Characterization of Cross-Linking in Guar Gum Hydrogels via the Analysis of Thermal Decomposition Behavior and Water Uptake Kinetics

Abstract

This study aimed to explore a test method for evaluating the effective cross-linking density of hydrogels. A guar gum–epichlorohydrin hydrogel (GEH) was prepared using guar gum (GG) as the raw material and epichlorohydrin (ECH) as the cross-linking agent. The thermal and mechanical properties, equilibrium swelling rate (ESR), water uptake (WU), and mass cross-linking degree of the hydrogels were assessed. Furthermore, the diffusion behavior of water molecules in the freeze-dried GEH was investigated. The experimental results showed the significance of the initial decomposition temperature (T_i) and final decomposition temperature (T_f) of the freeze-dried GEHs in determining the effective cross-linking density. The water uptake kinetics of the freeze-dried GEH was consistent with the linear fitting of the pseudo-second-order kinetic model and nonlinear fitting of the Fickian diffusion model, suggesting that chemisorption dominated the water absorption process in the GEH. Therefore, the effective cross-linking density of the hydrogels could be determined from the thermodynamic analysis and the diffusive behavior of water molecules in the gels. The thermal stability and water diffusion kinetics of the hydrogels were closely linked to the effective cross-linking density and pendant modification.

1. Introduction

There is a prevailing global trend to explore new plant-derived biomaterials and to use them in the development of new products because plant-based products are generally considered safe [1]. Guar gum (GG) is a plant polysaccharide composed of galactose and mannose that is present in the endosperm of guar seeds [2]. GG’s structure consists of a linear chain composed of (1 → 4)-β-D-mannopyranose units and a side chain composed of α-D-galactosyl pyranose units connected by (1 → 6) bonds [3]. GG is hydrophilic and water-soluble and can be used as a thickener and stabilizer in the food, petroleum, paper, and textile industries [4,5]. GG is a renewable biological resource that is relatively cheap and nontoxic, and it can be chemically and biochemically modified [6,7]. Owing to their remarkable characteristics, including an exceptional water absorption capacity, high viscosity, biocompatibility, and biodegradability [8,9], hydrogels prepared based on GG show a great potential for biomedical applications. These hydrogels are widely used in various domains, such as adsorption, separation, drug delivery, and other fields, as water-retaining agents [10,11].

GG hydrogels consist of physically or covalently cross-linked guar chains [12,13]. Chemical covalent cross-linking is a versatile approach for obtaining hydrogels with tunable structures and enhanced mechanical properties. A variety of cross-linking agents have been used to cross-link GG, including epichlorohydrin (ECH) [14], glutathione [15], borate [11], citric acid [16], silane coupling agents [17], and N,N-Dimethylacrylamide [18]. Under alkaline conditions, the affine hydroxyl group of GG reacts with the epoxide group of ECH, and some ECH molecules react with GG at both ends to form chemical cross-linking bonds. However, some ECH molecules react with GG only at one end, whereas the other end retains an epoxy group or is hydrolyzed during the process, leading to the formation of pendant hydroxyl group arms (Figure 1). After several water changes to remove the residual oligomers and facilitate the complete hydrolysis of the ECH molecules, the hydrogels form pendants of modified 1,2-propylene glycol ether, which increases the weight of the hydrogels. However, these pendants cannot be cross-linked efficiently. Therefore, 100% cross-linking efficiency (two hydroxyl groups of GG for each cross-linking agent molecule) is not possible for this cross-linking system. To explore the network properties of GG hydrogels and to assess their cross-linking density, an analytical method capable of distinguishing cross-linked ECH molecules from those with pendant modifications is required.

The performance of a hydrogel is contingent upon the stability of its network structure and the presence of functional groups, which influence various aspects, such as drug release and the adsorption of pollutants through solute diffusion within the 3D network structure [19]. The diffusion of solutes is dependent on the architecture of the hydrogel polymer network [20] and is affected by the properties and degree of the cross-linking agent, which, in turn, determine the thermal stability, mechanical strength, and expansion characteristics of the hydrogel [21,22]. Characterizing hydrogels presents a challenge due to the predominant presence of water in polysaccharide hydrogels. By investigating the behavior of water molecules within hydrogels, one can establish a correlation between the structure of the resulting gel network and its physical and chemical properties [23].

