THE JOURNAL OF CHEMICAL PHYSICS 127, 084701 共2007兲
Mechanistic study of proton transfer and H / D exchange in ice films
at low temperatures „100– 140 K…
Chang-Woo Lee, Poong-Ryul Lee, Young-Kwang Kim, and Heon Kanga兲
Department of Chemistry, Seoul National University, Gwanak-gu, Seoul 151-747, Republic of Korea
共Received 4 May 2007; accepted 22 June 2007; published online 22 August 2007兲
We have examined the elementary molecular processes responsible for proton transfer and H / D
exchange in thin ice films for the temperature range of 100– 140 K. The ice films are made to have
a structure of a bottom D2O layer and an upper H2O layer, with excess protons generated from HCl
ionization trapped at the D2O / H2O interface. The transport behavior of excess protons from the
interfacial layer to the ice film surface and the progress of the H / D exchange reaction in water
molecules are examined with the techniques of low energy sputtering and Cs+ reactive ion
scattering. Three major processes are identified: the proton hopping relay, the hop-and-turn process,
and molecular diffusion. The proton hopping relay can occur even at low temperatures 共⬍120 K兲,
and it transports a specific portion of embedded protons to the surface. The hop-and-turn
mechanism, which involves the coupling of proton hopping and molecule reorientation, increases
the proton transfer rate and causes the H / D exchange of water molecules. The hop-and-turn
mechanism is activated at temperatures above 125 K in the surface region. Diffusional mixing of
H2O and D2O molecules additionally contributes to the H / D exchange reaction at temperatures
above 130 K. The hop-and-turn and molecular diffusion processes are activated at higher
temperatures in the deeper region of ice films. The relative speeds of these processes are in the
following order: hopping relay⬎ hop and turn⬎ molecule diffusion. © 2007 American Institute of
Physics. 关DOI: 10.1063/1.2759917兴
I. INTRODUCTION
Fundamental molecular processes, such as the motions
of protons, defects, and water molecules, control the dielectric and conductive properties of ice.1,2 Ice is a model material for the study of proton transport mechanisms, which can
provide understanding applicable to many hydrogen-bonded
solids. The general concept of charge conduction by proton
transfer in an ice crystal, which is illustrated in Fig. 1, is now
well established.1,2 Protons can jump between adjacent molecules along successive hydrogen bonds. Such a proton hopping relay, however, cannot continue indefinitely in an ice
lattice constructed according to the “ice rules” and stops after
a certain distance. The proton passage along the hydrogenbonded chain polarizes the bond direction so that a second
proton cannot pass along the same path. Thus, for the continuous flow of protons it is necessary that orientational
共Bjerrum兲 defects exist and they move by reorientation of
water molecules. The combination of proton hopping and
molecular reorientation extends the passage of protons by the
so-called hop-and-turn mechanism.
Various experimental approaches have been made to examine the proton transfer mechanisms in ice.1–15 Since the
19th century the electrical conductivity of ice has been measured by placing metal electrodes on an ice crystal sample.3,4
However, such experiments are often hampered by the difficulty in controlling and characterizing the space charge layer
formed at the ice/electrode interfaces. More recently, specAuthor to whom correspondence should be addressed. Tel.: ⫹82-2-8757471; Fax: ⫹82-2-889-1568; Electronic mail: [email protected]
a兲
0021-9606/2007/127共8兲/084701/8/$23.00
troscopic techniques have been used to explore the proton
and defect dynamics in ice.5–15 Using IR spectroscopy, Devlin and co-workers5–7 studied the H / D isotopic exchange of
water molecules in ice nanocrystals doped with externally
provided protons, and they showed explicit evidence for the
occurrence of hop-and-turn processes at temperatures above
130 K. NMR spectroscopy has provided information about
FIG. 1. Illustration of proton transfer mechanism in ice. The threedimensional ice lattice is represented by the so-called square ice in two
dimensions for convenience. Hydrogen bonding is shown by the dotted
lines. 共a兲 H3O+ indicates a water molecule with an extra proton 共ionic defect兲, and D and L indicate two types of orientational 共Bjerrum兲 defects. 共b兲
A proton jumps along successive hydrogen bonds as shown by the arrows
until its passage is blocked, here, for example, by the D defect. 共c兲 Rotation
of a water molecule opens a new path, and 共d兲 proton hopping continues.
