Experimental investigation of the glass transition of polystyrene thin films in a broad frequency range

In this study, we investigate the α process of a polystyrene thin film using inelastic neutron scattering (INS), dielectric relaxation spectroscopy (DRS), and thermal expansion spectroscopy (TES). The DRS and TES measurements exhibited a decrease in glass transition temperature ($T_{\mathrm{g}}$) with film thickness. On the other hand, an increase in $T_{\mathrm{g}}$ was observed in INS studies. In order to interpret this contradiction, we investigated the temperature dependence of the peak frequency ($f_{\mathrm{m}}$) of the α process probed by DRS and TES. The experiments revealed an increase in the peak frequency ($f_{\mathrm{m}}$) with decreasing film thickness in the frequency region. This observation is consistent with the observed decrease in $T_{\mathrm{g}}$ with thickness. Interestingly, the increase in $T_{\mathrm{g}}$ with film thickness was confirmed by fitting the temperature dependence measurements of the peak frequency with the Vogel-Fulcher-Tammann equation, within the frequency region probed by INS. The discrepancy between INS and DRS or TES descriptions of the α process is likely to be attributed to a decrease in the apparent activation energy with film thickness and reduced mobility, due to the impenetrable wall effect.

Figure 1

Thickness dependence of thermal $T_{\mathrm{g}}$ values obtained from DRS, ellipsometry and INS with energy resolution of 0.8 μeV.

Figure 2

Temperature dependence of $\langle u^2\rangle$ measured with 0.8-μeV energy resolution for the bulk (red circles), and for film thicknesses of 100 nm (blue circles), 40 nm (green circles), and 20 nm (yellow circles). Solid arrows pointing downwards indicate the $T_{\mathrm{g}}$ value determined from INS measurements.

Figure 3

(a) Frequency dependence of the imaginary part of the complex capacitance (dielectric loss) for 18-nm thin PS at 386 K (red circles), 390 K (green circles), 394 K (yellow circles), 398 K (black circles), and 401 K (blue circles). Solid curves correspond to fits with the Havriliak-Negami equation. (b) Peak frequency of dielectric loss due to the α process as an inverse function of temperature for PS thin films with thicknesses of 18 nm (pink circles), 25 nm (blue circles), 62 nm (green circles), and 408 nm (pink circles), obtained through a combination of TES (filled symbol) and DRS (open symbol) methods. The solid curves with the same color as the corresponding symbols represent fits with VFT equation.

Figure 4

Energy resolution as a function of $T_{\mathrm{g}}$ for bulk polymer (red circles) and for films with thicknesses of 100 nm (blue circles), 40 nm (green circles), and 20 nm (yellow circles).

Figure 5

(a) Temperature dependence of $\langle u^2\rangle$ of bulk. First 30 data points were selected for glassy state, and the rest were selected for molten state. (b) Temperature dependence of $\langle u^2\rangle$ of bulk. First 27 data points were selected for glassy state, and the rest were selected for molten state. (c) Temperature dependence of $\langle u^2\rangle$ of bulk. First 24 data points were selected for glassy state, and the rest were selected for molten state.

Figure 6

Temperature dependence of total ${\chi }^2$ for bulk (a), for 100 nm thick (b), for 40 nm thick (c), and for 20 nm thick films. The dashed arrows correspond to the smallest total ${\chi }^2$ value among the temperature range examined.