Well that is something you need to determine by running experiments. The ability of PEG to protect your particles from aggregation largely depends on how does it adsorb to the surface. I do not understand the sonication question. You can sonicate anything you want. You need to remove excess PEG before claiming success. 

You can functionalize  Fe3O4 nanoparticles with PEG if it contains some dihydroxy type terminals, or diamino etc (multifunctionality, for strong binding/adsorption etc). May be a ligand exchange would be useful. And sonication will only disperse the nanoparticles, it has nothing to do with functionalization. 

Hello Amanda,

I know this paper coated  Fe3O4 with PEG, not sure about particle size though

ACS Appl. Mater. Interfaces, 2012, 4 (1), pp 142–149

DOI: 10.1021/am201166m

Regards

Amin

Particle size generally don't restrict the surface functionalization, yeah there come some problems when particles are too bigger, say from 50 nm and above the become slightly difficult to post functionalize, for the prefunctionalization there is almost no severe issue. Many thanks for mentioning the article @Amin.

Thanks for your answers!

@Oma @Muhammadr: With the sonication part I didn't mean functionalization, but if it's possible to disperse particles of that size using sonication. I'm not sure if it still has effect on such small particles.

@Amin: Thanks for the article.

If the particles are dried and you want to disperse them, it will be almost impossible. If they are already dispersed and you apply sonication nothing will happen, unless temperature rises considerably.