Parametric Study on Electric Field-Induced Micro-/Nanopatterns in Thin Polymer Films

Electric field-induced micro-/nanopatterns in thin polymer films, sometimes referred as electrohydrodynamic patterning, is a promising technique to fabricate micro-/nanostructures. Extensive attention has been attracted because of its advantages in microcontact (easy demolding) and low cost. Although considerable work has been done on this technique, including both experimental and theoretical ones, there still appears a requirement for understanding the mechanism of electrohydrodynamic patterning. Thus, we systematically studied the effect of different parameters on electrohydrodynamic patterning with a numerical phase field model. Previous researchers usually employed lubrication approximation (i.e., long-wave approximation) to simplify the numerical model. However, this approximation would lose its validity if the structure height is on the same scale or larger than the wavelength, which occurs in most cases. Thus, we abandoned the lubrication approximation and solved the full governing equations for fluid flow and electric field. In this model, the deformation of polymer film is described by the phase field model. As to the electric field, the leaky dielectric model is adopted in which both electrical permittivity and conductivity are considered. The fluid flow together with electric field is coupled together in the framework of phase field. By this model, the effect of physical parameters, such as external voltage, template structure height, and polymer conductivity, is studied in detail. After that, the governing equations are nondimesionalized to analyze the relationship between different parameters. A dimensionless parameter, electrical Reynolds number E_R, is defined, for which, a large value would simplify the electric field to perfect dielectric model and a small value leads it to steady leaky model. These findings and results may enhance our understanding of electrohydrodynamic patterning and may be a meaningful guide for experiments.