Benzene Internal Energy Distributions Following ... - ACS Publications

These studies were preceded by spectroscopic interrogations of the nascent internal energy content of Na2 molecules evaporating into a vacuum from liq...
0 downloads 0 Views 242KB Size
Download PDF
J. Phys. Chem. C 2009, 113, 637–643

637

Benzene Internal Energy Distributions Following Spontaneous Evaporation from a Water-Ethanol Solution Olivia J. Maselli,† Jason R. Gascooke,† Warren D. Lawrance,‡ and Mark A. Buntine*,† School of Chemistry and Physics, The UniVersity of Adelaide, Adelaide SA 5005, Australia, and School of Chemistry, Physics and Earth Sciences, The Flinders UniVersity of South Australia, Adelaide SA 5001, Australia ReceiVed: May 14, 2008; ReVised Manuscript ReceiVed: October 21, 2008

We use the liquid microjet technique coupled with laser spectroscopy to measure the rotational and vibrational energy content of benzene spontaneously evaporating from a water-ethanol solution. We find different temperatures for rotation (206 K) and for the two low-lying vibrational modes, ν6 (256 K) and ν16 (229 K). Collision-induced energy-transfer measurements reveal efficient rotational relaxation, from which we deduce that the rotational temperature indicates the translational energy of the evaporate. Conversely, the relaxation of ν6 is very inefficient, suggesting that the ν6 temperature indicates the surface temperature of the liquid. Modeling the relaxation of ν16 indicates that >102 collisions are occurring during the transition from liquid to vacuum, which is an order of magnitude more than has been reported to occur in the gas phase immediately above the liquid surface. Our results reveal that evaporative molecular energy transfer involves many collisions, resulting in moderate collisional cooling as molecules pass from liquid to vapor. Introduction Whereas the thermodynamics of evaporation have been understood for over a century,1,2 the molecular-level dynamics of the evaporation process remains inadequately defined. Apart from representing an important fundamental natural process worthy of study in its own right, developing a comprehensive molecular-level understanding of evaporative mass and energy transfer has wide-ranging practical importance in, for example, better understanding atmospheric3 and industrial4 processes. Recently, molecular dynamics (MD) simulations of evaporation have begun to provide insight into the mass and energy transfer across the liquid-vapor interface in unprecedented detail. Most commonly, simulations of monatomic liquids have made predictions about the translational energy content of the evaporate after it has passed through the interfacial region.5-7 However, MD simulations have rapidly evolved to the stage that they are able to describe polyatomic liquid interfaces and have, within a rigid rotor approximation, included predictions of the rotational energy content of the evaporate.8,9 Further extensions that explore the vibrational energy content of evaporating molecules have yet to be reported, although predictions of bulk thermodynamic properties from simulations that explicitly incorporate intramolecular flexibility are emerging.10 Structure of the Liquid-Vapor Interface. Particular attention, both theoretical and experimental, has been paid to the liquid-vapor interfacial structure of water. In a recent review of simulations describing this interface, Garrett and co-workers highlight that, whereas quantitative predictions of the nature of the interface are dependent upon the specific intermolecular interaction potentials employed, several qualitative trends have emerged.3 These include (i) the density transition from bulk liquid to water vapor occurring over a laterally averaged distance of 0.3-0.6 nm, that is, over molecular length scales, and (ii) * Corresponding author. E-mail: [email protected]. † The University of Adelaide. ‡ The Flinders University of South Australia.

the interface being rough over these molecular length scales. These simulations suggest that localized regions of the liquid-vapor interface are molecularly sharp, but as a whole, the interface appears as a rough outer layer consisting of molecules in direct contact with one another penetrating into the vacuum. Interestingly, X-ray scattering studies have measured liquid water surface roughness values that are in good agreement with the predictions from MD simulations.11 The simulated surface roughness lends itself to making predictions about surface molecular orientation.3,12,13 Such predictions have been compared to experimental results from optical interrogation,14-16 X-ray absorption,17-21 and photoemission studies.22,23 These experimental and theoretical investigations have provided valuable insight into, for example, the nature and extent of hydrogen bonding at the water surface. However, it remains unclear as to whether differences in the conclusions drawn from experiment and theory are primarily attributable to deficiencies in the theoretical models or experimental artifacts.3,17,24,25 An alternative experimental probe of the liquid-vapor interface is to explore the energy content of gas-phase molecules after they have interacted with the liquid surface. Nathanson has made seminal contributions toward understanding the structure, energetics, dynamics, and reactivity of gas-liquid and liquid-vacuum interfaces via molecular beam scattering studies.26-28 McCaffery and co-workers29-31 and most recently Nesbitt and co-workers32 have reported on the quantum stateresolved dynamics at gas-liquid interfaces via molecular beam scattering. These studies were preceded by spectroscopic interrogations of the nascent internal energy content of Na2 molecules evaporating into a vacuum from liquid sodium surfaces. In 1982, Miksch and Weber determined that the rotational and vibrational temperatures of the Na2 evaporate were identical to the liquid sodium surface temperature.33 This result was confirmed by Becker in 1985.34 In 1996, Nesbitt and coworkers reported the nascent quantum state distributions of CO2 subliming from thin solid films and determined that the

10.1021/jp804270v CCC: $40.75  2009 American Chemical Society Published on Web 12/19/2008

