Yuri Martínez-ratón - Academia.edu (original) (raw)
Papers by Yuri Martínez-ratón
Physical Review E, 1997
We propose a physical mechanism which leads to surface-enhanced smectic-A ordering ͑SESO͒ at the ... more We propose a physical mechanism which leads to surface-enhanced smectic-A ordering ͑SESO͒ at the free surface of a model liquid crystal. We also provide an explanation, based on a density-functional theory, for recent experimental results for the melting behavior of freely suspended smectic ͑FSS͒ films. It is shown that stepwise layer-thinning transitions do not usually occur during melting of FSS films, despite the presence of SESO. We find that thinning transitions similar to those observed experimentally occur under conditions such that the film interior melts to a nematic rather than isotropic liquid phase.
Soft Matter, 2015
We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with... more We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature, and the behaviour of the cholesteric pitch profile, are studied. In particular, the isotropic-cholesteric transition is calculated in the bulk and confined systems. In the slit pore, the transition exhibits an oscillatory structure with respect to pore width. Commensuration effects between cholesteric pitch and pore width causes an infinite set of winding transitions to exist. These transitions have been predicted and analysed by other authors for cholesterics confined in a fixed pore and subject to an external field promoting the uniaxial nematic phase; here we induce winding transitions by changing the pore width at zero external field, a setup recently explored in Atomic-Force Microscopy experiments that can detect these transitions. The structure of winding transitions terminates at the capillary isotropic-cholesteric transition via triple points where the confined isotropic phase coexists with two cholesterics with different helix indices. Complete phase diagrams in the temperature-pore width plane are obtained. For symmetric and asymmetric monostable plate anchorings the phase diagram are qualitatively similar. In the case where one plate presents a bistable anchoring potential, winding transitions exhibit a more complex structure, with a collection of triple points involving three cholesterics with different helix indices.
Physical Review E, 1998
We provide an exact mapping between the density functional of a binary mixture and that of the ef... more 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.
AIP Conference Proceedings, 2009
J. Chem. Phys., 2014
Orientational and positional ordering properties of liquid crystal monolayers are examined by mea... more 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. Their shapes are controlled by the aspect ratio κ = L/σ (>1 for prolate and <1 for oblate shapes). 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.
Journal of Physics: Condensed Matter 26, 463101 (2014), 2014
Hard models for particle interactions have played a crucial role in the understanding of the stru... more 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.
Lecture Notes in Physics, 2008
To the memory of our friend Yasha Rosenfeld, who discovered the Fundamental Measure Theory, makin... more To the memory of our friend Yasha Rosenfeld, who discovered the Fundamental Measure Theory, making this chapter grow into a thick one.
Phys. Chem. Chem. Phys., 2015
We extend our previous work on monolayers of uniaxial particles [J. Chem. Phys., 2014, 140, 20490... more We extend our previous work on monolayers of uniaxial particles [J. Chem. Phys., 2014, 140, 204906] 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 σ1 ≥ σ2 ≥ σ3, and the restricted-orientation approximation (Zwanzig model) is used. A density-functional formalism based on the fundamental-measure theory is used to calculate phase diagrams for a wide range of values with the largest aspect ratio κ1 = σ1/σ3 ∈ [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 κ1 > 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 κ1 > 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.
Physical Review Letters, 1997
We present a regularization of the recently proposed fundamental-measure functional for a mixture... more 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.
Physical Review Letters, 2002
The phase diagram of a polydisperse mixture of uniaxial rod-like and plate-like hard parallelepip... more 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. PACS numbers: 64.70.Md,64.75.+g,61.20.Gy Systems of anisotropic molecules with two symmetry axes may form a biaxial nematic phase. In this phase molecules align preferentially along two perpendicular axes. The biaxial phase is experimentally difficult to observe because in systems with biaxial molecules it is preempted by smectic or solid phases. This led Alben [1] to propose an alternative system which should behave similarly, but in which spatial ordering is difficulted: a mixture of hard rods and plates. His analysis of this system with a mean-field lattice model showed a phase diagram with four phases: isotropic fluid (I), rod-like nematic (N + ), plate-like nematic (N − ), and biaxial (B). The latter separates the two nematics with second-order transition lines when composition is varied from rod-rich to plate-rich. Upon increasing concentration, for a rodrich (plate-rich) composition the system first undergoes a first-order I-N + (I-N − ) transition and then a second order N + -B (N − -B) transition. At the crossover there is simply a continuous I-B transition. Two continuous and two first-order transitions meet at this multicritical point. At the conclusions of his work, Alben mentions that a N + -N − phase separation might replace the B phase, but does not considers this possibility in his analysis. A similar phase behavior has later been obtained by other authors using different models . They take into account the effect of having free (rather than restricted to a lattice) rotations and/or translations. From them one learns three main things: first of all, that Alben's phase diagram is qualitatively correct; secondly, that there is a symmetric mixture, namely that with rods and plates having the same molecular volume (hence parallel or perpendicular like particles have the same excluded volume), for which the multicritical point appears more or less at equimolar composition; and thirdly, that the phase diagram is perfectly symmetric about equimolarity only if virial coefficients higher than the second are neglected.
