## 3 Results  
The molecular weight between cross-links (cap M cap W sub c) is defined to provide a quantification parameter to characterize the molecular structure of the capsule wall. The MW between Cross-links is a parameter that characterizes the average distance between cross-linking points in the polymer network. Since acrylic monomer conversion is reported to reach full conversion [24; 25], it was reasonably assumed that the acrylic conversion was completed. Under this hypothesis, the MW between Cross-links can be calculated by dividing the average molecular weight of the monomers (\(M_{av}\)) by the number of acrylic groups per molecule (\(c\)) [26], as shown in Equation (4):  
\[MW_{c}=\frac{M_{av}}{c} \tag{4}\]  
In Table 4, the batches of capsules are characterized in terms of their molecular structures, such by \(MW_{c}\) and _HSP Distance_. The volume-weighted mean diameter (VW mean diameter) is reported as calculated via AccuSizer 780 AD, which leverages single-particle optical sensing (SPOS) [27]. The morphology of the prepared batches was characterized by scanning electron microscopy (SEM) using a FlexSEM 1000 from Hitachi (Chiyoda City, Tokyo, Japan). The images for the batches of Table 4 are shown in Figure 5.  
When the capsules with the highest \(MW_{c}\) (CAP \(|\) 0 1 1 0 1) were included in the SEM environment, they completely collapsed, presenting a highly distorted morphology. In contrast, the other capsules with lower \(MW_{c}\) exhibited a more intact appearance. This visual discrepancy suggests that CAP \(|\) 0 1 1 0 1 is characterized by poor encapsulation quality. The reason for this poor structural integrity will be discussed in the Discussion section. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample Name**} & \multicolumn{3}{c}{**Monomer Mixture**} & \multicolumn{2}{c}{**MW between**} & \multicolumn{2}{c}{**VW Mean**} \\  & **\% A** & **\% B** & **\% C** & **Cross-Links** & **HSP Distance** & **Diameter [\(\mu\)m]** \\ \hline CAP \(|\)11\(|\)0\(|\)0\(|\) & 100 & 0 & 0 & 128 & 1 & 20 \\ CAP \(|\)0\(|\)11\(|\)0\(|\) & 0 & 100 & 0 & 172 & 0.46 & 18 \\ CAP \(|\)0\(|\)3\(|\)0.7\(|\)0\(|\) & 30 & 70 & 0 & 147 & 0.58 & 24 \\ CAP \(|\)0\(|\)5\(|\)0\(|\)5\(|\)0\(|\) & 50 & 50 &The batch samples were then mechanically characterized with the abovementioned nanoindentation protocol. The rupture force of the individual capsules versus their diameters was then plotted in Figure 6.  
Figure 5: SEM photographs of the microcapsule slurries: (**a**) CAP111010, (**b**) CAP1011101, (**c**) CAP10.310.7101, (**d**) CAP10.510.5101, (**e**) CAP101011, (**f**) CAP10.31010.71, and (**g**) CAP10.51010.51. Figure 6: Rupture force for each sample population plotted in function of the diameter. Linear regression and 95% confidence intervals are reported for each sample. A linear relationship between the force required to break a capsule and its diameter can be evidenced, as highlighted in Figure 6. In other words, the size of the capsule has a direct impact on its mechanical properties. Larger capsules have a greater surface area and volume compared to smaller ones. This increased surface area allows for a more extensive stress distribution when external forces are applied. As a result, the load is distributed over a larger area, reducing the stress concentration on any particular point within the capsule. Consequently, the force required to cause rupture increases in proportion to the diameter of the capsule. Furthermore, the internal volume of the capsule also influences its mechanical properties. This higher internal volume for larger capsules can contribute to the capsule's overall structural stability and strength, requiring a higher force to break the capsule. A first-order linear regression analysis with a zero intercept was conducted to predict the value of rupture force as a function of the capsule diameter.