## 3 Results and Discussion
### Synthesis of Randomly Grafted Arborescent Copolymers
Within each generation, the elution volume decreased in the series PBG\({}_{65}\)-\(g\)-PEO < PBG\({}_{15}\)-\(g\)-PEO < PBG\({}_{29}\)-\(g\)-PEO. PBG\({}_{65}\)-\(g\)-PEO had the highest molecular weight, likely due to its more porous core structure minimizing steric crowding and facilitating the diffusion of the chains to the coupling sites in the grafting reaction. Properties of the Arborescent Copolymer Micelles  
The arborescent copolymers were evaluated for their potential to remain as unimolecular (non-aggregated) micelles in aqueous PBS solutions. The use of \({}^{1}\)H NMR spectroscopy \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & \multicolumn{3}{c}{**PBG Substrate**} & \multicolumn{3}{c}{**Graft Copolymer**} \\
**Copolymer** & **M\({}_{n}\) (g/mol) a** & \%-CO\({}_{2}\)H b & **G\({}_{y}\) c** & **M\({}_{n}\) (g/mol) a** & **M\({}_{w}\)/M\({}_{n}\) a** & \(f_{n}\)d & **\%-PEO e** \\ \hline G1 PBG\({}_{15}\)-\(g\)-PEO & 240,000 & 31 & 27 & 1.2 \(\times\) 10\({}^{6}\) & 1.07 & 96 & 80 \\ G1 PBG\({}_{29}\)-\(g\)-PEO & 200,000 & 31 & 27 & 1.0 \(\times\) 10\({}^{6}\) & 1.09 & 80 & 80 \\ G1 PBG\({}_{65}\)-\(g\)-PEO & 260,000 & 33 & 29 & 1.5 \(\times\) 10\({}^{6}\) & 1.08 & 124 & 82 \\ G2 PBG\({}_{15}\)-\(g\)-PEO & 1.2 \(\times\) 10\({}^{6}\) & 31 & 13 & 3.4 \(\times\) 10\({}^{6}\) & 1.08 & 220 & 65 \\ G2 PBG\({}_{29}\)-\(g\)-PEO & 1.0 \(\times\) 10\({}^{6}\) & 32 & 15 & 3.2 \(\times\) 10\({}^{6}\) & 1.09 & 220 & 69 \\ G2 PBG\({}_{65}\)-\(g\)-PEO & 1.4 \(\times\) 10\({}^{6}\) & 30 & 13 & 3.9 \(\times\) 10\({}^{6}\) & 1.06 & 250 & 64 \\ \hline \end{tabular}  
* Values from SEC-MALLS analysis in DMSO; b Mode fraction of carboxyl groups in the substrate; c Grafting yield: fraction of side chains attached to the substrate; d Branching functionality: number of side chains added in the last grafting cycle; e PEO weight fraction, from the difference in M\({}_{n}\) of the copolymer and the substrate.  
\end{table} 
Table 2: Characteristics of randomly grafted PBG-\(g\)-PEO arborescent copolymers. Figure 2: SEC traces for G1 (**left**) and G2 (**right**) arborescent copolymers. to investigate the formation of micellar structures is illustrated in Figure S5 (SM). Complete disappearance of the peak's characteristic for PBG such as the benzylic methylene (2H at 4.9 ppm) and phenyl protons (5H at 7.3 ppm) was observed in D\({}_{2}\)O, while these peaks were clearly visible in DMSO-\(d_{6}\), which confirms that G2 PBG-\(g\)-PEO has a core-shell morphology in aqueous solutions with a collapsed hydrophobic PBG core and a hydrophilic PEO shell. The hydrodynamic diameter of the copolymers, determined by DLS analysis in DMF (good solvent for PBG and PEO) and in aqueous PBS buffer (solvent selective for PEO) followed the expected trends for increasing generation numbers (Table S4, SM). The good agreement for the hydrodynamic diameters obtained in DMF and PBS confirms that the randomly grafted arborescent copolymers formed unimolecular micelles, with mean number-average diameters between 16-18 nm and 32-37 nm for the G1 and G2 in DMF, respectively. As shown in Table S4 (Supplementary Materials), the unimolecular micelles are uniform in size since the values of the three average diameters (number, volume, and intensity) are similar. The copolymers should form unimolecular, non-aggregated solutions in DMF, a good solvent for both the PBG and PEO components. Analysis of the same copolymers in phosphate-buffered saline (PBS) also yielded values for number-, volume-, and intensity-average diameters similar to those obtained in DMF, which suggests that all the arborescent copolymers also existed as unimolecular species under these conditions.