Glass transitions and dynamics in thin polymer films: Dielectric relaxation of thin films of polystyrene

The glass transition temperature $T_g$ and the temperature $T_{\alpha }$ corresponding to the peak in the dielectric loss due to the $\alpha$ process have been simultaneously determined as functions of film thickness d through dielectric measurements for polystyrene thin films supported on glass substrate. The dielectric loss peaks have also been investigated as functions of frequency for a given temperature. A decrease in $T_g$ was observed with decreasing film thickness, while $T_{\alpha }$ was found to remain almost constant for $d>\mathrm{}{d}_{\mathrm{c}}$ and to decrease drastically with decreasing d for $d<\mathrm{}{d}_{\mathrm{c}}.$ Here, $d_c$ is a critical thickness dependent on molecular weight. The relaxation time ${\tau }_{\alpha }$ of the $\alpha$ process, which was measured as the frequency at which the dielectric loss realizes its peak value at a given temperature, was found to have a d dependence similar to that of $T_{\alpha }.$ The relaxation function for the $\alpha$ process was obtained by using the observed frequency dependence of the peak profile of the dielectric loss. The exponent ${\beta }_{\mathrm{KWW}},$ which was obtained from the relaxation functions, decreases as thickness decreases. This suggests that the distribution of relaxation times for the $\alpha$ process broadens with decreasing thickness. The thickness dependence of $T_g$ is directly related to the distribution of relaxation times for the $\alpha$ process, not to the relaxation time itself. The value of the thermal expansion coefficient normal to the film surface was found to increase with decreasing film thickness below $T_g,$ but to decrease with decreasing film thickness above $T_g.$ These experimental results are discussed in the context of a three-layer model in which within thin films there are three layers with different mobilities and glass transition temperatures.