Single-walled carbon nanotubes are grafted with polystyrene chains employing a graft-to protocol. Thermogravimetric analysis allows calculation of the grafted chain density and average interchain separation on the nanotube surface as a function of molecular weight. The separation scales with molecular weight as a power law with an exponent of ca. 0.588, showing the grafted chains to be in a swollen random walk conformation. This implies that chain packing is controlled by coil size in solution. In addition, the dispersed concentration of functionalized nanotubes scales with the size of the steric potential barrier that prevents aggregation of polymer functionalized nanotubes. It is also shown that the molecular weight of the grafted chains significantly affects the mechanical properties of nanotube films.