## 7 The Key Parameters of Self-Assembly in Multi-Arm Polymers
### Linear versus Multi-Arm Copolymers
The multi-arm copolymer with a high volume fraction of PEG (f\({}_{\text{PEG}}\) = 0.55) and short PCL arm length self-assembled in an aqueous solution as a spherical micelle. However, cylindrical micelles were observed when the PCL arm length was longer (f\({}_{\text{PEG}}\) = 0.15-0.32). In contrast, linear diblock counterparts (PEG-PCL) consistently self-assembled in aqueous solutions as spherical micelles, regardless of the PCL arm length. The cylindrical micelles of PEG-PCL\({}_{2}\) with DOX as a model drug have demonstrated superior performance in terms of drug-loading capacity compared to the spherical micelles of the linear diblock counterparts. Additionally, DOX-loaded cylindrical micelles exhibited a slower release rate, increased cellular uptake, and improved cytotoxicity compared to DOX-loaded spherical micelles. The results indicate that DOX-loaded cylindrical micelles are more suitable for effectively administering drugs than other morphological forms. Similarly, [PERSON] and colleagues [204] have successfully synthesized linear-hyper-branched amphiphilic block copolymers, mPEG-(hb-PG)-g-PCL, with multiple arms using a simple two-step ring-opening polymerization strategy. They also synthesized linear mPEG-b-PCL block copolymers with a similar composition to compare the effects of hyperbranched architecture. The comparative studies have revealed that multi-branched copolymers are more advantageous than their linear counterparts, mPEG-b-PCL, for use as drug delivery vectors. The hyperbranched amphiphilic block copolymers mPEG-(hb-PG)-g-PCL had a higher drug-loading capacity (DLC) and encapsulation efficiency (EE) compared to linear mPEG-b-PCL block copolymers. Moreover, the hyperbranched amphiphilic block copolymers exhibited more sustained and durable drug release behavior. Therefore, these multi-armed block copolymers have the potential to be favorable biomaterials for controlled drug release. Figure 18: Schematic illustration of hydrodynamic radius changes as a function of PCL-b-PDMAEMA copolymer topology; Adapted from [203] (Copyright 2014, The Royal Society of Chemistry). However, in 2011, [PERSON] et al. (2015) introduced a different type of multi-arm architecture. This alternative design utilizes an ABC terpolymer that changes its aggregate morphology in response to temperature fluctuations in an aqueous solution. The terpolymer, called a multi-arm terpolymer (MPEG)(PCL)(PPE), is composed of a hydrophilic segment made of monomethoxy poly(ethylene glycol) (MPEG), a hydrophobic section of PCL, and thermosensitive polyphosphoester chains that are linked by a junction site. When formed in an aqueous solution, the micelles created by this multi-terpolymer demonstrate thermal sensitivity. At low temperatures, the micelles are spherical in shape, but at higher temperatures, they transform into a nano-rod morphology once the cloud point is surpassed. The morphological transition of this miktoarm terpolymer caused by temperature fluctuations suggests its potential for drug delivery that is regulated and intelligent (Figure 19). In 2014, a group of researchers led by [PERSON] (2018) successfully synthesized (PCL)\({}_{2}\) (PDEAEMA-b-PPEGMA)\({}_{2}\) amphiphilic miktoarm star polymers by combining ROP and atom transfer radical polymerization (ARGET ATRP). The CMC values of these polymers were remarkably low (ranging from 0.0024 to 0.0043 mg mL\({}^{-1}\)). The micelles, both empty and DOX-loaded, were spherical with average sizes of 63 and 110 nm, respectively. The in vitro drug release was pH-responsive, with a faster release at pH 5.0 compared to pH 7.4 and 6.5, due to the protonation of DEAs' tertiary amine groups. Intracellular uptake of DOX demonstrated its efficient delivery into cells after incubation with DOX-loaded micelles. Overall, the results suggest that pH-responsive (PCL)\({}_{3}\) (PDEAEMA-bPPEGMA)\({}_{3}\) polymeric micelles have the potential to be used as improved vehicles for cancer therapy.