## 3 Results and Discussion  
### Synthesis of Linear PBG Substrates  
The characteristics of arborescent copolymers can be tailored to meet specific requirements for different applications through variations in the synthetic procedure. For instance, the molecular weight of the linear substrate serving in the synthesis of the G0 polymer, the functionalization level of the substrate, and the number of grafting cycles used in their synthesis can be changed. In the current investigation, the length and the deprotection level of the linear PBG substrate used in the synthesis of G0 PBG were varied, while the length of the PBG side chains (core building blocks) had M\({}_{\rm n}\)\(\approx\) 5000 g/mol in all cases. Linear PBG substrates with three different lengths were synthesized with X\({}_{\rm n}\) = 15, 29, and 65, as shown in Table S1 (Supplementary Materials). The number of benzyl glutamate repeating units were controlled through the ratio of monomer (Glu-NCA) to the initiator (\(n\)-hexylamine) used in the polymerization reaction. Linear PBG substrates with different \(X_{\rm n}\) and deprotection levels were employed in the synthesis of GOPBG in the hope that the shape of the molecules could be controlled from spherical to brush-like topologies. The shape of micelles can significantly alter their behavior in living organisms and cells. For example, it was reported that worm-like polymer micelles of amphiphilic poly(ethylene glycol)-_block_-polycaprolactone copolymers had an increased circulation time in comparison with their spherical counterparts [32; 33]. Unfortunately, TEM and AFM imaging indicated that the molecules were all spherical. This approach nevertheless provided control over the branching density in the cores, which seems to correlate very well with the release properties of the micelles, as discussed in the release study.  
As shown in Figure 1, absolute values of \(M_{\rm n}\) and \(X_{\rm n}\) were determined from \({}^{1}H\) NMR analysis of the linear PBG samples, by comparing the integrated peak intensities for the benzylic methylene protons in the repeating units (4.9 ppm) and the terminal methyl group signal from the \(n\)-hexylamine initiator (0.77 ppm).  
The branching functionality (\(f_{\rm n}\)) of arborescent polymer molecules can be manipulated through the functionalization (deprotection) level of the substrate. In the current investigation, only the deprotection level of the linear PBG substrate serving in the G0 polymer synthesis was varied (Scheme S1, Supplementary Materials). The treatment of linear PBG with HBr in TFA allowed the cleavage of a controlled fraction of benzyl ester-protecting groups to generate coupling sites (carboxyl groups) for the grafting reaction. A target deprotection level of 30% was used for PBG\({}_{29}\) and PBG\({}_{65}\), while 100% deprotection was used for PBG\({}_{15}\) (Table S2, Supplementary Materials). The deprotection level was controlled through the amount of HBr added with respect to the benzyl ester moieties. The \({}^{1}H\) NMR spectra for partly deprotected PBG\({}_{29}\) and PBG\({}_{65}\), and fully deprotected PBG\({}_{15}\) are compared in Figure S1 (Supplementary Materials). The ratio of integrated intensities for the benzylic methylene protons (2H at 4.9 ppm) for the remaining protected structural units to the methine protons (1H at 3.9 ppm) served to determine the deprotection level of PBG\({}_{29}\) and PBG\({}_{65}\).