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Article

Moisture Sorption Isotherms of Fructooligosaccharide and Inulin Powders and Their Gelling Competence in Delaying the Retrogradation of Rice Starch

1
College of Grain and Strategic Reserves, Henan University of Technology, Zhengzhou 450001, China
2
Academy of National Food and Strategic Reserves Administration, National Engineering Research Center for Grain Storage and Transportation, Beijing 102209, China
3
College of Food Science and Engineering, Wuhan Polytechnic University, Wuhan 430048, China
*
Author to whom correspondence should be addressed.
Gels 2025, 11(10), 817; https://doi.org/10.3390/gels11100817
Submission received: 22 July 2025 / Revised: 27 August 2025 / Accepted: 10 October 2025 / Published: 12 October 2025
(This article belongs to the Special Issue Modification of Gels in Creating New Food Products (2nd Edition))

Abstract

The accurate determination of the equilibrium moisture content (EMC) of gel-related powdery samples requires strictly controlled conditions and a long time period. In this study, the adsorption and desorption isotherms of two fructooligosaccharide (FOS) powders and three inulin powders were determined using a dynamic moisture sorption analyzer at 0.1–0.9 water activity (aw) and 20–35 °C, respectively. The adsorption and desorption isotherms all exhibited type IIa sigmoidal curves; the desorptive isotherm was smooth, the FOS adsorption curves had three inflection points, and the inulin adsorption curves had five inflection points. Large hysteresis between the adsorption and desorption isotherms occurred at 0.1–0.7 aw for FOS and 0.1–0.6 aw for inulin. Seven equations, Boquet, Ferro–Fontan, Guggenheim–Anderson–de Boer (GAB), Generalized D’Arcy and Watt (GDW), modified GAB (MGAB), Peleg, and our developed Polynomial, were found to fit the isotherms of the FOS and inulin samples; for adsorption, the best equations were Ferro–Fontan and GDW, and for desorption, the best equations were Polynomial and MGAB. The GDW and MGAB equations could not distinguish the effect of temperature on the isotherms, while the Polynomial equation could. The mean adsorptive monolayer moisture content (M0) values in FOS and inulin samples were predicted as 7.29% and 7.94% wet basis, respectively. The heat of moisture sorption of FOS and inulin approached that of pure water at about 32.5% and 22.5% wet basis (w.b.) moisture content (MC), respectively. Fourier Transform Infrared Spectroscopy (FTIR) showed that the peaks in inulin with absorbance values above 0.52 and in FOS with absorbance values above 0.35 were at 1020, 1084, and 337 cm−1; these could represent the amorphous structure (primary alcohol C-OH), C-O group, and hydroxyl functional group, respectively. Microscopic structure analysis showed that inulin powder particles were more round-shaped and adhered together, resulting in hygroscopic and sticky characteristics, with a maximum equilibrium moisture content (EMC) of 34% w.b. In contrast, the FOS powders exhibited irregular amorphous particles and a maximum EMC of 60% w.b. As hydrogels, 3–10% FOS or inulin addition reduced the peak, trough, final, breakdown, and setback viscosities of rice starch pasting, but increased the peak time and pasting temperature. FOS addition gave stronger reduction in the setback viscosity and in amylose retrogradation of rice starch pasting than inulin addition. The differential scanning calorimeter (DSC) showed 3–10% FOS addition reduced the amylopectin aging of retrograded paste of rice starch, but 5–7% inulin addition tended to reduce. These results suggest that FOS and inulin have strong hygroscopic properties and can be used to maintain the freshness of starch-based foods. These data can be used for drying, storage, and functional food design of FOS and inulin products.

1. Introduction

Inulins are linear polysaccharides formed by fructose, usually with a glucose at the end; their degree of polymerization (DP) is usually 2–60 [1]. Fructooligosaccharides (FOSs) are a mixture of 1-kestose (GF2) to fructooligosaccharide (GF7) and fructodisaccharide (F2) to fructooligosaccharide (F8), produced from chicory (Cichorium intybus) or Jerusalem artichoke (Helianthus tuberosus) by partial enzymatic hydrolysis or membrane separation, purification, and drying, or a mixture of 1-kestose (GF2) to kestohexaose (GF5) produced from sucrose by the action of β-fructofuranosidase from Aspergillus niger or Aspergillus oryzae followed by purification and drying [2]. The functional food concept has recently become one of the essential elements to healthy nutrition and healthy living [3]. The utilization of FOSs and inulins in the food industry has grown in recent years because they offer the benefits of dietary fiber and can be employed as a carbohydrate or fat replacer due to their lower calorie production [4]. They also exhibit prebiotic functions, stimulating the growth of Bifidobacterium and Lactobacillus in the large intestine; thus, they can be employed in functional food formulations [5]. However, the equilibrium moisture content (EMC) of FOSs and inulins at similar physiological condition should be determined.
China has produced Jerusalem artichoke and chicory root crops since 2000. China’s inulin output was less than 1000 tons in 2009, but it surged to 15,000 tons by 2019 and exceeded 22,000 tons in 2023 [6]. However, amorphous inulins can exhibit caking and lumping phenomena during storage and transportation, and the reliable storage moisture content and optimal humidity conditions are required for the storage of inulin products.
During storage, the quality of food powders is influenced by ambient factors such as temperature, relative humidity, and oxygen level [7]. The water activity and moisture content are also considered parameters when describing food stability. With changes in the moisture content of inulin powder, various physical changes can occur, such as agglomeration, stickiness, and caking [8]. Moisture sorption isotherms shows that the equilibrium moisture content (EMC) of a food is related to its water activity at certain given temperatures [9]. Povolny et al. [8] investigated that the sorption isotherm behavior of commercial inulin samples is influenced by their degree of polymerization (DP) and molecular weight distribution. Ronkart et al. [10] reported the moisture adsorption and desorption isotherms of a kind of inulin powder (average DP of 10) supplied by Belgium Warcoing at a storage temperature of 20 °C. Zimeri and Kokini [11] measured the moisture sorption isotherm of inulin (Raftiline HP, DP ≥ 25) at 25 °C by applying the saturated salt solution and gravimetric method. Luo et al. [12] determined the 25 °C, 30 °C, and 45 °C adsorption isotherms of inulin with DP 10–12 using dilute sulfuric acidwater solution to condition the relative humidity and the static gravimetric method for determination, and revealed J-shaped isotherms. Jirayucharoensak et al. [5] used six saturated salt solutions to measure the 0 °C, 10 °C, and 30 °C adsorption isotherms of inulin powder. However, to date, there is a lack of studies of the adsorption/desorption isotherms and temperature-dependent EMC modeling of inulin and FOS powder products produced in China, plus limited linkage to starch retrogradation endpoints.
Thermodynamic functions like isosteric heat of sorption can be calculated from moisture sorption isotherm and have practical use in modelling energy consumption in the drying process of biomaterials [9]. No report on the isosteric heat moisture sorption of FOS and inulin products has been published to date. In order to overcome the difficulties associated with measuring the moisture adsorption and desorption isotherms of gel-like food powder samples, this study employed high-purity nitrogen as a drying gas and mould inhibitor, controlled the equilibrium relative humidity of the sample chamber with saturation vapour, and used the dynamic gravimetric method to measure the moisture adsorption and desorption curves of FOS and inulin powder samples, showing how FOS and inulin interacts with the moisture in the air. The aim was to predict the shelf life, determine the monolayer moisture content and proper storage conditions, give suitable drying and packaging design, and foretell the EMCs at physiological condition for gel-forming FOS and inulin products.

