Surface Dynamics of Polymer Films

The dynamics of supported polymer films were studied by probing the surface height fluctuations as a function of lateral length scale using x-ray photon correlation spectroscopy. Measurements were performed on polystyrene (PS) films of thicknesses varying from 84 to 333 nm at temperatures above the PS glass transition temperature. Within a range of wave vectors spanning ${10}^{-3}$ to ${10}^{-2}\mathrm{n}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$, good agreement is found between the measured surface dynamics and the theory of overdamped thermal capillary waves on thin films. Quantitatively, the data can be accounted for using the viscosity of bulk PS.

Figure 1

(a) Scheme of the experimental setup for XPCS in reflectivity geometry. (b) CCD image of time-averaged diffuse scattering. (c) Fit to capillary wave model for a sample of thickness 84 nm at $160°\mathrm{C}$. Axes are labeled with pixel numbers.

Figure 2

Autocorrelations obtained at four different in-plane wave vectors measured on a sample thickness of 84 nm at $160°\mathrm{C}$ (symbols), compared with single-exponential fits (lines). The time constant $\tau$ at each $q_{||}$ is also displayed.

Figure 3

(a) Measured time constant $\tau$ vs in-plane wave vector $q_{||}$ for the 177 nm-thick film at $150°\mathrm{C}$ (squares), $160°\mathrm{C}$ (circles), and $170°\mathrm{C}$ (triangles). (b) $\tau$ vs $q_{||}$ at $160°\mathrm{C}$ for films of thickness 84 nm (circles), 177 nm (triangles), and 333 nm (diamonds). (c) $\tau /h$ vs $q_{||}h$ for film thicknesses 84 nm (circles), 170, 177 nm (triangles), and 312.5, 318, 333 nm (diamonds). Lines represent least-squares fits based on Eq. (2).

Figure 4

(a) Viscosity of thin-film PS (diamonds) and bulk PS (crosses) as a function of temperature. (b) Comparison between the data (circles) and various model curves. The solid line corresponds to Eq. (2) and is also shown in Fig. 3c. The other two lines represent fits for inhomogeneous films according to the two-layer model described in the text. The total film thickness is 80 nm (dashed line, 1) and 20 nm (dotted line, 2), respectively. In both cases the viscosity of the high-mobility surface layer of thickness 10 nm is 10 times less than the measured viscosity given in (a) at $T=150°\mathrm{C}$.