Fig. 1.

(A–C) The glass transition temperatures $T_g$ of thin polymer films, defined from the $T$ dependence of (A) film height and (B) potential energy, and (C) a fixed relaxation time [$\tau \left(T_g\right)=10^3$] plotted as a function of film thickness $h$ for polymer–substrate interaction strengths $\epsilon \hspace{0.17em}=\hspace{0.17em}$0.1, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 2.0, 2.5, and 3.0 (bottom to top). On the right side of the vertical axis, we normalize each definition of $T_g$ by the corresponding glass transition temperature of the bulk polymer $T_g^{\mathrm{B}\mathrm{u}\mathrm{l}\mathrm{k}}$. For A, we use $T_g^{\mathrm{B}\mathrm{u}\mathrm{l}\mathrm{k}}$ defined by the $T$ dependence of density on heating, the nearest equivalent to film thickness. For both A and B, we average $T_g$ obtained from at least three independent runs and show the representative SE of the $T_g$ estimates. For extremely thin films $h\le 5$, polymers do not adhere to the substrate for weak substrate interactions ($\epsilon =$ 0.1, 0.25), and thus we exclude $T_g$ values for those films. The lines are a guide for the eye and come from a fit to a model for the thickness dependence of $T_g$ (ref. 37 and SI Appendix, section IV).