Thickness Dependence of the Young's Modulus of Polymer Thin Films

The Young's modulus of polymer thin films was measured from bulk films that are micrometers in thickness down to films having a thickness of ∼6 nm, which is less than the radius of gyration, R_g. A simple, noninvasive technique in the same geometry, i.e., the wrinkling of a free-floating film on a water surface with a droplet of water on the surface of the film, was used to determine the modulus over this very large range of film thicknesses. Unlike a solid substrate, there are no in-plane stresses exerted on the film by the underlying liquid substrate except at the boundary of the film. Using recent theoretical developments in the treatment of wrinkling phenomena, we extracted the film modulus from measurements of the wrinkle length. The Young's modulus does not show any systematic change with film thickness, from the thickest bulk films down to films with a thickness of ∼R_g for both PS and PMMA, although a slight increase of the Young's modulus was found for the thinnest sub-R_g thick PS film.