Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
THE JOURNAL OF CHEMICAL PHYSICS 133, 044709 共2010兲 Energy barrier of proton transfer at ice surfaces Eui-Seong Moon, Jinha Yoon,a兲 and Heon Kangb兲 Department of Chemistry, Seoul National University, Gwanak-ro 599, Seoul 151-747, South Korea 共Received 13 January 2010; accepted 7 June 2010; published online 27 July 2010兲 We estimated the energy barrier of proton transfer on ice film surfaces through the measurement of the H/D exchange kinetics of H2O and D2O molecules. The isotopomeric populations of water molecules and hydronium ions on the surface were monitored by using the techniques of reactive ion scattering and low energy sputtering, respectively, along the progress of the H/D reaction. When hydronium ions were externally added onto an ice film at a temperature of 70 K, a proton was transferred from the hydronium ion mostly to an adjacent water molecule. The proton transfer distance and the H/D exchange rate increased as the temperature increased for 90–110 K. The activation energy of the proton transfer was estimated to be 10⫾ 3 kJ mol−1 on a polycrystalline ice film grown at 135 K. The existence of a substantial energy barrier for proton transfer on the ice surface agreed with proton stabilization at the surface. We also examined the H/D exchange reaction on a pure ice film surface at temperatures of 110–130 K. The activation energy of the reaction was estimated to be 17⫾ 4 kJ mol−1, which was contributed from the ion pair formation and proton transfer processes on the surface. © 2010 American Institute of Physics. 关doi:10.1063/1.3457379兴 I. INTRODUCTION Hydronium ions present at ice surfaces may critically influence the physical and chemical properties of ice, such as interfacial charge distribution, electrical conduction,1 and reactivity of the ice surface.2 An interesting property of hydronium ions observed in recent studies3–9 is that they prefer to reside on the surface of ice rather than in the interior. Evidence for the thermodynamic affinity of hydronium ions for the ice surface has come from several experimental observations, including Fourier-transform infrared spectroscopic studies of the H/D exchange between H2O and D2O molecules in ice nanocrystals,3,4 soft-landing experiments of hydronium ions on ice films,9 and proton transfer studies at the surface and interior of ice films using reactive ion scattering 共RIS兲 and low energy sputtering 共LES兲 techniques.5–8 Devlin and co-workers3,4 observed that proton activity was greatly enhanced on the surface of ice nanocrystals relative to that in the ice interior. Park et al.5 observed that the adsorption of HCl onto ice films released protons which greatly promoted the H/D exchange of water molecules at the surface, while vertical proton transfer to the film interior was inefficient at a temperature of 95 K.5 Lee et al.6,7 reported that protons buried within an ice film moved to the surface and induced the H/D exchange reaction at temperatures above 130 K. UV photolysis studies of ice films observed the proton transfer from positive ionic defects 共H3O+兲 created in ice to methylamine molecules adsorbed onto the ice surface at 50–130 K.8 These observations provide a consistent picture for the properties of protons at ice surfaces, showing that a proton is energetically stabilized at the surface relative to its presence in the lattice as an ionic defect. a兲 Present address: Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784, South Korea. b兲 Author to whom correspondence should be addressed. FAX: 82-28898156. Tel.: 82-2-8757471. Electronic mail: [email protected]. 0021-9606/2010/133共4兲/044709/7/$30.00 There remains, however, a dilemma for the interpretation of the results of H/D exchange studies at ice surfaces. The adsorption of HCl onto ice films induces a very efficient H/D exchange of surface water molecules,5 and this observation appears to indicate that proton transfer occurs very easily on the ice surface with a negligible energy barrier. On the other hand, if a proton is energetically stabilized at the ice surface as a hydronium ion, as indicated by other studies mentioned above,3,6–8 the proton may not be expected to move so easily because the release of a proton from a surface hydronium ion requires a certain amount of activation energy. This dilemma has provoked us to inspect the proton transfer and the H/D exchange processes at ice surfaces more closely. In this paper, we examine the proton transfer on ice film surfaces by measuring the H/D exchange kinetics on the surface