## 7 The Key Parameters of Self-Assembly in Multi-Arm Polymers
### Linear versus Multi-Arm Copolymers  
As previously discussed, the branched or multi-arm architectures offer interesting properties to enhance the effectiveness of polymeric nanocariers as drug delivery vehicles. However, very few studies have sought to establish a direct comparison of the effectiveness of linear and multi-arm polymer architecture (Figure 16). [PERSON]'s [200,201] studies highlighted the ability of multi-arm sequenced copolymers to encapsulate hydrophilic compounds in a hydrophobic environment. This property could potentially allow their use as vectors for effective transdermal drug delivery. Although the limited number of arms (6 or 12) on amphiphilic sequenced star copolymers resulted in the formation of true unimolecular micelle properties, they showed improved encapsulation efficiency of polar dyes and reduced critical micelle concentration compared to linear analogues with only one arm. Furthermore, sequenc  
Figure 16: Ability of multi-arm architectures to respond to the various requirements of the drug delivery. notable improvement in transport. Multi-arm sequenced copolymer micelles also have a larger interior space, allowing them to contain more drugs. However, the majority of research on multi-arm polymers has focused on the synthesis of custom architectures and the relationship between structure and morphology [202]. [PERSON] and colleagues [197] have synthesized a series of miktoarm A\({}_{2}\)B copolymers consisting of a polyethylene glycol (PEG) A block and a polycaprolactone (PCL) B block for the delivery of nimodipine, a drug with low water solubility used to treat late-stage neurological ischemic disorders (Figure 17). These multi-arm copolymers (PEG)\({}_{2}\)-PCL generated micelles that displayed remarkable incorporation rates of up to 78%. Moreover, they facilitated sustained drug release, showed enhanced micellar stability, and exhibited reduced micelle size when compared to their linear analogues having a comparable composition and molecular weight. In 2014, [PERSON] et al. [203] conducted a study comparing the synthesis and characterization of a four-armed copolymer (Star-PCL-b-PDMAEMA) and its linear analogue (Linear-PCL-b-PDMAEMA) of similar composition. The study aimed to evaluate their ability to deliver a plasmid and doxorubicin, an anticancer drug. The results demonstrated that the amphiphilic copolymers effectively transported both substances. When the copolymers self-assembled in a pH 3.0 solution, the branched copolymer micelles had a hydrodynamic diameter of approximately 80 nm, whereas the linear copolymer micelles were 106 nm in diameter (Figure 18). Additionally, the critical micelle concentration (CMC) of the four-armed copolymers (8.01 ug mL\({}^{-1}\)) was much lower than that of the linear analogue (21.2 ug mL\({}^{-1}\)). This was due to the finer cationic density resulting from the molecular weight distribution over the four arms of the star-shaped polymer, which led to the formation of smaller micelles. Although both the star-shaped and linear copolymers exhibited a very similar DOX charge (DL% 16.6 and 15.8%), the star-shaped polymer had a slower drug release profile and an increased cellular uptake, which was highly efficient in killing cancer cells. The S-PCL-PDMAEMA delivered drugs to the nuclei of U87 cells during a 3-hour incubation, but L-PCL-PDMAEMA accumulated most of them in the cytoplasm. In addition, the cell-killing effect of DOX/S-PCLPDMAEMA was better than DOX/L-PCL-PDMAEMA against 293T, CRL-5802, MCF-7, and NCI-H358 cells. This result showed that S-PCL-PDMAEMA presents a promising system for co-diffusion of therapeutic pDNA and hydrophobic anticancer drugs. Figure 17: Controlled synthesis of miktoarm A\({}_{2}\)B copolymers with various PCL chain lengths. In the same area of study, [PERSON] et al. [181] found that the behaviors of the multi-arm PEG-PCL\({}_{2}\), such as drug loading efficiency, self-assembly, and controlled drug release characteristics, differed from their linear diblock counterparts (PEG-PCL).