$T_{g}$ depression and segmental dynamics of polystyrene thin films

The glass transition temperature ($T_{g})$ of polymer thin films has been a subject of intense debate in the last two decades. (Pseudo)thermodynamic determinations, such as calorimetry and ellipsometry, generally suggest a significant depression of $T_{g}$, whereas the dynamic $T_{g}$, measured by techniques such broadband dielectric spectroscopy and AC-calorimetry directly probing the molecular mobility, is found to be unchanged. The present study provides a resolution to this controversy on polystyrene by showing that the experimental relaxation time obtained from (pseudo)thermodynamic techniques, and the intrinsic molecular relaxation time can be rescaled on a master curve, only accounting for the thickness of the film. Furthermore the thickness and cooling rate dependence of the (pseudo)thermodynamic $T_{g}$ is quantitatively captured by the free volume holes diffusion model. In this framework, the $T_{g}$ depression emerges from the ability of thinner films to maintain equilibrium, due to the shortest distance free volume holes have to diffuse to the polymer interface.