## 7 The Key Parameters of Self-Assembly in Multi-Arm Polymers
### Arm Number and Branching Degree  
Another advantageous approach to reduce CMCs is adjusting the degree of branching in multi-arm amphiphilic copolymers, as this affects the packing of the monomers during self-assembly. For instance, [PERSON] et al. (2020) studied four multi-arm polymers of A\({}_{2}\)B, A\({}_{2}\)B\({}_{2}\), A\({}_{3}\)B, and AB\({}_{3}\) types with similar compositions, where A = PCL and B = polyoligo (ethylene glycol) methyl ether methacrylate (POEGMA). According to their findings, the three-arm polymer (PCL\({}_{2300}\))\({}_{2}\)-POEGMA\({}_{12300}\) had a larger hydrodynamic diameter (73 nm) and higher CMC (18.19 \(\mu\)g mL\({}^{-1}\)) than the other four-arm polymers (28-57 nm, 2.66-10.00 \(\mu\)g mL\({}^{-1}\)). Furthermore, they compared the effect of the degree of branching of the PCL halves on micelle stability. It is not surprising that the four-arm polymer (PCL\({}_{1600}\))\({}_{3}\)-PEGMA\({}_{11900}\) has the smallest hydrodynamic diameter (28 nm) and CMC (2.66 \(\mu\)g mL\({}^{-1}\)), likely due to the higher degree of branching of the hydrophobic core, resulting in a more compact core and thus a smaller size (Figure 20). Similarly, this same polymer also had the highest DL% (34.3%) and EE% (62.9%).  
Another study aimed at exploring the influence of different PLGA-PEG arms on DOX delivery was reported by [PERSON], et al. (2020). They successfully synthesized well-defined S-PLGA-PEG copolymers with different numbers of arms (3s/4s/6s-PLGA-PEG), which were utilized to investigate the relationship between the number of arms of PLGA-PEG copolymers and their micelle properties. The CMC value of st-PLGA-PEG copolymers decreased with an increase in the number of arms in S-PLGA-PEG copolymers, indicating that the formation of micelles becomes easier as the number of arms in copolymers increases. The size of DOX-loaded micelles and drug content also increased in the same order as the CMC. Among the three star-shaped copolymers (3s/4s/6s-PLGA-PEG), DOX-loaded S-PLGA-PEG micelles with four arms showed the highest cellular uptake and cytotoxicity,  
Figure 20: Structural Adaptation of Arm Number in Star-Shaped Copolymers (POEGMA-PCL) as a New Strategy for Designing Highly Effective Drug Delivery Carriers.  
possibly due to the difference in size and distribution of PEG on the surface of S-PLGA-PEG micelles. Thus, the structural design of the number of arms from S-PLGA-PEG copolymers could provide a new strategy for the design of highly efficient drug carriers.  
Drawing inspiration from the advantages offered by multi-arm topologies, new micelles formed from supramolecular structures based on \(\beta\)-cyclodextrintrin (\(\beta\)-CD) have been constructed [208]. These structures were linked to poly(N-vinylpyrrolidone) (PVP) chains with four and seven arms, terminated by a linear poly(\(\varepsilon\)-caprolactone). The micelles with PVP chains with seven arms on the outside showed the lowest amount of protein adsorption and the best stability in media, demonstrating the effect of the number of arms on encapsulation parameters. When cabazitaxel was loaded into the micelles, a drug content of 14.4% and an encapsulation efficiency of 85% were obtained. In vitro cytotoxicity studies showed that cabazitaxel-loaded micelles exhibited significant cytotoxicity against drug-resistant A2780/T cell lines. In vivo tumor inhibition experiments and survival rate observations demonstrated that PVP-PCL-loaded micelles had superior efficacy in tumor inhibition compared to free cabazitaxel (Figure 21).