127, 084701-1
© 2007 American Institute of Physics
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084701-2
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Lee et al.
the location and motion of protons in ice.8,9 Geil et al.9 performed NMR stimulated-echo experiments with ice crystals
in the temperature range of 160– 260 K and revealed two
types of proton transfer processes: a fast process mediated by
Bjerrum defect dynamics and a slow process that is attributed to interstitial diffusion of water molecules at the higher
temperatures. Cowin et al.13 deposited hydronium ions on ice
films from low energy beams and observed that the surface
protons were immobile across the films over the temperature
range of 30– 190 K. Park et al.14 adsorbed HCl onto ice films
and studied the H / D exchange reaction in surface water molecules. They observed that proton transfer was active only in
the lateral direction at the film surface, while vertical proton
transfer to the film interior was almost absent at 90– 140 K.14
The proton behaviors observed in these studies seem to contradict each other, while the IR and NMR experiments5–7,9
show that protons are mobile in ice at elevated temperatures,
for instance, at T ⬎ 130 K in ice nanocrystals, protons deposited at the surface of ice films do not transfer to the interior at
the corresponding temperatures.13,14
Recently, Lee et al.15 offered an explanation for this contradiction by showing that protons exhibit asymmetric transport behaviors at the surface and interior of ice due to the
thermodynamic affinity of protons for the ice surface. However, the detailed molecular features of proton transfer in ice
are not yet fully understood. It is desirable to identify specific elementary processes contributing to proton transfer and
explore their operating temperature and distance ranges. The
present study pursues these objectives in experiments with
thin ice films prepared at low temperatures 共100– 140 K兲.
excess protons are trapped between the D2O and H2O layers.
H2O and D2O molecules do not mix by self-diffusion at
100 K.16 The thickness of the ice films was checked by
temperature-programed desorption experiments.
The chemical composition and the isotopomeric abundance of molecules at the film surfaces were analyzed by the
techniques of Cs+ reactive ion scattering 共RIS兲 and low energy sputtering 共LES兲. The principle and instrumentation for
these techniques have been described in detail elsewhere.21,24
Briefly, a Cs+ beam of low energy 共⬍100 eV兲 is generated
from a surface-ionization source 共Kimball Physics兲 and is
scattered from a target surface. Neutral molecules at the surface are picked up by the Cs+ projectiles, forming
Cs+-molecule cluster ions 共RIS process兲. Ions preexisting at
the surface are ejected by the impact of low energy Cs+ ions
共LES process兲. These ions are detected by a quadrupole mass
spectrometer with its ionizer filament switched off. The Cs+
beam energy was 30 eV in the present experiments, unless
specified otherwise, and the beam current density was maintained below 1.0 nA cm−2 to avoid surface contamination by
incident Cs+ ions. The beam incidence and detection angles
were 65° and 75°, respectively, from the surface normal.
Such a low-angle geometry was effective for detecting molecules on ice films. Under these conditions the Cs+ impact
did not cause secondary ionization of water molecules at the
surfaces.19,20
II. EXPERIMENT
We studied the proton transfer in ice films by monitoring
the proton population at the surface of ice films embedded
with excess protons. For this study, ice films were prepared
by D2O deposition to a thickness of 2 BL at 140 K and then
HCl exposure to 0.1 L. Figure 2共a兲 shows the positive ion
mass spectrum of LES and RIS experiments obtained from
this surface. The RIS signal of CsD2O+ at
m / z = 153 amu/charge is due to the pickup of surface D2O
molecules by Cs+ projectiles. The LES peak at m / z
= 22 amu/charge represents D3O+ emitted from the surface
due to Cs+ impact, and the peak at m / z = 42 is its hydration
complex 共D5O+2 兲. The K+ peak is due to the scattering of
ionic impurities contained in the Cs+ beam. The hydronium
ion peaks, together with the absent RIS signal of CsHCl+
共m / z = 169兲, confirm the ionization of HCl to hydronium ions
at the surface.18–20 In the text, “hydronium ion” refers to any
or all of H3O+, H2DO+, HD2O+, and D3O+ species without
isotopomeric distinction. The isotopomeric abundance of
D3O+ is much higher than that of HD2O+ at the surface, in
agreement with the observations14,15 that H / D exchange reaction is facilitated at the ice surfaces in the presence of extra
protons.
