Contact angles, ordering, and solidification of liquid mercury in carbon nanotube cavities
A. Kutana and K. P. Giapis
*
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
Received 1 August 2007; published 29 November 2007
Optimized model potentials for mercury-mercury and mercury-carbon interactions are used in molecular
dynamics simulations to study wetting and solidification of liquid mercury encapsulated in single-walled
carbon nanotubes. The contact angle of mercury in the nanotube cavity increases linearly with wall curvature.
The solid-liquid transition becomes less well defined as nanotube diameter decreases, while the melting tem-
perature drops exponentially. A concentric cylindrical-shell structure is predicted for solidified mercury in
small
20,20
nanotubes, while a polycrystalline structure appears in larger
40,40
nanotubes.
DOI:
10.1103/PhysRevB.76.195444
PACS number
s
: 65.80.
n, 02.70.Ns, 64.70.Dv
Liquid mercury does not wet graphite spontaneously. In-
deed, fresh mercury forms droplets on highly ordered pyro-
lytic graphite with a contact angle of 152.5°.
1
Being equiva-
lent to graphene scrolls, carbon nanotubes too cannot be
wetted spontaneously by mercury, or for that matter, by any
liquid metal with surface tension greater than 180 mN
/
m.
2
However, wetting and filling of the inner cavity of a carbon
nanotube with mercury have been shown to occur as a result
of electrowetting.
3
Continuous columns of liquid mercury
form inside carbon nanotubes with their open end immersed
into a mercury droplet, following the application of a voltage
exceeding a threshold value between the nanotube and the
droplet. Once confined in a nanotube cavity, the wetting be-
havior of a nonwetting fluid becomes of fundamental and
practical interest for nanofluidics. Furthermore, studies of
freezing or melting transitions of metals under one-
dimensional confinement could lead to the discovery of new
crystalline phases and possibly to the existence of a solid-
liquid critical point.
4
New solid metal phases could lead to
unexpected mechanical, electrical, magnetic, and catalytic
properties.
Ordering and crystallization of materials in carbon nano-
tube cavities have attracted intense theoretical interest. New
ice phases, including ordered ice nanotubes, were predicted
to form by freezing water inside carbon nanotubes.
5
Simula-
tions of CCl
4
in nanotube cavities showed liquid ordering in
concentric layers, which solidify into two-dimensional
hexagonal crystals unlike those observed for bulk
crystallization.
6
Depending on the nanotube diameter,
helical-strand, cylindrical-shell, and fcc structures were pre-
dicted for Cu and Au confined inside nanotube cavities.
7
,
8
Experimental evidence for the existence of such new struc-
tures in nanotube cavities has been sparse. Using high-
resolution transmission electron microscopy, Fan
et al.
9
dem-
onstrated the formation of a double-strand helix of iodine
atoms inside a
10,10
single-walled nanotube
SWCNT
.In
slightly larger SWCNTs, Guan
et al.
10
found a new crystal-
line phase of iodine, in addition to a triple-strand helix. Us-
ing x-ray diffraction, Maniwa
et al.
11
studied water freezing
in SWCNT bundles and found a new peak appearing in the
diffraction spectrum at 235 K, which was attributed to the
formation of ordered ice nanotubes. In the absence of con-
finement, suspended gold nanowires in ultrahigh vacuum ex-
hibited a multishell structure composed of coaxial tubes.
12
As of this writing, helical-strand, cylindrical-shell, or other
new crystalline phases of metals encapsulated in SWCNTs
have not been demonstrated experimentally.
In this work, we report results of classical molecular dy-
namics
MD
simulations performed to predict the contact
angles and ordering of liquid mercury inside large single-
walled carbon nanotubes. The presence of a solid wall in-
duces ordering in the adjacent liquid, which is manifested in
density oscillations that extend several molecular diameters
into the bulk. Furthermore, we report on the solidification
process of liquid Hg under confinement and the structural
properties of the Hg nanowires thus formed. We employ the
optimized Hg-Hg and Hg-C potentials, developed for simu-
lating mercury imbibition in carbon nanotubes activated by
electrowetting.
