Practical loss tangent imaging with amplitude-modulated atomic force microscopy

Abstract

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<tan δ<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.

Fast, High Resolution, and Wide Modulus Range Nanomechanical Mapping with Bimodal Tapping Mode

“…A notable example of both the sensitivity and range of this technique is shown in Figure 3d where a 50:50 Sn/Pb alloy solder shows a pattern of softer and stiffer regions in the modulus channel that is not visible in topography (topography not shown; see Ref. 6). Often observed in optical and scanning electron micrographs, 29 this pattern is typical of Sn/Pb solder and is associated with softer, Pb-rich and stiffer, Sn-rich regions of solder.…”

“…1,2 A significant drawback of AM-AFM, which drives the cantilever at a single frequency, is its difficulty in quantifying sample mechanical properties.AM-AFM can only provide the ratio of storage to loss modulus, because the phase response is affected by both conservative and dissipative interactions. [3][4][5][6] Roughly a decade ago, it was recognized that simultaneously exciting higher resonance(s) of the cantilever provides additional information regarding the tip-sample interactions. 7-11 One…”

Time-resolved nanomechanics of a single cell under the depolymerization of the cytoskeleton

“…29,36 This parameter represents the ratio between the energy dissipated and the energy stored in one cycle of the oscillation. 44 The loss tangent avoids the estimation of the tip radius. However, this parameter has not been a straightforward link to the mechanical properties of a cell.…”

Local viscoelastic response of direct and indirect dental restorative composites measured by AFM

“…It should be pointed out that the viscous dissipation at the tip-sample interface may be affected not only by the sample properties but also by the environmental conditions (humidity of ambient air) as well as by surface contaminants. As a consequence, it is known that the loss tangent values measured by AM-FM can be considerably overestimated, of a factor up to one order of magnitude 17,27) . Nevertheless, the relative ranking of the 8 Dent Mater J 2018; : -materials in the same conditions (i.e.…”

“…AM-FM mode is based on a single-pass, during which the cantilever is dithered at two different resonance frequencies, namely the fundamental one in air, f 1,air, same as in standard Tapping mode, and a higher harmonic, in our case the second mode for AC160TS, which is at f 2,air~6.2 f1,air 16) . The amplitude of oscillation at the lower frequency is used in an AM feedback loop to track the surface and to obtain the loss tangent tanδ 17) . The phase of oscillation at the higher resonance frequency enters an FM feedback loop, which adjusts the frequency to keep the phase at 90° (i.e.…”