2. Results and Discussion

2.1. Experimental EMC/aw Data for FOS and Inulin Samples

The adsorption and desorption isotherms of the two FOS (FOS1 and FOS2) and three inulin (INU1, INU2, and INU3) samples (Table 1) were measured at four temperatures (20 °C, 25 °C, 30 °C, and 35 °C) and water activity ranging from 0.1 to 0.9, as shown in Figure 1 and Figure 2. Both the adsorption and desorption isotherms were sigmoidal in shape. The equilibrium moisture contents (EMCs) of FOS and inulin samples at constant aw decreased as the sorption temperature increased, because the kinetic energy of water molecules is high and water adsorption is low at high temperatures. With increase in the mobility of water molecules, water molecules cannot bind to the samples through hydrogen bonds, thereby the moisture content (MC) of the samples decreased with an increase in temperature [13].
For the FOS and inulin samples, the adsorption isotherms exhibited type-II sigmoidal curves with at least two inflection points, but the desorption isotherms exhibited smooth type-II sigmoidal curves. At the same temperature, there were big differences between the desorption and adsorption isotherms in the range of 0.1 to 0.69 aw. With an increase in the initial moisture content (IMC) of the samples, the isotherms at the same temperature were raised slightly for desorption or adsorption. The EMC of the samples showed a very slow increase at 0.1–0.2 aw and a slow increase at 0.21–0.6 aw for four temperatures, indicating water was only adsorbed on the surface, and monolayer and multilayer water regions were successively formed, while the solubility of sugar components and moisture content increased at all temperatures as the aw further increased [14].
At 0.3–0.7 aw, there were significant inflection points in the adsorption isotherms for the two FOS and three inulin samples, indicating surface adsorption and bulk absorption of gel-forming polysaccharides.
At 0.1–0.9 aw and 20–35 °C, the EMC range of the FOS samples was 2.0–59.5% and 4.8–59.5% wet basis (w.b.) for adsorption and desorption, respectively, while that of the inulin samples was 3.0–33.4% and 5.4–33.4% w.b. for adsorption and desorption, respectively. The EMC range of the inulin samples was similar to that of Jirayucharoensaket al. [5], where the EMCs of inulin powder were in the range of 2.1–36.8% at 0.1–0.9 aw and 0–30 °C. Ronkart et al. [10] suggested that the sigmoidal-shaped curves obtained for both desorption and adsorption isotherms of industrial spray-dried inulin (average DP of 5) were indicative of type II isotherms, according to Brunauer’s classification. Figure 1 and Figure 2 show that the desorption isotherms of Chinese FOS and inulin samples were more like type IIa sigmoidal curves.
The large hysteresis between adsorption and desorption occurred at aw < 0.7 for the FOS samples, and at aw < 0.6 for the inulin samples, suggesting the similar hygroscopic behavior of FOS and inulin to that of polydextrose reported by Liu et al. [15].

2.2. Fitting of Moisture Sorption Equations to Experimental Sorption Data

The EMC equations in Table 2 were used to fit the measured EMC/aw data of two FOS and three inulin samples. The statistical parameters such as residue sum of squares (RSS), standard error (SE), determination coefficient (R2), and relative percentage error (MRE) used to compare the model fits are given in Table 3, Table 4, Table 5, Table 6 and Table 7. The seven equations, namely Boquet, Ferro–Fontan, Guggenheim–Anderson–de Boer (GAB), Generalized D’Arcy and Watt (GDW), Peleg, the modified GAB (MGAB), and our developed seven-parameter Polynomial, all exhibited good fits to the measured sorption isotherm data of the FOS and inulin samples in the range of 0.1–0.9 aw, although GAB had larger MRE values for the adsorptive EMC data in the FOS1, FOS2, and INU2 samples, and Polynomial exhibited a larger MRE value for the adsorptive EMC data in the FOS2 sample.
The GAB and Peleg equations offered better fitting results to the desorption isotherms of the three inulin samples because the MRE values were <9.44% (Table 3 and Table 5). These results are similar to the results obtained for inulin powder containing FOS and inulin-type fructan at 0–30 °C and 0.1–0.9 aw by Jirayucharoensak et al. [5].
The monolayer moisture content (M0) is considered as an ideal moisture content to avoid changing the product’s quality [3], which was estimated by the parameter a in GAB and MGAB models in the present study. The GAB equation indicated that the monolayer moisture contents of three inulins were 5.07–7.76% w.b. and 6.29–7.37% w.b for adsorption and desorption, respectively. These values are smaller than those (8.47–10.16% w.b.) of inulin powder at 0–10 °C measured by Jirayucharoensak et al. [5].
The average adsorption M0 values in GAB were 7.071 and 7.485% w.b. for FOS and inulin, respectively, and those in MGAB were 7.507 and 8.392% w.b. for FOS and inulin. Meanwhile, the average desorption M0 values in GAB were 6.182 and 6.271% w.b. for FOS and inulin, respectively, and those in MGAB were 6.273 and 6.383% w.b. for FOS and inulin. The adsorption M0 values in FOS and inulin were all below the maximum monolayer moisture content (9.1% w.b.) given by Gül et al. [3] and Labuza [19].
Compared with the other equations used in the present study, the modified Chung–Pfost (MCPE) in a form of M = f a w , t fell short of expectation due to 0.875–0.960 of R2 and 20.76–79.00% of MRE for adsorptive samples, and 0.815–0.937 of R2 and 13.05–26.60% of MRE for desorptive samples (Table 7), but the MCPE in a form of a w = f M , t gave 0.931–0.970 of R2 and 15.73–22.41% of MRE for adsorptive samples, and 0.866–0.973 of R2 and 11.93–30.53% of MRE for desorptive samples; thus the MCPE parameters in FOS-aver and INU-aver samples could be used to analyze the isosteric heats of moisture sorption.
Further comparison of the sorption equations was performed for the five sets of FOS and inulin isotherm data (Table 8), and the average values of the R2 and error parameters (RSS, SE, and MRE) were calculated. For adsorption, the equations in a form of M = f a w , t were ranked in the following order of accuracy from the highest to the lowest: Ferro–Fontan, GDW, Boquet, Peleg, MGAB, Polynomial, GAB, and MCPE. In the case of desorption behavior, the order was Polynomial, MGAB, Peleg, Boquet, GDW, Ferro–Fontan, GAB, and MCPE. For adsorption, the Ferro–Fontan and GDW equations offered good descriptions of the equilibrium moisture data of the five samples of FOS and inulin in the range of 0.1–0.9 aw, and for desorption, the Polynomial and MGAB equations were the best fitting. The coefficients of the best-fitting equations for the average EMC/aw data in the FOS and inulin samples are summarized in Table 3, Table 4, Table 5 and Table 6. These calculated coefficients can be used to describe the dehydration process of FOS or inulin and can be employed to improve the physical control of moisture content during packaging and storage.

2.3. Prediction of Moisture Desorption and Adsorption Isotherms by the Best-Fitting Equation

The predicted mean adsorption and desorption isotherms of the FOS and inulin samples at 20 °C, 25 °C, 30 °C, and 35 °C using GDW and MGAB are displayed in Figure 3. It can be seen that these isotherms exhibited smooth curves and did not show the effect of temperature. Figure 4 presents the predicted mean isotherms of the FOS and inulin samples by the Polynomial equation. The Polynomial equation displayed the effect of temperature. At aw ≤ 0.8, the hysteresis between adsorption and desorption became bigger with decreases in the aw at the four temperatures. At aw ≤ 0.6, the adsorption and desorption isotherms of the FOS sample were lower than those of the inulin sample at the same temperature. These results suggest that the difference might occur due to the monolayer and multilayer water molecules sorption properties of the FOS and inulin samples.
The raw hysteresis degree curve of moisture sorption in FOS decreased so sharply with increases in the water activity below 0.5 aw, and then decreased gradually with increasing water activity. With increases in temperature, the hysteresis degree curve of FOS moved down (Figure 5). The fitted hysteresis degree curves of FOS using the Polynomial equation could be divided into three stages at ≤0.2 aw, 0.21–0.7 aw, and 0.71–0.9 aw, corresponding to a fast decrease in the hysteresis degree, a slow decrease, and a flat line, respectively. With decreases in the temperature, the Polynomial fitted hysteresis degree curve of FOS at 0.1–0.2 aw moved down. These results suggest that FOS has three inflection points at aw = 0.2, 0.5, and 0.7, respectively.
The raw hysteresis degree curve of moisture sorption in inulin first increased at 0.1 to 0.2 aw, then decreased sharply at 0.3 to 0.6 aw, but increased at 0.6 to 0.8 aw, and finally decreased slowly to 0.9 aw. With increases in temperature, the hysteresis degree curve of inulin moved down (Figure 5). The fitted hysteresis degree curves of inulin using the Polynomial equation could be divided into three stages at <0.2 aw, 0.2–0.6 aw, and 0.61–0.9 aw, corresponding to a fast decrease, slow decrease, and flat line in the hysteresis degree, respectively. With decreasing temperature, the Polynomial fitted hysteresis degree curve of inulin at 0.1–0.2 aw moved down. These results suggest that inulin has at least five inflection points at aw = 0.2, 0.3, 0.4, 0.6, and 0.7, respectively.
At 0.1 aw, the large hysteresis between the desorption and adsorption isotherms might derive from the reason that the semi-crystalline inulins or FOS are more hygroscopic than their amorphous counterparts. The further work will measure the glass transition temperature (Tg) and crystallinity of inulin or FOS samples by DSC and XRD to corroborate this semi-crystalline transition hypothesis.

