Modulus, Confinement, and Temperature Effects on Surface Capillary Wave Dynamics in Bilayer Polymer Films Near the Glass Transition

We report relaxation times ($\tau$) for surface capillary waves on 27–127 nm polystyrene (PS) top layers in bilayer films using x-ray photon correlation spectroscopy. At $\sim 10°\mathrm{C}$ above the PS glass transition temperature ($T_g$), $\tau$ tracks with underlayer modulus, being significantly smaller on softer substrates at low in-plane scattering wave vector. Relative to capillary wave theory, we also report stiffening behavior upon nanoconfinement of the PS layers. At PS $T_g+40°\mathrm{C}$, both effects become negligible. We demonstrate how neighboring polymer domains impact dynamics over substantial length scales.

Figure 1

Normalized autocorrelation function decays for (a) thin PS layers on various substrates ($q\sim 0.006{\mathrm{nm}}^{-1}$) at $110°\mathrm{C}$ and (b) ultrathin PS layers on the same substrates ($q\sim 0.014{\mathrm{nm}}^{-1}$) at $110°\mathrm{C}$. Curves are single exponential decay fits.

Figure 2

(a) Capillary wave relaxation times at $140°\mathrm{C}$ for PS on silicon and P4VP. (b) Relaxation times normalized by film thickness result in data overlap at $140°\mathrm{C}$ ($T_g+40°\mathrm{C}$).

Figure 3

Capillary wave relaxation times for (a) thin PS layers and (b) ultrathin PS layers on silicon, P4VP, cross-linked PDMS, and PiBMA substrates measured at $110°\mathrm{C}$ [51]. Substrate moduli measured by DMA at $110°\mathrm{C}$ were 1800, 5.4, and 1.3 MPa for P4VP, PDMS, and PiBMA, respectively. Gray areas correspond to surface relaxation times exceeding 40 000 s [47].

Figure 4

Capillary wave relaxation times normalized by PS layer thickness for thin (115 nm) and ultrathin (29 nm) PS layers on various substrates measured at $110°\mathrm{C}$. In the absence of confinement or substrate modulus effects, the $\tau /h$ values should overlap for thin and ultrathin films.