## 3 Results and Discussion
### Nanomechanical Properties of Electrospun PLLA Nanofibers
#### 3.4.2 Data Processing and Relevant Model  
For data analysis, the traditional way to extract contact modulus values requires determination of a contact point, which can be used for calculating the deformation as well as fitting the data (the contact point-based method). Determining the contact point is usually straightforward in the case of a rigid, non-deformable sample but becomes more difficult for soft, adhesive samples (e.g., polymeric materials). For example, there is no sharp contact in both cases of PLLA nanofibers, instead, we observe a force distance curve with a rounded bottom (compared to straight lines for more rigid samples) indicating that most probably the tip was gliding onto the sample surface. In addition, the signature of the adhesion force in the unloading/retraction part of the force curve also makes it more complicated to evaluate the contact point (Figure S5 of Supporting Information). Therefore, the most reliable method, in this case, is the linearized model which does not require the assignment of the contact point for the modulus calculation. For example, the linearized equation for the DMT model to fit the slope of the unloading curves can be described as:  
\[(F)^{2/3}=\left(\frac{4}{3}\cdot\frac{E}{(1-\
u^{2})}\cdot\sqrt{R_{Eff}} \right)^{2/3}\cdot\delta \tag{2}\]  
where \(F\) is the total applied force to the tip: \(F=F_{peakforce}+F_{adh}\) (nN), \(E\) is the fitted DMT's modulus of the sample (GPa), \(R_{Eff}\) is the effective tip radius (nm), \(\
u\) is the sample's Poisson ratio and \(\delta\) is the sample deformation (nm). In this study, \(\
u\) is taken as 0.3 for both pristine and thermal-treated samples. \(F_{adh}\) and \(\delta\) are experiment-dependent parameters that can be measured in real-time simultaneously with the topography.  
Furthermore, the choice of which relevant contact mechanic models (Hertz, Sneddon, DMT, or JKR) should be applied is also of great importance. The first model, Sneddon, can only be applied to cases in which the tip has a conical shape and when the indentation depth is large. In the case of PLLA nanofibers, the tip had a spherical shape with a radius of 29 nm while the indentation depths were around 2-4 nm. Therefore, the Sneddon model cannot be used. It is also clear that the Hertz model should be ruled out due to the presence of significant adhesion response in the force curves. The selection between DMT and JKR models is, however, more delicate. [PERSON] has proven that the Hertz, DMT and JKR models are all special cases of a more generalized contact mechanics model [48]. DMT only considers the long-range surface forces outside of the contact area while JKR assumes that adhesion forces are actually short-range surface forces within the contact area. In order to know if whether DMT is appropriate for the PLLA nanofibers system, we estimate the Maugis parameter, \(\lambda\), which can be written as [49]:  
\[\lambda=\frac{2.06}{D_{0}}.\sqrt[3]{\frac{R_{Eff}W_{adht}^{2}}{\pi E^{2}}} \tag{3}\]  
where \(D_{0}\) is the interatomic spacing describing the system, which is often taken as 0.165 nm. \(W_{adht}\) is the tip-sample adhesion energy per unit area: \(W_{adht}=F_{adht}/2\pi R_{Eff}\) and \(E\) is the Young modulus of the tip-sample system. If \(\lambda\) approaches 0, the DMT model is a good fit whereas if \(\lambda\) approaches infinity, the JKR model should be used. Based on the Equation (3), the value of the Maugis parameter for the as-spun and annealed samples are found to be in the range of 2-5, which indicates that the DMT model is indeed a suitable choice to describe the system in our case.