638 J. Phys. Chem. C, Vol. 113, No. 2, 2009 translational, rotational, and ν2 vibrational distributions are all described by the thin film surface temperature.35 In the late 1980s, Faubel pioneered the use of a liquid microjet (LµJ), or “liquid beam”, to measure the translational energy distributions of polar molecules evaporating into a vacuum.36,37 These studies provided unambiguous experimental data against which to test the validity of predictions made by simulations concerning the translational energy content of the evaporate.38 Faubel’s work showed that evaporation results in thermalized translational energy distributions. No measurements of the rotational or vibrational energy content were reported. We have developed a new experimental technique to quantify the rotational and vibrational energy content of molecules evaporating from a liquid surface. Specifically, we report results for benzene evaporating from a water-ethanol solution into vacuum using the LµJ approach coupled with laser spectroscopy. Our work provides a solid foundation upon which simulations of evaporative energy transfer and the structure of the liquid-vapor interface can be assessed and further theoretical developments proceed. In particular, we present experimental data that, when interpreted in terms of a purely gas-phase collision model, provides an estimation of the number of collisions experienced by the benzene solute as it undergoes evaporation. The interpretation of these data by more sophisticated MD simulations will undoubtedly provide deeper molecular-level insight into the relationship between interfacial structure and evaporative energy transfer. Liquid Microjets and Spontaneous Evaporation. An in vacuo LµJ is formed when a liquid sample is injected through a thin aperture or capillary at relatively high speed directly into a vacuum. LµJ techniques have gained popularity over the past two decades, with recent advances providing valuable experimental insight into physical and chemical processes occurring at the liquid-vacuum interface.39-41 In particular, the LµJ approach is well suited to the study of spontaneous evaporation.36,37,40,42-45 The mechanism by which molecules leave a liquid surface can be classified as “spontaneous” or “stimulated”.6 Spontaneous evaporation occurs only when molecules are liberated from the condensed phase in the absence of external forces; all of the energy needed to leave the surface is supplied either from the bulk phase beneath the evaporating molecule or by the molecule’s own internal energy. Stimulated evaporation involves vapor-phase molecules above the liquid surface contributing to mass and energy transfer. Experimental studies describing spontaneous evaporation have traditionally been challenging because of the presence of this vapor. Collisions between the emerging molecules and the vapor phase rapidly equilibrate the nascent energy distributions of the emerging molecules and thereby obscure the interrogation of the spontaneous process. The LµJ approach overcomes this complexity by presenting the evaporating liquid surface directly into a vacuum, thus enabling direct interrogation of spontaneous evaporation while minimizing competing processes. To date, most LµJ-based studies of evaporation have focused on measuring translational energy distributions. Faubel and coworkers have shown that the thickness of the LµJ influences the extent of translational cooling of the evaporate, attributed to vapor-phase collisions above the liquid surface. They report that the velocity distribution of water molecules evaporating from an LµJ of 5 µm radius is indicative of nearly collisionfree evaporation, whereas that for jets of 25 µm radius is significantly narrowed as a result of collisional cooling from a thin vapor layer above the liquid surface.36 Faubel’s work

Maselli et al. concludes that for sufficiently thin LµJs operating in a vacuum only a relatively small number of collisions occur in the vapor phase above the liquid surface. Saykally and co-workers have undertaken a quantitative investigation into the gas-phase collision number as a function of both liquid filament thickness and temperature.42 The LµJ evaporative translational energy distributions have been interpreted by Faubel and others using a model describing the liquid-vapor interface as a sharp boundary (on the molecular scale) that divides the bulk liquid from the vapor phase.37,38,42,45 In this classical thermodynamic model, it is assumed that the vapor pressure immediately above the liquid surface has the equilibrium value dictated by the local liquid surface temperature, decreasing rapidly with increasing distance from the liquid surface. We have previously noted that several MD simulations suggest local sharp boundaries at the liquid surface.3 However, other recent simulations of energy transfer on evaporation invoke a sigmoidal decrease in density upon moving from the bulk to the vapor phase, resulting in an “interphase” region several molecular layers thick.5,7-9 This latter model naturally involves a large number of collisions between the evaporate and its surroundings because the beginning of the interphase is commonly defined as the point where the molecular density has decreased to only 90% of the bulk value.46 Frezotti and co-workers5,7,8 predict that it is within this interphase region that molecular energy distributions begin to deviate from the equilibrium distribution found in the bulk. Clearly, such predictions of the interphase thickness, and hence the number of collisions undergone by a molecule passing through the interface, require experimental investigation. In particular, it is essential to experimentally interrogate properties of the evaporated molecules that are sensitive to different orders of magnitude in the number of collisions experienced. In this contribution, we extend the scope of the earlier LµJ studies by conducting a study of rotational and vibrational energy distributions of benzene following evaporation from a water-ethanol LµJ into the vacuum. In this context, benzene acts as a low-concentration molecular “spy” that probes the energy partitioning associated with evaporation. Benzene is an ideal candidate with which to determine the internal energy distribution of molecules liberated from an LµJ because its spectroscopy is well characterized.47-50 We report additional experiments to confirm that benzene displays ground electronic state collision-induced energy-transfer dynamics that are sensitive to widely different collision number regimes. As such, benzene can be conveniently used to quantify internal rotational and vibrational temperatures, from which the dynamics of evaporation can be further explored. Experimental Section A schematic illustration of the apparatus used to perform the experiments reported here is shown in Figure 1. In these studies, we produced a 7.5-µm-radius liquid microjet by forcing solutions at high pressure through a tapered silica capillary. Unless otherwise specified, all experiments were conducted using 10-3 M benzene with ethanol (Ajax Finechem, 99.5%) in deionized water (25% v/v EtOH in H2O) as the solvent. The water-ethanol solvent mix was used for two reasons. First, the ethanol assists in dissolving the benzene in the highly polar water solvent. Moreover, as noted in previous reports from this laboratory, ethanol is used to prevent premature disintegration of the liquid filament.44,51 Nonetheless, the use of a solvent mix does add potential complexity to the interpretation of experimental results. As noted by Klein and co-workers, the segregation of water

