# Moisture Sorption Behavior of Deproteinized Sunflower Meal and Patterned Food Extrudate
## 3 Results and Discussion
### Monolayer Moisture Content  
The MMC values at 20 \({}^{\circ}\)C for DSM were approximately close (7.21% d.b. at adsorption and 7.88% d.b. at desorption). For PFE, a higher hysteresis of MMC was observed--6.45% d.b. at adsorption and 7.40% d.b. at desorption. The MMCs of the PFE were lower than those of the DSM (Figure 3). This is probably due to the amorphous structure of the extrudate, which decreases the number of active sites. The MMC decreased with the temperature rise for both products, which is typical for most foods [51]. This probably could be explained by the fact that, when the temperature increases, the number of active centers able to keep the water molecules decreases. The linear equations described satisfactorily (\(R^{2}\) = 0.99) the functional dependence of monolayer moisture content on the temperature. This gave us a reason to apply the modified BET model including the linear temperature effect (Equations (11) and (12)). The modified BET model's coefficients for DSM and PFE are shown in Tables 2 and 3, respectively. The high values of the correlation coefficients and low values of _ARE_ and _SEE_ indicated that the modification of the BET model involving the temperature can be applied for the description of experimental data up to \(Rh\) < 0.45 and for the calculation of the MMC.  
\begin{table}
\begin{tabular}{c l c c c c} \hline \hline
**Model** & **Coefficients** & **R** & **SEE** & **ARE, \%** & **Plot of Residuals** \\ \hline \multirow{3}{*}{GAB} & \(a\) = 8.5282 & \multirow{3}{*}{0.97} & \multirow{3}{*}{1.31} & \multirow{3}{*}{8.18} & \multirow{3}{*}{Random} \\  & \(b\) = 0.7385 & & & & \\  & \(c\) = 682.19 & & & & \\  & \(a\) = 10.03405 & & & & \\ BET & \(b\) = \(-\)0.10825 & & & & \\  & \(c\) = 83.45321 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c l c c c c} \hline \hline
**Model** & **Coefficients** & **R** & **SEE** & **ARE, \%** & **Plot of Residuals** \\ \hline \multirow{3}{*}{Chung–Pfost} & \(a\) = 349.2721 & \multirow{3}{*}{0.99} & \multirow{3}{*}{1.16} & \multirow{3}{*}{4.92} & \multirow{3}{*}{Patterned} \\  & \(b\) = 24.3482 & & & & \\  & \(c\) = 0.2017 & & & & \\  & \(a\) = 4.231838 & & & & \\  & \(b\) = \(-\)0.023758 & & & & \\  & \(c\) = 1.617364 & & & & \\  & \(a\) = 13.47429 & & & & \\  & \(b\) = \(-\)0.08232 & & & & \\  & \(c\) = 2.76633 & & & & \\  & \(a\) = 0.00016 & & & & \\ Henderson & \(b\) = 56.2774 & & 0.98 & 1.22 & 11.08 & Random \\  & \(c\) = 71.80561 & & & & \\  & \(a\) = 6.9442 & & & & \\ GAB & \(b\) = 0.7921 & & & & \\  & \(c\) = 672.57 & & & & \\  & \(a\) = 8.07627 & & & & \\ BET & \(b\) = \(-\)0.07179 & & & & \\  & \(c\) = 39.37878 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Modified model coefficients (\(a\), \(b\), \(c\)) fitted to the equilibrium moisture content of PFE, correlation coefficients (\(R\)), standard error of estimation (_SEE_), and average relative error (_ARE_) obtained by adsorption.  
The substitution of Equation (12) in Equation (11) resulted in Equation (15), which was used for the calculation of the air equilibrium relative humidity (\(Rln_{m}\)) corresponding to the MMC:  
\[Rh_{m}=\frac{1}{1+\sqrt{C}}, \tag{15}\]  
The temperature does not participate in Equation (15), which means that it does not affect the coefficient \(C\). Therefore, for a product to be with MMC in the studied temperature range, it must be stored at \(Rh_{m}\). The values of \(Rln_{m}\) obtained by Equation (15) were 0.099 for DSM and 0.137 for PFE. This shows that the extruded product will have monolayer moisture if it is stored in the air with higher relative humidity than the meal.