The existence and origin of line tension has remained controversial in literature. To address this issue, we compute the shape of Lennard-Jones nanodrops using molecular dynamics and compare them to density functional theory in the approximation of the sharp kink interface. We show that the deviation from Young’s law is very small and would correspond to a typical line tension length scale (defined as line tension divided by surface tension) similar to the molecular size and decreasing with Young’s angle. We propose an alternative interpretation based on the geometry of the interface at the molecular scale.

1.
J. W.
Gibbs
,
The Collected Works of J. Willard Gibbs
(
Yale University Press
,
London
,
1957
).
2.
L.
Guzzardi
,
R.
Rosso
, and
E. G.
Virga
, “
Residual stability of sessile droplets with negative line tension
,”
Phys. Rev. E
73
,
021602
(
2006
).
3.
L.
Schimmele
and
S.
Dietrich
, “
Line tension and the shape of nanodroplets
,”
Eur. Phys. J. E
30
,
427
(
2009
).
4.
L.
Schimmele
,
M.
Napiorkowski
, and
S.
Dietrich
, “
Conceptual aspects of line tensions
,”
J. Chem. Phys.
127
,
164715
(
2007
).
5.
B. A.
Pethica
, “
Contact-angle equilibrium
,”
J. Colloid Interface Sci.
62
,
567
(
1977
).
6.
T.
Getta
and
S.
Dietrich
, “
Line tension between fluid phases and a substrate
,”
Phys. Rev. E
57
,
655
(
1998
).
7.
C.
Bauer
and
S.
Dietrich
, “
Quantitative study of laterally inhomogeneous wetting films
,”
Eur. Phys. J. B
10
,
767
(
1999
).
8.
H. T.
Dobbs
and
J. O.
Indekeu
, “
Line tension at wetting—Interface displacement model beyond the gradient-squared approximation
,”
Physica A
201
,
457
(
1993
).
9.
N. V.
Churaev
,
V. M.
Starov
, and
B. V.
Derjaguin
, “
The shape of the transition zone between a thin-film and bulk liquid and the line tension
,”
J. Colloid Interface Sci.
89
,
16
(
1982
).
10.
P. -G.
de Gennes
, “
Wetting—Statics and dynamics
,”
Rev. Mod. Phys.
57
,
827
(
1985
).
11.
A.
Amirfazli
and
A. W.
Neumann
, “
Status of the three-phase line tension: A review
,”
Adv. Colloid Interface Sci.
110
,
121
(
2004
).
12.
J. O.
Indekeu
, “
Line tension near the wetting transition—Results from an interface displacement model
,”
Physica A
183
,
439
(
1992
).
13.
J. O.
Indekeu
, “
Line tension at wetting
,”
Int. J. Mod. Phys. B
8
,
309
(
1994
).
14.
J.
Drelich
and
J. D.
Miller
, “
The effect of solid surface heterogeneity and roughness on the contact angle/drop (bubble) size relationship
,”
J. Colloid Interface Sci.
164
,
252
(
1994
).
15.
J.
Drelich
and
J. D.
Miller
, “
The line/pseudo-line tension in three-phase systems
,”
Part. Sci. Technol.
10
,
1
(
1992
).
16.
J.
Gaydos
and
A. W.
Neumann
, “
The dependence of contact angles on drop size and line tension
,”
J. Colloid Interface Sci.
120
,
76
(
1987
).
17.
D.
Li
and
A. W.
Neumann
, “
Determination of line tension from the drop size dependence of contact angles
,”
Colloids Surf.
43
,
195
(
1990
).
18.
R.
Vera-Graziano
,
S.
Muhl
, and
F.
Rivera-Torres
, “
The effect of illumination on contact angles of pure water on crystalline silicon
,”
J. Colloid Interface Sci.
170
,
591
(
1995
).
19.
J.
Drelich
, “
The significance and magnitude of the line tension in three-phase (solid-liquid-fluid) systems
,”
Colloids Surf., A
116
,
43
(
1996
).
20.
A.
Checco
,
P.
Guenoun
, and
J.
Daillant
, “
Nonlinear dependence of the contact angle of nanodroplets on contact line curvature
,”
Phys. Rev. Lett.
91
,
186101
(
2003
).
21.
D.
Li
,
F. Y.H.
Lin
, and
A. W.
Neumann
, “
Effect of corrugations of the 3-phase line on the drop size dependence of contact angles
,”
J. Colloid Interface Sci.
142
,
224
(
1991
).
