Polydispersity and ordered phases in solutions of rodlike macromolecules

We apply density functional theory to study the influence of polydispersity on the stability of columnar, smectic, and solid ordering in the solutions of rodlike macromolecules. For sufficiently large length polydispersity (standard deviation sigma > 0.25) a direct first-order nematic-columnar transition is found, while for smaller sigma there is a continuous nematic-smectic and first-order smectic-columnar transition. The length distribution of macromolecules changes neither at the nematic-smectic nor at the nematic-columnar transition. In the binary mixtures the nematic-smectic transition is also continuous. Demixing in the smectic phase is preempted by transitions to solid or columnar phases.