Deformation of an asymmetric thin film

TL;DR

This paper models how asymmetric swelling in polymer films causes shape changes, predicting curvature and stability of different shapes based on size and thickness, inspired by non-Euclidean geometry principles.

Contribution

It introduces a model for asymmetric swelling effects using an asymmetric target metric tensor, extending previous work on elastic sheet shaping by non-Euclidean metrics.

Findings

Smaller films favor spherical shapes due to energy minimization.

Larger films tend to form cylindrical shapes.

Critical size depends on film thickness.

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 be curvature 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.