To study diffusion and binding of polymers into surface-attached networks containing reactive groups, surface-attached polymer networks bound to oxidized silicon surfaces are generated, which contain succinimide ester groups. The surface-attached polymer layers are brought into contact with poly(ethylene glyco)s (PEG), which carry terminal amine end groups and which have systematically varied molecular weights. The coupling reaction between the active ester groups in the polymer networks and the amine groups in the incoming chains are studied by ellipsometry, surface plasmon spectroscopy, AFM, and Fourier transform infrared spectroscopy (FTIR). The degree of functionalization of the reactive layers by the PEG-NH2 depends strongly on the crosslink density of the network, the active ester content, and the molecular weight of the amine-terminated polymer. A model for the attachment reaction is proposed which suggests that the incoming polymer chains bind only at the outer periphery of the network in a narrow penetration zone. According to this model, when the incoming polymers are rather short, penetration into the layer and binding are prohibited by the high segment density and the anisotropic stretching of the surface-attached networks ("entropic shielding"). For incoming chains with a higher molecular weight and/or networks with a small mesh sizes, size exclusion effects determine diffusion and binding.