Water Accommodation and Desorption Kinetics on Ice - American

Article pubs.acs.org/JPCA

Water Accommodation and Desorption Kinetics on Ice Xiangrui Kong,† Panos Papagiannakopoulos,†,‡ Erik S. Thomson,† Nikola Marković,§ and Jan B. C. Pettersson*,† †

Department of Chemistry and Molecular Biology, Atmospheric Science, University of Gothenburg, SE-412 96 Gothenburg, Sweden Laboratory of Photochemistry and Kinetics, Department of Chemistry, University of Crete, 71003 Heraklion, Crete, Greece § Department of Chemical and Biological Engineering, Physical Chemistry, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden ‡

ABSTRACT: The interaction of water vapor with ice remains incompletely understood despite its importance in environmental processes. A particular concern is the probability for water accommodation on the ice surface, for which results from earlier studies vary by more than 2 orders of magnitude. Here, we apply an environmental molecular beam method to directly determine water accommodation and desorption kinetics on ice. Short D2O gas pulses collide with H2O ice between 170 and 200 K, and a fraction of the adsorbed molecules desorbs within tens of milliseconds by first order kinetics. The bulk accommodation coefficient decreases nonlinearly with increasing temperature and reaches 0.41 ± 0.18 at 200 K. The kinetics are well described by a model wherein water molecules adsorb in a surface state from which they either desorb or become incorporated into the bulk ice structure. The weakly bound surface state affects water accommodation on the ice surface with important implications for atmospheric cloud processes.

1. INTRODUCTION The rates of water condensation and evaporation on atmospheric ice particles influence the lifetime and properties of clouds1 and thereby affect the radiation budget of the atmosphere, the formation of precipitation, and climate.2 Acknowledging the ability of water to form hydrogen bonds, gas−ice collisions can be expected to result in efficient water uptake and ice growth, although the mechanism by which newly arrived water molecules become incorporated into the hydrogen-bonded network remains vague. The picture provided by earlier experimental studies yields estimates of the water accommodation coefficient, α, on ice that vary by more than 2 orders of magnitude.3−5 This spread in α values challenges our fundamental understanding of the behavior of water and introduces significant uncertainties in the description of ice particle growth in atmospheric models.6−8 Constraining α motivates further studies both from the perspective of fundamental scientific understanding and for the benefit of strengthening the validity of cloud and climate models.7 In molecular beam experiments, a directed gas flow collides with a surface in vacuum, and detailed information may be obtained on gas−surface interactions. The method has been used to investigate ice surfaces,9−11 but such studies at temperatures above 150 K have been problematic due to the finite vapor pressures required to maintain stable ice layers that result in molecular beam attenuation. This problem is partially overcome by the recently developed environmental molecular beam (EMB) method, which allows for ice experiments at temperatures up to 213 K, corresponding to temperatures in the upper troposphere.12−14 Here, we apply the EMB method to determine the accommodation and desorption kinetics of © 2014 American Chemical Society

water molecules on pure water−ice surfaces at temperatures from 170 to 200 K.

2. EXPERIMENTAL SECTION A schematic of the system used for EMB experiments is presented in Figure 1. The recently developed technique allows for molecular beam experiments at vapor pressures into the 10−2 mbar range, which is sufficient to form and maintain micrometer-thick ice layers on a substrate at temperatures above 200 K.12 A gas source produces 4.5 ms gas pulses that are introduced into a six-chamber vacuum system, with part of the

