## 4 Conclusions  
A library of water-soluble amphiphilic arborescent copolymers PBG-\(g\)-PEO was successfully prepared. Their aqueous solution behavior revealed that the copolymers existed mostly as unimolecular (non-aggregated) micellar species. The ability of these unimolecular micelles to encapsulate and release DOX was correlated with the generation number of the copolymers and the branching density (\(b_{\rm d}\)) of the hydrophobic cores. Both the DLC and the DLE increased with the generation number of the copolymers. For each generation, slightly higher values of DLE and DLC were obtained for the micelles with a denser core structure (G1 PBG\({}_{15}\) and G2 PBG\({}_{15}\)), with a DLE of about 50% and 65%, respectively, and a DLC of about 8.3% and 10.8%, respectively. Both the DLE and DLC decreased slightly as the grafting density of the cores decreased. The release profiles indicated that the drug release rate could be controlled through the generation number of the copolymers and by modulating the grafting density, and thereby the porosity of the cores. Micelles with highly branched cores (G2 PBG\({}_{15}\)) reduced the diffusion rate of the drug, while a lower branching density (G2 PBG\({}_{65}\)) facilitated the diffusion process. The versatile encapsulation and release properties of these unimolecular micelles show that they could be useful as nanocarriers for a broad range of drug release applications. While these unimolecular micelles have already displayed good potential for controlled and sustained drug release, it would be interesting to evaluate the release dynamics over a range of pH values from 5.5-7.4, as well as the cellular uptake of these systems both in vitro and in vivo. **Supplementary Materials:** The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/ma16062461/s1](https://www.mdpi.com/article/10.3390/ma16062461/s1)]([https://www.mdpi.com/article/10.3390/ma16062461/s1](https://www.mdpi.com/article/10.3390/ma16062461/s1)), Table S1. Synthesis of linear PBG substrates with different molecular weights. Table S2. Deprotected linear PBG serving as substrates. Table S3. Characteristics of upper generation PBG arborescent substrates. Table S4. Characteristics of randomly grafted PBG-\(g\)-PEO arborescent copolymers. Scheme S1. Partial and complete deprotection of the PBG substrates. Scheme S2. Polymerization of ethylene oxide with 3-aminophenpropanol and DPMK. Scheme S3. The reaction of 4-trifluoromethylbenzaldehyde (TFBA) with the primary amines end group in the PEO side chains. Figure S1. 1H NMR spectra for (a) fully deprotected linear PBG15, (b) partially deprotected linear PBG29, and (c) partially deprotected linear PBG65. Figure S2. SEC traces for G0 arborescent PBG samples. Figure S3. 1H NMR spectrum for \(\alpha\)-amino PEO in CDCl3. Figure S4. \({}^{19}\)F NMR spectrum for linear PEO synthesized using the 3-aminophen/DPMK initiator system, after treatment with 4-trifluoromethylbenzaldehyde (TFBA). Figure S5. \({}^{1}\)H NMR spectra for G2 PBG29-\(g\)-PEO in (a) D2O and (b) deuterated DMSO. Figure S6. Hydrodynamic diameter distributions for randomly grafted arborescent copolymers determined by DLS in DMF (left) and in PBS (right): (A) G2 PBC\({}_{15}\)-\(g\)-PEO, (B) G2 PBC\({}_{29}\)-\(g\)-PEO, and (C) G2 PBC\({}_{65}\)-\(g\)-PEO. Figure S7. TEM (left) and AFM phase scan (right) for randomly grafted arborescent copolymers: (A) G1 PBC\({}_{15}\)-\(g\)-PEO, (B) G1 PBC\({}_{62}\)-\(g\)-PEO, and (C) G1 PBC\({}_{65}\)-\(g\)-PEO. Figure S8. In vitro DOX release profiles over a 30-day period for (a) G2 PBC\({}_{15}\)-\(g\)-PEO/DOX, (b) G2 PBC\({}_{29}\)-\(g\)-PEO/DOX, and (c) G2 PBC\({}_{65}\)-\(g\)-PEO/DOX in PBS (pH 7.4 and 5.5) at 37 \({}^{\circ}\)C. Reference [41] is cited in the Supplementary Materials. Conceptualization, M.G. ; Methodology, M.A. ; Validation, M.A. ; Formal analysis, M.A. ; Investigation, M.A. ; Resources, M.G. ; Writing--original draft, M.A. ; Writing--review & editing, M.G. ; Supervision, M.G. ; Project administration, M.G.