Next, an H2O overlayer was deposited at a thickness of 4
BL at 100 K on top of the film. This forms a “protonsandwich” ice film, where excess protons are located at the
interface of the bottom D2O layer and the upper H2O layer,
as depicted in the inset of Fig. 2共b兲. Figure 2共b兲 shows that
CsH2O+ is the only RIS peak observed from the film surface,
A Ru共0001兲 single crystal was used as a substrate for
growing ice films, and it was installed on the temperaturecontrolled stage of a sample manipulator in an ultrahigh
vacuum chamber which has the base pressure of 5
⫻ 10−11 Torr. The Ru crystal was cleaned by repeated cycles
of Ar+ sputtering, O2 oxidation, and annealing at 1500 K. Ice
films were grown on the Ru surface by backfilling the chamber with H2O or D2O vapor at a partial pressure of 1
⫻ 10−8 Torr. Liquid water samples were degassed through
freeze-vacuum-thaw cycles, and HCl gas 共Aldrich, 99+ %
purity兲 was used as purchased. Separate leak valves were
used for these gases to prevent isotopic mixing in the introductory lines. HCl gas was guided close to the sample surface by a tube doser, which reduced its partial pressure in the
chamber below 1.0⫻ 10−9 Torr during the exposure. To prepare an ice film, we first deposited D2O on Ru共0001兲 at low
temperature to a thickness of 2 BL and warmed it to 140 K.16
The D2O film was used as the interface layer between the
Ru共0001兲 surface and the ice film to be grown, because D2O
forms a well-ordered ice structure without dissociation at the
surface.17 Subsequently, a small amount of HCl gas 共typically 0.1 L exposure兲 was adsorbed onto the D2O film at
140 K to provide excess protons. HCl completely ionizes to
hydronium and chloride ions on ice at this temperature.18–20
Then, a H2O overlayer was deposited at 100 K to give a
thickness of 2–8 BL, thereby providing a structure in which
III. RESULTS
A. Temperature dependence of proton transfer in ice
film
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084701-3
Proton transfer and H / D exchange in ice films
J. Chem. Phys. 127, 084701 共2007兲
FIG. 3. LES and RIS spectra measured from a proton-sandwiched film at
140 K. The sample consists of an underlying D2O layer 共2 BL兲, a protonsandwich layer 共0.1 ML兲, and a H2O overlayer 共4 BL兲. The H2O overlayer
is deposited at 100 K and warmed to 140 K in 2 min.
FIG. 2. 共a兲 LES and RIS spectra from a D2O-ice film adsorbed with HCl for
the exposure ⬃0.1 L at 140 K. 共b兲 LES and RIS spectra from a protonsandwiched ice film maintained at 100 K. The sample was prepared by
depositing a H2O overlayer on top of the film in 共a兲, as depicted in the
figure. The intensity scale is counts/s.
indicating negligible diffusional mixing of H2O and D2O
molecules in the film at this temperature. A LES spectrum
shows H3O+ and its hydrated cluster 共H5O+2 兲. These peaks
indicate that protons migrate from the sandwich layer to the
surface at 100 K. Noticeably, however, deuterated isotopomers of hydronium ions are absent from the surface. This
indicates that only H+ 共not D+兲 migrates to the surface. The
H3O+ peak appears immediately after the sample preparation
and its intensity does not increase noticeably with time.
The observed H+ migration to the surface indicates proton transfer by the hopping relay process. Note that in this
process only H+ can transfer through the H2O overlayer
without the rotation of water molecules 共see Fig. 1兲. The
proton hopping relay can only have a limited length of successful proton transfer in ice.2 However, it can transport a
specific portion of excess protons across a short distance
such as the present film thickness.
We examined proton transfer through the ice film at the
elevated temperature of 140 K. The ice film was prepared in
the same manner as that of Fig. 2共b兲, and then the film was
warmed to 140 K for subsequent LES and RIS measurements. The spectrum observed at 140 K 共Fig. 3兲 shows several features that can be distinguished from those appearing
at 100 K. First, the hydronium ion signal contains a large
portion of D-substituted species 共H2DO+, HD2O+, and
D3O+兲. Second, the total intensity of hydronium ions is increased. This increase is largely due to the appearance of
deuterated hydronium ions, but the H3O+ intensity is also
increased to a certain extent. Third, RIS signals of CsHDO+
and CsD2O+ reveal the presence of deuterated water molecules at the surface.
The deuterated forms of hydronium ions and water molecules in the spectrum indicate that the H / D exchange reaction propagates from the bottom D2O layer to the surface.
Also, the increased hydronium ion signals indicate an enhanced rate of proton transfer. These observations suggest a
new proton transfer channel operating at 140 K and causing
the H / D exchange between water molecules. This channel
can be attributed to the hop-and-turn mechanism. As illustrated in Fig. 1, the movement of Bjerrum defects by reorientation of water molecules creates additional paths for proton hopping, thus increasing both the length and rate of
proton transfers. The recurrence of such hop-and-turn processes can transport D+ from the bottom D2O layer to the
surface.
