Deformation of an asymmetric thin film

Jun Geng (耿 君) and Jonathan V. Selinger
Phys. Rev. E 86, 036602 – Published 12 September 2012

Abstract

Experiments have investigated shape changes of polymer films induced by asymmetric swelling by a chemical vapor. Inspired by recent work on the shaping of elastic sheets by non-Euclidean metrics [Y. Klein, E. Efrati, and E. Sharon, Science 315, 1116 (2007)], we represent the effect of chemical vapors by a change in the target metric tensor. In this problem, unlike that earlier work, the target metric is asymmetric between the two sides of the film. Changing this metric induces a curvature of the film, which may curve into a partial cylinder or a partial sphere. We calculate the elastic energy for each of these shapes and show that the sphere is favored for films smaller than a critical size, which depends on the film thickness, while the cylinder is favored for larger films.

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  • Received 2 November 2011

DOI:https://doi.org/10.1103/PhysRevE.86.036602

©2012 American Physical Society

Authors & Affiliations

Jun Geng (耿 君) and Jonathan V. Selinger*

  • Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA

  • *jselinge@kent.edu

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Issue

Vol. 86, Iss. 3 — September 2012

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