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liquid phase. Electrowetting is therefore most effective when the field polarizes
water along the wall, but is considerably weaker when the field tends to turn water
dipoles
toward
the wall. Consistent with the above picture, hydrogen bond popula-
tions, monitored as a function of field angle relative to the walls, are enhanced in
parallel fields and depleted especially at interfaces with field pointing toward the
wall [
66
]. Analogous preference for the interface/field alignment has been observed
and discussed in recent simulation studies of nanodroplet elongation [
109
] and
aqueous film evaporation [
110
] in the field. The surprisingly strong effect of field
direction and polarity on surface wetting is a signature of the nanoscale regime
where surface molecules represent a statistically significant constituency.
4.2 Wetting Free Energy
Field-enhanced wettability can be quantified in terms of wetting surface free
energy,
s
(
E
), here defined as the sum
Dg þ
W
el
(
E
)
¼g
cos
y
c
(
E
)[(
3
) and (
6
)].
For smooth surfaces,
inside an open nanopore of fixed width
D
has been shown
[
66
] to relate to the lateral component of the pressure tensor,
P
k
:
s
s ¼
@O
@
P
k
D
2
:
A
¼
(14)
is the grand potential of the wetted part of the confinement atop
the wetted area
A
with volume
AD
. A recent study reported systematic GCMC
calculations of
Here,
O
(
E
) in hydrocarbon-like nanopores [
66
]. To estimate contact angles
under the field also required calculations of surface tension (
s
g
lv
) as a function of
the field strength. Calculations for a free-standing aqueous slab were performed
using the conventional relation
sð
=
2. A novel finite-difference
technique for the calculation of pressure tensor components determined energy
differences
E
Þ¼ð
P
?
P
k
Þ
D
D
U
a
, associated with uniform scaling of molecular coordinates
a
(
a ¼
z
or
x, y
) and volume change
V
a
/2)
comprised changes in intermolecular and water-wall interactions. As described in
Supporting Information to [
66
], pressure tensor components were obtained from the
relation
D
V
a
[
66
].
D
U
a
¼
U
a
(
V
þ D
V
a
/2)
U
a
(
V
-
D
ð
D
U
a
kT
ln
<
exp
kT
Þ >
0
<
D
U
a
D
P
aa
¼ r
kT
þ
lim
¼ r
kT
lim
D
V
a
>:
(15)
D
V
a
D
V
a
!
0
V
a
!
Related finite-difference techniques have been studied in a number of contexts
involving fluids with hard-core [
111
] and soft potentials [
112
-
116
]. The central
finite-difference approximation, analyzed systematically in [
115
], was implemented
[
66
] through scaling by a factor of
f
10
5
in forward and backward
¼
1
e
with
e ¼
directions. Within the range 10
6
10
4
, no significant dependence on
has
been detected and exponential and linearized forms of (
15
) produced identical
e
e
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