2.4. The Isosteric Heat of Sorption of FOS and Inulin Samples

The coefficients a, b, and c of the MCPE equation with a form of a w = f M ,   t were used to calculate the sorption isosteric heats. Figure 6 shows the effect of moisture content (MC) on adsorption and desorption isosteric heats of FOS and inulin. The isosteric heats for both desorption and adsorption of FOS (Figure 6A) decreased rapidly with the increase in the sample MC until a moisture content of 32.5% w.b. (shown by short line) was achieved, but above 32.5% they decreased smoothly with increasing moisture content. At lower MCs below 30%, the isosteric heats of both FOS desorption and adsorption at lower temperatures were higher than those at higher temperatures. The isosteric heats of FOS desorption were higher than those of adsorption below 40% MC, but thereafter there was a minor difference found between desorption and adsorption (Figure 6A). The isosteric heats for both desorption and adsorption of inulin (Figure 6B) decreased rapidly with the increase in the sample MC until a moisture content of 22.5% w.b. (shown by short line) was achieved, but above 22.5% they decreased steadily with increase in MC.
The rapid rise in the heat of sorption at low MC might be due to the existence of considerably active polar sites on the surface of FOS and inulin samples, which were covered with water molecules forming a mono-molecular layer [9]. The reduction in the isosteric heats with higher amounts of sorbed water could be quantitatively explained by taking into account that sorption initially develops on the most active available sites bringing about high interaction energy. When these sites are occupied, sorption occurs on the less active ones, giving rise to lower heats of sorption [9]. In low MCs, the values of the isosteric heats were higher than the latent heat of water vaporization, showing that the binding energy of the water molecules and the sorption sites was higher than the energy which keeps the pure water molecules together in the liquid phase [20]. At high MCs, there was no appreciable difference between the sorption isosteric heat and the latent heat of water vaporization over the broad range of MCs. In the present study, the heat of sorption of FOS and inulin might approach that of pure water at about 32.5% and 22.5% w.b. MC, respectively. These isosteric heats can be used in drying calculation and modelling energy consumption in the drying process of FOS and inulin products.

2.5. FTIR Analysis of FOS and Inulin Samples

FOS powder had 11absorbance peaks in the FTIR spectrum, and inulin powder had 10 peaks (Figure 7 and Table 9). The peaks in inulin with absorbance above 0.52 and in FOS with absorbance above 0.35 were at 1020, 1084, and 3337 cm−1, which represent the amorphous structure (primary alcohol C-OH), C-O group, and hydroxyl functional group, respectively [21]. Peaks at 2892 and 2915 cm−1 show CH stretching and CH2 stretching, respectively [22]. Peaks at 1232, 1329, 1405, and 1628 cm−1 indicate C-OH and CH2OH, CH3 group, CH2 stretching and bending, and OH bending, respectively [23]. The peak at 925 cm−1 shows C-C stretching and C-O-C vibrations [24]. The peaks at 514, 556, and 814 cm−1 reflect skeletal vibrations of the fructose and glucose pyranose rings [25]. The peak at 749 cm−1 indicates C-H groups [22]. The main FTIR peaks in the present study are similar to the results of Pourfarzad et al. [22] who identified 14 FTIR peaks (577, 805, 875, 895, 1022, 1079, 1161, 1241, 1413, 1654, 2164, 2380, 2929, 3433 cm−1) in Serish inulin gel with a DP of 13.

2.6. Microstructure of FOS and Inulin Samples

Figure 8 shows the microstructures of the inulin and FOS powders. The inulin powders were more round-shaped and adhered together. The FOS powders had irregular particles. The round-shaped and sticky microstructures of inulin reflect the hygroscopic and sticky characteristics of these powder samples. Inulin powders are sticky and adhere together at temperatures higher than the glass transition temperature [5,26]. The further work will determine the particle size distributions from automated image analysis to support statements about “round” versus “irregular” particles, and quantify shape descriptors and agglomerate size.

2.7. Effect of FOS and Inulin on the Pasting Parameters of Rice Starch

Table 10 shows the influence of adding FOS or inulin on the pasting parameters of rice starch. The 3–10% FOS or inulin addition reduced the trough, peak, final, breakdown, and setback viscosities of rice starch pasting, but increased the peak time and pasting temperature. The present results are similar to the decrease in peak, trough, breakdown, final, and setback viscosities of wheat flour pasting and an increase in pasting temperature with additional amounts of short-chain and long-chain inulins from 0 to 8% [27].
The peak viscosity revealed the expansion degree of a starch granule and the capability to bind water molecules in the warming process of starch; when the additional amount of FOS and inulin was 10%, the peak viscosityreduced by 25.9% and 29.6%, respectively. The significant decrease in peak viscosity might come from the better moisture absorption properties of FOS and inulin, and the higher hygroscopicity in FOS and inulin could inhibit water molecules from entering the amorphous region of starch granules, influencing starch gelatinization [28]. The breakdown viscosity mainly revealed the stability of rice starch paste in the heating process; the 10% addition of FOS and inulin reduced the breakdown viscosity by 45.8% and 31.0%, respectively, indicating FOS had a better effect on improving the stability of starch granules than inulin, probably due to the better water-holding ability at high temperature [29]. The maximum increase inthe pasting temperature at the 10% addition amount suggested that the incorporation of FOS and inulin produced the FOS-starch or inulin-starch mixture more challenging to gelatinize.
The setback viscosity could reveal the recrystallization degree of starch during the cooling course of starch gelatinization, especially in the recrystallization and rearrangement of amylase. The 10% addition of FOS and inulin in rice starch reduced the setback viscosity by 22.9% and 16.4%, respectively. FOS and inulin could compete with rice starch for water molecules during starch gelatinization, and the hydrogen bonding of starch molecules was hindered by the interaction of FOS and starch molecules or inulin and starch molecules, making it more difficult for amylase to form a double-helix structure [30]. FOS addition produced a stronger reduction in the setback viscosity of rice starch pasting than inulin addition, indicating that these two polymers delay amylose retrogradation and could be used to improve the freshness of cooked rice as gel-forming agents.
The magnitude of setback viscosity measured by a rapid viscosity analyzer (RVA) is considered to reveal the retrogradation tendency of amylase in a starch paste, while in the case of retrograded starch, the endotherm of a differential scanning calorimeter (DSC) gives quantitative measure of enthalpy change and transition temperatures for the melting in recrystallized amylopectin [31]. The present study determined the aging of retrograded rice starch paste stored at 4 °C after 21 days. Table 11 shows the influence of adding FOS or inulin on the thermal parameters of rice starch. Compared with the control sample, 3–10% FOS addition increased the gelatinization enthalpy of rice starch (ΔH), and 3–7% FOS addition reduced the peak temperature of gelatinization (Tp), while 5–7% inulin addition kept the ΔH, and 3–10% inulin addition kept the Tp. The 3–10% FOS and inulin addition both kept the conclusion temperature of gelatinization (Tc). Furthermore, 3–10% FOS addition reduced the amylopectin aging of retrograded paste, but 5–7% inulin addition tended to reduce.
Tudoricâ et al. [32] showed that compared with the control sample, 7.5–10% inulin addition increased the peak and conclusion temperatures of gelatinization in raw pasta but decrease the gelatinization enthalpy value. In the present study, 7–10% inulin addition in rice starch kept the peak and conclusion temperature of gelatinization, which is different tothe reduction in starch gelatinization events in raw pasta by 7.5–10% inulin addition. These results suggest that rice starch and raw paste have different gelatinization responses to inulin addition.
General Linear Model (GLM) analysis (Table 12) further showed that, compared with the control sample, FOS addition increased the ΔH, but decreased the Tp and the aging of retrograded paste, while inulin addition kept the ΔH and the aging of retrograded paste, and increased the Tp. Both FOS and inulin addition kept the Tc value. With the increase in the addition amount of two prebiotics, the Tp increased, and the aging of retrograded paste decreased. The 5–7% addition amount increased the ΔH, and the 3–5% addition amount decreased the Tc value.
These results suggest 3–10% addition significantly reduced the aging of retrograded paste of rice starch, but 5–10% inulin addition also tended to reduce it. Compared with inulin, FOS has stronger competitiveness with rice starch for water molecules and thus delays starch retrogradation.
Inulin is currently more widely used as a food ingredient; to avoid its caking and lumping complaints, it is in urgent to know how it interacts with the moisture in air. Few studies have investigated its moisture sorption properties, possibly because there is a need for strict control of temperature and humidity over a long duration in order to determine its desorption isotherms. The present study is the first to measure the adsorption and desorption isotherms of inulin samples at 0.1–0.9 aw over a 45-day period. At 0.9 aw, the three inulin samples exhibited desorption EMCs of 27.0–33.36% w.b.at 20–35 °C. Inulin has a higher water-binding capacity than cereal grain (20–25% w.b., [9]), with a water-binding capacity of about 2:1 [33]. It is generally considered that amorphous materials are more hygroscopic than crystalline ones, but Ronkart et al. [34] observed that under low humidity (0–12%), semi-crystalline inulins are more hygroscopic than their amorphous counterparts. This might explain the large hysteresis between inulin adsorption and desorption at 0.1 aw, because the adsorption inulin powder is in an amorphous state, but the desorption inulin powder is in a semi-crystalline state.
According to the classification of sorption isotherms by Blahovec and Yanniotis [35], the shape of moisture sorption isotherms of FOS and inulin samples in the present study can be classified as type IIa isotherm curves. Gül et al. [3] categorized the moisture sorption isotherms of agglomerated boza powder as type III isotherms; we regarded that they should be type IIa isotherm curves because type III isotherms represent crystalline solids such as sugars and salt, and crystalline lactose powder adsorbs very little water over the low aw range (0–0.85), but adsorbs significant amounts of water at aw above 0.85 [36].
In the present study, the FOS (DP 2–8) and inulin (DP 2–60) powders exhibited type IIa isotherm curves, closer to that of Raftilose P95 (DP 5) [8], rather than the type IIb isotherm of Raftiline HP (DP 23) from Orifti, Tienen Belgium [8]. Compared with a type IIb isotherm, type IIa isotherm curves have lower moisture contents at aw below 0.6 and higher moisture contents at higher aw [8,35]. According to the result of Mazza [37], the water insoluble fractions in Jerusalem artichoke flour had a type II isotherm curve. Thus, we conclude that the FOS (DP 2–8) and inulin (DP 2–60) powders in the present study are water soluble fractions, and the short chain lengths of FOS and inulin have more hydroxyl groups available for water molecules to bind to at higher water activity during sorption.
Jirayucharoensak et al. [5] calculated the suitable water activity conditions for the storage of inulin samples using the Lewicki-3 model and found that the moisture content of inulin powder should be kept at ≤5.75% w.b. during storage and the ambient relative humidity should not exceed 18.32% and 37.12%, respectively. In the present study, when the moisture content was 5.75% w.b., the adsorption ERHs of inulin at 10, 20, and 30 °C calculated using the GAB equation were 17.99%, 26.58%, and 32.39%, respectively, which is very close to the results of Jirayucharoensak et al. [5]. The adsorption ERHs of the FOS samples at 10 °C, 20 °C, and 30 °C were 23.01%, 30.32%, and 35.07%, respectively, using the GAB equation. These results suggest that inulin and FOS powder should be kept in packaging that can prevent moisture transfer from the surrounding air into the package, especially in subtropical regions such as South China, where the relative humidity of the environmental air is usually high.
Our previous report [15] showed five polydextrose samples at approximate physiological conditions like 35 °C and 0.9 aw had the EMCs of 46.4–48.5%. In the present study, two FOS samples and three inulin samples at 35 °C and 0.9 aw, respectively, had the EMCs of 37.5–50.5% and 27.0–27.3%. Polydextrose, FOS, and inulin have a respective average DP of 12, 2.7–4, and 10 [15,38]. These combinations of average DP and the EMC value at physiological conditions might decide their functions that polydexrose plays a role based on dietary fiber, FOS makes a contribution by high-efficiency prebiotics and metabolic regulation, and inulins act as prebiotics and multi-effect regulation [38,39]. Further research will need to define the effects of FOS and inulin on the rice cooking properties, rice textural profile, and the microstructure of cooked rice, as well as the thermal, pasting, and thermo-mechanical properties of rice flour, and determine the optimal levels of FOS or inulin addition.

