Stability of the nematic phase of a mixture of aligned cylinders with respect to the smectic and columnar phases

Abstract

The theory for the stability of the nematic phase of parallel cylinders due to Mulder [Phys. Rev. A 35, 3095 (1987)] is generalized to binary mixtures. It is shown that adding cylinders of a different length to a one-component nematic phase of cylinders postpones the nematic–smectic A transition, enhancing the range of the nematic. This is a result of the two different length scales each favoring a density modulation of a different wavelength. When the ratio of the lengths of the cylinders is large a cusp appears in the limit of stability of the nematic phase. This cusp corresponds to a large jump in the wavelength of the density modulation from a wavelength characteristic of ordering of the short rods to that characteristic of the longer rods. The cusp is, however, masked by a transition to a columnar phase unless the diameters of the two species of rod are significantly different. The limit of stability with respect to the smectic phase bears a striking resemblance to the phase behavior of a mixture of two mesogens studied some time ago by Sigaud et al. [J. Phys. (Paris) Colloq. 40, C3 (1979)]. Their results have hitherto only been described by Landau theory and via lattice ‘‘analogs’’ which have no obvious connection with the underlying behavior at the molecular level. In contrast, theories of specific model molecules such as the cylinders studied here offer insight into behavior at the molecular level.