In this work, for the first time, the diameter limit of surfactant wrapped single walled carbon nanotubes (SWCNTs) in SWCNT:C60 solar cells is determined through preparation of monochiral small and large diameter nanotube devices as well as those from polychiral mixtures. Through assignment of the different nanotube chiralities by photoluminescence and optical density measurements a diameter limit yielding 0% internal quantum efficiency (IQE) is determined. This work provides insights into the required net driving energy for SWCNT exciton dissociation onto C60 and establishes a family of (n,m) species which can efficiently be utilized in polymer-free SWCNT:C60 solar cells. Using this approach the largest diameter nanotube with an IQE > 0% is found to be (8,6) with a diameter of 0.95 nm. Possible strategies to extend this diameter limit are then discussed.