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 [12]. 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:

Ub

a2

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

[12] 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

rCRIT —

• For higher graft densities (a > rCRIT), no further increase in joint frac­ture energy should be expected.