Collisions at the GasâLiquid Interface: Surface Temperature

J. Phys. Chem. B 2008, 112, 507-519

507

Quantum State-Resolved CO2 Collisions at the Gas-Liquid Interface: Surface Temperature-Dependent Scattering Dynamics† 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: September 17, 2007; In Final Form: NoVember 12, 2007

Energy transfer dynamics at the gas-liquid interface are investigated as a function of surface temperature both by experimental studies of CO2 + perfluorinated polyether (PFPE) and by molecular dynamics simulations of CO2 + fluorinated self-assembled monolayers (F-SAMs). Using a normal incident molecular beam, the experimental studies probe scattered CO2 internal-state and translational distributions with high resolution infrared spectroscopy. At low incident energies [Einc ) 1.6(1) kcal/mol], CO2 J-state populations and transverse Doppler velocity distributions are characteristic of the surface temperature (Trot ≈ Ttrans ≈ TS) over the range from 232 to 323 K. In contrast, the rotational and translational distributions at high incident energies [Einc ) 10.6(8) kcal/mol] show evidence for both trapping-desorption (TD) and impulsive scattering (IS) events. Specifically, the populations are surprisingly well-characterized by a sum of Boltzmann distributions where the two components include one (TD) that equilibrates with the surface (TTD ≈ TS) and a second (IS) that is much hotter than the surface temperature (TIS . TS). Support for the superthermal, yet Boltzmann, nature of the IS channel is provided by molecular dynamics (MD) simulations of CO2 + F-SAMs [Einc ) 10.6 kcal/ mol], which reveal two-temperature distributions, sticking probabilities, and angular distributions in near quantitative agreement with the experimental PFPE results. Finally, experiments as a function of surface temperature reveal an increase in both sticking probability and rotational/translational temperature of the IS component. Such a trend is consistent with increased surface roughness at higher surface temperature, which increases the overall probability of trapping, yet preferentially leads to impulsive scattering of more highly internally excited CO2 from the surface.

I. Introduction Dynamics at the gas-liquid interface represent a critically important focus of research effort for understanding heterogeneous chemistry on surfaces and within bulk liquids. Whether considering catalytic dissociation of acids on ice1-7 or chemical formation of acids in atmospheric aerosols,8-10 the detailed collision dynamics of gas molecules interacting with a surface control the resulting chemical pathways taken by the system. As has been true in countless areas of scientific endeavor, the process of understanding has been greatly stimulated by comparison of experimental measurements with theoretically tractable model systems, for which the elegant work of James T. “Casey” Hynes has long served as a source of inspiration. Of relevance to the current study, close comparison between (i) experiment, (ii) first principles theory, and (iii) high-level molecular dynamics simulations offer considerable promise for elucidating the fundamental paradigms of gas-liquid interactions, for example, the probability of a gas molecule sticking to a liquid surface upon impact.11,12 In our laboratory, we have recently developed methods for quantum state-resolved interrogation of molecular collision dynamics at the gas-liquid interface, based on ultrasensitive high-resolution direct absorption laser spectroscopy of the scattered projectile above the liquid surface.13-16 In the present work, we experimentally investigate how surface temperature (TS) of a perfluorinated liquid (PFPE) influences the interfacial †

Part of the “James T. (Casey) Hynes Festschrift”. * Corresponding author. E-mail: [email protected].

dynamics in terms of energy transfer and sticking probabilities. The conditions provide the opportunity to further characterize the CO2 + PFPE interaction, which has been previously studied in our laboratory as a function of incident energy14,16 and incident angle.13 In addition, we present a series of molecular dynamic (MD) simulations17 where CO2 is scattered from a fluorinated self-assembled monolayer surface (F-SAMs) over a range of temperatures that match the experimental conditions of CO2 + PFPE. From detailed comparison of these results, the synergism between molecular beam experimental results and theoretical modeling provide both validation of and key insights into simple models of the gas-liquid collision event. Historically, molecular beams were first used to study liquid surfaces by Fenn and co-workers. They investigated the angular distributions of Ar scattering off glycerol as a function of incident energy.18 Following these studies, extensive experiments in the Nathanson group further resolved many of the important parameters in the scattering mechanism such as the effects of incident energy, angle, projectile mass, surface structure, and temperature.19-26 In addition to liquids, self-assembled monolayer surfaces (SAMs) have been used for study, exploiting their unique ability to specifically control chemical and physical properties of moieties protruding into the liquidlike surface region.27-35 The current and yet rapidly evolving paradigm for describing the majority of gas-liquid scattering studies is depicted in Figure 1, which illustrates CO2 colliding with a surface of either PFPE liquid or F-SAM. In agreement with

10.1021/jp077488b CCC: $40.75 © 2008 American Chemical Society Published on Web 12/05/2007

508 J. Phys. Chem. B, Vol. 112, No. 2, 2008

Perkins and Nesbitt TABLE 1: Properties of Bulk PFPE Liquid chemical composition mass density melting point boiling point vapor pressure viscosity compressibility surface tension KH

F-[CF(CF3)CF2O]14a-CF2CF3 2400 amua 1.87 g/cm3 -45 °C 200 °C 7 × 10-7 Torrb 80 cpb 10-9 cm2/dyne 17 dyn/cmb 3.1 × 104 Torrc

a Average size of Krytox 1506 polymer. b 25 °C. c Henry’s law constant for CO2 with C10F22O2.

Figure 1. Physical picture of CO2 scattering from perfluorinated liquids (PFPE) and fluorinated self-assembled monolayers (F-SAMs). The dynamics incorporate trapping desorption (TD) and impulsive scattering (IS) trajectories for both surfaces.

numerous time-of-flight mass spectrometry (TOFMS) experiments,19-23,26 our previous quantum state-resolved IR studies at normal incidence have revealed that CO2 scatters from PFPE through two distinct pathways: trapping-desorption (TD) and impulsive scattering (IS). The TD channel incorporates diffuse scattering, where the final CO2 is characterized by cos(θ) angular distributions18,36 andMaxwell-Boltzmannenergydistributions12,37-39 characteristic of the surface temperature. The IS channel, however, guides the incoming gas through a series of interactions where either single or multiple collisions allow the projectile to retain a significant fraction of the incident energy.19,36,40,41 Under normal incidence conditions, the final IS rotational and translational energy distributions for CO2 + PFPE in the (x, y) plane parallel to the surface are wellcharacterized by an IS temperature where TIS > TS.13-16 Such a physical picture contrasts with many previous TOFMS experiments, for which the IS translational component could not be well-characterized by a single temperature.20,21,27,32,36 With such a discrepancy between quantum state-resolved/ unresolved experiments, the true nature of the IS collision event remains unclear, especially for molecular projectiles that tend to sample both single and multiple collisions with the surface. The physical picture of the interfacial dynamics has been strengthened in recent years by high-level theoretical studies of atoms and molecules interacting with SAM surfaces. Simulations have quantitatively reproduced experimental results for systems such as Ne + CH3(CH2)nS-Au,32,41-43 Ar + CH3(CH2)nS-Au,31,44,45 and CO2 + CF3(CF2)7S-Au.17 An explicit comparison between CO2 + F-SAM simulations with CO2 + PFPE experiments reveals quantitative agreement between the final CO2 rotational state distributions for normal incidence at Einc ) 10.6 kcal/mol. For example, a two-temperature Boltzmann analysis of the Martinez-Nuń˜ez and Hase trajectories17 reveals nearly identical final rotational-state distributions between the F-SAM simulation and the PFPE experiment, where both studies yield TD fractions (R) of ≈0.56 and IS rotational temperatures of ≈740 K. The similarity of the two sets of results suggests that CO2-PFPE interactions are quite well-modeled by those in the CO2 + F-SAM simulation, each dominated by

