arXiv subjects

Enrique Velasco

Publications and source records attributed to Enrique Velasco.

At least 19 recordsLinked to original sources

arXiv2026

Biaxial nematics and nematic-nematic demixing in polydisperse mixtures of hard board-like particle fluids

We study the bulk phase behavior of a polydisperse liquid crystal fluid made of biaxial boards with restricted orientations using both fundamental measure theory and Monte Carlo computer simulations. The continuous polydispersity is included in the intermediate particle length of the boards via a truncated Schulz distribution. By calculating several phase diagrams across a range of polydispersity coefficients, we find that polydispersity (i) enhances demixing between two uniaxial nematic phases and (ii) expands the stability region of the biaxial phase. Although metastable with respect to non-uniform phases, we identify certain mixtures exhibiting two-phase coexistence paths involving uniaxial-uniaxial and uniaxial-biaxial phase separations. Whether these paths can be completed depends on the precise shape of the parent distribution function. Monte Carlo simulations performed for a representative case exhibit the same phase diagram topology predicted by theory, thereby validating the theoretical approach. The main difference between both approaches lies in quantitative agreement, with simulated phase transitions systematically occurring at higher packing fractions than those predicted theoretically. Our combined theoretical and simulation results may prove relevant to the design and interpretation of sedimentation experiments on colloidal suspensions of polydisperse anisotropic particles.

cond-mat.soft↗

arXiv2025

Sedimentation profiles and phase stacking diagrams in polydisperse hard rounded rectangle fluids

We analyze the sedimentation behavior of a polydisperse two-dimensional liquid-crystal fluid using a local density functional theory based on scaled particle theory. Polydispersity is incorporated through variations in the roundness of hard rectangular particles interacting solely via excluded area effects. Despite its simplicity, the model displays a rich phenomenology. In bulk, the fluid exhibits isotropic, nematic, and tetratic phases. In sedimentation, we obtain complex phase stacking diagrams featuring multiphasic stacking sequences with up to four stacks of different bulk phases, inverted stacking sequences such as top isotropic and bottom nematic together with top nematic and bottom isotopic, as well as stacking sequences with reentrant stacks such as tetratic and nematic stacks floating between two isotropic stacks. This phenomenology arises as a result of an intricate coupling between particle polydispersity and the effect of gravity. Our approach can be easily adapted to investigate the sedimentation behaviour of other polydisperse colloidal systems.

cond-mat.soft↗

arXiv2025

Defects in vibrated monolayers of equilateral triangular prisms

We present experimental results in which a quasimonolayer of grains, shaped as equilateral triangular prisms, is vertically vibrated within circular and square confining cavities. The system exhibits a fluid phase characterized by sixfold orientational order. However, the specific geometries of the cavities frustrate this order, leading to the excitation of topological defects that adhere to topological principles. We analyze the distribution of topological charges of these defects and their evolution as a function of the container geometry. In particular, we find that in the circular cavity, both the number and charge of defects remain constant in the steady-state regime, with only defects of charge $+1$ being excited. In contrast, within the square cavity, with the same topology as the circular cavity, some defects become pinned to the corners of the cavity, developing charges of $+1$ or $+2$. Additionally, free defects with charges of $\pm 1$ can be excited. Notably, dynamic events occur, such as the fusion of two defects or the creation of two defects from a single one. These events are governed by the conservation of total charge within the cavity and give rise to various system configurations, with rapid transitions between them. The observed dynamic fluctuations in topological charge are remarkable, influenced by both particle shape and cavity geometry. This system of vertically vibrated (dissipative) granular monolayers presents a unique and simple platform for studying topological phenomena, with potential implications for topological effects in equilibrium-oriented fluids.

cond-mat.soft↗

arXiv2024

Cell theories for the chiral crystal phase of hard equilateral triangles

We derive several versions of the cell theory for a crystal phase of hard equilateral triangles. To that purpose we analytically calculated the free area of a frozen oriented or freely rotating particle inside the cavity formed by its neighbours in a chiral configuration of their orientations. From the most successful versions of the theory we predict an equation of state which, despite being derived from a crystal configuration of particles, describes very reasonably the equation of state of the 6-atic liquid-crystal phase at packing fractions not very close from the isotropic-6-atic bifurcation. Also, the same equation of state performs well when compared to that from MC simulations for the stable crystal phase. The agreement can even be improved by selecting adequate values for the angle of chirality.Despite the success of two of the versions of the theory for the pressure, we show that the free-energy is an increasing function of the angle of chirality, implying that the most stable phase is the achiral phase. Furthermore, we show that possible clustering effects, such as the formation of perfect chiral hexagonal clusters, which in turn crystallize into an hexagonal lattice, cannot explain the presence of the chirality observed in simulations.