Figure 1. Schematic view of the environmental molecular beam apparatus including the main components and the inner chamber surrounding the ice surface. The molecular beam and the direction of a specular reflection are marked in green and the laser beam in red. Received: April 9, 2014 Revised: May 8, 2014 Published: May 9, 2014 3973

dx.doi.org/10.1021/jp503504e | J. Phys. Chem. A 2014, 118, 3973−3979

The Journal of Physical Chemistry A

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gas passing through a skimmer and a subsequent mechanical chopper to form a directed low-density molecular beam. The beam source is run with a D2O/He gas mixture at a total pressure of 2 bar and a partial D2O pressure of approximately 22 mbar, which produces a beam with mean kinetic energies of 31.0 ± 2.0 and 8.0 ± 0.5 kJ mol−1 for D2O and He, respectively. The beam is directed toward a graphite surface (Advanced Ceramics Corp.; highly oriented pyrolytic graphite, grade ZYB) located in the center of the main ultrahigh vacuum (UHV) chamber. A separate inner environmental chamber surrounds the surface and allows for experiments with vapor pressures in the 10−2 mbar range.12 The finite pressure distinguishes the EMB method from traditional molecular beam experiments that are carried out under ultrahigh vacuum conditions. The apparatus has been designed to minimize the molecular beam path length (28 mm) within the high-pressure zone in order to reduce beam attenuation by collisions with the high pressure vapor phase surrounding the surface.12 Ice is formed by depositing deuterium-depleted H2O (≤1 ppm D2O, SigmaAldrich Co.) from a leak valve onto the temperature controlled graphite surface. The H2O−ice layer is maintained at constant thickness of about 1 μm during experiments and is monitored using the interference signal produced by a low power laser (860 μW) with a wavelength of 670 nm directed at the surface.12,13,15 The procedure produces polycrystalline ice surfaces that have been characterized in earlier work.13 The incident D2O/He beam enters the inner chamber through a circular opening with a diameter of 5 mm and collides with the surface at an angle of 45°. The outgoing flux in the forward direction passes through a second 5 mm opening in the inner chamber wall and is monitored with a quadrupole mass spectrometer (QMS) at an angle of 45° from the surface normal. The QMS is rotatable and is also used to measure the intensity of the incident beam. The flux from the surface measured by the QMS is recorded using a multichannel scaler with a 10 μs dwell time, and the intensity data are subsequently transformed into time-of-flight (TOF) distributions using the geometry of the system. The reported TOF distributions are based on 300,000 to 400,000 TOF passes corresponding to 7 to 10 h of data collection for each temperature, where the ice surface was reformed on a subhourly basis to ensure clean surface conditions. Figure 2. Time-of-flight data for D2O emitted from water−ice surfaces at temperatures from 170 to 200 K (red points), overlaid with a fit based on thermal desorption (black solid line; see text for details). The lower-most panel shows a measured TOF intensity distribution for the incident D2O beam. Displayed data are normalized to the beam intensity and averaged over 125 data points, except for the beam profile where all data are shown.

3. RESULTS In the experiments, short pulses of D2O are dosed onto an H2O−ice surface, and the flux from the surface is measured at 45° from the surface normal direction. Heavy water is used instead of H2O to enhance the signal-to-noise ratio in the mass spectrometer. The effect of isotopic composition on sticking probability in such a system has been shown to be negligible.16 Analyzed measurements consist of TOF distributions, with typical distributions obtained at the four temperatures illustrated in Figure 2 together with a D2O beam profile. A fraction of the incident molecules leaves the surface on the experimental time scale (60 ms), and both the total intensity and decay time depend on temperature. The TOF distributions are simulated assuming that D2O thermally desorbs from the ice surface at a rate described by first order desorption, where the intensity of desorbed molecules Fres(t) can be described as follows: Fres(t ) = C1 exp( −kobst )

where C1 is a fitted scaling factor, t is the surface residence time, and kobs is the observed rate constant. As discussed further below, the D2O surface population is depleted by simultaneous desorption and incorporation into the bulk ice, and kobs is therefore larger than the actual desorption rate constant. The TOF distributions are fit in a nonlinear least-squares manner assuming desorption results in an outgoing flux with a thermal velocity distribution.17 Thus, the result is a convolution of the D2O flow to the ice surface described by the beam profile, eq 1, and the outgoing thermal flux, where C1 and kobs act as free fitting parameters. The best-fit curves give a good representation of the experimental data within error limits, and we conclude that the D2O surface population decays exponentially

