## 3 Results and Discussion
### Dynamic Light Scattering Measurements  
DLS measurements were performed on the chain end CuAAC-grafted arborescent copolymers in DMF and in PBS to characterize their solution properties. The first- and second-order hydrodynamic diameters obtained are provided in Table 6, and the corresponding CONTIN size distributions are supplied in the Supporting Information (Figures S1-S3). There is good agreement between the \(d_{\text{h}1}\) and \(d_{\text{h}2}\) values for all the samples in DMF, which is also reflected in comparatively narrow size distributions. Sample G3 PBG-_eg_-PGly has \(d_{\text{h}1}\) and \(d_{\text{h}2}\) values similar to G2 PBG-_eg_-PGly in DMF, as observed previously for a series of arborescent copolymers with a randomly grafted PGlyAc shell [16]. The smaller than expected \(d_{\text{h}1}\) and \(d_{\text{h}2}\) values for G3 PBG-_eg_-PGly could be due to the lower weight fraction of polyglycidol in that sample (last column in Table 5), allowing the PGly chains to adopt a more coiled conformation to shield the PBG core from the surrounding environment. The arborescent copolymers containing PEO display decreasing \(d_{\text{h}1}\) and \(d_{\text{h}2}\) values for increasing generation numbers. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Copolymer \({}^{\text{a}}\)**} & \multicolumn{3}{c}{**PBG Substrate**} & \multirow{2}{*}{\(G_{\text{y}}\)\({}^{\text{d}}\)} & \multicolumn{5}{c}{**Graft Corollary**} \\ \cline{2-2} \cline{5-8}  & \(M_{\text{n}}\) **(g/mol)\({}^{\text{b}}\)** & \% Alkyne\({}^{\text{c}}\)** & & \(M_{\text{n}}\) **(g/mol)\({}^{\text{b}}\)** & \(M_{\text{w}}\)/\(M_{\text{n}}\)\({}^{\text{b}}\)** & \(f_{\text{n}}\)\({}^{\text{e}}\) & **\% Shell \({}^{\text{f}}\)** \\ \hline G1 PBG-_eg_-PGly & 322,000 & 7 & 98 & 906,000 & 1.09 & 89 & 69 \\ G2 PBG-_eg_-PGly & \(1.1\times 10^{6}\) & 12 & 47 & \(3.2\times 10^{6}\) & 1.02 & 294 & 65 \\ G3 PBG-_eg_-PGly & \(3.0\times 10^{6}\) & 11 & 30 & \(6.3\times 10^{6}\) & 1.01 & 467 & 52 \\ G1 PBG-_eg_-PEO & 280,000 & 7 & 50 \(\text{\SIUnitSymbolMicro}\) & h & 1.30 & & \\ G2 PBG-_eg_-PEO & \(1.1\times 10^{6}\) & 12 & 36 \(\text{\SIUnitSymbolMicro}\) & h & 1.23 & & \\ G3 PBG-_eg_-PEO & \(3.0\times 10^{6}\) & 11 & 24 & \(4.8\times 10^{6}\) & 1.04 & 738 & 38 \\ \hline \hline \end{tabular} \({}^{\text{a}}\) All reactions done with a 1:1 azide to alkyne ratio; \({}^{\text{b}}\) absolute values from SEC-MALLS in DMF; \({}^{\text{c}}\) functionalization level from \({}^{1}\)H NMR analysis; \({}^{\text{d}}\) grafting yield: fraction of side chains attached to the substrate; \({}^{\text{e}}\) branching functionality: number of side chains added in the last grafting cycle; \({}^{\text{f}}\) weight fraction of shell material, from the difference in absolute molecular weight of copolymer and substrate; \({}^{\text{g}}\) grafting yield from the peak area ratio in the DRI response; \({}^{\text{h}}\) absolute molecular weight not determined.  
\end{table} 
Table 5: Characteristics of arborescent copolymers obtained by chain-end CuAAC grafting. This trend was also observed when comparing the SEC traces for these samples, where G1 PBG-_eg_-PEO was eluted at a lower volume than both G2 PBG-_eg_-PEO and G3 PBG-_eg_-PEO. Despite this unusual trend, the differences between the \(d_{\text{h1}}\) and \(d_{\text{h2}}\) values for each sample remain small (\(\leq\)4 nm), indicating that these structures have a uniform size in DMF. The DLS results in PBS for the chain end CuAAC-grafted arborescent copolymer samples are more promising than for the random CuAAC-grafted samples in terms of unimolecular micelle formation. For example, G1 PBG-_eg_-PGly and G2 PBG-_eg_-PGly have much smaller \(d_{\text{h2}}\) values (54 and 53 nm, respectively) than their randomly-grafted counterparts (\(d_{\text{h2}}\) values of 199 and 67 nm for G1 PBG-_eg_-PGly and G2 PBG-_g_-PGly, respectively). However sample G1 PBG-_eg_-PGly has diameters larger than expected