Theory of the isotropic-nematic transition in dispersions of compressible rods

We theoretically study the nematic ordering transition of rods that are able to elastically adjust their mutually excluded volumes. The model rods, which consist of a hard core surrounded by a deformable shell, mimic the structure of polymer-coated, rod-like fd virus particles that have recently been the object of experimental study [K.~Purdy et al., Phys. Rev. Lett. \textbf{94}, 057801 (2005)]. We find that fluids of such soft rods exhibit an isotropic-nematic phase transition at a density higher than that of the corresponding hard-rod system of identical diameter, and that at coexistence the order parameter of the nematic phase depends non monotonically on the elastic properties of the polymer coating. For binary mixtures of hard and soft rods, the topology of the phase diagram turns out to depend sensitively on the elasticity of shell. The lower nematic-nematic critical point, discovered in mixtures of bare and polymer-coated fd virus particles, is not reproduced by the theory.