Benzene Spontaneous Evaporation from Water-Ethanol

Figure 1. Schematic illustration of the LµJ apparatus used to perform the experiments reported herein. The inset illustrates the relative positioning of the LµJ filament and the ionization laser that is propagating into the plane of the page.

and ethanol leads to an enhanced ethanol concentration at the liquid surface and possibly exacerbates the surface roughness.52-54 More recent water-alcohol simulations support these conclusions.55,56 As such, additional experiments were performed with a 10% v/v EtOH-H2O solvent mix to explore the influence of the ethanol concentration on the measured rotational energy distributions. Benzene (BDH, 99.7%) was used as supplied by the vendor without further purification. The aqueous solution was injected into the vacuum at a flow rate of 0.25 mL/min. Under these conditions, the source chamber operating pressure was 5 × 10-6 Torr. Solute benzene molecules that evaporated from the liquid surface were ionized by a collimated and telescoped ultraviolet (UV) laser beam (10 µJ/pulse, 150 µm radius fwhm) located a fixed distance downstream of the LµJ nozzle aperture and propagating orthogonally to the liquid filament. The UV laser radiation ionized the solute benzene molecules by 1 + 1 resonance-enhanced multiphoton ionization (REMPI) via the 1 B2u r 1A1g transition for the first absorption step. The UV laser did not directly irradiate the LµJ but rather ionized molecules that had moved a fixed distance away from the liquid filament. Typically, the UV laser was located 300 µm from the LµJ; however, studies with the laser as close as 200 µm and as far as 1200 µm from the LµJ were also undertaken. Resultant benzene ions were injected into a reflectron time-of-flight (TOF) mass spectrometer. Mass spectra were collected over 50 laser shots at each UV laser wavelength. Typically, two to four consecutive wavelength scans (depending upon ion signal strength) were averaged to generate the wavelength spectra used for spectral analysis. The rotational and vibrational energy content of the benzene molecules are reported in terms of rotational and vibrational mode-specific “temperatures”. Rotational temperatures in the vibrational ground state of benzene were determined by fitting the experimental 601 vibronic spectral band contours with those simulated from known spectroscopic constants and transition line strengths48,57,58 using a Levenberg-Marquardt nonlinear least-squares algorithm59 and assuming a Boltzmann distribution among the rotational energy levels. Measurements of the temperatures of select vibrational modes were made by comparing the integrated intensity ratios of the relevant vibronic hot bands to the 601 cold band.60

J. Phys. Chem. C, Vol. 113, No. 2, 2009 639

Figure 2. 1 + 1 resonance-enhanced multiphoton ionization (REMPI) spectra of the 610 vibronic transition of benzene (a) under roomtemperature gas cell conditions and (b) evaporated from the surface of a H2O/EtOH liquid microjet. Overlaid on each spectrum is a dashed line representing the best-fit spectral simulation for the 610 transition, assuming a Boltzmann distribution of rotational states.

Because of the large gas load introduced into the system by the evaporating liquid jet, the apparatus was equipped with a large pumping and cryotrapping system to minimize contributions from a warm (room-temperature) background signal. To assess the potential influence of a room-temperature background contribution on the shape of the recorded rotational contours, each contour was also fitted with a multitemperature algorithm. Any spectra that displayed a background temperature component (attributable to when the source chamber cyrotrap warmed up) were not included in subsequent analyses. To test the spectral simulation algorithm and to provide a benchmark against which the LµJ evaporation spectra can be interpreted, we recorded and analyzed room-temperature REMPI spectra of benzene in a static cell. The cell was equipped with a pair of 1 cm2 electrodes separated by a distance of 1 cm and biased with a potential difference of 90 V. These spectra were recorded at a benzene pressure of 0.45 Torr by passing the resulting photocurrent from each electrode through a differential amplifier. Results and Discussion Mode-Specific Evaporate Temperatures. Measured rotational contours of the 601 vibronic band of benzene at room temperature and after evaporating from the LµJ are shown in Figure 2. The lower LµJ spectrum in Figure 2 was recorded with the UV laser set at a distance of 300 µm from the liquid filament and 1 mm downstream of the nozzle orifice. Comparison with the upper room-temperature spectrum shows that the evaporation contour is significantly truncated at lower transition energies, revealing a considerably colder rotational energy distribution than found at room temperature. Overlaid on each spectrum is the best-fit spectral simulation. The simulated spectral contours, displayed as dashed lines in Figure 2, are convoluted with a Gaussian of 0.3 cm-1 (fwhm) to account for the laser bandwidth. Simulation of the gas-cell spectrum in Figure 2a yields a best-fit rotational temperature of 295 ( 6 K, where the uncertainty represents 1 standard error. This illustrates the accuracy of the rotational temperatures that can be extracted.