CO2 interaction with -CF3 and -CF2- groups near the surface. In fact, CO2-PFPE dynamics are likely to be especially sensitive to -CF3 and -CF2- groups, since studies have shown that the C-O-C ether linkages tend to solvate away from the surface and into the bulk liquid.46 By correctly capturing the essential physics of the CO2-surface interaction, these simulations provide a novel opportunity to both posit models for and validate detailed mechanistic questions concerning the gas-liquid collision dynamics. In terms of influential physical parameters in IS/TD scattering dynamics, the role of surface temperature has been investigated both experimentally and theoretically through detailed studies of atomic gases with perfluorinated liquids23,26 and SAM surfaces.32,47,48 Experimental studies have shown Ne, Ar, and Xe atoms have a greater probability to trap on the PFPE as the surface temperature increases.23,26 Such trends support a simple physical picture where an increase in TS leads to a dynamically rougher surface, which thereby promotes multiple collisions between the gas and the liquid. The TD fraction, therefore, tends to increase since each additional collision transfers more energy from the gas to the liquid. Such an increase in surface roughening has been correlated with the temperature dependence of bulk physical properties of PFPE (Table 1). For example, density decreases from 1.92 g/cm3 at 232 K to 1.78 g/cm3 at 323 K, while surface tension drops from 44 mN/m to12 mN/m over the same 90 K temperature range. These properties suggest the PFPE relaxes with increasing temperature into configurations where surface groups sample more volume, that is, with fewer steric restrictions from neighboring groups. An increase in local surface corrugation also couples to additional roughening caused by capillary waves, where random thermal oscillations increase the average thickness of the interface from ≈4.0 to 8.8 Å over the range of experimental surface temperatures.49 Simple properties of the liquid surface provide the foundation for physical insight into quantum state-resolved dynamics at the surface and how they change with temperature. The remaining sections of this paper are organized as follows. The key details of the CO2 + PFPE experiment are outlined in section II where the surface temperature is varied from 232 to 323 K. Quantum-state experimental populations are presented in section III along with high resolution Dopplerimetry analysis of the scattered flux absorption profiles. Section IV contains detailed results of molecular dynamics simulations where CO2 is scattered from F-SAM surfaces over a surface temperature range matching the experimental PFPE studies. Section V covers a discussion and further analysis of the experimental and theoretical results. A summary and conclusion are presented in section VI. II. Experiment The experiment consists of a supersonic molecular beam of jet-cooled CO2/buffer gas mixture that impinges upon a clean

Quantum State-Resolved CO2 Collisions

J. Phys. Chem. B, Vol. 112, No. 2, 2008 509 TABLE 2: Properties of the Incident Molecular Beam Einc carrier gas Trot (0000) Trot (0110) Tvib Vbeam ∆νD a

Figure 2. Schematic of experimental setup. A skimmed molecular beam impinges upon a temperature-controlled liquid surface in vacuum. The Pb-salt diode laser spectrometer measures scattered CO2(V,J) populations.

liquid surface in vacuum. As shown in Figure 2, a highresolution infrared spectrometer is used to detect both the incident and the scattered CO2 molecules throughout the experiment. The details of the molecular beam, liquid surface, and spectrometer have been discussed in previous papers.13,14,16 Therefore, we only present the important details of each component along with the specific modifications used to control surface temperature. By using methods developed by Lednovich and Fenn,50 the liquid surface is prepared on a 12.7 cm glass wheel that rotates at 0.5 Hz through a 300 mL reservoir of PFPE, viscously dragging a thin film onto the surface. A stainless steel razor blade scrapes off the top layer to yield a clean 1 mm thick surface for the impinging CO2 molecules. To control the temperature of the liquid, a refrigerated thermostat pumps ethanol from a fixed-temperature reservoir into tubing that runs through aluminum blocks in contact with the liquid reservoir inside the vacuum. The temperature of the liquid was monitored with a glass thermometer and remained constant to within (2 °C over the course of a single experiment. A molecular beam of CO2 is generated by a pulsed valve based on the designs of Proch and Trickl51 where incident energy is controlled by seeding CO2 either in argon or in hydrogen. The 10% gas mixture is supersonically expanded through a 0.5 mm pinhole orifice where the piezoelectric actuator generates 300 µs gas pulses. The angular divergence of the beam is confined to (6° around the centerline by a 5.0 mm skimmer positioned 2.5 cm downstream. With the pinhole fixed 10 cm from the surface, the molecular beam impinges the surface at normal incidence. The molecular beam and wheel assembly are housed within a 60 L aluminum vacuum chamber that is evacuated with a 6 in. liquid N2-trapped diffusion pump. The average pressure in the chamber remains below 3 × 10-5 Torr with the pulsed valve operating at 11 Hz and a backing pressure of 100 Torr. Quantum state CO2 populations in the incident molecular beam and scattered flux are measured by direct absorption with a high-resolution infrared spectrometer. A Pb-salt diode laser generates 1-2 µW of tunable infrared light around λ ) 4.2 µm. The light is used to excite the ν3 asymmetric stretch in both the ground (0000) and excited (0110) vibrational manifolds. The collimated laser beam is split into several subsequent beams to simultaneously measure the scattered CO2 populations and determine the frequency throughout the duration of the laser

1.6(1)a kcal/mol argon 19(4) K 24(5) K 255(15) K 5.51(9) × 104 cm/s 29(5) MHz

10.6(8) kcal/mol hydrogen 19(3) K 15(4) K 175(10) K 1.41(9) × 105 cm/s 63(2) MHz

Number in parenthesis indicates 1σ for multiple measurements.

scan. Specifically, the first third of the laser light is sent to a reference gas cell of CO2 to determine absolute frequencies, while a confocal Etalon provides the relative frequency axis throughout a single scan. To detect the scattered CO2 flux, the second third of the laser light is passed 1 cm directly above the liquid surface in a multipass52 configuration before being focused onto a liquid N2-cooled InSb photovoltaic detector. The final fraction of the laser beam passes directly onto a matched reference InSb detector, where the voltages from both the signal and the reference detectors are sent to fast servo-loop subtraction electronics to eliminate common mode noise from the laser. The detection scheme yields an absorption sensitivity of 1-2 × 10-6 Hz-1/2, which is within a factor of 2 of the shot noise limit for typical 1 µW laser power levels. A computer-controlled A/D records 2 ms absorption signals where the time window includes time before, during, and after the gas pulse collides with the surface. The time signals are stored as a function of laser frequency, which provides the opportunity to analyze both the time and the frequency-detuning dependence of the scattered signal. Data reported in this paper reflect absorption as a function of frequency where the time signals have been integrated over the central 200 µs of the rising edge of the scattered gas pulse. III. Experimental Results A. Incident Beam Characterization. The surface temperature dependence of CO2 scattering from PFPE has been investigated with two incident beam energies, 1.6(1) and 10.6(8) kcal/mol. Immediately prior to each scattering experiment, the internal state populations and translational distributions for the incident molecular beam are characterized in the absence of the liquid wheel assembly. Absorption profiles for populations in both ground (0000, J ) 0-54) and excited (0110, J ) 0-38) vibrational manifolds53 are measured for all J states accessible with the diode laser spectrometer, yielding the absolute density of CO2 in the laser beam as a function of Doppler-detuning frequency. The total population per quantum state is obtained by integration of the absorption profiles over all frequencies to produce column-integrated densities (Av,J) for each rotational state within a given vibrational manifold. The populations are analyzed in a standard Boltzmann fashion, where Av,J is scaled by the appropriate Ho¨nl-London factor (SJ) and degeneracy factor (2J + 1) and then plotted logarithmically against Erot ) BCO2J(J + 1). A linear least-squares fit reflects the characteristic rotational temperature (Trot) of CO2 in the incident molecular beam. Rotational populations in both the 0000 and 0110 states are cooled to Trot ≈ 15-25 K for both argon and hydrogen carrier gases, where each expansion exhibits modest “freezein” effects in the high rotational states.54,55 Furthermore, a direct comparison of the total population in each vibrational manifold reflects the vibrational temperature (Tvib) in the incident beam (Table 2). The excited bend state population cools to Tvib ) 255(15) K and 175(10) K for the argon and hydrogen beams, respectively. Inefficient vibrational cooling once again reflects the difficulty of relaxing large quanta of energy in a pinhole expansion.14,54,55


Perkins and Nesbitt

Figure 3. Sample data illustrating the scattered CO2 quantum state populations for a PFPE surface at TS ) 232 K. Incident energies of 1.6(1) and 10.6(8) kcal/mol are used to explore the surface temperature effects of TD and IS scattering dynamics.

