## 3 Results and Discussion
### Synthesis of GOPBG with Different Branching Densities  
The synthesis of arborescent GOPBG from amine-terminated PBG side chains and carboxyl-functionalized PBG substrates of different lengths and deprotection levels was  
Figure 1: Comparison of \({}^{1}H\) NMR spectra for the different linear PBG samples in DMSO-\(d_{\delta}\). achieved under previously optimized coupling reaction conditions [31]. The coupling reagents \(N\),\(N^{\prime}\)-diisopropylcarbodiimide (DIC) and 1-hydroxybenzotriazole (HOBt) were used to activate the carboxyl groups. All the reactions were carried out in DMSO at 25 \({}^{\circ}\)C, using a 5:1 molar ratio of coupling agents (DIC/HOBt) to CO\({}_{2}\)H groups on the substrate to maximize the grafting yield and the coupling efficiency. These optimized conditions were also subsequently used to synthesize the G1 and G2 arborescent PBG. The general coupling reaction for the synthesis of arborescent PBG is shown in Scheme 1, using a G0 polymer synthesis as an example. Different chain lengths and deprotection levels for the linear PBG substrate were used in the synthesis of GOPBG, while the PBG side chains had M\({}_{\text{n}}\)\(\approx\) 5000 g/mol in all cases. Three well-defined (dispersity D = M\({}_{\text{w}}\)/M\({}_{\text{n}}\)\(\leq\) 1.08) arborescent C0 (comb-branched) PBG were obtained in that manner: GOPBG\({}_{\text{15}}\) from a PBG substrate with X\({}_{\text{n}}\) = 15 and 100% deprotection, GOPBG\({}_{\text{29}}\) from a PBG substrate with X\({}_{\text{n}}\) = 29 and 31% deprotection, and GOPBG\({}_{\text{65}}\) from a PBG substrate with X\({}_{\text{n}}\) = 65 and 31% deprotection. The corresponding characterization data are summarized in Table 1.  
As shown in Table 1, the number-average branching functionality of the arborescent polypeptides, \(f_{\text{n}}\), defined as the number of side chains added in the grafting reaction, increased with the deprotection level since more coupling sites were available. However, despite the identical deprotection levels of PBG\({}_{\text{29}}\) and PBG\({}_{\text{65}}\), the branching functionality \(f_{\text{n}}\) achieved for GOPBG\({}_{\text{29}}\) was marginally lower. This is attributed to increased steric crowding leading to less accessible carboxylic acid moieties in the shorter PBG\({}_{\text{29}}\) substrate. The number-average branching density (\(b_{\text{d}}\)), defined as the number of side chains added in the grafting reaction divided by the number of repeating units in the linear substrate, clearly increased as the chain length of the substrate decreased. As a result, a compact and dense structure is expected for GOPBG\({}_{\text{15}}\) (\(b_{\text{d}}\) = 0.80), as opposed to a loose and more porous structure for GOPBG\({}_{\text{65}}\) (\(b_{\text{d}}\) = 0.11), and an intermediate (semi-compact) structure \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Deprotection Level** & **Molar Ratio** & **M\({}_{\text{n}}\)(g/mol)** & **D** & **G\({}_{\text{y}}\) (\%)** & **C\({}_{\text{e}}\) (\%)** & \(f_{\text{n}}\)** & \(b_{\text{d}}\) \\  & **of Substrate (\%)** & **CO\({}_{2}\)H:NH\({}_{2}\)** & & & & & & \\ \hline GOPBG\({}_{\text{15}}\) & 100 & 1.1:1 & 65,400 & 1.04 & 76 & 80 & 12 & 0.80 \\ GOPBG\({}_{\text{29}}\) & 31 & 1.7:1 & 35,300 & 1.08 & 87 & 54 & 5.4 & 0.19 \\ GOPBG\({}_{\text{65}}\) & 31 & 1.7:1 & 51,000 & 1.06 & 89 & 36 & 7.1 & 0.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of arborescent GOPBG with different structures. for G0 PBG\({}_{29}\) (\(b_{\rm d}=0.19\)). The synthesis of the arborescent G0 PBG samples with different branching densities (porosities) is illustrated with their SEC elution curves in Figure S2.