## 7 The Key Parameters of Self-Assembly in Multi-Arm Polymers  
### Solvophobic/Solvophilic Balance  
All linear or multi-arm amphiphilic copolymers are capable of self-assembling into nanoscale structures in the presence of a selective solvent, due to their dual nature. Indeed, amphiphiles are, by definition, made up of solvophobic and solvophilic parts that interact in diametrically opposed ways with a selective solvent. Whereas solvophilic parts maximize their contact with solvent molecules, solvophobic parts minimize this contact. The balance between these two interactions leads to the formation of specific supramolecular structures, whose architecture is finely controlled by the solvophobic/solvophilic molar ratio. Using simple geometric considerations, we can define a critical packing factor as: Cpp = v/a \(\times\) 1[187]. Where (v) and (l) are the molecular volume and the length of the solvophobic parts, respectively, and (a) is the optimal surface per molecule occupied by the solvophilic chains in the final assembly. Generally, structures with high curvature (such as spherical micelles) are formed when Cpp \(<\) 1/3, cylindrical micelles are formed when 1/3 \(\leq\) Cpp \(<\) 1/2, and low curvature bilayer membranes are formed when 1/2 \(\leq\) Cpp \(<\) 1 (Figure 11). In particular, amphiphilic block copolymers are the most useful, as the final structures can be finely controlled by the synthesis procedure. For amphiphilic block copolymers, the final packing factor is highly controlled by the ratio of hydrophobic and hydrophilic blocks. For example, experimental evidence has shown that for PEG-based systems, copolymers form spherical micelles with a PEG volumetric fraction (f) \(>\) 50%, cylindrical micelles with 40% \(<\) f \(<\) 50%, and vesicles with 25% \(<\) f \(<\) 40%. In 2017, [PERSON] et al. [188] conducted a significant study in which they demonstrated how the hydrophobicity of amphiphilic block copolymers allows for the control of the morphology of aggregates in water. This was achieved through RAFT dispersion polymerization, and they reported that the morphology of the nanoparticles is defined by the growth of the hydrophobic ratio during dispersion polymerization. In addition, predetermined morphologies can be targeted by controlling the degree of polymerization (DP) of the hydrophilic and hydrophobic monomers during synthesis. Therefore, this elucidation of the contributions of the hydrophobicity of block copolymers during self-assembly can provide new perspectives and powerful strategies for programming the morphology and dimensions of block copolymer aggregates in solution. Micelles, worms, and vesicles have been synthesized, and the highest control levels over worm elongation achieved during polymerization were reported, simply due to the hydrophobicity of the polymer chain (Figure 12). Figure 11: Variation of Critical Packing Parameter (Cpp) with Nanocarrier Morphology. Applying the universal approximations previously mentioned is challenging for multi-arm polymers, particularly due to the variable branching architectures they exhibit. [189; 190]. A comparison between AB and AB\({}_{2}\) polymers (A = PEG, B = PLLA) with variable hydrophilic volume fractions of PEG revealed that the self-assembly of multi-arm polymers into polymersomes is much more tolerant regarding the variation of volume fractions. The formation of polymersomes was observed for PEG volume fractions of f = 0.2-0.7, which is much broader than the range of 0.2-0.4 for the corresponding double-block linear counterparts. This study showed that multiarms favor the formation of polymersomes or vesicles in contrast to micelles, and in entirely different approximations than linear polymers [191]. In another example, multi-arm star polymer AB\({}_{3}\) (A = PAzo, B = PEG) had a hydrophobic/hydrophilic ratio of 78/22, slightly outside the typical range for polymersome formation, but was nevertheless found to be well suited for polymersome assembly.