in the presence of preexisting hydronium ions. The result is compared with the H/D exchange reaction induced by the adsorption of HCl onto an ice film surface and that due to the thermal ionization of water molecules on a pure ice film. II. EXPERIMENTAL SECTION We conducted experiments in an ultrahigh vacuum surface analysis chamber equipped with instrumentation for RIS, LES, and temperature programed desorption 共TPD兲.3 Ice films were grown on the 共0001兲 face of a Ru crystal mounted on a temperature control stage of a sample manipulator by backfilling the chamber with D2O vapor for a deposition rate of 0.02 BL s−1 共BL denotes bilayer兲 共1 BL = 1.14⫻ 1015 water molecules cm−2兲. The Ru substrate temperature was maintained at 135 K during D2O deposition, which probably resulted in a polycrystalline ice film with mixed domains of amorphous and crystalline structures. This ice sample produced more reproducible results in the H/D exchange experiments than a crystalline film prepared at a higher temperature 共⬎140 K兲, probably because the surface 133, 044709-1 © 2010 American Institute of Physics Downloaded 27 Jul 2010 to 147.47.217.45. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 044709-2 Moon, Yoon, and Kang roughening associated with cluster formation was reduced in the former sample.10 The ice film thickness was typically 8 BL, as deduced from the TPD experiments. H2O, D2O, and HCl vapors were introduced into the chamber through separate leak valves, thereby preventing the occurrence of the isotope exchange reactions before they condensed onto the sample surface. The ice film surface was analyzed by RIS and LES methods.2 In these experiments, a Cs+ beam from a low energy ion gun collided with the sample surface at an incident energy of 30 eV, and the ions emitted from the surface were detected by a quadrupole mass spectrometer with its ionizer filament switched off. In RIS, neutral species 共X兲 on the surface were picked up instantaneously 共⬍1 ps兲 by the scattering Cs+ projectiles to form Cs+-neutral clusters 共CsX+兲. In LES, ionic species 共Y+ and Z−兲 on the surface were ejected by the Cs+ impact. Thus, the RIS and LES signals revealed the identities of neutral 共X兲 and ionic species 共Y+ and Z−兲 on the ice film surface. The mechanisms of RIS and LES processes on thin ice films have been explained previously.2 RIS gives a quantitative measure for the isotopomeric distribution of water molecules on the surface owing to the nature of the instantaneous RIS process.11 However, LES measures the isotopomeric distribution of hydronium ions only qualitatively because the Cs+ impact may induce additional H/D exchange reactions of hydronium ions before they are ejected from the surface. The probing depth of LES and RIS methods is 1 BL of the ice surface at an energy below 35 eV.11 The surface contamination by the Cs+ beam was made to be negligible 关⬍0.01 ML 共monolayer兲兴 during the kinetic measurement by employing conditions of low Cs+ exposure, which were typically an incident Cs+ flux of 1 ⫻ 1011 ionscm−2 s−1 with a spectral acquisition time ⬍80 s. Whenever necessary, fresh ice films were prepared for the kinetic measurement to reduce the accumulated Cs+ beam dose. III. EXPERIMENTAL RESULTS AND ANALYSIS Figure 1 shows LES and RIS spectra obtained from ice samples prepared under various conditions. At first, a polycrystalline D2O-ice film was grown on Ru共0001兲 at 135 K for a thickness of 8 BL, as mentioned above. Then, H2O was added onto the film surface for a partial coverage 共0.5 BL兲 after the sample temperature was lowered to 70 K. Figure 1共a兲 shows RIS signals measured from this surface. CsH2O+ and CsD2O+ signals appeared with about equal intensities at m / z = 151 and 153 amu/charge, respectively, representing the relative populations of H2O and D2O on the surface. A low intensity CsHDO+ signal 共m / z = 152 amu/ charge兲 was attributed to adsorption of HDO impurities from the background residual gas. At this temperature, a H/D exchange reaction of water molecules does not occur on a pure ice film surface.5 When the sample was warmed to 110 K and held at the same temperature for 10 min, CsHDO+ intensity increased noticeably, as shown in Fig. 1共b兲. The increased proportion of the HDO population was attributed to the occurrence of H/D exchange between H2O and D2O at the higher temperature. J. Chem. Phys. 133, 044709 共2010兲 FIG. 1. LES and RIS spectra measured from polycrystalline ice films that were prepared under the following conditions: 共a兲 adsorption of H2O 共0.5 BL兲 onto a D2O-ice film 共8 BL兲 at 70 K. 