arXiv subjects

Yuri Martinez-Raton

Publications and source records attributed to Yuri Martinez-Raton.

At least 37 records · Page 2Linked to original sources

arXiv2015

Effect of orientational restriction on monolayers of hard ellipsoids

The effect of out-of-plane orientational freedom on the orientational ordering properties of a monolayer of hard ellipsoids is studied using Parsons-Lee scaling approach and replica exchange Monte Carlo computer simulation. Prolate and oblate ellipsoids exhibit very different ordering properties, namely, the axes of revolution of prolate particles tend to lean out, while those of oblate ones prefer to lean into the confining plane. The driving mechanism of this is that the particles try to maximize the available free area on the confining surface, which can be achieved by minimizing the cross section areas of the particles with the plane. In the lack out-of-plane orientational freedom the monolayer of prolate particles is identical to a two-dimensional hard ellipse system, which undergoes an isotropic-nematic ordering transition with increasing density. With gradually switching on the out-of-plane orientational freedom the prolate particles lean out from the confining plane and a destabilisation of the in-plane isotropic-nematic phase transition is observed. The system of oblate particles behaves oppositely to that of prolates. It corresponds to a two-dimensional system of hard disks in the lack of out-of-plane freedom, while it behaves similar to that of hard ellipses in the freely rotating case.

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arXiv2014

Effect of shape biaxiality on the phase behavior of colloidal liquid-crystal monolayers

We extend our previous work on monolayers of uniaxial particles [J. Chem. Phys. 140, 204906 (2014)] to study the effect of particle biaxiality on the phase behavior of liquid-crystal monolayers. Particles are modelled as board-like hard bodies with three different edge lengths $σ_1\geqσ_2\geqσ_3$, and use is made of the restricted-orientation approximation (Zwanzig model). A density-functional formalism based on the fundamental-measure theory is used to calculate phase diagrams for a wide range of values of the largest aspect ratio ($κ_1=σ_1/σ_3\in[1,100]$). We find that particle biaxiality in general destabilizes the biaxial nematic phase already present in monolayers of uniaxial particles. While plate-like particles exhibit strong biaxial ordering, rod-like ones with $κ_1>21.34$ exhibit reentrant uniaxial and biaxial phases. As particle geometry is changed from uniaxial- to increasingly biaxial-rod-like, the region of biaxiality is reduced, eventually ending in a critical-end point. For $κ_1>60$, a density gap opens up in which the biaxial nematic phase is stable for any particle biaxiality. Regions of the phase diagram where packing-fraction inversion occurs (i.e. packing fraction is a decreasing function of density) are found. Our results are compared with the recent experimental studies on nematic phases of magnetic nanorods.

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arXiv2014

Hard-body models of bulk liquid crystals

Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles, and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Hard models of anisotropic particles give rise to complex phase diagrams, including uniaxial and biaxial nematic phases, discotic phases, and spatially ordered phases such as smectic, columnar or crystal. Also, their mixtures exhibit additional interesting behaviours where demixing competes with orientational order. Here we review the different models of hard particles used in the theory of bulk anisotropic liquids, leaving aside interfacial properties, and discuss the associated theoretical approaches and computer simulations, focusing on applications in equilibrium situations. The latter include one-component bulk fluids, mixtures and polydisperse fluids, both in two and three dimensions, and emphasis is put on liquid-crystal phase transitions and complex phase behaviour in general.

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arXiv2014

Phase behavior of liquid-crystal monolayers of rod-like and plate-like particles

Orientational and positional ordering properties of liquid crystal monolayers are examined by means of Fundamental-Measure Density Functional Theory. Particles forming the monolayer are modeled as hard parallelepipeds of square section of size $σ$ and length $L$. The particle centers of mass are restricted to a flat surface and three possible and mutually perpendicular orientations (in-plane and along the layer normal) of their uniaxial axes are allowed. We find that the structure of the monolayer depends strongly on particle shape and density. In the case of rod-like shapes, particles align along the layer normal in order to achieve the lowest possible occupied area per particle. This phase is a uniaxial nematic even at very low densities. In contrast, for plate-like particles, the lowest occupied area can be achieved by random in-plane ordering in the monolayer, i.e. planar nematic ordering takes place even at vanishing densities. It is found that the random in-plane ordering is not favorable at higher densities and the system undergoes an in-plane ordering transition forming a biaxial nematic phase or crystallizes. For certain values of the aspect ratio, the uniaxial-biaxial nematic phase transition is observed for both rod-like and plate-like shapes. The stability region of the biaxial nematic phase enhances with decreasing aspect ratios for plate-like particles, while the rod-like particles exhibit a reentrant phenomenon, i.e. a sequence of uniaxial-biaxial-uniaxial nematic ordering with increasing density if the aspect ratio is larger than 21.34. In addition to this, packing fraction inversion is observed with increasing surface pressure due to the alignment along the layers normal. At very high densities the nematic phase destabilizes to a nonuniform phases (columnar, smectic or crystalline phases) for both shapes.