In this work, a guar gum–epichlorohydrin hydrogel (GEH) was prepared via chemical cross-linking under alkaline conditions, where GG was used as the raw material and where epichlorohydrin (ECH) was used as the cross-linking agent. To prepare GEH with excellent properties, this study explored the effect of different amounts of ECH and GG and other preparation conditions on the polymer properties. The structural properties of GEH were investigated through the FT-IR, ¹³C NMR, XRD, SEM, and TGA techniques. Additionally, the mechanical properties, the equilibrium swelling rate (ESR), the water uptake (WU), the mass cross-linking degree, and other characteristics of the hydrogels were investigated to infer the extent of cross-linking in the GEH. The water uptake kinetics of the freeze-dried GEH was investigated to elucidate the variation in the diffusion behavior of water molecules among different hydrogels. The purpose of this study was to explore a laboratory-based method for evaluating the effective cross-linking density of hydrogels and to lay a foundation for future studies on methods for testing the cross-linking density of hydrogels.

2. Materials and Methods

2.1. Materials

GG was purchased from Beijing Guarun Technology Co., Ltd. (Beijing, China), and the viscosity of GG was 5200 ± 150 mPa·s⁻¹. The M/G ratio (1.677 ± 0.004) of GG was obtained from the previous literature [24]. ECH, sodium hydroxide, and all other chemicals were obtained from Macklin Reagent Co., Ltd. (Shanghai, China).

2.2. GEH Preparation

The GEHs were synthesized in one step. In the reaction, 4.0 g of GG powder was mechanically stirred in 100 mL of distilled water at 70 °C for a duration of 2 h, and 1.0 g NaOH was added; stirring continued for an additional 30 min. Subsequently, a mold (glass tube) was charged with 10.0 g of GG solution and 0.5 g of ECH followed by magnetic stirring at 25 ± 2 °C for 10 min until homogenized. The magnetic stir bar was removed subsequently, and the glass tubes were sealed before being incubated at 40 °C for 6 h. Following the reaction, residual NaOH, ECH, and oligomers were eliminated by immersing the hydrogels in distilled water to obtain pure hydrogels. The reaction conditions for ECH preparation are listed in Table S1.

2.3. Characterization

Freeze-dried GG and the GEHs were pulverized into powder form followed by vacuum drying at 80 °C for 24 h prior to conducting FT-IR spectroscopy. The FT-IR spectra were obtained using a Bruker ALPHA spectrometer (Bruker Co., Ettlingen, Germany) in the range of 500–4000 cm⁻¹. The ¹³C NMR spectra of GG were obtained using a Bruker AVIII-400 MHz spectrometer (Bruker Co., Ettlingen, Germany) at 20 °C in D₂O with a concentration of approximately 0.5 wt%, and the internal reference was 2,2,3,3-D4-3-(trimethylsilyl)propionic acid sodium salt. The solid-state ¹³C NMR spectra of the freeze-dried GEHs were acquired at 60 °C using an Agilent VNMRS 600 instrument (Agilent Co., Palo Alto, CA, USA) equipped with a cross-polarization/magic-angle spinning unit. The crystal structures of GG and freeze-dried GEHs were investigated using an MXP21VAHF diffractometer (MAC Science Co., Ltd., Tokyo, Japan) equipped with Cu Kα radiation (λ = 0.154 nm at 40 kV and 100 mA) for wide-angle XRD analysis. The surface morphologies of the freeze-dried GEHs were examined through SEM (JSM-7001F, JEOL, Tokyo, Japan). The GEHs were rapidly frozen in liquid nitrogen, were immediately fractured, and were subsequently subjected to freeze-drying. Following, a cross-sectional view of each freeze-dried GEH sample was gold-sputtered for observation and photography. The thermal stabilities of GG and the freeze-dried GEHs were assessed through TGA (STA 449 F3, Netzsch, Selb, Germany). The 10.0 mg samples were precisely weighed into an aluminum crucible and were subsequently loaded onto a TGA instrument, and, under a nitrogen atmosphere, they were heated at a rate of 10 °C/min from 35 °C to 700 °C. The thermal degradation behavior of the GEHs was investigated by analyzing their TGA and derivative thermogravimetric curves as shown in Figure S1. The initial degradation temperature (T_i), maximum peak temperature (T_p), and end temperature (T_f) were determined using a built-in software program as illustrated in Figure S3.