13
For the former, we use an
ab initio
pairwise
potential for the mercury dimer developed by Schwerdtfeger
et al.
,
14
scaled to match the density of liquid Hg at 300 K.
This empirically adjusted potential improved the description
of multiple mercury properties as compared to standard
Lennard-Jones
LJ
potentials and was deemed a better can-
didate for studying wetting effects. Coincidentally, although
not specifically developed for describing the solid phase, this
potential reproduces the bulk freezing point and the inter-
atomic distance of solid mercury
3.0 Å
. However, it should
be emphasized that this potential is not a rigorous expansion
of the energy of the bulk phase in terms of
n
-body
n
2
interactions. When many-body terms are included, it has
been shown
15
that the convergence of the energy is poor at
interatomic distances
3Å
typical of the bulk phase, be-
cause the contributions from three-, four-, or even six-body
terms decrease very slowly with
n
. Thus, potentials that in-
clude three- or four-body corrections may not result in im-
provement while complicating the form of the potential. The
mercury-carbon interaction was modeled by a pairwise LJ
potential, with energy and distance parameters
HgC
/
k
B
=15.0 K,
HgC
=3.321 Å
optimized according to the proce-
dure described in Ref.
16
to predict the experimental contact
angle of a macroscopic mercury drop on graphite at 300 K.
Using these potentials, we calculated the shape of a liquid
mercury drop on graphite and the Hg density oscillations
ordering
near the solid surface. The drop consisted of 4000
Hg atoms and it was placed on a graphite surface formed by
two graphene layers with lateral dimensions of 108
107 Å
2
, separated by 3.354 Å. The atoms of the liquid
were coupled to a 300 K thermostat, while the positions of
PHYSICAL REVIEW B
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/195444
5
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195444-1
the surface atoms were fixed. Evaporated mercury atoms
were reflected toward the substrate to reproduce a saturated
vapor ambient. Random position fluctuations of the drop
center of mass were dampened mildly. The liquid density
was recorded in a two-dimensional histogram as a function
of the radial distance from the drop symmetry axis and
height above the graphene plane. From this density, the po-
sition of the drop surface was determined assuming
surf
=
1
/
2
bulk
.
17
For smoothness, the recorded density function
was averaged over a large time interval
1ns
after a pe-
riod of equilibration of the drop shape and vertical position.
The equilibrium density map is shown in Fig.
1
a
along with
a snapshot of the calculated drop shape where the Hg atoms
are depicted as hard spheres. Ordering of mercury atoms
adjacent to the graphene surface is apparent in the density
map.
Next, the equilibrium wetting of mercury droplets inside
carbon nanotubes is considered as a function of tube diam-
eter. Different numbers of mercury atoms
20,20
, 1279;
30,30
, 3571;
40,40
, 7123;
50,50
, 12 151
were placed in
the cavity of single-walled
n
,
n
nanotubes
SWCNT
at
regular positions within a cylinder of radius
r
=
R
SWCNT
−3.5 Å and were equilibrated for at least 1000 ps at 300 K
until a liquid slug was formed. Periodic boundary conditions
along the nanotube axis ensured that evaporated Hg atoms
did not escape. A Berendsen thermostat was applied to the
fluid while the nanotube atoms were kept fixed.
18
A snapshot
of the MD simulations after 1190 ps of equilibration inside a
40,40
SWCNT, shown in Fig.
1
b
, reveals that the free
surfaces of mercury are convex, as expected from a nonwet-
ting interaction. The liquid density map is also shown in Fig.
1
b
as a function of the radial distance
r
and axial length
z
.
The atom ordering in the liquid near the curved nanotube
walls is similar to that seen for the flat graphene surface.
However, a comparison of the Hg density oscillations in Fig.
