3,011 research outputs found

### Dimensional cross-over of hard parallel cylinders confined on cylindrical surfaces

We derive, from the dimensional cross-over criterion, a fundamental-measure
density functional for parallel hard curved rectangles moving on a cylindrical
surface. We derive it from the density functional of circular arcs of length
$\sigma$ with centers of mass located on an external circumference of radius
$R_0$. The latter functional in turns is obtained from the corresponding 2D
functional for a fluid of hard discs of radius $R$ on a flat surface with
centers of mass confined onto a circumference of radius $R_0$. Thus the curved
length of closest approach between two centers of mass of hard discs on this
circumference is $\sigma=2R_0\sin^{-1}(R/R_0)$, the length of the circular
arcs. From the density functional of circular arcs, and by applying a
dimensional expansion procedure to the spatial dimension orthogonal to the
plane of the circumference, we finally obtain the density functional of curved
rectangles of edge-lengths $\sigma$ and $L$. The DF for curved rectangles can
also be obtained by fixing the centers of mass of parallel hard cylinders of
radius $R$ and length $L$ on a cylindrical surface of radius $R_0$. The phase
behavior of a fluid of aligned curved rectangles is obtained by calculating the
free-energy branches of smectic, columnar and crystalline phases for different
values of the ratio $R_0/R$ in the range $1<R_0/R\leq 4$; the smectic phase
turns out to be the most stable except for $R_0/R=4$ where the crystalline
phase becomes reentrant in a small range of packing fractions. When $R_0/R<1$
the transition is absent, since the density functional of curved rectangles
reduces to the 1D Percus functional.Comment: 27 pages, 6 figure

### Stability of smectic phases in hard-rod mixtures

Using density-functional theory, we have analyzed the phase behavior of
binary mixtures of hard rods of different lengths and diameters. Previous
studies have shown a strong tendency of smectic phases of these mixtures to
segregate and, in some circumstances, to form microsegregated phases. Our focus
in the present work is on the formation of columnar phases which some studies,
under some approximations, have shown to become thermodynamically stable prior
to crystallization. Specifically we focus on the relative stability between
smectic and columnar phases, a question not fully addressed in previous work.
Our analysis is based on two complementary perspectives: on the one hand, an
extended Onsager theory, which includes the full orientational degrees of
freedom but with spatial and orientational correlations being treated in an
approximate manner; on the other hand, we formulate a Zwanzig approximation of
fundamental-measure theory on hard parallelepipeds, whereby orientations are
restricted to be only along three mutually orthogonal axes, but correlations
are faithfully represented. In the latter case novel, complete phase diagrams
containing regions of stability of liquid-crystalline phases are calculated.
Our findings indicate that the restricted-orientation approximation enhances
the stability of columnar phases so as to preempt smectic order completely
while, in the framework of the extended Onsager model, with full orientational
degrees of freedom taken into account, columnar phases may preempt a large
region of smectic stability in some mixtures, but some smectic order still
persists.Comment: 14 pages, 16 figures. To appear in JC

### Effect of particle geometry on phase transitions in two-dimensional liquid crystals

Using a version of density-functional theory which combines Onsager
approximation and fundamental-measure theory for spatially nonuniform phases,
we have studied the phase diagram of freely rotating hard rectangles and hard
discorectangles. We find profound differences in the phase behavior of these
models, which can be attributed to their different packing properties.
Interestingly, bimodal orientational distribution functions are found in the
nematic phase of hard rectangles, which cause a certain degree of biaxial
order, albeit metastable with respect to spatially ordered phases. This feature
is absent in discorectangles, which always show unimodal behavior. This result
may be relevant in the light of recent experimental results which have
confirmed the existence of biaxial phases. We expect that some perturbation of
the particle shapes (either a certain degree of polydispersity or even bimodal
dispersity in the aspect ratios) may actually destabilize spatially ordered
phases thereby stabilizing the biaxial phase.Comment: 9 pages, 7 figures, to appear in JC

