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.
Physical Review E
Copyright 2012 American Physical Society. Available on publisher's site at http://dx.doi.org/10.1103/PhysRevE.86.036602.
Geng, Jun; Selinger, Jonathan V. (2012). Deformation of an Asymmetric Thin Film. Physical Review E 86(3) doi: 10.1103/PhysRevE.86.036602. Retrieved from https://oaks.kent.edu/cpippubs/79