Using solution thermodynamics to describe the dispersion of rod-like solutes: application to dispersions of carbon nanotubes in organic solvents

We report a simple model describing the solubility of rods in solvents, expressing the final result explicitly in terms of the surface entropy and the enthalpy of mixing. This model can be combined with any expression for the mixing enthalpy depending on the requirements. For example, in one instance it predicts the dispersed concentration of rods to decrease exponentially with the Flory-Huggins parameter of the dispersion. Using a different enthalpy function, it predicts a Gaussian peak when concentration is plotted versus solvent surface energy. The model also suggests specific solvent-rod interactions to be important and shows the dispersed concentration to be very sensitive to ordering at the solvent-rod interface. We have used this model to describe experimental results for the concentration of dispersed nanotubes in various solvents. Qualitative agreement with these predictions is observed experimentally. However, we suggest that the fact that quantitative agreement is not found may be explained by solvent ordering at the nanotube surface.