共b兲 10 min after warming the sample in 共a兲 at 110 K. 共c兲 Adsorption and ionization of HCl 共0.1 ML兲 onto a D2O-ice film 共8 BL兲 at 130 K. 共d兲 Adsorption of H2O 共0.6 BL兲 onto the sample in 共c兲 at 70 K. 共e兲 After the sample in 共d兲 was warmed to 110 K at a rate of 1 K s−1 and kept at this temperature for 1 min. The LES spectral region 共m / z ⱕ 25兲 is shown in the magnified scale 共⫻10兲 for all spectra. The Cs+ beam energy was 30 eV. In Figs. 1共c兲–1共e兲, we provided excess hydronium ions on ice films by adsorbing HCl onto the surface for a coverage of 0.1 ML. HCl was adsorbed onto a D2O-ice film at 70 K, and the sample was then heated to 130 K for 1 min to ionize the HCl. The ionization of the HCl to hydronium and chloride ions on the surface was evidenced by the appearance of hydronium ion signals 共HD2O+ at m / z = 21 and D3O+ at m / z = 22兲, shown in Fig. 1共c兲. Also, as reported previously,12 CsHCl+ signal due to molecular HCl disappeared from the heated surface 共not shown兲. D3O+ was the strongest hydronium ion signal from the surface, indicating that hydronium ions underwent extensive H/D exchange reactions with D2O at 130 K. Figure 1共d兲 shows a spectrum measured after the deposition of a submonolayer 共0.6 BL兲 of H2O onto the sample prepared in Fig. 1共c兲. The sample temperature was kept at 70 K during the H2O adsorption and the LES/RIS measurements. The H2O adsorption shifted the isotopomeric distribution of hydronium ions to the lower masses, and the H2DO+ signal became the strongest. These changes indicated the occurrence of proton transfer from D3O+, which was the major hydronium ion isotopomer in Fig. 1共c兲, to H2O at 70 K 共reaction 1兲. D3O+ + H2O → D2O + H2DO+ 共reaction 1兲. The H2O adsorption did not noticeably increase the CsHDO+ intensity. This observation suggested that single proton transfer events occurred predominantly from the hydronium ions Downloaded 27 Jul 2010 to 147.47.217.45. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 044709-3 Proton transfer at ice surfaces FIG. 2. Kinetic data showing the changes in H2O, HDO, and D2O surface populations with time for ice films with externally provided protons. The ice films were prepared in a similar structure to that shown in Fig. 1共d兲, i.e., adsorption of H2O 共0.5 BL兲 on a HCl 共0.1 ML兲/D2O 共8 BL兲 film. The samples were heated to the indicated temperature at a rate of 1 K s−1 and then maintained at this temperature during the kinetic measurement. The kinetic origin 共t = 0兲 was set to be the time that the sample reached this temperature. The error bars indicate the signal intensity fluctuations in repeated measurements. The incident energy of the Cs+ beam was 30 eV. The lines indicate the numerical solutions of kinetic equations 关Eq. 共A6兲 in Appendix兴 fitted to the experimental data. to the nearest neighbor H2O molecules. Note that HDO is formed only via multiple proton transfers between D3O+ and H2O. HDO can also be produced by single proton transfer from HD2O+ to H2O, but the initial population of HD2O+ was much smaller than D3O+ on the present surface. Figure 1共e兲 shows a spectrum obtained after warming the sample in Fig. 1共d兲 to 110 K. The CsHDO+ intensity was significantly increased. This indicated that H/D exchange reactions efficiently occurred via multiple proton transfers on the heated surface, which contrasted with the inefficient occurrence of H/D exchange reactions on a pure ice surface at 110 K 关Fig. 1共b兲兴 and on a proton-rich surface at 70 K 关Fig. 1共d兲兴. The relative population of H2O:HDO:D2O was 0.19:0.41:0.40 in Fig. 1共e兲 according to their RIS intensities, if the screening effect of the H2O adsorbates was neglected for the RIS intensities. This ratio indicated that the deuterium content in surface water molecules increased. Also, the spectrum shows an overall decrease in hydronium ion intensities, reflecting the increased solvation of hydronium ions on the surface at 110 K, which reduced their sputtering yield.7 We examined the kinetics of the H/D exchange reaction by monitoring the changes in RIS intensities of H2O, HDO, and D2O as a function of time. The kinetic measurements were made in a temperature range of 90–110 K for the ice films with excess hydronium ions and 110–130 K for the pure ice films. The temperature ranges examined for these samples were different because the H/D exchange reaction on pure ice films occurred to a measurable extent above 110 K. Figure 2 shows the kinetic data measured for the ice films J. Chem. Phys. 133, 044709 共2010兲 FIG. 3. Kinetic measurement of H2O, HDO, and D2O populations on the pure ice film