Diffusion of HDO in pure and acid-doped ice films

Article abstract of DOI:10.1021/jp062270v

In these experiments, a few bilayers of D₂O were vapor-deposited on a pure crystalline H₂O ice film or an ice film doped with a small amount of HCl. Upon deposition, H/D isotopic exchange quickly converted the D₂O layer into an HDO-rich mixture layer. Infrared absorption spectroscopy followed the changes of the HDO from the initial HDO mixture layer to HDO isolated in the H₂O ice film. This was possible because isolated HDO in H₂O ice has a unique, sharp peak in the O-D stretch region that can be distinguished from the broad peak due to the initial HDO mixture layer. The absorbance of isolated HDO displayed first-order kinetics and was attributed to diffusion of HDO from the HDO-rich mixture layer into the underlying H₂O ice film. While negligible diffusion was observed for pure ice films and for ice films with HCl concentrations up to 1 × 10 ^-4 mole fraction, diffusion of HDO occurred for higher concentrations of (2-20) × 10^-4 mole fraction HCl with a concentration- independent rate constant. The diffusion under these conditions followed Arrhenius behavior for T = 135-145 K yielding E_a = 25 ± 5 kJ/mol. The mechanism for the HDO diffusion involves either (i) molecular self-diffusion or (ii) long-range H/D diffusion by a series of multiple proton hop and orientational turn steps. While these spectroscopic results compare favorably with recent studies of molecular self-diffusion in low-temperature ice films, the diffusion results from all the ice film studies at low temperatures (ca. T < 170 K) differ from earlier bulk ice studies at higher temperatures (ca. T > 220 K). A comparison and discussion of the various diffusion studies are included in this report.

Full text of DOI:10.1021/jp062270v

11064
J. Phys. Chem. A 2006, 110, 11064-11073
Diffusion of HDO in Pure and Acid-Doped Ice Films
Susan P. Oxley, Caitlin M. Zahn, and Christopher J. Pursell*
Department of Chemistry, Trinity UniVersity, One Trinity Place, San Antonio, Texas 78212-7200
ReceiVed: April 12, 2006; In Final Form: July 25, 2006
In these experiments, a few bilayers of D2O were vapor-deposited on a pure crystalline H2O ice film or an
ice film doped with a small amount of HCl. Upon deposition, H/D isotopic exchange quickly converted the
D2O layer into an HDO-rich mixture layer. Infrared absorption spectroscopy followed the changes of the
HDO from the initial HDO mixture layer to HDO isolated in the H2O ice film. This was possible because
isolated HDO in H2O ice has a unique, sharp peak in the O-D stretch region that can be distinguished from
the broad peak due to the initial HDO mixture layer. The absorbance of isolated HDO displayed first-order
kinetics and was attributed to diffusion of HDO from the HDO-rich mixture layer into the underlying H2O
ice film. While negligible diffusion was observed for pure ice films and for ice films with HCl concentrations
up to 1 × 10-4 mole fraction, diffusion of HDO occurred for higher concentrations of (2-20) × 10-4 mole
fraction HCl with a concentration-independent rate constant. The diffusion under these conditions followed
Arrhenius behavior for T ) 135-145 K yielding Ea ) 25 ( 5 kJ/mol. The mechanism for the HDO diffusion
involves either (i) molecular self-diffusion or (ii) long-range H/D diffusion by a series of multiple proton hop
and orientational turn steps. While these spectroscopic results compare favorably with recent studies of
molecular self-diffusion in low-temperature ice films, the diffusion results from all the ice film studies at low
temperatures (ca. T < 170 K) differ from earlier bulk ice studies at higher temperatures (ca. T > 220 K). A
comparison and discussion of the various diffusion studies are included in this report.
Introduction
as a function of temperature was measured. The results indicated
that the predominant point defects in ice are H2O interstitials
and not vacancies. Interstitials are H2O molecules in ice that
do not occupy regular crystal lattice sites, while vacancies are
unoccupied crystal lattice sites. Hondoh’s research group also
determined the diffusion coefficient of the H2O interstitials,
along with their equilibrium concentration. The energy of
activation was determined to be the sum of two components:
the energy of formation of interstitials and the activation energy
for motion. Because the total energy of activation was consistent
with those energies from the tracer studies, it was concluded
that the mechanism for self-diffusion of water molecules in ice
involves interstitial diffusion, at least for the temperature range
∼220-269 K. Recent molecular dynamic studies from Hon-
doh’s group confirmed this conclusion.8,9
The diffusion of water molecules in ice was studied in the
past by several research groups. Older results were conveniently
compiled by Hobbs,1 while more recent studies were reviewed
by Petrenko and Whitworth.2 Because the diffusion coefficient
is very small, all the older studies were performed at modestly
low temperatures between ∼238-271 K. These studies (i) used
the isotopic probes H218O, D2O, and T2O as tracers to follow
the diffusion process, (ii) included bulk ice samples of poly-
crystalline ice, artificially grown single-crystal ice, and naturally
grown single-crystal ice, and (iii) examined diffusion for
different crystallographic orientations. Microtome sectioning of
the bulk ice into very thin layers followed by scintillation or
mass spectrometric detection was used to measure the diffusion
of the tracer species. Studies indicated that diffusion of water
molecules in ice involves molecular self-diffusion of intact water
molecules since the diffusion coefficients for D2O and H218O
were approximately identical.1,2
More recently the diffusion of water in ice was examined
for thin vapor-deposited ice films at low temperatures (ca. T e
170 K). The results suggest that diffusion in low-temperature
ice films differs from diffusion in bulk ice samples at higher
temperatures.
George’s research group10-12 studied the diffusion of H218O
and HDO into H2O ice from 146 to 170 K using a laser-induced
thermal desorption technique with mass spectrometric detection.
Multilayer crystalline ice was grown epitaxially on a Ru(001)
metal substrate. After deposition of a thin ice film, a tracer
molecule (H218O or HDO) was adsorbed onto the surface.
Diffusion of the tracer molecule from the surface into the thin
ice film was detected by isothermally desorbing the ice
multilayer with a laser pulse and then monitoring the water
species with mass spectrometry. While the determined energy
of activation is similar to the values from the earlier bulk ice
As an example of the earlier tracer studies, Ramseier studied
T2O diffusion into artificially and naturally grown ice from 243
to 268 K.3 Diffusion perpendicular to the optical axis (c axis)
was observed to be greater (ca. ∼ 12%) than diffusion parallel
to the c axis. This anisotropy was attributed to the geometry of
the lattice structure. It was concluded that molecular self-
diffusion in ice takes place by a vacancy mechanism. However,
others argued that diffusion occurred by an interstitial mecha-
nism.4
The mechanism for molecular self-diffusion in ice was
examined by Hondoh’s laboratory5-7 for T ∼ 220-269 K. Using
X-ray topography the variation of the size of dislocation loops
* To whom correspondence should be addressed.
