On the isotropic-liquid crystal phase separation in a solution of rodlike particles of different lengths

The Onsager theory for the isotropic-anisotropic phase separation in a solution of rodlike particles is extended to the case of mixtures of such particles with different lengths. The concentration, composition, order parameters, and orientation dependent thermodynamic quantities of the coexisting phases are calculated for the case of a mixture of rods of two different lengths for different length ratios. It is found that there is a significantly higher mole fraction of the longer rods in the anisotropic phase than in the isotropic phase. The order parameter of the longer rods is higher than in the one component case, whereas the order parameter of the shorter rods first increases and then decreases as the mole fraction of the longer rods is increased. All these features are accentuated as the length ratio of the two kinds of rods increases