## 3 Results
Based on this change, we can see that the color in the loss tangent shows a similar result compared to previous case. However, when the excitation frequency is changed to the second eigenmode frequency, the loss tangent value is decreased (the colors in Figure 3b get darker). This trend continues when we increased the oscillation amplitude as well. This is an indication that the tip is penetrating less into the surface and therefore dissipating less energy. Based on this study, it can be concluded that if one is after loss tangent measurements of soft samples, measuring with the higher eigenmode frequencies while controlling the oscillation amplitudes can be advantageous. This can be extremely important for imaging sensitive samples, such as biological cells. In order to have a reliable characterization technique by AFM, a common approach is studying the contrast in the observable aspects on a sample where a portion of the sample can be considered as reference material. Figure 4 provides this set for this study. The sample shown in Figure 4 is a thin film of PS polymer that is intentionally spin-coated on a silicon wafer at high humidity to create the islands shown. The high humidity has caused some portions of the silicon wafer to be exposed during the measurements as a reference material that has very high stiffness and very low viscoelasticity. Therefore, we should expect a theoretical value of tan \(\delta\) for those portions to be close to zero. The left column in Figure 4 provides the height (Figure 4a) and loss tangent image (Figure 4c) using the first eigenmode frequency while the right column in Figure 4 represents the same measurements using the second eigenmode frequency. Although there is no obvious difference in topography measurements (Figure 4a,b), there is a major difference in loss tangent images shown in Figure 4c,d. The average loss tangent value is higher on the sample when imaged by the first eigenmode frequency compared to second eigenmode frequency. It should be noted both measurements are done on the same area of the same sample; therefore, one would expect identical results. However, it is clear that the second eigenmode measurements are showing less dissipation. With that said, if the aim is to distinguish the two different samples, imaging with the first eigenmode might be better since it can provide higher contrast. However, that comes with the disadvantage of penetrating more into the surface. If a sample is soft, imaging with the first eigenmode with large oscillation amplitudes can cause surface damages. On the other hand, although the second eigenmode stiffness is higher than the first one, due to lower oscillation amplitudes, imaging with the second eigenmode can be advantageous since it has been shown it can provide less dissipation of energy and have less penetration of the surface. Figure 3: PTFE loss tangent AFM study: (**a**) topography image and (**b**) tan \(\delta\) image. From bottom to top, the excitation frequency and free oscillation amplitudes are as follows: f\({}_{1}\) = 72 kHz and A 1 = 50 nm, f\({}_{1}\) = 72 kHz and A\({}_{2}\) = 100 nm, f\({}_{2}\) = 460 kHz and A\({}_{3}\) = 1.5 nm, and f\({}_{2}\) = 460 kHz and A\({}_{4}\) = 3.5 nm. The scale bar is 1 μm.