Structure and adhesion energy of the (10.4) calcite/(001) ice Ih and
(210) baryte/(001) ice Ih interfaces
BITTARELLO Erica,1 BRUNO Marco,*1,2 AQUILANO Dino2
1 SpectraLab s.r.l., Spin-off accademico dell’Università degli Studi di Torino, Via G. Quarello 15/a,
10135 Torino (TO), Italy
2 Dipartimento di Scienze della Terra, Università degli Studi di Torino, Via Valperga Caluso 35,
10125 Torino (TO), Italy *Corresponding author
marco.bruno@unito.it
Abstract
In this contribution we performed ab initio quantum-mechanical calculations to determine the equilibrium structures and specific adhesion energies (β) at 0K of the (10.4)-calcite/(001)-ice Ih and (210)-baryte/(001)-ice Ih interfaces; calcite (Cal), CaCO3, and baryte (Brt), BaSO4. Successively, by
means of the calculated adhesion energies and some approximations, the specific interface energy () at 273.15K of both interfaces was estimated and compared, in the case of calcite, with the (10.4)-calcite/water interface energy at the same temperature. Moreover, we made some general considerations on the role of the enthalpy and entropy to explain the hydrophilicity and
hydrophobicity of crystal surfaces.
We found that ice is strongly bounded to (10.4)Cal and (210)Brt surfaces, being their adhesion
energies not negligible: β(10.4)/(001)
Cal/ Ice
= 0.240 and β(210)/ (001)
Brt / Ice
= 0.336 J m-2. Moreover, we found
that the interface energy at 273.15K of the (10.4)Cal/(001)Ice system, γ(10.4 )/(001)
Cal / Ice
, is 0.333 J m-2,
significantly lower than the interface energy of the (10.4)Cal/water system ( γ(10.4 )
Cal /W
= 0.412 J m-2)
at the same temperature; the interface energy at 273.15K of the (210)Brt/(001)Ice system, γ(210)/(001)
Brt / Ice , is 0.117 J m-2, a value extremely lower than that obtained for the (10.4)
Cal/(001)Ice interface.
1. Introduction
An exhaustive knowledge of the interfaces among crystalline phases is essential to determine chemical and physical properties of composite materials for applications in several scientific fields, as medicine, electronics, mechanics, engineering and so on. Therefore, the study of surface and
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interface properties is essential in industrial applications and in a variety of pure and applied research.
A large numerous of papers focuses on crystalline interface study, and in particular: the surface and interface thermodynamics are exposed in exhaustive studies,1,2 whereas a complete analysis on
stress and strain in epitaxy is presented elsewhere.3,4 The formation of these interfaces correlated to
crystallographic observations has interested mineralogists from many years,5 but to study and
understand this complex mechanism are needed powerful techniques for the analysis of the interfaces,6 as well as theoretical and computational modeling.
Recently, theoretical and ab initio quantum-mechanical computational approach related to the determinations of the interface structure, adhesion energy, and interfacial energy of a system composed by two crystalline phases in epitaxial relationship has been discussed by Bruno et al.7,8 In
detail, they described the 2D lattice coincidences between two phases in epitaxial relationship, as well as all of the possible initial interface configurations. Then, they optimized at ab initio level the geometry of the interfaces and calculated their specific adhesion energies. The knowledge of the adhesion energy is fundamental to establish the probability to observe epitaxy: higher adhesion energies lead to higher probabilities.
In the present paper we used the computational approach described by Bruno et al.,7
focusing on the epitaxial relationships between two crystalline chemical phases, to evaluate the effect of ice Ih (H2O) on the most important calcite (CaCO3; S.G. R 3 c ) and baryte (BaSO4; S.G.
Pnma) surfaces: (10.4) and (210), respectively. Specifically, we simulated at ab initio level the
interfaces forming between the (001) surface of ice Ih, and the (10.4) and (210) surfaces of baryte and calcite, respectively: (10.4)Cal/(001)Ice and (210)Brt/(001)Ice. Then, taking advantage of their
epitaxial relationships, the structure and specific adhesion energy (β) of the (10.4)Cal/(001)Ice and
(210)Brt/(001)Ice interfaces at 0K were determined. Successively, by means of the calculated
adhesion energy and some approximations detailed in the following, the specific interface energy () at 273.15K of the (10.4)Cal/(001)Ice and (210)Brt/(001)Ice interfaces was estimated and compared, in
the case of calcite, with the (10.4)Cal/water interface energy at the same temperature. Moreover, we
made some considerations on the role of the enthalpy and entropy to explain the hydrophilicity and hydrophobicity of crystal surfaces.
