  Carbon nanotubes (CNTs) are stiff, all-carbon macromolecules with diameters
as small as one nanometer and few microns long. Solutions of CNTs in
chlorosulfonic acid (CSA) follow the phase behavior of rigid rod polymers
interacting via a repulsive potential and display a liquid crystalline phase at
sufficiently high concentration. Here, we show that small-angle X-ray
scattering and polarized light microscopy data can be combined to characterize
quantitatively the morphology of liquid crystalline phases formed in CNT
solutions at concentrations from 3 to 6.5 % by volume. We find that upon
increasing their concentration, CNTs self-assemble into a liquid crystalline
phase with a pleated texture and with a large inter-particle spacing that could
be indicative of a transition to higher-order liquid crystalline phases. We
explain how thermal undulations of CNTs can enhance their electrostatic
repulsion and increase their effective diameter by an order of magnitude. By
calculating the critical concentration, where the mean amplitude of undulation
of an unconstrained rod becomes comparable to the rod spacing, we find that
thermal undulations start to affect steric forces at concentrations as low as
the isotropic cloud point in CNT solutions.
