  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.
