Modeling the phase behavior of polydisperse rigid rods with attractive interactions, with applications to SWNTs in super acids

Abstract

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.