Elasticity of rubber-like materials measured by AFM nanoindentation

We exploit the force spectroscopy capabilities of the atomic force microscope in characterizing the local elasticity of rubber-like materials. Extraction of elastic properties from force curves usually relies on the linear theory pioneered by Hertz. While the Hertzian force-indentation relationships have been shown to be accurate in modeling the contact mechanics at sufficiently shallow indentation depths, the linear deformation regime of the probed material is exceeded in many practical applications of nanoindentation. In this article, a simple, nonlinear force-indentation equation based on the Mooney-Rivlin model is derived and used to fit data from the indentation of lightly crosslinked poly(vinyl alcohol) gels in equilibrium with water. The extracted values of Young's modulus show good agreement with those obtained by both macroscopic compression testing and by fitting truncated portions of the force curves with the Hertz equation