The isotropic-nematic phase transition in hard, slightly curved, lens-like particles.

Monte Carlo numerical simulations are used to study in detail how the characteristics of the isotropic-nematic phase transition change as infinitely thin hard platelets are bent into shallow lens-like particles. First, this phase transition in the former reference model system is re-examined and more accurately located. Then, it is shown quantitatively that this already quite weak but distinctly first-order phase transition weakens further upon curving the platelets to such an extent that, thanks to the thinness of these particles that does not favor its pre-emptying by a transition to a (partially) positionally ordered phase, an isotropic-nematic tricritical point limit can be arbitrarily closely approached

Hard convex lens-shaped particles: Densest-known packings and phase behavior

By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedomG.C. thanks the Government of Spain for the award of a Ramón y Cajal research fellowship and the financial support under the Grant No. FIS2013-47350-C5-1-R. S.T. was supported by the U.S. National Science Foundation under Grant Nos. DMR-0820341 and DMS-121108

Depletion effects in smectic phases of hard rod--hard sphere mixtures

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen--orientation approximation. These results are discussed in terms of the $\tau$ parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for $\tau$, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a Fundamental--Measure density--functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the $\tau$ parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard--rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, $d$, in contrast to Onsager approximation, which predicts $\tau\sim d^3$.Comment: 15 pages, 11 figure

Dense disordered jammed packings of hard spherocylinders with a low aspect ratio: a characterization of their structure

This work numerically investigates dense disordered (maximally random) jammed packings of hard spherocylinders of cylinder length L and diameter D by focusing on L/D ∈ [0,2]. It is within this interval that one expects that the packing fraction of these dense disordered jammed packings ϕMRJ hsc attains a maximum. This work confirms the form of the graph ϕMRJ hsc versus L/D: here, comparably to certain previous investigations, it is found that the maximal ϕMRJ hsc = 0.721 ± 0.001 occurs at L/D = 0.45 ± 0.05. Furthermore, this work meticulously characterizes the structure of these dense disordered jammed packings via the special pair-correlation function of the interparticle distance scaled by the contact distance and the ensuing analysis of the statistics of the hard spherocylinders in contact: here, distinctly from all previous investigations, it is found that the dense disordered jammed packings of hard spherocylinders with 0.45 ≲ L/D ≤ 2 are isostati

Dense packings of hard circular arcs

This work investigates dense packings of congruent hard infinitesimally--thin circular arcs in the two-dimensional Euclidean space. It focuses on those denotable as major whose subtended angle $\theta \in \left ( \pi, 2\pi \right ]$. Differently than those denotable as minor whose subtended angle $\theta \in \left [0, \pi \right]$, it is impossible for two hard infinitesimally-thin circular arcs with $\theta \in \left ( \pi, 2\pi \right ]$ to arbitrarily closely approach once they are arranged in a configuration, e.g. on top of one another, replicable ad infinitum without introducing any overlap. This makes these hard concave particles, in spite of being infinitesimally thin, most densely pack with a finite number density. This raises the question as to what are these densest packings and what is the number density that they achieve. Supported by Monte Carlo numerical simulations, this work shows that one can analytically construct compact closed circular groups of hard major circular arcs in which a specific, $\theta$-dependent, number of them (anti-)clockwise intertwine. These compact closed circular groups then arrange on a triangular lattice. These analytically constructed densest-known packings are compared to corresponding results of Monte Carlo numerical simulations to assess whether they can spontaneously turn up.Comment: 9 pages, 9 figures; to be published in Physical Review

Probing the sensitivity of orientational ordering as a way towards absolute enantiorecognition: Helical-particle solutes in helical-particle nematic solvents

To inquire into whether two enantiomers can be absolutely distinguished on the sole basis of their different degrees of orientational ordering when dissolved in a chiral nematic liquid crystal, several enantiomeric pairs of hard helical particles are dissolved in a cholesteric (nematic) liquid crystal made of slender hard helical particles as well as in a screwlike nematic liquid crystal made of tortuous hard helical particles. While in the former ordinary chiral nematic solvent their nematic order parameters are (almost) coincident, in the latter new chiral nematic solvent the two enantiomeric solutes not only usually have more appreciably different nematic order parameters, but also always have significantly different screwlike order parameters. If also the latter orientational order parameter could be measurable in real experiments, it would constitute an additional decisive piece of information on the way to absolutely distinguishing two enantiomers on the sole basis of their different degrees of orientational order when dissolved in a chiral nematic liquid crystal that is in the apter screwlike nematic phase. Even in that event, however, the general absence of regularity and systematicity in the trend of the orientational order parameters, already manifest in these elementary hard helical-particle binary systems, would make this coveted achievement experimentally arduous without the assistance of very accurate and precise theoretical calculations.Support from the Università della Calabria and that from the Government of Spain under Grants No. FIS2013-47350-C5-1-R, No. MDM-2014-0377, and No. FIS2017-86007-C3-1-P is acknowledge

Left or right cholesterics? A matter of helix handedness and curliness

We have investigated the relationship between the morphology of helical particles and the features of the cholesteric (N$^\ast$) phase that they form. Using an Onsager-like theory, applied to systems of hard helices, we show that the cholesteric handedness and pitch depend on both the pitch and the curliness of the particles. The theory leads to the definition of pseudoscalars that correlate the helical features of the phase to the chirality of the excluded volume of the constituent particles

Phase behavior of hard circular arcs

By using Monte Carlo numerical simulation, this work investigates the phase behavior of systems of hard infinitesimally thin circular arcs, from an aperture angle θ → 0 to an aperture angle θ → 2π, in the twodimensional Euclidean space. Except in the isotropic phase at lower density and in the (quasi)nematic phase, in the other phases that form, including the isotropic phase at higher density, hard infinitesimally thin circular arcs autoassemble to form clusters. These clusters are either filamentous, for smaller values of θ, or roundish, for larger values of θ. Provided the density is sufficiently high, the filaments lengthen, merge, and straighten to finally produce a filamentary phase while the roundels compact and dispose themselves with their centers of mass at the sites of a triangular lattice to finally produce a cluster hexagonal phas