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Kolb et al.19 In fact, in this case αs is close to unity because no inelastic scattering is observed. The α values from the present study decrease nonlinearly with temperature from close to unity at 170 K to 0.41 ± 0.18 at 200 K. A precursor model has previously been successfully applied to water−ice interactions,20−22 and it is applied here to simultaneously reproduce the observed α and kobs values. In the model, gas phase molecules are first trapped in a surface state before continuing to either desorb or transfer to a more strongly bound state in the solid ice structure. The reaction mechanism can be illustrated as follows:

with time. The signal-to-noise ratio decreases rapidly with increasing temperature due to background H218O from the vapor phase surrounding the ice surface that interferes with D2O detection at m/z = 20 in the mass spectrometer. No inelastic scattering component is distinguished in the experimental data, in agreement with earlier studies where the scattering probability was less than 0.001 under similar conditions.18 Figure 3 shows an Arrhenius plot of the calculated

kads

k1

kdes

k −1

D2 O(gas) XoooY D2 O(p) XooY D2 O(solid)

(2)

where D2O(p) is the precursor state, kads and kdes are the adsorption and desorption rate constants, respectively, k1 is the rate constant for transfer to a strongly bound surface state, and k−1 is the rate constant for the reverse reaction. The adsorption rate constant does not have to be considered here since no D2O adsorption takes place after the initial gas pulse is dosed onto the surface. The mechanism can be further simplified by also ignoring the back-reaction with rate constant k−1. Any significant back-reaction would be observed as an additional slow decay in the TOF distributions. The experimental data are, however, well described by a single exponential decay function, and k−1 can consequently be ignored. The incorporation of molecules into the ice is thus treated as an irreversible process on the time-scale of the experiments. The back-reaction may potentially be observed in experiments on longer time scales and/or at higher surface temperatures than those used here. According to the precursor model, the desorbing flux is proportional to the D2O population in the surface state, where the rate equation for that population can be written as follows:

Figure 3. Arrhenius plot of the experimentally observed rate constant kobs for D2O emission from ice (red points) and the precursor model fit to the data (black line) that utilizes a global difference minimization considering eqs 4 and 5 simultaneously. The deconvoluted components kdes (green line) and k1 (orange line) are also plotted. Error bars represent the 95% confidence intervals obtained from fitting individual TOF distributions.

kobs values including 95% confidence intervals, determined from the individual TOF distribution fitting. The data have a clear nonlinear appearance and are not well described by the Arrhenius equation. Instead, we find the data are better explained using a two-state kinetic model detailed below. The TOF data are also used to determine the D2O accommodation coefficient on ice using an analytical method that has been described in detail elsewhere.15 Briefly, the integral of the TOF distribution represents the thermally desorbed D2O molecules, while the remaining fraction of the incident molecules accommodate on the ice. Absolute values are obtained by normalizing each integral by comparison with a contiguously measured case of D2O scattering from bare graphite, for which the trapping-desorption probability is wellknown under the present conditions.15 No desorbing HDO is observed, eliminating the possibility of isotopic exchange between trapped D2O and surface H2O molecules as a major sink of heavy water. Figure 4 shows the calculated accommodation coefficients. The α values refer to bulk accommodation (αb) rather than surface accommodation (αs) according to the classification by

d[D2 O(p)] = −kdes[D2 O(p)] − k1[D2 O(p)] dt = −(kdes + k1)[D2 O(p)]

(3)

Thus, the experimentally observed rate constant kobs is kobs = kdes + k1

(4)

Similarly, the observed accommodation coefficient α results from competition between desorption and incorporation into ice:

α = k1/(kdes + k1)

(5)