The observed increase in hydronium ion intensity is not
due to a morphological change that an ice film undergoes as
it is heated from an amorphous state at 100 K to a crystalline
phase at 140 K. LES efficiency is not significantly affected
by the surface morphology of an ice film.14 The efficiency
with which the surface scatters Cs+ projectiles does increase
by two orders of magnitude from an amorphous to a crystalline ice surface.16 However, the ratio of Cs+-water to Cs+
signal intensity, which is a measure of the population of surface molecules, does not change significantly.
We examined the proton transfer efficiency by the hopping relay and hop-and-turn processes for the temperature
range of 100– 140 K. The H3O+ intensity gives a measure of
the occurrence of the hopping relay process, and the
D-substituted hydronium ion intensities 共H2DO+, HD2O+,
and D3O+兲 gives that of the hop-and-turn process. Figure 4
shows the variation in these ion intensities as the film temperature is increased from 100 to 140 K at a rate of
2 K min−1. The intensities shown are normalized against
those from a reference sample, which is an ice film with
excess protons at the surface rather than in the sandwich
layer, prepared by depositing 0.1 L of HCl on top of a pure
ice film at a fixed temperature of 140 K. In Fig. 4, the surface population of H3O+ is significant even at 100 K and
increases slowly with increasing temperature. In contrast, the
temperature dependence of D-substituted hydronium ions is
rather dramatic. The D-substituted signals are absent from
the surface below 120 K, but their intensity rapidly increases
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084701-4
Lee et al.
FIG. 4. Change in hydronium ion and chloride ion intensities measured by
LES as a function of ice film temperature. The ice film has a sandwich
structure of H2O共4 BL兲 / HCl共0.1 ML兲 / D2O共2 BL兲 / Ru共0001兲. The sample
is heated continuously during the measurement from 100 to 140 K at a rate
of 2 K min−1. The intensities for H3O+ 共䉭兲 and deuterated hydronium ions
共䉲兲 共HnD3−nO+, n = 0 – 2兲 are separately plotted. The intensities shown are
normalized against those from a reference sample, which is an ice film of 6
BL thickness with 0.1 L of HCl adsorbed at 140 K; the total hydronium ion
intensity 共HnD3−nO+, n = 0 – 3兲 from this reference surface is set to be 1.0 on
the ordinate. The chloride ion signal 共䊊兲 is basically absent from the surface
for T ⬍ 145 K; its abrupt increase at 150 K is due to rapid desorption of
water molecules. The error bars indicate the fluctuations in repeated
measurements.
above this temperature. This gives clear evidence for the
thermally activated nature of the hop-and-turn mechanism,
which requires the rotation of water molecules. At 140 K, the
total intensities of H3O+ and D-substituted hydronium ions
approach the value measured on the reference ice film which
has excess protons at the surface. This indicates that the major portion of excess protons move from the sandwich layer
to the surface at 140 K.
Also shown in Fig. 4 is the intensity of Cl− ions measured by LES in the negative ion detection mode, again normalized with respect to the reference surface adsorbed with
HCl. The result shows that Cl− does not migrate from the
sandwich layer to the surface at temperatures 艋140 K during
the time of measurement 共5 min兲, while protons build up a
substantial surface population. Thus, proton transport to the
surface is not driven by the electrostatic forces from Cl− but
by the thermodynamic forces originating from proton affinity
to the ice surface, as asserted in a previous work.15 The proton transport results in charge separation near the film surface, and somewhat analogous phenomena have been reported for the dissolution of electrolytes in ice films.22,23
We examined the effect of H2O overlayer thickness on
proton transfer efficiency. When the overlayer is deposited to
a thickness of 8 BL, in comparison to 4 BL in Fig. 4, 20% of
excess protons in the sandwich layer move to the surface
under similar conditions, i.e., upon raising the temperature
from 100 to 140 K at a rate of 2 K min−1. The composition
of surface hydronium ion is dominantly H3O+ at this stage.
Extension of the measurement time while maintaining the
sample at 140 K gradually increases the population of deuterated hydronium ions. After 30 min, 50% of excess protons
reach the surface. This shows that proton transfer efficiency
is substantially reduced by increasing the overlayer thickness
from 4 to 8 BL. According to this result, the hop-and-turn
process is relatively slow in the deeper regions of the thicker
ice film at 140 K, when compared to its occurrence at the
J. Chem. Phys. 127, 084701 共2007兲
FIG. 5. Changes in hydronium ion intensities as a function of time at the
temperatures of 120, 130, and 140 K. The results for H3O+ and
D-substituted hydronium ions 共HnD3−nO+, n = 0 – 2兲 are shown in
共a兲 and 共b兲, respectively. Ice films of a sandwich structure
关H2O共4 BL兲 / HCl共0.1 ML兲 / D2O共2 BL兲 / Ru共0001兲兴 were prepared at 100 K
and warmed to the indicated temperature at a rate of 20 K min−1 prior to the
kinetic measurement. The time zero indicates the start of the LES measurement, which takes 30 s for spectral acquisition. The intensities shown are
normalized against those measured on the reference ice film 共6 BL兲 adsorbed with HCl 共0.1 L兲 at 140 K.
