Effective-liquid approach to the generalized Onsager theories of the isotropic-nematic transition of hard convex bodies

Cuesta, José A.; Tejero, Carlos Fernández; Xu, Hòng; Baus, Marc

doi:10.1103/physreva.44.5306

Cited by 15 publications

(11 citation statements)

References 27 publications

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“…Ward and Lado [26] found based on the Percus-Yevick (PY) integral equation theory that the I-N transition does not take place in a fluid of hard ellipses although orientational ordering is allowed. While, the density-functional theory (DFT) [27] and the effective-liquid approach [28] indicate that the I-N transition is continuous for hard ellipses with arbitrary aspect ratios. The other forms of DFT [29,30], the Onsager theory-based approach [31], and the scaled particle theory (SPT) [32] predict the existence of the I-N transition in hard ellipses, but its location differs from these theoretical predictions.…”

Section: Introductionmentioning

confidence: 99%

Hard ellipses: Equation of state, structure, and self-diffusion

Sun

et al. 2013

The Journal of Chemical Physics

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Despite their fundamental and practical interest, the physical properties of hard ellipses remain largely unknown. In this paper, we present an event-driven molecular dynamics study for hard ellipses and assess the effects of aspect ratio and area fraction on their physical properties. For state points in the plane of aspect ratio (1 ≤ k ≤ 9) and area fraction (0.01 ≤ φ ≤ 0.8), we identify three different phases, including isotropic, plastic and nematic states. We analyze in detail the thermodynamic, structural and self-diffusive properties in the formed various phases of hard ellipses. The equation of state (EOS) is shown for a wide range of aspect ratios and is compared with the scaled particle theory (SPT) for the isotropic states. We find that SPT provides a good description of the EOS for the isotropic phase of hard ellipses. At large fixed φ, the reduced pressure p increases with k in both the isotropic and the plastic phases and, interestingly, its dependence on k is rather weak in the nematic phase. We rationalize the thermodynamics of hard ellipses in terms of particle motions. The static structures of hard ellipses are then investigated both positionally and orientationally in the different phases. The plastic crystal is shown to form for aspect ratios up to k = 1.4, while appearance of the stable nematic phase starts approximately at k = 3. We quantitatively determine the locations of the isotropic-plastic (I-P) transition and the isotropic-nematic (I-N) transition by analyzing the bond-orientation correlations and the angular correlations, respectively. As expected, the I-P transition point is found to increase with k, while a larger k leads to a smaller area fraction where the I-N transition takes place. Moreover, our simulations strongly support that the two-dimensional nematic phase in hard ellipses has only quasilong-range orientational order. The self-diffusion of hard ellipses is further explored and connections are revealed between the structure and the self-diffusion. We discuss the relevance of our results to the glass transition in hard ellipses. Finally, the results of the isodiffusivity lines are evaluated for hard ellipses and we discuss the effect of spatial dimension on the diffusive dynamics of hard ellipsoidal particles.

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Section: Introductionmentioning

confidence: 99%

Hard ellipses: Equation of state, structure, and self-diffusion

Sun

et al. 2013

The Journal of Chemical Physics

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“…We mention here that for the isotropic (p(x) = p) and nematic (p(x) = ph(u)) phases, (7) reduces to the same expression as that obtained from the factorized dcf in [18] (cf. [26]). This can partly explain why the latter leads to succussful results for the I-N transition of hard ellipsoids.…”

Section: The Direct Correlation Functionmentioning

confidence: 93%

“…This is due here to the perfect alignment of the HSCs, causing their excluded volume to be exactly 8v, just as for HS systems. This degeneracy disappears when the HSCs are free to rotate [26]. It could be interesting to replace the r.h.s, of (9) by the more general HS expression:…”

Section: The Nematic Phase Of Phscmentioning

confidence: 97%

A density functional study of nematic-smectic A-solid transitions of parallel hard spherocylinders

1992

Molecular Physics

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A density functional theory is formulated to study the nematic, smectic A and solid phases and phase transitions of a system of parallel hard spherocylinders (PHSC). For the direct correlation function the analytic expression suggested by Pynn is employed and an effective liquid approach is proposed to calculate the excess free energy of the inhomogeneous (smectic and solid) phases. The nematic-smectic A transition is found to be second order. The first-order nematic-solid and smectic A-solid transitions are calculated. As a function of the elongation of the spherocylinders, the phase behaviour and coexistence data obtained from the theory are in reasonable agreement with the available computer simulation results.

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“…The phase behavior has been explored extensively by various theoretical approaches and simulations in both two-dimensional hard ellipses [14][15][16][17][18][19][20][21][22] and three-dimensional hard ellipsoids.…”

Section: -13mentioning

confidence: 99%

Glass formation in a mixture of hard disks and hard ellipses

Duan

Sun

et al. 2015

The Journal of Chemical Physics

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We present an event-driven molecular dynamics study of glass formation in two-dimensional binary mixtures composed of hard disks and hard ellipses, where both types of particles have the same area. We demonstrate that characteristic glass-formation behavior appears upon compression under appropriate conditions in such systems. In particular, while a rotational glass transition occurs only for the ellipses, both types of particles undergo a kinetic arrest in the translational degrees of freedom at a single density. The translational dynamics for the ellipses is found to be faster than that for the disks within the same system, indicating that shape anisotropy promotes the translational motion of particles. We further examine the influence of mixture's composition and aspect ratio on the glass formation. For the mixtures with an ellipse aspect ratio of k = 2, both translational and rotational glass transition densities decrease with increasing the disk concentration at a similar rate and hence, the two glass transitions remain close to each other at all concentrations investigated. By elevating k, however, the rotational glass transition density diminishes at a faster rate than the translational one, leading to the formation of an orientational glass for the ellipses between the two transitions. Our simulations imply that mixtures of particles with different shapes emerge as a promising model for probing the role of particle shape in determining the properties of glass-forming liquids. Furthermore, our work illustrates the potential of using knowledge concerning the dependence of glass-formation properties on mixture's composition and particle shape to assist in the rational design of amorphous materials.

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Effective-liquid approach to the generalized Onsager theories of the isotropic-nematic transition of hard convex bodies

Cited by 15 publications

References 27 publications

Hard ellipses: Equation of state, structure, and self-diffusion

Hard ellipses: Equation of state, structure, and self-diffusion

A density functional study of nematic-smectic A-solid transitions of parallel hard spherocylinders

Glass formation in a mixture of hard disks and hard ellipses

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