We decided to investigate the faces (10.4) of calcite and (210) of baryte, for their relevant
occurrence in the morphology of these common and important minerals.9,10 Moreover, we selected
the (001) face of ice Ih, because the size of the 2D coincidence cells describing the (10.4)Cal/(001)Ice
and (210)Brt/(001)Ice epitaxy is sufficiently small to allow to perform ab initio calculations in a
reasonable time, compatibly with the resources of calculus actually in our hands.
Bernal and Fowler11 and Pauling12 discussed the noteworthy similarities between ice and
water and some studies affirmed that H2O molecules are intact in ice.13,14 Ice adhesion phenomena
were widely analyzed in several publications in the past few decades and an exhaustive and critical list is exposed in Meuler et al.15 Some of these studies include extensive discussion on the
relationships between ice adhesion and water wettability.15-17
There are eleven crystalline ice polymorphs: Ih, Ic, II, III, IV, V, VI, VII, VIII, IX and X. Water molecules in ice are always tetrahedrically coordinated, and the polymorphs differ primarily in H-bond angles and next-nearest neighbor separations. “Ordinary ice” (Ih), the most common crystalline form of ice on earth, is a hexagonal phase and is built by water molecules subjected to a set of rules known as the “ice rules”.11,18,19 The surfaces of ice Ih crystals are central to a wide
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variety of natural phenomena and several studies were carried out.20-25 Hirsch and Ojamäe26
investigated the properties and the structures of different ice polymorphs that may be used as benchmark structures for different quantum-chemical or force field methods in the future. The different possible proton-ordered structures of ice Ih for an orthorhombic unit cell with 8 water molecules were derived and 16 unique structures were found. In our work we have chosen one of these bulk ice structures with P1 symmetry (n.16).26 However, our results should be barely
influenced by the choice of the initial bulk ice structure, being the H2O molecule free to adjust at the
calcite (baryte)/ice interface.
This article is structured as follows: section 2 provides an outline of the computational details. In sections 3, the optimized structure and adhesion energies at 0K obtained at ab initio level of the (10.4) calcite and (210) baryte surfaces in contact with (001) ice Ih are described. Finally, in section 4, the specific interface energy at 273.15K of the (10.4)Cal/(001)Ice and (210)Brt/(001)Ice
interfaces is estimated.
2. Computational details
To investigate the interface structure between two phases in epitaxial relationship, a 2D periodic slab model27 and the ab initio CRYSTAL14 code28-30 were adopted.
The calculations for the calcite/ice system were carried out by testing several Hamiltonians:
B3LYP,31-33 B3LYP_DC (B3LYP hybrid functional + GRIMME long-range empirical Dispersion
Correction),34 HF (Hartree-Fock) and PBE0_DC (PBE0 hybrid functional + Grimme long-range
empirical Dispersion Correction),35 and successively the results were compared. Grimme
parameters used: s6 (scaling factor) = 1.0, d (steepness) = 20.0, Rcut (cutoff distance to truncate
direct lattice summation) = 25.0, C6 (dispersion coefficient for oxygen) = 1.52 J nm6 mol-1, Rvdw
(van der Walls radius of oxygen) = 1.342 Å.
The calculations for barite/ice system were performed by using only the B3LYP Hamiltonian, which provided accurate results for the surface properties of the minerals considered in the present work.
Further computational details (e.g., basis set, thresholds controlling the accuracy of the calculations) are reported in the ESI.
In detail, we studied the (10.4)Cal/(001)Ice and (210)Brt/(001)Ice epitaxial interfaces by
determining their structures and thermodynamic properties (i.e., specific adhesion energy at 0K). Composed slabs (ice Ih/Brt/ice Ih) and (ice Ih/Cal/ice Ih) were generated as follows: (i) the two-dimensional (2D) coincidence lattices between the two phases Brt/ice and Cal/ice in epitaxial relationship were identified;7 (ii) the slabs Brt or Cal and ice of a selected thickness were made by
cutting their respective bulk structures parallel to the hkl planes of interest and using the same 2D cell parameters describing the epitaxy; (iii) the slab Brt (or Cal) was placed in between two slabs ice; (iv) finally, the composed slab structure (atomic coordinates and 2D cell parameters) was optimized by considering all the atoms free to move. The slabs ice Ih/Brt/ice Ih and ice Ih/Cal/ice
Ih were generated preserving the symmetry center, to ensure the vanishing of the dipole component
perpendicular to the slab. The CRYSTAL14 output files, listing the optimized fractional coordinates and optimized 2D cell parameters of the composed slabs, are freely available at
http://mabruno.weebly.com/download. For the (10.4)Cal/(001)Ice system, the calculations were
performed by considering a composed slab with a thickness sufficient to obtain an accurate
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description of the interface; the slab thickness is considered appropriate when the bulk-like properties are reproduced at the center of the Cal and ice slabs. For the (210)Brt/(001)Ice system, it
has not possible to satisfy this criterion of convergence, since our calculus resources do not allow to treat systems with size larger than that considered in the present work.