depth of 4 BL. Further kinetic measurement for a longer
period at 140 K is hampered by the desorption of water molecules from the ice film, which reduces the film thickness
slowly but significantly 共⬃1 BL h−1兲.
B. Kinetic measurement of proton transfer
Proton transfer rates are examined by measuring the
temporal change in the hydronium ion population at the surface. Figures 5共a兲 and 5共b兲 show the kinetic plots for H3O+
and D-substituted hydronium ions, respectively, measured at
three different temperatures, 120, 130, and 140 K. The ice
films were prepared in the sandwich structure shown in Fig.
4 at 100 K and heated to each temperature at a rate of
20 K min−1 before the LES measurement. The LES spectral
acquisition took 30 s. In Fig. 5共a兲, a small surface population
of H3O+ is found at 120 K right from the beginning of the
kinetic measurement. The H3O+ population stays rather constant over time at this temperature. This shows that the H+
transfer occurs very fast. At 130 K, the initial population of
H3O+ is similar to that at 120 K, but the H3O+ population
further increases with the increase in time. At 140 K, the
H3O+ population level is significantly high from the beginning and decreases slightly over time.
In Fig. 5共b兲, D-substituted hydronium ions are absent
from the surface at 120 K during the entire period of kinetic
measurement. At 130 K, the population of D-substituted hydronium ions grows initially and reaches a plateau value after about 5 min. The slow appearance of the D-substituted
species at this temperature indicates that the hop-and-turn
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Proton transfer and H / D exchange in ice films
J. Chem. Phys. 127, 084701 共2007兲
FIG. 6. Variation in D-enrichment factor 共f DE兲 as a function of the temperature of a proton-sandwiched film 共i兲 and a pure ice film 共ii兲. The film structures are drawn in the figure. The sample temperature is gradually increased
during the measurement from 100 to 140 K at a rate of 2 K min−1.
process is triggered between 120 and 130 K. At 140 K, the
population of D-substituted hydronium ions is high and
shows a quick saturation; within experimental uncertainty
the proton transport is complete by the time of the first LES
measurement 共2 min for sample heating to 140 K plus
0.5 min for LES measurement兲.
The temporal variation in H3O+ population, shown in
Fig. 5共a兲, somewhat traces the trend of D-substituted hydronium ions, if the constant portion of H3O+ observed at 120 K
due to the H+-hopping relay is set aside. This additional increase in H3O+ population with time can be attributed to the
hop-and-turn mechanism, which concomitantly produces
D-substituted hydronium ions. It may also be due to the isotopic scrambling of hydronium ions that is induced by Cs+
impact. Owing to the possibility of this side reaction in LES
measurement, it is difficult to accurately deduce the isotopomeric distribution of surface hydronium ions from the LES
data.
In contrast to LES measurement, RIS detection of water
isotopomer is little affected by the collision-induced H / D
exchange reaction. This is because the RIS process occurs
instantaneously 共⬍1 ps兲, much faster than secondary reactions on the surface.16,24 The RIS result on the isotopomeric
distribution of water molecules will be presented in the following section.
C. H / D exchange in water molecules
The H / D exchange in water molecules gives additional
information on proton activity in ice films. Figure 6 presents
the result of RIS measurement of the H / D exchange reaction
of surface water molecules as a function of temperature. The
plot shows the D-enrichment factor of surface water molecules, defined by
f DE = 共关HDO兴 / 2 + 关D2O兴兲 / 共关H2O兴
+ 关HDO兴 + 关D2O兴兲, measured from the Cs共HxD2−xO兲+ 共x
= 0 – 2兲 signal intensities for the proton-sandwich ice film. If
isotopic scrambling is completed in the whole film made of
H2O 共4 BL兲 and D2O 共1.5 BL兲 layers, a value of f DE = 0.27
will be obtained. In this estimation D2O molecules in the first
chemisorbed water layer 共0.5 BL兲 共Ref. 25兲 are assumed not
FIG. 7. Kinetic measurement for the change in D-enrichment factor 共f DE兲 in
surface water molecules at 130 共a兲 and 140 K 共b兲. The results are shown for
a proton-sandwich film 共i兲 and a pure ice film 共ii兲, whose structures are
shown in Fig. 6. The films were prepared at 100 K and warmed to the
indicated temperature of the kinetic measurement at a rate of 20 K min−1.
