Letter pubs.acs.org/JPCL
Ballistic Evaporation and Solvation of Helium Atoms at the Surfaces of Protic and Hydrocarbon Liquids Alexis M. Johnson, Diane K. Lancaster, Jennifer A. Faust, Christine Hahn, Anna Reznickova, and Gilbert M. Nathanson* Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States S Supporting Information *
ABSTRACT: Atomic and molecular solutes evaporate and dissolve by traversing an atomically thin boundary separating liquid and gas. Most solutes spend only short times in this interfacial region, making them difficult to observe. Experiments that monitor the velocities of evaporating species, however, can capture their final interactions with surface solvent molecules. We find that polarizable gases such as N2 and Ar evaporate from protic and hydrocarbon liquids with Maxwell−Boltzmann speed distributions. Surprisingly, the weakly interacting helium atom emerges from these liquids at high kinetic energies, exceeding the expected energy of evaporation from salty water by 70%. This super-Maxwellian evaporation implies in reverse that He atoms preferentially dissolve when they strike the surface at high energies, as if ballistically penetrating into the solvent. The evaporation energies increase with solvent surface tension, suggesting that He atoms require extra kinetic energy to navigate increasingly tortuous paths between surface molecules. SECTION: Kinetics and Dynamics
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incoming molecules that dissolve.6 The evaporation experiments (panel b) are simpler to interpret than scattering experiments (panel a) because the direct scattering and trapping−desorption pathways are absent in evaporation and do not mask the pathways that transfer solute molecules between gas and liquid.12 Gas-phase molecules have a Maxwell−Boltzmann (MB) distribution of speeds that lead to a simple characterization of gas entry if the fraction of molecules that dissolve does not depend on the speed of the gas molecules.6 In this case, the reverse evaporation distribution must also be Maxwellian to match the speed distribution of molecules that dissolve. Our experiments verify this Maxwellian behavior for heavy and polarizable gases such as Ar, N2, O2, CO2, and H2O evaporating from a wide variety of liquids. The key experiments reported here, in contrast, demonstrate that He atoms evaporate in sharply non-Maxwellian distributions with high kinetic energies. This surprising observation implies in reverse that He atoms preferentially dissolve at high kinetic energies. Figure 1c,d illustrates this exceptional pathway for He dissolution and evaporation, where He atoms interact too weakly with surface molecules to undergo trapping. Instead, the He atoms dissolve by direct penetration through gaps between surface molecules.13 We show that the He evaporation energies increase with solvent surface tension, suggesting that He atoms require more energy to slip between molecules that
he gas−liquid interface acts as a gateway for the solvation and evaporation of solute species, selectively controlling the rates of transport between gas and liquid.1,2 Despite the diverse ways in which solute and solvent molecules interact with each other, the principle of detailed balance imposes a remarkable constraint: at equilibrium, where condensation and evaporation exactly balance, every trajectory of an incoming gas molecule must be matched by the reverse outgoing trajectory of another molecule.3−10 Strong and weak solute−solvent forces, however, can lead to starkly different mechanisms for interfacial transport. To explore these mechanisms, we monitor solute evaporation and apply detailed balancing to reconstruct the reverse dissolution pathways. Our studies reveal the special ability of helium atoms to ballistically traverse the gas−liquid boundary in ways that reflect the packing and attractive forces among the surface solvent molecules. Figure 1 illustrates the unexpected behavior of He atoms in comparison with common gases such as N2 as they dissolve in and evaporate from ethylene glycol, HOCH2CH2OH, an extensively hydrogen-bonded solvent. Panel a shows three representative trajectories for collisions of N2 with the liquid: direct impulsive scattering, momentary gas-surface binding (trapping) followed immediately by desorption, and trapping followed by solvation and diffusion into the bulk.11 The N2 evaporation pathway in panel b is the reverse of the trajectory leading to gas entry in panel a. Rather than disentangle the entry and exit pathways from each other at equilibrium, we isolate the evaporation pathways in panel b by monitoring gas evaporation in vacuum. Through detailed balance, the kinetic energies of the evaporating species are also the energies of the © XXXX American Chemical Society
Received: September 18, 2014 Accepted: October 22, 2014
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Figure 1. Representative pathways for collisions of N2 and He with ethylene glycol. (a) An impinging N2 molecule scatters from the surface (red dashed line), or it dissipates its excess energy and becomes momentarily trapped (black line) before either desorbing (blue dashed line) or dissolving into the bulk (green line). (b) The reverse N2 evaporation pathway, which occurs in the absence of direct scattering and trapping-desorption (dashed lines in panel a). (c) He atom direct penetration at high energies bypasses the two-step trapping and dissolution process for N2. (d) The penetration trajectory in reverse implies that He atoms preferentially evaporate at high kinetic energies.
