## 4 Discussion  
### Role of Interfaces in Pickering Emulsion Polymerization  
The calculated values for the work of adhesion between the nanoparticle and water (NP/w) and nanoparticle and polymer (NP/P) based on Equation (3) are given in Table 3. From the data, for NP/w, the magnitude of the work of adhesion decreases in order NP-Gly > NP-CN > NP-SH. The work of adhesion between the nanoparticle and polymer (NP/P) is significantly smaller than for NP/w and decreases in magnitude in the same order NP-Gly > NP-CN > NP-SH for all polymers. This confirms on one hand that the NP-Gly are most wetted by water and on the other hand that all the NPs are more strongly wetted by water than by the polymer and monomer. At this point, it is important to note that the surface energy of the monomer and its homopolymer in the cases of those that are polymerized through radical polymerization are close, the ratio of the surface tension of the monomer to the surface energy of the polymer is proportional to the square of polymer density divided by the monomer density, typically a factor of 1.1 [52], \(\left(\frac{\gamma_{P}}{T_{M}}\right)=\left(\frac{\rho_{P}}{\rho_{M}}\right)^ {2}\). Therefore, throughout this work we note that the contact angle determined for NPs with the polymers, by measuring the diameters of the circular traces left on the surface of the microspheres are equivalent to the contact angle of the NPs with the monomer (oil) in the emulsion droplet (colloidosome), from which microspheres are generated by polymerization to the extent given by the above relationship. Further, the contact angle of NPs will determine the size of the emulsion droplet and as soon as the polymerization starts, the contact angle will only slightly change until the equilibrium value with the polymer is reached, as the monomer is consumed, and more polymer is formed. As the time scale needed for polymerization of the emulsion droplets is 60 min, there is enough time for equilibration of the contact angle of NPs. Also, from the SEM studies, we observed that a change in density during the transition of the monomer to polymer \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Nanoparticle** & \(\gamma^{d}\)**\({}_{NP}\) (mN/m)** & \(\gamma^{p}\)**\({}_{NP}\) (mN/m)** & \(\gamma_{NP}\) (mN/m)** \\ \hline NP-SH & 20.96 & 26.60 & 47.56 \\ NP-CN & 25.40 & 26.94 & 52.34 \\ NP-Gly & 25.40 & 42.56 & 67.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Surface energy (interfacial energy of the nanoparticles with air) \(\gamma_{NP}\) and its disperse \(\gamma^{d}_{NP}\) and polar component, \(\gamma^{p}_{NP}\) of the silica nanoparticles with water, bearing different surface functional groups. The data for NP-CN and NP-SH were taken from reference [35]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Nanoparticle** & \(W^{dhesion}_{NP/inator}\) (m/m\({}^{2}\)) & \(W^{dhesion}_{NP/MM}\) (m/m\({}^{2}\)) & \(W^{dhesion}_{NP/BM}\) (m/m\({}^{2}\)) & \(W^{dhesion}_{NP/PRBA}\) (m/m\({}^{2}\)) \\ \hline NP-SH & 116.9 & 76.3 & 64.5 & 57.9 \\ NP-CN & 122.0 & 81.7 & 70.5 & 63.6 \\ NP-Gly & 140.2 & 87.9 & 72.0 & 64.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The calculated values of the work of adhesion based on Equation (3), where the surface energy values for the NPs were taken from Table 2 and for the polymers from reference [35]. causes [53] a small waviness of the surface of the final polymer microsphere. In this case, regions in the monolayer of NPs covering the microsphere could be jammed, being slightly pushed out or into the surface, decreasing or increasing the observed contact angle. While this jamming effect broadens the error, the average of the data should still represent the true value of the contact angle of the NPs with the polymer and as already mentioned with the monomer. However, as it can be seen in the SEM images of the Figure 1d, this effect is negligibly small for the polymers we investigated but can be better observed in the Figure S7 (top left corner of the image).