## 3 Results and Discussion
### Calculation of the Interfacial Tension by Contact Angle Measurements  
Table 4 summarizes the contact angle values measured for compression molded plates of the high-density polyethylene with and without acrylic acid grafting in the virgin and processed state. For the powder, the contact angle values shown in Table 4 are those measured by [PERSON] et al. [37] for pure zirconia, tetragonal yttria stabilized zirconia and zirconia with 5 mol% of yttria. According to the results of [PERSON] et al. [47] and [PERSON] et al. [48] with HDPE surface-grafted with acrylic acid, there is a large decrease in the contact angle of water onto the HDPE, even with low contents of AA in the surface [48]. Despite 5 mol% of AA being used in our study, only a slight difference exists between the values for AAHDPE00 and for HDPE00 (Table 4). Such disagreement might arise from the different distribution of the acrylic acid in the samples here employed [49]. For [PERSON] et al. [47] and [PERSON] et al. [48], all the AA was grafted and concentrated on the surface of the polymer. In our case, the commercial AAHPDE was used to produce the plates employed in the measurements. Therefore, after kneading and pressing, the polar and hydrophilic AA might be in the bulk of the compression molded plates rather than in the surface, and the polar chains might also be oriented towards the bulk and not to the surface. Using the contact angle values and Equation (1), the surface free energy values reported in Table 4 were obtained. The surface energy and its components were higher for the AAHDPE00 than for the HDPE00. Due to the small differences in the contact angle values, the difference in the \(\sigma^{P}\) of both materials is not as pronounced as expected [47]. Nevertheless, when comparing the values of both components, the \(\sigma^{P}\) of AAHDPE00 is 62% higher than the one of HDPE00, whereas the \(\sigma^{D}\) difference is only of 2%. Thus, it can be stated that the polarity of the AAHDPE00 is higher than the one of HDPE00. Following this, the interfacial tension between the AAHDPE00 and HDPE00 with the different types of zirconia was calculated with Equation (2) and with the surface energy values from Table 4. The interfacial tension is dependent on the surface energy and the polarity of the materials in contact, and it is inversely proportional to the adhesion between those materials [38; 50]. In Table 5, the interfacial tension values between the different material combinations are shown. The interfacial tension of the AAHDPE00 with the three types of zirconia was lower than for the HDPE00. Consequently, a better adhesion to the zirconia can be expected for the AAHDPE than for the HDPE. The increase in the adhesion for the grafted polymer is in agreement with the trend observed in the MD simulation, which showed the increase in the binding energy with the increase in the acrylic acid in the polymer and the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Contact Angle (\(\circ\))**} & \multicolumn{2}{c}{**Surface Energy (mN/m)**} \\ \hline
**Material** & \(\theta_{w}\) & \(\theta_{D}\) & \(\sigma^{D}\) & \(\sigma^{P}\) & \(\sigma^{T}\) \\ \hline
**AAHDPE00** & 97 & 53 & 32.6 & 0.55 & 33.14 \\
**HDPE00** & 99.3 & 54.2 & 31.9 & 0.34 & 32.24 \\
**ZrO\({}_{2}\)** & 71.8 & 40.9 & 39.15 & 6.75 & 45.9 \\
**Tetragonal Y\({}_{2}\)O\({}_{3}\)** & & 47 & 35.93 & 6.67 & 42.6 \\
**stabilized ZrO\({}_{2}\)** & & 48 & 40 & 39.61 & 9.14 & 48.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Contact angle with water (\(\theta_{w}\) and diiodomethane (\(\theta_{D}\)) measured for the polymers and values for zirconia as reported by [PERSON] et al. [37]. The precision of all the contact angle measurements was within \(\pm 2^{\circ}\). Polar (\(\sigma^{P}\)) and disperse (\(\sigma^{D}\)) components of the surface energy (\(\sigma^{T}\)) calculated with Equation (1).