Quantitative imaging of nanoscale mechanical properties using hybrid nanoindentation and force modulation

In this article, we present a quantitative stiffness imaging technique and demonstrate its use to directly map the dynamic mechanical properties of materials with nanometer-scale lateral resolution. For the experiments, we use a “hybrid” nanoindenter, coupling depth-sensing nanoindentation with scanning probe imaging capabilities. Force modulation electronics have been added, enhancing instrument sensitivity and enabling measurements of time dependent materials properties (e.g., loss modulus and damping coefficient) not readily obtained with quasi-static indentation techniques. Tip–sample interaction stiffness images are acquired by superimposing a sinusoidal force (∼1 μN) onto the quasi-static imaging force (1.5–2 μN), and recording the displacement amplitude and phase as the surface is scanned. Combining a dynamic model of the indenter (having known mass, damping coefficient, spring stiffness, resonance frequency, and modulation frequency) with the response of the tip–surface interaction, creates maps of complex stiffness. We demonstrate the use of this approach to obtain quantitative storage and loss stiffness images of a fiber-epoxy composite, as well as directly determine the loss and storage moduli from the images using Hertzian contact mechanics. Moduli differences as small as 20% were resolved in the images at loads two orders of magnitude lower than with indentation, and were consistent with measurements made using conventional quasi-static depth-sensing indentation techniques.