## 2 Results and Discussion
### Control of the Stability of the TiO\({}_{2}\) NC/Monomer Emulsion Droplets  
Since our TiO\({}_{2}\)/PS hybrid nanospheres are produced through _in situ_ polymerization, the stability of the TiO\({}_{2}\) NC/monomer droplets in water becomes crucial for the success of the polymerization. To this aim, a two-step strategy was developed. In the first step, we injected the TiO\({}_{2}\) NC/monomer mixture into an aqueous Tween 20 solution at a given concentration, and followed by sonication with a probe sonicator. Due to the steric stabilization of Tween 20, as well as the positive surface charges from the hydrolysis of TiO\({}_{2}\), the obtained mini-emulsion was very stable. However, after adding the initiator, KPS, to start the _in-situ_ polymerization, aggregation of the TiO\({}_{2}\) NC/monomer droplets occurred, leading to phase separation. This confirms that the stability of the mini-emulsion results from the synergistic role of both the steric stabilization of Tween 20 and the positive surface charges of TiO\({}_{2}\). When the polymerization started after adding KPS, the resulting oligomer or polymer chains with anionic end groups (-OSO\({}_{3}\)-) would interfere with the positive surface charges of TiO\({}_{2}\), leading to surface charge neutralization. Since the adsorbed Tween 20 molecules alone were unable to stabilize the emulsion droplets, phase separation occurred. One may propose to increase the amount of steric stabilizer, Tween 20, so that it alone can stabilize the system. However, our experiments revealed that this is not a feasible solution. In particular, we have prepared mini-emulsions at four different concentrations of Tween 20. Figure 3b (filled circles) shows the measured diameter of the emulsion droplets (\(D_{p}\)) at equilibrium as a function of the overall concentration of Tween 20, \(C_{\rm T20}\). It is seen that \(D_{p}\) decreases as \(C_{\rm T20}\) increases. However, we observed that the above instability problem (phase separation) remains for all the four cases. In fact, we have computed the amount of Tween 20, \(C_{\rm T20,\infty}\), required to fully cover the surface of the emulsion droplets:\[C_{\mathrm{T20},\infty}=\frac{6\phi W_{\mathrm{T20}}}{D_{p}A_{\mathrm{T20}}N_{A}} \tag{1}\]  
where \(\phi\) is the volume fraction of the TiO\({}_{2}\) NC/monomer mixture, \(W_{\mathrm{T20}}\) (=1.23 \(\times\) 10\({}^{3}\) g\(\cdot\)mol\({}^{-1}\)) is the molar mass of Tween 20, \(A_{\mathrm{T20}}\) is the surface area occupied by one Tween 20 molecule, which is equal to 46.5 A\({}^{2}\), taken from the work of [PERSON] and [PERSON] [47], and \(N_{A}\) is the Avogadro constant. The computed relation between \(C_{\mathrm{T20},\infty}\) and \(D_{p}\) for our system is shown in Figure 3b (continuous curve). It is seen that the \(C_{\mathrm{T20},\infty}\) curve is under the experimental data, indicating that in all the four cases the added amount of Tween 20 is more than enough to fully cover the surface of the droplets. The excess amount of Tween 20 is the dissolved partition, equilibrating with the surface adsorption. It should be noted that the \(C_{\mathrm{T20},\infty}\) curve depends on the \(A_{\mathrm{T20}}\) value reported in the literature, which may be slightly different for the present system. Thus, the comparison in Figure 3b is only qualitative. However, the trend of the experimental data is almost in parallel to that of the \(C_{\mathrm{T20},\infty}\) curve, which at least indicates that the density of Tween 20 on the surface is practically the same for the four cases. Thus, the stability of the given system cannot be improved by adding more Tween 20, which can only lead to reducing the droplet size. An alternative of course is to use a cationic initiator for the polymerization [42] so that the charge neutralization does not occur during the polymerization. This is indeed a proper solution, but the obtained hybrid nanospheres would be positively charged.