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arXiv2013

Interplay between columnar and smectic stability in suspensions of polydisperse colloidal platelets

The phase behavior of a model suspension of colloidal polydisperse platelets is studied using density-functional theory. Platelets are modelled as parallel rectangular prisms of square section $l$ and height $h$, with length and height distributions given by different polydispersities $δ_l$ and $δ_h$. We obtain the phase behavior of the model, including nematic, smectic and columnar phases and its dependence with the two polydispersities $δ_l$ and $δ_h$. When $δ_l>δ_h$ we observe that the smectic phase stabilises first with respect to the columnar. If $δ_h>δ_l$ we observe the opposite behavior. Other more complicated cases occur, e.g. the smectic stabilises from the nematic first but then exists a first-order transition to the columnar phase. Our model assumes plate-rod symmetry, but the regions of stability of smectic and columnar phases are non-symmetric in the $δ_l-δ_h$ plane due to the different dimensionality of ordering in the two phases. Microsegregation effects, i.e. different spatial distribution for different sizes within the periodic cell, take place in both phases.

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arXiv2013

Hard rods in a cylindrical pore: the nematic-to-smectic phase transition

The effect of cylindrical confinement on the phase behaviour of a system of parallel hard rods is studied using Onsager's second virial theory. The hard rods are represented as hard cylinders of diameter $D$ and length $L$, while the cylindrical pore is infinite with diameter $W$. The interaction between the wall and the rods is hard repulsive, and it is assumed that molecules are parallel to the surface of the pore (planar anchoring). In very narrow pores ($D 100 D$, results for bulk and confined fluids agree well due to the short range effect of the wall ($\sim 3-4D$).

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arXiv2013

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 $κ\equiv L/σ$, with $L$ the length and $σ$ the width of the rectangles ($L\geσ$), 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 $κ=1$, 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 $κ=1$ the crystal becomes stable with commensuration transitions taking place as $H$ is varied. In the case $κ=3$ the commensuration transitions involve columnar phases with different number of columns. Finally, in the case $κ=6$, 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.

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arXiv2013

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 $σ$ 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 $σ=2R_0\sin^{-1}(R/R_0)$, 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 $σ$ 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.

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arXiv2012

Two-dimensional nematics in bulk and confined geometries

Two-dimensional nematics possess peculiar properties that have been studied recently using computer simulation and various theoretical models. Here we review our own contribution to the field using density-functional theory, and present some preliminary simulation results on confined two-dimensional nematics. First we discuss the possible stable bulk phases and phase diagrams and the relation between phases and particle geometry. We then explore the adsorption properties on a single substrate and the confinement effects that arise when the fluid is confined between parallel walls. Next, confinement in circular cavities is presented; this geometry allows us to measure some properties of the simplest defects that arise in two-dimensional nematics. Finally, preliminary Monte Carlo simulation results of confined nematics in circular geometry are shown.

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arXiv2011

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.

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arXiv2011

Biaxial nematic phases in fluids of hard board-like particles

We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles with sizes $σ_1>σ_2>σ_3$. A restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio $κ_1=σ_1/σ_2$ while keeping $κ_2=σ_2/σ_3$, we predict phase diagrams for various values of $κ_2$ which include all the uniform phases: isotropic, uniaxial rod- and plate-like nematics, and biaxial nematic. In addition, spinodal instabilities of the uniform phases with respect to fluctuations of the smectic, columnar and plastic-solid type, are obtained. In agreement with recent experiments, we find that the biaxial nematic phase begins to be stable for $κ_2\simeq 2.5$. Also, as predicted by previous theories and simulations on biaxial hard particles, we obtain a region of biaxility centred on $κ_1\approxκ_2$ which widens as $κ_2$ increases. For $κ_2\agt 5$ the region $κ_2\approxκ_1$ of the packing-fraction vs. $κ_1$ phase diagrams exhibits interesting topologies which change qualitatively with $κ_2$. We have found that an increasing biaxial shape anisotropy favours the formation of the biaxial nematic phase. Our study is the first to apply FMT theory to biaxial particles and, therefore, it goes beyond the second-order virial approximation. Our prediction that the phase diagram must be asymmetric is a genuine result of the present approach, which is not accounted for by previous studies based on second-order theories.

