University of Wisconsin Madison College of Engineering



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From Pillars and Rings to Infinite Arrays: Pattern Formation in Thin Polymer Films due to Electrohydrodynamic Instabilities

Lecture by William B. Russel
Department of Chemical Engineering
Princeton University


This year's BSL Lecture is dedicated to the memory of Warren E. Stewart, who passed away March 27, 2006


Monday, May 1, 2006
Room 1800 Engineering Hall
Lecture at 4:00 p.m.
Refreshments at 3:45 p.m.


An intriguing process, known in some parts as lithographically induced self-assembly (LISA), is initiated by positioning a template parallel to a flat silicon wafer that is coated with a thin polymeric film and then raising the temperature above the glass transition/melting temperature of the film. Electric fields, either natural or imposed, exert a force on the polymer–air interface, placing the film in either tension or compression. This static equilibrium is unstable to disturbances with wavelengths for which the electrostatic force overcomes the surface tension. Flow ensues, generating a pattern in the film with periodicity that generally reflects the characteristic length of the instability. The geometry of the pattern varies according to the nature of the mask, the ratio of the film thickness to the gap, and a number of other parameters. Examples include square or triangular arrays of pillars or concentric rings, depending on the topology of the mask. Under some conditions the inverse appears: circular holes in a continuous polymer film.


Our goal is to create a sound understanding of the mechanism to facilitate the conversion of these microstructures into nano-structures and from modest areas to wafer-scale coverage. The variety of patterns observed in experiments for polymers under both unpatterned and patterned masks stimulated theoretical and numerical analyses that define the role of a linear instability in setting the characteristic length scale and nonlinear effects in selecting the final pattern. In particular, the nonlinear regime involves interactions among different Fourier modes that favor the growth of hexagonal patterns under a featureless mask, in agreement with experimental observations and supported by numerical simulations based on the fully nonlinear model. Furthermore, simulations for longer times reveal several “kinetically stable structures” along the path to the thermodynamically stable state of minimum surface area. Patterns on the mask guide the patterns into conformity with the geometric shape and the spacing preferred by the instability. Finally, we exploit the simulations to design a mask capable of producing large areas of well-ordered patterns.


William B. Russel

William B. Russel

William B. Russel is the A.W. Marks '19 Professor in the Department of Chemical Engineering and Dean of the Graduate School at Princeton University. He joined the faculty at Princeton in 1974 after BA and MChE degrees from Rice University (where he also played baseball), a PhD from Stanford, and a NATO Postdoctoral Fellowship in the Department of Applied Mathematics and Theoretical Physics at Cambridge University. At Princeton he has served as chairman of chemical engineering and director of the Princeton Materials Institute and pursues research in the field of complex fluids. His research includes studies of the crystallization of colloidal dispersions (akin to the formation of opals) in microgravity aboard the Space Shuttle, theory and fabrication of micro-patterns in thin polymer films, and the drying and cracking of paint films. He is the author or coauthor of two books, the Dynamics of Colloidal Systems and Colloidal Dispersions. Sabbaticals have taken him to the Australian National University, the University of Wisconsin, Bristol University, Twente University, and Utrecht University.