# The Effect of Freeze-Drying on the Properties of Polish Vegetable Soups
## 3 Results and Discussion
### The Sorption Properties of Freeze-Dried Soups  
The sorption isotherms describe the relationship between the water content and the water activity of the material. The selection of the best model of sorption behavior can be difficult due to the complex chemical composition and structure of food products [76]. Table 8 presents the estimated parameters of GAB, BET, Lewicki, Peleg, Hasley models. The model that best fit the observed data was conducted by the comparison of coefficients RMS, R\({}^{2}\), and P. The best model should be described by the highest coefficient of determination (R\({}^{2}\)) and the lowest values of root mean square (RMS) and P (mean relative deviation modulus) [77]. The parameter P has been used in several sorption experiments, and the sorption model was acceptable and good when P < 10% [42; 78]. A mathematical comparison of experimental and predicted results for freeze-dried soups gave P values ranging from 6.44 (Peleg model) to 56.34% (BET model). The values of RMS were very high for cucumber freeze-dried soup and varied from 21.31 (for Peleg model) to 80.49 (BET model). The Peleg model showed the lower values of RMS (11.89-21.31%) and P modulus (lower than 16.5%) than other models for the investigated freeze-dried soups. The values of determination coefficient R\({}^{2}\) (for Peleg model) ranged from 0.976 to 0.999, which was can be considered to be satisfying. By contrast, the GAB model has been frequently used to describe sorption isotherms of many food products because parameters of this model have a physical meaning. Also, the GAB model was reported as a very versatile sorption model that can be applied for a wide range of water activity [79]. However, Table 8 shows the GAB parameters obtained in this study did not fulfil the requirements of the GAB model because constant C should be in the range of \(5.67\leq\mathrm{C}\leq\infty\)[80]. Thus, the Peleg model was selected as an adequate model to characterize the sorption isotherms of all freeze-fried soups. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Product** & **Color** & **Consistency** & **Taste** & **Aroma** & **Overall Quality** \\ \hline Tomato soup & \(36\pm 3\) & \(5\pm 1\) & \(18\pm 2\) & \(24\pm 2\) & \(26\pm 3\) \\ Beetroot soup & \(42\pm 5\) & \(0\pm 0\) & \(9\pm 1\) & \(11\pm 1\) & \(16\pm 2\) \\ Pumpkin soup & \(31\pm 2\) & \(0\pm 0\) & \(11\pm 1\) & \(21\pm 2\) & \(20\pm 1\) \\ Cucumber & \(35\pm 3\) & \(4\pm 1\) & \(1\pm 0\) & \(17\pm 1\) & \(18\pm 2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Changes of sensory attributes (%) after rehydration of freeze-dried soups in comparison to freshly prepared soups. The experimental and predicted values calculated based on the Peleg model were presented in Figure 4a. The sigmoid shape of isotherm sorption was observed for freeze-dried beetroot and cucumber soup. The equilibrium moisture content of freeze-dried cucumber soup attained lower values than that observed for other dried soups in the water activity range of 0-0.53. Above the \(\mathrm{a_{w}}\) value, a rapid increase of equilibrium water was noted with the increase of water activity for dried cucumber soup. A similar behavior was reported for freeze-dried avocado when the water activity was higher than 0.5 [81]. The authors stated that this behavior could be related with the high concentration of hydrophobic fat in the dried avocado. The sigmoid shape of the sorption curve was also observed for dried tomato products. At low and intermediate water activities, the moisture content increased linearly with the water activity, but at high water \(\mathrm{a_{w}}\), the water content rapidly increased with the water activity, which was linked with capillary condensation [40]. The cucumber soup contained a high amount of water, and after drying, the layer of dried soup was more fragile and porous in comparison to other soups (visual observations).