## 2 Materials and Methods
### Research Methodology  
The thickness of the layers was measured with a Dualscope MP40 by [PERSON], using the eddy-current method. 10 measurements were performed along the length of the sample and then the average value was calculated.  
A scanning microscope (SEM) was used to produce images of the nanomorphology of the Al\({}_{2}\)O\({}_{3}\) layer surfaces and the nanostructure of those layers from metallographic specimens. A magnification of 50,000\(\times\) was used for surface analysis, which allows observation of the nanopore distribution. The magnification applied to analyze the structure was 30,000\(\times\).  
Microscopic digital images were used for computer analysis of the oxide layer surfaces. The ImageJ 1.50i program was employed for the analysis. By applying appropriate procedures of computer image analysis, the stereological parameters of the surface were calculated. The nanoporosity surface share, the number of nanopores per unit area, and the average nanopore size were determined. Based on the data, histograms showing the distribution of nanopore surface area were made. The chemical composition of the oxide layers was also analyzed using an EDS analyzer.  
To determine the surface roughness of the layers, surface geometric structure (SGS) tests were performed using a Form Talysurf Series 2, 3D profiler (Taylor Hobson). The tests were conducted using a systematic scanning method. The surface of the layers was measured over an area of x = 2.2 mm; y = 2.2 mm with a sampling step \(\Delta\)x = 0.001 mm; \(\Delta\)y = 0.002 mm. The preparation procedure consisted of levelling the sample and removing artifacts using two-sided thresholding--Tp = 1%. Next, the samples were rotated within the range of 0-2\({}^{\circ}\) and trimmed to an area of x = 2 mm; y = 2 mm. The analysis included determination of the basic stereometric parameters from the amplitude group: _Sa_; _Sq_; _Sp_; _Sv_; _St_; _Ssk_; _Sk_; _Sz_.  
The contact angle of the surface was measured using four liquids. Two of the liquids were polar (water and glycerin) and two were non-polar (diiodomethane and \(\alpha\)-bromonaphthalene). The measurement consisted of applying 10 drops of liquid, each of 0.5 \(\upmu\)L, onto the surface of the tested sample. Next, images of each drop were taken with a camera. The computer software enabled measurement of the contact angle for each drop, and the smallest and largest contact angles were rejected, while the remaining eight were used to calculate the average value. The contact angle values of the surface were used to determine the surface free energy (SFE) using the Owens-Wendt method. The Owens-Wendt method is applied for both polar and non-polar liquids. The contact angles of glycerin as a polar liquid and of \(\alpha\)-bromonaphthalene as a non-polar (dispersive) liquid were used for the calculations. In the Owens-Wendt method, it is assumed that the SFE value is the sum of two components: dispersive \(\gamma_{\mathrm{s}}\)d and polar \(\gamma_{\mathrm{s}}\)P, and that there is an additive relationship between the two values:  
\[\gamma_{\mathrm{s}}=\gamma_{\mathrm{s}}\mathrm{d}+\gamma_{\mathrm{s}}\mathrm{P} \tag{1}\]  
where:  
\(\gamma_{\mathrm{s}}\)--surface free energy of a solid;  
\(\gamma_{\mathrm{s}}\)d--dispersive component of the surface free energy of the investigated material;  
\(\gamma_{\mathrm{s}}\)P--polar component of the surface free energy of the investigated material.