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arXiv2011

Effect of polydispersity and soft interactions on the nematic vs. smectic phase stability in platelet suspensions

We discuss theoretically, using density-functional theory, the phase stability of nematic and smectic ordering in a suspension of platelets of the same thickness but with a high polydispersity in diameter, and study the influence of polydispersity on this stability. The platelets are assumed to interact like hard objects, but additional soft attractive and repulsive interactions, meant to represent the effect of depletion interactions are also considered. The aspect (diameter to thickness) ratio is taken to be very high, in order to model solutions of mineral platelets recently explored experimentally. In this regime a high degree of orientational ordering occurs; therefore the model platelets can be taken as completely parallel and are amenable to analysis via a fundamental-measure theory. Our focus is on the nematic vs. smectic phase interplay, since a high degree of polydispersity in diameter suppresses the formation of the columnar phase. When interactions are purely hard, the theory predicts a continuous nematic-to-smectic transition, regardless of the degree of diameter polydispersity. However, polydispersity enhances the stability of the smectic phase against the nematic phase. Predictions for the case where an additional soft interaction is added are obtained using mean-field perturbation theory. In the case of the one-component fluid, the transition remains continuous for repulsive forces, and the smectic phase becomes more stable as the range of the interaction is decreased. The opposite behaviour with respect to the range is observed for attractive forces, and in fact the transition becomes of first order below a tricritical point. Also, for attractive interactions, nematic demixing appears, with an associated critical point. When platelet polydispersity is introduced the tricritical temperature shifts to very high values.

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arXiv2011

Fluid-fluid versus fluid-solid demixing in mixtures of parallel hard hypercubes

It is well known that the increase of the spatial dimensionality enhances the fluid-fluid demixing of a binary mixture of hard hyperspheres, i.e. the demixing occurs for lower mixture size asymmetry as compared to the three-dimensional case. However, according to simulations, in the latter dimension the fluid-fluid demixing is metastable with respect to the fluid-solid transition. According to the results obtained from approximations to the equation of state of hard hyperspheres in higher dimensions, the fluid-fluid demixing might becomes stable for high enough dimension. However, this conclusion is rather speculative since none of the above works have taken into account the stability of the crystalline phase (nor by a minimization of a given density functional, neither spinodal calculations or MC simulations). Of course, the lack of results is justified by the difficulty for performing density functional calculations or simulations in high dimensions and, in particular, for highly asymmetric binary mixtures. In the present work, we will take advantage of a well tested theoretical tool, namely the fundamental measure density functional theory for parallel hard hypercubes (in the continuum and in the hypercubic lattice). With this, we have calculated the fluid-fluid and fluid-solid spinodals for different spatial dimensions. We have obtained, no matter of the dimensionality, the mixture size asymmetry nor the polydispersity (included as a bimodal distribution function centered around the asymmetric edge-lengths), that the fluid-fluid critical point is always located above the fluid-solid spinodal. In conclusion, these results point to the existence of demixing between at least one solid phase rich in large particles and one fluid phase rich in small ones, preempting a fluid-fluid demixing, independently of the spatial dimension or the polydispersity.

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arXiv2010

Phase transitions in nanoconfined binary mixtures of highly oriented colloidal rods