22.
B. M.
Borkent
,
S.
de Beer
,
F.
Mugele
, and
D.
Lohse
, “
On the shape of surface nanobubbles
,”
Langmuir
26
,
260
(
2010
).
23.
J.
Yang
,
J.
Duan
,
D.
Fornasiero
, and
J.
Ralston
, “
Very small bubble formation at the solid water interface
,”
J. Phys. Chem. B
107
,
6139
(
2003
).
24.
N.
Kameda
,
N.
Sogoshi
, and
S.
Nakabayashi
, “
Nitrogen nanobubbles and butane nanodroplets at Si(100)
,”
Surf. Sci.
602
,
1579
(
2008
).
25.
N.
Kameda
and
S.
Nakabayashi
, “
Size-induced sign inversion of line tension in nanobubbles at a solid/liquid interface
,”
Chem. Phys. Lett.
461
,
122
(
2008
).
26.
T.
Pompe
and
S.
Herminghaus
, “
Three-phase contact line energetics from nanoscale liquid surface topographies
,”
Phys. Rev. Lett.
85
,
1930
(
2000
).
27.
Z.
Zorin
,
D.
Platikanov
, and
T.
Kolarov
, “
The transition region between aqueous wetting films on quartz and the adjacent meniscus
,”
Colloids Surf.
22
,
133
(
1987
).
28.
J. D.
Halverson
,
C.
Maldarelli
,
A.
Couzis
, and
J.
Koplik
, “
Atomistic simulations of the wetting behavior of nanodroplets of water on homogeneous and phase separated self-assembled monolayers
,”
Soft Matter
6
,
1297
(
2010
).
29.
T.
Ingebrigtsen
and
S.
Toxvaerd
, “
Contact angles of Lennard-Jones liquids and droplets on planar surfaces
,”
J. Phys. Chem. C
111
,
8518
(
2007
).
30.
D.
Van Der Spoel
,
E.
Lindahl
,
B.
Hess
,
G.
Groenhof
,
A. E.
Mark
, and
H. J. C.
Berendsen
, “
GROMACS: Fast, flexible, and free
,”
J. Comput. Chem.
26
,
1701
(
2005
).
31.
J.-L.
Barrat
and
L.
Bocquet
, “
Large slip effect at a nonwetting fluid-solid interface
,”
Phys. Rev. Lett.
82
,
4671
(
1999
).
32.
S. M.
Dammer
and
D.
Lohse
, “
Gas enrichment at liquid-wall interfaces
,”
Phys. Rev. Lett.
96
,
206101
(
2006
).
33.
M. J.P.
Nijmeijer
,
C.
Bruin
,
A. F.
Bakker
, and
J. M.J.
Van Leeuwen
, “
Wetting and drying of an inert wall by a fluid in a molecular-dynamics simulation
,”
Phys. Rev. A
42
,
6052
(
1990
).
34.
J. S.
Rowlinson
and
B.
Widom
,
Molecular Theory of Capillarity
(
Clarendon
,
Oxford
,
1982
).
35.
J. -P.
Hansen
and
I. R.
McDonald
,
Theory of Simple Liquids
(
Academic
,
London
,
2006
).
36.
G. J.
Merchant
and
J. B.
Keller
, “
Contact angles
,”
Phys. Fluids A
4
,
477
(
1992
).
37.
J. H.
Snoeijer
and
B.
Andreotti
, “
A microscopic view on contact angle selection
,”
Phys. Fluids
20
,
057101
(
2008
).
38.
A.
Marmur
, “
Line tension and the intrinsic contact angle in solid-liquid-fluid systems
,”
J. Colloid Interface Sci.
186
,
462
(
1997
).
39.
B. M.
Borkent
,
S. M.
Dammer
,
H.
Schönherr
,
G. J.
Vancso
, and
D.
Lohse
, “
Superstability of surface nanobubbles
,”
Phys. Rev. Lett.
98
,
204502
(
2007
).
40.
M. A.
Hampton
and
A. V.
Nguyen
, “
Nanobubbles and the nanobubble bridging capillary force
,”
Adv. Colloid Interface Sci.
154
,
30
(
2010
).
41.
M. P.
Brenner
and
D.
Lohse
, “
Dynamic equilibrium mechanism for surface nanobubble stabilization
,”
Phys. Rev. Lett.
101
,
214505
(
2008
).
You do not currently have access to this content.