The thermal expansion behavior of polystyrene $\left(\mathrm{PS}\right)$ thin films was investigated using x-ray reflectivity, focusing on ultrathin films below $10\mathrm{nm}$. It was found that the glass transition temperature $T_{\mathrm{g}}$ decreases with thickness as reported by many researchers while it is almost independent of thickness and constant at $354\mathrm{K}$ for films below $\sim 10\mathrm{nm}$. The thickness dependence of $T_{\mathrm{g}}$ was well reproduced by a two-layer model consisting of a mobile surface layer with $T_{\mathrm{g}}$ of $354.5\mathrm{K}$ and a bulklike layer with $T_{\mathrm{g}}$ of $373\mathrm{K}\left(=\mathrm{bulk}{T}_g\right)$, suggesting that the so-called immobile dead layer near the substrate is negligible or very thin in this system. This surface $T_{\mathrm{g}}$ of $354\mathrm{K}$ was confirmed by the relaxation of surface roughness of as-deposited films at about $354\mathrm{K}$. It was also found that the thermal expansivity decreases with thickness in the glassy state as well as in the molten state while the reduction is smaller in the molten state.

• Received 16 November 2003

DOI:https://doi.org/10.1103/PhysRevE.69.061803