640 J. Phys. Chem. C, Vol. 113, No. 2, 2009

Maselli et al.

Figure 4. Rotational and vibrational temperatures of the benzene evaporate as a function of distance from the liquid filament. All data were collected at a distance of 1 mm downstream from the nozzle orifice. Rotational temperatures are represented by solid diamonds ((), whereas the vibrational temperatures for ν6 and ν16 are represented by open circles (O) and open squares (0), respectively. The error bars represent 3 standard deviations of the mean values.

Figure 3. Extended 1 + 1 REMPI spectra of benzene to lower photon energy of the 610 vibronic transition (a) under room-temperature gas cell conditions and (b) evaporated from the surface of a H2O/EtOH liquid microjet. Intensities to lower photon energy of the dashed vertical line in each spectrum have been multiplied by a factor of 5. Vibronic transitions discussed in the text are labeled. Vibrational temperatures are determined by the ratio of integrated band intensities for each hot band relative to that of the 610 transition.

The average of fitting nine spectra equivalent to that presented in Figure 2b yields a rotational temperature for the benzene evaporate of 206 ( 4 K. Here, the error in the measurement represents 3 times the standard error of the mean (3σ). Extended spectra of benzene recorded at room temperature in the static cell and under LµJ evaporation conditions are presented in Figure 3 (again, the evaporation spectrum was recorded 1 mm downstream from the nozzle orifice and 300 µm from the liquid filament). Here, several additional vibronic bands are labeled according to the assignments of Stephenson et al.50 In this study, the benzene vibrations under consideration are the ring deformation modes, ν6 (in plane) and ν16 (out of plane). The multipeaked band between 38 515 and 38 535 cm-1 is assigned to overlapping 621 and 6011120 transitions (ν11 involves an out-of-plane C-H wag). Although the peaks in this band involve mixed vibronic transitions, the initial vibrational level prior to laser excitation is 61, so the change in the ratio of the integrated intensity of this hot band relative to the 601 cold band between evaporation conditions and the equilibrated static cell allows us to determine the degree of evaporative cooling for the ν6 vibrational mode. Such analysis yields a ν6 evaporative vibrational temperature of 256 ( 11 K. Again, the uncertainty represents the 3σ confidence level. To lower transition energy, the series of peaks around 38 450 cm-1 are assigned to the 6011611 and 6011111 vibronic transitions. The analysis of this band to determine vibrational temperatures is less straightforward because the overlapping transitions arise from molecules initially populating both ν11 and ν16 in the ground electronic state. However, the vibrational energies of ν11 and ν16 are 674 and 399 cm-1, respectively,61,62 so by assuming a Boltzmann distribution at the static cell temperature of 295 K as well as equal electronic transition probabilities, the population ratio between ν11 and ν16 is 0.13. As such, 87% of the intensity from this band, at least in the upper trace of Figure 3, arises from the ground electronic state population in the lower-energy ν16 level. We therefore conclude that the contribution of ν11 to the spectral profile is minimal. Assuming

an identical ratio of vibrational populations under evaporation conditions yields a ν16 vibrational temperature of 229 ( 12 K. Because of its lower vibrational frequency, ν16 is expected to relax faster than ν11, so this temperature should be viewed as an upper limit.61,62 Again, the uncertainty represents the 3σ confidence level. It is important to ascertain that the measured temperatures represent the final values (i.e., collisional cooling is complete prior to laser ionization of the benzene evaporate). As such, spectra of benzene were recorded several distances away from the liquid microjet, but always at a distance of 1 mm downstream from the nozzle orifice. From these spectra, rotational and vibrational temperatures have been determined, and the results are presented in Figure 4. Here we see that, within experimental error, there is no significant change in either the rotational or the ν6 or ν16 vibrational temperatures as a function of distance from the liquid filament. This result indicates that collisional energy transfer is complete at a distance of 200 µm. In other words, all measurements have been made in the collision-free molecular flow regime, and our experiment probes the quantum state distributions of benzene after collisional energy transfer is complete. Moreover, the absence of a roomtemperature background signal in the recorded spectra is evident from the data displayed in Figure 4; even at very large distances from the liquid surface, the temperatures of the different molecular degrees of freedom show no evidence of warming. All remaining spectra reported in this study were recorded at a distance of 300 µm from the liquid filament. It is also important to verify that the rotational and vibrational temperatures reported are not artifacts of laser ionization at the specific 1 mm downstream distance from the liquid filament orifice. To test this possibility, we have recorded the 1 + 1 REMPI spectra of benzene evaporate at several downstream distances, from 0.5 to 3 mm. From these spectra, rotational and vibrational temperatures have been determined, and the results are presented in Figure 5. Here, we see that there is no evidence, within experimental error, of the rotational or vibrational energy content of the benzene evaporate varying with increasing residence time in the vacuum (that is, as a function of distance downstream from the nozzle orifice). Saykally and co-workers have used Raman thermometry to investigate evaporative cooling rates of water from liquid microjets42,45 and droplets63 into the vacuum. In the case of the LµJ studies, the liquid surface temperature was found to decrease with residence time inside the vacuum chamber. Moreover, the rate of surface cooling was found to increase with decreasing

Benzene Spontaneous Evaporation from Water-Ethanol

Figure 5. Rotational and vibrational temperatures of the benzene evaporate as a function of distance downstream from the nozzle orifice. All data were collected at a distance of 300 µm from the liquid filament. Rotational temperatures are represented by solid diamonds ((), whereas the vibrational temperatures for ν6 and ν16 are represented by open circles (O) and open squares (0), respectively. The error bars represent 3 standard deviations of the mean values.

