arXiv subjects

Yuri Martinez-Raton

Publications and source records attributed to Yuri Martinez-Raton.

53 records · Page 3Linked to original sources

arXiv2008

Biaxial nematic and smectic phases of parallel particles with different cross sections

We have calculated the phase diagrams of one--component fluids made of five types of biaxial particles differing in their cross sections. The orientation of the principal particle axis is fixed in space, while the second axis is allowed to freely rotate. We have constructed a free-energy density functional based on fundamental--measure theory to study the relative stability of nematic and smectic phases with uniaxial, biaxial and tetratic symmetries. Minimization of the density functional allows us to study the phase behavior of the biaxial particles as a function of the cross-section geometry. For low values of the aspect ratio of the particle cross section, we obtain smectic phases with tetratic symmetry, although metastable with respect to the crystal, as our MC simulation study indicates. For large particle aspect ratios and in analogy with previous work [Phys. Chem. Chem. Phys. 5, 3700 (2003)], we have found a four--phase point where four spinodals, corresponding to phase transitions between phases with different symmetries, meet together. The location of this point is quite sensitive to particle cross section, which suggests that optimizing the particle geometry could be a useful criterion in the design of colloidal particles that can exhibit an increased stability of the biaxial nematic phase with respect to other competing phases with spatial order.

cond-mat.soft↗

arXiv2008

Phase behavior of parallel hard cylinders

We test the performance of a recently proposed fundamental measure density functional of aligned hard cylinders by calculating the phase diagram of a monodisperse fluid of these particles. We consider all possible liquid crystalline symmetries, namely nematic, smectic and columnar, as well as the crystalline phase. For this purpose we introduce a Gaussian parameterization of the density profile and use it to minimize numerically the functional. We also determine, from the analytic expression for the structure factor of the uniform fluid, the bifurcation points from the nematic to the smectic and columnar phases. The equation of state, as obtained from functional minimization, is compared to the available Monte Carlo simulation. The agreement is is very good, nearly perfect in the description of the inhomogeneous phases. The columnar phase is found to be metastable with respect to the smectic or crystal phases, its free energy though being very close to that of the stable phases. This result justifies the observation of a window of stability of the columnar phase in some simulations, which disappears as the size of the system increases. The only important deviation between theory and simulations shows up in the location of the nematic-smectic transition. This is the common drawback of any fundamental measure functional of describing the uniform phase just with the accuracy of scaled particle theory.

cond-mat.soft↗

arXiv2008

A fundamental-measure density functional for mixtures of parallel hard cylinders

We obtain a fundamental measure density functional for mixtures of parallel hard cylinders. To this purpose we first generalize to multicomponent mixtures the fundamental measure functional proposed by Tarazona and Rosenfeld for a one-component hard disk fluid, through a method alternative to the cavity formalism of these authors. We show the equivalence of both methods when applied to two-dimensional fluids. The density functional so obtained reduces to the exact density functional for one-dimensional mixtures of hard rods when applied to one-dimensional profiles. In a second step we apply an idea put forward some time ago by two of us, based again on a dimensional reduction of the system, and derive a density functional for mixtures of parallel hard cylinders. We explore some features of this functional by determining the fluid-fluid demixing spinodals for a binary mixture of cylinders with the same volume, and by calculating the direct correlation functions.

cond-mat.soft↗

arXiv2008

Non-uniform liquid--crystalline phases of parallel hard rod-shaped particles: From ellipsoids to cylinders

In this article we consider systems of parallel hard {\it superellipsoids}, which can be viewed as a possible interpolation between ellipsoids of revolution and cylinders. Superellipsoids are characterized by an aspect ratio and an exponent $α$ (shape parameter) which takes care of the geometry, with $α=1$ corresponding to ellipsoids of revolution, while $α=\infty$ is the limit of cylinders. It is well known that, while hard parallel cylinders exhibit nematic, smectic, and solid phases, hard parallel ellipsoids do not stabilize the smectic phase, the nematic phase transforming directly into a solid as density is increased. We use computer simulation to find evidence that for $α\geα_c$, where $α_c$ is a critical value which the simulations estimate to be in the interval 1.2--1.3, the smectic phase is stabilized. This is surprisingly close to the ellipsoidal case. In addition, we use a density-functional approach, based on the Parsons--Lee approximation, to describe smectic and columnar ordering. In combination with a free--volume theory for the crystalline phase, a theoretical phase diagram is predicted. While some qualitative features, such as the enhancement of smectic stability for increasing $α$, and the probable absence of a stable columnar phase, are correct, the precise location of coexistence densities are quantitatively incorrect.

cond-mat.soft↗

arXiv2007

Large Attractive Depletion Interactions in Soft Repulsive-Sphere Binary Mixtures

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit, and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.

cond-mat.soft↗

arXiv2007

Capillary ordering and layering transitions in two-dimensional hard-rod fluids

In this article we calculate the surface phase diagram of a two-dimensional hard-rod fluid confined between two hard lines. In a first stage we study the semi-infinite system consisting of an isotropic fluid in contact with a single hard line. We have found complete wetting by the columnar phase at the wall-isotropic fluid interface. When the fluid is confined between two hard walls, capillary columnar ordering occurs via a first-order phase transition. For higher chemical potentials the system exhibits layering transitions even for very narrow slits (near the one-dimensional limit). The theoretical model used was a density-functional theory based on the Fundamental-Measure Functional applied to a fluid of hard rectangles in the restricted-orientation approximation (Zwanzig model). The results presented here can be checked experimentally in two-dimensional granular media made of rods, where vertical motions induced by an external source and excluded volume interactions between the grains allow the system to explore those stationary states which entropically maximize packing configurations. We claim that some of the surface phenomena found here can be present in two-dimensional granular-media fluids.

