Hard ellipsoids phase behaviour

It has not proved possible to develop general analytical hard-core models for liquid crystals, just as for nonnal liquids. Instead, computer simulations have played an important role in extending our understanding of the phase behaviour of hard particles. Frenkel and Mulder found that a system of hard ellipsoids can fonn a nematic phase for ratios L/D >2.5 (rods) or L/D <0.4 (discs) [73] however, such a system cannot fonn a smectic phase, as can be shown by a scaling... 

The first of these was by Vieillard-Baron [5] who investigated a system of spherocylinders but failed to detect a liquid crystal phase primarily because the anisometry, L/D, of 2 was too small [37]. He also attempted to study a system of 2392 particles with the larger L/D of 5 but these simulations had to be abandoned because of their large computational cost. However, in view of the ellipsoidal shape of the Gay-Berne particles it is the behaviour of hard ellipsoids of revolution which is of primary relevance to us. 

It is clear that systems of hard ellipsoids exhibit an intriguingly simple phase behaviour with some resemblance to that of real nematogens. However, such systems cannot form smectic or columnar phases and in addition the phase transitions are not thermally driven as they are for real mesogens. As we shall see in the following sections the Gay-Berne potential with its anisotropic repulsive and attractive forces is able to overcome both of these limitations. 

Fig. 3a,b. The phase behaviour of a system of hard ellipsoids, both prolate and oblate, as a function of the ellipticity, alb, plotted against a the packing fraction, p b the scaled number density, p ... 

FIGURE 1 The phase behaviour of hard ellipsoids as a fimctim of the aspect ratio x [2,9]. The reduced density p is defined such that the dmsity of regular close packing is equal to V2 fiv all x. The gr areas indicate the coexistence regions between the various diases, whidi are isotrr ic (I), nematic (N), solid (Cr) and plastic solid (PCr). The solid points indicate the simulation results. 

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