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 it 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.Financial support under Grant No. FIS2017-86007-C3-1-P from Ministerio de Economía, Industria y Competitividad (MINECO) of Spain. Y. M.-R. acknowledges the support from Grant No. PGC2018-096606-B-I00 (MCIU/AEI/FEDER, UE)

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 Schulz distribution function. We implemented the scaled particle theory for this model with the aim of 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 nemati

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

[Póster presentado a]: FisEs'14: XIX Congreso de Física Estadística: libro de resúmenes: Ourense, 2-4 de Abril de 2014The phase behavior of a model suspension of colloidal polydisperse platelets is studied using density-functional theory. Platelets are modelled as parallel rectangular prisms of square section l(2) and height h, with length and height distributions given by different polydispersities delta(l) and delta(h). The model is intended to qualitatively represent experimental colloidal platelet suspensions at high densities with a high degree of orientational ordering. We obtain the phase behavior of the model, including nematic, smectic and columnar phases and its dependence on the two polydispersities delta(l) and delta(h). When delta(l) >; delta(h) we observe that the smectic phase stabilises first with respect to the columnar. If delta(h) >; delta(l) we observe the opposite behavior. Other more complicated cases occur, e. g. the smectic stabilises from the nematic first but then exists a first-order transition to the columnar phase. Our model assumes plate-rod symmetry, but the regions of stability of smectic and columnar phases are non-symmetric in the delta(l) - delta(h) plane due to the different dimensionality of ordering in the two phases. Microsegregation effects, i.e. different spatial distribution for different sizes within the periodic cell, take place in both phases and, in each case, is more apparent in the variable associated with ordering

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.Comment: 16 pages, 13 figure

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 Schulz distribution function. We implemented the scaled particle theory for this model with the aim of 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.Financial support from Grant No. PGC2018-096606-B-I00 (MCIU/AEI/FEDER,UE) is acknowledged

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 analyze the orientational properties of a fluid of hard right isosceles triangles. This fluid has been analyzed 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 behavior. Our extended theory predicts that octatic correlations, associated to a symmetry under global rotations of the oriented fluid by 45∘, 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.Financial support from Grant No. PID2021-126307NB-C21 (MCIU/AEI/FEDER,UE) is acknowledged

Highly confined mixtures of parallel hard squares: A density-functional-theory study

Using the fundamental-measure density-functional theory, we study 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 analyze 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 obtain 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 lateral direction, i.e., the dividing interface is perpendicular to the walls, and phases exhibit symmetric density profiles. The possible experimental realization of this behavior (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 exclude the existence of true phase transitions in (1+[épsilon])-dimensional systems, density-functional theory is still successful in describing packing properties of large clusters of particles.Financial support from Ministerio de Economía, Industria y Competitividad (Spain) through Grants No. FIS2015-66523-P, No. PGC2018-096606-B-100, and No. FIS2017-86007-C3-1-P is acknowledged

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 the 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 pi, signaling 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 the 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.Financial support under Grant No. FIS2017–86007-C3–1-P from Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, and No. PGC2018–096606-B-I00 from Agencia Estatal de Investigación-Ministerio de Ciencia e Innovación of Spain, is acknowledged

Phase behaviour of very asymmetric binary mixtures

6 pages, 1 figure.-- PACS nrs.: 82.70.Dd, 64.75.-g, 64.70.K-, 64.70.D-.The phase behaviour of very asymmetric binary mixtures can be understood in terms of the depletion interaction. For hard particles this yields a narrow deep attractive well surrounding the hard core. Colloids with similar interaction potentials are known to destabilize the liquid, causing it to show a wide fluid-solid coexistence, and in extreme cases they exhibit an exotic solid-solid condensation. For a mixture this means that phase separation is not fluid-fluid, as previously thought, but normally fluid-solid, and if the asymmetry is very large, even solid-solid. We present in this work the result of devising a density functional theory for an infinitely asymmetric mixture of parallel hard cubes. This model is singular and undergoes a collapse in a close-packed solid (an extreme fluid-solid demixing). We avoid this collapse by introducing a small amount of polydispersity in the large particles; the resulting phase diagram shows the fluid-solid and solid-solid demixing scenarios described above.JAC’s work is part of the project PB96–0119 of the Dirección General de Enseñanza Superior (Spain).Publicad

Role of length polydispersity in the phase behavior of freely rotating hard-rectangle fluids

We use the density-functional formalism, in particular the scaled-particle theory, applied to a length-polydisperse hard-rectangle 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 are 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 divide 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 focus 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 coexistence 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.Financial support from MINECO (Spain) under Grant No. FIS2015-66523-P is acknowledged