2
reveals a lower density value for the first layer nearest to
the cavity walls, possibly due to the increased repulsion at
the curved surface. A mercury drop confined between two
parallel graphene sheets, separated by a distance of 54.24 Å
equal to the diameter of the
40,40
SWCNT, exhibits iden-
tical density oscillations to the free drop on graphene, sug-
gesting that confinement is less important for ordering than
wall curvature. Indeed, the amplitude of the near-wall den-
sity oscillations grows with the nanotube wall curvature
not
shown
. The effect is well pronounced and is not likely to be
artificially caused by the thermal motion of the nanotube
walls.
18
Instead, the stronger liquid ordering in smaller nano-
tubes may be caused by a hydrostatic capillary pressure
P
that is proportional to the mean meniscus curvature
H
,as
given by the Young-Laplace equation
P
=2
H
, where
is
the surface tension of the liquid in the drop. Enhanced order-
ing may occur when the spatial extent of the density oscilla-
tions becomes comparable with the tube radius. For example,
the liquid is ordered throughout the tube volume in a
20,20
SWCNT
R
=13.6 Å
.
The contact angle of the mercury free surface in the
SWCNT cavity varies with nanotube diameter as a result of
curvature. Figure
3
a
shows the meniscus outline and the
corresponding fitting curve
circle
inside the
30,30
,
40,40
, and
50,50
SWCNTs. Similarly to the flat surface,
the contact angle
was defined at the point of intersection of
the fitting line with the liquid boundary in contact with the
wall. The geometrical shape of the meniscus and the position
of the liquid surface were found by fitting the contour lines
corresponding to
=
1
/
2
bulk
with circular arcs.
19
To ensure
-60
-40
-20
0
20
40
60
r
(Å)
152.5
o
(b)
(
a
)
z
(Å)
-30 -20 -10 0 10 20 30
FIG. 1.
a
Snapshot of an equilibrated mercury drop
4000
atoms
on a graphene sheet
left
with averaged mercury density
contour
right
with contact angle determination.
b
Snapshot of an
equilibrated mercury slug
12 151 atoms
in a
40,40
single-walled
nanotube
top
with corresponding density contour
bottom
. Note
similarities in ordering of the liquid near the graphene sheet and
nanotube walls.
02468101214
0
2
4
6
8
10
12
14
16
ρ
ρ
ρ
ρ
(g/cm
3
)
r
(
Å
)
drop on graphene sheet
drop between graphene
sheets
drop in a (40,40) SWNT
FIG. 2. Radial density profile of mercury as a function of the
distance from a solid surface. Profiles are shown for a drop resting
on a graphene sheet
dotted line
, a drop confined between two
graphene sheets separated by 54.24 Å
dashed line
, and a drop in a
40,40
single-walled nanotube of diameter=54.24 Å
solid line
.
A. KUTANA AND K. P. GIAPIS
PHYSICAL REVIEW B
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the smoothness of the contour lines, at least 5
10
5
samples
of the liquid density were taken in calculating the average,
and the points within 5 Å from the wall and 2 Å from the
center axis were neglected in the fitting procedure.
Thus, obtained contact angles were larger than the 152.5°
value for a flat graphene sheet, suggesting a more mercuro-
phobic nanotube interior. The contact angle increases linearly
with the inverse of the tube radius, as inferred from Fig.
3
b
,
showing the contact angle of mercury inside
30,30
,
40,40
,
and
50,50
SWCNTs. For smaller nanotubes
R
SWCNT
17 Å
, contact angles could not be calculated reliably be-
cause of the smallness of the fitting region. The cutoff angle
of 153°, corresponding to a vanishing wall curvature, closely
matches the result obtained for the drop on planar
graphene.
20
This result confirms the importance of the wall
curvature in determining the mercury contact angle in the
nanotube cavity.
Remarkably, in one case of experimentally observed mer-
cury encapsulated in a
40,40
SWCNT, a contact angle of
150° ±5° was reported,
3
with a meniscus resembling the
curved surface of mercury in Fig.
