Interdigitation between surface-anchored polymer chains and an elastomer: Consequences for adhesion promotion

We study the adhesion between a crosslinked elastomer and a flat solid surface where polymer chains have been end-grafted. To understand the adhesive feature of such a system, one has to study both the origin of the grafted layer interdigitation with the network, and the end-grafted chains extraction out of the elastomer when it comes unstuck from the solid surface. We shall tackle here the first aspect for which we develop a partial-interdigitation model that lets us analytically predict a critical surface grafting density $\sigma^{*}\simeq P^{\frac{1}{10}}N^{-\frac{3}{5}}$ beyond which only the thermal fluctuations allow the layer to interdigitate with the elastomer. We then relate this result with recent adhesion measurements