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
American Physical Society (APS)
Geng, J., & Selinger, J. (2012). Deformation of an asymmetric thin film. Physical Review E. https://doi.org/10.1103/physreve.86.036602
Geng, Jun, and Jonathan Selinger. 2012. “Deformation of an Asymmetric Thin Film”. Physical Review E. https://doi.org/10.1103/physreve.86.036602.
Geng, J., and J. Selinger. Deformation of an Asymmetric Thin Film. Physical Review E, 12 Sept. 2012, doi:10.1103/physreve.86.036602.