Glass transition temperature of (ultra-)thin polymer films.

The glass transition temperature of confined and free-standing polymer films of varying thickness is studied by extended molecular dynamics simulations of bead-spring chains. The results are connected to the statistical properties of the polymers in the films, where the chain lengths range from short, unentangled to highly entangled. For confined films, perfect scaling of the thickness-dependent end-to-end distance and radius of gyrations normalized to their bulk values in the directions parallel and perpendicular to the surfaces is obtained. In particular, the reduced end-to-end distance in the perpendicular direction is very well described by an extended Silberberg model. For bulk polymer melts, the relation between the chain length and Tg follows the Fox-Flory equation. For films, no further confinement induced chain length effect is observed. Tg decreases and is well described by Keddie's formula, where the reduction is more pronounced for free-standing films. It is shown that Tg begins to deviate from bulk Tg at the characteristic film thickness, where the average bond orientation becomes anisotropic and the entanglement density decreases.