Quantification issues in the identification of nanoscale regions of homopolymers using modulus measurement via AFM nanoindentation

Since 1989, AFMs have been used to map the nanomechanical properties of surfaces using measurements such as force-distance curves. Quantification of the force and elastic parameters are critical to the nanomechanical analysis and positive identification of materials at the nanoscale, as well as for assessing behaviour at surfaces. In recent years, there have been AFM papers publishing “quantitative” values for the indentation modulus, however, many involved large uncertainties arising from the lack of calibration of key components, the use of manufacturers' nominal values for these components or the use of incorrect models. This paper addresses the quantification issues in modulus measurement at surfaces for homogeneous materials using force-distance curves and how to do this with sufficient accuracy to identify materials at the nanoscale. We review the available theory and describe two routes to quantitative modulus measurement using both the AFM on its own and the AFM combined with a nanoindenter. The first involves the direct measurement of modulus using a fully calibrated instrument and allows depth analysis. The second uses indirect measurement through calibration by reference materials of known reduced modulus. For depth analysis by this second route, these reference moduli need to be known as a function of depth. We show that, using the second route, an unknown polymer may be analysed using the nanoindenter, its modulus determined and, providing the moduli of the polymers to be identified or distinguished differ by more than 20%, identified with 95% confidence. We recommend that users evaluate a set of reference samples using a traceable nanoindenter via the first route, and then use these to calibrate the AFM by the second route for identification of nano-regions using the AFM.