10.1021/jp062270v CCC: $33.50 © 2006 American Chemical Society
Published on Web 08/31/2006

Diffusion of HDO in Pure and Acid-Doped Ice Film
J. Phys. Chem. A, Vol. 110, No. 38, 2006 11065
studies, their diffusion coefficients are more than 103 times larger
than the value obtained by extrapolation of the tracer data to
160 K.
steel tubing directed at the ZnSe window. H2O and HCl/H2O
vapors were introduced through a separate needle valve and
inlet system than the D2O vapor to prevent cross-contamination.
Vapors were from pure water (Aldrich, reagent grade), aqueous
solutions of HCl (dilutions of water and Aldrich 37 wt % HCl,
99.999%), and pure D2O (Cambridge Isotope Laboratories,
99.96%). The partial vapor pressures of HCl and H2O were
determined from the equilibrium pressures above the aqueous
acid solutions at either 0 °C or room temperature.17 The
concentrations of the HCl solutions were determined by titration
with a NaOH solution standardized with KHP. The mole fraction
of HCl in an ice film was determined according to condensation
kinetics, as explained below in the Results.
Experiments were performed by first introducing H2O or HCl/
H2O vapor at a rate of ∼0.5 mTorr/s onto the ZnSe window at
150 K. The thickness of the deposited crystalline ice layer was
determined using the known conversion value of 0.163 Abs/
µm of ice at 824 cm-1, giving a thickness of 0.50 ( 0.02 µm.18
The infrared spectrum of the ice films confirmed the polycrys-
talline nature of the ice. After the ice was annealed at 150 K
for at least 20 min, the window was cooled to the temperature
of interest. About 1-2 mTorr of D2O was then introduced into
the cryostat, leading to an absorbance of 1.5-3.5 mAbs at 2424
cm-1. Previous interference studies from this laboratory gave a
conversion value of 2.35 Abs/µm for the O-D stretching band
at 2424 cm-1 for pure crystalline D2O ice.15 Using this value,
it is estimated that approximately 6-15 Å or ∼2-5 bilayers
(BL) of D2O were deposited on the ice. Infrared spectra were
collected as a function of time for at least 1 h. To clearly observe
the resulting spectra, the spectrum of the underlying ice film
was used as the background. In all cases, spectra were acquired
by averaging 32 scans with a resolution of 4 cm-1 and an
acquisition time of 39.5 s.
Temperature Study. The experimental setup for the tem-
perature study was the same as that for the concentration study,
except the cryostat was also equipped with a turbomolecular
pump situated directly above the ZnSe window. The temperature
range for these experiments was dictated by extraneous ice
deposition below 135 K and ice loss by sublimation above 145
K. The minimal deposition or sublimation in this temperature
range was taken into account by calibration of ice films without
D2O. This calibration resulted in a small adjustment (∼10%)
in the measured k values.
Experiments were performed by first introducing 20 × 10-4
mole fraction HCl vapor at a rate of ∼0.5 mTorr/s onto the
ZnSe window at 150 K. The thickness of the deposited film
was 0.50 ( 0.01 µm, based upon the same conversion as in the
concentration study. The infrared spectrum of these acid-doped
ice films indicated that the films appeared to be essentially pure
crystalline ice. The ice was annealed at 150 K for at least 10
min and then cooled to the temperature of interest. The
temperature was recorded and maintained to (0.1 K throughout
the course of the experiment. Roughly 2-5 BL of D2O were
deposited on the ice, and infrared spectra were collected as a
function of time for at least 2 h. To clearly observe the resulting
spectra, the spectrum of the underlying ice film was used as
the background. In all cases, spectra were acquired by averaging
32 scans with a resolution of 4 cm-1 and an acquisition time of
39.5 s.
More recently Kang’s research group13,14 examined both
vertical water diffusion and H/D isotopic exchange on very thin
ice films using Cs+ reactive ion scattering (RIS) with mass
spectrometric detection. For this diffusion study, very thin
amorphous H2O ice films were vapor-deposited on Ru(0001)
between 100 and 140 K. A fractional coverage of D2O was then
added onto the ice film. Vertical diffusion of D2O into the H2O
ice film and reverse migration of H2O to the surface resulted in
a change in the surface concentration. This study provided
information directly at the ice surface with a depth resolution
of 1 BL. A first-order rate constant and activation energy were
determined for diffusion from the surface into the amorphous
ice film. The activation energy is similar to the energy associated
with the motion of interstitials mentioned above and suggests
that the measured diffusion is due to an interstitial mechanism.
Using the first-order rate constant and the assumption that the
probing depth for molecular diffusion is one interlayer spacing,
a diffusion coefficient was estimated. This estimated diffusion
coefficient is more than 105 times larger than the value obtained
by extrapolation of the tracer data to 140 K.
In this report, a spectroscopic study of the diffusion of HDO
into pure and acid-doped ice films is presented. These experi-
ments consisted of the vapor deposition of a few bilayers of
D2O on a pure crystalline H2O ice film or an ice film doped
with a small amount of HCl. Upon deposition, H/D isotopic
exchange quickly converted the D2O layer into an HDO mixture
layer. The diffusion of HDO from the mixture layer into the
underlying crystalline H2O ice film was monitored using infrared
absorption spectroscopy, which was possible because isolated
HDO in H2O ice has a unique, sharp peak that can be
distinguished from the initial broad peak of the HDO mixture
layer. Previously,15 the observed spectral changes were attributed
to H/D isotopic exchange of D2O occurring on H2O ice, which
is now believed to be wrong. In particular, (i) the initial D2O
layer was not pure D2O but an HDO isotopic mixture and (ii)
the spectral change observed for the acid-doped ice films was
not due to H/D exchange on the ice surface but to interdiffusion
of HDO and H2O between the isotopic mixture layer and the
H2O ice film. In this report additional data are presented
concerning the acid and temperature dependence, along with
an analysis that attributes the spectral changes to HDO diffusion
into an H2O ice film. The results compare favorably with the
other studies of diffusion in low-temperature ice films but differ
from the earlier bulk ice studies at higher temperatures. A
discussion of these differences for the diffusion of water in ice
films and in bulk ice samples is included in this report.
Experimental Methods
Concentration Study. The experimental setup for this system
has been described in detail.15,16 In brief, ice films were grown
by vapor deposition onto an infrared transparent ZnSe window
positioned at the end of a coldfinger contained in a closed-cycle
liquid-He cryostat (Advanced Research Systems DE 202
expander). The temperature of the window was measured and
regulated by a silicon diode sensor and a LakeShore 321
temperature controller. The pressure within the cryostat was
maintained at P < 10-6 Torr, as measured with a cold cathode
gauge. The cryostat system, with KBr outer windows, was
situated in the sample compartment of a purged Nicolet Magna
550 series FTIR spectrometer.