has shown that the chief criterion for minimizing these gas−gas collisions after evaporation is to choose a jet radius smaller than the gas-phase mean free path.14 Experimentally, this condition is achieved when the solvent or dissolved gases (other than He) evaporate in a Maxwellian distribution.12 Figure 2b shows TOF spectra of N2 and Ar evaporating from a 50 μm radius jet of squalane at 295 K. For both gases (and O2, CO2, and H2O),18 the velocity distributions are Maxwellian (dashed line) at Tliq = 295 K. The average flux-weighted energy of molecules desorbing in a MB distribution is 2RTliq = 4.9 kJ mol−1 at 295 K.7 No gas-squalane collisions occur in the vapor phase because of the low vapor pressure of squalane (10−8 Torr). Panel c displays the TOF spectrum of He atoms evaporating under the same conditions; these atoms arrive earlier than predicted by a MB distribution, and therefore their average kinetic energy is greater than 2RTliq. is found to be 5.9 kJ mol−1, equal to (1.20 ± 0.01) × 2RTliq (90% confidence interval for 10 measurements). Analogous measurements at 275 and 330 K yield similar multipliers of 1.18 ± 0.04 at 275 K and 1.19 ± 0.01 at 330 K. The constancy of these multipliers implies that scales with Tliq over the 55 K range; this scaling suggests that greater speeds are required for He atoms to pass through fluctuating gaps at higher temperatures, perhaps because the lifetimes of the gaps shorten as the temperature increases. In tandem, increased thermal motions of the surface C−H groups may also propel He atoms into the gas phase at higher velocities. Super-Maxwellian evaporation of He atoms is observed for every liquid investigated. Figure 3 displays TOF spectra of He atoms evaporating from dodecane, ethylene glycol, and salty water under conditions where O2, N2, Ar, CO2, and H2O evaporate in MB distributions (Figure S1 in the SI). In each case, the helium TOF spectra are shifted to earlier arrival times and therefore higher kinetic energies relative to a MB
are more tightly packed and attracted to each other to evaporate. Non-Maxwellian evaporation from liquids was first observed by Faubel and coworkers, who showed that water and acetic acid monomers evaporate in Maxwellian distributions from liquid water but that acetic acid dimers evaporate at higher speeds.14−17 This observation is attributed to the formation of the hydrophobic (CH3COOH)2 pair that is ejected as the surface flattens; in reverse, the surface must reorganize to accommodate the breakup of the adsorbed dimer. Our studies focus on the evaporation of individual He atoms, the most weakly interacting and least reactive of all chemical species. The four hydrocarbon and protic liquids we investigatesqualane (C30H62), dodecane (C12H26), ethylene glycol, and salty water (7.5 M LiBr/H2O)span wide variations in hydrogen bonding, viscosity, surface tension, and vapor pressure, and each produces different He speed distributions. The experiments were performed by monitoring the evaporation of dissolved He, Ar, N2, O2, CO2, and H2O from a microjet inside a vacuum chamber, as depicted in Figure 2a and described in the Supporting Information (SI).18 A cylindrical liquid jet is created by dissolving the solute gas into the liquid and then forcing the solution under high pressure through a 10−50 μm radius hole in a tapered glass nozzle. We monitor the velocities v = L/t and kinetic energies E = 1/2 mgasv2 of evaporating species by recording the arrival time t for these species to travel a distance L = 18.9 cm from the spinning chopper wheel to the mass spectrometer.11,12 The data are displayed by plotting the signal N(t) versus t as a timeof-flight (TOF) spectrum. Liquid microjets provide access to high-vapor pressure fluids in vacuum because of their narrow radius and small surface area, which suppress vapor-phase collisions by limiting the density of the solvent vapor cloud surrounding the jet. Faubel 3915
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Figure 3. TOF spectra of He atoms evaporating from (a) dodecane and ethylene glycol at 295 K and (b) 7.5 M LiBr/H2O at 236 K. The dashed lines are Maxwell−Boltzmann (MB) distributions.
