## 3 Results and Discussion  
PE-g-GMA is synthesized via radical polymerization [3; 5; 6; 7; 9; 10; 11; 14; 33]. Radicals are formed after the thermal decomposition of the peroxide and these formed radicals can react via several pathways (Figure 2). Figure 2: Reaction mechanism based on the literature [3; 5; 6; 7; 9; 10; 11; 14; 33; 34]. As depicted in Figure 2, the primary radical can abstract a hydrogen from PE to form a macro-radical (reaction 1). The formed macro radicals attack the GMA's sigma bond and, via termination, the growing chain forms a grafted polymer chain, PE-g-GMA. However, macro-radicals have limited accessibility to the GMA monomers due to steric hindrance. Therefore, PE crosslinking and recombination might occur (reaction 2). Furthermore, the primary radical might directly initiate GMA homo-polymerization (reaction 3) [7; 9; 14; 33]. Multiple side reactions are possible. They should be minimized to yield the highest FD. Several conditions, such as DCP and GMA concentration, temperature, pressure, and the use of scCO\({}_{2}\) can minimize these side reactions. In this study, we started by studying the influence of the feed composition (GMA and DCP) on the FD values for both virgin LDPE and RPE. Overall, the amount of GMA being grafted increased with the initiator intake until it reached a plateau, as shown in Figure 3. Similar results were found in the literature [6; 7; 9; 10; 11; 33]. The main reason for this was the increase in the number active sites, which enhanced unfavorable side reactions, such as crosslinking and the homo-polymerization of GMA [6; 7; 9; 10; 11; 35; 36]. Overall, the RPE yielded lower FD values compared to the LDPE. As shown in Figure 4, an increase in the amount of GMA at constant DCP concentration resulted in a higher FD. The highest FD was found when using 10 wt.% GMA for all the samples. Figure 4: Effect of GMA concentration on the FD for LDPE **(a)** and RPE **(b)**. Figure 3: Effect of initiator concentration on the FD for LDPE **(a)** and RPE **(b)**. This was in agreement with literature-based expectations because a larger amount of GMA monomers allows more molecules to be grafted onto the matrix and less active sites are available for the crosslinking of PE [11]. The grafting efficiency increased with the DCP intake for the LDPE, according to Figure 5a. However, the GMA grafting efficiency declined significantly for RPE, according to Figure 5b. It was assumed that GMA homo-polymerization may exceed GMA grafting in reaction rate with the increase in the monomer concentration. As a result, the efficiency decreased in the grafted GMA based on initial GMA concentration. These observations were also made in other grafting studies [6; 7; 9; 10; 11; 33]. To assess which parameters were more influential in changing the FD of the RPE-g-GMA, a statistical test using one-way ANOVA was conducted. The results are shown in Table 1.  
As shown in Table 1, \(p<0.05\) for the variation of the (GMA) was conducted on the RPE regardless of the presence of scCO\({}_{2}\). This indicated that the null hypothesis of equal means was rejected. Therefore, tuning the (GMA) had a higher influence on altering the FD compared to tuning the (DCP). This was also reported by [PERSON] et al. (2017) [36], through a mathematical modeling approach of grafting GMA onto HDPE. Overall, using pure, i.e., fresh and non-recycled, LDPE resulted in higher FD for all the samples, as expected. There are several possibilities that could account for this observation. First of all, it is very likely that there were radical quenchers present in the RPE, such as carbon black, which may have influenced the reaction rate and the grafting reaction. The presence of carbon black could also explain the color difference, with the RPE being light gray, as opposed to white, for the fresh LDPE. Moreover, there were traces of PP present in the RPE pellets, according to the DSC results.