2.4. Mechanical Strength

The mechanical strength of the hydrogels was evaluated in compression mode using a JS-II Bloom Tester (Tianjin Xuyang Instrument Equipment Co., Ltd., Tianjin, China) with a 1.0 kg load cell and TA5 round probe (12.7 × 35 mm) without any additional treatment by subjecting them to a single compression cycle at a test speed of 1.0 mm/s to achieve a target deformation of 4 mm followed by an immediate return to their original position.

2.5. Swelling Rate

The swelling rate of the hydrogels was calculated using gravimetry [25]. The hydrogels were immersed in distilled water at 25 °C for a duration of 7 days, with the replacement of the distilled water occurring every 12 h. After gently blotting the sample surfaces with filter paper to remove any excess water, the hydrogels’ equilibrium swelling ratio (ESR, g/g) was determined and calculated using Equation (1):

$$\mathrm{ESR}=W_{\mathrm{s}}/W_{\mathrm{d}},$$

(1)

where W_s represents the mass of swollen hydrogel, W_d is the mass of dry hydrogel, and ESR serves as an indicator for cross-linking density [26].

2.6. Water Uptake

The freeze-dried GEH samples were rehydrated in distilled water at 25 °C, and the kinetics of water uptake by the GEHs was subsequently measured. Each GEH sample was periodically extracted from the distilled water, whereupon the surface water of the hydrogel was removed using filter paper, and was subsequently weighed. The water uptake (WU, g/g) of the hydrogels was calculated using Equation (2).

$$\mathrm{WU}=\left(W_t-W_{\mathrm{d}}\right)/W_{\mathrm{d}},$$

(2)

where W_t represents the mass of the wet hydrogel at time t, and the reabsorption rate of the freeze-dried hydrogels was determined using the WU/ESR ratio.

2.7. Degree of Mass Cross-Linking

The degree of mass cross-linking (MCD) was calculated according to the literature with minor modifications. The hydrogels underwent swelling dialysis to remove the noncross-linked biopolymer chains, cross-linkers, and other chemicals. Fully swollen hydrogels were freeze-dried, with a mass assigned to W_d (g). The initial masses of GG and ECH in the synthetic hydrogels were labeled W_G and W_E (g), respectively. The MCD was calculated using Equation (3):

$$\mathrm{MCD} \left(\%\right)=W_{\mathrm{d}}/(W_{\mathrm{G}}+W_{\mathrm{E}})\times 100$$

(3)

The mass cross-linking degree only provided the masses of GG and ECH participating in the reaction, and pendant-modified ECH was also included; however, pendant-modified ECH did not provide effective cross-linking.

2.8. Statistical Analysis

All experiments were conducted in triplicate, and the mean values were reported. Statistical significance was determined at p < 0.05 level.