beam diameter.42,45 Specifically, the Raman thermometry studies indicate that under our experimental conditions a relatively minor liquid surface temperature reduction of ∼5 K can be expected over a distance of 1-3 mm downstream from the nozzle orifice, an outcome consistent with the insensitivity of our data to liquid filament residence time. Finally, to investigate the influence of solvent volatility on the temperature, determination experiments were also performed with solvent mixtures comprising 10% (v/v) EtOH in H2O. Within experimental error, no difference was observed in the benzene evaporative rotational temperature determined following laser ionization 300 µm from the solution surface and 1 mm downstream from the nozzle orifice. Such a result suggests that the presence of ethanol in the solvent mix does not add undue complexity to the interpretation of the measurements. Therefore, all subsequent analyses involve spectra recorded following benzene evaporation from a 25% v/v EtOH-H2O solution. Evaporative Collisional Energy Transfer. The important results to emerge from this study are that (i) the rotational and vibrational temperatures of the benzene evaporate are different and (ii) the temperatures of ν6 and ν16 are different. This is possible only if there have been insufficient collisions to establish equilibrium between the rotational and various vibrational degrees of freedom as benzene passes from the liquid into the collision-free region of the gas phase. As we have noted earlier, for sufficiently thin LµJ’s, gas-phase collisions above the liquid surface are largely, but not completely, eliminated.36-38,42 For example, the sharp boundary interface model used to analyze evaporative translational energy distributions predicts that, at a liquid surface temperature of 295 K, water molecules evaporating from a 7.5-µm-radius liquid jet, as used in the experiments reported here, will undergo no more than ∼7 hard-sphere gasphase collisions.42 As we demonstrate below, this small collision number is insufficient, by more than an order of magnitude, to cool ν16 to the extent observed. In principle, the data reported here allow for a comprehensive assessment of the number of collisions undergone by a molecule as it passes from the condensed phase, through the interphase region, and into the vacuum, thereby providing experimental insight into the dynamics occurring at the liquid-vapor interface. However, such a comprehensive assessment is problematic. The different rotational and vibrational temperatures arise as a consequence of the extent of collisional relaxation occurring as the benzene evaporate passes from the condensed phase into the vacuum. During this transition, benzene will

J. Phys. Chem. C, Vol. 113, No. 2, 2009 641 collide predominately with water and ethanol. Unfortunately, there are no data available in the literature quantifying ground electronic state collisional relaxation rates of benzene with either water or ethanol (although benzene-argon collisional energy transfer studies reveal very small relaxation efficiencies in the ground electronic state of benzene64). As such, we have undertaken experiments to estimate the collisional relaxation rates of benzene with water and ethanol, and we subsequently comment on the number of collisions experienced by benzene as it evaporates from the liquid surface into the vacuum. Initial experiments involved expanding benzene vapor with a water-ethanol vapor mixture (5 kPa benzene, 2 kPa H2O, 0.5 kPa EtOH) in an expansion created by passing the roomtemperature gas mixture through the LµJ orifice into the high vacuum. Expansion using the room-temperature vapor pressures of water and ethanol was found to be insufficient to observe collisional cooling, so N2 (15 kPa) was added as a carrier gas. Alternate experiments were performed with water and ethanol vapor present and absent in the expansions. Within experimental error, no differences in the benzene spectral profiles were observed, indicating that water and ethanol do not have unusually large ground electronic state collisional relaxation efficiencies with benzene and, for illustrative purposes, can therefore be considered to be comparable in efficiency to N2. In this study, we will use the collisional relaxation efficiencies of nitrogen, determined as described below, to represent a lower limit to the efficiencies expected for a water-ethanol system. The relaxation efficiencies for N2 were determined following the measurement of the REMPI spectrum of benzene vapor cooled in a free jet of N2 (10 kPa benzene in 350 kPa N2) by expanding through the LµJ orifice into vacuum. Consistent with previously reported trends,49 the temperatures 1 mm downstream from the nozzle orifice are 290:208:20 K for Tvib(ν6)/Tvib(ν16)/Trot. The key observations are that ν6 undergoes essentially no cooling, remaining at almost the initial temperature, ν16 undergoes moderate cooling, and rotations are substantially cooled, almost attaining the expected translational temperature of the expansion.65 Using established methods for characterizing the physical properties of free-jet expansions as a function of downstream distance,65 we quantify the collision number and translational temperature under the experimental conditions reported here. Such modeling of collision rates under point source (3D) free-jet expansion conditions indicates that ∼350 hard-sphere collisions have occurred in the free jet to yield the temperatures reported above. Simple models that describe the rate of rotational and vibrational collisional energy relaxation are given by Miller65 and Vincenti and Kruger,66 respectively. Both models predict that the rate of collisional energy transfer is linearly proportional to the extent that the particular mode deviates from its equilibrium value. Adopting a similar approach but expressing the energy-transfer rate in terms of collision number rather than time, a simple “temperature gap” model can be expressed as

dTi(Z) ) ki[Ttrans(Z) - Ti(Z)] dZ

(1)

where ki represents the collisional energy transfer efficiency of the particular mode, Ti(Z) is the temperature of the rotational or vibrational mode under investigation, and Ttrans(Z) is the translational temperature of the colliding gas. The latter two parameters are expressed as a function of collision number. Equation 1 yields the mode-specific collisional energy transfer efficiencies (i.e., ki) of benzene in N2. These data are reported in Table 1. Rotational relaxation is found to be occurring at

642 J. Phys. Chem. C, Vol. 113, No. 2, 2009

Maselli et al.

