Quantifying Strain via Buckling Instabilities in Surface Modified Polymer Brushes

A compressive strain applied to bilayer films (e.g. thin film adhered to a thick substrate) can lead to buckled or wrinkled morphologies, which has many important applications in stretchable electronics, anti-counterfeit technology, and high-precision micro and nano-metrology. A number of buckling-based metrology methods have been developed to quantify the residual stress and viscoelastic properties of polymer thin films. However, in some systems (e.g. solvent-induced swelling or thermal strain), the compressive strain is unknown or difficult to measure. We present a quantitative method of measuring the compressive strain of wrinkled polymer films and coatings with knowledge of the "skin" thickness, wrinkle wavelength, and wrinkle amplitude. The derived analytical expression is validated with a well-studied model system, e.g., stiff, thin film (PS) bonded to a thick, compliant substrate (PDMS). After validation, we use our expression to quantify the applied swelling strain of previously reported wrinkled poly(styrene-alt-maleic anhydride) brush surfaces. Finally, the applied strain is used to rationalize the observed persistence length of aligned wrinkles created during atomic force microscopy (AFM) lithography and subsequent solvent exposure.