Wall slip of polydisperse linear polymers using double reptation

The slip behavior of several high-density polyethylenes (HDPEs) is studied as a function of molecular weight (MW) and its distribution for a broad range of MW distributions. The slip velocity increases with decrease of MW, which is the case for several other linear polymers including monodisperse polybutadienes (PBDs), polystyrenes (PSs), and polylactides reported in the literature. For such polymers, the slip velocity, Vs, scales with weight or number average MW (due to monodispersity) as VS∝Mwβ, where β is about −2 for PBDs and −3.2 for PSs. For polydisperse HDPEs concepts from double reptation theory is used to develop an expression to relate slip velocity with MW and its distribution. Moreover, the slip velocity of linear polymers scales nonlinearly with the wall shear stress, namely, VS∝σWm. Using de Gennes' theory for slip, the values of m reported in the literature are explained on a theoretical basis and they are found to be equal to 1/n, where n is the local slope of the flow curve of the corresponding polymer, n≡ log(σw)/ log(γ̇w), which changes from 1 (Newtonian flow regime) to a constant value in the power-law flow regime.