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Polymers in Flatland : Self-Similarity and Nanorheology
The study of ultra-thin polymer nanofilms is a rich and productive field for applied mathematics, fundamental physics, physiology and engineering. It has been enlightened by the recent results on dewetting, nanoindentation, electrostatic instabilities and micro- bubbles. We report here on a novel and simple technique based on capillary leveling of a thin polystyrene stepped film far above the glass transition temperature [1]. We present as well the analytical [2] and numerical [3] tools that allow one to precisely understand the experimental profiles in various conditions. In particular, we study the self-similar in- termediate asymptotics of the solutions and we describe how they provide a direct and accurate viscosity probe for polymer materials and viscous flows in general. Finally, we show how those solutions can give quantitative insights on fundamental questions such as : the effect of confinement on the macromolecular mobility, the slip condition at the substrate in hydrodynamics, the spreading of a droplet onto a precursor film [4], or the evolution of the superficial mobility through the glass transition.
[1] McGraw, Salez, Bäumchen, Raphaël, Dalnoki-Veress, PRL 109 128303 (2012)
[2] Salez, McGraw, Bäumchen, Dalnoki-Veress, Raphaël, PoF in press (2012)
[3] Salez, McGraw, Cormier, Bäumchen, Dalnoki-Veress, Raphaël, EPJE in press (2012)
[4] Cormier, McGraw, Salez, Bäumchen, Raphaël, Dalnoki-Veress, PRL 109 154501 (2012)