Structure and phase diagram of self-assembled rigid rods: equilibrium polydispersity and nematic ordering in two dimensions.

We investigate the influence of directional or bonding interactions on the structure and phase diagram of complex fluids. Using a generalization of the theory of associating fluids we study the interplay between the self-assembly process, driven by the bonding interactions, and the isotropic-nematic transition, driven by the anisotropic shape of the equilibrium clusters, for a model consisting of particles with two bonding sites and discrete orientational degrees of freedom. The theory is applied over a wide range of temperature and density in two dimensions and the results are compared with Monte Carlo simulations on the square lattice. The specific heat is shown to exhibit pronounced structure at the onset of self-assembly and at the nematic-isotropic transition that occur over a narrow range of temperature, at fixed density. The results reveal that bonding is enhanced by the nematic ordering, although a bonding temperature still occurs in the isotropic phase at low densities. The average rod length is described quantitatively in both phases, while the location of the ordering transition, which was found to be continuous, is predicted semiquantitatively by the theory.