SLIPPAGE OF POLYMER MELTS ON GRAFTED SURFACES

We study the slippage of a highly viscous polymer melt (P monomers per chain) on a solid substrate grafted by a few smaller chains in the mu shroom regime (N monomers per chain, grafting density v). The friction is provided by the sliding motion of the P chains of the ''skin'' (th ickness R(p) = P(1/2)a) which are entangled with the tethered chains. At low grafting densities, only a fraction of the P chains in the skin are coupled to the N chains, and the friction on the mushrooms is add itive. Above a threshold v(c), all P chains of the skin are trapped, a nd the low-velocity friction becomes independent of the grafting densi ty. Above a certain threshold slippage velocity V(v), the N chains ar e strongly stretched and reach a ''marginal state'', corresponding to a constant shear stress. We expect that for v > v(c), V(v) increases linearly. Depending on N, P, v, and V, we predict a cascade of regimes , where the N chains may be ideal, stretched, or ''marginal'', while t he trapped chains may be ideal or stretched and progressively disentan gle from the N chains.