## 4 Discussion
### Size of Microspheres Function of NP Type for the Same Monomer
Figure 5: Normalized size distribution of the PtBA microspheres obtained from Pickering emulsion polymerization of tBA monomer with NPs bearing different surface functional groups NP-Gly, NP-CN, and NP-SH. The cartoon in Figure 6 was constructed based on the experimental findings in Table 3, Figures 4 and 5; the cartoon depicts the gradual change of the NPs immersion and contact angle \(\beta\) with the oil phase for an \(o/w\) emulsion, and its effect on the emulsion droplet radius R and curvature 1/R. Our experimental findings indicate that for an \(o/w\) emulsion, the increase in the contact angle with the oil phase, the NPs become less and less immersed in oil, the size of the obtained polymer colloidosomes also increases, e.g., the contact angle of the NPs with PtBA increases in the order NP-SH \(<\) NP-CN \(<\) NP-Gly. The value of the contact angle of the NPs with PBM also increases in the order NP-SH \(<\) NP-Gly, whereas the size of the microspheres also increases in the same order, see Figure S13. PMM only with NP-Gly microspheres could be obtained, whose size distribution is given in Figure S14. However, when the value of the contact angle \(\beta\) drops below 114\({}^{\circ}\) it seems that mixed or multiple emulsions are formed, as judged from the fact that no spherical microspheres are obtained anymore. Irregular polymer block shapes are obtained for NP-CN with PBM (114\({}^{\circ}\)), NP-CN with PMM (108\({}^{\circ}\)), NP-SH with PMM (106\({}^{\circ}\)), see Figure S15, indicating that the Pickering emulsion are complex below a critical contact angle \(\beta\), of approximately 114\({}^{\circ}\) with the oil, and 66\({}^{\circ}\) with water, signaling the beginning of the emulsion phase inversion and the coexistence of complex emulsions, mixed and multiple emulsions. By extrapolation, we hypothesize that the same is the case for the \(w/o\) emulsions, namely that the increase in the curvature of the water emulsion droplets decreases with the decrease in the contact angle \(\beta\) of the NPs with the oil. Our experimental values for the contact angle \(\beta\) finally confirm the theoretical predictions of [PERSON] and coworkers [38], which state  
Figure 6: Diagram depicting the relationship between the contact angle \(\beta\) of the NP with the oil, i.e., immersion depth of the nanoparticle at the oil/water interface and the curvature of the interface. For \(o/w\) emulsions, \(\beta\) > 90\({}^{\circ}\), the larger the value of the contact angle \(\beta\), the larger the emulsion droplets. For \(w/o\) emulsions, \(\beta\) < 90\({}^{\circ}\), the smaller the value of the contact angle \(\beta\), the larger the emulsion droplets. that the NPs whose contact angle with the water remains <75\({}^{\circ}\) and with the oil > 105\({}^{\circ}\) can only stabilize \(o/w\) emulsions, and NPs whose contact angle with water is >130\({}^{\circ}\) and with oil < 50\({}^{\circ}\), can only stabilize \(w/o\) emulsions, whereas in between these ranges complex multiple emulsion exist, signaling the approach of an emulsion phase inversion, when NPs have a contact angle of 90\({}^{\circ}\) with both phases. Further, from Table 3 and Table S4, there appears to be a relationship of direct proportionality between the increase in \(\Delta\)W and the microsphere diameter.