Measuring the modulus of soft polymer networks via a buckling-based metrology

We present a new method for measuring the modulus of soft polymer networks (E < 10 MPa). This metrology utilizes compression-induced buckling of a sensor film applied to the surface of the specimen, where the periodic buckling wavelength, assessed rapidly by laser light diffraction or optical microscopy, yields the modulus of the network specimen. To guide the development of this new technique, we use classical mechanical analysis to calculate the sensitivity of the critical strain and resulting wavelength of the buckling instability to the modulus and thickness of the sensor film as well as the modulus of the soft material being probed. Experimental validation of our technique employed a series of model cross-linked poly(dimethylsiloxane) elastomers. To further demonstrate the versatility of this method, we measure the moduli of a set of pertinent biomaterials, i.e., cross-linked 2-hydroxyethyl methacrylate ( HEMA) hydrogels. Using a hydrogel substrate possessing a gradient in the cross-link density, we also show how this metrology can be used to map spatial differences and heterogeneity in modulus within a specimen.