Results
Figure 1 shows the change in the infrared absorption spectra
of the O-D stretch region as a function of time when 2-5 BL
of D2O were deposited at 145 K on (a) a pure H2O ice film and
Vapor was introduced from a glass line (volume ≈ 2 L) into
the cryostat through a needle valve and a 6-in. piece of stainless

11066 J. Phys. Chem. A, Vol. 110, No. 38, 2006
Oxley et al.
Figure 1. Infrared absorption spectra as a function of time for 2-5 BL of D2O deposited at 145 K on (a) pure H2O ice film, showing negligible
spectral changes, and (b) 2 × 10-4 mole fraction HCl-doped H2O ice film (ca. 1 HCl to 5000 H2O molecules), indicating the appearance of isolated
HDO in ice. The spectra situated below the dashed line are the subtraction of t ) 0 from the t ) 3285 and 3004 s spectra for pure ice and 2 × 10-4
mole fraction HCl-doped ice, respectively. For this particular data, approximately twice as much D2O was deposited on the acid-doped ice film as
on the pure ice film, as evidenced by the ∼2× absorbance at t ) 0 s. D2O deposition was complete after ∼200 s. The absorbance scales for (a) and
(b) are the same, and the spectra are offset for clarity.
(b) an acid-doped H2O ice film. On the pure ice film, the shape
of the resulting broad peak did not appear to change appreciably
during the time probed (ca. up to 2 h). However, when the H2O
ice film was doped with HCl (ca. 2 × 10-4 mole fraction HCl,
or 1 molecule of HCl to 5000 H2O molecules), the O-D stretch
spectrum changed significantly as the band at 2424 cm-1
narrowed and increased in absorbance, indicative of HDO
isolated in H2O ice. It should be noted that well over 50
experiments have been performed on pure and acid-doped ice
films, consistently yielding these results. The t ) 0 s spectra in
Figure 1 correspond to the first spectra acquired; since spectral
acquisition takes a definite period of time (39.5 s), the t ) 0
spectra correspond to the average of the first 39.5 s. The
deposition of the D2O layer was complete within the first 200
s of exposure.
exchange occur very quickly at the surface (ca. 1-5 BL) of ice
films from 90 to 140 K. Therefore, upon vapor deposition of
D2O on an H2O ice film over the temperature range 135-145
K, short-range vertical diffusion and H/D isotopic exchange
quickly convert the thin D2O layer into an isotopic HDO mixture
layer. George’s group observed the same type of rapid isotopic
exchange of D2O on an H2O film at 120 K.11
To confirm that H/D isotopic exchange occurred and to
determine the composition of the resulting HDO mixture layer,
various D2O ice spectra were collected for comparative pur-
poses. Figure 2a shows the spectrum for 2-5 BL of D2O
deposited on a pure H2O ice film just after deposition at 145 K
(ca. the t ) 210 s spectrum from Figure 1a). This peak is broad
(fwhm ) 114 cm-1) and featureless. An amorphous D2O ice
film at 80 K (Figure 2e) is broader and shifted to a higher
frequency, while a crystalline D2O ice film at 150 K (Figure
2d) shares a common maximum with the D2O layer spectrum
but has two pronounced shoulders. Thus, the initial D2O layer
is not “pure” amorphous or crystalline D2O ice. Ice films
prepared by mixing an ∼1:1 ratio of D2O and H2O in the vapor
phase and then depositing at 80 K (cf. amorphous) and 150 K
(cf. crystalline) are shown in Figure 2b and c, respectively. The
vapors were mixed in the ∼2 L glass line where isotopic
scrambling on the glass surface produced an equilibrium gas
composition of 25% D2O:50% HDO:25% H2O. The amorphous
ice spectrum is broader and shifted to a higher frequency, while
the crystalline ice spectrum appears to match the spectrum of
the initial D2O layer. The crystalline ice-mixture spectrum also
matches the published ice spectrum of Haas and Horning for
this same composition.21
Previously,15 the results displayed in Figure 1 had been
interpreted in terms of H/D isotopic exchange of D2O occurring
on the H2O ice surface. Since the initial spectrum of D2O on a
pure ice film did not appear to change during the course of the
experiment, it was concluded that no isotopic exchange occurred.
This conclusion conflicted with the extensive and thorough work
from Devlin’s laboratory concerning isotopic exchange in
ice.2,19,20 Furthermore, since isotopic exchange involves a proton
hop step, it was suggested that there are few active protons on
the pure ice surface, thus the need for doping the ice film with
acid in order for exchange to occur. It was concluded15 that the
results were unique and differed from Devlin’s work because
isotopic exchange was being examined on the ice surface as
opposed to in ice. However, the previous interpretation of these
results in terms of H/D isotopic exchange now appears to be
wrong. In particular and as demonstrated below, (i) the initial
D2O layer was not pure D2O but an HDO isotopic mixture and
(ii) the spectral change observed for the acid-doped ice films
was not due to H/D exchange but to the diffusion of HDO into
the H2O ice film.
Thus, the spectrum observed just after the deposition of 2-5
BL D2O layer on crystalline H2O ice films, for both pure and
acid-doped ice at 145 K (Figure 2a), closely resembles the
spectrum of the crystalline ice mixture of Figure 2b. The initial
D2O layer is therefore not a pure D2O ice layer but is actually
an isotopically mixed layer of D2O, HDO, and H2O. On the
basis of a comparison of the spectra in Figure 2 (parts a and b),
the composition of the layer is estimated to be 25% D2O:50%
Concerning the initial D2O, the 2-5 BL D2O layer is not a
pure layer but an isotopic mixture. According to the recent work
from Kang’s laboratory,13,14 vertical diffusion and H/D isotopic

Diffusion of HDO in Pure and Acid-Doped Ice Film
J. Phys. Chem. A, Vol. 110, No. 38, 2006 11067
Figure 2. Infrared absorption spectra of the O-D stretch region for (a) 2-5 BL of D2O on pure crystalline H2O ice film just after deposition at
145 K, (b) crystalline ice film from deposition of ∼1:1 gas mixture of D2O and H2O at 150 K (film composition is 25% D2O:50% HDO:25% H2O),
(c) amorphous ice film from deposition of ∼1:1 gas mixture of D2O and H2O at 80 K (film composition is 25% D2O:50% HDO:25% H2O), (d) pure
crystalline D2O ice film at 150 K, (e) pure amorphous D2O ice film at 80 K, (f) 2-5 BL of D2O on 2 × 10-4 mole fraction HCl-doped ice film
1 h after deposition at 145 K, and (g) isolated HDO in crystalline H2O ice film at 150 K. Spectra have been offset for clarity. Reference spectra
(b-e, g) have been scaled to the same absorbance as the unscaled reaction spectra (a, f).