### Demixing behavior in two-dimensional mixtures of anisotropic hard bodies

Scaled particle theory for a binary mixture of hard discorectangles and for a
binary mixture of hard rectangles is used to predict possible liquid-crystal
demixing scenarios in two dimensions. Through a bifurcation analysis from the
isotropic phase, it is shown that isotropic-nematic demixing is possible in
two-dimensional liquid-crystal mixtures composed of hard convex bodies. This
bifurcation analysis is tested against exact calculations of the phase diagrams
in the framework of the restricted-orientation two-dimensional model (Zwanzig
model). Phase diagrams of a binary mixture of hard discorectangles are
calculated through the parametrization of the orientational distribution
functions. The results show not only isotropic-nematic, but also
nematic-nematic demixing ending in a critical point, as well as an
isotropic-nematic-nematic triple point for a mixture of hard disks and hard
discorectangles.Comment: 13 pages, 14 figures. To appear in PR

### Liquid-crystal patterns of rectangular particles in a square nanocavity

Using density-functional theory in the restricted-orientation approximation,
we analyse the liquid-crystal patterns and phase behaviour of a fluid of hard
rectangular particles confined in a two-dimensional square nanocavity of side
length $H$ composed of hard inner walls. Patterning in the cavity is governed
by surface-induced order, capillary and frustration effects, and depends on the
relative values of particle aspect ratio $\kappa\equiv L/\sigma$, with $L$ the
length and $\sigma$ the width of the rectangles ($L\ge\sigma$), and cavity size
$H$. Ordering may be very different from bulk ($H\to\infty$) behaviour when $H$
is a few times the particle length $L$ (nanocavity). Bulk and confinement
properties are obtained for the cases $\kappa=1$, 3 and 6. In the confined
fluid surface-induced frustration leads to four-fold symmetry breaking in all
phases (which become two-fold symmetric). Since no director distorsion can
arise in our model by construction, frustration in the director orientation is
relaxed by the creation of domain walls (where the director changes by
$90^{\circ}$); this configuration is necessary to stabilise periodic phases.
For $\kappa=1$ the crystal becomes stable with commensuration transitions
taking place as $H$ is varied. In the case $\kappa=3$ the commensuration
transitions involve columnar phases with different number of columns. Finally,
in the case $\kappa=6$, the high-density region of the phase diagram is
dominated by commensuration transitions between smectic structures; at lower
densities there is a symmetry-breaking isotropic $\to$ nematic transition
exhibiting non-monotonic behaviour with cavity size.Comment: 31 pages, 15 figure

### Depletion effects in smectic phases of hard rod--hard sphere mixtures

It is known that when hard spheres are added to a pure system of hard rods
the stability of the smectic phase may be greatly enhanced, and that this
effect can be rationalised in terms of depletion forces. In the present paper
we first study the effect of orientational order on depletion forces in this
particular binary system, comparing our results with those obtained adopting
the usual approximation of considering the rods parallel and their orientations
frozen. We consider mixtures with rods of different aspect ratios and spheres
of different diameters, and we treat them within Onsager theory. Our results
indicate that depletion effects, and consequently smectic stability, decrease
significantly as a result of orientational disorder in the smectic phase when
compared with corresponding data based on the frozen--orientation
approximation. These results are discussed in terms of the $\tau$ parameter,
which has been proposed as a convenient measure of depletion strength. We
present closed expressions for $\tau$, and show that it is intimately connected
with the depletion potential. We then analyse the effect of particle geometry
by comparing results pertaining to systems of parallel rods of different shapes
(spherocylinders, cylinders and parallelepipeds). We finally provide results
based on the Zwanzig approximation of a Fundamental--Measure
density--functional theory applied to mixtures of parallelepipeds and cubes of
different sizes. In this case, we show that the $\tau$ parameter exhibits a
linear asymptotic behaviour in the limit of large values of the hard--rod
aspect ratio, in conformity with Onsager theory, as well as in the limit of
large values of the ratio of rod breadth to cube side length, $d$, in contrast
to Onsager approximation, which predicts $\tau\sim d^3$.Comment: 15 pages, 11 figure

### Efficient approach to the free energy of crystals via Monte Carlo simulations

We present a general approach to compute the absolute free energy of a system of particles with constrained center of mass based on the Monte Carlo thermodynamic coupling integral method. The version of the Frenkel-Ladd approach [J. Chem. Phys. 81, 3188 (1984)]JCPSA60021-960610.1063/1.448024, which uses a harmonic coupling potential, is recovered. Also, we propose a different choice, based on one-particle square-well coupling potentials, which is much simpler, more accurate, and free from some of the difficulties of the Frenkel-Ladd method. We apply our approach to hard spheres and compare with the standard harmonic methodFinancial support from MINECO (Spain) under Grant No. FIS2013-47350-C5-1-R is acknowledge

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