  We present a study of the charge state conversion of single nitrogen-vacancy
(NV) defects hosted in nanodiamonds (NDs). We first show that the proportion of
negatively-charged NV$^{-}$ defects, with respect to its neutral counterpart
NV$^{0}$, decreases with the size of the ND. We then propose a simple model
based on a layer of electron traps located at the ND surface which is in good
agreement with the recorded statistics. By using thermal oxidation to remove
the shell of amorphous carbon around the NDs, we demonstrate a significant
increase of the proportion of NV$^{-}$ defects in 10-nm NDs. These results are
invaluable for further understanding, control and use of the unique properties
of negatively-charged NV defects in diamond