The time zero corresponds to the start of the RIS measurement 共which takes
30 s兲 right after the temperature rise. The solid curves for sample 共ii兲 represent a theoretical model 共see text兲. The dotted curves for sample 共i兲 are just
there as an eye guide.
to participate in the isotopic exchange reaction. Figure 6
shows that f DE is close to zero at temperatures of
100– 120 K, indicating negligible H / D exchange in water
molecules. This observation is in conformity with the absence of deuterated hydronium ions at these temperatures
共Figs. 4 and 5兲, since the H / D exchange in water molecules
is mediated by hydronium ions. The population of deuterated
water molecules rapidly increases above 120 K.
Also shown in Fig. 6 is f DE measured for an ice film
consisting of H2O 共4 BL兲 and D2O 共2 BL兲 layers in the
absence of a proton-sandwich layer 关structure 共ii兲兴. Without
the externally provided protons the proton transfer rate is
very slow. In this case D2O molecules are carried to the
surface mostly by self-diffusion. Therefore, the difference
between the two f DE curves in the figure represents the contribution of the H / D exchange reaction catalyzed by excess
protons. The D-enrichment factor for sample 共i兲 is noticeably
higher than that for sample 共ii兲 in the temperature range
120– 135 K. This extra portion indicates the contribution of
the hop-and-turn mechanism to D+ transfer to the surface. At
140 K, the f DE values are high for both samples and are close
to each other. This suggests that D2O migration by selfdiffusion becomes as efficient as the D+ transfer in the hopand-turn process for increasing the deuterium content at the
surface.
The progress in the H / D exchange of surface water molecules is examined as a function of time. Figure 7共a兲 shows
f DE measured for structures 共i兲 and 共ii兲 at 130 K, a temperature at which the hop-and-turn process is activated but with
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084701-6
Lee et al.
only a moderate speed. For a proton-sandwich film 关structure
共i兲兴 f DE increases for the initial 10 min and then the increase
rate slows down. However, the increase in f DE for a pure ice
film 关structure 共ii兲兴 is very slow and continuous after activation. Assuming that the migration of water molecules by selfdiffusion is solely responsible for the D-enrichment in the
pure ice film, we simulate the D-enrichment kinetics curve
by using a kinetic model. The model treats molecule diffusion as consecutive processes of molecule exchange between
two neighboring ice bilayers.16 A convenient feature of this
treatment is that we can directly use the rate coefficient for
the interlayer molecule exchange process that is experimentally measured.16 The rate coefficient at 130 K is ks = 2.7
⫻ 10−2 s−1 for molecule exchange between the first and second ice bilayers.16 In bulk ice, the rate coefficient kb = 3.4
⫻ 10−4 s−1 at 130 K is extrapolated from the self-diffusion
coefficients measured at T = 153– 170 K for hexagonal
ice.26,27 The rate coefficient for molecule exchange and the
self-diffusion coefficient are interconvertible through the
one-dimensional diffusion equation, 具x2典 = 2Dt, where x is
the interlayer spacing in ice 共3.66 Å兲 and D is the diffusion
coefficient.16 The best fit of the model to the experimental
data, shown in Fig. 7共a兲, is found when the top 4 BL of ice
film is treated as the “surface region” that is characterized by
the given ks value and the rest of the film as the interior
characterized by kb. The thickness of the surface region as
estimated here is based on the assumption that molecular
mobility is uniform at this depth. In reality, however, molecular mobility should gradually decrease from the outermost surface of ice toward the interior.
Figure 7共b兲 shows the result obtained at 140 K, where
f DE increases much faster than that at 130 K for both
samples. For the proton-sandwich film, deuterium enrichment has already substantially progressed at the beginning of
the measurement, and after 5 min f DE reaches ⬃0.25, which
is close to the full scrambling value of 0.27. f DE for the pure
ice film increases relatively more slowly from zero to ⬃0.18
in 30 min. The theoretical model fitting to the D-enrichment
kinetics of the pure ice film at 140 K uses ks = 6.7
⫻ 10−2 s−1 共Ref. 16兲 and kb = 8.5⫻ 10−4 s−1 extrapolated from
the diffusion coefficients.26,27 The ks value is applied to the
top 5 BL of the film for the curve shown in Fig. 7共b兲.
