Cylindrically symmetric electrohydrodynamic patterning

Abstract

Cylindrically symmetric structures such as concentric rings and rosettes arise out of thin polymeric films subjected to strong electric fields. Experiments that formed concentric rings and theory capable of explaining these and other cylindrical structures are presented. These rings represent an additional member of a class of structures, including pillars and holes, formed by electrohydrodynamic patterning of thin films, occasionally referred to as lithographically induced self-assembly. Fabrication of a set of concentric rings begins by spin coating a thin poly(methyl methacrylate) film onto a silicon wafer. A mask is superimposed parallel to the film leaving a similarly thin air gap. Electric fields, acting in opposition to surface tension, destabilize the free interface when raised above the glass transition temperature. Central pillars nucleate under small cylindrical protrusions patterned on the mask. Rings then emerge sequentially, with larger systems having as many as 10 fully formed rings. Ring-to-ring spacings and annular widths, typically on the order of a micron, are approximately constant within a concentric cluster. The formation rate is proportional to the viscosity and, consequently, has the expected Williams-Landel-Ferry dependence on temperature. In light of these developments we have undertaken a linear stability analysis in cylindrical coordinates to describe these rings and ringlike structures. The salient feature of this analysis is the use of perturbations that incorporate their radial dependence in terms of Bessel functions as opposed to the traditional sinusoids of Cartesian coordinates. The theory predicts approximately constant ring-to-ring spacings, constant annular widths, and growth rates that agree with experiment. A secondary instability is observed at higher temperatures, which causes the rings to segment into arcs or pillar arrays. The cylindrical theory may be generalized to describe hexagonal pillar/hole packing, gratings, and rosettes with the first being of particular importance given the ubiquitous observation of hexagonal packing. The perturbation analysis presented here is relevant to any system with cylindrical symmetry, for which the radial dependence can be described in terms of Bessel functions.

Optically induced electrohydrodynamic instability-based micro-patterning of fluidic thin films

“…The randomly generated nucleation sites limit the applicability of this process for patterning polymers over large areas (Lei et al 2003). In order to pattern pillars into other shapes and structures, such as arrays of rings (Deshpande et al 2004), squares (Deshpande et al 2001), rectangles, triangles (Chou and Zhuang 1999;Wu and Russel 2009;Lei et al 2005), or multiscale patterns over large areas, it is necessary to use electrodes with corresponding patterns of protrusions which can generate a heterogeneous electric field. However, the electrode patterns in these aforementioned methods require a complex fabrication process that after which cannot be changed.…”

“…For example, various groups have used an electric field which is perpendicular (or normal) to an air/polymer interface (Deshpande et al 2004;Schaffer et al 2001), or a polymer/ polymer interface (Lin et al 2001), or an ionic liquid/ polymer interface (Lau and Russel 2011), or air/polymer/ polymer interfaces (Morariu et al 2003;Reddy et al 2012) to create micro-patterns. The interfacial stresses, however, can also be generated by a tangential electric field (Roberts 2009;Melcher 1974).…”

Numerical studies of electrically induced pattern formation by coupling liquid dielectrophoresis and two‐phase flow

“…The template can be either a flat one (i.e. non-patterned), generating an array of periodic pillars [1,4], or a periodically patterned one in an attempt to duplicate various microstructures on the polymer, such as gratings and grids [1,[5][6][7], which coincide with the template pattern, as desired.…”

Charge driven, electrohydrodynamic patterning of thin films

“…4 One method towards achieving arrays of pillars, 5,6 gratings, 7,8 and sets of concentric rings 9 is the electrohydrodynamic patterning as explored by Schäffer et al 8 and Chou and Zhuang ͓see Fig. 1͑a͔͒.…”