Optimization of Mechanical and Setting Properties in Acrylic Bone Cements Added with Graphene Oxide

: The extended use of acrylic bone cements (ABC) in orthopedics presents some disadvan-tages related to the generation of high temperatures during methyl methacrylate polymerization, thermal tissue necrosis, and low mechanical properties. Both weaknesses cause an increase in costs for the health system and a decrease in the patient’s quality of life due to the prosthesis’s loosening. Materials such as graphene oxide (GO) have a reinforcing effect on ABC’s mechanical and setting properties. This article shows for the ﬁrst time the interactions present between the factors sonication time and GO percentage in the liquid phase, together with the percentage of benzoyl peroxide (BPO) in the solid phase, on the mechanical and setting properties established for cements in the ISO 5833-02 standard. Optimization of the factors using a completely randomized experimental design with a factorial structure resulted in selecting nine combinations that presented an increase in compression, ﬂexion, and the setting time and decreased the maximum temperature reached during the polymerization. All of these characteristics are desirable for improving the clinical performance of cement. Those containing 0.3 wt.% of GO were highlighted from the selected formulations because all the possible combinations of the studied factors generate desirable properties for the ABC.


Introduction
Acrylic bone cements (ABC) are biomaterials used since 1960 in orthopedics, and their applications extend from arthroplasty procedures [1] to neurosurgery [2], vertebroplasty, and kyphoplasty [3][4][5]. Arthroplasty procedures generally use ABCs with impressive results [6]. The cement mantle's prominent roles are to stabilize the implant and transfer body weight and service loads from the prosthesis to the bone [1,7,8]. Successful arthroplasty is related to the implants; therefore, the cement's good mechanical properties must be guaranteed [7].
Several types of research have demonstrated that GO content in ABCs generates a reinforcement on the mechanical properties' flexion [34,35], compression, fracture toughness [8], and fatigue performance [3]. Reduction in the maximum temperature reached during polymerization (T max ), increase in the setting time (t set ) [3,[36][37][38], and additionally, improvements in bioactivity [38][39][40] and antibacterial properties [37,41]. Despite these improvements, it has also been reported that GO in ABCs can inhibit the polymerization reaction, which can be counteracted by increasing the radical species. However, since the BPO content influences the polymerization exotherm (T max ) [1], it is necessary to optimize its content.
The effect of GO's sonication time has been studied in materials different from ABCs [42][43][44], and it has been found that this parameter is related to two key characteristics of GO: the lateral size and the thickness of the sheets [45,46]. Increasing the sonication time decreases the thickness and particle size, as previously reported [47]. However, excessive sonication decreases hydrophilicity and functional groups in GO sheets [48] with a simultaneous increase in GO structure defects [49,50].
Although there are several types of research where the GO content alone is studied, there are no studies on the interactive effects of the size and content of GO and the BPO content. This article shows for the first time the interactions present between the factors sonication time and GO percentage in the liquid phase, together with the percentage of benzoyl peroxide (BPO) in the solid phase, on the mechanical and setting properties established for cements in the ISO 5833-02 standard [51]. Optimization of the factors using a completely randomized experimental design with factorial structure resulted in selecting nine formulations that presented an increase in compression, flexion, and the setting time and decreased the maximum temperature reached during the polymerization. Some of these combinations have not yet been studied, which broadens the possibilities for new formulations with desirable characteristics to improve ABCs' clinical performance, which could be used in orthopedics.

Experimental Design
A completely randomized experimental design with a factorial structure was applied to analyze the information obtained in this study statistically. The study factors considered and their levels are shown in Table 1. Each level selected for the factors was based on a review of the values used in the formulations of cements containing GO. A total of 60 tests were conducted (20 treatments with 3 repetitions) for each of the 6 response variables.
The tests were performed at random under identical conditions. The analysis of variance (ANOVA), post-ANOVA tests (Tukey test), and graphs of the data obtained was carried out in the statistical package MINITAB version 19 (Minitab, LLC, State College, PA, USA). Simultaneously evaluated was the interaction significance and the factor effects over the response variables. Simultaneously, the importance of the interaction and each factor's primary effects on the response variable was assessed [52,53]. Equation (1), expressing the completely randomized design model with a factorial structure, is given by where Y is the response variable, µ is the general mean, Z is the effect due to sonication time, β is the effect due to BPO/solid ratio, and α is the effect due to GO/liquid ratio. (Zβ), (Zα), and (βα) are the interaction effects, and ε is the experimental error. A completely randomized experimental design with a structure factorial has several assumptions that need to be fulfilled, such as (1) normality, (2) homoscedasticity, and (3) independence.