HDO:25% H2O. The thickness is estimated to be 4-10 BL, or
two times 2-5 BL of D2O. This estimate is consistent with a
study from George’s research group, where rapid and complete
H/D exchange was observed that converted 1.5 BL of D2O on
a thin H2O ice film at 120 K into a localized 3 BL HDO
adlayer.11
If we return to Figure 1, while no spectroscopic changes were
observed for the pure ice films, significant changes occurred
for the acid-doped ice films. These spectroscopic changes are
attributed to the interdiffusion (or isotopic mixing) of HDO from
the HDO-rich mixture layer into the underlying H2O ice film
and of H2O from the film into the HDO-rich mixture layer. The
sharp peak at 2424 cm-1 that grows in with time is due to the
formation of HDO isolated in the H2O ice film, which can easily
be distinguished from the initial spectrum of the HDO mixture
layer. The resulting spectrum (Figure 2f) is significantly sharper
(fwhm ) 26 cm-1) than the spectrum for the HDO mixture
layer (Figure 2a) and compares favorably with the spectrum of
HDO isolated in bulk crystalline ice (Figure 2g). The reference
spectrum of isolated HDO was obtained by depositing an H2O
ice film that possessed a very small amount of HDO. This was
accomplished in the following way: D2O vapors were intro-
duced into the glass line and removed; H2O vapors were then
introduced and H/D exchange occurred on the glass line
producing a very small amount of HDO. The resulting H2O
vapors with a very small amount of HDO (ca. < 1%) were
then deposited as an ice film. The resulting spectrum of isolated
HDO in crystalline H2O ice (Figure 2g) agrees with that reported
by Devlin.19
Figure 3. Infrared absorption spectra of the O-D stretch region at
145 K for (a) 2-5 BL of D2O on 2 × 10-4 mole fraction HCl-doped
ice film after 1 h, (b) isolated HDO in H2O ice film, and (c) spectral
subtraction (a) - (b), revealing the spectrum for (HDO)2. Spectra are
offset for clarity.
This fast preequilibrium step maintains a steady-state amount
of the (HDO)2 species. Step 2 represents the slower diffusion
of HDO into the underlying ice film.
According to step 1, the (HDO)2 species should be present
in the initial mixture spectrum and should slowly decrease with
time. On the basis of the relative amount of the isotopes in the
initial mixture (ca. 25% D2O:50% HDO:25% H2O), 50% of
the HDO should exist as the (HDO)2 nearest neighbor, which
Devlin identified in his studies.19,20,22 To observe this species,
an isolated HDO spectrum can be subtracted from the reaction
spectrum, as shown in Figure 3. The subtraction yields two
peaks at 2447 and 2403 cm-1, in agreement with the (HDO)2
spectrum reported by Devlin and co-workers.22 To obtain this
(HDO)2 spectrum, it was assumed that 85% of the absorbance
at 2424 cm-1 could be attributed to HDO. The HDO spectrum
was then scaled accordingly, and the two spectra were subtracted
with a subtraction factor of 1. This method is similar to that
employed by Devlin and co-workers to isolate the (HDO)2
spectrum.22
The present spectroscopic results can be explained by the
following expressions:
D2O + H2O T (HDO)2
(1)
(2)
(HDO)2 f 2HDO (isolated)
Step 1 represents the isotopic exchange equilibrium that is
quickly established on the ice films, both pure and acid-doped,
giving rise to the initial isotopic mixture layer (see Figure 2a).

11068 J. Phys. Chem. A, Vol. 110, No. 38, 2006
Oxley et al.
The data for the acid-doped ice film (filled circles) fit well to
the single exponential, indicating first-order behavior and
yielding a first-order rate constant, k, associated with step 2
above. The recent vertical diffusion studies by Kang’s labora-
tory13 also produced first-order behavior. For the 2 × 10-4 mole
fraction HCl data shown in Figure 5, k ) 1.5 × 10-3 s-1 at
145 K. Since the initial deposition of D2O occurred over the
first 200 s, these data were not included in the kinetic fits and
are not included in Figure 5.
The absorbance at 2424 cm-1 for the HDO mixture layer on
pure ice is also presented in Figure 5 (open circles). It is virtually
constant for the first 1500 s and then slowly decreases at longer
times as a result of sublimation. This slight sublimation loss is
the only evidence of the dynamic nature of the ice surface from
our study. Assuming an equilibrium vapor pressure of 7 × 10-9
Torr at 145 K, the condensation rate should equal the sublima-
tion rate, which is calculated to be 0.02-0.2 BL/min for H2O
ice and 0.007-0.04 BL/min for D2O ice at this temperature.23-25
This constant reconstruction of the ice surface is believed to
occur to only 2-3 BL deep, according to a molecular dynamics
study for T ) 180-210 K.26 It is possible that our results may
be affected by this fast exchange at the surface, where the depth
of reconstruction is perhaps 1-2 BL deep for the present
experimental temperatures. For example, if net condensation
of H2O were occurring throughout the experiment, then the D2O/
HDO layer would become embedded in the ice film. This would
lead to rapid H/D exchange and the formation of isolated HDO.
However, this was not observed on the pure ice films. If the
vapor pressure of D2O in the cryostat is much less than 7 ×
10-9 Torr, this would lead to net sublimation of D2O from the
surface. Calculations, using the larger sublimation rate, indicate
that ∼2 BL of D2O ice should sublime after 3000 s at this
temperature, which agrees with the data in Figure 5 and with
the estimate of the HDO mixture layer thickness. Therefore,
concerning the dynamic nature of the ice surface, the spectro-
scopic data indicate only the very slow sublimation of D2O from
the surface of pure ice films. On acid-doped ice films, this
sublimation would compete with the HDO diffusion, causing
the measured rate constants to be slightly smaller. The amount
of sublimation was therefore taken into account by calibration
of the sublimation of pure ice films at the appropriate temper-
atures. This calibration resulted in a small adjustment (∼10%)
in the measured k values.
Concerning the acid concentration study, the first-order rate
constant was determined according to eq 3 for ice films with
various concentrations of HCl. The rate constant displays an
“off-on” behavior as a function of HCl concentration, as shown
in Figure 6. At concentrations below 1 × 10-4 mole fraction,
negligible diffusion was observed, while, at concentrations of
2 × 10-4 mole fraction and above, HDO diffusion occurred.
Within experimental error, the rate constant is constant for (2-
20) × 10-4 mole fraction HCl with an average value of (1.5 (
0.5) × 10-3 s-1 at 145 K (ca. the average for the data from
Figure 6).
