# Engineering and Clinical Study of Surface Geometry of Clear Aligners at the Nanoscale
## 3 Results and Discussion
### Statistical and Mechanical Parameters  
Table 1 reports the basic statistical measures of surface variations of worn and new (reference) Invisalign aligners under investigation derived from AFM images. This includes the rms roughness Sq (deviation of the height samples from the mean plane), texture anisotropy ratio Str (directionality of surface patterns--unity indicates perfectly isotropic surfaces, whereas zero indicates highly anisotropic surfaces) and surface development ratio Str (the surplus of the surface triangulated using the height samples over the plane with the same edges). On the other hand, Table 1 also provides the results of the nanomechanical mapping of the pseudo-Young's modulus Y and tip-surface adhesion force Fadh taken in the PF-QNM mode together with the topography data. Apart from that, all the numbers presented therein are supplied with the results of the test of normality using the Shapiro-Wilk method, with a confidence level of \(\alpha=0.05\)[21]. The results of the S-W test shown in Table 1 allow us to reject the null hypothesis that the data tested are normally distributed in almost all cases, even though the data from a single measurement nearly passed the normality test (see Figure 2C). Only the surface development ratio Sdr in worn aligners and the texture anisotropy ratio Str in the new aligners (marked with gray colors) provide enough evidence that the null hypothesis cannot be rejected. Therefore, to find out whether or not there is a significant difference between worn and new aligners on any of the studied levels (topographical and mechanical), an additional non-parametric Mann-Whitney U test was carried out. The obtained results are summarized in Table 2, whereas the graphical comparison of these results is shown in Figure 4. Table 2 reveals that all surface roughness parameters (Sq, Str  
Figure 4: (**A**) Histogram of the height samples of the Invisalign® aligner (blue bars) and their corresponding AFC (solid red line) obtained from the AFM image, (**B**) functional areal parameters of the surface texture from the AFC: thicknesses of the three main layers: peaks (Spk), core (Sk) and valleys (Svk) with the corresponding material ratios (Smrk1 and Smrk2), (**C**) functional volumetric parameters from the AFC (the volumes of specific areas per surface unit at the respective material share levels): peak volume (Vmp), core volume (Vmc) and valley void volume (Vvv). and Sdr) do not change significantly upon daily use of the aligners, while their ranges of variability decrease. In terms of mechanical parameters, Table 2 reveals that adhesion force Fadh remains the same regardless of the daily use of the aligners. However, the pseudo-Young's modulus (marked with gray colors) becomes statistically lower as its median value decreases from 1010 MPa to 917 MPa in new and worn aligners, respectively; that is, within ca. 10% compared to the reference value. The lower elasticity of the material might be due to the chemical transformation occurring in the structure of the aligner material, caused by contact with food and saliva. Alternatively, this could be also due to the growth of a new layer on the surface of the aligners--a biofilm that produces its own enzymes. On the other hand, the unaffected adhesion force might prove that both the tip-surface contact area and capillary layer remain the same, which is supported by the similar behavior of the roughness parameters. All of this strongly suggests that daily use provides no significant abrasive wear to the surface under study, and that the life span of the aligners is limited by the chemical stability of the material rather than specific geometry of residual surface. Plots in Figure 5 not only show the trends in statistical measures of the parameters under investigation, but also reveal how the points corresponding to single measurements are spread around.