surface. The ice samples were prepared to have the same structure as that in Fig. 1共a兲, i.e., H2O 共0.5 BL兲 on a D2O-ice film 共8 BL兲. The lines indicate the numerical solutions of kinetic equation 共A6兲. The experimental details are the same as those described in Fig. 2, except for the sample temperature. with excess hydronium ions. The ice films were prepared in a similar structure to that used in Fig. 1共d兲. At a temperature of 90 K 关Fig. 2共a兲兴, HDO population increased gradually during 10 min with the concomitant decrease in H2O and D2O populations. This showed a slow progress of the H/D exchange reaction. The reaction occurred more rapidly at 110 K 关Fig. 2共b兲兴. The surface populations of water isotopomers changed during ⬃2 min, after which the population ratio of H2O:HDO:D2O approached 0.17:0.44:0.39. The rapid increase of HDO population and the decrease of H2O population indicated that the H/D exchange reaction efficiently occurred on the surface. However, D2O population did not decrease as much as it was expected from the H/D exchange reaction. Since the initial isotopomeric composition of the surface was H2O : D2O = 0.6: 0.4, the observed population ratio indicated that D2O molecules were continually supplied to the surface while they were consumed by the H/D exchange reaction. As will be discussed later in detail, we consider that D2O molecules migrate from the film interior to the surface via self-diffusion at this temperature.11 In addition, H/D exchange reactions may occur between H2O on the surface and D2O in the second bilayer. Figures 3共a兲 and 3共b兲 present the kinetic measurements on the pure ice film surfaces performed at 110 and 130 K, respectively. The samples were prepared by depositing H2O 共0.5 BL兲 on a D2O-ice film 共8 BL兲 at 70 K, and then they were warmed to the indicated temperatures for the kinetic study. The surface population of D2O was higher than that of H2O at time “zero,” indicating that significant molecular Downloaded 27 Jul 2010 to 147.47.217.45. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 044709-4 J. Chem. Phys. 133, 044709 共2010兲 Moon, Yoon, and Kang mixing already occurred via self-diffusion during the sample heating period. Figure 3共a兲 shows that water isotopomeric populations changed slowly with time at 110 K. In Fig. 3共b兲, HDO population rapidly increased during the initial period of ⬃1 min at 130 K, but afterward it did not drastically change up to ⬃5 min. H2O population continuously decreased in this period, and D2O population increased. These behaviors indicated that self-diffusion was active at this temperature. The results of the kinetic measurement, such as those presented in Figs. 2 and 3, were analyzed in terms of a kinetic model that incorporates H/D exchange reactions and self-diffusion. The details of the underlying assumptions and the kinetic equations are given in Appendix. In brief, the overall reaction for the H/D exchange between H2O and D2O can be written as kf → H 2O + D 2O ← 2HDO 共reaction 2兲, FIG. 4. Arrhenius plot of the H/D exchange rate coefficients 共k兲 on ice film surfaces. The rate coefficients and the associated error bars are obtained by using the refined kinetic analysis 共see text兲. kb where kf and kb are the forward and backward rate coefficients. When the isotope effect is ignored, the microscopic reversibility predicts a relationship, kf = 4kb共=k兲, for the overall reaction. This relationship holds independent of the H/D exchange mechanism and the hydrogen bonding structure of the system. As a first-order approximation, we assume that H/D exchange reaction is solely responsible for the change in the surface populations of water isotopomers and that H/D exchange occurs only on the surface. With these assumptions, the differential rate expression for the H/D exchange can be analytically solved. The resulting first-order kinetic equation 关Eq. 共A3兲 in Appendix兴 explains the observed variation in HDO population reasonably well, as can be seen in the linear plots presented in Fig. 5. However, this simplified model does not satisfactorily explain the variation in H2O and D2O populations at high temperatures and at long observation times. Therefore, we make improvements on the kinetic model by incorporating the H/D exchange reaction occurring in the vertical direction 关reactions A4兴 and the interlayer migration of water isotopomers due to self-diffusion 关reactions A5兴, as described in Appendix. The differential rate expression resulting from this refined kinetic model is rather complex 关Eqs. 共A6兲–共A8兲兴. The solutions of Eqs. 