## 4 Discussion  
A common method for producing antibacterial polystyrene involves mixing the resin with metal nanoparticles, such as silver. However, unlike ADIP-PS, silver can react with hydrogen sulfide in the environment, leading to discoloration and reduced transparency [43]. Additionally, silver-zeolite-containing PS has shown reduced antibacterial effects under wet conditions [25], resulting in long-term performance challenges. High-molecular-weight antibacterial agents, such as polyhexamethylene biguanide (PHMB) and chitosan, are also commonly used [44; 45; 46]. However, adding PHMB to polyurethane at concentrations as low as 5% significantly decreases the tensile strength of polyurethane fibers [44]. Similarly, chitosan incorporation into polylactic acid (PLA) results in substantial strength loss because of solubility issues [47] resulting from the incompatibility of chemical structures and polarity differences between the two polymers. Consequently, the interactions between the base polymer and additives are affected. In the case of chitosan and PLA, blending caused discontinuities in the PLA matrix because of poor solubility [47]. Using the same polymer as an antibacterial additive could resolve such challenges but is not straightforward. Nevertheless, this study demonstrates the effectiveness of using ADIP-PS, a contact-killing antibacterial agent synthesized with a  
Figure 8: TNS adsorption on PS and GPPS blended with 10% ADIP-PS sheets. Error bars represent the SD with \(n=3\). Figure 7: Antibacterial activity of GPPS blended with 10% ADIP-PS sheets. Error bars represent the SD with \(n=3\). cationic polymerization initiator. Typically, lower-molecular-weight polymers are more likely to be exposed on the surface when blended with the same polymer type [48; 49], providing a potential advantage for ADIP-PS in maintaining antibacterial functionality. Theoretical analysis suggests several reasons for the tendency of low-molecular-weight polymers to be positioned more easily on the surface. These include entropy-driven behavior, shorter chains being closer to the surface, and fewer possible configurations compared to longer chains, which lowers the entropy penalty [50; 51]. As shown in Figure 7, the 10% AD-40K blend, which has a higher molecular weight, showed slightly reduced antibacterial activity. Additionally, Figure 8 shows a lower level of exposed cationic groups. However, this does not mean that a lower molecular weight always improves the antibacterial properties. Previous studies have reported a significant decrease in the glass transition temperature (\(T_{g}\)) of linear PS when the \(M_{n}\) falls below 18,000 [52; 53]. Blending polymers with significantly different \(T_{g}\) values can affect the bulk resin properties, making extremely low-molecular-weight ADIP-PS unsuitable as an antibacterial agent. Based on these factors, AD-23K (\(M_{n}\) = 23,000) was considered within the optimal molecular weight range. We also investigated the surface segregation potential because of the presence of cationic groups at the ends of ADIP-PS chains. Our results demonstrate that even with a 5% blend and a molecular weight of approximately 23,000, ADIP-PS shows sufficient antibacterial activity. Notably, each ADIP-PS chain contained at most two cationic groups, representing an extremely small weight percentage. In the 5% ADIP-PS blend, cationic groups comprised only about 0.1% by weight, significantly lower than high-molecular-weight cationic agents such as PHMB [44] and chitosan [47]. Previous studies on polymer end-group chemistry have shown that PS with hydrophilic end-groups tends to undergo internal segmentation, resulting in the accumulation of hydrophilic groups on the surface [54]. Given the hydrophilic nature of the imidazolium groups used in our study, a similar effect likely occurred. Surface segregation is more common in low-molecular-weight polymers. In this study, AD-15K, the lowest molecular weight polymer, had the highest concentration of cationic groups on its surface (Figure 8).