Preparation of GO
GO was obtained by the Hummers method modified as reported by Valencia et al. [37]. Briefly, 3 g of graphite were oxidized with H 2 SO 4 and KMnO 4 for 4 days, purified by dialysis, and dried by lyophilization. The characterizations made to GO are reported in previous studies [37,38]. The lateral size of GO dispersed for 1 h measured by dynamic light scattering (DLS) was 400 nm, while the one spread for 5 h was 367 nm. The GO thickness determined by Atomic force microscopy (AFM) was <30 nm, the level of oxidation by X-ray photoelectron spectroscopy (XPS) was 67.84%, and the interlaminar distance determined by X-ray diffraction (XRD) was 7.953 Å.

Preparation of ABCs
The solid phase (SP) of the cement consisted of 10 wt.% BaSO 4 , the BPO content was taken from the experimental design shown in Table S1 (Supporting Information), and the amount of PMMA was adjusted to complete 100% of the SP. The SP components were mixed manually.
In the liquid phase (LP), the percentage of DMPT and comonomers were constant for all formulations at 2.5 wt.% and 2.0 wt.%, respectively. The total comonomer consisted of a 50:50 mixture of the alkaline comonomers DEAEA and DEAEM. The GO content was taken from the experimental design shown in Table S1 (Supporting Information), and the amount of MMA was adjusted to complete 100% of the LP. LP was obtained by mixing the components and subsequent sonication in an ultrasonic bath (Branson, Danbury, CT, USA) at 25 • C and 40 kHz frequency by 1 or 5 h according to the treatment given in the experimental design.
LP was added to SP in an SP/LP ratio of 2 g/mL, and the dough was manually mixed and deposited in Teflon molds with the form required for each test (Figure 2). amount of MMA was adjusted to complete 100% of the LP. LP was obtained by the components and subsequent sonication in an ultrasonic bath (Branson, Danb USA) at 25 °C and 40 kHz frequency by 1 or 5 h according to the treatment give experimental design.
LP was added to SP in an SP/LP ratio of 2 g/mL, and the dough was manual and deposited in Teflon molds with the form required for each test (Figure 2).

Characterization of ABCs
The cements' characterization was based on the evaluation methods proposed in the ISO 5833-02 [51] standard for ABCs.

Setting Properties
After mixing SL and LP, the dough was put in molds 68 mm in diameter and 20 mm in height, and the temperature and time were registered with a data acquisition system with a USB port containing a thermocouple for temperature sensing (Figure 3a). T max was the higher temperature reached during the polymerization reaction, and the t set was calculated as the time where the T set was reached. T set was determined by Equation (2). The test was conducted in duplicated.
where: T set is the setting temperature, and T amb is the ambient temperature.

Characterization of ABCs
The cements' characterization was based on the evaluation methods proposed in the ISO 5833-02 [51] standard for ABCs.

Setting Properties
After mixing SL and LP, the dough was put in molds 68 mm in diameter and 20 mm in height, and the temperature and time were registered with a data acquisition system with a USB port containing a thermocouple for temperature sensing (Figure 3a). Tmax was the higher temperature reached during the polymerization reaction, and the tset was calculated as the time where the Tset was reached. Tset was determined by Equation 2. The test was conducted in duplicated. , (2) where: Tset is the setting temperature, and Tamb is the ambient temperature.

Mechanical Properties
Mechanical properties were characterized in a universal testing machine Tinius Olsen-H50KS (Tinius Olsen, Redhill, United Kingdom). Compressive strength and compressive modulus were measured in cylinders with 6 mm in diameter and 12 mm in height to crosshead displacement rate of 20 mm/min ( Figure 3b). Each formulation tested six samples. A four-point bending test was conducted on rectangular beams of 75 mm × 10 mm × 3 mm with a 5 mm/min crosshead displacement rate ( Figure 3c). Bending strength and bending modulus were calculated according to the ISO 5833-02 [51] specifications.

Setting Properties
For analysis of the maximum temperature and setting time variables based on the effect of sonication time, BPO/SP ratio, and GO/LP ratio, a completely randomized design model with a factorial structure was proposed, which meets the assumptions of normality about error of the model, at significance levels greater than p-value = 0.15.