TABLE 1: Mode-Specific Collisional Energy Transfer Efficiencies of Benzene with N2 benzene internal energy mode

collisional energy transfer efficiency (collision-1)

rotation ν16 ν6

0.9 4.3 × 10-3 9.0 × 10-5

almost the hard-sphere collision rate; it is ∼200 times more efficient than the relaxation of ν16 and 10 000 times more efficient than the relaxation of ν6. ν16 relaxation is ∼50 times more efficient than the relaxation of ν6. As discussed earlier, we now use the collisional relaxation efficiencies given in Table 1 to model the collisional energy transfer of benzene following evaporation from a water-ethanol LµJ in order to estimate the number of collisions involved in the fluid-phase change. Two constraints are imposed on this analysis. The first is that because ∼350 hard-sphere collisions result in negligible cooling of the ν6 vibrational mode of benzene in the free jet this mode is considered to be insensitive to collision number. Indeed, because of this insensitivity the experimentally determined evaporative ν6 vibrational temperature of 256 K provides a measure of the liquid filament surface temperature. Cooling of the liquid surface by ∼40 K is consistent with previous reports of the extent of cooling of water-based liquid beams.37,67 The second constraint is that because the free-jet results demonstrate that the rotational temperature of benzene closely follows the translational temperature due to efficient collisional energy transfer, the experimentally determined evaporative rotational temperature of 206 K provides a measure of the translational temperature of the benzene evaporate. This conclusion is consistent with predictions arising from very recent MD simulations that indicate that the translational and rotational temperatures of the evaporate rapidly converge.8 The translational temperature is therefore fixed at 206 K in our subsequent modeling of evaporative energy transfer. The constraints above leave ν16 as the internal mode of benzene whose temperature is sensitive to the number of collisions involved in evaporation. Using the collisional energy transfer efficiencies reported in Table 1 together with the constraints given above (i.e., a liquid surface temperature of 256 K and a fixed translational temperature of 206 K), the modespecific temperatures as a function of collision number are presented in Figure 6. The translational temperature is fixed in recognition that this degree of freedom reaches an asymptotic limit almost instantaneously during the evaporative phase transition. From Figure 6, we see that the temperature of ν6 is independent of collision number whereas the rotational temperature rapidly equilibrates to the translational temperature within just a few collisions. Finally, we note that 170 hardsphere binary collisions are required to produce the observed ν16 vibrational temperature of 229 K. In other words, this simple analysis suggests that molecules undergoing the transition from liquid to vacuum are subjected to several hundred collisions. This estimated collision number is sufficient to result in some cooling of the evaporate as it leaves the liquid surface but is insufficient to equilibrate the various molecular degrees of freedom. Having determined a liquid surface temperature of 256 K, our experiments indicate that the benzene rotational temperature is cooled by ∼50 K during evaporation. Rotational cooling has been predicted in recent MD simulations of the evaporation process.8,9 However, the predicted extent of cooling for water

Figure 6. Mode-specific temperatures of benzene as a function of collision number from the simple model developed here. See the text for details. The translational temperature (Ttrans), represented by the thick dashed line, is fixed at 206 K. The rotational temperature (Trot), represented by a thin continuous line, is initially set to 256 K and rapidly (within three hard-sphere collisions) converges to the translational temperature of 206 K. The ν6 vibrational temperature, represented by the thin dashed line, is initially set at 256 K and is considered to be an indication of the liquid surface temperature. This temperature is essentially invariant to collision number. The ν16 vibrational temperature, represented by the dashed-dotted line, is initially set at 256 K and smoothly decreases with increasing collision number. Our model indicates that ∼170 hard-sphere binary collisions are required to achieve the experimentally determined temperature of 229 K.

and methanol is not as extensive as observed in the experimental studies reported here.9 Rotational cooling is efficient for these polyatomics,65 so the difference between our observations and the simulations is not likely to be a consequence of our use of benzene as a spy for behavior at the water-ethanol liquid surface. This suggests that current MD simulations underestimate the extent of rotational cooling following evaporation. There are no simulation data yet available to compare to the observed vibrational cooling of ∼27 K involving ν16 of benzene. Conclusions We have directly measured the rotational and mode-specific vibrational energy content of benzene that has spontaneously evaporated into the vacuum from a water-ethanol liquid microjet. The rotational and ν6 and ν16 vibrational temperatures of benzene are all different, pointing to nonequilibrated collisional energy transfer occurring during the transition from liquid to vapor, consistent with predictions arising from recent MD simulations.5,7 The insensitivity of the benzene ν6 vibrational temperature to collision number provides a convenient measure of the local liquid surface temperature. We contend that, because of efficient rotational energy transfer via collisions, the observed benzene rotational temperature of 206 ( 4 K is indicative of the translational temperature of the evaporate. The ν16 vibrational mode of benzene provides a reasonable probe of the number of hard-sphere binary collisions experienced by the evaporate as it passes into the vacuum. Our modeling reveals that benzene experiences ca. 102 hard sphere collisions to bring about this vibrational temperature. This study provides important experimental insight into the molecular-level aspects of mass and energy transfer from the liquid to the vapor phase. The data are consistent with the notion of the liquid-vapor interphase region playing a dominant role in collisional energy transfer dynamics. Our data are in broad agreement with predictions arising from recent MD simulations of spontaneous evaporation and indicate that refinements in the simulation algorithms are required to (i) account for rotational energy transfer better and (ii) incorporate the role of molecular vibrations in the energy-transfer process. Such refinements will allow for a more rigorous assessment of the number of collisions involved in evaporative phase transfer.