The specific adhesion energy, β(A / Bhkl)/(h k lʹ ʹ ʹ) (J m-2), is the energy gained once the boundary interface is formed and it is calculated by means of the relation:
β(A / Bhkl)/(h k lʹ ʹ ʹ)
=E (2 A )+ E (B )−E(2 A+B) 2 S
where A is barite or calcite slab and B is the ice slab; (hkl) and (hʹkʹlʹ) define the crystallographic faces in epitaxy of A and B, respectively. E(2A + B), E(2A), and E(B) are the static energies (at 0K) of the optimized slab A/B/A, slab A/vacuum/A and slab B, respectively, and S is the area of the 2D common epitaxial unit cell.
3. Results and discussion
3.1. Structure and adhesion energy of the (10.4)Cal/(001)Ice interface
Surface structural discrepancies of the (10.4) of calcite in contact with (001) ice Ih were analyzed. The optimized interface structures obtained with the B3LYP, B3LYP_DC, HF and PBE0_DC functionals are reported in (Figs. 1 and 2).
Fig. 1 Optimized structures of the (10.4)Cal/(001)Ice interface obtained with the B3LYP, B3LYP_DC,
HF and PBE0_DC functionals. Some O−O distances (Å) in the (001)Ice slab are reported for
comparison. A, B, C and D are the independent tetrahedra in the first layer of the (10.4)Cal slab.
In order to describe the structural modifications we have considered the distortion of the CO3 polyhedra belonging to the first layer of the (10.4)Cal slab in contact with the (001)Ice slab. The
statistical indices we employed to summarize the effects of atomic modification are: (i) the average C−O bond distance per polyhedron, ⟨C−O⟩(Å), (ii) the difference between the maximum and minimum bond distance per polyhedron, Δmax-min, and (iii) the difference between ⟨C−O⟩ distance
4 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 7
obtained at B3LYP_DC, HF and PBE0_DC level, and that in the structure optimized with the B3LYP functional, ΔB3LYP and ΔB3LYP%. These values are listed in Table 1.
⟨C−O⟩ distances determined with the functional B3LYP are in the range 1.2910-1.2933 Å and the
average difference between the maximum and minimum C−O distances, ⟨Δmax-min⟩, is 0.0188 Å. |
ΔB3LYP%| is 0.13% and ⟨C−O⟩ distances are between 1.2910 and 1.2920 Å when the B3LYP_DC
functional is used. |ΔB3LYP%| values are between 0.70 % and 0.82% and ⟨C−O⟩ distances are 1.2830,
1.2817 and 1.2827 Å, when using the PBE0_DC computational method. As expected, we observed remarkable differences in the C−O distances using the HF functional: |ΔB3LYP%| values are between
1.68 % and 1.83% and the ⟨C−O⟩ distances correspond to 1.2690, 1.2693 and 1.2697 Å.
Table 1 Optimized C‒O distance per polyhedron (Å) of (10.4)Cal performed using different computational methods (B3LYP, B3LYP_DC, HF and PBE0_DC)
B3LYP B3LYP_DC polyhedra A B C D A B C D C‒O 1.2790 1.2900 1.2840 1.2720 1.2800 1.2900 1.2840 1.2740 1.2990 1.2910 1.2890 1.2980 1.2940 1.2910 1.2890 1.2970 1.3020 1.2920 1.3000 1.3060 1.3010 1.2920 1.3000 1.3050 ⟨C‒O⟩ 1.2933 1.2910 1.2910 1.2920 1.2917 1.2910 1.2910 1.2920 Δmax-min 0.0230 0.0020 0.0160 0.0340 0.0210 0.0020 0.0160 0.0310 ⟨Δmax-min⟩ 0.0188 0.0175 ΔB3LYP -0.0016 0.0000 0.0000 0.0000 ΔB3LYP% -0.13 0.00 0.00 0.00 HF PBE0_DC polyhedra A B C D A B C D C‒O 1.2520 1.2640 1.2660 1.2510 1.2710 1.2780 1.2760 1.2690 1.2760 1.2710 1.2700 1.2760 1.2850 1.2820 1.2820 1.2870 1.2810 1.2730 1.2710 1.2820 1.2920 1.2850 1.2870 1.2930 ⟨C‒O⟩ 1.2697 1.2693 1.2690 1.2697 1.2827 1.2817 1.2817 1.2830 Δmax-min 0.0290 0.0090 0.0050 0.0310 0.0210 0.0070 0.0110 0.0240 ⟨Δmax-min⟩ 0.0185 0.0158 ΔB3LYP -0.0237 -0.0217 -0.0220 -0.0223 -0.0107 -0.0093 -0.0093 -0.0090 ΔB3LYP% -1.83 -1.68 -1.70 -1.73 -0.82 -0.72 -0.72 -0.70
Surface data are reported for the symmetry-independent CO3 polyhedron of the first layer. ⟨C‒O⟩ (Å) is the average
C‒O bond length per polyhedron; Δmax-min is the difference between maximum and minimum C‒O distance values;
ΔB3LYP and ΔB3LYP% are the difference and the relative percentage difference of ⟨C‒O⟩ respect to the C‒O distance
value for (10.4)Cal using the B3LYP functional.