In addition to the internal state populations, the translational distributions for the incident CO2 are characterized with (i) timeof-flight measurements along the molecular beam expansion axis and (ii) high-resolution Dopplerimetry analysis of the absorption profiles. First, the centerline beam velocity is measured with a hearing aid microphone in a time-of-flight configuration.56 The microphone measures the arrival time of each gas pulse as a function of downstream distance, the slope of which readily permits determination of a mean velocity. Centerline velocity measurements for the low and high energy beams are 5.51(9) × 104 and 1.41(9) × 105 cm/s, respectively, which agree quite well with beam velocity values (5.56 × 104 and 1.42 × 105 cm/s) calculated from supersonic gas flow formulas.54 By virtue of our laser probe method, the transverse velocity components parallel to the surface can be characterized by line shape analysis of the incident absorption profiles, based on nonlinear leastsquares fitting14 to a Voigt line shape function. The Gaussian component of such a line shape reflects the translational velocity distribution parallel to the laser multipass, while the Lorentzian component accounts for frequency noise (≈20 MHz) in the diode laser. Such deconvolution yields Gaussian full-width-halfmaximum (fwhm) values for the low and high energy beams of 29(5) MHz and 63(2) MHz, respectively, which corresponds quantitatively to the expected broadening (26 and 66 MHz) arising from different jet speeds and finite angular divergence of the skimmer. B. Low Incident Energy CO2 + PFPE (Einc ) 1.6 kcal/ mol). High-resolution absorption profiles of CO2 in the scattered flux have been measured for low and high incident energies at normal incidence for TS ) 232 to 323 K. Sample absorption profiles for quantum states in the 0000 manifold are presented in Figure 3 to illustrate the qualitative differences between the low and high Einc for the lowest surface temperature, TS ) 232 K. The progression of rotational state populations for both incident energies appears roughly Boltzmann in character; J states below 10 are not included because of signal contamination in the normal scattering configuration by the incident CO2 beam. The clear qualitative difference between the two measured populations is the substantially enhanced fraction of high J state populations observed under high incident energy conditions. The qualitative nature of the two distributions at TS ) 232 K parallels the populations measured when CO2 is scattered from a roomtemperature surface. To analyze the quantum state populations more quantitatively, however, we again use a Boltzmann analysis to extract characteristic rotational temperatures for the scattered distributions.

Figure 4. Surface temperature dependence of scattered CO2 populations where Einc ) 1.6 kcal/mol and TS ranges from 232 to 323 K. Boltzmann plots illustrate Trot ≈ TS for both the (a) 0000 ground state and the (b) 0110 excited vibrational manifolds.

On the basis of previous experiments at TS ) 298 K that reveal nearly complete accommodation with the surface (i.e., R ) 1, Trot ≈ TS) for Einc ) 1.6 kcal/mol,14 we first examine the distributions for the low incident energy beam over the full range of surface temperatures. As described above, populations in the 0000 and 0110 manifolds are obtained by integration of the high resolution absorption profiles over Doppler detunings, corrected at normal incidence for low J residual contamination due to the incident beam, scaled by the appropriate line strength and degeneracy factors, and logarithmically plotted against Erot. Sample results are shown in Figure 4a for the rotational state populations in the 0000 manifold, which illustrate that the populations are well fit by a single rotational temperature for each TS. Indeed, within uncertainty of the least-square fits, the scattered distributions are well-characterized by a single Trot ≈ TS over the full temperature range from 232 to 323 K, with Figure 4b supporting the same conclusion for all rotational states in the vibrational hot band. The results of these fits are summarized in Table 3 and plotted in Figure 5; simply stated, at these low collision energies, the CO2 rotational degrees of freedom clearly have enough time to equilibrate with the liquid surface temperature. Interestingly, this is not true for vibrational degrees of freedom. Indeed, as shown in Figure 5, relative population analysis of the vibrational states demonstrates Tvib


J. Phys. Chem. B, Vol. 112, No. 2, 2008 511

TABLE 3: One-Temperature Results for CO2 + PFPE for Einc ) 1.6 kcal/mol TS

Trot (0000)

Trot (0110)

Tvib

Ttrans (0000)

323a 298 273 254 232

321(3)b 308(4) 275(2) 256(3) 244(4)

330(30) 303(10) 265(15) 243(15) 232(20)

273(3) 289(3) 266(2) 258(2) 268(5)

313(12)c 287(10) 270(6) 261(6) 231(6)

a All temperatures are Kelvin. b Numbers in parentheses represent the estimated error from a single temperature fit over several data sets. c Average Ttrans over J ) 14-44 from high resolution Dopplerimetry line shape analysis.

Figure 5. Summary of characteristic translational, rotational, and vibrational temperatures for CO2 scattered from PFPE at Einc ) 1.6 kcal/mol.

is approximately constant at ≈270 K and relatively independent of the surface temperature. This apparent inability to thermalize the bending mode in CO2 to the surface temperature suggests that gas-surface interactions, even for a dominantly TD scenario at low incident energies, are of limited duration and specifically insufficient to either excite or relax bend quanta as low as 667 cm-1. In addition to providing internal state populations, the narrow line width of the diode laser allows one to characterize parallel translational distributions for the scattered flux from line shape analysis of the absorption profiles. Figure 6 illustrates sample Doppler profiles for J ) 36 at each surface temperature, for which the line shapes clearly broaden systematically as TS increases. To account for residual laser line width, each profile is fit to a Voigt line shape, where the Gaussian component reflects a thermal distribution of velocities parallel to the surface. The fwhm of the line shape, ∆νD, is equal to

x

∆νD ) 2‚ν0

2 ln(2)‚kTtrans mCO2c2

(1)

where ν0 is the rovibrational transition frequency and Ttrans reflects a characteristic translational temperature parallel to the liquid surface. Within uncertainties determined from repeated measurements, the translational distributions for J ) 36 are all consistent with Ttrans ≈ TS. Indeed, with the exception of low J profiles (with residual incident beam contributions), Doppler analysis results in Ttrans ≈ TS for all measured 0000 J states, which is reported as an average Ttrans value in Table 3 and plotted in Figure 5 with the internal state temperatures. As expected, the translational degree-of-freedom equilibrates with the surface

Figure 6. Sample temperature dependent absorption profiles for J ) 36 (TS ) 232 to 323 K). Doppler profiles are fit to Voigt line shapes where the Gaussian component characterizes translation of the scattered flux and the Lorentzian accounts for small residual laser line width of ≈20 MHz. The extracted translational distributions for low incident energy (Einc ) 1.6 kcal/mol) are all well-characterized by Ttrans ≈ TS at each temperature.

in the same fashion as rotation but not like vibration. Although Dopplerimetry probes only the velocity component along the laser axis, that is, Vy, the normal incidence beam-liquid collision geometry implies cylindrical symmetry for the distribution for Vx. The present probe geometry offers no information on Vz, but on the basis of the thermally equilibrated x and y components, it is most likely a flux-weighted distribution also at Ttrans ≈ TS. The low collision energy experiments provide us with an important physical picture for the nature of the TD scattering channel. As determined in a previous study at TS ) 298 K, the measured sticking-probability of ≈1 now can be extended through the entire temperature range of 232-323 K. Our definition for sticking for the TD channel continues to be based


