## 2 Materials and Methods  
### Characterization and Sample Preparation  
\({}^{1}\)H Nuclear magnetic resonance (NMR) spectroscopy was performed on a Bruker 300 MHz instrument (Bruker Ltd., Milton, ON, Canada), at a sample concentration of 15-20 mg/mL. Infrared analysis was performed on a Bruker Vector 22 FT-IR spectrometer (Bruker Ltd., Milton, ON, Canada), supplied with the OPUS 6.0 software package, to acquire and manipulate the spectra. The analysis was performed with 64 scans from 400 to 4000 cm\({}^{-1}\) at 1 cm\({}^{-1}\) resolution. Size exclusion chromatography (SEC) analysis was done on a Viscotek GPCmax instrument (Malvern, Montreal, QC, Canada) with a TDA 305 triple detector array and a Viscotek UV Detector 2600. Three PolyAnalytik Supere(tm) Series linear mixed bed columns of 300 \(\times\) 8 mm\({}^{2}\), with polystyrene molecular weight exclusion limits of 400 \(\times\) 10\({}^{3}\), 4 \(\times\) 10\({}^{6}\), and 20 \(\times\) 10\({}^{6}\) g/mol (PolyAnalytik, London, ON, Canada) were used in series with tetrahydrofuran (THF) as the mobile phase at a flow rate of 1.0 mL/min and 35 \({}^{\circ}\)C. Analysis of the PEO and P(HEA-TMS) linear chains, and all the arborescent copolymers were performed on a SEC instrument with a Waters 510 HPLC pump (Waters Ltd., Mississauga, ON, Canada), a 50 \(\upmu\)L injection loop, a Waters 2410 differential refractometer (DRI) detector (Waters, Mississauga, ON, Canada), and a Wyatt MiniDAWN laser light scattering detector (Wyatt Technology Corp., Santa Barbara, CA, USA) operating at 690 nm to determine the absolute molecular weight of the polymers. The column was a 500 \(\times\) 10 mm\({}^{2}\) Jordi Gel Xstream H2O Mixed Bed model (Jordi Labs, Mansfield, MA, USA) with a polystyrene molecular weight range of 10\({}^{2}\)-10\({}^{7}\) g/mol. \(N\),\(N\)-Dimethylformamide (DMF) with LiCl (1 g/L, to minimize polymer adsorption) was used at 1.0 mL/min and room temperature (RT). Knowledge of the refractive index increment (d\(n\)/d\(c\)) of linear \(\alpha\)-azido polyglycidol, \(\omega\)-azido poly(ethylene oxide) and \(\omega\)-azido poly(2-trimethylsilylethyl acrylate) was necessary to determine the absolute molecular weight by SEC. These were determined on a Brookhaven Instruments BI-DNDC 620 differential refractometer (Brookhaven Instruments Corp., Holtsville, NY, USA), using five solutions in DMF at concentrations ranging from 1 to 5 mg/mL at 30 \({}^{\circ}\)C. Preparative SEC was carried out with a Waters M45 pump (Waters Ltd., Mississauga, ON, Canada), a 2-mL sample injection loop, a Waters R401 differential refractometer detector (Waters Ltd., Mississauga, ON, Canada), and a [PERSON] DVB 1000 A ([PERSON], Mansfield, MA, USA) or a Mixed Bed 250 \(\times\) 22 mm\({}^{2}\) column ([PERSON], Mansfield, MA, USA). DMF with 0.2 g/L LiCl at 3.0 mL/min and RT served as the mobile phase, and the polymer was injected as a 20-30 mg/mL solution. Dynamic light scattering measurements were carried out batch-wise on a Brookhaven BI-200 SM light scattering goniometer (Brookhaven Instruments Corp., Holtsville, NY, USA) with a BI-APD (avalanche photo diode) detector and a Claire Lasers CLAS2-660-140C (120 mW) laser (Claire Lasers Corp., Kitchener, ON, Canada) operating at 660 nm. All the samples were measured at 25 \({}^{\circ}\)C and a scattering angle of 90\({}^{\circ}\) after filtration twice with 3.0 \(\upmu\)m polytetrafluoroethylene (PTFE) membrane filters. The correlator was operated in the exponential sampling mode and the hydrodynamic diameters were calculated from the \(Z\)-average translational diffusion coefficients obtained from first- and second-order cumulant analysis of the correlation function, to better account for polydispersity effects. CONTIN analysis of the data was also used to generate size distributions for the samples. Solutions were prepared at 0.1-2% \(w/v\), depending on the molecular weight (generation number) of the sample.