# Effect of the Sulfonation on the Swollen State Morphology of Styrene Cross-Linked Polymers
## 3 Results and Discussion  
### Proton Exchange Capacity (PEC)  
The comparison of the PECs of the ion-exchange resins obtained with different sulfonation methods with the respective sulfur contents from the elemental analysis can give valuable information. The PECs of the polymer materials determined by back-titration are reported in Table 1.  
The PEC of a gel-type styrenic resin cannot exceed 5.4 mmol H\({}^{+}\) g\({}^{-1}\), corresponding to the functionalization of all the aromatic rings with one sulfonic group each. The simple inspection of PECs suggests that oleum gave an oversulfonated resin (_Gel_oleum_), and concentrated H\({}_{2}\)SO\({}_{4}\) introduced more or less one sulfonic group per phenyl ring in _Gel_H\({}_{2}\)_SO\({}_{4}\)_. This simple analysis would also suggest that sulfonation was not quantitative in _Gel_HCISO\({}_{3}\)_, which seems rather surprising. Whereas sulfuric acid and oleum are neither soluble in the swelling \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample 1** & **PEC 2** & **C\% wt** & **Total S\% wt** & **Cl\% wt** & **x 3** \\ \hline _Gel\_oleum_ & 5.51 & 44.96 & 19.99 (6.24) 2 & – & 1.33 \\ _Gel\_H\({}_{2}\)SO\({}_{4}\)_ & 5.20 & 50.64 & 17.31 (5.40) 2 & – & 1.02 \\ _Gel\_HCISO\({}_{3}\)_ & 4.16 & 50.40 & 17.33 (5.40) 2 & 3.9 4 (0.11) & 1.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Analytical data on the composition of the sulfonic resins. agent (DCE) nor able to swell the starting resin, chlorosulfonic acid is miscible with DCE. On this basis, chlorosulfonic acid should access the swollen polymer framework easily in comparison with sulfuric acid or oleum. The difficulty of the latter two sulfonation agents to diffuse into the polymer framework is shown by the egg-shell distribution of sulfonic groups in partially sulfonic resins [11]. In these cases, the sulfonation starts from the external surface, then the first sulfonic (and hydrophilic) layer is swollen by H\({}_{2}\)SO\({}_{4}\) (or oleum) which sulfonates a second layer just beneath the surface and so on. However, the comparison of PECs with the total sulfur and carbon from the elemental analysis gives a more detailed and appropriate insight on the effects of the different sulfonation methods. Sulfur can be distributed among three different types of \"sulfo\"-groups: sulfonic (-SO\({}_{2}\)OH), sulfone bridges (-SO\({}_{2}\)-) and chlorosulfonic (-SO\({}_{2}\)Cl). The latter were found, in little amount, only in \(Gel\_HClSO_{3}\) as shown by the presence of chlorine in the material. To estimate the actual degree of sulfonation of the phenyl rings we assumed that the resins were essentially sulfonic polystyrene with a formula weight C\({}_{2}\)H\({}_{3}\)-C\({}_{6}\)H\({}_{5}\)\(\cdot\)\(x\)SO\({}_{3}\) (we neglected both the presence of DVB, which is nominally only 2% of the resin and the different nature of the sulfo-groups), where \(x\) is straightforward to be obtained from the ratio of the C and S weight percentages (Equation (1)):  
\[x=8\times\frac{S(\%wt)\times AW(C)}{AW(S)\times C(\%wt)}\approx 3\times \frac{S(\%wt)}{C(\%wt)} \tag{1}\]  
This number is also the degree of sulfonation, defined as the average number of \"sulfo\" groups per phenyl ring. The values of \(x\) show that the starting gel-type resin is fully (at least) sulfonated in each case and confirm that a remarkable oversulfonation takes place with oleum. In line with previous reports of sulfonation of PS-DVB resins with oleum exceeding the limit of one sulfonic group per each phenyl ring of the polymer [18], the PEC of \(Gel\_oleum\) is consistent with the presence of 1.17(5) sulfonic groups per phenyl ring i.e., ca. 17% of the phenyl rings bear two acidic groups. However, this does not entirely account for the total content of sulfur of \(Gel\_oleum\). It can be estimated that there are on average 0.15(5) sulfone bridges per phenyl ring, which amounts to ca. 11% of total sulfur in the resin. This also implies that ca.