Equations 4 and 5 are used to simultaneously fit the measured kobs and α values assuming that Arrhenius behavior k = A· exp(E/kbT) governs the transition between states. Thus, the best fit values for eqs 4 and 5 are computed by minimizing the squares of the differences with weighting to ensure that each measurement contributes equally. Figure 3 shows the measurement data and fitting result for kobs and includes the deconvoluted kdes and k1 that constrain the fit. At low temperatures, k1 is significantly higher than kdes, and gas− surface interactions are dominated by efficient bulk accommodation, while the two rate constants are comparable at 200 K resulting in partial desorption of the surface population. The Arrhenius type fitting yields a desorption activation energy Edes = 42 ± 9 kJ mol−1 and a pre-exponential factor Ades = 1 × 10(13.1±2.5) s−1, given with their respective 95% confidence intervals. Similarly, E1 = 6 ± 5 kJ mol−1 and A1 = 1 × 10(3.4±1.3) s −1 for the incorporation process. In Figure 4, the

Figure 4. Bulk accommodation coefficient α computed from the TD integrals plotted as a function of temperature (red points) and overlaid by the precursor model fit to the data (black line; see text for details). Error limits on α represent the 95% confidence intervals obtained by propagating the uncertainty in the TD distribution coefficients. 3975



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surface. As a consequence, desorption may be identified with ordinary desorption from ice. The question then arises if the experimentally observed kinetics are compatible with the sublimation enthalpy and equilibrium vapor pressure over ice. Under equilibrium conditions, mass conservation implies that the flux to and from the ice surface are equal:

accommodation data are plotted with the simultaneously achieved fit described above. Thus, we observe that the precursor model well describes the combined accommodation and desorption kinetics data.

4. DISCUSSION The observed water−ice collision dynamics are consistent with previous studies which show efficient trapping of molecules on ice surfaces and negligible inelastic scattering under the conditions employed here.16 The precursor model utilized here successfully describes the experimentally observed kinetics for these processes, whereby trapped molecules either desorb or remain in the ice structure on the 60 ms time-scale of the experiments. The determined pre-exponential factor for the desorption process Ades = 1 × 10(13.1±2.1) s−1 has a large error envelope but is centered on the 1013 s−1 expected for an ordinary desorption process. The desorption energy Edes = 42 ± 8 kJ mol−1 is lower than the sublimation enthalpy of water−ice of 51.04 kJ mol−1.23 George and co-workers4,9 reported a desorption activation barrier of 48.25 ± 0.80 kJ mol−1 using optical and molecular beam methods, and Rossi and co-workers21,22,24 obtained a comparable desorption activation energy below 190 K by utilizing a Knudsen flow-reactor method. However, Rossi and co-workers22,24,26 observed a shift in evaporation and condensation behavior near 190 K and reported a lower desorption energy above 190 K that agrees favorably with the present results.26 Davy and Somorjai hypothesized that water molecules need to break two hydrogen bonds to desorb from bulk ice, with each hydrogen bond corresponding to about 23 kJ mol−1,20 which is also consistent with the present results. The interpretation of the Arrhenius parameters for incorporation of water molecules into the ice structure (E1 = 6 ± 5 kJ mol−1; A1 = 1 × 10(3.4±1.3) s−1) requires a more detailed analysis of the ice surface conditions. The rate-limiting step may correspond to several processes in the ice surface layer and may be affected by gradual changes in surface structure with increasing temperature. Earlier studies provide complementary information concerning the nature of the surface under the conditions investigated here. Elastic He scattering has been used to probe changes in the uppermost molecular layer above 180 K that relate to either strongly anharmonic surface vibrations or surface disorder,26 and sum frequency generation vibrational spectroscopy has detected an onset of orientational disorder of surface OH groups around 200 K.27,28 Molecular dynamics (MD) simulations at 180−210 K also show that surface molecules are substantially more mobile than bulk molecules and that adsorbed molecules are incorporated into the uppermost bilayer on ice on the nanosecond time scale and may reach the second bilayer from the surface within 50 ns.29 Simulations at 250 K confirm this and show enhanced diffusion into the ice structure compared to that at the lower temperatures, and the surface water molecules are also shown to have significantly lower binding energies than the molecules in bulk.30 These earlier studies strongly support a scenario where adsorbed molecules are rapidly incorporated into the uppermost molecular layers of the ice from where they are able either to escape and desorb on the millisecond time scale or to slowly reach larger depths with kinetics characterized by k1 and become part of the bulk structure. These arguments suggest that the intermediate precursor state corresponds to the complete surface layer rather than weakly bound molecules trapped in a state on top of the ice

