How does tack depend on time of contact and contact pressure?

The tack of polymer melts on rigid substrates under conditions of short contact times and low pressures is examined. The substrate is modeled as a random rough surface with a distribution of asperities heights. The true contact area between the adhesive and the substrate is calculated for a given total load and elastic modulus of the substrate. The dependence of tack on contact time is accounted for by introducing the relaxation of the adhesive through a time-dependent elastic modulus. For relatively high pressures the tack is predicted to scale with 1/E so that for short contact times, tc, the tack is predicted to scale with (tc/τe)1/2, where τe is the entanglement time. For lower pressures this simple scaling law is no longer valid and we predict a complex variation of tack with contact time and molecular parameters.