3. Conclusions

The present study is the first to determine the adsorption and desorption isotherms of FOS and inulin samples at 0.1–0.9 aw over a 45-day period, and obtain the isotherms of 20–35 °C. Their shape showed type IIa isotherm curves. At 0.1 aw, the large hysteresis between the desorption and adsorption isotherms might come from the reason that the semi-crystalline inulins or FOSs are more hygroscopic than their amorphous counterparts. For adsorption, the Ferro–Fontan and GDW equations are best for describing the isotherms of FOS and inulin, respectively, and for desorption, the Polynomial and MGAB equations are best. Inulin powder is more round-shaped and the particles adhere together, resulting in hygroscopic and sticky characteristics, with a maximum EMC of 34% wet basis (w.b.). In contrast, FOS powders are characterized by irregular amorphous particles with a maximum EMC of 60% w.b. The mean adsorptive monolayer moisture content (M0) values in FOS and inulin samples were predicted as 7.289% and 7.939% wet basis, respectively. The heat of sorption of FOS and inulin approaches that of pure water at about 32.5% and 22.5% w.b. MC, respectively. Both FOS and inulin were found to have rich amorphous structures (primary alcohol C-OH), C-O groups, and hydroxyl functional groups. Two FOS samples and three inulin samples at approximate physiological conditions like 35 °C and 0.9 aw, respectively, had the EMCs of 37.5–50.5% and 27.0–27.3% w.b. These powders can be used as gel-forming agents to maintain the freshness of starch-based foods by competing with starch for water molecules during pasting. This study provides useful insights for the dehydration, storage, packaging, and food addition of FOS and inulin products. The effects of FOS and inulin addition on the rice cooking properties, textural profile, thermal properties, and the microstructure of cooked rice will be studied.

4. Materials and Methods

4.1. The Samples

Two samples of FOS and three inulins were provided by Runloy Biotechnology Co., Ltd., Shanghai, China (Table 1). The two FOS powders met the China national standard GB1903.40-2022 with DP 2–8 [2]. The three inulin samples met the quality requirement of GB/T 41377-2022 with DP 2–60 [1]. The initial moisture contents (MCs) of the samples were determined by the AOAC method [40].

4.2. Moisture Desorption and Adsorption Isotherms and Their Fitting

The moisture desorption and adsorption isotherms of the FOS and inulin samples were measured with a dynamic moisture sorption analyzer (SPS11-10μ, ProUmid GmbH & Co. KG, Ulm, Germany), as described by Liu et al. [15]. This instrument is a merged system for self-acting gravimetric determination of the water vapor adsorption and desorption of eleven samples in a test atmosphere chamber with controlled water activity (aw) and temperature. The temperature accuracy is ±0.1 K and the precision of water activity varying with time is ±0.6% at (23 ± 5 °C) in the range of 0–1 aw. The equilibrium moisture contents (EMCs) of two parallel samples (each ca. 2.0000 g) under one of four constant temperatures (20 °C, 25 °C, 30 °C, and 35 °C) over an aw range of 0.1–0.9 were determined with the use of deionized water to produce humidity and high-purity nitrogen to blow the samples dry and prevent them from going mouldy. The interval size between gravimetric cycles was set at 10 min. The adsorption measurement cycle was begun at 0.1 aw and first boosted with a 0.1 aw step to 0.2 aw. Then, aw was boosted successively to 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9. The desorption measurement cycle was carried out from 0.8 aw to 0.1 aw with 0.1 aw step and seven steps. The time per cycle was set up to a minimum of 50.1 min and a maximum of 50.1 h. The default weight limit was +100%, and balance bandwidth (dm/dt) was ±0.01%/40 min. During a measurement cycle, the samples were automatically placed on an analytical balance (0.00001 g) and weighed. The sample pan remained unloaded and was adoptedfor drift compensation of the measured values. The recorded data were analyzed using SPS-Toolbox Basic Rel. 1.15 software.
The experimental EMC/aw data were used to draw isotherms in Kaleidagraph version 4.54 software [41], with the aw and EMC data shown on the x- and y-axis, respectively. The EMC equations in Table 2 were employed to fit the actually measured moisture isotherms of the samples.
To show the influence of temperature on the moisture isotherms, we supposed that EMC is the function of temperature and aw, and developed a seven-parameter Polynomial,
M = a + b · t + c · t 2 + d · t 3 + e · a w + f · a w 2 + g · a w 3 ,
where M is equilibrium moisture content (%w.b.), t is temperature (°C), aw is water activity (decimal), and a–g are parameters.
Fitting was carried out by non-linear regression analysis in SPSS v17.1 for Windows (SPSS Inc., Chicago, IL, USA, [42]). The criteria used to decide the equation for the EMC/aw data were the residue sum of squares (RSS), and standard error (SE), determination coefficient (R2), as well as the mean relative percentage error (MRE). Equations (2)–(5) were, respectively, used to calculate RSS, SE, R2, and MRE.
R S S = i = 1 n m i m pi 2
S E = i = 1 n m i m pi 2 / n 1
R 2 = 1 i = 1 n m i m pi 2 / i = 1 n m i m mi 2
M R E % = 100 n i = 1 n m i m pi m i
where mi, the experimental value; mpi, the predicted value; mmi, the average of experimental values; n, the total number of observations. The fitting of an equation to the EMC/aw data of a sample was considered more satisfactory if the MRE value was lower than 20% [15].
The hysteresis degree (Hy) between moisture desorptionand adsorption was determined as,
Hy   % = E M C des E M C ads E M C ads × 100

4.3. Determination of the Isosteric Heat of Sorption

The isosteric heat of moisture sorption (hs) is the quantity of energy needed to change one unit mass of product from liquid to vapour at a certain temperature and aw [9]. The hs for FOS and inulin samples was assayed using the following equations [9]:
h s h v = 1 + P s E R H · d t d P s · a w t M
h v = 2501.33 2.363 t
P s = 6 × 10 25 273.15 + t 5 · exp 6800 t + 273.15
d P s d t = P s t + 273.15 · 6800 t + 273.15 5
a w t M = a · a w T + b 2 · exp c · M
where hs is the isosteric heat of moisture sorption (kJ/kg), hv is the latent heat of free water vaporization (kJ/kg), t is temperature, M is equilibrium moisture content (% wet basis), and P s is the saturated vapor pressure (Pa). Equation (7) was adopted to calculate the hs-to-hv ratio from d P s / d t and a w t M , which can be calculated using Equations (10) and (11), respectively. The hv in Equation (8) is dependent on temperature. The Ps was calculated using Equation (9). The a w t M term depends on the sorption isotherm equation used; this studyused the modified Chung–Pfost equation (MCPE), a, b, and c are the parameters of MPCE in the form of a w = f M ,   t .

