Investigation of Transition States in Bulk and Freestanding Film Polymer Glasses

We have performed transition state searches on the potential energy landscape for bulk and freestanding film polymer glasses and identified connected minima. An analysis of the displacements between minima shows that the sites that undergo the greatest displacement are highly localized in space for both the bulk and the thin-film systems studied. In the case of the thin film, the clusters originate at the surface and penetrate into the center of the film thereby coupling the relaxation in the center of the film to the mobile surface layer. Furthermore, the energy barriers between minima are lower in the thin film than in the bulk system. These findings can rationalize the experimentally observed depression of the glass transition temperature in freestanding polymer films.

Figure 1

(a) Probability of finding an energy barrier less than $\Delta U_{\mathrm{barr}}$. The open symbols are for the film and the filled symbols are for the bulk system. The dashed lines are for the transition to a saddle point from the original minimum, and the solid lines are for the transition from the saddle point to the new minimum. (b) The inset shows the correlation between mean square displacement (${\overline{r}}^2$) between the minima and saddle point and corresponding energy barriers for the film. (◇, from $M_1$ to the transition state; ⊳, from $M_2$ to transition state). The values have been scaled to lie between 0 and 1.

Figure 2

Weighted mean square displacement of fast sites between the connected minima (filled circles) and between transition state and original minimum (open circles), as a function of distance into the film. The dashed and dotted horizontal lines are the corresponding average values for the bulk system.

Figure 3

Probability of a cluster of size $N_c$ in the freestanding film (squares) and bulk (diamonds).

Figure 4

Typical clusters of fast sites for (a) freestanding film and (b) bulk system. The fast sites are shown as spheres while the other sites are shown as circles. The arrows indicate the magnitude and direction of displacement on the fast sites between connected minima.