Three-dimensional analysis of spontaneous surface instability and pattern formation of thin soft films

Abstract

For soft films with a thickness on the order of microns or nanometers, the long-range surface∕interface interaction can be sufficiently strong to induce their surface instability or even rupture. By using the bifurcation theory of elasticity, we here present a three-dimensional theoretical model to study the spontaneous surface instability of a soft elastic thin film supported by a rigid substrate. By accounting for the competition of van der Waals interaction energy with elastic strain energy and surface energy, we obtain the analytical solutions for the critical conditions of three-dimensional surface morphology instability. The effects of surface energy, thickness, and elastic properties of the film on the characteristic wavelength of surface wrinkling are examined. It is found that the characteristic wavelength of the deformation bifurcation mode depends on the film thickness via an exponential relation, with the power index in the range of 0.75–1.0, which mainly depends on the ratio between the surface energy and shear modulus of the film but not on the nature of the surface∕interface interaction. Furthermore, it is shown that the interface condition between the film and the substrate significantly influences the critical condition of surface bifurcation. The theoretical solution proves to be a good agreement with the corresponding experiment results.