Adhesion between a flat solid and a rubber is considerably increased b
y grafting chains (chemically identical to the rubber) on the solid su
rface. Similarly, a population of mobile chains dissolved into rubber
can increase the strength of a rubber/rubber contact. A third (more re
cent) type of promoter is a ''Guiselin brush'', obtained by incubating
certain polymer melts against a suitable solid. A major practical pro
blem is to understand how the adhesive energy varies with the surface
concentration sigma of ''connector molecules'': very often, at high co
nnector density, the strength goes down. We set up a theoretical pictu
re of polymer interdigitation, covering most of the cases listed above
. We also describe peeling measurements of the adhesion energy G(sigma
) for Guiselin brushes (silica/PDMS/PDMS network). For the Guiselin br
ush, the statistical problem is much more complex. The main experiment
al result is the presence of a clear maximum in the plot of G(sigma).