IV. DISCUSSION
The results indicate several mechanisms of proton transfer and H / D exchange operating within different temperature
regimes. H+ transfer producing H3O+ at the surface occurs
even at low temperatures 共⬍120 K兲. As mentioned in Sec.
III A, the H+ transfer can be explained by the hopping relay
process involving proton tunneling between adjacent water
molecules. Since this process does not require molecular rotation, it can occur even at a low temperature and also instantaneously, which is consistent with observation. It is well
known that a proton hopping relay is an essential component
of the proton transfer mechanism in ice as well as the Grotthuss mechanism of proton transfer in liquid water. Yet, its
direct observation in bulk ice has been difficult owing to its
short distance range. The present study demonstrates that the
J. Chem. Phys. 127, 084701 共2007兲
proton hopping relay in thin ice films does occur and is the
only operating mechanism of proton transport at the low
temperatures.
The observed H+ transfer, however, may also take place
during the deposition of the H2O overlayer of a protonsandwich film. In this case a proton can move from one
depositing water molecule to another as the ice film grows,
rather than in a concerted hopping process across several
molecules after the film structure is completed. However, in
these two processes the essential molecular picture might be
regarded as the same in that a proton jumps through water
molecules that are held in fixed orientations. In the frozen
molecular arrangement at low temperature, a large number of
excess protons are still trapped in the vicinity of the sandwich layer, as they cannot access the hopping relay channels.
Importantly, Fig. 4 shows a small but noticeable increase in
H3O+ intensity as the film is warmed to 120 K, a temperature
at which the rotational motions of water molecules are still
inactive. This indicates the occurrence of additional H+ transfer by the hopping relay process, made accessible probably
by the reorientation of water molecules located in defect sites
where the reorientation is easier than at normal sites. Another
evidence of the hopping relay process comes from the UV
irradiation experiment of ice films;29 photogenerated protons
migrate through the film at low temperatures 共⬍100 K兲 and
are trapped by acceptor molecules at the surface.
Several pieces of evidence have been presented in this
work for the occurrence of the hop-and-turn process at temperatures above 125 K, which include 共i兲 the appearance of
deuterated hydronium ions 共H2DO+, HD2O+, and D3O+兲 at
the surface in Fig. 3, 共ii兲 the enhanced rate of proton transfer,
shown in Figs. 4 and 5, 共iii兲 the increased D enrichment of
surface water molecules by the presence of extra protons,
shown in Fig. 6. The strong temperature dependence of these
observations indicates the thermally activated nature of this
mechanism involving the reorientation of water molecules.
The hop-and-turn mechanism has already been explicitly
demonstrated in other studies.5–7,9 For example, by identifying water isotopomers with IR spectroscopy, Devlin and
co-workers5–7 observed that the motions of Bjerrum defects
and the hop-and-turn processes are activated in ice nanocrystals at temperatures above 130 K. A slightly higher onset
temperature observed in this study is in conformity with our
result, considering the difference in dimensions between ice
nanocrystals 共radii of 12– 45 nm兲 and the present ice films
共thickness ⬍4 nm兲.
At elevated temperatures 共艌130 K兲, the diffusion of water molecules begins to contribute to the formation of
D-substituted molecules at the surface. At 140 K, molecule
diffusion alone can advance the D enrichment in water molecules near completion in about 30 min 共Fig. 7兲. At this stage
H2O and D2O molecules in the ice film are well mixed by
self-diffusion, and thermally generated protons catalyze the
H / D exchange process between neighboring water
molecules.16 According to the theoretical analysis of
D-enrichment kinetics, shown in Fig. 7, molecule diffusion
in the ice films occurs much faster than in bulk ice, because
the major part of the ice films can be considered as a surface
region with a higher concentration of defects which promote
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084701-7
J. Chem. Phys. 127, 084701 共2007兲
Proton transfer and H / D exchange in ice films
diffusion. The theoretical analysis suggests that the depth of
the surfacelike region increases from 4 BL at 130 K to 5 BL
at 140 K. Though this estimation is based on the rather
simple assumption, considering the surfacelike region to be a
few bilayers deep is reasonable in view of the observations
made in a thickness-dependent study of molecule migration
kinetics for ice films at the same temperatures.16 The deeper
surface region at the higher temperature is also consistent
with the dynamic nature of ice surfaces.28
Since the rate of molecule migration is quite different in
the surface and bulk regions of ice, we should take into consideration that the present results have relevance only for the
processes occurring near the surface, i.e., to the depth of the
proton-sandwich layer in the ice films. The quantitative rate
and operating temperature range of each proton transfer
mechanism will change somewhat in bulk ice, if it involves a
thermally activated process. For example, although molecular migration plays a major role in H / D exchange of water
molecules in the present ice films at 140 K, its contribution
in bulk ice may not be so important because its speed is
reduced by two orders of magnitude compared to that near
the ice surface at the same temperature.16 As the temperature
increases, however, the rate of molecule migration increases
more rapidly than that of Bjerrum defect migration owing to
the
higher
activation
energy
of
the
former
共70± 7 kJ mol−1兲26,27 than the latter 共52± 3 kJ mol−1兲.5 Thus,
at a substantially high temperature, molecular migration may
become a major contributor to the H / D exchange process in
bulk ice. In accordance with this expectation, NMR
stimulated-echo experiments9 have observed two proton
transfer processes in the temperature range of 160– 260 K,
one mediated by Bjerrum defect dynamics at the lower temperatures and the other related to interstitial diffusion of water molecules at the higher temperatures. For similar reasons,
the efficiency of the hop-and-turn mechanism also depends
on the film depth. Figure 5共b兲 shows that at the depth of 4
BL, proton transfer by the hop-and-turn process rapidly occurs and almost reaches completion in 5 min at 140 K. On
the other hand, the same process occurs significantly more
slowly at the depth of 8 BL, progressing only by 50% even
after 30 min. This obviously indicates slower migration of
Bjerrum defects in the deeper region of ice film.
