Capillary-driven flow as a probe of enhanced surface mobility in glassy polymer films

We present the use of a novel experimental arrangement [\textit{McGraw et al. Soft Matter }\textbf{\textit{7}}\textit{, 7832 (2011)] }to directly distinguish the dynamical behavior and heterogeneity of polymer thin films above and below the glass transition temperature T$_{\mathrm{g}}$. In particular, by monitoring the capillary-driven evolution of a stepped thin polystyrene film over a temperature range encompassing the bulk T$_{\mathrm{g}}$ value, we find evidence suggesting enhanced surface mobility. Furthermore, by varying the initial aspect ratio of the sample we can examine the heterogeneity of the sample dynamics. The results of these experiments above T$_{\mathrm{g}}$ are consistent with homogenous viscous flow [\textit{McGraw et al. PRL }\textbf{\textit{109}}\textit{, 128303 (2012)],} whereas those below T$_{\mathrm{g}}$ indicate a localization of the flow over a thin surface layer only. We thus develop a linear thin film equation for superficial viscous flows, which is analogous to the surface diffusion model, and for which exact analytical solutions are known and in good agreement with the present experimental data.