Evidence for Viscoelastic Effects in Surface Capillary Waves of Molten Polymer Films

The surface dynamics of supported ultrathin polystyrene films with thickness comparable to the radius of gyration were investigated by surface sensitive x-ray photon correlation spectroscopy. We show for the first time that the conventional model of capillary waves on a viscous liquid has to be modified to include the effects of a shear modulus in order to explain both static and dynamic scattering data from ultrathin molten polymer films.

Figure 1

Transverse diffuse scattering at $q_z=0.2{\AA }^{-1}$ for PS ($123k$) films with thickness $2R_g$ and $4R_g$ at $195°\mathrm{C}$. Solid lines represent the fits described in the text, and vertical dash-dotted lines indicate the low wave vector cutoffs from the fitting for two films, respectively, $q_{l,c}=4.51$ and $1.14\times {10}^{-4}{\AA }^{-1}$. The upper inset shows the in-plane scattering geometry. The lower inset shows $\mu$ versus $M_W$ for $2R_g$ films at $195°\mathrm{C}$.

Figure 2

$g_2$ functions obtained from PS ($123k$) films with thickness (a) $4R_g$, (b) $2R_g$ at $195°\mathrm{C}$ at wave vector $5.4\times {10}^{-4}{\AA }^{-1}$ (○), $7.7\times {10}^{-4}{\AA }^{-1}$ (◊) . Solid lines are best single-exponential fits described in the text, with fitted $\tau$ values labeled. For clarity the curves are shifted vertically.

Figure 3

Measured time constant $\tau$ versus in-plane wave vector $q_{\parallel }$ for $2R_g$ films with molecular weight (a) $123\mathrm{kg}/\mathrm{mol}$ and (b) $400\mathrm{kg}/\mathrm{mol}$. Solids lines and dashed lines are fits to viscoelastic [Eq. (2)] and viscous [Eq. (3)] models, respectively.

Figure 4

Viscosity (◊) as a function of molecular weight for (a) $2R_g$ films at $185°\mathrm{C}$ and (b) $4R_g$ films at $176°\mathrm{C}$. Lines are power-law fits with slopes labeled underneath. Viscosity values for PS bulk (+) are taken from Ref. 25.