(186aa) Coarsening Dynamics of the Electrohydrodynamic Instability In Thin Polymer Films

The polymer-air interface is unstable during annealing when subject to an electric field applied normal to it. Hexagonal arrays of polymer pillars generally evolve with a periodic spacing ranging from 800 nm to 50 microns, depending on the properties of the polymer, the voltage applied, and the film thickness. Our numerical simulations, however, indicate that those microstructures are themselves unstable at longer time simulation (corresponding to annealing time in experiments). Therefore, we performed experiments on thin films of polydimethylsiloxane with a series of viscosities and film thicknesses at room temperature. Microscopic observations clearly show three distinct stages of the nonlinear dynamics. In the first stage, the average size of pillars increased slowly due to occasional merging between neighboring pillars, while the overall pattern remained almost unchanged. Most coarsening took place during the faster second stage, characterized by a power-law relationship between the average pillar size and time. In the final stage, coalescence became much slower presumably because the ultra thin residual layer between pillars rendered transport of polymer more difficult. The effect of fill ratio on the coarsening dynamics is also significant.

This phenomenon, in morphology, resembles coarsening in spinodal decomposition of a binary mixture and dewetting of thin liquid films due to van der Waals forces. However, the mechanism differs qualitatively due to the significant effect of Maxwell stresses and geometric confinement on the disjoining pressure, which leads to quantitatively different coarsening laws. We have employed two different methods to derive scaling laws for the second and third stages of coarsening in one dimension. For the second stage where pillars are still connected by a significantly thick residual layer, we performed a linear stability analysis for near-equilibrium periodic pillars with separations equal to or larger than the most unstable wavelength. The maximal growth rates of disturbances provide a power law relationship between the size of pillars and time. For the third stage in which the pillars are connected by an ultra thin film, we reduced the partial differential equation governing the interface asymptotically to a set of ordinary differential equations for the evolution of the pillars. From this, a logarithmic scaling law is obtained, which is consistent with experimental observations of a much slower coarsening in the third stage.