Download Energy barrier of proton transfer at ice surfaces

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
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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
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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
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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,
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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-
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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,
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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.
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N. Uras-Aytemiz, C. Joyce, and J. P. Devlin, J. Chem. Phys. 115, 9835
共2001兲.
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R. Vácha, V. Buch, A. Milet, J. P. Devlin, and P. Jungwirth, Phys. Chem.
Chem. Phys. 9, 4736 共2007兲.
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S.-C. Park, K.-H. Jung, and H. Kang, J. Chem. Phys. 121, 2765 共2004兲.
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C. W. Lee, P. R. Lee, Y. K. Kim, and H. Kang, J. Chem. Phys. 127,
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E.-S. Moon, C.-W. Lee, and H. Kang, Phys. Chem. Chem. Phys. 10,
4814 共2008兲.
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E.-S. Moon, C.-W. Lee, J.-K. Kim, S.-C. Park, and H. Kang, J. Chem.
Phys. 128, 191101 共2008兲.
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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.
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K.-H. Jung, S.-C. Park, J.-H. Kim, and H. Kang, J. Chem. Phys. 121,
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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
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