Multicomponent solubility parameters for single-walled carbon nanotube-solvent mixtures.

We have measured the dispersibility of single-walled carbon nanotubes in a range of solvents, observing values as high as 3.5 mg/mL. By plotting the nanotube dispersibility as a function of the Hansen solubility parameters of the solvents, we have confirmed that successful solvents occupy a well-defined range of Hansen parameter space. The level of dispersibility is more sensitive to the dispersive Hansen parameter than the polar or H-bonding Hansen parameter. We estimate the dispersion, polar, and hydrogen bonding Hansen parameter for the nanotubes to be <delta(D)> = 17.8 MPa(1/2), <delta(P)> = 7.5 MPa(1/2), and <delta(H)> = 7.6 MPa(1/2). We find that the nanotube dispersibility in good solvents decays smoothly with the distance in Hansen space from solvent to nanotube solubility parameters. Finally, we propose that neither Hildebrand nor Hansen solubility parameters are fundamental quantities when it comes to nanotube-solvent interactions. We show that the previously calculated dependence of nanotube Hildebrand parameter on nanotube diameter can be reproduced by deriving a simple expression based on the nanotube surface energy. We show that solubility parameters based on surface energy give equivalent results to Hansen solubility parameters. However, we note that, contrary to solubility theory, a number of nonsolvents for nanotubes have both Hansen and surface energy solubility parameters similar to those calculated for nanotubes. The nature of the distinction between solvents and nonsolvents remains to be fully understood.