Computer Simulations of Biaxial Nematics

Berardi, Roberto; Zannoni, Claudio

doi:10.1002/9781118696316.ch6

Cited by 15 publications

(19 citation statements)

References 197 publications

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“…The first was to allow for different particle shapes and in particular, apart from biaxial [57], bowl like mesogens [58] with the aim of modelling pyramidic liquid crystals [59] and polyphilic [60] tapered shapes to try to obtain ferroelectric nematics [61].…”

Section: Molecular Modelsmentioning

confidence: 99%

From idealised to predictive models of liquid crystals

Zannoni

2018

Liquid Crystals

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Section: Molecular Modelsmentioning

confidence: 99%

From idealised to predictive models of liquid crystals

Zannoni

2018

Liquid Crystals

Self Cite

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“…We reported a novel crystalline packing of self-dual ellipsoids (β=1/2), which are widely used models for the simulation of biaxial nematics [29][30][31] . Our new crystal is significantly denser than the corresponding SM2 packing for aspect ratios α in (1.365, 1.5625).…”

Section: Discussionmentioning

confidence: 99%

Dense crystalline packings of ellipsoids

et al. 2017

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An ellipsoid, the simplest non-spherical shape, has been extensively used as models for elongated building blocks for a wide spectrum of molecular, colloidal and granular systems [1][2][3][4] . Yet the densest packing of congruent hard ellipsoids, which is intimately related to the high-density phase of many condensed matter systems, is still an open problem. We discover a novel dense crystalline packing of ellipsoids containing 24 particles with a quasi-square-triangular (SQ-TR) tiling arrangement, whose packing density ɸ exceeds that of the SM2 crystal 5 for aspect ratios α in (1.365, 1.5625), attaining a maximal ɸ ≈ 0.75806… at α = 93/64. We show that SQ-TR phase is thermodynamically stable at high densities over the aforementioned α range and report a novel phase diagram for self-dual ellipsoids. The discovery of SQ-TR crystal suggests novel organizing principles for non-spherical particles and self-assembly of colloidal systems.Dense packings of hard particles have been widely used as models for a variety of condensed matter systems, including glasses, crystals, heterogeneous materials, and granular media [1][2][3][4] . The optimal (maximally dense) packing arrangement is also intimately related to the crystalline phase of the associated particle system and its high-density phase behavior 3 . The pursuit of the optimal packing for given particle shape has long been an intriguing and challenging problem in discrete geometry 6 . Indeed, it took almost four centuries to prove the famous Kepler's conjecture 6 posed in 1611 that the densest packing of spheres is the face-centered cubic (FCC) lattice with a packing density ɸ = π/√18 ≈ 0.7405 7 . For congruent nonspherical particles that do not tile three-dimensional (3D) Euclidean space R 3 , the optimal packing problem is only solved for infinite cylinders 8 and rhombic dodecahedra with a clipped corner 9 . So far no rigorous mathematical theory has been put forth for constructing or proving optimal packings of nonspherical particles. Recently, the discovery of the candidate optimal packings is significantly advanced via computer simulations. [13][14][15][20][21][22][23][24] , to name but a few. No counterexample of the Ulam's conjecture 25 that all convex shapes in R 3 pack better than spheres has been found yet.An ellipsoid, the simplest non-spherical shape, can be obtained from a sphere through an affine transformation. The ratios of the semiaxes of an ellipsoid can be expressed as a:b:c=α: β :1 (a≥b≥c), where α is the aspect ratio, and β (0≤β≤1) is the skewness. When β = 1/2, the ellipsoid is neither prolate (β=0) nor oblate (β=1), and is referred to as the self-dual ellipsoid. In this work, we discover via Monte Carlo simulations a novel crystalline packing of self-dual ellipsoids (β=1/2) that is denser than the corresponding SM2 packing for aspect ratios α in (1.365, 1.5625), attaining a maximal φ ≈ 0.75806… at α = 93/64. The smallest periodic unit cell contains 24 ellipsoids with a quasi-square-triangle tiling arrangement. Henceforth, we refer to...

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“…Biaxiality, that is the simultaneous orientation along two mutual orthogonal axes, is one of the most intriguing properties of Liquid Crystals being the subject matter of numerous modern theoretical studies (see e.g. [3,4,5,6,7,8]).…”

Section: Introductionmentioning

confidence: 99%

Exact equations of state for nematics

2018

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We propose a novel approach to the solution of nematic Liquid Crystal models based on the derivation of a system of nonlinear wave equations for order parameters such that the occurrence of uniaxial and biaxial phase transitions can be interpreted as the propagation of a two-dimensional shock wave in the space of thermodynamic parameters. We obtain the exact equations of state for an integrable model of biaxial nematic liquid crystals and show that the classical transition from isotropic to uniaxial phase in absence of external fields is the result of a van der Waals type phase transition, where the jump in the order parameters is a classical shock generated from a gradient catastrophe at a non-zero isotropic field. The study of the equations of state provides the first analytical description of the rich structure of nematics phase diagrams in presence of external fields.

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Computer Simulations of Biaxial Nematics

Cited by 15 publications

References 197 publications

From idealised to predictive models of liquid crystals

From idealised to predictive models of liquid crystals

Dense crystalline packings of ellipsoids

Exact equations of state for nematics

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