  We study the adhesion between a cross-linked 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 $\sigma^{*}
\simeq P^{{1/10}}N^{-{3/5}}$ beyond which the layer no longer interdigitates
with the elastomer. We then relate this result with recent adhesion
measurements.