Physical Review E, 2011
We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Mont... more We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Monte Carlo simulation and mean-field theory. A film of material is sandwiched between two planar, parallel plates that couple to the adjacent spins via a surface strength ǫ s . We consider the cases where the favoured alignments at the two walls are the same (symmetric cell) or different (asymmetric or hybrid cell). In the latter case, we demonstrate the existence of a single phase transition in the slab for all values of the cell thickness. This transition has been observed before in the regime of narrow cells, where the two structures involved correspond to different arrangements of the nematic director. By studying wider cells, we show that the transition is in fact the usual isotropic-to-nematic (capillary) transition under confinement in the case of antagonistic surface forces. We show results for a wide range of values of film thickness, and discuss the phenomenology using a mean-field model.
Physical Review E, 2009
We report the nematic and smectic ordering in a new aqueous suspension of monolayer α-Zirconium p... more 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.
Physical Review E, 2007
Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientati... more Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientational degrees of freedom, we analyse the stability of phases with orientational order and the demixing phase behaviour of a variety of mixtures. Our study is focused on cases where at least one of the components consists of hard rectangles, or a particular case of these, hard squares. A pure fluid of hard rectangles has recently been shown to exhibit, aside from the usual uniaxial nematic phase, an additional oriented phase, called tetratic phase, possessing two directors, which is the analog of the biaxial or cubatic phases in three-dimensional fluids. There is evidence, based on computer simulation studies, that the tetratic phase might be stable with respect to phases with lower translational symmetry for rectangles with low aspect ratios. As hard rectangles are mixed, in increasing concentration, with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilised, via a first-or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio (hard squares in particular), tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry and dimensions, and also on the thermodynamic conditions of the mixture.
Physical Review E, 2008
We obtain a fundamental-measure density functional for mixtures of parallel hard cylinders. For t... more We obtain a fundamental-measure density functional for mixtures of parallel hard cylinders. For 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 those 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.
Physical Review E, 2013
Using density-functional theory in the restricted-orientation approximation, we analyze the liqui... more Using density-functional theory in the restricted-orientation approximation, we analyze the liquid-crystal patterns and phase behavior 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 as well as capillary and frustration effects and depends on the relative values of the particle aspect ratio κ≡L/σ, with L the length and σ the width of the rectangles (L≥σ), and cavity size H. Ordering may be very different from bulk (H→∞) behavior 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 bulk the isotropic phase is always stable at low packing fractions η=Lσρ_{0} (with ρ_{0} the average density) and nematic, smectic, columnar, and crystal phases can be stabilized at higher η depending on κ: For increasing η the sequence of isotropic to columnar is obtained for κ=1 and 3, whereas for κ=6 we obtain isotropic to nematic to smectic (the crystal being unstable in all three cases for the density range explored). In the confined fluid surface-induced frustration leads to fourfold symmetry breaking in all phases (which become twofold symmetric). Since no director distortion 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^{∘}); this configuration is necessary to stabilize periodic phases. For κ=1 the crystal becomes stable with commensurate transitions taking place as H is varied. These transitions involve structures with different number of peaks in the local density. In the case κ=3 the commensurate transitions involve columnar phases with different number of columns. In the case κ=6 the high-density region of the phase diagram is dominated by commensurate transitions between smectic structures; at lower densities there is a symmetry-breaking isotropic to nematic transition exhibiting nonmonotonic behavior with cavity size. Apart from the present application in a confinement setup, our model could be used to explore the bulk region near close packing in order to elucidate the possible existence of disordered phases at close packing.
Physical Review E, 2008
We have calculated the phase diagrams of one-component fluids made of five types of biaxial parti... more 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.
Physical Review E, 2005
Scaled particle theory for a binary mixture of hard discorectangles and for a binary mixture of h... more 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.
