# Moisture Sorption Behavior of Deproteinized Sunflower Meal and Patterned Food Extrudate
## 3 Results and Discussion
### Net Isosteric Heat of Sorption  
In order to create the dependence \(\ln(a_{\text{w}})=\text{f}(1/T)\), we used the modified Oswin model, transforming it into:  
\[a_{\text{w}}=\frac{1}{1+\left[\left(A+Bt\right)M^{-1}\right]^{C}}, \tag{16}\]  
Figure 2: Residuals (blue dots) from the modified Oswin model during adsorption at several moisture contents.  
By setting different moisture contents in the range from 6 to 30% d.b. according to Equation (16), we calculated the corresponding values of the water activity for the three investigated temperatures (Table 4). The results in the table show that at equal moisture contents of both products, the water activity of PFE was significantly higher, especially at lower moisture contents.  
For each investigated product, we determined the slope of the straight line called isoster using the plot of \(\mathrm{In}\mathrm{{}_{w}}\) versus \(1/T\), and we calculated the values of \(q_{\mathrm{st}}\) for different moisture contents. Figure 4 shows the change of the net heat of sorption with dependence on the moisture content. For both products, the isosteric heat initially decreased significantly up to 15% (d.b.) moisture content. After that point, the further decrease was slower. The sharp increase in isosteric heat of sorption at low moisture content may be explained by the fast exposure of extremely active polar sites of the product's surface, which are encircled by water molecules that form a monolayer coat. As the active sites are occupied, sorption begins to occur in fewer active sites in the multilayer, where less energy is involved in the binding, reflected by lower values of isosteric heats of sorption [37]. The net heat of sorption of both products is significantly lower than the heat of phase transition of pure water (43.6 kJ/mol), indicating a relatively weak interaction between the water molecules  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(\mathbf{M}\)} & \multicolumn{4}{c}{**DSM**} & \multicolumn{4}{c}{**PFE**} \\ \hline  & \(T\) & **293** & **303** & **313** & **293** & **303** & **313** \\ \hline
7 & \(a_{\mathrm{w}}\) & 0.105 & 0.136 & 0.179 & 0.190 & 0.222 & 0.262 \\
10 & & 0.261 & 0.322 & 0.397 & 0.386 & 0.434 & 0.488 \\
12 & & 0.383 & 0.455 & 0.536 & 0.510 & 0.560 & 0.612 \\
15 & & 0.554 & 0.625 & 0.698 & 0.659 & 0.702 & 0.745 \\
18 & & 0.686 & 0.746 & 0.803 & 0.762 & 0.796 & 0.829 \\
20 & & 0.752 & 0.803 & 0.849 & 0.810 & 0.839 & 0.866 \\
23 & & 0.8245 & 0.863 & 0.897 & 0.863 & 0.885 & 0.905 \\
25 & & 0.8589 & 0.890 & 0.918 & 0.888 & 0.906 & 0.9231 \\
30 & & 0.914 & 0.935 & 0.952 & 0.929 & 0.941 & 0.952 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Water activities (\(a_{\mathrm{w}}\)) of DSM and PFE calculated by modified Oswin model for different values of moisture content (\(M\), % d.b.) and in the range of the absolute temperatures of the experiment (\(T\), K).  
Figure 3: BET monolayer moisture of DSM and PFE at several temperatures obtained using a standard algorithm [31] at adsorption.  
and the dry solid. Similar results were obtained for the net isosteric heat of sorption of other products [52], including for extrudates [37]. The DSM had higher values of net isosteric heat than PFE in all intervals of the moisture content's change. Obviously, extrusion reduces the bond energy between the solid matrix and the water molecules. The comparison of the results obtained for net isosteric heat of sorption of DSM with the published literature data for sunflower seeds in Ref. [53] showed that the heat was significantly higher for the DSM than for the seeds. This was probably due to the lower fat and protein contents of DSM. Simultaneously, our results for PFE were lower than those obtained for extrudates prepared from a blend composition of maize, finger millet, defatted soy, and elephant foot yam [37].