In Table 2 the O−C−O bond angles are listed for the CO3 polyhedra belonging to the first
layer of the (10.4)Cal slab in contact with (001)Ice. Again, statistical indices are adopted to evaluate
the effect of structural variation: (i) the average O−C−O bond angle per polyhedron, ⟨O−C−O⟩(°),
(ii) the difference between the maximum and minimum bond angle per polyhedron, Δmax-min(°), and
5 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 9
(iii) the difference between the average O−C−O bond angle per polyhedron obtained at B3LYP_DC, HF and PBE0_DC level, and that in the structure optimized with the B3LYP functional, ΔB3LYP and ΔB3LYP%.
⟨O−C−O⟩ angles are in the range 119.996°-120.000° when using the B3LYP functional, and the average difference between the maximum and minimum O−C−O bond angle, <Δmax-min>, is 1.6935°.
|ΔB3LYP%| is slight in all cases: |ΔB3LYP%| values are 0.002% for B3LYP_DC and HF, whereas the
values are lower than 0.015% when using PBE0_DC. These values are shown in Table 2 as well.
Table 2 Optimized O‒C‒O bond angles (°) of (10.4) calcite performed using different computational
methods (B3LYP, B3LYP_DC, HF and PB0_DC)
B3LYP B3LYP_DC polyhedra A B C D A B C D O‒C‒O 118.670 119.775 119.302 118.21 0 118.829 119.681 119.363 118.256 120.444 119.996 120.174 120.68 0 120.271 120.150 120.179 120.551 120.885 120.217 120.521 121.10 8 120.900 120.157 120.456 121.188 ⟨O‒C‒O⟩ 120.000 119.996 119.999 119.99 9 120.000 119.996 119.999 119.998 Δmax-min 2.215 0.442 1.219 2.898 2.071 0.476 1.093 2.932 ⟨Δmax-min⟩ 1.6935 1.643 ΔB3LYP 0.000 0.000 0.000 -0.001 ΔB3LYP% 0.000 0.000 0.000 -0.001 HF PBE0_DC polyhedra A B C D A B C D O‒C‒O 118.501 119.503 119.789 118.38 4 119.051 119.733 119.633 118.669 120.591 120.138 119.885 120.52 0 120.290 119.734 120.063 119.814 120.906 120.354 120.323 121.096 120.637 120.515 120.302 121.463 ⟨O‒C‒O⟩ 119.999 119.998 119.999 120.000 119.993 119.994 119.999 119.982 Δmax-min 2.405 0.851 0.534 2.712 1.586 0.782 0.669 2.794 ⟨Δmax-min⟩ 1.626 1.458 ΔB3LYP -0.001 0.002 0.000 0.002 -0.007 -0.004 0.000 -0.018 ΔB3LYP% -0.001 0.002 0.000 0.001 -0.006 -0.004 0.000 -0.015
Surface data are reported for the symmetry-independent CO3 polyhedron of the first layer. ⟨O‒C‒O⟩ (°) is the
average bond angle per polyhedron; Δmax-min is the difference between maximum and minimum O‒C‒O angular
measures; ΔB3LYP and ΔB3LYP% are the difference and the relative percentage difference of ⟨O‒C‒O⟩ with respect to
the O‒C‒O angular value for (10.4)Cal using the B3LYP functional.
6 178 179 180 181 182 183 184 185 186 187 188 11
Fig. 2 shows the structural variations in the layers of (001)Ice slab in contact with (10.4)Cal. To
evaluate the order of magnitude of these modifications we considered the distance between two hydrogen apical atoms of H2O molecules that belong to the different layers of ice.