共A6兲–共A8兲 are obtained by numerical integration, and they are fitted to the experimental kinetic data. From the optimized kinetic curve fitting, the H/D exchange rate coefficient 共k兲 and the diffusion rate coefficient 共kd兲 are deduced. Figures 2 and 3 show the theoretical kinetic curves fitted to the experimental data for the proton-rich and pure ice films, respectively. The k values deduced from this process are plotted in Fig. 4. The k values obtained from the simple and refined models agree within 30% when the temperature is 90–100 K for the proton-rich film and 110–120 K for the pure ice film. This indicates that the H/D exchange reaction on the surface dominates the kinetic features observed at the low temperatures, whereas the self-diffusion and the vertical H/D exchange reaction are relatively suppressed, thereby justifying the assumptions of the simple kinetic model. However, the k values from the two models differ by 2.7 times for the proton-rich surface at 110 K, and by 2.1 times for the pure ice surface at 130 K. Close inspection of the factors contributing to the kinetic curves at the high temperatures reveals that self-diffusion is the most important, and H/D exchange reactions have only minor contributions. Accordingly, the k values deduced from the high-temperature kinetic data have large uncertainty. The activation energy of the H/D exchange on the ice surface is estimated from the Arrhenius plot of k, as shown in Fig. 4. Only the two values at low temperatures are used for each surface to calculate the activation energy, for the reason mentioned above. The estimated activation energy is Ea = 10⫾ 3 kJ mol−1 for the proton-rich surface and Ea = 17⫾ 4 kJ mol−1 for the pure ice surface. Apparently, excess protons on the ice surface significantly reduce the energy barrier of H/D exchange reaction. However, the barrier height still remains substantial on the proton-rich surface. It must be emphasized that the result of the Ea measurement for the ice surfaces varies depending sensitively on the experimental conditions, in particular, the ice surface structure, regardless of whether excess protons are present on the surface or not. Even for a polycrystalline ice film, we observed that the absolute Ea value changed by 4 kJ mol−1 when the ice films were grown in slightly different conditions. Such sensitivity of Ea to the ice surface condition was most likely due to the fact that the activation energy was measured for the reaction occurring at the outermost surface. In this respect, the Ea values reported here may be relevant only for a polycrystalline ice film grown specifically at 135 K, rather than for ice films in general. Despite the variance of Ea with the ice surface conditions, the experiments performed with different sample sets showed consistently that a proton-rich surface had a substantially lower Ea value than a pure ice surface. IV. DISCUSSION Depending on whether an ice film surface has excess protons or not, H/D exchange reactions on the surface may occur in different mechanisms. On the proton-rich surface, Downloaded 27 Jul 2010 to 147.47.217.45. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 044709-5 J. Chem. Phys. 133, 044709 共2010兲 Proton transfer at ice surfaces the H/D exchange occurs via the transport of excess protons. The passage of excess protons 共or deuterons兲 through the hydrogen bond in the H2O – D2O mixture surface eventually generates HDO species and various hydronium ion isotopomers. Such processes can be exemplified by reaction 1 in Sec. III. Note that HDO can be formed without the reorientational motion of water molecules on the surface, and the water reorientation is energetically more difficult to occur than the proton transfer.13 On this surface, the study of H/D exchange reaction reveals proton transfer kinetics. On the other hand, the pure ice surface has a very small population of intrinsic hydronium ions. For a H/D exchange reaction to occur on this surface, thermal ionization of water molecules 共reaction 3兲 is necessary, 2H2O ↔ H3O+ + OH− 共reaction 3兲. Therefore, the H/D exchange mechanism on the pure ice surface involves at least two basic steps: ion pair formation 共reaction 3兲 and proton transfer 共reaction 1兲. The ion pair formation is energetically more demanding and it is most likely the rate-limiting step of the reaction. As a result, the H/D exchange kinetics observed on the pure ice surface contains convoluted information of ion pair formation and proton transfer. The analysis of the H/D exchange kinetics on the protonrich surface in Sec. III reveals