Three-dimensional model of electrostatically induced pattern formation in thin polymer films

Abstract

Experiments have shown that a thin polymer film subjected to an electrostatic field may lose stability at the polymer-air interface, leading to uniform self-organized pillars emerging out of the film surface. This paper presents a three-dimensional model to account for this behavior. Attention is focused on a fully nonlinear evolution simulation to reveal the dynamic process from an early perturbation to late structure formation. Energetic components involving the interface energy and dielectric effect and the kinetics of coupled viscous flow and diffusion are incorporated into a phase field framework. The semi-implicit Fourier spectral method and preconditioned biconjugate-gradient method are applied for high efficiency and numerical stability. The simulations reveal rich dynamics of the pattern formation process, and show that the kinetic constraint of the substrate can essentially limit structure coarsening. The pillar size is insensitive to the film thickness while the distance between pillars and the growth rate are significantly affected. The study also suggests an approach to control structural formation in thin films with a designed electric field.