cond-mat.soft↗

arXiv2024

Density-functional theory for clustering of two-dimensional hard particle fluids

Fluids made of two-dimensional hard particles with polygonal shapes may stabilize symmetries which do not result directly from the particle shape. This is due to the formation of clusters in the fluid. Entropy alone can drive these effects, which represent a challenge for standard theories. In this article we present a general density-functional theory for clustering effects in fluids of hard particles in two dimensions. The theory combines a free-energy functional of the angular distribution function with an association energy term which qualitatively reproduces the clustering tendencies of the particles found in Monte Carlo simulations. Application is made to a fluid of hard right-angled triangles.

cond-mat.soft↗

arXiv2023

Prediction of the liquid-crystal phase behavior of hard right triangles from fourth-virial density-functional theories

We have used an extended Scaled-Particle Theory that incorporates four-body correlations through the fourth-order virial coefficient to analyse the orientational properties of a fluid of hard right-angle triangles. This fluid has been analysed by computer simulation studies, with clear indications of strong octatic correlations present in the liquid-crystal phase, although the more symmetric order tetratic phase would seem to be the most plausible candidate. Standard theories based on the second virial coefficient are unable to reproduce this behaviour. Our extended theory predicts that octatic correlations, associated to a symmetry under global rotations of the oriented fluid by $45^{\circ}$, are highly enhanced, but not enough to give rise to a thermodynamically stable phase with strict octatic symmetry. We discuss different scenarios to improve the theoretical understanding of the elusive octatic phase in this intriguing fluid.

cond-mat.soft↗

arXiv2022

Exotic liquid crystalline phases in monolayers of vertically vibrated granular particles

Vibrated monolayers of granular particles confined into horizontal cavities form a variety of fluid patterns with orientational order that resemble equilibrium liquid-crystal phases. In some cases one can identify nematic and smectic patters that can be understood in terms of classical statistical mechanics of hard bodies. Low aspect ratio cylinders project as rectangles and form uniaxial, or 2-atic, and tetratic, or 4-atic, nematic phases. Other polygonal particles may exhibit different liquid-crystal phases, in general $p$-atic phases, of higher symmetries. We give a brief summary of theoretical work on rectangles and triangles, and provide some experimental results on vibrated monolayers. In the case of equilateral triangles, the theory predicts an exotic triatic phase, or 6-atic phase, with six-fold symmetry and three equivalent directors. Right-angled triangles exhibit a 4-atic phase with strong octatic (8-atic) correlations. Experiments on cylinders show 4-atic textures and, even more remarkable, geometric frustration caused by confinement excites topological defects, which seem to follow the same topological rules as standard liquid crystals. Some of our findings can be understood with the help of simulations of hard particles subject to thermal equilibrium, although standard Density-Functional Theories fail to account for the correct equilibrium phases in some cases.

cond-mat.soft↗

arXiv2022

The effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids

We introduce a model for a fluid of polydisperse rounded hard rectangles where the length and width of the rectangular core are fixed, while the roundness is taken into account by the convex envelope of a disk displaced along the perimeter of the core. The diameter of the disk has a continuous polydispersity described by a Schultz distribution function. We implemented the scaled particle theory for this model with the aim to studying: (i) the effect of roundness on the phase behavior of the one-component hard-rectangle fluid, and (ii) how polydispersity affects phase transitions between isotropic, nematic and tetratic phases. We found that roundness greatly affects the tetratic phase, whose region of stability in the phase diagram strongly decreases as the roundness parameter is increased. Also the interval of aspect ratios where the tetratic-nematic and isotropic-nematic phase transitions are of first order considerably reduces with roundness, both transitions becoming weaker. Polydispersity induces strong fractionation between the coexisting phases, with the nematic phase enriched in particles of lower roundness. Finally, for high enough polydispersity and certain mean aspect ratios, the isotropic-to-nematic transition can change from second (for the one-component fluid) to first order. We also found a packing-fraction inversion phenomenon for large polydispersities: the coexisting isotropic phase has a higher packing fraction than the nematic.