The acidic ice films were not created under equilibrium
conditions but by the co-condensation of HCl and H2O vapors
onto a cold infrared window. Since diffusion of HCl at these
temperatures is thought to be very slow, the HCl should be
evenly distributed in the ice films and the composition should
be controlled by condensation kinetics.27 Accordingly, the mole
fraction of HCl in the ice has been determined as
Figure 4. Infrared absorption spectra of (HDO)2 as a function of time
for 2-5 BL D2O on 2 × 10-4 mole fraction HCl-doped ice at 145 K.
Normalized isolated HDO spectra (Figure 3b) were subtracted from
raw absorption spectra (Figure 1b) as described in the text. Spectra are
offset for clarity.
Figure 5. Absorbance at 2424 cm-1 as a function of time for an HDO
mixture layer (4-10 BL) at 145 K on (O) pure H2O ice film and (b)
2 × 10-4 mole fraction HCl-doped ice film. The solid line corresponds
to a first-order fit (see eq 3). The data in this figure correspond to the
spectra in Figure 1. A small amount of sublimation is observed for
this pure ice sample as evidenced by the slight negative slope of the
data after ∼1500 s (see text).
The evolution of the (HDO)2 peak with time is shown in
Figure 4. These spectra were obtained by subtracting an
appropriately scaled isolated HDO spectrum from each spectrum
in Figure 1b. The isolated HDO scaling factor was determined
from the longest time spectrum (t ) 3004 s) and the measured
first-order rate constant (see below). The (HDO)2 spectrum
slowly decreases with time, and the two peaks become more
distinct. These results indicate that the (HDO)2 forms very
quickly and is then slowly depleted over time by diffusion of
HDO into the underlying ice film, consistent with step 1 (the
fast preequilibrium step) and step 2 (the slower diffusion step)
above. Note that even though the diffusion is ∼99% complete
at t ) 3004 s, (HDO)2 is still clearly present.
According to step 2, the slow formation of isolated HDO
dominates the observed spectral changes (see Figure 1b). To
quantitatively characterize these changes, the absorbance at 2424
cm-1 was measured as a function of time, an example of which
is shown in Figure 5. The data presented correspond to the
spectra in Figure 1 at 145 K. These data were fit to a single
exponential, first-order expression of the following form:
1/2
XHCl ) (PHCl/PH2O)(RHCl/RH2O)(MH O/MHCl
)
(4)
2
absorbance ) A(1 - e-kt) + B
(3)
For the experimental temperature range, it was estimated that

Diffusion of HDO in Pure and Acid-Doped Ice Film
J. Phys. Chem. A, Vol. 110, No. 38, 2006 11069
Figure 6. Averaged first-order rate constant as a function of mole
fraction HCl in the ice film. Error bars for k * 0 points are ( one
standard deviation from at least 3 measurements, while error bars for
k ) 0 points are the average of the nonzero standard deviation values.
Figure 7. Arrhenius plot for the diffusion of an HDO mixture layer
(4-10 BL) into 20 × 10-4 mole fraction HCl-doped ice film between
135 and 145 K. Circles represent data, and the line represents a linear
fit of the data, yielding Ea ) 25 ( 5 kJ/mol. Error bars correspond to
( one standard deviation from at least four experiments. For T ) 135
K the error bars are smaller than the size of the data point.
RHCl ≈ RH O ) 0.8-1, based upon measured mass accommoda-
2
tion coefficients.23,28 The partial vapor pressures of HCl and
H2O were determined from the equilibrium pressures above the
aqueous acid solutions. For the present experimental conditions,
the HCl probably exists in ice in the form of an ionic solid
solution, according to the HCl-H2O temperature-composition
phase diagram.27
on” behavior may therefore be explained as follows. For the
very lowest HCl concentrations, the protons may be more or
less mixed in the ice. At the higher concentrations, the larger
proton activity drives the protons to the surface. Once near the
surface, the hydrated protons turn on the H/D diffusion, at which
point the diffusion process is then controlled by the orientational
turn step (see Discussion below).
The reason for the “off-on” behavior is unclear at this time.
For the low concentrations up to 1 × 10-4 mole fraction (ca. 1
molecule of HCl to 104 molecules of H2O), the HCl has probably
been incorporated and ionized in the ice structure, forming
protonic and Bjerrum L-defects but otherwise not significantly
disrupting the ice lattice structure, at least in terms of increasing
diffusion. For higher acid concentrations of 2 × 10-4 mole
fraction and above, local microcrystals of the HCl hexahydrate
may form within the solid ionic mixture. Hobbs has suggested
that local clustering of impurities can occur in ice.1 Formation
of an HCl hydrate in the ice might be revealed by the infrared
spectra. For both pure and acid-doped ice films, the spectra were
qualitatively and quantitatively very similar due to the very low
HCl concentrations and the spectroscopic detection limits.
However, at the very highest acid concentration, a small broad
absorption band between 1700 and 1900 cm-1 and a small sharp
peak at 1635 cm-1 were detected, indicative of H3O+ due to
the HCl hexahydrate.29 A mixed ice-acid-hydrate solid would
have an increased number of defects, especially dislocations
and grain boundaries between the two microcrystalline solid
regions.27,30 Enhanced diffusion would then occur due to the
increased number of defects. It is possible that once these
microcrystalline regions are established, increasing the acid
content of the ice films simply increased the relative size of
the microcrystals but not necessarily the number of grain
boundaries.
An additional explanation for the “off-on” behavior comes
from very recent work by Kang’s group.31 They examined
proton transfer and H/D diffusion in very thin ice films using
Cs+ reactive ion scattering and low-energy sputtering. Briefly,
the results indicate that (1) protons can very quickly migrate
from inside an “ice sandwich” to the surface, which is followed
by a slower H/D diffusion by recurrence of a proton hop-
molecular turn process, and (2) excess protons tend to collect
at the surface where they become hydrated with increasing
temperature and thereby buried just below the surface. For this
study, this means that for the HCl-doped ice films the excess
protons may not be homogeneously mixed throughout the ice
film but may become concentrated near the surface. The “off-
George’s group also observed concentration-independent
processes in ice with acid dosing. The rate of D2O desorption
from and the rate of HDO diffusion into a thin film of ice was
observed as a function of HCl and HNO3 surface coverage.24,32
The surface coverage of the acid was 0.3-5 BL for HCl and
0.5-3 BL for HNO3. Over this range, the D2O desorption rate
and the HDO diffusion rate were independent of acid coverage.
The changes in the measured rates relative to pure ice films
were attributed to an increase in the number of protonic and
Bjerrum L-defects in the case of HCl dosing and to the possible
formation of acid hydrates for the HNO3 dosing. No further
explanation was given for the acid concentration independence.
