Tactoidal state and phase transitions in systems of linear polymers of variable length

The tactoidal state in systems containing long, rod-like molecules consists of partially aligned solute molecules in equilibrium with and at a concentration not much higher than that in the conjugate isotropic phase. Under the liquid lattice model of Flory [Proc. R. Soc. London Ser. A, (1956) 234, 73-89], as well as under other models, tactoid formation by molecules of fixed axial ratio depends on nonideality induced by excluded volumes; the process is wholly entropy driven and requires no direct interactions between rods. Many rod-like biological polymers exhibit reversible polymerization, so that axial ratio and length are not fixed. Polymerization and rod length will then not only induce nonideality, alignment, and phase separation, but will be affected by these. In this work these interrelations are treated under the model of Flory, modified to include a free energy of polymerization and to permit reversible changes in rod length. The primary conclusion is that, in contrast to the situation for fixed lengths, excluded volume-dependent nonideality alone does not suffice to induce a tactoidal phase separation. In the absence of attractions or repulsions between rods the anisotropic phase is highly concentrated. This phase only becomes tactoidal when a minimal level of repulsive interaction between rods is reached. Under this model, tactoid formation in systems such as deoxygenated hemoglobin S and tobacco mosaic virus depends on repulsive interactions or metastability or both. As a secondary result it is shown that rod length in the anisotropic phase is much greater than in the conjugate isotropic phase.