# The Effect of Freeze-Drying on the Properties of Polish Vegetable Soups
## 2 Materials and Methods
### Methodology for the Determination of the Selected Properties of Soups
#### 2.2.6 Sorption Isotherms--Static Method  
Experimental Determination of Moisture Sorption Isotherms  
The freeze-dried soup samples were brought in equilibrium after storage in a desicator with anhydrous calcium chloride. Then, the selected salts were mixed with distilled water until a solution with excess crystals was formed. The salt solutions were poured in the glass desiccator to a depth of 3 cm. Afterward, dry samples (1.5 g) in aluminum weighing boats were placed in 9 desiccators containing anhydrous CaCl\({}_{2}\), and saturated solutions of selected salts: LiCl, CH\({}_{3}\)COOK, MgCl\({}_{2}\), K\({}_{2}\)CO\({}_{3}\), Mg(NO\({}_{3}\))\({}_{2}\), NaClO, NaCl, (NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\)), which generated an environment with different water activity of 0, 0.113, 0.225, 0.329, 0.438, 0.529, 0.648, 0.753, 0.810 (Figure 2). The desiccators with water activity higher than 0.529 contained a dish with thymol to prevent mold growth. The experiment was terminated when the mass of samples did not differ in three sequential measurements. The mass of samples was controlled every month. The triplicate samples of the same type of dried soup were stored for 3 months at a constant temperature of 25 \({}^{\circ}\)C. The moisture content of samples after storage was determined using the vacuum drying method in selected conditions (temperature of 70 \({}^{\circ}\)C, a pressure of 1 kPa for 24 h). The equilibrium water content was calculated from dry matter of samples. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Attributes** & **Definition** & **Scale-Boundary Conditions** \\ \hline \multirow{4}{*}{Color} & Color typical for the main vegetable & \\  & ingredient of a selected soup: tomato & 1-very bright color \\  & (red), pumpkin (yellow), beetroot & 10-dark, deep color \\  & (red-violet), pickled cucumber (green) & \\ \hline \multirow{2}{*}{Consistency} & \multirow{2}{*}{Consistency from thin, watery, to thick} & 1-thin \\  & & 10-thick \\ \hline \multirow{2}{*}{Taste} & Taste typical for the main ingredient of & 1-no perceptible flavor \\  & the soup & 10-intensive perceptible flavor \\ \hline \multirow{2}{*}{Aroma} & Aroma typical of the main vegetable & 1-no perceptible aroma \\  & ingredient of the soup & 10-Intensive perceptible aroma \\ \hline \multirow{2}{*}{Overall quality} & \multirow{2}{*}{Overall evaluation} & 1-low \\  & & 10-high \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sensory attributes and their definitions. Modelling of Moisture Sorption Isotherms  
The non-linear regression analysis with the application of Table Curve 2D program (Systat Software Inc., San Jose, CA, USA) was performed to select the best equation for modelling the sorption isotherms. The following Equations (5)-(9) were used to describe the moisture sorption isotherms:  
GAB model [58]:  
\[\mathrm{u}\ =\ \frac{\mathrm{u}_{\mathrm{m}}\mathrm{C}\mathrm{a}_{\mathrm{w}}}{(1- \ \mathrm{ka}_{\mathrm{w}})[1+(\mathrm{C}-1)\mathrm{ka}_{\mathrm{w}}]} \tag{5}\]  
BET model [58]:  
\[\mathrm{u}\ =\ \frac{\mathrm{u}_{\mathrm{m}}\mathrm{c}\mathrm{a}_{\mathrm{w}}}{(1- \ \mathrm{a}_{\mathrm{w}})[1+(\mathrm{c}-1)\mathrm{a}_{\mathrm{w}}]} \tag{6}\]  
[PERSON] model [59]:  
\[\mathrm{u}\ =\ \frac{\mathrm{F}}{(1-\mathrm{a}_{\mathrm{w}})^{\mathrm{G}}}- \frac{\mathrm{F}}{1+\ \mathrm{a}_{\mathrm{w}}\mathrm{H}} \tag{7}\]  
[PERSON] model [60]:  
\[\mathrm{u}\ =\ \mathrm{A}\mathrm{a}_{\mathrm{w}}\mathrm{}^{\mathrm{D}}+\ \mathrm{B} \mathrm{a}_{\mathrm{w}}\mathrm{}^{\mathrm{E}} \tag{8}\]  
[PERSON] model [28]:  
\[\mathrm{a}_{\mathrm{w}}\ =\ \mathrm{exp}\bigg{(}\frac{-\mathrm{g}}{\mathrm{u}^{ \mathrm{n}}}\bigg{)} \tag{9}\]  
where: u\({}_{\mathrm{m}}\)--monolayer moisture content (g water/100 g d.m. ); a\({}_{\mathrm{w}}\)--water activity; C, k--constants of GAB model; c--constant of BET model; A, B, D, E--constants of [PERSON] model; F, G, H--constants of [PERSON] model; g, n--constants of [PERSON] model.