Clarifying the controversy of the Tg depression in polystyrene thin films

The glass transition temperature ($T_g$) of polymer thin films has been a subject of controversy in the last two decades. (Pseudo)thermodynamic determinations of $T_g$ generally suggest a significant depression, whereas the molecular mobility is found to be unchanged. The present study clarifies this apparent controversy by assuming that the $T_g$ in thin films is determined not only by the molecular mobility but also by the thickness of the film. This hypothesis is supported by the analysis of literature results on polystyrene thin films showing that the $T_g$ dependence on the cooling rate obtained on samples with different thicknesses can be rescaled onto a master curve. The thickness dependence of $T_g$ is quantitatively captured by an equilibration mechanism based on free volume holes diffusion. This dependence emerges from the ability of thinner films to maintain equilibrium, due to the shorter distance free volume holes have to diffuse to the polymer interface, the molecular motion determining the diffusion coefficient being thickness independent.