2.4.1. Determination of the Reaction Yield

The yield of the polymerization reaction was determined by weighing the resulting freeze-dried sample (xerogel) and comparing it with the total mass of the reagents using Equation (1).

$$\%Y = \frac{mass\_{\text{xrogeel}}(\text{g})}{mass\_{\text{total}}(\text{g})} \times 100\% \tag{1}$$

where *massxerogel* (g) is the mass of the xerogel in grams, and *masstotal* (g) is the total mass of the reactive compounds.

#### 2.4.2. Determination of Water Absorption Capacity

To determine the maximum water absorption capacity of each of the synthesized hydrogels, 100 mg of xerogel was added to 80 mL of distilled water. The hydrated hydrogel was weighed and deposited in water. The water absorption capacity (%*WA*) was determined using Equation (2).

$$\%WA = \left(\frac{W\_1 - W\_0}{W\_0}\right) \times 100\% \tag{2}$$

where *W*<sup>1</sup> and *W*<sup>0</sup> are the weights in grams of the swollen and initial hydrogels, respectively.

2.4.3. Determination of the Effective Cross-Link Density of a Cross-Linked Structure

To determine the degree of cross-linking, 0.01 g of xerogel was taken in a petri dish, and 1 mL of demineralized ether type I was added. The swollen gels were dried superficially with filter paper and left to stand for 10 min, and the weight of the petri dish with the hydrated polymer material was recorded with XB220 Precisa Analytical Balance. The measurements continued until a constant weight was obtained for each sample. This weight was used to calculate the volume fraction *ν*2m according to Equation (3):

$$w = 1 - \frac{\%WA}{100\%} \tag{3}$$

where *w* is the weight fraction of polymer in swollen gel [32].

$$\mathbf{C}\_d = \frac{mass\_{\text{xrogeel,net}}(\mathbf{g})}{mass\_{\text{total,dry}}(\mathbf{g})} \tag{4}$$

where *Cd* is the equilibrium degree of swelling of the polymer in a gel sample that is swollen to equilibrium in water, *massxerogel,wet* (g) is the wet mass of the xerogel in grams, and *masstotal,dry* (g) is the total mass of the dry sample. The hydrated material was dried in an oven (BIOBASE model BOV-T50F) at 50 ◦C for 24 h. The dried mass of the material was measured again.

$$
\upsilon\_{2m} = 1/\mathbb{C}\_d \tag{5}
$$

where *ν*2*<sup>m</sup>* is the polymer volume fraction of the cross-linked polymer in the swollen gel.

$$\frac{1}{\upsilon\_{2m}} - 1 - \frac{\rho\_{polymer}}{\rho\_{water\ 25\ ^\circ\text{C}}} \* \left(\frac{1}{w} - 1\right) = 0\tag{6}$$

where *ρpolymer* is the polymer density in g cm<sup>−</sup>3, and *ρwater* is the water density at 25 ◦C. By using the Excel solver function, it is possible to determine the value of the density of the polymeric part of the hydrogel using Equation (6).

$$\overline{M\_{\mathbb{C}}} - \frac{\left(1 - \frac{2}{\phi}\right) \times V\_1 \times \upsilon\_{2m}^{\frac{2}{3}} \times \upsilon\_{2r}^{\frac{1}{3}}}{\overline{v} \times \left(\ln(1 - \upsilon\_{2m}) + \upsilon\_{2m} + \chi \times \upsilon\_{2m}^2\right)} = 0 \tag{7}$$

where *MC* is the average molecular weight of the network chains (g mol−1), *ν*2*<sup>r</sup>* is the polymer volume fraction in the relaxed state, *V*<sup>1</sup> (18,07 cm3 mol−1) 1 is the molar volume of the swelling agent (water, in this study), and *υ* is the specific volume of the polymer. In this study, the reference value of cellulose is taken as 0.664 cm3 g−1) [33]. By using the Excel solver function, it is possible to determine the value of *MC* using Equation (7).

$$
\phi = \mathbf{3} \tag{8}
$$

where *φ* is functional at the cross-linking site [34,35].

$$
\chi = \frac{1}{2} + \frac{v\_{2m}}{3} \tag{9}
$$

where *χ* is the polymer–solvent interaction [35].

$$
\sigma\_{\varepsilon} \left( \frac{mol}{cm^3} \right) = \rho\_{polymer} / M\_{\mathbb{C}} \tag{10}
$$

where *υ<sup>e</sup>* is the effective cross-linking density of a cross-linked structure [36].