Perkins and Nesbitt

PTD/IS(J) )

(2J + 1)‚e-Erot/kTrot(TD/IS) Qrot(TD/IS)

Pvib(V) )

Figure 7. Boltzmann analysis of high incident energy (10.6 kcal/mol) CO2 scattered from PFPE over surface temperatures of 232 to 323 K. The 0000 and 0110 populations are fit to a two-temperature Boltzmann function that consists of the TD fraction (R), Trot(IS), and Trot(TD). Details of the fit are outlined in section III.C.

on the equilibration of the rotational and translational degreesof-freedom with the surface, yet excludes vibrational equilibration since the ground and excited-state populations never reach a TS distribution. Such a definition deviates from traditional gassurface studies where a trapping event explicitly requires that all memory of the incident trajectory is lost.38 With this in mind, CO2 + PFPE provides an important example where the duration of the gas-surface interaction is long enough to thermally equilibrate rotations and translations in the molecular gas, yet not vibrations. C. High Incident Energy CO2 + PFPE: Internal State Distributions. At higher incident energy, the rotational and translational populations no longer thermally equilibrate with the surface. This is quantified in Figure 7 by a Boltzmann plot analysis analogous to Figure 4, which clearly shows rotational populations for Einc ) 10.6 kcal/mol no longer follow a straight line as observed under low Einc conditions. Similar deviations have been measured as a function of both incident energy and incident angle,14,16 for which a two-temperature Boltzmann model has proven effective in characterizing the scattered populations in terms of TD and IS components. We employ a similar analysis to analyze quantum state distributions as a function of TS. The two-temperature model assumes that the total population is the sum of two subpopulations, TD and IS, each of which is characterized by a rotational temperature. The data are fit to extract Trot(TD), Trot(IS), and microscopic branching between TD and IS events, with the 0000 and 0110 populations fit simultaneously to estimate a vibrational temperature in the scattered flux. Explicitly, the column-integrated absorbances are fit to:

AV,J ) N‚{R‚PTD(J) + (1 - R)‚PIS(J)}‚Pvib(V) SJ

(2)

where R is the TD sticking-coefficient fraction based on rotational populations and P is the normalized Boltzmann factor for either rotation or vibration,

e-hν/kTVib Qvib

(3)

(4)

As in previous studies, we assume that the rotational temperature of the TD component achieves thermal equilibrium with the surface. This has been further confirmed by the low Einc results and allows us to fix Trot(TD) ) TS to reduce parameter correlation in a nonlinear least-squares fit of the data. The extracted fit parameters are listed in Table 4 for all five surface temperatures investigated. This two-temperature fit can be used to normalize the scattered J state populations for ground and excited vibrational states (see Table 5). The results are plotted in Figure 8a as a function of J state and surface temperature, where the fit curve is displayed along with the individual TD and IS component contributions. Qualitatively, the fractional area under the TD curve increases with surface temperature, corresponding to an increase in sticking coefficient R from 0.43(2) to 0.58(3) as TS increases from 232 to 323 K (Figure 9). Such a behavior is consistent with a surface roughening of the liquid with increasing temperature and is in agreement with previous atom + PFPE studies.23,26 What is somewhat less obvious is that, over the same temperature range, CO2 projectiles colliding with a hotter surface tend to scatter through the IS channel with a hotter rotational temperature. Specifically, Trot(IS) increases from 600(30) K to 860(40) K, which is about three times more than the increase in surface temperature, as illustrated in Figure 10a. By way of contrast, Tvib remains at or below TS for each surface temperature, clearly underscoring a large difference in relaxation dynamics between rotational and vibrational degrees of freedom. The combination of these two trends, that is, a correlated increase in R and Trot(IS) as TS increases, suggests a possible microscopic picture where a rougher liquid surface not only is more effective at temporarily trapping CO2 but also provides more local structure to torque CO2 into higher rotational states through a collision. Additionally, the surface itself could impart energy into the scattered CO2, where the energy gained in the projectile increases with surface temperature.57 Alternatively, one could argue that rougher liquid surfaces generated at higher temperatures are more efficient at trapping the lower rotational energy fraction of CO2 emerging from first interaction with the surface. This argument would both preferentially enhance R by reducing escape probability into what would have otherwise constituted a “low J state” IS event, thereby elevating Trot(IS). The importance and validity of such “inelastically competitive” mechanisms would be interesting to explore further theoretically with trajectory calculations, which we are currently starting to pursue. However, such a mechanism whereby heating of the J state distribution by preferential trapping of low J states after an initial encounter may already be analogous to work by McKendrick and co-workers on hyperthermal O(3P) + squalane.58 Specifically, their studies reveal an increase in OH(V ) 1) versus OH(V ) 0) branching fraction with increasing liquid temperature, which they argue arises from a decreased relaxation rate and therefore increased escape probability for OH(V )1) on a rougher and more open surface.58 D. High Incident Energy CO2 + PFPE: Translational Distributions. At high collision energy, there is ample evidence in the CO2 rotational distributions for microscopic branching into dual temperature TTD ) TS and TIS . TS channels. Within this picture, we explore details in the corresponding translational



TABLE 4: Two-Temperature Results CO2 + PFPE/F-SAMs for Einc ) 10.6 kcal/mol PFPE

F-SAMs

TS

R

Trot(IS)

Tvib

Ttrans(IS)

〈Escat〉/Einc

〈Escat(IS)〉/Einc

323a 298 273 254 232

0.58(3)b 0.55(2) 0.53(1) 0.47(3) 0.43(2)

780(50)b 720(20) 660(20) 610(10) 580(10)

250(3)b 230(4) 228(3) 228(5) 230(2)

860(40)b 820(30) 700(30) 640(40) 600(30)

0.30(3) 0.30(3) 0.26(2) 0.25(2) 0.25(2)

0.47(4) 0.45(4) 0.39(3) 0.35(3) 0.33(3)

TS

R

Trot(TD)

Trot(IS)

Rtrans

Ttrans(IS)

〈Escat(IS)〉/Einc

323 298 273 254 232

0.54(9)b 0.48(10) 0.51(11) 0.45(6) 0.44(9)

330(40) 290(40) 300(40) 280(40) 240(30)

760(90)b 740(80) 700(90) 680(60) 650(50)

0.22(2)b 0.23(2) 0.28(1) 0.22(2) 0.22(2)

740(30)b 770(20) 720(20) 680(20) 680(10)

0.42(4) 0.43(4) 0.40(4) 0.38(3) 0.38(3)

a All temperatures are Kelvin. b Numbers in parentheses represent the estimated error from the two-temperature fit over several data sets for CO2 + PFPE. Errors reported for CO2 + F-SAMs represent the estimated statistical error from the least-squares analysis over ≈3500 trajectories.