3. Results and Discussion

3.1. Characterization of Physical and Chemical Properties

The peaks observed in the FT-IR spectra at 3410 and 2926 cm⁻¹ are attributed to O-H and C-H stretching vibrations, respectively (Figure 2a). The GEH peak exhibited a sharper profile at 3410 cm⁻¹. The discernible peaks observed at 1140, 1075, and 1027 cm⁻¹ are associated with the stretching vibrations of the C-C-O and C-O-C bonds in the GG backbone. The sharp peaks at 1379 cm⁻¹ indicate that more methylene bridges were formed through cross-linking [27,28]. The cross-linking of the GEHs was verified through a ¹³C NMR analysis (Figure 2b). The ¹³C NMR spectra of GG’s exhibited peaks in the range of 90–110 ppm, which corresponded to mannose and galactose, with resonant in the range of 60–80 ppm, were consistent with the previous literature [29,30]. The characteristic peaks of GG were observed in the solid-state ¹³C NMR spectra of the GEHs [31,32]. The GEHs also showed a peak at 26.7 ppm, which was attributed to the -CH- of ECH, indicating that the hydrogels were cross-linked by GG and ECH. As can be seen from the XRD curves of GG and the GEHs (Figure 2c), the overall crystallinity of natural GG was poor as reflected at 19.9° and as reported in the literature [27]. However, this characteristic diffraction peak did not exist in the XRD spectra of the GEHs, which means that the crystallization region of GG was destroyed by the cross-linking reaction and that the hydrogels presented an amorphous structure [33].

TGA was performed on GG and the GEHs to analyze their thermal stabilities. According to Figure 2d, the initial stage occurred at about 120 °C, which corresponded to the loss of absorbed and bound water [32]. The thermal degradation of GG began at temperatures above 230 °C, and further oxidation and carbonization took place in the range of 280 to 500 °C. The initial decomposition temperature and maximum weight loss rate of the GEHs were higher than those of GG, indicating that cross-linking with ECH enhanced the thermal stability of the GEHs [34]. For polysaccharide hydrogels, the cross-linking bridge and polysaccharide backbone broke with increasing temperature [35]. Therefore, the thermal stability and cross-linking degree of the hydrogels could be determined by the initial decomposition temperature (T_i), maximum weight loss rate temperature (T_p), and final decomposition temperature (T_f). The TG and DTG curves of the freeze-dried GEHs, prepared under different conditions, are shown in Figure S1. In order to make the analysis of the TG data more intuitive, the T_i, T_p, T_f, and ΔT(T_f − T_i) of the polymer were obtained from the DTG curves through the built-in software of the device (Figure 2e). In addition, the SEM image of the GEHs (Figure 2f and Figure S2) shows abundant connected pores inside the hydrogel.

3.2. Influence of GG Concentration on the Cross-Linking Characteristics of the GEHs

As shown in Figure 3a, the mechanical strength and MCD of the GEHs increased with an increase in the GG concentration. This is because, as the concentration of GG increased, the density of the chemical cross-links increased. Owing to the increase in the number of GG chains, the degree of chain curling and entanglement increased, resulting in an increase in the physical cross-linking density [36]. The MCD data shows that, as the GG concentration and degree of cross-linking increased, the microstructure of the aerogel changed from an open 3D porous nanofiber network to a 2D sheet skeleton, which is consistent with the literature [37]. According to the swelling and water uptake properties of the hydrogels (Figure 3b), both the ESR and WU of the hydrogels exhibited a decreasing trend with an increase in the concentration of GG, whereas the WU/ESR ratio increased with an increase in the concentration of GG. The water uptake capacity of the freeze-dried GEHs decreased with an increase in the GG concentration, which is consistent with the data reported in the literature [37]. The ESR reflects the swelling property of the network structure and is a manifestation of the cross-linking density [38]. The WU/ESR ratio was used to evaluate the network stability of the GEHs. The greater the WU/ESR value was, the higher the stability of the network structure in the GEHs. The results of the thermal analysis are shown in Figure 3c. As can be seen, the T_i of the GEHs did not change significantly with an increase in the GG concentration; T_p showed a gradual decrease, whereas T_f showed a sharp decrease. The thermal properties of a polymer are predominantly dictated by its degree of cross-linking [35]. Specifically, a polymer network structure with branched chains and low cross-linking densities for the chain segments is the first to break down at T_i [39,40]. The final decomposition process occurred in the dense portion and the main chain of the polymer network at the T_f.

