# Optimization of Mechanical and Setting Properties in Acrylic Bone Cements Added with Graphene Oxide
## 3 Results and Discussion
### Mechanical Properties  
#### 3.2.1 Compressive Properties  
The models proposed for the variables compressive strength and compressive modulus met the assumption of normality on errors with significance levels greater than 10%. The variance analysis presented in Table S3 showed that in both properties, the sum of squares (SS) of the effects studied is greater than the sum of squares of the errors, evidenced by R\({}^{2}\) values of 96.26% and 96.6% for the strength and modulus, respectively. These results indicate a more outstanding contribution from the controlled effects (studied factors) than the random effects (they are random variables, and they are all those effects that could not be controlled or are not controllable and will go into error). * Compressive strength  
Figure 6 shows that the compressive strength is maximum when the sonication time is 5 h with BPO/solid ratio of 2.0% and GO/liquid ratio of 0.3%, and decreases when sonication time drops to 1 h, BPO/solid ratio increases to 2.5% and GO/liquid ratio is 0.5% in the formulation. All the formulations studied presented compression strength values higher than the minimum established in ISO 5833-02 of 70 MPa [51]. The decrease in the compressive strength with the increase in the BPO content can be related to the fact that the higher amount of free radicals generated by BPO during the polymerization reaction activates more monomers that act as nucleation sites for the growth of the polymer chain,  
Figure 5: Interaction plot between the effect sonication time vs. BPO/solid ratio and sonication time vs. GO/liquid ratio for the variable \(t_{set}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Sonication Time**} & \multicolumn{1}{c}{**Mean**} & \multicolumn{1}{c}{**Grouping *} & \multicolumn{1}{c}{**Sonication Time**} & \multicolumn{1}{c}{**Mean**} & \multicolumn{1}{c}{**Grouping *} \\ \multicolumn{1}{c}{*} & **BPO/Solid Ratio** & **(s)** & & **\multicolumn{1}{c}{**Grouping *} & \multicolumn{1}{c}{**’GO/Liquid ratio**} & \multicolumn{1}{c}{**(s)**} & \multicolumn{1}{c}{**Grouping *} \\ \hline
1-2.0 & 413 & A & & 1-0.5 & 482 & A & \\ \hline
1-2.5 & 393 & B & 5-0.5 & 460 & A & \\
5-2.0 & 292 & B & & 5-0.3 & 425 & B & \\
5-2.5 & 386 & B & 1-0.3 & 420 & B & \\  & & & 1-0.2 & 400 & B & C & \\  & & & 1-0.1 & 377 & C & D \\  & & & 5-0.2 &causing lower molecular weights that directly influence the mechanical behavior of the cement [5]. Some researchers reported an association between the sonication time, the degree of dispersion, and the thickness of the GO particle [44]. Therefore, the degree of mechanical reinforcement is generated in the matrix [62]. This higher dispersion in the matrix favored the compression strength of the studied ABCs [38]. The presence of GO provides a high surface area [63] that tends and increases the chemical interaction between the OH groups of GO and OCH\({}_{3}\) and oxygenated groups of PMMA, improving the interfacial adhesion and the strength of the cements [36; 64]. On the other hand, GO contents above 0.3 wt.% aggregate and decrease the mechanical properties of the cement [3; 37]. Because the transfer of mechanical forces in arthroplasty is achieved through the cement interface, it is necessary to provide good mechanical performance in the cement [63]. The results obtained for verifying the hypothesis tests on the interactions and main effects (Table S3) indicate that in the strength and the compressive modulus, the third and second-order interactions were significant at levels significantly lower than 0.007 (\(p\)-value). The analysis of the multiple comparison tests (Tukey's test) is presented in Table 4.  
Table 4 shows the comparisons between all treatments for compressive strength. Each of the six treatments of group A has the same statistical effect on the compressive strength, and all of them presented values higher than 100 MPa.