Dynamics of end-tethered chains at high surface coverage

A molecular model for wall slip based on recent tube theories is extended to account for the effects of entanglements between tethered chains that occur at higher surface coverage. Three regimes of surface coverage are identified. Regime I is a low surface coverage regime (the mushroom regime), which has been discussed earlier by us. In regime II the tethered chains undergo a cooperative constraint release process due to which the slip velocity increases with surface coverage while the slip length becomes independent of the surface coverage. In regime III the tethered chains start to become entangled with each other thereby causing the interfacial modulus, the critical wall shear stress and the critical shear rate to decrease with surface coverage. Our model is different from previous scaling models in that it provides a constitutive equation for tethered chains. As a result, it offers scope for quantitative prediction of microscopic and macroscopic experimental slip data based solely on molecular information. Our model also predicts scaling laws for the various slip parameters in the three regimes of surface coverage. These laws are in general agreement with previously reported scaling models and experimental data