αkadsPice = kdes[H 2O(surface)]

where Pice is the equilibrium vapor pressure, the evaporating surface population and kads = (2πmkBT )−1/2

(6) 23

H2O(surface) is (7)

where m is the molecular mass of H2O. By employing the α and kdes values determined for D2O and ignoring any differences in D2O and H2O interactions with the ice surface, we conclude that eq 6 is consistent with an evaporating surface population of (2.0−2.6)·1015 cm−2 over the range of experimental temperatures, 170 to 200 K. The calculation confirms that the surface state has a population that is comparable to the molecular density on a basal facet of ice.29,30 Thus, the experimentally determined kinetic parameters are consistent with the equilibrium vapor pressure over ice and with the sublimation enthalpy that determines the temperature dependence of Pice. A more elaborate model will require knowledge of molecular diffusion in layers near the ice surface as a function of temperature, information that is only partially available based on MD simulations.29,30 Figure 5 shows the observed accommodation coefficients together with experimental values from earlier laboratory

Figure 5. Accommodation coefficient α for D2O on water−ice from the present study and a comparison with experimental values for the H2O−ice system from the literature: this study (closed red circle); Koros et al.11 (red criss-cross); Brown et al.9 (closed red bar); Bryson et al.10 (open red rectangle); Tolbert and Middlebrook33 (open gray diamond); Davis and Strickland-Constable34 (closed brown circle); Haynes et al.4 (open black circle); Fluckiger and Rossi25 (closed blue circle); Leu37 (closed green sqaure); Kramers and Stemerding36 (closed marron circle); Delval et al.31 (open blue square); Delval and Rossi24 (open blue circle); Pratte et al.22 (blue star); Chaix et al.21 (closed blue square); Isono and Iwai35 (green striped rectangle); Earle et al.32 (inverted green triangle); Magee et al.8 (closed pink square); and Choularton and Latham3 (open orange circle). The black line is the Figure 4 fit extrapolated to higher temperatures. The gray shading indicates the 95% confidence interval straddling the fitted curve.

studies.3−5,8−11,21,24,25,31−37 The present results are comparable to or higher than other data in the 170−200 K range and in good agreement with several earlier studies. Studies employing molecular beam techniques (all red symbols) show a similar trend and in general produce relatively high values.9−11 The temperature dependence observed in the present study is also qualitatively similar in earlier work,22,24,25,31,34,35 and although 3976



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ficient values and values from several modeling studies. The present results for temperatures ≤200 K are consistent with modeling of cloud chamber data below 200 K5,42 and atmospheric modeling by Lohmann et al.,43 while Saunders et al. preferred a lower value of 0.1 in the modeling of cloud chamber results.44 Above 200 K, the spread in employed accommodation coefficients is considerably larger. Most studies overlap with the estimate from the precursor model in some range, but modeling studies have either employed a temperature-independent accommodation coefficient43,45 or evaluated the effect of α at a given temperature.6,46 Gierens et al. used α = 0.01−0.1 at 225 K to explain high particle concentrations observed in cirrus observations,6 which agrees favorably with the predictions from the precursor model.

