Practical loss tangent imaging with amplitude-modulated atomic force microscopy

<jats:p>Amplitude-modulated (AM) atomic force microscopy (AFM), also known as tapping or AC mode, is a proven, reliable, and gentle imaging method with widespread applications. Previously, the contrast in AM-AFM has been difficult to quantify. AFM loss tangent imaging is a recently introduced technique that recasts AM mode phase imaging into a single term tan δ that includes both the dissipated and stored energy of the tip-sample interaction. It promises fast, versatile mapping of variations in near-surface viscoelastic properties. However, experiments to date have generally obtained values larger than expected for the viscoelastic loss tangent of materials. Here, we explore and discuss several practical considerations for AFM loss tangent imaging experiments. A frequent limitation to tapping in air is Brownian (thermal) motion of the cantilever. This fundamental noise source limits the accuracy of loss tangent estimation to approximately 0.01&lt;tan δ&lt;5 in air. In addition, surface effects including squeeze film damping, adhesion, and plastic deformation can contribute in a manner consistent with experimentally observed overestimations. For squeeze film damping, we demonstrate a calibration technique that removes this effect at every pixel. Finally, temperature-dependent imaging in a two-component polymeric film demonstrates that this technique can identify temperature-dependent phase transitions, even in the presence of such non-ideal interactions. These results help understand the limits and opportunities not only of this particular technique but also of AM mode with phase imaging in general.</jats:p>