## 3 Results and Discussion
### Optimization of CuAAC Reactions with PBG and Synthesis of G0 Copolymers  
All the grafting reactions reported herein used a 1:1 ratio of azide to alkyne functionalities. This ratio was purposely maintained constant in all the reactions, to determine how the efficiency of the coupling reaction was affected by parameters such as the composition of the side chains being grafted, but particularly by the characteristics (generation number and location of the coupling sites) of the arborescent substrates used in the reaction. The yield of the grafting reactions is correspondingly  
Figure 4: \({}^{1}\)H NMR spectra for (top to bottom) G1 PBG with _tert_-butyl-protected chain ends, deprotected chain ends (7 mol % CO\({}_{2}\)H), and alkyne-functionalized chain ends (7 mol % alkyne) in \(d_{6}\)-DMSO. Figure 3: \({}^{1}\)H NMR spectra for (top to bottom) G1 PBG substrate, randomly deprotected (19 mol % CO\({}_{2}\)H), and randomly alkyne-functionalized (19 mol % alkyne) in \(d_{6}\)-DMSO. low in some cases, but it is clear that it could be increased by modifying the reaction conditions used (e.g., using a larger ratio of PBG substrate to side chains). In recognition of the lower grafting yields achieved under the conditions selected for this investigation, the grafting procedures are identified as CuAAC coupling reactions rather than \"click\" reactions, for which consistently higher yields would be expected. The grafting yield (fraction of side chains grafted onto the substrate) was determined from the weight fraction of each component in the copolymers, along with the known amounts of substrate and side chains used in the grafting reaction as described earlier [16]. The solubility characteristics of the PBG substrates limited the solvents for the CuAAC reaction to either DMF or DMSO, and also influenced the selection of the catalyst. Due to its solubility in DMF a combination of CuBr and PMDETA was explored initially, as this catalyst system has been widely used for polymer-related CuAAC reactions [21]. Given the poor results obtained with CuBr/PMDETA, another less reactive catalyst, bromotris(triphenylphosphine) copper(I) bromide, was also investigated but gave even lower grafting yields. It was determined that CuSO\({}_{4}\) with sodium ascorbate (NaAsc) provided the best results, so these reactions will be discussed in more detail. The CuSO\({}_{4}\)/NaAsc combination also has been widely used as a source of Cu(I) [22]. This catalyst system is generally employed in aqueous or aqueous/alcoholic mixtures, due to the limited solubility of NaAsc in organic solvents. One benefit of this approach is that the reactions can proceed in the presence of residual oxygen, since NaAsc acts as a reducing agent for copper(II) and can regenerate copper(I) continuously during the reaction. Because NaAsc has limited solubility in DMF, two FPT cycles were, nevertheless, used to remove dissolved oxygen prior to the addition of NaAsc to ensure the presence of a maximum amount of copper(I) catalyst in the reaction. The color of the solution started as greenish blue but turned bright yellow minutes after adding NaAsc, and persisted over the 24 h reaction period. Removal of the copper catalyst by preparative SEC was efficient, as indicated by the absence of color in the purified copolymer solutions. This synthetic protocol was, therefore, applied to the preparation of the GoPBG copolymers with the different \(\alpha\)-azido side chains. The characteristics of the purified arborescent copolymers derived from randomly alkyne-functionalized G0 PBG substrates coupled with \(\omega\)-azido P(HEA-TMS), \(\alpha\)-azido PGly, and \(\omega\)-azido PEO are summarized in Table 2, and the SEC traces obtained for the crude copolymers and the G0 substrate are compared in Figure 5. The peak for the copolymer (leftmost peak) is shifted relatively to the G0 substrate in all cases, while unreacted P(HEA-TMS), PGly or PEO side chains give the rightmost peak.