cond-mat.stat-mech↗

arXiv2007

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 $τ$ parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for $τ$, 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 $τ$ 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 $τ\sim d^3$.

cond-mat.soft↗

arXiv2006

Orientational ordering in hard rectangles: The role of three-body correlations

We investigate the effect of three-body correlations on the phase behavior of hard rectangle two-dimensional fluids. The third virial coefficient, $B_3$, is incorporated via an equation of state that recovers scaled particle theory for parallel hard rectangles. This coefficient, a functional of the orientational distribution function, is calculated by Monte Carlo integration, using an accurate parameterized distribution function, for various particle aspect ratios in the range 1-25. A bifurcation analysis of the free energy calculated from the obtained equation of state is applied to find the isotropic (I)-uniaxial nematic (N$_u$) and isotropic-tetratic nematic (N$_t$) spinodals and to study the order of these phase transitions. We find that the relative stability of the N$_t$ phase with respect to the isotropic phase is enhanced by the introduction of $B_3$. Finally, we have calculated the complete phase diagram using a variational procedure and compared the results with those obtained from scaled particle theory and with Monte Carlo simulations carried out for hard rectangles with various aspect ratios. The predictions of our proposed equation of state as regards the transition densities between the isotropic and orientationally ordered phases for small aspect ratios are in fair agreement with simulations. Also, the critical aspect ratio below which the N$_t$ phase becomes stable is predicted to increase due to three-body correlations, although the corresponding value is underestimated with respect to simulation.

cond-mat.soft↗

arXiv2005

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.

cond-mat.soft↗

arXiv2005

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.

cond-mat.soft↗

arXiv2004

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.

cond-mat.soft↗

arXiv2004

Bulk inhomogeneous phases of anisotropic particles: A fundamental measure functional study of the restricted orientations model

The phase diagram of prolate and oblate particles in the restricted orientations approximation (Zwanzig model) is calculated. Transitions to different inhomogeneous phases (smectic, columnar, oriented, or plastic solid) are studied through minimization of the fundamental measure functional (FMF) of hard parallelepipeds. The study of parallel hard cubes (PHC's) as a particular case is also included motivated by recent simulations of this system. As a result a rich phase behavior is obtained which include, apart from the usual liquid crystal phases, a very peculiar phase (called here discotic smectic) which was already found in the only existing simulation of the model, and which turns out to be stable because of the restrictions imposed on the orientations. The phase diagram is compared at a qualitative level with simulation results of other anisotropic particle systems.

cond-mat.soft↗

arXiv2003

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, $κ$. The phase diagram containing the homogeneous phases as well as the spinodals of the transitions to inhomogeneous phases is determined for the cases $κ=5$ 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.

cond-mat.soft↗

arXiv2002

Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates

The phase diagram of a polydisperse mixture of uniaxial rod-like and plate-like hard parallelepipeds is determined for aspect ratios $κ=5$ and 15. All particles have equal volume and polydispersity is introduced in a highly symmetric way. The corresponding binary mixture is known to have a biaxial phase for $κ=15$, but to be unstable against demixing into two uniaxial nematics for $κ=5$. We find that the phase diagram for $κ=15$ is qualitatively similar to that of the binary mixture, regardless the amount of polydispersity, while for $κ=5$ a sufficient amount of polydispersity stabilizes the biaxial phase. This provides some clues for the design of an experiment in which this long searched biaxial phase could be observed.

cond-mat.soft↗

arXiv2002

Close to the edge of Fundamental Measure Theory: density functional for hard sphere mixtures

We analyze the structure of the Fundamental Measure Theory for the free energy density functional of hard sphere mixtures. A comparative study of the different versions of the theory, and other density functional approaches, is done in terms of their generic form for the three-points direct correlation function, which shows clearly the main advantages and problems of the different approximations. A recently developed version for the monocomponent case is extended to mixtures of hard spheres with different radii, and a new prescription is presented to obtain the exact dimensional crossover of those mixtures in the one-dimensional (1D) limit. Numerical results for planar wall-fluid interfaces and for the 1D fluid are presented.

cond-mat.soft↗

arXiv1998

Phase behaviour of additive binary mixtures in the limit of infinite asymmetry

We provide an exact mapping between the density functional of a binary mixture and that of the effective one-component fluid in the limit of infinite asymmetry. The fluid of parallel hard cubes is thus mapped onto that of parallel adhesive hard cubes. Its phase behaviour reveals that demixing of a very asymmetric mixture can only occur between a solvent-rich fluid and a permeated large particle solid or between two large particle solids with different packing fractions. Comparing with hard spheres mixtures we conclude that the phase behaviour of very asymmetric hard-particle mixtures can be determined from that of the large component interacting via an adhesive-like potential.

cond-mat.soft↗

arXiv1997

Dimensional crossover of the fundamental-measure functional for parallel hard cubes

We present a regularization of the recently proposed fundamental-measure functional for a mixture of parallel hard cubes. The regularized functional is shown to have right dimensional crossovers to any smaller dimension, thus allowing to use it to study highly inhomogeneous phases (such as the solid phase). Furthermore, it is shown how the functional of the slightly more general model of parallel hard parallelepipeds can be obtained using the zero-dimensional functional as a generating functional. The multicomponent version of the latter system is also given, and it is suggested how to reformulate it as a restricted-orientation model for liquid crystals. Finally, the method is further extended to build a functional for a mixture of parallel hard cylinders.

cond-mat.soft↗