cond-mat.soft↗

arXiv2022

Effect of clustering on the orientational properties of a fluid of hard right isosceles triangles

Recent studies have shown the fluid of hard right triangles to possess fourfold and quasi-eightfold (octatic) orientational symmetries. However, the standard density-functional theory for two-dimensional anisotropic fluids, based on two-body correlations, and an extension to incorporate three-body correlations, fail to describe these symmetries. To explain the origin of octatic symmetry we postulate strong particle clustering as a crucial ingredient. We use Scaled Particle Theory to analyze four binary mixtures of hard right triangles and squares, three of them being extreme models for a one-component fluid, where right triangles can exist as monomeric entities together with triangular dimers, square dimers or square tetramers. Phase diagrams exhibit a rich phenomenology, with demixing and three-phase coexistences. More important, under some circumstances the orientational distribution function of triangles has equally high peaks at relative particle angles 0, $π/2,$ and $π$, signalling fourfold, tetratic order, but also secondary peaks located at $π/4$ and $3π/4$, a feature of eightfold, octatic order. Also, we extend the binary mixture model to a quaternary mixture consisting of four types of clusters: monomers, triangular and square dimers, and square tetramers. This mixture is analyzed using Scaled Particle Theory under the restriction of fixed cluster fractions. Apart from the obvious tetratic phase promoted by tetramers, we found that, for certain cluster compositions, the total orientational distribution function of monomers can exhibit quasi-eightfold (octatic) symmetry. The study gives evidence on the importance of clustering to explain the peculiar orientational properties of liquid-crystal phases in some two dimensional fluids.

cond-mat.soft↗

arXiv2021

Failure of standard density functional theory to describe the phase behavior of a fluid of hard right isosceles triangles

A fluid of hard right isosceles triangles was studied using an extension of Scaled-Particle Density-Functional Theory which includes the exact third virial coefficient. We show that the only orientationally ordered stable liquid-crystal phase predicted by the theory is the uniaxial nematic phase, in agreement with the second-order virial theory. By contrast, Monte Carlo simulations predict exotic liquid-crystal phases exhibiting tetratic and octatic correlations, with orientational distribution functions having four and eight equivalent peaks, respectively. This demonstrates the failure of the standard Density Functional Theory based on two and three-body correlations to describe high-symmetry orientational phases in two-dimensional hard right-triangle fluids, and points to the necessity to reformulate the theory to take into account high-order body correlations and ultimately particle self-assembling and clustering effects. This avenue may represent a great challenge for future research, and we discuss some fundamental ideas to construct a modified version of Density-Functional Theory to account for these clustering effects.

cond-mat.soft↗

arXiv2020

Orientational ordering in a fluid of hard kites: A density-functional-theory study

Using Density Functional Theory we theoretically study the orientational properties of uniform phases of hard kites -- two isosceles triangles joined by their common base. Two approximations are used: Scaled Particle Theory, and a new approach which better approximates third virial coefficients of two-dimensional hard particles. By varying some of their geometrical parameters kites can be transformed into squares, rhombuses, triangles, and also very elongated particles, even reaching the hard-needle limit. Thus a fluid of hard kites, depending on the particle shape, can stabilize isotropic, nematic, tetratic and triatic phases. Different phase diagrams are calculated, including those of rhombuses, and kites with two of their equal interior angles fixed to $90^{\circ}$, $60^{\circ}$ and $75^{\circ}$. Kites with one of their unequal angles fixed to $72^{\circ}$, which have been recently studied via Monte Carlo simulations, are also considered. We find that rhombuses and kites with two equal right angles and not too large anisometry stabilise the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to $60^{\circ}$ stabilize the triatic phase to some extent, although it is very sensitive to changes in particle geometry. Kites with the two equal interior angles fixed to $75^{\circ}$ have a phase diagram with both tetratic and triatic phases, but we show the nonexistence of a particle shape for which both phases are stable at different densities. Finally the success of the new theory in the description of orientational order in kites is shown by comparing with Monte Carlo simulations for the case where one of the unequal angles is fixed to $72^{\circ}$. These particles also present phase diagrams with stable tetratic and triatic phases.