Physical Review E, 1997
We propose a physical mechanism which leads to surface-enhanced smectic-A ordering ͑SESO͒ at the ... more We propose a physical mechanism which leads to surface-enhanced smectic-A ordering ͑SESO͒ at the free surface of a model liquid crystal. We also provide an explanation, based on a density-functional theory, for recent experimental results for the melting behavior of freely suspended smectic ͑FSS͒ films. It is shown that stepwise layer-thinning transitions do not usually occur during melting of FSS films, despite the presence of SESO. We find that thinning transitions similar to those observed experimentally occur under conditions such that the film interior melts to a nematic rather than isotropic liquid phase.
Soft Matter, 2015
We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with... more We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature, and the behaviour of the cholesteric pitch profile, are studied. In particular, the isotropic-cholesteric transition is calculated in the bulk and confined systems. In the slit pore, the transition exhibits an oscillatory structure with respect to pore width. Commensuration effects between cholesteric pitch and pore width causes an infinite set of winding transitions to exist. These transitions have been predicted and analysed by other authors for cholesterics confined in a fixed pore and subject to an external field promoting the uniaxial nematic phase; here we induce winding transitions by changing the pore width at zero external field, a setup recently explored in Atomic-Force Microscopy experiments that can detect these transitions. The structure of winding transitions terminates at the capillary isotropic-cholesteric transition via triple points where the confined isotropic phase coexists with two cholesterics with different helix indices. Complete phase diagrams in the temperature-pore width plane are obtained. For symmetric and asymmetric monostable plate anchorings the phase diagram are qualitatively similar. In the case where one plate presents a bistable anchoring potential, winding transitions exhibit a more complex structure, with a collection of triple points involving three cholesterics with different helix indices.
Physical Review E, 1998
We provide an exact mapping between the density functional of a binary mixture and that of the ef... more 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.
AIP Conference Proceedings, 2009
J. Chem. Phys., 2014
Orientational and positional ordering properties of liquid crystal monolayers are examined by mea... more 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. Their shapes are controlled by the aspect ratio κ = L/σ (>1 for prolate and <1 for oblate shapes). 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.
Journal of Physics: Condensed Matter 26, 463101 (2014), 2014
Hard models for particle interactions have played a crucial role in the understanding of the stru... more 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.
Lecture Notes in Physics, 2008
To the memory of our friend Yasha Rosenfeld, who discovered the Fundamental Measure Theory, makin... more To the memory of our friend Yasha Rosenfeld, who discovered the Fundamental Measure Theory, making this chapter grow into a thick one.
Phys. Chem. Chem. Phys., 2015
We extend our previous work on monolayers of uniaxial particles [J. Chem. Phys., 2014, 140, 20490... more We extend our previous work on monolayers of uniaxial particles [J. Chem. Phys., 2014, 140, 204906] 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 σ1 ≥ σ2 ≥ σ3, and the restricted-orientation approximation (Zwanzig model) is used. A density-functional formalism based on the fundamental-measure theory is used to calculate phase diagrams for a wide range of values with the largest aspect ratio κ1 = σ1/σ3 ∈ [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 κ1 > 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 κ1 > 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.
Physical Review Letters, 1997
We present a regularization of the recently proposed fundamental-measure functional for a mixture... more 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.
Physical Review Letters, 2002
The phase diagram of a polydisperse mixture of uniaxial rod-like and plate-like hard parallelepip... more 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. PACS numbers: 64.70.Md,64.75.+g,61.20.Gy Systems of anisotropic molecules with two symmetry axes may form a biaxial nematic phase. In this phase molecules align preferentially along two perpendicular axes. The biaxial phase is experimentally difficult to observe because in systems with biaxial molecules it is preempted by smectic or solid phases. This led Alben [1] to propose an alternative system which should behave similarly, but in which spatial ordering is difficulted: a mixture of hard rods and plates. His analysis of this system with a mean-field lattice model showed a phase diagram with four phases: isotropic fluid (I), rod-like nematic (N + ), plate-like nematic (N − ), and biaxial (B). The latter separates the two nematics with second-order transition lines when composition is varied from rod-rich to plate-rich. Upon increasing concentration, for a rodrich (plate-rich) composition the system first undergoes a first-order I-N + (I-N − ) transition and then a second order N + -B (N − -B) transition. At the crossover there is simply a continuous I-B transition. Two continuous and two first-order transitions meet at this multicritical point. At the conclusions of his work, Alben mentions that a N + -N − phase separation might replace the B phase, but does not considers this possibility in his analysis. A similar phase behavior has later been obtained by other authors using different models . They take into account the effect of having free (rather than restricted to a lattice) rotations and/or translations. From them one learns three main things: first of all, that Alben's phase diagram is qualitatively correct; secondly, that there is a symmetric mixture, namely that with rods and plates having the same molecular volume (hence parallel or perpendicular like particles have the same excluded volume), for which the multicritical point appears more or less at equimolar composition; and thirdly, that the phase diagram is perfectly symmetric about equimolarity only if virial coefficients higher than the second are neglected.