Concerning the temperature studies, the first-order rate
constant as a function of temperature was measured for 20 ×
10-4 mole fraction HCl ice films. The k values were obtained
according to eq 3 for T ) 135-145 K. At least four experiments
were performed at each temperature. The resulting first-order
rate constants display Arrhenius behavior as shown in Figure 7
producing an activation energy Ea ) 25 ( 5 kJ/mol. This
measured Ea value compares well with the reported value for
the energy associated with the breaking of an ice-like hydrogen
bond of ∼23 kJ/mol.2,33-35 Additionally, it agrees with the
energy value from a study of the dielectric properties of HCl-
doped ice by Takei and Maeno.36 In their model, an HCl
molecule is considered to replace an H2O in the ice lattice,
generating a Bjerrum L-defect and an H3O+ ion (i.e. extrinsic
protonic defect). The temperature dependence of the ac (or high-
frequency) and dc conductivity was measured. The energy of
activation for the ac conductivity was attributed to the liberation
and migration of L-defects. Their reported value is Ea ) 25.0
( 0.3 kJ/mol. The agreement with the present value suggests a
common mechanism. For this study, the addition of HCl into
the ice films increases the number of protonic and Bjerrum
L-defects.2 One proposed mechanism for diffusion of water
molecules in ice includes the combined migration of interstitials
with L-defects.1,2 If, under the present experimental conditions,
the diffusion is mostly limited by L-defect migration, then the

11070 J. Phys. Chem. A, Vol. 110, No. 38, 2006
Oxley et al.
TABLE 1: Recent Results for Diffusion in Low-Temperature Ice Films
1018D(140 K)
measuremnt
Trange (K) Ea (kJ/mol)
(cm2/s)
ref (year)
H218O diffusion into crystalline H2O ice
HDO diffusion into crystalline H2O or D2O ice
(HDO from isotopic mixture)
HDO diffusion into crystalline D2O ice
(HDO from H/D exchange of HCl on D2O ice surface)
HDO diffusion into D2O crystalline ice
(HDO from H/D exchange of HNO3 on ice surface)
D2O diffusion into surface (ca. 1-5 BL) of amorphous H2O ice 100-140
HDO diffusion into HCl-doped crystalline H2O ice film
(HDO from isotopic mixture)
155-165
153-170
69.9
71.1
0.8
1.2
S. M. George10 (1996)
S. M. George11,12,24 (1997, 1998, 1999)
146-161
146-161
79.5
55.2
5.2
0.2
S. M. George24 (1999)
S. M. George24 (1999)
13.7
25
80
11
H. Kang13 (2004)
this work (2006)
135-145
mechanism is similar to the ac conductivity measurements by
Takei and Maeno, thereby yielding a similar activation energy.
coefficients show just the opposite trend for these acid-dosed
ices. This group suggested that a compensation effect relates
Ea and the diffusion coefficient. It was further suggested that
HCl enhances diffusion by creating ionic and Bjerrum L-defects
while HNO3 reduces diffusion by forming stable HNO3-hyrate
cages that limit HDO migration.32
Discussion
In the discussion that follows, the present results are compared
with the results from the previous ice film studies and discussed
in terms of a molecular self-diffusion mechanism. Then, the
differences between the film studies and the previous bulk ice
studies are discussed. Finally, the present results are discussed
in terms of an alternative mechanism, namely, a long-range H/D
diffusion mechanism by a proton hop-orientational turn
sequence.
Kang’s research group13 examined vertical water diffusion
into very thin ice films using Cs+ reactive ion scattering (RIS)
with mass spectrometric detection. Amorphous H2O ice films
were vapor-deposited on Ru(0001) between 100 and 140 K with
thicknesses of 1-5 BL. A fractional coverage of D2O was then
added onto the ice film. Self-diffusion of D2O into the H2O ice
film and reverse migration of H2O to the surface resulted in a
change in the surface concentration of the isotopic species,
which was detected with a depth resolution of 1 BL. Diffusion
into just the top 3 BL was probed. The diffusion followed first-
order kinetics, yielding a first-order rate constant. The rate
constant showed Arrhenius-like temperature dependence, yield-
ing an energy of activation of 13.7 kJ/mol. While this energy
of activation is rather low, it is very important to note that
changes right at the ice surface were probed and the ice sample
was amorphous and not crystalline. Interestingly, the activation
energy is similar to the energy associated with the motion of
interstitials. Hondoh’s group5-7 determined that the energy of
activation of interstitials in ice is composed of two components,
the energy for interstitial formation and the energy for interstitial
motion; i.e., Ea ) Eif + Eim. If the energy for interstitial
formation is very low, ca. Eif ≈ 0, for the amorphous ice surface
due to molecular disorder and high defect concentrations, then
Ea ≈ Eim, where Eim ) 15.4 kJ/mol. Thus, the close agreement
between Kang’s Ea and Hondoh’s Eim suggests that the measured
diffusion is due to an interstitial mechanism. Finally, a diffusion
coefficient at 140 K was estimated using the diffusion equation,
x2 ) 2Dt, equating the first-order half-life with the diffusion
time and assuming that the diffusion length for was one
interlayer spacing (ca. 1 BL ) 0.366 nm). This produced D(140
K) ) 8 × 10-17 cm2/s.
Comparison of Ice Film Studies. George’s research group10-12
had previously studied diffusion of water in low-temperature
ice films. In particular, the diffusion of H218O and HDO into
H2O ice from 146 to 170 K was examined using a laser-induced
thermal desorption technique with mass spectrometric detection.
The ice samples were multilayer ice films grown epitaxially on
a Ru(001) metal substrate to thicknesses of ∼25-200 BL and
were reported to be crystalline according to LEED measure-
ments.10 After deposition of a thin ice film, a tracer molecule
was adsorbed onto the surface. Experiments included H218O (ca.
1 BL) diffusing into H2O ice and HDO (ca. 2-9 BL) diffusing
into H2O or D2O ice. The HDO was produced on the ice surface
by the rapid H/D isotopic exchange of D2O on H2O ice (or H2O
on D2O ice). The HDO production and thickness were es-
sentially the same as the present experiments (cf. 2-9 BL to
4-10 BL). Diffusion of the tracer molecule from the surface
into the thin ice film was detected by isothermally desorbing
the ice multilayer with a laser pulse and then monitoring the
water species with mass spectrometry. Diffusion was measured
throughout the entire crystalline ice film. An experiment
involving 1 BL of H218O sandwiched between two H2O ice
layers was also performed and yielded similar results. A
summary of these results is provided in Table 1. Over the
temperature range 146-170 K, the reported energy of activation
for self-diffusion of water into crystalline ice films is between
69.9 and 71.1 kJ/mol.10-12 These values are close to the energy
values from the earlier tracer experiments and might suggest a
similar mechanism, namely, molecular self-diffusion by inter-
stitials.