cond-mat.soft↗

arXiv2020

Domain walls in vertically vibrated monolayers of cylinders confined in annuli

Liquid-crystalline ordering in vertically vibrated granular monolayers confined in annuli of different sizes is examined. The annuli consist of circular cavities with a central circular obstruction. In the absence of the central obstruction cylinders of low aspect-ratio exhibit tetratic order, except for the existence of four defects which restore the symmetry broken by the circular confinement. This behaviour is demanded by topology in systems with strong anchoring properties at the surface. By contrast, topology dictates that the annular geometry is compatible with a distorted tetratic phase without point defects. However, the effect of restricted geometry and limited size on phases possessing finite anchoring energy at the wall and elastic stiffness leads to different configurations, showing finite ordered regions separated by domain walls. We argue that highly packed nonequilibrium vibrated granular monolayers respond to geometrical frustration and extreme confinement as corresponding equilibrium systems of particles do, and that the former can be analysed in terms of surface free energies, elastic distortions and defects, much as equilibrium liquid crystals. Therefore, selective confinement of vertically-vibrated monolayers of rods could be used with advantage as a new tool to study the creation and dynamics of various types of defects in ordered systems.

cond-mat.soft↗

arXiv2019

Highly confined mixtures of parallel hard squares: A Density Functional Theory study

Using the Fundamental-Measure Density Functional Theory, we have studied theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting of two consecutive big squares, or three small squares, in the transverse direction, perpendicular to the walls, are forbidden. We analyzed two different mixtures with edge-lengths of species selected so as to allow or forbid one big plus one small square to fit into the channel. For the first mixture we obtained first-order transitions between symmetric and asymmetric packings of particles: small and big squares are preferentially adsorbed at different walls. Asymmetric configurations are shown to lead to more efficient packing at finite pressures. We argue that the stability region of the asymmetric phase in the pressure-composition plane is bounded so that the symmetric phase is stable at low and very high pressure. For the second mixture, we observe strong demixing between phases which are rich in different species. Demixing occurs in the transverse direction, i.e. the dividing interface is perpendicular to the walls, and phases exhibit symmetric density profiles. The possible experimental realization of this behaviour (which in practical terms is precluded by jamming) in strictly two-dimensional systems is discussed. Finally the phase behavior of a mixture with periodic boundary conditions is analyzed and the differences and similarities between the latter and the confined system are discussed. We claim that, although exact calculations discard the existence of true phase transitions in $1+ε$-dimensional systems, Density Functional Theory is still successful to describe packing properties of large clusters of particles.

cond-mat.soft↗

arXiv2019

Defects in vertically vibrated monolayers of cylinders

We analyse liquid-crystalline ordering in vertically vibrated monolayers of cylinders confined in a circular cavity. Short cylinders form tetratic arrangements with C$_4$ symmetry. This symmetry, which is incompatible with the geometry of the cavity, is restored by the presence of four point defects with total topological charge $+4$. Equilibrium Monte Carlo simulations predict the same structure. A new method to measure the elastic properties of the tetratic medium is developed which exploits the clear similarities between the vibrated dissipative system and the thermal equilibrium system. Our observations open up a new avenue to investigate the formation of defects in response to boundary conditions, an issue which is very difficult to realize in colloidal or molecular systems.

cond-mat.soft↗

arXiv2018

Uniform phases in fluids of hard isosceles triangles: one component and binary mixtures