Maximum Temperature
The analysis of variance is shown in Table S2 (support information). The Tmax delivers

Mechanical Properties
Mechanical properties were characterized in a universal testing machine Tinius Olsen-H50KS (Tinius Olsen, Redhill, United Kingdom). Compressive strength and compressive modulus were measured in cylinders with 6 mm in diameter and 12 mm in height to crosshead displacement rate of 20 mm/min ( Figure 3b). Each formulation tested six samples. A fourpoint bending test was conducted on rectangular beams of 75 mm × 10 mm × 3 mm with a 5 mm/min crosshead displacement rate ( Figure 3c). Bending strength and bending modulus were calculated according to the ISO 5833-02 [51] specifications.

Setting Properties
For analysis of the maximum temperature and setting time variables based on the effect of sonication time, BPO/SP ratio, and GO/LP ratio, a completely randomized design model with a factorial structure was proposed, which meets the assumptions of normality about error of the model, at significance levels greater than p-value = 0.15.

Maximum Temperature
The analysis of variance is shown in Table S2 (support information). The T max delivers that all the effects of the interaction were significant at levels below 0.021 (sonication time * BPO/solid ratio; sonication time * GO/liquid ratio; BPO/solid ratio * GO/liquid ratio and sonication time * BPO/solid ratio * GO/liquid ratio). A determination coefficient of 94.64% was obtained, which is a good measure of the controlled effects' contribution (studied factors) to the total variation. Figure 4 exhibits the interaction plot for T max . Increasing the sonication time and the BPO/solid ratio promoted the higher values of T max , while the higher GO percentages decrease the T max reached during polymerization. T max values of all the formulations studied were found between 41 and 58 • C, below the maximum value allowed by the ISO 5833-02 standard, 90 • C. In ABC, a reduction in the T max reached during polymerization is desirable since it reduces the thermal necrosis of the periprosthetic tissue [6,12,54], which is related to the loosening of the prosthesis [55]. Several researchers have highlighted the influence of the BPO content on the maximum temperature [5,6,55], finding that a higher BPO content can increase the concentration of free radicals available during polymerization, generating an increase in the amount of energy released during the reaction [11,56,57].
Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 18 Figure 4 exhibits the interaction plot for Tmax. Increasing the sonication time and the BPO/solid ratio promoted the higher values of Tmax, while the higher GO percentages decrease the Tmax reached during polymerization. Tmax values of all the formulations studied were found between 41 and 58 °C, below the maximum value allowed by the ISO 5833-02 standard, 90 °C. In ABC, a reduction in the Tmax reached during polymerization is desirable since it reduces the thermal necrosis of the periprosthetic tissue [6,12,54], which is related to the loosening of the prosthesis [55]. Several researchers have highlighted the influence of the BPO content on the maximum temperature [5,6,55], finding that a higher BPO content can increase the concentration of free radicals available during polymerization, generating an increase in the amount of energy released during the reaction [11,56,57]. The sonication time is related to the degree of dispersion [50] and the thickness of the GO particle [44]. Longer exfoliation times decrease the size of GO [45,47] and possibly the heat dissipation capacity during the polymerization reaction due to the increase of the defects in the GO structure [49,50,58]. The decrease of Tmax with the increase in GO content has been attributed to this component's inhibitory effect during the polymerization reaction because it acts as a sink for free radicals [34,37,38,59]. According to the results reported by Paz et al. [60], this inhibitory effect is concentration-dependent because, in their study, they showed by differential scanning calorimetry that the addition of 0.1 wt.% GO had no significant impact on the heat generation during the polymerization reaction of MMA.
Tukey's multiple comparison tests shown in Table 2 indicate that group G formulations are the most suitable from a Tmax point of view since they had the lowest Tmax (<48 °C). This suggests that formulations 1-2. The sonication time is related to the degree of dispersion [50] and the thickness of the GO particle [44]. Longer exfoliation times decrease the size of GO [45,47] and possibly the heat dissipation capacity during the polymerization reaction due to the increase of the defects in the GO structure [49,50,58]. The decrease of T max with the increase in GO content has been attributed to this component's inhibitory effect during the polymerization reaction because it acts as a sink for free radicals [34,37,38,59]. According to the results reported by Paz et al. [60], this inhibitory effect is concentration-dependent because, in their study, they showed by differential scanning calorimetry that the addition of 0.1 wt.% GO had no significant impact on the heat generation during the polymerization reaction of MMA.
Tukey's multiple comparison tests shown in Table 2 indicate that group G formulations are the most suitable from a T max point of view since they had the lowest T max (<48 • C). This suggests that formulations 1-2.5-0.5; 1-2.0-0.5; 5-2.0-0.3; 1-2.5-0.3; 5-2.0-0.5 are statistically equal to a significance level of 5%. All group G samples are characterized by presenting the highest GO contents studied, which indicates that this variable's effect was the most significant on T max . Compared to the other two studies, the lower p-value shown for the GO/liquid ratio confirms the previous statement (Table S2). Table 2. Grouping information for T max using Tukey's test and 95% confidence.

