The liquid crystalline behavior of a two dimensional (2D) model of hard needles bent into a “zigzag shape” is studied. This model, originally designed to study two dimensional chiral segregation, also shows liquid crystalline behavior and has some anomalous features which are contrasted in relation to the following: (i) Most of the microscopical models used to study liquid crystals have a symmetry axis that coincides with a molecular axis; (ii) in three-dimensions, chiral molecules can form cholesteric instead of nematic phases; (iii) the smectic phase is usually found when attractions are present or at least when the molecules have finite volume. Despite the fact that the present 2D model does not have any of these characteristics, numerical evidence is found for the occurrence of nematic and smectic phases. Since these molecules are athermal, infinitely repulsive, and infinitesimally thin, the liquid crystalline characteristics are attributed to excluded volume effects. To determine the mesophases of the model, both nematic and smectic order parameters as well as distribution functions are computed.
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This kind of plot is necessary for those cases where the density is high and it is very difficult to see the structure of the configuration, for this reason from now on most of the snapshots presented in this paper, are drawn following this criterion.
For those cases where there is not an anisotropic behavior, the parallel and perpendicular directions are arbitrary.
It is convenient to note that a large value of does not necessarily imply a nematic phase, as in this case. This is only a coincidence that in the smectic phase orientational order also exists.