Benzene Spontaneous Evaporation from Water-Ethanol Acknowledgment. Financial support for this work was provided by the Australian Research Council and The University of Adelaide. O.J.M. is the recipient of an Australian Postgraduate Award. References and Notes (1) Sadtler, P. B. J. Franklin Inst. 1909, 166, 291–296. (2) Sadtler, P. B. J. Ind. Eng. Chem. 1910, 1, 644–653. (3) Garrett, B. C.; Schenter, G. K.; Morita, A. Chem. ReV. 2006, 106, 1355–1374. (4) Innocenzi, P.; Malfatti, L.; Costacurta, S.; Kidchob, T.; Piccinini, M.; Marcelli, A. J. Phys. Chem. A 2008, 112, 6512–6516. (5) Frezzotti, A.; Gibelli, L.; Lorenzani, S. Phys. Fluids 2005, 17, 012102. (6) Matsumoto, M. Fluid Phase Equilib. 1998, 144, 307–314. (7) Meland, R.; Frezzotti, A.; Ytrehus, T.; Hafskjold, B. Phys. Fluids A 2004, 16, 223–243. (8) Frezzotti, A. Eur. J. Mech. B-Fluids 2007, 26, 93–104. (9) Ishiyama, T.; Yano, T.; Fujikawa, S. Phys. Fluids 2004, 16, 4713– 4726. (10) Raabe, G.; Sadus, R. J. J. Chem. Phys. 2007, 126, 7. (11) Penfold, J. Rep. Prog. Phys. 2001, 64, 777–814. (12) Kuo, I. F. W.; Mundy, C. J. Science 2004, 303, 658–660. (13) Kuo, I. F. W.; Mundy, C. J.; Eggimann, B. L.; McGrath, M. J.; Siepmann, J. I.; Chen, B.; Vieceli, J.; Tobias, D. J. J. Phys. Chem. B 2006, 110, 3738–3746. (14) Gan, W.; Wu, D.; Zhang, Z.; Feng, R.; Wang, H. J. Chem. Phys. 2006, 124, 15. (15) Gan, W.; Wu, D.; Zhang, Z.; Guo, Y.; Wang, H. F. Chin. J. Chem. Phys. 2006, 19, 20–24. (16) Shen, Y. R.; Ostroverkhov, V. Chem. ReV. 2006, 106, 1140–1154. (17) Cappa, C. D.; Smith, J. D.; Wilson, K. R.; Saykally, R. J. J. Phys.: Condens. Matter 2008, 20, 7. (18) Smith, J. D.; Cappa, C. D.; Wilson, K. R.; Messer, B. M.; Cohen, R. C.; Saykally, R. J. Science 2004, 306, 851–853. (19) Wilson, K. R.; Cavalleri, M.; Rude, B. S.; Schaller, R. D.; Nilsson, A.; Pettersson, L. G. M.; Goldman, N.; Catalano, T.; Bozek, J. D.; Saykally, R. J. J. Phys.: Condens. Matter 2002, 14, L221–L226. (20) Wilson, K. R.; Rude, B. S.; Catalano, T.; Schaller, R. D.; Tobin, J. G.; Co, D. T.; Saykally, R. J. J. Phys. Chem. B 2001, 105, 3346–3349. (21) Wilson, K. R.; Schaller, R. D.; Co, D. T.; Saykally, R. J.; Rude, B. S.; Catalano, T.; Bozek, J. D. J. Chem. Phys. 2002, 117, 7738–7744. (22) Winter, B.; Aziz, E. F.; Hergenhahn, U.; Faubel, M.; Hertel, I. V. J. Chem. Phys. 2007, 126, 6. (23) Winter, B.; Faubel, M. Chem. ReV. 2006, 106, 1176–1211. (24) Davidovits, P.; Worsnop, D. R.; Williams, L. R.; Kolb, C. E.; Gershenzon, M. J. Phys. Chem. B 2005, 109, 14742–14746. (25) McCoustra, M. R. S. Phys. Chem. Chem. Phys. 2008, 10, 4676– 4677. (26) Nathanson, G. M. Annu. ReV. Phys. Chem. 2004, 55, 231–255. (27) Benjamin, I.; Wilson, M. A.; Pohorille, A.; Nathanson, G. M. Chem. Phys. Lett. 1995, 243, 222–228. (28) Saecker, M. E.; Nathanson, G. M. J. Chem. Phys. 1993, 99, 7056– 7075. (29) Kenyon, A. J.; McCaffery, A. J.; Quintella, C. M.; Zidan, M. D. Faraday Discuss. 1993, 245–254. (30) Kenyon, A. J.; McCaffery, A. J.; Quintella, C. M.; Zidan, M. D. J. Chem. Soc., Faraday Trans. 1993, 89, 3877–3884. (31) Quintella, C. M.; McCaffery, A. J.; Zidan, M. D. Chem. Phys. Lett. 1993, 214, 563–568. (32) Perkins, B. G.; Haber, T.; Nesbitt, D. J. J. Phys. Chem. B 2005, 109, 16396–16405. (33) Miksch, G.; Weber, H. G. Chem. Phys. Lett. 1982, 87, 544–547. (34) Becker, C. H. Surf. Sci. 1985, 149, 67–80. (35) Weida, M. J.; Sperhac, J. M.; Nesbitt, D. J. J. Chem. Phys. 1996, 105, 749–766.