Sonication Time * BPO /Solid
Ratio * GO/Liquid Ratio 3 G * Means that do not share a letter are significantly different.

Setting Time
According to Table S2 (supporting information), for the setting time variable, only the interactions sonication time * BPO/solid ratio, and sonication time * GO/liquid ratio were significant, at levels below 0.076. A determination coefficient of 97.2% was obtained, indicating an adequate contribution of the controlled effects to the total variation. Following Figure 5, higher values in sonication time and BPO/solid ratio reduced t set , while the GO/liquid ratio increase increased t set . ISO 5833-02 indicates that the t set should be between 180 and 900 s (3-15 min), which means that all formulations studied are within the acceptable range. Setting time is one of the most representative setting parameters of the ABCs [5,55], and in orthopedics, it is expected to have a moderate value [7] because it is directly related to the time the surgeon has to mold and apply the cement during the procedure [37].
The concentration of BPO plays a vital role in the kinetic parameters of ABC [1,55,56], and it is found that the decrease in t set with the increase of the BPO content is due to the higher amount of free radicals available to initiate the polymerization reaction faster [5,56]. The longer exfoliation time when generating smaller GO sizes with reduced heat dissipation capacity promotes that the cement hardening reaction occurs in less time.
According to the research of Goncalves et al. [34], the presence of the double bonds C=C in the GO generates extensive electron donor-acceptor capability, so it becomes remarkably reactive toward free radicals, acting as polymerization retardation and polymerization inhibition simultaneously during the polymerization reaction of the MMA in the ABC. The same behavior has been reported by other authors who studied the radical polymerization of some typical vinyl monomers [61].
while the GO/liquid ratio increase increased tset. ISO 5833-02 indicates that the be between 180 and 900 s (3-15 min), which means that all formulations studied the acceptable range. Setting time is one of the most representative setting par the ABCs [5,55], and in orthopedics, it is expected to have a moderate value [7 is directly related to the time the surgeon has to mold and apply the cement procedure [37].  According to Tukey's post-ANOVA test for the t set variable (Table 3), although all the formulations are within the range allowed by ISO 5833-02, group A provides higher values in both interactions for cement setting time. Formulation with 1 h of sonication time, 2.0 wt. % of BPO and 0.5 wt.% of GO presented the highest setting time.

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, causing lower molecular weights that directly influence the mechanical behavior of the cement [5].
ppl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 18 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 mechanica 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 OCH3 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 (pvalue). The analysis of the multiple comparison tests (Tukey's test) is presented in Table  4.  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. The treatments are statistically equal within each group B, C, D, E, F, and G. It is essential to highlight that the formulations with 0.3 wt.% of GO predominated in group A, indicating that this percentage of GO in the formulation could optimize the compressive strength.

• Compressive modulus
According to Figure 7, shorter sonication time and higher BPO and GO content increase the compression modulus in the solid and liquid phase. ISO 5833-02 does not establish a reference value for this property; however, since the cement is responsible for transferring the mechanical loads between the implant and the bone [1], the compressive type arthroplasty [7] is necessary to understand how this property performs.  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. The treatments are statistically equal within each group B, C, D, E, F, and G. It is essential to highlight that the formulations with 0.3 wt.% of GO predominated in group A, indicating that this percentage of GO in the formulation could optimize the compressive strength.

