Glass transition of star-shaped thin polymer films

We show that the glass transition temperatures, $T_{\mathrm{g}}$, of thin polystyrene (PS) films, supported by oxidized silicon substrates (SiOx), depends on functionality, $f$, and the degree of polymerization of the arm, N$_{\mathrm{arm}}$, of the macromolecule. The $T_{\mathrm{g}}$s of star-shaped PS films with thickness H$=$30nm, $T_{\mathrm{g}}$(30nm) with $f$ as high as 64 were investigated. The $T_{\mathrm{g}}$(30nm) of linear PS thin films, is less than the average bulk $T_{\mathrm{g}}$, $T_{\mathrm{g}}$(bulk). For molecules of N$_{\mathrm{arm}}$ about100, the $T_{\mathrm{g}}$(30nm) of a macromolecule with $f=$3 was equal to that of a linear PS. However, the $T_{\mathrm{g}}$(30nm) increased with increasing $f$, reaching a maximum of at $f=$8 where $T_{\mathrm{g}}$(30nm) was higher than $T_{\mathrm{g}}$(bulk). For larger values of $f$, T$_{\mathrm{g}}$ (30nm) decreased monotonically with increasing $f$ and for $f=$64the$ T_{\mathrm{g}}$(30nm) became comparable to $T_{\mathrm{g}}$(bulk). The magnitude of this effect is weaker for much larger values of N$_{\mathrm{arm}}$. We rationalized these observations in term of two competing entropic: the increasing entropic attraction of the macromolecules to interfaces, with increasing $f$, and an increasing intermolecular entropic repulsion of these macromolecules with increasing f, and/or decreasing N$_{\mathrm{arm}}$.