TABLE 5: Quantum State-Resolved Populations: CO2 + PFPE surface temperature (TS) 232 K

254 K

J

population

J

population

12 14 16 18 20 22 24 26 28 30 34 36 38 40 42 44 46 50 54

5.88(11)c 6.24(20) 6.33(32) 6.47(22) 6.01(12) 6.12(28) 5.26(13) 5.61(16) 4.39(11) 4.02(9) 3.16(4) 2.97(14) 2.35(6) 1.94(2) 1.81(1) 1.45(2) 1.36(5) 0.88(2) 0.65(1)

12 14 16 18 20 22 24 26 28 30 34 36 38 40 42 44 46 50 54

6.05(14) 5.97(16) 6.52(22) 6.35(13) 6.27(26) 5.57(7) 5.62(16) 4.86(4) 4.87(8) 4.21(2) 3.13(5) 3.10(6) 2.63(10) 2.21(6) 2.06(4) 1.67(2) 1.49(2) 1.08(2) 0.76(3)

9 10 11 13 14 15 16 21 24 25 26 29 30

8.6(7) 8.6(6) 9.5(8) 9.0(3) 9.0(5) 10.6(3) 9.4(4) 8.0(4) 7.6(9) 7.1(7) 6.5(4) 5.1(4) 4.8(3)

4 6 8 10 11 12 14 15 16 23 24 25 33 38

3.9(17) 7.4(8) 9.3(11) 11(2) 12(3) 8.5(8) 9.7(11) 11(1) 9.3(6) 11(2) 8(2) 7(2) 4.9(8) 6(4)

273 K

298 K

0000 J - State Populations (×10-2)a,b J population J 12 14 16 18 20 22 24 26 28 30 34 36 38 40 42 44 46 50 54

5.68(7) 6.13(5) 5.90(11) 6.15(10) 5.98(10) 5.54(19) 5.35(12) 4.74(6) 4.68(6) 4.16(4) 3.42(4) 3.15(8) 2.52(5) 2.25(2) 1.92(2) 1.63(7) 1.43(1) 1.03(2) 0.78(3)

0110 J - State Populations (×10-4) 6 6.0(6) 7 4.6(9) 8 7.2(3) 10 7.2(7) 11 7.5(2) 12 9.0(18) 14 9.2(9) 15 9.2(14) 16 9.2(11) 19 7.7(3) 23 7.5(4) 24 6.5(5) 25 6.6(4) 33 4.6(4) 38 3.1(6)

12 14 16 18 20 22 24 26 28 30 34 36 38 40 42 44 46 50 54 6 8 10 12 13 14 16 21 23 24 31 38

323 K

population

J

population

5.45(11) 6.02(18) 5.90(8) 6.18(20) 6.14(9) 5.48(10) 5.42(9) 4.79(8) 4.55(3) 4.29(3) 3.40(3) 3.15(15) 2.76(2) 2.32(1) 1.99(2) 1.71(5) 1.53(1) 1.10(2) 0.78(2)

12 14 16 18 20 22 24 26 28 30 34 36 38 40 42 44 46 50 54

5.32(9) 5.95(9) 5.99(11) 5.94(11) 6.03(7) 5.51(9) 5.55(19) 4.98(2) 4.65(7) 4.37(4) d 3.31(2) 2.86(3) 2.46(2) 2.14(2) 1.79(5) 1.65(6) 1.23(3) 0.86(2)

5.6(9) 7.6(5) 9.0(6) 9.1(7) 9.6(4) 11(1) 10.0(2) 9.1(9) 7.4(4) 8.7(5) 4.8(3) 2.7(5)

6 8 10 12 14 15 16 23 24 25 33

5.6(8) 8.1(9) 11.4(8) 11.0(3) 13(1) 11(1) 13(1) 9(1) 15(5) 14(2) 7(5)

a Normalized to total populations predicted from the two-temperature analysis described in section III. b Low J-state populations are not reported because of contamination from the incident molecular beam. c Values in parenthesis represent 1σ for multiple measurements. d Approximately 10% of the rovibrational transitions are inaccessible because of discontinuity in the diode laser gain profile.

distributions to support the dual channel dynamics evident in the internal state populations. As the simplest starting point, the Voigt line shape analysis outlined in section III.B has been employed to fit a single effective Ttrans for CO2 + PFPE at Einc ) 10.6 kcal/mol. Unlike low Einc studies, where translational temperatures were independent of J state, the high Einc experiments indicate a systematic increase in Ttrans with J. Figure 11 illustrates this trend for all five surface temperatures where Ttrans

is plotted against J, indicating a significant increase in line width with both (i) J state and (ii) surface temperature. Consistent with our analysis in section III.C, the simplest way to think of this line broadening is that it reflects a superposition of TD and IS Doppler contributions, where the sticking probability, RJ, is now an explicit function of J state. Similar J state dependent translational distributions have been observed under other incident collision energy conditions,13,14,16 where


Perkins and Nesbitt

Figure 9. Trapping desorption fraction for CO2 + PFPE (experiment) and CO2 + F-SAMs (MD simulation). Values are extracted from the two-temperature Boltzmann rotation state analysis.

Figure 8. Fractional population distributions (a) for CO2 + PFPE experimental measurements and (b) for CO2 + F-SAM theoretical simulations over TS ) 232 to 323 K and at Einc ) 10.6 kcal/mol. The two-temperature Boltzmann function is plotted along with the individual IS and TD components. Note the hotband populations for the PFPE experiment have been magnified by a factor of 10.

each has been characterized by a two-temperature line shape that reflects a weighted contribution of the TD and IS components. The increase in an effective Ttrans is now simply explained by a systematic increase in the IS to TD branching ratio as a function of J. Consistent with the quality of the data, the TD and IS Doppler components are assumed to be Gaussian and characterized by parameters Ttrans(TD) and Ttrans(IS). The total line shape function is therefore

SJ(ν - ν0) ) N{RJ‚gTD(ν - ν0) + (1 - RJ)‚gIS(ν - ν0)} (5) where N is a normalization constant, RJ is the J state dependent TD fraction,

RJ )

R‚PTD(J) R‚PTD(J) + (1 - R)‚PIS(J)

(6)

and PTD/IS is calculated from eq 2 with the values from Table 4. To minimize parameter correlation, we again assume that the TD component has thermalized with the surface; thus, Ttrans(TD) is held fixed at TS. This assumption is of course consistent with Dopplerimetry analysis in low Einc studies, where Ttrans(TD) ≈ TS was found to be true over a 232 to 323 K range of liquid temperatures. Since RJ values are known, the total absorption profiles can be fit to extract Ttrans(IS) for each J state (Table 6). The extracted Ttrans(IS) values prove to be remarkably constant (within 5%) over all J states, the averages of which are shown as the top dotted lines in Figure 11, summarized in Table 4, and plotted alongside Trot(IS) in Figure 10a as a function of surface temperature. Most interestingly, Figure 10a indicates the fitted Ttrans(IS) and Trot(IS) values to be very nearly the same, which lends support to the rather unexpectedly simplifying

Figure 10. Extracted IS and TD temperatures for (a) CO2 + PFPE experiment and (b) CO2 + F-SAMs simulation. Values are based on two-temperature models developed to fit the rotational and translation distributions for scattered CO2 populations.

notion of a single internally consistent rotational/translational “temperature” corresponding to a hot, albeit largely internally thermalized, IS channel. As a final consistency check, a single line shape is reconstructed from the sum of TD and IS Gaussian line shapes, each of which is generated by Ttrans(TD/IS) and a corresponding amplitude to match the given RJ value. Sample line shapes over all J states are then fit with a single temperature Gaussian to extract Ttrans, which is plotted in Figure 11 as a solid line to show the excellent agreement with experiment.


J. Phys. Chem. B, Vol. 112, No. 2, 2008 515 TABLE 6: Quantum Dopplerimetry Analysis of CO2 (0000) Absorption Profiles surface temperature (TS) 232 K

254 K

273 K

298 K

323 K

0000 Translational Temperatures J Ttrans (K) J Ttrans (K) J Ttrans (K) J Ttrans (K) J Ttrans (K) 20 22 24 26 28 30 34 36 38 40 42 44 46 48 50 54

330(10) 350(20) 360(10) 370(10) 390(20) 400(10) 450(10) 450(20) 500(20) 500(10) 490(50) 520(10) 530(10) 620(20) 640(30) 640(40)

20 22 24 26 28 30 34 36 38 40 42 44 46 48 50 54

330(20) 330(20) 340(10) 380(10) 380(20) 410(10) 440(20) 470(10) 510(10) 540(10) 550(40) 590(20) 620(10) 610(10) 600(20) 630(50)

20 22 24 26 28 30 34 36 38 40 42 44 46 48 50 54

330(10) 370(40) 370(10) 410(10) 400(10) 420(5) 470(20) 510(10) 520(30) 510(20) 590(10) 590(20) 600(40) 610(10) 610(60) 650(20)

18 20 22 24 26 28 30 34 36 38 40 42 44 46 50 54

400(10) 430(30) 470(10) 460(10) 500(20) 490(20) 520(20) 570(20) 570(20) 600(10) 620(30) 640(20) 630(20) 680(20) 700(50) 740(20)

20 22 24 26 28 30 34 36 38 40 42 44 46 48 50 54

410(20) 430(30) 440(10) 450(20) 460(20) 490(10) 540(20) 530(30) 540(10) 590(20) 600(20) 640(20) 650(30) 640(10) 690(20) 700(50)

a Absorption profiles for low J states are not analyzed due to contamination from the incident molecular beam.

can be inferred from large scale molecular dynamics simulations, as discussed in the following section. IV. Theoretical Results

Figure 11. Experimental quantum state-dependent translational distributions of scattered CO2 from PFPE. A single-temperature line shape analysis extracts Ttrans(J), while a two-temperature line shape analysis extracts Ttrans(IS). The solid line represents a single Gaussian fit for a reconstructed two-temperature line shape based on the known TD and IS populations at each J state.

