Non-nematicity of the filamentary phase in systems of hard minor circular arcs.

This work further investigates an aspect of the phase behavior of hard circular arcs whose phase diagram has been recently calculated by Monte Carlo numerical simulations: the non-nematicity of the filamentary phase that hard minor circular arcs form. Both second-virial density-functional theory and further Monte Carlo numerical simulations find that the positional one-particle density function undulates in the direction transverse to the axes of the filaments while further Monte Carlo numerical simulations find that the mobility of the hard minor circular arcs across the filaments occurs via a mechanism reminiscent of the mechanism of diffusion in a smectic phase: the filamentary phase is not a {"modulated" ["splay(-bend)"]} nematic phase.

Densest-known packings and phase behavior of hard spherical capsids.

By mostly using Monte Carlo numerical simulation, this work investigates the densest-known packings and phase behavior of hard spherical capsids, i.e., hard infinitesimally thin spherical caps with a subtended angle larger than the straight angle.

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 and diameter by focusing on / ∈ [0,2]. It is within this interval that one expects that the packing fraction of these dense disordered jammed packings ϕ attains a maximum. This work confirms the form of the graph ϕ versus /: here, comparably to certain previous investigations, it is found that the maximal ϕ = 0.

Dense disordered jammed packings of hard very elongate particles: A new derivation of the random contact equation.

This work describes a derivation of the random contact equation that predicts the packing fraction ϕ of a dense disordered (maximally random) jammed state of hard, very elongate particles. This derivation is based on (i) the compressibility equation connecting the compressibility of a uniform system with its pair-correlation function: it is assumed equal to zero at jamming; (ii) the pair-correlation function of the interparticle distance scaled with respect to the orientationally dependent contact distance: it is assumed equal to the sum of a delta function and a unit-step function at jamming, where the former function accounts for the interparticle contacts, while the latter function accounts for the background. On assuming that the hard, very elongate particles are cylindrically symmetric with a length L and a diameter D and isostaticity occurs at jamming, the prediction, in particular that, in the limit of L/D → +∞, ϕ L/D = (10 + 1)/2, is compared to the available experimental data.

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 two-dimensional 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.

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 θ∈(π,2π]. Differently than those denotable as minor whose subtended angle θ∈[0,π], it is impossible for two hard infinitesimally thin circular arcs with θ∈(π,2π] to arbitrarily closely approach once they are arranged in a configuration, e.

Hard convex lens-shaped particles: Characterization of dense disordered packings.

Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is "optimal" in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction ϕ_{MRJ}≃0.73 [G. Cinacchi and S.

Phase behavior of hard C_{2h}-symmetric particle systems.

Using Monte Carlo numerical simulation, this work sketches the phase diagram of systems of certain hard C_{2h}-symmetric particles, formed by gluing two aligned and displaced hard spherocylinders with a cylindrical-length-to-diameter ratio realistically, if viewed not only from the lyotropic colloidal liquid-crystal side but also from the thermotropic low-molecular-mass liquid-crystal side, equal to 5, as a function of the displacement. Several distinctive phases are observed, such as a nonperiodic smectic-B-like phase, a nonperiodic smectic-H-like phase, a smectic-C phase, and a short-layer-spacing uniaxial smectic-A phase but no biaxial nematic phase.

Hard convex lens-shaped particles: metastable, glassy and jammed states.

We generate and study dense positionally and/or orientationally disordered, including jammed, monodisperse packings of hard convex lens-shaped particles (lenses). Relatively dense isotropic fluid configurations of lenses of various aspect ratios are slowly compressed via a Monte Carlo method based procedure. Under this compression protocol, while 'flat' lenses form a nematic fluid phase (where particles are positionally disordered but orientationally ordered) and 'globular' lenses form a plastic solid phase (where particles are positionally ordered but orientationally disordered), 'intermediate', neither 'flat' nor 'globular', lenses do not form either mesophase.

Cholesteric and screw-like nematic phases in systems of helical particles.

Recent numerical simulations of hard helical particle systems unveiled the existence of a novel chiral nematic phase, termed screw-like, characterised by the helical organization of the particle C symmetry axes round the nematic director with periodicity equal to the particle pitch. This phase forms at high density and can follow a less dense uniform nematic phase, with relative occurrence of the two phases depending on the helix morphology. Since these numerical simulations were conducted under three-dimensional periodic boundary conditions, two questions could remain open.

Diffusion of helical particles in the screw-like nematic phase.

The mechanism of diffusion of helical particles in the new screw-like nematic phase is studied by molecular dynamics numerical simulation. Several dynamical indicators are reported that evidence and microscopically characterise the special translo-rotational motion by which helical particles move in this chiral liquid-crystalline phase. Besides mean square displacements and diffusion coefficients resolved parallel and perpendicular to the nematic director, a suitable translo-rotational van Hove self-correlation function and a sequence of translational and rotational velocity, self- and distinct-, time correlation functions are calculated.

Chiral self-assembly of helical particles.

The shape of the building blocks plays a crucial role in directing self-assembly towards desired architectures. Out of the many different shapes, the helix has a unique position. Helical structures are ubiquitous in nature and a helical shape is exhibited by the most important biopolymers like polynucleotides, polypeptides and polysaccharides as well as by cellular organelles like flagella.

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.

Detection of Significant Aprotic Solvent Effects on the Conformational Distribution of Methyl 4-Nitrophenyl Sulfoxide: From Gas-Phase Rotational to Liquid-Crystal NMR Spectroscopy.