that the reaction occurs with substantial activation energy 共10⫾ 3 kJ mol−1兲. This energy is interpreted as a proton transfer energy barrier on the surface, as explained above. The observation shows that the proton transfer requires overcoming an energy barrier and it must be assisted by thermal energy. As Fig. 1共d兲 shows, the proton transfer occurs from hydronium ions mostly to adjacent water molecules at a temperature of 70 K. The proton transfer rate and distance increase upon raising the temperature above 90 K, increasing the H/D exchange efficiency at a higher temperature 共Fig. 2兲. On the pure ice surface, the H/D exchange reaction occurs relatively inefficiently due to the lack of protons to mediate the reaction. The reaction involves a higher activation energy 共Ea = 17⫾ 4 kJ mol−1兲 than that on the proton-rich surface, and perhaps a larger pre-exponential factor as can be seen from the Arrhenius plots of k 共Fig. 4兲. These Arrhenius parameters may be associated with the ion pair formation, which is most likely the rate-limiting step of the reaction, and the proton transfer process. The existence of a substantial energy barrier for proton transfer on the ice surface agrees with recent observations on the properties of protons at ice surfaces.3–7 They show that a proton exhibits thermodynamic affinity for the ice surface due to its being energetically stabilized as a surface hydronium ion relative to its presence in the tetrahedral ice lattice as an ionic defect.3,6,7 Therefore, the release of a proton from a stable hydronium ion for the proton transfer will require extra energy. This interpretation is also consistent with the incomplete proton transfer between a hydronium ion and weak base molecules on ice surfaces observed in another investigation,14 although the acid-base reactions readily proceed to completion in aqueous solutions. The present observations indicate that proton transfer characteristics may be quite different at the surface and interior of an ice crystal. There is a consensus that an excess proton in a crystalline ice lattice moves with negligible energy barrier in a concerted fashion.15,16 The present result contrasts with the observation of a very efficient H/D exchange reaction on a H2O – D2O mixture film when HCl is directly adsorbed onto the surface at a low temperature 共95 K兲.5 Such different observations in the two experiments can be attributed to the fact that the adsorption and ionization of HCl on the ice surface releases a large amount of exothermic chemical energy. This extra energy induces additional proton transfers before the energy is dissipated into the solid. On the other hand, such an extra energy effect is eliminated in the present experiment where the H/D exchange reaction is examined on the ice surface with preexisting excess protons. The adsorption of water molecules on the ice surface also releases a certain amount of exothermic energy. Apparently, however, this energy is relatively small and produces a minor effect compared to that of direct HCl adsorption. V. CONCLUSION This work examined the energy barrier of proton transfers at the outermost surface of an ice film through the measurement of the H/D exchange reaction on the surface with excess protons. The energy barrier was estimated to be 10⫾ 3 kJ mol−1 on a polycrystalline ice film that was grown at 135 K, although this energy varied with the ice surface morphology. At a temperature of 70 K, proton transfer occurred from hydronium ions mostly to adjacent water molecules, and the proton transfer rate and distance increased with temperatures above 90 K. The present result, combined with observations from previous studies,3–7 offers a coherent explanation for the properties of protons at ice surfaces, by demonstrating that a proton is energetically trapped at the surface and its movement along the surface involves a substantial energy barrier. The activation energy of the H/D exchange reaction on a pure ice surface was estimated to be 17⫾ 4 kJ mol−1, which was contributed from the ion pair formation energy as well as the proton transfer barrier. ACKNOWLEDGMENTS This work was supported by the National Research Foundation grant funded by the Korean government 共MEST兲 through the Center for Space-Time Molecular Dynamics 共No. R11-2010-0001638兲. APPENDIX: EVALUATION OF THE H/D EXCHANGE RATE COEFFICIENTS FROM THE KINETIC DATA We consider two kinetic models for analyzing the H/D exchange kinetics observed on the ice film surfaces. In the first model, it is assumed that H/D exchange reaction is confined in the outermost surface layer of an ice film and that the molecular mixing of water isotopomers due to selfdiffusion is suppressed. As we will see shortly, these approximations are reasonable when the H/D exchange reac- Downloaded 27 Jul 2010 to 147.47.217.45. