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Cylindrically symmetric electrohydrodynamic patterning.

Paru Deshpande1, Leonard F Pease, Lei Chen

  • 1Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA. pad@princeton.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
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Strong electric fields induce concentric rings and other structures in thin polymer films through electrohydrodynamic patterning. A new cylindrical theory using Bessel functions accurately predicts ring spacing and formation rates, explaining self-assembly phenomena.

Area of Science:

  • Materials Science
  • Physics
  • Nanotechnology

Background:

  • Thin polymeric films subjected to strong electric fields can form cylindrically symmetric structures.
  • Electrohydrodynamic patterning, also known as lithographically induced self-assembly, is a key phenomenon in this area.
  • Previous studies have observed structures like pillars and holes, but concentric rings were less understood.

Purpose of the Study:

  • To experimentally form and theoretically explain the emergence of concentric rings in thin polymeric films under electric fields.
  • To develop a theoretical framework capable of describing various cylindrical structures formed by electrohydrodynamic patterning.
  • To investigate the relationship between film properties, electric fields, and the resulting self-assembled patterns.

Main Methods:

Related Experiment Videos

  • Fabrication of concentric rings using spin-coated poly(methyl methacrylate) films on silicon wafers.
  • Application of electric fields above the glass transition temperature to destabilize the film interface.
  • Development of a linear stability analysis in cylindrical coordinates using Bessel functions for radial dependence.
  • Experimental observation and measurement of ring formation, spacing, and width.

Main Results:

  • Concentric rings, with up to 10 fully formed rings, were successfully fabricated.
  • Ring-to-ring spacings and annular widths were found to be approximately constant, on the order of a micron.
  • The formation rate showed a temperature dependence consistent with the Williams-Landel-Ferry equation.
  • The cylindrical theory accurately predicted constant ring spacing, width, and growth rates, aligning with experimental data.
  • A secondary instability at higher temperatures led to ring segmentation into arcs or pillar arrays.

Conclusions:

  • The study presents a successful experimental and theoretical explanation for the formation of concentric rings in thin films under electric fields.
  • The developed cylindrical stability analysis, utilizing Bessel functions, provides a robust model for electrohydrodynamic patterning.
  • The findings contribute to the understanding of lithographically induced self-assembly and can be generalized to other symmetric structures like hexagonal patterns.