Figure 2. (a) Apparatus for monitoring evaporation from a liquid microjet in vacuum. (b) Time-of-flight (TOF) spectra of Ar and N2 evaporating from squalane in comparison with Maxwell−Boltzmann (MB) distributions (dashed lines). (c) TOF spectrum of He atoms evaporating at higher speeds than a MB distribution.
distribution. For 7.5 M LiBr/H2O at 236 K, reaches 6.7 ± 0.3 kJ mol−1 or (1.7 ± 0.1) × 2RTliq. These TOF spectra may be transformed into distributions P(E) versus E displaying the kinetic energies of the evaporating He atoms; two examples are shown in Figure 4 for squalane and LiBr/H2O. They are shifted to higher energies when compared with the corresponding MB curves (dashed lines) but do not reveal additional maxima or minima. Detailed balancing of the evaporating and dissolving He atom fluxes enables the energy distributions in Figure 4 to be converted into relative He atom entry probabilities, β(E) = P(E)/PMB(E), by dividing the normalized kinetic energy distribution P(E) by the analogous MB distribution.6,18 The β(E) plots describe how the probability of gas entry (and evaporation) varies with the kinetic energy of the impinging atom or molecule. Because we do not measure absolute evaporation fluxes, β(E) is computed from the area-normalized energy distributions, and only its shape or relative values are meaningful. The Maxwellian evaporation of Ar, N2, CO2, and H2O in Figure 2 and Figure S1 in the SI implies that β(E) is independent of collision energy over the range of energies
Figure 4. Kinetic energy distributions P(E) for He evaporation from (a) squalane and (b) LiBr/H2O. The dashed lines are Maxwell− Boltzmann (MB) distributions PMB(E). Each distribution is areanormalized. The relative entry and evaporation probabilities, β(E) = P(E)/PMB(E), are shown on the same scale in each panel.
populated in a MB distribution. In contrast, Figure 4 demonstrates that β(E) increases steadily with He kinetic energy for squalane and even more sharply for water. These curves emphasize that He atoms dissolve preferentially at higher incident energies; the entry probability jumps 12-fold between 2 and 12 kJ mol−1 (1−6 RTliq) for 7.5 M LiBr/H2O and two-fold for squalane. The cumulative data for He evaporation from the four liquids are collected in Figure 5, along with additional measurements 3916
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entry and evaporation, requiring that He atoms evaporate at high energies when the incoming trajectories are reversed.5 In this way, molecules at the surfaces of protic and hydrocarbon liquids act to filter low-velocity He atoms from dissolving and evaporating by deflecting them back into the gas or liquid phases. The present measurements suggest that the high-energy evaporation of He atoms is universal, spanning hydrogenbonded, alkane, and aromatic liquids. In particular, the trend in Figure 5 implies that interfacial hydrogen bonds may block lowenergy He atoms from escaping, while the similar He evaporation energies from squalane, dodecane, and octane indicate that the length of the alkyl chain does not significantly alter interfacial He atom transport. The high excess energy for He evaporation from salty water may also depend on the identity of the interfacial alkali and halide ions, which can vary in mass, ion−ion and ion−water interactions, and surface propensity.24−26 These potential correlations make us hopeful that He evaporation measurements can become an incisive probe to explore packing and bonding at the surfaces of ionic solutions and liquid mixtures and the means by which they control solvation and evaporation.