1
b
. This value is smaller
than the contact angle of
166 °, predicted for a
40,40
SWCNT. A larger value for the nanotube cavity makes sense
given the more mercurophobic character of the curved walls
of the nanotube interior. Perhaps the smaller contact angle
seen experimentally is a result of reduced surface tension
because of oxidation or the presence of other impurities on
the mercury surface. Indeed, a trace of the meniscus with
lighter contrast was left behind when the mercury evaporated
as a result of electron beam heating during imaging of the
experimental profile.
3
We next considered the solidification of mercury droplets
encapsulated in SWCNT cavities. The internal energy of a
droplet is determined as a function of temperature as follows.
Each droplet is formed initially by joining two parts: one-
half liquid at 400 K and one-half solid at 50 K. The number
of atoms in each droplet varies with the nanotube diameter to
keep the nanowire length fixed at 7.9 nm for all nanotube
sizes studied. Then, the temperature is set to a desired value,
and the system is allowed to equilibrate before calculating
the total energy. The equilibration time increases substan-
tially for the larger nanotubes
most runs were executed for
800 ps but a few points around the solidification temperature
were allowed to equilibrate for 1600 ps
. This procedure per-
mits a more accurate determination of the solidification tem-
perature by avoiding supercooling effects. Figure
4
illustrates
results from calculations of the total energy of Hg droplets in
20,20
and
40,40
SWCNTs, plotted as a function of tem-
perature. While the solid-liquid phase transition is readily
apparent in both cases, it is less pronounced for the smaller
nanotube. In fact, a mere change in the slope of the energy vs
temperature plot indicates the phase transition for the Hg
0.0
0.2
0.4
0.6
150
155
160
165
170
175
θ
θ
θ
θ
(deg)
1/
r
(nm
-1
)
(50,50)
(40,40)
(30,30)
(b)
0 5 10 15 20 25 30 3
5
30
40
50
60
(50,50)
(40,40)
(30,30)
z
(
Å
)
r
(Å)
(a)
FIG. 3.
a
Outline of menisci for mercury slugs inside the in-
dicated single-walled carbon nanotubes as a function of the distance
from the tube centerline. Each shape is fitted with an arc
dotted
line
.
b
Mercury contact angles obtained from
a
as a function of
nanotube curvature.
-380
-360
-340
-320
-300
-280
-
260
150
200
250
-2200
-2100
-2000
-1900
-1800
T(K)
(40,40)
(20,20)
E(eV)
FIG. 4. Total energy of a mercury slug
7.9 nm long
encapsu-
lated in the cavity of
20,20
and
40,40
single-walled nanotubes,
calculated as a function of temperature after equilibration.
CONTACT ANGLES, ORDERING, AND SOLIDIFICATION
...
PHYSICAL REVIEW B
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195444-3
slug in the
10,10
SWCNT
not shown
. This trend is con-
sistent with the Landau fluctuation theorem as applied to
phase transitions in reduced dimensionality systems. Figure
5
shows the solidification point for the fixed-length Hg nano-
wire in each nanotube as a function of nanotube radius. The
melting transition occurs at exponentially lower temperatures
as the nanotube size decreases. Note that the solidification
point predicted for a macroscopic drop on graphite is 234 K.
The cylindrical concentric shell structures predicted for
solidified Cu and Au in SWCNTs,
7
,
8
are also found for mer-
cury in
20,20
and smaller nanotubes. Figure
6
a
illustrates
radial snapshots of the encapsulated mercury in a
20,20
SWCNT at various temperatures above and below the solidi-
fication point
173 K
. The Hg atoms are plotted as small
hard spheres to facilitate observation. The first two snapshots
correspond to a liquid phase with wall ordering, while the
last two correspond to the solid phase. The radial density
profile for each temperature, averaged over many snapshots,
is shown in Fig.
6
b
. Above the solidification point, the
density oscillations have minima larger than zero, indicating
motion of Hg atoms across layers and randomness character-
istic of a liquid. However, below the solidification point, the
density drops to zero between layers, suggesting that the Hg
atoms are confined in each cylindrical shell. The lack of
atom exchange between concentric shells occurs at the same
temperature as the discontinuity in total energy and thus
marks the solidification transition without ambiguity.