3.3. Influence of Cross-Linking Agent Concentration on the Cross-Linking Characteristics of the GEHs

Generally, the cross-linking density of hydrogels increases with the concentration of the cross-linker within a certain range [41], and the effect of ECH on the GEH characteristics is shown in Figure 4a. The mechanical strength of the GEHs exhibited an initial increase followed by a subsequent decrease upon increasing the concentration of the cross-linker, while the MCD of the GEHs demonstrated a significant reduction with an increase in the concentration of the cross-linker. As shown in Figure 4b, the ESR of the GEHs first increased and then remained constant with an increase in the cross-linker concentration, while the WU of the freeze-dried GEHs gradually increased. At the same time, the WU/ESR values showed a gradual increase, indicating the enhanced water uptake capacity of the freeze-dried GEHs, which was due to the overhanging modifications formed by the large amount of ECH on the gum backbone. This increased the number of hydroxyl groups and enhanced water absorption [42]. As seen from the thermal stability data (Figure 4c), the thermal stability of the GEHs was enhanced through the addition of a cross-linker. Within the range of the experimental concentration, the maximum decomposition rate temperature, the final decomposition temperature, and ΔT(T_f − T_i) showed an increasing trend.

3.4. Influence of Catalyst Concentration on the Cross-Linking Characteristics of the GEHs

According to the cross-linking mechanism (Figure 1), the amount of NaOH, as an activator of polymerization, affects the cross-linking reaction [43,44]. In addition, GG chain breakage in alkaline solutions affects the cross-linking density of hydrogels and their properties [45,46]. As shown in Figure 5a, both the mechanical strength and MCD of the GEHs initially increased and then decreased with an increase in the NaOH concentrations. Figure 5b shows that, as the NaOH concentration increased, the ESR and WU of the GEHs initially decreased before subsequently increasing, whereas the WU/ESR ratio gradually increased.

According to the thermal stability data (Figure 5c), T_i, T_p, T_f, and ΔT(T_f − T_i) first increased and then decreased with an increase in the concentration of NaOH. This is because the degree of cross-linking in the hydrogels increased with an increase in the concentration of NaOH, and both the T_i and T_f of the hydrogels increased. However, as the concentration of NaOH continued to increase, the degradation of the polysaccharide backbone [45], the pendant modification of ECH, and the formation of o-diol increased the branched chains in the hydrogels and reduced the MCD of the hydrogels; therefore, both the T_i and T_f of the hydrogels decreased.

3.5. Influence of Cross-Linking Temperature and Time on the Cross-Linking Characteristics of the GEHs

The effects of the cross-linking temperature and time on the cross-linking properties of the hydrogel are shown in Figure 6. As shown in Figure 6a, the mechanical strength of the hydrogel gradually increased with an increase in the temperature. The MCD of the hydrogels initially increased and then decreased. Figure 6d shows that the mechanical strength of the hydrogel first increased and then decreased as the cross-linking time increased. As seen from Figure 6b, with an increase in the temperature, the ESR of the GEHs first decreased and then remained nearly constant, while the ratio of WU and WU/ESR increased significantly after 40 °C. As shown in Figure 6e, the ESR of the hydrogel gradually decreased as the cross-linking time increased, while the WU remained constant for the first 6 h and then increased slightly. Furthermore, the WU/ESR ratio gradually increased as the cross-linking time extended. As seen from Figure 6c, T_i significantly decreased after 40 °C, and the T_f of the hydrogels first increased and then decreased with an increase in the temperature. The increase was due to the increase in the hydrogel cross-linking density, while the decrease was probably because the alkali accelerated the pendant modification of ECH on the GG main chain and the breakage of the polysaccharide backbone at higher reaction temperatures [46]. As seen in Figure 6f, the T_f of the hydrogels showed an increasing trend with an increase in the cross-linking time, whereas T_p and T_i first increased and then decreased.