Stated alternatively, if one were to assume (rather than experimentally infer) that Ttrans(IS) ≈ Trot(IS), the solid lines in Figure 11 would represent parameter-free predictions in excellent agreement with experiment for all J states and for all liquid temperatures. How general is such a description is yet to be determined. It is worth noting that this analysis reflects vx and vy components only; the laser probe geometry yields no information on vz component distributions. However, within the signal-to-noise limitations of the absorption profiles, such a twotemperature fit provides a remarkably simple and yet internally self-consistent description of near equilibration between (x, y) translational and rotational degrees of freedom into the IS channel, for normal incidence CO2 scattering at the PFPE interface. Further theoretical support for this elementary picture

A. Molecular Dynamics Simulation. The physical picture of gas-liquid scattering dynamics has been greatly strengthened by the development of high-quality interaction potentials and molecular dynamic trajectory calculations. Previous work by Hase and co-workers has established the similarity between PFPE and fluorinated self-assembled monolayer surfaces.17 Stimulated by their remarkably quantitative success reproducing our experimental CO2-PFPE results with CO2-F-SAMs trajectories, we have used their CO2-F-SAM intermolecular potential from ref 17 to study scattering trajectories over a range of surface temperatures, which allows us to compare and contrast our experimental results with a theoretical perspective. Detailed descriptions of the interaction potential and molecular dynamics simulation are presented in the previous work of Hase and coworkers.17 The F-SAM surface in the simulation consists of 48 chains of the CF3(CF2)7S radical adsorbed on a single layered surface of 225 Au atoms, where the S atoms are adsorbed on the hollow site of the Au(111) surface to match the experimentally observed hexagonal close-packed structure.59 Such a structure results in a well-ordered perfluorinated alkane surface that we can characterize and compare to the bulk properties of the PFPE liquid. For example, analysis of the CF3(CF2)7 layer reveals a density of 1.9 g/cm3 and a thermal expansion of ∼1 × 10-3 K-1, which, as expected, are nearly the same as measured for PFPE60 and other perfluorinated alkanes.59,61-63 In addition, surface roughness can be estimated from the ≈1 Å root-meansquare (rms) z displacement of the terminal CF3 groups. Such an estimate matches atomic force microscopy (AFM) experiments of n-alkane thiol64 and fluorinated n-alkane thiols65 on Au(111), where rms roughness of 1-2 Å is observed over large monolayer domains on the surface. In the simulation, the CO2 starts 25 Å above the F-SAM surface with an incident energy of 10.6 kcal/mol and an internal temperature of 15 K, consistent with our experimental conditions. The normal incident trajectory is integrated throughout


Perkins and Nesbitt

the simulation with a fixed step size of 0.3 fs using the AdamsMoulton algorithm in VENUS05, with the trajectory finishing when the CO2 center-of-mass passes its initial starting height. At the end of each simulation, the final translational, rotational, and vibrational energies of CO2 are calculated from the atomic Cartesian coordinates and momenta. In addition, the final scattering angles are extracted to generate an angular distribution with respect to the surface normal. The 3500 trajectories were simulated for each of the 5 surface temperatures, which ranged from 232 to 323 K to match the experimental PFPE studies. Within the ensemble of trajectories, fewer than ≈1% of the incident CO2 molecules solvated into the bulk and reached the foundation of Au atoms. These CO2 molecules failed to escape on the trajectory time scale of 150 ps and were not included in the analysis. The final CO2 internal state, translational, and angular distributions are analyzed and discussed in the following sections, which provide supporting evidence for two-channel scattering dynamics in agreement with the experimental measurements at all surface temperatures. B. Rotational State Distributions. To compare quantum state populations with the CO2 + PFPE experiment, the final J state for each scattered CO2 is calculated from classical angular momentum, j, by

j ) xJ(J + 1)p

(7)

The resulting P(J) distribution is plotted versus J in Figure 8b at each TS to permit direct comparison with the CO2 + PFPE experimental data. The theoretical J state populations show distinctly non-Boltzmann distributions, in close agreement with those measured in experiment. To illustrate the parallel nature between experiment and theory, each P(J) is treated exactly as experimental data and fit with the twotemperature Boltzmann function in eq 2 to extract Trot(TD), Trot(IS), and R. As a further test of our assumptions, however, the TD temperature is now allowed to float as a free parameter; the resulting two-temperature fit to each P(J) is plotted in Figure 8b along with the individual TD and IS components. Qualitatively, the trend over surface temperatures matches the experimental results where the TD fraction increases with TS. Interestingly, the results encompass all variations of trajectories including direct scattering, physisorption, and partially solvated pathways, which are not easily parsed into IS and TD channels. We will come back to this point later in the discussion. To compare quantitatively with PFPE experimental results, the extracted TD fraction and Trot(IS/TD) are plotted in Figures 9 and 10b, respectively. The TD fraction R for CO2 + F-SAMs trajectories shows an identical trend with surface temperature; indeed, within statistical uncertainty, the extracted values are in agreement with the PFPE results. Trot(IS) values also parallel the PFPE results nearly quantitatively. Most importantly, the Trot(TD) values from the trajectory analysis are independently in agreement with Trot(TD) ≈ TS within the error estimates from the two-temperature fits. Such a result further strengthens our previous assumption that the TD channel desorbs with thermal distributions characteristic of TS. Note that these results are still consistent with detailed balance considerations and an overall sticking coefficient less than unity, since the net scattered flux (i.e., the sum of TD + IS channels) is not in thermal equilibrium with the surface.38,66 To summarize our comparisons in the framework of a two-temperature Boltzmann picture, the overall agreement between the F-SAM simulations and the PFPE experiments is remarkably good and appears to reproduce all temperature-dependent trends in the data.

