J. J. Chem. Phys. 2004, 120, 2417. (25) Gibson, K. D.; Isa, N.; Sibener, S. J. J. Chem. Phys. 2003, 119, 13083. (26) Darling, S. B.; Rosenbaum, A. M.; Sibener, S. J. Surf. Sci. 2001, 478, L313. (27) Waclawik, E. R.; Goh, M. C.; Donaldson, D. J. J. Chem. Phys. 1999, 110, 8098. (28) Stevenson, K. P.; Kimmel, G. A.; Dohnalek, Z.; Smith, R. S.; Kay, B. D. Science 1999, 283, 1505. (29) Lipkin, N.; Gerber, R. B.; Moiseyev, N.; Nathanson, G. M. J. Chem. Phys. 1994, 100, 8408. (30) Troya, D.; Schatz, G. C. J. Chem. Phys. 2004, 120, 7696. (31) Becker, C. H. Surf. Sci. 1985, 149, 67. (32) Miksch, G.; Weber, H. G. Chem. Phys. Lett. 1982, 87, 544. (33) Quintella, C. M.; McCaffery, A. J.; Zidan, M. D. Chem. Phys. Lett. 1993, 214, 563. (34) Kenyon, A. J.; McCaffery, A. J.; Quintella, C. M.; Zidan, M. D. Chem. Phys. Lett. 1992, 190, 55. (35) Cohen, S. R.; Naaman, R.; Sagiv, J. J. Chem. Phys. 1988, 88, 2757. (36) Kelso, H.; Kohler, S. P. K.; Henderson, D. A.; McKendrick, K. G. J. Chem. Phys. 2003, 119, 9985. (37) Lednovich, S. L.; Fenn, J. B. AIChE J. 1977, 23, 454. (38) Kaur, D.; Desouza, A. M.; Wanna, J.; Hammad, S. A.; Mercorelli, L.; Perry, D. S. Appl. Opt. 1990, 29, 119. (39) Proch, D.; Trickl, T. ReV. Sci. Instrum. 1989, 60, 713. (40) Johns, J. W. C. J. Mol. Spectrosc. 1989, 134, 433. (41) Guelachvili, G.; Rao, K. N. Handbook of Infrared Standards With Spectral Maps and Transitions Assignments between 3 and 2600 microns; Academic Press: London, UK, 1986. (42) Guelachvili, G. J. Mol. Spectrosc. 1980, 79, 72. (43) Michaels, C. A.; Mullin, A. S.; Flynn, G. W. J. Chem. Phys. 1995, 102, 6682. (44) Pradeep, T.; Miller, S. A.; Cooks, R. G. J. Am. Soc. Mass Spectrosc. 1993, 4, 769. (45) Herzberg, G. Molecular Spectra and Molecular Structure; D. Van Nostrand Company, Inc.: New York, 1945; Vol. II, Infrared and Raman Spectra of Polyatomic Molecules. (46) Weida, M. J.; Sperhac, J. M.; Nesbitt, D. J. J. Chem. Phys. 1996, 105, 749. (47) Miller, D. R. Free Jet Sources. In Atomic and Molecular Beam Methods; Scoles, G., Ed.; Oxford University Press: New York, 1988; Vol. 1, p 14. (48) Zacharias, H.; Loy, M. M. T.; Roland, P. A.; Sudbo, A. S. J. Chem. Phys. 1984, 81, 3148. (49) Nizkorodov, S. A.; Harper, W. W.; Chapman, W. B.; Blackmon, B. W.; Nesbitt, D. J. J. Chem. Phys. 1999, 111, 8404. (50) Morris, J. R.; Behr, P.; Antman, M. D.; Ringeisen, B. R.; Splan, J.; Nathanson, G. M. J. Phys. Chem. A 2000, 104, 6738. (51) King, M. E.; Fiehrer, K. M.; Nathanson, G. M.; Minton, T. K. J. Phys. Chem. A 1997, 101, 6556. (52) Ringeisen, B. R.; Muenter, A. H.; Nathanson, G. M. J. Phys. Chem. B 2002, 106, 4988. (53) Tully, J. C. J. Chem. Phys. 1990, 92, 680. (54) Doll, J. D. J. Chem. Phys. 1973, 59, 1038. (55) Nichols, W. L.; Weare, J. H. J. Chem. Phys. 1975, 62, 3754. (56) Yardley, J. T. Introduction to Molecular Energy Transfer; Academic Press: New York, 1980.