Physical Review E, 2011
We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Mont... more We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Monte Carlo simulation and mean-field theory. A film of material is sandwiched between two planar, parallel plates that couple to the adjacent spins via a surface strength ǫ s . We consider the cases where the favoured alignments at the two walls are the same (symmetric cell) or different (asymmetric or hybrid cell). In the latter case, we demonstrate the existence of a single phase transition in the slab for all values of the cell thickness. This transition has been observed before in the regime of narrow cells, where the two structures involved correspond to different arrangements of the nematic director. By studying wider cells, we show that the transition is in fact the usual isotropic-to-nematic (capillary) transition under confinement in the case of antagonistic surface forces. We show results for a wide range of values of film thickness, and discuss the phenomenology using a mean-field model.
Physical Review E, 2009
We report the nematic and smectic ordering in a new aqueous suspension of monolayer α-Zirconium p... more 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.
Physical Review E, 2007
Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientati... more Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientational degrees of freedom, we analyse the stability of phases with orientational order and the demixing phase behaviour of a variety of mixtures. Our study is focused on cases where at least one of the components consists of hard rectangles, or a particular case of these, hard squares. A pure fluid of hard rectangles has recently been shown to exhibit, aside from the usual uniaxial nematic phase, an additional oriented phase, called tetratic phase, possessing two directors, which is the analog of the biaxial or cubatic phases in three-dimensional fluids. There is evidence, based on computer simulation studies, that the tetratic phase might be stable with respect to phases with lower translational symmetry for rectangles with low aspect ratios. As hard rectangles are mixed, in increasing concentration, with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilised, via a first-or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio (hard squares in particular), tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry and dimensions, and also on the thermodynamic conditions of the mixture.
Physical Review E, 2008
We obtain a fundamental-measure density functional for mixtures of parallel hard cylinders. For t... more We obtain a fundamental-measure density functional for mixtures of parallel hard cylinders. For 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 those 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.
Physical Review E, 2013
Using density-functional theory in the restricted-orientation approximation, we analyze the liqui... more Using density-functional theory in the restricted-orientation approximation, we analyze the liquid-crystal patterns and phase behavior 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 as well as capillary and frustration effects and depends on the relative values of the particle aspect ratio κ≡L/σ, with L the length and σ the width of the rectangles (L≥σ), and cavity size H. Ordering may be very different from bulk (H→∞) behavior 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 bulk the isotropic phase is always stable at low packing fractions η=Lσρ_{0} (with ρ_{0} the average density) and nematic, smectic, columnar, and crystal phases can be stabilized at higher η depending on κ: For increasing η the sequence of isotropic to columnar is obtained for κ=1 and 3, whereas for κ=6 we obtain isotropic to nematic to smectic (the crystal being unstable in all three cases for the density range explored). In the confined fluid surface-induced frustration leads to fourfold symmetry breaking in all phases (which become twofold symmetric). Since no director distortion 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^{∘}); this configuration is necessary to stabilize periodic phases. For κ=1 the crystal becomes stable with commensurate transitions taking place as H is varied. These transitions involve structures with different number of peaks in the local density. In the case κ=3 the commensurate transitions involve columnar phases with different number of columns. In the case κ=6 the high-density region of the phase diagram is dominated by commensurate transitions between smectic structures; at lower densities there is a symmetry-breaking isotropic to nematic transition exhibiting nonmonotonic behavior with cavity size. Apart from the present application in a confinement setup, our model could be used to explore the bulk region near close packing in order to elucidate the possible existence of disordered phases at close packing.
Physical Review E, 2008
We have calculated the phase diagrams of one-component fluids made of five types of biaxial parti... more 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.
Physical Review E, 2005
Scaled particle theory for a binary mixture of hard discorectangles and for a binary mixture of h... more 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.