Near-Surface Nanomechanics of Medical-Grade PEEK Measured by Atomic Force Microscopy

The PEEK samples were medical-grade sheets (10 × 10 × 6 mm height; Direct Plastics Ltd., Sheffield, UK) with semimachined surfaces, as described previously [43]. AFM measurements were performed by a NT-MDT (Moscow, Russia) system equipped with an upright optical microscope. NSG10 and NSG30 tips (NT-MDT, Moscow, Russia) with resonant frequencies in the range of 140–390 kHz were used. Topographies were taken at a 256 × 256-pixel resolution and acquired in tapping mode of operation. The cantilever stiffness k was measured according to Sader [35], a procedure implemented into the acquisition software (NOVA, MT-MDT, Moscow, Russia). The cantilever deflection sensitivity was calibrated from a set of indentation curves previously obtained under hard-contact regime on a clean and nanometrically flat silica slice (~80 GPa in stiffness); such procedure prevents from damages the tips actually used. PEEK slices were mounted on the sample stage and characterized both topographically and by extraction of force curves. Before and after mapping, the integrity of the tips was checked via z-axis calibration on a TGS1 calibration grating (NT-MDT, Moscow, Russia; grid TGZ1 with a height of (21 ± 1) nm). Two-dimensional arrays of F-d curves (1000 points each) were acquired at six non-overlapped 5 × 5 µm² areas on 20 × 20 grids. Note that the spatial resolution of the mapping is equal to the distance between the indents. In this work, a distance of 5000 nm/20 = 250 nm was set according to theoretical considerations [44,45] and to reduce the acquisition time of a single map (<1 h). The loading/unloading rate was fixed at 500 nms⁻¹ for all indentation tests. Several survey curves were taken before mapping to verify that h_max fell in the range suitable to the model used (see later).

Figure 1a illustrates a typical loading–unloading or force–distance (F-d) curve, with indication of the adhesion force F_ad (typically, <10 nN in our measurements) and contact point. The calibration operation converts the F-d into the corresponding F-h curve (Figure 1b), where h is the penetration depth. Referring to the areas in colors in Figure 1b, η_el = S_unload/S_load for each curve was calculated; for a totally plastic sample, η_el = 0, while for a totally elastic sample, η_el = 1 [35].

According to the Hertz theory, in case of a spherical indenter of radius R, purely elastic deformation and negligible adhesion force F_ad, the Young’s modulus E of an isotropic, homogeneous sample will follow the well-known h^−3/2 dependence [35,44]. Following a previous work of this group [41], in this study E is calculated by the modified Hertz formula introduced by Kontomaris [44,45], which accounts for indentations comparable to or higher than the dimension of the indenter (h ≥ R). This modified Hertz formula differs from the original by a factor depending on h/R; if h < R, the original Hertz formula is obtained. If h >> R, linear dependence is obtained [45].

Indentation maps obtained by AFM were processed using an assembly of different algorithms implemented as a Python module [46] that could be adapted to a user’s computational needs, as described previously [43]. In brief, the software processes the F-d curves, aligning them and separating loading and unloading curves to generate F-h curves. Then, the indentation modulus E was calculated applying the modified Hertz formula of Section 2.2 to the loading part of the F-h curve. The Poisson’s ratio of PEEK (ν = 0.38) and the radius R enters into calculation of E. Following previous studies [33,43], an uncertainty of 10% on these quantities was propagated. Then, the uncertainty ΔE and the correlation coefficient of the fitting r² were computed. Afterward, to assess the correctness and the consistency of the data, rejection criteria based on r² and ΔE/E can be tailored according to the given experimental context. In the present study, the conditions r² > 0.95 and ΔE/E < 30% were required; this caused -in average- rejection of <3% of the acquired curves.

PEEK indentations by cantilevers with different stiffness produced, in general, different mechanical responses. Thus, cantilevers with different k were used while η_el was continuously monitored during data acquisition to ensure that the condition η_el ~ 1 (elastic behavior) was fulfilled. Furthermore, an uncertainty of 10–15% on F¯¯¯max�¯��� was determined by statistical analysis; such statistical fluctuations are due to instrumental and local contact instabilities. For each map, η¯el�¯�� and the corresponding F¯¯¯max�¯��� were extracted as an average. Assuming homogeneous mechanical response of the surface, the six η¯el�¯��(F¯¯¯max)�¯���) values were plotted in Figure 2a at increasing F¯¯¯max�¯���. Note that elastic deformations were produced up to a load of ~450 nN, which represents the transition point for plastic deformation in this work (η_el~0.6). For the sake of clarity, two representative F-h curves corresponding to the lowest and highest loads (the first and last points of Figure 2a, respectively), are shown (Figure 2b). Note that the h_max values (6.3 nm and 21.8 nm respectively) fall in the range of validity of the modified Hertz model used to fit the data (Section 2.2). On the other hand, the effective penetration depth h_f is less than 1 nm for the left curve, while exceeds 12 nm for the right one. The larger h_f value implies a lower fitting quality with higher deformations, as only elastic deformations were assumed, as discussed in the following.

Sample areas 5 × 5 µm² large were considered for the AFM analysis, based on a preliminary survey of the surface and previous studies [34,40]. In Figure 3a, a topographic image (roughness 15.6 nm, peak-to-peak height 184 nm) is shown along with the corresponding maps of E, η_el and h_max. (Figure 3b–d). By way of example, two features 1 and 2 are evidenced in the topography. These features are separated by a step height of (20 ± 5) nm along the z-axis. At the same positions, two distinct regions or “islands” of localized moduli at ~0.9 GPa can be observed (Figure 3b). Significantly, both the regions exhibited purely elastic response (η_el~0.95), with the same deformation h_max~12 nm (Figure 3c,d). Although similar correspondences between topographies and maps can be observed likewise at different positions, they are—in general- quite elusive. This is the case of Figure 4 (roughness 17.5 nm, peak-to-peak height 166 nm), where several small (<1 µm) islands were detected; remarkably, these islands appear prevalently elastic in nature and correspond to the smallest h_max within the image. Nevertheless, the topographic step heights measured in correspondence of the islands are too small (<5–10 nm) to be significant in relation to the image roughness.

For quantitative analysis, statistical histogram plots of moduli were extracted from each map, as in Figure 5. To account for the presence of two distinct peaks in the distributions, two-Gaussian functions were used to fit the data, corresponding to lower and higher distributions of moduli with calculated peaks at E₁ and E₂, respectively. The results obtained for the six regions considered are summarized in Table 1 at increasing loads.