We analyse a binary mixture of colloidal parallel hard cylindrical particles with identical diameters but dissimilar lengths $L_1$ and $L_2$, with $s=L_2/L_1=3$, confined by two parallel hard walls in a planar slit-pore geometry, using a fundamental--measure density functional theory. This model presents nematic (N) and two types of smectic (S) phases, with first- and second-order N-S bulk transitions and S-S demixing, and surface behaviour at a single hard wall which includes complete wetting by the S phase mediated (or not) by an infinite number of surface-induced layering (SIL) transitions. In the present paper the effects of confinement on this model colloidal fluid mixture are studied. Confinement brings about profound changes in the phase diagram, resulting from competition between the three relevant length scales: pore width $h$, smectic period $d$ and length ratio $s$. Four main effects are identified: (i) Second-order bulk N-S transitions are suppressed. (ii) Demixing transitions are weakly affected, with small shifts in the $μ_1-μ_2$ (chemical potentials) plane. (iii) Confinement-induced layering (CIL) transitions occurring in the two confined one-component fluids in some cases merge with the demixing transition. (iv) Surface-induced layering (SIL) transitions occurring at a single surface as coexistence conditions are approached are also shifted in the confined fluid. Trends with pore size are analysed by means of complete $μ_1-μ_2$ and $p-\bar{x}$ (pressure-mean pore composition) phase diagrams for particular values of pore size. This work, which is the first one to address the behaviour of liquid-crystalline mixtures under confinement, could be relevant as a first step to understand self-assembling properties of mixtures of metallic nanoparticles under external fields in restricted geometry.

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arXiv2010

Competition between capillarity, layering and biaxiality in a confined liquid crystal

The effect of confinement on the phase behaviour and structure of fluids made of biaxial hard particles (cuboids) is examined theoretically by means of Onsager second-order virial theory in the limit where the long particle axes are frozen in a mutually parallel configuration. Confinement is induced by two parallel planar hard walls (slit-pore geometry), with particle long axes perpendicular to the walls (perfect homeotropic anchoring). In bulk, a continuous nematic-to-smectic transition takes place, while shape anisotropy in the (rectangular) particle cross section induces biaxial ordering. As a consequence, four bulk phases, uniaxial and biaxial nematic and smectic phases, can be stabilised as the cross-sectional aspect ratio is varied. On confining the fluid, the nematic-to-smectic transition is suppressed, and either uniaxial or biaxial phases, separated by a continuous trasition, can be present. Smectic ordering develops continuously from the walls for increasing particle concentration (in agreement with the supression of nematic-smectic second order transition at confinement), but first-order layering transitions, involving structures with n and n+1 layers, arise in the confined fluid at high concentration. Competition between layering and uniaxial-biaxial ordering leads to three different types of layering transitions, at which the two coexisting structures can be both uniaxial, one uniaxial and another biaxial, or both biaxial. Also, the interplay between molecular biaxiality and wall interactions is very subtle: while the hard wall disfavours the formation of the biaxial phase, biaxiality is against the layering transitions, as we have shown by comparing the confined phase behaviour of cylinders and cuboids. The predictive power of Onsager theory is checked and confirmed by performing some calculations based on fundamental-measure theory.

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arXiv2009

Stable smectic phase in suspensions of polydisperse colloidal platelets with identical thickness

We report the nematic and smectic ordering in a new aqueous suspension of monolayer $α$-Zirconium phosphate platelets possessing a high polydispersity in diameter but uniform thickness. We observe an isotropic--nematic transition as the platelet volume fraction increases, followed by the formation of a smectic, an elusive phase that has been rarely seen in discotic liquid crystals. The smectic phase is characterized by X-ray diffraction, high-resolution transmission electron microscopy, and optical microscopy. The phase equilibria in this highly polydisperse suspension is rationalized in terms of a theoretical approach based on density--functional theory.

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arXiv2009

Smectic and columnar ordering in length-polydisperse fluids of parallel hard cylinders

We apply a recently proposed density functional for mixtures of parallel hard cylinders, based on Rosenfeld's fundamental measure theory, to study the effect of length-polydispersity on the relative stability between the smectic and columnar liquid crystal phases.To this purpose we derive from this functional an expression for the direct correlation function and use it to perform a bifurcation analysis. We compare the results with those obtained with a second and a third virial approximation of this function. All three approximations lead to the same conclusion: there is a terminal polydispersity beyond which the smectic phase is less stable than the columnar phase. This result is in agreement with previous Monte Carlo simulations conducted on a freely rotating length-polydisperse hard spherocylinder fluid, although the theories always overestimate the terminal polydispersity because the nematic-columnar phase transition is first order and exhibits a wide coexistence gap. Both, the fundamental-measure functional and the third virial approximation, predict a metastable nematic-nematic demixing. Conversely, according to second virial approximation this demixing might be stable at high values of the polydispersity, something that is observed neither in simulations nor in experiments. The results of the fundamental-measure functional are quantitatively superior to those obtained from the other two approximations. Thus this functional provides a promising route to map out the full phase diagram of this system.

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arXiv2008

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 $κ$ 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. $i\simeqκ$), 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.

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