For the present experiments, a few bilayers of D2O were
vapor-deposited on a pure crystalline H2O ice film or an HCl-
doped ice film. Upon deposition, H/D isotopic exchange quickly
converted the D2O layer into an HDO-rich mixture layer.
Infrared absorption spectroscopy was used to follow the changes
of the HDO from the initial HDO mixture layer to HDO isolated
in the H2O ice film. The absorbance of isolated HDO displayed
first-order kinetics on acid-doped ice films and was attributed
to diffusion of HDO. An Arrhenius analysis produced an
activation energy of 25 ( 5 kJ/mol.
A diffusion coefficient can be estimated, similar to Kang’s
study as presented above,13 using the measured first-order rate
constant, an assumed diffusion length, and the one-dimensional
Einstein-Smoluchowski diffusion equation, x2 ) 2Dt. The
George’s group also examined the diffusion of HDO diffusing
into acid-dosed crystalline D2O ice films.32 In these experiments,
the HDO was produced by the reaction of HCl or HNO3 dosed
onto the D2O ice surface. The surface coverage of the acid was
0.3-5 BL for HCl and 0.5-3 BL for HNO3. The derived
diffusion coefficients were independent of acid surface coverage.
Relative to the pure ice studies, the HCl-dosed ice films gave
increased HDO diffusion, while the HNO3-dosed ice films gave
decreased diffusion (see Table 1). The presence of HCl appears
to increase Ea while HNO3 decreases it. Puzzling, the diffusion

Diffusion of HDO in Pure and Acid-Doped Ice Film
J. Phys. Chem. A, Vol. 110, No. 38, 2006 11071
diffusion time was equated to the first-order half-life at 140 K
(ca. the midrange temperature): k ) 7.2 × 10-4 s-1 and the
half-life is 960 s (or 16 min). Therefore, a diffusion time of t )
16 min was assumed. Since the initial HDO mixture layer was
4-10 BL thick, it was assumed that the HDO would have to
diffuse a typical length of about 4 BL (ca. 1.464 nm) from the
HDO-rich mixture layer into the ice film. Using these values
for t and x in the one-dimensional diffusion equation, gives an
estimated diffusion coefficient of D(140 K) ) 1.1 × 10-17 cm2/
s. This value is obviously an estimate that is highly dependent
upon the stated approximations. For comparative purposes, the
diffusion coefficient at 140 K was calculated for the other ice
film studies using the published diffusion data. A summary of
the results are presented in Table 1.
ficient at 140 K from the higher temperature bulk ice studies to
those in Table 1 for the low-temperature ice films indicates a
large discrepancy of 103 times and more.
At least three possible explanations have been presented in
the literature for the large difference in the diffusion coefficients
and activation energies between the previous, higher temperature
bulk ice studies and the more recent, low-temperature ice film
studies. The first and simplest explanation is that the extrapola-
tion of Arrhenius-like behavior is not valid from ∼250 K to
the lower temperatures.10 Small uncertainties in the preexpo-
nential factor and the energy term are greatly magnified when
the extrapolation is as great as 100 K. Thus, it is simply
inappropriate to expect the diffusion results from the two types
of studies to overlap.
In a comparison of the film results, the activation energy
varies from 13.7 to 79.5 kJ/mol while the diffusion coefficient
at 140 K varies from (0.2-80) × 10-18 cm2/s. In an explanation
of these differences, there are at least two important aspects to
keep in mind: (1) the ice morphology (i.e. amorphous,
polycrystalline, or crystalline ice); (2) the depth probed (i.e.
surface, subsurface, or interior ice). George’s ice films were
thought to be single crystals with fairly few defects. Diffusion
was probed through the entire thickness of the ice film (ca. 25-
200 BL). The Ea values are large and very similar to those
reported for diffusion in bulk ice. The calculated diffusion
coefficients represent the smallest values. Kang’s ice films were
amorphous and presumably had many structural defects. Dif-
fusion was probed at the surface to a depth of ∼3 BL. This
study yielded the lowest Ea and the largest diffusion coefficient.
The present ice films were thought to be mostly polycrystalline
and therefore possessed more defects than single-crystal ice but
less than amorphous ice. Furthermore, the addition of HCl
increases the number of defects. Diffusion was probed across
the interface between the HDO mixture layer and the underlying
acid-doped ice film, ∼4-10 BL below the ice surface. The Ea
and diffusion coefficient values are intermediate between the
other studies. Thus, the results agree with expectations on the
basis of the ice morphology and the experimental depth probed
by the different techniques.
The second explanation is that the mechanism for molecular
self-diffusion in ice changes between the two temperature
ranges. The mechanism involves migration of lattice defects,
either interstitials or vacancies, where interstitials are H2O
molecules in ice that do not occupy regular crystal lattice sites,
while vacancies are unoccupied crystal lattice sites. Migration
by these molecular defects may also be assisted by ionic and
Bjerrum defects.1,2 The research by Hondoh’s group5-7 appears
to confirm that the major mechanism involves migration by
interstitials for T g 220 K. For this mechanism, the diffusion
depends on the number or concentration of interstitials in ice.
For the lower temperatures, the concentration of interstitials may
become vanishingly small. Thus, George’s group has suggested
that the mechanism may involve migration by vacancies at the
lower temperature range.37 Recent work from this group
concerning diffusion of other small molecules in ice films
appears to suggest a vacancy mechanism.37
The third explanation concerns the structure or morphology
of vapor-deposited, low-temperature ice films. Microstructures
in ice films including increased defects, dislocations, and grain
boundaries may increase diffusion relative to diffusion in bulk
ice samples.1,2,27,30 For example, assuming that the mechanism
involves interstitials and the diffusion coefficient is proportional
to the concentration of interstitials, then the increased diffusion
coefficient at low temperature may reflect an increase in the
concentration of interstitial defects for the vapor-deposited ice
films. George’s group previously suggested that since the very
thin ice films have a large surface-to-volume ratio, the concen-
tration of interstitials in the ice multilayers may be increased
due to perturbations of the nearby surface.10 Alternatively, if
the low-temperature ice films are polycrystalline rather than
single crystals, these ice films will have an increased number
of defects, dislocations, and grain boundaries. Self-diffusion
along these ice defects may be enhanced relative to the higher-
temperature, bulk ices. This would be especially true for the
acid-doped ice films, where clusters of acid hydrates may
increase the number of defects.27 Finally, and unique to vapor-
deposited ice films, cubic crystalline ice (Ic between 130 and
150 K), hexagonal crystalline ice (Ih for T > 150 K), or a
mixture can be formed depending upon the temperature and
deposition procedure.2 A mixture would have an increased
number of structural defects that might increase diffusion.
Comparison to Bulk Ice Studies. To compare these recent
ice film studies to the previous bulk ice studies, the bulk ice
results are first summarized.1 These studies were performed at
modestly low temperatures between ∼238 and 271 K and used
the isotopic probes H218O, D2O, and T2O as tracers to follow
the diffusion process. Bulk ice samples of polycrystalline ice,
artificially grown single-crystal ice, and naturally grown single-
crystal ice, including diffusion for different crystallographic
orientations, were examined. Microtome sectioning of the bulk
ice (ca. 1 cm thick) into very thin layers (ca. 5 µm) followed
by scintillation or mass spectrometric detection was used to
measure the diffusion of the tracer species. Over the temperature
range studied, the diffusion coefficient fits the standard Arrhe-
nius expression, D ) D0 e-E /RT, with the following range of
a
values: D0 ) 0.6-330 cm2/s and Ea ) 52.1-65.6 kJ/mol.
Hobbs summaries the data from all the tracer experiments as
D(263 K) ∼ 2 × 10-11 cm2/s and Ea ∼ 62.7 kJ/mol;1 the study
by Ramseier gave the typical results of D(263 K) ) 1.49 ×
10-11 cm2/s and Ea ) 59.8 kJ/mol3, and the interstitial study
by Hondoh’s group gave D(263 K) ≈ 2 × 10-11 cm2/s and Ea
) 54.0 kJ/mol.5-7 From these values, the diffusion coefficient
was estimated by extrapolation to the midrange temperature of
140 K to be D(140 K) ∼ 2 × 10-22, 6 × 10-22, and 1 × 10-22
cm2/s, respectively, or simply an average value of D(140 K) ∼
3 × 10-22 cm2/s. Comparison of this average diffusion coef-
Presently, it is suggested that differences in the ice morphol-
ogy are probably responsible for the differences in the results
for diffusion of water in vapor-deposited ice films and bulk
crystalline ice. As discussed above, the results for the film
studies appear to be dependent upon the morphology, whether
amorphous, polycrystalline, or crystalline, and the depth of
diffusion probed, whether surface, subsurface, or interior ice.
Structural defects must play an important role. Vapor-deposited

11072 J. Phys. Chem. A, Vol. 110, No. 38, 2006
Oxley et al.
films, controlled by condensation kinetics, have more defects
than bulk ice samples that have been carefully prepared under
equilibrium conditions by freezing water. Films have a larger
surface-to-volume ratio, and the surface may induce more
defects deeper into the films compared to bulk ice samples.
Finally, the diffusion depth probed for the ice film studies varied
from 1 to ∼100 nm, while the bulk ice studies probed interior
ice on the order of 1 cm thick.
These new results and analysis correct an earlier study15 in which
the spectral changes were attributed to H/D isotopic exchange
on H2O ice.
These spectroscopic results compare favorably with recent
studies of diffusion in low-temperature ice films.10-14 The
present activation energy falls between the values for diffusion
in crystalline ice films and amorphous ice films, while the
estimated diffusion coefficient at 140 K is very similar to the
value from a study of HDO diffusion in HCl-dosed ice films.30
However, the results from all the ice film studies at low
temperatures differ from earlier bulk ice studies at higher
temperatures. In particular, extrapolation of the results from the
bulk ice studies to 140 K yields an estimated diffusion
coefficient that is at least 103 times smaller than the values
determined from the ice film studies. The discrepancy is
probably due to differences in the ice structure or morphology
between vapor-deposited ice films and bulk ice samples.
Microstructures in ice films including increased defects, disloca-
tions, and grain boundaries would increase diffusion relative to
diffusion in bulk crystalline ice samples.
Furthermore, in comparing studies, it is important to note
that HDO can diffuse in ice by two mechanisms: (1) self-
diffusion by either interstitial or vacancy migration; (2) H/D
diffusion by a series of proton hop-molecular orientational turn
steps. In “neutral” ice, the self-diffusion mechanism operates
and is slow. Again, on the basis of the bulk ice studies, it is
therefore surprising that self-diffusion in low-temperature films
has been observed. For acid-doped ice, the excess protons turn
on the long-range hop-turn mechanism, thereby enhancing
HDO diffusion in low-temperature ice films.
Long-Range H/D Diffusion Mechanism. Finally, an alterna-
tive explanation for the present spectroscopic results involves
long-range H/D diffusion rather than a molecular self-diffusion
mechanism. This diffusion mechanism is effectively the same
as the H/D isotopic exchange mechanism proposed and devel-
oped by Devlin and co-workers.2,19,20 They have successfully
applied this mechanism to the observed H/D exchange in pure
bulk ice and both pure and HCl-doped ice nanocrystals.
According to this mechanism, the first step involves the passage
of a protonic defect through adjacent H2O and D2O molecules
in the ice lattice to form the nearest-neighbor group (HDO)2.
The second step involves the passage of an orientational Bjerrum
L-defect. This defect flips the orientation of the HDO molecules
in the (HDO)2 species to form two isolated HDO molecules
separated by two oxygen atoms. For the present results, the
(HDO)2 species already exists in the isotopic mixture layer, due
to the initial rapid H/D exchange of D2O on the ice film, as
shown in Figure 2a. It is the formation of isolated HDO by
step 2 above that could involve long-range, multiple passage
of a protonic defect followed by the passage of an orientational
Bjerrum L-defect. Thus, a series of multiple proton hopping
and orientational turning steps could move D toward the interior
and H toward the surface, leading to isotopic mixing and the
formation of isolated HDO molecules. This long-range H/D
diffusion is highly unlikely in pure ice films because of slow
proton hopping over the estimated distance (ca. 4 BL), which
is consistent with the present results for diffusion on pure ice
films. However, for the acid-doped ice films, the increased
proton activity could increase the proton hopping step, such that
a series of multiple hopping followed by orientational turn steps
could cause the observed H/D diffusion. Concerning the “off-
on” behavior with acid concentration, once the acid reaches a
certain activity level that turns on the H/D diffusion, the
diffusion would then be limited by the turn step. Thus, additional
acid would not necessarily cause the diffusion to be faster but
would be limited by the rate of the orientational turn step. This
alternative H/D diffusion mechanism therefore appears to
account for the present results. Additionally, this mechanism is
consistent with the very recent work from Kang’s group,31 as
pointed out in the Results. For these reasons, it is the favored
mechanism for explaining the present results.
Acknowledgment. This research has greatly benefited from
many helpful and insightful discussions with Professor Devlin.
We gratefully acknowledge the financial support of the Welch
Foundation and the Dreyfus Foundation.
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