### Collection of materials

The exudate karaya (*Sterculia urens* Roxb.) gum samples were collected from the forest area of Dantewada and Bastar Districts of Chhattisgarh under the Network Project on Harvesting, Processing, and Value Addition of Natural Resin and Gums, which is operated by Indira Gandhi Krishi Vishwavidyala (IGKV), Raipur (Chhattisgarh).

### Sample preparation

Karaya gum samples were dried under the sun drying method and a proper cleaning operation was performed before the study of sorption characteristics (Fig. 1). The cleaned test gum samples were grinded and converted into uniform fine particles. To attain this, the gum samples were grounded with the help of a laboratory crusher and passed through a sieve BSS-16 (width of aperture = 1 mm) and retained on BSS-22 (width of aperture = 0.71 mm). The uniform sizes of samples were used for the sorption study.

### Procedure and equipment applied for sorption isotherm

Moisture sorption isotherms of karaya gum samples were determined using a static gravimetric technique (Lazou and Krokida 2011; Sahu et al. 2021). The sample was exposed to the humid atmosphere in the container maintained by the saturated salt slurries. The water activities (*a*_{w}) of saturated salt solutions were acquired from the data presented by Greenspan (1977) and Labuza (1984). Saturated salts made from pre-decided laboratory reagent grade salts were used in the study to retain different water activity (0.10–0.95) as shown in Table 1. The experiment was carried out at four different temperatures, namely 30, 40, 50 and 60 °C. Saturated salt solutions were prepared in the distilled water at 100 °C, followed by cooling to the desired temperatures for crystallization and placed in the desiccators. Saturated salt solutions with excess salts gave the required ERH or water activity environments inside the desiccators and to compensate possible solution dilution by the liberation of moisture from samples (Igathinathane et al. 2005). Before placing the test samples for actual study, the desiccators filled with saturated salt solution were equilibrated at respective temperatures for 4 days using BOD incubator.

The gum samples (2.5 ± 0.5 g) were taken in sterilized bottles and placed inside the pre-prepared desiccators, which maintain different water activity conditions. Desiccators were placed carefully inside the BOD incubator to equilibrate samples over the period. The samples were allowed to equilibrate until there was no discemible weight change (± 0.001 g). The weight of each of the samples was recorded at an interval of 3–4 days until the difference between two consecutive readings was negligible. The effect of temperature on the water activity of karaya gum was calculated by comparing moisture loss or gain from the sample inside the sorbostats at different water activities and at corresponding temperatures. The moisture content in the samples during this study was determined as per the method adopted by Sahu and Patel (2020).

The graph plotted between equilibrium moisture content (EMC) versus water activity (*a*_{w}) at experimental temperature was the indication of the sorption isotherm of karaya gum.

### Mathematical modeling of sorption behavior

Various sorption models for moisture sorption behavior of food and agricultural materials exist in order to model the experimental data obtained from the sorption testing. In order to model the experimental data obtained from the sorption experiments were analyzed and fitted on five different mathematical sorption models at four selected temperatures (30, 40, 50 and 60 °C). The isotherm equations of these models are described in Table 2. Nonlinear second-order least square regression analysis method was adopted for fitting in the sorption models. The regression analysis was applied to find out the model parameters by minimizing the residual sum of square under the required water activity conditions (0.10–0.95).

### Statistical evaluation

The accuracy or goodness of fit for each of the isotherm models was obtained by applying various statistical coefficients like adjusted *R*^{2}, percentage relative deviation modulus (%*P*), root mean square percentage error (%RMSE) and standard error (SE). The best-fitted model was selected as the one with the highest adjusted R^{2} and the least errors (% RMSE and *P*). To be considered a good fit, the values of % RMSE and % P should be less than 10% (Jena and Das 2012). The equations used to calculate the goodness of fit as suggested by Sahu and Patel (2020) are as follows:

$${text{Adjusted}};R^{{2}} = {1} – frac{{left( {N – 1} right)sumnolimits_{1}^{N} {left( {WY – Y^{prime } } right)^{2} } }}{{left( {N – M} right)sumnolimits_{1}^{N} {left( {WY – Y^{prime prime } } right)^{2} } }}$$

(1)

$$Pleft( % right) = frac{100}{N}left[ {sumnolimits_{1}^{N} {left( {frac{{Y – Y^{prime } }}{Y}} right)} } right]$$

(2)

$$% {text{RMSE}} = sqrt {frac{1}{N}left[ {sumnolimits_{1}^{N} {left( {frac{{Y – Y^{prime } }}{Y}} right)^{2} } } right]} times 100$$

(3)

$${text{SE}} = sqrt {frac{{sumnolimits_{i = 1}^{N} {left( {Y – Y^{prime } } right)^{2} } }}{{left( {N – M – 1} right)}}}$$

(4)

where *Y* Experimental moisture content, %; *Y*ʹ Predicted moisture content, %; *Y*ʺ Mean of experimental EMC, %; *W* Weightage useful to each data point (*W* = 1); *N* Number of observations; *M* Number of coefficients.

All the experiments were conducted in three replications to overcome possible errors.

### Evaluation of net isosteric heat of sorption

The determination of net isosteric heat of sorption was performed by the application of the generalized Clausius–Clapeyron equation (Eq. 5) as suggested by Labuza (1984).

$${text{ln}}left( {frac{{a_{{{text{w}}_{{2}} }} }}{{a_{{{text{w}}_{{1}} }} }}} right) = frac{{q_{{{text{st}}}} }}{R}left( {frac{1}{{T_{1} }} – frac{1}{{T_{2} }}} right)$$

(5)

where *q*_{st} Net isosteric heat, kJ/mol; *R* Universal gas constant (8.314 J/K mol); (a_{{{text{w}}_{1} }}) Water activity at temperature *T*_{1}; (a_{{{text{w}}_{2} }}) Water activity at temperature *T*_{2}.

The Eq. (6) is used to calculate the isosteric heat of sorption (*Q*_{st})

$$Q_{{{text{st}}}} = q_{{{text{st}}}} + Delta H_{{text{v}}}$$

(6)

where **Δ***H*_{v} Latent heat of vaporization of pure water.

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