Phase diagram of two-dimensional hard ellipses

Bautista-Carbajal, Gustavo; Odriozola, Gerardo

doi:10.1063/1.4878411

Cited by 50 publications

(57 citation statements)

References 47 publications

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“…[31][32][33][34][35][36] The studies show there are differences between the nature of 2D nematic ordering and 3D one. So, we examined the orientation ordering properties of 2D hard ellipsoids.…”

Section: Resultsmentioning

confidence: 99%

The study of uniaxial–biaxial phase transition of confined hard ellipsoids using density functional theory

Moradi

Ghotbabadi

Aliabadi

2017

Int. J. Mod. Phys. C

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The density profiles and corresponding order parameters of the hard ellipsoids confined between two hard walls and also in contact with a single hard wall are studied using the density functional theory. The Hyper-Netted Chain (HNC) approximation is used to write excess grand potential of the system with respect to the bulk value. To simplify the calculations we use restricted orientation model (ROM) for the orientation of ellipsoids to find the density profiles and order parameters. Density functional theory shows that there is a uniaxial-biaxial phase transition near a single hard wall and also between two hard walls for a fluid consisting of uniaxial hard ellipsoidal particles with finite elongation.

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Section: Resultsmentioning

confidence: 99%

The study of uniaxial–biaxial phase transition of confined hard ellipsoids using density functional theory

Moradi

Ghotbabadi

Aliabadi

2017

Int. J. Mod. Phys. C

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“…Thus, this study did not demonstrate the formation of a disordered glass under slow near-equilibrium compression. Simulations show that hard, elongated ellipses having aspect ratios (i.e., semimajor axis divided by semiminor axis) greater than 2.4 form nematic phases (25). In the limit of very high aspect ratios, dispersions of rod-like fd virus, when slowly compressed, have yielded liquid crystals that possess long-range orientational order and are therefore not glasses (26).…”

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confidence: 99%

Shape-designed frustration by local polymorphism in a near-equilibrium colloidal glass

Zhao

Mason

2015

Proc. Natl. Acad. Sci. U.S.A.

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We show that hard, convex, lithographic, prismatic kite platelets, each having three 72°vertices and one 144°vertex, preferentially form a disordered and arrested 2D glass when concentrated quasistatically in a monolayer while experiencing thermal Brownian fluctuations. By contrast with 2D systems of other hard convex shapes, such as squares, rhombs, and pentagons, which readily form crystals at high densities, 72°kites retain a liquid-like disordered structure that becomes frozen-in as their long-time translational and rotational diffusion become highly bounded, yielding a 2D colloidal glass. This robust glass-forming propensity arises from competition between highly diverse few-particle local polymorphic configurations (LPCs) that have incommensurate features and symmetries. Thus, entropy maximization is consistent with the preservation of highly diverse LPCs en route to the arrested glass.A lthough much is known about many different kinds of glassy materials, including entangled polymers, dispersions of hard particles at high densities, and spin glasses (1-7), no single universal mechanism for glass formation describes them all. When isotropic Brownian systems of hard shapes are compressed slowly, the development of long-range order, typical of equilibrium crystal or liquid crystal phases, can either occur or be suppressed. By contrast, fast quenching processes, such as cooling molecular liquids or osmotically compressing dispersions of hard colloids, are known to produce nonequilibrium glassy states even if the components could, in principle, form highly ordered equilibrium high-density phases through slower processes (8-13). For instance, hard spheres in three dimensions (3D) undergo a first-order crystallization disorderorder transition when slowly compressed, yet can also be forced into a disordered and arrested (i.e., nonergodic) glassy solid through a rapid quench in their volume fraction to a value that is near but below the point at which the spheres actually jam (4, 14-18). Other types of glasses can be formed through mechanisms such as attractive interactions or entanglements between constituent objects (1-3). Disordered glasses differ from disordered gels, because gels result from strong attractions between constituents compared with thermal energy, and gels typically have much larger local spatial inhomogeneities than glasses (19). Thus, dispersions of colloidal particles that are not highly attractive and have hard interactions can be model glassy systems. Molecular and colloidal glass formers have been classified according to the notion of fragility (2, 20), which involves relative differences in attractive interactions. Nevertheless, a general theory of the glass-forming propensity of hard Brownian particles as a function of shape remains elusive. Moreover, dense glassy states typically have a significant residual entropy (21), reflecting orientational and positional randomness of constituent particles. The role of residual entropy in the general context of entropy maximization (22, 23) of hard...

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“…(The formation of a nematic crystal may be avoided for larger systems since the nematic order parameter is expected to decrease with the system size. 36 For instance, the replica exchange MC simulations 36 indicate that an isotropic-plastic transition occurs for monodisperse hard ellipses with aspect ratios up to k ≃ 1.6, while a nematic liquid crystal forms at sufficiently high densities when k ≥ 2.4. 34,35 Instead, we have found that a binary hard-ellipse system with an aspect ratio of around k = 2 exhibits characteristic glassy dynamics on increasing density for the chosen size disparities both translationally and rotationally.…”

Section: Model and Simulation Detailsmentioning

confidence: 99%

Relaxation dynamics in a binary hard-ellipse liquid

Sun

2015

Soft Matter

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Structural relaxation in binary hard spherical particles has been shown recently to exhibit a wealth of remarkable features when size disparity or mixture composition is varied. In this paper, we test whether or not similar dynamical phenomena occur in glassy systems composed of binary hard ellipses. We demonstrate via event-driven molecular dynamics simulation that a binary hard-ellipse mixture with an aspect ratio of two and moderate size disparity displays characteristic glassy dynamics upon increasing density in both the translational and the rotational degrees of freedom. The rotational glass transition density is found to be close to the translational one for the binary mixtures investigated. More importantly, we assess the influence of size disparity and mixture composition on the relaxation dynamics. We find that an increase of size disparity leads, both translationally and rotationally, to a speed up of the long-time dynamics in the supercooled regime so that both the translational and the rotational glass transition shift to higher densities. By increasing the number concentration of the small particles, the time evolution of both translational and rotational relaxation dynamics at high densities displays two qualitatively different scenarios, i.e., both the initial and the final part of the structural relaxation slow down for small size disparity, while the short-time dynamics still slows down but the final decay speeds up in the binary mixture with large size disparity. These findings are reminiscent of those observed in binary hard spherical particles. Therefore, our results suggest a universal mechanism for the influence of size disparity and mixture composition on the structural relaxation in both isotropic and anisotropic particle systems.

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Phase diagram of two-dimensional hard ellipses

Cited by 50 publications

References 47 publications

The study of uniaxial–biaxial phase transition of confined hard ellipsoids using density functional theory

The study of uniaxial–biaxial phase transition of confined hard ellipsoids using density functional theory

Shape-designed frustration by local polymorphism in a near-equilibrium colloidal glass

Relaxation dynamics in a binary hard-ellipse liquid

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