Spherocylinders phase behaviour

It has not proved possible to develop general analytical hard core models for liquid crystals, just as for normal liquids. Instead, computer simulations have played an important role in extending our understanding of the phase behaviour of hard particles. It has been found that a system of hard ellipsoids can form a nematic phase for ratios L/D > 2.5 (rods) or L/D < 0.4 (discs). However, such a system cannot form a smectic phase, as can be shown by a scaling argument in statistical mechanical theory. However, simulations show that a smectic phase can be formed by a system of hard spherocylinders. The critical volume fractions for stability of a smectic A phase depend on whether the model is that of parallel spherocylinders or, more realistically, freely rotating spherocyHnders. 

FIGURE 3 The phase behaviour of 2D spherocylinders as a function of inverse aspect ratio D/L and density p [33]. The phases exhibited are isotropic (I), nematic (N) and crystal (Cr). 

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. 

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