4.4. Fourier Transform Infrared Spectroscopy (FTIR)

The FTIR spectra of the FOS and inulin samples were measured on a Nicolet 6700 FTIR (Thermo Fisher Scientific, Greater Mumbai, MA, USA). The determination conditions were given as follows:64 scans, spectral resolution of 4 cm−1 with 100% T-line signal/noise ratio in the range of 4300–4400 cm−1. All measurements were treated with OMNIC software 9.1 (Thermo Fisher Scientific, Greater Mumbai, MA, USA). Samples were ground with potassium bromide (KBr) under a mass ratio of 100:1 and made into tablets. The scanning wavenumber was 400–4000 cm−1.

4.5. Scanning Electron Microscopy (SEM)

The FOS and inulin samples were separately fixed on a sample holder and then splashed with gold in the vacuum ion particle sprayer (JEC-3000FC, Japan Electronics Co., Ltd., Tokyo, Japan). The sputtering situation was given as follows: working distance of 10 mm, sputtering working pressure of 2.0 Pa, sputtering current of 30 mA, and sputtering time of 130 s. The samples were then set on the holder of the scanning electron microscope (JSM-IT 700HR, Japan Electronics Co., Ltd.), and photographed at the accelerating voltage of 25 kV with 100 to 1000 times magnification. The pressure in the observation room was 7.50 × 10−8 Pa, with the distance between the sample and the lens of 10mm and an emission current of 88 μA.

4.6. The Pasting Properties of Rice Starch with AddingFOS or Inulin

FOS (FOS2) or inulin (INU3) were added as gel-forming agents to rice starch powder (sigma) with w/w proportions of 0%, 3%, 5%, 7%, and 10%. The rapid viscosity analyzer (RVA–TecMaster, PertenRuihua Scientific Instrument Co., Ltd., Beijing, China) was adopted to measure the pasting parameters of the starch samples, according to the China national standard GB/T24852–2010 [43]. During each measurement, the stirring paddle was set up at 960 r/min for the initial 10 s, then reduced to 160 r/min within 20 s and remained at 180 r/min. The temperature was set initially at 50 °C for 1 min, then increased to 95 °C within 3.70 min and kept there for 2.5 min, before being lowered to 50 °C within 2.8 min and remained for 2 min.

4.7. Thermal Properties

FOS (FOS2) or inulin (INU3) was uniformly mixed with rice starch on amass basis to obtain adding levels of 0% to 10%. A 5.0 mg sample was used to measure the gelatinization parametersusingadifferential scanning calorimeter (DSC 214, NetzschGmbH, Selb, Germany), using the means of Wang et al. [44]. After measurement, the retrograded sample was placed in a numbered small plastic bag at 4 °C for 21 d and again determined for gelatinization enthalpy. The result wasanalyzedwith the same software. The aging of the retrograded starch paste was obtained using Equation (12):
Aging (%) = (Gelatinization enthalpy determined at day 21)/(Gelatinization enthalpy determined at day 0) × 100

4.8. Data Analysis

Aside from parallel samples for the measurement of the EMC/aw data, three replicates were measured to determine the physicochemical parameters of each FOS or inulin sample. SPSS software (Version 17.0, SPSS Inc., Chicago, IL, USA [42]) was adopted for data analysis. One-way analysis of variance and Duncan’s new multiple-range test were selected to compare pairs of means and multiple means, respectively. For considering the effect of FOS and INU species and addition amount, General Linear Model (GLM) analysis was adopted. Statistical significance is declared at p < 0.05.

Author Contributions

B.D., data collection, methodology, and writing; R.C., data collection, and methodology; Z.W., methodology, and investigation; J.W., supervision and review; X.L., writing—review and editing, methodology, investigation, supervision, results interpretation, and data curation. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the research fund for institute–enterprise cooperation (H24051).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in this article;the raw EMC–aw matrices, fits, code, and other inquiries can be directed to the corresponding author.