Figure 5. Average He atom evaporation energy versus solvent surface tension. The vertical axis is the multiplier of 2RTliq. Tliq is 295 K for squalane, dodecane, ethylene glycol, and 1-methylnaphthalene; 241 K for octane; 236 K for 7.5 M LiBr/H2O; and 215 K for isooctane. The best-fit line has a slope of 0.93 ± 0.04 (kJ mol−1)/(dyn cm−1). The error bars reflect both reproducibility and fitting uncertainty.18
for octane at 241 K, isooctane at 215 K, and 1methylnaphthalene at 295 K. The average evaporation energies, represented by the multipliers of 2RTliq, are plotted against the solvent surface tensions. Figure 5 demonstrates that increases steadily from 1.14 × 2RTliq for dodecane to 1.7 × 2RTliq for 7.5 M LiBr/H2O, while the multiplier is close to one for Ar, N2, O2, CO2, and H2O. Solvent surface tension was found to provide the best macroscopic correlation; parameters such as viscosity, compressibility, vaporization enthalpy, and helium solubility do not correlate well with (Figure S2 in the SI). The surface tension itself depends on the bonding and packing of interfacial solvent molecules;19 the trend in Figure 5 suggests that more strongly interacting solvent molecules create increasingly tortuous paths for He atoms as they cross the liquid−gas boundary, inhibiting the slower and lower energy atoms from passing through the interfacial region. We also find good correlations between and solvent mass density, perhaps because the light He atom retains more momentum when it ricochets from a heavier surface group of atoms and enters the gas phase.18 Figure 1 provides an intuitive explanation for the superMaxwellian behavior of evaporating and dissolving He atoms, which we attribute to weak He−solvent interactions. Helium atoms have the lowest polarizability (0.2 Å3) of all chemical species, generating He-surface binding energies of only ∼0.2 and ∼0.7 kJ mol−1 for He-ice and He-alkane surfaces.20−22 These well depths are much smaller than the several kJ mol−1 kinetic energies of moving He and surface species, prohibiting the momentary trapping of He atoms upon collision with the liquid. In these circumstances, He atoms cannot follow the twostep trapping and diffusion/solvation pathway in Figure 1a, which should be dominant for more polarizable gases.5,11 We instead hypothesize that He atoms enter each liquid by ballistically penetrating through fluctuating gaps between solvent molecules at the interface (Figure 1c). The frequency and size of the gaps should shrink with increasing surface tension.1 Figure 5 suggests that He atoms require more energy to traverse the tighter pathways between surface ethylene glycol molecules or water molecules than between hydrocarbon molecules. These higher energies may allow the He atom to move more freely through fluctuating gaps or to translate or rotate C−H or O−H groups as it penetrates between them.23 The same He-liquid potential energy function governs both
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EXPERIMENTAL METHODS Liquid jets were prepared by forcing filtered liquid mixed with 1−10 atm of He or other gas through a tapered glass nozzle with an exit radius between 10 and 50 μm, as illustrated in Figure 2a. The 30 min gap between mixing and jetting allows the gas to dissolve, and no bubbles were evident in the liquid. After passing through the vacuum chamber, the liquid was trapped in a cooled glass flask. Atoms and molecules evaporating from the jet were viewed by the mass spectrometer over a 5 mm diameter region located just below the nozzle exit. The smooth P(E) and β(E) distributions were obtained by trial-and-error fitting of the TOF spectra when convolved with the 45 μs chopper wheel pulses. The SI lists cooling temperatures (3 mm), and He-vapor collision probabilities (
