The unique carbon nanotube (CNT) properties are mainly determined by their geometry, e.g., their aspect ratio, diameter, and number of walls. So far, chlorosulfonic acid is the only practical true solvent for carbon nanotubes, forming thermodynamically stable molecular solutions. Above a critical concentration the system forms an ordered, nematic liquid-crystalline phase. That phase behavior is the basis for liquid phase processing and the optimal translation of the carbon nanotube molecular properties to the macroscopic scale. The final material properties depend on the phase behavior of the "dope" from which it is prepared, which depends on the CNT parameters themselves. Earlier work determined that CNT aspect ratio controls the phase behavior, in accordance with classical rigid-rod theories. Here we use cryogenic transmission electron microscopy and Raman spectroscopy to understand the relation between the geometry of the CNTs, the chemical interaction with chlorosulfonic acid, and the phase behavior of crowded solutions. We show that the CNT diameter and number of walls also play an independent role in the phase transition and phase morphology of the system because of their effect on the CNT bending stiffness.