Two-dimensional symmetry breaking of fluid density distribution in closed
nanoslits
Gersh O. Berim and Eli Ruckenstein
a͒
Department of Chemical and Biological Engineering, State University of New York at Buffalo,
Buffalo, New York 14260, USA
͑Received 17 September 2007; accepted 1 November 2007; published online 9 January 2008͒
Stable and metastable fluid density distributions ͑FDDs͒ in a closed nanoslit between two identical
parallel solid walls have been identified on the basis of a nonlocal canonical ensemble density
functional theory. Similar to Monte Carlo simulations, periodicity of the FDD in one of the lateral
͑parallel to the walls surfaces͒ directions, denoted as the x direction, was assumed. In the other
lateral direction, y direction, the FDD was considered uniform. It was found that depending on the
average fluid density in the slit, both uniform as well as nonuniform FDDs in the x direction can
occur. The uniform FDDs are either symmetric or asymmetric about the middle plane between
walls; the latter FDD being the consequence of a symmetry breaking across the slit. The nonuniform
FDDs in the x direction occur either in the form of a bump on a thin liquid film covering the walls
or as a liquid bridge between those walls and provide symmetry breaking in the x direction. For
small and large average densities, the stable state is uniform in the x direction and is symmetric
about the middle plane between walls. In the intermediate range of the average density and
depending on the length L
x
of the FDD period, the stable state can be represented either by a FDD,
which is uniform in the x direction and asymmetric about the middle of the slit ͑small values of L
x
͒,
or by a bump- and bridgelike FDD for intermediate and large values of L
x
, respectively. These
results are in agreement with the Monte Carlo simulations performed earlier by other authors.
Because the free energy of the stable state decreases monotonically with increasing L
x
, one can
conclude that the real period is very large ͑infinite͒ and that for the values of the parameters
employed, a single bridge of finite length over the entire slit is generated. © 2008 American Institute
of Physics. ͓DOI: 10.1063/1.2816574͔
I. INTRODUCTION
A fluid in a long nanoslit between two planar identical
solid walls is exposed to an external potential due to fluid-
solid interactions, which is symmetrical about the middle of
the slit in the direction across the slit ͑perpendicular to the
walls͒. For this reason, one usually expects the fluid density
distribution ͑FDD͒ to possess the same symmetry. However,
in Refs. 1 and 2, it was shown that in a closed slit this
symmetry can be broken in some ranges of the parameters
characterizing the system ͑fluid average density, strength of
the fluid-solid interactions, and temperature͒ and that the
stable FDD can become asymmetrical about the middle of
the slit. The existence of such a symmetry breaking, which
was unknown previously, is in agreement with the Monte
Carlo ͑MC͒ simulations.
3
Similarly, in a long ͑infinite͒ slit the fluid-solid interac-
tion potential possesses translational symmetry in lateral
͑parallel to the walls͒ directions suggesting uniformity of the
FDD along the walls. The same symmetry is also inherent
for long cylindrical pores in the axial direction. For the latter
system, it was shown using canonical ensemble MC
simulations,
4
the Laplace theory of capillarity and the Der-
jaguin model,
5
and the nonlocal density functional theory
6
that the translational symmetry in the axial direction of the
FDD can be broken through the formation of bumps,
bubbles, and bridges on and between the solid surfaces.
These results were used to explain the Everett-Haynes
7
sce-
nario of bridging through the formation of a bump on the
film adsorbed on the solid surface, which grows with in-
creasing fluid average density and transforms into a bridge
connecting the solid surfaces. They also explain the capillary
condensation in open pores as a morphological transition
from a low average density state ͑thin film adsorbed on the
solid surface͒ to a high average density state ͑liquid com-
pletely filling the pore͒, both states being uniform in the
lateral direction.
5
During such a transition, the bridges and
bumps play the roles of unstable nuclei of the new liquid
phase. Because the states of interest ͑bridges and bumps͒ are
not present in open systems which are described by the grand
canonical ensemble, but occur in closed systems which are
described by the canonical ensemble, MC simulations in ca-
nonical ensemble were used in Ref. 4 to obtain information
about them. In addition, the canonical ensemble version of
the density functional theory ͑CEDFT͒ was used to describe
the unstable states in open systems. This approach allowed
one to calculate the work of formation of droplets or bubbles
in a metastable configuration on a solid substrate
8
and inside
slit pores.
9
It was also used to describe the backward part of
a͒
Author to whom correspondence should be addressed. Tel.: ͑716͒645-2911,
Ext. 2214. Fax: ͑716͒645-3822. Electronic mail:
feaeliru@acsu.buffalo.edu.
THE JOURNAL OF CHEMICAL PHYSICS 128, 024704 ͑2008͒
0021-9606/2008/128͑2͒/024704/7/$23.00 © 2008 American Institute of Physics128, 024704-1