The average distances between the two H atoms belonging to the first and the second layer (after the contact surface with calcite), ⟨ΔH1,2⟩, using different computational methods (B3LYP,
B3LYP_DC, HF and PBE0_DC) are respectively: 4.536, 4.503, 4.629, 4.486 Å. The ⟨ΔH2,3⟩
distance values from the second and the third layer are 5.029, 5.005, 5.049, 4.965 Å, whereas from the third and the fourth layer, ⟨ΔH3,4⟩, are 5.008, 4.990, 5.059, 4.930 Å.
Fig. 2 A detailed view of the optimized structures of the (001)Ice in contact with the (104)Cal
obtained with the B3LYP, B3LYP_DC, HF and PBE0_DC functionals. Some O-O distances (Å) in the (001)Ice slab are reported for comparison.
Generally, it is possible to observe that the average bond distances (⟨C-O⟩ and ⟨H-H⟩) are similar both in calcite and ice structure when the B3LYP and B3LYP_DC are used, whereas they are stretched when considering HF and shortened for PBE0_DC. Instead, the optimized O‒C‒O and O‒ H‒O bond angles are approximately constant for all the different computational methods.
In Table 3 the adhesion energies at 0K between (10.4)Cal and (001)Ice, β(10.4)/(001)Cal/ Ice (J m-2),
calculated with B3LYP, B3LYP_DC, HF and PB0_DC, are listed. The highest value (0.315 J m-2)
was obtained with HF, whereas the lowest one (0.143 J m-2) with B3LYP. Instead, B3LYP_DC and
PBE0_DC give very similar results: 0.253 and 0.250 J m-2, respectively. The average value results
to be 0.240 J m-2. Such a value is almost twice the one we estimated for the (10.4)
Cal in contact with
water (W) at 300K, β(10.4)Cal/ W = 0.124 J m-2.9
Table 3 Adhesion energy at 0K between (10.4)Cal and (001)Ice, β(10.4)/(001)
Cal/ Ice
(J m-2), as resulting from calculations with B3LYP, B3LYP_DC, HF and PBE0_DC
B3LYP HF B3LYP_DC PBE0_DC
β(10.4)/(001) Cal/ Ice 0.143 0.315 0.253 0.250 ⟨ β(10.4)/(001) Cal / Ice ⟩ 0.240 7 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 13
3.2. Structure and adhesion energy of the (210)Brt/(001)Ice interface
The structure of the face (210)Brt in contact with (001)Ice was compared with the one in dry condition
(i.e., in contact with the vacuum) at T = 0 K and with the optimized bulk structure of baryte.10 The
following analysis was performed by considering the distortion of the SO4 tetrahedra belonging to
the first layer of the (210)Brt slab in contact both with vacuum and (001)Ice. People interested in
in-depth structural analysis can carry it out by using the CRYSTAL14 output files reporting the optimized atomic coordinates. The optimized structures of the (210)Bar surfaces are shown in Fig. 3.
Fig. 3 (210)Brt optimized surfaces viewed along the [100] direction in dry condition (a) and in contact with the (001)Ice (b). Independent tetrahedra in the first layer of the (210)Brt slab are marked
with orange circles in (a) and blue circles in (b).
Tables 4 and 5 report the values of the S−O bond distances and O−S−O bond angles for the bulk, the (210)Brt surface in dry condition and in contact with (001)Ice. The first layer of the (210)Bar
slab in dry condition is constituted by two independent SO4 tetrahedra,10 while the same slab in
contact with (001)Ice consists of four independent SO4 tetrahedra.
In Table 4 are reported the statistical indices we employed to summarize the effects of atomic relaxation: in particular, (i) the average S−O bond distance per tetrahedron, ⟨S−O⟩(Å), (ii) the
difference between the maximum and minimum bond distances per tetrahedron, Δmax-min, and (iii) the
difference between ⟨S−O⟩ in the slab and ⟨S−O⟩ in the bulk, Δbulk and Δbulk%.
⟨S−O⟩ is 1.5655 Å in the bulk, whereas ⟨S−O⟩ values in the (210)Brt/vacuum and (210)Brt/(001)Ice
systems are in the range 1.5670-1.5703 Å and 1.5665-1.5690 Å, respectively. Then, the average percentage deviations from the bulk, Δbulk%, are 0.31% in all the independent tetrahedra both in contact with vacuum and with (001)ice.
