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 mushroom regime ( N monomers per chain, grafting density ν). The friction is provided by the sliding motion of the P chains of the “skin” (thickness 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 additive. Above a threshold ν c, all P chains of the skin are trapped, and the low-velocity friction becomes independent of the grafting density. Above a certain threshold slippage velocity V *(ν), the N chains are strongly stretched and reach a “marginal state”, corresponding to a constant shear stress. We expect that for ν > ν c, V *(ν) increases linearly. Depending on N, P, ν, and V, we predict a cascade of regimes, where the N chains may be ideal, stretched, or “marginal”, while the trapped chains may be ideal or stretched and progressively disentangle from the N chains.