C. Angular and Translational Distributions. The angular distributions from our trajectories are constructed from a histogram of final scattering angles (θscat, measured with respect to the surface normal), binned by angle and normalized by sin(θscat) to extract the probability, P(θscat). Note that these distributions reflect all types of interactions, since it is not, in general, meaningful to unambiguously identify an “IS” or “TD” trajectory by its final state outcome. The plots P(θscat) in Figure 12 for each of the five surface temperatures follow a cos(θscat) curve reasonably well, with little or no dependence as TS is varied. In terms of two-channel-scattering dynamics, the TD trajectories are expected to desorb isotropically, that is, PTD(θscat) ∝ cos(θscat).18,36 Within statistical uncertainty for the number of trajectories, therefore, the remaining IS distribution must also be largely governed by PIS(θscat) ≈ cos(θscat). This type of distribution implies CO2 scatters more or less isotropically from the surface in both TD and IS channels for normal incidence geometry, simply with more rotational and translational energy in the IS than the TD channel. One might presume that these distributions obtained at normal incidence must break down at some point, in agreement with the more or less specular contributions to the IS channel noted previously by TOF studies for beams impinging on the surface at non-normal incidence. Indeed, initial hints of such behavior may be evident in minor deviations from cos(θscat) at intermediate scattering angles, which may indicate possible lobular scattering patterns. However, we are currently investigating these deviations both experimentally and theoretically with off-normal incident scattering geometries. One drawback of the direct absorption experimental method is that our Dopplerimetry analysis is only sensitive to velocity components parallel to the surface; however, our trajectory calculations suffer no such limitation. The full three-dimensional translational energy distributions for the scattered CO2 flux have been analyzed with a two-temperature Maxwell energy-distribution function to extract Rtrans, Ttrans(TD), and Ttrans(IS). This analysis differs from traditional methods, whereby the lowenergy regime is typically fit to a single (TTD ≈ TS) temperature distribution,12 where the IS contribution is simply characterized as the remaining fraction of the total signal. Instead, our final translational energy distributions, P(Etrans), are constructed from a normalized histogram and then fit to the following twotemperature Maxwell distribution;

P(Etrans) ) Rtrans

Etrans e-Etrans/kTtrans(TD) [kTtrans(TD)]2

+ Etrans e-Etrans/kTtrans(IS)

(1 - Rtrans)

[kTtrans(IS)]2

(8)

where Rtrans is the TD fraction based on the total threedimensional translation distribution. As explained previously, we assume Ttrans(TD) thermally accommodates with the surface; thus, its value is fixed at TS in a nonlinear least-squares fitting algorithm. P(Etrans), the two-temperature fit, and the TD/IS components are each plotted in Figure 13 for all surface temperatures. The fits reveal probability distributions characterized by a sum of two populations corresponding empirically to a well-defined IS and TD temperature. This two-temperature analysis of translational energies provides an opportunity to compare and contrast with theoretical and experimental trends already noted via rotational state analysis. The extracted values of Ttrans(IS) are summarized in Table 4 and plotted in Figure 10b as a function of surface



Figure 12. P(θscat) angular distributions for the total population recorded in the CO2 + F-SAMs simulation for TS ) 232 to 323 K.

temperature. The Ttrans(IS) values increase systematically with TS and are in agreement with the theoretical Trot(IS) results. Furthermore, quantitative comparison of the full three-dimensional theoretical F-SAM Ttrans(IS) values with the experimental PFPE values in Figure 10a (which only sample x, y velocity components) reveals both temperatures also to be equivalent within the uncertainty of the measurements and fits. This apparent ability to characterize the full three-dimensional translational degrees of freedom by a single temperature is consistent with and provides additional support for the nearly isotropic scattering nature of the IS channel. V. Discussion Within the normal approach geometry, the low incident energy experiments with CO2 + PFPE reveal that molecules scatter predominantly through a TD channel, where both translational and rotational degrees of freedom have thermalized with the surface. While angular distributions are not explicitly determined, the P(Vx) and P(Vy) velocity component distributions are well fit by Gaussians with Ttrans ≈ TS, from which P(θscat) may be inferred to be ≈ cos(θscat). On the other hand, the vibrational temperature after scattering is Tvib ≈ 260-280 K and largely independent of temperature; this is only marginally warmer than the incident beam, which arrives at the surface at Tvib ≈ 250-260 K because of inefficient cooling of the 667 cm-1 degenerate bend in the supersonic expansion. Thus, in contrast to rotation and translation motion, the vibrational degree of freedom appears to be largely decoupled from the surface, at least on time scales sampled under the current scattering conditions. To reach equilibrium, CO2 must remain on the surface sufficiently long to exchange 667 cm-1 of energy into and/or out of the bending vibrational manifold. A possibly appropriate comparison system, therefore, might be studies by Hynes and co-workers on relaxation of the 670 cm-1 C-Cl vibration in liquid CH3Cl, for which the relaxation time was estimated to be ≈ 5 ps.67 To the best of our knowledge, no experimental or theoretical studies of vibrational relaxation have been performed for CO2 physisorbed on a PFPE liquid surface. However, on the basis of the lack of appreciable thermalization of the bend, the data suggests that vibrational relaxation of CO2 takes place on a longer time scale than ≈10 ps, which represents an average residence time for CO2 on PFPE from the low-energy MD simulations.17 At high collision energies and normal approach, the TD fraction R clearly drops to less than unity, which by detailed balance considerations is consistent with a scattering flux out of equilibrium with the surface temperature. We have chosen

Figure 13. Final translational energy distribution for scattered CO2 from F-SAMs surface. P(Etrans) is fit with a two-temperature Maxwell energy distribution to extract Rtrans, Ttrans(TD), and Ttrans(IS). The individual TD and IS components are plotted along with the total fit to the distribution.

to analyze this nonequilibrium distribution as a sum of two Boltzmann components with different temperatures. Rather remarkably, the internal rotational distributions are very wellrepresented by this simple model, with one component thermalized to the surface (TTD ≈ TS) and a second component at a temperature TIS . TS. Consistent with interpretation of previous TOF studies, it is reasonable to associate the one component with TD events, where all memory of the incident collision dynamics has been lost, and the other as a measure of IS events, which escape with some memory of and sensitivity to the initial interaction. However, it is important to note that the time scales for TD and IS events overlap considerably, and thus, there is no meaningful way to distinguish them, for example, by inspection of individual MD trajectories. It is only by inspection of the ensemble of results, both experimentally and theoretically, that the potential utility of such a classification emerges.

518 J. Phys. Chem. B, Vol. 112, No. 2, 2008 What is remarkable and dynamically meaningful is the fidelity with which the IS distributions can be described by an effective temperature. This description has been shown to be true not only for rotational degrees of freedom (by direct spectroscopic selection), but also for x, y velocity components by highresolution Dopplerimetry. The similarity between the rotational state populations of the F-SAMs simulation with the PFPE experiment provides us with the confidence to extrapolate the physical picture from one to the other. The IS population angular distribution of ≈cos(θscat) implies a hot but nearly thermal distribution of final translational energies. Experimentally, the Gaussian nature of the IS line shape analysis in section III.D fulfills this requirement where the translational temperatures range from 600 to 860 K. In parallel with experiment, the final energy distributions for the F-SAMs simulations were also fit to a thermal energy distribution with final Ttrans(IS) similar to the PFPE values. On the basis of the Ttrans(IS) and P(θscat) distributions for both PFPE and F-SAMs scattering, a coherent physical picture can be constructed where the IS channel scatters CO2 from the surface in an isotropic distribution, yet with hyperthermal temperatures in equilibrium with the rotational degree-of-freedom. The extraordinary agreement between the CO2 + PFPE experiments and the CO2 + F-SAMs simulations reflects the similarities between the liquid and the self-assembled monolayer surface, at least in terms of an interaction with a gas like CO2. Comparison of bulk and surface properties between the two systems provides insight into the important physical parameters that lead to two-channel scattering dynamics, where notably, the IS population is well-characterized by a single IS temperature. From previous studies,13-16,21,41,68 the hyperthermal nature of the rotational and translational distributions reflects the importance of single, double, and multiple interactions with the surface. While the effective mass of specific surface groups is important in terms of energy transfer dynamics, the local roughness certainly provides pathways for multiple CO2-surface interactions that result in an IS temperature. As a result, the important comparison between PFPE and F-SAMs must include the degree of surface roughness that enables the CO2 to sample single-to-multiple interactions with the surface. As previously noted, the temperature dependence TD fraction implies that hotter surfaces tend to trap molecules more efficiently than colder ones. To compare CO2 + PFPE with similar TOFMS experiments, the TD fraction for Ar scattered from PFPE at Einc ) 10 kcal/mol increases from 0.25 at TS ) 278 K to 0.30 at TS ) 363 K.26 The 20% increase in trapping efficiency over an 85 K temperature range reflects the dynamical increase of activity on the microscopic scale of the liquid. For a similar ∆T ) 90 K range in TS, R shifts from 0.43 to 0.58 for CO2 + PFPE and 0.50 to 0.63 for CO2 + F-SAMs. While the trend in TD probability is qualitatively similar, the CO2 molecules tend to stick more efficiently and increase more dramatically with the temperature of the surface. Both points reflect the additional structural complexity of linear CO2 molecules as compared with atomic Ar. For CO2, an impulsive collision may torque the molecule into an excited rotational state, whereas a similar interaction for Ar may only excite translation in the scattered projectile. Excited rotational CO2 may presumably interact with the surface again since energy has not been transferred into recoil translation. The increased number of interaction events would plausibly cause the CO2 to stick more efficiently than an atomic projectile. Similarly, the effects of the rotational degree of freedom are amplified as the surface is roughened at higher temperatures.