Table 4 Optimized S‒O distances (Å) in baryte bulk and (210)Brt slab at 0K in vacuum and in contact with (001)Ice
bulk Brt (210)Brt/vacuum (210)Brt/(001)Ice
S‒O 1.5471 1.5542 1.5337 1.5570 1.5570 1.5380 1.5510 1.5603 1.5629 1.5712 1.5590 1.5640 1.5720 1.5610 1.5772 1.5679 1.5750 1.5640 1.5670 1.5790 1.5680 1.5772 1.5828 1.6013 1.5880 1.5840 1.5870 1.5860 8 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 15
⟨S‒O⟩ 1.5655 1.5670 1.5703 1.5670 1.5680 1.5690 1.5665
Δmax-min 0.0301 0.0286 0.0676 0.0310 0.0270 0.0490 0.0350
Δbulk 0.0015 0.0048 0.0015 0.0025 0.0035 0.0010
Δbulk% 0.10 0.31 0.10 0.16 0.22 0.06
Surface data are reported for the symmetry-independent SO4 tetrahedra of the first layer of the
(201)Brt slab. ⟨S‒O⟩ (Å) is the average S‒O bond length per tetrahedron; Δmax-min is the difference
between maximum and minimum S‒O distance values inside the tetrahedron; Δbulk and Δbulk% are
the difference and the relative percentage difference of ⟨S‒O⟩ with respect to the bulk value.
Table 5 lists the O−S−O bond angles (°) for the baryte bulk, the (210)Brt slab at the contact with
vacuum and (001)Ice. Again, statistical indices are adopted to evaluate the effect of geometry
optimization: (i) the average O−S−O bond angles per tetrahedron, ⟨O−S−O⟩(°), (ii) the difference
between the maximum and minimum bond angles per tetrahedron, Δmax-min(°), and (iii) the difference
between ⟨O−S−O⟩ in the slab and ⟨O−S−O⟩ in the bulk, Δbulk and Δbulk%.
⟨O−S−O⟩ is 109.63° in the bulk, whereas ⟨O−S−O⟩ values in the (210)Brt/vacuum and (210)Brt/
(001)Ice systems are in the range 108.94°-109.06° and 108.46°-109.52°, respectively. |Δbulk%| are 1.1% in all the independent tetrahedra both in contact with vacuum and with ice.
These values, both bond length and angle, are overall indicative of low atomic distortion degree of the barite structure at the interface with ice.
The adhesion energy, β(210)/ (001)Brt / Ice (J m-2), of the (210)Brt/(001)Ice interface at B3LYP level is
0.336 J m-2, a value significantly higher with respect to that obtained at B3LYP level for the
(10.4)Cal/(001)Ice interface.
Table 5 Optimized O‒S‒O bond angles (°) of barite and its (210) surface at 0K in vacuum and in contact
with (001)Ice
bulk Brt (210)Brt/vacuum (210)Brt/(001)Ice
O‒S‒O 107.88 106.00 106.21 106.53 106.13 106.62 106.84 108.94 106.56 108.61 108.52 106.77 108.76 108.92 109.27 109.04 108.99 108.72 110.36 109.50 109.23 112.42 114.16 112.41 112.57 110.56 111.95 113.07 ⟨O‒S‒O⟩ 109.63 108.94 109.06 109.09 108.46 109.21 109.52 Δmax-min 4.54 8.16 6.20 6.0390 4.4210 5.3290 6.2290 Δbulk -0.69 -0.57 -0.5397 -1.1727 -0.4217 -0.1155 Δbulk% -0.63 -0.52 -0.49 -1.07 -0.38 -0.11 9 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 17
Surface data are reported for the symmetry-independent SO4 tetrahedra of the first layer. ⟨O‒S‒O⟩ (°)
is the average bond angle per tetrahedron; Δmax-min is the difference between maximum and minimum
O‒S‒O bond angles; Δbulk and Δbulk% are the difference and the relative percentage difference of ⟨O‒S‒
O⟩ with respect to the bulk value.
4. An estimate of the (10.4)Cal/(001)Ice and (210)Brt/(001)Ice specific
interface energies at 273.15K and some considerations about
hydrophilic and hydrophobic surfaces
The specific interfacial energy, γ(hkl )/(h k lʹ ʹ ʹ) A / B
(J m-2), is the energy needed to create, per unit area, the
(hkl)A/(h’k’l’)B interface, and is related to the specific adhesion energy, β(hkl)/(h ʹ k ʹ lʹ ) A / B
, by means of the Dupré’s relation:36
γ(hkl )/(h ʹ k ʹ l ʹ) A / B =γ(Ah kl)+γ(hʹ k ʹ l ʹ) B −β(A /Bhkl)/(h ʹ k ʹ lʹ ) where γ(h kl) A and γ(h ʹ k ʹ l ʹ) B
are the specific surface energies of the (hkl) and (h’k’l’) faces of the crystals A and B in contact with vapour, respectively. When the phase B in contact with A is water (W), the Dupré’s relation reads:
γ(hkl ) A /W =γ(h kl ) A +γW−β(hkl) A / W
where γW is the surface tension of water.