Acknowledgments

We thank Guoqing Ning from Runloy Biotech (Shanghai) Co., Ltd., Shanghai, China, for supplying the fructooligosaccharide (FOS) and inulin samples.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. The measured moisture sorption isotherms of two FOS samples. Notes: ads, adsorption; des, desorption; FOS1 and FOS2 are two FOS samples; FOS-aver is the average adsorptive or desorptive EMC/aw data of two FOS samples.
Figure 1. The measured moisture sorption isotherms of two FOS samples. Notes: ads, adsorption; des, desorption; FOS1 and FOS2 are two FOS samples; FOS-aver is the average adsorptive or desorptive EMC/aw data of two FOS samples.
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Figure 2. The measured moisture sorption isotherms of three inulin samples. Notes: ads, adsorption; des, desorption; INU1, INU2 and INU3 are three inulin samples; INU-aver is the average adsorptive or desorptive EMC/aw data of three inulin samples.
Figure 2. The measured moisture sorption isotherms of three inulin samples. Notes: ads, adsorption; des, desorption; INU1, INU2 and INU3 are three inulin samples; INU-aver is the average adsorptive or desorptive EMC/aw data of three inulin samples.
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Figure 3. The predicted mean isotherms of FOS or inulin samples by GDW and MGAB equations. Note: FOS-aver is the mean adsorptive or desorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive or desorptive EMC/aw data of three inulin samples; ads, desorption; des, desorption; Generalized D’Arcy and Watt; MGAB, the modified GAB.
Figure 3. The predicted mean isotherms of FOS or inulin samples by GDW and MGAB equations. Note: FOS-aver is the mean adsorptive or desorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive or desorptive EMC/aw data of three inulin samples; ads, desorption; des, desorption; Generalized D’Arcy and Watt; MGAB, the modified GAB.
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Figure 4. The predicted mean isotherms of FOS or inulin samples by Polynomial equation. Notes: FOS-aver is the mean adsorptive or desorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive or desorptive EMC/aw data of three inulin samples; ads, adsorption; des, desorption.
Figure 4. The predicted mean isotherms of FOS or inulin samples by Polynomial equation. Notes: FOS-aver is the mean adsorptive or desorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive or desorptive EMC/aw data of three inulin samples; ads, adsorption; des, desorption.
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Figure 5. The hysteresis degree of inulin and FOS. Notes: FOS-aver is the mean adsorptive or desorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive or desorptive EMC/aw data of three inulin samples.
Figure 5. The hysteresis degree of inulin and FOS. Notes: FOS-aver is the mean adsorptive or desorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive or desorptive EMC/aw data of three inulin samples.
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Figure 6. Comparison of adsorption and desorption isosteric heats of FOS and inulin at different temperatures predicted by the Modified Chung–Pfost equation. Notes: (A), FOS-aver; (B), INU-aver.
Figure 6. Comparison of adsorption and desorption isosteric heats of FOS and inulin at different temperatures predicted by the Modified Chung–Pfost equation. Notes: (A), FOS-aver; (B), INU-aver.
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Figure 7. The absorbance of main peaks in the FTIR of FOS (FOS2) and inulin (INU3).
Figure 7. The absorbance of main peaks in the FTIR of FOS (FOS2) and inulin (INU3).
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Figure 8. The microstructure of inulin (INU3) and FOS (FOS2). Note: (A,B), INU3; (C,D), FOS2. The photos were enlarged at 100× (A,C) and 1000× (B,D), respectively.
Figure 8. The microstructure of inulin (INU3) and FOS (FOS2). Note: (A,B), INU3; (C,D), FOS2. The photos were enlarged at 100× (A,C) and 1000× (B,D), respectively.
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Table 1. The samples used by this study.
Table 1. The samples used by this study.
Sample
No.
SpeciesAbbr.Moisture Content
(% Wet Basis)
a1FructooligosaccharideFOS14.07
a2FructooligosaccharideFOS22.49
a3InulinINU14.25
a4InulinINU23.89
a5InulinINU33.87
Table 2. EMC equations used in the present study.
Table 2. EMC equations used in the present study.
EquationsFormulaReference
Ferro–Fontan M = b ln a a w 1 / c Saberi et al. [16]
GAB M = a · b · c · a w 1 b · a w 1 b · a w + b · c · a w Li et al. [9]
GDW M = a · b · a w 1 + b · a w · 1 c · 1 d · a w 1 c · a w Furmaniak, et al. [17]
Boquet M = a w a + b · a w + c · a w 2 Liu, et al. [15]
MCPE a w = exp a · exp c · M b + t
M = 1 c ln t + b ln a w a
Li, et al. [9]
MGAB M = a · b · c / t · a w 1 b · a w 1 b · a w + b · c / t · a w
a w = 2 + c t a M 1 2 + c t a M 1 2 4 1 c t 0.5 2 b 1 c t
Cao, et al. [18]
Peleg M = a · a w c + b · a w d Liu, et al. [15]
Note: M is equilibrium moisture content (% w.b.), aw is water activity (decimal), t is temperature (°C). a, b, c, and d are the equation parameters. GAB, Guggenheim–Anderson–de Boer; GDW, Generalized D’Arcy and Watt; MCPE, the modified Chung–Pfost; MGAB, the modified GAB.
Table 3. The fitting results for the moisture adsorption isotherms of FOS and inulin samples.
Table 3. The fitting results for the moisture adsorption isotherms of FOS and inulin samples.
EquationSamplesEquationParameters StatisticalParameters
abcRSSSER2MRE (%)
BoquetFOS15.824 × 10−22.022 × 10−2−6.754 × 10−275.652.38730.984913.7316
FOS29.647 × 10−2−7.920 × 10−2−1.135 × 10−2111.37023.37490.989112.4943
INU14.020 × 10−26.256 × 10−2−8.209 × 10−268.42992.07350.973912.4264
INU24.131 × 10−25.890 × 10−2−7.953 × 10−262.56611.89590.976412.2518
INU37.397 × 10−2−1.966 × 10−2−4.674 × 10−278.65172.38340.989410.8291
FOS-aver4.603 × 10−27.125 × 10−2−9.184 × 10−258.98741.78750.976713.3542
INU-aver4.072 × 10−26.405 × 10−2−8.433 × 10−261.48951.86330.976312.4709
Ferro–FontanFOS11.1764.9840.78571.31892.16220.986410.3899
FOS21.1523.6080.666101.29583.06960.99019.7479
INU11.3126.2370.82669.51262.10640.973510.4663
INU21.3266.0890.81163.66291.92920.97597.9618
INU31.1514.2540.73770.84492.14680.99057.7725
FOS-aver1.2626.2250.86156.43281.71010.977711.1907
INU-aver1.2986.1920.83361.33951.85870.976410.4688
GABFOS15.0450.978−4.04 × 108201.34465.10140.961530.695
FOS25.1531.011−2.90 × 108368.378211.16290.963750.5032
INU17.6440.8493.83 × 10068.42992.07360.973912.4264
INU27.7590.8473.68 × 10062.56611.89590.976412.2518
INU35.0710.998−3.37 × 108256.08957.76040.965637.5305
FOS-aver7.0710.8644.03 × 10058.98741.78750.976713.3542
INU-aver7.4850.8533.84 × 10061.48951.86330.976412.4709
MGABFOS19.3970.89242.41954.91151.66390.989515.4482
FOS211.0080.93323.83965.93371.99790.993515.0965
INU19.0880.81469.46650.18011.52060.980912.7239
INU28.7950.82274.07547.17071.42940.982212.4161
INU39.9990.91831.60745.06251.36550.993913.9382
FOS-aver7.5070.85291.86251.14111.54970.979813.7313
INU-aver8.3920.83178.09448.02151.45520.981512.7838
Note: Boquet, Ferro–Fontan, GAB and MGAB are in a form of M = f a w , t ; GAB, Guggenheim–Anderson–de Boer; MGAB, the modified GAB; a, b, and c are the equation parameters; FOS-aver is the mean adsorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive EMC/aw data of three inulin samples; RSS residue sum of squares; SE, standard error; R2, determination coefficient; MRE, mean relative percentage error.
Table 4. The fitting results for the moisture desorption isotherms of FOS and inulin samples.
Table 4. The fitting results for the moisture desorption isotherms of FOS and inulin samples.
EquationSamplesEquationParameters StatisticalParameters
abcRSSSER2MRE (%)
BoquetFOS16.041 × 10−31.380 × 10−1−1.345 × 10−185.32992.58580.98059.7775
FOS2−4.772 × 10−31.368 × 10−1−1.264 × 10−1194.99335.90890.97179.382
