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Boundary Curvature Effect on the Wrinkling of Thin Suspended Films

In this letter, we demonstrate a relation between the boundary curvature $κ$ and the wrinkle wavelength $λ$ of a thin suspended film under boundary confinement. Experiments are done with nanocrystalline diamond films of thickness $t \approx 184$~nm grown on glass substrates. By removing portions of the substrate after growth, suspended films with circular boundaries of radius $R$ ranging from approximately 30 to 811 $μ$m are made. Due to residual stresses, the portions of film attached to the substrate are of compressive prestrain $ε_0 \approx 11 \times 10^{-4}$ and the suspended portions of film are azimuthally wrinkled at their boundary. We find that $λ$ monotonically decreases with $κ$ and present a model predicting that $λ\propto t^{1/2}(ε_0 + ΔR κ)^{-1/4}$, where $ΔR$ denotes a penetration depth over which strain relaxes at a boundary. This relation is in agreement with our experiments and may be adapted to other systems such as plant leaves. Also, we establish a novel method for measuring residual compressive strain in thin films.