In order to estimate γ(10.4 )/(001)Cal / Ice and γ(210)/(001)Brt / Ice at 273.15K, we have to know γ(001)Ice at
the same temperature. Fortunately, we are able to estimate this quantity since all the terms entering into Dupré’s relation, γ(001)Ice =γ(001)Ice/ W+β(001)Ice /W−γW , are either well known or estimated with good
precision at the temperature of interest, 273.15K. Indeed, γ(001)Ice /W at 273.15K results to be 0.033 J
m-2, according to the simulations performed by Ambler et al.;37 γW at 273.15K is 0.076 J m-2;38
β(001)
Ice /W
at 273.15K can be approximated at the value 2 γW = 0.152 J m-2, being probable an
almost perfect adhesion of water on ice at the melting point. Then, γ(001)Ice is estimated to be 0.109
J m-2, a value rather reliable if compared with the (001)
Ice surface energy calculated at
quantum-mechanical level at 0K by Hermann,39 0.119 J m-2. According to our estimate of γ (001)
Ice at 273.15K, we observe that the (001)Ice surface energy at 0K is only slightly modified with the
increase of the temperature.
Now, we can use our estimate of γ(001)Ice to calculate γ(10.4 )/(001)Cal / Ice and γ(210)/(001)Brt / Ice at
273.15K, always by means of the Dupré’s relation: γ(10.4 )/(001)Cal / Ice =γ(10.4 )Cal +γ(001)Ice −β(10.4 )/ (001)Cal / Ice
γ(210)/(001)Brt / Ice =γ(210)Brt +γ(001)Ice −β(210)/(001)Brt / Ice
10 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 19
where γ(10.4 )Cal and γ(210)Brt are the (10.4)Cal and (210)Brt surface energies, respectively, at 273.15K;
β(10.4)/(001)
Cal/ Ice
and β(210)/ (001)
Brt / Ice
are the (10.4)Cal/(001)Ice and (210)Brt/(001)Ice adhesion energies,
respectively, at 273.15K.
As concerns calcite, Bruno et al.9 estimated a value of 0.464 J m-2 for γ (10.4 )
Cal
at 298.15K, which should not be significantly affected by small variations of temperature and, consequently, we hypothesize that γ(10.4 )
Cal (273.15K) γ
(10.4 )
Cal
(298.15K). Moreover, in the present paper we calculated β(10.4)/(001)
Cal/ Ice
at 0K, but we do not know the effect of the temperature on this quantity. Then, we are forced to insert in the Dupré’s relation the average value ⟨ β(10.4)/(001)
Cal / Ice ⟩ = 0.240
J m-2 (Table 3), obtaining in this way the following estimate of γ(10.4 )/(001)
Cal / Ice
at 273.15K: 0.333 J m-2.
As concerns baryte, there are not estimates of the γ(210)
Brt
value at 298.15K. Therefore, as
calculated for the (10.4) surface of calcite by Bruno et al.,9 we assume that the surface energy at 0K
of the (210) face of baryte, γ(210)
Brt = 0.382 J m-2,10 is reduced by 10% at 298.15K, 0.382 J m-2. Then, supposing γ(210) Brt (273.15K) γ (210) Brt (298.15K) and using β(210)/ (001) Brt / Ice = 0.336J m-2, we obtain γ(210)/(001) Brt / Ice = 0.117 J m-2 at 273.15K. Interestingly, γ(10.4 )/(001)
Cal / Ice is lower by 20% than γ
(10.4 )
Cal /W
= 0.412 J m-2,9 suggesting that it
is less expensive from an energetic point of view to build an unit area of the (10.4)Cal/(001)Ice
interface than to increase of an unit area the (10.4)Cal/water interface. This finding suggests that an
ordered interface, (10.4)Cal/(001)Ice, is more stable than a disordered one, (10.4)Cal/water, where
order/disorder is given by the disposition of the H2O molecule above the (10.4)Cal surface. Probably,
the entropy variation, S 0, when passing from disordered water molecules to ordered ice
molecules at the (10.4)Cal surface, is significantly lesser than the enthalpic variation, H << 0, due to
stronger interactions forming between H2O molecules in ice and (10.4)Cal surface with respect to
those between H2O molecules in water and (10.4)Cal surface. This implies a negative variation of the
free energy of the system, G = H - TS 0.
