Surface-Grafted Connector Molecules Chemically Bonded to an Adjacent Adhesive
The theoretical principles of interfacial reinforcement by surface-grafted connector molecules capable of chemically bonding with an adjacent adhesive were developed and discussed by Brochard-Wyart and de Gennes . Their theory predicts that the adhesion enhancement provided by surface-grafted and chemically bonded macromolecular chains can be expressed as:
Gb = Wa + WbNr (5)
where N is the degree of polymerization of connector molecules, Wa is a reversible energy of adhesion between the bare (ungrafted substrate) and the adjacent polymer (because of van der Waals forces only), and Wb describes the energy required to disrupt a dense array of chemical bonds as given by the following:
where Ub is the energy of a bond occupying an areas of a2.
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Figure 6 illustrates the following findings of Brochard-Wyart and de Gennes
 in relation to interfaces reinforced by macromolecular connector chains grafted onto the substrate surface and chemically bonded to the adhesive:
• An increase in graft density from zero to a certain cut-off value (rCRIT), as described by Eq 7, results in a linear increase of interfacial fracture energy
• For higher graft densities (a > rCRIT), no further increase in joint fracture energy should be expected.