the absolute values may differ, there appears to be a general trend that α decreases with increasing temperature beginning around 190 K. This is particularly clear in the work by Rossi and co-workers (all blue symbols) where a marked decrease in α is observed above 190 K.21,22,24,25,31 Figure 5 also includes an extrapolation to temperatures above 200 K based on the kinetic parameters determined for the precursor model. The calculated α value decreases significantly +0.061 with increasing temperature and reaches 0.096−0.039 and +0.010 0.019−0.007 at 220 and 240 K, respectively. However, the assumption that the back-reaction described by k−1 can be ignored may not hold above 200 K, and any back-reaction would tend to further decrease α. In addition, we expect water accommodation to be strongly affected by the formation of a liquid-like surface layer as the temperature approaches the melting point,38−40 and the validity range for the present kinetic model remains to be determined. A majority of earlier studies suggest that α deviates significantly from unity above 200 K. The prediction from the precursor model agrees favorably with experimental data from Rossi and co-workers21,22,24,25,31 and Earle et al.,32 while other data sets are either lower3,8 or higher36 than the predicted values. There are several possible uncertainties that may have affected the different types of experiments. As pointed out by Skrotzki et al.,5 the determination of the ice saturation ratio of water vapor near the ice surface is often a major source of uncertainty that may have influenced some of the studies. The experimental timescales also vary between studies, which may potentially affect the determination of α values. In addition, effects of surfaceactive impurities may play a role and need to be considered. In a related recent study, experimental investigations of water accommodation on liquid water have been reanalyzed to assess the sensitivity of the measurements to thermophysical quantities and experimental parameters,41 and a similar investigation would be required to critically review the existing ice experiments. We note that the present methodology simplifies the analysis since gas diffusion outside the surface does not have to be considered, the time-scale for gas−ice interactions is well-defined, nevertheless an extension of the method to include higher ice temperatures would be valuable. The estimated temperature trend of the accommodation coefficient may affect ice growth under atmospheric conditions and need to be considered in cloud models.6−8 Figure 6 shows a comparison between our measured accommodation coef-

5. CONCLUSIONS We have studied D2O interactions with an H2O ice surface at temperatures from 170 to 200 K. The accommodation coefficient decreases rapidly with temperature above 190 K, and a fraction of the adsorbed D2O molecules desorb within tens of milliseconds. The population of adsorbed D2O molecules decays exponentially with time and displays a nonArrhenius temperature dependence. A kinetics model that assumes initial adsorption in a surface state followed by either desorption or incorporation into the ice crystal structure agrees well with all experimental data, and the determined kinetic parameters are shown to be consistent with the equilibrium pressure over ice. We conclude that α values below 200 K are relatively well constrained by the available experimental and modeling studies, and the present study confirms the previously observed decrease in α with temperature above 190 K. Extrapolation of the present results to temperatures above 200 K suggests a relatively strong temperature dependence with α values below 0.1 above 220 K. The situation at these temperatures remains unresolved and calls for further experimental and modeling efforts. Suggested studies include atmospheric modeling of cirrus clouds that include a temperature dependent α and MD simulations focusing on diffusion perpendicular to the surface to improve the understanding of the water uptake process. Development of the EMB method is currently under way to allow for accommodation experiments at temperatures above 200 K.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +46 31 786 90 72. E-mail: [email protected]. Notes

The authors declare no competing financial interest. (X.K.) E-mail: [email protected].

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ACKNOWLEDGMENTS This work is supported by the Swedish Research Council, and the Nordic Top-Level Research Initiative CRAICC. P.P. thanks the Wenner-Gren Foundation for providing funding for an extended stay at the University of Gothenburg. Riccardo Iannarelli and Michel Rossi are thanked for early discussions.

Figure 6. Accommodation coefficient α values for H2O on water−ice used in modeling studies are reproduced for comparison with the present measurements. This study (closed red circle); Gierens et al.6 (dark green rectangle); Kärcher and Ström45 (olive green rectangle); Lohmann et al.43 (peach rectangle); Kay and Wood46 (teal rectangle); Saunders et al.44 (purple rectangle); and Haag et al.42 (light green rectangle). The curve (black line) from Figure 5 is reproduced with the gray shading indicative of the 95% confidence interval.

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REFERENCES

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Water Accommodation and Desorption Kinetics on Ice - American

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