INU11.129 × 10−31.558 × 10−1−1.377 × 10−141.29751.25130.97845.4797
INU21.075 × 10−31.569 × 10−1−1.389 × 10−139.89481.20890.97935.6076
INU3−2.422 × 10−31.451 × 10−1−1.355 × 10−1120.71913.65820.97829.3627
FOS-aver1.869 × 10−31.584 × 10−1−1.411 × 10−129.22680.88570.98464.2232
INU-aver1.342 × 10−31.571 × 10−1−1.392 × 10−136.29561.09980.98115.0535
Ferro–FontanFOS11.02622.3811.37886.28542.61470.98039.6767
FOS20.899131.5191.979253.93997.69510.923512.9858
INU10.99882.4881.95739.85881.20780.97925.4127
INU20.99682.8281.96238.10941.15480.98035.5501
INU30.96692.0381.843152.10414.60920.972510.0406
FOS-aver1.00662.7111.86328.78710.87230.98484.2237
INU-aver1.00075.3361.92735.11981.06420.98164.9664
GABFOS16.6790.93426.53685.32992.58580.98059.7775
FOS28.4930.9415.42 × 108268.85058.14690.960911.9103
INU16.3360.878159.28441.29351.25130.97845.4797
INU26.2980.879167.82539.89481.20890.97935.6076
INU37.3650.9433.15 × 108128.29073.88760.97689.2657
FOS-aver6.1820.88198.26729.22690.88570.98464.2232
INU-aver6.2710.879135.11536.29561.09980.98115.0538
MGABFOS16.9130.928465.66274.60882.26090.98298.8713
FOS28.4930.9414.22 × 109268.85098.14690.960911.9103
INU16.4580.8732035.81739.43081.19490.97944.8227
INU26.4210.8752073.62138.07291.15370.98034.9639
INU37.3650.9431.64 × 109128.29073.88760.97689.2657
FOS-aver6.2730.8771720.98927.49630.83320.98553.6035
INU-aver6.3830.8751935.7334.46381.04440.98194.3433
Note: Boquet, Ferro–Fontan, GAB and MGAB are in a form of M = f a w , t ; GAB, Guggenheim–Anderson–de Boer; MGAB, the modified GAB; a, b, and c are the equation parameters; FOS-aver is the mean desorptive EMC/aw data of two FOS samples; INU-aver is the mean desorptive EMC/aw data of three inulin samples; RSS, residue sum of squares; SE, standard error; R2, determination coefficient; MRE, mean relative percentage error.
Table 5. Fitting the moisture sorption isotherms of FOS and inulin samples using GDW and Peleg.
Table 5. Fitting the moisture sorption isotherms of FOS and inulin samples using GDW and Peleg.
EquationSorptionSamplesEquationParameters Statistical Parameters
abcdRSSSER2MRE (%)
GDWAdsFOS11.624−1.011 × 10100.8935.98570.03972.18870.986612.9
FOS20.6388.091 × 10130.94715.145107.43913.35750.989410.302
INU11.9393.201 × 10150.7776.17369.03472.15730.97379.577
INU21.884−3.402 × 10150.7756.44563.00021.96880.97629.4799
INU31.176−5.219 × 10140.9278.07371.83812.24490.99047.7725
FOS-aver2.026−1.432 × 10150.8025.22755.53231.73540.978110.3702
INU-aver1.9545.358 × 10150.7855.90460.70271.89690.97669.5277
GDWDesFOS15.0793.479 × 10130.9111.57382.42212.57570.98129.7117
FOS210.7161.895 × 10140.9860.538199.96686.24890.97099.3569
INU16.284−3.539 × 10140.8850.97341.83341.30730.97825.8434
INU26.276−9.768 × 10130.8880.96240.34331.26070.97915.9754
INU38−6.846 × 10140.9580.815123.11433.84730.97779.3528
FOS-aver5.901−7.167 × 10130.8811.06130.39860.94990.98394.6303
INU-aver6.154−2.450 × 10130.8850.99737.05551.15790.98065.4111
PelegAdsFOS114.67349.7550.8375.57280.99862.53120.984512.5587
FOS216.39684.1281.0116.73192.42572.88830.990911.4296
INU124.36640.7341.21914.45764.05732.00180.975614.2233
INU224.69841.8271.23714.85458.04271.81380.978114.1289
INU316.46666.6140.9716.44173.37752.29310.990210.4121
FOS-aver22.69133.3751.19411.60161.00831.90650.975915.7294
INU-aver24.02138.4711.22213.70859.29581.85290.977214.606
PelegDesFOS114.17250.0570.4245.63587.40582.73040.98019.7695
FOS215.04580.2660.088836.352166.86395.21450.97589.2847
INU113.80431.6880.3585.94340.34111.26070.97895.4666
INU213.84832.1350.3626.03538.92841.21650.97985.5801
INU314.22265.2680.2095.998118.12493.69140.97869.4316
FOS-aver13.40131.1040.3695.79629.18310.91240.98464.3630
INU-aver13.68531.6360.3635.92435.6931.11540.98135.0454
Note: GDW and Peleg are in a form of M = f a w , t ; GDW, Generalized D’Arcy and Watt; a, b, c, and d are the equation parameters; FOS-aver is the mean adsorptive or desorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive or desorptive EMC/aw data of three inulin samples; Ads, adsorption; Des, desorption; RSS, residue sum of squares; SE, standard error; R2, determination coefficient; MRE, mean relative percentage error.
Table 6. The fitting results for the moisture sorption isotherms of FOS and inulin samples using a Polynomial.
Table 6. The fitting results for the moisture sorption isotherms of FOS and inulin samples using a Polynomial.
SorptionSamplesEquationParameters StatisticalParameters
abcdefgR2MRE (%)
AdsFOS122.263−2.07146.41 × 10−2−6.80 × 10−436.532−98.016116.2640.985112.9000
FOS2−63.8836.691−2.48 × 10−12.93 × 10−399.468−276.555268.8530.988224.3912
INU1−20.7282.767−1.09 × 10−11.33 × 10−320.955−31.75148.2740.975811.9344
INU2−19.8542.619−1.02 × 10−11.23 × 10−320.257−29.92847.2110.977311.5841
INU3−20.8112.309−9.18 × 10−27.12 × 10−367.999−187.285194.0580.988116.4874
FOS-aver15.452−1.334.41 × 10−2−5.09 × 10−414.83−23.36644.8520.976811.2958
INU-aver−8.3791.352−5.54 × 10−26.87 × 10−418.681−28.34746.7790.977111.4668
DesFOS1−89.64110.631−3.96 × 10−14.72 × 10−356.274−145.635146.7710.99116.0063
FOS2−76.45210.133−3.91 × 10−14.75 × 10−384.953−263.627255.9190.98975.7773
INU1−12.4332.081−8.55 × 10−21.07 × 10−345.291−106.639100.2120.98883.8617
INU2−14.52.309−9.40 × 10−21.17 × 10−345.966−108.619101.8130.98943.8712
INU3−83.04610.382−3.93 × 10−14.73 × 10−370.614−204.631201.3450.99115.6422
FOS-aver18.026−1.4394.47 × 10−2−4.90 × 10−443.723−102.51597.2560.99053.6893
INU-aver−2.9690.9837−4.49 × 10−25.82 × 10−444.993−105.92599.7610.98963.8198
Note: FOS-aver is the mean adsorptive or desorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive or desorptive EMC/aw data of three inulin samples; Ads, adsorption; Des, desorption; a, b, c, d, e, f, and g are the Polynomial parameters; R2, determination coefficient; MRE, mean relative percentage error.
Table 7. Fitting the moisture sorption isotherms of FOS and inulin samples using MCPE.
Table 7. Fitting the moisture sorption isotherms of FOS and inulin samples using MCPE.
EquationSorptionSamplesEquationParameters StatisticalParameters
abcRSSSER2MRE (%)
M = f a w , t AdsFOS1192.97374.5478.07 × 10−2441.184413.36920.915542.2929
FOS2188.21990.9795.93 × 10−21271.34438.52560.874579.0006
INU1242.25575.7621.14 × 10−1127.20493.85470.949823.3271
INU2171.27144.6411.16 × 10−1109.60013.32120.958120.7637
INU3188.45852.2621.11 × 10−1107.11593.24590.959520.9011
FOS-aver189.84283.4966.84 × 10−2782.6723.71730.894956.9353
INU-aver195.94855.4881.12 × 10−1112.97113.42340.956521.3975
desFOS1133.03525.2778.88 × 10−2383.657411.62590.912324.3588
FOS2127.44712.4017.52 × 10−21278.41438.73980.814526.5989
INU1234.02336.3411.33 × 10−1119.8043.63040.936813.5253
INU2197.59724.2491.33 × 10−1126.49413.83320.933913.0525
INU3195.98824.2851.32 × 10−1128.49743.89390.933413.2478
FOS-aver128.78317.4398.14 × 10−2758.074422.97190.862825.2102
INU-aver207.37627.7131.33 × 10−1124.62823.77660.934913.2529
a w = f M , t AdsFOS1692.292303.7199.99 × 10−20.14194.30 × 10−30.940922.4137
FOS2376.423168.0419.33 × 10−20.16595.03 × 10−30.930919.893
INU1708.351268.9841.21 × 10−10.10253.11 × 10−30.957318.2084
INU2342.882113.2511.19 × 10−10.072142.19 × 10−30.969915.8039
INU3374.672127.4171.18 × 10−10.071042.15 × 10−30.970415.7335
FOS-aver501.712222.5939.65 × 10−20.14574.41 × 10−30.939320.7755
INU-aver431.559150.9141.19 × 10−10.078942.39 × 10−30.967116.3496
DesFOS1181.48328.7621.18 × 10−10.12793.88 × 10−30.946719.294
FOS2225.796−0.099541.45 × 10−10.32113.73 × 10−30.866230.5305
INU1431.37657.7771.70 × 10−10.066992.02 × 10−30.972112.6296
INU2332.97433.8611.71 × 10−10.063771.93 × 10−30.973411.9331
INU3324.54132.5611.71 × 10−10.064361.95 × 10−30.973211.9689
FOS-aver188.18710.8051.29 × 10−10.20746.28 × 10−30.913624.2068
INU-aver355.42139.5961.71 × 10−10.064541.96 × 10−30.973112.1971
Note: FOS-aver is the mean adsorptive or desorptive EMC/aw data of two FOS samples; INU-aver is the mean adsorptive or desorptive EMC/aw data of three inulin samples; Ads, adsorption; Des, desorption; a, b, and c are MCPE parameters; RSS, residue sum of squares; SE, standard error; R2, determination coefficient; MRE, mean relative percentage error.