The final part of our discussion concerns the relative
speeds of proton transfer, H / D exchange, and molecular diffusion. The hopping relay process producing H3O+ at the
surface is extremely fast even at low temperatures. The hopand-turn process occurs more slowly than the hopping relay
process, as it involves the thermal rotation of molecules,
which is activated at temperatures above 125 K at the film
depth of 4 BL. Despite a slower propagation speed, the hopand-turn process greatly increases the distance and overall
rate of proton transfer. This process also results in the H / D
exchange of water molecules. Kinetic measurements show
that proton transfer by the hop-and-turn mechanism precedes
the D-enrichment of surface water molecules. For example,
proton transfer to the surface reaches saturation in 5 min at
130 K 关Fig. 5共b兲兴, but it takes 10– 20 min to accomplish the
H / D exchange of surface water molecules at the same temperature 关Fig. 7共a兲兴. This is because the build up of
D-enriched water molecules requires the recurrence of the
hop-and-turn process,7 i.e., the repeated passage of protons
and Bjerrum defects between the bottom D2O layer and the
film surface. Molecule diffusion is quite inactive in ice films
at temperatures below 130 K, but it catches up to the speed
of the hop-and-turn process at 140 K at a depth of 4 BL with
regard to its contribution to the D-enrichment of water molecules.
V. SUMMARY
We have identified that the proton hopping relay, the
hop-and-turn process, and molecular diffusion are three major molecular mechanisms responsible for proton transport
and H / D exchange in thin ice films in the temperature range
of 100– 140 K. Their observed characteristics are summarized as follows.
共i兲
共ii兲
共iii兲
共iv兲
共v兲
Proton hopping relay can transfer protons only across
a short distance, and as such it can move a specific
fraction of protons across a thin ice film. Though its
range is limited, it makes protons a unique mobile
species in a low-temperature ice film, where the motions of water molecules and other foreign species are
virtually frozen.
Upon the activation of molecular rotation at temperatures above 125 K, the hop-and-turn process starts to
occur and additionally contributes to the proton transfer. It increases the proton transfer rate and distance
and induces the H / D exchange reactions. D-enriched
water isotopomers are transported through the ice film
by the recurrence of this mechanism.
D-enriched water molecules are formed also by molecular diffusion at the higher temperatures
共艌130 K兲.
The quantitative features of the present observations
are relevant only for the processes occurring near the
ice surface. In the interior region of ice, molecule diffusion and Bjerrum defect migration may occur more
slowly and at higher temperatures.
The relative speeds of three processes are in the following order: proton hopping relay⬎ proton transfer
by the hop-and-turn mechanism⬎ H / D exchange by
the hop-and-turn mechanism⬎ H / D exchange by
molecule diffusion. This behavior can be explained in
terms of the characteristic time scale of the related
molecular motions in ice films between 100 and
␶共proton tunneling兲 ⬍ ␶共molecule rotation兲
140 K:
⬍ ␶共molecule translation兲
ACKNOWLEDGMENTS
This project was supported in part by the Korea Science
and Engineering Foundation 共R01-2006-000-10019-0兲 and
Korea Research Foundation 共C00206兲. We thank Professor
C. W. Lee 共Ajou University兲 for critical reading of this paper.
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