arXiv subjects

Yuri Martinez-Raton

Publications and source records attributed to Yuri Martinez-Raton.

At least 19 recordsLinked to original sources

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.

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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.

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arXiv2023

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.

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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.

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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.

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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.

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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, $\pi/2,$ and $\pi$, signalling fourfold, tetratic order, but also secondary peaks located at $\pi/4$ and $3\pi/4$, 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.

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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.

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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 $1+\epsilon$-dimensional systems, Density Functional Theory is still successful to describe packing properties of large clusters of particles.

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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.

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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 ($\kappa_i$) symmetric with respect to the equilateral one: $\kappa_1\kappa_2=3$. 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.

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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.

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arXiv2017

Ordering of hard rectangles in strong confinement

Using transfer operator and fundamental measure theories, we examine the structural and thermodynamic properties of hard rectangles confined between two parallel hard walls. The side lengths of the rectangle ($L$ and $D$, $L>D$) and the pore width ($H$) are chosen such that maximum two layers are allowed to form in planar order ($L$ is parallel to the wall), while only one in homeotropic order ($D$ is parallel to the wall). We observe three different structures: (i) a low density fluid phase with parallel alignment to the wall, (ii) an intermediate and high density fluid phase with two layers and planar ordering and (iii) a dense single fluid layer with homeotropic ordering. The appearance of these phases and the change in the ordering direction with density is a consequence of the varying close packing structures with $L$ and $H$. Interestingly, even three different structures can be observed with increasing density if $L$ is close to $H$.

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arXiv2017

Role of length-polydispersity on the phase behavior of freely-rotating hard-rectangle fluid

We used the Density Functional formalism, in particular the Scaled Particle Theory, applied to a length-polydisperse hard-rectangular fluid to study its phase behavior as a function of the mean particle aspect ratio ($\kappa_0$) and polydispersity ($\Delta_0$). The numerical solutions of the coexistence equations were calculated by transforming the original problem with infinite degrees of freedoms to a finite set of equations for the amplitudes of the Fourier expansion of the moments of the density profiles. We divided the study into two parts: The first one is devoted to the calculation of the phase diagrams in the packing fraction ($\eta_0$)- $\kappa_0$ plane for a fixed $\Delta_0$ and selecting parent distribution functions with exponential (the Schulz distribution) or Gaussian decays. In the second part we study the phase behavior in the $\eta_0$-$\Delta_0$ plane for fixed $\kappa_0$ while $\Delta_0$ is changed. We characterize in detail the orientational ordering of particles and the fractionation of different species between the coexisting phases. Also we study the character (second vs. first order) of the Isotropic-Nematic phase transition as a function of polydispersity. We particularly focused on the stability of the Tetratic phase as a function of $\kappa_0$ and $\Delta_0$. The Isotropic-Nematic transition becomes strongly of first order when polydispersity is increased: the coexisting gap widens and the location of the tricritical point moves to higher values of $\kappa_0$ while the Tetratic phase is slightly destabilized with respect to the Nematic one. The results obtained here can be tested in experiments on shaken monolayers of granular rods.

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arXiv2017

Clustering in vibrated monolayers of granular rods

We investigate the ordering properties of vertically-vibrated monolayers of granular cylinders in a circular container at high packing fraction. In line with previous works by other groups, we identify liquid-crystalline ordering behaviour similar to that of two-dimensional hard rectangular particles subject to thermal equilibrium fluctuations. However, due to dissipation, there is a much stronger tendency for particles to cluster into parallel arrangements in the granular system. These clusters behave as a polydisperse mixture of long life-time `superparticles', and some aspects of the system behaviour can be understood by applying mean-field theories for equilibrium hard rectangles, based on two-body correlations, to these `superparticles'. Many other features of the granular system are different: (i) For small particle length-to-breadth ratio $\kappa$, we identify tetratic ordering at moderate packing fractions and smectic fluctuations at higher packing fractions, with no sharp transition between the two states. Both types of ordering can be explained in terms of clustering. (ii) For large $\kappa$, strong clustering precludes the stabilisation of a uniaxial nematic state, and the system exhibits a mixture of randomly-oriented clusters which, as packing fraction is increased, develops into states with smectic fluctuations, again through a diffuse transition. (iii) Vorticity excitations of the velocity field compete with smectic ordering, causing dynamic fluctuations and the absence of steady states at high densities; the tetratic state, by contrast, is very stiff against vorticity, and long-standing steady states, spatially and orientationally homogeneous except for four symmetrical defects located close to the wall, can be observed.

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arXiv2016

Biaxial nematic phase stability and demixing behaviour in monolayers of rod-plate mixtures

We theoretically study the phase behaviour of monolayers of hard rod-plate mixtures using a fundamental-measure density functional in the restricted-orientation (Zwanzig) approximation. We consider both species to be subject to an attractive potential proportional to the particle contact area on the surface and with adsorption strengths that depend on the species type. Particles have board-like shape, with sizes chosen using a symmetry criterion: same volume and same aspect ratio $\kappa$. Phase diagrams were calculated for $\kappa=10$, 20 and 40 and different values of adsorption strengths. For small adsorption strengths the mixtures exhibit a second-order uniaxial nematic-biaxial nematic transition for molar fraction of rods $0\leq x\lesssim 0.9$. In the uniaxial nematic phase the particle axes of rods and plates are aligned perpendicular and parallel to the monolayer, respectively. At the transition, the orientational symmetry of the plate axes is broken, and they orient parallel to a director lying on the surface. For large and equal adsorption strengths the mixture demixes at low pressures into a uniaxial nematic phase, rich in plates, and a biaxial nematic phase, rich in rods. This demixing is located between two tricritical points. Also, at higher pressures and in the plate-rich part of the phase diagram, the system exhibits a strong first-order uniaxial nematic-biaxial nematic phase transition with a large density coexistence gap. When rod adsorption is considerably large while that of plates is small, the transition to the biaxial nematic phase is always of second order. At very high pressures the mixture can effectively be identified as a two-dimensional mixture of squares and rectangles which again demixes above a certain critical point. We also studied the relative stability of uniform phases with respect to density modulations of smectic, columnar and crystalline symmetry.

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arXiv2015

Phase behaviour and correlations of parallel hard squares: From highly confined to bulk systems

We study a fluid of two-dimensional parallel hard squares in bulk and under confinement in channels, with the aim of evaluating the performance of Fundamental-Measure Theory (FMT). To this purpose, we first analyse the phase behaviour of the bulk system using FMT and Percus-Yevick theory, and compare the results with MD and MC simulations. In a second step, we study the confined system and check the results against those obtained from Transfer Matrix Method and from our own Monte Carlo simulations. Squares are confined to channels with parallel walls at angles of 0$^{\circ}$ or 45$^{\circ}$ relative to the diagonals of the parallel hard squares, respectively, which allows for an assessment of the effect of the external-potential symmetry on the fluid structural properties. In general FMT overestimates bulk correlations, predicting the existence of a columnar phase (absent in simulations) prior to crystallisation. The equation of state predicted by FMT compares well with simulations, although the PY approach with the virial route is better in some range of packing fractions. The FMT is highly accurate for the structure and correlations of the confined fluid due to the dimensional crossover property fulfilled by the theory. Both density profiles and equations of state of the confined system are accurately predicted by the theory. The highly non-uniform pair correlations inside the channel are also very well described by FMT.

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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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