## 2 Block Copolymer Self-Assembly: Strategies for Controlling Nanostructure Formation  
The self-assembly of copolymers, whether linear or multi-arm, is a spontaneous process in which molecular units transform spontaneously into ordered structures through local interactions [47; 48]. This process is well-known biologically in living cells, where it occurs during the formation of the DNA double helix, the folding of polypeptides, and the arrangement of phospholipids in the cell membrane [49; 50]. Nanotechnologies draw inspiration from this biological phenomenon, using molecular blocks to self-assemble into organized structures applicable to drug administration and biomedicine, sensors, circuits, and devices [51; 52]. As their capacity can be adapted, the encapsulation and controlled administration of drugs in self-assembled structures should be more versatile [53]. This review demonstrates this capacity, particularly that of multi-arm copolymers. The self-assembly of copolymers results in various types of aggregates, among the most interesting of which are micelles, vesicles, and polymersomes. Micelles are amphiphilic aggregates formed by amphiphilic block copolymers, in which the hydrophilic blocks come into contact with a polar solvent to form the corona, whereas the hydrophobic blocks form the core of the micelle. The size of spontaneously formed micelles generally ranges from 10 to 100 nm [54]. The structure and size of micelles depend on parameters such as the size of the hydrophobic domain, the size of the polar group, ionic strength, concentration, temperature, pH, and, more specifically, on the topology of the copolymer, which will be further discussed [55]. Depending on the topology, micellar structures can include sphere, lamella, worm-like, and disk shapes [56; 57]. Figure 1: Bibliographic metrics from Scopus ([[https://www.scopus.com/](https://www.scopus.com/)]([https://www.scopus.com/](https://www.scopus.com/)), accessed on 26 February 2023), with “polycaprolactone multi arms for drug delivery” keywords, from 1990 to 2022. On the other hand, vesicles are another type of self-assembled system that were first reported just over twenty years ago by [PERSON] and colleagues [58], who observed polymer vesicles from the self-assembly of block copolymers of polystyrene-poly(acrylic acid) (PS-PAA). Initially, polymer vesicles were assumed to be out-of-equilibrium structures due to the glassy nature of the PS membrane, but their thermodynamic stability was subsequently established [59; 60]. Further work confirmed that vesicular morphologies are not dictated by the kinetically-frozen glassy nature of the hydrophobic block because vesicles can be formed with low glass transition temperature (T\({}_{g}\)) hydrophobes such as Poly butadiene (PBD) and poly(propylene oxide) (PPO) [61]. Since these initial reports, hundreds of articles have described the formation of polymer vesicles, and a high number of review papers have been published [62]. Polymersomes and liposomes are types of self-assembled vesicles characterized by their hollow spherical structure and composition, consisting of phospholipids for liposomes/vesicles and sequenced copolymers for polymersomes [63]. The discovery of liposomes dates back to the early 1960s, when [PERSON] first identified these structures as models for cell membranes [64]. Firstly, liposomes were employed for this purpose. However, in the 1970s [65], they were proposed as a straightforward drug delivery system. They offer an ideal solution for combination therapy, as they enable the simultaneous delivery of hydrophilic and hydrophobic compounds, unlike micelles, which can only encapsulate one type of compound [66; 67]. Hydrophilic compounds are encapsulated in the hollow core, whereas hydrophobic compounds are loaded into the bilayer. The robust, stable, and tunable membranes, high loading capacity, and long blood circulation time of the liposomes further enhance their value for targeted delivery of a wide variety of therapeutic products with appropriate pharmacokinetics.