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 044709-6 J. Chem. Phys. 133, 044709 共2010兲 Moon, Yoon, and Kang proton-rich ice film and Ea = 20⫾ 4 kJ mol−1 for the pure ice film. This model, however, does not satisfactorily explain the kinetic curves of 关H2O兴 and 关D2O兴 at a high-temperature and at a long observation time. The disagreement indicates that other processes than the lateral H/D exchange reaction on the surface also take place under these conditions. Next, we improve the kinetic model by incorporating the H/D exchange reaction occurring in the vertical direction and the migration of water isotopomers due to self-diffusion. We consider that the vertical H/D exchange occurs between the water molecules in the adjacent ice bilayers. These processes are represented by reactions 共A4兲, kv FIG. 5. First-order kinetic fitting to the change in HDO surface concentration with time for ice films with externally provided protons 共solid symbols兲 and for pure ice films 共open symbols兲. The straight lines indicate the rate expression shown in Eq. 共A3兲. The kinetic data are the same ones as those presented in Figs. 2 and 3. H2Oi + D2Oadj ↔ HDOi + HDOadj , 1/4kv kv D2Oi + H2Oadj ↔ HDOi + HDOadj , 1/4kv tion occurs at a low temperature. In this case, the H/D exchange reaction between H2O and D2O at the ice surface can be written as 1/2kv 共A4兲 HDOi + H2Oadj ↔ H2Oi + HDOadj , 1/2kv k H2O共s兲 + D2O共s兲 ↔ 2HDO共s兲. 1/4k 共A1兲 1/2kv HDOi + D2Oadj ↔ D2Oi + HDOadj . 1/2kv The forward and backward rate coefficients have the ratio of 4:1, as explained for reaction 2 in Sec. III.A mass conservation relationship holds for the molecules in the outermost surface layer, 关HDO兴 − 关HDO兴0 = −2共关H2O兴 − 关H2O兴0兲 = −2共关D2O兴 − 关D2O兴0兲, where 关HDO兴 is the surface coverage of HDO at time t, 关HDO兴0 is the initial surface coverage, and so forth. The rate expression of reaction 共A1兲 is given by 1 1 d关HDO兴 = k关H2O兴关D2O兴 − k关HDO兴2 . 2 dt 4 共A2兲 This differential rate expression can be integrated to the firstorder kinetic equation and its analytical solution is given by Eq. 共A3兲, 关HDO兴t = 2关H2O兴0关D2O兴0 + 关HDO兴0 − 21 关HDO兴20 − 共2关H2O兴0关D2O兴0 + 21 关HDO兴20兲exp共− kt兲 = 2f H f D − 共2f H f D − 关HDO兴0兲exp共− kt兲 = c2 − c1 exp共− kt兲. 共A3兲 Here, f D represents the fraction of deuterium in surface water molecules, defined by f D = 关HDO兴 / 2 + 关D2O兴. The integrated rate expression of Eq. 共A3兲 is used to fit the experimental kinetic data in the form of ln关共c2 − 关HDO兴t兲 / c1兴 = −kt. Figure 5 presents the kinetic plot, which shows a good straight line for the variation in 关HDO兴. The slope of the linear plot gives the H/D exchange rate coefficient k. As we estimate the activation energy of the H/D exchange from the Arrhenius plot of the k values, we obtain Ea = 7.5⫾ 1.5 kJ mol−1 for the Here, H2Oi denotes a H2O molecule located in the ith layer, H2Oadj denotes a molecule in the adjacent layer 关共i + 1兲th or 共i − 1兲th layer兴, and so forth. kv is the rate coefficient of the vertical H/D exchange reaction between the water molecules in the adjacent layers connected through a hydrogen bond. The forward and backward rate coefficients for these reactions have a specific ratio due to the microscopic reversibility, and the ratio is indicated in the reaction formula. The kv value cannot be determined from the experiment. Therefore, we seek for a theoretical relationship between kv and the lateral H/D exchange rate coefficient 共k兲 from the consideration of the proton transfer path degeneracy. For this, we assume that the ice sample has a full-bilayer terminated 共0001兲 surface of hexagonal ice.1 Also, it is assumed that the rate of each proton transfer event through a hydrogen bond is the same independent of the direction of the proton transfer, i.e., whether it occurs along the 共0001兲 basal plane or in the normal direction. Water molecules at the surface are hydrogen-bonded to three neighboring molecules located in the first bilayer. Among these surface molecules, only half of them 共those in the lower part of the first bilayer兲 make one vertical hydrogen bond to a molecule in the second bilayer. Therefore, the number of the proton transfer events occurring along the surface plane and in the vertical direction has the ratio of 6:1, and a relationship k = 6kv can be deduced for surface water molecules. Self-diffusion in the ice sample can also change the relative surface population of water isotopomers without the occurrence of H/D exchange reactions. The interlayer migration of water isotopomers is described by reactions 共A5兲 with the corresponding rate coefficient kd, Downloaded 27 Jul 2010 to 147.47.217.45. