## 3 Results and Discussion
### Nanomechanical Properties of Electrospun PLLA Nanofibers
#### 3.4.3 Evaluation of the Viscoelastic Contribution  
Apart from the plastic deformation, there is another factor that hampers obtaining the true elastic modulus of a sample, i.e., the effect of viscoelasticity [50]. Such viscous response, in many cases, dominates over the elastic response and should be identified separately if we want to obtain a meaningful contact modulus value from the measurements. Unfortunately, a technique like peakforce QNM normally involves applying a contact mechanic model to the obtained quasi-static force-distance curves. Such models are only applicable under the assumption that the tip-sample interaction is linearly dependent on the cantilever deflection and, therefore, those models do not take into account the dependence on the tip velocity or, in other words, the viscous response. Therefore, we employed ImAFM which is a dynamic, multi-frequency, AFM-based measurement method. In this technique, the tip is driven and oscillated at two different frequencies that are close to the resonant frequency of the cantilever. The tip-surface interaction results in an intermodulation spectrum (a mixing product of frequencies) from which, by Fourier transformation, one can generate the dynamic force quadratures \(F_{I}\) and \(F_{Q}\) at each pixel. These force quadratures do not display force as a function of tip position but represent integrals of the force over a single oscillation cycle. The F\({}_{\rm I}\) curve shows the integrated force that is in phase with the cantilever motion and can be described as conservative force whereas F\({}_{\rm Q}\) shows the integrated force that is in phase with the velocity and is attributed to the dissipative force or energy lost during each tapping cycle of the cantilever. The \(F_{I}\) and \(F_{Q}\) can be considered as force curves in dynamic AFM and can be used to explain various tip-surface interactions.  
To validate the efficiency of the method, we first characterize a reference sample which is a polymer blend of poly(styrene) (PS) and low-density poly(ethylene) (LDPE) using the same tip that was used for PFQNM measurements. PS acts as the stiff matrix with a modulus of 2.5-2.8 GPa whereas LDPE acts as the soft viscous filler with an elastic modulus around 0.3 GPa. The ImAFM results of the polymer blends are shown in Figure S6 of the Supporting Information. The \(F_{I}\) and \(F_{Q}\) curves on PS and LDPE regions are completely different. The \(F_{I}\) value of the PS region displays a large negative value at large amplitude, meaning that the force is fundamentally repulsive and the \(F_{Q}\) value is significantly smaller. On the contrary, the \(F_{I}\) curve of LDPE shows positive values corresponding to a dominantly attractive force, even at maximum amplitude. Its \(F_{Q}\) curve also displays a sizable negative value. Finally, for the stiff and mostly elastic response of PS region, we can fit the DMT model to the slopes of \(F_{I}\) (A) to generate a map of the modulus from which we find a value for the PS region is about 2.5 GPa, i.e., fully consistent with the macroscopic measurements.  
After successfully calibrating with the reference sample, we analyzed the PLLA nanofibers with ImAFM. Figure 5 shows the \(F_{I}\) and \(F_{Q}\) curves of both as-prepared and annealed electrospun fibers. At small oscillation amplitudes, the tip is far away from the surface resulting in the zero values for both \(F_{I}\) and \(F_{Q}\). With the gradual increase of oscillating amplitude, the tip starts to touch and penetrate to the surface sample, reaching the largest value of \(F_{I}\) and \(F_{Q}\) at the maximum amplitude. It is clear that, in both cases, the \(F_{I}\) shows large negative values while smaller values are observed for \(F_{Q}\). It is important to note the absence of any hysteresis loop in the \(F_{I}\) curves of both as-spun and annealedelectrospun fibers meaning that their surface is completely recovered after each cycle, or in other words, a dominantly elastic response.