  The phase behavior of rodlike molecules with polydisperse length and
solvent-mediated attraction and repulsion is described by an extension of the
Onsager theory for rigid rods. A phenomenological square-well potential is used
to model these long-range interactions, and the model is used to compute phase
separation and length fractionation as a function of well depth and rod
concentration. The model closely captures experimental data points for
isotropic/liquid crystalline phase coexistence of single-walled carbon
nanotubes (SWNTs) in superacids. The model also predicts that the
isotropic-biphasic boundary approaches zero as acid strength diminishes, with
the possibility of coexistence of isotropic and liquid crystalline phases at
very low concentrations; this counterintuitive prediction is confirmed
experimentally. Experimental deviations from classical theories for rodlike
liquid crystals are explained in terms of polydispersity and the balance
between short range repulsion and long range attractions. The predictions of
the model also hold practical import for applications of SWNT/superacid
solutions, particularly in the processing of fibers and films from liquid
crystalline SWNT/superacid mixtures.