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp 044709-7 J. Chem. Phys. 133, 044709 共2010兲 Proton transfer at ice surfaces kd H2Oi↔ H2Oadj , kd kd HDOi↔ HDOadj , 共A5兲 kd kd D2Oi↔ D2Oadj . kd The ice surface layer that is diffusionally activated gets thicker at a higher temperature.6 We estimate that the thickness of the diffusion layer increases from 2 BL at 110 K to 4 BL at 130 K, based on the information about the amount of D atoms contained in the surface water molecules in the data shown Figs. 2 and 3, and the result of self-diffusion studies in the ice surface region.6 When the kinetic model includes the lateral H/D exchange reaction, the vertical H/D exchange reaction, and the self-diffusion, the following kinetic equations are derived for the changes in H2O, D2O, and HDO surface populations: d 关H2O兴i = − k关H2O兴i共关D2O兴i + 61 关D2O兴i+1 + 61 关D2O兴i−1 dt + 1 12 共关HDO兴i+1 + 1 12 k关HDO兴i + 关HDO兴i−1兲兲 + 关H2O兴i+1 + 21 共关HDO兴i−1 + 关HDO兴i+1兲兲 共A6兲 d 关D2O兴i = − k关D2O兴i共关H2O兴i + 61 关H2O兴i+1 + 61 关H2O兴i−1 dt + 1 12 共关HDO兴i+1 + 1 12 k关HDO兴i + 关HDO兴i−1兲兲 共3关HDO兴i + 关D2O兴i−1 + 关D2O兴i+1 + 21 共关HDO兴i−1 + 关HDO兴i+1兲兲 + kd共关D2O兴i−1 + 关D2O兴i+1 − 关D2O兴i兲, d关HDO兴i = − d关H2O兴i − d关D2O兴i . V. F. Petrenko and R. W. Whitworth, Physics of Ice 共Oxford University, Oxford, 1999兲, Chap. 10. 2 H. Kang, Acc. Chem. Res. 38, 893 共2005兲. 3 N. Uras-Aytemiz, C. Joyce, and J. P. Devlin, J. Chem. Phys. 115, 9835 共2001兲. 4 R. Vácha, V. Buch, A. Milet, J. P. Devlin, and P. Jungwirth, Phys. Chem. Chem. Phys. 9, 4736 共2007兲. 5 S.-C. Park, K.-H. Jung, and H. Kang, J. Chem. Phys. 121, 2765 共2004兲. 6 C. W. Lee, P. R. Lee, Y. K. Kim, and H. Kang, J. Chem. Phys. 127, 084701 共2007兲. 7 E.-S. Moon, C.-W. Lee, and H. Kang, Phys. Chem. Chem. Phys. 10, 4814 共2008兲. 8 E.-S. Moon, C.-W. Lee, J.-K. Kim, S.-C. Park, and H. Kang, J. Chem. Phys. 128, 191101 共2008兲. 9 J. P. Cowin, A. A. Tsekouras, M. J. Iedema, K. Wu, and G. B. Ellison, Nature 共London兲 398, 405 共1999兲. 10 A. Hodgson and S. Haq, Surf. Sci. Rep. 64, 381 共2009兲. 11 K.-H. Jung, S.-C. Park, J.-H. Kim, and H. Kang, J. Chem. Phys. 121, 2758 共2004兲. 12 S.-C. Park and H. Kang, J. Phys. Chem. B 109, 5124 共2005兲. 13 P. J. Wooldridge and J. P. Devlin, J. Chem. Phys. 88, 3086 共1988兲. 14 S.-C. Park, J.-K. Kim, C.-W. Lee, E.-S. Moon, and H. Kang, ChemPhysChem 8, 2520 共2007兲. 15 M. Eigen, Angew. Chem., Int. Ed. Engl. 3, 1 共1964兲. 16 C. Kobayashi, S. J. Saito, and I. Ohmine, J. Chem. Phys. 113, 9090 共2000兲. 1 共3关HDO兴i + 关H2O兴i−1 + kd共关H2O兴i−1 + 关H2O兴i+1 − 关H2O兴i兲, from Eqs. 共A6兲–共A8兲 with predetermined values of k and kd; the initial k value is obtained from a kinetic plot using the first model 共Fig. 5兲 and kd is from literature.6 The kinetic curves thus calculated are fitted to the experimental kinetic data. Then, the kinetic curves are improved by adjusting the k and kd values until the mean-square error in the curve fitting is minimized. Figures 2 and 3 show the result of the optimized curve fitting for the proton-rich and pure ice films, respectively. The k value derived from this refined kinetic analysis differs by less than 30% from the initial k value deduced from the first kinetic model when the temperature is 90–100 K for the proton-rich film and 110–120 K for the pure ice film. This illustrates that the dominant process at the low temperatures is the H/D exchange reaction on the surface, and the self-diffusion and the vertical H/D exchange reaction are relatively suppressed, justifying the assumptions used in the first kinetic model. The observation also agrees with the result of previous studies.5 On the other hand, the refined kinetic analysis changes the k value by 2.7 times for the proton-rich film at 110 K and by 2.1 times for the pure ice film at 130 K. Close inspection of the factors contributing to these kinetic curves reveals that the curve shape is determined mainly by self-diffusion at the high temperatures and the H/D exchange reactions are less important. 共A7兲 共A8兲 The differential equations 共A6兲–共A8兲 cannot be solved analytically, and thus we obtain their numerical solutions. A software package embedded in MATHEMATICA is used. The kinetic curves for 关H2O兴, 关D2O兴, and 关HDO兴 are calculated Downloaded 27 Jul 2010 to 147.47.217.45. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp