Adsorbate-induced distortion of solid surfaces. Application to HCl on ice at stratospheric conditions
It is shown that the adsorption of HCl molecules at the surface of ice increases, if the HCl binding energy increases with the distortion amplitude of the oxygen sites of ice. At the same time, the adsorption stimulates an increase of the Lindemann parameter for the ice lattice, driving its melti...
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irk-123456789-1204002017-06-13T03:04:44Z Adsorbate-induced distortion of solid surfaces. Application to HCl on ice at stratospheric conditions Vakarin, E.V. Holovko, M.F. Badiali, J.P. It is shown that the adsorption of HCl molecules at the surface of ice increases, if the HCl binding energy increases with the distortion amplitude of the oxygen sites of ice. At the same time, the adsorption stimulates an increase of the Lindemann parameter for the ice lattice, driving its melting at temperatures (T = 190 K) relevant to the polar stratosphere. Similar effects take place when the lateral interaction between HCl molecules becomes more attractive due to the coupling through the ice lattice. Показано, що адсорбція молекул HCl на поверхню льоду зростає, якщо зростає енергія зв’язку молекул HCl при збільшенні амплітуди спотворення кисневих вузлів льоду. В той же час адсорбція стимулює зростання параметра Ліндемана для гратки льоду, приводячи до її плавлення при температурах (T = 190 K), відповідних до полярної стратосфери. Подібні ефекти спостерігаються, коли латеральна взаємодія між молекулами HCl стає більш притягальною внаслідок з’єднання через гратку льоду. 2001 Article Adsorbate-induced distortion of solid surfaces. Application to HCl on ice at stratospheric conditions / E.V. Vakarin, M.F. Holovko, J.P. Badiali // Condensed Matter Physics. — 2001. — Т. 4, № 2(26). — С. 251-260. — Бібліогр.: 22 назв. — англ. 1607-324X PACS: 05.70.Np, 68.45.Da, 92.60.Jq DOI:10.5488/CMP.4.2.251 http://dspace.nbuv.gov.ua/handle/123456789/120400 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| description |
It is shown that the adsorption of HCl molecules at the surface of ice increases,
if the HCl binding energy increases with the distortion amplitude
of the oxygen sites of ice. At the same time, the adsorption stimulates an increase
of the Lindemann parameter for the ice lattice, driving its melting at
temperatures (T = 190 K) relevant to the polar stratosphere. Similar effects
take place when the lateral interaction between HCl molecules becomes
more attractive due to the coupling through the ice lattice. |
| format |
Article |
| author |
Vakarin, E.V. Holovko, M.F. Badiali, J.P. |
| spellingShingle |
Vakarin, E.V. Holovko, M.F. Badiali, J.P. Adsorbate-induced distortion of solid surfaces. Application to HCl on ice at stratospheric conditions Condensed Matter Physics |
| author_facet |
Vakarin, E.V. Holovko, M.F. Badiali, J.P. |
| author_sort |
Vakarin, E.V. |
| title |
Adsorbate-induced distortion of solid surfaces. Application to HCl on ice at stratospheric conditions |
| title_short |
Adsorbate-induced distortion of solid surfaces. Application to HCl on ice at stratospheric conditions |
| title_full |
Adsorbate-induced distortion of solid surfaces. Application to HCl on ice at stratospheric conditions |
| title_fullStr |
Adsorbate-induced distortion of solid surfaces. Application to HCl on ice at stratospheric conditions |
| title_full_unstemmed |
Adsorbate-induced distortion of solid surfaces. Application to HCl on ice at stratospheric conditions |
| title_sort |
adsorbate-induced distortion of solid surfaces. application to hcl on ice at stratospheric conditions |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2001 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120400 |
| citation_txt |
Adsorbate-induced distortion of solid
surfaces. Application to HCl on ice at
stratospheric conditions / E.V. Vakarin, M.F. Holovko, J.P. Badiali // Condensed Matter Physics. — 2001. — Т. 4, № 2(26). — С. 251-260. — Бібліогр.: 22 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT vakarinev adsorbateinduceddistortionofsolidsurfacesapplicationtohcloniceatstratosphericconditions AT holovkomf adsorbateinduceddistortionofsolidsurfacesapplicationtohcloniceatstratosphericconditions AT badialijp adsorbateinduceddistortionofsolidsurfacesapplicationtohcloniceatstratosphericconditions |
| first_indexed |
2025-07-08T17:49:00Z |
| last_indexed |
2025-07-08T17:49:00Z |
| _version_ |
1837101950656577536 |
| fulltext |
Condensed Matter Physics, 2001, Vol. 4, No. 2(26), pp. 251–260
Adsorbate-induced distortion of solid
surfaces. Application to HCl on ice at
stratospheric conditions
E.V.Vakarin 1 , M.F.Holovko 1 , J.P.Badiali 2
1 Institute for Condensed Matter Physics
of the National Academy of Sciences of Ukraine,
1 Svientsitskii Str., 79011 Lviv, Ukraine
2 Structure et Réactivité des Systèmes Interfaciaux,
Université Pierre et Marie Curie,
4 Place Jussieu, 75230 Paris Cedex 05, France
Received December 20, 2000
It is shown that the adsorption of HCl molecules at the surface of ice in-
creases, if the HCl binding energy increases with the distortion amplitude
of the oxygen sites of ice. At the same time, the adsorption stimulates an in-
crease of the Lindemann parameter for the ice lattice, driving its melting at
temperatures (T = 190 K) relevant to the polar stratosphere. Similar effects
take place when the lateral interaction between HCl molecules becomes
more attractive due to the coupling through the ice lattice.
Key words: adsorption of HCl on ice, two-dimensional lattice gas, lattice
distortion, surface melting
PACS: 05.70.Np, 68.45.Da, 92.60.Jq
1. Introduction
Adsorption of HCl on ice is believed to be one of the preliminary steps, involved
into the ozone depletion over the Antarctic [1]. The exceptional importance of the
problem has initiated extensive theoretical [2–5] and experimental [7–11] investiga-
tions in this field. One of the most important points is the mechanism for chlorine
accumulation through the HCl ionization upon adsorption on ice. Semiempirical cal-
culations suggest [12] that at least four to six water molecules are needed to ionize
HCl, while the natural coordination of the honeycomb lattice (ice Ih) at the surface
is three. It should be stressed that the solvation mechanism is strongly correlated
with the mechanism of HCl adsorption.
Several theoretical approaches were developed to explore this phenomenon. One
of them [3] takes into account the dynamic nature of ice-vapour interface. In the
c© E.V.Vakarin, M.F.Holovko, J.P.Badiali 251
E.V.Vakarin, M.F.Holovko, J.P.Badiali
course of water and HCl co-adsorption the latter can be encapsulated during the
process of ice growth. However, the collision frequency (partial pressure) of water
molecules with the ice surface should be high enough to account for the formation
of the solvation shell before HCl has time to desorb.
Another model [4] assumes that the ionization is assisted by a quasi-liquid layer
which exists on the surface of ice, providing in this way an appropriate coordination
for adsorbed HCl molecules. Nevertheless, the nature of the quasi-liquid layer at
stratospherically relevant conditions (low temperatures, T ≈ 200 K and pressures,
pHCl ≈ 10−7 − 10−6 Torr) remains to be investigated.
The nonideality of the ice surface was examined as a source of increasing ad-
sorption. For instance, the defect-assisted adsorption [5] is consistent with the en-
capsulation scenario. However, our preliminary estimation [6] implies that point-like
defects (like vacancies) do not give a significant increase of the binding energy. To
recover the experimentally measured adsorption energy (46 kJ/mole), one has to
assume a binding energy of about 60–80 kJ/mole at the defect sites, depending on
their concentration. This suggests the investigation of more extended defects (like
cracks or pores).
Moreover, recent experiments [7–9] give a convincing evidence that adsorbate-
induced effects should be considered in order to make a link between all the aspects
concerning the HCl-ice interface. In particular, we have already demonstrated that
in the quite general case (when the cohesion energy of a crystal is comparable to the
adsorbate-substrate or adsorbate-adsorbate interactions), the adsorbate-substrate
coupling may lead to a distortion [13] or restructuring [14] of the substrate lattice.
In addition, it was shown that the adsorption may facilitate a local melting [15] and
roughening [16] of the substrate, such that the corresponding disordering tempera-
tures are much lower than those for a clean surface. Since both the HCl-ice binding
energy and the ice cohesion energy are of the order of the hydrogen bond strength
(≈ 20 kJ/mole), we expect these effects to be especially pronounced.
In this paper, based on previous experience, we argue that the adsorbate-induced
effects may lead to the formation of quasi-liquid droplets [15], involving a local dis-
tortion (or even melting) of the ice lattice supplemented by the condensation of HCl
molecules around the distorted domains. We take into account the dynamic nature
of the ice surface, that is, the lattice sites are allowed to displace from their equilib-
rium positions, distorting in this way an ideal lattice arrangement. Then the binding
energy of HCl at a given site should depend on the distortion amplitude. Dynamical
effects are discussed within the harmonic approximation, which is known [17] to
be quite reliable for the bulk ice-Ih. Application of these simple models together
with order of magnitude estimations, based on experimental data, demonstrate that
the formation of quasi-liquid droplets can be realized at stratospherically relevant
conditions. Nevertheless, the distortion alone does not explain experimental results
regarding coverage and adsorption energy. For that reason, our approach should be
modified to include a solvation mechanism.
252
Adsorbate-induced distortion of solid surfaces
2. Single-site approach
The surface of ice is modelled as a planar honeycomb lattice of N adsorbing
sites whose equilibrium positions are given by the set {R0
i }. More precisely, we
associate the lattice with the arrangement of oxygen atoms. The lattice is taken as
non-rigid, that is the sites are allowed to deviate from their equilibrium positions
(for instance, due to vibration at non-zero temperatures, or dynamic distortion). We
consider the displacements ui = Ri − R
0
i , where Ri is a vector specifying the site
location. To provide an adequate lattice dynamics calculation we have to take into
account the random heterogeneity of the force constants [18]. As we only focus on
certain dynamic aspects, it is sufficient to consider a single-site approach, capable of
recovering the mean square displacements with a reasonable choice of the effective
rigidity coefficient. Thus the surface of ice is described by the effective Hamiltonian
HI =
γ
2
∑
i
u
2
i , (1)
where γ is the rigidity coefficient determining the mean square displacement (or the
lattice distortion)
δ20 = 〈
∑
i
u
2
i 〉/N = kT/γ. (2)
Here 〈...〉 denotes thermodynamic averaging. This Gaussian form can be taken as a
mean-field limit of the harmonic approximation [17] used for the description of the
lattice dynamics of ice. By introducing such an approach we underestimate the pair
correlations and neglect the heterogeneity [18] in the force constants. Nevertheless,
our model gives a reasonably good agreement with the lattice dynamics calculations.
In particular, at T = 190 K, the mean square displacement for the ice bulk is
[19] δ20 = 0.0083 Å2, which is consistent with experimental data. To recover this
value (using equation (2)) we have to assume γ = 1.97 eV/Å2, which is in the
range between the weaker (1.1 eV/Å2) and the stronger (2.1 eV/Å2) intermolecular
stretching force constants [19] used in the lattice dynamics calculations of the ice-Ih
bulk.
The lattice is in contact with a fluid of HCl that occupies the half-space above
the surface. An HCl molecule is modelled as a hard sphere with a point-like sticky
site, that may bind with the lattice sites. Therefore, the interaction of HCl molecules
with the surface is described by the lattice gas Hamiltonian
H =
W
2
∑
ij
titj −
∑
i
(µ+ ǫ0 + ǫ(ui))ti, (3)
where W is the pair interaction between the two adsorbed nearest neighbour HCl
molecules and µ is their chemical potential. The set of occupation numbers t i = 0, 1
controls the distribution of adsorbates at the lattice sites. As it was shown in our
earlier works [13,14], such a Hamiltonian can be obtained, by integrating out the
fluid bulk. In this way, W and µ+ ǫ0 + ǫ(ui) are related to the mean force potential
253
E.V.Vakarin, M.F.Holovko, J.P.Badiali
and the density profile in the fluid, respectively. The binding energy ǫ0 corresponds
to a lattice “frozen” at equilibrium (rigid lattice). This case corresponds to the
conditions studied by Kroes and Clary [2]. In addition, we have a term, ǫ(ui), which
depends on the lattice distortion.
ǫ(ui) =
ǫ
2
u
2
i + ... . (4)
The expansion above implies that ǫ(ui) is an isotropic function. To proceed further
we have to decide on whether ǫ(ui) increases or decreases with ui. A recent theoret-
ical study [20], which allowed HCl to vibrate, gave an adsorption energy (roughly,
the average binding energy) of 25 kJ/mole, which is about 6 kJ/mole larger than
that for a rigid HCl model. We may expect a similar increase, if the lattice of ice
is not rigid. Also, we argue that ǫ0 does not correspond to a maximum, because of
the quite limited ability of the Cl atom to interact with the surface. A distortion of
the oxygen lattice may distort the HCl-ice hydrogen bonds, reducing the distance
between a Cl atom and the surface and allowing for a larger binding energy. Based
on this, we assume ǫ > 0. Of course, such a mechanism cannot give an unlimited gain
in the binding energy. If the distortion is too strong, then it may break the hydro-
gen bonds between HCl and ice. This can be reproduced by taking additional terms
in the expansion (4). Instead of doing so, we retain the quadratic approximation,
keeping in mind its restricted validity (|u i| 6 umax). On the other hand, we have to
keep ǫ < γ, in order to avoid instabilities because of the Gaussian approximation of
the lattice displacements. The free energy, in the mean field approximation (MFA)
for the occupation numbers, is given by
Φ =
βF
N
=
βF 0
I
N
− 3βWΘ2
2
− ln
(
1 +
1
1− ǫ/γ
eβ(µ+ǫ0−3WΘ)
)
, (5)
where F 0
I is the lattice free energy at zero coverage and β = 1/kT . Minimizing Φ
with respect to Θ, we obtain the equilibrium coverage
Θ =
1
N
∑
i
〈ti〉 =
1
1−ǫ/γ
eβ(µ+ǫ0−3WΘ)
1 + 1
1−ǫ/γ
eβ(µ+ǫ0−3WΘ)
. (6)
For a rigid lattice (ǫ = 0, ǫ0 = 20 kJ/mole) and at stratospherically relevant con-
ditions (pHCl = 10−7 Torr, T = 190 K) equation (6) gives Θ = 4.3 · 10−8, which is
exactly of the same order of magnitude as in the simulation [2]. It is clear that Θ
increases as ǫ/γ → 1, since the effective binding energy
E = ǫ0 + kT ln [1/(1− ǫ/γ)] (7)
grows with ǫ/γ. This gives a shift of the adsorption isotherm towards lower pressures
(see figure 1). This, in turn, gives a larger adsorption energy than that corresponding
to a rigid lattice. To demonstrate this we rearrange equation (6) to the conventional
form [21], involving the free energy of adsorption ∆G
e−β∆G = eβ(E−3WΘ) Θ
1−Θ
. (8)
254
Adsorbate-induced distortion of solid surfaces
0,0
0,2
0,4
0,6
0,8
1,0
-8 -6 -4 -2 0 2
ε/γ=0.9
ε/γ=0.6
exp[β(µ+ε0)]
Θ
0,6 0,8
5
10
15
20
Θ=0.8
Θ=1
( δ
/ δ
0)
2
ε/γ
Figure 1. Coverage, calculated at W = 0, as a function of the dimensionless
pressure P = exp[β(µ + ǫ0)] (single-site approach). Relative mean square dis-
placement (δ/δ0)
2 as a function of ǫ/γ is shown in the inset. Stratospheric con-
ditions (T = 190 K, pHCl = 10−7 − 106 Torr, ǫ0 = 20 kJ/mole) correspond to
P = 4.3 · (10−8 − 10−7).
The so-called standard value ∆G0 (calculated at Θ = 1/2) is then proportional to
the binding energy ∆G0 = −E + 3W/2. If we neglect the lateral interaction W
between HCl molecules, then E is a measure of the adsorption free energy. The
distortion implies an increase in the coverage up to Θ = 4 · 10−6 (at ǫ/γ = 0.99),
which is still too far from the experimental results Θ ≈ 0.4− 0.8.
Taking a derivative of Φ with respect to γ and using the result (2) for δ20, we
obtain the coverage-dependent mean square displacement of the lattice
δ2 = δ20
[
1 +
ǫ/γ
1− ǫ/γ
Θ
]
(9)
increases with increasing ǫ (the inset in figure 1). The mean square displacement is
closely related to the Lindemann parameter L =
√
δ2/d, which is a semiempirical
measure of melting. Recall that the Lindemann criterium states that a crystal melts
when L ≈ 0.1, where d is the equilibrium lattice spacing. The equilibrium spacing
in the bulk ice is d = 2.76 Å (at T = 190 K). Thus, to match the Lindemann
criterium, we must have δ = 0.276 Å. Returning to equation (9) we see that this
255
E.V.Vakarin, M.F.Holovko, J.P.Badiali
is the case when δ/δ0 = 3.03. The latter occurs when ǫ/γ = 0.91 and ǫ/γ = 0.89
for Θ = 0.8 and Θ = 1, respectively. Therefore, if the gain in the binding energy
ǫ becomes comparable with the rigidity coefficient γ, then the ice surface is driven
towards melting (provided that we know how to explain Θ ≈ 1). It is instructive to
calculate the molar energy excess ∆E due to the lattice distortion
∆E = 〈E − ǫ0〉 =
ǫ
2
NAδ
2. (10)
For ǫ = 1.95 eV/Å2 and δ = 0.276 Å we obtain ∆E = 7.23 kJ/mole. Then the total
energy E ≈ 28 kJ/mole, which is far below the experimental data (46 kJ/mole).
Our estimation is closer to the result [20] (25 kJ/mole), obtained when the HCl
molecules were allowed to vibrate. Based on this we may conclude that the dis-
tortion energy is not enough to explain experimental values for both coverage and
adsorption energy. Nevertheless, this does not mean that the distortive mechanism
should be abandoned. Simply, the adsorbate-induced distortion is not the only ef-
fect. If the mean square displacements of oxygen sites become large enough, then
an adsorbed HCl molecule is found in a quasi-liquid environment [4] that may facil-
itate its dissociation. The latter is beyond the scope of our simple model. However,
the model does explain how such distorted (or quasi-liquid) domains may appear at
stratospherically relevant conditions.
3. Dynamic effects
In the previous section we neglected the pair correlations. For that reason we
were not able to determine the extent of the distorted domains. It is known [22] that
an indirect (through the substrate) interaction between the adsorbates is inversely
proportional to the substrate shear modulus. Therefore, pair-wise effects should
become quite important with increasing distortion. We keep the same model for the
lattice and HCl molecules, but now the ice Hamiltonian is given by the following
harmonic approximation
HI =
∑
ij
Dij(ui − uj)
2, (11)
where Dij is the force constant (or elastic) matrix. The HCl-HCl pair interaction is
represented by the expansion
W (Ri,Rj) = W +∆ij(ui − uj)
2 + ... , (12)
where W is the pair interaction between two HCl molecules, adsorbed at the equi-
librium positions of the ice lattice. The second term corresponds to the interac-
tion,which is mediated by the lattice distortion. For simplicity, we drop the linear
term, by assuming that the equilibrium lattice spacing is close to an extremum of
W (|Ri−Rj |), such that, ∆ij represents the curvature of the HCl mean force poten-
tial, calculated at distances of the order of the equilibrium lattice spacing. Therefore,
the adsorption of HCl is described by the lattice gas model
H =
∑
ij
[W +∆ij(ui − uj)
2]titj ,−(µ+ ǫ0)
∑
i
ti (13)
256
Adsorbate-induced distortion of solid surfaces
in which the lateral HCl interaction is coupled to the lattice distortion. As we are
interested in estimating the difference due to this additional interaction, it is rea-
sonable to apply a perturbative technique, developed in our previous studies [15,16].
Choosing a system with ∆ij = 0 as reference and performing a summation over {ti}
we obtain the following effective Hamiltonian for the displacements
Hef =
∑
ij
[Dij + χij∆ij](ui − uj)
2, (14)
where χij = 〈titj〉 − 〈ti〉〈tj〉 ≈ ξ2 exp(−Rij/ξ) is the adsorbate correlation function
and ξ is the correlation length. It is now clear that the range of the adsorbate-
induced perturbation is of an order of the adsorbate correlation length. The latter
determines an average size of the distorted domains, as mentioned in the previous
section. The Hamiltonian (14) allows us, at least in principle, to explore all the
lattice dynamic aspects. Instead of doing so, we restrict ourselves by an order of
magnitude estimation to determine the conditions under which quasi-liquid droplets
may be formed. Clearly, everything depends on the symmetry of the Dij and ∆ij
matrices and on the magnitude of their elements. Also, the range and symmetry of
χij plays a role. If the HCl gas is correlated at distances much larger than the lattice
spacing, then the correlation function may be replaced by a number proportional
to ξ2. Fourier transformation allows one to diagonalize the Hamiltonian (14). This
gives a dispersion law. At small wave vectors k, the frequency splits according to
the splitting of the dynamic matrix
D(k) + ξ2∆(k) → Ω(k) = ω0(k) + ξ2ω1(k), (15)
where ω0(k) is the frequency spectrum of the pure ice lattice, while ξ 2ω1(k) gives the
shift due to the adsorbate-induced effects. To estimate the mean square displacement
δ2 we use the so-called flat spectrum approximation Ω(k) = Ω ∝ D+ ξ 2∆, in which
the collective frequency Ω(k) for a given mode is replaced by an effective one-body
frequency Ω. Then we obtain
δ2 =
δ20
1 + ξ2∆/D
. (16)
It is seen that δ2 increases with ξ2 when ∆ is negative. Then we are restricted to
ξ2∆/D < 1 in order to keep the stability of Hef . Therefore, the surface of ice is
strongly distorted when the HCl-HCl interaction becomes more attractive due to
the coupling through the ice substrate. Conditions at which an indirect interaction
between the adsorbates is attractive are extensively discussed in [22]. Note, however,
that W (Ri,Rj) is a mean force potential for HCl, so that an additional attraction
through the gas phase may exist [13,14]. However, the distortion is not monotonic
with the coverage, since ξ2 ∝ Θ(1−Θ). The maximum is at Θ = 1/2, that is, when
the strongest density fluctuations in the adsorbate take place [15].
Using the same perturbative technique we calculate the coverage
Θ =
eβ(µ+ǫ0)e−3β[W+∆δ2]Θ
1 + eβ(µ+ǫ0)e−3β[W+∆δ2]Θ
, (17)
257
E.V.Vakarin, M.F.Holovko, J.P.Badiali
0,0
0,2
0,4
0,6
0,8
1,0
-8 -6 -4 -2 0 2
β∆ δ2=1
β∆ δ2=1.5
β∆ δ2=2
exp[β(µ+ε0)]
Θ
Figure 2. Coverage, calculated at W = 0, as a function of the dimensionless
pressure P = exp[β(µ+ ǫ0)] (pair approach) at different β∆δ2. Other parameters
are the same as for the previous figure.
where we have replaced δ20 by δ2 in order to correct our approximate treatment. As is
seen in the figure 2, the coverage increases with increasing distortion, provided that
∆ < 0. The adsorption isotherms exhibit a liquid-gas coexistence when the interac-
tion parameter β∆δ2 increases. This implies a droplet formation for the adsorbate
around the distorted lattice domains. To observe this effect at stratospheric condi-
tions (P = eβ(µ+ǫ0) = 4 · 10−8) we have to accept an unphysically large distortion.
Nevertheless, we were able to obtain a reasonably high coverage out of the critical
regime. For instance, Θ = 1/2 can be achieved if NA∆δ2 ≈ 4.74 kJ/mole. For a
distortion amplitude δ = 0.276 Å, satisfying the Lindemann criterium, this corre-
sponds to ∆ = 2.4 eV/Å2 (that is ∆ ≈ D). The total binding energy (25 kJ/mole)
is still below the experimental value. As is discussed above, we have to incorporate
a solvation mechanism in order to remove this discrepancy.
4. Conclusion
In this paper an adsorbate-induced mechanism of the ice lattice distortion is
suggested. It is shown that the adsorption of HCl molecules at the surface of ice
258
Adsorbate-induced distortion of solid surfaces
increases, if either the HCl binding energy or the HCl-HCl attraction increase with
increasing distortion amplitude for the oxygen sites of ice. Simultaneously, the ad-
sorption stimulates an increase of the Lindemann parameter for the ice lattice, driv-
ing its local melting at temperatures (T = 190 K) relevant to the polar stratosphere.
This may cause the ionization of HCl, since the local coordination of HCl-water com-
plexes increases with the lattice distortion. The range of the distorted domains is
shown to be comparable with the adsorbate correlation length. The coverage varies
from Θ ≈ 10−6 to Θ ≈ 1/2 for a realistic choice of the parameters. The adsorption
energy is estimated to be about 28 kJ/mole, that is, below the experimental results.
This discrepancy is attributed to the neglect of HCl solvation upon adsorption.
5. Acknowledgements
This work was supported by INTAS (Grant INTAS99–01162).
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E.V.Vakarin, M.F.Holovko, J.P.Badiali
Адсорбційно індуковане спотворення поверхні
твердого тіла. Застосування до адсорбції HCl на
льоді при стратосферних умовах
Е.В.Вакарін 1 , М.Ф.Головко 1 , Ж.П.Бадіалі 2
1 Інститут фізики конденсованих систем НАН України,
79011 Львів, вул. Свєнціцького, 1
2 Лабораторія структури та реактивності поверхневих систем
Університету ім. П’єра і Марії Кюрі.
Франція, 75230 Париж, площа Жюсс’є 4
Отримано 20 грудня 2000 р.
Показано, що адсорбція молекул HCl на поверхню льоду зростає, як-
що зростає енергія зв’язку молекул HCl при збільшенні амплітуди
спотворення кисневих вузлів льоду. В той же час адсорбція стиму-
лює зростання параметра Ліндемана для гратки льоду, приводячи до
її плавлення при температурах (T = 190 K), відповідних до полярної
стратосфери. Подібні ефекти спостерігаються, коли латеральна вза-
ємодія між молекулами HCl стає більш притягальною внаслідок з’єд-
нання через гратку льоду.
Ключові слова: адсорбція HCl на льоді, двовимірний гратковий
газ, спотворення гратки, поверхневе плавлення
PACS: 05.70.Np, 68.45.Da, 92.60.Jq
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