3.6. Relationship between the Water Uptake Kinetics and Cross-Linking Characteristics of the Freeze-Dried Hydrogels

Water uptake is important for controlled drug release and the adsorption properties of hydrogels [47]. It was assumed that the higher the degree of hydrogel swelling was, the larger the space occupied by water would be, resulting in larger pores after lyophilization [48]. However, in the process of lyophilization, if the strength of the polymer matrix is not sufficient to support the stability of its structure, it will lead to the accumulation of polymer chains [49] and the collapse of the capillary structure [50], which will have an impact on the water uptake performance of the freeze-dried hydrogels. The water uptake kinetic curve of the freeze-dried GEHs is shown in Figure 7. As shown in Figure 7a, the saturation water absorption of the GEHs and water uptake rate in the diffusion phase decreased with an increase in the GG concentration. Figure 7b shows that, as the cross-linker concentration increased from 3 wt% to 7 wt%, the water uptake of the GEHs increased significantly. As shown in Figure 7c, when the amount of NaOH was larger than 3 wt%, the quantity and rate of the water uptake during the diffusion phase increased. As seen from Figure 7d, when the reaction temperature was over 40 °C, the water uptake rate in the diffusion stage increased significantly. Figure 7e shows that the reaction time had little effect on the water uptake performance of the GEHs.

Water absorption is an important parameter for water diffusion in freeze-dried gels. In this study, the first-order swelling kinetics model (Equation (4)) and second-order swelling kinetics model (Equation (5)) were used for calculations [51,52] to elucidate the mechanism of water diffusion in the freeze-dried GEHs, and the Fickian diffusion model, Equation (6), was used for fitting [51].

Pseudo-first-order kinetic model:

Nonlinear fitting model:

$$W{U}_t=W{U}_{\infty }\left(1-e^{-k_{1}t}\right)$$

(4a)

Linear fitting model:

$$-\ln \left(1-W{U}_t/W{U}_{\infty }\right)=k_{1}t$$

(4b)

Pseudo-second-order kinetic model:

Nonlinear fitting model:

$$W{U}_t=k_{2}W{U}_{\infty }^{2}t/\left(1+k_{2}W{U}_{\infty }t\right)$$

(5a)

Linear fitting model:

$$t/W{U}_t=1/\left(k_2·W{U}_{\infty }^2\right)+t/W{U}_{\infty }$$

(5b)

Fickian diffusion model:

Nonlinear fitting model:

$$W{U}_t/W{U}_{\infty }=k_3{t}^n$$

(6a)

Linear fitting model:

$$\ln \left(W{U}_t/W{U}_{\infty }\right)=\ln k_3+n·\ln t$$

(6b)

Here, t represents the adsorption time (h); WU_t and WU_∞ are the WU capacity at time t and equilibrium, respectively; k₁ represents the WU rate constant (h⁻¹); k₂ (g·g⁻¹h⁻¹) is the rate constant of the second-order kinetic model; and k₃ denotes the swelling constant obtained from the truncation, which is a material constant that varies with the structure. A low k₃ value indicates a weak interaction between the material and water, implying poor water absorption. n is the diffusion index that is determined from the slope, and it indicates the mode of the infiltration transmission mechanism [53]. When n < 0.5, the hydrogel volume did not change during swelling, and the diffusion was dominated by the chemical potential gradient. Furthermore, the diffusion mechanism was Fickian.

The linear and nonlinear fitting graphs of the pseudo-first- and pseudo-second-order kinetic models are shown in Figure S3. The kinetic parameter k, theoretical maximum adsorption capacity WU_∞, and correlation coefficient R² of the two models are listed in Table S2. The analysis of the experimental results showed that the correlation coefficient of the linear fit was larger than that of the nonlinear fit, and the R² values obtained from the pseudo-second-order model with the linear fit were higher than those obtained from the pseudo-first-order kinetic model. In addition, the theoretical maximum absorption WU_∞, calculated by the pseudo-second-order model, was almost equal to the experimental value, which proves that the water uptake behavior of the freeze-dried GEHs conformed to the pseudo-second-order kinetic model. Because the pseudo-second-order kinetic model is based on chemisorption, the results show that the water absorption process was dominated by chemisorption. Moreover, water absorption was affected by the hydroxyl group at the adsorption site, which is similar to the literature [54].

