## 2 Results and Discussion
### Polymerization Rate and Average Number of Radicals per Particle  
The variation of the polymerization rate (\(R_{p}\)) and the average number of radicals per particle (\(\tilde{n}\)) as the polymerization evolves is shown in Figure 10 and Table 3, respectively. The \(R_{p}\) values (in mol/L water-min) were obtained by fitting _X vs._\(t\) data to a polynomial equation and evaluating its derivative at some given points along the polymerization using the recipe data. On the other hand, \(\tilde{n}\) values were calculated from the well-known equation representing the polymerization rate in an emulsion polymerization and which applies in our case:  
\[R_{p}=\frac{k_{p}\big{[}M_{p}\big{]}N_{p}\tilde{n}}{N_{A}} \tag{5}\]  
where \(k_{p}\) is the propagation rate constant and \(N_{A}\), the Avogadro's number. Given that this equation would be used in a copolymerization where St and DVB are monomer 1 and 2, respectively, the terms _[M]\({}_{p}\)_ and \(k_{p}\) were redefined, obtaining:  
\[R_{p}=\ \big{(}k_{p11}[St]+k_{p22}[DVB]+k_{p12}[DVB]+k_{p21}[St]\big{)}\frac{ \tilde{n}N_{p}}{N_{A}} \tag{6}\]  
where \(k_{11}\) and \(k_{22}\) are the homo-propagation rate constants for St and DVB, respectively and \(k_{12}\) and \(k_{21}\), the corresponding cross-propagation rate constants. Despite the fact that DVB is a mixture of \(m\)-DVB and \(p\)-DVB, to simplify the calculations it was assumed that DVB is only composed of \(m\)-DVB. The values taken from literature [27] for \(k_{11}\), \(k_{22}\), \(k_{12}\) and \(k_{21}\) are 480, 456, 1140 and 456 L\(\cdot\)mol\({}^{-1}\cdot\)s\({}^{-1}\), respectively. Once all the constants and the rest of the variables in Equation (6) were known, \(\tilde{n}\) was calculated at different points along the polymerization. Figure 9: Evolution of total monomers concentration inside nanoparticles with global conversion in polymerizations at 0.05 (**a**) and 0.15 (**b**) g/min in organic dosing rate. Runs M (\(\blacklozenge\)); runs MR (\(\blacktriangle\)). Figure 10 shows that \(R_{p}\) increases at the beginning of the polymerization, remaining almost constant from approximately 20% up to 90% global conversion, with a pronounced increase at the end of the reaction for the polymerization at the higher dosing rate. In contrast, the \(R_{p}\) values at the lower dosing rate are significantly lower and show a slightly decrease as polymerizations evolve. On the other hand, Table 3 reveals that \(\tilde{n}\) behavior is similar for both polymerizations, that is to say, a decrease from the beginning to the end of the organic phase dosing, followed by an increase at the end of the polymerization. However, the \(\tilde{n}\) values for the polymerization at higher dosing rate are significantly higher; furthermore, the final increase is also more marked, attaining values around to \(3.4\times 10^{-2}\)-\(4.8\times 10^{-2}\) radicals per particle against \(3.8\times 10^{-4}\)-\(4.4\times 10^{-4}\) for the polymerization at the other dosing rate. The above results suggest that the direct dependence of \(x_{i}\) on the organic-phase dosing rate arises from the higher values of \(\tilde{n}\) in the polymerization at the higher dosing rate, which would lead to an increase in the monomer consumption. This supports the previous explanation given to understand the direct dependence of gel percentage on dosing rate (Figure 5), which said that the probability of cross-linking reactions occurrence was increased due to the increase of the propagation reactions occurrence inside the particles. Figure 10: Evolution of polymerization rate with global conversion in polymerizations at 0.05 (**a**) and 0.15 (**b**) g/min in organic phase dosing rate. Runs M (\(\blacklozenge\)); runs MR (\(\blacktriangle\)).