The density peaks become narrower in width and more
pronounced at lower temperatures, indicating smaller fluc-
tuations in atom positions in each shell. Detailed analysis of
atom packing below the corresponding melting transition
showed that the atoms in each shell assume a close-packed
configuration. This packing gives the impression that the at-
oms organize in helices along the 60° diagonal of the ben-
zene rings of the carbon nanotube with respect to the tube
axis, which could be interpreted as order imposed by the
nanotube through templating. The lack of direct coordination
between the Hg atoms and benzene rings suggests that tem-
plating would be an overinterpretation of close packing.
Increasing the nanotube diameter influences packing and
ordering of the encapsulated mercury. Figure
7
presents
snapshots for mercury in
30,30
and
40,40
SWCNTs at a
select temperature below the corresponding solidification
point. These solid structures must be contrasted with the con-
centric shells found in the
20,20
SWCNT. While
cylindrical-shell ordering persists near the walls, the order
becomes much less discernible near the center of the
30,30
SWCNT. Remarkably, the cylindrical-shell structure near the
walls of the
40,40
SWCNT changes into a different crys-
talline phase near the center axis. The mercury atoms orga-
nize in intersecting planar sheets parallel to the nanotube
axis. We believe that cohesive interactions between mercury
atoms become dominant away from the walls resulting in a
bulklike ordering in the larger nanotubes. While new crystal-
line phases have been found for materials solidified in carbon
nanotubes, a polycrystalline phase with a continuous transi-
tion from cylindrical order to a bulk phase has not been
discussed. Such order should influence the structural and
electronic properties of the solidified nanowire. Similar
structures should also exist for encapsulated nanowires of
5 1015202530
100
120
140
160
180
200
T(K)
R
(
Å
)
FIG. 5. Solidification temperature as a function of single-walled
nanotube radius for a fixed-length mercury slug encapsulated in the
nanotube.
0246810121
4
0
10
20
30
40
50
60
70
80
90
100
ρ
ρ
ρ
ρ
(g/cm
3
)
r
(
Å
)
T=250K
T=175K
T=170K
T=150K
T=170K
T=150K
T=250K
T=175K
(
a
)
(b)
FIG. 6.
a
Front view of typical equilibrium configurations of
encapsulated mercury in a
20,20
single-walled nanotube at vari-
ous temperatures above and below the solidification point
173 K
. Only the centers of mass of the mercury atoms are de-
picted in the snapshots to facilitate observation.
b
Radial density
profiles for the indicated temperatures, averaged over many
snapshots.
A. KUTANA AND K. P. GIAPIS
PHYSICAL REVIEW B
76
, 195444
2007
195444-4
higher melting point metals, which may be easier than mer-
cury to verify experimentally.
In conclusion, molecular dynamics simulations of liquid
mercury encapsulated in carbon nanotube cavities predict or-
dering near the walls and density oscillations, which extend
several molecular diameters into the bulk. The mercury wet-
ting angle is found to increase linearly with wall curvature,
suggesting that the nanotube interior is more mercurophobic
than a flat graphene surface. Solidification of encapsulated
mercury in small
20,20
nanotubes results in close-packed
concentric cylindrical-shell structures. In
40,40
and larger
nanotubes, the solidified mercury becomes polycrystalline:
The cylindrical-shell order persists near the walls but evolves
into a periodic planar structure away from the walls. The
solid-liquid transition becomes less well defined as nanotube
diameter decreases while the solidification temperature drops
exponentially.
This work was based on research supported by NSF
CTS-0508096
.
*
Corresponding author; giapis@cheme.caltech.edu
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at a nonzero tempera-
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A separate simulation of a mercury droplet on a single graphene
layer produced a contact angle identical to that for the two-layer
case.
(30
,
30) T=150K
(40
,
40) T=160K
(20
,
20) T=120K
FIG. 7. Radial snapshots of solidified mercury, encapsulated in
20,20
,
30,30
, and
40,40
single-walled nanotubes at a representative
temperature below the solidification point for each nanotube.
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2007
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