Hierarchical line-defect patterns in wrinkled surfaces

We demonstrate a novel approach for controlling the formation of line-defects in wrinkling patterns by introducing step-like changes in the Young's modulus of elastomeric substrates supporting thin, stiff layers. Wrinkles are formed upon treating the poly(dimethylsiloxane) (PDMS) substrates by UV/Ozone (UVO) exposure in a uniaxially stretched state and subsequent relaxation. Line defects such as minutiae known from fingerprints are a typical feature in wrinkling patterns. The position where these defects occur is random for homogenous substrate elasticity and film thickness. However, we show that they can be predetermined by using PDMS substrates consisting of areas with different cross-linking densities. While changing the cross-linking density is well known to influence the wrinkling wavelength, we use this parameter in this study to force defect formation. The defect formation is monitored in situ using light microscopy and the mechanical parameters/film thicknesses are determined using imaging AFM indentation measurements. Thus the observed wrinkle-wavelengths can be compared to theoretical predictions. We study the density and morphology of defects for different changes in elasticity and compare our findings with theoretical considerations based on a generalized Swift-Hohenberg-equation to simply emulate the observed pattern-formation process, finding good agreement. The fact that for suitable changes in elasticity, well-ordered defect patterns are observed is discussed with respect to formation of hierarchical structures for applications in optics and nanotechnology.