Smectic, nematic, and isotropic phases in binary mixtures of thin and thick hard spherocylinders

A second-virial Onsager theory, based on Parsons-Lee rescaling and suitably extended to deal with multicomponent systems and smectic phases, has been used to calculate the phase diagram of a collection of binary mixtures of thin and thick hard spherocylinders. In particular, two types of phase diagrams are investigated. First, a number of binary mixtures where the two components have the same total length have been considered; in addition, the phase diagram of a binary mixture where the two components have the same volume has been calculated. For the particles of one of the two components, the length of the cylindrical part and the diameter have always been set equal to 5 and 1, respectively. Spherocylinders of the same total length and different diameter tend to demix considerably as soon as the diameter ratio deviates from unity. This happens especially at high pressures, when at least the phase richer in the thicker component is smectic. In the case where the two components have equal volumes, demixing is further increased due to the disparity not only in particle diameter but also in particle lengths. The incorporation of inhomogeneous layered phases is seen to alter significantly the phase diagrams calculated if only homogeneous phases are allowed, since transitions to a smectic phase often preempt those to a nematic or an isotropic phase. The apparent versatility of the recent experimental techniques suggests that the phase diagram features predicted by the theory might be also observed in real systems.