•
Compressive modulus According to Figure 7, shorter sonication time and higher BPO and GO content increase the compression modulus in the solid and liquid phase. ISO 5833-02 does not establish a reference value for this property; however, since the cement is responsible for transferring the mechanical loads between the implant and the bone [1], the compressive type arthroplasty [7] is necessary to understand how this property performs. Larger particles (shorter sonication time) and the higher quantity of polymer chains (higher BPO content) generated a physical impediment for the chains' movement, which increased the stiffness of the ABCs. As in the compressive strength, the GO content in- Larger particles (shorter sonication time) and the higher quantity of polymer chains (higher BPO content) generated a physical impediment for the chains' movement, which increased the stiffness of the ABCs. As in the compressive strength, the GO content increased the compression modulus of the cement. This mechanical reinforcement of GO over ABCs formulations has been reported by several authors . It is possible to establish that the formulations with 1 h of sonication time, 2.5 wt.% of BPO, and 0.3 or 0.5 wt.% maximize the compression module and present an equal effect on this property ( Table 5). The module's lowest values are reached with the lowest GO percentages (Groups H and I). Although the behavior reported for the compressive modulus of the cements added with GO is similar to that reported by Pahlevanzadeh et al. [63] with the use of reduced graphene oxide (rGO), it is noted that the values obtained with GO are higher, possibly due to the greater ease of chemical interaction of the functional groups of GO, which are found in lower proportion in rGO.

Bending Properties
To model the effect of the sonication time, BPO/solid ratio, and GO/liquid ratio, a completely randomized design model with a factorial structure was proposed, which meets the assumptions of normality about error of the model, at significance levels more significant than the p-value = 0.15. Through the analysis of variance, the hypotheses about the interaction between effects are tested (Table S4), showing that effects interaction (Sonication time * GO/Solid ratio; BPO/Solid ratio * GO/Liquid ratio) were significant at levels below 0.001 in the proposed model. For both bending strength and bending modulus, with these models, determination coefficients of 93.47% and 92.13%, respectively, were obtained, which are a good measure of the controlled effects' contribution to the total variation.

•
Bending strength The increase in sonication time and GO content increases ABCs' bending strength, as shown in Figure 8. In contrast, the rise in BPO content decreases this property. ISO 5833-02 [51] establishes a minimum bending strength of 50 MPa, so formulations without GO and the highest GO content studied do not achieve this requirement.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of Figure 8. Interaction plot between the effect sonication time vs. GO/liquid ratio and BPO/solid ratio vs. GO/liquid ratio for the variable bending strength.
As mentioned earlier, for the compressive strength, a higher BPO content has an e sential influence on the molecular weight and polymerization degree of PMMA [12] an therefore, lower cement's mechanical performance. The size reduction generated by th longer sonication time generated a higher mechanical reinforcement [49] and a GO co tent of 0.3 wt. % produced the highest bending strengths, which coincides with the on reported by Paz et al. [3] and by our group in other investigations [37,38].
Tukey's post-ANOVA test for the variable bending strength shown in Table 6 ind cates that the formulations that maximize bending strength are those with GO conten between 0.1 and 0.3 wt.%. There are no significant differences in the bending streng value of the formulations to which the same letter is assigned so that all formulation grouped as A generate the highest possible values in this property and are above the mi imum requirement in ISO 5833-02 [51].  As mentioned earlier, for the compressive strength, a higher BPO content has an essential influence on the molecular weight and polymerization degree of PMMA [12] and, therefore, lower cement's mechanical performance. The size reduction generated by the longer sonication time generated a higher mechanical reinforcement [49] and a GO content of 0.3 wt. % produced the highest bending strengths, which coincides with the one reported by Paz et al. [3] and by our group in other investigations [37,38].
Tukey's post-ANOVA test for the variable bending strength shown in Table 6 indicates that the formulations that maximize bending strength are those with GO contents between 0.1 and 0.3 wt.%. There are no significant differences in the bending strength value of the formulations to which the same letter is assigned so that all formulations grouped as A generate the highest possible values in this property and are above the minimum requirement in ISO 5833-02 [51]. On the other hand, the addition of 0.5 wt.% of GO does not benefit the ABC from the bending strength perspective. The results of Tukey's test show that the addition of the maximum GO content statistically has the same effect on this property as the basic formulation without the addition of GO (Group D in both interactions) and that both GO contents are below the minimum strength required in the standard (50 MPa).

•
Bending modulus According to Figures 7 and 9, the bending modulus and the compression modulus increase with higher BPO content, shorter sonication time, and higher GO content up to 0.3 wt.%. The higher the polymer chains during polymerization, the larger particle size, and GO nanoparticles' presence increases the ABCs' stiffness [66]. Other researchers found a similar modulus behavior concerning the BPO content in ABCs formulations [1,57]. In addition, it has been reported the increase in the mechanical properties of ABCs [3,35,67] and other types of polymeric materials with the addition of GO thanks to the presence of hydroxyl, carboxylic, and epoxy groups on their surface and is consequently more accessible to disperse [47,68,69]. maximum GO content statistically has the same effect on this property as the basic fo lation without the addition of GO (Group D in both interactions) and that both GO tents are below the minimum strength required in the standard (50 MPa).

