Supplementary Material to:
Vapor deposition of water on graphitic surfaces: formation of
amorphous ice, bilayer ice, ice I and liquid water.
Laura Lupi, Noah Kastelowitz and Valeria Molinero
A. Calculation of the line tension of mW water on graphite.
We calculated the line tension for water in contact with graphite for the size dependence of
the contact angle through1,2
cos 𝜃 = cos 𝜃∞ − 𝛾
𝜏
1
𝐿𝑉 𝑅𝑏
,
(S1)
where 𝜃 is the contact angle of microscopic droplets, 𝜃∞ is the contact angle in the limit of
very large droplets, 𝜏 is the line tension, 𝛾𝐿𝑉 is the liquid-vapor surface tension, and 𝑅𝑏 is the
radius of the circumference of contact between the droplet and the surface. The surface
tension of mW water droplets with diameters as small as 1 nm was found to be independent
on curvature,3 therefore in our calculations we approximated the liquid-vapor surface tension
∞
of the spherical interface with 𝛾𝐿𝑉
(this was taken from ref.
4
at 220 K for mW water).
1
Through linear fitting of cos 𝜃 versus 𝑅 of the data of Table 1 we determined cos 𝜃∞ = 85°
𝑏
and 𝜏 = 12 pN for water in contact with graphite (Figure S1).
Table 1. Contact angles, and radius of base, Rb, of droplets containing Nw water
molecules in contact with graphite.
Nw  (°) Rb (nm)
550 89
1.9
1035 87
2.5
5241 86
4.2
1
cos (q)
0.06
Tf droplet
0.04
0.02
0.2
0.3
0.4
1/Rb (1/nm)
0.5
Figure S1. Cosine of the contact angle of mW water on graphite as a function of
inverse droplet radius. Blue symbols are the data points and the blue line is the linear fit of
the data using equation 1.
B. Bilayer ice and graphitic surfaces lattice.
Bilayer ice and graphitic sheets have hexagonal symmetry with a lattice domain mismatch of
only 3% when two cells of the graphitic surface are compared with one cell of bilayer ice.
Nevertheless, we do not observe alignment between the two structures even for the most
attractive surfaces of this study. Snaphots of bilayer ice on these graphitic surfaces are shown
in Figures S2 to S4.
2
Figure S2. Bilayer ice deposited on graphite at T = 180 K. The first layer of water
molecules from the surfaces is showed with red sticks, the second in blue, carbon atoms of
the graphite surface are shown in silver. Only the first layer of water is shown in left panel,
and both layers are shown in right panel.
Figure S3. Bilayer ice deposited on graphitic surface with ε = 0.16 kJ/mol at T = 200
K. The first layer of water molecules from the surfaces is showed with red sticks, the second
in blue, carbon atoms of the graphite surface are shown in silver. Only the first layer of water
is shown in left panel, and both layers are shown in right panel.
3
Figure S4. Bilayer ice deposited on graphitic surface with ε = 0.18 kJ/mol at T = 210
K. The first layer of water molecules from the surfaces is showed with red sticks, the second
in blue, carbon atoms of the graphite surface are shown in silver. Only the first layer of water
is shown in left panel, and both layers are shown in right panel.
Supporting References.
(1)
(2)
(3)
4508 (2014).
(4)
J. Wang; S. Betelu; B. Law, Phys. Rev. E 63, 031601 (2001).
A. I. Rusanov, Surf. Sci. Rep. 23, 173 (1996).
M. H. Factorovich; V. Molinero; D. A. Scherlis, J. Am. Chem. Soc. 136,
A. Hudait; V. Molinero, J. Am. Chem. Soc. 136, 8081 (2014).
4