# Improving Sorbents for Glycerol Capture in Biodiesel Refinement
## 2 Results
### Glycerol Capture from Aqueous Solution  
Batch type experiments were used for comparison of sorbent variants with regard to their potential for capture of glycerol from water. Analysis was completed by determination of the glycerol remaining in solution following overnight incubation of varying sorbent masses with glycerol solutions of varied concentration. Analysis of glycerol was based on a modification of the ASTM D6584-13 method [27]. Figure 6 provides single point comparison of glycerol binding by the synthesizedorbents. As shown, under identical conditions, the D13-Ph2(5) variant (Type 6) bound more target on a per mass basis than all other sorbents including the commercially available materials. D13b(6) and the Type 3 materials also stand out, with greater performance than other sorbents. Complete isotherms were generated for more thorough comparison of the materials. Figure 7 provides examples of the binding isotherms collected; additional isotherms are included in the Supporting Information, Figures S1-S5. We have shown previously that binding of targets by these sorbents can be described by a phenomenological model such as the Langmuir-Freundlich formulation [20; 28; 29],  
\[q=\frac{q_{\mathrm{s}}AkL^{n}}{1+kL^{n}} \tag{1}\]  
where \(q\) is the amount of target bound per unit sorbent surface area, \(L\) is the free ligand, \(k\) is the affinity coefficient, \(n\) is the homogeneity factor, and \(A\) is the total sorbent surface area. The typically used saturation capacity is \(q_{\mathrm{s}}\). Table 2 provides a summary of the calculated parameters. The dynamic range of the analytical method utilized for these studies limits the range of target concentrations that can be interrogated. Due to this limited range, it was necessary to access a series of isotherms at different sorbent masses to obtain a data set that could be fit with confidence. Sorbent masses were varied from 2.5 to 50 mg in a fixed solution volume (20 mL). This variation is captured by the area (\(A\)) in Equation (1). All data not representing binding of 0 or 100% of target was used in the generation of the isotherm for a given sorbent material. ED11, with ethane and diethylbenzene bridging groups, and E25, with ethane bridging groups, sorbents provide points for comparison of the sulfonated materials. There was no significant binding of glycerol by the E25 sorbent. ED11 bound some glycerol but less than any of the sulfonated sorbents (Figure 6). The addition of pendant sulfonatopnyl groups (E25-Ph(2)) dramatically increased capture of glycerol by E25. The similar sorbent, E50-Ph(2), showed a lower glycerol saturation capacity (see isotherms for E25-Ph(2) and E50-Ph(2) in the Supporting Information, Figure S1). The E50-Ph(2) sorbent shows a broad pore size distribution with no defined peak and an increased percentage of pores at smaller diameters while the E50 sorbent had a defined peak around 76 A (Figure 3). It is likely that the smaller saturation capacity of the E50-Ph(2) material is related to inhibited access to the total surface area of the sorbent owing to collapsed or restricted pores. The capacity could be impacted by  
Figure 6: Glycerol binding by the sorbents evaluated from identical batch type experiments using 271 \(\upmu\)M glycerol (10 mL) with 15 mg sorbent. incomplete sulfonation of the total surface area; however, the affinity of the sorbent for the target is higher than that of the E25-Ph(2) sorbent. Saturation capacities for the binding of glycerol by TEOS based sorbents with pendant sulfonatophenyl groups (S65-Ph(1) and S85-Ph(1)) were greater than those of the ethane-bridge sorbents while affinity coefficients were lower. These sorbents retained the pore structure of the base sorbents to a greater degree following functionalization. Sulfonation of the sorbent synthesized with a mixture of ethane and diethylbenzene bridging groups (ED11a(4); 18.0 mg/g) did not yield an increase in per mass binding when compared to the base sorbent (ED11; 38.8 mg/g).