The motion of confined polymers is measured experimentally between parallel, atomically smooth solid surfaces, separated by 2 nm. In particular, the kinetics of intercalation of monodispersed polystyrene in alkylammonium modified mica-type silicates were studied using X-ray diffraction. The kinetics of the neat polymers and their functionalized derivatives were measured as functions of molecular weight, extent of functionalization, and silicate surface organic modification, at various temperatures. Selective corroborative studies were also performed using in-situ small-angle neutron scattering (SANS). The kinetic data are interpreted in terms of an effective diffusion coefficient (D-eff) of the polymer, which undergoes a dramatic decrease with stronger silicate surface-polymer interaction. This interaction is varied by either changing the silicate surface modification or by increasing the extent of functionalization of the polystyrene chains. Furthermore, the diffusion coefficient exhibits an inverse dependence on chain length (N), i.e., D-eff proportional to N-1, for chains up to 900 000 molecular weight.