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Hard ellipses: Equation of state, structure, and self-diffusion
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10.1063/1.4812361
/content/aip/journal/jcp/139/2/10.1063/1.4812361
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/2/10.1063/1.4812361
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Reduced pressure as a function of area fraction ϕ for (a) hard disks and hard ellipses with = 1.1–2 and (b) hard ellipses with = 3–9. The results are shifted up by 5 from the preceding small for clarity. The dotted lines are simulation results and the solid lines are the results of the SPT [Eq. (5) ]. The green dashed line in (a) is the SPT prediction for the equation of state of hard disks in the isotropic state, i.e., Eq. (10) in Ref. . The circles indicate the area fractions where the system starts to form stable plastic crystals in (a) and stable nematic crystals in (b), respectively (see the structural analysis in Subsection III B ). The semi-log plot in the inset of Fig. 1(b) highlights the change of dependence of on ϕ with increasing .

Image of FIG. 2.
FIG. 2.

Reduced pressure as a function of γ at fixed densities. The solid lines are the results of Eq. (5) .

Image of FIG. 3.
FIG. 3.

-dependence of at the highest densities studied. The dotted lines are a guide to the eye. For these densities, the system has a plastic phase for ⩽ 1.4, a nematic phase for ⩾ 3 and an isotropic phase in between.

Image of FIG. 4.
FIG. 4.

Pair correlation function () of hard ellipses at ϕ = 0.8 for ⩾ 1.5. The results are shifted up by 0.5 from the preceding small for clarity. As there are two basic length scales in a system of hard ellipses, () also peaks at = 2, as indicated by the arrows for = 9.

Image of FIG. 5.
FIG. 5.

()/() of hard ellipses with = 1.2 in the vicinity of the isotropic-plastic transition. The solid lines are the results of the OZ fittings and the dash dotted lines are the results of the power-law fittings. The green dashed line indicates ()/() ∼ . The results are similar for other aspect ratios with ⩽ 1.4.

Image of FIG. 6.
FIG. 6.

Isotropic-plastic transition point ϕ as a function of . The solid line is a guide to the eye.

Image of FIG. 7.
FIG. 7.

Nematic order parameter as a function of nematic director θ for hard ellipses with = 6 for various ϕ. Note that the result is shown for a single sample because ) cannot be averaged among different samples since the nematic direction differs from one sample to another.

Image of FIG. 8.
FIG. 8.

Upper: as a function of ϕ for various . Lower: contour plot of in the plane of ϕ and .

Image of FIG. 9.
FIG. 9.

Angular correlation function () for hard ellipses with ⩽ 2 at ϕ = 0.8. The green dashed line indicates () ∼ .

Image of FIG. 10.
FIG. 10.

Angular correlation function () for a system of hard ellipses with = 6 in the vicinity of the isotropic-nematic transition. The solid lines are the results of the power-law fittings. The green dashed line indicates () ∼ . The results are similar for other aspect ratios with ⩾ 3.

Image of FIG. 11.
FIG. 11.

Isotropic-nematic transition point ϕ as a function of . The triangle and the squares are the MC results taken from Refs. and , respectively. The dashed and solid lines are the fits to the EDMD data by ϕ = / with = 2.90 and ϕ = ϕ/( + ) with ϕ = 6.37 and = 5.14, respectively.

Image of FIG. 12.
FIG. 12.

Angular correlation function () for hard ellipses with ⩾ 3 at ϕ = 0.8.

Image of FIG. 13.
FIG. 13.

(a) Phase diagram of hard ellipses in the plane of aspect ratio and area fraction ϕ. (b)–(e) Representative snapshots for a high-density isotropic phase with = 1.5 and ϕ = 0.8, a low-density isotropic phase with = 6 and ϕ = 0.5, a plastic phase with = 1.2 and ϕ = 0.8, and a nematic phase with = 9 and ϕ = 0.8. Note that there is visually no distinction for the orientation of an ellipse with θ and θ + π so that particles with θ are shown as the same color as those with θ + π in the snapshots.

Image of FIG. 14.
FIG. 14.

Time evolution of (a) translational and (b) rotational MSDs at ϕ = 0.8 for three aspect ratios. The system has a plastic phase for = 1.1, an isotropic phase for = 2, and a nematic phase for = 6.

Image of FIG. 15.
FIG. 15.

(a) Translational diffusion constant and (b) rotational diffusion constant as a function of area fraction ϕ for various .

Image of FIG. 16.
FIG. 16.

Rotational diffusion constant as a function of translational diffusion constant for various . The green dashed line indicates = .

Image of FIG. 17.
FIG. 17.

Isodiffusivity lines in the plane of aspect ratio and area fraction ϕ. The solid lines are isodiffusivity lines from translational diffusion coefficients and the dashed lines are isodiffusivity lines from rotational diffusion coefficients . The green squares and the red circles indicate the locations of the isotropic-plastic transition and the isotropic-nematic transition, respectively.

Image of FIG. 18.
FIG. 18.

For hard ellipses with = 2 and 4, effect of the system size on (a) reduced pressure, (b) nematic order parameter, (c) translational diffusion constant, and (d) rotational diffusion constant. The results for = 4 in (a) are shifted up by 5 for clarity, and the error bars in (b) correspond to the standard deviation over four independent samples. The system shows an isotropic phase in the whole density range in the case of = 2, while the I-N transition occurs at ϕ ≈ 0.7 for = 4.

Image of FIG. 19.
FIG. 19.

Effect of the system size on the angular correlation function () for = 4 at ϕ = 0.7 and 0.8.

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/content/aip/journal/jcp/139/2/10.1063/1.4812361
2013-07-08
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hard ellipses: Equation of state, structure, and self-diffusion
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/2/10.1063/1.4812361
10.1063/1.4812361
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