Table 8. Determination of the best-fitting equations for FOS and inulin.
Table 8. Determination of the best-fitting equations for FOS and inulin.
SorptionEquationStatisticalParameters Order
RSSSER2MRE (%)
AdsBoquet73.8778 ± 18.09442.2523 ± 10.55110.9809 ± 0.006612.5083 ± 0.92253
Ferro–Fontan70.6296 ± 14.59782.1404 ± 0.44230.9815 ± 0.00729.7139 ± 1.33011
GAB153.8979 ± 123.75364.5207 ± 3.70490.9706 ± 0.006724.1760 ± 15.53667
GDW71.0838 ± 17.04482.2214 ± 0.53260.9816 ± 0.00699.9899 ± 1.54232
MCPE421.7273 ± 452.950512.7796 ± 13.72580.9298 ± 0.034837.8026 ± 22.86978
MGAB51.7744 ± 6.99521.5689 ± 0.21190.9859 ± 0.006213.7340 ± 1.19005
Polynomial75.4104 ± 22.37682.6003 ± 0.77160.9812 ± 0.005714.2942 ± 4.80636
Peleg69.8866 ± 12.96742.1839 ± 0.40530.9818 ± 0.006713.2983 ± 1.89454
DesBoquet78.2510 ± 61.21382.3712 ± 1.85490.9791 ± 0.00396.9837 ± 2.40554
Ferro–Fontan90.6006 ± 84.37032.7454 ± 2.55670.9717 ± 0.02167.5509 ± 3.33126
GAB89.8831 ± 86.54072.7237 ± 2.62240.9774 ± 0.00777.3311 ± 2.94227
GDW79.3049 ± 62.69932.4782 ± 1.95940.9788 ± 0.00417.1831 ± 2.18855
MCPE417.0814 ± 447.383412.6388 ± 13.55710.9041 ± 0.047518.4638 ± 6.51258
MGAB87.3163 ± 87.44992.6459 ± 2.64990.9782 ± 0.00816.8258 ± 3.16292
Polynomial34.1896 ± 20.11321.1789 ± 0.69350.9900 ± 0.00094.6668 ± 1.07491
Peleg73.7915 ± 52.58182.3059 ± 1.64310.9799 ± 0.00276.9916 ± 2.37853
Note: Ads, adsorption; Des, desorption; GAB, Guggenheim–Anderson–de Boer; GDW, Generalized D’Arcy and Watt; MCPE, the modified Chung–Pfost; MGAB, the modified GAB; RSS, residue sum of squares; SE, standard error; R2, determination coefficient; MRE, mean relative percentage error.
Table 9. The comparison of the absorbance values of main peaks in FTIR of FOS and inulin.
Table 9. The comparison of the absorbance values of main peaks in FTIR of FOS and inulin.
Sample AbsorbanceValues
514 cm−1556 cm−1749 cm−1814 cm−1
FOS20.2675 ± 0.0075 0.1926 ± 0.0038-
INU3-0.3082 ± 0.0035-0.2338 ± 0.0034
Sample918 cm−1925 cm−11020 cm−11084 cm−1
FOS20.2820 ± 0.0050-0.4101 ± 0.00720.3556 ± 0.0058
INU3-0.3525 ± 0.00450.6609 ± 0.00570.5216 ± 0.0061
Sample1232 cm−11329 cm−11405 cm−11628 cm−1
FOS20.2216 ± 0.0025-0.2317 ± 0.00250.1342 ± 0.0022
INU3-0.2968 ± 0.0060-0.2046 ± 0.0062
Sample2072 cm−12892 cm−12915 cm−13337 cm−1
FOS20.0460 ± 0.00690.1987 ± 0.0044-0.3559 ± 0.0033
INU30.1057 ± 0.0100-0.2913 ± 0.01040.6138 ± 0.0117
Note: - shows no clear peak.
Table 10. Effect of adding FOS or inulin on the pasting parameters of rice starch.
Table 10. Effect of adding FOS or inulin on the pasting parameters of rice starch.
AdditionPeak Viscosity (cp)Trough
Viscosity(cp)
Breakdown Viscosity (cp)Final
Viscosity (cp)
Setback Viscosity (cp)Peak Time (min)Pasting Temp. (°C)
0%2724 ± 24 a2117 ± 10 a609 ± 21 a3001 ± 22 a885 ± 19 a6.44 ± 0.07 e75.43 ± 0.01 c
3% FOS22539 ± 34 b1967 ± 68 c573 ± 50 a2839 ± 32 b872 ± 43 ab6.47 ± 0.14 de74.77 ± 0.49 d
5% FOS22378 ± 35 c1954 ± 103 c424 ± 81 bc2702 ± 20 c748 ± 93 bcde6.67 ± 0.14 bcd75.57 ± 0.45 bcd
7% FOS22228 ± 10 d1801 ± 48 d427 ± 38 bc2568 ± 5 d767 ± 44 cd6.58 ± 0.10 de75.30 ± 0.48 bcd
10% FOS22019 ± 6 f1689 ± 3 e330 ± 3 d2371 ± 3 f682 ± 2 e6.67 ± 0.07 cd76.13 ± 0.45 b
3% INU32527 ± 14 b2107 ± 7 b422 ± 21 b2855 ± 3 b749 ± 10 c6.75 ± 0.04 bc75.60 ± 0.48 bcd
5% INU32357 ± 14 c1996 ± 22 c361 ± 36 cd2699 ± 5 c703 ± 23 de6.75 ± 0.04 bc75.88 ± 0.03 b
7% INU32157 ± 1 e1778 ± 30 d378 ± 29 bc2502 ± 6 e723 ± 34 cd6.84 ± 0.08 b76.07 ± 0.46 b
10% INU31918 ± 8 g1502 ± 9 f416 ± 8 b2243 ± 9 g740 ± 8 c6.98 ± 0.04 a76.63 ± 0.03 a
Note: All data are expressed as mean ± SD; number of repetitions—n = 3. Different superscript letters indicate significant differences (p < 0.05) within the column.
Table 11. Effect of adding FOS or inulin on the thermal properties of rice starch samples.
Table 11. Effect of adding FOS or inulin on the thermal properties of rice starch samples.
AdditionΔH (J/g)To
(°C)
Tp
(°C)
Tc
(°C)
Peak Width
(°C)
Peak Height
(0.01 mW/mg)
Aging (%)
0%9.54 ± 0.10 e62.95 ± 1.16 abcde69.85 ± 0.94 a77.87 ± 1.08 abc7.70 ± 0.23 abc16.16 ± 0.45 bcd38.20 ± 2.60 b
3% FOS29.71 ± 0.06 d61.97 ± 0.31 e69.17 ± 0.15 c77.37 ± 0.67 c7.43 ± 0.15 c17.14 ± 0.34 a29.39 ± 0.70 c
5% FOS29.85 ± 0.01 c62.15 ± 0.15 de69.45 ± 0.25 bc77.90 ± 0.70 bc7.60 ± 0.30 bc17.01 ± 0.63 abc26.12 ± 0.76 d
7% FOS29.95 ± 0.02 b62.53 ± 0.25 d69.70 ± 0.17 b78.07 ± 0.47 bc7.53 ± 0.35 bc17.16 ± 0.81 abc20.44 ± 0.97 e
10% FOS210.11 ± 0.03 a63.03 ± 0.23 c70.50 ± 0.26 a79.23 ± 0.32 a7.70 ± 0.17 bc16.82 ± 0.32 ab15.55 ± 0.54 f
3% INU39.21 ± 0.09 f64.10 ± 0.14 a70.70 ± 0.42 a78.25 ± 0.49 bc7.75 ± 0.07 b15.70 ± 0.17 d43.62 ± 0.15 a
5% INU39.70 ± 0.17 cde63.80 ± 0.44 ab70.77 ± 0.25 a77.70 ± 0.36 c7.83 ± 0.12 ab16.10 ± 0.32 cd35.17 ± 1.95 b
7% INU39.76 ± 0.34 abcde63.63 ± 0.06 b70.80 ± 0.10 a78.37 ± 0.51 bc7.97 ± 0.06 a16.20 ± 0.54 bcd33.68 ± 2.80 b
10% INU38.57 ± 0.17 g64.17 ± 0.21 a71.03 ± 0.47 a78.70 ± 0.44 ab7.63 ± 0.15 c15.00 ± 0.26 e33.07 ± 7.13 bcd
Note: ΔH, Gelatinization enthalpy; To, Tp, and Tc are the onset temperature, peak temperature, and conclusion temperature of gelatinization, respectively. All data are expressed as mean ± SD; number of repetitions—n = 3. Different superscript letters indicate significant differences (p < 0.05) within the column.
Table 12. Influence of FOS or inulin on the thermal properties of rice starch using General Linear Model (GLM) analysis.
Table 12. Influence of FOS or inulin on the thermal properties of rice starch using General Linear Model (GLM) analysis.
FactorsLevelsΔH (J/g)To
(°C)
Tp
(°C)
Tc
(°C)
Peak Width
(°C)
Peak Height
(0.01 mW/mg)
Aging (%)
SpeciesFOS29.81 ± 0.091 a62.32 ± 0.09 d69.58 ± 0.09 d77.96 ± 0.17 bc7.59 ± 0.06 c16.82 ± 0.16 a25.79 ± 1.04 c
INU39.37 ± 0.09 c63.940 ± 0.09 a70.78 ± 0.09 a78.30 ± 0.17 b7.78 ± 0.06 a15.87 ± 0.16 d36.90 ± 1.04 a
Addition09.54 ± 0.15 bc62.95 ± 0.14 c69.85 ± 0.14 c77.87 ± 0.27 b7.70 ± 0.09 abc16.16 ± 0.25 cd38.21 ± 1.64 a
(%)39.46 ± 0.15 c63.03 ± 0.14 c69.94 ± 0.14 c77.81 ± 0.27 c7.59 ± 0.09 bc16.41 ± 0.25 bc36.51 ± 1.64 a
59.77 ± 0.15 ab62.98 ± 0.14 c70.11 ± 0.14 bc77.80 ± 0.27 c7.72 ± 0.09 abc16.54 ± 0.25 abc30.64 ± 1.64 b
79.85 ± 0.15 a63.09 ± 0.14 c70.25 ± 0.14 b78.22 ± 0.27 bc7.75 ± 0.09 ab16.70 ± 0.25 ab27.06 ± 1.64 c
109.34 ± 0.15 c63.60 ± 0.14 b70.77 ± 0.14 a78.97 ± 0.27 a7.67 ± 0.09 abc15.90 ± 0.25 d24.31 ± 1.64 c
Note: ΔH, Gelatinization enthalpy; To, Tp, and Tc are the onset temperature, peak temperature, and conclusion temperature of gelatinization, respectively. All data are expressed as mean ± SD; number of repetitions—n = 3. Different superscript letters indicate significant differences (p < 0.05) within the column.
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Dai, B.; Chen, R.; Wei, Z.; Wu, J.; Li, X. Moisture Sorption Isotherms of Fructooligosaccharide and Inulin Powders and Their Gelling Competence in Delaying the Retrogradation of Rice Starch. Gels 2025, 11, 817. https://doi.org/10.3390/gels11100817

AMA Style

Dai B, Chen R, Wei Z, Wu J, Li X. Moisture Sorption Isotherms of Fructooligosaccharide and Inulin Powders and Their Gelling Competence in Delaying the Retrogradation of Rice Starch. Gels. 2025; 11(10):817. https://doi.org/10.3390/gels11100817

Chicago/Turabian Style

Dai, Bing, Ruijun Chen, Zheng Wei, Jianzhang Wu, and Xingjun Li. 2025. "Moisture Sorption Isotherms of Fructooligosaccharide and Inulin Powders and Their Gelling Competence in Delaying the Retrogradation of Rice Starch" Gels 11, no. 10: 817. https://doi.org/10.3390/gels11100817

APA Style

Dai, B., Chen, R., Wei, Z., Wu, J., & Li, X. (2025). Moisture Sorption Isotherms of Fructooligosaccharide and Inulin Powders and Their Gelling Competence in Delaying the Retrogradation of Rice Starch. Gels, 11(10), 817. https://doi.org/10.3390/gels11100817

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