Evolving Thin Polymer Film Driven by Electrostatic Field
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Evolving Thin Polymer Film Driven by Electrostatic Field Dongchoul Kim and Wei Lu Department of Mechanical Engineering, University of Michigan Ann Arbor, MI 48109, USA 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 dynamic model that accounts for the behavior. Attention is focused on the interplay of the thermodynamic forces and the kinetic processes. The coupled diffusion, viscous flow, and dielectric effect are incorporated into a phase field framework. The semi-implicit Fourier spectral method and the preconditioned biconjugategradient method are applied in the simulations for high efficiency and numerical stability. Numerical simulations reveal rich dynamics of the pattern formation process. INTRODUCTION Recent experimental findings show that a flat interface between two dielectric media may lose stability in an electrostatic field and self-assemble into morphological patterns [1-5]. The phenomenon is also known as the electrohydrodynamic instability. The fundamental mechanism has been explained by two competing energetics: surface energy and electrostatic energy. Linear or weakly nonlinear perturbation analyses under the lubrication approximation of a viscous flow have been performed [6-8]. These studies have provided valuable insights into the instability mechanism and the system behavior at early stage. However, the critical dynamic process that links the early perturbation and the final structure is still unknown. The nonlinear evolution regime may significantly change the system behavior. Experiments have shown that diffusion can be another important mass transport mechanism in a thin polymer film [9-11], which needs to be considered in addition to viscous flow to provide more accurate prediction. A thorough consideration of these issues suggests that the phenomenon may have a complex nature and involve rich dynamics. Its potential application for nanofabrication relies on an effective computational approach to simulate and understand the entire self-assembly process. This paper presents a three dimensional dynamic model that considers coupled diffusion, viscous flow, surface energy and dielectric effect. The evolving surface and multiple energetics and kinetics pose a computational challenge. This is addressed by modeling the system with a
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diffuse interface framework, where an interface is represented by a thin continuous transition region. For the computational work, we propose a semi-implicit Fourier spectral method and the preconditioned biconjugate-gradient method, which leads to high efficiency and numerical stability. MODEL Consider a thin polymer film on a substrate subjected to an electrostatic field. The field is generated by two electrodes parallel to the film, one above the polymer surface and the other underneath the substrate. When heated, the polymer fil
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