Rubbery layer on polystyrene surface well below the glassy temperature

The dynamics of polymer surfaces is a controversial subject. Many experimental evidences support the existence of a surface mobile layer, while there are a few equally strong experimental evidences that contradict it. Here we show, through careful studies of the topological evolution of nanometer-size ridges and ditches on rubbed polystyrene surfaces, that there is indeed a surface rubbery layer whose mobility decreases rapidly with depth. The segments in the layer can only be displaced by a finite distance comparable to the depth. The temperature and depth dependence of the surface effective compliance is quantitatively determined. At tens of degrees below the bulk glass transition temperature the thickness of the surface rubbery layer is only a fraction of nanometer while the rest of the polymer sample remains frozen. Such surface mobile layer can qualitatively explain the seemingly contradictory behaviors of polymer surfaces and resolve most of the controversy among the results obtained from different experimental approaches.