On the Equivalence of Glass Transition Temperatures In Polymer Nanocomposites and Polymer Thin Films

Motivated by recent experiments, we examine within a percolation model whether there is a quantitative equivalence in the glass transition temperatures ($T_g$) of polymer thin films and polymer nanocomposites (PNCs). Our results indicate that while the qualitative behaviors of these systems are similar, a quantitative equivalence cannot be established in general. However, we propose a phenomenological scaling collapse of our results which suggests a simple framework by which the results of the thin films may be used to quantitatively predict the properties of PNCs.