Anti-oxidant properties usually have to do with an interaction at the surface. Decreasing particle size increases surface area to volume ratio, so if you can decrease size (while holding all other things constant and ensuring it is stable - not an easy thing), you can expect an increase in surface area related properties, such as anti-oxidant behavior.
I don't know any good references off the top of my head. I published a paper a few years ago that makes the same point I made above in greater detail. You can get it here: dx.doi.org/10.1016/j.carbon.2012.05.063. If you don't have access to the site, you can get it off my profile here.
Here's the article reference: Chu, C.C., K.L. White, P. Liu, and H.-J. Sue, “Electrical conductivity and thermal stability of polypropylene containing well-dispersed multi-walled carbon nanotubes disentangled with exfoliated nanoplatelets,” Carbon, 50(12) (2012), p. 4711-21, doi:10.1016/j.carbon.2012.05.063.
We discuss the change the change in transition in conductivity and thermal degradation behavior based on size effect, and also mention some negative consequences that might be associated.