How does a polymer brush repel proteins?

The captioned question has been addressed by the steric effect; namely, the adsorption of proteins on a surface grafted with linear polymer chains decreases monotonically as the grafting density increases. However, there is no quantitative and satisfactory explanation why the adsorption starts to increase when the grafting density is sufficiently high and why polyethylene glycol (PEG) still remains as one of the best polymers to repel proteins. After considering each grafted chain as a molecular spring confined inside a "tube" made of its surrounding grafted chains, we estimated how its free energy depends on the grafting density and chain length, and calculated its thermal energy-agitated chain conformation fluctuation, enabling us to predict an adsorption minimum at a proper grafting density, which agrees well with previous experimental results. We propose that it is such a chain fluctuation that slows down the adsorption kinetically.