## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & \begin{tabular}{c} **Grafting Density** \\ **(Chains nm\({}^{-2}\))** \\ \end{tabular} & \begin{tabular}{c} **M\({}_{\rm a}\), NMR** \\ **(kDa)** \\ \end{tabular} & \
\begin{tabular}{c} **M\({}_{\rm a}\), sec** \\ **(kDa)** \\ \end{tabular} &
\begin{tabular}{c} **D** \\ **(nm)** \\ \end{tabular} \\ \hline PS-\(\sigma_{\rm low}\) & & 0 & & & & \(81\pm 20\) \\ PS-PMA\({}_{\rm 3k}\)-\(\sigma_{\rm low}\) & & 35 & 3 & 4 & \(1.8\) & \(86\pm 20\) \\ PS-PMA\({}_{\rm 6k}\)-\(\sigma_{\rm low}\) & & 70 & 6 & 8 & 2.1 & \(85\pm 30\) \\ PS-PMA\({}_{\rm 18k}\)-\(\sigma_{\rm low}\) & \(0.07\pm 0.01\) & 209 & 18 & 19 & 2.3 & \(90\pm 20\) \\ PS-PMA\({}_{\rm 28k}\)-\(\sigma_{\rm low}\) & & 325 & 28 & 15 & 2.2 & \(100\pm 30\) \\ PS-PMA\({}_{\rm 41k}\)-\(\sigma_{\rm low}\) & & 476 & 41 & 18 & 2.7 & \(100\pm 20\) \\ PS-PMA\({}_{\rm 49k}\)-\(\sigma_{\rm low}\) & & 569 & 49 & 34 & 2.2 & \(110\pm 20\) \\ \hline PS-\(\sigma_{\rm medium}\) & & 0 & & & & \(70\pm 20\) \\ PS-PMA\({}_{\rm 3k}\)-\(\sigma_{\rm medium}\) & & 30 & 3 & 4 & 1.9 & \(90\pm 30\) \\ PS-PMA\({}_{\rm 7}\)-\(\sigma_{\rm medium}\) & & 81 & 7 & 9 & 2.6 & \(90\pm 30\) \\ PS-PMA\({}_{\rm 20k}\)-\(\sigma_{\rm medium}\) & \(0.46\pm 0.02\) & 232 & 20 & 20 & 2.2 & \(120\pm 40\) \\ PS-PMA\({}_{\rm 30k}\)-\(\sigma_{\rm medium}\) & & 348 & 30 & 27 & 2.1 & \(170\pm 30\) \\ PS-PMA\({}_{\rm 42k}\)-\(\sigma_{\rm medium}\) & & 488 & 42 & 29 & 2.1 & \(160\pm 30\) \\ PS-PMA\({}_{\rm 51k}\)-\(\sigma_{\rm medium}\) & & 592 & 51 & 35 & 2.4 & \(180\pm 40\) \\ \hline PS-\(\sigma_{\rm high}\) & & 0 & & & & \(90\pm 20\) \\ PS-PMA\({}_{\rm 3k}\)-\(\sigma_{\rm high}\) & & 35 & 3 & 4 & 1.7 & \(110\pm 50\) \\ PS-PMA\({}_{\rm 10k}\)-\(\sigma_{\rm high}\) & & 116 & 10 & 12 & 2.1 & \(130\pm 30\) \\ PS-PMA\({}_{\rm 20k}\)-\(\sigma_{\rm high}\) & \(1.00\pm 0.12\) & 232 & 20 & 21 & 2.1 & \(160\pm 70\) \\ PS-PMA\({}_{\rm 33k}\)-\(\sigma_{\rm high}\) & & 383 & 33 & 27 & 2.4 & \(190\pm 30\) \\ PS-PMA\({}_{\rm 42k}\)-\(\sigma_{\rm high}\) & & 488 & 42 & 40 & 2.5 & \(200\pm 60\) \\ PS-PMA\({}_{\rm 55k}\)-\(\sigma_{\rm high}\) & & 639 & 55 & 44 & 2.0 & \(240\pm 60\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Library of PS-PMA core-canopy NPs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Grafting Density** & **Grafting Density in** & **Grafting Density in** & **Scaling Exponent** & **Scaling Exponent** \\
**(\(\sigma\))** & **H\({}_{2}\)O (Chains nm\({}^{-2}\))** & **DCM (Chains nm\({}^{-2}\))** & **in H\({}_{2}\)O** & **in DCM** \\ \hline Low & 0.17 & 0.07 & 0.27 & 0.63 \\ Medium & 0.80 & 0.46 & 0.50 & 0.88 \\ High & 2.50 & 1.00 & 0.55 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Grafting density and scaling exponent of PS-PMA core-canopy NPs in DCM and H\({}_{2}\)O.  
gels was observed [18]. However, the NMR experiments were performed below the solution-to-gel transition to study the dynamics of single particles rather than the dynamics of the NPs network. The NMR relaxation of the NPs suspension was measured at different magnetic fields and different temperatures to understand the local subsegmental chain dynamics in both the PS core and the PMA canopy. Both the spin-lattice relaxation (\(T_{1}\)) and spin-spin relaxation (\(T_{2}\)) were measured. The relaxation times obtained by NMR spectroscopy are influence by \(\tau_{\mathrm{c}}\) of the relaxation process and the interactions between the spin under study and their environment. Typically, \(T_{2}\) is not largely influenced by the magnetic field used and the values of \(T_{2}\) can be directly correlated to the subsegmental relaxation [35]. As the local mobility of the molecules under investigation decreases, the value of the \(T_{2}\) time decreases, and for very slow systems, it can be difficult to quantify the \(T_{2}\) relaxation precisely without using alternative pulse sequences. Consequently, the measurement of the \(T_{2}\) of the crosslinked PS core was challenging.