Perkins and Nesbitt

Figure 14. Fraction of incident energy remaining in CO2 after collision with the surface.

The correlation between the sticking probability and energy transferred to the surface through the IS collisions provides further insight into the nature of the IS population and how it changes with a rougher surface. The internal energy of the scattered CO2 from both the PFPE and the F-SAMs is determined from simple statistical mechanics where Erot(IS) ) kTrot(IS). As for translational energy, the ≈cos(θscat) angular distribution allows us to estimate Etrans(IS) ≈ 2kTtrans(IS) for both the PFPE experiment and the F-SAM simulation. The total energy remaining in the scattered CO2 is then

〈Escat(IS)〉 ≈ kTrot(IS) + 2kTtrans(IS)

(9)

The average energy for CO2 in the IS channel is calculated for each surface temperature, divided by Einc ) 10.6 kcal/mol, and then plotted in Figure 14 as a function of TS. As expected from the extracted IS temperatures, the fraction of incident energy that remains with the scattered projectile increases from 0.33 to 0.48 for PFPE and 0.38 to 0.42 for F-SAMs as TS changes from 232 to 323 K. The trend indicates that only the high-energy fraction of the scattering distribution escapes from the rougher surface at TS ) 323 K. VI. Conclusion and Summary Experimental gas-liquid scattering dynamics have been investigated with low and high incident energy in a normal incidence configuration to control the ratio of TD to IS populations in the scattered flux. At Einc ) 1.6 kcal/mol, the final translational and rotational distributions for CO2 are wellcharacterized by a surface temperature where Trot ≈ Ttrans ≈ TS over a ∆T ) 90 K range. The vibrational degree of freedom remains out of equilibration with the surface, which invokes a limited time scale for the CO2-surface interaction. From these measured distributions, the TD populations are well-characterized by isotropic scattering from the surface where P(θscat) ) cos(θscat) for all TS. In contrast to these low Einc studies, high collision energy experiments explored the IS dynamics as a function of TS. Two-temperature Boltzmann and Dopplerimetry analysis reveal that the IS component is also well-characterized by a temperature, where Trot(IS) and Ttrans(IS) show a strong dependence on the temperature of the surface. In addition,

Quantum State-Resolved CO2 Collisions molecular dynamic simulations for CO2 + F-SAMs at Einc ) 10.6 kcal/mol provide nearly quantitative confirmation of this two-temperature description of the scattering mechanism, as well as showing that the total, TD, and IS components each scatter with a cos(θscat) angular distribution. Acknowledgment. We would like to express our long term appreciation to Prof. J. T. Hynes as both an excellent teacher and colleague, with whom we have enjoyed exploring many topics in physical chemistry. In addition, we would like to thank Thomas A. Baker, Emilio Martıńez-Nuń˜ez, and William L. Hase for their valuable assistance with the molecular dynamics simulations and VENUS05 software. Funding for this research has been provided primarily through the Air Force Office of Scientific Research, with additional support for computation from the National Science Foundation. References and Notes (1) Gertner, B. J.; Hynes, J. T. Science 1996, 271, 1563. (2) Ando, K.; Hynes, J. T. J. Phys. Chem. B 1997, 101, 10464. (3) Gertner, B. J.; Hynes, J. T. Faraday Discuss. 1998, 301. (4) Solomon, S. ReV. Geophys. 1999, 37, 275. (5) Abbatt, J. P. D. Chem. ReV. 2003, 103, 4783. (6) Tolbert, M. A.; Rossi, M. J.; Golden, D. M. Science 1988, 240, 1018. (7) Tolbert, M. A.; Rossi, M. J.; Malhotra, R.; Golden, D. M. Science 1987, 238, 1258. (8) Hanson, D. R.; Lovejoy, E. R. J. Phys. Chem. 1996, 100, 6397. (9) Hanson, D. R.; Lovejoy, E. R. Science 1995, 267, 1326. (10) Ellison, G. B.; Tuck, A. F.; Vaida, V. J. Geophys. Res-Atmosph. 1999, 104, 11633. (11) Nathanson, G. M.; Davidovits, P.; Worsnop, D. R.; Kolb, C. E. J. Phys. Chem. 1996, 100, 13007. (12) Nathanson, G. M. Annu. ReV. Phys. Chem. 2004, 55, 231. (13) Perkins, B. G.; Nesbitt, D. J. J. Phys. Chem. A 2007, 111, 7420. (14) Perkins, B. G.; Nesbitt, D. J. J. Phys. Chem. B 2006, 110, 17126. (15) Zolot, A. M.; Harper, W. W.; Perkins, B. G.; Dagdigian, P. J.; Nesbitt, D. J. J. Chem. Phys. 2006, 125, 021101. (16) Perkins, B. G.; Haber, T.; Nesbitt, D. J. J. Phys. Chem. B 2005, 109, 16396. (17) Martinez-Nunez, E.; Rahaman, A.; Hase, W. L. J. Phys. Chem. C 2007, 111, 354. (18) Sinha, M.; Fenn, J. Proc. 5th Int. Symp. Mol. Beams; 1975, Nice. (19) Saecker, M. E.; Govoni, S. T.; Kowalski, D. V.; King, M. E.; Nathanson, G. M. Science 1991, 252, 1421. (20) Saecker, M. E.; Nathanson, G. M. J. Chem. Phys. 1993, 99, 7056. (21) Saecker, M. E.; Nathanson, G. M. J. Chem. Phys. 1994, 100, 3999. (22) King, M. E.; Nathanson, G. M.; Hanninglee, M. A.; Minton, T. K. Phys. ReV. Lett. 1993, 70, 1026. (23) King, M. E.; Fiehrer, K. M.; Nathanson, G. M.; Minton, T. K. J. Phys. Chem. A 1997, 101, 6556. (24) Morris, J. R.; Behr, P.; Antman, M. D.; Ringeisen, B. R.; Splan, J.; Nathanson, G. M. J. Phys. Chem. A 2000, 104, 6738. (25) Benjamin, I.; Wilson, M. A.; Pohorille, A.; Nathanson, G. M. Chem. Phys. Lett. 1995, 243, 222. (26) King, M. E.; Saecker, M. E.; Nathanson, G. M. J. Chem. Phys 1994, 101, 2539. (27) Day, B. S.; Shuler, S. F.; Ducre, A.; Morris, J. R. J. Chem. Phys. 2003, 119, 8084. (28) Day, B. S.; Morris, J. R. J. Phys. Chem. B 2003, 107, 7120. (29) Ferguson, M. K.; Lohr, J. R.; Day, B. S.; Morris, J. R. Phys. ReV. Lett. 2004, 92, 073201. (30) Darling, S. B.; Rosenbaum, A. M.; Sibener, S. J. Surf. Sci. 2001, 478, L313. (31) Gibson, K. D.; Isa, N.; Sibener, S. J. J. Chem. Phys. 2003, 119, 13083.

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Collisions at the GasâLiquid Interface: Surface Temperature

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Collisions at the GasâLiquid Interface: Surface Temperature