Heterogeneous nature of the dynamics and glass transition in thin polymer films

Recent experiments have demonstrated that the dynamics in liquids close to and below the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. We use here a model proposed recently for explaining these features, and show that the heterogeneous nature of the dynamics has important consequences when considering the dynamics of thin films. We show how the dominant relaxation time in a thin film is changed as compared to the bulk, as a function of the thickness, the interaction energy with the substrate, and the temperature. The corresponding time scales cover the so-called VFT (or WLF) regime and vary between 10 -8 s to 10 4 s typically. In the absence of interaction, our model allows for interpreting suspended films experiments, in the case of small polymers for which the data do not depend on the polymer weight. The interaction leads to an increase of $T_ g$ for an interaction per monomer of the order of the thermal energy T . This increase saturates at the value corresponding to strongly interacting films for adsorption energies slightly larger and still of order T . In particular, we predict that the $T_ g$ shift can be non-monotonous as a function of the film thickness, in the case of intermediate interaction strength.