•
Bending modulus According to Figures 7 and 9, the bending modulus and the compression mod increase with higher BPO content, shorter sonication time, and higher GO content 0.3 wt.%. The higher the polymer chains during polymerization, the larger particle and GO nanoparticles' presence increases the ABCs' stiffness [66]. Other resear found a similar modulus behavior concerning the BPO content in ABCs formula [1,57]. In addition, it has been reported the increase in the mechanical properties of A [3,35,67] and other types of polymeric materials with the addition of GO thanks t presence of hydroxyl, carboxylic, and epoxy groups on their surface and is consequ more accessible to disperse [47,68,69].
Concerning the sonication time, Ormsy et al. [70] reported an improvement i cement mechanical properties by mixing multilayer carbon nanotubes in the liquid p with ultrasound due to the homogenization and dispersion of the nanotubes in the l phase. According to ISO, the bending modulus of all formulations was between 2.4 an GPa (Table 7), which means that all formulations studied present bending modulus v above 1800 MPa, which is the minimum required for ABCs 5833-02 [51]. The formula with 0.3 wt.% of GO, 1 or 5 h of sonication, and 2.5 wt.% of BPO presented the hi values in this property, represented in higher stiffness of the cements. Concerning the sonication time, Ormsy et al. [70] reported an improvement in the cement mechanical properties by mixing multilayer carbon nanotubes in the liquid phase with ultrasound due to the homogenization and dispersion of the nanotubes in the liquid phase.
According to ISO, the bending modulus of all formulations was between 2.4 and 2.7 GPa (Table 7), which means that all formulations studied present bending modulus values above 1800 MPa, which is the minimum required for ABCs 5833-02 [51]. The formulations with 0.3 wt.% of GO, 1 or 5 h of sonication, and 2.5 wt.% of BPO presented the highest values in this property, represented in higher stiffness of the cements. In the ABCs formulations, it is necessary to comply with the mechanical and setting properties described in ISO 5833-02 [51] to guarantee the implant's long-term stability [11]. Considering that most of the formulations studied met all the mechanical and set requirements specified in the standard, a selection criterion based on the bending strength was employed since some formulations did not reach the minimum value required. In an ABC, it is desirable low values of T max , moderate t set to facilitate the application of cement (in applications such as vertebroplasties and kyphoplasties, longer setting times are desirable as it allows the surgeon to inject the cement), and high mechanical performance that allows the adequate transfer of loads during the patient's daily activities. Table 8 presents a summary of the formulation's properties with better performance in bending strength. Although all the formulations mentioned in this table accomplish the requirements outlined in ISO 5833-02, those with 0.3 wt.% of GO independent of sonication time and BPO content showed the highest mechanical performance. That allows adequate load transfer during the patient's daily activities [7]. The longest t set that facilitates cement application and the lowest T max values decrease the risk of thermal necrosis of the surrounding tissue. The characteristics mentioned in the formulations with 0.3 wt.% of GO make them promising to be applied as ABCs; therefore, complementary studies of properties such as residual monomer content, cell viability, antiviral activity, among others, are suggested to evaluate how these properties are affected by the BPO content and the sonication time of GO nanoparticles, to limit these factors.

Conclusions
Using a factorial experiment design completely randomized for evaluating the mechanical and setting properties of ABCs allowed the optimization of BPO/solid ratio, sonication time, and GO/liquid ratio factors, obtaining a group of formulations that satisfy the requirements proposed in ISO 5833-02.
The increase in the BPO content favored the stiffness of the cement by increasing the compression and bending modulus; however, it increased the T max and decreased the t set , compression, and bending strength.
The sonication time favored the compressive and bending strength of the ABCs and simultaneously increased T max when incorporating more effective content of BPO, reducing the t set and the stiffness of the cement using the reduction of the compressive and bending modulus.
The increase in GO content favored the setting properties, as it decreased T max and increased t set . Moreover, GO up to 0.3 wt.% had a beneficial effect on the mechanical properties in compression and bending. The addition of 0.5 wt.% of GO generated a significant decrease in the mechanical properties possibly due to the formation of agglomerates. The formulations with a GO content of 0.3 wt.% are of interest in the formulations that meet the mechanical and setting requirements since they presented higher mechanical performance, longer t set , and the lowest T max values.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.