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

Abstract

The glass transition temperature ${T}_{g}$ and the temperature ${T}_{\ensuremath{\alpha}}$ corresponding to the peak in the dielectric loss due to the $\ensuremath{\alpha}$ 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 ${T}_{\ensuremath{\alpha}}$ was found to remain almost constant for $d>{d}_{\mathrm{c}}$ and to decrease drastically with decreasing d for $d<{d}_{\mathrm{c}}.$ Here, ${d}_{c}$ is a critical thickness dependent on molecular weight. The relaxation time ${\ensuremath{\tau}}_{\ensuremath{\alpha}}$ of the $\ensuremath{\alpha}$ 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 ${T}_{\ensuremath{\alpha}}.$ The relaxation function for the $\ensuremath{\alpha}$ process was obtained by using the observed frequency dependence of the peak profile of the dielectric loss. The exponent ${\ensuremath{\beta}}_{\mathrm{KWW}},$ which was obtained from the relaxation functions, decreases as thickness decreases. This suggests that the distribution of relaxation times for the $\ensuremath{\alpha}$ process broadens with decreasing thickness. The thickness dependence of ${T}_{g}$ is directly related to the distribution of relaxation times for the $\ensuremath{\alpha}$ 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.