At variance with calcite, there are not estimates of γ(210)
Brt /W
and a comparison with γ(210)/(001)
Brt / Ice
does not result possible. But, it is likely that the behavior of the (210)Brt surface is similar to that of
the (10.4)Cal surface, since both the crystal faces show a strong affinity towards H2O molecules in
ice.
The experimental observed partial ordering of the water molecules on the (10.4)Cal surface at
room temperature can be also explained with the same thermodynamic argument: the interface is
energetically favored when H2O molecules organize in such a way to maximize the enthalpic
variation to contrast the entropy reduction. All hydrophilic surfaces, e.g. (10.4)Cal, should be
subjected to this interplay between entropy and enthalpy, where the interaction between H2O
molecules of water and crystal surface (i.e., H << 0) reduces the entropy (e.g., translational and rotational motion of the H2O molecules) at the interface.
Instead, the enthalpic effect for a hydrophobic surface is less important than that observed for a hydrophilic one (i.e., Hhydrophilic < Hhydrophobic): the water molecule are slightly bonded to the
crystal surface. In spite of this, there is a strong reduction of the entropy due to the “hydrophobic effect”: loss of entropy by the 3D network of water molecules when they interact with non-polar molecules and surfaces (S 0); introducing a non-hydrogen-bonding surface does disrupt this
11 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 21
network. The water molecules rearrange themselves around the surface to minimize the number of disrupted hydrogen bonds. This implicates a higher free energy variation for the hydrophilic surfaces than that for hydrophobic ones, Ghydrophilic < Ghydrophobic. The enthalpic contribution should
be the dominant one to establish either a surface is hydrophilic or hydrophobic, being the entropic contribution probably similar for both the cases.
5. Conclusions
We performed ab initio calculations to determine the structure and adhesion energy at 0K of the (10.4)Cal/(001)Ice and (210)Brt/(001)Ice interfaces. The interface energies at 273.15K were also
estimated. By means of these interface energies, we were also able to make some considerations about the role of entropy and enthalpy to explain the hydrophilicity and hydrophobicity of the crystal surfaces.
The (10.4)Cal and (210)Brt surfaces are extremely compact; indeed, their structures are slightly
modified by the presence of ice. According to our calculations, the ice is strongly bounded to (10.4)Cal and (210)Brt surfaces, being their adhesion energies not negligible: β(10.4)/(001)Cal/ Ice = 0.240
and β(210)/ (001)Brt / Ice = 0.336 J m-2. Obviously, this paper has not the presumption to give a conclusive
estimate of the adhesion energy between (10.4) calcite [(210) baryte] and (001) Ih ice, but it aims only at furnish a reliable value of this quantity. Many others calculations should be performed to validate our estimates, in particular by using DFT functionals with a more recent London dispersion correction (DFT-D3)40 implemented, e.g., in CRYSTAL17,41 and by testing several Gaussian basis
sets.
According to our calculations, the interface energy of the (10.4)Cal/(001)Ice system,
γ(10.4 )/(001)
Cal / Ice
, is 0.333 J m-2 at 273.15K, significantly lower than the interface energy of the
(10.4)Cal/water system ( γ(10.4 )
Cal /W
= 0.412 J m-2) at the same temperature. We explained such a
difference with stronger interactions forming between H2O molecules in ice and (10.4)Cal surface
with respect to those between H2O molecules in water and (10.4)Cal surface.
The interface energy at 273.15K of the (210)Brt/(001)Ice system, γ(210)/(001)
Brt / Ice
, is 0.117 J m-2, a value
extremely lower than that obtained for the (10.4)Cal/(001)Ice interface. We can speculate that the
(210) surface of baryte shows a water affinity greater than that of the (10.4) face of calcite. An interesting development of this work should concern the study of others calcite (baryte)/ice interfaces, in order to evaluate the ability of the different crystallographic forms to interact with ice and water molecules. Different faces of the same crystal should show different behaviours, then different adhesion and interface energies.
Conflicts of interest
There are no conflicts to declare.
Acknowledgements
12 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 23The work was supported by Regione Piemonte - Grant LR34/2004 - "Studio preliminare e sviluppo di soluzioni innovative di materiali d’attrito in ambito Automotive”.
Electronic Supplementary Information (ESI) Available
Computational details concerning the ab initio simulations of the (10.4)Cal/(001)Ice and (210)Brt/
(001)Ice interfaces.
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