15 research outputs found

### Phase behavior of mixtures of hard ellipses: A scaled particle density functional study

We present a scaled particle density functional study of two-dimensional
binary mixtures of hard convex particles with one or both species being
ellipses. In particular, we divide our study into two parts. The first part is
devoted to the calculation of phase diagrams of mixtures with the same
elliptical shapes, but with (i) different aspect ratios and equal particle
areas, (ii) equal aspect ratios and different particle areas and (iii) with the
former and the later being different. In the second study we obtain the phase
diagrams corresponding to crossed-mixtures of particles with species having
elliptical and rectangular shapes. We compare the phase diagram topologies and
explain their main features from the entropic nature of particle interactions
directly related to the anisotropies, areas, and shapes of species. The results
obtained can be corroborated by experiments on granular rods where the entropic
forces are very important in the stabilization of liquid-crystal textures at
the stationary states.Comment: Preprint format. 22 pages and 10 figure

### 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

### Phase diagrams of Zwanzig models: The effect of polydispersity

The first goal of this article is to study the validity of the Zwanzig model
for liquid crystals to predict transitions to inhomogeneous phases (like
smectic and columnar) and the way polydispersity affects these transitions. The
second goal is to analyze the extension of the Zwanzig model to a binary
mixture of rods and plates. The mixture is symmetric in that all particles have
equal volume and length-to-breadth ratio, $\kappa$. The phase diagram
containing the homogeneous phases as well as the spinodals of the transitions
to inhomogeneous phases is determined for the cases $\kappa=5$ and 15 in order
to compare with previous results obtained in the Onsager approximation. We then
study the effect of polydispersity on these phase diagrams, emphasizing the
enhancement of the stability of the biaxial nematic phase it induces.Comment: 11 pages, 12 figure

### 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

### 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

### 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

### Enhanced stability of tetratic phase due to clustering

We show that the relative stability of the nematic tetratic phase with
respect to the usual uniaxial nematic phase can be greatly enhanced by
clustering effects. Two--dimensional rectangles of aspect ratio $\kappa$
interacting via hard interactions are considered, and the stability of the two
nematic phases (uniaxial and tetratic) is examined using an extended
scaled--particle theory applied to a polydispersed fluid mixture of $n$
species. Here the $i$--th species is associated with clusters of $i$
rectangles, with clusters defined as stacks of rectangles containing
approximately parallel rectangles, with frozen internal degrees of freedom. The
theory assumes an exponential cluster size distribution (an assumption fully
supported by Monte Carlo simulations and by a simple chemical--reaction model),
with fixed value of the second moment. The corresponding area distribution
presents a shoulder, and sometimes even a well-defined peak, at cluster sizes
approximately corresponding to square shape (i.e. $i\simeq\kappa$), meaning
that square clusters have a dominant contribution to the free energy of the
hard--rectangle fluid. The theory predicts an enhanced region of stability of
the tetratic phase with respect to the standard scaled--particle theory, much
closer to simulation and to experimental results, demonstrating the importance
of clustering in this fluid.Comment: 9 pages, 9 figure

### Effect of polydispersity, bimodality and aspect ratio on the phase behavior of colloidal platelet suspensions

We use a Fundamental-Measure density functional for hard board-like
polydisperse particles, in the restricted-orientation approximation, to explain
the phase behaviour of platelet colloidal suspensions studied in recent
experiments. In particular, we focus our attention on the behavior of the total
packing fraction of the mixture, $\eta$, in the region of two-phase
isotropic-nematic coexistence as a function of mean aspect ratio,
polydispersity and fraction of total volume $\gamma$ occupied by the nematic
phase. In our model, platelets are polydisperse in the square section, of side
length $\sigma$, but have constant thickness $L$ (and aspect ratio
$\kappa\equiv L/$ the mean side length). Good
agreement between our theory and recent experiments is obtained by mapping the
real system onto an effective one, with excluded volume interactions but with
thicker particles (due to the presence of long-ranged repulsive interactions
between platelets). The effect of polydispersity in both shape and particle
size has been taken into account by using a size distribution function with an
effective mean-square deviation that depends on both polydispersities. We also
show that the bimodality of the size distribution function is required to
correctly describe the huge two-phase coexistence gap and the nonlinearity of
the function $\gamma(\eta)$, two important features that these colloidal
suspensions exhibit.Comment: 12 pages, 9 figure