It depends on the peptide sequence, the size and composition of the particle, the molecular weight and density of your PEG layer. If you can provide those information I think people would be able to give you a better idea.

It depends on the structure of the peptide sequence. More precisely, the side chains in the aminoacids of the peptide. If they are nonpolar then there could be vander waals interaction; if the side chain is polar then you would see stronger interaction due to dipole-dipole forces of attraction in addition to vander waals. The degree of interaction may differ. You should be able to do calculations and study the models using chembiodraw ultra.

Thank you for the answers. I was assuming that stable binding to a PEG coat might be extremely rare or be restricted to peptides with a very specific conformation and charge, simply due to the relatively inert nature of PEG. Do you think there may exist a class of peptides which form high affinity interaction with PEG polymers/coats?

First, you need to decide the size of the peptide that is compatible to the size or length of PEG chain. Then come up with proper amino acids that can make the peptide. B-glycine and B-alanine could be the "must present" amino acids in my opinion.