The conformational equilibrium of methyl 4-nitrophenyl sulfoxide (MNPSO) was experimentally investigated in the gas phase by using microwave spectroscopy and in isotropic and nematic liquid-crystal solutions, in which the solvents are nonaqueous and aprotic, by using NMR spectroscopy; moreover, it was theoretically studied in vacuo and in solution at different levels of theory. The overall set of results indicates a significant dependence of the solute conformational distribution on the solvent dielectric permittivity constant: when dissolved in low-polarity media, the most stable conformation of MNPSO proved to be strongly twisted with respect to that in more polar solvents, in which the conformational distribution maximum essentially coincides with that obtained in the gas phase. We discuss a possible explanation of this behavior, which rests on electrostatic solute-solvent interactions and is supported by calculations of the solute electric dipole moment as a function of the torsional angle.

Isotropic-nematic phase transition in hard platelets as described by a third-virial theory.

This work discusses a few second- and third-virial (density functional) theory approaches aimed at describing the isotropic-nematic phase transition in three-dimensional freely rotating infinitesimally thin hard discs, the basic model for (colloidal) discotic liquid crystals. Both plain and resummed versions are considered, those resummed being based on a simple yet rather accurate analytic equation of state for the isotropic phase. Extensive Monte Carlo simulations, carried out to locate accurately the phase transition, are used to test the performance of these approaches and guide toward an improved ansatz.

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.

Self-assembly of hard helices: a rich and unconventional polymorphism.

Hard helices can be regarded as a paradigmatic elementary model for a number of natural and synthetic soft matter systems, all featuring the helix as their basic structural unit, from natural polynucleotides and polypeptides to synthetic helical polymers, and from bacterial flagella to colloidal helices. Here we present an extensive investigation of the phase diagram of hard helices using a variety of methods. Isobaric Monte Carlo numerical simulations are used to trace the phase diagram; on going from the low-density isotropic to the high-density compact phases a rich polymorphism is observed, exhibiting a special chiral screw-like nematic phase and a number of chiral and/or polar smectic phases.

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

Using an Onsager-like theory, we have investigated the relationship between the morphology of hard helical particles and the features (pitch and handedness) of the cholesteric phase that they form. We show that right-handed helices can assemble into right- (R) and left-handed (L) cholesterics, depending on their curliness, and that the cholesteric pitch is a non-monotonic function of the intrinsic pitch of particles. The theory leads to the definition of a hierarchy of pseudoscalars, which quantify the difference in the average excluded volume between pair configurations of helices having (R) and (L)-skewed axes.

Communication: from rods to helices: evidence of a screw-like nematic phase.

Evidence of a special chiral nematic phase is provided using numerical simulation and Onsager theory for systems of hard helical particles. This phase appears at the high density end of the nematic phase, when helices are well aligned, and is characterized by the C2 symmetry axes of the helices spiraling around the nematic director with periodicity equal to the particle pitch. This coupling between translational and rotational degrees of freedom allows a more efficient packing and hence an increase of translational entropy.

Phase behavior of hard spherical caps.

This work reports on the phase behavior of hard spherical caps in the interval of particle shapes delimited by the hard platelet and hemispherical cap models. These very simple model colloidal particles display a remarkably complex phase behavior featuring a competition between isotropic-nematic phase separation and clustering as well as a sequence of structures, from roundish to lacy aggregates to no ordinary hexagonal columnar mesophases, all characterized by groups of particles tending to arrange on the same spherical surface. This behavior parallels that one of many molecular systems forming micelles but here it is purely entropy-driven.

The isotropic-to-nematic phase transition in hard helices: theory and simulation.

We investigate the isotropic-to-nematic phase transition in systems of hard helical particles, using Onsager theory and Monte Carlo computer simulations. Motivation of this work resides in the ubiquity of the helical shape motif in many natural and synthetic polymers, as well as in the well known importance that the details of size and shape have in determining the phase behaviour and properties of (soft) condensed matter systems. We discuss the differences with the corresponding spherocylinder phase diagram and find that the helix parameters affect the phase behaviour and the existence of the nematic phase.

Smectic order parameters via liquid crystal NMR spectroscopy: Application to a partial bilayer smectic A phase.

Solute molecules were dissolved in the liquid crystal 4-cyano-4'-n-octyloxybiphenyl (8OCB), known to form a partial bilayer smectic-A phase. Through measurement of solutes' and solvent's orientational order parameters via nuclear magnetic resonance spectroscopy, and their analysis via a statistical thermodynamic density functional theory, values of the solvent's positional order parameters and solutes' positional-orientational distribution functions were obtained. Near to the transition to the nematic phase, the main positional order parameter of the smectic liquid crystal turned out to be comprised in the interval 0.

Rigid probe solutes in a smectic-A liquid crystal: an unconventional route to the latter's positional order parameters.

Biphenylene and pyrene were dissolved in the nematic and smectic-A phases of the liquid crystal 4,4'-di-n-heptyl-azoxybenzene and the orientational order parameters of both solutes and solvent measured via proton and deuteron nuclear-magnetic-resonance spectroscopy. This new data set was then merged with the one previously obtained, formed by 4,4'-di-chloro-benzene and naphthalene as solutes in the same solvent, and the resulting overall data set analyzed with a statistical thermodynamic density-functional theory to provide positional-orientational distribution functions of the various solutes along with the smectic solvent's positional order parameters.

On the distribution functions of depletion interactions.

Molecular dynamics computer simulations were performed on model colloidal binary mixtures of two large and many small soft repulsive spheres. Depletion forces arise between the two large spheres, as a function of their distance, because of the nonadditivity of the volume they exclude to the small spheres. The probability distribution functions of both longitudinal and transverse component of the total force exerted by the small particles were calculated and generally turned out non-Gaussian.