We formulate the scaled particle theory for a general mixture of hard isosceles triangles and calculate different phase diagrams for the one-component fluid and for certain binary mixtures. The fluid of hard triangles exhibits a complex phase behavior: (i) the presence of a triatic phase with sixfold symmetry, (ii) the isotropic-uniaxial nematic transition is of first order for certain ranges of aspect ratios, and (iii) the one-component system exhibits nematic-nematic transitions ending in critical points. We found the triatic phase to be stable not only for equilateral triangles but also for triangles of similar aspect ratios. We focus the study of binary mixtures on the case of symmetric mixtures: equal particle areas with aspect ratios ($κ_i$) symmetric with respect to the equilateral one: $κ_1κ_2=3$. For these mixtures we found, aside from first-order isotropic-nematic and nematic-nematic transitions (the latter ending in a critical point): (i) A region of triatic phase stability even for mixtures made of particles that do not form this phase at the one-component limit, and (ii) the presence of a Landau point at which two isotropic-nematic first-order transitions and a nematic-nematic demixing transition coalesce. This phase behavior is analog to that of a symmetric three-dimensional mixture of rods and plates.

cond-mat.soft↗

arXiv2018

Positional ordering of hard adsorbate particles in tubular nanopores

The phase behaviour and structural properties of a monolayer of hard particles is examined in such a confinement, where the adsorbed particles are constrained to the surface of a narrow hard cylindrical pore. The diameter of the pore is chosen such that only first and second neighbour interactions occur between the hard particles. The transfer operator method of Percus and Zhang [Mol. Phys., 69, 347 (1990)] is reformulated to obtain information about the structure of the monolayer. We have found that a true phase transition is not possible in the examined range of pore diameters. The monolayer of hard spheres undergoes a structural change from fluid-like order to a zigzag-like solid one with increasing surface density. The case of hard cylinders is different in the sense that a layering takes place continuously between a low density one-row and a high density two-row monolayer. Our results reveal a clear discrepancy with classical density functional theories, which do not distinguish smectic-like ordering in bulk from that in narrow periodic pores.

cond-mat.soft↗

arXiv2017

Ordering transitions of weakly anisotropic hard rods in narrow slit-like pores

The effect of strong confinement on the positional and orientational ordering is examined in a system of hard rectangular rods with length L and diameter D (L>D) using the Parsons-Lee modification of the second virial density functional theory. The rods are nonmesogenic (L/D<3)and confined between two parallel hard walls, where the width of the pore (H) is chosen in such a way that both planar (particle's long axis parallel to the walls) and homeotropic (particle's long axis perpendicular to the walls) orderings are possible and a maximum of two layers are allowed to form in the pore. In the extreme confinement limit of ,where only one layer structures appear, we observe a structural transition from a planar to a homeotropic fluid layer with increasing density, which becomes sharper as L->H. In wider pores (2D<H<3D) planar order with two layers, homeotropic order, and even combined bilayer structures (one layer is homeotropic, while the other is planar) can be stabilized at high densities. Moreover, first order phase transitions can be seen between different structures. One of them emerges between a monolayer and a bilayer with planar orders at relatively low packing fractions.

cond-mat.soft↗

arXiv2017

Dynamical properties of heterogeneous nucleation of parallel hard squares

We use the Dynamic Density-Functional Formalism and the Fundamental Measure Theory as applied to a fluid of parallel hard squares to study the dynamics of heterogeneous growth of non-uniform phases with columnar and crystalline symmetries. The hard squares are (i) confined between soft repulsive walls with square symmetry, or (ii) exposed to external potentials that mimic the presence of obstacles with circular, square, rectangular or triangular symmetries. For the first case the final equilibrium profile of a well commensurated cavity consists of a crystal phase with highly localized particles in concentric square layers at the nodes of a slightly deformed square lattice. We characterize the growth dynamics of the crystal phase by quantifying the interlayer and intralayer fluxes and the non-monotonicity of the former, the saturation time, and other dynamical quantities. The interlayer fluxes are much more monotonic in time, and dominant for poorly commensurated cavities, while the opposite is true for well commensurated cells: although smaller, the time evolution of interlayer fluxes are much more complex, presenting strongly damped oscillations which dramatically increase the saturation time. We also study how the geometry of the obstacle affects the symmetry of the final equilibrium non-uniform phase (columnar vs. crystal). For obstacles with fourfold symmetry, (circular and square) the crystal is more stable, while the columnar phase is stabilized for obstacles without this symmetry (rectangular or triangular). We find that, in general, density waves of columnar symmetry grow from the obstacle. However, additional particle localization along the wavefronts gives rise to a crystalline structure which is conserved for circular and square obstacles, but destroyed for the other two obstacles where columnar symmetry is restored.

cond-mat.soft↗