J. Phys. Chem. C, Vol. 113, No. 2, 2009 643 (36) Faubel, M.; Kisters, T. Nature 1989, 339, 527–529. (37) Faubel, M.; Schlemmer, S.; Toennies, J. P. Z. Phys. D: At., Mol. Clusters 1988, 10, 269–277. (38) Sibold, D.; Urbassek, H. M. Phys. Fluids A: Fluid Dynamics 1991, 3, 870–878. (39) Charvat, A.; Bo¨gehold, A.; Abel, B. Aust. J. Chem. 2006, 59, 81– 103. (40) Kondow, T.; Mafune´, F. Annu. ReV. Phys. Chem. 2000, 51, 731– 761. (41) Faubel, M.; Steiner, B.; Toennies, J. P. Mol. Phys. 1996, 90, 327– 344. (42) Cappa, C. D.; Drisdell, W. S.; Smith, J. D.; Saykally, R. J.; Cohen, R. C. J. Phys. Chem. B 2005, 109, 24391–24400. (43) Faubel, M.; Steiner, B.; Toennies, J. P. J. Chem. Phys. 1997, 106, 9013–9031. (44) Maselli, O. J.; Gascooke, J. R.; Kobelt, S. L.; Metha, G. F.; Buntine, M. A. Aust. J. Chem. 2006, 59, 104–108. (45) Wilson, K. R.; Rude, B. S.; Smith, J.; Cappa, C.; Co, D. T.; Schaller, R. D.; Larsson, M.; Catalano, T.; Saykally, R. J. ReV. Sci. Instrum. 2004, 75, 725–736. (46) Matsumoto, M.; Takaoka, Y.; Kataoka, Y. J. Chem. Phys. 1993, 98, 1464–1472. (47) Callomon, J. H.; Dunn, T. M.; Mills, I. M. Philos. Trans. R. Soc. London, Ser. A 1966, 259, 499–532. (48) Okruss, M.; Muller, R.; Hese, A. J. Mol. Spectrosc. 1999, 193, 293–305. (49) Murakami, J.; Kaya, K.; Ito, M. J. Chem. Phys. 1980, 72, 3263– 3270. (50) Stephenson, T. A.; Radloff, P. L.; Rice, S. A. J. Chem. Phys. 1984, 81, 1060–1072. (51) Otten, D. E.; Trevitt, A. J.; Nichols, B. D.; Metha, G. F.; Buntine, M. A. J. Phys. Chem. A 2003, 107, 6130–6135. (52) Tarek, M.; Klein, M. L. J. Phys. Chem. A 1997, 101, 8639–8642. (53) Tarek, M.; Tobias, D. J.; Klein, M. L. Physica A 1996, 231, 117– 122. (54) Tarek, M.; Tobias, D. J.; Klein, M. L. J. Chem. Soc., Faraday Trans. 1996, 92, 559–563. (55) Chen, B.; Siepmann, J. I.; Klein, M. L. J. Am. Chem. Soc. 2002, 124, 12232–12237. (56) Chen, B.; Siepmann, J. I.; Klein, M. L. J. Am. Chem. Soc. 2003, 125, 3113–3118. (57) Herzberg, G. Molecular Spectra and Molecular Structure. III. Electronic Spectra and Electronic Structure of Polyatomic Molecules; Van Nostrand: New York, 1966. (58) Wilson, E. B., Jr. J. Chem. Phys. 1935, 3, 276–285. (59) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes: The Art of Scientific Computing; Cambridge University Press: New York, 1986. (60) Demtro¨der, W. Visible and Ultraviolet Spectroscopy: Physical Aspects. In Atomic and Molecular Beam Methods; Scoles, G., Ed.; Oxford University Press; New York, 1992; Vol. 2, pp 231-233. (61) Hollenstein, H.; Piccirillo, S.; Quack, M.; Snels, M. Mol. Phys. 1990, 71, 759–768. (62) Page, R. H.; Shen, Y. R.; Lee, Y. T. J. Chem. Phys. 1988, 88, 4621–4636. (63) Smith, J. D.; Cappa, C. D.; Drisdell, W. S.; Cohen, R. C.; Saykally, R. J. J. Am. Chem. Soc. 2006, 128, 12892–12898. (64) Lyman, J. L.; Mu¨ller, G.; Houston, P. L.; Piltch, M.; Schmid, W. E.; Kompa, K. L. J. Chem. Phys. 1984, 82, 810–821. (65) Miller, D. R. Free Jet Sources. In Atomic and Molecular Beam Methods; Scoles, G., Ed.; Oxford University Press; New York, 1988; Vol. 1, pp 35-38. (66) Vincenti, W. G.; C. H. Kruger, J. Introduction to Physical Gas Dynamics; Wiley: New York, 1965. (67) Wattenberg, A.; Sobott, F.; Barth, H. D.; Brutschy, B. Int. J. Mass Spectrom. 2000, 203, 49–57.

JP804270V