The linear fitting of the water uptake curves using the Fickian diffusion model is shown in Figure S4, and the kinetic parameters are listed in Table S3. The n values of the GEH samples were all less than 0.5, indicating that the water transport mechanism in the freeze-dried GEHs was of the Fickian diffusion type, and the large value of n indicated that the material had a rich pore structure. For example, the values of n for alginate/starch-based hydrogels cross-linked with different ions are generally below 0.45 [55]. To better understand the effect of the structure of the freeze-dried GEHs on the diffusion of water molecules, Fickian diffusion was used to perform the piecewise fitting of the water absorption kinetics curve, with an adsorption capacity of 60% of the weight for the first stage and 40% for the second stage, as shown in Figure 7f. The transport of water molecules in the freeze-dried gels occurred in two stages. The first stage was the percolation and adsorption of water molecules in the 3D network structure of the gels, and the second stage was the diffusion within it. The schematic diagram illustrating these stages is shown in Figure 7g. The swelling of the gel mainly depends on three factors: the pore size of the gel surface, the intermolecular space generated within the 3D network structure, and the presence of hydrophilic functional groups [56]. The water uptake rate and the amount in the initial stage were determined by the stability of the freeze-dried gel network, whereas the water uptake rate in the diffusion stage was determined by the capillary structure of the frozen gel and the number and hydrophilic properties of the hydrophilic groups.

According to Figure S5 and Table S4, the correlation coefficient of the nonlinear fit to Fickian diffusion was larger than that of the linear fit. The effects of fitting the GG concentration, ECH concentration, NaOH concentration, reaction temperature, and time to the Fickian diffusion model showed that the value of k₃ exhibited an initial increase followed by a subsequent decrease as the concentrations of ECH and NaOH were increased and that it increased with an increase in the GG concentration and reaction temperature. As the cross-linking time increased, it first decreased, then increased, and finally decreased again. In addition, k₃₁ in the first stage was higher than k₃₂ in the second stage, indicating that the water diffusion rate in the first stage was higher than that in the second stage. This was because the water molecules in the first stage were primarily diffused in the macroporous network channels of the freeze-dried gel and were adsorbed on the surface. In the second phase, the network channels in the freeze-dried gel matrix were smaller, and the water molecules diffused more slowly. The values of n in the first stage were all lower than those in the second stage, indicating that the polysaccharide backbone swelled in water, the gel network relaxed as the immersion time was extended, and the water molecules diffused. The lower the cross-linking density of the gel network and the higher the number of adsorption sites (hydroxyl), the larger the value of n is, and the more likely the occurrence of the gel network relaxation phenomenon is.

4. Conclusions

In this study, GEHs were prepared by chemically cross-linking GG and ECH in an alkaline solution. A thermogravimetric analysis showed that the thermal stability of the cross-linked GEHs significantly improved. The analysis of the T_i and T_f of the GEHs was helpful for determining the effective cross-linking density. If the T_i value was low, the polymer contained more branched chains, and if the cross-linking density was low, the T_f value was high, indicating a high degree of cross-linking. The diffusion kinetics of the water molecules in the freeze-dried GEHs was consistent with the linear fitting of the pseudo-second-order kinetic model and the nonlinear fitting of the Fickian diffusion model, suggesting that the water absorption process in the GEHs was dominated by chemisorption. Fitting the Fickian diffusion model in stages showed that the water diffusion rate in the first stage was higher than that in the second stage. The lower the cross-linking density of the gel network was, the larger the number of adsorption sites and the value of n. Therefore, the thermodynamic analysis and the diffusive behavior of the water molecules in a gel can be used to determine the effective cross-linking density of the hydrogel. This approach not only enhances the comprehension of cross-linking mechanisms but also provides a novel means to investigate the properties and applications of hydrogels.