## 3 Results and Discussion
This unexpected result is related to the deswelling of crosslinked PS observed at high temperatures in specific solvent systems (Figure S6 Supplementary Material, ) [12; 42]. The energy of activation of the PMA chains of PS-PMA core-canopy NPs was calculated using the \(\tau_{\rm c}\) measured at different temperatures (Figure 4a). As expected, the activation energy associated with the subsegmental dynamics of the untethered PMA chains did not change significantly with \(N\). However, short grafted chains displayed lower activation energy than the free chains, indicative of a decrease in the degree of cooperativity associated with the relaxation process, in keeping with the conformational changes of the PMA chains upon grafting when the chains adopted a partially stretched conformation. As the \(N\) increases, the difference in the extent of cooperativity of the relaxation process between the grafted chain and the free chains decreased. As a result of the limited weight fraction of PMA in the PS-PMA samples prepared at a low \(\sigma\), the measurements were not as precise, and no clear conclusion to the effect of the \(\sigma\) can be drawn. In the case of the PS core, the results are more complex; the deswelling of the PS core led to the reduction in the local subsegmental mobility of the PS core and  
Figure 3: Temperature dependence of correlation time of PMA canopy with (**a**) short chains (\(N<50\)), (**b**) long chains (\(N>500\)), PS core with (**c**) short PMA chains and (**d**) long PMA chains. For PS-PMA NPs with low (0.17 chains nm\({}^{-2}\), \(\square\)), medium (0.8 chains nm\({}^{-2}\), \(\triangle\)), high (2.5 chains nm\({}^{-2}\), \(\Circinus\)) grafting density and free PMA chain (\(\Diamond\)). resulted in apparent negative activation energy for the relaxation process (Figure S4, Supplementary Material). Nonetheless, the results clearly show that the grafting of the PMA chains facilitated the relaxation of the PS core, and this effect was more pronounced for long chains grafted with \(\sigma_{\text{high}}\) and \(\sigma_{\text{medium}}\) than with \(\sigma_{\text{low}}\). The activation energy measured for the DCM suspensions of the PS-PMA NPs clearly demonstrated an interaction between the dynamics of the PS core and the dynamics of the PMA canopy. Similar trends are also observed in the solid-state. The thermal behavior of dried PS-PMA (Figure 4c,d) showed that both the glass transition temperature of the PS core and of the PMA canopy was affected by the architecture of the PMA canopy. The untethered PMA chains displayed a moderate increase (ca. 2 \({}^{\circ}\)C) of glass transition temperature with the \(N\) as expected from the Flory-Fox equation [43; 44]. Short PMA chains grafted to the PS core displayed a glass transition temperature systematically higher than free PMA chains of the same molecular weight. The difference in the glass transition temperature of free and tethered chains decreased with increasing \(N\). The results observed for the grafted PMA chains were consistent with what has been observed when polymer chains tethered to rigid NP cores transitioned between a highly stretched to a more relaxed brush regime [21; 45]. In addition, it was found that the glass transition temperature of PS core (Figure 4b; Table S1, Supplementary Material) significantly decreased by grafting PMA chains to the PS core. The grafting of the PMA chains on the surface of the PS core softened the core, in keeping with the increased local subsegmental mobility observed by NMR relaxation in the swollen nanoparticles suspensions.