## 3 Results and Discussion  
Using SI-ATRP, the PMA chains were successfully grafted from the surface of initiator immobilized PS NPs prepared by miniemulsion, and resulted in the formation of PS NPs having PMA canopies with different \(\sigma\) and varying \(N\) (Table 1). The increase in size created by the grafting of the PMA canopy resulted in a larger solvodynamic radius (\(R_{\mathrm{s}}\)) for the samples with longer PMA chains or higher \(\sigma\) (Figure 1b); similar results were also observed in the dry state by TEM measurements (Figure S3, Supplementary Material). The comparison of the size of the NPs in DCM and in H\({}_{2}\)O by DLS (Figure 1b,c) made it possible to study the swelling of the NPs and the evolution of thickness of the layer of end-grafted polymer chains. The size of the NPs in both DCM and water increased with increasing \(N\) and \(\sigma\). In addition, DCM is a good solvent for both the PS core and the PMA canopy and both components were swollen in suspension, while water is a poor solvent for both the PS and PMA, and the NPs were in a collapsed state. This variable swelling of the core had a consequence on the apparent \(\sigma\) of the system. In water, because the NP cores were collapsed, the number of chains per unit of surface area was larger than for the same NP in DCM (Table 2). In DCM, \(R_{\rm s}\) of bare PS NPs with \(\sigma_{\rm low}\) was 81 nm and the size increased up to 110 nm for NPs functionalized with PMA chains with \(N=569\) units. For NPs with \(\sigma_{\rm high}\), \(R_{\rm s}\) of bare PS NPs was 90 nm and increased up to 240 nm when PMA chains with \(N=639\) units were grafted. The variation of the size of the swollen NPs with the increase of \(N\) (Figure 1b,c) follows the scaling relation:  
\[R_{\rm s}-R_{\rm s,0}\propto N^{\rm v} \tag{1}\]  
where \(R_{\rm s}\) is the thickness of grafted chains, \(N\) is the degree of polymerization, \(v\) is the scaling exponent and \(R_{\rm s,0}\) is the size of the PS core. The scaling factor was shown to change for different grafting regime [14; 15; 31; 32]. Here, at \(\sigma_{\rm low}\) in DCM the scaling factor (\(v=0.63\)) was typical of grafted chains in the semi-collapsed chain regime in a good solvent. For the NPs with \(\sigma_{\rm medium}\) and \(\sigma_{\rm high}\), the scaling exponent of 0.88 and 0.91 were observed, respectively (Table 2), typical of grafted chains in the stretched regime [14; 15]. In water, a poor solvent for the PMA canopy, the stretching factor of the canopy with a \(\sigma_{\rm low}\) was 0.27 typical of collapsed chains. The particles prepared at higher \(\sigma_{\rm medium}\) and \(\sigma_{\rm high}\) dispersed in water showed a stretching parameter corresponding to the semi-collapsed regime. The result obtained for the stretching parameter of the grafted chains the PS-PMA NPs was in keeping with the decrease in solvent quality going from DCM to water. In a good solvent, as a consequence of the polymer-solvent enthalpic attraction and the polymer-polymer entropic repulsion, the grafted polymer chains adopt a stretched and extended conformation [33; 34] resulting in a large \(v\). Conversely, in a poor solvent, the favorable polymer-polymer attraction results in the adoption of a collapsed conformation. If the NPs were dispersed in a good solvent at a high enough concentration, the formation of colloidal